A car is driving away from El Paso with constant velocity. At 1 p.m., it is 145 miles away from El Paso. At 3 p.m., it is 275 miles away from El Paso.

Part A: Write a linear function that describes the distance (in miles) the car is from El Paso in terms of time (in hours after 12:00 p.m.).

The proportional relationship is complete as follows:

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

The constant for this problem is given as follows:

k = 146/19

k = 7.684.

Hence the equation is:

y = 7.684x.

The input for an output of 438 is given as follows:

7.684x = 438

x = 438/7.684

x = 57.

The output for an input of 76 is obtained as follows:

y = 7.684 x 76

y = 584.

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According to the information, the least number of committees that need to be formed to meet all of the conditions is 8.

To minimize the number of committees, we can try to use each student in as many committees as possible. Since each student must be in exactly 2 committees, and there are 12 students, we need a total of 24 "student committee slots".

Now we need to figure out how to assign the students to committees so that no two committees have more than one student in common. One way to do this is to use a "round-robin" approach:

Assign the first student to committees 1, 2, and 3.

For the next student, assign them to committees 1, 4, and 5.

For the third student, assign them to committees 2, 4, and 6.

Continue in this way, cycling through the remaining students and assigning them to three committees at a time, making sure to avoid any duplicates.

After assigning all 12 students to committees in this way, we will have a total of 8 committees. We can check that each committee contains exactly 3 students, and that no two committees have more than one student in common.

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The  three equivalent numerical expressions are; Options M, R and S

To determine the expressions, we need to take note that index forms are described as forms that are used for the representation of numbers or variables that are too large or small to be written.

Some rules of index forms are;

From the information given, we have that;

(2^-3)(2^5)/2^7)

add the exponents of the numerator

2⁻³⁺⁵/2⁷

Add the values

2²/2⁷

Subtract the exponents

2⁻⁵

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The ratio of Student Ambassadors to total Students in Mr. Thompson's class is 1:4.

Ratios and proportions are two fundamental concepts in mathematics that are used to compare quantities and express relationships between them.

A ratio is a comparison of two quantities that are expressed in the same units. Ratios are typically written in the form of "a:b" or "a to b", where a and b are two quantities being compared. For example, the ratio of the number of boys to the number of girls in a class of 20 students might be 3:2, indicating that there are 3 boys for every 2 girls.

A proportion is a statement that two ratios are equal. Proportions are used to solve problems involving ratios by setting up an equation that equates two ratios.

The total number of students in Mr. Thompson's class is 6 + 18 = 24.

The ratio of Student Ambassadors to total Students is 6:24, which can be simplified by dividing both the numerator and denominator by 6 to get 1:4.

Therefore, the ratio of Student ambassadors to total Students in Mr. Thompson's class is 1:4.

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Option B is the actual length of the playground, which is 27 feet.

First, find the scale factor from the drawing to the actual playground. Since the width of the drawing is 2 inches and the actual width is 6 feet, the scale factor is:

6 feet / 2 inches = 3 feet/inch

Next, use this scale factor to find the actual length of the playground. The length in the drawing is 9 inches, so the actual length is:

9 inches x 3 feet/inch = 27 feet

Therefore, the actual length of the playground is 27 feet.

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The value of function (f - g)(x) will be; 2x² - 3x

Since Function is a type of relation, or rule, that maps one input to specific single output. A Linear function is a function whose graph is a straight line

We are given that the function;

f(x)=-2x²-2x+1

g(x)=x+1

(f - g)(x) = f(x) - g(x)

(f - g)(x) =2x²-2x+1  - (x+1)

(f - g)(x) = 2x²-2x+1  - x - 1

(f - g)(x) = 2x² - 3x

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When the figure is decomposed, we will have 3 triangles and one square figure

In this problem, we have a given figure in which we are asked to break down or decompose and identify the individual shapes.

At the center of the figure, we have a square shape. A square is a figure or shape that has all it's edges equal and are at equal angle to one another. The edges of a square are at 90 degrees to one another.

At the edges of the square, we have three triangles attached to it to the edges of the square.

From the image, the triangles must also be of equal size since they're attached to the base of a square which has an equal sides across all it's edges.

