Answer:
90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].
Step-by-step explanation:
We are given that a sample of 37 cars traveling on a particular stretch of highway revealed an average speed of 70.7 miles per hour with a standard deviation of 6.3 miles per hour.
Firstly, the pivotal quantity for 90% confidence interval for the true mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average speed of cars = 70.7 miles per hour
s = sample standard deviation = 6.3 miles per hour
n = sample of cars = 37
[tex]\mu[/tex] = true mean speed
Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.
So, 90% confidence interval for the true mean, [tex]\mu[/tex] is ;
P(-1.688 < [tex]t_3_6[/tex] < 1.688) = 0.90 {As the critical value of t at 36 degree of
freedom are -1.688 & 1.688 with P = 5%}
P(-1.688 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.688) = 0.90
P( [tex]-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90
P( [tex]\bar X-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90
90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]70.7-1.688 \times {\frac{6.3}{\sqrt{37} } }[/tex] , [tex]70.7+1.688 \times {\frac{6.3}{\sqrt{37} } }[/tex] ]
= [68.9517 miles per hour , 72.4483 miles per hour]
Therefore, 90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].
The interpretation of the above interval is that we are 90% confident that the true mean speed of all cars will lie between 68.9517 miles per hour and 72.4483 miles per hour.
We want to use this information to determine if there is an effect of friendship. In other words, is the mean price when buying from a friend the same as (or different from) the mean price when buying from a stranger? Assume the two groups have the same population standard deviation, and use significance level 0.05. Suppose that mu1 is the true mean price when buying from a friend and mu2 is the true mean price when buying from a stranger. (a) What are the null and alternative hypotheses?
Answer:
H0 : mu1 = mu2
Ha : mu1 ≠ mu2
Which means
Null hypothesis H0; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is the same/equal
Alternative hypothesis Ha; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is different (not equal)
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean(i.e it tries to prove that the old theory is true). While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
Therefore, for the case above;
H0 : mu1 = mu2
Ha : mu1 ≠ mu2
Which means
Null hypothesis H0; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is the same/equal
Alternative hypothesis Ha; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is different (not equal)
A person has 5 tickets for a concert and she wants to invite 4 of her 8 best friends. How many choices does she have, if two of her friends do not get along and cannot be both invited?
Answer:
55
Step-by-step explanation:
Combinations formula is used to make choice of 'R' out of 'N' options =
N(C)R = N ! / [ R ! . (N-R)! ]
Total choices to choose 4 out of 8 friends = 8C4
= 8! / (4! 4!)
= 70
Choices for calling them 2 together = 2C2 x 6C2
= 1 x [ 6! / (2! 4!)]
= 15
So : Number of choices that the 2 friends are not called together = Total choices - choices they are called together
= 70 - 15 = 55
It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose you randomly survey 11 California residents. We are interested in the number who have adequate earthquake supplies.What is the probability that at least 8 have adequate earthquake supplies?
Is it more likely that none or that all of the residents surveyed will have adequate earthquake
supplies? Why?
Answer:
[tex]P(X\geq 8)=0.0043\\\\[/tex]
It's more likely that all of the residents surveyed will have adequate earthquake supplies since it has a probability of 98.02% which is very close to 100%.
