Answer:
The smallest poster has dimension 25.6 cm by 32.05 cm.
Step-by-step explanation:
Let "x" and "y" be the length and the width of the poster.
The margin of a poster are 4 cm and the side margins are 5 cm.
The length of the print = x - 2(4) = x - 8
The width of the print = y - 2(5) = y - 10
The area of the print = (x- 8)(y -10)
The area of the print is given as 388 square inches.
(x-8)(y -10) = 388
From this let's find y.
y -10 = [tex]\frac{388}{(x - 8)}[/tex]
y = [tex]\frac{388}{x - 8} + 10[/tex] -------------------(1)
The area of the poster = xy
Now replace y by [tex]\frac{388}{x - 8} + 10[/tex], we get
The area of the poster = x ([tex]\frac{388}{x - 8} + 10[/tex])
= [tex]10x + \frac{388x}{x - 8}[/tex]
To minimizing the area of the poster, take the derivative.
A'(x) = [tex]10 + 388(\frac{-8}{(x-8)^{2} } )[/tex]
A'(x) = [tex]10 - \frac{3104}{(x-8)^2}[/tex]
Now set the derivative equal to zero and find the critical point.
A'(x) = 0
[tex]10 - \frac{3104}{(x-8)^2}[/tex] = 0
[tex]10 = \frac{3104}{(x-8)^2}[/tex]
[tex](x - 8)^2 = \frac{3104}{10}[/tex]
[tex](x - 8)^2 = 310.4[/tex]
Taking square root on both sides, we get
x - 8 = 17.6
x = 17.6 + 8
x = 25.6
So, x = 25.6 cm takes the minimum.
Now let's find y.
Plug in x = 25.6 cm in equation (1)
y = [tex]\frac{388}{25.6 - 8} + 10[/tex]
y = 22.05 + 10
y = 32.05
Therefore, the smallest poster has dimension 25.6 cm by 32.05 cm.
The minimum area of the poster given that the printed area is 388 sq.cm and the margins are 4cm top/bottom and 5cm on the sides, is found by using calculus and the area constraints. The problem can be solved by expressing width and height in terms of one another and then optimizing the area equation.
To solve the problem, we use calculus and the area constraint to find the dimensions with a minimum area. Let's denote that width of the poster is w and height is h. The entire area of the poster would then be expressed as:
(w+2*5cm)*(h+2*4cm) = poster area
On the other hand, we have a fixed constraint that states the printed area is 388cm², so we have:
w*h = 388 cm²
We can express h as 388/w and substitute this in the poster's area equation, and then use calculus to find the minimum area given these constraints.
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Gina was earning $10 per hour. Then she received a 10% pay rate increase. Next month, her pay rate will decrease by 10%. What will Gina's pay rate be next month?
Answer:
Gina's pay rate next month will be =$9.9 per hour
Step-by-step explanation:
Gina was initial earnings was = $10 per hour
She received an increase by = 10%
Increase in amount received = [tex]10\%\ of\ \$10= 0.1\times\$10 =\$1 [/tex]
New earnings = [tex]\$10+\$1=\$11[/tex] per hour
Next month her pay rate will decrease by = 10%
Decrease in pay rate next month will be = [tex]10\%\ of\ \$11= 0.1\times\$11 =\$1.1 [/tex]
Thus, Gina's pay rate next month will be = [tex]\$11-\$1.1=\$9.9[/tex] per hour
A political analyst found 43% of 300 randomly selected republican voters feel that the federal government has too much power. Find the 95% confidence interval of the population proportion of republican voters who feel this way.
Answer:
Step-by-step explanation:
We want to determine 95% confidence interval of the population proportion of republican voters who feel that the federal government has too much power.
43% of 300 randomly selected republican voters feel that the federal government has too much power. This means that
p = 43/100 = 0.43
q = 1 - p = 1 - 0.43 = 0.57
n = 300
mean, u = np = 300 × 0.43 = 129
Standard deviation, s = √npq = √129×0.57 = 8.575
For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.
We will apply the formula
Confidence interval
= mean +/- z ×standard deviation/√n
It becomes
129 +/- 1.96 × 8.575/√300
= 129 +/- 0.9704
= 129 +/- 0.9704
The lower end of the confidence interval is 129 - 0.9704 =128.0296
The upper end of the confidence interval is 129 + 0.9704 =129.9704
Therefore, with 95% confidence interval, the mean of the population proportion of republican voters who feel that the federal government has too much power is between 128.0296 and 129.9704
To find the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power, use the formula CI = p ± Z * √((p*(1-p))/n), where p is the sample proportion, Z is the Z-score for the desired confidence level, and n is the sample size. Given the sample proportion of 0.43, sample size of 300, and desired confidence level of 95%, the confidence interval is approximately 0.381 to 0.479.
Explanation:To find the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power, we can use the formula:
CI = p ± Z * √((p*(1-p))/n)
Where:
p is the sample proportionZ is the Z-score for the desired confidence level (in this case, 95%)n is the sample sizeGiven that the sample proportion is 0.43, the sample size is 300, and the desired confidence level is 95%, we can calculate the 95% confidence interval:
CI = 0.43 ± 1.96 * √((0.43*(1-0.43))/300)
Simplifying the equation, we get:
CI = 0.43 ± 0.049
Therefore, the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power is approximately 0.381 to 0.479.
99 POINTS BRAINLIEST!! no fake answers please!
In a game, you have a 1/36 probability of winning $94 and a 35/36 probability of losing $8. What is your expected value?
ALSO ANSWER QUESTIONS IN PICTURE, THANK YOU
I think the answer would be -$5.17 because you would have to find the unexpected value.
I think the answer to this picture is 0.122
Game:
1/36(94) + 35/36(-8) = 94/36 -280/36 = -186/36 = -5.17
4. Add the probabilities together for 5 and under:
0.122 + 0.061 + 0.022 + 0.006 + 0.001 = 0.212
Airline :
Given: P = 70, P = 97% = 0.97, q = 1-0.97 = 0.03
Probability of being greater than 68:
(70 * 0.97^69 * 0.03^1) + (1*0.97^70*1)
= 0.2567 + 0.1185
= 0.375
Calc AB! Please show work, the answers are provided. I need all work for part A AND B!!!
Need ASAP!
Step-by-step explanation:
24. A
B' ( t ) = 10 [ 20 CDS ( t/10) ] = 2 COS ( t/10 )
B' ( 7 ) = 1.5
After 7 days the number of beds in use is increasing at the rate of 1 1/2 beds per day.
24.B
2 COS ( t/10) =0
using calculator t = 15.7
B (12) = 20 Sin (1.2) + 50 = 68.6 = 69
B (15.7) = 20 Sin (1.57) + 50 = 70
B (20) = 20 SIn (20) + 50 = 68.25 = 68
Maximum number of beds in use occurs in afternoon of 15th day and is 70 beds.
I hope that helps and I hope it's right
the probabilities that a b and c can solve a particular problem are 3/5 2/3 and 1/2 respectively if they all try determine the probability that at least one of the group solves the problem
Answer: The required probability is [tex]\dfrac{14}{15}.[/tex]
Step-by-step explanation: Given that the probabilities that A, B and C can solve a particular problem are [tex]\dfrac{3}{5},~ \dfrac{2}{3},~\dfrac{1}{2}[/tex] respectively.
We are to determine the probability that at least one of the group solves the problem , if they all try.
Let E, F and G represents the probabilities that the problem is solved by A, B and C respectively.
Then, according to the given information, we have
[tex]P(E)=\dfrac{3}{5},~~~P(F)=\dfrac{2}{3},~~P(G)=\dfrac{1}{2}.[/tex]
So, the probabilities that the problem is not solved by A, not solved by B and not solved by C are given by
[tex]P\bar{(A)}=1-P(A)=1-\dfrac{3}{5}=\dfrac{2}{5},\\\\\\P\bar{(B)}=1-P(B)=1-\dfrac{2}{3}=\dfrac{1}{3},\\\\\\P\bar{(C)}=1-P(C)=1-\dfrac{1}{2}=\dfrac{1}{2}.[/tex]
Since A, B and C try to solve the problem independently, so the probability that the problem is not solved by all of them is
[tex]P(\bar{A}\cap \bar{B}\cap \bar{C})=P(\bar{A})\times P(\bar{B})\times P(\bar{C})=\dfrac{2}{5}\times\dfrac{1}{3}\times\dfrac{1}{2}=\dfrac{1}{15}.[/tex]
Therefore, the probability that at least one of the group solves the problem is
[tex]P(A\cup B\cup C)\\\\=1-P(\bar{A\cup B\cup C})\\\\=1-P(\bar{A}\cap \bar{B}\cap \bar{C})\\\\=1-\dfrac{1}{15}\\\\=\dfrac{14}{15}.[/tex]
Thus, the required probability is [tex]\dfrac{14}{15}.[/tex]
Final answer:
To find the probability that at least one of A, B, or C solves the problem, calculate 1 minus the probability that none solve it. The individual non-solving probabilities are multiplied together and subtracted from 1, resulting in a final answer of 14/15.
Explanation:
To determine the probability that at least one person out of A, B, and C solves a problem, we must first understand that the probability of at least one event occurring equals 1 minus the probability that none of the events occur (in this case, that none of the people solve the problem).
We have the individual probabilities as follows:
Probability A solves the problem: 3/5
Probability B solves the problem: 2/3
Probability C solves the problem: 1/2
The probabilities that A, B, or C do not solve the problem are then 1 - (3/5), 1 - (2/3), and 1 - (1/2), respectively. To find the probability that none of them solve the problem, we multiply these probabilities:
P(none solve) = (1 - 3/5) × (1 - 2/3) × (1 - 1/2)
Calculating this gives us P(none solve) = (2/5) × (1/3) × (1/2) = 2/30 = 1/15. Thus, the probability that at least one person solves the problem is:
P(at least one solves) = 1 - P(none solve) = 1 - 1/15 = 14/15.
find the quotient following this pattern
image attached
Answer:
x ^5 + x ^4 + x ^3 + x ^2 + x + 1
Answer:
The answer to your question is below
Step-by-step explanation:
[tex]\frac{x^{6}- 1 }{x -1} = \frac{x^{6}+ 0x^{5} + 0x^{4} + 0x^{3} + 0x^{2} + 0x - 1 }{x - 1}[/tex]
Synthetic division
1 0 0 0 0 0 -1 1
1 1 1 1 1 1
1 1 1 1 1 1 0
Quotioent = x⁵ + x⁴ + x³ + x² + x
Remainder = 0
Mofor's school is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 7 adult tickets and 6 tickets for a total of $143. The school took in $187 on the second day by selling 4 adult tickets and 13 student tickets. Find the price of an adult ticket and the price of a student ticket.
Answer: the price of an adult ticket is $11
the price of a child ticket is $11
Step-by-step explanation:
Let x represent the price of an adult ticket.
Let y represent the price of a student ticket.
On the first day of ticket sales the school sold 7 adult tickets and 6 student tickets for a total of $143. This means that
7x + 6y = 143 - - - - - - - - - -1
The school took in $187 on the second day by selling 4 adult tickets and 13 student tickets. This means that
4x + 13y = 187 - - - - - - - - - -2
Multiplying equation 1 by 4 and equation 2 by 7, it becomes
28x + 24y = 572
28x + 91y = 1309
Subtracting
-67y = -737
y = -737/-67 = 11
Substituting y = 11 into equation 1, it becomes
7x + 6×11 = 143
7x + 66 = 143
7x = 143 - 66 = 77
x = 77/7 = 11
On Saturday,4 friends ordered a large pizza to share altogether they pay 9.80 for the pizza . They share the cost equally .How much does each person pay?
Answer:
each paid $2.45
Step-by-step explanation:
9.80/4 = 2.45
Radiation machines, used to treat tumors, produce an intensity of radiation that varies inversely as the square of the distance from the machine. At 3 meters, the radiation intensity is 62.5 milliroentgens per hour. What is the intensity at a distance of 2.7 meters?The intensity is______milliroentgens per hour. (Round to the nearest tenth as needed.)
The intensity at a distance of 2.7 meters is 77.17 milliroentgens per hour.
Given:
I= 62.5 milliroentgens per hour
Distance = 3 meters
If the intensity of radiation varies inversely as the square of the distance from the machine, use the inverse square law formula:
[tex]I = k/d^2[/tex]
Where:
I represents the intensity of radiation,
k is a constant,
d represents the distance from the machine.
Substituting the value back to formula as
62.5 = k/(3²)
62.5 = k/9
k = 62.5 x 9
k = 562.5
So, the intensity at a distance of 2.7 meters:
I = 562.5/(2.7²)
I = 562.5/7.29
I = 77.17 milliroentgens per hour
Therefore, the intensity is 77.17 milliroentgens per hour.
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The intensity of radiation from a machine at a distance of 2.7 meters is 77.16 milliroentgens per hour, according to the inverse square law in Physics.
Explanation:The question is related to inverse square law in Physics. The intensity (ℤ) of radiation varies inversely as the square of the distance (d) from the machine. Mathematically, this relationship is represented as ℤ = k/d^2 where k is a constant. Given that at a distance of 3 meters, the intensity is 62.5 milliroentgens per hour, we can find the constant k = ℤ * d^2, i.e., k = 3^2 * 62.5 = 562.5.
Now, you want to know the intensity at a distance of 2.7 meters, which we can find by substituting this value and the constant k in our equation: ℤ = k/d^2, which results in ℤ = 562.5/(2.7^2) = 77.16 milliroentgens per hour. Therefore, the intensity at a distance of 2.7 meters from the radiation machine is 77.16 milliroentgens per hour.
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The sum of both digits, of either of two two-digit numbers , in whatever order the digits are written, is 9. The square of either of the digits of either number, minus the product of both digits, plus the square of the other digit is the number 21. The numbers are?
a. 36, 63
b. 81, 18
c. 27, 72
d. 45, 54
e. none
Answer:
(d.) 45, 54
Step-by-step explanation:
Let the first digit = y
Let the second digit = z
y +z = 9 ------------------------------------------ (1)
y²- yz +z² = 21------------------------------------(2)
From equation (2),
z = 9-y-------------------------------------------------(3)
Substitute equation (3) into (2):
y²- y(9-y) +(9-y)² = 21
y²-9y+y²+y²-18y+81 = 21
3y²-27y+ 81 = 21
3y²-27y+ 81-21= 0
3y²-27y+ 60= 0
y²- 9y +20= 0
(y -5) (y-4) =0
y= 5 or y =4
z = 4 or 5 (substituting into (3))
So the numbers are 54 or 45.
A volleyball league collected $2,040 for both division of volleyball teams the blue division costs &160 per team and the red division costs $180 per team.How many teams will play in each division
Answer:
There are 6 teams will play for each team.
Step-by-step explanation:
Given;
Total amount of money = $ 2040
Cost for blue team = $ 160
Cost for red team = $ 180
Solution,
Let number of blue teams be x and the number of red teams be y.
Total cost =[tex]160x + 180y = 2040[/tex]
Since it is a league match and so both divisions must have equal teams.
∴ x=y
∴ [tex]160x + 180x = 2040[/tex]
[tex]340x = 2040\\x = 6[/tex]
Hence the number of teams in each division is 6.
Two non-common sides of adjacent supplementary angles form a _____ angle.
A. reflex
B. acute
C. straight
D. obtuse
Answer:
C. straight
Step-by-step explanation:
A Linear Pair is two adjacent angles whose non-common sides form opposite rays.
If two angles form a linear pair, the angles are supplementary.
A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary.
In the figure given in attachment, AB and BC are two non common sides of ∠ABD and ∠DBC.
∠1 and ∠2 form a linear pair.
The line through points A, B and C is a straight line.
∠1 and ∠2 are supplementary.
Thus two non-common sides of adjacent supplementary angles form a straight angle.
circles pls help decent amount of points
The volume of a cylinder is 4x3 cubic units and its height is x units.
Which expression represents the radius of the cylinder, in units?
2x
4x
2pi x²
4pi x2
Answer:
The answer to your question is r = 2x
Step-by-step explanation:
Volume of a cylinder = V = π r² h
r = radius
h = height = x
Volume = 4x³
Then
r² = [tex]\frac{volume}{\pi h}[/tex]
r² = [tex]\frac{4x^{3} }{\pi x}[/tex]
r² = 4x²
r = 2x
Assume that the heights of men are normally distributed with a mean of 66.9 inches and a standard deviation of 2.1inches. If 36 men are randomly selected, find the probability that they have a mean height greater than 67.9 inches.
A. 0.0021
B. 0.0210
C. 0.9979
D. 0.9005
Answer:
A. 0.0021
Step-by-step explanation:
Given that the heights of men are normally distributed with a mean of 66.9 inches and a standard deviation of 2.1inches.
Sample size = 36
Std dev of sample = [tex]\frac{2.1}{\sqrt{36} } =0.35[/tex]
The sample entries X the heights are normal with mean= 66.9 inches and std deviation = 0.35 inches
Or we have
Z = [tex]\frac{x-66.9}{0.35}[/tex]
Hence the probability that they have a mean height greater than 67.9 inches
=[tex]P(X>67.9)\\=P(Z>\frac{1}{0.35)} \\=0.00214[/tex]
So option A is right answer.
Final answer:
To find the probability that the mean height of 36 randomly selected men is greater than 67.9 inches, calculate the z-score and find the corresponding area under the standard normal distribution curve.
Explanation:
To find the probability that the mean height of 36 randomly selected men is greater than 67.9 inches, we need to calculate the z-score and find the corresponding area under the standard normal distribution curve.
The z-score is calculated using the formula:
z = (x - μ) / (σ / √n)
Where x is the value we want to find the probability for, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the given values into the formula, we have:
z = (67.9 - 66.9) / (2.1 / √36) = 1.71
Using a standard normal distribution table or a calculator, we can find that the area to the right of a z-score of 1.71 is approximately 0.0436.
Since we want the probability of having a mean height greater than 67.9 inches, we need to calculate the area to the right of the z-score. Therefore, the probability is approximately 1 - 0.0436 = 0.9564.
Given that Ray E B bisects ∠CEA, which statements must be true? Select three options. m∠CEA = 90° m∠CEF = m∠CEA + m∠BEF m∠CEB = 2(m∠CEA) ∠CEF is a straight angle. ∠AEF is a right angle.
The statements that must be true are:
a. m∠CEA = 90°
b. m∠CEF = m∠CEA + m∠BEF
e. ∠AEF is a right angle.
Here's why:
a. m∠CEA = 90°
The diagram shows a small square marking ∠CEA, which is the standard notation for a right angle, indicating it measures 90 degrees.b. m∠CEF = m∠CEA + m∠BEF
This statement is true by the Angle Addition Postulate, which states that the measure of an angle formed by two adjacent angles is equal to the sum of their individual measures. In this case, ∠CEF is formed by ∠CEA and ∠BEF, so its measure is the sum of their measures.c. m∠ CEB = 2(m∠ CEA)
This statement is not true. Since EB bisects ∠CEA, it divides it into two equal angles, meaning m∠CEB = m∠CEA, not twice its measure.d. ∠ CEF is a straight angle.
