Answer: There are 4 more wrenches in the toolbox then the screwdrivers.
Step-by-step explanation: Add the 6 wrenches Sid put in the toolbox with the 8 wrenches Bella added to get 14 wrenches in total. Then, subtract the 10 screwdrivers from the 14 wrenches to get 4 wrenches.
Final answer:
Bella added 8 wrenches to the toolbox, making a total of 14 wrenches. There were initially 10 screwdrivers, so there are now 4 more wrenches than screwdrivers.
Explanation:
Calculating the Difference Between Wrenches and Screwdrivers in a Toolbox
Initially, there are 10 screwdrivers and 6 wrenches in the toolbox. Bella adds 8 more wrenches, which brings the total number of wrenches to 6 + 8, which equals 14 wrenches. The question asks how many more wrenches there are than screwdrivers. To find this, we subtract the number of screwdrivers from the number of wrenches:
14 wrenches - 10 screwdrivers = 4 more wrenches than screwdrivers in the toolbox.
The response times of technicians of a large heating company follow a Normal distribution with a standard deviation of 10 minutes. A supervisor suspects that the mean response time has increased from the target of 30 minutes. He takes a random sample of 25 response times and calculates the sample mean response time to be 33.8 minutes. What is the value of the test statistic for the appropriate hypothesis test?
Answer:
The value of z test statistics for the appropriate hypothesis test is 1.90.
Step-by-step explanation:
We are given that the response times of technicians of a large heating company follow a Normal distribution with a standard deviation of 10 minutes.
He takes a random sample of 25 response times and calculates the sample mean response time to be 33.8 minutes.
Let [tex]\mu[/tex] = mean response time.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 30 minutes {means that the mean response time is 30 minutes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 30 minutes {means that the mean response time has increased from the target of 30 minutes}
The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean response time = 33.8 minutes
[tex]\sigma[/tex] = population standard deviation = 10 minutes
n = sample of response times = 25
So, test statistics = [tex]\frac{33.8-30}{\frac{10}{\sqrt{25} } }[/tex]
= 1.90
Hence, the value of z test statistics for the appropriate hypothesis test is 1.90.
6.8 Use the Normal approximation. Suppose we toss a fair coin 100 times. Use the Normal approximation to find the probability that the sample proportion of heads is (a) between 0.3 and 0.7. (b) between 0.4 and 0.65. Moore, David. Exploring the Practice of Statistics & Student CD (p. 325). W.H. Freeman & Company. Kindle Edition.
Answer:
(a) The probability that proportion of heads is between 0.30 and 0.70 is 1.
(b) The probability that proportion of heads is between 0.40 and 0.65 is 0.9759.
Step-by-step explanation:
Let X = number of heads.
The probability that a head occurs in a toss of a coin is, p = 0.50.
The coin was tossed n = 100 times.
A random toss's result is independent of the other tosses.
The random variable X follows a Binomial distribution with parameters n = 100 and p = 0.50.
But the sample selected is too large and the probability of success is 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of [tex]\hat p[/tex] (sample proportion of X) if the following conditions are satisfied:
np ≥ 10 n(1 - p) ≥ 10Check the conditions as follows:
[tex]np=100\times 0.50=50>10\\n(1-p)=100\times (1-0.50)=50>10[/tex]
Thus, a Normal approximation to binomial can be applied.
So, [tex]\hat p\sim N(p,\ \frac{p(1-p)}{n})[/tex]
[tex]\mu_{p}=p=0.50\\\sigma_{p}=\sqrt{\frac{p(1-p)}{n}}=0.05[/tex]
(a)
Compute the probability that proportion of heads is between 0.30 and 0.70 as follows:
[tex]P(0.30<\hat p<0.70)=P(\frac{0.30-0.50}{0.05}<\frac{\hat p-p}{\sigma_{p}}<\frac{0.70-0.50}{0.05})\\[/tex]
[tex]=P(-4<Z<4)\\=P(Z<4)-P(Z<-4)\\=(\approx1)-(\approx0)\\=1[/tex]
Thus, the probability that proportion of heads is between 0.30 and 0.70 is 1.
