Answer:
-16, -25, -34, -43, and -52
Step-by-step explanation:
a, = - 9n - 7.
Sequence given by
a_n, = - 9n - 7.
a_1 = -9*1 - 7 = -16
a_2 = -9*2 - 7 = -18 - 7 = -25
a_3 = -9*3 - 7 = -27 - 7 = -34
a_4 = -9*4 - 7 = -36 - 7 = -43
a_5 = -9*5 - 7 = -45 - 7 = -52
A rectangular sheet of paper is folded diagonally. What is the length of XY?
15 in
8 in
OA) 23 in.
OB) 19 in.
OC) 15 in.
OD) 17 in.
Answer:
17 inches
Step-by-step explanation:
the quesiton is in the picture
Answer:
The three equivalent options are: [tex]\frac{1}{6}x+47[/tex], [tex]\frac{5}{3}x+35-\frac{3}{2}x+12[/tex], and [tex]5(\frac{1}{3} x+(5)(7)-(3)(\frac{1}{2}x)+(3)(4)[/tex]
Step-by-step explanation:
Expand [tex]5(\frac{1}{3}x+7)-3(\frac{1}{2}x-4)[/tex] to get [tex]\frac{5}{3}x+35-\frac{3}{2}x+12[/tex].
Simplifying this gets you [tex]\frac{1}{6}x+47[/tex].
Which choice are equivalent to the fraction below? Check all that apply 6^7/6^5
Answer:36
Step-by-step explanation:u
6^7/6^5
6^(7-5)
6^2
6x6=36
tina has a doll which she can dress with a hat, a scarf and a jacket.
she has 3 different colour hat, 4 different colour scarves and 5 different colour jackets
Tina chose a hat a scarf and a jacket for her doll
how many combinations of hat scarf and jacket can she choose
Answer:
60 combinations
Step-by-step explanation:
3 × 4 × 5 = 60
Hope i helped!
Tina can choose from 60 different combinations of hat, scarf, and jacket for her doll.
To find the total number of combinations Tina can choose for her doll's outfit, you can use the multiplication principle.
Tina has 3 choices for the hat, 4 choices for the scarf, and 5 choices for the jacket.
To find the total number of combinations, multiply the number of choices for each item together:
3 (choices for the hat) × 4 (choices for the scarf) × 5 (choices for the jacket) = 60
Tina can choose from 60 different combinations of hat, scarf, and jacket for her doll.
for such more question on combinations
https://brainly.com/question/28065038
#SPJ3
A research company desires to know the mean consumption of milk per week among males over age 25. A sample of 650 males over age 25 was drawn and the mean milk consumption was 3.4 liters. Assume that the population standard deviation is known to be 1.3 liters. Construct the 95% confidence interval for the mean consumption of milk among males over age 25. Round your answers to one decimal place.
Answer:
[tex]3.3\leq x\leq 3.5[/tex]
Step-by-step explanation:
The 95% confidence interval can be calculated as:
[tex]x'-z_{\alpha/2}\frac{s}{\sqrt{n}} \leq x\leq x'+z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]
Where [tex]x[/tex] is the mean consumption of milk, [tex]x'[/tex] is the sample mean, [tex]s[/tex] is the population standard deviation, [tex]n[/tex] is the size of the sample, [tex]\alpha[/tex] is 5% and [tex]z_{\alpha /2}[/tex] is the z-value that let a probability of [tex]\alpha /2[/tex] on the right tail.
So, replacing [tex]x'[/tex] by 3.4 liters, [tex]s[/tex] by 1.3 liters, n by 650 and [tex]z_{\alpha /2}[/tex] by 1.96, we get that the 95% confidence interval is equal to:
[tex]3.4-(1.96*\frac{1.3}{\sqrt{650}})\leq x\leq 3.4+(1.96*\frac{1.3}{\sqrt{650}}) \\3.4-0.1\leq x\leq 3.4+0.1\\3.3\leq x\leq 3.5[/tex]
Answer:
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.