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By the theorem of triangles, the calculated value of y in the triangle ABC is 50 degrees

From the question, we have the following parameters that can be used in our computation:

The triangle ABC

Also, the angles in the triangle are given as y, y and 80 degrees

By the theorem of triangles, the sum of angles in a triangle is 180 degrees

Representing the above statement as an equation, we have

y + y + 80 = 180

Evaluate

y = 50

So, we can conclude that the value of y is 50 degrees

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The volume of the oblique cylinder can be calculated as:

833π cm³

The formula that would be used to find the volume of any given oblique cylinder can be expressed as:

Volume = πr²h, where:

radius of the cylinder = r

height of the cylinder = h

π is a constant

We are given the values for the cylinder as:

r = 14/2 = 7 cm

h = 17 cm

Volume of the oblique cylinder =  πr²h =  π × 7² ×  17

Volume of the oblique cylinder = 833π cm³

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Answer:

$68,796.57

Step-by-step explanation:

approx $68,796.57 at 18 years

Answer:

(x + 1)² + y² = 3

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 1, 0 ) and r = [tex]\sqrt{3}[/tex] , then

(x - (- 1) )² + (y - 0)² = ([tex]\sqrt{3}[/tex] )² , that is

(x + 1)² + y² = 3

The two ways of rewritting the fraction are.

6/10 = 60/100

6/10 = 0.6

Here we know that of the trees in a park 6/10 have red leaves. And we want to write that fraction with a 100 as the denominator (the second number of the fraction)

To do so, we can multiply our fraction by 10/10

Notice that the quotient is equal to 1 so it does not change the value of our fraction, then we will get:

(6/10)*(10/10) = 60/100

And the fraction written as a decimal is:

6/10 = 0.6

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The solution is, the value of the angle & x is:

x = 43

43°, 51°, 86°

We have,

The sum of the angles is ...

 x° + (x +8)° + 2x° = 180°

 4x +8 = 180 . . . . . . . . . . . collect terms, divide by °

 x +2 = 45 . . . . . . . . . . divide by 4

 x = 43 . . . . . . . . . . subtract 2

 x +8 = 51

 2x = 86

The angles are 43°, 51°, 86°.

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complete question:

The sum of the angle measures of a triangle is 180°. Find the value of x. Then find the angle measures of the triangle.

The fencing that Wally needs more in 81 feet

A D = E F

A F = DE

AD = AB + BC + CD

Length of the back wall = 15 m

1 y ard = 3 ft

15 ya rds = 15 x 3 = 45

AD EF is a rectangle

5 + 45 + 3 feet

= 53 feet

Then the amount of the fencing that would be required is given as

5 feet + 3 feet + 10 feet + 10 feet + 53 feet

= 81 feet

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Answer:

The equation that shows how the cost of the baby shower, y, depends on the number of guests, x is:

y = 9x + 43

In this equation, x represents the number of guests and y represents the cost of the baby shower. The term 9x represents the cost of food for each guest, multiplied by the number of guests. The term 43 represents the cost of decorations that has already been spent. Therefore, the total cost of the baby shower can be calculated by multiplying the number of guests by the cost of food per guest and adding the cost of decorations that have already been spent.

Answer: y = 9x + 43

Step-by-step explanation: y =  cost of the baby shower

x = number of guests

$9 per guest would be 9x

Answer:

6x-50-7(3x+10)=0

Distribute the -7:

6x - 50 - 21x - 70 = 0

Combine like terms:

-15x - 120 = 0

Add 120 to both sides:

-15x = 120

Divide both sides by -15:

x = -8

Answer: volume of the cone is 324pi cm^3

Step-by-step explanation:

the volume of the cone is derived by the formula

V= 1/3 pi r^2 h

v= volume of the cone

h= height of the cone

r= radius of the cone

V= 1/3 x pi x 9 x 9 x 12

V= 324pi cm^3

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Step-by-step explanation:

to find the volume use the formula (1/3)πr2h,

[tex]( \frac{1}{3})h\pi \: r {}^{2} \\ \frac{1}{ 3} \times \pi \times 9 \times 9 \times 12 \\ \frac{1}{3} \times 972\pi \: cm \\ = 324\pi \: cm {}^{3} [/tex]

Answer:

1.

a) 3 cubes

b) 5 cubes

c) 15 cubes

d) 45 cubes

2.

a) 2 cubes

b) 4 cubes

c) 8 cubes

d) 8 , 1/8

Step-by-step explanation:

1.

a) 3 cubes because 1.5/0.5=3

b) 5 cubes because 2.5/0.5=5

c) 15 cubes because 5x3=15

d) 45 cubes because the height 1.5/0.5=3 so 3x15=45

2.

a) 2 cubes beacuse 1/0.5=2

b) 4 cubes because the lenght is 1/0.5=2

c) 8 cubes because the height is 1/0.5=2 4x2=8

d) 8 , 1/8

Answer:

El volumen en cm cúbicos es 108 cm cúbicos (o a la tercera potencia). La fórmula utilizada para encontrar el volumen es largo por ancho por alto.

