Answer:
[tex]\frac{dV}{dt} = 155.82[/tex] [tex]\frac{ft^{3}}{min}[/tex]
Step-by-step explanation:
Since it is circular slick, it's volume can be modeled as,
[tex]V = \pi R^{2}h[/tex]
Where R is the radius in feet and h is the thickness of slick.
taking derivative of the above equation with respect to time yields,
[tex]\frac{dV}{dt} = \pi 2Rh \frac{dR}{dt}[/tex]
Where the rate of change of radius of the slick (dR/dt) is given,
[tex]\frac{dV}{dt} = \pi 2(400)(0.2)(0.31)[/tex]
[tex]\frac{dV}{dt} = 155.82[/tex] [tex]\frac{ft^{3}}{min}[/tex]
Therefore, the rate of change of volume is 155.82 cubic feet per minute.
The value of dV/dt using pi almost equal to 3.14 gives; dV/dt = 155.82 ft³/min
dV/dt = 155.82 ft³/min
We are given;
Radius; R = 400 ft
Height; h = 0.2 ft
Rate of Increase of radius; dr/dt = 0.31 ft/min
Formula for Volume of a cylinder is;
V = πr²h
Differentiation of both sides of V and r with respect to t gives;
dV/dt = 2πrh(dr/dt)
Plugging in the relevant values gives;
dV/dt = 2π × 400 × 0.2 × 0.31
dV/dt = 155.82 ft³/min
Read more at; https://brainly.com/question/23611212
Solve for x.
3x− 8 = −x −8
Answer:
x=0
Step-by-step explanation:
Cancel -8 on both sides.
3x=−x
Subtract -x from both sides.
3x+x=0
Simplify 3x+x to 4x.
4x=0
Divide both sides by 4
x=0
Brainliest please!
Answer:
Step-by-step explanation:
0
A bag contains 32 red blocks, 47 green blocks, 21 yellow blocks, and 25 purple blocks. You pick one block from the bag at random. Find the indicated theoretical probability.
P(green or purple)
Answer:
P(green or purple) = 0.576
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
32 + 47 + 21 + 25 = 125 blocks.
Of those, 47 + 25 = 72 are green of purple
P(green or purple) = 72/125 = 0.576
To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed 4 times. The resulting measurements (in grams) are: 0.95,1.02, 1.01, 0.98. Assume that the weighings by the scale when the true weight is 1 gram are normally distributed with mean μ. Use these data to compute a 95% confidence interval for μ.
Final answer:
To calculate a 95% confidence interval for the mean (μ) of a laboratory scale's measurements, the sample mean, standard deviation, and t-distribution are utilized to find the interval, which is approximately 0.9444 to 1.0356 grams. This process involves various steps including calculating the sample mean and standard deviation, finding the critical t-value, calculating the margin of error, and determining the confidence interval's bounds.
Explanation:
To compute a 95% confidence interval for μ, the mean of the weighings when the true weight is 1 gram, we first calculate the sample mean (μ) and the standard deviation (s) of the given measurements. The measurements are: 0.95, 1.02, 1.01, and 0.98 grams. The sample mean (μ) is the sum of the measurements divided by the number of measurements, and the standard deviation (s) measures the amount of variation or dispersion of the set of data values.
Calculate the sample mean (μ): (μ) = (0.95 + 1.02 + 1.01 + 0.98) / 4 = 0.99 grams.
Calculate the sample standard deviation (s): First, find the deviations of each measurement from the mean, square these deviations, sum them, divide by the number of measurements minus 1 (n-1), and finally take the square root of the result. (s) ≈ 0.02887 grams.
Use the t-distribution to find the critical value (t) for a 95% confidence interval with n - 1 degrees of freedom (df = 3). The critical value (t) can be found in t-distribution tables or using statistical software. For df = 3 and a 95% confidence level, (t) ≈ 3.182.
