A vehicle is running at a constant speed of 60 miles per hour on a highway. When it started, it had 10 gallons of gasoline in its cylinder. The vehicle travels 30 miles on each gallon of gasoline. Ignore the initial acceleration at the start and final deceleration when the vehicle runs out of gasoline and comes to halt. The amount of gasoline in the vehicle can be modeled as a linear function G(t)=10−2t, where t is time, in hours. How much gas is consumed in the first 3 hours?
1, 3 gallons
2, 4 gallons
3, 6 gallons
7, gallons

Answer:

3,418.32yd³

Step-by-step explanation:

For volume you do the area (8)² multiplied by the height (17). 8 x 8 = 64. 64 x 17 = 1,088. you then multiply 1,088 by 3.14, the π, which is 3,416.32. We are using yards so the end result is 3,418.32yd³.

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Therefore , the solution of the given problem of rational comes out to be  53.00 for the given rational number after rounding off.

The percentage (not the percentage) of two integers can be used to represent rational numbers. A reasonable fraction is one with a non-zero denominator. Rational values are including 1/2, 1/5, but they also include 3/4. Additionally, "0" could be expression as a real purpose in a variety of forms, including 0/1, 0/2, and 0/3. However, 1/0, 2/0, 3/0, along with others. Seven is a reasonable amount. A rational number can be obtained by dividing two factors.

Here,

Given :

rational number or integer is 53.121

To round it to the nearest half so ,

According to rounding off the integer , we can round off to 54 when it is 53.5 or above .

But since it is below than that

We get answer as 53.00 for the given rational number after rounding off.

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Archimedes went to sleep about 9.24 meters away from the rock where its shadow should end when it was 7 AM.

Trigonometric ratios are ratios of the sides of a right triangle to its angles. The three primary trigonometric ratios are

Sine = opposite/hypotenuse.

Cosine = adjacent/hypotenuse.

Tangent = opposite/adjacent.  

Here we have

Archimedes wanted to get up at 7. AM, but the alarm clock was yet to be invented. Archimedes knew that at 7.AM, the sunlight reaches the ground at an angle of 31°.

The rock beside which he slept was 5.55 meters tall.

Let's assume that the distance from the rock where Archimedes went to sleep is "x".  

Form a right triangle where the height of the triangle is the height of the rock (5.55 meters) and the angle between the ground and the sunlight at 7 AM is 31° and the opposite side to that angle is x.

Using trigonometry, we can solve for x as follows

tan(31°) = 5.55 / x

x = 5.55 / tan(31°)

x = 5.55/0.60086

x = 9.24 meters    

Therefore,

Archimedes went to sleep about 9.24 meters away from the rock where its shadow should end when it was 7 AM.

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Answer:

Step-by-step explanation:

Let's call the number of gallons of gas consumed by the first car "x" and the number of gallons of gas consumed by the second car "y". We can set up a system of two equations to represent the information given in the problem:

x + y = 45 (equation 1: total gas consumption is 45 gallons)

35x + 25y = 1375 (equation 2: total distance traveled is 1375 miles)

To solve for x and y, we can use the first equation to solve for one variable in terms of the other. For example, we can solve for y as:

y = 45 - x

We can then substitute this expression for y into the second equation, and simplify:

35x + 25(45 - x) = 1375

35x + 1125 - 25x = 1375

10x = 250

x = 25

So the first car consumed 25 gallons of gas that week. We can substitute this value into equation 1 to find the number of gallons consumed by the second car:

25 + y = 45

y = 20

Therefore, the second car consumed 20 gallons of gas that week.

Answer:

Tahlia was correct in remembering that you can find the slope of a line using the slope formula.

She was also correct that the slope is 0.5.

However, if you use the slope-intercept formula y = mx + b, you still have to find b (the y-intercept) by plugging in one of the two points and the slope.

So, if we plug in the first point and the slope into the line, we can find b and thus the full equation of the line:

[tex]-7.5=0.5(-3)+b\\-7.5=-1.5+b\\b=-6\\\\y=0.5x-6[/tex]

The square root of 45 lies between the two whole numbers 36 and 49.

Number is a mathematical object used to count, measure, and label. It is an abstract concept that can be represented in various forms, such as a numeral, a word, or an image. Numbers can be used to represent any quantity, such as a person's age, a distance, a temperature, or a length. They can also be used to represent abstract or intangible concepts, such as a feeling or a thought.

To determine this, we can use a process called the square root algorithm. The first step is to find the largest perfect square that is less than the number you are taking the square root of. In this case, that would be 36. Then, you subtract that perfect square from your number. In this case, you would subtract 36 from 45, leaving you with 9. The next step is to find the two whole numbers that the square root of this difference lies between. Since 9 is the square root of 81, the two numbers that the square root of 9 lies between are 3 and 4. Therefore, the square root of 45 lies between the two whole numbers 36 and 49.

