Step-by-step explanation:
a) 24 / 250 = 0.096
b) Standard error for a proportion is:
σ = √(pq/n)
σ = √(0.096 × 0.904 / 250)
σ = 0.0186
c) At 98% confidence, the critical value is 2.326. The margin of error is therefore:
2.326 × 0.0186 = 0.0433
d) At 95% confidence, the critical value is 1.960. The margin of error is therefore:
1.960 × 0.0186 = 0.0365
So the confidence interval is:
(0.0960 − 0.0365, 0.0960 + 0.0365)
(0.0595, 0.1325)
e) 0.10 is within the 95% confidence interval, so the null hypothesis would not be rejected.
Final answer:
a) The point estimate of the proportion of components in the shipment that fail to meet the company's specifications is 9.6%. b) The standard error of the estimated proportion is 1.9%. c) The margin of error at the 98% confidence level is 4.4%. d) The 95% confidence interval estimate for the true proportion is approximately 5.9% to 13.3%. e) The null hypothesis that the proportion is 0.10 is rejected if the z-test statistic falls outside the range (-1.96, 1.96).
Explanation:
a) Point estimate:
The point estimate of the proportion of components in the shipment that fail to meet the company's specifications is the number of failed components divided by the total number of components tested. In this case, the point estimate is 24/250 = 0.096, or 9.6%.
b) Standard error:
The standard error of the estimated proportion is calculated using the formula SE = sqrt((phat * (1 - phat)) / n), where phat is the point estimate and n is the sample size. In this case, the standard error is sqrt((0.096 * (1 - 0.096)) / 250) = 0.019, or 1.9%.
c) Margin of error:
The margin of error is determined by multiplying the standard error by the appropriate critical value from the standard normal distribution. For a 98% confidence level, the critical value is approximately 2.33. Therefore, the margin of error is 2.33 * 0.019 = 0.044, or 4.4%.
d) Confidence interval:
The 95% confidence interval estimate for the true proportion of components that fail to meet the specifications is given by the formula phat +/- z * SE, where phat is the point estimate, z is the appropriate critical value from the standard normal distribution (for 95% confidence, z is approximately 1.96), and SE is the standard error. Therefore, the confidence interval is 0.096 +/- 1.96 * 0.019, or approximately 0.059 to 0.133.
e) Hypothesis test:
To test the null hypothesis H_0: p = 0.10 against the alternative hypothesis H_a: p != 0.10, we can use a two-tailed z-test. The test statistic is calculated as (phat - p_0) / sqrt((p_0 * (1 - p_0)) / n), where p_0 is the null hypothesis value (0.10), phat is the point estimate, and n is the sample size. The critical value for a significance level of 0.05 is approximately 1.96 from the standard normal distribution. If the test statistic is outside the range (-1.96, 1.96), we reject the null hypothesis. In this case, if the test statistic falls outside the range (-1.96, 1.96), we would reject the null hypothesis and conclude that the true proportion of components that fail to meet the specifications is not 0.10.
you have 5 red crayons, 3 yellow crayons, 4 blue crayons and purple crayons. what multiplication would you do to find the probability of picking a blue then a red crayon.
Answer:
3/46
Step-by-step explanation:
is The polar form of a complex number is unique?
Answer:
no
Step-by-step explanation:
The angle in the polar form of a complex number can have any multiple of 2π radians added to it, and the number will be the same number. That is, there are an infinite number of representations of a complex number in polar form.
Final answer:
The polar form of a complex number is not unique due to the angle component, which can vary by multiples of full rotations (2π). However, when considering the principal value of the angle, the polar form becomes unique.
Explanation:
The polar form of a complex number is not entirely unique, the reason being that the angle (θ) in the polar form can be expressed as θ + 2πk, where k is any integer.
This is because complex numbers are represented in the complex plane, which is similar to a circle, where angles that differ by full rotations (2π radians) represent the same point.
However, the magnitude (or modulus) and the principal value of the angle (typically between -π and π) combine to give a unique representation of a complex number in polar form.
Help fast!!! Pls!!!!!
Answer:
The height is 5 and the base is 9
Step-by-step explanation:
The area of a parallelogram is given by
A = bh
45 =x(x+4)
Distribute
45 =x^2+4x
Subtract 45 from each side
45-45 =x^2 +4x-45
0 = x^2 +4x-45
Factor
What two numbers multiply to -45 and add to 4
9+-5 = -45
9-5 =4
0=(x+9) (x-5)
Using the zero product property
0= x+9 0 = x-5
x=-9 x=5
Since length cannot be negative
x=5 is the solution
x=5
x+4 = 5+4 =9
A travelling salesman sells milkshake mixing machines and on average sells 8.9 machines per month. He needs to sell at least 3 machines each month order to stay in business, otherwise he will shut down. Using the Poisson distribution, what is the probability he will have to shut down after this month
Answer:
0.67% probability he will have to shut down after this month
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
On average sells 8.9 machines per month.
So [tex]\mu = 8.9[/tex]
Using the Poisson distribution, what is the probability he will have to shut down after this month
If he sells less than 3 machines.
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-8.9}*8.9^{0}}{(0)!} = 0.0001[/tex]
[tex]P(X = 1) = \frac{e^{-8.9}*8.9^{1}}{(1)!} = 0.0012[/tex]
[tex]P(X = 2) = \frac{e^{-8.9}*8.9^{2}}{(2)!} = 0.0054[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0001 + 0.0012 + 0.0054 = 0.0067[/tex]
0.67% probability he will have to shut down after this month
Write a logical argument which determines what I ate for dinner. Number eachstep in your argument and cite which rule you use for each step.a. I did not have a coupon for buns or I did not have a coupon for hamburger.b. I had hamburgers or chicken for dinner.c. If I had hamburgers for dinner then I bought buns.d. If I did not have a coupon for buns then I did not buy buns.e. If I did not have a coupon for hamburger then I did not buy buns.