Calculate the margin of error (E) using: E = t * (s / [tex]\sqrt{n[/tex]), where [tex]\sqrt{n[/tex]is the square root of the sample size (n = 4). E ≈ 3.182 * (0.02887 / [tex]\sqrt{4[/tex] ) ≈ 0.0456 grams.
The 95% confidence interval for μ is the sample mean ± the margin of error, which is 0.99 ± 0.0456 grams, or approximately 0.9444 to 1.0356 grams.
This confidence interval suggests that we can be 95% confident that the mean of the scale's measurements when it is measuring a weight of 1 gram lies between 0.9444 grams and 1.0356 grams.
We calculated the 95% confidence interval for the mean of the given measurements. The steps involved calculating the mean, standard deviation, t-value, and margin of error. The confidence interval is 0.9397 g to 1.0403 g.
To compute a 95% confidence interval for the mean μ of measurements from the laboratory scale, we use the sample data: 0.95 g, 1.02 g, 1.01 g, and 0.98 g. We need to follow these steps:
Compute the sample mean ([tex]\bar_x[/tex]):[tex]\bar_x[/tex] = (0.95 + 1.02 + 1.01 + 0.98) / 4
= 0.99 g
Calculate the sample standard deviation (s):s = [tex]\sqrt{\frac{{(0.95 - 0.99)^2 + (1.02 - 0.99)^2 + (1.01 - 0.99)^2 + (0.98 - 0.99)^2}}{{4 - 1}}}[/tex]
≈ 0.0316 g
Find the critical t-value for 3 degrees of freedom (df = n - 1 = 4 - 1 = 3) at the 95% confidence level.
This value is roughly t0.025,3 ≈ 3.182.
Compute the margin of error (ME):ME = t0.025,3 * [tex](s / \sqrt{n})[/tex]
≈ 3.182 * (0.0316 / 2)
≈ 0.0503 g
Determine the confidence interval:([tex]\bar_x[/tex] - ME) to ([tex]\bar_x[/tex] + ME) = (0.99 - 0.0503) to (0.99 + 0.0503)
= 0.9397 g to 1.0403 g
Therefore, the 95% confidence interval for the mean mass μ of the standard weight is 0.9397 g to 1.0403 g.
Find the circumference of the circle.Use 3.14 pi
Looks like pizza
13in
Answer:
do you know your radius or diameter?
Identify the graph of the equation. What is the angle of rotation for the equation?
y2 + 8x - 0
a hyperbola, 30°
b. parabola; 90°
c.hyperbola; 180°
d. parabola, 0°
Answer:
d. parabola, 0°
Step-by-step explanation:
y² + 8x - 0
y² = -8x
Where x = cos t , y = sin t
Sin² t = -8 Cos t
1 - Cos² t = -8 Cos t
- Cos² t + 8 Cos t + 1 = 0
t = 2лπ ± (3 + √10) , л∈Z
Angle of rotation
Jake earned $62.50 in 5 hours. At the
same rate, how much will he earn in
8 hours?
Answer:
one hundred which is 100
which property of addition is used in the following (7+9)+5=7+(9+5)
Answer:
associative property of addition
Step-by-step explanation:
The 5 is substituted into the parentheses and the 7 is taken out.
he one-way ANOVA null hypothesis is rejected when the _________.Multiple Choiceratio of the within-treatments variance and the between-treatments variance is 1variability in the sample means can be explained by chanceratio of the within-treatments variance and the between-treatments variance is signficialy greater than 1two estimates of the variance are relatively close together
Answer: two estimates of the variance are relatively close together
Step-by-step explanation:
Melanie’s bedroom walls are 45% painted. The area of her walls totals 420 square feet.
What is the number of square feet of Melanie’s walls that still need to be painted?
Answer:
231 sq. ft.
Step-by-step explanation:
Total of anything is 100%
45% are painted, so not painted:
100 - 45 = 55%
The number of sq. ft. that still needs to be painted is basically 55% of 420 (total sq. ft.).
