if necessary.
21. A company makes specialized fish tanks, like the one shown below. If 1 gallon = 0.134 ft³, how many
gallons of water will it take to fill the fish tank completely?
9 ft
2 ft
3 ft
V = 6

Answer:

[tex]tringle = \frac{1}{2} \times base \times hieght[/tex]

1/2 × 8×5

0.5×40

=20m

according to the question, the PLUS Loan will have a higher balance due at the time of repayment by $233.80 ($11,966.11 - $11,732.31).

Divide the principal times the interest rates, the length of time, and various other factors to arrive at simple interest. Simple return = principle + interest + hours is the marketing formula. The easiest way to compute interest is with this method. The most typical technique to figure out interest is to use a portion of the principal sum. He is only going to pay his share of the 100% interest, for example, if he loans $100 form a friend then agrees to pay it off with 5% interest. $100 (0.05) corresponds to $5. Interest must be paid as you borrow money and must be added to any loans you make. Interest is often determined as a yearly proportion of the loan total. The interest on the loan is this percentage.

given,

To compare the two loans, we need to calculate the total balance due for each loan at the time of repayment. We can start by calculating the balance due for the Unsubsidized Stafford Loan:

Principal: $10,720

Interest rate: 5.95% per year, compounded monthly

Time: 6 months grace period + 6 months repayment = 1 year

Number of periods: 12 months x 1/12 month per period = 12 periods

Using the formula for compound interest, the balance due on the Unsubsidized Stafford Loan after 1 year is:

B = P(1 + r/n)^(nt) + I [(1 + r/n)^(nt) - 1]/(r/n)

where B is the balance due, P is the principal, r is the annual interest rate, n is the number of times per year the interest is compounded, t is the time in years, and I is the monthly payment.

Plugging in the numbers, we get:

B = $10,720(1 + 0.0595/12)^(121) + $0 [(1 + 0.0595/12)^(121) - 1]/(0.0595/12)

B = $11,732.31

Now, let's calculate the balance due for the PLUS Loan:

Principal: $11,443.63

Interest rate: 6.55% per year, compounded monthly

Time: 6 months repayment

Number of periods: 6 periods

Using the same formula for compound interest, the balance due on the PLUS Loan after 6 months is:

B = $11,443.63(1 + 0.0655/12)^(120.5) + $0 [(1 + 0.0655/12)^(120.5) - 1]/(0.0655/12)

B = $11,966.11

Therefore, the PLUS Loan will have a higher balance due at the time of repayment by $233.80 ($11,966.11 - $11,732.31). Thus, the Unsubsidized Stafford Loan will have a lower balance due at the time of repayment compared to the PLUS Loan.

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Answer:

The lateral area of a cone is given by the formula:

L = πrs

Where r is the radius of the base, s is the slant height, and π is pi.

We are given that the lateral area L is 587π cm^2 and the radius r is 32 cm. Substituting these values into the formula, we get:

587π = π(32)s

Simplifying, we can cancel the π on both sides of the equation:

587 = 32s

Dividing both sides by 32, we get:

s = 18.34375

Rounding to the nearest tenth, we get:

s ≈ 18.3 cm

Therefore, the slant height is approximately 18.3 cm.

Step-by-step explanation:

Answer:

a) 3/4

b) 21/4  

Step-by-step explanation:

To find the scale factor from A to B take any side of B and divide it by the corresponding side of A

The ratio will be the same for all sides

We have
scale factor = 3/4

We see that the sides 9 and 12 are also in this ratio: 9/12 = 3/4

a) So scale factor from A to B is 3/4

b) w of shape B corresponds to the side with length 7 in shape A

The ratio of w to 7 must be equal to the scale factor

So w/7 = 3/4

w = 7 x 3/4

w = 21/4

Hence, 7, 22, 37, and 52 are the first four terms in the arithmetic series with initial term 7 and common difference 15.

Algebraic progression is a series of numbers where each term following the first is derived by multiplying the previous president by a constant known as the common difference (d). An arithmetic progression often takes the form: A, A+D, A+2D, A+3D,... where "a" stands for the initial keyword and "d" for the common distinction.

given

The sequence's initial term is 7, and the shared discrepancy is 15. We can continuously add 15 to the preceding word to find the next terms.

