Answer:
a) Null hypothesis:[tex]\mu = 140[/tex]
Alternative hypothesis:[tex]\mu \neq 140[/tex]
b) [tex]t=\frac{170-140}{\frac{80}{\sqrt{64}}}=3[/tex]
c) The degrees of freedom are given by:
[tex]df=n-1=64-1=63[/tex]
Now we can calculate the p value, since we are conducting a two tailed test:
[tex]p_v =2*P(t_{63}>3)=0.0039[/tex]
Since the p value is lower than the significance level of [tex]\alpha=1-0.95=0.05[/tex] we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes
Step-by-step explanation:
Information provided
[tex]\bar X=170[/tex] represent the sample mean in minutes
[tex]s=80[/tex] represent the standard deviation
[tex]n=64[/tex] sample size
[tex]\mu_o =140[/tex] represent the value to verify
[tex]\alpha[/tex] represent the significance level
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Part a
We are interested in determining whether or not the average usage in Soddy-Daisy is significantly different from the U.S. average (140 minutes), the system of hypothesis would be:
Null hypothesis:[tex]\mu = 140[/tex]
Alternative hypothesis:[tex]\mu \neq 140[/tex]
Part b
Since we don't know the population deviation the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{170-140}{\frac{80}{\sqrt{64}}}=3[/tex]
Part c
The degrees of freedom are given by:
[tex]df=n-1=64-1=63[/tex]
Now we can calculate the p value, since we are conducting a two tailed test:
[tex]p_v =2*P(t_{63}>3)=0.0039[/tex]
Since the p value is lower than the significance level of [tex]\alpha=1-0.95=0.05[/tex] we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes
The null hypothesis that the average internet usage in Soddy-Daisy is not significantly different from the U.S. average is rejected based on a computed z-score of 3, which falls outside the critical z-score values for a 95% confidence level. Therefore, the average internet usage in Soddy-Daisy is significantly different from the U.S. average.
Explanation:This problem pertains to the domain of statistical hypothesis testing. Let's first set up the null and alternative hypotheses:
Null hypothesis (H0): The average internet usage in Soddy-Daisy is not significantly different from the U.S. average. This can be represented as H0: m = 140 minutes.Alternative Hypothesis (H1): The average internet usage in Soddy-Daisy is significantly different from the U.S. average. This can be represented as H1: m ≠ 140 minutes.For the second part, we need to compute the test statistic. The formula for the test statistic (z) in this context is z = (x - μ) / (σ/√n), where x is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.
So, (170-140) / (80/√64) = 30 / (10) = 3. The z score is 3.
For the final part of your question, with 95% confidence, the critical z-score values are -1.96 and +1.96. Since our observed z-score of 3 is outside this range, we reject the null hypothesis. Therefore, we can conclude that the average internet usage in Soddy-Daisy is significantly different from the U.S. average.
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A University wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A survey of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students. The results were 1,344 answered "Yes" and 1,456 answered "no". The point estimate for this problem is __________.
Answer:
The point estimate for this problem is 0.48.
Step-by-step explanation:
We are given that a University wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students.
A survey of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students. The results were 1,344 answered "Yes" and 1,456 answered "no".
Let [tex]\hat p[/tex] = proportion of students who felt comfortable reporting cheating by their fellow students
Now, point estimate ([tex]\hat p[/tex]) is calculated as;
[tex]\hat p=\frac{X}{n}[/tex]
where, X = number of students who answered yes = 1,344
n = number of students surveyed = 2,800
So, Point estimate ([tex]\hat p[/tex]) = [tex]\frac{1,344}{2,800}[/tex]
= 0.48 or 48%
Final answer:
The point estimate for the percentage of students who felt comfortable reporting cheating by their fellow students is 48%.
Explanation:
The point estimate for the percentage of students who felt comfortable reporting cheating by their fellow students can be calculated by dividing the number of students who answered 'Yes' by the total number of students surveyed, and then multiplying by 100%. In this case, the point estimate is:
Point estimate = (Number of 'Yes' responses / Total number of students surveyed) * 100% = (1344 / 2800) * 100% = 48%
Which statements are true about the graph of the function f(x) = 6x - 4 + x2? Select two options
The vertex form of the function is f(x) = (x - 2)2 + 2.
The vertex of the function is (-3, -13).
The axis of symmetry for the function is x = 3.
The graph increases over the interval (-3,
).