55% in decimal is 55/100 = 0.55
Now we multiply this with total:
0.55 * 420 = 231 sq. ft. (remaining)
In a test of the effectiveness of garlic for lowering cholesterol, 8181 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg/dL) have a mean of 0.40.4 and a standard deviation of 16.216.2. Use a 0.010.01 significance level to test the claim that with garlic treatment, the mean change in LDL cholesterol is greater than 00. What do the results suggest about the effectiveness of the garlic treatment? Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. What are the null and alternative hypotheses?
Answer:
With garlic treatment, the mean change in LDL cholesterol is not greater than 0.
Step-by-step explanation:
The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.
In this case a paired t-test is used to determine the effectiveness of garlic for lowering cholesterol.
A random sample of 81 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment.
The hypothesis for the test can be defined as follows:
H₀: With garlic treatment, the mean change in LDL cholesterol is not greater than 0, i.e. d ≤ 0.
Hₐ: With garlic treatment, the mean change in LDL cholesterol is greater than 0, i.e. d > 0.
The information provided is:
[tex]\bar d=0.40\\SD_{d}=16.2\\\alpha =0.01[/tex]
Compute the test statistic value as follows:
[tex]t=\frac{\bar d}{SD_{d}/\sqrt{n}}\\\\=\frac{0.40}{16.2/\sqrt{81}}\\\\=0.22[/tex]
The test statistic value is 0.22.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
Compute the p-value of the test as follows:
[tex]p-value=P(t_{n-1}>0.22)\\=P(t_{80}>0.22)\\=0.4132[/tex]
*Use a t-table.
The p-value of the test is 0.4132.
p-value= 0.4132 > α = 0.01
The null hypothesis was failed to be rejected.
Thus, it can be concluded that with garlic treatment, the mean change in LDL cholesterol is not greater than 0.
A survey published in the American Journal of Sports Medicine reported the num- ber of meters (m) per week swum by two groups of swimmers—those who competed exclusively in breaststroke and those who competed in the individual medley (which includes breaststroke). The number of meters per week practicing the breaststroke 1 was recorded for each swimmer, and the summary statistics are given below. Is there sufficient evidence to indicate that the average number of meters per week spent prac- ticing breaststroke is greater for exclusive breaststrokers than it is for those swimming individual medley?
Answer:
see explaination
Step-by-step explanation:
Let mu1 be the mean for exclusively breaststroke
Let mu2 be the mean for individual medley
----------------------------------------------------------------------------------------------------------
(a) H o: mu1=mu2 (i.e. null hypothesis)
Ha: mu1> mu2 (i.e. alternative hypothesis)
----------------------------------------------------------------------------------------------------------
(b) Since both sample sizes are grearter than n=30, we can use normal distriubtion.
It is a one-tailed test.
Given a=0.01, the critical value is Z(0.01) =2.33 (from standard normal table)
So the rejection region is Z>2.33
----------------------------------------------------------------------------------------------------------
(c) The test statistic is
Z=(xbar2-xbar2)/sqrt(s1^2/n1+s2^2/n2)
=(9017-5853)/sqrt(7162^2/130+1961^2/80)
=4.76
----------------------------------------------------------------------------------------------------------
(d) Since Z=4.76 is larger than 2.33, we reject the null hypothesis.
----------------------------------------------------------------------------------------------------------
(e) In conclusion there is sufficient evidence to indicate that the average number of meter per week spent practicing breaststroke is greater for exclusive breaststrokers than it is for those swimming individual medley
There is sufficient evidence to indicate that the mean number of breaststroke is greater for exclusive breaststrokers than for swimming individual medley.
What are null hypotheses and alternative hypotheses?In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
Let μ₁ be the mean for the exclusive breaststroke.
Let μ₂ be the mean for the individual medley.