This statement is not necessarily true. A straight angle measures 180 degrees, and we don't have enough information to determine if ∠CEF has that measure.e. ∠ AEF is a right angle.
This statement is true. Since EB bisects ∠CEA, which is a right angle, it creates two right angles: ∠CEB and ∠AEF.You have $10 to spend on charms and stickers. The equation 0.5x + 0.25y=10 represents this situation, where x is the number of charms and y is the number of stickers. How many stickers can you buy when you do not buy any charms?
Answer:
40
Step-by-step explanation:
Since your only buying stickers you divide 10 by 0.25 to see how many you can purchase.
Answer:
It means a sticker costs $0.25 and a charm costs $0.5
Therefore without buying any charm
You can use $10 to buy 10/0.25
40 stickers
Step-by-step explanation:
sec^-1(csc(-45))
help me figure this out pleaseee
Answer: -1.17522136 hertz
there you go :) just to let you know I’m in 7th
Find the number solutions of the equation
Answer:
A. 0
Step-by-step explanation:
The value of the discriminant is ...
b² -4ac = (-3)² -4(1)(4) = 9 - 16 = -7
The negative discriminant means the roots will be complex.
There are 0 real solutions.
A private plane traveled from Seattle to a rugged wilderness, at an average speed of 312312 mph. On the return trip, the average speed was 364364 mph. If the total traveling time was 44 hours, how far is Seattle from the wilderness?
Final answer:
The distance from Seattle to the rugged wilderness, calculated using the average speeds and total travel time, is found to be 7424 miles.
Explanation:
Given that a private plane traveled to and from a rugged wilderness, with average speeds of 312 mph on the way to the wilderness and 364 mph on the return trip to Seattle, and the total flying time for round trip was 44 hours, we can calculate the distance by using the formula for average speed, which is average speed = total distance/total time.
Let's denote the distance between Seattle and the wilderness as x miles. The time taken to fly to the wilderness is then x/312 and the time taken to fly back is x/364.
The total flying time of 44 hours can be split into the sum of the time going to the wilderness and coming back, which gives us:
(x/312) + (x/364) = 44.
To solve for x, we need to find a common denominator and solve the equation.
Common denominator for 312 and 364 is 114,048.
Convert the equation: (364x + 312x) / 114048 = 44.
Multiply both sides by 114048: 676x = 5018112.
Divide both sides by 676: x = 7424.
Therefore, the distance from Seattle to the rugged wilderness is 7424 miles.
You have the opportunity to lease space for your business with a fixed-rate lease. The property owner has proposed a three-year lease with a rent of $3,800 per month. How much is the rent over the life of the lease?a) $129,240b) $129,440c) $136,800d) $139,240
Answer:
Easy, it is C) $136,800
Step-by-step explanation:
All you need to do is multiply $3,800 by 12 to get the yearly rent. To get $45,600 per year. You now multiply $45,600 by 3 to get the total price of the 3 year lease. You now have a total cost of $136,800 over the 3 year time period of the lease.
Last year Ariq made 6 1-cup servings of soup for a party this year you will make 8 times the amount of soup that he made last year how many gallons of soup will he make this year?
Answer:
3 gallons
Step-by-step explanation:
He will make 8×(6 cups) = 48 cups of soup. There are 16 cups in a gallon, so 3·16 = 48 cups in 3 gallons.
Ariq will make 3 gallons of soup this year.
Olivia and her three siblings bring a sack lunch to school each day, consisting of a bagel, an apple, a cookie, and a juice box. When Olivia's mom goes grocery shopping, she likes to purchase the same amount of each lunch item so that she can make complete lunches, with no leftover items. However, each item comes in a different sized package, as shown below: Bagels: six in a bag Apples: eight in a bag Cookies: twelve in a box Juice Boxes: nine in a box Find the least number of packages she must purchase in order to have the same amount of each item. With the amount of items Olivia's mom is purchasing, she'll be able to make enough lunches to feed all four siblings for days.
Answer:
72/4=18 so she could make their lunch for 18 days
Step-by-step explanation:
so it would be 6x12 for the bagels which would be 72
for the apples it would be 8x9 which is 72
the cookies would be 12x6 to get 72
and the juice boxes would be 9x8 to get 72
divide that by 4 to get 18
When 3010 adults were surveyed in a poll, 27% said that they use the Internet. Is it okay for a newspaper reporter to write that "1 divided by 4 of all adults use the Internet"? Why or why not? Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.
The test statistic is z = ?. (Round to two decimal places as needed.)The P-value is ?. (Round to four decimal places as needed.)Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim. (Assume a 0.05 significance level.)
Answer:
Null hypothesis:[tex]p=0.25[/tex]
Alternative hypothesis:[tex]p \neq 0.25[/tex]
z=2.53
pv=0.0114
So based on the p value obtained and using the significance given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they use the Internet differs from 0.25 or 25% .
Step-by-step explanation:
1) Data given and notation
n=3010 represent the random sample taken
X represent the people who says that said that they use the Internet.
[tex]\hat p=\frac{X}{106}=0.27[/tex] estimated proportion of people who says that said that they use the Internet.
[tex]p_o=0.25[/tex] is the value that we want to test
[tex]\alpha[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that 50% of people who says that they would watch one of the television shows.:
Null hypothesis:[tex]p=0.25[/tex]
Alternative hypothesis:[tex]p \neq 0.25[/tex]
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.27 -0.25}{\sqrt{\frac{0.25(1-0.25)}{3010}}}=2.53[/tex]
4) Statistical decision
P value method or p value approach . "This method consists on determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
We have the significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z>2.53)=2*(0.0057)=0.0114[/tex]
So based on the p value obtained and using the significance given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they use the Internet differs from 0.25 or 25% .
H-20
———— = 0
-3
Solve for h
Answer:
H = 30
Step-by-step explanation:
The value of a fraction is zero when its numerator is zero. The value of h that makes the numerator zero is 20.
h = 20
Consider the following class declaration: class Thing { private: int x; int y; static int z; public: Thing() { x = y = z; } static void putThing(int a) { z = a; } }; int Thing:: z = 0: Assume a program containing the class declaration defines three Thing objects with the following statement: Thing one, two, three; A) How many separate instances of the x member exist? B) How many separate instances of the y member exist? C) How many separate instances of the z member exist? D) What value will be stored in the x and y members of each object?
There are 3 individual instances of each of the 'x' and 'y' members, while there's only one instance of static member 'z'. The value of 'x' and 'y' members in each object is 0.
Explanation:The subject of this question pertains to class declarations in the field of programming, with a focus on how variables are instantiated among objects of a class. Specifically, the interest is on the number of instances and values of private and static member variables in the class Thing which includes private int x, private int y and static int z.
A) For every new object created from the class Thing, new instances of x are also created. Since Thing one, two, three created three objects, that means there are three separate instances of the x member.B) Similar to x, there are also three separate instances of the y member, since it is an non-static member variable, and each object has its own copy of non-static member variables.C) Unlike x and y, there is only one instance of the static member z. Static members are shared among all objects of a class, so no matter how many objects are created, there is only one z. D) In the Thing constructor, 'x = y = z' sets the x and y members for each object to the value of z which in this case, as defined in 'int Thing:: z = 0', means that x and y for each object will have the value 0.Learn more about Class Declarations here:https://brainly.com/question/32923899
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Final answer:
There are three separate instances each of the non-static members x and y, one instance of the static member z, and since the constructor initializes x and y to z's value, they will both have the value 0.
