1) (14 - 8)* 8 + 5
What is this
Answer:
53
Step-by-step explanation:
Answer:
53
Step-by-step explanation:
[tex](14 - 8) \ast8 + 5 \\ =6 \ast8 + 5 \\ = 48 + 5 \\ = 53 \\ \\ \red{ \boxed{\bold {\therefore \: (14 - 8) \ast8 + 5 = 53}}}[/tex]
What is the approximate length of the missing side in the triangle below?
18 miles
15 miles
80 degrees
[Not drawn to scale]
Answer: 21.3 miles
Step-by-step explanation:
(Photo attached) Trig question. I partially understand it, but not completely. Please explain! :) Thanks in advance.
Answer:
A = 2B = 3Step-by-step explanation:
You can start by recognizing 19/12π = π +7/12π, so the desired sine is ...
sin(19/12π) = -sin(7/12π) = -(sin(3/12π +4/12π)) = -sin(π/4 +π/3)
-sin(π/4 +π/3) = -sin(π/4)cos(π/3) -cos(π/4)sin(π/3)
Of course, you know that ...
sin(π/4) = cos(π/4) = (√2)/2
cos(π/3) = 1/2
sin(π/3) = (√3)/2
So, the desired value is ...
sin(19π/12) = -(√2)/2×1/2 -(√2)/2×(√3/2) = -(√2)/4×(1 +√3)
Comparing this form to the desired answer form, we see ...
A = 2
B = 3
A survey reported in Time magazine included the question ‘‘Do you favor a federal law requiring a 15 day waiting period to purchase a gun?" Results from a random sample of US citizens showed that 318 of the 520 men who were surveyed supported this proposed law while 379 of the 460 women sampled said ‘‘yes". Use this information to find a 95% confidence interval for the difference in the two proportions, , where is the proportion of men who support the proposed law and is the proportion of women who support the proposed law. Round your answers to three decimal places. The 95% confidence interval is Enter your answer; The 95%confidence interval, value 1 to Enter your answer; The 95%confidence interval, value 2 .
Answer:
Step-by-step explanation:
Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
For the men,
x = 318
n1 = 520
p1 = 318/520 = 0.61
For the women
x = 379
n2 = 460
p2 = 379/460 = 0.82
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96
Margin of error = 1.96 × √[0.61(1 - 0.61)/520 + 0.82(1 - 0.82)/460]
= 1.96 × √0.0004575 + 0.00032086957)
= 0.055
Confidence interval = 0.61 - 0.82 ± 0.055
= - 0.21 ± 0.055
Which statements are true about the shapes? Select three options.
Figure A is a cylinder. Figure B is a cone. Figure C is a sphere. Figure D is a pyramid with rectangular base.
Figure A is a cylinder.
Figure B is a square pyramid.
Figure C has no bases.
Figure D is a triangular prism.
Figure D has four lateral faces that are triangles
Correctly identifying shapes involves recognizing defining features. Figures A, C, and E are accurately labeled, while B and D need correction due to misclassifications.
In mathematics, shapes are defined by their boundaries or contours, often enclosed by points, lines, curves, and more. These characteristics categorize shapes into various types. The identification of shapes involves recognizing their defining features.
Analyzing the provided shapes:
Figure A is correctly identified as a cylinder. Its appearance aligns with the characteristics of a cylinder.
Figure B is mistakenly labeled as a square pyramid when, in fact, it resembles a cone. This discrepancy points to an incorrect classification.
Figure C is accurately described as having no bases, resembling a sphere. The absence of a base is a defining feature of a sphere.
Figure D is erroneously labeled as a triangular prism, whereas it more closely resembles a rectangular prism. This misclassification may lead to confusion.
Additionally, Figure D is correctly recognized for having four lateral faces that are triangles, aligning with the characteristics of a rectangular prism.
In summary, the accurate identifications are A, C, and E, while B and D require correction based on their actual geometric features.
What are the lowest fractions of 20 and12
Answer:4
Step-by-step explanation:
Is the square root of 95 less than 10
Answer:
Yes,it is
Step-by-step explanation:
95's square root is 9.7467943448
10 is greater than 9.7 and so forth.
So the square root of 95 is less than 10.
The square root of 95 is approximately 9.74679434, thus the square root of 95 is less than 10. The question pertains to the mathematical operation of finding square roots that are indeed pivotal while solving various mathematical problems.
