Answer:
y -6 = 2/5(x+3)
Step-by-step explanation:
The point slope form of an equation is
y -y1 = m(x-x1)
where m is the slope and (x1,y1) is the point
y -6 = 2/5(x- -3)
y -6 = 2/5(x+3)
C.) y - 6 = 2/5(x + 3)
The original point slope equation is the following
[tex]y - y_1 = m(x-x_1)[/tex]
When you plug in negative point values into this equation, the sign changes from '-' to '+'. This is how you can determine which equation accurately represents the line.
Which best describes the complement of spinning any number less than 3?
spinning a 4
spinning a 3 or 4
spinning a 1 or 2
spinning a 1, 2 or 3
Answer:
spinning a 1 or 2
Step-by-step explanation:
less than 3 is 1 or 2
Answer:
B
Step-by-step explanation:
taking the test too
HURRY PLEASE
morgan poured 3/4 gallon of punch into each of 6 bottles. how many gallons of punch did she pour in all
Answer:
gallons of punch in all = 4.5 gallons
Step-by-step explanation:
Morgan poured 3/4 gallons of punch into each of 6 bottles . This means Morgan poured 3/4 gallons of punch in each of the available 6 bottle .
He pours 3/4 gallons of punch in 1 bottle . For 6 bottles the gallons of punch poured is calculated below
1 bottle = 3/4 gallons of punch
6 bottles = ? gallons of punch
cross multiply
gallons of punch in all = 3/4 × 6
gallons of punch in all = 18/4
gallons of punch in all = 9/2 gallons
gallons of punch in all = 4.5 gallons
A trampoline has a diameter of 10ft. What is it’s area ?
Answer: 78.5 feet squared for short answer
Step-by-step explanation:
If the diameter is 10 feet, then the radius is half of that, or 5 feet. feet squared is the EXACT answer, and we surely didn't need a calulator for this one. However, a real world answer is probably more appropriate if you were trying to measure the area. So the area of our trampoline is about 78.5 feet squared.
Answer:
78.54 square feet
Step-by-step explanation:
The formula to find the area of a circle is πr², and since we know the diameter is 10 ft we know the radius is 5 feet, so π5²=78.54
A country's balance of payments is divided up into three categories, the
current account, capital account and financial account. The current account
mainly measures
A) the flow of credit.
B) the flow of goods and services.
c) purchases and sales of nonfinancial assets.
D) purchases of sales of stocks and bonds and other financial assets.
Answer:
B) the flow of goods and services
Step-by-step explanation:
Balance of payments (BOP) is a statement of all transactions made between one country and the rest of the world at a particular period of time. It is also called balance of international payment. BoP is divided into current and capital account.
1. The current account: This is account of country's net trade in goods and services, net earnings on cross-border investments, and its net transfer payments. The current account measures the flow of goods and services.
2. The capital account: This is a country's imports and exports of capital and foreign aid. It can also be called financial account.
The sum of all transactions recorded in the balance of payments should be zero.
Balance of payment deficit is when a country's import is higher than its export.
Balance of payment surplus is when a country's export is greater than its import.
HELP!! pls pls pls
The average price of a movie ticket in 1990 was $4.22. Since then, the price has increased by approximately 3.1% each year. Write an exponential function to model this situation, then find the price of a ticket in 2016. Is this growth or decay?
Answer:
$9.33
Exponential growth.
Step-by-step explanation:
The formula for an exponential function is:
abˣ = y OR
a(1 + r)ˣ = y
a is the initial value (4.22)
r is the rate of increase (3.1% or 0.031 in dec. form) where 1 + r is b
x is the time (26 years)
y is the ending value.
If we plug those values in, the equation will turn out to be 4.22(1 + 0.031)²⁶ = y
Plug it into a calculator and you will get 9.333354216
This is exponential growth because x, the initial value, increases to get to y, the ending value.
A graph shows the horizontal axis numbered 2 to 8 and the vertical axis numbered 10 to 50. A line increases from 0 to 4 then decreases from 4 to 9.
Which type of function best models the data shown on the scatterplot?
Answer:
Quadratic
Step-by-step explanation:
Took a test and got it right
Answer:
quadratic
Step-by-step explanation:
Is the environment a major issue with Americans? To answer that question, a researcher conducts a survey of 1255 randomly selected Americans. Suppose 735 of the sampled people replied that the environment is a major issue with them. Construct a 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them. What is the point estimate of this proportion?