As a result, the arithmetic sequence's first four terms are:

Initial term = 7

Term two: 7 plus 15 equals 22

Third term = 22 plus 15 equals 37

Fourth term: 37 plus 15 equals 52

Hence, 7, 22, 37, and 52 are the first four terms in the arithmetic series with initial term 7 and common difference 15.

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The values of the a gles using trigonometric ratios are;

tan L = (1/√3)

sin L = 0.5

cos L = ½√3

sin M = 2/√3

cos M = 0.5

The three most basic trigonometric ratios are;

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We are given;

l = 12

m = 12√3

n = 24

Using trigonometric ratios, we have;

12/(12√3) = tan L

tan L = (1/√3)

L = tan¯¹(1/√3)

L = 30°

Similarly;

12/24 = sin L

sin L = 0.5

cos L = (12√3)/24

cos L = ½√3

Similarly;

sin M = 24/12√3

sin M = 2/√3

cos M = 12/24

cos M = 0.5

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The supplied value 4 is a solution to the equation m + 2(m + 1) = 14.

To solve the equation m + 2(m + 1) = 14 for the supplied value of m = 4, we substitute the value of m into the equation and simplify both sides of the equation.

First, we replace every occurrence of m in the equation with 4:

m + 2(m + 1) = 14

Substitute m with 4

4 + 2(4 + 1) = 14

The parentheses around (4 + 1) indicate that we need to add 4 and 1 together first, before multiplying by 2. This gives us:

4 + 2(5) = 14

We simplify further by performing the multiplication:

4 + 10 = 14

14 = 14

Therefore, when we substitute m = 4 into the equation, we get a true statement. Therefore, 4 is a solution to the equation.

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according to the given information we can say that the fraction of the area of the circle that is shaded is 1/4 or 0.25.

Every point in a horizontal surface that is a certain distance above another point forms a circle (centre). It is a circle made out of point that are separated from each other in a horizontal direction as a result. At all angles, it is rotating symmetric about the centre. In the closed, two-dimensional plane of a circle, each pair of points is evenly separated from the "centre." A line that pierces the circle creates a specular symmetrical line. At all angles, it rotates symmetrically about the centre.

given,

If the circle is divided into two equal parts and one of them is shaded, then the shaded area is half of the total area of the circle. So the fraction of the area of the circle that is shaded is 1/2 or 0.5.

If the circle is divided into four equal parts and one of them is shaded, then the shaded area is one-fourth of the total area of the circle. So the fraction of the area of the circle that is shaded is 1/4 or 0.25.

Therefore, the answer depends on how many equal parts the circle is divided into and the number of shaded parts.

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24  boxes were used this week

12 boxes of recycled paper were used last week
For this week double of this amount was used

When calculating double the amount that was used, this means we have to multiply the initial amount by 2

In this case, we have to multiply 12 by 2

= 12 × 2

= 24

Hence 24 boxes of recycled paper was used this week

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The true statements are (a) A sphere with half the radius has 1/8 of the volume and (c) A sphere with 3 times the radius has 27 times the volume

Given that the radius of the sphere is represented as

Radius, r = 4 inches

The formula of the volume of the sphere is represented as

V = 4/3πr³

For the transformed volume, we have

V₂ = 4/3πR³

Where

R = kr and k is the scale factor

So, we have

V₂ = 4/3π(kr)³

V₂ = 4/3πr³k³

This gives

V₂ = Vk³

Testing the statements, we have

(a) A sphere with half the radius has 1/8 of the volume

V₂ = V(1/2)³

Evaluate

V₂ = 1/8V

So, the statement is true

(b) A sphere with twice the radius has 6 times the volume

V₂ = V(2)³

Evaluate

V₂ = 8V

So, the statement is false

(c) A sphere with 3 times the radius has 27 times the volume

V₂ = V(3)³

Evaluate

V₂ = 27V

So, the statement is true

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Complete question

A sphere has a radius of 4 inches.