(b)
Compute the probability that proportion of heads is between 0.40 and 0.65 as follows:
[tex]P(0.40<\hat p<0.65)=P(\frac{0.40-0.50}{0.05}<\frac{\hat p-p}{\sigma_{p}}<\frac{0.65-0.50}{0.05})\\[/tex]
[tex]=P(-2<Z<3)\\=P(Z<3)-P(Z<-2)\\=0.9987-0.0228\\=0.9759[/tex]
Thus, the probability that proportion of heads is between 0.40 and 0.65 is 0.9759.
Through the Law of Large Numbers, we can approximated the binomial distribution with a normal distribution when the number of repetitions is quite high. We find the mean and standard deviation for the distribution and convert the asked proportion of heads to equivalent X and Z values. The probabilities are found by referring to a Standard Normal Distribution Table.
Explanation:Normal Approximation to Binomial DistributionIn this problem, we are dealing with a binomial distribution -- a coin flip with two outcomes, heads or tails. But since the number of flips is high (100), we can use Normal approximation to solve the problem.
Whenever a fair coin is tossed, the chance of getting a head is 0.5. This is our theoretical probability, which doesn't guarantee exact outcomes but gives an estimated figure when the size of event repetitions is high. The main principle here is the Law of Large Numbers, which states that as the number of repetitions of an experiment increases, we expect the empirical probability to approach the theoretical probability.
Let's calculate the mean (μ) and standard deviation (σ) for this distribution.
Mean (μ) = np = 100*0.5 = 50Standard Deviation (σ) = √[np(1-p)] = √[100*0.5*0.5] = 5(a) To find the probability of the sample proportion of heads being between 0.3 and 0.7, we convert these into equivalent X values and then find the corresponding Z values.
X for 0.3 is 0.3*100 = 30X for 0.7 is 0.7*100 = 70We calculate Z for each using Z = (X - μ) / σ. After that, we refer to the Z table (Standard Normal Distribution Table) or use a calculator to find the probabilities.
Repeat similar steps for part (b) for the probabilities between 0.4 and 0.65.
Note: While using Normal approximation, we apply a Continuity Correction factor of ±0.5 depending upon the problem.
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This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x1, x2, ..., xn) = x1 + x2 + ... + xn; x12 + x22 + ... + xn2 = 9
Answer:
Maximum value: [tex] 3* \sqrt{n} [/tex]
Minimum value: [tex] -3* \sqrt{n} [/tex]
Step-by-step explanation:
Let [tex] g(x) = x_1^2 + x_2^2+x_3^2+ ----+ x_n^2[/tex] , the restriction function.The Lagrange Multiplier problem states that an extreme (x1, ..., xn) of f with the constraint g(x) = 9 has to follow the following rule:
[tex] \nabla{f}(x_1, ..., x_n) = \lambda \nabla{g} (x_1,...,x_n) [/tex]
for a constant [tex] \lambda [/tex] .
Note that the partial derivate of f respect to any variable is 1, and the partial derivate of g respect xi is 2xi, this means that
[tex] 1 = \lambda 2 x_1 [/tex]
Thus,
[tex] x_i = \frac{1}{2\lambda} = c [/tex]
Where c is a constant that doesnt depend on i. In other words, there exists c such that (x1, x2, ..., xn) = (c,c, ..., c). Now, since g(x1, ..., xn) = 9, we have that n * c² = 9, or
[tex] c = \, ^+_- \, \sqrt{\frac{9}{n} } = \, ^+_- \frac{3}{\sqrt{n}} [/tex]
When c is positive, f reaches a maximum, which is [tex] \frac{3}{\sqrt{n}} + \frac{3}{\sqrt{n}} + \frac{3}{\sqrt{n}} + ..... + \frac{3}{\sqrt{n}} = n * \frac{3}{\sqrt{n}} = 3 * \sqrt{n} [/tex]
On the other hand, when c is negative, f reaches a minimum, [tex]-3 * \sqrt{n} [/tex]
A jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of 44 cm3. If nickel plating costs $1 per cm2 and silver plating costs $3 per cm2, find the dimensions of the box to minimize the cost of the materials. (Round your answers to two decimal places.) The box which minimizes the cost of materials has a square base of side length
Answer:
Base= 5.09 cm x 5.09 cm; height = 1.69 cm
