Mateus recorded the number of miles driven and the amount
of gasoline used in the table below.
Gas Mileage
Distance Gas Usage
(in miles) (in gallons)
105
5
210
10
315
15
420
20
At this rate, what is the maximum miles that can be driven
with 12 gallons of gasoline?
A) 220 miles
B) 236 miles
C) 252 miles
D) 262.5 miles

Answer:

Step-by-step explanation:

Given

slope =6/5

point =(5, -4)

So

the equation of the line =

(y-y1)=m(x-x1)

Where X1=5,y1=-4,m=6/5

Put the values

(Y+4)=6/5(x-5)

5(Y+4)=6(x-5)

5y+20=6x-30

5y-6x=-30-20

-6x+5y=-50

6x-5y=50.

So the equation of the line is 6x-5y=50.

The cost of one apple is $0.70.

Let's assume that the cost of one apple is "a" dollars and the cost of one banana is "b" dollars. We can create two equations based on the information given:

4a + 9b = 12.70 ...(1)

8a + 11b = 17.70 ...(2)

To solve for "a", we can use elimination method by multiplying equation (1) by 8 and equation (2) by -4, so that the coefficients of "a" in both equations will be equal and opposite:

32a + 72b = 101.60

-32a - 44b = -70.80

Adding these two equations, we get:

28b = 30.80

Simplifying and solving for "b", we get:

b = 1.10

Now, we can substitute the value of "b" in equation (1) and solve for "a":

4a + 9(1.10) = 12.70

4a + 9.90 = 12.70

4a = 2.80

a = 0.70

Therefore, the cost of one apple is $0.70.

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The correct answer is the triangle

Triangle : 239 yards

Square : 224 yards

The expression is factorized to give j = -10  and j = 4

From the information given, we have the quadratic equation as;

j²+ 6j - 40

Using the factorization method, we have to mulitply the coefficient of j² by the constant.

After this, find the pair factors of the product that adds up to give 6

Substitute the values

Then, we have;

j² + 10j - 4j - 40

group the expression in pairs

(j² + 10j) - (4j- 40)

factor the common terms

j(j + 10) - 4(j + 10)

We have;

(j + 10) (j - 4)

j + 10 = 0

collect the terms

j = -10

j = 4

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Linear expressions are expressions in which the highest power of the variable is 1.

Linear expressions 3x - 2 and 2x - 3 have a difference of 3x - 2

The given parameter is:

\(\mathbf{difference = x + 1}\)

Let one of the linear expressions be 2x - 3, and the other expression be y.

So, the difference would become

\(\mathbf{y -(2x -3) = x + 1}\)

Open bracket

\(\mathbf{y -2x +3 = x + 1}\)

Collect like terms

\(\mathbf{y = 2x + x + 1 - 3}\)

Evaluate like terms

\(\mathbf{y = 3x - 2}\)

Hence, 3x - 2 and 2x - 3 have a difference of 3x - 2

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The equivalent fraction for 2/3 and 8/11 is 22/33 and 24/33.

What is least common denominator?

The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.

Given fractions are

2/3 and 8/11

L.C.M of 3 and 11 is 33.

We get,

2/3 ×11/11 = 22/33

and

8/11×3/3 = 24/33

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Answer:

No

Step-by-step explanation:

Six times negative three is negative eighteen and that plus four is negative 14

Answer:

5/33

......................................................

The surface area of the cylinder is approximately 2,260.8 square units.

To calculate the surface area of a cylinder, you can use the formula SA = 2πr(r + h), where r is the radius and h is the height of the cylinder. If the diameter of the cylinder is given, you can find the radius by dividing it by 2. In this case, the diameter is 24, so the radius is 24/2 = 12. Now we can substitute the values into the formula:

SA = 2π(12)(12 + 18)
SA = 2π(12)(30)
SA = 720π

Therefore, the surface area of the cylinder is 720π square units. To find an approximate decimal value, we can use the approximation π ≈ 3.14:

SA ≈ 720(3.14)
SA ≈ 2,260.8

So the surface area of the cylinder is approximately 2,260.8 square units.

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Answer:

East

Step-by-step explanation:

Starting position = North

Condition = each time you turn, you are going to turn 90 degrees

Using the image attached as a guide;

If you turn 2 times to the right

- Turning the first time to the right changes the direction to East

- Turning the second time to the right changes the direction to South

1 time to the left

- Turning once to the left changes the direction to East

3 times to the right

- Turning the first time to the right changes the direction to South

- Turning the second time to the right changes the direction to West

- Turning the second time to the right changes the direction to North

2 times to the right

- Turning the first time to the right changes the direction to East

- Turning the second time to the right changes the direction to South

1 time to the left

- Turning once to the left changes the direction to East

Answer:

\(|-3|=3\\-3=-3\)

Step-by-step explanation:

The absolute value represents the distance from the zero on the numberline, so \(|-3|\) represents the distance between number -3 and 0, which is 3 units, and \(-3\) is only the point (value) on the numberline.

So, the value of \(|-3|\) is equal to 3, and the value of -3 is -3.

