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Answer:

113.1 is the volume of the sphere.

Answer:

[tex]volume = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times 3.14 \times {(3)}^{3} \\ = 113.04 \: {cm}^{3} [/tex]

a) The equation that models Alice's total cost of filling up her car tank using regular unleaded gas and premium gas is 4.65r + 4.95p = 874.80.

b) Based on the above equation, if Alice purchases 87 gallons of regular unleaded gas, it means that she also purchases 95 gallons of premium gas.

An equation is a mathematical statement equating two or more mathematical expressions using the equation sign (=).

The cost per gallon of regular unleaded gas = $4.65

The cost of premium gas per gallon = $4.95

The total cost for gas = $874.80

Let gallons of regular unleaded gas = r

Let gallons of premium gas = p

4.65r + 4.95p = 874.8

If r = 87, the value of p is:

4.65(87) + 4.95p = 874.8

404.55 + 4.95p = 874.8

4.95p = 470.25

p = 95 gallons

Thus, during Alice's first leg from the East Coast to the West Coast, she purchases 87 gallons of unleaded and 95 gallons of premium gas for her car.

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Answer:

x = 24

Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180°.

4x + x + 60 = 180

5x + 60 = 180

5x = 120

x = 24

Answer:

it 33 pts not 50

Answer:

Point E

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

You don't move on the x axis, so no side to side movement.

You do move on the y axis, but only down 1.

D is the only one that can work.

Answer:

chicken pot pie

Step-by-step explanation:

ain't good

The number of cans needed will be 3.divide the total surface area by the area the spray paint can cover.

The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.

The total surface area to be painted;

A = Area 1 + Area 2 +Area 3+Area 4 \\\\\ A= Area of rectangular face 1 + Area of triangular surface 1+Area of triangular face 2 +Area of rectangular face 2

[tex]\rm \ A = 36 \times 50 + \frac{1}{2}\times 48 \times 14 +\frac{1}{2} \times 48 \times 14 + 36 \times 14 \\\\ A = 1800 +672+504 \\\\ A = 2976 \ inch^2[/tex]

The total surface area to be painted is 2976 inch².

To find the number of cans, divide the total surface area by the area that the spray paint can cover;

[tex]\rm n = \frac{2976}{1000} \\\\ n = 2.976 \\\\ n \approx 3[/tex]

Hence, the number of cans required will be 3.

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Answer:

106 boys

Step-by-step explanation:

7th grade = 159 students

Boys to girls ratio:

2:1

Find two thirds of 159:

2/3*159 = 106 boys

159-106= 53 girls

Check:

53*2 = 106

Answer:

318 boys

Step-by-step explanation:

Easy mutiplication

159*2=318

Answer: x=-1/4 and x=-1

Step-by-step explanation:

The answer choices you give are extremely hard to figure out, so I hope my explanations and answers help.

The quadratic formula is [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]. Once we figure out a, b, c, we can plug them into the formula and solve for x.

The standard form equation is ax²+bx+c=0. The equation given matches this so we know that:

a=4

b=5

c=1

Plug them into the formula. There is a [tex]\pm[/tex] symbol, which stands for "plus or minus". This means we solve the formula with addition and subtractions separately. We should have 2 solutions at the end. Let's do them separately to show work.

Solution 1: addition

[tex]x_1=\frac{-5+\sqrt{5^2-4(4)(1)} }{2(4)}[/tex]             [exponents]

[tex]x_1=\frac{-5+\sqrt{25-4(4)(1)} }{2(4)}[/tex]             [multiply]

[tex]x_1=\frac{-5+\sqrt{25-16} }{8}[/tex]                    [inside square root]

[tex]x_1=\frac{-5+\sqrt{9} }{8}[/tex]                          [square root]

[tex]x_1=\frac{-5+3}{8}[/tex]                            [add]

[tex]x_1=\frac{-2}{8}[/tex]                                [divide top and bottom by 2]

[tex]x_1=-\frac{1}{4}[/tex]

Solution 2: subtraction

[tex]x_2=\frac{-5-\sqrt{5^2-4(4)(1)} }{2(4)}[/tex]             [exponents]

[tex]x_2=\frac{-5-\sqrt{25-4(4)(1)} }{2(4)}[/tex]             [multiply]

[tex]x_2=\frac{-5-\sqrt{25-16} }{8}[/tex]                    [inside square root]

[tex]x_2=\frac{-5-\sqrt{9} }{8}[/tex]                          [square root]

[tex]x_2=\frac{-5-3}{8}[/tex]                            [subtract]

[tex]x_2=\frac{-8}{8}[/tex]                                [divide]

[tex]x_2=-1[/tex]

I am not able to find the answer choices, but we know that x=-1/4 and x=-1.

The length and width of the rectangle will be 16 centimeters and 13 centimeters, respectively.

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be

Perimeter of the rectangle = 2(L + W) units

The length of a rectangle is 3cm longer than its width. If the perimeter of the rectangle is 58 cm. Then the equations are given below.

L = 3 + W                ...1

2(L + W) = 58

L + W = 29                ...2

From equations 1 and 2, then we have

3 + W + W = 29

2W = 26

W = 13 cm

Then the length of the rectangle will be given as,

L = 3 + 13

L = 16 cm

The length and width of the rectangle will be 16 centimeters and 13 centimeters, respectively.

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Answer:

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

i think b because it makes more sense than a or c

Answer:

The answer is a because the sign should be facing right but not be greater than or equal to.

