a. The GRP (Gross Rating Points) for the four-week media buy with a 62 reach and 3.2 frequency can be calculated by multiplying the reach by the frequency. Therefore, the GRP for this buy is 62 * 3.2 = 198.4 GRPs.
b. In the case of the similar buy with 230 GRPs and a 50% reach, we can calculate the frequency by dividing the GRPs by the reach. So the frequency is 230 / 50 = 4.6.
When you reach fewer people, you gain a higher frequency. The difference in frequency between the two buys can be calculated by subtracting the initial frequency (3.2) from the frequency in the second buy (4.6). Therefore, the gain in frequency is 4.6 - 3.2 = 1.4.
c. To determine which buy is better, we need to consider the marketing objectives and strategies. If the objective is to maximize reach and exposure to a wider audience, the first buy with a higher reach of 62 would be better. However, if the objective is to focus on repetition and frequency of message delivery to a more targeted audience, the second buy with a higher frequency of 4.6 might be more suitable. The choice depends on the specific goals and priorities of the advertising campaign.
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1. What is 5,509 rounded to the thousands place?
А
6,000
B
5,500
5,600
D
5,000
Using mirrors installed on the moon by Apollo astronauts to reflect laser waveforms, its possible to measure the distance from earth to moon to high precision. Due to the physics of the detectors, the measurement errors have a uniform distribution of -3.0 to + 5.0 cm
a. What is the probability that a particle measurement will be accurate to within +- 1.0 cm?
b. Find the mean of the measurement errors
c. Find the standard deviation of the measurement errors
A.the probability that a particle measurement will be accurate to within +- 1.0 cm is 0.25 B. the mean of the measurement errors is 1 cm. C. the standard deviation of the measurement errors is 2.311 cm.
a. For a uniform distribution of -3.0 to + 5.0 cm, the total distance is 5.0 - (-3.0) = 8.0 cm.
The probability that a particle measurement will be accurate to within +- 1.0 cm is given by:
P(-1.0 ≤ X ≤ 1.0) = (1/(8.0)) * (1.0 - (-1.0))= (1/8.0) * 2= 0.25
b. Find the mean of the measurement errors
The formula to calculate the mean (μ) of the measurement errors is:μ = (a + b) / 2
where, a is the lower limit of the distribution, and b is the upper limit of the distribution.μ = (-3.0 + 5.0) / 2= 2 / 2= 1
Therefore, the mean of the measurement errors is 1 cm.
c. Find the standard deviation of the measurement errors
The formula to calculate the standard deviation (σ) of a uniform distribution is:σ = (b - a) / √12
where, a is the lower limit of the distribution, b is the upper limit of the distribution, and √12 is the square root of 12.σ = (5.0 - (-3.0)) / √12= 8 / 3.464= 2.311
Therefore, the standard deviation of the measurement errors is 2.311 cm.
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Picking a purple marble from a jar with 3 green and 3 purple marbles. What is the probability of picking a purple marble?
Answer:
1/2
Step-by-step explanation:
The total number of marbles in the jar is equal to 6
Since we have 3 purple marbles and 3 green marbles,
The probability of picking a purple marble =
Number of purple marbles in the jar / total number of marbles
= 3/6
= 1/2
From this calculation the probability of picking a purple marble is 1/2 or 0.5
The circle graph shows how William spends his day on average. If he sticks
to this schedule, how many hours will William spend sleeping over the
course of a week (7 days)? ()
17% 11%
10%
А
A) 75.6 hours
B) 78.2 hours
C) 814 hours
Watching TV
Video Games
Fating
Working
45 %Sleeping
27%
D) 848 hours
Answer:
d
Step-by-step explanation:
i did the math
What's the equation to use to solve x?
Use the Euler method to solve the differential equation
dy/dx= x/y ; y(0) = 1
with h = 0.1 to find y(1). Improve the result using h= 0.05 and compare both results with the analytical solution.
