A cooking magazine shows a photo of a main dish on the front cover of 5 out of the 12 issues it publishes each year,how many times will it be on front cover for 5 years

Answer:

V = [tex]\frac{15}{2x}[/tex]

Step-by-step explanation:

Using the volume formula

V = [tex]\frac{12}{x}[/tex] × [tex]\frac{x+4}{4}[/tex] × [tex]\frac{5}{2x+8}[/tex] ← cancel 12 and 4 by 4 and factor 2x + 8

   = [tex]\frac{3}{x}[/tex] × [tex]\frac{x+4}{1}[/tex] × [tex]\frac{5}{2(x+4)}[/tex] ← cancel (x + 4) on numerator/denominator

  = [tex]\frac{3}{x}[/tex] × 1 × [tex]\frac{5}{2}[/tex]

  = [tex]\frac{15}{2x}[/tex]

Final answer:

To find the length of the child's shadow, set up a proportion comparing the woman's height and shadow length to the child's height and unknown shadow length. Solving the proportion 64/40 = 58/Child's shadow, we find that the child's shadow is approximately 36.25 inches long.

Explanation:

The question involves using proportions to calculate the length of the child’s shadow. Since the child is shorter than the woman, we can expect that the child’s shadow will also be shorter in proportion to her height. The woman is 5 feet and 4 inches tall, which converts to 64 inches. The shadow to height ratio is the same for both individuals because they are standing under the same lighting conditions.

We can set up a proportion using the woman’s height and shadow length to find the child’s shadow length:

Woman’s height / Woman’s shadow = Child’s height / Child’s shadow

64 inches / 40 inches = 58 inches / Child’s shadow

To solve for the child’s shadow, we cross-multiply:

64 * Child’s shadow = 58 * 40

Child’s shadow = (58 * 40) / 64

Child’s shadow = 2320 / 64

Child’s shadow = 36.25 inches

Therefore, the child’s shadow is roughly 36.25 inches long.

Answer:

1. D & F

2. A, C, D

Step-by-step explanation:

DID ON EDGE

None of the given graphs are identical. Their differences arise from the distinct characteristics of their specific square root or cube root functions, as well as the range of x-values they apply to.

None of the aforementioned graphs are identical. The syntax y=√x corresponds to the graph of the square root function, which is always positive and only defined for x≥0. On the other hand, the syntax y=-√x describes the graph that's a reflection of y=√x in the x-axis. However, y=∛x and y=-∛x both entail the cube root function, which is distinguishable from the square root function by its shape and the fact it includes values for negative x. Lastly, y=√-x and y=∛-x are not properly defined real functions, since taking square or cube roots of negative x values leads to complex numbers.

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Answer:

$50

Step-by-step explanation:

Let's write an equation to solve:

We can represent the profit as "p"

In that case, we have:

(p - 25) = 35

Adding 25:

p = 25.

If you charge 50, you will get 25 dollars back.

If you charge 10, you will get no profit.

Thus, the answer is $50.

Answer:

The answer to your question is Volume = 80000 cm³

Step-by-step explanation:

Data

height = 50 cm

radius = 20 cm

Process

1.- The smallest dimensions of the prism must have the same dimensions that the cylinder.

Radius = 20 cm then the length of a side = 2 x radius = 40 cm

2.- Calculate the area of the base

     Area = 40 x 40

              = 1600 cm²

3.- Calculate the volume of the prism

    Volume = Area x height

                  = 1600 x 50

                  = 80000 cm²

Given:

The given triangle is a right angled triangle.

One of the angle is 64° and the length of one of the leg is x.

The length of the hypotenuse is 28.

We need to determine the value of x.

Value of x:

The value of x can be determined using the trigonometric ratio.

Thus, we have;

[tex]cos \ \theta=\frac{adj}{hyp}[/tex]

where [tex]\theta= 64[/tex], adj = x and hyp = 28

Substituting the values, we get;

[tex]cos\ 64=\frac{x}{28}[/tex]

Multiplying both sides by 28, we have;

[tex]cos \ 64 \times 28=x[/tex]

 [tex]0.438\times 28=x[/tex]

       [tex]12.264=x[/tex]

Rounding off to the nearest hundredth, we get;

[tex]12.26=x[/tex]

Therefore, the value of x is 12.26

Answer:

14

Step-by-step explanation:

Answer: The answer is: 14

Step-by-step explanation: I just took that test!

Have a great day!

-Sunny

Answer:

Kidnappers

Step-by-step explanation:

Answer:

kidnappers

Step-by-step explanation:

Marian and Robin, by combining their efforts, can weed a garden together in approximately 1 hour and 43 minutes by adding their individual work rates and calculating the time taken to complete one whole task at this combined rate.

