Answer:
Claim is rejected
Step-by-step explanation:
Solution:-
- The claim was made on the effectiveness of medication on the market of Parkinson's disease to be p = 75%.
- A random sample was taken of N = 150 individuals and n = 100 number of people reported that it was effectively.
- We are to test the claim made by the manufacturer of the medication based on the statistics available for the sample N.
- State the hypothesis for the effectiveness of medication:
Null Hypothesis: p = 0.75 ... Claim
Alternate hypothesis: p < 0.75 .... Test
- The conditions of standard normality:
n*p > 5 , 150*0.75 = 112.5 .. ( Check )n*(1-p) > 5 , 150*0.25 = 37.5 .. ( Check )Hence, the standard normal test is applicable. Assuming the population proportion to be normally distributed.
- We will estimate the population proportion with the sample proportion ( p* ):
p* = n / N
p* = 100 / 150
p* = 2/3 = 0.667
- Testing against the claimed population proportion ( p ) = 0.75. The standard normal statistic value is given by:
[tex]Z-test= \frac{(p^* - p)}{\sqrt{p(1-p) / N} } \\\\Z-test= \frac{(0.6667 - 0.75)}{\sqrt{0.75(0.25) / 150} } \\\\Z-test= \frac{-0.0833}{\sqrt{0.00125} } \\\\Z-test= -2.35607 \\[/tex]
- We will see whether the Z-test statistic falls in the rejection region defined by the critical value of Z at significance level ( α ) of 0.05.
- The rejection region is defined by the Alternate hypothesis which is less than the claimed value. So, the rejection region defined by the lower tail of the standard normal.
- So for lower tailed test the critical value of statistics is:
P ( Z < Z-critical ) = α = 0.05
Z-critical = - 1.645
- The rejected values all lie to the left of the Z-critical value -1.645
- The claim test value is compared the rejection region:
-2.35607 < -1.645
Z-test < Z-critical
Hence, Null hypothesis rejected because test lies in the rejection region.
Conclusion:
The Null hypothesis or claim made by the manufacturer of Parkinson's disease medication of 75% effectiveness is without sufficient evidence. Hence, the claim made is false or has no statistical evidence.
By calculating the Z-score and corresponding p-value for the statistical test, we found that there is significant evidence at the 0.05 level to suggest that the medication's effectiveness is less than the 75% claimed.
Explanation:The subject we're dealing with here is hypothesis testing in statistics, where we have a claim (the effectiveness of the medication is 75%) and we are testing whether the observations (effectiveness in 100 out of 150 individuals) support this claim.
Firstly, the parameter of interest here is the proportion (p) of individuals for whom the medication is effective. Our null hypothesis (H0) is that p = 0.75 and our alternate hypothesis (Ha) is that p < 0.75.
To conduct the hypothesis test, let's check the conditions:
Random: It's not mentioned, but assuming these 150 individuals were chosen randomly, this condition is met.Normal: Since both np (150 * 0.75 = 112.5) and n(1-p) (150 * 0.25 = 37.5) are greater than 10, the sampling distribution will be approximately normal.Independent: Again, this is not stated, but let's assume the responses from the individuals are independent.The sample proportion (p-hat) = 100/150 = 0.67
Next, we calculate the Z score, which is (p-hat - p) / sqrt[p(1-p)/n] = (0.67 - 0.75) / sqrt[0.75 * (0.25) / 150] = -1.65. The p-value associated with a Z score of -1.65 is 0.0495.
Since the p-value is less than the significance level of 0.05, we reject H0 and conclude that there is statistically significant evidence at the 0.05 level that the effectiveness of medication is less than 75% as claimed by the manufacturer.
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Maya picks 16 vegetables from her garden.
6 of them are carrots. The rest are cucumbers.
Then she gives away 5 cucumbers.
How many cucumbers does Maya have now?
16 - 6 = 10
10 - 5 = ?
16 + 6 = 22
22 - 5 = ?
16 - 6 = 10
10 + 5 = ?