2. Use the predictor-corrector method to solve dy/dx = x^2+y^2 ; y(0)=0
with h = 0.01. Repeat for h= 0.05 and then give an estimate of the accuracy of the result of the first calculation.
Using Euler's method we get:
y_1 = 1
using the analytical solution:
y = 1.225
We can estimate the accuracy of the result of the first calculation to be approximately `0.0003927`.
Let's begin by solving the given differential equation using Euler's method.
Using Euler's method we can estimate the value of `y` at a point using the following equation:
y_n+1 = y_n + h*f(x_n,y_n), where h is the step size given by
`h=x_(n+1)-x_n`.
Given that `dy/dx = x/y` we have that `y dy = x dx`. Integrating both sides we get:
(1/2)y^2 = (1/2)x^2 + C where C is the constant of integration.
To find `C` we use the initial condition `y(0)=1`.
This gives:
(1/2)(1)^2 = (1/2)(0)^2 + C => C = 1/2
Therefore the solution is given by: y^2 = x^2 + 1/2 => y = sqrt(x^2 + 1/2)
Now to estimate `y(1)` using the Euler's method, we have:
x_0 = 0, y_0 = 1, h = 0.1
Using Euler's method we get:
y_1 = y_0 + h*(x_0/y_0) = 1 + 0.1*(0/1) = 1
Now, we will improve the result using h= 0.05 and compare both results with the analytical solution.
x_0 = 0, y_0 = 1, h = 0.05
Using Euler's method we get:
y_1 = y_0 + h*(x_0/y_0) = 1 + 0.05*(0/1) = 1
Now, using the analytical solution:
y = sqrt(x^2 + 1/2) => y(1) = sqrt(1 + 1/2) = sqrt(3/2) = 1.225
Using Euler's method we get y(1) = 1.0 (with h = 0.1) and 1.0 (with h = 0.05). As we can see the result is not accurate. To improve the result we can use a more accurate method like the Runge-Kutta method.
Next, we will use the predictor-corrector method to solve the given differential equation.
dy/dx = x^2+y^2 ; y(0)=0
with h = 0.01
To use the predictor-corrector method we need to first use a predictor method to estimate the value of `y` at `x_(n+1)`. For that we can use the Euler's method. Then, using the estimate, we correct the result using a better approximation method like the Runge-Kutta method.
The Euler's method gives:
y_n+1(predicted) = y_n + h*f(x_n,y_n) = y_n + h*(x_n^2 + y_n^2)y_1(predicted)
= y_0 + h*(x_0^2 + y_0^2) = 0 + 0.01*(0^2 + 0^2) = 0
Next, we will correct this result using the Runge-Kutta method of order 4.
The Runge-Kutta method of order 4 is given by: y_n+1 = y_n + (1/6)*(k1 + 2*k2 + 2*k3 + k4)
where k1 = h*f(x_n,y_n)
k2 = h*f(x_n + h/2, y_n + k1/2)
k3 = h*f(x_n + h/2, y_n + k2/2)
k4 = h*f(x_n + h, y_n + k3)
Using the given differential equation: f(x,y) = x^2 + y^2y_1 = y_0 + (1/6)*(k1 + 2*k2 + 2*k3 + k4)
where k1 = h*f(x_0,y_0) = 0
k2 = h*f(x_0 + h/2, y_0 + k1/2) = h*f(0.005, 0) = 0.000025
k3 = h*f(x_0 + h/2, y_0 + k2/2) = h*f(0.005, 0.0000125) = 0.000025
k4 = h*f(x_0 + h, y_0 + k3) = h*f(0.01, 0.0000125) = 0.000100y_1 = 0 + (1/6)*(0 + 2*0.000025 + 2*0.000025 + 0.000100) = 0.0000583
Now, we will repeat this process for `h=0.05`.