Step-by-step explanation:
-> materials has a square base of side length, dimension will be: x . x = x²
'y' represents height
->For dimensions of 4 silver plated sides= xy each
->dimensions of the nickel plated top= x²
Volume = yx²
44=yx² => y= 44/x²
Cost of the sides will be( 4 * xy * $3 )
Cost of the top and the bottom will be (2 * x² * $1)
For the Total cost: 12xy + 2x²
substituting value of 'y' in above equation,
=> Total cost = 12x (44/x²) + 2x² = 528 / x + 2x²
To Minimum critical point => d [cost] / dx = 0
=> - 528/x² + 4x =0
132/x² - x =0
132 - x³ = 0
x³ = 132
Taking cube root on both sides
∛x³ = ∛(132)
x= 5.09
=> y = 44/5.09² =>1.69
Dimensions of the box :
Base= 5.09 cm x 5.09 cm; height = 1.69 cm
Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. Some governments have a safety limit for cadmium in dry vegetables at 0.6 parts per million (ppm). A hypothesis test is to be performed to decide whether the mean cadmium level in a certain mushroom is less than the government's recommended limit. Complete parts (a) through (c) below.
a) Perform a hypothesis test at the 5% significance level to determine if the mean
cadmium level in the population of Boletus pinicoloa mushrooms is greater than the
government’s recommended limit of 0.5 ppm. Suppose that the standard deviation of
this population’s cadmium levels is o( = 0.37 ppm. Note that the sum of the data is 6.31 ppm. For this problem, be sure to: State your hypotheses, compute your test statistic, give the critical value.
(b) Find the p-value for the test.
Answer:
There is not enough evidence to support the claim that the mean cadmium level in Boletus pinicoloa mushrooms is greater than the government's recommended limit (0.5 ppm).
The P-value for this test is P=0.404.
Step-by-step explanation:
The question is incomplete:
The sample size is n=12 and the sample mean is M=6.31/12=0.526 ppm.
This is a hypothesis test for the population mean.
The claim is that the mean cadmium level in Boletus pinicoloa mushrooms is greater than the government's recommended limit (0.5 ppm).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=0.5\\\\H_a:\mu> 0.5[/tex]
The significance level is 0.05.
The sample has a size n=12.
The sample mean is M=0.526.
The standard deviation of the population is known and has a value of σ=0.37.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{0.37}{\sqrt{12}}=0.107[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{0.526-0.5}{0.107}=\dfrac{0.026}{0.107}=0.242[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]P-value=P(z>0.242)=0.404[/tex]
As the P-value (0.404) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the mean cadmium level in Boletus pinicoloa mushrooms is greater than the government's recommended limit (0.5 ppm).
6.- Find the area under the standard normal distribution: to the left of z=-1.55.
Answer:
[tex] P(z<-1.55)=0.0606[/tex]
Step-by-step explanation:
For this case we want to find this probability:
[tex] P(z<-1.55)[/tex]
Because they want the area to the left of the value. We need to remember that the normal standard distribution have a mean of 0 and a deviation of 1.
We can use the following excel code: =NORM.DIST(-1.55,0,1,TRUE)
And we got:
[tex] P(z<-1.55)=0.0606[/tex]
The other possibility is use the normal standard table and we got a similar result.
Gina has 3 yards of fabric.She needs to cut 8 pieces,each 1 foot long.Does she have enough fabric
Answer:
Yes, she does
Step-by-step explanation:
A yard is equivalent to 3 feet and there is 3 yards of fabric. Therefore there are 9 feet of fabric available and 8<9
Answer:
yes there is enough
Step-by-step explanation:
1 yard = 3 ft
We need to convert yards to ft
3 yds * 3ft/ 1yds = 9 ft
We can cut 9 1ft pieces from 3 yds
Which of the following best describes the equation below? y=-6x+7
Answer:
y=-6x+7 (Negative Slope)
Step-by-step explanation:
This equation is in slope intercept form.
7= y-intercept
-6= slope
This means that when you plot this on a graph, your slope will be negative.
what % of 75 is 19? round to 1 decimal
Answer:
25.3%
Step-by-step explanation:
Let P be the percent
Of means multiply and is means equals
P *75 = 19
Divide each side by 75
P* 75/75 = 19/75
P =.25333333
Change from decimal to percent form
P = 25.33333333%
Rounding to one decimal
25.3%
Answer:
25.3
Step-by-step explanation:
19/75 = 0.253
0.253 x 100% = 25.3%
Find the inverse of the function: { (3,5), (1, 6), ( -1, 7), (-3, 8)}
Answer:
{(5,3) , (6,1), (7,-1), (8,-3)}
Step-by-step explanation:
inverse of (x,y) is (y,x)
inverse of { (3,5), (1, 6), ( -1, 7), (-3, 8)} is
{(5,3) , (6,1), (7,-1), (8,-3)}
Simplify 8(x - 4).
A. 8x-4
B. 8x-32
C. x-32
D. x-4
Answer:
8x-32
Step-by-step explanation:
Because 8 multiples X and gives 8x and also multiples-4 and gives you -32
:.8x-32
Using the distributive property to find the product (y−4x)(y2+4y+16) results in a polynomial of the form y3+4y2+ay−4xy2−axy−64x. What is the value of a in the polynomial?
4
8
16
32
Answer:
16
Step-by-step explanation:
Answer:
16, AKA C
Step-by-step explanation:
Edge 2021 :)
Sara is watching a movie that is 1hr. And 38 mins. long she has already watched 48mins. If the 6:10pm what time will the movie be over?
Answer: 7:48pm
Step-by-step explanation:
Convert 1h to mins
[tex]1h(\frac{60min}{1h} )=60min[/tex]
add the 38 extra mins.
60+38=98mins
The movie started at 6:10pm, and she has already watched 48 mins of it.
Add 48 to the time and subtract from the length of the movie.
6:10pm + 48 mins=6:58pm (this is the current time)
98-48=50
Let's add 2 mins to make it 7:00pm.
6:58pm+2mins=7:00pm
50-2=48mins
So now it's 7:00pm and we still have 48 mins to watch. Add that to the time.
7:00pm+48mins=7:48pm
Find the horizontal asymptote off of x equals quantity 3 x squared plus 3x plus 6 end quantity over quantity x squared plus 1.
y = −3
y = −1
y = 3
y = 1
Answer:
y = 3
Step-by-step explanation:
y = (3x² + 3x + 6) / (x² + 1)
The power of the numerator and denominator are equal, so as x approaches infinity, y approaches the ratio of the leading coefficients.
y = 3/1
The horizontal asymptote will be;
⇒ y = 3
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The algebraic expression is,
''The horizontal asymptote off of x equals quantity 3 x squared plus 3x plus 6 end quantity over quantity x squared plus 1.''
Now,
We can formulate;
⇒ f (x) = ( 3x² + 3x + 6 ) / (x² + 1)
Hence, We get the horizontal asymptote as;
We know that;
A function f is said to have a horizontal asymptote y = a;
⇒ [tex]\lim_{x \to \infty} f (x) = a[/tex]
So, We get;
⇒ [tex]\lim_{x \to \infty} f (x) = \lim_{x \to \infty} \frac{(3x^2 + 3x + 6)}{x^2 + 1}[/tex]
⇒ [tex]\lim_{x \to \infty} \frac{(3x^2 + 3x + 6)}{x^2 + 1} = \lim_{x \to \infty} \frac{3x^2 (1+1/x + 6/x^2)}{x^2(1 + 1/x^2)}[/tex]
⇒ [tex]\lim_{x \to \infty} \frac{3x^2 (1+1/x + 6/x^2)}{x^2(1 + 1/x^2)} = 3[/tex]
⇒ y = 3
Thus, The horizontal asymptote will be;
⇒ y = 3
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A fair dice is rolled.
Work out the probability of getting a multiple of 3.
Give your answer in its simplest form.
Answer:
2/6 or 1/3
Step-by-step explanation:
3 and 6 are multiples of 3
so that is 2 out of 6 numbers on a fair dice.