Step-by-step explanation:
-This is a binomial probability problem with the function:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}[/tex]
-Given p=0.3, n=11, the is calculated as:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X\geq 8)=P(X=8)+P(X=9)+P(X=10)+P(X=11)\\\\={11\choose 8}0.3^8(0.7)^3+{11\choose 9}0.3^9(0.7)^2+{11\choose 10}0.3^{10}(0.7)^1+{11\choose 11}0.3^{11}(0.7)^0\\\\=0.0037+0.0005+0.00005+0.000002\\\\=0.0043[/tex]
Hence, the probability that at least 8 have adequate supplies 0.0043
#The probability that non has adequate supplies is calculated as;
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X= 0)={11\choose 0}0.3^{0}(0.7)^{11}\\\\=0.0198[/tex]
#The probability that all have adequate supplies is calculated as:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X= All)=1-{11\choose 0}0.3^{0}(0.7)^{11}\\\\=1-0.0198\\\\=0.9802[/tex]
Hence, it's more likely that all of the residents surveyed will have adequate earthquake supplies since [tex]P(All)>P(None)\ \[/tex] and that this probability is 0.9802 or 98.02% a figure close to 1
Final answer:
The probability that at least eight California residents have adequate earthquake supplies when surveying 11 can be calculated with the binomial distribution, summing probabilities for exactly 8, 9, 10, and 11. None having adequate supplies is more likely than all, given the 30% success rate. The average number of surveys before finding a resident without supplies is close to 2, and before finding one with supplies, it is approximately 3.
Explanation:
The probability of at least eight California residents having adequate earthquake supplies when surveying 11 residents can be calculated using the binomial distribution formula. Given that the success probability (having adequate supplies) is 30% (0.3), we can calculate the probability for exactly 8, 9, 10, and 11 residents and sum these probabilities to get the total probability for 'at least 8'.
The random variable X can be defined as the number of successes in n independent Bernoulli trials, with success on each trial having probability p. Here, X represents the number of California residents with adequate earthquake supplies in our sample of 11. The values that X can take on are 0, 1, 2, ..., 11.
To find the probability of none or all residents having adequate supplies, we calculate the probabilities for X = 0 and X = 11. The probability of none (X = 0) would be 0.7¹¹, and the probability of all (X = 11) would be 0.3¹¹. Between these, the probability of none is higher due to the lower success probability.
For the expected number of surveys until finding a resident without adequate supplies, we can use the geometric distribution where the expected value E(X) is 1/p. In this case, p = 0.7 (probability of not having adequate supplies), so E(X) would be approximately 1.43, meaning on average we would have to survey close to one or two residents before finding one without adequate supplies.
Conversely, the expected number of surveys until finding one with adequate supplies would be 1/q, where q = 0.3 (probability of having adequate supplies), giving us an expected value of around 3.33 surveys.
A student's tuition was 2800. They took a loan out for 6/7 of the tuition. How much was the loan
What is the volume of a hemisphere with a diameter of 52.9 inch, rounded to the nearest tenth of a cubic inch ?
Answer:
38755.7
Step-by-step explanation:
The volume of the hemisphere is 55495.5 cubic inches.
Explanation:To find the volume of a hemisphere, we can use the formula for the volume of a sphere and divide it by 2.
The volume of a sphere can be calculated using the formula:
V = (4/3)πr³
Given that the diameter of the hemisphere is 52.9 inches, we can find the radius by dividing the diameter by 2:
Radius = Diameter / 2 = 52.9 inches / 2 = 26.45 inches
Now we can calculate the volume of the hemisphere:
Volume = (4/3)π(26.45 inches)³ / 2
Using the value of π as approximately 3.14159, we can substitute the values into the formula:
Volume ≈ (4/3) × 3.14159 × (26.45 inches)³ / 2
Simplifying the calculation:
Volume ≈ 55495.5314 cubic inches
Rounding to the nearest tenth of a cubic inch, the volume of the hemisphere is approximately 55495.5 cubic inches.
The National Center for Health Statistics interviewed 5409 adults smokers in 2015, and 2636 of them said they had tried to quit smoking during the past year. Consider this to be a random sample. a) Find a 95% confidence interval for the proportion of smokers who have tried to quit within the past year.
Answer:
0.4740<p<0.5006
Step-by-step explanation:
-Given [tex]n=5409, \ x=2636 , \ CI=0.95[/tex]
#we calculate the proportion of trial quitters;
[tex]\hat p=\frac{2636}{5409}\\\\=0.4873[/tex]
For a confidence level of 95%:
[tex]z_{\alpha/2}=z_{0.025}\\\\=1.96[/tex]
The confidence interval is calculated as follows:
[tex]Interval= \hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\\\\\=0.4873\pm 1.96\times\sqrt{\frac{0.4873(1-0.4873)}{5409}}\\\\\\\\=0.4873\pm0.0133\\\\\\=[0.4740,0.5006][/tex]
Hence, the 95% confidence interval is 0.4740<p<0.5006
The 95% confidence interval for the proportion of smokers who have tried to quit within the past year is (0.4738, 0.5004), calculated using the sample proportion and the z-score for the 95% confidence level.
Explanation:To find the 95% confidence interval for the proportion of smokers who have tried to quit within the past year, we use the formula for a confidence interval for a population proportion:
CI = p± z*(√p(1-p)/n)
Where:
CI = Confidence Interval
p = Sample proportion (successes/sample size)
z = z-score associated with the confidence level
n = Sample size
Given:
p = 2636/5409
n = 5409
And for a 95% confidence level, the z-score is typically about 1.96.
Step 1: Calculate the sample proportion (p):
2636/5409 = 0.4871
Step 2: Calculate the standard error (SE):
SE = √[0.4871*(1-0.4871)/5409] = 0.0068
Step 3: Calculate the margin of error (ME):
ME = z * SE = 1.96 * 0.0068 = 0.0133
Step 4: Calculate the confidence interval:
Lower bound = p - ME = 0.4871 - 0.0133 = 0.4738
Upper bound = p + ME = 0.4871 + 0.0133 = 0.5004
So, the confidence interval is (0.4738, 0.5004).
PLEASE HELP WILL MARK BRAINLIEST!
For the function below, is the discriminant positive, negative, zero
y=x^2 + 4x + 4
A group of n people enter an elevator in a building with k floors. Each person independently selects a floor uniformly at random (each with equal probability 1/k). The elevator stops at each floor selected (by at least one person). Let N be the number of stops. (a) [3 marks] Find a simple expression for EN, the average number of stops. Bonus [2 marks] Suppose that n
Answer:
Hence the person stop at floor by at least one person will be
E(X)=(summation from K=1 to k)[1-{(k-1)/k}^n]
Step-by-step explanation:
Given:
There are n peoples and k floors in a building.
Selects floor with 1/k probability .
To find :
Elevator stop at each floor by at least one person.
Solution:
Now
let K= number of floor at which at least one person will be stopping.
For getting E(X)
consider a variable Ak =1 if a least one person get of the elevator
and values for k=1,2,3.....k
K=(summation From k=1 to k)Ak
E(K)=((summation From k=1 to k) E[Ak]
=(summation From k=1 to k)[[tex]1-{(k-1/k)^n[/tex]
Hence the person stop at floor by at least one person will be
E(K)=(summation from K=1 to k)[1-{(k-1)/k}^n]
Create a list in steps, in order, that will solve the following equation. 3(x+1^2)=108
Answer: x=35
Step-by-step explanation:
1. Divide both by 3
2. Simplify-x+1=36
3. Subtract 1 form both sides
You answer will be x=35
Answer:
Divide Both Sides by 3
Take the Square Root of Both Sides
Subtract 1 from Both Sides
Step-by-step explanation:
Pray!
1. A group of 400 town residents is asked to attend a
town hall meeting. Of the 400 residents asked to
attend, 36 were able to attend. What percentage of the
town residents were able to attend?
Answer:
9%
Step-by-step explanation:
36/400=9/100=9%
What is the probability that X is between 12 and 60?
Certain car manufacturers install a gauge that tells the driver how many miles they can drive until they will run out of gas. A study was conducted to test the accuracy of these gauges. Each driver was assigned a certain gauge reading until empty to watch for. When their car announced it had that many miles remaining until empty, they began to measure their distance traveled. After they ran out of gas, they reported the distance they were able to drive (in miles) as well as the gauge reading they were assigned (in miles). Here is computer output showing the regression analysis: Regression Analysis: Distance versus Gauge Reading Predictor Coef SE Coet Constant -0.7928 3.2114 -0.2469 0.8060 Gauge 1.1889 0.0457 26.0310 0.0000 B = 7.0032 R-39 = 0.9326 2-3q(adj) = 0.9312 Identify and interpret the slope of the regression line used for predicting the actual distance that can be driven based on the gauge reading.
Answer:
that a hard question
Step-by-step explanation:
i tried to use a calculator and graphs to solve it but I couldn't
Answer:
Slope = 1.1889. The predicted distance the drivers were able to drive increases by 1.1889 miles for each additional mile reported by the gauge.
Step-by-step explanation:
The slope is the second value under the “Coef” column. The interpretation of slope must include a non-deterministic description (“predicted”) about how much the response variable (actual number of miles driven) changes for each 1-unit increment of change in the explanatory variable (the gauge reading) in context.
Step by step
Help ?
Given:
The given figure consists of a triangle, a rectangle and a half circle.
The base of the triangle is 2 mi.
The height of the triangle is 4 mi.
The length of the rectangle is 9 mi.
The diameter of the half circle is 4 mi.
The radius of the half circle is 2 mi.
We need to determine the area of the enclosed figure.
Area of the triangle:
The area of the triangle can be determined using the formula,
[tex]A=\frac{1}{2}bh[/tex]
where b is the base and h is the height
Substituting b = 2 and h = 4, we get;
[tex]A=\frac{1}{2}(2\times 4)[/tex]
[tex]A=4 \ mi^2[/tex]
Thus, the area of the triangle is 4 mi²
Area of the rectangle:
The area of the rectangle can be determined using the formula,
[tex]A=length \times width[/tex]
Substituting length = 9 mi and width = 4 mi, we get;
[tex]A=9 \times 4[/tex]
[tex]A=36 \ mi^2[/tex]
Thus, the area of the rectangle is 36 mi²
Area of the half circle:
The area of the half circle can be determined using the formula,
[tex]A=\frac{\pi r^2}{2}[/tex]
Substituting r = 2, we get;
[tex]A=\frac{(3.14)(2)^2}{2}[/tex]
[tex]A=\frac{(3.14)(4)}{2}[/tex]
[tex]A=\frac{12.56}{2}[/tex]
[tex]A=6.28[/tex]
Thus, the area of the half circle is 6.28 mi²
Area of the enclosed figure:
The area of the entire figure can be determined by adding the area of the triangle, area of rectangle and area of the half circle.
Thus, we have;
Area = Area of triangle + Area of rectangle + Area of half circle
Substituting the values, we get;
[tex]Area=4+36+6.28[/tex]
[tex]Area = 46.28 \ mi^2[/tex]
Thus, the area of the enclosed figure is 46.28 mi²
The caffeine content (in mg) was examined for a random sample of 50 cups of black coffee dispensed by a new machine. The mean and the standard deviation were 110 mg and 7.1 mg respectively. Use the data to construct a 98% confidence interval for the mean caffeine content for cups dispensed by the machine. Interpret the interval!
Answer:
We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 mg .
Step-by-step explanation:
Given -
The sample size is large then we can use central limit theorem
n = 50 ,
Standard deviation[tex](\sigma)[/tex] = 7.1
Mean [tex]\overline{(y)}[/tex] = 110
[tex]\alpha =[/tex] 1 - confidence interval = 1 - .98 = .02
[tex]z_{\frac{\alpha}{2}}[/tex] = 2.33
98% confidence interval for the mean caffeine content for cups dispensed by the machine = [tex]\overline{(y)}\pm z_{\frac{\alpha}{2}}\frac{\sigma}\sqrt{n}[/tex]
= [tex]110\pm z_{.01}\frac{7.1}\sqrt{50}[/tex]
= [tex]110\pm 2.33\frac{7.1}\sqrt{50}[/tex]
First we take + sign
[tex]110 + 2.33\frac{7.1}\sqrt{50}[/tex] = 112.34
now we take - sign
[tex]110 - 2.33\frac{7.1}\sqrt{50}[/tex] = 107.66
We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 .