Answer:
she has 5
Step-by-step explanation:
16 vegetables subtracted by 6 = 10 carrots
10 carrots subtracted by 5 that she gives away = 5 that she has left
A nonlinear function with at least one term raised to the power of two is known as a a. logarithmic function. b. quadratic function. c. hyperbolic function. d. cubic function.
Answer:
The option b) quadratic function is correctA nonlinear function with at least one term raised to the power of two is known as a quadratic functionStep-by-step explanation:
A nonlinear function with at least one term raised to the power of two is known as a quadratic function
FOR :
A non-linear system of equations is a set of equations where one or more terms have a variable of power two or higher .
In Algebra, linear functions are polynomials with highest exponent equal to 1 or of the form y = c where c is constant. Non-linear functions are all other rest functions with exponent atleast 2.
Hence A nonlinear function with at least one term raised to the power of two is known as a quadratic function
Therefore the option b) quadratic function is correctHow many black cherry trees have a height of 80 or more feet?
(Group of answer choices)
A) 7
B) 5
C) 10
D) 17
What is the ratio of our solar system's radius to the Milky Way's radius given that the distance from Pluto to the sun is 5.9 * 10^12 meters; and the Milky Way's disk radius is 3.9 * 10^20 meters. Round the coefficient to the nearest tenth.
Answer:
Just divide the sun-pluto distance by the milky way radius and you get the following ratio:
6.6 x 10^7 : 1
Solve the equation for x, and enter your answer below.
7 x -5= 65
x=10
Step-by-step explanation:
7x - 5=65
+5 +5 so the 5's cancel so add 5 to 65
7x =70 because you add 5 to 65 to get 70
7x 7
7 x cancels out so you answer will be
x=10
Answer:
x = 10Step-by-step explanation:
7 x -5 = 65
7 times what? (x) - 5 equals 65
Well we know that x has to be less than 65 and more than 7 and -5.
So 7 must be multiplied by numbers 8, and up.
7 * 8 -5 = 51, NOT 65.
7 * 9 -5 = 58, NOT 65.
7 * 10 -5 = Does equal 65.
Therefore, x is equivalent to 10.
According to this site, if you know the coordinates of two points on a line, what form would you use to write the equation of the
line? Explain the process for writing the equation. (Site 1)
You would use the POINT SLOPE FORMULA and the Slope Formula
which is as follows ...
slope formula : [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
point slope formula: [tex]y - y_{1} = m(x - x_{1} )[/tex]
Find the theoretical probability of the event when rolling a standard number cube. P(6)
The theoretical probability of rolling a 6 on a standard number cube is 1/6 or approximately 0.1667.
Explanation:The theoretical probability of rolling a 6 on a standard number cube is 1/6 or approximately 0.1667.
To find the probability, we divide the number of successful outcomes (rolling a 6) by the total number of possible outcomes (numbers 1 to 6), which is 6.
So the probability is 1/6 or 0.1667.
Since a standard number cube has equal chances of landing on any number from 1 to 6, each outcome has the same probability of occurring, which is 1/6.
Thus, the theoretical probability of the event when rolling a standard number cube is found to be 1/6 or approximately 0.1667.
Final answer:
The theoretical probability of rolling a six on a standard six-sided die is 1 in 6, or P(6) = 1/6.
Explanation:
The student has asked about finding the theoretical probability of rolling a six, P(6), with a standard six-sided die. In a fair six-sided die, the outcomes are equally likely, meaning the probabilities for each number 1 through 6 are the same. Given that there are six possible outcomes, the probability of rolling any one specific number, for example 6, is 1 out of the 6 total possible outcomes. Therefore, P(6) = 1/6. This probability reflects that, theoretically, if we were to roll the die many times, we'd expect to roll a 6 in approximately one-sixth of all the rolls.
Determine the center of the following data set by finding
the median.
Test Scores
47,50,43, 42, 42, 38, 49, 47, 42, 50
Answer:
The median of this set is 45.