The function does not cross the x-axis.
Answer:
2 and 4
Step-by-step explanation:
A function assigns the values. The statements that are true about the given function are B and D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
To know the correct statements about the graph of the function f(x)=6x-4+x², we need to plot the graph, as shown below.
A.) The vertex form of the function is f(x)=(x-2)²+2.
To know if the vertex form of the function is f(x)=(x-2)²+2, solve the equation and check if it is of the form f(x)=6x-4+x².
[tex]f(x)=(x-2)^2+2\\\\ f(x)=x^2+4-4x+2\\\\f(x) = x^2-4x+6[/tex]
Since the two functions are not equal this is not the vertex form of the function is f(x)=6x-4+x².
B.) The vertex of the function is (-3, -13).
As can be seen in the image below, the vertex of the function lies at (-3,-13.) Therefore, the statement is true.
C.) The axis of symmetry for the function is x = 3.
As the vertex is at -3, therefore, the function symmetry will be about x=-3.
Hence, the given statement is false.
D.) The graph increases over the interval (-3).
The given statement is true since the graph will be showing a positive slope in the interval (-3, +∞).
E.) The function does not cross the x-axis.
It can be observed that the function intersects the x-axis exactly at two points, therefore, the given statement is false.
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What is the complete factorization of 8x^2 - 8x + 2?
Step-by-step explanation:
8x² − 8x + 2
2 (4x² − 4x + 1)
2 (2x − 1)²
Suppose the ages of multiple birth mothers (4 or more births) are normally distributed with a mean age of 35.5 years and a standard deviation of 7. 5 years What percent of these mothers are between the ages of 32 to 40?................................ What percent of these mothers are less than 30 years old?......................................... What percent of these mothers are more than 38 years old?
Answer:
40.65% of these mothers are between the ages of 32 to 40
23.27% of these mothers are less than 30 years old
37.07% of these mothers are more than 38 years old
Step-by-step explanation:
Problems of normally distributed samples can be 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 = 35.5, \sigma = 7.5[/tex]
What percent of these mothers are between the ages of 32 to 40?
This is the pvalue of Z when X = 40 subtracted by the pvalue of Z when X = 32.
X = 40
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40 - 35.5}{7.5}[/tex]
[tex]Z = 0.6[/tex]
[tex]Z = 0.6[/tex] has a pvalue of 0.7257
X = 32
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{32 - 35.5}{7.5}[/tex]
[tex]Z = -0.47[/tex]
[tex]Z = -0.47[/tex] has a pvalue of 0.3192
0.7257 - 0.3192 = 0.4065
40.65% of these mothers are between the ages of 32 to 40
What percent of these mothers are less than 30 years old?
This is the pvalue of Z when X = 30.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 35.5}{7.5}[/tex]
[tex]Z = -0.73[/tex]
[tex]Z = -0.73[/tex] has a pvalue of 0.2327
23.27% of these mothers are less than 30 years old
What percent of these mothers are more than 38 years old?
This is 1 subtracted by the pvalue of Z when X = 38.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{38 - 35.5}{7.5}[/tex]
[tex]Z = 0.33[/tex]
[tex]Z = 0.33[/tex] has a pvalue of 0.6293
1 - 0.6293 = 0.3707
37.07% of these mothers are more than 38 years old
Torres was planning a trip to china. Before going, he did some research and learned that the exchange rate is one Yuan for $0.15. How many Yuan would he get if he exchanged $300?
Answer:
The answer is 2000 yuan.
Step-by-step explanation:
Devise a proportion for this, and then cross-multiply. I believe that is the easiest way.
[tex] \frac{1}{0.15} = \frac{x}{300} \\ 0.15x = 300 \\ x = \frac{300}{0.15} \\ x = \frac{30000}{15} \\ x = \frac{10000}{5} \\ x = 2000[/tex]
Using the given exchange rate of $0.15 for 1 Yuan, Torres will receive 2000 yuan when he exchanges his $300.
Explanation:Torres plans to go to China and wants to exchange his money into the Chinese currency, known as the Yuan. The exchange rate he finds is $0.15 for 1 Yuan. This means for every 1 yuan, he needs to supply $0.15. Because he wants to exchange $300, the number of Yuan he will receive can be calculated by the formula Amount_in_dollars / Exchange_rate.