h = 0.05
The Euler's method gives:
y_1(predicted) = y_0 + h*(x_0^2 + y_0^2) = 0 + 0.05*(0^2 + 0^2) = 0
The Runge-Kutta method of order 4 gives:
y_1 = y_0 + (1/6)*(k1 + 2*k2 + 2*k3 + k4)
where k1 = h*f(x_0,y_0) = 0
k2 = h*f(x_0 + h/2, y_0 + k1/2) = h*f(0.025, 0) = 0.000313
k3 = h*f(x_0 + h/2, y_0 + k2/2) = h*f(0.025, 0.000156) = 0.000312
k4 = h*f(x_0 + h, y_0 + k3) = h*f(0.05, 0.000156) = 0.001242y_1 = 0 + (1/6)*(0 + 2*0.000313 + 2*0.000312 + 0.001242) = 0.000451
The estimate of the accuracy of the result of the first calculation is given by the difference between the two results obtained using `h=0.01` and `h=0.05`. This is:
y_1(h=0.05) - y_1(h=0.01) = 0.000451 - 0.0000583 = 0.0003927
Therefore, we can estimate the accuracy of the result of the first calculation to be approximately `0.0003927`.
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Help there are five people at the carnival they are 15 people at the other carnival how many people are there
Let W be the set of all vectors of the form shown on the right, where a and b represent arbitrary real numbers. Find a set S of vectors that spans W, or give an example or an explanation showing why W is not a vector space.
To determine whether the set W is a vector space, we need to check if it satisfies the properties of a vector space. In this case, W represents the set of all vectors of the form:
W = {(a, b, -2a + 3b) | a, b ∈ ℝ}
To show that W is a vector space, we need to demonstrate that it is closed under vector addition and scalar multiplication, and that it contains the zero vector. Let's verify each of these properties.
Closure under vector addition:Consider two arbitrary vectors in W, (a₁, b₁, -2a₁ + 3b₁) and (a₂, b₂, -2a₂ + 3b₂). Their sum is given by:
(a₁, b₁, -2a₁ + 3b₁) + (a₂, b₂, -2a₂ + 3b₂) = (a₁ + a₂, b₁ + b₂, -2(a₁ + a₂) + 3(b₁ + b₂))
We can rewrite the last expression as:
(a₁ + a₂, b₁ + b₂, -2a₁ - 2a₂ + 3b₁ + 3b₂) = (a₁ + a₂, b₁ + b₂, -2(a₁ + a₂) + 3(b₁ + b₂))
This shows that the sum of two arbitrary vectors in W is also in W. Therefore, W is closed under vector addition.
Closure under scalar multiplication:Consider an arbitrary vector in W, (a, b, -2a + 3b), and a scalar c ∈ ℝ. The scalar multiple of this vector is given by:
c(a, b, -2a + 3b) = (ca, cb, c(-2a + 3b)) = (ca, cb, -2ca + 3cb)
This expression can be rewritten as:
(ca, cb, -2(ca) + 3(cb))
Thus, the scalar multiple of an arbitrary vector in W is also in W. Therefore, W is closed under scalar multiplication.
Contains the zero vector:To check if W contains the zero vector, we need to find values of a and b that make the expression (-2a + 3b) equal to zero. If we set a = 0 and b = 0, then (-2a + 3b) = (-2(0) + 3(0)) = 0. Thus, the zero vector (0, 0, 0) is in W.
Since W satisfies all the properties of a vector space, we can conclude that W is indeed a vector space.
To find a set S that spans W, we can choose two arbitrary vectors that are linearly independent. One possible set is:
S = {(1, 0, -2), (0, 1, 3)}
These vectors can be expressed in the form of W:
(1, 0, -2) = (a, b, -2a + 3b) when a = 1 and b = 0
(0, 1, 3) = (a, b, -2a + 3b) when a = 0 and b = 1
Any vector in W can be represented as a linear combination of these two vectors, which demonstrates that S spans W.
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write the equation of a function whose parent function, f(x) = x 8, is shifted 2 units to the right.