Answer:
88
Step-by-step explanation:
this is my answer it will help you
You roll a six-sided die twice. What is the probability of rolling a 3 and then a 5?
My guess is that it is 2/12 chance to get it, or 16.6
Answer:
1/36
Step-by-step explanation:
Multiply the two independent probabilities to find the compound probability.
P(3 and 5) =
1
6
×
1
6
=
1
36
Problem 15-05 (Algorithmic) Consider the following time series data. Week 1 2 3 4 5 6 Value 16 13 18 11 15 14 Choose the correct time series plot. (i) Time Series ValueWeek(t) (ii) Time Series ValueWeek(t) (iii) Time Series ValueWeek(t) (iv) Time Series ValueWeek(t) Plot (i) What type of pattern exists in the data? Horizontal Pattern Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places. Week Time Series Value Forecast 1 16 2 13 3 18 4 11 15.67 5 15 14 6 14 14.67 MSE: 7.74 The forecast for week 7: 13.33 Use = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places. Week Time Series Value Forecast 1 16 2 13 16 3 18 15.4 4 11 15.92 5 15 14.94 6 14 14.95 MSE: 8.17 The forecast for week 7: 14.76 Compare the three-week moving average forecast with the exponential smoothing forecast using = 0.2. Which appears to provide the better forecast based on MSE? Three-week moving average Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. Use trial and error to find a value of the exponential smoothing coefficient that results in a smaller MSE than what you calculated for = 0.2. Find a value of for the smallest MSE. Round your answer to three decimal places. = 0.157
This answer involves time series analysis concepts, specifically focusing on three-week moving averages and exponential smoothing methods. It explains the results obtained from both methods for predicting week 7's forecast, comparing them using the Mean Squared Error (MSE). It suggests that the three-week moving average provides a better prediction due to a lower MSE.
Explanation:The question asked is a problem in time series analysis, a category of statistics that involves the use and interpretation of data points ordered in time. The method used to analyze this data includes calculating a three-week moving average, computing mean squared error (MSE), and conducting exponential smoothing.
In the scenario given, a three-week moving average tracks an average of data over the past three weeks. It showed a forecast for week 7 as 13.33 with an MSE value of 7.74. In contrast, the exponential smoothing method, which uses a weight assigned to historic data (referred to as alpha, =0.2 in this case) forecasted a higher value of 14.76 with a slightly greater MSE of 8.17.
Between the two methods, the three-week moving average forecast provided a better model due to its lower MSE, indicating a smaller average squared distance between predicted and actual values. Although the calculations for the best value are not included here, a lower MSE (compared to =0.2) was obtained with the value =0.157. This example showcases how using different methods and changing parameters within methods can provide different forecasting results in time series analysis.
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Researchers are conducting a study in an attempt to establish a linear relationship between the number of online music video views and the number of guitar sales. A computer output for regression is shown and is based on a sample of seven observations. Predictor Coeff St. Dev t Ratio p-Value Constant 7.85671094 1.316226455 5.969118 0.001889 Music Video Views 0.094781123 0.027926367 3.393965 0.019378 What represents the 99% confidence interval for the slope of the regression line?
a. 0.0948 ± 3.499(1.3162)
b. 0.0948 ± 4.032(1.3162)
c. 0.0948 ± 3.707(0.0279)
d. 0.0948 ± 4.032(0.0279)
Answer:
d. 0.0948 ± 4.032(0.0279)
Step-by-step explanation:
A 99% confidence interval for the coefficient of promotional expenditures is, First, compute the t critical value then find confidence interval.
The t critical value for the 99% confidence interval is,
The sample size is small and two-tailed test. Look in the column headed es = 0.01 and the row headed in the t distribution table by using degree of freedom is here
for (n-2=5) degree of freedom and 99% confidence ; critical t =4.032
therefore 99% confidence interval for the slope =estimated slope -/+ t*Std error
= 0.094781123 -/+ 4.032* 0.027926367 = -0.017822 to 0.207384
Safety regulations state that roller coasters cannot operate safely in high winds. Throughout the day, ride operators measure the wind speed at several random locations along the track to verify that the speed is below an established threshold value, allowing the ride to operate safely. The collected data is used to conduct a one-sample z -test of the null hypothesis that the mean wind speed is moderate against the alternative that the mean wind speed is too high. If the null hypothesis is rejected in favor of the alternative, the ride is shut down due to unsafe conditions. Choose the correct description of a type I error and a type II error in this context.
Answer:
Type I error would be to conclude that the mean wind speed is too high and decide to shut down the ride but in actual the wind speed was moderate and it is safe to do riding.
Type II error would be to conclude that the mean wind speed is moderate and decide to go on riding but in actual the wind speed is too high and it unsafe to go on riding and should be shut down.
Step-by-step explanation:
We are given that the collected data is used to conduct a one-sample z -test of the null hypothesis that the mean wind speed is moderate against the alternative that the mean wind speed is too high.
If the null hypothesis is rejected in favor of the alternative, the ride is shut down due to unsafe conditions.
So, Null Hypothesis, [tex]H_0[/tex] : The mean wind speed is moderate.
Alternate Hypothesis, [tex]H_A[/tex] : The mean wind speed is too high.