Choose True or False for each statement.

(a) A sphere with half the radius has 1/8 of the volume

(b) A sphere with twice the radius has 6 times the volume

(c) A sphere with 3 times the radius has 27 times the volume

The equations that will make a linear function are

A linear equation, also referred to as a linear function in mathematics, is used to identify relationships between variables that can be plotted on a straight line.

This class of polynomial functions have a degree of 1, indicating that the highest power of the variable within the formula cannot exceed 1.

It takes on the standardized form:

y = mx + b

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Answer: 1.8

Let's put our whole number and fraction side by side so we can visualize the problem we're trying to solve:

3 ÷

5

3

The trick to working out 3 divided by 5/3 is similar to the method we use to work out dividing a fraction by a whole number.

All we need to do here is multiply the whole number by the numerator and make that number the new numerator. The old numerator then becomes the new denominator. Let's write this down visually:

3 x 3

5

=

9

5

So, the answer to the question "what is 3 divided by 5/3?" is:

9

5

Sometimes, after calculating the answer we can simplify the resulting fraction down to lower terms. In this example though 9/5 is already in it's lowest possible form.

If you made it this far you must really love your fractions and dividing whole numbers by them. Hopefully this simple guide was easy for you to follow along and you can now go forth and divide more whole numbers by as many fractions as your heart desires.

Convert 3 divided by 5/3 to Decimal

One last little calculation before you go. It's common to want to express your result as a decimal and, to do that, all you need to do is divide your numerator by your denominator:

9

5

= 1.8

Answer:

The party opposed to expanding slavery in the United States was the Republican Party. It was actually formed to go against slavery.  

The slope-intercept form of the equation is y = 18x.

To find the function in slope-intercept form, we have to write the general form below as;

y = mx + c

m = slope

c = y-intercept

To find the slope, we need to take two points from the table given;

slope (m) = y2 - y1 / x2 - x1

m = 720 - 450 / 40- 25

m = 18

The slope of the line is 18

we can use this with any point to find the y - intercept

y = mx + c

720 = 18(40) + c

720 = 720 + c

c = 720 - 720

c = 0

The equation of the line in slope-intercept form is y = 18x

b. To determine how far he travelled with 55 gallons of gas

y = 18x

y = 18(55)

y = 990 miles

c. How many gallons will be required to cover 630 miles

y = 18x

630 = 18x

x = 630 / 18

x = 35 gallons

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The surface area of the solid created upon dilation is equal to 36 units².

In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):

SA = 2πrh + 2πr²

Where:

By substituting the given parameters into the formula for the surface area (SA) of a cylinder, we have the following;

Surface area = 2πrh + 2πr²

Surface area = 2(π)(9)(9) + 2(π)(9²)

Surface area = 324π units²

After applying a dilation with a scale factor of 1/3, the surface area of the cylinder is given by;

Surface area = 324π × (1/3)²

Surface area = 324π × 1/9

Surface area = 36 units²

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The equation that represents the relationship between the distances each girl has run is: Marcia = -3/4 * k + 6.5

Let x be the distance run by Tamara in kilometers.

Since Tamara has completed 3/4 of the race, then x = 3/4 * k.

Since Tamara is 2.5 kilometers ahead of Marcia, then x - 2.5 = 4 - Marcia.

Substituting the first equation into the second equation, we get:

3/4 * k - 2.5 = 4 - Marcia

Multiplying both sides by -1, we get:

Marcia - 4 = -3/4 * k + 2.5

Adding 4 to both sides, we get:

Marcia = -3/4 * k + 6.5

Therefore, the equation that represents the relationship between the distances each girl has run is:

Marcia = -3/4 * k + 6.5

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Answer:

Step-by-step explanation:

7.3 is the anwser

Answer:

We can use the cosine double angle formula to find cos(2π/3):

cos(2θ) = cos^2(θ) - sin^2(θ)

Letting θ = π/3, we get:

cos(2π/3) = cos^2(π/3) - sin^2(π/3)

Using the values of cosine and sine of π/3 (which are known), we have:

cos(2π/3) = (1/2)^2 - (√3/2)^2

Simplifying, we get:

cos(2π/3) = 1/4 - 3/4

cos(2π/3) = -1/2

Therefore, cos(2π/3) is equal to -1/2.