To find the equation of a function whose parent function, f(x) = x^8, is shifted 2 units to the right, we can use the formula given below: g(x) = f(x - a) + bwhere f(x) is the parent function, a is the horizontal shift (positive for right and negative for left), b is the vertical shift (positive for up and negative for down), and g(x) is the new function.So, in this case, we need to shift the parent function f(x) = x^8 two units to the right.
This means that a = 2 and b = 0 (since there is no vertical shift).So, substituting these values in the formula, we get:g(x) = f(x - 2) + 0g(x) = (x - 2)^8Thus, the equation of the new function, g(x), is (x - 2)^8 when the parent function, f(x) = x^8, is shifted 2 units to the right.
To shift the parent function f(x) = x^8 two units to the right, we need to modify the equation by replacing 'x' with 'x - 2'. This will shift the graph horizontally to the right by 2 units.
Therefore, the equation of the shifted function, let's call it g(x), becomes:
g(x) = (x - 2)^8
To shift the parent function, f(x) = x^8, two units to the right, we can use the transformation equation:
g(x) = f(x - h)
where h represents the horizontal shift. In this case, h = 2 because we want to shift the function two units to the right. Substituting the values into the equation, we get:
g(x) = (x - 2)^8
Therefore, the equation of the function after shifting the parent function, f(x) = x^8, two units to the right is g(x) = (x - 2)^8.
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The given parent function is f(x) = x 8. We are supposed to write the equation of a function that is shifted two units to the right. It can be done by taking a new function g(x) and writing it as g(x) = f(x − 2).
Therefore, the equation of the new function g(x) is g(x) = (x − 2)8.
Step-by-step explanation: The given parent function is f(x) = x 8. We are supposed to write the equation of a function that is shifted two units to the right. It can be done by taking a new function g(x) and writing it as g(x) = f(x − 2).
The value of f(x) = x 8
Write it as follows:
when x is 0, 0 8 = 0 and
when x is 1, 1 8 = 8.
Now, we can write the equation for g(x) by using f(x) = x 8.
We have g(x) = f(x − 2)
= (x − 2)8.
Therefore, the equation of the new function g(x) is g(x) = (x − 2)8.
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what is the first 5 cubic numbers
Answer:
1,8,27,64,125
Step-by-step explanation:
Minh wants to buy a car costing $9,950. She can put $1,000 down and finance the rest at 10.9% APR, making the monthly payments for 3 years. How will Minh pay in finance charges? What will her monthly payments be?
Answer:
piip;[-p-o-ul0i
Step-by-step explanation:
7 + k = 11 step explanation
Answer:
k = 4
Step-by-step explanation:
11 - 7 = 4
Jamie bought 4 pounds of sugar for $2.56. What is the cost of sugar per pound?
a.$10.24
b.$1.56
c.$0.64
d.$6.04
The cost of sugar per pound can be found by dividing the total cost of sugar by the number of pounds purchased. In this case, the correct option is C).
To calculate the cost of sugar per pound, we divide the total cost by the number of pounds purchased. In this case, Jamie bought 4 pounds of sugar for $2.56. Therefore, the cost per pound is given by:
Cost per pound = Total cost / Number of pounds
Cost per pound = $2.56 / 4 pounds
Simplifying this calculation, we find:
Cost per pound = $0.64
Hence, the cost of sugar per pound is $0.64, which corresponds to option c. $0.64 in the given choices. This means that Jamie paid $0.64 for each pound of sugar purchased.
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For a hypothesis test using the single-factor ANOVA formula:
The obtained overall F ratio = MS between treatments divided by MS within treatments.
Calculate the obtained overall F ratio for: MS between treatments= 8 and MS within treatments = 2.
Then describe the null hypothesis decision for = .05, df numerator: 3, and df denominator: 4.
Reject of fail to reject null hypothesis?
We can conclude that there is not enough evidence to suggest that the means of the different groups are different.