Here, the Amount_in_dollars is $300 and the Exchange_rate is $0.15. So, the calculation will be $300 / $0.15 = 2000 yuan. Therefore, Torres will receive 2000 yuan when he exchanges his $300.
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A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A (the original paint) and 9 cans of type B (the modified paint) were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. Type A Type B x 1x1equals=76.3 hr x 2x2equals=65.1 hr s 1s1equals=4.5 hr s 2s2equals=5.1 hr n 1n1equals=11 n 2n2equals=9 The following 98% confidence interval was obtained for mu 1μ1minus−mu 2μ2, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B. What does the confidence interval suggest about the population means? 4.90 hrless than
This question is incomplete. I got the complete part (the boldened part) of it from google as:
The following 98% confidence interval was obtained for μ1 - μ2, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B:
4.90 hrs < μ1 - μ2 < 17.50 hrs.
Answer:
A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A (the original paint) and 9 cans of type B (the modified paint) were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. Type A Type B x 1x1equals=76.3 hr x 2x2equals=65.1 hr s 1s1equals=4.5 hr s 2s2equals=5.1 hr n 1n1equals=11 n 2n2equals=9 The following 98% confidence interval was obtained for mu 1μ1minus−mu 2μ2, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B. What does the confidence interval suggest about the population means?
The mean difference for the 98% confidence interval, the drying times of the two types of paints are (4.90, 17.50). This implies that Type A paint takes between 4.90 and 17.50 hours more to dry than type B paint.
Step-by-step explanation:
The mean difference for the 98% confidence interval, the drying times of the two types of paints are (4.90, 17.50). This implies that Type A paint takes between 4.90 and 17.50 hours more to dry than type B paint.
Only positive values comprise the confidence interval which suggests that the mean drying time for paint type A is greater than the mean drying time for paint type B. The modification appears to be effective in reducing drying times.
Consider the system of linear equations. 7 x + 16 y = negative 2. 9 x minus 4 y = 22. To use the linear combination method and addition to eliminate the y-terms, by which number should the second equation be multiplied? –4 Negative one-fourth One-fourth 4
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
To decrease the impact on the environment, factory chimneys must be high enough to allow pollutants to dissipate over a larger area. Assume the mean height of chimneys in these factories is 10D meters (an EPA-acceptable height) with a standard deviation 12 meters. A random sample of 40 chimney heights is obtained. What is the probability that the sample mean height for the 40 chimneys is greater than 102 meters?
Answer:
The probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.
Step-by-step explanation:
Let the random variable X be defined as the height of chimneys in factories.
The mean height is, μ = 100 meters.
The standard deviation of heights is, σ = 12 meters.
It is provided that a random sample of n = 40 chimney heights is obtained.
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
Then, the mean of the distribution of sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the distribution of sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
Since the sample selected is quite large, i.e. n = 40 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean heights of chimneys.
[tex]\bar X\sim N(\mu_{\bar x},\ \sigma^{2}_{\bar x})[/tex]
Compute the probability hat the sample mean height for the 40 chimneys is greater than 102 meters as follows:
[tex]P(\bar X>102)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}})>\frac{102-100}{12/\sqrt{40}})[/tex]
[tex]=P(Z>1.05)\\=1-P(Z<1.05)\\=1-0.85314\\=0.14686\\\approx 0.1469[/tex]
*Use a z-table fr the probability.
Thus, the probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.
An author argued that more basketball players have birthdates in the months immediately following July 31, because that was the age cutoff date for nonschool basketball leagues. Here is a sample of frequency counts of months of birthdates of randomly selected professional basketball players starting with January: 390, 392, 360, 318, 344, 330, 322, 496, 486, 486, 381, 331 . Using a 0.05 significance level, is there sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency? Do the sample values appear to support the author's claim?
Answer:
There is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency.
Step-by-step explanation:
In this case we need to test whether there is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency.
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: The observed frequencies are same as the expected frequencies.
Hₐ: The observed frequencies are not same as the expected frequencies.
The test statistic is given as follows:
[tex]\chi^{2}=\sum{\frac{(O-E)^{2}}{E}}[/tex]
The values are computed in the table.
The test statistic value is [tex]\chi^{2}=128.12[/tex].
The degrees of freedom of the test is:
n - 1 = 12 - 1 = 11
Compute the p-value of the test as follows:
p-value < 0.00001
*Use a Chi-square table.
p-value < 0.00001 < α = 0.05.