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We simplify the summation to get:

S₄ = 8*(3ⁿ⁻¹)

Remember that the large sigma means that we need to add from the lower number to the larger number.

The particular problem here is that "n" is not the index in the summation, so we can't evaluate that variable, we will just have 4 terms (for k = 1 to k = 4) but the variable k does not appear, so we will  have 4 times the same term:

S₄ = 2*(3ⁿ⁻¹) +  2*(3ⁿ⁻¹) +  2*(3ⁿ⁻¹) +  2*(3ⁿ⁻¹)

S₄ = 4*2*(3ⁿ⁻¹)

S₄ = 8*(3ⁿ⁻¹)

That is the simplification we can do.

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The total number of cars that will fit in the spaces at school is less than or equal to 155, which means that the combined number of parking spaces in the parking lot and on the side of the building cannot exceed 155.

What is expression ?

In mathematics, an expression is a combination of numbers, variables, and operators (such as addition, subtraction, multiplication, and division) that represents a quantity or a relationship between quantities. Expressions can be as simple as a single number or variable, or they can be complex, involving multiple variables and operations.

Let x be the number of parking spaces in each row of the school parking lot. Then, the total number of parking spaces in the parking lot is 6x.

The total number of parking spaces in the school is the sum of parking spaces in the parking lot and parking spaces on the side of the building, which is 6x + 35.

Since the total number of cars that will fit in the spaces at school is at most 155, we can write the inequality:

6x + 35 ≤ 155

Simplifying this inequality, we get:

6x ≤ 120

x ≤ 20

Therefore, the total number of cars that will fit in the spaces at school is less than or equal to 155, which means that the combined number of parking spaces in the parking lot and on the side of the building cannot exceed 155.

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Answer:

Step-by-step explanation:

If you know how to subtract which you should the answer is 2.

How many more means subtraction.

Hope that is helpful!

The inequality 2d+20<=120 is a valid inequality. It means that some value of d can be substituted into the inequality to make it a true statement.

In mathematics, an inequality is a statement that compares two values and indicates how they are related in terms of magnitude or size. Inequalities use symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to) to show the relationship between the two values.

In the given question,

Yes, the inequality 2d+20<=120 is a valid inequality. It means that some value of d can be substituted into the inequality to make it a true statement.

In this case, the inequality is saying that 2 times the value of d plus 20 is less than or equal to 120. To solve for d, we can subtract 20 from both sides to get:

2d <= 100

Then, we can divide both sides by 2 to isolate d:

d <= 50

So the solution to the inequality is that d must be less than or equal to 50 for the inequality to be true.

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Answer: -17a^4

Step-by-step explanation:

Combine like terms

12a^4 +(-29a^4)

(12a^4-12a^4) - (29a^4-12a^4) =

-17a^4

Hope this helps

The response to the given question would be that Because it has a interest higher interest rate and a longer term than option 3, option 1 would generate the greatest interest.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The interest rate of the loan is defined as this ratio.

The following would be the order of 2000 simple interest generated on an investment, from least to most:

2000 invested for 20 years at 3% simple interest

2000 invested for three years at 10% simple interest

2000 invested at 10% simple interest for nine years

Because of its longer length and lower interest rate than the other two alternatives, Option 2 would yield the least amount of interest.

Due to its higher interest rate and longer period, option 3 would generate more interest than option 2.

Because it has a higher interest rate and a longer term than option 3, option 1 would generate the greatest interest.

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Answer:

1 term (monomial).

Step-by-step explanation:

A term includes at least either a number, a variable, or both together, and can have more than one.

In this case, there is 1 term, which denotes that a variable, has an exponent of 9.

[tex]b^9[/tex] is one term.

Examples of more than 1 term can include:

[tex]b^9 + 1[/tex] , which is two terms (Binomial).

[tex]a^2 + b + 3[/tex] is three terms (Trinomial).

* One thing to note is to always simplify when possible.

~

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Answer:

The interest earned would be $600.

To calculate this, you would subtract the initial investment from the final amount:

$5,600 - $5,000 = $600.

Therefore, the interest earned is $600.

Answer: We can start by evaluating g(2):

g(2) = 2 + 9 = 11

Now we can use the definition of function composition to evaluate (f ∙ g)(2):

(f ∙ g)(2) = f(g(2)) = f(11)

To find f(11), we need to substitute 11 for x in the expression for f(x):

f(11) = (11 - 3)^2 + 1 = 8^2 + 1 = 65

Therefore, (f ∙ g)(2) = f(g(2)) = f(11) = 65.