The obtained overall F ratio for MS between treatments = 8 and MS within treatments = 2 can be calculated using the formula for a hypothesis test using the single-factor ANOVA. The formula is given below: Obtained overall F ratio = MS between treatments/MS within treatments Substituting the values in the above formula, we get, Obtained overall F ratio = 8/2 = 4
The obtained overall F ratio for MS between treatments = 8 and MS within treatments = 2 is 4.Now, let's describe the null hypothesis decision for α = .05, df numerator: 3, and df denominator: 4.The null hypothesis decision can be made using the F-distribution table. Using the table, the critical value of F is 9.49.
Therefore, if the obtained overall F ratio is greater than 9.49, then we reject the null hypothesis. If the obtained overall F ratio is less than or equal to 9.49, then we fail to reject the null hypothesis.Obtained overall F ratio = 4 is less than the critical value of F, i.e., 9.49.Therefore, the null hypothesis is not rejected at α = .05, df numerator: 3, and df denominator: 4.
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The obtained overall F ratio for MS between treatments = 8 and MS within treatments = 2 will be 4. The null hypothesis decision for α = 0.05, df numerator: 3, and df denominator: 4 is Fail to reject null hypothesis.
Explanation: ANOVA (analysis of variance) is a statistical method used to determine if two or more population means are equal.
It is used to analyze the variation between sample group means and is frequently used in hypothesis testing.
Therefore, we will now calculate the obtained overall F ratio for the given values.
The obtained overall F ratio formula is: Overall F Ratio = MS between treatments / MS within treatments.
Given, MS between treatments = 8 and MS within treatments = 2.
Therefore, Overall F Ratio = MS between treatments / MS within treatments
= 8/2
= 4
Hence, the obtained overall F ratio for MS between treatments= 8 and MS within treatments = 2 is 4.
The null hypothesis decision for α = 0.05, df numerator: 3, and df denominator: 4 is Fail to reject null hypothesis.
The test statistic value, F, is 3.71. The p-value is greater than 0.05. Therefore, we fail to reject the null hypothesis.
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Is x = 5 a solution to the equation 19 - x = 14?
Answer:
Yes
Step-by-step explanation:
Test the equation by substituting 5 in for x:
19- 5 =14
14=14
TRUE
If I helped, a brainliest would be greatly appreciated!
Answer: If you replace x with 5 then 19-5=14
Step-by-step explanation:
pls help i’m so confused omg!!
Answer:
C or B
Step-by-step explanation:
Answer:
Your answer is A.
Step-by-step explanation:
You can count the arrow lines as the 2s. Such as, 2, 4, 6, 8 and 10.
So, the line 'x' is being divided by how many lines touching it.
Therefore, it is 1.
Then you add x and 6, the number which the line is ending with.
Your final answer is, F(x) = 1
x+6
Hope this helped!
24 Hour Fitness charges svara spatee plus so per months to poun thensyn time has podszes por s gym membership so farHow many monohis has he been a member at 24 Hour Fitness monks
Answer:
4 months
Step-by-step explanation:
Equation:
y = 55 + 30x
y = gym membership
x = per month
Work:
y = 55 + 30x
175 = 55 + 30x
30x = 175 - 55
30x = 120
x = 4
4 months
Question Progress
boel
21/40 Marks
Find the area of this parallelogram.
13 cm
15 cm
20 cm
Please help.
a+67a+3ab-2ab-1=
Answer:
68a+ab-1
Step-by-step explanation:
Have a good day!
2222222 help me plz plz plz plz
Answer:
○ B) m∠XOA = m∠OYC
Step-by-step explanation:
Since Point O is circumcentered into the square, we keep it in the midst when we are making comparisons, and since this was simple to identify, this automatically is a false statement. Point O stays in the midst at all times.
- Hope this helps!
Help me please with the answer
tell me how to answer this
The mid point of the line segment is (-2, 5 / 2).
How to find the mid point of a line segment?The midpoint of a line segment is a point that lies exactly halfway between two points.
Therefore, let's find the mid point of the line segment indicated above.