Answer: in explination

Step-by-step explanation:

annual interest = .05(4000) = 200  

to double, you need another $4000  

number of years = 4000/200 = 20  

annual interest = .05(4000) = 200  

to double, you need another $4000  

number of years = 4000/200 = 20  

it will take 20 years  

to check if you are right you would...

Check:

simple interest on $4000 for 20 years at 5%  

= .05(20)(4000) = 4000  

the amount = what we had + new amount  

= 4000 + 4000 = 8000 which is double what we started with  

So the answer would be it took 20 years.

Length of side of patio A = 12 yards

Area of patio A which is a square :

\( =\tt side \times side\)

\( =\tt 12 \times 12\)

\(\color{plum} = \tt144 \: {yards}^{2} \)

Thus, Area of patio A = 144 yards²

Length of side of patio B = 6.1 yards

Area of patio B which is a square :

\( =\tt side \times side\)

\( = \tt6.1 \times 6.1\)

\(\color{plum} = \tt37.21 \: {yards}^{2} \)

Length of side of the second patio B = 6.1 yards

Area of this patio :

\( =\tt 6.1 \times 6.1\)

\(\color{plum} = \tt37.21 \: yards\)

Total area of Patio B :

= Area of first patio B + Area of second patio B

\( =\tt 37.21 + 37.21\)

\(\color{plum} = \tt74.42 \: {yards}^{2} \)

Thus :

▪︎Area of patio A = 144 yards²

▪︎Area of patio B = 74.42 yards²

▪︎Therefore, the correct option is (a) 74.42

The hexadecimal instruction 2888006416 is associated with the MIPS32 command "d. sub $v0, $t9, $t8".

In MIPS32 assembly language, "sub" is a command used for subtraction. In this particular instruction, the command is subtracting the value stored in register $t8 from the value stored in register $t9 and storing the result in register $v0.

It's important to note that hexadecimal instructions are machine code instructions that are represented in hexadecimal format for ease of reading. They are not typically used by programmers directly. Instead, programmers write code in assembly language and then use an assembler to translate it into machine code.

In summary, the MIPS32 command associated with the hexadecimal instruction 2888006416 is "sub $v0, $t9, $t8", which subtracts the value stored in register $t8 from the value stored in register $t9 and stores the result in register $v0.

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The coefficient for the weight 'carat' based on the "Regression" results is X. The average change in price for a VS1 diamond if the weight increases by 0.1 carat would be Y.

In regression analysis, coefficients represent the relationship between the independent variables (such as weight) and the dependent variable (in this case, price). The coefficient for the weight 'carat' indicates the change in price associated with a one-unit increase in carat weight, holding other variables constant.

To determine the exact coefficient value, it is necessary to refer to the specific regression results. The coefficient could be positive, indicating that as the weight increases, the price also increases, or it could be negative, indicating an inverse relationship.

Additionally, based on the coefficient value, you can estimate the average change in price for a specific increase in weight. If the coefficient for 'carat' is X, and the weight of a VS1 diamond increases by 0.1 carat, the average change in price would be Y.

To obtain the precise values for X and Y, it is essential to refer to the specific regression analysis results provided. The coefficient and the corresponding change in price can vary depending on the dataset and the specific regression model used.

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(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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Answer: (-2,1)

Step-by-step explanation:

The point (1,2) is in quadrant 1.

When rotated 90 degrees counter clockwise, it moves to quadrant 2.

The new point becomes (-2,1)

Answer:81030m

Step-by-step explanation:1km=1000m, 81km=81000+30=81030m

A. The equations for the amounts of money Lyle and Shaun have in their accounts are represented as:

f(x) = 20x + 100

g(x) = 10x + 500

B. When f(x) = g(x), x = 40.

A linear equation can be written in slope-intercept form y = mx + b. Here, the value of m is the unit rate or slope, while the value of b is its y-intercept or initial value.

Part A:

Equation for Lyle:

y-intercept / initial value (b) = $100

Slope / unit rate (m) = $20

To write the equation, substitute m = 20 and b = 100 into f(x) = mx + b:

f(x) = 20x + 100.

Equation for Lyle:

y-intercept / initial value (b) = $500

Slope / unit rate (m) = $10

To write the equation, substitute m = 10 and b = 500 into g(x) = mx + b:

g(x) = 10x + 500.

Part B: To solve the system, we would do the following:

20x + 100 = 10x + 500

20x - 10x = -100 + 500

10x = 400

x = 400/10

x = 40

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Answer:

30 cm²

Step-by-step explanation:

Step 1: Find the value of xy using the formula for area of triangle with 2 sides and an angle between

Area = ½*x*y*sinB

Area of ∆ABC = 30 cm²

sin B = sin 70 = 0.9397

Thus,

30 = ½*x*y*0.9397

30 = (x*y*0.9397)/2

Multiply both sides by 2

60 = xy*0.9397

Divide both sides by 0.9397

60/0.9397 = xy

xy = 63.85

Step 2: calculate the area of ∆PQR with the same formula used in step 1, and also, using the value of the product of x and y gotten in step 1

Area of ∆PQR = ½*x*y*sinQ

x*y = xy = 63.85

sin Q = sin 110 = 0.9397

Area = ½*63.85*0.9397

Area of ∆PQR ≈ 30 cm²

Answer:

the answer is

The answer is

The answer is

The answer is 73

Step-by-step explanation:

To find (f+g)(x), we need to add the functions f(x) and g(x) together. the answer is c. 7x-1

we can add the two functions as follows:

(f+g)(x) = f(x) + g(x)
= (5x - 2) + (2x + 1)

To add the terms with the same variables (x),

we combine the coefficients: = 5x + 2x - 2 + 1

Simplifying the equation: = 7x - 1

To find the sum of two functions, we add the corresponding terms. In this case, we add the coefficients of x and the constants separately. After simplifying the expression, we get 7x - 1 as the result.