Answer:
The point estimate of this proportion is [tex]\pi = 0.5857[/tex]
The 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them is (0.5584, 0.6130).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 1255, \pi = \frac{735}{1255} = 0.5857[/tex]
The point estimate of this proportion is [tex]\pi = 0.5857[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5857 - 1.96\sqrt{\frac{0.5857*0.4143}{1255}} = 0.5584[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5857 + 1.96\sqrt{\frac{0.5857*0.4143}{1255}} = 0.6130[/tex]
The 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them is (0.5584, 0.6130).
Answer:
The best point of estimate is given by:
[tex]\hat p =\frac{X}{n}= \frac{735}{1255}=0.586[/tex]
[tex]0.586 - 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.559[/tex]
[tex]0.586 + 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.613[/tex]
And we have 95% of confidence that the true proportion of Americans who feel that the environment is a major issue with them is between 0.559 and 0.613
Step-by-step explanation:
The interest is the real proportion of Americans who feel that the environment is a major issue with them. The best point of estimate is given by:
[tex]\hat p =\frac{X}{n}= \frac{735}{1255}=0.586[/tex]
Confidence interval
The confidence interval for the true proportion of interest is given by this:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
We want an interval at 95% of confidence, so then the significance level is [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value for this case are:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
Replacing into the confidence interval formula we got:
[tex]0.586 - 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.559[/tex]
[tex]0.586 + 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.613[/tex]
And we have 95% of confidence that the true proportion of Americans who feel that the environment is a major issue with them is between 0.559 and 0.613
n is an integer and -2
Answer:
-1, 0,1
Step-by-step explanation:
Hope this helps.
-3+(-4) • 5 + 10???? I need help!!!
Answer:
-13
Step-by-step explanation:
used a calculator ._.
Jean-Patrick found an old unopened bag of lawn fertilizer in his shed. The bag weighs 36 pounds, and the instructions claim it can cover 10,000 ft^2. If his lawn is 7,000 ft^2, how many pounds will he need? Round to the nearest tenth if needed.
Answer:
25.2
Step-by-step explanation:
Weight of one bag of lawn fertilizer = 36
area one bag of lawn fertilizer can cover = 10,000 ft^2
Total area of lawn in the given problem = 7,000 ft^2
no. of bags of lawn fertilizer needed to cover the lawn = total area of lawn in the given problem / area, one bag of lawn fertilizer can cover
= 7,000/10,000 = 7/10 = 0.7 bags
Weight of full bags has 36 pounds of lawn fertilizer.
therefore,
Pounds of lawn fertilizer in 0.7 part of bag = 36 * 0.7 = 25.2 pounds (Answer)
Mr. De Leon's Geometry class has 34 students. After lunch everyone returns to the classroom. Within an hour, each person produces 800 BTUs. The room is 25 feet by 32 feet by 12 feet. How many BTUs per cubic foot were produced?
Plz provide the work.
Answer:
2.833 BTUs per cubic foot were produced.
Step-by-step explanation:
BTU's produced by one person = 800
No. of students = 34
Therefore no. of BTU's produced by 34 person = 800 * 34 = 27,200 BTU
Dimension of class 25 feet by 32 feet by 12 feet
Volume of class = length * width * height = 25 * 12 * 32 = 9,600 cubic feet
________________________________________________
BTUs per cubic foot produced = Total BTU's produced by 34 person/ Volume of class
Substituting the value of Total BTU produced and volume of class
BTUs per cubic foot produced = 27,200 BTU/ 9,600 cubic feet
= 2.833 BTUs per cubic foot
2.833 BTUs per cubic foot were produced.
plz answer this asap
Answer:
100 inches square
Step-by-step explanation:
The surface is a trapezoid
Area = ½ × (sum of // sides) × height
= ½ × (5+15) × 10
= ½ × 20 × 10
= 100 in²
Please help 15 points
Answer:
D) Alternate exterior angles
Step-by-step explanation:
Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.
Is 9/10 greater than 3/20
Answer:
Yes.
Step-by-step explanation:
9/10 is equal to 18/20, which is evidently greater than 3/20.
The average age of online consumers a few years ago was 24.1 years. As older individuals gain confidence with the Internet, it is believed that the average age has increased. We would like to test this belief. Answer parts a) through e) below. a) Write the appropriate hypotheses. Choose the correct answer below. A. Upper H 0 : mugreater than24.1 years Upper H Subscript Upper A Baseline : muequals24.1 years B. Upper H 0 : muless than24.1 years Upper H Subscript Upper A Baseline : muequals24.1 years C. Upper H 0 : muequals24.1 years Upper H Subscript Upper A Baseline : mugreater than24.1 years D. Upper H 0 : muequals24.1 years Upper H Subscript Upper A Baseline : muless than24.1 years
Answer:
The correct option is (C).