Step-by-step explanation:
Maximum height___feet
Answer:
you are not aloud to cheat on tests please don't do that sorry can't answer to a cheater
Step-by-step explanation:
What function is graphed below?
y = cot(x)-2
y=tan(x)-2
y = cot(x)+2
y=tan(x)+2
Answer:
d
Step-by-step explanation:
The function y = tan(x) + 2 is shown in the provided graph option fourth is correct.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
The missing figure is in the picture please refer to the picture.
As we have a trigonometric function.
In the picture, the graph of a tanx is shown but 2 units up.
Thus, the function y = tan(x) + 2 is shown in the provided graph option fourth is correct.
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Find the complete solution of the linear system, or show that it is inconsistent. (If the system has infinitely many solutions, express your answer in terms of t, where x = x(t), y = y(t), and z = t. If there is no solution, enter NO SOLUTION.) 2x + 3y − z = −1 x + 2y = 5 x + 3y + z = 12
Answer:
inconsistent
Step-by-step explanation:
The sum of the first and last equations is ...
(2x +3y -z) +(x +3y +z) = (-1) +(12)
3x +6y = 11
Three times the second equation is ...
3(x +2y) = 3(5)
3x +6y = 15
There are no values of x, y, or z that can make both of these equations true. They are inconsistent.
A simple random sample of 5 months of sales data provided the following information: Month:12345 Units Sold:9480859492 (a)Develop a point estimate of the population mean number of units sold per month. x
Answer:
89 units
Step-by-step explanation:
-The population's mean point estimate is equivalent to the sample mean.
Given the 5 month units sold is 94,80,85,94 and 92
-Mean is the average of the units sold over the 5 month period:
[tex]\bar X=\frac{\sum {x_i}}{n}\\\\=\frac{94+80+85+84+92}{5}\\\\=89[/tex]
Hence, the point estimate for the population mean is 89 units
The mean weekly earnings of a sample of 30 construction workers was $759, with a standard deviation of $73, and the mean weekly earnings of a sample of 28 manufacturing workers was $658, with a standard deviation of $65. Construct a 85% confidence interval for the difference between the mean weekly earnings for construction workers and the mean weekly earnings for manufacturing workers. Round to the second decimal place.
Answer:
[tex] (759-658) -1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 74.54[/tex]
[tex] (759-658) +1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 127.46[/tex]
And the confidence interval for the difference of the two means is given by (74.54, 127.46)
Step-by-step explanation:
Information given:
[tex]\bar X_1 = 759[/tex] the sample mean for construction workers
[tex] s_1 =73[/tex] the sample standard deviation for construction workers
[tex]n_1 =30[/tex] sample size of construction workers
[tex]\bar X_2 = 658[/tex] the sample mean for manufacturing workers
[tex] s_2 =65[/tex] the sample standard deviation for manufacturing workers
[tex]n_2 =28[/tex] sample size of construction workers
Confidence interval
The confidence interval for the difference of means are given by:
[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]
We need to find the degrees of freedom given by:
[tex] df = n_1 +n_2 -2= 30+28-2=56[/tex]
The confidence is 0.85 and the significance level would be [tex]1-0.85=0.15[/tex] and [tex]\alpha/2 = 0.075[/tex]. We need to find a critical value in the t distribution who accumulates 0.075 of the area on each tail and we got:
[tex] t_{\alpha/2}= \pm 1.46[/tex]
And then we can replace and we got:
[tex] (759-658) -1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 74.54[/tex]
[tex] (759-658) +1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 127.46[/tex]
And the confidence interval for the difference of the two means is given by (74.54, 127.46)
Part (a): The 80% confidence interval for the earnings difference is $77.51 to $124.49.
Part (b): The interval suggests 80% confidence in the true earnings difference falling within $77.51 to $124.49.
Part (c): Since zero isn't in the interval, there's a significant pay difference between construction and manufacturing workers.
Part (a): Construct an 80% confidence interval for the difference between the mean weekly earnings
Step 1: Identify the given data
- Construction workers:
- Mean [tex](\(\bar{X_1}\)) = \$759[/tex]
- Standard deviation [tex](\(s_1\)) = \$73[/tex]
- Sample size [tex](\(n_1\))[/tex] = 30
- Manufacturing workers:
- Mean [tex](\(\bar{X_2}\)) = \$658[/tex]
- Standard deviation [tex](\(s_2\)) = \$65[/tex]
- Sample size [tex](\(n_2\)) = 28[/tex]
Step 2: Determine the formula for the confidence interval
We use the formula for the confidence interval of the difference between two independent means:
[tex]\[ (\bar{X_1} - \bar{X_2}) \pm t_{\alpha/2} \cdot \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \][/tex]
Step 3: Calculate the standard error (SE) of the difference
[tex]\[ SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \][/tex]
[tex]\[ SE = \sqrt{\frac{73^2}{30} + \frac{65^2}{28}} \][/tex]
[tex]\[ SE = \sqrt{\frac{5329}{30} + \frac{4225}{28}} \][/tex]
[tex]\[ SE = \sqrt{177.63 + 150.89} \][/tex]
[tex]\[ SE = \sqrt{328.52} \approx 18.12 \][/tex]
Step 4: Determine the degrees of freedom (df) using the Welch-Satterthwaite equation
[tex]\[ df = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\right)^2}{\frac{\left(\frac{s_1^2}{n_1}\right)^2}{n_1-1} + \frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2-1}} \][/tex]
[tex]\[ df \approx \frac{328.52^2}{\frac{(177.63)^2}{29} + \frac{(150.89)^2}{27}} \][/tex]
[tex]\[ df \approx \frac{107,922.4}{1090.15 + 843.48} \][/tex]
[tex]\[ df \approx \frac{107,922.4}{1933.63} \approx 55.83 \approx 56 \][/tex]
Step 5: Find the t-value for an 80% confidence interval
For df ≈ 56 and [tex]\(\alpha/2 = 0.10\),[/tex] the t-value [tex](\(t_{0.10}\))[/tex] is approximately 1.296.
Step 6: Construct the confidence interval
[tex]\[ (\bar{X_1} - \bar{X_2}) \pm t_{\alpha/2} \cdot SE \][/tex]
[tex]\[ (759 - 658) \pm 1.296 \cdot 18.12 \][/tex]
[tex]\[ 101 \pm 23.49 \][/tex]
[tex]\[ (77.51, 124.49) \][/tex]
So, the 80% confidence interval for the difference between the mean weekly earnings is [tex]\((77.51, 124.49)\).[/tex]
Part (b): Explanation of the Confidence Interval
The 80% confidence interval [tex]\((77.51, 124.49)\)[/tex] means that we are 80% confident that the true difference between the mean weekly earnings of construction workers and manufacturing workers lies between [tex]\$77.51[/tex] and [tex]\$124.49[/tex]. In other words, if we were to take many samples and compute the confidence interval for each, about 80% of those intervals would contain the true difference in mean earnings.
Part (c): Is there a significant difference in pay?
To determine if there is a significant difference in pay, we look at whether the confidence interval includes zero. Since the 80% confidence interval for the difference in mean earnings (\(77.51, 124.49\)) does not include zero, we can conclude that there is a statistically significant difference in pay between construction workers and manufacturing workers at the 80% confidence level.
Complete Question:
ILL GIVE BRAINLIEST please please help (only help if u know the right answer)
Okay, to find the answer,
All we need to do it multiply !
[tex]\frac{f}{-3.2}[/tex] = 0.01
f = (0.01) × (-3.2)
f = -.032
I hope I helped :) Just comment if you have any questions and remember to vote me "brainliest" if you like my answer !!!
If $5958 is invested in an account at 5.9% annual interest compounded quarterly, how much will be in the account in 7 years if no money is withdrawn (Round your answer to the nearest hundredth)?