Therefore, the correct answer is option c) 7x-1.

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Answer:

Ben receives 75%

Step-by-step explanation:

sum the parts of the ratio, 1 + 3 = 4 parts

Ben receives 3 parts of the 4 , that is

\(\frac{3}{4}\) × 100%

= 0.75 × 100%

= 75%

Answer:

Share of Alex = £130

Share of Ben = £390

Percentage Ben received \(=75\%\)

Step-by-step explanation:

Answer:

18 + 16 n

Step-by-step explanation:

does that equation equal anything??

Answer:

Step-by-step explanation:

-5n+3(6+7n)

-5n+18+21n

16n+18

As per the mentioned informations, the cash paid for rent during 2014 is calculated to be  $395,000. So, the correct  answer is option (C) i.e. $395,000.

To calculate the cash paid for rent during 2014, we need to use the information given in the problem and apply the following formula:

Cash paid for rent = Rent expense + Prepaid rent at the beginning of the period - Prepaid rent at the end of the period

Substituting the values given in the problem, we get:

Cash paid for rent = $420,000 + $70,000 - $95,000

Cash paid for rent = $395,000

Therefore, it can be concluded that the correct answer is (C) $395,000.

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The net advantage to repairing the defective autos compared to selling them for scrap is $9,592,000.

To calculate the net advantage, we need to compare the total revenue from selling the repaired autos to the total revenue from selling them as scrap.

If Luxury Motors sells the defective autos as scrap, they would earn $7,300 per auto, resulting in a total revenue of $7,300 * 6,300 = $45,390,000.

Alternatively, if Luxury Motors chooses to repair the autos, they would incur an additional cost of $17,620,000. However, they can then sell the repaired autos for $11,300 per unit. The total revenue from selling the repaired autos would be $11,300 * 6,300 = $71,190,000.

To calculate the net advantage, we subtract the cost of repairs from the revenue generated from selling the repaired autos: $71,190,000 - $17,620,000 = $53,570,000.

Finally, we subtract the revenue from selling the autos as scrap from the net revenue generated by repairing them: $53,570,000 - $45,390,000 = $9,592,000.

Therefore, the net advantage to repairing the autos compared to selling them for scrap is $9,592,000.

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Entonces, el precio de cada nucita es $35 y el precio de cada paleta payaso es $12.50.

Sea "x" el precio de cada nucita y "y" el precio de cada paleta payaso. Entonces, podemos plantear el siguiente sistema de ecuaciones:

2x + 4y = 120

5x + 2y = 200

Podemos utilizar el método de eliminación para resolver este sistema. Multiplicando la primera ecuación por 5 y la segunda por 2, obtenemos:

10x + 20y = 600

10x + 4y = 400

Restando la segunda ecuación de la primera, obtenemos:

16y = 200

Por lo tanto:

y = 12.5

Sustituyendo este valor en la primera ecuación, podemos despejar "x":

2x + 4(12.5) = 120

2x = 70

x = 35

Entonces, el precio de cada nucita es $35 y el precio de cada paleta payaso es $12.50.

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Using a standard normal distribution table, we can find that the percentage of values below a z-score of -1.6 is approximately 5.0%. Therefore, we can say that Carl has a higher GPA than approximately 95% of other students at UTA.

To determine Carl's z-score, we need to know the mean and standard deviation of GPAs at UTA. Without this information, we cannot calculate the z-score. However, we can still determine the percentage of other students at UTA who have a lower GPA than Carl. We can use a standard normal distribution table to find this percentage, assuming that GPAs at UTA are approximately normally distributed.

First, we need to calculate the z-score corresponding to Carl's GPA of 2.2. Assuming a mean GPA of 3.0 and a standard deviation of 0.5, we can use the formula: z = (x - μ) / σ

where x is Carl's GPA, μ is the mean GPA, and σ is the standard deviation. Plugging in the values, we get:

z = (2.2 - 3.0) / 0.5 = -1.6

Using a standard normal distribution table, we can find that the percentage of values below a z-score of -1.6 is approximately 5.0%. Therefore, we can say that Carl has a higher GPA than approximately 95% of other students at UTA.

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Answer:

The given equation Y=4x^3+6 is a nonlinear equation because it contains a term with a power of 3, which means that the relationship between Y and x is not linear. In a linear equation, the power of the variable is always 1. Therefore, the answer is B. Nonlinear.

Step-by-step explanation: