First, we find how much 1 baseballs card costs.
1 card = 0.60
12*0.6 = $7.20
For A B and C, you just plug in the given number
A
![2(15) + 5 = 35](https://tex.z-dn.net/?f=2%2815%29%20%2B%205%20%3D%2035)
B
![4(20) + 2 = 82](https://tex.z-dn.net/?f=4%2820%29%20%2B%202%20%3D%2082)
C
![6(10) + 5 = 65](https://tex.z-dn.net/?f=6%2810%29%20%2B%205%20%3D%2065)
And for D, you set the equation to 26 and solve for n
![3x + 5 = 26 \\ 3x = 21 \\ x = 7](https://tex.z-dn.net/?f=3x%20%2B%205%20%3D%2026%20%5C%5C%203x%20%3D%2021%20%5C%5C%20x%20%3D%207)
I had to use x instead of n, but for D n=7. :)
Using the z-distribution, it is found that the 95% confidence interval for the difference is (-1.3, -0.7).
<h3>What are the mean and the standard error for each sample?</h3>
Considering the data given:
![\mu_S = 3.8, n = 175, s_S = \frac{1.7}{\sqrt{175}} = 0.1285](https://tex.z-dn.net/?f=%5Cmu_S%20%3D%203.8%2C%20n%20%3D%20175%2C%20s_S%20%3D%20%5Cfrac%7B1.7%7D%7B%5Csqrt%7B175%7D%7D%20%3D%200.1285)
![\mu_N = 4.8, n = 152, s_N = \frac{1.2}{\sqrt{152}} = 0.0973](https://tex.z-dn.net/?f=%5Cmu_N%20%3D%204.8%2C%20n%20%3D%20152%2C%20s_N%20%3D%20%5Cfrac%7B1.2%7D%7B%5Csqrt%7B152%7D%7D%20%3D%200.0973)
<h3>What is the mean and the standard error for the distribution of differences?</h3>
The mean is the subtraction of the means, hence:
![\overline{x} = \mu_S - \mu_N = 3.8 - 4.8 = -1](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%3D%20%5Cmu_S%20-%20%5Cmu_N%20%3D%203.8%20-%204.8%20%3D%20-1)
The standard error is the square root of the sum of the variances of each sample, hence:
![s = \sqrt{s_S^2 + s_N^2} = \sqrt{0.1285^2 + 0.0973^2} = 0.1612](https://tex.z-dn.net/?f=s%20%3D%20%5Csqrt%7Bs_S%5E2%20%2B%20s_N%5E2%7D%20%3D%20%5Csqrt%7B0.1285%5E2%20%2B%200.0973%5E2%7D%20%3D%200.1612)
<h3>What is the confidence interval?</h3>
It is given by:
![\overline{x} \pm zs](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%5Cpm%20zs)
We have a 95% confidence interval, hence the critical value is of z = 1.96.
Then, the bounds of the interval are given as follows:
More can be learned about the z-distribution at brainly.com/question/25890103
#SPJ1
Answer:
<h2>The value of y is <u>0.5</u>, so the answer is <u>C</u>.</h2>
Step-by-step explanation:
Find first the constant of variation.
Given: x = 3, y = 4
Find: k = ?
Formula:
![y = \frac{k}{x}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7Bk%7D%7Bx%7D%20)
Solution:
![y = \frac{k}{x} \\ 4 = \frac{k}{3} \\ 12 = k](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7Bk%7D%7Bx%7D%20%20%5C%5C%204%20%3D%20%20%5Cfrac%7Bk%7D%7B3%7D%20%20%5C%5C%2012%20%3D%20k)
Then, find the value of y in the third box.
Given: x = 24, k = 12
Find: y = ?
Formula:
![y = \frac{k}{x}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7Bk%7D%7Bx%7D%20)
Solution:
![y = \frac{k}{x} \\ y = \frac{12}{24} \\ y = \frac{1}{2} \\\boxed{y = 0.5}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7Bk%7D%7Bx%7D%20%20%5C%5C%20y%20%3D%20%20%20%5Cfrac%7B12%7D%7B24%7D%20%5C%5C%20y%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%5Cboxed%7By%20%3D%200.5%7D)
Answer:
3.2 units
Step-by-step explanation:
Use the law of sines
z/sin 76 = 2.6/sin 51
z = 2.6 sin 76/sin 51 = 3.2