Also, it is provided that if the null hypothesis is rejected in favor of the alternative, the ride is shut down due to unsafe conditions.
Now, Type I error states the Probability of rejecting null hypothesis given the fact that it was true or Probability of rejecting the true hypothesis.
So, in the given context, Type I error would be to conclude that the mean wind speed is too high and decide to shut down the ride but in actual the wind speed was moderate and it is safe to do riding.
On the other hand, Type II error states the Probability of accepting null hypothesis given the fact that it was false or Probability of accepting the false hypothesis.So, in the given context, Type II error would be to conclude that the mean wind speed is moderate and decide to go on riding but in actual the wind speed is too high and it unsafe to go on riding and should be shut down.
From a point along a straight road, the angle of elevation to the top of a hill is . From farther down the road, the angle of elevation to the top of the hill is . How high is the hill?
Complete Question:
From a point along a straight road, the angle of elevation to the top of a hill is 33° . A distance of 200 ft farther down the road, the angle of elevation to the top of the hill is 20°. How high is the hill?
Answer:
The hill is 165.87 ft high
Step-by-step explanation:
Check the file attached below for a pictorial understanding of the question
[tex]tan \theta = \frac{opposite}{Adjacent}[/tex]
From ΔABC
[tex]tan 33 = \frac{y}{x} \\[/tex]
[tex]y = x tan 33[/tex]..........(1)
From ΔABD
[tex]tan 20 = \frac{y}{x + 200} \\[/tex]
[tex]y = (x + 200) tan 20[/tex]............(2)
Equating (1) and (2)
[tex]x tan 33 = (x+200) tan20\\xtan33 = xtan20 + 200tan20\\0.649x = 0.364x + 72.794\\0.649x - 0.364x = 72.794\\0.285x = 72.794\\x = 72.794/0.285\\x = 255.42 ft[/tex]
Substitute the value of x into equation (1)
[tex]y = 255.42 tan 33[/tex]
y = 165.87 ft
The height of the hill is 550 feet.
Given:
- [tex]\(\theta_1 = 31^\circ\)[/tex]
- [tex]\(\theta_2 = 24^\circ\)[/tex]
- [tex]\(d = 320\) feet[/tex]
We use the formula for the height of the hill \(h\):
[tex]\[h = \frac{d \tan(\theta_2) \tan(\theta_1)}{\tan(\theta_1) - \tan(\theta_2)}\][/tex]
First, we calculate [tex]\(\tan(31^\circ)\)[/tex] and [tex]\(\tan(24^\circ)\)[/tex]:
[tex]\[\tan(31^\circ) \approx 0.6009\][/tex]
[tex]\[\tan(24^\circ) \approx 0.4452\][/tex]
Now, substitute these values into the formula:
[tex]\[h = \frac{320 \times 0.4452 \times 0.6009}{0.6009 - 0.4452}\][/tex]
Calculate the numerator:
[tex]\[320 \times 0.4452 \times 0.6009 \approx 85.676256\][/tex]
Calculate the denominator:
[tex]\[0.6009 - 0.4452 \approx 0.1557\][/tex]
Now, divide the numerator by the denominator:
[tex]\[h = \frac{85.676256}{0.1557} \approx 550.41\][/tex]
Rounding to the nearest foot, the height of the hill is:
550 feet.
Complete question is here
From a point along a straight road, the angle of elevation to the top of a hill is 31º. From 320 n farther down the road, the angle of elevation to the top of the hill is 24º. How high is the hill? Round to the nearest foot.
Toxaphene is an insecticide that has been identified as a pollutant in the Great Lakes ecosystem. To investigate the effect of toxaphene exposure on animals, groups of rats were given toxaphene in their diet. An article reports weight gains(in grams) for rats given a low dose (4ppm) and for control rats whose diet did not include the insecticide. The sample standard deviation for 23 female control rats was 32g and for 20 female low-dose rats was 54g. Does this data suggest that there is more variability in low-dose weight gains than in control weight gains? Assuming normality, carry out a test of hypotheses at significance level .05.
Answer:
Check the explanation
Step-by-step explanation:
The details of the given samples are as follows:
Low dose. Number numbers of rats 20
The standard deviation . [tex]S_1[/tex]=54g
Control:
Number of rats [tex]N_2[/tex]=23
The standard deviation [tex]S_1[/tex]=32g
[tex]H_0[/tex]: there is no more variability in low — dose weight gains than in the control weight gins
[tex]H_1[/tex]: There is mere In-viability in low — dose weight gains than in control weight gains
>4 The level of significance.
a= 0.05 The test statistic to test the above hypothesis is Larger variance Smaller variance
The critical value of F (19.22) dr and at 0.05
significance level is 2.0837
The P-Value is 0.01 The test significance value is greater the the critical level is 20837.
Also. the 8-value is less then the significance level Hence, we reject the null hypothesis.
Therefore, we conclude that there is sufficient evidence to conclude that there is more variability in low — dose weight gains than in control weight gains .
DEFINE PARALLELLOGRAM
Answer:
Parallelograms are shapes that have four sides with two sides that are parallel. For example, some shapes that are parallelograms are squares, rectangle, rhombus and rhomboid.
Step-by-step explanation:
No explanation :)
Final answer:
A parallelogram is a quadrilateral with parallel and congruent opposite sides, congruent opposite angles, and diagonals that bisect each other.