Final answer:
A 98% confidence interval for the mean caffeine content of cups dispensed by the machine is calculated using the sample mean, the standard deviation, and the Z-score for a 98% confidence level, leading to an interval of (107.72 mg, 112.28 mg). We can be 98% confident that the true mean caffeine content lies within this range.
Explanation:
To construct a 98% confidence interval for the mean caffeine content of cups dispensed by the machine, we use the provided sample mean (μ), which is 110 mg, and the standard deviation (s), which is 7.1 mg, of the 50 cups sampled. Since the sample size is 50, which is more than 30, we can use the Z-distribution as an approximation of the T-distribution for this confidence interval as the Central Limit Theorem suggests that the distribution of sample means will be normally distributed if the sample size is large enough. Using a Z-score for 98% confidence, which typically is approximately 2.33 (you would obtain the exact value from a Z-table), the margin of error (E) can be calculated using the formula E = Z * (s/√n), where n is the sample size (50 in this case).
The margin of error is then 2.33 * (7.1/√50), which equals approximately 2.28 mg. The 98% confidence interval is therefore the sample mean plus or minus the margin of error, which is 110 mg ± 2.28 mg or (107.72 mg, 112.28 mg).
The interpretation of this confidence interval is that we can be 98% confident that the true mean caffeine content of all cups of coffee dispensed by the machine falls between 107.72 mg and 112.28 mg.
Mr. Jackson had $110 to purchase school supplies for his class. He bought 32 boxes of colored pencils and 32 dry erase markers. Each box of colored pencils cost $2.40, and each dry erase marker cost $0.79. How much money did Mr. Jackson have left after these purchases?
Answer:
$7.92
Step-by-step explanation:
110 - ((32 x 2.40) + (32 x 0.79)) = $7.92
Answer:
$7.92 dollars left over
Step-by-step explanation:
32* 2.40= 76.8
32*0.79= 25.28
25.28+ 76.8= 102.08
110-102.08
===========7.92
Suppose SAT Writing scores are normally distributed with a mean of 493 and a standard deviation of 108. A university plans to send letters of recognition to students whose scores are in the top 10%. What is the minimum score required for a letter of recognition
Answer:
The minimum score required for a letter of recognition is 631.24.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 493, \sigma = 108[/tex]
What is the minimum score required for a letter of recognition
100 - 10 = 90th percentile, which is the value of X when Z has a pvalue of 0.9. So X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 493}{108}[/tex]
[tex]X - 493 = 1.28*108[/tex]
[tex]X = 631.24[/tex]
The minimum score required for a letter of recognition is 631.24.
Answer:
[tex]b=493 +1.28*108=631.24[/tex]
The minimum score required for a letter of recognition would be 631.24
Step-by-step explanation:
Let X the random variable that represent the writing scores of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(493,108)[/tex]
Where [tex]\mu=493[/tex] and [tex]\sigma=108[/tex]
On this questio we want to find a value b, such that we satisfy this condition:
[tex]P(X>b)=0.10[/tex] (a)
[tex]P(X<b)=0.90[/tex] (b)
Both conditions are equivalent on this case. We can use the z score again in order to find b.
As we can see on the figure attached the z value that satisfy the condition with 0.90 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1
If we use condition (b) from previous we have this:
[tex]P(X<b)=P(\frac{X-\mu}{\sigma}<\frac{b-\mu}{\sigma})=0.90[/tex]
[tex]P(z<\frac{b-\mu}{\sigma})=0.90[/tex]
[tex]z=1.28<\frac{b-493}{108}[/tex]
And if we solve for a we got
[tex]b=493 +1.28*108=631.24[/tex]
The minimum score required for a letter of recognition would be 631.24
PLZ HURRY!!!
THE QUESTION AND ANSWER BUBBLE IN PHOTO!
Which inequality is represented by this graph?
Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = [infinity] e−stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. to find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = te9t ℒ{f(t)} = (s > 9)
Answer:
e^-s/s + e^-s/s^2
Step-by-step explanation:
See the attachment please
The question asks for the Laplace transform of f(t) = te^9t using the given definition of the Laplace Transform. This can be calculated using the integral ℒ{f(t)} = ∫ (from 0 to ∞) e^{-st} te^9t dt and likely requires the technique of integration by parts for evaluation.
Explanation:The question is asking for the Laplace transform of the function f(t) = te9t, using the definition of the Laplace transform. The Laplace Transform is a method that can be used to solve differential equations. In general, the Laplace Transform of a function f(t) is defined as ℒ{f(t)} = ∫ (from 0 to ∞) e-st f(t) dt, provided that the integral converges.
In this case, f(t) is equal to te9t so the integral becomes ℒ{f(t)} = ∫ (from 0 to ∞) e-st te9t dt. To find the integral, you would generally need to use integration by parts, which is a method of integration that is typically taught in a calculus course. Note that the given condition (s > 9) will affect the convergence of the integral.
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Evaluate \dfrac {15}k
k
15
start fraction, 15, divided by, k, end fraction when k=3k=3k, equals, 3.
Answer:
5
Step-by-step explanation:
We desire to evaluate the fraction: [tex]\dfrac{15}{k}[/tex] when k=3.
This is a simple substitution, so what is required is
Replace k with the given numberSimplify the resulting expressionTherefore, when k=3
[tex]\dfrac{15}{k}=\dfrac{15}{3}=5[/tex]
You can try the same for any value of k.
The question requires to evaluate the mathematical expression 15/k when k=3. Substituting k with 3, we get 15/3 which equals to 5.
In the subject of Mathematics, the expression 15/k represents a simple division. The value of this expression changes depending on the value assigned to k. In the case where k = 3, we simply substitute 3 in place of k in the expression. This gives us: 15/3 which equals 5. So, 15/3 = 5. So when k = 3, 15/k equals 5.
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A textbook company claims that their book is so engaging that less than 55% of students read it. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted?
a. There is sufficient evidence to support the claim that less than 55% of students read this text
b. There is not sufficient evidence to support the claim that less than 55% of students read this text
c. There is sufficient evidence to support the claim that no more than 55% of students read this text
d. There is not sufficient evidence to support the claim that no more than 55% of students read this text
Answer:
The answer is B.
Step-by-step explanation:
The example given in the question uses the null hypothesis versus the alternative hypothesis. Null hypothesis is the statement that is tested to be true or not and if it is not true, then the alternative hypothesis is accepted.
In the example, it is stated that the hypothesis test for the null hypothesis failed which means that the statement given on the percentage of students who read the book is false.
Then the option b is going to be interpreted which claims that the null hypothesis is false and there is not enough evidence to say that less than 55% of students read the textbook.
I hope this answer helps.
Final answer:
When a hypothesis test does not reject the null hypothesis with a p-value greater than the alpha level of 0.05, it indicates that there is not sufficient evidence to support the claim being tested, in this case, that less than 55% of students read the textbook.
Explanation:
If a hypothesis test is performed and fails to reject the null hypothesis, the interpretation depends on the results related to the alpha level and the p-value. In this case, where the claim is that less than 55% of students read the textbook and the p-value is greater than the alpha level (0.05 or 5%), the correct interpretation is that there is not sufficient evidence to support the claim that less than 55% of students read the text. This means that the sample data does not provide strong enough evidence to infer that the proportion of students who read the textbook is less than 55% for the entire population of students.
Therefore, the correct answer is:
b. There is not sufficient evidence to support the claim that less than 55% of students read this text.
What percentage of job opening are published?
a. 10% - 15%
b. 15% - 20%
30% - 35%
35% - 40%
Please select the best answer from the choices provided
Ο
Α
Answer:
a. 10% - 15%
Step-by-step explanation:
The percentage of a job opening, that gets published, is 15% to 20%, just since just scarcely any occupations can be seen on a paper, commercials, and employment sheets. A large portion of the employment opportunities can be gotten notification from those representatives that worked inside the organization since there is only two job vacancies.
Answer:
the answer is b
Step-by-step explanation:
Problem 2. (4 points) Suppose A is a matrix of size 4 by 4. Which of the following statements must be TRUE? (I) If the rank of A is 4, then the matrix A must be invertible. (II) If the matrix A is invertible, then the rank of A is 4. (III) If A is invertible, then the nullity of A is 0. (A) I only (B) II only (C) III only (D) II and III only (E) I, II, and III
Answer:
(E) I, II, and III
Step-by-step explanation:
Suppose the matrix A has rank 4.
A has 4 linearly independent columns.
As the matrix A is 4 by 4 matrix so all columns of A are linearly independent.
=> det(A) ≠ 0.
=> A must be invertible.
Suppose A is invertible.
Columns of A are linearly independent.
As A has 4 columns and all columns of A are linearly independent so A has 4 linearly independent columns.
As Rank of A = Number of linearly independent columns of A.
=> Rank of A = 4.
Suppose A is invertible.
=> Rank of A = 4.
By rank nullity theorem,
Rank of A + Nullity of A= 4
=> 4 + Nullity of A= 4
=> Nullity of A= 0.
Hence the nullity of A is 0.
Which behavior was observed when one and of the earthworm was placed on a wet paper towel while the other end was placed on a dry paper towel
Answer:
the awnser is c
Answer:
C
Step-by-step explanation:
its on egunity ik u hate it im here for u
If each edge equals 5 inches, what will be the surface area of the cube?? Need answer quick!
Answer:
C
Step-by-step explanation:
A cube has 6 faces
Each face is a square of area:
5² = 25
Surface area: 6 × 25
= 150 in²
Answer:
150 in^2
Step-by-step explanation:
The surface area of a cube is given by
SA = 6 s^2 where s is the side length
SA = 6 (5)^2
= 6 * 25
= 6*25
= 150 in^2
Assume that the profit generated by a product is given by where x is the number of units sold. If the profit keeps changing at a rate of per month, then how fast are the sales changing when the number of units sold is 1100? (Round your answer to the nearest dollar per month.) $30/month $132,665/month $16,583/month $33,166/month
Answer:
P'(1100)=0.06
(see explanation below)
Step-by-step explanation:
The answer is incomplete. The profit function is missing, but another function will be used as an example (the answer will not match with the options).
The profit generated by a product is given by [tex]P=4\sqrt{x}[/tex].
The changing rate of sales can be mathematically expressed as the derivative of the profit function.
Then, we have to calculate the derivative in function of x:
[tex]\dfrac{dP}{dx}=\dfrac{d[4x^{0.5}]}{dx}=4(0.5)x^{0.5-1}=2x^{-0.5}=\dfrac{2}{\sqrt{x}}[/tex]
We now have to evaluate this function for x=1100 to know the rate of change of the sales at this vlaue of x.
[tex]P'(1100)=\frac{2}{\sqrt{1100} } =\frac{2}{33.16} =0.06[/tex]
0.24 + 4.25 equals what ?
Answer:
4.49
Step-by-step explanation:
Answer:
4.49
Step-by-step explanation:
*Imagine it as money, you have $4.25 and you find $0.24
1) 4.25 + 0.24= 4.49
You now have $4.49
Hoped that helped ;)
A researcher is studying the effect of ten different variables on a critical measure of business performance. In selecting the best set of independent variables to predict the dependent variable, a forward selection method is used. How are variables selected for inclusion in the model?
A. Smallest p-value
B. Highest increase in the multiple r-squared
C. smallest coefficient
D. Largest p-value
Answer:
D. Largest p-value
Step-by-step explanation:
P-value assists statistician to know the importance of their result. It assists them in determining the strength of their evidence.