Answer:
Pretty sure in 7 years with no money withdrawn it would be $8,418.65
Step-by-step explanation:
because you would find out what 5.9% of $5958 which would be $351.522 you get that by multiplying [5958*5.9%=351.522]
Then multiply 351.522 by 7 and you get 2460.654 [351.522*7=2460.654]
Finally you add 2460.654 and 5958 and you get 8418.654 [5958+2460.522=8418.654]
Then you round down .654 and you get [8418.65]
The price of a movie ticket after a 16% increase is $8.99. What was the price before increase?
Answer:
The price before the increase was $7.75.
Step-by-step explanation:
This question can be solved using a rule of three.
The price of a movie ticket after a 16% increase is $8.99.
This means that the current price, of $8.99, is 100+16 = 116% = 1.16 of the original
x, the original price, is 100% = 1. So
8.99 - 1.16
x - 1
[tex]1.16x = 8.99[/tex]
[tex]x = \frac{8.99}{1.16}[/tex]
[tex]x = 7.75[/tex]
The price before the increase was $7.75
Answer:
$7.75
Step-by-step explanation:
When a number is increased by a certain percentage, it means that the product of the percentage and the number is added to the number. The result is the increase of the original number by the given percentage.
As such, if the original number is x and it is increased by 16%, to get $8.99, this may be expressed mathematically as
16% * x + x = 8.99
1.16x = 8.99
x = 8.99/1.16
= $7.75
The price before the increase was $7.75
In March, April, and June it rained 2 inches. In February, May, and September it rained 1 inch In August and
October, it rained 3 inches. And in January it only rained 4 inches. Which line plot represents the data?
x
x
.
X
.
X
X
X
1
2
3
4
5
✓ Done
Intro
Answer:
d
Step-by-step explanation:
What is the density of an object with a mass of 20 g and volume of 10 cm3?
Answer:
2 g/cm^3
Step-by-step explanation:
D=m/V
=20g/10cm^3
=2g/cm^3
Density calculation based on mass and volume of an object is 2 g/cm³.
The density of an object is calculated by dividing its mass by its volume. In this case, with a mass of 20 g and volume of 10 cm³, the density can be calculated as:
Density = Mass / Volume = 20 g / 10 cm³ = 2 g/cm³
Answer the question bellow
Answer:
D
Step-by-step explanation:
All of the other functions are functions that are just multiplicative. When we substitute any x for A, B,or C, y/x will be the same. In D y/x will vary.
HELP! will give brainliest if given right answers
7. tails, odd, 4
P(tails) = 1/2
P(odd) = 3/6 = 1/2
P(4) = 1/6
P(tails then odd then 4) = (1/2)×(1/2)×(1/6) = 1/24 ≈ 0.041666
Answer: 1/24, 4.2%
8. tails, 6 or 1, 3
P(6 or 1) = 2/6 = 1/3
P(3) = 1/6
P( tails, 6 or 1, 3) = (1/2)(1/3)(1/6) = 1/36 ≈ 0.027777
Answer: 1/36, 2.8%
9. heads, not 2, even
P(heads) = 1/2
P(not 2) = 5/6
P(even) = 1/2
P(heads, not 2, even) = (1/2)(5/6)(1/2) = 5/24 ≈ 0.208333
Answer: 5/24, 20.8%
Answer:
7. 1/24 = 4.2%
8. 1/36 = 2.8%
9. 1/6 = 16.67%
All percentages are rounded
The number of cell phone accounts in a certain country has increased exponentially for the last decade. The number of cell phone accounts (in millions) in this country can be approximated by the following function. Estimate the number of cell phone accounts in 2003.
f(x)= 114.8e.125x (0
What was the approximate number of cell phone accounts in 2003?
Answer:
See Below
Step-by-step explanation:
The equation estimating the number of cellphones in the country is:
[tex]f(x)=114.8 e^{0.125x}[/tex]
Where x = 0 corresponds to year 2000
thus,
x = 1 is year 2001
x = 2 is year 2002
x = 3 is year 2003
and so on...