For the null hypothesis, we have
H₀: μ₁ = μ₂
For the alternative hypothesis, we have
Hₐ: μ₁ > μ₂
The sample size of both is greater than 30, then the normal distribution will be
a = 0.01
The critical value is z(0.01) = 2.33 (From standard normal table)
So the rejection region is z > 2.33
The test statistic will be
[tex]z = \dfrac{\mu_2 - \mu_1}{\sqrt{s^2_1/n_1 + s^2_2/n_2}}\\\\\\z = \dfrac{9017 - 5853}{\sqrt{7162^2/130+1961^2/80}}\\\\\\z = 4.76[/tex]
Since the value of z is greater than 2.33, then we reject the null hypothesis.
More about the null hypotheses and alternative hypotheses link is given below.
https://brainly.com/question/9504281
The percentage of adult height attained by girls who are x years old can be modeled by f(x)equals 62 plus 35 log (x minus 4 )where x represents the girl's age (from 5 to 15) and f(x) represents the percentage of her adult height. Use this function to determine approximately what percent of her adult height girls are at age 15.
Answer:
[tex]98.45\%[/tex]
Step-by-step explanation:
The percentage of adult height attained by girls who are x years old can be modeled by: [tex]f(x)= 62 +35 log (x -4 )[/tex]
Where x represents the girl's age (from 5 to 15); and
f(x) represents the percentage of her adult height.
If a girl's age, x=15
Then, from f(x), the percentage of her adult height:
[tex]f(15)= 62 +35 log (15 -4 )\\=62+35log11\\=98.45\%[/tex]
The percentage of adult height attained by a girl who is 15 years old is approximately 98.45%.
A square-based prism made of clay had dimensions of 6 by 6 by 10. A pyramid was removed from the prism so the prism has no top. what is the total surface area of the remaining clay solid if the slant height of the pyramid is 10.5
Answer:
Step-by-step explanation:
Given that,
The square based prism has dimensions is
6 by 6 by 10
Length = 6
Width = 6
Height = 10
Slant height of pyramid is given as
h = 10.6
Note: The base of the pyramid matches the top of the square prism, so it's square-based prism.
So, we are going to have
4 rectangular faces(i.e the square Base prism rectangular faces)
1 square face ( the based of the prism)
four triangular faces( the top pyramid)
So, area of the four face
It is a rectangular shape and it is calculated using
A = length × Breadth
Area of one face is
A = L × W
A = 6 × 10 = 60 Square units
And there are 4 similar rectangle
So, area of the four rectangles is
A' = 4 × 60 = 240 square unit
Now, area of the square base below can be calculated using
A = s²
A" = L² = 6² = 36 Square units
Now, area of the four triangle pyramid at the top
Area of triangle is given as
A = ½bh
A = ½ × 6 × 10.6
A = 31.8 square units.
The area of the four triangles becomes
A"' = 4 × 31.8
A"' = 126 square units
Then, the total area of the shape is
A(total ) = A' + A" + A"'
A(total) = 240 + 36 + 126
A(total) = 402 Square units
So, the total area of the solid shape is 402 Square units
a) A standard deck consists of 52 cards. Four of the cards are aces. Twenty-six of the cards are red. A poker hand consists of 5 cards dealt at random from the deck. Without calculation, say which has the bigger SD and explain why: the number of aces in the poker hand the number of red cards in the poker hand b) Use a code cell to find the numerical values of the SDs
Answer:
a)The number of aces in the poker hand is greater
b)It is about[tex]\sqrt{2}[/tex] as accurate.
Piecewise and Combining Functions
It has been determined with 95% confidence that the proportion of on-line students at SPC who live in Pinellas County is between 0.73 and 0.77. Determine the sample proportion of on-line SPC students who live in Pinellas County.
Answer:
sample proportion is 0.75
Step-by-step explanation:
given data
confidence = 95%
Pinellas County between = 0.73 and 0.77
solution
We write confidence interval in terms of p and E as
(p - E ) < P < ( p + E ) ................1
when we compare it 0.73 < p < 0.77
we get
so here
p - E = 0.73 ................2
and E is 0.02 so
p - 0.02 = 0.73
p = 0.75
The sample proportion of on-line SPC students who live in Pinellas County is 0.75.