Margin of error = z × σ/√n
Where
σ = population standard Deviation
n = number of samples
From the information given
x = 3.4
σ = 1.3
n = 650
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96
Margin of error = 1.96 × 1.3/√650 = 0.1
Confidence interval = 3.4 ± 0.1
The lower end of the confidence interval is
3.4 - 0.1 = 3.3 litres
The upper end of the confidence interval is
3.4 + 0.1 = 3.5 litres
The monthly demand equation for an electric utility company is estimated to be p equals 59 minus (10 Superscript negative 5 Baseline )x, where p is measured in dollars and x is measured in thousands of killowatt-hours. The utility has fixed costs of $3 comma 000 comma 000 per month and variable costs of $27 per 1000 kilowatt-hours of electricity generated, so the cost function is Upper C (x )equals 3 times 10 Superscript 6 Baseline plus 27 x. (a) Find the value of x and the corresponding price for 1000 kilowatt-hours that maximize the utility's profit. (b) Suppose that the rising fuel costs increase the utility's variable costs from $27 to $41, so its new cost function is Upper C 1 (x )equals 3 times 10 Superscript 6 Baseline plus 41 x. Should the utility pass all this increase of $14 per thousand kilowatt-hours on to the consumers?
Answer:
a) The price that maximizes profit is p =$43.
b) The utility shouldn't pass all this increase on the consumers because this would mean a decrease in the profits. They should pass only $7 to consumers price.
Step-by-step explanation:
We have an electric utility company which has a demand function defined by:
[tex]p=59-10^{-5}x[/tex]
where p is the price and x is the the energy in thousands of kWh.
The cost of the company is defined as:
[tex]C(x)=3\cdot 10^6+27x[/tex]
We have to calculate the price that maximizes the utility's profit R(x).
We can define the profit as:
[tex]R(x)=p\cdot x-C=(59-10^{-5}x)\cdot x-(3\cdot 10^6+27x)\\\\R(x)=-10^{-5}x^2+(59-27)x-3\cdot10^6\\\\R(x)=-10^{-5}x^2+32x-3\cdot10^6[/tex].
To maximize R, we have to derive it and equal to zero
[tex]\dfrac{dR}{dx}=0\\\\\\\dfrac{dR}{dx}=-2\cdot10^{-5}x+32=0\\\\\\x=(32/2)\cdot 10^5=16\cdot 10^5=1.6\cdot 10^6[/tex]
The price that maximizes the profit is then:
[tex]p=59-10^{-5}x=59-10^{-5}(16\cdot 10^5)=59-16=43[/tex]
b) When the unit cost rise from $27 to $41, the utility profit function changes.
We have to calculate the new price that maximizes profit, and then we will know if the rise in cost was transferred to price completely.
The new profit function is:
[tex]R(x)=p\cdot x-C=(59-10^{-5}x)\cdot x-(3\cdot 10^6+41x)\\\\R(x)=-10^{-5}x^2+(59-41)x-3\cdot10^6\\\\R(x)=-10^{-5}x^2+18x-3\cdot10^6[/tex]
To maximize R, we have to derive it and equal to zero
[tex]\dfrac{dR}{dx}=0\\\\\\\dfrac{dR}{dx}=-2\cdot10^{-5}x+18=0\\\\\\x=(18/2)\cdot 10^5=9\cdot 10^5[/tex]
We calculate the new price as:
[tex]p=59-10^{-5}x=59-10^{-5}(9\cdot 10^5)=59-9=50[/tex]
The new price is $7 dollars above the previous maximizing price, so the rise in unit cost is only transferred 50% to the price.
The utility shouldn't pass all this increase on the consumers because this would mean a decrease in the profits. They should pass only $7 to consumers price.
Hundreds, tens, and ones
hat number represents the same amount as 3 hundreds + 4 tens +16 ones?
