Answer:A
Step-by-step explanation:
She has to pay 7.50 for admission and golf is 6.25 each round. We don’t know how many rounds she golfs so it will be 6.25x.
A market researcher would like to know how much time the average college student spends watching sports. Suppose he does a preliminary study based upon a sample of 25 college students. The mean amount of time spent watching sports, by those in the sample, is 90 minutes per day with a standard deviation of 15 minutes per day.
(a) Which of the following numbers gives the value of the point estimate?
a. 15.
b. 25.
c. 90.
d. 0.
e. 95.
(b) Using the information given above, calculate the margin of error (in minutes) of the point estimate. Assume we would like to estimate the population mean with 95% confidence.
(c) Suppose that the researcher is not content with the current margin of error. He would like the margin of error of the point estimate to be no more than 4 minutes with 95% confidence. The researcher is unwilling to trust that the sample standard deviation from his previous study accurately estimates the true population standard deviation. He does, however, know that college students tend to watch sports between 0 and 120 minutes per day. What is the minimum sample size needed to obtain this amount of precision?
Answer:
a) c. 90.
b) The margin of error of the point estimate is of 6.19 minutes.
c) The minimum sample size needed to obtain this amount of precision is 289.
Step-by-step explanation:
(a) Which of the following numbers gives the value of the point estimate?
The value of the point estimate is the sample mean, of 90 minutes. So the answer is given by option c.
(b) Using the information given above, calculate the margin of error (in minutes) of the point estimate. Assume we would like to estimate the population mean with 95% confidence.
We have the standard deviation for the sample, which means that the t-distribution is used 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 = 25 - 1 = 24
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0639.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
Here, we have [tex]s = 15, n = 25[/tex]. So
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
[tex]M = 2.0639\frac{15}{\sqrt{25}}[/tex]
[tex]M = 6.19[/tex]
The margin of error of the point estimate is of 6.19 minutes.
Question c:
College students tend to watch sports between 0 and 120 minutes per day, which means that the standard deviation for population can be estimated as the standard deviation of an uniform distribution with [tex]a = 0, b = 120[/tex]. This standard deviation is:
[tex]\sigma = \sqrt{\frac{(b-a)^2}{12}}[/tex]
Then
[tex]\sigma = \sqrt{\frac{(120-0)^2}{12}}[/tex]
[tex]\sigma = 34.64[/tex]
Minimum sample size:
Now, since we have an estimate for the standard deviation of the population, we use the z-distribution.
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].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
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.
The minimum sample size is n for which M = 4. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]4 = 1.96\frac{34.64}{\sqrt{n}}[/tex]
[tex]4\sqrt{n} = 1.96*34.64[/tex]
[tex]\sqrt{n} = \frac{1.96*34.64}{4}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*34.64}{4})^2[/tex]
[tex]n = 288.1[/tex]
Rounding up:
The minimum sample size needed to obtain this amount of precision is 289.
pls pls help i realy need help
Answer:
a <= 3
Step-by-step explanation:
Select the correct answer. What is the domain of the function represented by this graph? the graph of a quadratic function y = x^2 – 4 with a minimum value at the point (0,-4) A. x ≤ 0 B. -2 ≤ x ≤ 2 C. x ≥ 4 D. all real numbers
WILL GIVE BRAINLIEST
Answer:
For a general function f(x), the domain is the set of the possible values of x that we can input in the function.
The trick to find the domain is first to assume that the domain is the set of all real numbers, and then let's try to find the values of x that cause a problem in the function. (If the graph is cut in some value of x, such that it ends with an open or a closed point, then these values define the domain).
Such that one of these problems can be like x = 1 in the function:
g(x) = 1/(x - 1)
Because that value causes the denominator to be equal to zero, then the domain of that function will be the set of all real numbers except the value x = 1.
In this case, we have:
f(x) = x^2 - 4
There is no value of x that causes a problem for this function, then the domain is the sett of all real numbers.
Correct option D.
Someone help
A statistican is analyzing data to find a model. She has determined the following characteristics of the data. Which characteristics of the data defines the period?