A large P-value which is less than 0.05 depicts that an evidence is week against null hypothesis, therefore the null hypothesis must be accepted.
A small P-value <0.05 depicts a strong evidence against null hypothesis, so the null hypothesis must be rejected.
Answer:
B. Highest increase in the multiple r-squared
Step-by-step explanation:
Forward selection is a type of stepwise regression which begins with an empty model and adds in variables one by one. In each forward step, you add the one variable that gives the single best improvement to your model.
We know that when more variables are added, r-squared values typically increase with probability 1. Based on this and the above definition, we select the candidate variable that increases r-Squared the most and stop adding variables when none of the remaining variables are significant.
Full-price tickets for a concert cost $ 58.50. Students can purchase a discounted ticket for $ 48.50. If a total of 3250 tickets are sold and if the total amount of ticket sales was $ 160,045a) how many full-price tickets were sold? b) how many student tickets were sold?
Answer:
242 Full Tickets were sold; and
3008 Student Tickets were sold.
Step-by-step explanation:
Let the number of full tickets sold=x
Let the number of student tickets sold =y
A total of 3250 tickets were sold, therefore:
x+y=3250Cost of a Full Ticket =$58.50.
Cost of a Discounted Ticket=$48.50
Total Amount =(58.50. X Number of Full Tickets sold)+(58.50 X Number of Student Tickets sold)
Total amount of ticket sales was $ 160,045
Therefore:
58.50x+48.50y=160045We solve the two equations simultaneously to obtain the values of x and y.
From the First Equation, x=3250-y
Substitute x=3250-y into the Second Equation.
58.50x+48.50y=160045
58.50(3250-y)+48.50y=160045
Open the brackets
190125-58.50y+48.50y=160045
-10y=160045-190125
-10y=-30080
Divide both sides by -10
y=3008
Recall: x=3250-y
x=3250-3008
x=242
Therefore:
242 Full Tickets were sold; and
3008 Student Tickets were sold.
Final answer:
To solve for the number of full-price and student tickets sold, a system of two linear equations is set up and solved using the elimination method. The solution shows that 242 full-price tickets and 3008 student tickets were sold.
Explanation:
To solve this problem, we will use a system of linear equations. Let's define x as the number of full-price tickets and y as the number of student tickets. The two equations based on the information provided will be:
x + y = 3250 (the total number of tickets sold)
58.50x + 48.50y = 160,045 (the total revenue from ticket sales)
To find the number of full-price and student tickets sold, we need to solve this system of equations. We can do this using either the substitution or elimination method. I'll demonstrate the elimination method.
Step 1: Multiply the first equation by 48.50 to align the y terms.
48.50x + 48.50y = 157,625
Step 2: Subtract this new equation from the second equation.
58.50x + 48.50y = 160,045
- (48.50x + 48.50y = 157,625)
10x = 2,420
Step 3: Solve for x
x = 242
Step 4: Use the value of x to solve for y in the first equation.
242 + y = 3250
y = 3250 - 242
y = 3008
So, 242 full-price tickets were sold, and 3008 student tickets were sold.
A circle with radius 5 has a sector with a central angle of 9/10 pi radians
Answer: 4.5 pi to this question
Please Help, Will give Brainliest!
Law Of Cosines.
Answer:
B) a = 6.7, B = 36°, C = 49°
Step-by-step explanation:
Fill in the numbers in the Law of Cosines formula to find the value of "a".
a² = b² + c² -2bc·cos(A)
a² = 4² +5² -2(4)(5)cos(95°) ≈ 44.4862
a ≈ √44.4862 ≈ 6.66980
Now, the law of sines is used to find one of the remaining angles. The larger angle will be found from ...
sin(C)/c = sin(A)/a
sin(C) = (c/a)sin(A)
C = arcsin(5/6.6698×sin(95°)) ≈ 48.31°
The third angle is ...
B = 180° -A -C = 180° -95° -48.31° = 36.69°
The closest match to a = 6.7, B = 37°, C = 48° is answer choice B.