Explanation:
A parallelogram is a four-sided polygon, also known as a quadrilateral, where opposite sides are parallel and equal in length. There are several properties that define a parallelogram:
Opposite sides are congruent (equal in length).Opposite angles are congruent (equal in measure).Consecutive angles are supplementary (their measures add up to 180 degrees).The diagonals of a parallelogram bisect each other.Each diagonal divides the parallelogram into two congruent triangles.An example of a parallelogram is a rectangle, which also has all angles equal to 90 degrees, making it a special type of parallelogram. Another example is a rhombus, which has all sides of equal length. The term parallelogram comes from the Greek 'parallelos' and 'gramme', meaning 'parallel lines' and 'line' respectively.
What is the domain of f(x) = 3x – 22
Answer: 7.3333
Step-by-step explanation:
the plane that delta airlines uses to travel from New York to Los Angeles has a total of 80 seats. On the most recent flight, only 4/5 of the seats were filled with passengers. Of those filled with passagers 3/4 were people traveling for business. How many people on the flight were traveling for business?
Answer:
48
Step-by-step explanation:
If only 4/5 of the 80 seats were filled, then 4/5*80=64 of the seats were filled. Of those filled, if 3/4 were travelling for business, then 3/4*64=48 of the people were travelling for business. Hope this helps!
A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if they are different colors, then you win -$1.00. (This is, you lose $1.00.) Calculate (a) the expected value of the amount you win; (b) the variance of the amount you win.
The expected value of the amount you would win from this game is $0.85 and the variance of the amount you win is $0.06.
Explanation:To calculate the expected value, we need to multiply each outcome with its probability and sum them up. The outcomes and corresponding probabilities are as follows:
Winning $1.10 (drawing two marbles of the same color): The probability is 4/9 (for blue) + 4/9 (for red) = 8/9Losing $1.00 (drawing two marbles of different colors): The probability is 1/9Then, the expected value is (8/9)*$1.10 + (1/9)*(-$1.00) = $0.96 - $0.11 = $0.85. So, (a) expected value of the amount you win is $0.85.
To calculate the variance, we need to subtract the expected value from each outcome, square the result, multiply by the probability of each outcome and sum it all up. Variance = (8/9)*($1.10-$0.85)^2 + (1/9)*(-$1.00-$0.85)^2 = $0.06. So, (b) the variance of the amount you win is $0.06.
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The expected value of the amount you win is approximately -$0.0667 and the variance of the amount you win is approximately $1.0888.
(a) To calculate the expected value of the amount you win, we first need to determine the probability of each outcome:
1. Probability of drawing two red marbles: [tex]\( P(\text{red-red}) = \frac{5}{10} \times \frac{4}{9} = \frac{20}{90} = \frac{2}{9} \)[/tex]
2. Probability of drawing two blue marbles: [tex]\( P(\text{blue-blue}) = \frac{5}{10} \times \frac{4}{9} = \frac{20}{90} = \frac{2}{9} \)[/tex]
3. Probability of drawing one red marble and one blue marble: [tex]\( P(\text{red-blue}) = 2 \times \frac{5}{10} \times \frac{5}{9} = \frac{50}{90} = \frac{5}{9} \)[/tex]
Now, let's calculate the expected value (\( E \)):
[tex]\[ E = (P(\text{red-red}) \times \$1.10) + (P(\text{blue-blue}) \times \$1.10) + (P(\text{red-blue}) \times -\$1.00) \]\[ E = \left(\frac{2}{9} \times \$1.10\right) + \left(\frac{2}{9} \times \$1.10\right) + \left(\frac{5}{9} \times -\$1.00\right) \]\[ E = \left(\frac{4}{9} \times \$1.10\right) + \left(\frac{5}{9} \times -\$1.00\right) \]\[ E = \$\left(\frac{4}{9} \times 1.10\right) + \$\left(\frac{5}{9} \times -1.00\right) \][/tex]
[tex]\[ E = \$\left(\frac{4.40}{9} - \frac{5.00}{9}\right) \]\[ E = \$\frac{-0.60}{9} \]\[ E = -\$0.0667 \][/tex]
So, the expected value of the amount you win is approximately -$0.0667.
(b) To calculate the variance of the amount you win, we'll use the formula for variance:
[tex]\[ \text{Var}(X) = E(X^2) - (E(X))^2 \][/tex]
We already know E(X) from part (a). Now, let's calculate E(X)²:
[tex]\[ E(X^2) = (P(\text{red-red}) \times (\$1.10)^2) + (P(\text{blue-blue}) \times (\$1.10)^2) + (P(\text{red-blue}) \times (-\$1.00)^2) \]\[ E(X^2) = \left(\frac{2}{9} \times (\$1.10)^2\right) + \left(\frac{2}{9} \times (\$1.10)^2\right) + \left(\frac{5}{9} \times (-\$1.00)^2\right) \]\[ E(X^2) = \left(\frac{4}{9} \times (\$1.21)\right) + \left(\frac{5}{9} \times \$1.00\right) \]\[ E(X^2) = \$\left(\frac{4 \times 1.21}{9} + \frac{5}{9}\right) \][/tex]
[tex]\[ E(X^2) = \$\left(\frac{4.84}{9} + \frac{5}{9}\right) \]\[ E(X^2) = \$\frac{9.84}{9} \]\[ E(X^2) = \$1.0933 \][/tex]
Now, we can calculate the variance:
[tex]\[ \text{Var}(X) = E(X^2) - (E(X))^2 \]\[ \text{Var}(X) = \$1.0933 - (-\$0.0667)^2 \]\[ \text{Var}(X) = \$1.0933 - \$0.0045 \]\[ \text{Var}(X) = \$1.0888 \][/tex]
So, the variance of the amount you win is approximately $1.0888.
Therefore, the solution is (a) Expected value: -$0.0667 and (b) Variance: $1.0888
what is the slope of the line y=8 ?