Explanation:
The period of a function measures how long a cycle takes. Think of tides on a beach. There's a regular pattern that can be predicted whether its high tide or low tide. Time is often the critical component with the period. Since choice D mentions time and the key term "repeat", this is why it's the answer.
The other values, while useful elsewhere, aren't going to tell us anything about the period. The initial value being 5 doesn't tell us when y = 5 shows up again, and if the function is repeating itself at this point or not. So info about choice A is not sufficient to determine the period. The same goes for choices B and C as well.
A force of 350 pounds is resolved into component forces. If it makes an angle of 67° with the horizontal, find the larger component. 322 lb 235 lb 137 lb 380 lb
Answer: [tex]322\ lb[/tex]
Step-by-step explanation:
Given
The magnitude of the force [tex]F=350\ \text{Pounds}[/tex]
The force makes an angle of [tex]67^{\circ}[/tex] with the horizontal
So, the components of the force are
[tex]\Rightarrow F\cos 67^{\circ}, F\sin 67^{\circ}\\\Rightarrow F\cos 67^{\circ}=350\cos 67^{\circ}\\\quad \quad =136.75\ lb\\\text{Similarly, }\\\Rightarrow F\sin 67^{\circ}=350\sin 67^{\circ}\\=322.17\ lb[/tex]
The larger among the two is [tex]F\sin 67^{\circ}[/tex] i.e. [tex]322\ lb[/tex]
which system of equations does this graph represent?
1) y=x^2-5
y=-x+1
2) y=x^2-5
y=-x-1
3) y=x^2+5
y=-x+1
4) y=x^2+5
y=-x-1
Answer:
1
Step-by-step explanation:
First, we can find the equation of the parabola. The standard form of a parabola is ax^2 + bx + c,
where c is the y-intercept. The y-intercept on the graph is -5, and every option starts with x^2, so the equation must be x^2 - 5. This rules out options 3 and 4.
Next, we can find the equation of the line. The options are all given in slope-intercept form: y = mx + b, where b is the y-intercept. The y-intercept on the graph is 1, and option 1 has 1 in the place of b. Therefore, option 1 is the answer.
Daryl can jump 2 1/2 yards. sarah can jump 8 feet michell can jump 72 inches, witch statement is true.
Answer:
Where are the statements?
Step-by-step explanation:
Where are the statements?
Solve
W times 4 - 10=42
Please help quick thank you
Answer:
13
Step-by-step explanation:
4w-10=42
4w=52
w=52/4
w=13
USING A2+B2=c2
For the following right triangle, find the side length x.
DELL
Answer:
[tex]x=15[/tex]
Step-by-step explanation:
Pythagorean theorem: [tex]c^2 = a^2 + b^2[/tex], where c is the longest side (hypotenuse), a and b are the other sides of the right angled triangle.
In this question, c is labelled as [tex]x[/tex].
Therefore, we can use the theorem to find [tex]x[/tex].
[tex]x^2 = a^2+b^2[/tex]
So, substitute in the other sides and solve for [tex]x[/tex].
[tex]x^2 = (9)^2 + (12)^2\\x^2 = 81 + 144\\x^2 = 225\\x = 15[/tex]
We can see the answer is correct because it is meant to be the largest side and [tex]15> 12>9[/tex].
A leasing firm claims that the mean number of miles driven annually, , in its leased cars is less than miles. A random sample of cars leased from this firm had a mean of annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is miles. Assume that the population is normally distributed.
Is there support for the firm's claim at the level of significance?
Perform a one-tailed test.
null hypothesis?
alternative hypothesis?
type of test statistic?
value of the test statistic?
the p-value?
Can we support the leasing firm's claim that the mean number of miles driven annually is less than 12800 miles?
Complete question is;
A leasing firm claims that the mean number of miles driven annually, u , in its leased cars is less than 12800 miles. A random sample of 50 cars leased from this firm had a mean of 12499 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 3140 miles. Is there support for the firm's claim at the 0.05 level of significance?
Perform a one-tailed test.
null hypothesis?
alternative hypothesis?
type of test statistic?
value of the test statistic?
the p-value?
Can we support the leasing firm’s claim that the mean number of miles driven annually is less than 12800 miles?