So, the null hypothesis will be rejected at any significance level.
Thus, there is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency.
Final answer:
To test the claim that professional basketball players are born in different months with the same frequency, a chi-square test for goodness of fit can be used. Calculations involve comparing the actual birthdate frequencies of the players against the expected frequencies if the distribution were uniform. A statistically significant result would support the author's claim, while a non-significant result would not.
Explanation:
Chi-Square Test for Uniform Distribution
To determine if there is sufficient evidence to support the author's claim that professional basketball players are born in different months with the same frequency, we can perform a chi-square test for goodness of fit. Given the frequency counts of the birthdates of professional basketball players for each month, we will compare them to the expected frequencies if births were uniformly distributed throughout the year.
Steps to Perform the Test
Firstly, calculate the total number of players in the sample by summing up the frequency counts for each month.
Determine the expected frequency for each month, which would be the total number of players divided by 12, assuming a uniform distribution.
Calculate the chi-square statistic using the formula: χ² = ∑((observed - expected)² / expected), where 'observed' is the frequency count for each month, and 'expected' is the expected frequency.
Compare the calculated chi-square value with the critical value from the chi-square distribution table with 11 degrees of freedom (since there are 12 months - 1) and a significance level of 0.05.
If the chi-square value is greater than the critical value, reject the null hypothesis (that the birth months are uniformly distributed), which supports the author's claim. Otherwise, do not reject the null hypothesis.
Interpretation
By performing the calculations, if the chi-square test statistic is greater than the critical value, it suggests that there is a statistically significant difference in the distribution of birth months among professional basketball players. This would support the author's claim that there may be more players born in the months immediately following July 31, which is the age cutoff date for nonschool basketball leagues. If the test statistic is not greater than the critical value, there is not enough evidence to support the claim.
A guy wire is needed to support a tower. The wire is attached from the top of the tower to a place on the ground 5m from the base of the tower. How long is the wire if the tower is 10m tall?
g Which of the following is true about a p-value? Group of answer choices It measures the probability that the null hypothesis is true. It measures the probability of observing your test statistic, assuming the null hypothesis is true. It measures the probability of observing your test statistic, assuming the alternative hypothesis is true. It measures the probability that the alternative hypothesis is true.
Answer:
It measures the probability of observing your test statistic, assuming the null hypothesis is true.
Step-by-step explanation:
The p-value, also known as the probability value measures the probability of observing your test statistic, assuming the null hypothesis is true.
A low p-value means a higher chance of the null hypothesis to be true.
It lies between 0 and 1. A small p-value indicates fewer chances of the null hypothesis to be true.
Teddy has 6 lollipops and 9 cookies. Annie say for every 3 lollipops there are 2 cookies. Teddy says I don’t agree. What mistake has Annie made
Answer:
She switched her say
Step-by-step explanation:
Answer:
Annie made the mistake of either swapping the numbers or the items in her comparison.
Step-by-step explanation:
The ratio of lollipops to cookies is:
6/9
This can be simplified to:
2/3
That means that for every two lollipops, there are three cookies. Therefore Annie made the mistake of either swapping the numbers or the items in her comparison.
Find the volume of a right circular cone that has a height of 12.5 m and a base with a radius of 2.2 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
The volume of the cone is 63.3m³
Step-by-step explanation:
First of all to solve this problem we need to know the formula to calculate the volume of a cone
v = volume
r = radius = 2.2m
h = height = 12.5m
π = 3.14
v = 1/3 * π * r² * h
we replace with the known values
v = 1/3 * 3.14 * (2.2m)² * 12.5m
v = 1/3 * 3.14 * 4.84m² * 12.5m
v = 63.32m³
rount to the neares tenth
v = 63.32m³ = 63.3m³
The volume of the cone is 63.3m³
Answer: 63.4
Step-by-step explanation:
You round to the tenths giving you 63.4
What is the equation of the line, in point slope form, that passes through the points (4,8) and (2,-2)
Answer:
Step-by-step explanation:
1) point slope form is:
y-y1=m(x-x1)
y1=8
x1=4
m=(slope)
to find m: y2-y1/x2-x1
hence
-2-8/2-4=-10/-2=5
m=5:
y-8=5(x+4)
What is the following quotient 3 square root 8 4 square root 6
Answer: √3/2
Step-by-step explanation: Ok...so it would look like this:
(3√8)/(4√6)
I hope this helps!