The sample proportion is the point estimate that lies in the middle of the confidence interval.
To find the sample proportion from the given confidence interval, you calculate the average of the lower and upper bounds.
The lower bound is 0.73, and the upper bound is 0.77.
0.73 + 0.77 = 1.50
1.50 / 2
= 0.75
Therefore, the sample proportion of on-line SPC students who live in Pinellas County is 0.75.
Which correctly describes a cross section of the right rectangular prism if the base is a rectangle measuring 15 inches by 8 inches? Select three options..
1.) A right rectangular prism with length 15 inches, width of 8 inches, and height of 6 inches.
2.) A cross section parallel to the base is a rectangle measuring 15 inches by 8 inches.
3.) A cross section parallel to the base is a rectangle measuring 15 inches by 6 inches.
4.) A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.
5.) A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 4 inches by 15 inches.
6.) A cross section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.
The correct options, given the base dimensions and assuming a height of 6 inches, would be 2 and 4, while options 1, 3, 5, and 6 cannot be confirmed without more information.
When analyzing the cross sections of a rectangular prism, it is crucial to consider the orientation of the cut in relation to the base and sides of the prism. The correct descriptions of the cross sections for a right rectangular prism with a base measuring 15 inches by 8 inches and an unspecified height would be as follows:
A cross section parallel to the base will have the same dimensions as the base, which is 15 inches by 8 inches.
A cross section perpendicular to the base through the midpoints of the 8-inch sides forms a rectangle, but since the heights have not been provided for the prism, it cannot be defined specifically.
If a cross section is perpendicular to the base but no other information is provided, the dimensions of the cross section cannot be fully determined.
However, based on the options given, we can discern the following:
Option 2 is correct because a cross section parallel to the base would be identical to the base, measuring 15 inches by 8 inches.
Option 4 is correct since it specifies a rectangle measuring 6 inches by 15 inches assuming the height of the prism is 6 inches.
Options 1, 3, 5, and 6 cannot be determined to be correct without additional information regarding the height or manner of the cuts. Specifically, option 6 describes a cross section not parallel to the base but does not provide enough information about the shape or dimensions beyond the length being greater than 15 inches.
Research at the University of Toledo indicates that 50 percent ofthe students change their major area of study after their firstyear in a program. A random sample of 100 students in the Collegeof Business revealed that 48 had changed their major area of studyafter their first year of the program.Has there been a significant decrease in the proportion of studentswho change their major after the first year in this program? Testat the .05 level of significance.(a) What is the decisionrule? (Round youranswer to 3 decimal places.)(b) The value ofthe test statistic is . (Roundyour answer to 2 decimal places.)(c) What is yourdecision regarding ?
Answer:
a) The decision rule is:
Reject the null hypothesis if P-value is under 0.05 (or the test statistic is larger than z=-1.645).
b) Test statistic z=-0.30
c) The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that there has been a significant decrease in the proportion of students who change their major after the first year in this program.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim we have to test is that there has been a significant decrease in the proportion of students who change their major after the first year in this program.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi< 0.5[/tex]
The significance level is α=0.05.
The sample has a size n=100.
The sample proportion is p=0.48.
[tex]p=X/n=48/100=0.48[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{100}}\\\\\\ \sigma_p=\sqrt{0.0025}=0.05[/tex]
We can calculate the test statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.48-0.5+0.5/100}{0.05}=\dfrac{-0.015}{0.05}=-0.3[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]P-value=P(z<-0.3)=0.3821[/tex]
The P-value (0.3821) is bigger than the significance level (0.05), then the effect is not significant.
The null hypothesis failed to be rejected.
If we use the critical value approach, the critical value of z for this test with 5% significance level is z=1.645.
There is not enough evidence to support the claim that there has been a significant decrease in the proportion of students who change their major after the first year in this program.
964 two correct wrong place
147 one correct wrong place
189 one correct right place
286 one correct wrong place
523 all wrong
Answer:
679
Step-by-step explanation:
The goal of this exercise is to find a three digit number given five statements.
1 - We can conclude that two digits out of 964 are correct but in the wrong place.
2 - One digit out of 147 is correct, but in the wrong place
3 - One digit out of 189 is correct and in the right place. Since 1 is on the same place in 147 and 189, 1 is not the correct digit. The correct digit is either 8 or 9.
4 - One digit out of 286 is correct, but in the wrong place. Since 8 is on the same place in 189 and 286, 8 is not the correct digit. We can then conclude that 9 is correct (statement 3) and in the right place (third) and that either 2 or 6 are correct but in the wrong place.
5 - 523 are all wrong. We can then conclude that 6 is correct and that is not in the third or second place, which leaves it in the first place.
If 1 and 4 are incorrect, from the second statement, we infer that 7 is the remaining correct digit at the second place.
Therefore the number is 679
Future scientists: Education professionals refer to science, technology, engineering, and mathematics as the STEM disciplines. A research group reported that 28% of freshmen entering college in a recent year planned to major in a STEM discipline. A random sample of 90 0 freshmen is selected. Round the answer to at least four decimal places.
Answer:
The probability that the proportion of freshmen in the sample of 90 who plan to major in a STEM discipline is between 0.29 and 0.37 is P=0.0166.
Step-by-step explanation:
The question is incomplete. You have to add:
Find the probability that the proportion of freshmen in the sample of 90 who plan to major in a STEM discipline is between 0.29 and 0.37.
We have a sample of n=90 out of a population with a proportion p=0.28.
We have to calculate the probability that the sample has a proportion between 0.29 and 0.37.
First, we calculate the standard deviation of the sampling distribution:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.28*0.72}{90}}=\sqrt{0.0024}=0.047[/tex]
We can now calculate the z-score for 0.29 and 0.37
[tex]z_1=\dfrac{p_1-p}{\sigma}=\dfrac{0.29-0.28}{0.0047}=\dfrac{0.01}{0.0047}=2.13\\\\\\z_2=\dfrac{p_2-p}{\sigma}=\dfrac{0.37-0.28}{0.0047}=\dfrac{0.09}{0.0047}=19.15[/tex]
Now, we can calculate the probability as:
[tex]P(0.29<\hat p<0.37)=P(2.13<z<19.15)=P(z<19.15)-P(z<2.13)\\\\P(0.29<\hat p<0.37)=1-0.9834=0.0166[/tex]
The situation is describing a binomial probability scenario. Given the probability of a freshman choosing a STEM discipline as 28% (0.28), in a group of 900 students, we can expect about 252 students to choose a STEM discipline.
Explanation:The reported statistic suggests that 28% of freshmen entering college in a recent year planned to major in a STEM discipline. Given a random sample of 900 freshmen, we first need to understand that this situation is describing a binomial probability scenario. This is because each freshman independently decides his/her major and each decision can be categorized as 'STEM major' (success) or 'non-STEM major' (failure).
1. The probability of success (p) = 0.28.
2. The size of the collection of individuals (n) = 900.
Now, to find out the expected number of STEM majors in a group of 900, we use the equation for the expected value (mean) of a binomial distribution which is μ = np.
Substitute: μ = (900)(0.28) = 252. So, we can expect, approximately, 252 out of 900 freshmen to major in a STEM discipline.
Learn more about Binomial probability here:https://brainly.com/question/39666605
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the point A(7,1) is reflected over the point (4,0) and its image is point B. What are the coordinates of point B?
Answer: The coordinates of point be are (1,-1)
Step-by-step explanation:
The reflected point will be equidistant from the point over which it is reflected as the original point and in the same line as the original point and the reflected point.
Find the difference between the x and y values of the given points and add that value (distance) to the reflection point.
x-values: 4-7 = -3 y-values: 0-1 = -1
Add to reflection point x: 4-3 = 1 y: 0 -1 = -1
Final answer:
To reflect point A(7, 1) over point (4, 0) to find point B, calculate the horizontal and vertical distances from A to (4, 0) and subtract these distances from (4, 0) to get B's coordinates, resulting in point B being at (1, -1).
Explanation:
To find the coordinates of point B after reflecting point A(7, 1) over point (4, 0), we need to apply the concept of reflections in the Cartesian plane. When a point is reflected over another, the line joining the original point and the point of reflection is bisected perpendicularly by the point of reflection. This means that point B will have the same distance from (4, 0) as point A, but in the opposite direction.
Here's the step-by-step method to find the coordinates of B:
Calculate the horizontal and vertical distances from A to the mirror point (4, 0): Horizontal distance = 7 - 4 = 3, Vertical distance = 1 - 0 = 1.
Subtract these distances from the mirror point to find B's coordinates: B's x-coordinate = 4 - 3 = 1, B's y-coordinate = 0 - 1 = -1.
So, the coordinates of point B after the reflection are (1, -1).
Which is true?
A) 6 inches = 2 feet
B) 6 yards = 2 feet
C) 6 feet = 2 yards
D) 6 feet = 2 inches
Answer:
C.
Step-by-step explanation:
It is believed that as many as 23% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group. Question 1. How many of this younger age group must we survey in order to estimate the proportion of non-grads to within .10 with 90% confidence
Answer: here are 48 adults of this younger age group.
Step-by-step explanation:
Since we have given that
Error = 0.10
p = 23% = 0.23
At 90% level of significance, i.e. α = 0.10
So, the value of z = 1.645
[tex]n=(\dfrac{z}{E})^2p(1-p)\\\\n=(\dfrac{1.645}{0.1})^2(0.23)(1-0.23)\\\\n=270.6025\times 0.23\times 0.77\\\\n=47.92\\\\n\approx 48[/tex]
Hence, there are 48 adults of this younger age group.
A newsletter publisher believes that 49% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.05 level to refute the publisher's claim? State the null and alternative hypotheses for the above scenario.
Answer:
A newsletter publisher believes that 49% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.05 level to refute the publisher's claim? State the null and alternative hypotheses for the above scenario.
Null hypothesis ⇒ H₀: p = 0.49
Alternative hypothesis ⇒ Hₐ: p ≠ 0.49
Step-by-step explanation:
Given that α = 0.05
From the given information, the null and alternative hypothesis is expressed below:
Null hypothesis ⇒ H₀: p = 0.49
Alternative hypothesis ⇒ Hₐ: p ≠ 0.49
Write an expression to represent the amount of water remaining in a 4th tank which is the same size
as the others and which contains 512 spheres. Leave your expression in terms of pie
Answer:
Amount of water = x³- 4/3 π (x/2)³
Step-by-step explanation:
Let's assume there is a cubic tank, we have 512 spheres in it. Now we have to write an expression in terms of pie.
Let's suppose:
x = edge of the tank
volume of a cube = x³
volume of sphere = 4/3 π r³
where, r = radius of a sphere.
So, we have 512 spheres in total, it means there are 8 spheres in a single row.
(8)³ = 512
It means radius of a single sphere will be = x/16, where x represents the edge of the cubic tank.
Radius of sphere = x/16
So, the formula to calculate the amount of water in the tank will be:
Amount of water in the tank = Volume of cube - Volume of all spheres.