Answer:

cos(2π/3) = cos(π/3 + π/3)

= cos²(π/3) - sin²(π/3)

= (1/2)² - (√3/2)²

= 1/4 - 3/4

= -2/4

= -1/2

Step-by-step explanation:

here are the steps:

Therefore, cos(2π/3) = -1/2

Answer: bellshaped

Step-by-step explanation:

The above prompts are related to the concepts of Degrees, Radians, Sines and Cosines. See the solutions below.

1)

(a) Cos 150 degrees

To convert 150 degrees to radians, we multiply by π/180:

150 degrees = (150π/180) radians = (5π/6) radians

We can use the unit circle and reference angle of π/6 to find the cosine of 5π/6:

cos(5π/6) = -cos(π/6) = -(√3/2) = -√3/2

Therefore, cos 150 degrees = -√3/2.

(b) Sin 240 degrees

To convert 240 degrees to radians, we multiply by π/180:

240 degrees = (240π/180) radians = (4π/3) radians

We can use the unit circle and reference angle of π/3 to find the sine of 4π/3:

sin(4π/3) = -sin(π/3) = -(√3/2) = -√3/2

Therefore, sin 240 degrees = -√3/2.

2)

To use the law of cosines, we need either a side and the two angles opposite that side, or two sides and the angle between them. In this case, we have two angles and the side opposite one of them, so we can use the law of sines to find the other side and then use the law of cosines to find the remaining side or angle.

Using the law of sines, we have:

sin A / AB = sin B / AC

where AC is the side opposite angle B. Substituting the given values, we get:

sin 52 / 26.7 = sin 70 / AC

Solving for AC, we get:

AC = sin 70 / sin 52 * 26.7 = 30.4

Now we can use the law of cosines to find the remaining side, x:

x^2 = AB^2 + AC^2 - 2ABACcos A

Substituting the given values, we get:

x^2 = 26.7^2 + 30.4^2 - 226.730.4*cos 52

Solving for x, we get:

x ≈ 22.1

Therefore, the missing side is approximately 22.1.

To find the area of the triangle, we can use the formula:

Area = (1/2) * a * b * sin C

where a and b are the lengths of the two sides, and C is the included angle. Substituting the given values, we get:

Area = (1/2) * 7 * 9 * sin 30

Using the fact that sin 30 = 1/2, we can simplify this to:

Area = (1/2) * 7 * 9 * (1/2) = 15.75

Therefore, the area of the triangle is 15.75 square units.

From the law of sines, we have:

sin A / a = sin B / b

Substituting the given values, we get:

sin 45° / (7√2) = sin B / 7

Solving for sin B, we get:

sin B = (7/7√2) * sin 45° = √2/2

Therefore, B = 45° or 135°. We can use the fact that the angles of a triangle sum to 180° to find C:

C = 180° - A - B = 90° or 0°

If C = 0°, then the triangle is degenerate and the sides a and b lie on top of each other. Therefore, we must have C = 90°.

Now we can use the Pythagorean theorem to find the remaining side:

c^2 = a^2 + b^2 - 2ab*cos C

Substituting the given values, we get:

c^2 = (7√2)^2 + 7^2 - 2(7√2)(7)*cos 90°

Solving for c, we get:

c = √(98 + 49) = √147 = 7√3

Therefore, the sides of the triangle are:

a = 7√2

b = 7

c = 7√3

Using the law of cosines to find x:

In triangle ABC with side lengths AB = 18, AC = 15, and angle A = 108 degrees, we want to find the length of side BC (denoted by x). Using the law of cosines:

x^2 = 18^2 + 15^2 - 2(18)(15)cos(108 degrees)

We can evaluate the cosine of 108 degrees using the identity cos(180 - 108) = -cos(108):

cos(108 degrees) = -cos(180 - 108 degrees) = -cos(72 degrees)

Substituting this into the equation above, we get:

x^2 = 18^2 + 15^2 - 2(18)(15)(-cos(72 degrees))

Simplifying:

x^2 = 729

Taking the square root of both sides:

x = ±27

Since x represents a length, we take the positive root:

x = 27

Therefore, the length of BC is 27 units.

Using the law of cosines to find theta:

In triangle ABC with side lengths AB = 20, BC = 12, and AC = 10, we want to find the measure of angle B (denoted by theta). Using the law of cosines:

cos(B) = (12^2 + 10^2 - 20^2) / (2(12)(10)) = -1/2

Since -1/2 is the cosine of an angle in the second quadrant, we have:

B = 180 degrees - arccos(-1/2)

Using a calculator, we find:

B ≈ 150.5 degrees

Therefore, the measure of angle B is approximately 150.5 degrees (or theta = 150.5 degrees).

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The one to one functions in the options includes

A one-to-one function, also known as an injective function, is a type of function in mathematics where every element in the domain maps to a unique element in the range.

So we can say that, each input value corresponds to exactly one output value, and no two distinct input values have the same output value.

Graphically, one-to-one functions pass the horizontal line test, meaning that no horizontal line intersects the graph of the function more than once.

Applying the horizontal line test shows that the one-to-one function are: Graph 1, 4 and 6

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 [tex]1.[/tex] The answers are given below

   Equation: [tex]6xt +4yz -3 +10a = 1[/tex]

   Number of terms: [tex]4[/tex]

  Coefficients: [tex]6,4,10[/tex]

   Constants: [tex]-3,1[/tex]

 [tex]2.[/tex] Expression: [tex]25abc -2b +3ac -6bc +25[/tex]

    Number of terms: [tex]5[/tex]

    Coefficients: [tex]25,-2,3,-6[/tex]

    Constants: [tex]25[/tex]

  [tex]3.[/tex] Equation: [tex]25y -3xy+5x = 100[/tex]

     Number of terms: [tex]3[/tex]

     Coefficients: [tex]25,-3,5[/tex]

      Constants: [tex]100[/tex]

To break down each equation or expression and identify the number of terms, coefficients, and constants.

[tex]1.[/tex] Equation: [tex]6xt +4yz -3 +10a = 1[/tex]

   Number of terms: 4. There are four terms in this equation separated     by addition and subtraction operators.

Coefficients: [tex]6,4,10[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (xt, yz, a) in each term.

 Constants: [tex]-3,1[/tex]. These are the constants, which are the numerical values without any variables that are added or subtracted in the equation.

[tex]2.[/tex]  Expression:[tex]25abc -2b +3ac -6bc +25[/tex]

   Number of terms: [tex]5[/tex] There are five terms in this expression separated by addition and subtraction operators.

  Coefficients: [tex]25,-2,3,-6[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (abc, b, ac, bc) in each term.

  Constants: [tex]25[/tex]. This is the constant, which is the numerical value without any variables that is added in the expression.

[tex]3.[/tex]  Equation: [tex]25y -3xy+5x = 100[/tex]

    Number of terms:[tex]3[/tex]. There are three terms in this equation separated by addition and subtraction operators.

    Coefficients: [tex]25,-3,5[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (y, xy, x) in each term.

   Constants: [tex]100[/tex]. This is the constant, which is the numerical value without any variables on the right-hand side of the equation.

Therefore,   [tex]1.[/tex] The answers are given below

   Equation: [tex]6xt +4yz -3 +10a = 1[/tex]

   Number of terms: [tex]4[/tex]

   Coefficients: [tex]6,4,10[/tex]

   Constants: [tex]-3,1[/tex]

 [tex]2.[/tex] Expression: [tex]25abc -2b +3ac -6bc +25[/tex]

    Number of terms: [tex]5[/tex]

    Coefficients: [tex]25,-2,3,-6[/tex]

    Constants: [tex]25[/tex]

  [tex]3.[/tex] Equation: [tex]25y -3xy+5x = 100[/tex]

     Number of terms: [tex]3[/tex]

     Coefficients: [tex]25,-3,5[/tex]

      Constants: [tex]100[/tex]

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