Step-by-step explanation:
A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.
It is a hypothesis of no difference.
It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.
Whereas the alternative hypothesis is a contradicting statement tot he null hypothesis. It is denoted by Hₐ.
In this case we need to test whether the average age of online consumers has increased or not.
From previous data we know that the average age of online consumers a few years ago was 24.1 years.
A one-sample mean test can be used to determine whether the mean age has increased or not.
The hypothesis for the test can be defined as follows:
H₀: The average age of online consumers is 24.1 years, i.e. μ = 24.1.
Hₐ: The average age of online consumers is more than 24.1 years, i.e. μ > 24.1.
Thus, the correct option is (C).
several years ago wolves were reintroduced in to a national park in north carolina in north carolina. Researchers have monitored the populations over the last severals years and the per capita growth rate of the population is .5. If the current population size is 100, what equation would you use to determine how large the population will be in ten years
Answer: [tex]5766.503\ \text{wolves}[/tex]
Step-by-step explanation:
Given
Current Population of wolves is [tex]P_o=100[/tex]
If the growth rate is [tex]=0.5[/tex]
So the population in next year is
[tex]P_1=100+100\times 0.5[/tex]
[tex]P_1=100(1+0.5)[/tex]
similarly [tex]P_2=100(1+0.5)^2[/tex]
So population after n years is [tex]P_n=P_o(1+r)^n[/tex]
Population after 10 years is
[tex]P_{10}=100(1+0.5)^{10}[/tex]
[tex]P_{10}=5766.503\ \text{wolves}[/tex]
The mayor of a large city claims that the average net worth of families living in this city is at most $300,000. A random sample of 25 families selected from this city produced a mean net worth $288,000. Assume that the net worth of all families in this city have a normal distribution with the population standard deviation of $80,000. What is the parameter of interest?
Answer:
Check the explanation
Step-by-step explanation:
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 300000
Alternative Hypothesis, Ha: μ < 300000
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (288000 - 300000)/(80000/sqrt(25))
z = -0.75
P-value Approach
P-value = 0.2266
As P-value >= 0.05, fail to reject null hypothesis.
The parameter of interest is the average net worth of families living in the city. Hypothesis testing can be used to evaluate the mayor's claim using a random sample of households. The test statistic can be calculated using the sample mean, sample standard deviation, and sample size.
Explanation:The parameter of interest in this question is the average net worth of families living in the city. The mayor claims that the average net worth is at most $300,000. To determine if this claim is true, a random sample of 25 families is selected. The mean net worth of this sample is $288,000. This mean is an estimate of the population mean net worth.
Based on the information given, the population standard deviation of net worth for all families in the city is $80,000. This information allows us to perform hypothesis testing to evaluate the claim made by the mayor.
Null Hypothesis (H0): The average net worth of families living in the city is $300,000.Alternative Hypothesis (Ha): The average net worth of families living in the city is less than $300,000.Using the sample mean of $288,000, the sample standard deviation ($80,000), and the sample size (25), we can calculate the test statistic.The test statistic is calculated as follows:Test Statistic = (Sample Mean - Population Mean) / (Sample Standard Deviation / sqrt(Sample Size))
Plugging in the values:
Test Statistic = (288,000 - 300,000) / (80,000 / √25)
After calculating the test statistic, we can compare it to the critical value of the test (based on the desired significance level) to determine if we reject or fail to reject the null hypothesis. If the test statistic is less than the critical value, we reject the null hypothesis and conclude that there is evidence to support the claim that the average net worth of families living in the city is less than $300,000.
By providing a random sample from the population, we can use hypothesis testing to evaluate the mayor's claim and determine if there is evidence to support it.