Josh wants to convince his mother to stop buying single-ply toilet paper. Josh believes that even though Fluffy, a two-ply toilet paper costs more, it will last longer because it is more absorbent. To help substantiate his claim, Josh performed a study. He purchased a random sample of 18 rolls of Fluffy. For each roll, he determined how many squares are needed to completely absorb one-quarter cup of water. Here is a dotplot of the data. The mean of the sample is 24.444 squares with a standard deviation of 2.45 squares. Single-ply toilet paper requires 26 squares to absorb one-quarter cup of water. Josh would like to carry out a test to determine if there is convincing evidence that the mean number of squares of Fluffy that are needed to absorb one-quarter cup of water is fewer than 26 squares. What is the appropriate test statistic and P-value of this test?
Answer: the correct answer is B
Step-by-step explanation:
t= -2.69, P- value = 0.0078
Two types of plastics are suitable for an electronics component manufacturer to use. The breaking strength of this plastic is important. It is known that the standard deviations of the two types of plastics are the same, with a value of 1.0 psi. From a random sample of 10 and 12 for type 1 and type 2 plastics, respectively, we obtain sample means of 162.5 and 155. The company will not adopt plastic 1 unless its mean breaking strength exceeds that of plastic 2 by at least 10 psi.
(a) Based on the sample information, should it use plastic 1? Use α = 0.05 in reaching a decision. find the P-value.
(b) Calculate a 95% confidence interval on the difference in means. Suppose that the true difference in means is really 12 psi.
(c) Find the power of the test assuming that α = 0.05.
(d) If it is really important to detect a difference of 12 psi, are the sample sizes employed in part (a) adequate, in your opinion?
Answer:
a. We fail reject to the null hypothesis because zo = -5.84 < 1.65 = zα and P-value = 1 (approximately)
b. The confidence Interval for u1 - u2 is; 6.79 ≤ u1 - u2
c. The power of the test = 1 -
β = 0.998736
d. The sample size is adequate because the power of the test is approximately 1
Step-by-step explanation:
Given
Standard Deviations; σ1 = σ2 = 1.0 psi
Size: n1 = 10; n2 = 12
X = 162.5; Y = 155.0
Let X1, X2....Xn be a random sample from Population 1
Let Y1, Y2....Yn be a random sample from Population 2
We assume that both population are normal and the two are independent.
Therefore, the test statistic
Z = (X - Y - (u1 - u2))/√(σ1²/n1 + σ2²/n2)
See attachment for explanation
The p-value is 0.028, indicating that plastic 1's breaking strength exceeds that of plastic 2 by at least 10 psi. A 95% confidence interval for the difference in means is (4.858, 22.142). The power of the test is 0.858, indicating a high probability of correctly rejecting the null hypothesis. The sample sizes employed may not be adequate to detect a difference of 12 psi.
To determine whether the electronics component manufacturer should use plastic 1, we will conduct a Hypothesis testing and calculate a confidence interval for the difference in means.
(a) We will test the null hypothesis that the mean breaking strength of plastic 1 is less than or equal to the mean breaking strength of plastic 2 by at least 10 psi.
Using a t-test, we find the p-value to be 0.028.
Since this is less than the significance level of 0.05, we reject the null hypothesis and conclude that plastic 1's breaking strength exceeds that of plastic 2 by at least 10 psi.
(b) To calculate a 95% confidence interval for the difference in means, we use the formula: difference in means ± (t-value * standard error).
With a true difference in means of 12 psi, the confidence interval is (4.858, 22.142).
(c) The power of a test is the probability of correctly rejecting the null hypothesis when it is false.
We can calculate the power using the formula: 1 - Beta. Given alpha = 0.05, the power of the test is 0.858.
(d) To determine if the sample sizes are adequate, we can calculate the minimum sample size required to detect a difference of 12 psi with a power of at least 0.8.
Using a power analysis, we find that a sample size of 16 for each type of plastic would be adequate.
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The table shows the relationship, "Taiga reads 250 words Which equation models this relationship?
per minute."
O wm = 250
The independent variable, the number of minutes he
O w = 250m
reads, causes a change in the dependent variable, the
O m = 250w
number of words read.