Answer:

0.0005

Step-by-step explanation:

this is a binomial experiment -- they are either cured or not, and the outcome is random

probability = n choose r * p^r * q^(n-r)

here, n = number of trials, r = number of successes desired, p = probability event occurs, and q = probability event doesn't occur

probability = n choose r * p^r * q^(n-r) = 6 choose 3 * 0.97^3 * 0.03^(6-3)

= 0.00049284342 rounding to 0.0005

Answer:

D 28/36

Step-by-step explanation:

A person's debt-to-income can be calculated by dividing all his/her monthly debt payments by the gross monthly income. This number can be used for determining your ability to manage your monthly payments to repay the money you plan to borrow. In general, 43% is the highest DTI ratio a borrower can have and still get qualified for a mortgage, but lenders prefer a ratio lower than 36%, with no more than 28% of that debt going towards servicing a mortgage or rent payment. Thus, someone should spend at most 28% of his/her gross income on total housing expense and maximum of 36% on total debt service.

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

I gave you all of the information to fill out the first page

i also answered some of the questions on the 2nd page. They are written sideways on the page. The other questions I didn’t answer yneed calculations after you add all of the expenses together.

put the amounts from each category I listed in the image and put them into the respective category and get the total for each category. Use those totals to fill out page two. If you get stuck I don’t mind helping but I thought this is the best way to get you started.  

Answer:

21

Step-by-step explanation:

If the mean of the data set is 20, we know that it is the sum of all the values in the data set, divided by the number of values. So, with s representing the sum, the mean is s/6 = 20

To undo division, multiply 20 by 6. 20*6 = 120.

120 is the sum of all of the values. Since we're taking out the number 15, subtract it from 120. You're left with 105, which is the sum of the rest of the numbers. Since you now only have 5 numbers, divide 105 by 5 and you get the new mean, which is 21.

An undecidable problem is one that should have a "yes" or "no" answer but has no algorithm that can correctly answer on all inputs.

According to the theories of computational complexity and computability, an undecidable problem is one for which it has been demonstrated that it is impossible to create an algorithm that always yields the right yes-or-no response. As an illustration, it can be shown that there is no algorithm that can accurately predict whether arbitrary programmes will eventually halt when run.

Any question that is simply yes or no on an infinite list of inputs is a decision problem. It is customary to define the decision problem as the set of inputs for which the problem returns yes because of this. Natural numbers as well as values of other kinds, such as strings in a formal language, can be used as these inputs.

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Step-by-step explanation:

Volume of displaced water = (10cm)(10cm)(1.6cm)

= 160 cm^3

density = mass/vol of displaced water

= 3088 grams/160 cm^3

= 19.3 g/cm^3

P.S. This is most likely a pure gold medallion.

Answer:

13, 14, 15, 16

Step-by-step explanation:

Call the first number  n.  Then the next three consecutive numbers (assuming integers) are  n + 1, n + 2, n + 3.

The mean is the total of the numbers divided by how many there are.

[tex]\frac{n+(n+1)+(n+2)+(n+3)}{4}=14.5[/tex]

Simplify and multiply by 4.

[tex]4n+6=58\\4n=52\\n=13[/tex]

The first number is 13.

The median is 14.5, halfway between the "middle" numbers 14 and 15.  This is just a check; no additional equation is necessary.

Jake and Hakeem's rocket's flight is approximately modeled by the equation h(t) = - 12t ^ 2 + 36t + 3. The rocket's highest point is 30m

Generally, Since we are not instructed on what to look for, we are able to determine the highest point that the rocket ever achieved.

Given that the rocket's flight can be approximated approximatively using the equation,

h(t) = - 12t ^ 2 + 36t + 3

At maximum height dh/dt = 0

dh/dt = --24t + 36

0 = -24t + 36

24t = 36

t= 36/24

t = 1.5s

Find out the maximum height.

h(1.5) = - 12 (1.5)^ 2 + 36(1.5) + 3

h(1.5) = - 12(2.25) + 54 + 3

h(1.5) = -27 + 57

h(1.5) = 30m

As a result, the rocket is only capable of reaching a height of 30 meters at its highest point.

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Zero is the middle point of a number line.

On the number line, all positive (natural numbers) numbers are on the right side of zero, while all negative numbers are on the left. A number's value lowers as we turn to the left. As an illustration, 1 is greater than -2.

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point. [1]

The integers are frequently represented as specially designated, uniformly spaced dots on a line. It is frequently employed as a teaching tool for basic addition and subtraction, particularly when negative numbers are involved.

The number line may also be referred to as a real line or real number line in advanced mathematics.

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Answer:

x > 3

Step-by-step explanation:

6x - 2 - 3x + 9 > 16

3x + 7 > 16

3x > 9

x > 3

Answer:

1/4 of 60= 15

15+60=75

75 is 125% of 60

Step-by-step explanation:

Answer:

[tex]use \: this \: formula \\ circumference = dimeter \times 3.14 = 2 \times radius \times 3.14 \\ \\ area = 0.25 \times {diameter}^{2} \times 3.14 = {radius}^{2} \times 3.14[/tex]

Answer:

5^5+4/5^6

5^9/5^6

5^9-6

5^3

125

Step-by-step explanation:

Firstly the powers of 4 adds up

Then net power is formed by (9-6) ie 3

Lastly 5^3 is result which is 125

The correct option is option (c)-"The distribution is skewed right."

The distribution of the ages of the Best Actor Oscar winners is slightly skewed to the right.

A histogram of the ages of the Best Actor Oscar winners shows that the majority of the ages are centered around the mean age, with a few ages on the higher end that extend the right tail of the distribution. This creates a small skewness to the right.

The distribution seems to be centered at around 42-43.

The age distribution ranges from about 30 to about 75, without taking into account an outlier.

It's worth noting that the distribution is not extremely skewed, and the majority of the ages are still grouped around the center of the distribution.

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