Answer:
We need a sample size of at least 97.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 2 dollars.
We need a sample size of at least n.
n is found when [tex]M = 2, \sigma = 10[/tex].
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 1.96*\frac{10}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 1.96*10[/tex]
[tex]\sqrt{n} = \frac{1.96*10}{2}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96*10}{2})^{2}[/tex]
[tex]n = 96.04[/tex]
Rouding up
We need a sample size of at least 97.
The hypotenuse of a right triangle is 10 feet long the longer leg is 2 feet longer than the shorter leg find the side side of the triangle
Answer:
square root of 96 or 9.79
Step-by-step explanation:
a2+b2=c2
2square+b2=10square
4+b2=100
(4-4)+b2=(100-4)
b2=square root96 or 9.79
need help with this question
Answer:
2√11
Step-by-step explanation:
The square of the hypotenuse (h) of the smaller triangle is given by the Pythagorean theorem:
h² = 6² +8² = 100
The length of x is given by that same theorem:
h² +x² = 12²
x² = 12² -h² = 144 -100 = 44 . . . . . subtract h², fill in its value
x = √44 . . . . . . . . take the square root
x = 2√11 . . . . . . . simplify the root
n a survey of 700 year 2005 high school graduates, it was found that 50.3% had enrolled in colleges, 11.1% in vocational institutions, while the other 38.6% did not pursue any further studies. Perform a test of hypotheses to determine whether the college enrollment rate in the population of year 2005 high school graduates was significantly higher than 48%. (Calculate the P-value.) Round to four decimal places.
Answer:
[tex]z=\frac{0.503-0.48}{\sqrt{\frac{0.48(1-0.48)}{700}}}=1.218[/tex]
Now we can calculate the p value given by:
[tex]p_v =P(z>1.218)=0.1116[/tex]
Step-by-step explanation:
Information provided
n=700 represent the random sample selected
[tex]\hat p=0.503[/tex] estimated proportion of college enrollment
[tex]p_o=0.48[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value (variable of interest)
System of hypothesis
we want to check if the true proportion for the college enrollment is higher thna 0.48, the system of hypothesis are:
Null hypothesis:[tex]p\leq 0.48[/tex]
Alternative hypothesis:[tex]p > 0.48[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we have:
[tex]z=\frac{0.503-0.48}{\sqrt{\frac{0.48(1-0.48)}{700}}}=1.218[/tex]
Now we can calculate the p value given by:
[tex]p_v =P(z>1.218)=0.1116[/tex]
A spinner has a 12 equal sized sections. Three of the sections are orange. What is the probability that the spinner will land on orange?
1/4
Step-by-step explanation:
1/4 is the original fraction of 3/12 simplified
Final answer:
The probability of the spinner landing on an orange section is 1/4 or 0.25, meaning there is a 25% chance it will land on orange.
Explanation:
The question involves calculating the probability of a spinner landing on a specific color. If a spinner has 12 equal-sized sections and three of them are orange, to find the probability of landing on orange, we use the ratio of the number of orange sections to the total number of sections. In this case, there are 3 orange sections and 12 sections in total, so the probability (P) is:
P(orange) = Number of orange sections / Total number of sections
P(orange) = 3 / 12
P(orange) = 1 / 4
Therefore, the probability that the spinner will land on orange is 1/4 or 0.25, which means there's a 25% chance the spinner will land on an orange section.
The formula for the surface area of a cylinder is SA= 2 pi r (h + r). What is the surface area of a cylinder when r = 3 centimetres and h = 4 centemeters?
The surface area of the cylinder, when the radius is 3 centimeters and the height is 4 centimeters, is approximately 131.88 square centimeters.