Answer:
0
Step-by-step explanation:
It is a horizontal line, the slope is 0 and it crosses the y-axis at 8
The line is a horizontal line, which has a slope that is equal to zero (0).
Given the following equation:
[tex]y = 8[/tex]To calculate or determine the slope of the given line:
The slope of a line can be defined as the gradient of a line.
In Mathematics, a slope is typically used to describe both the direction and steepness of an equation of a straight line.
Generally, the standard form of an equation of line is given by the following formula;
[tex]y = mx+b[/tex]
Where:
x and y are the points. m is the slope. b is the intercept.Comparing the two equations, we can deduce that the slope of the given line is equal to zero (0).
This ultimately implies that, the line is a horizontal line, which would cross the y-axis of a graph at point 8.
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9. A contractor is considering a sale that promises a profit of $27,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $12,000 with a probability of 0.3. What is the expected value?
Answer:
Hence the expected value for the contractor for sales is 15,300 $.
Step-by-step explanation:
Given:
Winning $27000 is 0.7 and losing 12000 $ of it about 0.3
To find :
Expected value for the contractor for sales.
Solution:
Th expected value is the average occurred of the event.
{Suppose
a series of number like 10,30,30,30,30,60,78.
for this expected value will be
(10+30+30+30+30+60+78+78) / 8
=10(1/8)+30(4/8)+60(1/8)+78(2/8).
78 ,10 ,30 and 60 are just like cost and 1/8 ,4/8,2/8 are probabilities of respective cost.
}
Similar for given values
Expected value with probability is =
Winning probability *cost of winning +(-losing probability * losing cost)
losing means negative impact on value so it is negative
=27000*0.7-12000*0.3
=18900-3600.
=15300 $.
What is true about the function graphed below?
see image v v v
A. The coordinates of the vertex are (3, 0).
B. The function graphed is look at the picture.
C. The axis of symmetry is the x-axis.
D. The axis of symmetry is the y-axis.
Answer:
D. The axis of symmetry is the y-axis.
Step-by-step explanation:
The vertex is at coordinates (0, 3). Since this parabola opens vertically, its axis of symmetry is the x=coordinate of the vertex: x = 0. That is the equation of the y-axis.
The axis of symmetry is the y-axis.
Which expression is equivalent to
2(5m) + m?
a) 11m
b) 12m
c) 5m + 2
d) 7m + 2m
Answer:
choice a.) 11m
Step-by-step explanation:
2(5m) + m = 10m + m = 11m
A university administrator was interested in determining if there was a difference in the distance students travel to get from class from their current residence(in miles). Men and women at UF were randomly selected. The Minitab output is below. What is the best interpretation for the output? Difference = mu (F) - mu (M) T-Test of difference = 0 (vs not =): T-Value = -1.05 P-Value = 0.305 DF = 21
The Minitab output from the t-test signifies that there is no statistically significant difference in the distances traveled by men and women at UF to get to class. The t-value and p-value obtained don't give enough evidence to reject the null hypothesis. The degrees of freedom (DF) indicate the number of independent observations in the sample.
Explanation:The output from Minitab that you've shared is the result of a paired t-test comparing the mean distances traveled by men and women to get to class at UF. The null hypothesis in this context is that there is no difference in the average distances traveled by men and women (Difference = mu (F) - mu (M)). The t-value of -1.05 and the p-value of 0.305 do not provide enough evidence to reject the null hypothesis at the conventional 0.05 level of significance. Therefore, we could interpret the output as not detecting a statistically significant difference between the mean distances men and women travel to get to class at UF.
The 'DF' or degrees of freedom, indicates the number of independent observations in your sample that are free to vary once certain constraints (like the sample mean) are calculated. In this case, DF = 21, which is the sample size (pairs of men and women) minus 1.
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(1 point) Suppose that f(x) and g(x) are given by the power series f(x)=6+7x+3x2+5x3+⋯ and g(x)=7+8x+3x2+4x3+⋯. By multiplying power series, find the first few terms of the series for the product h(x)=f(x)⋅g(x)=c0+c1x+c2x2+c3x3+⋯.
Answer:
f(x).g(x) = c0+c1x+c2x2+c3x3+⋯.
[tex]f(x).g(x) = 42 +97x +95x^{2} + 104x^{3} +77x^{4} +27x^{5} + 20x^{6}+....[/tex]
c₀ = 42 , c₁ =97 , c₂ = 95, c₃ =104, ...…...
Step-by-step explanation:
Suppose that f(x) and g(x) are given by the power series
f(x)=6+7x+3x2+5x3+⋯ and
g(x)=7+8x+3x2+4x3+⋯
By multiplying power series ,
f(x).g(x) = (6+7x+3x2+5x3+⋯).(7+8x+3x2+4x3+⋯)
= 6(7+8x+3x2+4x3+⋯)+7x(7+8x+3x2+4x3+⋯)+3x2(7+8x+3x2+4x3+⋯) + 5x3(7+8x+3x2+4x3+⋯)+......
[tex]f(x).g(x) = 42 +97x +95x^{2} + 104x^{3} +77x^{4} +27x^{5} + 20x^{6}+....[/tex]
f(x).g(x) = c0+c1x+c2x2+c3x3+⋯.is the form
[tex]f(x).g(x) = 42 +97x +95x^{2} + 104x^{3} +77x^{4} +27x^{5} + 20x^{6}+....[/tex]
c₀ = 42 , c₁ =97 , c₂ = 95, c₃ =104, ...……
In this problem, power series f(x) and g(x) are multiplied together term by term to produce the product h(x). The first few terms of the h(x) series are found by sequentially multiplying the corresponding terms of f(x) and g(x). The procedures produced the first four terms as 42, 98, 170, and 356 respectively.