Hence, using (-4, 0) and (0, 5)
Hence,
mid point = (x₁ + x₂ / 2, y₁ + y₂ / 2)
Therefore,
mid point = (0 - 4 / 2, 5 + 0 / 2)
mid point = (-4 /2, 5 / 2)
mid point = (-2, 5 / 2)
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b) Which phrases are used to describe an upper-tail test? (Select all that apply.) is greater than is less than is not the same as is smaller than is bigger than is shorter than is longer than is different from is decreased from is increased from has changed from is above is below is not equal to (c) Which phrases are used to describe a two-tail test? (Select all that apply.) is greater than is less than is not the same as is smaller than is bigger than is shorter than is longer than is different from is decreased from is increased from has changed from is above is below is not equal to
The phrases used to describe an upper-tail test are "is greater than," "is bigger than," "is above," and "is not equal to." and the phrases used to describe a two-tail test are "is not the same as," "is different from," and "is not equal to."
a) The hypothesis testing process is based on the assumption that the null hypothesis is true, which means that there is no significant difference between the observed and expected data. The alternative hypothesis is a statement that contradicts the null hypothesis and suggests that the observed data is different from the expected data. A hypothesis test involves testing the null hypothesis against the alternative hypothesis using a test statistic and a significance level. The significance level is the probability of rejecting the null hypothesis when it is true. If the p-value is less than the significance level, then we reject the null hypothesis and accept the alternative hypothesis. Otherwise, we fail to reject the null hypothesis.
b) The phrases used to describe an upper-tail test are "is greater than," "is bigger than," "is above," and "is not equal to." An upper-tail test is a one-tailed test that is used to determine if the sample mean is significantly greater than the population mean. The null hypothesis for an upper-tail test is that the population mean is less than or equal to the sample mean. The alternative hypothesis is that the population mean is greater than the sample mean.
c) The phrases used to describe a two-tail test are "is not the same as," "is different from," and "is not equal to." A two-tail test is used to determine if the sample mean is significantly different from the population mean. The null hypothesis for a two-tail test is that the population mean is equal to the sample mean. The alternative hypothesis is that the population mean is not equal to the sample mean.
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please please I really need help this depends on my life
Answer:
39.4 divided by (-7.2)= -5.472
6.7-39.31=-32.61
Step-by-step explanation:
"
Perform the following test of hypothesis. H0: μ 10.70, H1: μ # 10.70, n = 47, t = 12.234, = H0 is
"
Based on the given information, we have sufficient evidence to conclude that the population mean (μ) is not equal to 10.70.
To perform the test of hypothesis, we can use a t-test to determine whether there is sufficient evidence to reject the null hypothesis (H0) in favor of the alternative hypothesis (H1).
The given hypotheses are:
H0: μ = 10.70 (null hypothesis)
H1: μ ≠ 10.70 (alternative hypothesis)
The sample size is n = 47, and the test statistic is t = 12.234.
To conduct the test, we need to compare the calculated test statistic to the critical value(s) based on the desired significance level (α).
The steps to perform the hypothesis test are as follows:
Step 1: Set the significance level (α)
Let's assume a significance level of α = 0.05. This means we want to be 95% confident in our decision.
Step 2: Determine the critical value(s)
Since the alternative hypothesis is two-sided (μ ≠ 10.70), we need to find the critical values for a two-tailed t-test.
Since n = 47, we have n - 1 = 46 degrees of freedom (df). Looking up the critical values in the t-distribution table or using a statistical calculator, the critical values for a two-tailed test with α = 0.05 and df = 46 are approximately ±2.013.
Step 3: Calculate the p-value
The p-value is the probability of obtaining a test statistic as extreme as the one observed (t = 12.234), assuming the null hypothesis is true.
Using a t-table or statistical software, we can determine the p-value associated with the given t-value and degrees of freedom. The p-value turns out to be very small (p < 0.001).
Step 4: Make a decision
If the p-value is less than the significance level (α), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Since the p-value is smaller than α (p < 0.001), we reject the null hypothesis (H0).
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The diameter of a circle is 4 feet. What is the circumference?
d=4 ft
Give the exact answer in simplest form.
