Answer:
{ 4,8}
Step-by-step explanation:
The intersection is what the sets have in common
{1, 4, 8, 12}∩ {2, 4, 6, 8}
{ 4,8}
Answer:
{4, 8}
Step-by-step explanation:
The intersection of sets are the terms that appear in both sets. In this case, the only numbers that appear in both sets are 4 and 8.
The radius of a sphere is 3 inches. Which represents the volume of the sphere? 12π cubic inches 36π cubic inches 64π cubic inches 81π cubic inches
Answer:
36pi
Step-by-step explanation:
Answer:
36pi
Step-by-step explanation:
i got it right on my test
Given the sequence rn defined recursively below, find r3. r1rn=2=−rn−1+n−2
Answer:
[tex]r_3=3[/tex]
Step-by-step explanation:
Given:
[tex]r_1=2\\r_n=-r_{n-1}+n-2[/tex]
We want to find the value of [tex]r_3[/tex] .
[tex]\\r_2=-r_{2-1}+2-2\\r_2=-r_1\\r_2=-2\\\\r_3=-r_{3-1}+3-2\\r_3=-r_{2}+1\\r_3=-(-2)+1\\r_3=2+1\\r_3=3[/tex]
A cash prize is randomly placed into certain cereal boxes that sell for $5. A $1 prize is placed in 10% of cereal boxes, a $5 prize is placed in 5% of cereal boxes, while 10% of boxes receive a $20 prize. The other boxes do not receive any cash prizes. What is the expected value of the cash prizes if you include the cost of purchasing the cereal in your calculations?
Answer:
-2.65 usd
Step-by-step explanation:
1. Note that 10%= probability 0.1 5%= 0.05 .
Lets find the average prize value :
1 usd *P(1 uzd)+5usd *P(5usd)+20,usd*P(20usd)=
= 1*0.1+5*0.05+20*0.1=2.35 USD is a value average prize brutto.
However for 1 turn the player has to pay 5 USD.
That means the net value is 2.35-5=-2.65 USD
Actually it means that every turn the player loses 2.65 USD averagly.
Please help!!! a.) Describe a series of at least two congruent transformations that will transform heptagon ABCDEFG into heptagon A’B’C’D’E’F’G’. b.) There is more than one way to transform heptagon ABCDEFG into heptagon A’B’C’D’E’F’G’. Describe a second sequence of transformations that will accomplish this goal. Explain what tool you used as an aid in identifying a transformation sequence.
Answer:
you can rotate it around point (1.5,3.5) or you can rotate it counter clockwise and translate it (x+2) (y+6).
Step-by-step explanation: i hope this helps
The graph of f(x) = x2 is shifted 3 units to the left to obtain the graph of g(x). Which of the following equations best describes g(x)?
g(x) = (x + 3)2
g(x) = x2 − 3
g(x) = x2 + 3
g(x) = (x − 3)2
Answer:
g(x) = (x + 3)^2
Step-by-step explanation:
When a function is shifted to the left or right we can think of a change of units, like a new independent variable is used.
If we have a quadratic function
[tex]f(x)=x^2[/tex]
and the graph is shifted 3 units to the left, then we can think of a new unit u that is:
[tex]g(x)=u^2[/tex]
The vertix of this parabola, that happens for u=0, happens for x=-3, as the graph is shifted 3 units to the left.
Then, the relation between u and x is:
[tex]u-x=0-(-3)=3\\\\u=x+3[/tex]
We can use this relation in the new graph and replace u as:
[tex]g(x)=(x+3)^2[/tex]
Answer:
g(x) = (x + 3)^2
Step-by-step explanation:
I took the practice test as well.
Solve this correctly for brainliest !!!!!! 3(7) + 2 • |7 - 8| - 12
Answer:
3(7) + 2* |7 - 8| - 12 = 11
Step-by-step explanation:
3(7) + 2* |7 - 8| - 12
21 + 2* |-1| - 12
21 + 2* 1 - 12
21 + 2 - 12
23 - 12 = 11
Hope this helps! :)
11. What's the approximate area of a segment of a circle with a height 6 m and the length of the chord is 20 m? round to the nearest whole number.