The question involves discovering the collective work rate of Marian and Robin when weeding a garden. To solve, we first identify the individual rates: Marian can weed a garden in 3 hours, which means her rate is 1/3 of the garden per hour. Robin's rate is 1/4 of the garden per hour, as he can complete it in 4 hours. To find the rate at which they can weed the garden together, we add their individual rates: (1/3) + (1/4) = 4/12 + 3/12 = 7/12.

Thus, their combined rate is 7/12 of the garden per hour. To find the total time taken, we divide the whole task (1 garden) by their collective rate (7/12). Hence, the time taken for them to complete the weeding together is 12/7 hours, which can be simplified to approximately 1 hour and 43 minutes.

The area of the cake that is frosted is 464 in²

What is the area of the cake that is frosted?

Bottom cake = 10 inches

Top cake = 6 inches

The lateral area of the bottom cube is 4 faces, each of which is a 10-inch square.

Lateral area = 4 × s²

= 4 × (10 in)²

= 400 in²

Top cube

The top area is the difference in area between a 10-inch square and a 6-inch square;

= (10 in)² - (6 in)²

= (100 -36) in²

= 64 in²

Therefore,

Area of the cake frosted = the sum of the lateral area and the top frosted area.

Area of the cake frosted = 400 in² +64 in²

= 464 in²

U means "Union" or all the numbers from one set and all the numbers from the other set combined.  So your answer is any of the numbers included in one set or the other or both.

Answer:

SAS

Step-by-step explanation:

The sides have the same ratio and the angle between them is congruent, so it's SAS

Replacing the ordered pairs into the equation, we find that the correct option is:

The equation is:

[tex]y + 1 = 3(x - 4)[/tex]

An ordered pair (x,y) is a solution to the equation if we replace (x,y) in the equation and get an identity.

Test if (4,-1) is a solution:

[tex]-1 + 1 = 3(4 - 4)[/tex]

[tex]0 = 0[/tex]

Identity, so it is.

Test if (5,2) is a solution:

[tex]2 + 1 = 3(5 - 4)[/tex]

[tex]3 = 3[/tex]

Identity, so it is.

Hence, both is the correct option.

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Answer:

The answer is A

Step-by-step explanation:

Answer:

the answer is c

Step-by-step explanation:

Answer: C. 25π/3 cm²

Step-by-step explanation:

The sector is an area of a circle bounded by two radii. The formula for determining the area of a sector is expressed as

Area of sector = θ/360 × πr²

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 10 cm

θ = 30 degrees

Therefore,

Area of sector = 30/360 × π × 10²

= 3000π/360 = 25π/3 cm²

Answer:

55 and 7.5 for number 3

Step-by-step explanation:

Answer:

[tex]625 m^2[/tex]

Step-by-step explanation:

In this problem, we are told that the area of the garden is given by the expression

[tex]A(w)=-(w-25)^2+625[/tex]

where

w is the width of the garden (in meters)

Here we want to find the maximum possible area.

The maximum of a function f(x) can be found by requiring that its first derivative is zero:

[tex]f'(x)=0[/tex]

Therefore, here we have to calculate the derivative of [tex]A(w)=0[/tex] and find the value of w for which it is equal to zero.

Let's start by rewriting the area function as

[tex]A(w)=-(w^2-50w+625)+625=-w^2+50w[/tex]

Now we calculate the derivative with respect to w:

[tex]A'(w)=-2w+50[/tex]

Now we require this derivative to be zero, so

[tex]-2w+50=0\\w=-\frac{50}{-2}=25 m[/tex]

So now we can substitute this value of w into the expression of A(w) to find the maximum possible area:

[tex]A(25)=-(25-25)^2+625 = 625 m^2[/tex]

This value is allowed because we know that the maximum length of the perimeter of the fence is 100 meters; If the garden has a square shape, the length of each side is [tex]L=\frac{100}{4}=25 m[/tex], and the area of the squared garden is

[tex]A=L^2=(25)^2=625 m^2[/tex]

Which is equal to what we found earlier: this means that the maximum area is achieved if the garden has a squared shape.

Answer:

Step-by-step explanation:

The known acute angle of the triangle is 46 degrees, so the unknown acute angle of that triangle is 90-46 = 44 degrees. In other words, the two acute angles of any right triangle must add to 90, so 46+44 = 90.

The 44 degree angle is adjacent to angle ADC, and it adds to angle ADC to form 180 degrees.

If x is the measure of angle ADC, then

44+(angleADC) = 180

44+x = 180

x = 180-44

x = 136

angle ADC = 136 degrees

For any parallelogram, the opposite angles are always congruent. Therefore, angle ABC is equal to angle ADC = 136, making ABC = 136 as well.