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Katrina bought a package of 500 stickers. These sheet in the package has 20 stickers. 25% of the stickers on each sheet our hearts. The remaining stickers are stars. Select all the statements that are true. A Katrina has 100 heart stickers B Katrina has 375 star stickers C the package contains 20 sheets of stickers D 75% of the stickers on each sheet our stars see the number of heart stickers is the same number I start stickers
Answer:B
Step-by-step explanation:
Given
There are total of 500 stickers
Each sheet has 20 stickers out of which 25 % is Hearts and remaining are stars
So in each sheet 5 are hearts and 15 are stars
therefore in [tex]\frac{500}{20}=25[/tex] sheet
There are [tex]25\times 5=125[/tex] heart stickers
and [tex]25\times 15=375[/tex] star stickers
So statement B is true
HELP ASAP timed question. A table is 4 ft high. A model of the table is 6 in high. What is the ratio of the height of the actual table to the helght of the model table? 3/2 8/1 2.3 1/8
Answer:
The ratio of the height of the actual table to the height of the model table is .
Step-by-step explanation:
As given
A table is 4 ft high. A model of the table is 6 in. high.
As
1 foot = 12 inch
Now convert 4 ft into inches .
4 ft = 4 × 12
= 48 inches
Height of the actual table = 48 inches
Now the ratio of the height of the actual table to the height of the model
table .
Therefore the ratio of the height of the actual table to the height of the model table is .
Determine Whether the triangle with the given side lengths is a right triangle
6,8,10
Right Triangle
Not A Right Triangle
Answer:
Yes, right triangle
Step-by-step explanation:
Since it is a right triangle, we can use Pythagorean Theorem.
a^2+b^2=c^2
a and b are the legs, or shorter sides, and c is the hypotenuse, or the longest side.
We have 3 side lengths: 6, 8 and 10
6 and 8 are the shorter legs, so they are a and b.
10 is the longest leg, so it is c
Substitute the values into the equation, and see if it is true.
6^2+8^2=10^2
Evaluate the exponents
36+64=100
100=100
Since this is a true statement, these sides can make a right triangle.
The operator of a beachfront hotel in a tropical island wishes to select a new paint for the hotel’s exterior walls. Three different paints are applied to sample pieces of plywood, then exposed to a heat lamp and sprayed continuously with salt water until the paint begins to peel. Five plywood samples are used for testing each paint. The hours needed in order for the paint to begin to peel are listed below: • Paint A: 25, 27, 28, 28, and 30 hours. • Paint B: 23, 28, 30, 31, and 32 hours. • Paint C: 30, 31, 33, 33, and 37 hours. The hotel operator believes that there is no fundamental difference in longevity/endurance between the three types of paint. Do you agree or disagree? Perform ANOVA to justify your answer.
Find the given attachment for complete answer and solution
Is the mean age at which American children learn to walk less than 15 months? A study of 40 American children found a mean walking age of = 13.2 months. If the population of all American children has mean age μ until they begin to walk and standard deviation σ, which of the following null and alternative hypotheses should we test to answer this question? H 0 : μ ≥ 13.2 vs. Ha : μ < 13.2 H 0 : μ = 13.2 vs. H a : μ ≠ 13.2 H 0 : μ = 15 vs. H a : μ ≠ 15 H 0 : μ ≥ 15 vs. Ha : μ < 15
Answer:
We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.
Null hypothesis: [tex]\mu \geq 15[/tex]
Alternative hypothesis: [tex]\mu <15[/tex]
And for this case the best answer would be:
H 0 : μ ≥ 15 vs. Ha : μ < 15
Step-by-step explanation:
We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.
Null hypothesis: [tex]\mu \geq 15[/tex]
Alternative hypothesis: [tex]\mu <15[/tex]
And for this case the best answer would be:
H 0 : μ ≥ 15 vs. Ha : μ < 15
And the data given from the sample is:
[tex]\bar X = 13.2[/tex] represent the sample mean
[tex]\sigma[/tex] represent the population deviation
[tex] n = 40[/tex] represent the sample size
And the statistic would be given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The radial spokes of a bicycle tire are 13 inches long. What is the diameter of the tire?
Answer:
the answer is 5
Step-by-step explanation:
the
The snack bar at the soccer field is charging $12 for 9 hamburgers. At that rate, how many hamburgers could you get for $20?
Answer:
6
Step-by-step explanation:
12 = 9 so u do 12 divided by 9
$20 to get 15 hamburgers. By dividing the price to produce one unit of your product by the number of items you have created, you can use the total variable cost.
locate total variables cost?By dividing the price to produce one unit of your product by the number of items you have created, you can determine the total variable cost.
Multiply the cost of producing one unit of your product by the total number of items you have produced to determine variable costs. Total Variable Costs = Cost Per Unit x Total Number of Units is the calculation for this cost.
For instance, if producing one unit of your product costs $12 and you produced 9 pieces, your total variable cost would be $12 x 9, or $108.