We want approx. number of cellphones in the country in 2003. This corresponds to x = 3. So substituting in the equation we get:
[tex]f(x)=114.8 e^{0.125x}\\f(3)=114.8 e^{0.125(3)}\\f(3)= 167.03[/tex]
So, approximately there were 167.03 million cellphones in the country in 2003
Several years ago, Dirk bought some gold at a price of $710 per ounce. When he went to sell it, the gold was worth 60% more than it was when he purchased it. What was the new value of the gold?
Answer:
$1,136 per ounce.
Step-by-step explanation:
To find the new value of gold, you have to find what 60% of 710 is. You do this by converting 60% into a decimal and multiplying it by 710. This results in 0.6*710. 60% of 710 is 426. 426 + the original price of 710 is equal to 1,136.
You can also solve this problem in a condensed manner by multiplying 710 by 1.6: the 1.0 stands for the original price (710) so you don't have to add it later. The 0.6 stands for the 60% more. Multiplying 710 by 1.6 gets you 1,136, which is the new value of gold/ounce.
The Tauroto region contains 31 different species of IceCream-type small monsters. Each capture of an IceCream-type small monster has an equal chance of being any of the 31 species. If a collector captures five of these small monsters, what is the probability that they have captured at least two small monsters of the same species?
Answer:
0.28
Explanation:
You can determine the probability of the collector has captured at least two small monsters of the same species is the complent of that all the monsters captured are of different species, i.e. none are of the same species.
The probability than none of the five captured small monsters are of the same species are:
1. Probability than the one monster is of the species One, and the others are not of the species One:
(1/32) × (31/32) × (30/32) × (29/32) × (28/32)2. Probability that the first monster is of the species Two, and the others are not of the species Two:
(1/32) × (31/32) × (30/32) × (29/32) × (28/32)3. Probability that the first monster is of the species Three and the others are not of the same species:
(1/32) × (31/32) × (30/32) × (29/32) × (28/32)4. Inference
As you see you have to do this 32 times, and then add all the equal 32 probabilities, which is
32 × (1/32) × (31/32) × (30/32) × (29/32) × (28/32) = 0.72That is the probability that none of the five small monsters are of the same species. Then, the probability that at leas two small monsters are of the same species is 1 - 0.72 = 0.28
If I sent out 200 letters and got 80 responses. If I want 20 more responses how many more letters do I have to send out
Answer:
Step-by-step explanation:
50
What is the area of the triangle below?
Answer:
9 square units
Step-by-step explanation:
Draw a rectangle around the triangle. The rectangle is 4 units tall by 6 units wide. The area of the triangle equals the area of the rectangle minus the triangles in the corners.
A = (4)(6) − ½(2)(4) − ½(1)(4) − ½(3)(6)
A = 24 − 4 − 2 − 9
A = 9
A spinner has 8
equal-sized sections. Two
of the sections are yellow
.
a. What is the probability that the spinner will land on yellow
?
b. Use words to describe the probability.
Answer:
1/4
Step-by-step explanation:
The probability that the spinner will land on yellow is 2/8 because 2 is how many of the sections are yellow and 8 is how many sections there are in total. However, you need to simplify this to 1/4 and that is your answer
Final answer:
The probability that a spinner with 8 equal sections will land on yellow is 2 out of 8, which simplifies to 1/4 or a 25% chance.
Explanation:
The question asks about the probability of a spinner with 8 equal-sized sections landing on yellow, where 2 of the sections are yellow. To calculate the probability:
Count the number of favorable outcomes (the yellow sections): 2 sections.Count the total number of possible outcomes (all sections of the spinner): 8 sections.Divide the number of favorable outcomes by the total number of possible outcomes to get the probability.a. The probability that the spinner will land on yellow is 2 out of 8, or 1/4.
b. In words, the probability can be described as having a one in four chance or a 25% chance of landing on yellow when the spinner is spun.