Answer: C. 136 degrees

Step-by-step explanation:

From the diagram, angle C is a right angle because it is formed by a perpendicular line. It means that

Angle BCD + 46 = 90

angle BCD = 90 - 45 = 44 degrees

The opposite angles in a parallelogram are equal while the adjacent angles are supplementary. Angle ABC and angle BCD are supplementary and the sum of supplementary angles is 180 degrees. Therefore,

Angle ABC + 44 = 180

Angle ABC = 180 - 44

Angle ABC = 136 degrees

Answer:

3 1/2 pounds or 3.5 pounds

Step-by-step explanation:

Two ingredients are measured in pounds while one is measured in ounces.  Recall that 1 pound = 16 ounces.  Thus, 12 ounces of cocoanut comes out to

(12/16) pound.  Next, we sum up 1 1/2 pounds of flour, 12/16 pound of cocoanut and 1 1/4 pounds of sugar, after rewriting these mixed numbers with the same denominator (4):

1 1/2 pounds       stays 1 2/4 pounds;

12 ounces becomes       3/4 pound; and

1 1/4 pounds stays        1 1/4 pounds

Summing up the fractions results in 6/4 pounds, or 1 1/2 pounds; and summing up the integers results in 2 pounds.

The final sum is 1 1/2 pounds + 2 pounds, or 3 1/2 pounds.

Dwayne buys 3 1/2 pounds of ingredients.

Alternatively, we could convert all of these measurements to decimal fractions and then add up those fractions:

1.5 pounds + 0.75 pounds + 1.25 pounds = 3.5 pounds (same as before).

Answer:

45

Step-by-step explanation:

Taking into account the definition of equation and percentage, 30 percent of 120 is the same as 80 percent of 45.

An equation is defined as an established equality between two expressions, in which there may be one or more unknowns or variables.

So solving an equation consists of finding the value or values ​​of the variables so that they fulfill the equality represented in the equation. That is, when changing the variable for the solution found, the equality must be true.

On the other side, the percentage is a value that represents the proportionality between two established quantities. That is, the percentage tells what part of a total represents a quantity.

Mathematically, the percentage is the division between an initial quantity and the total quantity, all multiplied by one hundred.

And to calculate the percentage of a quantity, the quantity is multiplied by the percentage and divided by 100. Then, 30 percent of 120 can be expressed as: (30×120)÷100

On the other hand, 80 percent of a number can be expressed as: (80×number)÷100

Since 30 percent of 120 must be the same as 80 percent of an unknown number, the following equation can be expressed:

(30×120)÷100= (80×number)÷100

Solving:

3600 ÷100= (80×number)÷100

36= (80×number)÷100

36×100= 80×number

3600= 80× number

3600÷ 80= number

45= number

The, 30 percent of 120 is the same as 80 percent of 45.

Learn more about percentage with this examples:

Answer:

We use Simultaneous Equation to express the problem

From the equation, a bag of popcorn will cost $5

Step-by-step explanation:

We can represent drink with d and bad of popcorn with p

If Tristan spent $38.75 on 5 drinks and 2 bags of popcorn, the we can interpret it as

5d + 2p = 38.75 ....................... eqn 1

And if Noah spent $37.25 on 3 drinks and 4 bags of popcorn, we can interpret it also as

3d + 4p = 37.25 ........................ eqn 2

This is now a Simultaneous Equation

Since we are to state the price of a bag of popcorn, then we can use the elimination method to eliminate d and solve for p

To do this, Multiply eqn 1 by 3 and eqn 2 by 5

(5d + 2p = 38.75)*3

(3d + 4p = 37.25)*5

The we will have

15d + 6p = 116.25 .......................... eqn 3

15d + 20p = 186.25 ...................... eqn 4

If we subtract eqn 3 from eqn 4, we will have

14p = 70

Divide both sides by 14 to get the value of p, and we will have

p = 70/14

p = 5

Therefore a bag of popcorn equals to $5

Answer:

1/8

Step-by-step explanation:

1/4 divided by 2

Final answer:

Each friend received 1/8 of the original pie after equally sharing 1/4 that was left over.

Explanation:

Marge and Kimo equally shared 1/4 of a pie that was left over. To determine the fraction of the original pie that each friend got, we divide that 1/4 by two, since there are two people sharing it. So, each friend received 1/8 of the original pie.

Step-by-step explanation:

Answer:

99000 meters.

Step-by-step explanation:

We have the swimmer going at 50 m / s, and we want to know where he is going in 33.3 minutes.

The first thing is to pass the time from minutes to seconds, we know that 1 minutes is 60 seconds, therefore:

33.3 min * 60 s / 1 min = 1998 seconds

Now to know the distance is to multiply this time by the speed they give us, like this:

1998s * 50m / s = 99900 m

Which means that in that time and at the speed of the swimmer, he has traveled 99000 meters.