O w + m = 250
Minutes
(m)
Words
(w)
250
500
750
1000
9514 1404 393
Answer:
w = 250m
Step-by-step explanation:
As the problem statement tells you, the independent variable, the number of minutes he reads, causes a change in the dependent variable, the number of words read. This is modeled by ...
w = 250m
Answer: B. w = 250m
Step-by-step explanation: i answered the question and got it right :)
A camera has a listed price of $778.95 before tax. If the sales tax rate is 9.75%, find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary.
Answer:
$854.90
Step-by-step explanation:
List Price Before Tax = $778.95
Sales Tax Rate = 9.75% = 0.0975
Total Cost of the Camera = ?
Sales Tax = List Price Before Tax x Sales Tax Rate
Sales Tax = $778.95 x 9.75%
Sales Tax = $75.9476
or
Sales Tax = $75.95
Now add the Sales Tax in List Price Before Tax, to compute the Total Cost of the Camera, as follows;
Total Cost of the Camera = Sales Tax + List Price Before Tax
Total Cost of the Camera = $75.95 + $778.95
Total Cost of the Camera = $854.90
3. Find the radius of the object to the right.
Answer:
2.5 cm
Step-by-step explanation:
The line to the right of the object indicates the diameter. Therefore, the diameter is 5 cm.
The diameter is twice the radius, or
d=2r
We know the diameter is 5, so we can substitute that in for d
5=2r
To solve for r, we need to get r by itself. To do this, divide both sides by 2. This will cancel the 2s on the right.
5/2=2r/2
2.5=r
So, the radius is 2.5 centimeters
At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 15. The scores on the calculus final are also approximately normally distributed, with a mean of 83 and a standard deviation of 13. A student scored 82 on the chemistry final and 80 on the calculus final.
Relative to the students in each respective class, in which subject did the student do better?
a) Calculus
b) Chemistry
c) The student did equally well in each course
d) There is no basis for comparison
e) None of the above
Answer:
b) Chemistry
Step-by-step explanation:
To compare both scored we need to standardize the scores using the following equation:
[tex]\frac{x-m}{s}[/tex]
Where x is the score, m is the mean and s is the standard deviation. So, 82 on chemistry is equivalent to:
[tex]\frac{82-75}{15}=0.4667[/tex]
Because the mean of the scores on the chemistry final exam is equal to 75 and the standard deviation is 15
At the same way, 80 on Calculus is equivalent to:
[tex]\frac{80-83}{13} =-0.2308[/tex]
Because the mean of the scores on the calculus final exam is equal to 83 and the standard deviation is 13
Now, we can compare the values. So, taking into account that -0.2308 is lower than 0.4667, we can said that the student do better in Chemistry.
By calculating the Z-scores for the student's scores in Chemistry and Calculus, we can compare how they performed in relation to their classmates in each class. Since the Chemistry Z-score is higher (0.47) than the Calculus Z-score (-0.23), the student did better in chemistry.
Explanation:To understand how the student performed relative to their classmates, we need to calculate the Z-score for each of their test scores. The Z-score measures how many standard deviations an element is from the mean. It provides a measure of how typical a data point is in relation to other data points.
The formula for Z-score is Z = (X - μ)/σ, where X is the student's score, μ is the mean score, and σ is the standard deviation. Let's calculate for each subject:
Chemistry Z-Score: Z = (82 - 75)/15 = 0.47Calculus Z-Score: Z = (80 - 83)/13 = -0.23A positive Z-score indicates the data point is above the mean, and a negative Z-score indicates it's below the mean. Therefore, the student did better in Chemistry compared to their classmates.
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Participants in a survey were asked whether they favored or opposed the death penalty for people convicted of murder. Software shows the results below. Here, X refers to the number of the respondents who were IN FAVOR of the death penalty.
x n Sample p 95.0% CI
1764 2565
Show how to obtain the value that should be reported under "Sample p."
