Jarrod helped his teachers pack textbooks into boxes for the summer. He packed 6 boxes of science textbooks with 14 books per box. He also packed math textbooks with 12 books per box.

If x represents the total number of boxes he packed, which of the following equations can be used to find the total number of books that Jarrod packed into boxes?
A. y = 84(x - 6) + 12
B. y = 12x + 84
C. y = 84x + 12
D. y = 12(x - 6) + 84

The value of k is 1 and -5.

What is factorization?

A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, typically smaller or simpler things of the same kind.

Here, we have

Given function: 5k²+20k-25 = 0

Now, we factorize the given function and we get

5k²+20k-25 = 0

5(k²+4k-5) = 0

k² + 4k - 5 = 0

k² + 5k - k -5 = 0

k(k+5) -1(k+5) = 0

(k+5)(k-1) = 0

k+5 = 0, k-1 = 0

k = -5, k = 1

Hence, The value of k is 1 and -5.

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So, the maximum volume of the cone is approximately 1047.19 cubic inches.

The volume of a cone is given by the formula V = (1/3) * pi * r^2 * h, where r is the radius of the base and h is the height of the cone. In this case, the height of the cone is the radius of the circle, which is 10 inches, and the radius of the base is half the length of the circumference of the sector, which is (theta/360) * 2 * pi * 10 inches.

We want to find the value of theta that maximizes the volume of the cone. We can do this by taking the derivative of the volume formula with respect to theta, setting it equal to 0, and solving for theta.

V = (1/3) * pi * r^2 * h

= (1/3) * pi * ((theta/360) * 2 * pi * 10)^2 * 10

= (1/3) * pi * (theta/36)^2 * 100

dV/dtheta = (2/3) * pi * (theta/36) * (100/36)

= (2/3) * pi * theta/36

Setting dV/dtheta = 0 and solving for theta, we get theta = 0.

Since the magnitude of theta must be positive, the maximum volume occurs when theta = 0, which means that the entire circle is used to form the cone. The maximum volume of the cone is then

V = (1/3) * pi * r^2 * h

= (1/3) * pi * (10)^2 * 10

= (1/3) * pi * 100 * 10

= (1/3) * pi * 1000

= approximately 1047.19 cubic inches

So, the maximum volume of the cone is approximately 1047.19 cubic inches.

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We want to find the value of theta that maximizes the volume of the cone. We can do this by taking the derivative of the volume formula with respect to theta, setting it equal to 0, and solving for theta.

V = (1/3) * pi * r^2 * h

= (1/3) * pi * ((theta/360) * 2 * pi * 10)^2 * 10

= (1/3) * pi * (theta/36)^2 * 100

dV/dtheta = (2/3) * pi * (theta/36) * (100/36)

= (2/3) * pi * theta/36

Setting dV/dtheta = 0 and solving for theta, we get theta = 0.

Since the magnitude of theta must be positive, the maximum volume occurs when theta = 0, which means that the entire circle is used to form the cone. The maximum volume of the cone is then

V = (1/3) * pi * r^2 * h

= (1/3) * pi * (10)^2 * 10

= (1/3) * pi * 100 * 10

= (1/3) * pi * 1000

= approximately 1047.19 cubic inches

So, the maximum volume of the cone is approximately 1047.19 cubic inches.

answer: yes.

since y = 6 and x = -1 are parallel to the y and x axis, respectively, they hit each other at a 90° angle when graphed, making a plus sign. they are perpendicular lines.

Answer:

  (c)  y = -1

Step-by-step explanation:

You want the equation of the horizontal line through (0, -1).

A horizontal line has the same y-value for every x-value. Its equation is ...

   y = constant

If you want the line to go through a point with a y-coordinate of -1, then the constant must be -1.

  y = -1 . . . . . . . horizontal line through (0, -1)

Answer: $45.3

Step-by-step explanation:

1 hour of mowing: $8.80

5 hours of babysitting: $7.30 x 5 = $36.5

$36.5 + 8.80 = $45.3

$45.3 is your answer.

Answer:

45.30

Step-by-step explanation:

its simple math bro lol

Answer:

37.237%

Step-by-step explanation:

Use the Formula I = P x R x T

P = Principal amount (the beginning balance).