Answer:

B. 1/2

Step-by-step explanation:

This problem involves the use of the Pythagorean theorem. In the unit circle, the hypotenuse of any right triangle formed is 1 while the coordinates of the point are then the two legs that make up the triangle.

a = 1 (given)

b = √3/2 (given)

a² = b² + c² (Pythagorean Theorem)

1² = (√3/2)² + c² (Substitute information)

Now, we need to solve for c

1 = (3/4) + c² (square the hypotenuse and one of the legs)

1 - (3/4) = (3/4) + c² - (3/4) (subtract 3/4 on both sides)

1/4 = c² (combine like terms)

√(1/4) = √(c²) (square root both sides)

√1 / √4 = c (square root both sides)

1/2 = c (final answer)

Therefore the other leg of the right triangle is 1/2, this also means that the other coordinate, or x, is 1/2, so the answer is B. 1/2.

Final answer:

The x-coordinate for the point (x, √3/2) on the unit circle is determined using the Pythagorean theorem for a unit circle. After substituting √3/2 for y and solving for x, the x-coordinate can be ±1/2. The correct option from the given choices is B. 1/2.

Explanation:

If the point (x, √3/2) is on the unit circle, we must use the Pythagorean theorem that applies to the unit circle, which states that x² + y² = 1, where x and y are the coordinates of a point on the circle. For a unit circle, the radius is 1. Since the y-coordinate is given as √3/2, we can substitute this value into the equation and solve for x:

x² + (√3/2)² = 1

x² + (3/4) = 1

x² = 1 - 3/4

x² = 1/4

x = ±√(1/4)

x = ±(1/2)

Therefore, x could be either 1/2 or -1/2. Since the question doesn't specify which quadrant the point is in, both answers are correct. However, within the given options, the correct answer is B. 1/2.

Final answer:

John's new balance after 6 years with an original investment of $18,000 at a 4.5% annual compound interest rate will be approximately $23,362.65.

Explanation:

To calculate John's new balance after 6 years with a principal investment of $18,000 at an annual compound interest rate of 4.5%, we use the formula for compound interest:

A = P[tex](1+r/n)^{(nt)}[/tex]

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the time the money is invested for, in years.

In this case, P = $18,000, r = 0.045 (4.5%), n = 1 (since it's compounded annually), and t = 6 years.

Now we plug the values into the formula:

A = 18000(1 + 0.045/1)⁶

A = 18000(1 + 0.045)⁶

A = 18000(1.045)⁶

Calculating this, we get:

A ≈ 18000(1.297925)

A ≈ $23,362.65

Therefore, after 6 years, John will have approximately $23,362.65 in his account.

Answer: 144

Step-by-step explanation: To find a value of c that would make this a perfect square, take -24 and divide it by 2 to get -12. Next, simply square -12 to get 144.

x^2 - 24x + 144 can be factored into (x - 12)(x - 12)

Answer:

144 is the correct answer

Answer:

The lines will have one positive y-intercept and one negative y-intercept is NOT true.

Step-by-step explanation:

If a graphed system has infinitely many solutions, that means that the two equations are the exact same. This means that they'll have the same slope, y-intercept, and will share all of the same points. Answer b is the only choice left.

The lines will have one positive y-intercept and one negative y-intercept that is not true.

The graph is a diagram showing the relation between variable quantities, typically of two variables, each measured along with one of a pair of axes at right angles.

The lines will have one positive y-intercept and one negative y-intercept is NOT true.

If a graphed system has infinitely many solutions, that means that the two equations are the exact same. This means that they'll have the same slope, and y-intercept, and will share all of the same points. Answer b is the only choice left.

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Answer: 36 pi over 7.5

Step-by-step explanation:

Answer:

$81,269.53

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 3.4% into a decimal:

3.4% -> [tex]\frac{3.4}{100}[/tex] -> 0.034

Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:

[tex]A=56,000(1+\frac{0.034}{4})^{4(11)}[/tex]

[tex]A=81,269.53[/tex]

After 11 years, you will have $81,269.53

Answer:

Therefore it will take 28 years.

Step-by-step explanation:

To find the years, we use the following formula,

[tex]A=P(1+r)^n[/tex]

A= Total balance after n years

P= Initial amount.

r= Rate of interest per year.

n = Time in years.

Given that, Josh's grandparents put $3,000 into a college saving account when he was born. The account earn 6% interest per years.

Here A=$15,000,P=$3,000, r=6%=0.06 ,n=?

[tex]\therefore 15,000=3,000(1+0.06)^n[/tex]

[tex]\Rightarrow (1.06)^n=\frac{15,000}{3,000}[/tex]

[tex]\Rightarrow (1.06)^n=5[/tex]

Taking ln both sides

[tex]\Rightarrow ln(1.06)^n=ln(5)[/tex]

[tex]\Rightarrow n=\frac{ln(5)}{ln(1.06)}[/tex]

[tex]\Rightarrow n\approx 28[/tex]

Therefore it will take 28 years.