Use the provided formula for the surface area of a cylinder:
[tex]\[ SA = 2\pi r (h + r) \][/tex]
Given:
[tex]r = 3 \text{ centimeters}[/tex]
[tex]h = 4 \text{ centimeters}[/tex]
Now, substitute these values into the formula and calculate the surface area:
[tex]SA = 2\pi \times 3 \times (4 + 3)[/tex]
[tex]SA = 2\pi \times 3 \times 7[/tex]
[tex]SA = 6\pi \times 7[/tex]
[tex]SA = 42\pi[/tex]
Now, let's calculate the numerical value:
[tex]SA \approx 42 \times 3.14[/tex]
[tex]SA \approx 131.88 \text{ square centimeters}[/tex]
Therefore, the surface area of the cylinder, when the radius is 3 centimeters and the height is 4 centimeters, is approximately 131.88 square centimeters.
2/3 x G = 1/4
Solve for G!
(FIRST ANSWER GETS BRAINLIEST!)
Answer:
The value of G is 3/8 .
Step-by-step explanation:
In order to solve G, you have to divide 2/3 to both sides :
[tex] \frac{2}{3} \times G = \frac{1}{4} [/tex]
[tex] \frac{2}{3} \times G \div \frac{2}{3 } = \frac{1}{4} \div \frac{2}{3} [/tex]
[tex]G = \frac{1}{4} \times \frac{3}{2} [/tex]
[tex]G = \frac{3}{8} [/tex]
Answer:
3/8
Step-by-step explanation:
Convert to common denominator which would be 12.
8/12 x G=3/12
Then divide 3/12 by 8/12 and you get 3/8
Evaluate the following expression
40 -8 - 102
Answer:
-70
Step-by-step explanation:
40-8-102
= 32 - 102
= -70
To evaluate the expression 40 - 8 - 102, subtract 8 from 40 to get 32, then subtract 102 from 32 to arrive at -70.
40 - 8 - 102
To solve this expression, we need to follow the order of operations. In this case, since there are only subtraction operations involved, we can proceed from left to right.
40 - 8 = 32
32 - 102 = -70
This gives us the final answer: -70.
Each group of students receives a bag that has 8 red cubes, 2 green cubes, and 10 blue cubes. If each group makes 100 pulls and replaces the cube after each pull, how many times would you expect them to draw a green cube?
Answer:
10 green cubes
Step-by-step explanation:
The total number of cubes is 8+2+10 = 20
The probability of drawing a green cube when there is replacement is
P(green) = green cubes/ total
=2/ 20
= 1/10
Multiply the probability by the number of draws to get the total number of cubes
1/10 * 100 draws = 10 green cubes
Expect 10 green cube draws in 100 pulls, with 8 red and 10 blue cubes also present.
To calculate the expected number of times a green cube is drawn, we can use the concept of probability.
In each pull, there are 20 cubes in total (8 red + 2 green + 10 blue). So, the probability of drawing a green cube in a single pull is:
[tex]\[ P(\text{green}) = \frac{\text{number of green cubes}}{\text{total number of cubes}} = \frac{2}{20} = \frac{1}{10} \][/tex]
Since each pull is independent and the cubes are replaced after each pull, the probability of drawing a green cube remains the same for each pull.
Therefore, the expected number of times a green cube is drawn in 100 pulls is:
[tex]\[ \text{Expected number of green draws} = P(\text{green}) \times \text{Total number of pulls} = \frac{1}{10} \times 100 = 10 \][/tex]
So, you would expect them to draw a green cube about 10 times in 100 pulls.
Rainwater was collected in water collectors at thirty different sites near an industrial basin and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 5.2 and 1.8 respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.2 pH units to all of the values and then multiply the result by 1.2. Find the mean and standard deviation of the corrected pH measurements.
Answer:
mean = 7.98; standard deviation = 2.52
Step-by-step explanation:
Kindly check the attached images below to see the step by step explanation to the question above.
A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. At how many seconds will the lights first blink at the same time?
Answer:
20 seconds
Step-by-step explanation:
The least common multiple of 4 and 5 is 20. So the two lights will blink at the same time every 20 seconds.
Based on the number of seconds it takes for each light to blink, they will both blink at 20 seconds.
The green light blinks every 4 seconds and the yellow, every 5 seconds.
The time that they will blink together depends on the lowest common multiple of both numbers.