The student question asks if the square root of 95 is less than 10. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 95 is approximately 9.74679434, which is indeed less than 10. The concept of square roots comes from the realm of Mathematics, more specifically Algebra. It's crucial to understand this mathematical operation as it is frequently encountered in various mathematical problems, especially ones involving quadratic equations where an unknown variable is squared. Usually, these equations will yield two solutions, as both a positive and a negative number squared gives the same result. However, the context of a problem can sometimes restrict the solution to only one value, typically the positive.
As an example, let's consider an equation like x² = 49. The solutions to this are x = -7 and x = 7 because both (-7)² and 7² equals 49. But if this equation was describing a real-world scenario where negative values could not apply (like time or distance), the meaningful solution would only be x = 7.
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Peanuts cost $12.00 for 2.5 pounds.How much for 1 pound
Answer:
$4.80
Step-by-step explanation:
Make a proportion
$12 for 2.5 pounds, and $x for 1 pound
12/2.5=x/1
x/1 is equivalent to x
12/2.5=x
Divide
x=4.8
So, one pound of peanuts costs $4.80
Answer:
4.8
Step-by-step explanation:
divide 12.00 by 2.5 to find the unit rate which is 4.8.
A mass of 1 slug is attached to a spring whose constant is 5 lb/ft. Initially, the mass is released 1 foot below the equilibrium position with a downward velocity of 7 ft/s, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity. (a) Find the equation of motion if the mass is driven by an external force equal to f(t) = 16 cos 2t + 4 sin 2t.
The equation of motion for the given scenario, involving a 1-slug mass attached to a spring, an applied external force and a damping force, is determined by formulating a differential equation from Newton's 2nd law, incorporating the spring's force and the damping force. (a) The final equation is: d²x/ dt² + 2(dx/dt) + 5x = (16 cos 2t + 4 sin 2t).
Explanation:The given scenario relates to the field of physics, specifically harmonic motion and dampening force. Harmonic motion can be studied in the context of a mass attached to a spring, such as in this question. Here, it's specified that we have a 1-slug mass attached to a spring with a spring constant of 5lb/ft, and that an external force, f(t) = 16 cos 2t + 4 sin 2t, is applied.
To find the equation of motion, you can use the general formula from Newton's 2nd law, F=ma. Given that the movement takes place in a medium providing a damping force numerically equal to two times the instantaneous velocity, the force equation of the damped harmonic oscillator becomes relevant.
The damping force can be represented as - 2v and the spring force represented as - 5x (as F= -kx). Hence, the differential equation F=ma can be represented as: m* d²x/ dt² = -2v * dx/dt – 5x + f(t), translating to: d²x/ dt² + 2(dx/dt) + 5x = (16 cos 2t + 4 sin 2t). This equation represents the equation of motion for the given conditions.
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A hypnosis program designed to help individuals quit smoking claims a 57% success rate. A consumer watch group suspects that this claim is high and randomly selects 50 individuals who have completed the program in order to conduct a hypothesis test. What are the appropriate null and alternative hypotheses?
a) H0: p = 0.57 vs. Ha: p < 0.57
b) H0: p = 0.57 vs. Ha: p > 0.57
c) H0: p = 0.57 vs. Ha: p ≠ 0.57
d) H0: p < 0.57 vs. Ha: p > 0.57
The appropriate null and alternative hypotheses for the consumer watch group's hypothesis test on the hypnosis program's success rate are:
option a) H0: p = 0.57 vs. Ha: p < 0.57
The Null Hypothesis (H0):The success rate of the hypnosis program is 57%.
Alternative Hypothesis (Ha): The success rate is less than 57%.
We use a one-tailed test because we have a directional hypothesis (suspecting a lower success rate).
If we suspected a higher or different rate, we'd use a two-tailed test.
The consumer watch group is challenging the claim of a 57% success rate by testing if the actual success rate is lower than 57%. This setup allows for a focused investigation into the program's effectiveness.
The complete question is :A hypnosis program designed to help individuals quit smoking claims a 57% success rate. A consumer watch group suspects that this claim is high and randomly selects 50 individuals who have completed the program in order to conduct a hypothesis test. What are the appropriate null and alternative hypotheses?
a) H0: p = 0.57 vs. Ha: p < 0.57
b) H0: p = 0.57 vs. Ha: p > 0.57
c) H0: p = 0.57 vs. Ha: p ≠ 0.57
d) H0: p < 0.57 vs. Ha: p > 0.57
A student obtained the Rydberg constant to be 2.16*10-18 J. What is the % error of the measurement? Answer as percentage and keep one decimal place. For example, if your answer is 12.5%, please either use 12.5% or 12.5. The fraction 0.125 will NOT be counted as correct answer.