A mechanic finds that 30% of his customers own foreign cars, and that 40% own dogs. Assuming that these events are independent, what percent of the customers have neither a foreign car nor a dog
Answer:
42%
Step-by-step explanation:
Answer:
Since the events are independent, 30% of his customers have neither a foreign car nor a dog.
Step-by-step explanation:
Let the total number of his customers = 100.
Since the events are independent,
customers with foreign cars + customers that own dogs + customers that have neither a foreign car nor a dog = 100.
But,
Customers with foreign cars = 30% = 30
Customers that own dogs = 40% = 40
Customers with neither foreign car nor dog = x%
So that,
30 + 40 + x = 100
70 + x = 100
x = 100 - 70
x = 30
Customers with neither foreign car nor dog = 30.
Converting this value to percentage,
= [tex]\frac{30}{100}[/tex] × 100
= 30%.
Therefore, 30% of his customers have neither a foreign car nor a dog.
What is the surface area of a square pyramid with a slant height of 6cm and the length of one side of the square base is 5cm
Answer:
S = 85cm^2
Step-by-step explanation:
The surface area of a square pyramid is given by the following formula:
[tex]S=2hb+b^2[/tex]
where it has taken into account the sum of the area of a square and four triangles:
[tex]4(\frac{hb}{2})+b*b=2bh+b^2[/tex]
h: slant height = 6cm
b: base = 5cm
By replacing in the formula you obtain:
[tex]S=2(5cm)(6cm)+(5cm)^2=85cm^2[/tex]
hence, the surface area is 85cm^2
Immediately after a ban on using hand-held cell phones while driving was implemented, compliance with the law was measured. A random sample of 1,250 drivers found that 98.9% were in compliance. A year after the implementation, compliance was again measured to see if compliance was the same (or not) as previously measured. A different random sample of 1,100 drivers found 96.9% compliance.
(2 Points) State an appropriate null and alternative hypothesis for testing whether or not there is any statistical difference (i.e., a two-sided test) in these two proportions measured initially and then one year later. Conduct the test of hypothesis using a significance level of α= 0.05. Be sure to check the assumptions and conditions for your test. State the P-value of your test and also state your conclusion. (Feel free to use R in showing your work - and show your commands and output if using R.)
(2 points) Develop a 95% confidence interval for the true difference in proportions between the first survey and the second survey and explain what this confidence interval means in context of this problem. (Feel free to use R in showing your work - and show your commands and output if using R.
Answer:
Step-by-step explanation:
* The Null hypothesis was rejected.
* The confidence interval for the true difference in proportions between the first and second survey are:
0.008238357 and 0.003176164 respectively in 95% situations.
Please kindly go through the attached files for a step by step explanation of how these answer are gotten.
George works for a shipping company, loading packages into a truck. How much work does George do on a 2-kg package when he lifts it to a height of 1.8 m?
Answer:
Work done by george = 35.28J
Step-by-step explanation:
We are given;
Mass; m = 2 kg
Height;h = 1.8 m
Now, we want to find how much work does George do on a 2-kg package at the height of 1.8m.
This is a potential energy problem.
The formula for work done is therefore;
W = mgh
Where;
m is mass
g is acceleration due to gravity which has a constant value of 9.8 m/s²
h is height
Thus, plugging in relevant values;
W = 2 x 9.8 x 1.8
W = 35.28 J
Final answer:
The work done by George on the 2-kg package when he lifts it to a height of 1.8 meters is calculated using the equation W = mgh, which results in 35.28 joules.
Explanation:
The question How much work does George do on a 2-kg package when he lifts it to a height of 1.8 m? requires the calculation of the work done against the force of gravity. To find the work done, the equation W = mgh is used, where W is the work done in joules, m is the mass in kilograms, g is the acceleration due to gravity (9.8 m/s2), and h is the height in meters.
To solve for the work done in this case: W = (2 kg)(9.8 m/s2)(1.8 m).
When you calculate this, it gives you the work done by George as W = 35.28 J (joules).