Explanation:
The question involves understanding the concept of members and static members in the C++ programming language, specifically within the context of class instances. When considering the provided class declaration and the creation of three instances of the Thing class, we are dealing with object-oriented programming principles.
A) Each instance of a class has its own separate set of non-static members. Since x is a non-static member and we have three instances, there are three separate instances of the x member.
B) Similarly, y is a non-static member. Thus, there are also three separate instances of the y member.
C) The z member is declared as static, meaning that it is shared across all instances of the class. Therefore, there is only one instance of the z member that exists across all instances of the class.
D) Because the constructor initializes x and y with the value of z, and z is initially set to 0, the value stored in the x and y members of each object will be 0.
The music department of a department store sold 12 jazz CDs last month. Jazz sales during that month made up 2% of the music departments total sales. Determine the number of CDs that the store sold during that month
12 CDs ............... 2 %
x CDs .............100 %
x = 12×100/2 = 1200/2 = 600 Cds/month
The required number of CD that was sold last month is 600 CD's.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the number of total CDs sold be x,
The music department of a department store sold 12 jazz CDs last month.
Jazz sales during that month made up 2% of the music department's total sales.
2% of x = 12
x = 12 / 2%
x = 12 / 0.02
x = 600
Thus, the required number of CD that was sold last month is 60 CD's.
Learn more about percentages here:
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Please Help!
30. Write an equation in point-slope form for the line through the given point with the given slope. (-7,9); m=4/5
A. y+7= 4/5(x-9)
B. y-7=4/5(x+9)
C. y-9=4/5(x+7
D. y+9=4/5(x-7)
Answer:
C. [tex]y - 9 = \frac{4}{5}(x + 7)[/tex]
Step-by-step explanation:
The equation of a straight line through a point [tex](x_{1}, y_{1})[/tex] with slope m is given by
[tex]y - y_{1} = m(x - x_{1})\\y - 9 = \frac{4}{5}(x - (-7))\\y - 9 = \frac{4}{5} (x + 7)[/tex]
Therefore the answer is C. [tex]y - 9 = \frac{4}{5}(x + 7)[/tex]
you guysss pls help me
Answer:
option B)[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
According to the given conditions, the total number of outcomes are 24.
The probability that of drawing hearts card is
P=[tex]\frac{(total number of hearts cases)}{(total number of cases)}[/tex]
total number of hearts cases= 6
thus P= [tex]\frac{6}{24} = \frac{1}{4}[/tex]
now the probability of 4 or 6 is,
P=[tex]\frac{(total number of 4 or 6 cases)}{(total number of cases)}[/tex]
thus P= [tex]\frac{8}{24} = \frac{1}{3}[/tex]
thus, by multiplication law,
final probality is P= [tex](\frac{1}{4})(\frac{1}{3})[/tex]
P= [tex]\frac{1}{12}[/tex]
A soccer ball is thrown upward from the top of a 204 foot high building at a speed of 112 feet per second. The soccer ball's height above ground can be modeled by the equation . When does the soccer ball hit the ground?
Answer:
8.5 seconds to hit the ground
Step-by-step explanation:
A soccer ball is thrown upward from the top of a 204 foot high building at a speed of 112 feet per second.
[tex]h(t)=-16t^2+V_0t+h_0[/tex]
Vo is the speed 112 feet per second
h0 is the initial height = 204 foot
So the equation becomes
[tex]h(t)=-16t^2+112t+204[/tex]
When the soccer ball hit the ground then the height becomes 0
[tex]0=-16t^2+112t+204[/tex]
Apply quadratic formula
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]t=\frac{-112+\sqrt{112^2-4 (-16) \cdot 204}}{2(-16)}[/tex]
[tex]t=\frac{-112+\sqrt{25600}}{-32}=-1.5[/tex]
[tex]\frac{-112-\sqrt{25600}}{-32}=8.5[/tex]
time cannot be negative
so it takes 8.5 seconds to hit the ground