Using the correct measure of center, the team that typically has the tallest players is C. The Champs, with a mean of about 66.4 inches.

The three typical measures of center are the mean, the median, and the mode.

The mean is the average value, obtained as the quotient of the total value of the data set divided by the number of items.

The median is the middle value of the data set arranged in descending or ascending order.

The mode refers to the value that occurs most in the data set.

66 66 66 = 198

63 63 63 = 189

65 65 65 = 195

64 64 64 = 192

58 58 58 = 174

Total =      948

Mean = 63.2 (948 ÷ 15)

Median = 64 (58, 58, 58, 63, 63, 63, 64, 64, 64, 65, 65, 65, 66, 66, 66)

62 69 65 = 196

68 60 70 = 198

70 58 67 = 195

66 75 70 = 211

69 67 60 = 196

Total = 996

Mean = 66.4 (996 ÷ 15)

Median = 67 (58, 60, 60, 62, 65, 66, 67, 67, 68, 69, 69, 70, 70, 70, 75)

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For any matrices A and B, where A is a m x n matrix and B is a n x p matrix, the inequality rank(AB) ≤ min rank(A), rank(B) holds.

To see why this is so, examine the rank of a matrix, which is defined as the matrix's greatest number of linearly independent rows or columns.

In other words, it is the dimension of the vector space covered by the matrix's rows or columns.

When we multiply matrices A and B to obtain AB, we get a matrix with m rows and p columns.

The dot product of a row from A and a column from B yields each element in the matrix.

Because the rows and columns of AB are linear combinations of the rows and columns of A and B, the rank of AB is at most the minimum of the rank of A and the rank of B.

If either A or B has a lower rank than the other, there will be some linear dependency between the rows or columns of one of the matrices, which will carry over to AB. This indicates that AB's rank will be strictly less than the bigger matrix's rank.

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Answer:

Salon des Refusés. Is the correct answer

Edouard Manet's Luncheon on the Grass was shown in the Salon des Refusés after it was rejected for the annual salon.

Answer:  Yes, (-4, 24) is a solution to the given equation.

Step-by-step explanation:

24 = -6(-4)

24 = 24

Answer:106

Step-by-step explanation:

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$975\\ r=rate\to \text{\LARGE 5.7\%}\to \frac{5.7}{100}\dotfill &0.057\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years \end{cases} \\\\\\ A = 975\left(1+\frac{0.057}{1}\right)^{1\cdot t} \implies A = 975(1.057)^t[/tex]

At a drug research testing facility:

To find the probability that the drug will wear off in less than 200 minutes:

The z-score is (200-240)/40 = -1.

Using a standard normal distribution table or calculator, P(z < -1) = 0.1587. Therefore, the requested probability is P(x < 200) = 0.1587.

To find the probability that the drug will wear off after 220 minutes:

The z-score is (220-240)/40 = -0.5.

Using a standard normal distribution table or calculator, P(z < -0.5) = 0.3085. Therefore, the requested probability is P(x > 220) = 0.3085.

To find the probability that the drug will wear off between 200 and 220 minutes:

Using the z-scores calculated above, find the area between them on the standard normal distribution. P(-1 < z < -0.5) = 0.1867.

Therefore, the requested probability is P(200 < x < 220) = 0.1867.

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The bond yield is approximately 5.0% to the nearest tenth of a percent.

We have,

To find the total cost of the 10 State Farm bonds, we can multiply the price per bond by the number of bonds:

10 bonds x $99.40 per bond = $994.00

So, we paid $994.00 for the 10 State Farm bonds.

To calculate the amount of interest we will receive each year from the bonds, we can use the following formula:

Interest = Principal x Rate

where:

The principal is the amount invested in the bonds

Rate is the interest rate

In this case, our principal is $994.00 and our rate is 5%, or 0.05 as a decimal.

So, the annual interest we will receive from the bonds is:

Interest = $994.00 x 0.05 = $49.70

So,

We will receive $49.70 in interest each year from the bonds.

To calculate the bond yield, we need to use the following formula:

Bond yield = (Annual interest / Total cost) x 100%

In this case, the annual interest is $49.70 and the total cost is $994.00, so we can plug these values into the formula:

Bond yield = ($49.70 / $994.00) x 100% ≈ 5.0%

Therefore,

The bond yield is approximately 5.0% to the nearest tenth of a percent.

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