Step-by-step explanation:

Answer: 10 / 5 = 2

Step-by-step explanation:

Using the Pythagorean theorem we know that the rest 2 sides of the given right triangle are 27 inches long.

The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry.

The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

The side opposite the right angle is always the hypotenuse of a right triangle. In a right triangle, it is the longest side.

So, we know the Pythagorean theorem which is:

H² = a² + b²

We know that:

H² = a² + b²

54² = a² + b²

Suppose that the given right triangle is also an isosceles triangle with the rest of the sides being of the same length. Then,

54/2 = 27

Similarly,

54² = a² + b²

54² = 27² + 27²

Therefore, using the Pythagorean theorem we know that the rest 2 sides of the given right triangle are 27 inches long.

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Answer:

below

Step-by-step explanation:

Given cos, you will have to use this to calculate sin because csc is  1/ sin

Remember    cos^2 + sin^2 = 1

                        (2/5)^2 + sin^2 = 1

                                  sin^2 = 21/25  

                                    sin = sqrt (21) / 5     (ignoring negative root)

csc = 1/sin = 5 / sqrt(21)

Answer:

1. 6/18 = 1/3

   9/21 = 3/7

2. 4/6 = 2/3

   2/4 = 1/2

3. 6/12 = 1/2

   8/12 = 2/3

4. 2/8 = 1/4

   3/6 = 1/2

5. 7/21 = 1/3

   8/10 = 4/5

6. 9/12 = 3/4

   12/20 = 3/5

7. 8/16 = 1/2

   10/25 = 2/5

Answer:

Using the slope-intercept form, the slope is −2 .

Step-by-step explanation:

Step-by-step explanation:

solution

Equation of line,

y=-2x-2

2x+y=2 - - - - - - -1

Now,

slope of line,

m= -x coefficient/ y coefficient

= -2/1

= -2

Slope of required line which is perpendicular to the line

m.m = -1

-2.m = -1

m = -1/-2

m =1/2

One hot wing costs 60 cents at this restaurant.

A variable in an equation that has to be solved for is known as an unknown.

A polynomial or formal power series may contain an indeterminate symbol, often known as a variable. In the polynomial ring or the ring of formal power series, an indeterminate is a constant rather than a variable. Nonetheless, many writers view indeterminates as a distinct class of variables because of the close connection between polynomials or power series and the functions that they describe.

Let's us assume that the cost of one hot wing is x dollars.

Then,

Total amount spent by each customer:

8x + 4 = 10x + 2.8

8x - 10x = 2.8 - 4

-2x = -1.2

x = 0.6

Therefore, one hot wing costs 60 cents at this restaurant.

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Answer:

$0.06/yrd

Step-by-step explanation:

you want to divide the cost by the amount of units purchased.

.30/5=.06

this would mean your price per unit is 6 cents

Answer:

15 + t = greather than 180

Step-by-step explanation:

Answer:

I’m pretty sure 3

Step-by-step explanation:

Answer:

D. I, II, III

Step-by-step explanation:

Social security is the only plan managed by the government

Answer:

The heaviest piece of chocolate weighed 2.94 ounces.

Step-by-step explanation:

Answer:im confused

Step-by-step explanation:

Random condition:

✔ met

10% condition:

✔ not met

Large counts condition:

✔ not met

Are the conditions for inference met?

✔ no

Answer: As a fraction: 1/2

              As a decimal: 0.005

Step-by-step explanation:

FRACTION:

To figure out how to write 0.5% as a fraction, all you need to know is that 0.5 = to a half, or 1/2 because 0.5 is half of 1.

DECIMAL:

0.5% as a decimal form is 0.005 because it is 1000 times less than 1, so you move the 0 3 times right.

Given - The expression as

[tex]\frac{3.07+2^4}{5.03-1.79}[/tex]

To find - the solution of the expression

Explanation To simplify the expression, we will simply the terms in the expression

[tex]\frac{3.07+2^4}{5.03-1.79} =\frac{3.07+16}{3.24} =5.885[/tex]

Hence the value of the expression is 5.885

Final answer- The value is 5.885

Explanation:

The front and back faces are triangles. They have a base of 10 ft and height of 4 ft.

The front face has area 20 sq ft. The same applies for the back face as well.

Now imagine rotating the prism so that the front face is now laying on the floor. The floor and ceiling are triangles. Each wall is a rectangle.

Answer: 110 ft^3

Step-by-step explanation:

Base is 10ft

Height is 4ft (distance from base to uppermost point)

0.5*10*4=20

20*5.5 (length)=110