$12/9 = 1.34 then $20 to get 15 hamburgers.
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It was claimed that when tossing a fair coin 4 times it is quite likely to not obtain 2 heads and 2 tails. However, when tossing a fair coin 4,000 times one should expect to obtain number of tails in the range between 1940 and 2060. Let us compare the situation for 2 versus 2,000 coins. Let X be the number of heads when tossing a fair coin 2 times and let Y be the number of heads when tossing a fair coin 2,000 times.
1. P(940 ≤ Y ≤ 1,060) is equal to:______.2. E(X) is equal to:______.3. The standard deviation of X is equal to:______.4. E(Y) is equal to:_______.
Final answer:
The expected value of flipping a coin twice (X) is 1 head, with a standard deviation of 0.7071. The expected value of flipping a coin 2,000 times (Y) is 1,000 heads, but we cannot calculate P(940 ≤ Y ≤ 1,060) from the given information.
Explanation:
The question involves the concept of probability, expected value (E), and standard deviation (SD) in the context of flipping coins. We'll address each part of the query using basic probability and statistics principles.
P(940 ≤ Y ≤ 1,060) would require the use of the Central Limit Theorem for large sample sizes; however, with the information given, we cannot calculate this probability without additional statistical tables or tools, so we must refuse to answer this part.
The expected value of X, E(X), when flipping a coin twice would be the sum of products of each outcome's value and its probability. E(X) = (0 * 0.25) + (1 * 0.5) + (2 * 0.25) = 1.
The standard deviation of X requires calculating the variance first, then the square root of the variance. σ(X) = √[((0-1)^2 * 0.25) + ((1-1)^2 * 0.5) + ((2-1)^2 * 0.25)] = √(0.5) = 0.7071.
The expected value of Y, E(Y), when flipping a coin 2,000 times is simply 0.5 * 2,000 = 1,000 because the probability of a head for each flip is 0.5.
The probability P(940 ≤ Y ≤ 1,060) is approximately 99.63%, E(X) equals to 1, and the standard deviation of X is approximately 0.707. E(Y) is 1000.
To understand the probability and expectations for tossing fair coins, we will address your questions step by step.
P(940 ≤ Y ≤ 1,060) involves using the normal approximation to the binomial distribution.
For large numbers of coin tosses, the binomial distribution can be approximated by a normal distribution.
Since we are tossing the coin 2,000 times, our mean (μ) and variance (σ²) need to be calculated.
μ = n * p = 2000 * 0.5 = 1000 σ² = n * p * (1 - p) = 2000 * 0.5 * 0.5 = 500Hence σ ≈ 22.36.
Now, we standardize the range [940, 1060].
Z-score = (940 - 1000) / 22.36 ≈ -2.68 and (1060 - 1000) / 22.36 ≈ 2.68.From the Z-table, P(-2.68 ≤ Z ≤ 2.68) is approximately 0.9963, or 99.63%.
E(X) represents the expected number of heads when tossing 2 coins. Since each coin is fair and has a probability of 0.5 for heads,
E(X) = n * p = 2 * 0.5 = 1.Standard Deviation = √(n * p * (1 - p)). Here, n = 2, p = 0.5.
= √(2 * 0.5 * 0.5) = √0.5 = 0.707.E(Y) is the expected number of heads when tossing 2,000 coins. Similarly,
E(Y) = n * p = 2000 * 0.5 = 1000.Therefore, probability P(940 ≤ Y ≤ 1,060) is 99.63%, E(X) is 1, and the standard deviation is 0.707. E(Y) is 1000.
A manager at a shipping company will purchase boxes in the shape of right rectangular prisms. He wants the volume of each box to be exactly 98 cubic feet. Which figure shows a box with the dimensions, in feet, that the manager will purchase?
The manager needs to select dimensions for a right rectangular prism that when multiplied together equal 98 to achieve a volume of 98 cubic feet. Possible dimensions could be 7 feet by 7 feet by 2 feet, or 14 feet by 7 feet by 1 foot.
The question pertains to calculating the volume of right rectangular prisms (boxes) and understanding the relationship between their dimensions and volume. To find a box with a volume of 98 cubic feet, one can use the formula for the volume of a right rectangular prism, which is Volume = length * width * height. The manager needs to identify the dimensions that, when multiplied together, equal 98. For instance, if a box has dimensions of 7 feet, 7 feet, and 2 feet, the volume would be 7 * 7 * 2 = 98 cubic feet, as required. Other possible dimensions could be 14 feet by 7 feet by 1 foot, as 14 * 7 * 1 also gives 98 cubic feet.