R = Interest rate (usually per year, expressed as a decimal).

T = Number of time periods (generally one-year time periods).

Plug in the values

I = 5305 x R x 20

Solve for R by dividing 20 by 5305

I=5305 x R x 20

20 / 5305 = 0.0037

Answer: 10.56 or 10.6 %

Step-by-step explanation:

5305 x x^20 = 39534

39534/5305 = x^20

20√39534/5305 = x

x = 1.1056

1.1056 x 100 = 110.56

110.56 - 100 = 10.56 or 10.6

Answer:

  117.79 m

Step-by-step explanation:

You have an observer 337 m from a skyscraper who measures the angle of elevation from a point 1.75 m above the ground to be 19°. You want to know the height of the skyscraper.

The tangent relation tells you ...

  Tan = Opposite/Adjacent

Solving for the side opposite the angle, we get ...

  Opposite = Adjacent · Tan

In this scenario, the height of the building above the eye height is ...

  height above eyes = (337 m)(tan 19°) = 116.038 m

Then the height of the building is ...

  skyscraper height = eye height + height above eyes

  skyscraper height = 1.75 m + 116.038 m = 117.788 m

The height of the skyscraper is about 117.79 meters.

The amount needed to be deposited in an account in order to have $5000 in 27 month is $4997.74.

Simple interest is based on the principal amount of a loan or the first deposit in a savings account.

To calculate the amount that needed to be deposited, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the amount needed to be deposited is $4997.74.

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Answer:

$1 per movie

$5.50 per video game

Step-by-step explanation:

We know 5 movies and 2 video games cost $16 and 3 movies and 8 video games cost $47.

Let x be the cost of 1 movie and y be the cost of a video game.

5x + 2y = 16

3x + 8y = 47

In the first equation, lets solve for y

2y = 16 - 5x

y = 8 - 2.5x

Now, we can substitute this into the other equation.

3x + 8(8 - 2.5x) = 47

3x + 64 - 20x = 47

-17 x = - 17

x = 1

So a movie costs $1 to rent.

2y = 16 - 5(1)

2y = 11

y = 5.5

A video game costs $5.50 to rent.

Answer: x + 8 - 8 = 10 - 8

Simplifying the left side of the equation gives us:

x = 2

Therefore, the value of x in this equation is 2.

The x-coordinates where the line y = 2x + 3 intersects the circle is equal to -2 and -4.

Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²  

Where:

From the information provided, we have the following system of equations:

(x - 3)² + (y + 6)² = 50      ......equation 1.

y = 2x + 3              .............equation 2.

In order to determine the x-coordinates at the point of intersection, we would substitute the equation 2 into equation 1:

(x - 3)² + (2x + 3 + 6)² = 50

(x - 3)² + (2x + 9)² = 50

x² - 6x + 9 + 4x² + 36x + 81 - 50 = 0

5x² + 30x + 40 = 0

x² + 6x + 8 = 0

x² + 6x + 9 = 1

(x + 3)² = 1

Taking the square of both sides of the equation, we have;

x + 3 = ±1

x = ±1 - 3

x = -2 and -4

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The maximum speed of the linear function is y = -7x + 90

a. we have two points connecting (speed, degree) are (+5,55) and (-2,104) representing (x₁ , y₁) and (x₂, y₂)

Slope = (y₂ - y₁) / (x₂ - x₁)

slope = (104-55) / (-2-5) = 49/-7 = -7 mph/1°

speed = slope x (degree) + b

Solve 'b':

55 = -7 x (5) + b

55 = -35 + b

b = 55 + 35

b = 90

y₁ = -7x₁ + 90

b) What does the speed-intercept equal and what does it represent?  

The speed is 90 mph when there is no hill.

c ) What does the degree of steepness-intercept and what does it represent?

Up the hill, the steepness is roughly 12.9 degrees at its maximum. Whenever there is a slope, the car will not move.

d) Interpret the slope in words.

The speed drops by 7 mph for every 1 degree that the hill's steepness increases.

e) If your top speed is 83 mph, how steep is the hill?  Be sure to include whether the direction is up or down.

