At one gas station, gas costs $2.75 per gallon. Write an equation that relates total cost, C, to the number of gallons of gas purchased

Given:

The scale factor between two circles is \(\dfrac{2x}{5y}\).

To find:

The ratio of their areas.

Solution:

We know that, all circles are similar.

The ratio of the areas of similar figures is equal to the ratio of squares of their corresponding sides or equal to the square of ratio of their corresponding sides.

The scale factor is the ratio of the corresponding sides.

Ratio of areas of circles = Square of scale factor between two circles

\(\text{Ratio of areas of circles}=\left(\dfrac{2x}{5y}\right)^2\)

\(\text{Ratio of areas of circles}=\dfrac{(2x)^2}{(5y)^2}\)

\(\text{Ratio of areas of circles}=\dfrac{4x^2}{25y^2}\)

Therefore, the correct option is D.

Answer:

5

−21

÷

10

−7

= \frac{-21}{5} \times \frac{-10}{7}=

5

−21

×

7

−10

= \frac{21\times 10}{5 \times 7 }=

5×7

21×10

/* After cancellation , we get */

= 6=6

Therefore.,

\red{ \frac{-21}{5} \div \frac{-7}{10}}\green { = 6}

5

−21

÷

10

−7

=6

•••♪

Answer: -6

Step-by-step explanation:

(-21/5) / (-7/-10)

Since there is two negatives in -7/-10 the negative will cancel out, but only in -7/-10

(-21/5)/(7/10)

You can now divide what’s in the parentheses (which will give you (-21/5)/(10/7)

(-21/5) / (10/7) =  -3 X 2 (just divide 10 by 5 and -21 by 7, when dividing fractions you divided the opposing numerator by the denominatior)

-3 x 2 = -6

Hope that makes sense :)

Equating the expressions, if Li Wei can read 30 pages in an hour and Colleen Henry 24 pages an hour, they will be on the same page in 6 hours.

Equivalent expressions are two or more algebraic expressions that have the same value when the variables are substituted with real numbers.

In this situation, we can determine the time that Li Wei and Colleen Henry can be on the same page by equating the expressions representing their reading rates.

The number of pages Li Wei can read in a week = 90

The number of pages Collen can read in a week = 126

Li Wei's reading rate per hour = 30 pages

Collen's reading rate per hour = 24 pages

Let the hours that Li Wei and Colleen can be on the same page= x

The total number of pages Li Wei can read = 90 + 30x

The total number of pages Colleen can read = 126 + 24x

For Li Wei and Colleen to be on the same, the two expressions are equated.

90 + 30x = 126 + 24x

6x =  36

x = 6

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Answer:

There is not enough evidence to support the claim that the fat percentage of at least one of the four ethnic groups is different.

Step-by-step explanation:

The Analysis of Variance (ANOVA) test is used to determine whether there is any significant difference between the mean of various independent groups.

In this case an ANOVA test is being performed to determine whether the fat percentage of four different ethnic groups are different or not.

The hypothesis can be defined as:

H₀: The fat percentage of four different ethnic groups are same, i.e. μ₁ = μ₂ = μ₃ = μ₄.

Hₐ: The fat percentage of at least one of the four ethnic groups is different, i.e. at least one μ\(_{i}\) is different.

The significance level of the test is, α = 0.05.

The decision rule is:

The p-value of the ANOVA test is computed as, p-value = 0.11.

p-value = 0.11 > α = 0.05.

The null hypothesis was failed to be rejected.

Hence, it can be concluded that there is not enough evidence to support the claim that the fat percentage of at least one of the four ethnic groups is different.