Answer:
A) Null hypothesis; μ ≥ 12800
Alternative hypothesis; μ < 12800
B) type of test statistic: z-score test
C) test statistic; z = -0.678
D) p - value = 0.2489
E) No, we can't support the leasing firms claim
Step-by-step explanation:
We are given;
Population mean; μ = 12800 miles
Sample mean; x¯ = 12499 miles
Sample size; n = 50
Population standard deviation; σ = 3140
Let's define the hypothesis;
Null hypothesis; μ ≥ 12800
Alternative hypothesis; μ < 12800
The alternative hypothesis is the claim.
Since sample size is greater than 30, we will use z-score test.
Formula for z-score;
z = (x¯ - μ)/(σ/√n)
z = (12499 - 12800)/(3140/√50)
z = -0.678
From online p-value from z-score calculator attached, using z = -0.678 with one tailed hypothesis and significance value of 0.05,we have;
p - value = P(z < -0.678) = 0.2489
The p-value is greater than the significance value, so we will fail to reject the null hypothesis and conclude that there is no sufficient information to support the leasing firm's claim
х
The table of values below represent an exponential function. Write an exponential equation that models the data.
у
-2 23
-1 16.1
0 11.27
1 7.889
2 5.5223
a.
y = 23(0.7)
y = 16.1(1.7)
C. y = 11.27(0.7)
d.
y = 11.27(1.3)
b.
9514 1404 393
Answer:
C. y = 11.27(0.7^x)
Step-by-step explanation:
The table value (x, y) = (0, 11.27) tells you the multiplier of the exponential term will be 11.27. The decreasing values tell you the base of the exponential term is less than 1. Only answer choice C matches these requirements.
PLS HELPPPP ! I need itttt
Answer:
x = 10
Step-by-step explanation:
A number is greater than 8. The same number is less than 10. The inequalities x > 8 and x < 10 represent the situation
Which best explains the number of possible solutions to the inequality?
There is one solution because 9 is the only number between 8 and 10.
O There are a three solutions because 8, 9, and 10 are possible solutions.
O There are a few solutions because there are some fractions and decimals between 8 and 10.
There are infinite solutions because there is always another number between any two numbers.
Answer:
Option 4
Step-by-step explanation:
Let any two real number a and b (no matter +ve, -ve or 0). a ≥ b
The average of them will always lie in between them or be equal(if 0).
Let's prove : According to the statement,
a ≥ (a + b)/2 ≥ b
2a ≥ a + b ≥ 2b
2a ≥ a + b and a + b ≥ 2b
a ≥ b and a ≥ b, as we assumed.
Moreover, as the average exists in between a and b, we have the average (a + b)/2. Similarly, there exists one more average of (a + b)/2 and a or b, which definitely lie between a and b as (a + b)/2 lies there and smaller than a and b.
In the same order, we can have many average and the process would stop. This leads to infinite number between a and b.
Notice that we talked about all the numbers moreover there are many irrational(non-terminating like 9.898989.... etc numbers as well.
Option (4), infinite solutions.
Note: we solved for all the number (not specifically odd, even, natural, whole, integer, etc).
A clock lost 2 minutes and 36 seconds in 78 days. How many seconds did it lose per day?
the clock lost 2 seconds per day
You are going to use an incline plane to lift a heavy object to the too of shelving unit with a height of 7 ft. The base if the incline plane is 26 ft from the shelving unit. What is the length of the incline plane? FAST HELPPP MEE PLEASEE IM STUCK
Answer:
17.46 ft
Step-by-step explanation:
The inclined plane is in the shape of a right triangle, therefore we can use the Pythagorean theorem to find the length of the inclined plane. The formula for this theorem is the following
[tex]a^{2} + b^{2} = c^{2}[/tex]
Where a and b are the two sides and c is the hypotenuse/inclined side. Therefore, we can simply plug in the lengths of the two sides into the formula and solve for c.
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]7^{2} + 16^{2} = c^{2}[/tex]
[tex]49 + 256 = c^{2}[/tex]
[tex]305 = c^{2}[/tex] ... square root both sides
17.46 = c
The table shows all possible outcomes when Juan tosses a penny, a nickel, and a quarter at the same time.