Multiples of 4 = 4, 8, 12, 16, 20
Multiples of 5 = 5, 10, 15, 20
The lowest common multiple is 20 which means they will blink together after 20 seconds.
Find out more at https://brainly.com/question/7419041.
Which object has the mass of about one kilogram?
Answer:
A one-liter bottle of soda has a mass of about 1 kilogram.
Write an expression, using an exponent, that is equivalent to 9 x 9 x 9 x 9 x 9 x 9 x 9.
Answer:
[tex]9^{2}[/tex]
Step-by-step explanation:
Answer:
[tex]9^{7}[/tex]
Step-by-step explanation:
There are 7 9s being multiplied together. This can be written as 9 to the 7th power or [tex]9^{7}[/tex]
The two box plots show the data of the pitches thrown by two pitchers throughout the season. Which statement is correct? Check all that apply.
Answer:
Doesn’t show image
Step-by-step explanation:
Answer:
B,C
Step-by-step explanation
Pitcher 1 does not have a symmetric data set.
Pitcher 2 has a symmetric data set.
Question 5
A restaurant bill is $80. Juan leaves a $20 tip. What percent tip is that?
Answer:
25%
Step-by-step explanation:
Plz mark me brainliest.
Answer:
25%
Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Perform the following computation with radicals. Simplify the answer.
Answer:
[tex]\sqrt[4]{10x^2}[/tex]
Step-by-step explanation:
[tex]\sqrt[4]{5x}.\sqrt[4]{2x} = \sqrt[4]{5x * 2x} = \sqrt[4]{10x^2}[/tex]
Answer:
(10x²)^¼
Or,
10^¼ × x^½
Step-by-step explanation:
(5x)^¼ × (2x)^¼
[5x × 2x]^¼
(10x²)^¼
10^¼ × (x²)^¼
10^¼ × x^½
Weight of a rock: In a geology course, students are learning to use a balance scale to accurately weigh rocks. One student plans to weigh a rock 20 times and then calculate the average of the 20 measurements to estimate her rock's true weight. A second student plans to weigh a rock 5 times and calculate the average of the 5 measurements to estimate his rock's true weight. The student who weighs his rock 5 times uses the mean to calculate the 95% confidence interval for the rock weight (in grams). His interval is (25.2, 29.1). What does a 95% confidence interval for rock weight tell us in this case? Group of answer choices We are 95% confident that this interval includes the mean of the 5 weight measurements taken by this student. We are 95% confident that most rocks of this type weigh between 25.2 g and 29.1 g. We are 95% confident that the true weight of the rock is between 25.2 g and 29.1 g.
Answer:
We are 95% confident that the true weight of the rock is between 25.2 g and 29.1 g.
Step-by-step explanation:
Hello!
A geology student weighted a rock 5 times and estimated the average weight using a 95% CI [25.2; 29.1]gr
The confidence interval is used to estimate the value of the population mean, it gives you a range of values for it.
The 95% level of confidence of the interval indicates that if you were to construct 100 confidence intervals to estimate the population mean, you'd expect 95 of them to include the true value of the parameter.
So with a 95% confidence level, you'd expect the true average weight of the rock to be included in the interval [25.2; 29.1]gr
I hope this helps!
A research center poll showed that 81% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?
Answer:0.19
Step-by-step explanation:
Alice’s scores for five math test are: 85, 76, 81, 90, 88. What score must she achieve on the sixth test to give her an average of 85?
Find the slope of the line passing through the points (-9. -6) and (-4, 5)
Answer:
The slope of the line is 2.2 or 11/5
Step-by-step explanation:
I graphed the points on the graph below and found the slope of the line.
The slope of the line is 11/ 5.
What is the slope of a line?The slope is equal to the change in y over the change in x, or rise over run.
m = change in y/change in x
The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).
m = (y₂−y₁)/(x₂−x₁)
Substituting the values of x and y into the equation to find the slope.
m = (5 − ( − 6 ))/(−4−(−9))
m =11/5
Therefore, the Slope of the line is 11/ 5.
To learn more about the slope of the line refer to :
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Am isosceles triangle has at least 2 equal sides and equilateral triangle has all sides equal which sentence is true
all isosceles triangles are equilateral triangle
all equilateral triangles are isosceles triangles all equilateral triangles does not necessarily have to be isosceles triangles
An isosceles triangle cannot be an equilateral triangle
Answer:an isosceles triangle cannot be an equilateral triangle
Step-by-step explanation:
An isosceles triangle cannot be an equilateral triangle
Final answer:
An isosceles triangle has at least 2 equal sides and an equilateral triangle has all sides equal. All equilateral triangles are isosceles triangles, but not all isosceles triangles are equilateral triangles.
Explanation:
An isosceles triangle has at least 2 equal sides, while an equilateral triangle has all sides equal. Therefore, the sentence 'All isosceles triangles are equilateral triangles' is not true because not all isosceles triangles have all sides equal. On the other hand, the sentence 'All equilateral triangles are isosceles triangles' is true because every equilateral triangle automatically has at least 2 equal sides. Furthermore, it is possible for an equilateral triangle to not be an isosceles triangle if all three sides are not equal in length. So, the sentence 'An isosceles triangle cannot be an equilateral triangle' is not true.
A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study examined the scores of a random sample of 81 graduating seniors and found the mean score to be 506 with a standard deviation of 83. At the 95% confidence level, find the margin of error for the mean, rounding to the nearest tenth. (Do not write \pm±).
Answer:
The margin of error for the mean is of 165.18 points.
Step-by-step explanation:
We have the standard deviation of the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 81 - 1 = 80
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 80 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.9901
The margin of error is:
M = T*s = 1.9901*83 = 165.18.
In which s is the standard deviation of the sample.
The margin of error for the mean is of 165.18 points.
Final answer:
The answer discusses z-scores for SAT scores, calculating scores above the mean, and comparing performance on different tests.
Explanation:
Z-score for SAT score of 720:
Calculate the z-score: z = (720 - 520) / 115 = 1.74.
Interpretation: A score of 720 is 1.74 standard deviations above the mean.
Math SAT score 1.5 standard deviations above the mean:
Calculate the score: 520 + 1.5(115) ≈ 692.5.
The score of 692.5 is 1.5 standard deviations above the mean of 520.
Better performance on math tests:
For SAT: z = (700 - 514) / 117 ≈ 1.59.
For ACT: z = (30 - 21) / 5.3 ≈ 1.70.
Person with a z-score closer to 2 performed better relative to the test they took.
Mrs.Golden wants to cover her 6.5 by 4 bulletin board with silver paper that comes in 1-foot squares how many squares does Mrs.Golden need to cover her bulliten board will there be any pieces left over why or why not
Final answer:
Mrs. Golden will need 26 squares of silver paper to cover her bulletin board, and there will not be any pieces left over.
Explanation:
To find out how many 1-foot squares Mrs. Golden needs to cover her bulletin board, we first need to calculate the area of the bulletin board. The area of a rectangle can be found by multiplying the length and width. In this case, the length is 6.5 feet and the width is 4 feet, so the area is 6.5 feet x 4 feet = 26 square feet.
Since the silver paper comes in 1-foot squares, we can divide the area of the bulletin board by the area of each square to find out how many squares are needed. In this case, we divide 26 square feet by 1 square foot, giving us a result of 26 squares.
There will not be any pieces left over because 26 squares fully cover the area of the bulletin board. If there were any remaining space, we would need a fraction of a square to cover it.
If A is 3 and C is 12, then 4AC equals...?
A. 19
B. 36
C.48
D.144
E. None correct
Answer:
144
Step-by-step explanation:
James and Karlee caught a lizard in their backyard. Its length from head to the end of the tail is
3/5 meters and the length of its tail is1/5
Answer:
what do you need answered?
Step-by-step explanation:
Answer:
2/5
Step-by-step explanation:
khan academy
A 3% fee is taken out of an initial amount of $3,460, and then a $100 fee is taken after that, leaving a new amount of $
Answer:
$3,256.2
Step-by-step explanation:
First, we need to get 3% of 3,460. Find the decimal value of 3%:
3% -> [tex]\frac{3}{100}[/tex] -> 0.03
Next, lets multiply 3,460 by 0.03:
[tex]x=3,460(0.03)[/tex]
[tex]x=103.8[/tex]
Now subtract that number from 3,460:
[tex]3,460-103.8=3,356.2[/tex]
Lastly, lets take the $100 fee off of the number we just got:
[tex]3,356.2-100=3,256.2[/tex]
The new amount is $3,256.2
Answer:
3% fee is taken out of an initial amount of $3,460, and then a $100 fee is taken after that, leaving a new amount of $3,256.2.
explanation:
The following data was collected to explore how the number of square feet in a house, the number of bedrooms, and the age of the house affect the selling price of the house. The dependent variable is the selling price of the house, the first independent variable (x1) is the square footage, the second independent variable (x2) is the number of bedrooms, and the third independent variable (x3) is the age of the house.
Effects on Selling Price of Houses
Square Feet Number of Bedrooms Age Selling Price
2049 5 5 282900
10101 4 8 268600
1033 3 9 137900
1286 2 8 114900
2920 4 4 113000
2443 10 10 154700
2206 2 5 234000
1360 3 4 183400
2405 3 1 193100
Copy Data
Step 1 of 2 :
Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.
HOW TO PULL THIS UP IN EXCEL-----------------------------------------
To find the p-value from the given data in Excel, populate your data in Excel sheet into various columns for each variable. Then, use the 'Regression' tool under 'Data Analysis' in the 'Data' tab, selecting the appropriate ranges for dependent and independent variables. Ensure that the 'P-Values' box is checked before clicking 'OK'. Excel will then generate the regression analysis with the p-value.
Explanation:In Excel, you can perform regression analysis to deduce the p-value from this data using the following steps:
First, you want to load your data into the Excel sheet. Each independent variable (Square Feet, Number of Bedrooms, Age) should have its own column and the dependent variable (Selling Price) too.Once the data is spread across columns, go to the 'Data' tab, under which you'll find 'Data Analysis'. If it's not visible, you'll have to add it in from 'Excel Options' > 'Add-Ins' > 'Excel Add-Ins' > 'Analysis ToolPak'.After clicking 'Data Analysis', a window will pop up. Choose 'Regression' and click 'OK'.A dialog box will appear. Under 'Input', select the Y Range (dependent variable: Selling Price) and X Range (independent variables: Square Feet, Number of Bedrooms, Age).Mark the box 'Labels' if you have header rows. Also check the box for 'P-Values'.Finally, click 'OK' and Excel will generate the regression analysis including the p-value for your data.Learn more about Regression Analysis and P-Value in Excel here:https://brainly.com/question/30590416
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8.73e16 in standerd form
Answer:
Hello,
Here is your answer:
The proper answer to this question is 87300000000000000.
Here is how:
8.73e16=87300000000000000.
Your answer is 87300000000000000.
If you need anymore help feel free to ask me!
Hope this helps!
(P.S. REMEMBER E IS EXPONET OR ^)
The equation having null set as its solution set is
A) x = cos x
B) x = e^x
C) x = sin x
D) x = tan x
Answer:
B) x = e^x
Step-by-step explanation:
The graphs of y = e^x and y = x never intersect, so the solution set will be the empty (null) set for ...
x = e^x
_____
There is one intersection of y=x with cos(x) and with sin(x). There are an infinite number of solutions for x = tan(x).
2x+9+3x+x=
what is it in all 3 solutions
Answer:
6x+9
3(2x+3)
Step-by-step explanation:
Combine like terms
2x+9+3x+x
6x+9
We can factor out 3
3(2x+3)
Answer:
6x + 9
Step-by-step explanation:
2x + 9 + 3x + x =
6x + 9
What is the value of 7 in the number 8.07
0.07 or 7 hundredths.