Answer:

Step-by-step explanation:

Line s

slope m = Δy / Δx =  (22 - 4) / (4 - (-5)) = 18/9 = 2

y = mx + b

22 = 2(4) + b

b = 14

y = 2x + 14

which can be rearranged to

2x - y = -14

Line t

slope = ( -4 - 14) / (5 - (-4)) = -18/9 = -2

-4 = (-2)(5) + b

b = 6

y = -2x + 6

2x + y = 6

2x − y = −14             2x + y = 6

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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Answer:

Rs. 18080

Step-by-step explanation:

Given :

Marked price = Rs. 20000

Discount = 20%

Discounted price = (100-20)% * marked price

Discounted price = 80% * 20,000 = Rs. 16,000

The VAT = 13%

VAT charge = 13% * 16,000 = Rs. 2080

Final price = discounted price + VAT charge

Final price = 16000 + 2080 = Rs. 18080

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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The inequality is:

So, we have two options:

Therefore solving both options, we get:

So, the answer is the set of all the x greater or equal to zero and smaller or equal to 5.

Answer: 0 ≤ x ≤ 5

The y-coordinate of -3f(x-1) when x = 0 is -63

From the question, we have the following parameters that can be used in our computation:

The table of values

So, we have

-3f(x - 1)

When x = 0, we have

y = -3f(0 - 1)

This gives

y = -3f(-1)

From the table, we have

y = -3 * 21

Evaluate

y = -63

Hence, the y-coordinate is -63

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Answer:

Hope this helps

Step-by-step explanation:

7850 ft²

Hi there !

d = 2r => r = d/2 = 100ft/2 = 50 feet

A = πr²

= 3.14×(50ft)²

= 3.14×2500ft²

= 7850 ft²

Good luck !

Answer:

Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value. For example, 2/4 and 3/6 are equivalent fractions, because they both are equal to the ½. A fraction is a part of a whole. Equivalent fractions represent the same portion of the whole.

Answer:

1244 DCD

Step-by-step explanation:

A' - (-1,4)

B' - (-1,8)

C' - (-5,4)

hope this helps

The mistake is when you try to divide by X - 1, because you can't divide by zero.

Here we start by defining:

X = 1

The second step makes sense, we are adding the same value in both sides:

X + X = X + 1

2X = X + 1

Now subtract 2 in both sides:

2X - 2 = X + 1 - 2

2X - 2 = X - 1

Here is the mistake, you divide both sides by X - 1

But we already defined that X = 1

Then you are trying to divide by zero, and that opeartion is not defined, that is why you reach a false equation.

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the equation of straight line y=-x+5

A straight line is a geometric object that extends infinitely in both directions and has a constant slope or gradient. It is the shortest path between two points in Euclidean space and is characterized by the equation y = mx + b, where m is the slope or gradient of the line and b is the y-intercept, which is the point where the line intersects the y-axis.

Let the equation of straight line be y=mx+c

Putting the values;

x=5

y=0

5m+c=0…..Equation 1

Putting the values;

x=0

y=5

5=c

Putting value of c in equation1, we get

5m+5=0

m=-1

Hence, the equation of straight line y=-x+5

Image  of graph is attached below

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The expression without absolute value bars is 3.84.

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,

|√10 - 7 |

= | 3.16 - 7 |

= | -3.84 |

= 3.84

Thus,

The value of the expression is 3.84.

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Answer:

Step-by-step explanation:

You want the simplified form of (5b^1c^-5)^-3(4b^0a^2)^-5.

There are several useful rules of exponents here:

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

  a^-b = 1/(a^b)

Simplifying the top-level exponents first, we have ...

  \((5b^1c^{-5})^{-3}(4b^0a^2)^{-5}=(5^{-3}b^{1(-3)}c^{(-5)(-3)})(4^{-5}b^{0(-5)}a^{2(-5)})\\\\=(5^{-3}4^{-5})a^{-10}b^{-3+0}c^{15}=\dfrac{1}{5^34^5}a^{-10}b^{-3}c^{15}=\boxed{\dfrac{1}{128000}a^{-10}b^{-3}c^{15}}\)

In terms of answer requirements:

  n = 1/128000

  r = -10

  s = -3

  t = 15

From the given scatter plot it is a positive trend.

We need to describe the trend of given scatter plots.