I need the answers
Answer: 4π
Step-by-step explanation: C= 2πr; 2r=d; C=dπ; C=4π!
Answer:
4π ft
Step-by-step explanation:
C = 2πr (Circumference formula for a circle)
diamater = 4, so diamter = 2 x radius, 4 = 2 x r , so r = 2
Use formula:
C = 2π(2) = 4π
4π ft (Exact answer)
Tony borrows $7,000 from a friend
at a rate of 5% interest for 4 months.
What is the total that needs
to be repaid after this time
to the nearest dollar?
Answer:
5%100 ×R200
Step-by-step explanation:
Address and u the one for me please
Please help! if do you will get 'Brainliest' (Right answers only, and please show your work)
Answer:
The answer should be B
[tex]3c \: + \: 43 \: \geqslant \: 100[/tex]
The center and a point on a circle are given. Find the circumference to the nearest tenth.
center:(−15, −21);
point on the circle: (0, −13)
The circumference is about ?
Answer:
Circumference ~ 106.8
Step-by-step explanation:
Use the distance formula to find the radius of the circle with the two coordinates given. The radius of this circle is 17. Plug 17 into the formula 2(pi)r to find the Circumference. The answer is 106.8 rounded to the nearest tenth.
IQ is normally distributed with a mean of 100 and a standard deviation of 15. When selecting samples of size n = 16, find the probability a randomly selected sample has a mean greater than 105. 0.0981 0.0936 O None of these 0.0973 0.0912
Given that IQ is normally distributed with a mean of 100 and a standard deviation of 15 and the sample size, n=16
We need to find the probability that a randomly selected sample has a mean greater than 105.
The z-score is given by;[tex]z = \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\[/tex]
The sample mean of size n=16 is [tex]\bar{x}=105[/tex], the population mean is [tex]\mu=100[/tex] and the standard deviation is [tex]\sigma=15[/tex]. Now we need to find the probability that the z-score is greater than z. Since the sample size is greater than 30, we can use the z-distribution to approximate the standard normal distribution. Since the sample size is n=16 which is less than 30, we cannot use the z-distribution to approximate the standard normal distribution. Instead, we use the t-distribution, which is a set of distributions that are similar to the standard normal distribution but are dependent on the sample size. The formula for the t-score is given by;
[tex]t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\[/tex]Where [tex]s[/tex] is the sample standard deviation. Since the population standard deviation is unknown, we use the sample standard deviation instead.
The sample mean of size n=16 is [tex]\bar{x}=105[/tex],
the population mean is [tex]\mu=100[/tex],
the sample standard deviation is [tex]s=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{16}}=3.75[/tex].
The t-score is given by[tex]t=\frac{105-100}{\frac{3.75}{\sqrt{16}}}=4.267\[/tex]
The degrees of freedom is given by n-1 = 16-1 = 15. Using the t-table with 15 degrees of freedom and a two-tailed test at the 0.05 level of significance, the critical value is 2.131. Since the t-score is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the sample mean is greater than the population mean. The p-value is the area under the curve to the right of the t-score. We find the p-value using the t-table. The p-value is 0.0002. Hence, the probability that a randomly selected sample has a mean greater than 105 is 0.0002 (or 0.02%). Therefore, the option with the correct answer is 0.0002.
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Write a clear explanation summarizing what you have learned about defining expressions that have zero or a negative integer as an exponent. Then explain, using examples, why these definitions makes sense. Give as many reasons as you can. Also indicate which exclamation makes the most sense to you.
Answer:
Any number raised to zero is one.
Examples:
[tex]4^{0} = 1\\\\178^0=1\\\\15^0 = 1[/tex]
Any number raised to a negative integer is 1 over that exponential term without the negative exponent.
Examples:
[tex]5^{-1} = \frac{1}{5}\\\\324^{-13}=\frac{1}{324^{13}}\\\\17^{-6} = \frac{1}{17^{6}}[/tex]