What is the volume of a cube with side lengths that measure 8 cm?
Answer: 512 cm³
Explanation: Since the length, width, and height of a cube are all equal,
we can find the volume of a cube by multiplying side × side × side.
So we can find the volume of a cube using the formula v = s³.
In the cube in this problem, we have a side length of 8 cm.
So plugging into the formula, we have (8 cm)³
or (8 cm)(8 cm)(8 cm), which is 512 cm³.
So the volume of the cube is 512 cm³.
Answer:512[tex]cm^{3}[/tex]
Step-by-step explanation:
All sides are equal. Hence, volume =[tex]l^{3} = 8^{3} =512cm^{3}[/tex]
The graph of g(x) = x – 8 is a transformation of the graph of f(x) = x. Which of
the following describes the transformation?
(A) translation 8 units down
(B) translation 8 units up
(C) translation 8 units right
(D) translation 8 units left
Aaron wants to mulch his garden. His garden is x^2+18x+81 ft^2 One bag of mulch covers x^2-81 ft^2 . Divide the expressions and simplify to find how many bags of mulch Aaron needs to mulch his garden.
Answer:
Step-by-step explanation:
Given
Garden: [tex]x^2+18x+81[/tex]
One Bag: [tex]x^2 - 81[/tex]
Requires
Determine the number of bags to cover the whole garden
This is calculated as thus;
[tex]Bags = \frac{x^2+18x+81}{x^2 - 81}[/tex]
Expand the numerator
[tex]Bags = \frac{x^2+9x+9x+81}{x^2 - 81}[/tex]
[tex]Bags = \frac{x(x+9)+9(x+9)}{x^2 - 81}[/tex]
[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 81}[/tex]
Express 81 as 9²
[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 9\²}[/tex]
Evaluate as difference of two squares
[tex]Bags = \frac{(x+9)(x+9)}{(x - 9)(x+9)}[/tex]
[tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]
Hence, the number of bags is [tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]
How to find which ratio is largest
A clothing business finds there is a linear relationship between the number of shirts, n, it can sell and the price, p, it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $30, while 3,000 shirts can be sold at a price of $10. Find a linear equation in the form p(n)=mn+b that gives the price p they can charge for n shirts.
Answer:
p(n) = -1/100 n 40
Step-by-step explanation:
Use the two points (n, p): (1000, 30) and (3000, 10).
Now we find the equation of the line that passes through these two points.
m = (10 - 30)/(3000 - 1000)
m = -20/2000
m = -1/100
p(n) = mn + b
30 = -1/100 * 1000 + b
30 = -10 + b
b = 40
The equation is:
p(n) = -1/100 n 40
A number is chosen at random from 1 to 50. Find
the probability of selecting multiples of 10.
Step by step.
Answer:
1/10
Step-by-step explanation:
There are 5 numbers in the range that are multiples of 10: 10, 20, 30, 40, 50. The probability of choosing one of those at random from the set of 50 numbers is ...
5/50 = 1/10
The Airline Passenger Association studied the relationship between the number of passengers on a particular flight and the cost of the flight. It seems logical that more passengers on the flight will result in more weight and more luggage, which in turn will result in higher fuel costs. For a sample of 21 flights, the correlation between the number of passengers and total fuel cost was 0.668.
(1)
State the decision rule for 0.10 significance level: H0: Ï â‰¤ 0; H1: Ï > 0 (Round your answer to 3 decimal places.)
Reject H0 if t >
(2)
Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
Answer:
Decision Rule: To reject the null hypothesis if t > 1.328
t = 3.913
Step-by-step explanation:
The summary of the given statistics include:
sample size n = 21
the correlation between the number of passengers and total fuel cost r = 0.668
(1) We are tasked to state the decision rule for 0.10 significance level
The degree of freedom df = n - 1
degree of freedom df = 21 - 1
degree of freedom df = 19
The null and the alternative hypothesis can be computed as:
[tex]H_o : \rho < 0\\ \\ Ha : \rho > 0[/tex]
The critical value for [tex]t_{\alpha, df}[/tex] is [tex]t_{010, 19}[/tex] = 1.328
Decision Rule: To reject the null hypothesis if t > 1.328
The test statistics can be computed as follows by using the formula for t-test for Pearson Correlation:
[tex]t = r*\sqrt{ \dfrac{(n-2)}{(1-r^2)}[/tex]
[tex]t = 0.668*\sqrt{ \dfrac{(21-2)}{(1-0.668^2)}[/tex]
[tex]t = 0.668*\sqrt{ \dfrac{(19)}{(1-0.446224)}[/tex]
[tex]t = 0.668*\sqrt{ \dfrac{(19)}{(0.553776)}[/tex]
[tex]t = 0.668*5.858[/tex]
t = 3.913144
t = 3.913 to 3 decimal places
There are 2229 students in a school district. Among a sample of 452 students from this school district, 163 have mathematics scores below grade level. Based on this sample, estimate the number of students in this school district with mathematics scores below grade level.
a. 804
b. 844
c. 884
d. 0.36
Answer:
A. 804Step-by-step explanation:
Given the total number of students in the school to be 2229 students. If among a sample of 452 students from this school district, 163 have mathematics scores below grade level, then we can determine the number of students in this school district with mathematics scores below grade level based on the sample scores using ratio.
Let the number of students in this school district with mathematics scores below grade level be x. The ratio of the students with math score below grade level to total population will be x:2229
Also, the ratio of the sample students with math score below grade level to sample population will be 163:452
On equating both ratios, we will have;
x:2229 = 163:452
[tex]\dfrac{x}{2229} = \dfrac{163}{452}\\ \\cross\ multiplying;\\\\\\452*x = 2229*163\\\\x = \dfrac{2229*163}{452}\\ \\x = \frac{363,327}{452}\\ \\x = 803.8\\\\x \approx 804[/tex]
Hence the estimate of the number of students in this school district with mathematics scores below grade level based on the sample is 804
Is math a feature of the universe or a feature of human creation?
Answer:
a feature of the universe
Step-by-step explanation:
Math is a feature of the universe because what we call math is just a way of explaining how things work.
Which statement best describes a sequence? a.All sequences have a common difference. b.A sequence is always infinite. c.A sequence is an ordered list. d.A sequence is always arithmetic or geometric.
Answer:
C
Step-by-step explanation:
A sequence is defined as a list of numbers or objects in a special order.
They may be arithmetic or geometric or neither.
For example
0, 1, 4, 9, 16, 25, ..... ← is the sequence of square numbers.
Note it is neither arithmetic or geometric.
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen, and bedroom)?
Answer:
A
Step-by-step explanation:
How many different sets of polar coordinates can be given for a point, within one rotation? I thought it was infinite, but the given options are 1, 2, 3, and 4.
Answer:
the answer is 4
Step-by-step explanation:
so 1 rotation is like a circle 1 unit circle requires 4 quadrant to be in this is the most simplified i can get
Answer:
Solution : 4
Step-by-step explanation:
The question asks us how many polar coordinates are possible for one rotation. For one rotation there will be 4 polar coordinates, one present in each quadrant such that,
( r, theta ), ( r, theta ), ( - r, theta ), ( - r, theta )
Respectively if theta was q say,
( r, q ), ( r, - q ), ( - r, q ), ( - r, -q )
Therefore there are 4 sets of polar coordinates for one rotation, in each of the 4 quadrants.
A potato chip company makes potato chips in two flavors, Regular and Salt & Vinegar. Riley is a production manager for the company who is trying to ensure that each bag contains about the same number of chips, regardless of flavor. He collects two random samples of 10 bags of chips of each flavor and counts the number of chips in each bag. Assume that the population variances of the number of chips per bag for both flavors are equal and that the number of chips per bag for both flavors are normally distributed. Let the Regular chips be the first sample, and let the Salt & Vinegar chips be the second sample. Riley conducts a two-mean hypothesis test at the 0.05 level of significance, to test if there is evidence that both flavors have the same number of chips in each bag. (a) H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test. (b) t≈1.44 , p-value is approximately 0.167 (c) Which of the following are appropriate conclusions for this hypothesis test?
A. There is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag.B. There is sufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag.C. Reject H0.D. Fail to reject H0.
Answer:
A. There is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag.
D. Fail to reject H0.
Step-by-step explanation:
From the summary of the given test statistics.
The null and the alternative hypothesis are:
[tex]H_0:\mu_1=\mu_2 \\ \\ Ha:\mu_1 \neq \mu_2[/tex]
This test is also a two tailed test.
Similarly, the t value for the test statistics = 1.44
The p- value - 0.167
The level of significance ∝ = 0.05
The objective we are meant to achieve here is to determine which of the following from the given options are appropriate conclusions for this hypothesis test.
From what we have above:
Decision Rule: We fail to reject the null hypothesis since the p-value is greater than the level of significance at 0.05
CONCLUSION: Therefore, we can conclude that there is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag as we fail to reject H0.
These girts stasts jogging from the same point around
acircular track and they complete one round in 24
Seconds 36 seconds and 48 seconds respectively,
After.
how much time will they meet atone point?
Answer:
2hrs 24mins
Step-by-step explanation:
Very simple the time they will meet again at the point will be the LCM of their various time taken to complete a cycle.
Ans LCM(24, 36, 48) = 144 mins
= 2hrs 24mins
Answer:
The answer is 2 hours and 24 minutes
Step-by-step explanation:
Hope you get this right:)
Let x represent the number of times a student visits a gym in a one month period. Assume that the probability distribution of X is as follows:
x 0 1 2 3
p(x) 0.37 0.29 0.22 0.12
Find the mean, of this distribution. Report your answer to two decimal places.
Answer:
1.86
Step-by-step explanation:
Given the following :
X : - - - - 0 - - - - 1 - - - - 2 - - - - - 3 - - - - 4
P(x) - 0.37 - - 0.28 - - 0.22 - - 0.22 - - 0.12
The mean of the distribution can be calculated by evaluated by determining the expected value of the distribution given that the data above is a discrete random variable. The mean value can be deduced multiplying each possible outcome by the probability of it's occurrence.
Summation of [P(x) * X] :
(0.37 * 0) + (0.28 * 1) + (0.22 * 2) + (0.22 * 3) + (0.12 * 4)
= 0 + 0.28 + 0.44 + 0.66 + 0.48
= 1.86
If xy = 1 what is the arithmetic mean of x and y in terms of y? Please show work as detailed as possible
Answer:
(1+y^2) /2y
Step-by-step explanation:
arithmetic mean is the average of x and y
(x+y)/2
Using the equation
xy = 1
and solving for x
x = 1/y
Replacing x in the first equation
(1/y + y) /2
Multiply by y/y
(1/y + y) /2 * y/y
(1/y + y)*y /2y
(1+y^2) /2y
Sarah needs to go to five different stores. How many ways can she go to two of them before lunch?
Answer:
10
Step-by-step explanation:
Solution 1: At first, you might think that because there are 5 ways to choose the first store and 4 ways to choose the second store, the answer is 5 * 4 = 20 but this is over-counting by a factor of 2. Say that two of the stores are A and B. If she went to A then B, that's the same as going to B then A since you still go to the same stores, therefore, the answer is 20 / 2 = 10.
Solution 2: We need to find the number of ways to choose 2 stores from 5, we can do this by calculating ₅C₂ which equals:
5! / 2! * 3!
= 5 * 4 * 3 * 2 * 1 / 2 * 1 * 3 * 2 * 1
= 5 * 4 / 2 * 1
= 10
coordinates of England
Answer:
52.3555 north
1.1745 west
I don't understand word problems can someone please answer it for me and I need it ASAP.
Answer:
Inequality: 3 + 1.2c
What you'd put on graph: 1 ≥ 13.50
there are 5 discs, 6 jump ropes, 3 balls, and 12 pieces of sidewalk chalk in a bin. If two items are drawn at random without replacement, what is the probability that both items removed are not jump ropes?
Answer: 0.584
Step-by-step explanation:
We have:
5 discs
6 jump ropes
3 balls
12 pieces of sidewalk.