Answer:
356
Step-by-step explanation:
3 hundreds = 3 * 100 = 300
4 tens = 4 * 10 = 40
16 ones = 16 * 1 = 16
Combine the terms: 300 + 40 + 16 = 356
356 is your answer.
~
If 15 bahs are equal to 24 rahs, and 9 rahs are equal in value to 15 yahs, how many bahs are equal in value to 1000 yahs?
Answer:
375
Step-by-step explanation:
b : r = 15 : 24
r : y = 9 : 15 = 3 : 5 = 24 : 40
Then ...
b : r : y = 15 : 24 : 40
The number of bahs equivalent to 1000 yahs is ...
bahs = (15/40)(1000) = 375
375 bahs are equal in value to 1000 yahs.
Mr. Hobbs has 10 blue markers, 6 black markers, and 8 red markers
on his desk. What fraction of black markers can be found on Mr.
Hobbs' desk?
Select one:
1.3/9
2.5/12
3.1/4
4.1/3
Answer:
4
Step-by-step explanation:
Im not completely sure
Jenny is 12 years older than Nancy. Five years ago Jenny was three times as old as Nancy. How old is each now?
Answer:
Jenny = 23 | Nancy = 11
Step-by-step explanation:
Please help 6th grade math ! :)
Answer:
2.50 per two bottles of sprite
Step-by-step explanation:
Poornima is a stay-at-home parent who lives in San Francisco and teaches tennis lessons for extra cash. At a wage of $30 per hour, she is willing to teach 3 hours per week. At $50 per hour, she is willing to teach 7 hours per week. Using the midpoint method, the elasticity of Poornima's labor supply between the wages of $30 and $50 per hour is approximately(1.6,0.13,0.63,25) , which means that Poornima's supply of labor over this wage range is (elastic, inelastic)
Answer:
We can deduce that the elasticity of the labor supply is greater than 1 the labor supply is considered elastic
Step-by-step explanation:
The formula to use is the following:
Elasticity = (Change in working hours / Average working hours) / (Change in wage rate / Average wage rate)
we replace the data
Elasticity = [(7 - 3) / (7 + 3) / 2] / [(50 - 30) / (50 + 30) / 2]
Elasticity = [4 / (10/2)] / [20 / (80/2)]
Elasticity = (4/5) / (20/40)
Elasticity = 0.8 / 0.5
OUTCOME
Elasticity = 1.6
We can deduce that the elasticity of the labor supply is greater than 1 the labor supply is considered elastic
The elasticity of Poornima's labor supply between the wages of $30 and $50 per hour is approximately 1.5. This shows that Poornima's supply of labor in this wage range is elastic, indicating responsiveness to wage changes.
Explanation:The elasticity of labor supply can be calculated using the midpoint method. This method measures elasticity as the percent change in quantity supplied divided by the percent change in wage. The percent change in quantity supplied is calculated as (Q2-Q1)/[(Q1+Q2)/2], where Q1 = 3 and Q2 = 7. That gives us (7-3)/[(3+7)/2] = 1. The percent change in wage is calculated similarly as (P2-P1)/[(P1+P2)/2], where P1 = $30 and P2 = $50, giving us (50-30)/[(30+50)/2] = 0.67. By dividing the percent change in quantity supplied by the percent change in wage, we get the elasticity of labor supply: 1/0.67 = 1.5 (rounded).
Therefore, the elasticity of Poornima's labor supply between wages of $30 and $50 per hour is approximately 1.5. Because the elasticity is greater than 1, Poornima's supply of labor over this wage range is elastic, meaning she is responsive to wage changes.
Learn more about Elasticity of Labor Supply here:https://brainly.com/question/34322494
#SPJ3
A restaurant sells four combo meals. Jolly Meal, which cost $7, consists of 2 yogurt cups and 1 sandwich. The Special Meal, which is made up of 2 sandwiches and 1 yogurt cup, cost $12.50. Calculate the cost of the following combo meals if the charge for sandwiches and yogurt cups are the same for all combo meals.