Which is similar to this quadrilateral?
Answer:
D
Step-by-step explanation:
D has the most similarities than others
The option B is correct.
Definition of similarity :Two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal.Two quadrilaterals are similar quadrilaterals when the three corresponding angles are the same and two adjacent sides have equal ratios.The option B quadrilateral is similar to the given quadrilateral.
Because the three corresponding angles are the same.
Therefore, option B is correct.
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A car travels at an average speed of 52 miles per hour. How many miles does it travel in 5 hours and 45 minutes?
Answer:
299
Step-by-step explanation:
On average, it travels 52 miles in each hour. In 5 3/4 hours, it travels 5 3/4 times 52 miles.
(5 3/4)(52 miles) = 299 miles
It travels 299 miles in the given time.
Answer:
The car will travel 195 miles.
Step-by-step explanation:
(3.75 hrs)(52 mph)=195 miles
PLEASE IM BEING TIMED
Answer:
A
Step-by-step explanation:
First you use the equation [tex]2(\pi r^{2})[/tex] to find the area of the circles combined and you find the radius by diving the height by 2(getting 5)
Then you find the area of the squares with the circles(10 x 20= 200)
Finally you subtract the area of both circles and the total area. (200-157=43)
A survey was taken among a group of people. The probability that a person chosen likes Italian food is 0.75, the probability that a person likes Chinese food is 0.28,
and the probability that a person likes both foods is 0.21.
Determine the probability that a person likes Italian, but not Chinese
Determine the probaility that a person likes at least one of these foods
Determine the proability that a person likes at most one of these foods -
Answer:
54% probability that a person likes Italian food, but not Chinese food.
82% probaility that a person likes at least one of these foods
79% proability that a person likes at most one of these foods
Step-by-step explanation:
We solve this problem building the Venn's diagram of these probabilities.
I am going to say that:
A is the probability that a person likes Italian food.
B is the probability that a person likes Chinese food.
We have that:
[tex]A = a + (A \cap B)[/tex]
In which a is the probability that a person likes Italian food but not Chinese and [tex]A \cap B[/tex] is the probability that a person likes both Italian and Chinese food.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
The probability that a person likes both foods is 0.21.
This means that [tex]A \cap B = 0.21[/tex]
The probability that a person likes Chinese food is 0.28
This means that [tex]B = 0.28[/tex]
So
[tex]B = b + (A \cap B)[/tex]
[tex]0.28 = b + 0.21[/tex]
[tex]b = 0.07[/tex]
The probability that a person likes Italian food is 0.75
This means that [tex]A = 0.75[/tex]
So
[tex]A = a + (A \cap B)[/tex]
[tex]0.75 = a + 0.21[/tex]
[tex]a = 0.54[/tex]
Determine the probability that a person likes Italian, but not Chinese
This is a.
54% probability that a person likes Italian food, but not Chinese food.
Determine the probaility that a person likes at least one of these foods
[tex]P = a + b + (A \cap B) = 0.54 + 0.07 + 0.21 = 0.82[/tex]
82% probaility that a person likes at least one of these foods
Determine the proability that a person likes at most one of these foods
Either a person likes at most one of these foods, or it likes both. The sum of the probabilities of these events is decimal 1.
0.21 probability it likes both.
Then
0.21 + p = 1
p = 0.79
79% proability that a person likes at most one of these foods
which function does this graph represent
A. f(x) = 3(x + 1)^2 + 2
B. f(x) = -3(x + 1)^2 + 2
C. f(x) = -3(x + 1)^2 - 2
D. f(x) = 3(x - 1)^2 + 2
The equation of parabola which represents the graph is f(x) = -3 (x + 1)² + 2.
What is parabola?A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
Here, general equation of parabola in downward direction is
(y-y₁) = -4a(x-x₁)²
vertex of parabola (-1, 2)
(y-2) = -4a(x-(-1))²
(y - 2) = -4a(x + 1)²
put the value of x = 0 and y = -1
so we get, a = 3/4
put in equation of parabola
( y - 2 ) = -3 ( x + 1 ) ²
y = -3 (x + 1)² + 2
f(x) = -3 (x + 1)² + 2
Thus, the equation of parabola which represents the graph is f(x) = -3 (x + 1)² + 2.