Answer:
A
Step-by-step explanation:
Please this a really easy question. Does this mean I got an A on this test?! Please answer!!!!!!!!!!!!!!!
Answer:
yes it does. good job on your A.
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
find the common difference of the arithmetic sequence 3, -2, -7
Answer:
-5
Step-by-step explanation:
To find the common difference, take the second term and subtract the first term
-2 - 3 = -5
Check with the third term and the second term
-7 - (-2) = -7 +2 = -5
The common difference is -5
Can someone help me I am stuck on this question it would mean the world if u helped me! and TYSM! for the people who helped me have a wonder full day!
Answer:
1.25 gallons of orange juice needed
Step-by-step explanation:
2(3/4)=3/2 cups per 1 person
24 x 3/2=36 cups for everyone
36 cups=18 pints
18-8=10 pints of orange juice
10 pints = 1.25 gallon
Answer:
1.25 gallons of orange juice
Step-by-step explanation:
24x2=48
3/4x48=36
36 cups into pints is 18 pints
18-8=10
10 pints into gallons is 1.25 gallons
Find the slope
2/3
-2/3
3/2
-3/2
Please help I really need help. I am super confused and would really appreciate it
Answer:
[tex] a^{5} [/tex]
Step-by-step explanation:
Given the mathematical expression;
a⁸/a³
To rewrite the expression in the form [tex] a^{m} [/tex]
We would have to apply the law of indices.
[tex] Law \; of \; division = \frac {a^{x}}{a^{y}} = a^{x - y} [/tex]
[tex] Law \; of \; division = \frac {a^{8}}{a^{3}} = a^{8 - 3} [/tex]
[tex] a^{m} = a^{8 - 3} = a^{5} [/tex]
Are all cones similar?
Answer: all cones with the same height are always similar. False... radii could differ. ... Doubling the radius of a sphere doubles its surface area.
Step-by-step explanation:
Classify the following triangle. Check all that apply.
A
I A. Equilateral
B. Right
C. Acute
I D. Isosceles
O E Obtuse
O F. Scalene
Answer:
A and C
Step-by-step explanation:
The triangle given has three equal sides and three equal angles.
Since the sum of a triangle = 180°, therefore, each angle equals 60°
Thus, we can conclude that the triangle is an acute triangle because an acute triangle has all three sides measuring less than 90°. This implies that all it's angles are acute angles.
Also, since all its sides are equal and the same as well as it's three angles, based on this, we can equally say the triangle is an equilateral triangle.
The triangle can be referred to as an acute triangle and also as an equilateral triangle.
A watermelon that weighed 12 pounds cost $5.76. What was the cost per ounce of the watermelon?
Answer:
69.12
Step-by-step explanation:
12x5.76
Answer
69
Step-by-step explanation:
12×5.75=69
An equation with real coefficients has (1-i), 3, and 4 among its roots. What is the lowest possible degree of the equation?
A: 3
B: 4
C: 5
D: 6
Answer:
D
Step-by-step explanation:
PLEASE ANSWER ASAP WILL MARK BRAINLIEST!!
Select the favorable outcomes for rolling a sum of seven.
O (5-1) (5-2) (5-3) (5-4) (5-5) (5-6)
O (1-6) (2-5) (3-4) (4-3) (5-2) (6-1)
O (1-1) (1-2) (1-3) (2-1) (2-2)(3-1)
O (1-1) (2-2) (3-3) (4-4) (5-5) (6-6)
Answer:
The second one
O (1-6) (2-5) (3-4) (4-3) (5-2) (6-1)
Step-by-step explanation:
Favorable outcome is the outcome that we are looking for
The outcome that we are looking for when rolling two = die is a sum of 7
The set (1-6) (2-5) (3-4) (4-3) (5-2) (6-1) all add up to equal 7
( 1 , 6 ) 1 + 6 = 7
( 2 , 5 ) 2 + 5 = 7
( 3 , 4 ) 3 + 4 = 7
etc.