Amount of water = x³ - 512 x ( 4/3 π r³)
Amount of water = x³- 512 x ( 4/3 π (x/16)³)
Amount of water = x³- 512 x ( 4/3 π x³/4096)
Amount of water = x³- 4/3 π x³/8
Amount of water = x³- 4/3 π (x/2)³
Hence, this will be the expression required.
an eggseller charged Mrs ada#1450 for 100 eggs . how much did she pay for each egg
Answer:
14.5
step by step explanation:
1450÷100= 14.5
Final answer:
Mrs. Ada paid #14.50 for each egg after being charged #1450 for 100 eggs. This is calculated by dividing the total cost by the number of eggs.
Explanation:
To calculate the cost of each egg when Mrs. Ada charged #1450 for 100 eggs, we need to divide the total cost by the number of eggs. This is a simple division problem under the subject of mathematics.
The formula to find the cost per egg is:
Total cost of eggs ÷ Number of eggs = Cost per egg
#1450 ÷ 100 eggs = #14.50 per egg
Therefore, Mrs. Ada paid #14.50 for each egg.
A survey of 1,565 households estimated that 72% of the households in a given state owned a television. What is the population?
Answer:
all the households in given state. part 2 is 1565 households surveyed.
Step-by-step explanation:
Part 1
A. all the households given state
Part 2
B. 1565 households surveyed.
Save & Ext
Solving Exponential and Logarithmic Functions: Tutorial
brief evaluation of your work
Activity
Question 1
The growth of the Dow Jones Industrial Average from can be modeled through an exponential function. The graph of this function has been
extrapolated through 2012 to forecast a prediction. Use this graph to estimate the DJIA in the years 2002, 2004, 2006, 2008, and 2010. Then, use
the Internet to research the yearly performance of the DJIA and compare your predictions with the actual value at the end of those years.
Answer:
Year Prediction Actual
2002 12,500 8,342
2004 16,250 10,783
2006 21,250 12,463
2008 26,250 8,776
2010 32,500 11,578
Step-by-step explanation:
look at the graph and look for where the year and average meet fir each year. then look up online the actual closing price.
Without specific input data and a graph, it is not possible to perform this task here. However, typically, one would estimate values from the graph for specified years and then compare with the actual DJIA values researched online.
Explanation:This task requires estimations based on an exponential function graph for the Dow Jones Industrial Average (DJIA) for specified years and then comparing these estimations with the actual values. However, without the graph and data, this is not possible to demonstrate here specifically.
Usually, to estimate the values from the graph from years 2002, 2004, 2006, 2008, and 2010, we would look at the y-axis (representing DJIA's value) for the corresponding years on the x-axis. The estimated values can then be compared with the actual yearly performance of DJIA, which can be researched online on credible financial platforms.
It's worth noting that this task combines mathematical skills and research ability, employing both to draw a comparison between actual and predicted results from a mathematical model.
Learn more about Exponential Function here:https://brainly.com/question/37289664
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Anwer question bellow
Answer:
C) y=4x-12.5
Step-by-step explanation:
8x-2y=25
-2y=25-8x
y=-12.5+4x
y=4x-12.5
Therefore C is the right answer
An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:
418 421 422 422 425 429 431 434 437
439 446 447 449 452 457 461 465
Calculate a two-sided 95% confidence interval for true average degree of polymerization. (Round your answers to two decimal places.)
Answer:
[tex]438.53-2.12\frac{14.988}{\sqrt{17}}=430.82[/tex]
[tex]438.53+2.12\frac{14.988}{\sqrt{17}}=446.24[/tex]
So on this case the 95% confidence interval would be given by (430.82;446.24)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the mean and the sample deviation we can use the following formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
The mean calculated for this case is [tex]\bar X=438.53[/tex]
The sample deviation calculated [tex]s=14.988[/tex]
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=17-1=16[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,16)".And we see that [tex]t_{\alpha/2}=2.12[/tex]
Now we have everything in order to replace into formula (1):
[tex]438.53-2.12\frac{14.988}{\sqrt{17}}=430.82[/tex]
[tex]438.53+2.12\frac{14.988}{\sqrt{17}}=446.24[/tex]
So on this case the 95% confidence interval would be given by (430.82;446.24)