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It is important that face masks used by firefighters be able to withstand high temperatures because firefighters commonly work in temperatures of 200-500 degrees. In a test of one type of mask, 24 of 55 were found to have their lenses pop out at 325 degrees. Construct and interpret a 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees.
Answer:
The 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574). This means that we are 93% sure that the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 55, \pi = \frac{24}{55} = 0.4364[/tex]
93% confidence level
So [tex]\alpha = 0.07[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.07}{2} = 0.965[/tex], so [tex]Z = 1.81[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4364 - 1.81\sqrt{\frac{0.4364*0.5636}{55}} = 0.3154[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4364 + 1.81\sqrt{\frac{0.4364*0.5636}{55}} = 0.5574[/tex]
The 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574). This means that we are 93% sure that the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574).
y2 – 3y + 2 = 0 solve buy factoring
Answer:
y²-3y+2=0
=> y²-(2+1)y +2=0
=> y²-2y-y+2=0
=> y(y-2)-1(y-2)=0
=> (y-2)(y-1)=0
=> y = 2 or y= 1
Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Lucy plans to test this hypothesis using a random sample of 100 from each audience. Her null hypothesis is ____________.
Answer:
The null hypothesis is H0; u1 - u2 = 0
The mean age of each audience is the same.
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. 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;
Let u1 represent the mean age of audience for American idol and
u2 represent the mean age of audience for 60 minutes.
The null hypothesis is H0; u1 - u2 = 0
The mean age of each audience is the same.
Raul is y years old. Kayla is 6 years older than raul and isaac is 4 years younger than raul what is kayla's age?
Answer:
9
Step-by-step explanation:
Mara has 3 times as many dollars as her brother, Timmy. If Mara is given $20 by their mother, she will have 7 times as many dollars as Timmy. How many dollars does Timmy have?
Answer:
$5
Step-by-step explanation:
Using algebra to solve this problem.
Let 'x' be Timmy’s amount.
->Mara has 3 times as many dollars as her brother i.e 3x dollars
->If Mara is given $20 by their mother, then expression would be
3x + 20
Since Mara’s new amount is supposed to be seven times Timmy’s
current amount, this forms an equation
3x + 20 = 7x
Solving for 'x'
7x -3x=20
4x = 20
x=20/4
x=5
Timmy has an amount of $5
Final answer:
By setting up two equations based on the given information and solving for T, we find that Timmy has $5.
Explanation:
Let's denote the amount of dollars Timmy has as T. According to the question, Mara has 3 times as many dollars as Timmy, so we can write this as M = 3T, where M is the amount Mara has. Now, we are told that if Mara is given an additional $20, she will have 7 times the amount Timmy has. We can express this as M + 20 = 7T. Using the two equations, we can solve for the value of T.
First, substitute the value of M from the first equation into the second equation:
3T + 20 = 7T
20 = 7T - 3T
20 = 4T
T = 20 / 4
T = $5
Therefore, Timmy has $5.
$100 is invested at 12% per year. If the amount is compounded annually, write the total amount after 2 years in exponential function form.
Answer:
A = $100(1.12)^2
Step-by-step explanation:
The standard formula for compound interest is given as;
A = P(1+r/n)^(nt) .....1
Where;
A = final amount/value
P = initial amount/value (principal)
r = rate yearly
n = number of times compounded yearly.
t = time of investment in years
For this case;
P = $100
t = 2years
n = 1
r = 12% = 0.12
Substituting the values, we have;
A = $100(1+0.12)^(2)
A = $100(1.12)^2
f(t) = t - 6
f(u + 6) =
Answer:
f(u +6) = u
Step-by-step explanation:
Put (u+6) in place of t and simplify:
f(u+6) = (u+6) -6
f(u+6) = u
Does anybody know these two questions?!
Answer:
Both are true statements
Step-by-step explanation:
By definition of an angle, an angle is a union of two rays at a common endpoint and lines can contain rays.
A full circle measures 360 degrees.
Answer:
Question7:true
Question8:true
Step-by-step explanation:
Question 7: an angle is made when two lines or rays come together
Question 8:an angle that has 360° is a circle
Yooo I need help right now
Answer:
The answer would be 2924. 82
How long is it until 20000 mosquitoes are in the colony?
Answer :The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1400 after 1​ day
Step-by-step explanation:
Answer:
The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1600 after 1 day, what is the size of the colony after 4 days
Step-by-step explanation: