Write two expressions
that represent the volume of the cube, one with
exponents and one without.
Answers
The two expressions for the volume of a cube with a side length of S are:
V = S^3
V = S*S*S
How to express the volume of the cube?A cube is a rectangular prism where the 3 dimensions have the same measure, which we will call the side-length of the cube.
So, if S is the sidelength of the cube, the volume will be given by the product between the product between the dimensions of the cube, and the 3 dimensions measure the same thing, which is S, then:
V = S*S*S
That is the expression without exponents, and the expression with an exponent is really trivial, we have S multiplied by itself 3 times, so we get:
V = S^3
These are the two expressions for the volume.
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Related Questions
please help fast!!!! trig/ geometry
Answers
Answer:
b = 5.7
A = 51.1°
B = 38.9°
Step-by-step explanation:
a = 7
c = 9
✔️Find b using Pythagorean theorem:
b = √(9² - 7²) ≈ 5.7
✔️Find A using trigonometric function:
Reference angle = A
Opposite = a = 7
Hypotenuse = c = 9
Apply SOH:
\( sin(A) = \frac{Opp}{Hyp} \)
\( sin(A) = \frac{7}{9} \)
\( A = sin^{-1}(\frac{7}{9}) \)
A = 51.0575587° = 51.1°
✔️B = 180 - (90 + 51.1) (sum of triangles)
B = 38.9°
Among all pairs of numbers whose sum is 24, find a pair whose product is as large as possible. Show the work(the steps)! Write an equation of the corresponding quadratic function. How parabola opens? What is the maximum product? Does this function has a maximum value or the minimum value? Explain. Graph the function and upload the image.
Answers
The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.
To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.
Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.
To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:
P(x) = x(24 - x)
This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.
The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.
To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.
Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.
So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.
Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.
To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]
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Sarah goes to the grocery store and buys
four packs of gum. Sales tax in
Connecticut is 6.35%. If g is the price of a
single pack of gum, write a function p(g)
to model the scenario.
Answers
Based on the fact that sales tax in Connecticut is 6.35%, the price of a single pack of gum can be shown by the function, p(g) = 4g + 0.254g
What is the function?The price of a single pack of gum is g and Sarah bought 4 packets.
The total cost of her purchase is:
= (4 x price of single pack) x ( 1 + Sales tax rate)
When expressed in terms of g, the function is:
= 4g x (1 + 6.35%)
p(g) = 4g + 0.254g
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A farmer has only dogs and chickens. The animals total 60. There are 148 legs in all How
many dogs are there? How many chickens are there?
Answers
Answer:
46 chickens14 dogsStep-by-step explanation:
You want to know the number of dogs and chickens a farmer has if there are 60 total, having a total of 148 legs.
SetupLet d represent the number of dogs. Then 60-d is the number of chickens, and the total number of legs is ...
4d + 2(60 -d) = 148
SolutionSimplifying gives ...
2d +120 = 148
d +60 = 74 . . . . divide by 2
d = 14 . . . . . . . subtract 60
60 -d = 46 . . . . the number of chickens
The farmer has 14 dogs and 46 chickens.
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Find the equation of the line through (2,1) which is parallel to the line y=−7x−1.
Give your answer in the form y=mx+b
Answers
Answer:
y=-7x+15
Step-by-step explanation:
At a dinner, the meal cost $22 and a sales tax of $2.09 was added to the bill. How much would the sales tax be on a $88 meal?
Answers
Find two square numbers that total 45
Answers
x^2+^2=45
if ×=3 and y=6
then 9+36=45
What's the range in the question below. Please answer one of the answer choices.
Answers
Answer:
yo I'm doing the same thing
You start at (0,-4). You move left 1 unit and right 4 units. where do you end?
Answers
If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)
Calculating the endpoint of the pointFrom the question, we have the following parameters that can be used in our computation:
Start = (0, -4)
Also, we have
You move left 1 unit and right 4 units
Mathematically, this can be expressed as
(x, y) = (x - 1 + 4, y)
Substitute the known values in the above equation, so, we have the following representation
Endpoint = (0 - 1 + 4, -4)
Evaluate the expression
Endpoint = (3, -4)
Hence, the endpoint is (3, -4)
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The zero product property indicates that if “ab = 0,” then ___?___ = 0 or ___?___ = 0. Substitute the correct variable for the question mark.
Select one:
a
b
a ; b
none of the above
Answers
Answer: a; b
Step-by-step explanation: Both answers are possibilities because 0a = 0 and 0b = 0. Hope this helps!
you are sent to the local tea shop to pick up 9 drinks. You purchase 3 sweet teas and 6 unsweetened teas. Unfortunately, you forgot to label them. If you pick 3 drinks at random, find the probability of each event below. Give your answers as simplified fractions.
Answers
The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21
The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:
Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84
Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14
Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28
Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21
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If 600 people were polled and 240 said the the approved of the mayor's action, what percent approved of her actions?
Answers
In order to calculate the percentage of people that approved the mayor's actions, we just need to divide the number of people that approved the actions by the total number of people polled. So we have:
\(\frac{240}{600}=\frac{40}{100}=40\text{\%}\)So the percentage is 40%.
Find the area and perimeter of the figure
Answers
The perimeter and area of the given composite shape are respectively; 10a² + 10b and 37a²b
How to find the area and perimeter of a composite figure?The perimeter of the composite figure here will simply be the sum of the entire boundary lengths and as such we have;'
Perimeter = 2(a² + 3a² + a²) + 2(4b) + b + b
= 10a² + 8b + 2b
= 10a² + 10b
The area of a rectangle is;
Area = Length * width.
Thus;
Area of composite shape = Overall area of rectangle - Area of cut out rectangle
Area = (10a² * 4b) - (3a² * b)
Area = 40a²b - 3a²b
Area = 37a²b
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Please help me with this question
Answers
The values of tht missing part of the triangle are;
A= 20.9°
a = 13.06
c = 33.6
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
To find side c
sinB/b = sinC/c
sin45.9/26.30 = sin113.2/c
csin 45.9 = 26.30 × sin113.2
0.718c = 23.90
c = 23.90/0.718
c = 33.6
Angle A = 180-(113.2+ 45.9)
angle A = 20.9°
sinA/a = sinB/b
sin20.9/a = 0.718/26.30
0.357 × 26.30 = 0.718a
a = 9.389/0.718
a = 13.06
Therefore A = 20.9°
a = 13.06
c = 33.6
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PLZZZZZZ IL do anything give brainilest 5 star i'll like My grade depends on this PLEASE I NEED THIS TO BE CORRECT AND SHOW YOUR WORK PLZ NO TROLLSSSS PLZZZZ ANSWER CORRECT
Answers
Answer:
$195.00
Step-by-step explanation:
perimeter is 54 feet
area is 152 \(ft^{2}\)
54' * $1.50 = $81.00
152/8 = 19 bags of mulch needed
19*$6.00= $114.00
$195.00 you get away from the store for under 200 :P
P.S. since you said you'll do anything, send me $1,000,000.00 dollars :D
For any positive integer n, the value of n! is the product of the first n positive integers. For example, 4! = 4 * 3 * 2 * 1 =24. What is the greatest common divisor of 5! and 7! ?
Answers
The greatest common divisor of 5! and 7! is 840.
To find the greatest common divisor (GCD) of 5! and 7!, we need to calculate the prime factorization of both numbers.
First, let's calculate the prime factorization of 5!:
5! = 5 * 4 * 3 * 2 * 1 = 120.
The prime factorization of 120 is 2^3 * 3 * 5.
Now, let's calculate the prime factorization of 7!:
7! = 7 * 6 * 5! = 7 * 6 * 120 = 5040.
The prime factorization of 5040 is 2^4 * 3^2 * 5 * 7.
To find the GCD of 5! and 7!, we need to find the common factors in their prime factorizations. We take the smallest exponent for each prime factor that appears in both factorizations.
From the prime factorizations above, we can see that the common factors are 2^3, 3, 5, and 7. Multiplying these factors together gives us:
GCD(5!, 7!) = 2^3 * 3 * 5 * 7 = 8 * 3 * 5 * 7 = 840.
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Solve the exponential equation for x
Answers
Answer:
6^3 = 6^(4x + 11)
3 = 4x + 11
-8 = 4x
x = -2
Patricia needs 2 pints of purple icing to decorate cupcakes. She will use the following recipe for 1 pint of purple icing.
• 1 pint of white icing
4 1/4 teaspoons of blue food coloring
2 1/2 teaspoons of red food coloring.
explain two different ways for patricia to find total number of teaspoons of blue and red food coloring necessary to make 2 pints of purple icing
Answers
Answer:
Step-by-step explanation:
i’m thinking of the second way right now, but one way is doubling the recipe
2 pints of white icing
8 1/2 teaspoons of blue food coloring
5 teaspoons of red food coloring
B) Given: y = 2x - 1 (x-3) (x+1) what is the I. VAII. HAIII. X-intercept IV. Y-Intercept
Answers
SOLUTION:
Case: Equations
Method:
\(\begin{gathered} y=2x-1(x-3)(x+1) \\ y=2x-[x^2+x-3x-3] \\ y=2x-[x^2-2x-3] \\ y=2x-x^2+2x+3 \\ y=3-x^2+2x+2x \\ y=3+4x-x^2 \end{gathered}\)The following:
1. Vertical asymptote: None
2. Horizontal asymptote: None
3. x-intercept
\(\begin{gathered} y=3+4x-x^2 \\ 0=3+4x-x^2 \\ x^2-4x-3=0 \\ x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-3)}}{2(1)} \\ x=-0.646\text{ }or\text{ }4.646 \end{gathered}\)4. y-intercepts
\(\begin{gathered} y=3+4x-x^2 \\ y=3+4(0)-(0)^2 \\ y=3 \end{gathered}\)Final answer:
I) None
II) None
III) (-0.646, 0), (4.646, 0)
IV) (0, 3)
Informatne problem and woube mostAfter taking 4 pieces of fruit out of a bag, 12 pieces of fruit remained. Howmany pieces of fruit were in the bag to start?A. 12 + f= 4OB. 12 ÷ f= 4O C. 12-4 = fOD. f÷4=12E. f- 4 = 12OF. 4+f=12
Answers
Answer:
E. f - 4 = 12
Explanation:
f represents the initial number of pieces of fruit.
They say that after taking 4 pieces of fruit, 12 pieces remained. Therefore, if we subtract 4 from f, we will get 12. It means that the expression is
E. f - 4 = 12
Ten less than three times a number is 2.
Answers
Answer:
the number is 4
Step-by-step explanation:
4 times 3=12
12-10=2
hope this helps!
Answer:
it's 7!
Step-by-step explanation:
I need it please I will give 20
Answers
i need help quick! please!
Assume that random guesses are made for nine multiple choice questions on an SAT test, so that there are nequals9 trials, each with probability of success (correct) given by pequals0.35. Find the indicated probability for the number of correct answers.
Find the probability that the number x of correct answers is fewer than 4.
P(x<4)= ???
Answers
Answer: the probability that the number x of correct answers is fewer than 4 is 0.61
Step-by-step explanation:
Let x be a random variable representing the answers to the SAT questions. This is a binomial distribution since the outcomes are two ways. It is either the answer is correct or incorrect. Also, the probability of success or failure is constant for each trial. The probability of success, p = 0.35
The probability of failure, q would be 1 - p = 1 - 0.35 = 0.65
We want to determine P(x < 4)
n = number of trial = 9
x = 4
From the binomial distribution calculator,
P(x < 4) = 0.61
D.Solve the following problems.Show your solution
1.A boy ran a distance of 5.8 kilometers. How many meters did he run?
2. Jose walks 378 meters while Rene walks 0.67 kilometers.What is the difference between the distances which they walked,in centimeters
SHOW YOUR SOLOTION PLSSS
I will ggive u points
sana
Answers
2. 29200 centimeters. there are 100 centimeters in a meter, and 1000 meters in a kilometer, so 0.67x1000 gives you 670 meters, which if multiplied by 100 gives you 67000 centimeters, and if you multiply 378 by 100 you get 37800 centimeters. 67000-37800=29200cm
The values of x and y vary directly
and one pair of values are given.
Write an equation that relates x
and y. Simplify completely.
x = 4, y = 6
[?]
y =
Answers
Answer:
\(y=-\frac{3}{2}\)
Step-by-step explanation:
\(\text{y = kx where k is a constant.}\)
\(6 = -4k\\k = \frac{6}{-4} =-\frac{3}{2}\)
Solve:
-14 + (-3) =
O 11
0 -17
O 17
0-11
Answers
Answer:
-17 ...............................
The following multiple regression printout can be used to predict a person's height (in inches) given his or her shoe size and gender, where gender = 1 for males and 0 for females.
Regression Analysis: Height Versus Shoe Size, Gender
Coefficients
Term Coef SE Coef T-value P-value
Constant 55.24 1.05 52.61 0.000
Shoe Size 1.164 0.13 0.000
Gender 2.574 0.489 5.26 0.000
Required:
a. Find the value of the test statistic for shoe size.
b. Is the regression coefficient of shoe size statistically significant?
c. Does the variable shoe size belong in the model?
d. Interpret the regression coefficient of Gender.
Answers
Answer:
a. 8.95
b. it is
c. yes it belongs
d. males are 2.574 taller than females on average.
Step-by-step explanation:
GIven the regression outpuit that we have in this question, the value of the t test statistics for the shoe size can be solved as
a. test statistic = 1.164/0.13
t test = 8.95
b. the regression coefficient of shoe size is 1.164, this is statistically significant
c. Yes the variable shoe size does belong to the model.
d. The regression coefficient of gender shows that on the average, while holding other variables constant, males are 2.574 inches taller than the their female counterparts.
To the questions circled in the pink/red, can I ask these be solved with work too? Thank you.
Answers
The factorized form for the given polynomials are:
8. 5n(3n² - 4).
10. x²(x - 8).
11. 4x(2x² - 3x + 10).
12. 6x³(1 + 5x).
13. 2w(w² + 3w - 18).
14. 3c²(4c - 1).
15. 2x(x + 3 - 80).
In the question, we are asked to factor the given polynomials.
8. 15n³ - 20n.
The given polynomial is 15n³ - 20n.
The terms are 15n³ and - 20n.
The HCF of the terms is 5n.
Taking the HCF common in the given polynomial, we get 5n(3n² - 4), which is the required form.
Going by the same method, the errors will have a solution as:-
10. x³ - 8x².
The factorized form is x²(x - 8).
11. 8x³ - 12x² + 40x.
Factorized form is 4x(2x² - 3x + 10).
12. 6x³ + 30x⁴.
The factorized form is 6x³(1 + 5x).
13. 2w³ + 6w² - 36w.
The factorized form is 2w(w² + 3w - 18).
14. 12c³ - 3c².
The factorized form is 3c²(4c - 1).
15. 2x² + 6x - 80.
The factorized form is 2x(x + 3 - 80).
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What is the domain of the function in this table?
Answers
Answer: B
Step-by-step explanation:
The domin is X and range is Y so that the domin is 1,2,3,4 and range is 2,3,4 we dont take the same number twice
Answer: B.
Step-by-step explanation:
Just took the quiz
Which shapes are similar but not congruent to shape 1
Answers
There are countless possibilities for shapes that are similar but not congruent to shape 1, as long as they maintain the same proportions and shape.
There are many shapes that are similar but not congruent to shape 1. Similar shapes have the same shape, but their sizes may be different. In contrast, congruent shapes have the same shape and size.
One example of a similar shape to shape 1 is a rectangle that is twice as long and half as wide. Another example could be a square that is three times larger in area than shape 1.
A parallelogram that has the same base as shape 1 but is three times as tall is also similar but not congruent.
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