Which sentence is written correctly? Kino said that if play practice does not start on time, the director “will be mad.” Kino said that if play practice does not start on time, the director “Will be mad”. Kino said that if play practice does not start on time, the director “will be mad”. Kino said that if play practice does not start on time, the director “Will be mad.”
The correct sentence is: Kino said that if play practice does not start on time, the director "will be mad."
Explanation:The correct sentence is: Kino said that if play practice does not start on time, the director "will be mad."
In this sentence, the verb "will" is correctly written in lowercase, as it is not a proper noun or the start of a sentence. Additionally, the punctuation marks, such as the quotation marks and the comma, are correctly placed.
It is important to use proper capitalization and punctuation to ensure clear and effective communication in writing.
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A car travels at an average speed of 52 mph. Jow long does it take to travel 169 miles?
To calculate the time it takes for the car to travel 169 miles at an average speed of 52 mph, divide the distance by the speed. The car would take approximately 3.25 hours.
Explanation:To calculate the time it takes for the car to travel 169 miles, we can divide the distance by the average speed. The formula for speed is:
Speed = Distance / Time
Rearranging the formula to solve for time, we get:
Time = Distance / Speed
Plugging in the values, we have:
Time = 169 miles / 52 mph
Calculating this, the car would take approximately 3.25 hours to travel 169 miles.
Use the Venn diagram to calculate probabilities.
Which probabilities are correct? Select two options.
P(AIC) =
PCB) = 0
PLA) =
PC)
PBIA) = 3
Corrected Question
These are the given probabilities. The Venn diagram is also attached. are (A) P(A|C) = 2/3
(B) P(C|B) = 8/27
(C) P(A) = 31/59
(D) P(C) = 3/7
(E) P(B|A) = 13/27
Answer:
A and C
Step-by-step explanation:
[tex]P(A|C)=\dfrac{P(A\cap C)}{P(C)}= \dfrac{14/59}{21/59}=\dfrac{14}{21}=\dfrac{2}{3}[/tex]
[tex]P(C|B) =\dfrac{P(C\cap B)}{P(B)}= \dfrac{11/59}{27/59}=\dfrac{11}{27}\neq \dfrac{8}{27}\\\\P(A) = \dfrac{31}{59}\\\\P(C) =\dfrac{21}{59}\neq \dfrac{3}{7}\\\\P(B|A)=\dfrac{P(B\cap A)}{P(A)}= \dfrac{13/59}{31/59}=\dfrac{13}{31}\neq\dfrac{13}{27}[/tex]
From the above, only A and C are correct.
Answer: A and C
Step-by-step explanation:
Edg 2021
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.21. How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03
Answer:
We need a sample size of at least 383.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
85% confidence level
So [tex]\alpha = 0.15[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.15}{2} = 0.925[/tex], so [tex]Z = 1.44[/tex].
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03
We need a sample size of at least n.
n is found with [tex]M = 0.03, \pi = 0.21[/tex]
Then
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.44\sqrt{\frac{0.21*0.79}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.44\sqrt{0.21*0.79}[/tex]
[tex]\sqrt{n} = \frac{1.44\sqrt{0.21*0.79}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.44\sqrt{0.21*0.79}}{0.03})^{2}[/tex]
[tex]n = 382.23[/tex]
Rounding up
We need a sample size of at least 383.
To estimate the proportion of tenth graders reading at or below the eighth grade level with an 85% confidence level and a 0.03 margin of error, a sample size of 550 students is needed.
To estimate the fraction of tenth grade students with reading skills at or below the eighth grade level with an 85% confidence interval and a margin of error of at most 0.03, we use the following formula for sample size:
⇒ n = (Z² × p × (1 - p)) ÷ E²
Where:
Z is the z-value corresponding to the desired confidence level.p is the estimated population proportion (0.21).E is the desired margin of error (0.03).For an 85% confidence level, the z-value is approximately 1.44. Plugging in the values:
Calculate the numerator:⇒ Z² × p × (1 - p) = 1.44² × 0.21 × (1 - 0.21)
≈ 0.494668.
Calculate the denominator:⇒ E² = 0.03²
= 0.0009.
Divide the numerator by the denominator:⇒ 0.494668 ÷ 0.0009 ≈ 549.63.
Round up to the next integer: 550.Therefore, the required sample size is 550 students.
Complete question:
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.21. How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03? Round your answer up to the next integer.