5 + 6 + 3 + 12 = 26
If all of them have exactly the same probability of being removed, then:
in the first selection, we do not want to remove a jump rope, so we can remove one disc, one ball or one piece of sidewalk.
The total number of those objects is:
5 + 3 + 12 = 20.
Then the probability of removing one of those objects is:
P1 = 20/26 = 0.769
Now in the second selection, we have the same situation, but now we have 25 objects in total, and because in the previous selection we removed one ball, or one disc, or one piece of sidewalk, the total number of these things now is 19.
So the probability of removing another object of that set is:
P2 = 19/25 = 0.76
The joint probability is equal to the product of the individual probabilities, so we have:
P = P1*P2 = 0.769*0.76 = 0.584
Based on the dot plots shown in the images, which of the following is a true statement? A. Set B has the greater mode. B. Set A has more items than set B. C. Set A is more symmetric than set B. D. Set B has the greater range.
Using the power series methods solve the 1st order Lane-Emden Equation:
xy = 2y + xy = 0
You may only use a power series solution to find both linearly independent functions. This means you may not use Abel’s theorem, variation of parameters or reduction of order.
Answer:
Step-by-step explanation:
xy = 2y + xy = 0
Hence, 2y + xy = 0 ---------(1)
Differentiating equation (1) n times by Leibnitz theorem, gives:
2y(n) + xy(n) + ny(n - 1) = 0
Let x = 0: 2y(n) + ny(n - 1) = 0
2y(n) = -ny(n - 1)
∴ y(n) = -ny(n - 1)/2 for n ≥ 1
For n = 1: y = 0
For n = 2: y(1) = -y
For n = 3: -3y(2)/2
For n = 4: -2y(3)
Suppose that 80% of all registered California voters favor banning the release of information from exit polls in presidential elections until after the polls in California close. A random sample of 25 registered California voters is selected.
Required:
a. Calculate the mean and standard deviation of the number of voters who favor the ban.
b. What is the probability that exactly 20 voters favor the ban?
Answer:
a. Mean = 20
Sd = 4
b. Probability of X = 20 = 0.1960
Step-by-step explanation:
we have
n = 25
p = 80% = 0.8
mean = np
= 0.8 * 25
= 20
standard deviation = √np(1-p)
= √25*0.8(1-0.8)
=√4
= 2
probability that exactly 20 favours ban
it follows a binomial distribution
= 25C20 × 0.8²⁰ × 0.2⁵
= 53130 × 0.01153 × 0.00032
= 0.1960
Probability of X = 20 = 0.1960
Which of the following is an example of closure? (1 point)
The equation 5 - 5 = 0 is an example of the natural numbers being closed under subtraction
The equation 1.5 +1.6 = 3.1 is an example of the rational numbers being closed under addition
The equation 4 - 6 = -2 is an example of the whole numbers being closed under subtraction
The equation 1+0= 1 is an example of the natural numbers being closed under addition
Answer:
The equation 1+0=1
Step-by-step explanation:
Other options are not eligible because
1 option -Natural numbers cannot be closed under subtraction
2 option-The equation is not having proper rational numbers, they are decimals
3 option-Whole numbers cannot be closed under subtraction
Thank you!
Factor.
x2 + 11x
x2 + 11x
x(x + 11)
11(x + 11)
0(x2 + 11x)
Answer:
x(x + 11)
Step-by-step explanation:
x^2 + 11x when factored gives a result of x(x + 11)
Answer:
x(x+11)
Step-by-step explanation:
We are given the expression:
[tex]x^2+11x[/tex]
This can be factored using the Greatest Common Factor (GCF).
The GCF of x^2 and 11x is x.
Factor out an x.
[tex]x(x+11)[/tex]
x^2+11x factored is: x(x+11).
the temp fell 3 degrees every hour for 5 hours what's the change in temperature
Answer:
-15
Step-by-step explanation:
If it fell 3 deg every hour for 5 hours so the equation is 3*5 plus a - sign because it dropped degrees
what is the diameter of a circular swimming pool with a radius of 9 feet? enter only the number
Answer:
The answer is 18 feet
Step-by-step explanation:
To find the diameter of a circle given it's radius we use the formula
diameter = radius × 2
From the question
radius = 8
So the diameter is
diameter = 9 × 2 = 18 feetHope this helps you
Answer:
18
Step-by-step explanation:
Hey there!
Well radius is half the diameter so,
D = r*2
Plug in 9
D = 9*2
D = 18
Hope this helps :)
Please solve this question by using the strategy Elimination Method or Solve By Substitution. This is the math equation: 1/2x+y=15 and -x-1/3y=-6
2nd Question: 5/6x+1/3y=0 and 1/2x-2/3y=3
First pair of equations :
[tex]\dfrac{1}{2}x+y=15\ ..(i)\\\\-x-\dfrac{1}{3}y=-6\ ..(ii)[/tex]
Multiply 2 to equation (i), we get
[tex]x+2y=30\ ..(iii)[/tex]
By Elimination Method, Add (i) and (ii) (term with x eliminate), we get
[tex]2y-\dfrac{1}{3}y=30-6\\\\\Rightarrow\ \dfrac{5}{3}y=24\\\\\Rightarrow\ y=\dfrac{24\times3}{5}=14.4[/tex]
put y= 14.4 in (iii), we get
[tex]x+2(14.4)=30\Rightarrow\ x=30-28.8=1.2[/tex]
hence, x=1.2 and y =14.4
Second pair of equations :
[tex]\dfrac{5}{6}x+\dfrac13y=0\ ..(i)\\\\ \dfrac12x-\dfrac{2}{3}y=3\ ..(ii)[/tex]
Multiply 2 to equation (i), we get
[tex]\dfrac{5}{3}x+\dfrac{2}{3}y=0\ ..(iii)[/tex]
Elimination Method, Add (i) and (ii) (term with y eliminate) , we get
[tex]\dfrac53x+\dfrac12x=3\Rightarrow\ \dfrac{10+3}{6}x=3\\\\\Rightarrow\ \dfrac{13}{6}x=3\\\\\Rightarrow\ x=\dfrac{18}{13}[/tex]
put [tex]x=\dfrac{18}{13}[/tex] in (i), we get
[tex]\dfrac{5}{6}(\dfrac{18}{13})+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{15}{13}+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{1}{3}y=-\dfrac{15}{13}\\\\\Rightarrow\ y=-\dfrac{45}{13}[/tex]
hence, [tex]x=\dfrac{18}{13}[/tex] and [tex]y=\dfrac{-45}{13}[/tex] .
What is the slope of the line that passes through (2, 12) and (4, 20)?On the graph of the equation 3x + 2y = 18, what is the value of the y-intercept?
Answer: The slope of the line that passes through (2, 12) and (4, 20) is 4.
The value of the y-intercept is 9.
Step-by-step explanation:
Slope of line passing through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]
Then, the slope of the line that passes through (2, 12) and (4, 20) = [tex]\dfrac{20-12}{4-2}[/tex]
[tex]=\dfrac{8}{2}=4[/tex]
So, the slope of the line that passes through (2, 12) and (4, 20) is 4.
To find the y-intercept of 3x + 2y = 18, first write in slope intercept form y=mx+c ( where c= y-intercept ).
[tex]2y=-3x+18\\\\\Rightarrow\ y=-\dfrac{3}{2}x+9[/tex]
By comparison, c= 9
Hence, the value of the y-intercept is 9.
Consider the following functions. f={(−1,1),(1,−2),(−5,−1),(5,3)} and g={(0,2),(−3,−4),(1,−2)} Step 1 of 4: Find (f+g)(1).
Answer:
-4
Step-by-step explanation:
(f+g)(1) = f(1) +g(1)
In each case, you need to locate the ordered pair with 1 as the first element.
(1, f(1)) = (1, -2) . . . . f(1) = -2
(1, g(1)) = (1, -2) . . . . g(1) = -2
f(1) +g(1) = (-2) +(-2) = -4
(f+g)(1) = -4