Explanation:In the field of mathematics, specifically calculus, you can multiply two power series together term by term. In this case, function f(x) = 6 + 7x + 3x2 + 5x3 + ⋯ and g(x) = 7 + 8x + 3x2 + 4x3 + ⋯ are provided. When you multiply these two power series, the product h(x) = f(x) ⋅ g(x) is obtained by multiplying each corresponding term in the series of f(x) and g(x) together.
To find the first few terms we consider it like
First term, c0: f0*g0 = 6*7 =42Second term, c1: f1*g0 + g1*f0 = 7*6 + 8*7 = 98Third term, c2: f2*g0 + f1*g1 + g2*f0 = 18*3*6 + 7*8 + 21*6 = 170Fourth term, c3: f3*g0 + f2*g1 + f1*g2 + f0*g3 = 30*7 + 18*8 + 21*7 + 6*0 = 356and so on for the subsequent terms.
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which is greater, 7 or 24/4
Answer:
7
Step-by-step explanation:
24/4=6. 7>6
Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.3. (Round your answers to four decimal places.)
(a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 12 pins is at least 51?
The probability that the sample mean hardness for a random sample of 12 pins is at least 51 is approximately 0.0228.
Explanation:To determine the probability, we can use the central limit theorem. Since the distribution of the Rockwell hardness is normal, the distribution of the sample mean will also be normal. The formula for calculating the standard deviation of the sample mean (standard error) is given by the population standard deviation divided by the square root of the sample size. In this case, the standard error is calculated as 1.3 / sqrt(12), which is approximately 0.3746.
To find the z-score, we use the formula: z =[tex](X - μ) / σ[/tex], where X is the desired value (51), μ is the mean (50), and σ is the standard error (0.3746). Plugging in these values, we get a z-score of approximately 2.6744.
Using a standard normal distribution table, we find the probability that a z-score is greater than 2.6744 is approximately 0.0057. However, since we are interested in the probability that the sample mean hardness is at least 51, we need to consider the tail of the distribution on both sides. Therefore, the final probability is[tex]2 * 0.0057[/tex] = 0.0114.
To round the answer to four decimal places, the final probability is approximately 0.0228.
Probability that the sample mean hardness for 12 pins is at least 51 is approximately 0.0038.
To solve this problem, we'll use the Central Limit Theorem (CLT) and the properties of the normal distribution.
Given:
- Population mean[tex](\( \mu \))[/tex] = 50
- Population standard deviation [tex](\( \sigma \))[/tex] = 1.3
- Sample size (( n )) = 12
- Desired sample mean[tex](\( \bar{x} \)) = 51[/tex]
The CLT states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
For a sample size of 12, we can use the following formula to calculate the standard error[tex](\( \text{SE} \))[/tex]:
[tex]\[ \text{SE} = \frac{\sigma}{\sqrt{n}} \][/tex]
Substitute the given values:
[tex]\[ \text{SE} = \frac{1.3}{\sqrt{12}} \][/tex]
[tex]\[ \text{SE} \approx \frac{1.3}{3.4641} \][/tex]
[tex]\[ \text{SE} \approx 0.3749 \][/tex]
Now, we need to find the z-score for the sample mean of 51 using the standard normal distribution formula:
[tex]\[ z = \frac{\bar{x} - \mu}{\text{SE}} \][/tex]
Substitute the given values:
[tex]\[ z = \frac{51 - 50}{0.3749} \][/tex]
[tex]\[ z = \frac{1}{0.3749} \][/tex]
[tex]\[ z \approx 2.6679 \][/tex]
Now, we look up the probability corresponding to this z-score in the standard normal distribution table.
The probability that the sample mean hardness for a random sample of 12 pins is at least 51 is the area under the standard normal curve to the right of ( z = 2.6679 ).
Consulting a standard normal distribution table or using statistical software, we find:
[ P(Z > 2.6679) ]
This probability represents the area to the right of ( z = 2.6679 ).
Now, if we're using a standard normal distribution table, we might find the value closest to 2.67 or 2.67 itself, then look up the corresponding probability.
This probability gives us the likelihood that the sample mean hardness for a random sample of 12 pins is at least 51.
Point A is at (-2, -7) and point M is at (2.5, -1.5).
Point M is the midpoint of point A and point B.
What are the coordinates of point B?
Answer:
B = (7, 4)
Step-by-step explanation:
B = 2M -A = 2(2.5, -1.5) -(-2, -7)
B = (5+2, -3+7)
B = (7, 4)
__
Derivation
You know the midpoint is calculated from ...
M = (A+B)/2
Solving for B, we get ...
2M = A+B
B = 2M-A . . . . the formula we used above
Answer:
Give more points
Step-by-step explanation:
Work out the length X.
Answer:
17.67 cm
Step-by-step explanation:
[tex]\sqrt{a^2+b^2}[/tex] = x
16^2 = 256
7.5^2 = 56.25
Add.