Answer:
0.826%
Step-by-step explanation:
The Rydberg constant = 2.178 × [tex]10^{-18}[/tex] J.
students record = 2.16 x [tex]10^{-18}[/tex]J.
error = 0.018 x [tex]10^{-18}[/tex]J.
Percentage error = [tex]\frac{error}{actual measurement}[/tex] x 100
= [tex]\frac{ 0.018 * 10^{-18} }{2.178 * 10^{-18} }[/tex] x 100
= 0.826%
An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic. Step 2 of 2: Suppose a sample of 972 new car buyers is drawn. Of those sampled, 700 preferred domestic rather than foreign cars. Using the data, construct the 85% confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars. Round your answers to three decimal places.
Answer:
[tex]0.72 - 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.696[/tex]
[tex]0.72 + 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.744[/tex]
The 85% confidence interval would be given by (0.696;0.744)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
The estimated proportion for this case is [tex]\hat p =\frac{700}{972}=0.720[/tex]
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 85% of confidence, our significance level would be given by [tex]\alpha=1-0.85=0.15[/tex] and [tex]\alpha/2 =0.075[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.44, z_{1-\alpha/2}=1.44[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
If we replace the values obtained we got:
[tex]0.72 - 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.696[/tex]
[tex]0.72 + 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.744[/tex]
The 85% confidence interval would be given by (0.696;0.744)
Which of the following equations is in proper standard form?
-5x + 3y = 15
½x + 4y = 8
y = 3x + 4
2x - 3y = 6
Answer:
y= 3x+4
Step-by-step explanation:
standard form is always y equals first
According to an IRS study, it takes a mean of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. This distribution of times follows the normal distribution and the standard deviation is 80 minutes. A consumer watchdog agency selects a random sample of 40 taxpayers. What is the likelihood the sample mean is greater than 320 minutes?
Answer:
78.52% probability that the sample mean is greater than 320 minutes
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 330, \sigma = 80, n = 40, s = \frac{80}{\sqrt{40}} = 12.65[/tex]
What is the likelihood the sample mean is greater than 320 minutes?
This is 1 subtracted by the pvalue of Z when X = 320. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{320 - 330}{12.65}[/tex]
[tex]Z = -0.79[/tex]
[tex]Z = -0.79[/tex] has a pvalue of 0.2148
1 - 0.2148 = 0.7852
78.52% probability that the sample mean is greater than 320 minutes
One factor of 7x2 +33x–10 is
Answer:
OptionB
Step-by-step explanation:
Each marble bag sold by Hans's Marble Company contains 8 purple marbles for every 5 green marbles. If a bag has 30 green marbles, how many purple marbles does it contain?
We can set up a proportion since we know the ratio between the # of purple marbles and the # of green marbles.
A ratio is a way to compare two different values: for every 8 purple marbles there are 5 green marbles
[tex]\frac{8}{5} = \frac{p}{30}[/tex]when we cross multiply, we get 5p = 240 we divide both sides by 5 to isolate the variable There are 48 purple marbles
which of these expressions is equivalent to log (3 x 8)
Answer:log3 + log8
Step-by-step explanation:
log(3x8)=log3 + log8
a study examined the effectiveness of an ear molding technique used to correct ear deformities in newborns without the need for surgery. a plastic mold was placed around the deformed ear shortly after birth for about 2 weeks. the study reports that 152 of 158 procedures were successful. what is the sample proportion of successful procedures
Answer:
The sample proportion of successful procedures is 0.962.
Step-by-step explanation:
The sample proportion of successful procedures is the number of successfiç procedures divided by the total number of procedures.
In this problem:
158 procedures, of which 152 were successful. So
p = 152/158 = 0.962
The sample proportion of successful procedures is 0.962.
The sample proportion is the ratio of the number of successes to the total number of samples or trials, Hence, the sample proportion is 0.962
Given the Parameters :
Number of successful procedures, x = 152 Total number of procedures, n = 158The sample proportion can be calculated using the relation :
Sample proportion = x/nSample proportion = 152/158 = 0.962
Hence, the sampling proportion of successful procedures is 0.962.
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Find the vertices and foci of the hyperbola with equation quantity x plus 2 squared divided by 144 minus the quantity of y minus 4 squared divided by 81 = 1.
Answer:
Vertices:(-14,4) and (10,4).Foci: (–17, 4) and (13, 4)Step-by-step explanation:
Given the equation of the hyperbola
[tex]\dfrac{(x+2)^2}{144}-\dfrac{(y-4)^2}{81} =1[/tex]
Since the x part is added, then
[tex]a^2=144; b^2=81\\a=12,b=9[/tex]
Also, this hyperbola's foci and vertices are to the left and right of the center, on a horizontal line paralleling the x-axis.
From the equation, clearly the center is at (h, k) = (–2, 4). Since the vertices are a = 12 units to either side, then they are at (-14,4) and (10,4).
From the equation
[tex]c^2=a^2+b^2=144+81=225\\c=15[/tex]
The foci, being 15 units to either side of the center, must be at (–17, 4) and (13, 4)
A real estate appraiser is developing a regression model to predict the market value of single family residential houses as a function of heated area, number of bedrooms, number of bathrooms, age of the house, and central heating (yes, no). The response variable in this model is _______.
a. heated area
b. number of bedrooms
c. market value
d. central heating
e. residential houses
The response variable in this model is: Market value .
Hence the correct option is C.
Given, that a regression model is developed.
A real estate appraiser is developing a regression model to predict the market value of single family residential houses as a function of heated area, number of bedrooms, number of bathrooms, age of the house, and central heating (yes, no). The response variable in this model is market value .
Therefore the correct option is C .
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In the regression model being developed by the real estate appraiser, the response variable is the market value of the single-family residential houses.
Explanation:In the regression model described by the question, the market value of single-family residential houses is being predicted based on several predictive variables (heated area, number of bedrooms, number of bathrooms, age of the house, and presence of central heating). Therefore, the response variable or the dependent variable in this model is the market value of the houses.
A response variable is the feature or quantity that the model outputs. In this context, the real estate appraiser is trying to produce a model that will tell him how changes in the variables like heated area, bedrooms etc. will change the output, which is the market value.
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Find X: 5x=45
A) 9
B) 2
C) 12
D) 0
Answer: [tex]x=9[/tex]
Divide both side by 5
[tex]5x/5=45/5\\x=9[/tex]
Answer:
[tex]x = 9[/tex]
Step-by-step explanation:
[tex]5x = 45 \\ \frac{5x}{5} = \frac{45}{5} \\ x = 9[/tex]
hope this helps you.....
A simple random sample of 450 residents in the state of New York is taken to estimate the proportion of people who live within one mile of a hazardous waste site. If 135 of the residents in the sample live within one mile of a hazardous waste site, what are the values of the sample proportion of people who live within one mile of a hazardous waste site and its standard error?
A. 0.3 and 0.01
B. 0.3 and 0.022
C. 0.3 and 0.21
D. 0.7 and 0.022
Answer:
B. 0.3 and 0.022
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a sample proportion p in a sample of size n, the standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
135 of the 450 residents sampled live within one mile of a hazardous waste site.
So the sample proportion is [tex]p = \frac{135}{450} = 0.3[/tex]
Standard error
[tex]s = \sqrt{\frac{0.3*0.7}{450}} = 0.022[/tex]
So the correct answer is:
B. 0.3 and 0.022
Final answer:
The sample proportion of people who live within one mile of a hazardous waste site is 0.3, and the standard error for this sample proportion is 0.022. The correct answer is B. 0.3 and 0.022.
Explanation:
To estimate the proportion of people who live within one mile of a hazardous waste site using a sample, we divide the number of residents living within one mile by the total number of residents sampled. In this case, 135 residents live within one mile out of a sample of 450 residents, which makes the sample proportion 135/450 = 0.3.
To calculate the standard error (SE) for the sample proportion, we use the formula SE = √(p(1-p)/n), where p is the sample proportion and n is the sample size. Plugging in the values, we get SE = √(0.3(1-0.3)/450), which approximates to 0.022.
The correct answer is B. 0.3 and 0.022 for the sample proportion and its standard error, respectively.
. Suppose you wish to find out the answer to the questions "Do Americans prefer Coke or Pepsi?" You conduct a blind taste test in which individuals are randomly asked to drink one of the colas first, followed by the other cola, and then asked to disclose which drink they prefer. Results of your taste test indicate that 53 of 100 individuals prefer Pepsi. Conduct a hypothesis test to determine if more than 50% of people prefer Pepsi to coca cola. Use the ???? = 0.05 level of significance.