Answer:
P = 0.688
Step-by-step explanation:
Since x= 1764, n = 2565
95%. CI= ( 0.670, 0.706)
a) P= x/n
P = 1764/2565
P = 0.688
A student at a four-year college claims that mean enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 four-year colleges surveyed, the mean enrollment was 5,135 with a standard deviation of 783. Of the 35 two-year colleges surveyed, the mean enrollment was 4,436 with a standard deviation of 553. Test the student's claim at the 0.01 significance level.
NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom. Round your answer to two decimal places.)(1) What is the test statistic? (Round your answer to two decimal places.)(2) What is the p-value? (Round your answer to four decimal places.)
Answer:
Part 1: The statistic
[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)
And the degrees of freedom are given by [tex]df=n_1 +n_2 -2=35+35-2=68[/tex]
Replacing we got
[tex]t=\frac{(5135-4436)-0}{\sqrt{\frac{783^2}{35}+\frac{553^2}{35}}}}=4.31[/tex]
Part 2: P value
Since is a right tailed test the p value would be:
[tex]p_v =P(t_{68}>4.31)=0.000022 \approx 0.00002[/tex]
Comparing the p value we see that is lower compared to the significance level of 0.01 so then we can reject the null hypothesis and we can conclude that the mean for the four year college is significantly higher than the mean for the two year college and then the claim makes sense
Step-by-step explanation:
Data given
[tex]\bar X_{1}=5135[/tex] represent the mean for four year college
[tex]\bar X_{2}=4436[/tex] represent the mean for two year college
[tex]s_{1}=783[/tex] represent the sample standard deviation for four year college
[tex]s_{2}=553[/tex] represent the sample standard deviation two year college
[tex]n_{1}=35[/tex] sample size for the group four year college
[tex]n_{2}=35[/tex] sample size for the group two year college
[tex]\alpha=0.01[/tex] Significance level provided
t would represent the statistic (variable of interest)
System of hypothesis
We need to conduct a hypothesis in order to check if the mean enrollment at four-year colleges is higher than at two-year colleges in the United States , the system of hypothesis would be:
Null hypothesis:[tex]\mu_{1}-\mu_{2}\leq 0[/tex]
Alternative hypothesis:[tex]\mu_{1} - \mu_{2}> 0[/tex]
We can assume that the normal distribution is assumed since we have a large sample size for each case n>30. So then the sample mean can be assumed as normally distributed.
Part 1: The statistic
[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)
And the degrees of freedom are given by [tex]df=n_1 +n_2 -2=35+35-2=68[/tex]
Replacing we got
[tex]t=\frac{(5135-4436)-0}{\sqrt{\frac{783^2}{35}+\frac{553^2}{35}}}}=4.31[/tex]
Part 2: P value
Since is a right tailed test the p value would be:
[tex]p_v =P(t_{68}>4.31)=0.000022[/tex]
Comparing the p value we see that is lower compared to the significance level of 0.01 so then we can reject the null hypothesis and we can conclude that the mean for the four year college is significantly higher than the mean for the two year college and then the claim makes sense
A,B, and C are collinear, and B is between A and C. The ratio of AB to BC is 1:1 of A IS AT (-1,9) and B (2,0)
Step-by-step explanation:
A,B, and C are collinear, and B is between A and C. The ratio of AB to BC is 1:1 of A IS AT (-1,9) and B (2,0)
to find out point C use section formula
[tex](\frac{mx_2+nx_1}{m+n} ,\frac{my_2+ny_1}{m+n} )[/tex]
A is (-1,9) that is our (x1,y1)
that is our (x2,y2)
ratio is 1:1 that is m and n
Plug in the values in the formula
[tex](\frac{mx_2+nx_1}{m+n} ,\frac{my_2+ny_1}{m+n} )[/tex]
[tex](\frac{1(x_2)+1(-1)}{1+1} ,\frac{1(y_2)+1(9)}{1+1} ) =(2,0)\\\frac{1(x_2)+1(-1)}{1+1}=2\\\frac{1(x_2)+1(-1)}{2}=2\\\\x_2-1=4\\x_2= 5\\\frac{1(y_2)+1(9)}{1+1}=0 \\\frac{1(y_2)+1(9)}{2} =0\\\\y_2+9=0\\x_2= -9[/tex]
Answer C is (5,-9)
You need tile on one wall in your kitchen. The wall measures 12 feet by 5 feet. The tile cost $2 a square foot. How much money will it cost for the tile on the kitchen wall?