O A. 746 67 m2
O B. 74 6 m2
O C.85 4 m2
O D. 8 54 m2
Answer:
85.4
Step-by-step explanation:
first you have to find the radius before you find the area. so given the height, the radius is 11.3 meters. then, you need to find the area behind the arc, which is 85.4 meters/
A study of the use of social media asked a sample of 488 American adults under the age of 40 and a sample of 421 American adults aged 40 or over about their use of social media. Based on their answers, each subject was assigned a social media usage score on a scale of 0 to 25. Higher scores indicate greater usage. The subjects were chosen at random. Are the conditions for two-sample t inference satisfied?
a. Maybe: the SRS condition is OK but we need to look at the data to check Normality
b. No: scores in a range between 0 and 25 cant be Normal
c. Yes: the STS condition is OK and large sample sized makes the Normality condition unnecessary.
Answer:
a
Step-by-step explanation:
Maybe: the SRS condition is OK but we need to look at the data to check Normality.
The normality inference is important in that the null compares the difference in the sample means to the difference that one would expect by random variation, or by chance, alone meaning that the sample is assumed to have being from a normal distribution with a mean and standards deviation.
Find the length of AB. Leave
your answer in terms of 7.
A
20° AB = [ ? ]
27
1B
Enter
Answer:
AB = 3π
Step-by-step explanation:
See attachment for correct format of question.
Given
From the attachment, we have that
θ = 20°
Radius, r = 27
Required
Find length of AB
AB is an arc and it's length can be calculated using arc length formula.
[tex]Length = \frac{\theta}{360} * 2\pi r[/tex]
Substitute 20 for θ and 27 for r
[tex]Length = \frac{20}{360} * 2\pi *27[/tex]
[tex]Length = \frac{20 * 2\pi * 27}{360}[/tex]
[tex]Length = \frac{1080 \pi}{360}[/tex]
[tex]Length = 3\pi[/tex]
Hence, the length of arc AB is terms of π is 3π
Given the following diagram, are OC and OE opposite rays ?
Answer:
No
Step-by-step explanation:
If they were opposite, they would be equal.
But they are not, (on one of the spaces in between them is smaller and one is larger.)
Hope I have helped you, since it seems I haven't helped "other people" the last time :/
Answer:
No
Step-by-step explanation:
Use synthetic division to solve What is the quotient?
Answer:
[tex]3{x}^{3} + 2x + 5[/tex]
Step-by-step explanation:
Sorry if my notes weren't very clear.
Answer:B
Step-by-step explanation: got it right
WILL GIVE BRAINLIEST! EASY! Give detailed answer
Bill and Ben each have three cards numbered 4,5,6 they each take one of their own cards then they add the two numbers on the cards what is the probability that their answer is an odd number. What is the probability that their answer is a number less than 11.
Answer:
P(odd) = 4/9P(<11) = 2/3Step-by-step explanation:
There are 9 possible outcomes for (Bill, Ben)'s cards:
(4, 4) total 8; (4, 5) total 9; (4, 6) total 10;
(5, 4) total 9; (5, 5) total 10; (5, 6) total 11;
(6, 4) total 10; (6, 5) total 11; (6, 6) total 12.
Of these 9 outcomes, 4 have an odd total; 6 are less than 11.
P(odd) = 4/9
P(sum < 11) = 2/3
The whole sale cost of bicycle is $75. There is a mark up of 55%. What is the new sale price of the bike
Answer:
$116.25
Step-by-step explanation:
10% = $7.50
5% = $3.75
7.50 x 5 = 37.50
37.50 + 3.75 = $41.25
$75 + $41.25 = $116.25
Hope this helps !
The mean water temperature downstream from a power plant cooling tower discharge pipe should be no more than 100 degrees F. Past experience has indicated that the standard deviation of temperature is 2 degrees F. The water temperature is measured on nine randomly chosen days, and the average temperature is found to be 98 degrees F.
A) Is there evidence that the water temperature is acceptable at α = 0.05?
B) What is the P-value for this test?
C) What is the probability of accepting the null hypothesis at α = 0.05 if the water has a true mean temperature of 104 degrees F?
Answer:
A) Yes. At a significance level of 0.05, there is enough evidence to support the claim that the mean water temperature is significantly below 100 °F.
B) P-value = 0.001
C) The probability of not rejecting the null hypothesis at α = 0.05 if the true mean is 104 °F is P(M>98.9)=1. This means that is almost impossible to reject the null hypothesis μ≤100 given that the true mean is 104.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the mean water temperature is significantly below 100 °F.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=100\\\\H_a:\mu< 100[/tex]
The significance level is 0.05.
The sample has a size n=9.
The sample mean is M=98.
The standard deviation of the population is known and has a value of σ=2.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{2}{\sqrt{9}}=0.667[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{98-100}{0.667}=\dfrac{-2}{0.667}=-3[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-3)=0.001[/tex]
As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the mean water temperature is significantly below 100 °F.
The critical value for this left-tailed test is zc=-1.645.
The null hypothesis would be accepted if the test statistic is higher than zc=-1.645. For a normal distribution with the parameters of the null hypothesis (μ=100, σ=2), this would correspond to a value of:
[tex]X=\mu+z\sigma/\sqrt{n}=100+(-1.645)\cdot 2/\sqrt{9}=100-1.1=98.9[/tex]
This means that if we get a sample of size n=9 and mean bigger than 98.9, we will failed to reject the null hypothesis.
If the true mean is 104 °F, the probability of getting a sample mean over 98.9 for this sample size can be calculated as:
[tex]z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{98.9-104}{2/\sqrt{9}}=\dfrac{-5.1}{0.6667}=-7.65\\\\\\P(M>98.9)=P(z>-7.65)=1[/tex]
The probability of not rejecting the null hypothesis at α = 0.05 if the true mean is 104 °F is P(M>98.9)=1. This means that is almost impossible to reject the null hypothesis μ≤100 given that the true mean is 104.
0.3y+ z y 0, point, 3, y, plus, start fraction, y, divided by, z, end fraction when y=10y=10y, equals, 10 and z=5z=5z, equals, 5.
Answer:
5
Step-by-step explanation:
Substitute the given values and do the arithmetic.
[tex]0.3y+\dfrac{y}{z}=0.3\cdot 10+\dfrac{10}{5}=3+2=\boxed{5}[/tex]
Two ships leave a port at the same time.
Ship A sails 12 knots on a bearing of 035°
Ship B sails 16 knots on a bearing of 270°
Calculate the distance between the ships after 2 hours
(1 knot = 1 nautical mile per hour)
Answer: 49.8 nautical miles
Step-by-step explanation:
Angle between routes = 125⁰
after 2 hours :-
d² = 24² + 32² - 2 x 24 x 32 cos 125⁰
d = 49•8 nautical miles
From 1960 to 2010, a certain money stock measure was growing at the rate of approximately 43e(1/2)x billion dollars per decade, where x is the number of decades since 1950. Find the total increase in the money stock measure from 1960 to 2010. (Round your answer to the nearest billion dollars.)
Answer:
1222 billion dollars.
Step-by-step explanation:
To find the total increase from 1960 to 2010, we need to find the growth of each decade and sum them all:
In the period 1960-1970, we have x = 1, and the growth is:
[tex]y(1) = 43e(1/2) = 70.895[/tex]
In the period 1970-1980, we have x = 2, and the growth is:
[tex]y(2) = 43e(2/2) = 116.8861[/tex]
The growth in the following 3 periods are:
[tex]y(3) = 43e(3/2) =192.7126[/tex]
[tex]y(4) = 43e(4/2) = 317.7294[/tex]
[tex]y(5) = 43e(5/2) =523.8472[/tex]
So the total growth in the period 1960 - 2010 is:
[tex]Total = y(1) + y(2) + y(3) + y(4) + y(5)[/tex]
[tex]Total = 70.895 + 116.8861+192.726+317.7294+523.8472[/tex]
[tex]Total = 1222.08\ billion\ dollars[/tex]
Rounding to the nearest billion dollars, we have a total of 1222 billion dollars.
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean 1261 and a standard deviation of 118. (a) Determine the 30th percentile for the number of chocolate chips in a bag. (b) Determine the number of chocolate chips in a bag that make up the middle 98% of bags. (c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Answer:
(A) 1199.168
(B) 1503.372
(C) 159.17728
Step-by-step explanation:
(A) To determine the 30th percentile for the number of chocolate chips in the bag, we find the z-score for the 30th percentile.
Found using a z-table or z-calculator, the z-score for the 30th percentile is -0.524
The formula for finding X (the number of items in a given percentile) is:
X = M + Z(S.D.)
Where M is the mean, Z is the specific z-score of the sought percentile and S.D. is the standard deviation.
So for the 30th percentile,
X = 1261 + (-0.524)(118)
X = 1261 - 61.832 = 1199.168
(B) The number of chocolate chips that make up the middle 98% of chips in the bag is
X = 1261 + (2.054)(118)
X = 1261 + 242.372 = 1503.372
(C) For normal distributions, Interquartile range is Q3 - Q1, that is; 3rd quartile minus 1st quartile.
This is within 1.34896 standard deviations of the mean.
IQR = (1.34896)(118)
IQR = 159.17728
A is any nonnegative real number and b is a square root of that number. Is a a function of b, b a function of a, both, or neither?