A scatter plot shows a positive trend if y tends to increase as x increases. A scatter plot shows a negative trend if y tends to decrease as x increases. A scatter plot shows no trend if there is no obvious pattern.

Here, from the given graph it is a positive trend.

Hence, from the given scatter plot it is a positive trend.

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Step-by-step explanation:

The Perimeter of Equilateral triangle = 60cm

According to the question,

To find the height of the triangle,

Perimeter of Equilateral triangle = Area of Equilateral triangle.

\(60 = \frac{ \sqrt{3} }{4} a {}^{2} \\ \)

\(60 \times 4 = \sqrt{3a {}^{2} } \)

\(a {}^{2} = 240 \sqrt{3} \\ \)

\(a = 120 \sqrt{3} cm\)

Answer: -16.66

Reason: 10*-5/3=−16.66666667 or −50/3​

Answer:

The answer is a

Step-by-step explanation:

it’s a because each dude is 1/2 and you add another one half that’s one and you keep on doing until the last one.

brainliest pls

I hope this helped and was right.

Step-by-step explanation:

Length: 6

width: 4

height:3

Formula :

Volume= l x w x h

6x4x3 =72

72 x 1/2= 36in3/A

Answer:

I don't have a clue

Step-by-step explanation:

Answer:

\(\frac{-29}{72}\)

Step-by-step explanation:

use a calculator

Answer:

Exact Form:

x = 6 + 3 square root sign 10, 6 - 3 sqaure root sign 10

Decimal Form:

x = 15.48683298...-3.48683298 ...

Step-by-step explanation:

The cost of one small box of fruit and the cost of one large box of fruit is $11.5 and $14.5 respectively.

Let

cost of one small box of fruit = x

cost of one large box of fruit = y

15x + 15y = 390

20x + 25y = 592.50

From (1)

x + y = 26

x = 26 - y

Substitute x = 26 - y into (2)

20x + 25y = 592.50

20(26 - y) + 25y = 592.50

520 - 20y + 25y = 592.50

- 20y + 25y = 592.50 - 520

5y = 72.50

divide both sides by 5

y = 72.50/5

y = 14.5

Substitute y = 14.5 into

15x + 15y = 390

15x + 15(14.5) = 390

15x + 217.5 = 390

15x = 390 - 217.5

15x = 172.5

divide both sides by 15

x = 172.5/15

x = 11.5

Therefore, small box cost $11.5 and large box cost $14.5

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After simplifying a mixed number is 5 1/16

A mixed number is a combination of a whole number and a fraction.

It is typically written in the form "a b/c", where "a" is the whole number, "b" is the numerator of the fraction, and "c" is the denominator of the fraction.

For example, 3 1/2 is a mixed number, where 3 is the whole number, 1 is the numerator of the fraction, and 2 is the denominator of the fraction. This mixed number can also be expressed as an improper fraction as follows:

3 1/2 = (3 × 2 + 1) / 2 = 7/2.

Conversely, an improper fraction can be converted to a mixed number by dividing the numerator by the denominator to obtain the whole number and expressing the remainder as a fraction.

To multiply 2 1/4, follow these steps:
1. Convert the mixed number to an improper fraction: 2 1/4 = (2 × 4 + 1) / 4 = 9/4
2. Multiply the improper fraction by itself: (9/4) × (9/4)
3. Multiply the numerators: 9 × 9 = 81
4. Multiply the denominators: 4 × 4 = 16
5. Write the result as a fraction: 81/16
6. Simplify the fraction by converting it to a mixed number:

81 ÷ 16 = 5, with a remainder of 1.

So, 81/16 = 5 1/16.

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Answer:

12m

Step-by-step explanation:

To find the area of the rectangle we multiply l by w

so

lw=a

if l=2+w we can substitute l with 2+w

so now

w(w+2)=168

distribute

w^2+2w=168

Now we use guess and check to solve

13^2 is 169

so 12^2 is 144 and 2*12=24

and 144+24=168