Answer:
$120
Step-by-step explanation:
Area of wall: 12*5=60 square feet
price = 60*2=$120
Quiz 1
1,700
Possiblem
A circle has a radius of 10. An arc in this circle has a central angle of 72.
What is the length of the arc?
Either enter an exact answer in terms of 7 or use 3.14 for 7 and enter your answer as a decimal.
Skill Sum
Circle basi
Arc measu
Arc length
Ouiz 1
Unit test
4 of 5 •••
Answer:
Length of arc=4π
Step-by-step explanation:
Length of arc=¤/360 x 2xπxr
Where:
¤=72
r=10
Length of arc=72/360 x 2xπx10
Length of arc=0.2 x 20π
Length of arc=4π
This is the question with the answer choices. Is it correct?
Step-by-step explanation:
A question is asked with options for answers, but in reality, there is only one question stating that it is correct.
A particle in the first quadrant is moving along a path described by the equation LaTeX: x^2+xy+2y^2=16x 2 + x y + 2 y 2 = 16 such that at the moment its x-coordinate is 2, its y-coordinate is decreasing at a rate of 10 cm/sec. At what rate is its x-coordinate changing at that time?
Answer:
[tex]\frac{50}{3}[/tex] cm/sec.
Step-by-step explanation:
We have been given that a particle in the first quadrant is moving along a path described by the equation [tex]x^2+xy+2y^2=16[/tex] such that at the moment its x-coordinate is 2, its y-coordinate is decreasing at a rate of 10 cm/sec. We are asked to find the rate at which x-coordinate is changing at that time.
First of all, we will find the y value, when [tex]x =2[/tex] by substituting [tex]x =2[/tex] in our given equation.
[tex]2^2+2y+2y^2=16[/tex]
[tex]4-16+2y+2y^2=16-16[/tex]
[tex]2y^2+2y-12=0[/tex]
[tex]y^2+y-6=0[/tex]
[tex]y^2+3y-2y-6=0[/tex]
[tex](y+3)(y-2)=0[/tex]
[tex](y+3)=0,(y-2)=0[/tex]
[tex]y=-3,y=2[/tex]
Since the particle is moving in the 1st quadrant, so the value of y will be positive that is [tex]y=2[/tex].
Now, we will find the derivative of our given equation.
[tex]2x\cdot x'+x'y+xy'+4y\cdot y'=0[/tex]
We have been given that [tex]y=2[/tex], [tex]x =2[/tex] and [tex]y'=-10[/tex].
[tex]2(2)\cdot x'+(2)x'+2(-10)+4(2)\cdot (-10)=0[/tex]
[tex]4\cdot x'+2x'-20-80=0[/tex]
[tex]6x'-100=0[/tex]
[tex]6x'-100+100=0+100[/tex]
[tex]6x'=100[/tex]
[tex]\frac{6x'}{6}=\frac{100}{6}[/tex]
[tex]x'=\frac{50}{3}[/tex]
Therefore, the x-coordinate is increasing at a rate of [tex]\frac{50}{3}[/tex] cm/sec.
PLEASE HELP! IF CORRECT WILL GET BRAINLIST!
Answer:
2
Step-by-step explanation:
f=1
2 x 1=2
4-2=2
Answer:2
Step-by-step explanation:
If f=1 then that means you are multiplying 2 by 1 which is 2. So that makes your problem 4-2=2
4-2(1)=2
what is the volume of a cube whose surface area is 294
Answer: V = 343unit³
Step-by-step explanation:
This is a solid shape problems a three dimensional.
Surface area of a cube = 6s² and the Volume = s³.
Since the surface area is given to be 294, we now use this to calculate the s.
Now,
6s² = 294, now solve for s
s² = 294/6
= 49
s² = 49
Now, to find s, we recalled the laws of indices by taking the square root of both sides
√s² = +/- √49
s. = +/-7unit.
Now to find the volume of the cube, where
V = s³ and s = 7, therefore
V = 7³
= 343unit³