Which means that they are the favorable outcomes for rolling a seven
X/4 < 1.5 show steps please
Step-by-step explanation:
x/4<1.5x<1.5×4x<6stay safe healthy and happy...The management of a relatively new social networking website named BooglePlus is conducting a pilot study comparing use of its own site with use of a longer established social networking site named FaceList. Some articles published on the Internet give the reader the opportunity to register votes (called "likes") for the article on social networking sites to which the reader belongs. A BooglePlus employee selects from the Internet a random sample of 28 articles where the opportunity is given for registering votes for the article on both BooglePlus and Face List. Letting x be the number of votes on FaceList and y be the number of votes on the BooglePlus, the slope of the least squares regression line of y on x is found to be 0.0623, with a standard error of 0.0224.
Required:
What could be used to compute a 95% confidence interval for the slope of the population regression line of y on x?
Answer:
0.0623 ± ( 2.056 )( 0.0224 ) can be used to compute a 95% confidence interval for the slope of the population regression line of y on x
Step-by-step explanation:
Given the data in the question;
sample size n = 28
slope of the least squares regression line of y on x or sample estimate = 0.0623
standard error = 0.0224
95% confidence interval
level of significance ∝ = 1 - 95% = 1 - 0.95 = 0.05
degree of freedom df = n - 2 = 28 - 2 = 26
∴ the equation will be;
⇒ sample estimate ± ( t-test) ( standard error )
⇒ sample estimate ± ( [tex]t_{\alpha /2, df[/tex]) ( standard error )
⇒ sample estimate ± ( [tex]t_{0.05 /2, 26[/tex]) ( standard error )
⇒ sample estimate ± ( [tex]t_{0.025, 26[/tex]) ( standard error )
{ from t table; ( [tex]t_{0.025, 26[/tex]) = 2.055529 = 2.056
so we substitute
⇒ 0.0623 ± ( 2.056 )( 0.0224 )
Therefore, 0.0623 ± ( 2.056 )( 0.0224 ) can be used to compute a 95% confidence interval for the slope of the population regression line of y on x
Raw scores on a certain standardized test one year were normally distributed, with a mean of 156 and a standard deviation of 23. If
48,592 students took the test, about how many of the students scored less than 96?
Answer:
About 220 of the students scored less than 96
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 156 and a standard deviation of 23.
This means that [tex]\mu = 156, \sigma = 23[/tex]
Proportion that scored less than 96:
p-value of Z when X = 96. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{96 - 156}{23}[/tex]
[tex]Z = -2.61[/tex]
[tex]Z = -2.61[/tex] has a p-value of 0.00453.
About how many of the students scored less than 96?
0.00453 out of 48592.
0.00453*48592 = 220.1.
Rounding to the closest integer:
About 220 of the students scored less than 96
Answer:
220
Step-by-step explanation:
#platolivesmatter
Find the volume of the prism below if each cube has a side length of 1/8 of a foot
Answer:
[tex]Volume = \frac{3}{128}ft^3[/tex]
Step-by-step explanation:
Given
[tex]Length = 1\ cube[/tex]
[tex]Width = 3\ cubes[/tex]
[tex]Height = 4\ cubes[/tex]
[tex]1\ cube = \frac{1}{8}ft[/tex]
Required
The volume of the cube
Start by calculating the dimension in ft
[tex]Length = 1\ cube[/tex]
[tex]Length = 1 * \frac{1}{8}ft[/tex]
[tex]Length = \frac{1}{8}ft[/tex]
[tex]Width = 3\ cubes[/tex]
[tex]Width = 3 * \frac{1}{8}ft[/tex]
[tex]Width = \frac{3}{8}ft[/tex]
[tex]Height = 4\ cubes[/tex]
[tex]Height = 4 * \frac{1}{8}ft[/tex]
[tex]Height = \frac{1}{2}ft[/tex]
So, the volume is:
[tex]Volume = Length * Width * Height[/tex]
[tex]Volume = \frac{1}{8}ft * \frac{3}{8}ft * \frac{1}{2}ft[/tex]
[tex]Volume = \frac{1}{8} * \frac{3}{8} * \frac{1}{2}ft^3[/tex]
Using a calculator, we have:
[tex]Volume = \frac{3}{128}ft^3[/tex]