256 + 56.25 = 312.25
[tex]\sqrt{312.25}= 17.67[/tex]
The missing side of the triangle is x = 17.67 cm
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
The Pythagorean theorem formula:
a² + b² = c²
Replacing by the values we have;
16² + 7.5² = x²
x² = 256 + 56.25
x² = 312.25
x = √312.25 cm
x = 17.67 cm
Therefore, the correct answer is x = 17.67 cm
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farmer ed has 3000 meters of fencing and wants to enclose a rectangle plot that borders on a river. if farmer ed does not fence the side along the river what is the largest area that can be enclosed
Answer:
area = 1500× 750 = [tex]1125000 m^2[/tex]
Step-by-step explanation:
we know area of rectangle
for length = l m
and width = b m
[tex]A = lb[/tex]
and perimeter
[tex]Perimeter = 2 (length + width)[/tex]
but one side length measures is not required because of the river so
He does not use the fence along the side of the river
so we use this formula
Perimeter = P = L + 2 b
Perimeter is 3000 m
[tex]so \ \ 3000 = l +2b[/tex]
[tex]l = 3000 - 2b[/tex]
so area will be
[tex]A = (3000-2b)b[/tex]
it is a quadratic function whose max or min will
occur at the average of the Solutions.
on Solving (3000 - 2b)b = 0
3000 - 2b = 0 or b=0
2b =3000
[tex]b =\frac{3000}{2} \\b = 1500 m[/tex]
or [tex]b = 0 m[/tex]
The average of the values are [tex]\frac{(0+1500)}{2} = 750[/tex]
so for max area we use b= [tex]750 m[/tex]
The Length is then L=3000 - 2(750) = 3000 - 1500 = 1500
for max area
length = 1500 m
bredth = 750 m
area = 1500× 750 = [tex]1125000 m^2[/tex]
The largest area that can be enclosed by Farmer Ed with 3000 meters of fencing along a river (with only three sides fenced) equals 1,125,000 square meters by using principles of mathematical optimization.
Explanation:In this question, Farmer Ed wants to maximize the area of a rectangle with only three sides fenced, since one side borders on a river. We can use the principles of optimization in mathematics to solve this problem.
With 3000 meters of fencing for three sides, if we denote one side perpendicular to the river as X and the side parallel to the river (which forms the base of the rectangle) as Y, then, the perimeter would be Y+2X which is equal to 3000 meters. So, Y = 3000-2X.
The area A of a rectangle is length times width, or, in this case, A = XY. Substituting Y from the equation above: A = X(3000-2X) = 3000X - 2X^2. To maximize this area, we need to find values of X for which this equation has its maximum value.
The maximum or minimum of a function can be found at points where its derivative is zero. So, we take the derivative of A with respect to X, set it equal to zero, and solve for X.
The derivative, dA/dX is 3000 - 4X. Setting this equal to 0 gives X = 3000/4 = 750. So, the maximum area that Farmer Ed can enclose is when X is 750, and Y is 3000 - 2X = 1500, so the maximum area is 750 * 1500 = 1,125,000 square meters.
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Further, Boris must also take into consideration the chicken calorie specifications which, as you know, are imposed by customers and competitors. The target for the chicken calorie content is 475 calories---with a tolerance level of 50 calories in each direction. The upper control limit of the X-bar chart is: (Please round up) a) More than 520 calories but less than or equal to 540 calories. b) More than 540 calories but less than or equal to 560 calories. c) More than 560 calories but less than or equal to 580 calories. d) More than 580 calories but less than or equal to 600 calories. e) None of the above.The lower control limit of the X-bar chart is:a) More than 415 calories but less than or equal to 430 calories.b) More than 430 calories but less than or equal to 445 calories.c) More than 445 calories but less than or equal to 460 calories.d) More than 460 calories but less than or equal to 475 calories.The process capability index, Cp, is:a) Negative.b)Less than 1.c)More than 1 but less than 1.3d)More than 1 but less than 1.4.e)None of the above.The process capability index, Cpk, is:a) Negative.b) Less than 1.c) More than 1 but less than 1.05d) More than 1 but less than 1.08e) None of the above.
Answer:
a, a, b,b
Step-by-step explanation:
Upper bound: 475+50= 525
lower bound: 475-50= 425
Cp= (Upper bound-lower bound)/ 6σ
Cp= (525-525)/ (6× 50)
Cp= 0.33
Cpk is minimum of two following values: (Upper bound-mean)/ 3σ, (mean -lower bound)/ 3σ
Cpk in this case is: Min (0.33,0.33)
The Cp and Cpk values are calculated from the actual process values. Here target Cp and Cpk value is 0.33
Roster's Chicken can monitor their caloric content using an X-chart with control limits calculated at either three or four standard deviations from the mean. The analysis reveals that grilled chicken breast is more energy-dense than tortilla chips. After consuming 16 tortilla chips, significant portions of the daily values (DV) for fat, sodium, and fiber remain for other meals.
Control Limits for X-Chart
To design an X-chart for monitoring the caloric content of Roster's Chicken, we need to establish the upper and lower control limits based on the given parameters.
Part a) Control Limits with Four Standard Deviations
The average caloric content of the chicken breast is 420 calories with a standard deviation of 20 calories. For a sample size of 25, the standard error is:
Standard Error = σ / √n = 20 / √25 = 20 / 5 = 4
Therefore, the four standard deviation limits from the target mean of 420 calories are:
Upper Control Limit (UCL) = 420 + 4 * 4 = 420 + 16 = 436 calories
Lower Control Limit (LCL) = 420 - 4 * 4 = 420 - 16 = 404 calories
Part b) Control Limits with Three Standard Deviations
Using the same standard error, the three standard deviation limits are:
Upper Control Limit (UCL) = 420 + 3 * 4 = 420 + 12 = 432 calories
Energy Density Comparison
A serving of grilled chicken breast (4 oz) has about 190 calories. In comparison, 16 tortilla chips typically have around 140 calories. Chicken breast is more energy-dense because it has more calories per ounce compared to tortilla chips, which makes it a denser source of calories.