Answer:
B is a function of A
Step-by-step explanation:
If you do something to another thing, it is a function of that.
Suppose that 3 is a factor of a, a is a divisor of 12, and a is positive. What is the number of possible values of a?
Answer:
3
Step-by-step explanation:
12 is divisible by: 1, 2, 3, 4, 6, 12
Because 3 is a factor of a, that means 3 multiplied by another number equals a. Additionally, a is a divisor of 12, meaning a multiplied by another number equals 12.
Out of the numbers, 12 is divisible by, only 3 are also divisible by 3: 3, 6, 12 This gives three possible values of a.
Makayla is teaching Rodney how to construct a square inscribed in a circle.
I need help ...... Makayla says Rodney should draw diameter AB, and then use a compass and a straightedge to find chord CD that bisects diameter AB. Makayla also tells Rodney he should use a straightedge to draw the four chords that make up the square: chords AC, AD, BC, and BD.
What error, if any, is Makayla making in her instructions to Rodney?
Answer:
A.) Chord CD must not only bisect but must also be perpendicular to diameter AB.
Step-by-step explanation:
The error, Makayla is making in her instructions to Rodney is that the chords that make up the square are chords AB, BC, CD, and DA.
What is Geometric construction?Geometric construction is method todraw any sketch lines, angles, and other geometric forms and figures only using a compass and a straightedge. It generally is done without employing precise measurements of length, angle, etc.
Now the steps taken by Makayle are,
→draw diameter AB
→use a compass and a straightedge to find chord CD that bisects diameter AB.
→use a straightedge to draw the four chords that make up the square: chords AC, AD, BC, and BD.
Now here the error she is making is that the required chords will be AB, BC, CD, and DA, not AC, AD, BC, and BD.
Hence,the error, Makayla is making in her instructions to Rodney is that the chords that make up the square are chords AB, BC, CD, and DA.
To learn more about Geometry:
https://brainly.com/question/7558603
#SPJ2
Questlon 3 of 10
2 Points
The volume of a cube depends on the length of its sides. This can be written
in function notation as (s). What is the best interpretation of (4) = 64?
O A. 4 sides of the cube have a total length of 64 feet.
B. A cube with side lengths of 4 feet has a volume of 64 cubic feet.
C. A cube with a volume of 4 cubic feet has side lengths of 64 feet.
O D. 4 of these cubes will have a total volume of 64 cubic feet.
SUBMIT
Answer:
b)A cube with side lengths of 4 feet has a volume of 64cubic feet
Step-by-step explanation:
volume=length×width×height
=4×4×4
=64feet³
4) A large number of people were polled and asked which of four different animals were their
favorite. 13% said Penguin, 21% said Iguana, 22% said Parrot, and 44% said Turtle. Suppose you
decide to carry out a simulation given these percentages. You decide to select two digits at a
time. Which would be a proper assignment of digits for these teams?
a) 01-13 = Penguin, 01-21 = Iguana, 01-22 = Parrot, 01-44 = Turtle
b) 00-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 = Turtle
c) 01-13 = Penguin, 14-35 = Iguana, 36-58 = Parrot, 59-99 & 00 = Turtle
d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle
e) None of these
Answer:
d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle
Step-by-step explanation:
13 − 01 + 1 = 13
34 − 14 + 1 = 21
56 − 35 + 1 = 22
99 − 57 + 1 + 1 = 44
Dr. Pagels is a mammalogist who studies meadow and common voles. He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices. So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.
Indicate which of the following is the null hypothesis, and which is the alternate hypothesis.
There food preferences among vole species are independent of one another. _____
There is a relationship between voles and food preference. ______
To test for independence, we need to calculate the Chi-square statistic.
These are the data that Dr. Pagels collected:
meadow voles common voles
apple slices 26 32
peanut butter-oatmeal 35 25
When transferring your answers, make sure you carry them out to AT LEAST SIX SIGNIFICANT FIGURES unless otherwise stated.
_____= expected meadow vole/apple slices
_____= expected common vole/apple slices
_____= expected meadow vole/peanut butter-oatmeal
_____= expected common vole/peanut butter-oatmeal
_____= chi-square value
_____= degrees of freedom (whole number only)
_____= using Statistical Table A (pg 704 of your textbook), what is the chi-square critical value with significance level of alpha=0.05?
_____= will you reject or fail to reject the null hypothesis? (answer either reject or fail to reject)
Answer:
Null hypothesis = H₀ = There food preferences among vole species are independent of one another.
Alternate hypothesis = H₁ = There is a relationship between voles and food preference.
Expected meadow vole/apple slices = 29.983051
Expected common vole/apple slices = 28.016949
Expected meadow vole/peanut butter-oatmeal = 31.016949
Expected common vole/peanut butter-oatmeal = 28.983051
Chi-square value = χ² = 2.154239
Degree of freedom = 1
Critical value = 3.841
χ² < Critical value
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.
Step-by-step explanation:
He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices.
So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.
Null hypothesis = H₀ = There food preferences among vole species are independent of one another.
Alternate hypothesis = H₁ = There is a relationship between voles and food preference.
Data collected by Dr. Pagels:
meadow voles common voles Row Total
apple slices 26 32 58
peanut butter-oatmeal 35 25 60
Column Total 61 57 118
Where 118 is the grand total.
The expected number is given by
Expected = (row total)×(column total)/grand total
Expected meadow vole/apple slices = 58×61/118
Expected meadow vole/apple slices = 29.983051
Expected common vole/apple slices = 58×57/118
Expected common vole/apple slices = 28.016949
Expected meadow vole/peanut butter-oatmeal = 60×61/118
Expected meadow vole/peanut butter-oatmeal = 31.016949
Expected common vole/peanut butter-oatmeal = 60×57/118
Expected common vole/peanut butter-oatmeal = 28.983051
The chi-square statistic value is given by
χ² = Σ(Observed - Expected)²/Expected
χ² = (26 - 29.983051)²/29.983051 + (32 - 28.016949)²/28.016949 + (35 - 31.016949)²/31.016949 + (25 - 28.983051)²/28.983051
χ² = 2.154239
The degrees of freedom is given by
DoF = (row - 1)×(col - 1)
For the given case, we have 2 rows and 2 columns
DoF = (2 - 1)×(2 - 1)
DoF = 1
The given level of significance = 0.05
The critical value from the chi-square table at α = 0.05 and DoF = 1 is found to be
Critical value = 3.841
Conclusion:
Reject H₀ If χ² > Critical value
We reject the Null hypothesis If the calculated chi-square value is more than the critical value.
For the given case,
χ² < Critical value
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.
y = 0.8x+ 7.2
20x + 32y = 48
Step-by-step explanation:
y = 0.8x+ 7.2 ..........(1)
20x + 32y = 48 .........(2)
Substitute (1) in (2)
20x +32*(0.8x+7.2) = 48 expand
20x + 25.6x+230.4 = 48 add
45.6x+230.4 = 48 transpose and simplify
45.6x = 48-230.4 = -182.4
x = -182.4 / 45.6
x = -4
Answer:
x=-4, Y=4
Step-by-step explanation:
20x+32(0.8x+7.2)=48
45.6x =48-230.4
x=-4
substitute x=-4 in y eqn
y=-3.2+7.2
y=4
Find the distance from R to S on the graph. Round to the nearest tenth.
Answer:
7.2
Step-by-step explanation
plug the values in in the distance formula
the points are -3,3 and 1, -3
sqrt((-3-1)^2+(3-(-3))^2)
sqrt(16)+(36)
sqrt(52)
approximately 7.2
ASAP will give brainliest Which of the following formulas would find the surface area of a right cylinder where h is the height, r is the radius, LA is the lateral area, and BA is the base area?
Answer:
A. BA + 2πrh
C. 2πr² + 2πrh
Step-by-step explanation:
height of cylinder = h
Radius of cylinder = r
=>Lateral area of cylinder = LA (THis is the area of the cylinder excluding the area of its circular bases)
L.A of a cylinder = 2πrh
=>Base area = BA (this is the area of both circular bases of the cylinder)
Area of circle = πr²
Area of the 2 circular bases of the cylinder (BA) = 2(πr²) = 2πr²
=>Surface area of a right cylinder = B.A + L.A
= 2πr² + 2πrh
The formulas that can be used to find surface area of a right cylinder from the given options are:
A. BA + 2πrh (note: BA = 2πr², LA = 2πrh)
C. 2πr² + 2πrh
Which is greater 36÷(4×3) or 54-48-(16÷4
Step-by-step explanation:
36 ÷ (4 x 3)
36 ÷ 12
= 3
54 - 48 - (16 ÷ 4)
54 - 48 - 4
= 2
So first one is greater
which regression equation best fits these data
Answer:
D. y = 2.13x² +0.13x +6.39
Step-by-step explanation:
The quadratic regression function of a spreadsheet or graphing calculator will tell you the best choice is D.