Answer:
Yogurt: $0.50 Sandwich: $6
Step-by-step explanation:
Because if you make the combos equations it would be Y+Y+X=7 and X+X+Y=12.5 so you would solve with those and for it to work with both, 0.50 for yogurt, and 6 for sand which would work.
Box measure 4 units by 2.5 by 1.5 units what is the greatest number of cubes side length o 1/2 unit can be pack inside the box
Show details
Answer:120
Step-by-step explanation:
Volume=length x width x height
volume of box=4x2.5x1.5
Volume of box=15
Length of side of cube=1/2=0.5
Volume of cube=0.5x0.5x0.5
Volume of cube=0.125
Number of cube that can pack inside there box=15 ➗ 0.125=120
help. If 20 men can survive for 24 days on 15 cans of rations, how many cans will be needed for 16 men to survive for 36 days?
Answer: 29 cans.
Step-by-step explanation:
20 can survive 24 days with 15 cans.
If X is the number of days that a man can survive with one can of rations.
so X is in the units can/day
then we have that:
24/15*X = 20
X = 20*15/24 = 12.5
This means that a man can live 12.5 days with a can of food.
then, for 16 men and 36 days we have:
(36/C)*12.5 = 16
C = (36/16)*12.5 = 28.1215
And we can not have a 0.1215 of a can, so we should round it up to 29 cans.
Sam is creating a homemade lava lamp using an empty 0.6-liter water bottle. He fills the 1.25 bottle with deciliters of colored water, and plans to fill the rest of the bottle with oil. How many milliliters of oil will he need?
Answer:
475 milliliters of oil
Step-by-step explanation:
1 liter =1000 milliliters
1 deciliter =100 milliliters
To make it easier, we convert all our units to milliliters.
Volume of the water bottle =0.6 liter
=0.6 X 1000 =600 milliliters
Volume of colored water = 1.25 deciliters
=1.25 X 100 =125 milliliters
Therefore:
Volume of oil needed to fill the bottle = 600-125
=475 milliliters
Sam will need to add 475 milliliters of oil to the 0.6-liter bottle after adding 1.25 deciliters of colored water to create his homemade lava lamp.
Explanation:The question involves calculating the volume of oil needed to fill the remainder of a 0.6-liter bottle after adding some colored water. To solve this, we need to convert the measurements into the same units and perform subtraction. In this case, we convert deciliters to milliliters, as we know that 1 deciliter is equivalent to 100 milliliters. The student has filled the bottle with 1.25 deciliters of colored water, which is 1.25 × 100 milliliters = 125 milliliters of water.
Since the bottle can hold 0.6 liters, which is equal to 600 milliliters, the amount of oil required will be the total bottle capacity minus the volume of colored water already added. Thus, we calculate 600 milliliters (bottle capacity) – 125 milliliters (water added) to find the volume of oil needed.
So, Sam will need 600 mL – 125 mL = 475 milliliters of oil to fill the rest of his homemade lava lamp.
The operations manager of a manufacturer of television remote controls wants to determine which batteries last the longest in his product. He took a random sample of his remote controls and tested two brands of batteries. Here are the number of minutes of continuous use before the batteries failed for each brand. Is there statistical evidence of a difference in longevity between the two batteries?
Answer:
There is not enough evidence to support the claim that the longevity of the two brand of batteries differs.
Step-by-step explanation:
The question is incomplete:
The sample data for each battery is:
Battery 1: 106 111 109 105
Battery 2: 125 103 121 118
The mean and STD for the sample of battery 1 are:
[tex]M_1=\dfrac{1}{4}\sum_{i=1}^{4}(106+111+109+105)\\\\\\ M_1=\dfrac{431}{4}=107.75[/tex]
[tex]s_1=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s_1=\sqrt{\dfrac{1}{3}\cdot [(106-(107.75))^2+(111-(107.75))^2+(109-(107.75))^2+(105-(107.75))^2]}\\\\\\ s_1=\sqrt{\dfrac{1}{3}\cdot [(3.06)+(10.56)+(1.56)+(7.56)]}\\\\\\ s_1=\sqrt{\dfrac{22.75}{3}}=\sqrt{7.58333333333333}\\\\\\s_1=2.754[/tex]
The mean and STD for the sample of battery 2 are:
[tex]M_2=\dfrac{1}{4}\sum_{i=1}^{4}(125+103+121+118)\\\\\\ M_2=\dfrac{467}{4}=116.75[/tex]
[tex]s_2=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s_2=\sqrt{\dfrac{1}{3}\cdot [(125-(116.75))^2+(103-(116.75))^2+(121-(116.75))^2+(118-(116.75))^2]}\\\\\\ s_2=\sqrt{\dfrac{1}{3}\cdot [(68.06)+(189.06)+(18.06)+(1.56)]}\\\\\\ s_2=\sqrt{\dfrac{276.75}{3}}=\sqrt{92.25}\\\\\\s_2=9.605[/tex]
This is a hypothesis test for the difference between populations means.
The claim is that the longevity of the two brand of batteries differs.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
The significance level is α=0.05.
The sample 1, of size n1=4 has a mean of 107.75 and a standard deviation of 2.754.
The sample 2, of size n2=4 has a mean of 116.75 and a standard deviation of 9.605.
The difference between sample means is Md=-9.
[tex]M_d=M_1-M_2=107.75-116.75=-9[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{2.754^2+9.605^2}{4}}\\\\\\s_{M_d}=\sqrt{\dfrac{99.841}{4}}=\sqrt{24.96}=4.996[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-9-0}{4.996}=\dfrac{-9}{4.996}=-1.8014[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-1=4+4-2=6[/tex]
This test is a two-tailed test, with 6 degrees of freedom and t=-1.8014, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=2\cdot P(t<-1.8014)=0.122[/tex]
As the P-value (0.122) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the longevity of the two brand of batteries differs.
12 more than 8.2 times a number n is
Answer:
12+ 8.2n
Step-by-step explanation:
12 more than 8.2 times a number n is:
First, 12 more indicates that whatever we get has to add 12 on since it is 12 more.
Second, 8.2 times a number is multiplication and that number is filled in by a variable (n).
Therefore, the equation is 8.2n + 12
−15x + 60 ≤ 105 AND 14x + 11 ≤ −31
Answer:
X=-3
Step-by-step explanation:
The volume of a cube is 343 cubic inches. What is the length of each edge of the cube?
Answer:7 inches
Step-by-step explanation:
Volume of cube=343
volume of cube=length x length x length
length =L
Volume of cube=LxLxL
343=L^3
L^3=343
Taking the cube root of both sides we get
L=cube root of 343
L=7
Length =7 inches
Type the expressions as radicals.
[tex] \sqrt{ {q}^{3} } [/tex]
Step-by-step explanation:
[tex] {q}^{ \frac{3}{2} } = ( {q}^{3} )^{ \frac{1}{2} } = \sqrt{ {q}^{3} } \\ [/tex]
Multiply and simplify: (6x + 3y)(6x − 3y)
Answer:
36x² - 9y²
Step-by-step explanation:
We see that the given expression (6x + 3y)(6x - 3y) looks just like the expression (a + b)(a - b). When multiplied out, this is a difference of squares identity that I highly recommend you memorise:
(a + b)(a - b) = a² - b²
Here, a = 6x and b = 3y, so plug these in:
(6x + 3y)(6x - 3y) = (6x)² - (3y)² = 36x² - 9y²
Answer:
36x² - 9y²
Step-by-step explanation:
(6x + 3y)(6x − 3y)
(6x)² - (3y)²
36x² - 9y²
The cost, not including tax, of paper and pens
at the card store is $21.79. The tax is 9% of
the selling price. What is the total cost of the
pens and pencils including tax?
The volume of a cone is 565.2 cubic inches. The height of the cone is 15 inches. What is the radius of the cone, rounded to the nearest inch? (Use π = 3.14.) (1 point)
Group of answer choices
3
6
18
36
Answer:
Radius, r = 6 inches
Step-by-step explanation:
We have,
Volume of a cone is 565.2 cubic inches
Height of the cone is 15 inches
It is required to find the radius of the cone. Volume of a cone is given by :
[tex]V=\dfrac{1}{3}\pi r^2 h[/tex]
r is radius of cone
[tex]r=\sqrt{\dfrac{3V}{\pi h}} \\\\r=\sqrt{\dfrac{3\times 565.2}{3.14\times 15}} \\\\r=6\ \text{inch}[/tex]
So, the radius of the cone is 6 inches. The correct option is (b).
A car that normally sells for $20,000 is on sale for $16,000. What percent of the original price of the car is the final price?
Answer:
80%
Step-by-step explanation:
20000. take out 3 zeros from both numbers and you get 20 and 16. 20 is 4 times 5 and 16 is 4 times 4 if 20 is 100% then 4 over 5 is 80%
Use what you have learned about filing income taxes to complete these sentences.
If a citizen pays too much in taxes throughout the year, then after filing a tax return, he or she will receive a .
Employers supply a each January to help citizens file their tax returns.
Taxes returns can by filed either by mail or
Answer: refund, w-2, online
Answer:
See Explanation
Step-by-step explanation:
The W-2 form is a form which an employer must send to an employee and the Internal Revenue Service (IRS) at the end of each year. Every January, the employee should receive a Form W-2 Wage and Tax Statement from his/her employer. The contents of this form are the amount of money made by the employee during the previous year and how much was paid as tax.
Therefore, Employers supply a w-2 each January to help citizens file their tax returns.When a citizen gets their W-2 form for the previous year, they can use it to decide if they qualify for a tax refund which could be in cash or used towards the next years' tax.
If a citizen pays too much in taxes throughout the year, then after filing a tax return, he or she will receive a refund.Finally,
Taxes returns can by filed either by mail or online.Answer:
1. refund
2. w-2
3. online
corse hereo Joe has two drawers containing socks. The first contains three pairs of red socks, two pairs of black socks, and one pair of white socks. The second drawer contains two pairs of red socks, one pair of black socks, and two pairs of white socks. Each morning Joe flips a fair coin and picks two socks at random from the first drawer if heads is flipped; if tails is flipped he instead picks two socks at random from the second drawer. Joe is observed leaving his house this morning wearing one red and one black sock. What is the probability he flipped heads today?
Answer:
P(H/A) = 0.6716
Step-by-step explanation:
Let's call H the event that Joe flipped heads, T the event that Joe flipped tails and A the event that Joe wear one read and one black sock.
So, the probability that he flipped heads given that Joe wears one read and one black sock is calculated as:
P(H/A) = P(H∩A)/P(A)
Where P(A) = P(H∩A) + P(T∩A)
On the other hand, nCx gives the number of combinations in which we can select x elements from a group of n elements. nCx is calculated as:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, the probability that Joe wear one red and one black sock given that he picks the socks from the first drawer is:
[tex]\frac{6C1*4C1*2C0}{12C2}=0.3636[/tex]
Because he need to choose one red sock from the 6 that are in the first drawer, one black sock from the 4 that are in the first drawer and 0 white socks. Additionally there are 12C2 ways to choose a pair of socks.
Therefore the probability P(H∩A) that that Joe flipped heads and Joe wear one read and one black sock is:
P(H∩A) = 0.5*0.3636 = 0.1818
Because there is a probability of 0.5 to flipped heads and the probability that Joe wear one red and one black sock given that he flipped heads is 0.3636.
At the same way, the probability that Joe wear one red and one black sock given that he picks the socks from the second drawer is:
[tex]\frac{4C1*2C1*4C0}{10C2}=0.1778[/tex]
Therefore the probability P(T∩A) that that Joe flipped tails and Joe wear one read and one black sock is:
P(T∩A) = 0.5 * 0.1778 = 0.0889
Finally, P(A) and P(H/A) is equal to:
P(A) = 0.1818 + 0.0889 = 0.2707
P(H/A) = 0.1818/0.2707 = 0.6716
Suppose the true proportion of students at a college who study abroad is 0.25. I select a random sample of 40 students from the college and record if they have studied abroad. What is the probability that the proportion of students in my sample who have studied abroad is less than 0.2
Answer:
[tex]\mu_{\hat p} = 0.25[/tex]
[tex]\sigma_{\hat p}= \sqrt{\frac{0.25*(1-0.25)}{40}}= 0.0685[/tex]
[tex] z = \frac{0.2-0.25}{0.0685}= -0.730[/tex]
And we can use the normal standard distribution or excel to find this probability and we got:
[tex] P(\hat p <0.2) = P(z<-0.730)= 0.233[/tex]
Step-by-step explanation:
We define the parameter as the proportion of students at a college who study abroad and this value is known [tex]p =0.25[/tex], we select a sample size of n =40 and we are interested in the probability associated to the sample proportion, but we know that the distirbution for the sample proportion is given by:
[tex]\hat p \sim N(p , \sqrt{\frac{p(1-p)}{n}}[/tex]
And the paramters for this case are:
[tex]\mu_{\hat p} = 0.25[/tex]
[tex]\sigma_{\hat p}= \sqrt{\frac{0.25*(1-0.25)}{40}}= 0.0685[/tex]
We want to find the following probability:
[tex]P(\hat p< 0.2)[/tex]
For this case since we know the distribution for the sample proportion we can use the z score formula given by:
[tex] z = \frac{\hat p -\mu_{\hat p}}{\sigma_{\hat p}}[/tex]
Replacing the info given we got:
[tex] z = \frac{0.2-0.25}{0.0685}= -0.730[/tex]
And we can use the normal standard distribution or excel to find this probability and we got:
[tex] P(\hat p <0.2) = P(z<-0.730)= 0.233[/tex]
To find the probability that the proportion of students in your sample who have studied abroad is less than 0.2, you can use the normal distribution approximation for sampling proportions.
Explanation:To find the probability that the proportion of students in your sample who have studied abroad is less than 0.2, you can use the normal distribution approximation for sampling proportions. First, find the mean of the sampling distribution, which is equal to the true proportion (0.25) multiplied by the sample size (40), giving a mean of 10.
Next, find the standard deviation of the sampling distribution, which is calculated as the square root of (p(1-p)/n), where p is the true proportion (0.25) and n is the sample size (40). The standard deviation is approximately 0.071.
Finally, use the normal distribution to find the probability that the proportion is less than 0.2. Using the z-score formula, calculate the z-score as (sample proportion - mean)/(standard deviation). In this case, the z-score is approximately -1.41. Use a standard normal distribution table or calculator to find the corresponding probability, which is approximately 0.079.
Learn more about probability here:https://brainly.com/question/32117953
#SPJ3
The right rectangular prism below is made up of 8 cubes. Each cube has an edge length of 12inch.
What is the volume of this prism?
Answer:
13824 cubic inches
Step-by-step explanation:
So all we need to do is:
1) Find the volume of 1 cube of the 8
2) Multiply that by 8, because 8 of them make the prism.
SO 1)
the volume of cube = side * side * side = 12*12*12 = 1728
SO 2)
the volume of prism = vol(cube) * 8 = 1728 * 8 = 13824
ANSWER: 13824 cubic inches ;)
Brent’s after-school game club has 12 members from which a six-member team is created. Miguel’s after-school sports club has 10 members from which a six-member team is created. Which student’s club has more possible combinations for his six-member team?
Answer:
Brent
Step-by-step explanation:
More numbers = More combinations
Answer:
Brent’s club has more possible team combinations because there are more members to choose from.
Step-by-step explanation:
I completed it on edg 2020