Percentage Daily Values (DV) in 16 Tortilla Chips
If 16 tortilla chips contribute 10% DV of fat, 8% DV of sodium, and 4% DV of dietary fiber, the remaining percentages for a healthy diet would be:
• Fat: 100% - 10% = 90% DV remaining
• Sodium: 100% - 8% = 92% DV remaining
• Fiber: 100% - 4% = 96% DV remaining
Complete Question:- Roster's Chicken advertises "lite" chicken with 30% fewer calories than standard chicken. When the process for "lite chicken breast production is in control, the average chicken breast contains 420 calories, and the standard deviation in caloric content of the chicken breast population is 20 calories. Roster's wants to design an X-chart to monitor the caloric content of chicken breasts, where 25 chicken breasts would be chosen at random to form each sample. a) What are the lower and upper control limits for this chart? These limits are chosen to be four standard deviations from the target. Upper Control Limit (UCL): 436 calories (enter your response as an integer) Lower Control Limit (LCL): 404 calories (enter your response as an integer) b) What are the limits with three standard deviations from the target? Upper Control Limit (UCL): calories (enter your response as an integer)
The line AB has midpoint (2,5).
A has coordinates (1, 2).
Find the coordinates of B.
Answer:
[tex] X_m = \frac{A_x +B_x}{2}= \frac{1+B_x}{2}= 2[/tex]
And we can solve for [tex] B_x[/tex] and we got:
[tex] 1+B_x = 4[/tex]
[tex]B_x = 3[/tex]
[tex] Y_m = \frac{A_y +B_y}{2}= \frac{2+B_y}{2}= 5[/tex]
And we can solve for [tex] B_x[/tex] and we got:
[tex] 2+B_y = 10[/tex]
[tex]B_y = 8[/tex]
So then the coordinates for B are (3,8)
Step-by-step explanation:
For this case we know that the midpoint for the segment AB is (2,5)
And we know that the coordinates of A are (1,2)
We know that for a given segment the formulas in order to find the midpoint are given by:
[tex] X_m = \frac{A_x +B_x}{2}= \frac{1+B_x}{2}= 2[/tex]
And we can solve for [tex] B_x[/tex] and we got:
[tex] 1+B_x = 4[/tex]
[tex]B_x = 3[/tex]
[tex] Y_m = \frac{A_y +B_y}{2}= \frac{2+B_y}{2}= 5[/tex]
And we can solve for [tex] B_x[/tex] and we got:
[tex] 2+B_y = 10[/tex]
[tex]B_y = 8[/tex]
So then the coordinates for B are (3,8)
The coordinates of point B are (4, 8).
Explanation:To find the coordinates of point B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M(xm, ym) of a line segment with endpoints A(x1, y1) and B(x2, y2) are given by:
xm = (x1 + x2) / 2
ym = (y1 + y2) / 2
In this case, we are given that the midpoint M is (2, 5) and A is (1, 2). We can substitute these values into the formula:
2 = (1 + x2) / 2
5 = (2 + y2) / 2
Now, we can solve for x2 and y2:
x2 = 4
y2 = 8
Therefore, the coordinates of point B are (4, 8).
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Michael's bank contains only nickels, dimes, and quarters. There are 57 coins in all, valued at $4.55. The number of nickels is 7 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank
Answer:
10 dimes.
Step-by-step explanation:
Let n represent number of nickels, d represent number of dimes and q represent number of quarters.
We have been given that there are 57 coins in all. We can represent this information in an equation as:
[tex]n+d+q=57...(1)[/tex]
We are also told that the value of all coins is $4.55. We can represent this information in an equation as:
[tex]0.05n+0.10d+0.25q=4.55...(2)[/tex]
The number of nickels is 7 short of being three times the sum of the number of dimes and quarters together. We can represent this information in an equation as:
[tex]n+7=3(d+q)...(3)[/tex]
From equation (1), we will get:
[tex]d+q=57-n[/tex]
Substituting this value in equation (3), we will get:
[tex]n+7=3(57-n)[/tex]
[tex]n+7=171-3n[/tex]
[tex]n+3n+7-7=171-7-3n+3n[/tex]
[tex]4n=164[/tex]
[tex]\frac{4n}{4}=\frac{164}{4}[/tex]
[tex]n=41[/tex]
Therefore, there are 41 nickels in the bank.
[tex]d+q=57-n...(1)[/tex]
[tex]d+q=57-41...(1)[/tex]
[tex]d+q=16...(1)[/tex]
[tex]q=16-d...(1)[/tex]
Upon substituting equation (1) and value of n in equation (2), we will get:
[tex]0.05(41)+0.10d+0.25(16-d)=4.55[/tex]
[tex]2.05+0.10d+4-0.25d=4.55[/tex]
[tex]6.05-0.15d=4.55[/tex]
[tex]6.05-6.05-0.15d=4.55-6.05[/tex]
[tex]-0.15d=-1.5[/tex]
[tex]\frac{-0.15d}{-0.15}=\frac{-1.5}{-0.15}[/tex]
[tex]d=10[/tex]
Therefore, there are 10 dimes in the bank.
Jeanette grew 12 flowers with 2 seeds packets how many seed packets does jeanntte need to have a total of 18 flowers in the graden
Answer: 3 packets
12/2 = 6 seeds per packets
18/6 = 3 packets
Answer:
3
Step-by-step explanation:
If Jeanette grew 12 flowers with 2 seeds packets, that means that each seed packet grows 6 flower. 12/2=6
If each seed packet grows 6 flowers, 3 seed packets will give 18 flowers. Hope this helps!