Using the Central Limit Theorem, it is found that the standard deviation is of 0.0971.
What does the Central Limit Theorem states?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].It also states that when two variables are subtracted, the standard deviation is the square root of the sum of the variances.In this problem, for each sample, the standard error is given by:
[tex]s_I = \sqrt{\frac{0.25(0.75)}{50}} = 0.0612[/tex]
[tex]s_{II} = \sqrt{\frac{0.35(0.65)}{40}} = 0.0754[/tex]
Hence, for the distribution of differences, it is given by:
[tex]s = \sqrt{s_I^2 + s_{II}^2} = \sqrt{0.0612^2 + 0.0754^2} = 0.0971[/tex]
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3.
Which system of equations has infinite solutions? Select all that apply.
A. y = 4x + 4
y=x - 4
B. y = -2x + 4
y=x+4
-6
C. y=4
x=-2
D. y = 5x + 3
3y = 15x +9
Answer:
B and D
Step-by-step explanation:
in D 15x+9=15x+9
in B x=0
Jamie needs to lease a car. At Big City Nissan, Jamie can lease an Altima for $3,000 down plus $420 per month. Big City will also give her the first two months of her lease free. At Rye Town Nissan, they offer her the same car for $3960 down plus $400 per month. Rye Town will give her the first four months free. After how many months would both deals cost the same?
Answer:
90 months
Step-by-step explanation:
Let x = number of months
Let y = total cost of deal
Big City Nissan
y = 3000 + 420x - 840
⇒ y = 2160 + 420x
Rye Town
y = 3960 + 400x
Equate the equations and solve for x
2160 + 420x = 3960 + 400x
⇒ 420x - 400 x= 3960 - 2160
⇒ 20x = 1800
⇒ x = 90
Ann sells beaded necklaces. Each large necklace sells for $5.40 and each small necklace sells for $4.30. How much will she earn from selling 3 large necklaces and 1 small necklace?
Answer
20.5
Step-by-step explanation:
You multiply 5.4 and 3 to get 16.2. Then you add 16.2 and 4.3 to get 20.5.
FIRST TO ANSWRR GETS 30 POINTS!
A jewellery shop is having a sale.
A bracelet is now reduced to £420.
This is 70% of the original price.
a) Work out the original price of the bracelet.
A ring is now reduced to £840.
This is a saving of 40% of the original price.
b) Work out the original price of the ring.
Answer:
a) £600
b) £1400
Step-by-step explanation:
a) Set up a ratio of price to percentage of original price.
Let x = original price
⇒ £420 : 70 = £x : 100%
[tex]\sf \implies 420 : 70 = x : 100[/tex]
[tex]\sf \implies \dfrac{420}{70}=\dfrac{x}{100}[/tex]
[tex]\sf \implies x=100\cdot\dfrac{420}{70}[/tex]
[tex]\sf \implies x=600[/tex]
Therefore, the original price of the bracelet was £600
b) Set up a ratio of price to percentage of original price.
If the ring is reduced by 40% then it is now 60% of the original price, since 100% - 40% = 60%
Let x = original price
⇒ £840 : 60% = £x : 100%
[tex]\sf \implies 840 : 60 = x : 100[/tex]
[tex]\sf \implies \dfrac{840}{60}=\dfrac{x}{100}[/tex]
[tex]\sf \implies x=100\cdot\dfrac{840}{60}[/tex]
[tex]\sf \implies x=1400[/tex]
Therefore, the original price of the ring was £1400
I NEED THAT ANSWER ASAP
Answer:
2064.19 km^3
Step-by-step explanation:
Formula for volume of a sphere
V = 4/3 pi r^3
= 4/3 * 3.14 * 7.9^3 =
Answer:
[tex]2064\ km^3[/tex]
Step-by-step explanation:
Volume of a Sphere: [tex]\frac{4}{3}\pi r^3[/tex]
r (radius) = 7.9 km[tex]V=\frac{4}{3}\pi r^3[/tex]
[tex]V=\frac{4}{3}*3.14*(7.9)^3 \\\\V=\frac{4}{3}*3.14*493.039\\\\V=\frac{4}{3}*1548.142\\\\V=\frac{4}{3}*\frac{1548.142}{1}\\\\V=\frac{6192.568}{3}\\\\V=2064.18933 < == round\ to\ the\ nearest\ whole\ number\\\\V=2064\ km^3[/tex]
Therefore, the volume of the sphere is [tex]2064\ km^3[/tex]
Hope this helps!
calculate the value of s and t
Answer:
s = 4, t = 1.2.
Step-by-step explanation:
y = k/x (Inverse variation, k is some constant)
Substituting:
2 = k/3
k = 2*3 = 6
So the relation is y = 6/x.
So 1.5 = 6/s
s = 6/1.5 = 4.
t = 6/5 = 1.2.
Videos Incorporated charges a membership fee of $4.99 plus $0.99 for each movie you watch. Videos Plus does not charge a membership fee but charges $2.99 per movie. Videos Plus is a better deal than Videos Incorporated. Which inequality represents this situation?
What is the inequality symbol for the situation? Answer Chocies: >, <, =.
Videos Incorporated Expression: Answer choices: 4.99x + 0.99, 4.99 + 0.99x, 4.99 - 0.99x
Videos Plus Expression: Answer Choices: 2.99x, 2.99x + 1, 2.99x - 1.
Which inequality represents this situation?
Videos Incorporated Expression:
-> Starting membership fee of $4.99, and then adding onto the overall cost is $0.99 for every movie watched.
4.99 + 0.99x
Videos Plus Expression:
-> There is no membership fee, but adding to the cost is $2.99 per movie.
2.99x
Which inequality represents this situation?
-> You do not have answer options, so this is a guess.
-> It states that "Videos Plus is a better deal than Videos Incorporated" which means Videos Incorporated costs more than Videos Plus
2.99x < 4.99 + 0.99x
Simplify the equation
X^2 +x
x^2 + x
---Both of these terms both contain an x, which means we can factor out one x.
x(x + 1)
Simplified: x(x + 1)
Hope this helps!
Tiffany ate ¼ of a pizza. If there were 16 slices of pizza to begin with, how many slices did Tiffany eat?
Answer:
she ate 4 slices
Step-by-step explanation:
Answer:
1/4 × 16
=4
therefore she ate 4 slices
use the intersect method to solve the equation
-2x+1=-x^2+4
The intersect method involves spliting an equation to a system of equations
The solutions to the equation are (-1, 3) and (3,-5)
How to solve the equation?The equation is given as:
-2x + 1 = -x^2 + 4
Using the intersect method, we have the following equations
y = -2x + 1
y = -x^2 + 4
Next, we plot the graph of both equations
From the graph (see attachment), we have the following points of intersection
(x,y) = (-1, 3) and (3,-5)
Hence, the solutions to the equation are (-1, 3) and (3,-5)
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Help plsss 60 points
Step-by-step explanation:
please mark me as brainlest
Answer:
a) 5, -3, -4, 0
b) Curve B
Step-by-step explanation:
Given equation:
[tex]y=x^2-4x[/tex]
Inputting the values of x into the equation to find the missing values of y:
[tex]x=-1 \implies y=(-1)^2-4(-1)=5[/tex]
[tex]x=1 \implies y=(1)^2-4(1)=-3[/tex]
[tex]x=2 \implies y=(2)^2-4(2)=-4[/tex]
[tex]x=4 \implies y=(4)^2-4(4)=0[/tex]
[tex]\large\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} x & -1 & 0 & 1 & 2 & 3 & 4 & 5\\\cline{1-8} y & 5 & 0 & -3 & -4 & -3 & 0& 5\\\cline{1-8}\end{array}[/tex]
According to the table:
y-intercept of the curve = (0, 0)x-intercept of the curve = (4, 0)Therefore, Curve B matches the graph of [tex]y=x^2-4x[/tex]
which of the follwing is true?
Answer:
The correct one is B)
Step-by-step explanation:
Dividing with the same base subtracts the power
The table shows the number of points Malik and Alexia scored while playing a video game together.
The table is titled Video Game Scores. The table has two columns and three rows. The first column is labeled Malik's Score represented by m, the second column is labeled Alexia's Score represented by a. Malik scored sixty, Alexia scored ninety. Malik scored seventy, Alexia scored one hundred. Malik scored eighty, Alexia scored one hundred ten.
Which equation relates Alexia’s score, a, to Malik’s score, m
Answer:
a = m+30
Step-by-step explanation:
malik is always 30 points under alexia so in order for malik to be equal to alexia he would have to add an additional 30. i hope this helps :)
A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole. A right triangle with side length 10 feet, hypotenuse of 22 feet, and side of h. What is the height of the pole? Round to the nearest hundredth. 12. 00 feet 19. 60 feet 24. 17 feet 38. 40 feet.
The height of the pole from the ground is 19.60 feet round to the nearest hundredth.
How to find the length of longest side in right angle triangle?To find the lenght of longest side in right angle triangle, the Pythagoras theorem is used.
According to this theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole.
A right triangle with side length 10 feet, hypotenuse of 22 feet, and side of h. Thus, the length of side of h by the Pythagoras theorem can be given as,
[tex]h^2=22^2-10^2\\h=\sqrt{484-100}\\h=\sqrt{384}\\h=19.60\rm\; ft[/tex]
Thus, the height of the pole from the ground is 19.60 feet round to the nearest hundredth.
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(За + 2b) (2а — b) HELP ME PLEASE
Answer:
6a^2 + ab - 2b^2
Step-by-step explanation:
[insert something smart]
Choose the amount of money that is equal to 1 dollar 1 nickel.
25 nickels
21 nickels
22 nickels
23 nickels
HELLPPPP!!
So that is how it goes hope this helps
Answer: I think the answer is 25 nickels? Im sorry if I get it wrong
Step-by-step explanation:
Debbie has 65 tubs of yogurt and 16 boxes of granola. All four kids continue to eat the same amount of food each morning. Which kind of food will get used up first?_________
show your calculations and explain how you figured it out.
The kind of food that will finish and get used up first is the boxes of granola.
What is word problem?Word problem in mathematics is the use of critical understanding of the problem which then employs basic arithmetic operations, fractions, ratios, algebraic expression, etc to solve real-life problems.
From the parameters given:
Debbie has = 65 tubs of yogurtThe boxes of granola = 16The number of kids that consume the same quantity of both food types = 4The time at which the 65 tubs of yogurt will finish:
= 65/4
= 16th rounds with a remainder of 1 tub
The time at which 16 boxes of granola will finish:
= 16/4
= 4th round
A tub of yogurt is roughly 17 ounces while a box of granola is 1 ounce.
Therefore, we can conclude that the kind of food that will finish and get used up first is the boxes of granola.
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Jackson recorded the following data: 2,5, X, 2, 4, 3. If the mean
of the data is 3, what is the value of x? Explain how you found your answer
Answer:
x = 2
Step-by-step explanation:
mean = sum of data / number of data
3 = 2 + 5 + x + 2 + 4 + 3 / 6
3 = 16 + x / 6
18 = 16 + x
2 = x
The missing value of data is 2.
What is arithmetic Mean?The simplest and most popular way to measure a mean or average is the arithmetic mean. It simply entails adding up a collection of numbers, then dividing that total by the total number of numbers in the series.
We have,
Data: 2,5, X, 2, 4, 3
Mean= 3
So, Mean
3 = Sum of data/ Total number of data
3 = (2 + 5 +x + 2 + 4 +3)/ 6
18 = 16 + x
x = 18 - 16
x= 2
So, the missing value of data is 2.
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A 2,000 piece puzzle is in the shape of a trapezoid. The lengths of the bases are 7012 and 6512 inches long. The area of the puzzle is 1,224 square inches. What is the height of the puzzle?
in.
Answer:
0.18
Step-by-step explanation:
Maths big brain
PLEASE HELP!!! I am stuck!!
How do I get question c)?
-15/-21 -14/x
-15x = -21 * -14
x = -19.6
answer -14c = -19.6 or about -20
answer 3c = .6 or about 1
formula would be
y= 1.2x -3
partial variation means the line doesn't go through (0,0)
Max made a journey of 700km partly by train and partly by bus.He started his journey at 8.00am. by train which travelled at 50km/hr. After alighting from the train, he took a lunch break of 30 minutes. He then continued his journey by bus which travelled at 75km/hr.The whole journey took 11.75hours. Determine the distance travelled by bus.
I really don't know I'm not big on school subjects
What is the answer to how many 1/2 are in 3 1/2?
Please help ASAP!!! Thank you!
Answer: 58 1/3 in^3.
Step-by-step explanation: To find the volume of a pyramid, you need to multiply the length, width, and height and divide it by 3. The length and width are both 5 and the height is 7, so the equation is 5 x 5 x 7. The answer to that is 175. Now, you have to divide 175 by 3, which is 58.33, or 58 1/3, which is your answer.
Let me know if this is right! :)
If the vertex of a parabola is (2,9), what is the axis of symmetry?
Answer:
x=2
Step-by-step explanation:
The Axis of Symmetry is when a line is put where it splits the parabola in the half perfectly. The vertex is where the parabola starts. The line x=2 is when it splits it into two congruent parts.
Graph the inequality of x>15
Answer:
Hope this helps!
To control pollination, pollen-producing flowers are often removed from the top of corn in a process called detasseling. The hourly rates for detasselers in Iowa are roughly normally distributed, with a mean of $12/hr and a standard deviation of $2/hr. What are the z-scores for a detasseler making $13 and $17 an hour? z13 = 0. 9, z17 = 1. 25 z13 = 0. 5, z17 = 1. 25 z13 = 0. 5, z17 = 2. 5.
The z-scores for a deta seller making $13 and $17 an hour will be [tex]Z_{13}=0.5 \ \ \ Z_{17}=2.5[/tex]
What is z- value ?The z-scores give us information about how many standard deviations from the mean the data are. This difference can be negative, if the data are n deviations to the left of the mean, or it can be positive if the data are n deviations to the right of the mean.
To calculate the Z scores, we calculate the difference between the value of the data and the mean and then divide this difference by the standard deviation.
[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]
Where x is the value of the data, μ is the mean and σ is the standard deviation
In this case :
μ = 12 $/h
[tex]\sigma[/tex] = 2 $/h
We need to calculate the Z-scores for x=17 and x=13
[tex]Z_{13}=\dfrac{13-12}{2}=0.5[/tex]
[tex]Z_{17}=\dfrac{17-12}{2}=2.5[/tex]
Thus the z-scores for a deta seller making $13 and $17 an hour will be [tex]Z_{13}=0.5 \ \ \ Z_{17}=2.5[/tex]
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The bases of a trapezoid are 11 meters and 14 meters. It’s height is 10 meters. What is the area of the trapezoid?
Answer:
120 m²
Step-by-step explanation:
A = (1/2) · (p + q) · h
A = (1/2)(14 + 10)(10)
A = (1/2)(24)(10)
A = 120
Hope this helps :)
IM STUCK IN THIS ONES AND THEY KEEP DELETING THE ANSWERS
Answer:
c
Step-by-step explanation:
40 cubic units
divide the shape into 2 pieces first.
4 × 4 ×2 = 32
4×2 = 8
32 + 8 = 40
the idea being that, each cube in the stack, is a 1x1x1 = 1 unit³, now if that's so, then, Check the picture below.
Samir and Ayisha are on one side of a river. Katia is on the other side. The distance between Samir and
Katia is 82 ft. The distance between Ayisha and Katia is 80 ft. If the angle from Samir to Katia to Ayisha is 18°, how far apart are Samir and Ayisha?
The distance between Samir and Ayisha is 2 ft.
Samir and Ayisha are on one side of a river. Since they are on the same side, they may likely be close to each other.
Katia is on the other side of the river. It is likely Katia is far from Samir and Ayisha.
The distance between Samir and Katia is 82 ft. Therefore, the distance between Ayisha and Katia is 80 ft.
How to find distance between between Samir and AyishaThe distance between Samir and Ayisha = 82 ft - 80 ft
The distance between Samir and Ayisha = 2 ft
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I really need help on understanding how the exponents relate to each other ?
because after the exponents it devides