A car is traveling at a speed of 80 miles per hour. What is the car's speed in kilometers per hour? How many kilometers will the car travel in 4 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.

Answer:

Step-by-step explanation:

After the first year, the number of rabbits will double from 50 to 100.

After the second year, the number of rabbits will double again from 100 to 200.

This doubling process will continue for a total of 5 years, so after 5 years, the number of rabbits will be:

Number of rabbits after 5 years = 50 x 2^5 = 50 x 32 = 1600

Therefore, there will be 1600 rabbits on Groff Farm after 5 years.

Similarly, after 10 years, the number of rabbits will double 10 times:

Number of rabbits after 10 years = 50 x 2^10 = 50 x 1024 = 51200

Therefore, there will be 51,200 rabbits on Groff Farm after 10 years.

Mr. Brust is standing at a height of approximately 90.6 feet in the tree. When they shoot him, he will fall from this height.

Let's break down the problem and solve it step by step.

First, we'll find the height from which Mr. Brust falls, and then we'll find the total distance he falls considering the tree's height and the height of the shed.

Find the height of the tree where Mr. Brust is standing:

We can use the tangent function to find the height of the tree above the shed where Mr. Brust is hiding.

tan(θ) = opposite/adjacent

We know the angle of elevation (θ) is 65°, and the tree is 40 feet in front of the shed. So, we have:

tan(65°) = height_above_shed / 40 ft

height_above_shed = 40 ft * tan(65°)

Using a calculator, we find:

height_above_shed ≈ 40 ft * 2.14 ≈ 85.6 ft

Find the total height of the tree where Mr. Brust is standing:

Since Mr. Kelly and Mr. Sullivan are 5 feet off the ground, we need to add this height to the height_above_shed we just calculated:

total_height = height_above_shed + height_of_shed

total_height = 85.6 ft + 5 ft = 90.6 ft

So, Mr. Brust is standing at a height of approximately 90.6 feet in the tree. When they shoot him, he will fall from this height.

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Since the function is already in standard form (ax^2 + bx + c form) you don't have to change anything and simply rewrite it.

For the vertex, if you have a quadratic function in standard form -b/2a is the x value of the vertex.

-b/2a = -4/(2(2)) = -1

Since we now know the x-value of the vertex we can plug it into the function to find the corresponding y-value.

h(-1) = 2(-1)^2 + 4(-1) - 10 = -12

So, the vertex is at (-1,-12)

A = [-4/3 -1/3; 10 10/3] is the matrix that fulfills the equation A × [1 0; -1 3] = [-1 -3; 1 6].

Rows and sections of integers are arranged in a matrix. Learn about matrices' lengths and components as you begin your study of them. A rectangle matrix is a grouping of integers into rows as well as columns. The matrix A, for instance, has two rows along with three columns.

To find the matrix A, we need to solve the matrix equation:

A × [1 0; -1 3] = [-1 -3; 1 6]

We can do this by multiplying both sides by the inverse of [1 0; -1 3] on the left:

A × [1 0; -1 3] × [3 0; 1 1/3] = [-1 -3; 1 6] × [3 0; 1 1/3]

Simplifying the left-hand side using the associative and commutative properties of matrix multiplication, we get:

A × [3 0; -1 1] = [-3 -1; 10 3]

Now, we can solve for A by multiplying both sides by the inverse of [3 0; -1 1]:

A × [3 0; -1 1] × [1/3 0; 1/3 1] = [-3 -1; 10 3] × [1/3 0; 1/3 1]

Simplifying the left-hand side using the associative and commutative properties of matrix multiplication, we get:

A × [1 1/3; 0 1] = [-2/3 -1/3; 10/3 3]

Multiplying both sides by the inverse of [1 1/3; 0 1]:

A = [-2/3 -1/3; 10/3 3] × [1 1/3; 0 1]⁻¹

We can easily find the inverse of [1 1/3; 0 1]:

[1 1/3; 0 1]⁻¹ = [1 -1/3; 0 1]

So, substituting this into the equation for A, we get:

A = [-2/3 -1/3; 10/3 3] × [1 -1/3; 0 1]

Multiplying the matrices on the right-hand side, we get:

A = [-2/3 -1/3; 10/3 3] × [1 -1/3; 0 1] = [-4/3 -1/3; 10 10/3]

Therefore, the matrix A that satisfies the equation A × [1 0; -1 3] = [-1 -3; 1 6] is:

A = [-4/3 -1/3; 10 10/3]

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Answer: The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Step-by-step explanation:

I hope it helped! :)

Answer:

The average rate of change of the function from x=-1 to x=1 is 6.

Step-by-step explanation:

The average rate of change of a function from x=-1 to x=1 is the change in the output of the function (y-value) divided by the change in the input of the function (x-value). In other words, it is the slope of the line connecting the two points (x=-1 and x=1).

Answer:

To find the interest rate, we can use the formula for simple interest:

I = Prt

Where:

I = Interest earned

P = Principal (initial investment)

r = Interest rate

t = Time

We are given that P = $100, t = 3 years, and I = $15. Substituting these values, we get:

15 = 100 * r * 3

Solving for r, we get:

r = 15 / (100 * 3) = 0.05

Therefore, the interest rate on the savings account is 5%.

Answer:

The question you provided is a math problem involving fractions, specifically solving for an unknown quantity using a proportion. Here is how you can solve it:

1/15 = 5/8

To solve for the unknown quantity, you can use cross-multiplication, which means multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa:

1 * 8 = 15 * 5

Simplifying this equation, we get:

8 = 75

This is a contradiction, so the given equation has no solution. Therefore, none of the answer choices (A, B, C, D) are correct.

I hope this helps! If you have any further questions, feel free to ask.

Answer:

Step-by-step explanation:

The figure is a rectangular trapezoid, and this answers one question, the second question is the area, which we find by making the major base plus the minor base multiplied by the height and we divide everything by two, the two bases are the parallel ones (12 and 8) and the height is 7.

Then it is resolved with this expression

Area = [(12 + 8) ×  7] : 2

Area = (20 × 7) : 2

Area = 140 : 2

Area = 70 cm²

Answer: Sally will earn $4,830.00 in interest over 7 years.

Step-by-step explanation:

If the interest is not compounded, then Sally will earn simple interest, which can be calculated using the formula:

I = P * r * t

where:

I = the interest earned

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

t = the time period, in years

In this case, we have:

P = $9,000 (the initial deposit)

r = 7% = 0.07 (the annual interest rate)

t = 7 (the number of years)

So, plugging in the values:

I = $9,000 * 0.07 * 7

I = $4,830.00

Therefore, Sally will earn $4,830.00 in interest over 7 years.

Answer: 6

Step-by-step explanation:

21 - 1 = 20

20 - 2 = 18

18 - 3 = 15

15 - 4 = 11

11 - 5 = 6

Answer:

correct answer

c. 0.07 × $350

Answer:

Let x be the number of miles completed by the participant before the mark. Then, the total distance of the triathlon is:

2.6 + 110 + 26.2 = 138.8 miles

At the mark, the participant has completed x miles and has the remaining distance to complete, which is:

138.8 - x

According to the problem, x is equal to the remaining distance:

x = 138.8 - x

Solving for x, we get:

2x = 138.8

x = 69.4

Therefore, the participant had completed 69.4 miles at the mark.

Answer:

D) 115.2π cm².

Step-by-step explanation:

The surface area of a cylinder can be calculated using the formula:

Surface Area = 2πr² + 2πrh

where r is the radius and h is the height of the cylinder.

In this case, r = 4 cm and h = 10.4 cm. Substituting these values in the formula, we get:

Surface Area = 2π(4)² + 2π(4)(10.4)

Surface Area = 2π(16) + 2π(41.6)

Surface Area = 32π + 83.2π

Surface Area = 115.2π

Therefore, the exact surface area of the candle is 115.2π cm².

The answer is (D) 115.2π cm².

Answer: The answer is D, 115.2π cm²

Step-by-step explanation: When we use the formula of 2πrh+2πr2=2·π·4·10.4+2·π·42 to get the surface area, which equals 361.91

We can divide this by pi to get 115.2π cm²

Hope this helped!

We may conclude after answering the presented question that where equation V(z) is the value of the car z years after 1964.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry.

To model the value of the car, we can use the exponential growth formula:

[tex]V(t) = V0 * (1 + r)^t\\V(t) = ab^t\\a = V0 = $2000\\b = 1 + r = 1 + 0.113 = 1.113\\V(z) = 2000 * 1.113^z\\[/tex]

where V(z) is the value of the car z years after 1964.

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Answer:

53 in2 is the answer for this question

Answer:

53

Step-by-step explanation:

If you divide the figure into two parts by extending the 4 in side, you get a right triangle and a rectangle.

Area of rectangle:

6*8 = 48 in²

Area of triangle:

1/2*(13 - 8)*(6 - 4) = 1/2 times 5 times 2 = 5 in²

Total area is:

48 + 5 = 53 in²

hope this helps x

Answer:

421.875 ft³

Step-by-step explanation:

Since the length, width, and heigh are equal, this is a cube.