83 = -7 x + 90

83 -90 = -7x

-7 = -7x

x = 1° up the hill

f) How fast could you go down a 7º hill?

y = -7 (-7) + 90

y = 139 mph

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The prevalence of asthma on January 1, 2019 is 0.055, the prevalence of asthma on September 1, 2019 is 0.080, the incidence of asthma between January 1 and September 1 is 0.025, there is not possible to calculate asthma incidence rate for the year 2018.

Prevalence is the formula to determine the rate of some case based on population. This can be calculated by divide the case by the population.

Incidence rate is same as prevalence in some factor except it only calculate time range and for this case it have same formula which is we can calculate incidence rate by divide the case by the population.

So, for January 1, 2019 is

Prevalence = 1,098 / 19,800

= 0.055

For September 1, 2019 is

Prevalence = (1,098 +  new 495) / 19,800

= 1,593 / 19,800

= 0.080

For incidence of asthma between January 1 and September 1 is

Incidence = 495 / 19,800

= 0.025

For 2018 because we are not provided with data for that year so it is impossible to calculate it.

Thus, the prevalence in January 1 is 0.055, September 1 is 0.080, and incidence between January 1 and September 1 is 0.025, and also there is not possible to calculate asthma incidence rat for the year 2018.

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The y-intercept of Function A is greater than the y-intercept of Function B.

What is y-intercept ?

The y intercept of a graph is the point where the graph intersects the y-axis. We know that the x-coordinate of any point on the y-axis is 0. So the x-coordinate of a y-intercept is 0.

Here are the steps to find the y intercept of a function y = f(x),

Given:

Function A : y=x-1

y-intercept of Function A (x=0) is y = -1

y-intercept of Function B are  -6 , -4 and -3.

Since , -1 > -6  , -1 > -4 and -1 > -3

Hence , the y-intercept of Function A is greater than the y-intercept of Function B.

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The statement is true. Functions that are concave upward are always increasing.

What is Concave Upward Function?

Where the derivative f′ is growing, a function f is concave up (or upwards). This is equivalent to the derivative of f′, which is represented by the notation f′′f, start superscript, prime, end superscript, positive.

Explanation:

If a function is concave upward on an interval, it must be increasing on the interval. Given statement is true. Functions that are concave upward are always increasing.

A function is said to be concave upward on an interval if f″(x) > 0 at each point in the interval and concave downward on an interval if f″(x) < 0 at each point in the interval.

At interval if function is increasing then functions that are concave upward are always increasing.

Hence, The statement is true. Functions that are concave upward are always increasing.

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Answer:

4/15

Step-by-step explanation:

1/3 x 5/5 = 5/15, 2/5 x3/3 = 6/15

5/15+6/15= 11/15

15/15- 11/15= 4/15

so 4/15 people don't have neither blue nor brown eyes.

Answer:

C. The solution to the system is (-4,3) where the 2 lines MEET

Step-by-step explanation:

D. The system has no solution only if the lines are PARALLEL

A. The system has infinite solutions only if both equations give ONE and the same line

minute math

Answer:

A.-7-100. [Since it is -107]

Answer:

0.27563735723563.

Step-by-step explanation:

74 is an acute angle since it is less than 90° cos (74) = 0.27563735723563. Write cos (74) in terms of sin Since 74° is less than 90, we can express this in terms of a cofunction.

The value of MW in the given figure is 5.

In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.

Given,

In the figure,

PM=MW

It means PM is similar to MW

As given in the figure,

PM=5

Since PM is similar to MW

Then,

MW=5

Therefore, the value of MW in the given figure is 5.

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Answer:

91.4%

Step-by-step explanation:

First do: 32,000/35,000 = X/100

Then multiply 32,000 by 100 which is 3,200,000

Then divide 3,200,000 by 35,000

You will get 91.42857142857143

The actual annual value of this job to Karla is 33000.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

the job will pay 2400 per month,

if the full cost of the medical insurance is 450 a month and Karla plans to contribute the full 1500 every year tpa retirement plan,

the actual annual value of this job to Karla is:

2400 per month

annual value  = 2400 * 12 = 28,800

the medical insurance is 450 a month

half the cost of medical insurance is  225 a month

annual value  = 225  * 12 = 2700

the full 1500 every year tpa retirement plan,

So, the total value is:

= 28,800 + 2700 + 1500

= 33000

Hence,  the actual annual value of this job to Karla is 33000.

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Answer:

x is equal to 87

Step-by-step explanation:

42 +51=93

93-180=x

x=87

The green grapes weigh 0.125 pounds more than the red grapes.

1/4 of a pound = 0.25 pounds

1/8 of a pound = 0.125 pounds

0.25 - 0.125 = 0.125 pounds

Hope this helps :)

The Fourier transform of this sequence does not exist

What is Fourier Transform?

The output of a Fourier transform is a function of frequency and is a mathematical transformation that breaks down functions into frequency components.

To determine the z-transform of a given sequence, we need to find the sum of the sequence's terms multiplied by z raised to the negative of the term's position. For example, given a sequence x[n], the z-transform X(z) is given by:

[tex]X(z) = sum_{n=-infinity}^{infinity} x[n] * z^{-n}[/tex]

To sketch the pole-zero plot of a z-transform, we need to plot the poles (values of z where the z-transform is infinite) and zeros (values of z where the z-transform is zero) in the complex plane. The region of convergence (ROC) is the set of values of z for which the sum defining the z-transform converges.

[tex]x[n] = a^n u[n][/tex], where a is a constant and u[n] is the unit step function[tex](u[n] = 1 for n > = 0[/tex] and [tex]u[n] = 0 for n < 0)[/tex]

The z-transform of this sequence is given by:

[tex]X(z) = sum_{n=0}^{infinity} a^n * z^{-n}= 1 / (1 - a*z^{-1})[/tex]

This z-transform has a pole at z = 1/a and a zero at z = 0. The pole-zero plot consists of a single pole at 1/a in the complex plane. The ROC is the set of values of z such that [tex]|a*z^{-1}| < 1[/tex], which is the region inside the unit circle centered at the origin. The Fourier transform of this sequence exists.

[tex]x[n] = (-1)^n u[n].[/tex]

The z-transform of this sequence is given by:

[tex]X(z) = sum_{n=0}^{infinity} (-1)^n * z^{-n}= 1 / (1 + z^{-1})[/tex]

This z-transform has a pole at z = -1 and a zero at z = 0. The pole-zero plot consists of a single pole at -1 in the complex plane. The ROC is the set of values of z such that [tex]|z^{-1}| < 1[/tex], which is the region inside the unit circle centered at the origin. The Fourier transform of this sequence exists.

[tex]x[n] = n^2 u[n].[/tex]

The z-transform of this sequence is given by:

[tex]X(z) = sum_{n=0}^{infinity} n^2 * z^{-n}= z^{-2} / (1 - z^{-1})^3[/tex]

This z-transform has poles at z = 1, z = 1, and z = 1. The pole-zero plot consists of three poles at the origin in the complex plane. The ROC is the set of values of z such that [tex]|z^{-1}| > 1[/tex], which is the region outside the unit circle centered at the origin.

Hence, The Fourier transform of this sequence does not exist.

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Answer:

  0.5 oz

Step-by-step explanation:

You want the greatest possible error associated with the measurement 19 oz.

The possible error is generally considered to be half the place value of least-significant digit. Here, the least significant digit has a place value of units, so the greatest error is 1/2 unit, or 0.5 ounces.

__

Additional comment

We know that values of 18.5 oz up to 19.4999... oz will round to 19 oz. That is why the greatest error is considered to be 0.5 oz.

In practice, there can be some difficulty associated with knowing that a value is 18.5 instead of 18.49. Hence real-world error may actually be slightly larger than 0.5 oz. In math, we ignore that case.

To find the time it took the cruise ship to travel to Madagascar, we need to use the formula for distance, which is distance = speed x time. We are given the distance and the speed of the ship on the trip there, so we can solve for the time by dividing the distance by the speed:

time = distance / speed

We are told that the distance of the trip there was the same as the distance of the return trip, which took 6 hours. We are also told that the ship traveled 12 km/h on the trip there, so the distance of the trip there was 12 km/h x 6 h = 72 km.

Now we can plug this information into the formula to solve for the time:

time = 72 km / 12 km/h = <<72/12=6>>6 hours

Therefore, it took the cruise ship 6 hours to travel to Madagascar. The correct answer is therefore (A) 12 hours.