Answer:
[tex]z=\frac{0.53 -0.5}{\sqrt{\frac{0.5(1-0.5)}{100}}}=0.6[/tex]
[tex]p_v =P(z>0.6)=0.274[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 5% of significance the proportion of people who prefer Pepsi is not higher than 0.5 or 50%
Step-by-step explanation:
Data given and notation
n=100 represent the random sample taken
X=53 represent the people who prefer Pepsi
[tex]\hat p=\frac{53}{100}=0.53[/tex] estimated proportion of people who prefer PEsi
[tex]p_o=0.5[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is higher than 0.5.:
Null hypothesis:[tex]p\leq 0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.53 -0.5}{\sqrt{\frac{0.5(1-0.5)}{100}}}=0.6[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
[tex]p_v =P(z>0.6)=0.274[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 5% of significance the proportion of people who prefer Pepsi is not higher than 0.5 or 50%
To determine if more than 50% of people prefer Pepsi to Coca-Cola, conduct a one-sample proportion test using the given data and a significance level of 0.05.
Explanation:To conduct a hypothesis test to determine if more than 50% of people prefer Pepsi to Coca-Cola, you can use a one-sample proportion test. The null hypothesis, denoted as H0, is that the proportion of people who prefer Pepsi is equal to 50%. The alternative hypothesis, denoted as H1, is that the proportion is greater than 50%. Using the given data, you would calculate the test statistic and compare it to the critical value or p-value associated with a significance level of 0.05. If the test statistic falls in the rejection region, you would reject the null hypothesis and conclude that more than 50% of people prefer Pepsi.
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The mean hourly wage for employees in goods-producing industries is currently (Bureau of Labor Statistics website, April, 12, 2012). Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of for the goods-producing industries. a. Select the null hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries. 1. : 2. : 3. :
Complete Question:
The mean hourly wage for employees in goods-producing industries is currently $24.57 (Bureau of Labor Statistics website, April, 1 2, 201 2). Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries. State the null and alternative hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries
Answer:
Null hypothesis, H₀ : μ = 24.57
Alternative hypothesis, [tex]H_{a}[/tex] : μ ≠ 24.57
Step-by-step explanation:
The mean hourly wage for the goods producing industry = $24.57
Since we want to see if the mean of hourly wage for the manufacturing industry is equal to $24.57( The mean f hourly wage for the good producing industry)
Therefore the, null hypothesis will be that there is no significant difference between the means of the hourly wages of both the goods producing and the manufacturing industries, while the alternative hypothesis will be that the means of their hourly wages are significantly different
Null hypothesis, H₀ : μ = 24.57
Alternative hypothesis, [tex]H_{a}[/tex] : μ ≠ 24.57
Kathy and her brother Clay recently ran in a local marathon. The distribution of finishing time for women was approximately normal with mean 259 minutes and standard deviation 32 minutes. The distribution of finishing time for men was approximately normal with mean 242 minutes and standard deviation 29 minutes.
(a) The finishing time for Clay was 289 minutes. Calculate and interpret the standardized score for Clay’s marathon time. Show your work.
(b) The finishing time for Kathy was 272 minutes. What proportion of women who ran the marathon had a finishing time less than Kathy’s? Show your work.
(c) The standard deviation of finishing time is greater for women than for men. What does this indicate about the finishing times of the women who ran the marathon compared to the finishing times of the men who ran the marathon?
Answer:
a) Clay's marathon time is 1.62 standard deviations above the mean finishing time for men.
b) 69.51% of those who ran the marathon has a finishing time less than 272.
c) The spread in the distribution of women's finishing time is greater as compared to the spread in the distribution of men's finishing time.
Step-by-step explanation:
Part a) It was given that, the finishing time for Clay's marathon time is 289 minutes.
To calculate the standardized test score for Clay's marathon time, we use the formula:
[tex]z = \frac{x - \mu}{ \sigma} [/tex]
where
[tex]x = 289[/tex]
[tex] \mu = 242[/tex]
and
[tex] \sigma = 29[/tex]
We substitute the values into the formula to get:
[tex]z = \frac{289 - 242}{29} = 1.62[/tex]
Interpretation: Clay's marathon time is 1.62 standard deviations above the mean finishing time for men.
b) To calculate the proportion of women that had a finishing time less than Kathy , we again need to calculate the z-score for x=272, with mean for women being 259 minutes and standard deviation 32 minutes.
We substitute to get:
[tex]z = \frac{272 - 259}{32} = 0.41[/tex]
From the standard normal distribution table, P(z<0.41)=0.6951
Therefore 69.51% of those who ran the marathon has a finishing time less than 272.
c) The standard deviation measures the variation of a distribution. This means the standard deviation measures how far away the data set of a distribution are from the mean.
If the standard deviation of finishing time is greater for women than for men, then it indicates that, women's finishing time are far away from the mean finishing time as compared to men's finishing time.
What shape is formed when a plane slices through a sphere at any angle?
oval
rectangle
triangle
circle
Answer:
Triangle
Step-by-step explanation:
I got done taking the quiz and it wasn't oval For k12 people this is the answer. Hope this helps
A computer manufacturer is testing a batch of processors. They place a simple random sample of processors from the batch under a stress test and record the number of failures, their guidelines specify the percentage of failures should be under 4%. Of the 300 processors tested, there were 54 failures.
a. State the hypotheses for the test. Assume the manufacturer wants to assume there is a problem with a batch, that is, they will only accept that there are fewer than 4% failures in the population if they have evidence for it.
b. Calculate the test statistic and p-value. Your test statistic should be either a z-value or a t-value, whichever is appropriate for the problem
Answer:
a)We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.04 or no.:
Null hypothesis:[tex]p \leq 0.04[/tex]
Alternative hypothesis:[tex]p > 0.04[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
b) We need to use a z statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.135 -0.04}{\sqrt{\frac{0.04(1-0.04)}{300}}}=8.396[/tex]
Since is a right tailed test the p value would be:
[tex]p_v =P(z>8.396) \approx 0[/tex]
Step-by-step explanation:
Data given and notation
n=400 represent the random sample taken
X=54 represent the number of failures
[tex]\hat p=\frac{54}{400}=0.135[/tex] estimated proportion of adults that said that it is morally wrong to not report all income on tax returns
[tex]p_o=0.04[/tex] is the value that we want to test
[tex]\alpha[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Part a: Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.04 or no.:
Null hypothesis:[tex]p \leq 0.04[/tex]
Alternative hypothesis:[tex]p > 0.04[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Part b: Calculate the statistic
We need to use a z statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.135 -0.04}{\sqrt{\frac{0.04(1-0.04)}{300}}}=8.396[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
[tex]p_v =P(z>8.396) \approx 0[/tex]
So the p value obtained was a very low value and using the significance level for example [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of defectives is significantly higher than 0.04 or 4%
halla la altura de la torre con los datos ofrecidos `por el equipo de ingenieros la longitud entre el niño y la punta de la torre es de 250 metros
Answer:
The height of the tower is 245 m
Step-by-step explanation:
The complete question in English is
Find the height of the tower with the data provided by the engineering team. Value of the segment ab= 50 m. The length between the child and the tip of the tower is 250 m
The picture in the attached figure
we know that
In the right triangle ABC
Applying the Pythagorean Theorem
[tex]AC^2=AB^2+BC^2[/tex]
we have
[tex]AB=50\ m\\AC=250\ m[/tex]
substitute
[tex]250^2=50^2+BC^2[/tex]
[tex]BC^2=250^2-50^2[/tex]
[tex]BC^2=60,000\\BC=245\ m[/tex]
An eccentric philanthropist undertakes to give away $100,000. He is eccentric because he insists that each of his gifts be a number of dollars that is a power of two, and he will give no more than one gift of any amount. How does he distribute the money? Dudley, Underwood. Elementary Number Theory: Second Edition (Dover Books on Mathematics) (p. 113). Dover Publications. Kindle Edition.
Answer:
Step-by-step explanation:
An eccentric philanthropist undertakes to give away $100,000. He is eccentric because he insists that each of his gifts be a number of dollars that is a power of two, and he will give no more than one gift of any amount. How does he distribute the money?
To solve this problem, we will simply write 1,00,000 in base 2.
2^17 gives 131072, 2^16 gives 65536.
So, the first gift is 65536, we then need to repeat this process for 34,464 ((100,000-65536 = 34,464), to get all gifts in succession.
6 gifts in all: one each of $32, $128, $512, $1024, $32768, and $65536.
find the value of x and tan x in the given trigonometric equation:
sin 2x= cos(3x+10)
Answer:
x = 16°, tan x = 0.3
Step-by-step explanation:
[tex]sin \: 2x = cos \: (3x + 10) \\ cos(90 - 2x) = cos \: (3x + 10) \\ 90 - 2x = 3x + 10 \\ 90 - 10 = 3x + 2x \\ 80 = 5x \\ x = \frac{80}{5} \\ \huge \red{ \boxed{x = 16 \degree }}\\ \\ tan \: x = tan \: 16 \degree \\ = 0.2867453858 \\ = 0.3[/tex]