V = s³

V = (7.5 ft)³

V = 421.875 ft³

Answer:421.875 ft^3

Step-by-step explanation:

Answer:

585 miles

Step-by-step explanation:

845 miles ÷ 13 hours = 65 mph

645 mph * 9 hours = 585 miles

10³•10⁵•10³

Step-by-step explanation:

10³means 10×3,10⁵means 10×5and 10³means 10×3 30+50+30=110

Answer:

0.9973 or 364/365

Step-by-step explanation:

Assuming that every day of the year is equally likely to be someone's birthday, the probability that a randomly selected person has a birthday on the 1st day of the month is 1/365, since there are 365 possible birthdays in a year.

Therefore, the probability that a randomly selected person does not have a birthday on the 1st day of the month is:

P(not on 1st day) = 1 - P(on 1st day)

P(not on 1st day) = 1 - 1/365

P(not on 1st day) = 364/365

So, the probability that a randomly selected person does not have a birthday on the 1st day of the month is 364/365 or approximately 0.9973.

Therefore, the measure of the intercepted arc by the inscribed angle of 61 degrees is 122 degrees.

A circle is a closed shape in geometry that is defined as the set of all points in a plane that are at a fixed distance from a given point, called the center of the circle. The distance between any point on the circle and the center is called the radius of the circle.

Given by the question.

In a circle, an inscribed angle is an angle formed by two chords of the circle that have a common endpoint on the circle. The measure of an inscribed angle is half the measure of its intercepted arc.

Let's call the intercepted arc by the inscribed angle "x". Then, the measure of the inscribed angle is 61 degrees, and we can use the formula mentioned above to find the measure of the intercepted arc:

61 = x/2

To solve for x, we can multiply both sides of the equation by 2:

122 = x

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Answer:

1. 90 students x (2/9) = 20 sixth graders

2. 27 students x (2/9) = 6 sixth graders

3. 42 sixth graders x (9/2) = 189 students

the container needs to have a volume of  0.01514 cubic meters to hold 205 kg of mercury.

Volume is the measure of the amount of three-dimensional space enclosed by an object or space. It is typically expressed in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).

The density of mercury is approximately 13,534 kg/m³.

We can use the formula:

Volume = mass/density

To find the volume of mercury that has a mass of 205 kg:

Volume = 205 kg / 13,534 kg/m³

Volume ≈ 0.01514 m³

Therefore, the container needs to have a volume of approximately 0.01514 cubic meters to hold 205 kg of mercury.

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The complete question is:

What volume should a container have to hold 205 kg of mercury?

Algebraic expressions are useful for solving different and complex equations in mathematics, as well as for modelling real-life situations such as revenue, cost, inference, etc

The algebraic expression is: [tex]6x - 9[/tex].

To represent the sentence as an algebraic expression, we can follow these steps: Identify the variable. In this case, “a number” is x. Identify the operation. In this case, “less than” means subtraction and “times” means multiplication.

An algebraic expression is an expression that contains variables, constants and mathematical operations. Algebraic expressions are useful because they can help us solve different and complex equations.

For example, if you want to calculate the area of a rectangle with length x and width y, you can use the algebraic expression xy to represent the area.

Write the expression using the order of operations. In this case, we need to multiply six by x first, then subtract nine from the result.

Therefore, The algebraic expression is: [tex]6x - 9[/tex]

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Answer:

18

Step-by-step explanation:

siz times three is eighteen

Step-by-step explanation:

SA = 2πrh + 2πr²

where;

π = 3.14

r = 8

h = 11

Slotting in those parameters, we have;

= (2 x 3 x 8 x 11) + ( 2 x 3 x 8²)

= 528 + 384

= 912 inches²

To the nearest 100th, answer becomes 900inches²

Problem 7)  The model labelling p, q and p + q is given in the attached. The addition equation using integers that could represent p, q, and p +  q are:
(-1) + 2 = 1

Problem 8) The model would change if p > q

7) Addition equation is given as:

(-1) + 2) = 1

Where ;

p = -1

q = 2

Hence,

-1 + 2 = 1

8) The model in the equation above would change if p > q

That is

|p| > |q|

⇒ p > q

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached image.

Answer:

We are given the function S = m^2 + 6m + 8 which models the growth of book sales in m months, where S is an amount in thousands of dollars. We want to find in how many months book sales reach $80,000.

We can set up an equation as follows:

S = m^2 + 6m + 8 = 80

Subtracting 80 from both sides, we get:

m^2 + 6m - 72 = 0

We can factor this quadratic equation as:

(m + 12)(m - 6) = 0

This gives us two possible solutions:

m + 12 = 0 or m - 6 = 0

Solving for m in each case, we get:

m = -12 or m = 6

Since we are looking for a number of months, we can discard the negative solution.

Therefore, book sales reach $80,000 in 6 months.

So, the answer is: 6 months.