What is the answer to this question?
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Answer:

5.625 gallons are being leaked per hour.

Step-by-step explanation:

Since every fluid ounce = 0.0078125 of a gallon,

0.0078125 x 12 (the amount of fluid ounces leaked per minute) = 0.09375

Since 0.09375 is the number of gallons leaked per minute, we have to multiply by 60 (because an hour is 60 minutes long).

12 x 60 = 720 (the number of fluid ounces leaked per minute)

0.09375 x 60 = 5.625 (the number of gallons are being leaked per hour)

The account will reach $5500 after approximately 33.3 years have passed.

The simple interest formula is I = P x r x t, where I is the interest earned, P is the principal (the initial amount of money deposited), r is the annual interest rate, and t is the time in years.

You can rearrange this formula to solve for t: t = I / (P x r).

In this case, I = $500 (the difference between the final balance and the initial balance), P = $5000 (the initial amount deposited), and r = 0.3% (the annual interest rate).

Plugging these values into the formula, we get:

t = $500 / ($5000 x 0.3%)

t = $500 / ($5000 x 0.003)

t = $500 / $15

t = 33.333...

To the nearest tenth of a year, it will take approximately 33.3 years for the account to reach $5500.

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Given trigonometric expression in algebraic form would be,

cos(arcsin(x - h/r)) =  ± [√(r² - (x - h)²)]/r

In this question, we need write the expression in algebraic form.

Given trigonometric expression is cos(arcsin(x - h/r))

Let y = arcsin(x - h/r)

so, sin(y) = (x - h)/r

By trigonometric identity,

sin^2(y) + cos^2(y) = 1

we have cos(y) = ±√(1 - sin²y)

cos(arcsin(x - h/r)) = ±√[1 - ((x - h)/r)^2]

                             = ± [√(r² - (x - h)²)]/r

Therefore, given trigonometric expression in algebraic form would be,

cos(arcsin(x - h/r)) =  ± [√(r² - (x - h)²)]/r

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Answer:

25 & 37

Step-by-step explanation:

Constant of Proportionality = 15.20

What's proportionality?

Suppose there are two amounts. Proportionality indicates that if there's a change in the value of one number, the value of other number also changes but maintaining a constant ratio

Proportionality can be direct or inverse

Direct proportion

Two amounts are said to be in direct proportion if on increasing the value of one number, the value of other number also increases and vice versa.

For illustration cost of a commodity and volume of a commodity are in direct proportion

Inverse proportion

Two amounts are said to be in inverse proportion if on increases the value of one number, the value of other volume diminishes and vice versa.

For illustration Number of men and number of days taken by those men to complete a job

From the table, we can calculate the constant of proportionality

Constant of Proportionality =

                                                [tex]\frac{304 - 243.20}{20 -16}\\\frac{60.80}{4}\\15.20[/tex]

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Answer:

Step-by-step explanation:

T₁ = 1² + 4·1 + 2 = 7

T₂ = 2² + 4·2 + 2 = 14

T₃ = 3² + 4·3 + 2 = 23

After any particular a, the next a in the sequence must appear exactly 2 or 3 positions down the line. In this case, we start at position b and end at position 19. answer is 65

i.e. we move a total of 18 positions down the line. Therefore, we must add a series of c's and d's to get 18. There are several ways to do this:

Case 1: nine c's - there is only 1 way to arrange them.

Case 2: two d's and six c's - there are 28 ways to arrange them.

Case 3: four d's and three c's - there are 35 ways to arrange them.

Case 4: six c's - there is only 1 way to arrange them.

Summing the four cases gives 1+28+35+1 = 65

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The side of the cube is 6 cm.

What is the Volume of a prism?

The area that a prism takes up is referred to as its volume. A prism is a solid, three-dimensional structure with two identical faces and additional faces that resemble parallelograms. It is a polyhedron whose nomenclature is influenced by the various basic forms. Every prism has a particular base, whether it be a triangular prism (triangular base), square prism (square base), rectangular prism (rectangular base), pentagonal prism (pentagonal base), hexagonal prism (hexagonal base), or an octagonal prism (octagonal base). Consequently, because a prism is a three-dimensional form, its volume likewise exists in a three-dimensional plane. Prisms are measured in terms of their volume in cubic meters, cubic millimeters, cubic inches, or cubic feet. Following are the steps to calculate the prism's volume:

Write down the prism's dimensions as specified in step one.

Step 2: Use the formula V = B H to calculate the prism's volume. V, B, and H stand for the prism's volume, base area, and height, respectively.

Step 3: After obtaining the volume of the prism's value, add the unit of prism volume at the conclusion (in terms of cubic units).

In the question, we have given that:

Prism is made up of 120 equal cubes;

The volume of the prism is 25, 920[tex]cm^{3}[/tex];

So, we can equate the volume of 120 equal cubes with the prism's volume;

⇒ 120 × [tex](a)^{3}[/tex] = 25, 920;

⇒[tex](a)^{3}[/tex] = [tex]\frac{25920}{120}[/tex]

⇒[tex](a)^{3}[/tex] = 216;

So, the value of a is 6 cm;

That is the side of the cube is 6 cm;

Hence, The side of the cube is 6 cm.

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Answer:

THE SLOPE IS 16

Answer: The slope is 16/1 which is just 16.

Step-by-step explanation:                                                                                                              

Answer:

33.4%

Step-by-step explanation:

60+33.4%=80

60x1.334=80

The ∠3+ ∠1 = 90°. in the given figure are the same just using the properties of Vertically angles.

What is Vertically opposed angles?

Two lines intersecting at a point create vertical angles. Every time they are on an equal footing. Alternatively stated, four angles are created anytime two lines cross or intersect. Two opposed angles are equal and are referred to as vertical angles, as we can see. Due to their position opposite one another, they are also known as "Vertically opposed angles."

Angles that are vertically opposed to one another at a certain vertex are formed by two straight lines intersecting. The equality of the vertically opposed angles has been established.

∠1  and ∠2 are vertical angles, which means ,

∠1  =∠2

Given in the question is ∠3+ ∠2 = 90

As both ∠1  and ∠2 are the same so we can write ∠3+ ∠1 = 90°.

Hence, The ∠3+ ∠1 = 90°. in the given figure are same.

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The option that could be the diameter of a baseball used by a professional baseball team is A. 2 7/8 inches.

From the information, the baseball used by a professional baseball team must have a diameter that is between 2.86 inches and 2.94 inches.

In this case, 2 7/8 inches to decimal is 2.875

2 7/9 inches will be 2.778

2 8/10 will be 2.8

2 9/11 inches will be 2.818

Therefore, the correct option is A as it fits tye value given.

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Complete question

A baseball used by a professional baseball team must have a diameter that is between 2.86 inches and 2.94 inches. which of the following could be the diameter of a baseball used by a professional baseball team?

A. 2 7/8 inches

B 2 7/9 inches

C 2 9/11 inches

D. 2 8/10 inches.

The equation, 4 - 0.25g + 0.5h, will be evaluated as equal to: 4.

To evaluate an equation, plug in the values of the variables in the equation and solve to get the simplified value.

Given the equation, 4 - 0.25g + 0.5h, where:

g = 10

h = 5

Substitute g = 10 and h = 5 into the equation 4 - 0.25g + 0.5h, then evaluate:

4 - 0.25(10) + 0.5(5)

Simplify

= 4 - 2.5 + 2.5

= 4 + 0

= 4

Therefore, if g = 10 and h = 5, the equation 4 - 0.25g + 0.5h, is evaluated as: 4.

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The Question:

Evaluate 4 - 0.25g + 0.5h when g = 10 h = 5.

The converse of the given statement is if b+6 is odd then b is odd

And the converse statement is valid

The correct statement is option 1)

What is an odd number?

A number which on dividing by 2 gives remainder as 1 is known as odd number and a number which gives remainder 0 on dividing by 2 is known as even number

We are given a statement as if b is odd then b+6 is odd

The converse of the given statement would be

if b+6 is odd then b is odd

And the statement is true as 6 is an even number then if b+6 is odd iff b is odd

Hence the correct statement is option 1

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Answer:

[tex]y = -\frac{7}{20}x + 1[/tex]

Step-by-step explanation:

We have to find the equation of the line that would be made by the stars

This line is parallel to the one already given

Gradients of both lines will be the same

Find out the gradient of the line already given

chose 2 coordinates of the line, I'll choose (0,0) and (-10,3.5)

use the formula

[tex]\frac{y2 - y1}{x2 - x1}[/tex]

[tex]\frac{3.5-0}{-10-0}[/tex]

[tex]-\frac{3.5}{10}[/tex]

-7/20 is the gradient

the star crosses the y axis at y = 1 so the y intercept is 1

y = mx + c

[tex]y = -\frac{7}{20}x + 1[/tex]

the probability that each of the four players is dealt exactly one ace is about 0.11. this means that in a very large number of bridge deals, the percentage of deals on which each player has one ace will be very close to 11%

The probability of each of the four players is dealt exactly one ace is about 0.11

so,

the probability is always approximately the corresponding percent obtained for very large samples.

Hence it means that in a very large number of bridge deals, the percentage of deals on which each player has one ace will be very close to 11%

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Answer:

1: Supplementary angle; x = 95

2: Complementary angle; x = 31 [(2x-3)+x]

3: vertical angle; x = 90

4: supplementary angle; x = 92 [x+(x-4)]

Step-by-step explanation:
1: 180-85 = 95 (x)

2: (2x-3)+x = 90 evaluates into x = 31

3: all sides are equal so if one side is 90 then the rest are

4: x+(x-4) = 180 evaluates into x = 92

Let me know if you need any more help.

A total of 640 cubes of 3cm size can fit into a box with internal dimensions of 54, 40, and 8 cm.

By using volume, et’s assume that ’n’ cubes can be cut out from the cuboid. The volume of n cubes will be equal to the total volume of the cuboid.

The volume of 1 cube of side 3 cm is (3)^3 = 27 c.c. [volume of a cube of side 'a' is (a)^3]

Now, the volume of cuboid from which the cubes will be cut is 54 X 40 X 8 = 17280 c.c. [volume of a cuboid is length X breadth X height].

Now, the number of cubes that can be cut out from the cuboid (n) = (volume of cuboid)/(volume of 1 cube) => n = 17280/27 = 640.

Hence, a total of 640 cubes of side 3cm can beput into a box which had internal measurement of 54cm 40cm and 8 cm

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The percentage error of Bob’s measurement to the nearest tenth of a percent is 3.87%

The percentage error is The difference between the estimated value and the actual value in relation to the actual value is given as a percentage. Analyst use this formula to determine how big is the error in a relation to true value.

Here, given that

The experimental volume of liquid is 18.8 ml, and the actual volume of liquid is 18.1 ml

i.e. exprimental volume=18.8 mL

and, actual volume=18.1 mL

Now, we will calculate the percentage error

So,

percentage error=((Exprimental value-Actual value)/(Actual value))∙100

percntage error=((18.8-18.1))/18.1∙100

percentage error=0.7/18.1∙100

percentage error=0.0387∙100

percentage error=3.87%

Thus,

       We got percentage error of 3.87% in measurement

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The blanks in this two-column proof should be completed (filled) as follows:

Statements                                                       Reasons_______________

∠A and ∠B are complementary angles.         Given

∠B and ∠C are complementary angles.    

m∠A + m∠B = 90°                               Definition of complementary angles

m∠B + m∠C = 90°

m∠A + m∠B = m∠B + m∠C                  Substitution property of equality

m∠A = m∠C                                          Subtraction property of equality

∠A ≅ ∠C                           Angles that have equal measure are congruent.  

In Mathematics, a complementary angle can be defined as two (2) angles or arc whose sum is equal to 90 degrees (90°).

Mathematically, a complementary angle can be represented by using this mathematical expression:

Q + R = 90°

Where:

Q and R are measure of the angles subtended.    

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Answer:A

Step-by-step explanation:

The initial height is 12 feet.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

3 (x + 4)² + 12

The constant value = 12

The constant in the simplified form of the expression represents the initial height, in feet, of the ball.

So,

The initial height is 12 feet.

Thus,
Initial height = 12 feet.

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Answer:

d=8

t=9

Step-by-step explanation:

2.75x8=$22

2x9=$18

22+18=40

d=8

t=9

Answer:

2.75d+2t <= 40

Step-by-step explanation:

The equation in standard form is, [tex]y=-6x^2+48x-97[/tex].

What is quadratic form?

A polynomial with all terms of degree two is known as a quadratic form in mathematics. A quadratic form with the variables x and y is, for instance, 4x^2 + 2xy - 3y^2. It is common to refer to a quadratic form over K when the coefficients are typically members of a specified field K, such as the real or complex numbers.

Consider, the given quadratic form

[tex]y=-6(x-4)^2-1\\[/tex]

Simplifying this,

[tex]y=-6(x^2-8x+16)-1\\y=-6x^2+48x-96-1\\y=-6x^2+48x-97[/tex]

Therefore, the standard form of the given quadratic form is, .[tex]y=-6x^2+48x-97[/tex]

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The three digit number you thought of is 111.

We now have:

According to the question:

N = a*100 + b*10 + c.

where:

b = c^2

a = b^2.

Let's now assign values to c. (here we can start with zero).

If c = 0, then b = 02 = 0 and a = 02 = 0 are the results.

Then N = 0*100 + 0*10 + 0 = 0 (this is not a 3-digit number) is the expression

If c = 1, then b = 12 = 1, then a = 12, and so on.

N = 1*100 + 1*10 + 1 = 111

If c = 2, then b = 2 2 4 a = 4 2 16 will follow.

111 is the only viable choice in this case.

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Answer: 9-11 = -2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

11 - 9 = 2

2 -----> -2

OR

9 - 11 = -2

Answer:  6  -3  

Step-by-step explanation: i just took the test

Answer:

(-6,3) (5,-9)

Step-by-step explanation:

The value of y when x = 24 is 272.

Proportionality indicates that two quantities or variables are related linearly.

Given that, y varies directly with x when y = 68 and x = 6

y/x = 68/6 = 34/3

Therefore, the proportion is 34/3

when x = 24

34/3 = y/24

y = 272

Hence, y = 272 when x = 24

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The unit rate of weeks to pounds is 2.5 pounds in just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.

Given that,

In just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.

We have to find how many weeks are there in a pound.

A rate is a ratio that is utilized to compare the quantities of several commodities. A unit rate is a rate with one as the denominator. Whenever a rate's denominator, such as the price per unit of a certain number of items, is not 1.

So, we can write has

This is the fraction of the number of pounds and number of weeks.

=30pounds / 12 weeks

=2.5 pounds

Therefore, The unit rate of weeks to pounds is 2.5 pounds in just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.

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