Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of
cubic feet, HCF). When graphed, the function gives a line with a slope of 1.65. See the figure below.
If the monthly cost for 21 HCF is $49.58, what is the monthly cost for 24 HCF?
Monthly cost 49.58
(in dollars)
21
Water usage
(in HCF)
$0
X
5
INIC

Answer:

the original price of each costume was $25, and the sale price was $(25-3.50) = $21.50.

Step-by-step explanation:

Let the original price of each costume be $x. The sale price of each costume will be $(x-3.50). Ms. Monroe ordered 24 costumes, so the cost of 24 costumes at the sale price will be:

24 × (x-3.50) = $24x - $84

Ms. Monroe paid $516 in all, so we can write:

24x - 84 = 516

Adding 84 to both sides, we get:

24x = 600

Dividing both sides by 24, we get:

x = 25

Therefore, the original price of each costume was $25, and the sale price was $(25-3.50) = $21.50.

Answer: so Ms.Monroe got $84 off her entire purchase

Step-by-step explanation: I hope it helps

The number of hours till Ed and Julie were 875 miles apart was 7 hours.

Since Ed and Julie are traveling in opposite directions, we can think of their distances from Good Life City as two separate distances that are adding up to their total distance apart.

For Ed, his distance from Good Life City is:

= 60 t

For Julie :

=  65t

We want to know how many hours it took for their total distance to be 875 miles. So we can set up the equation:

875 = 60t + 65t

Simplifying, we get:

875 = 125t

t = 875 /  125

t = 7 hours

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Answer:

10^9 = 1,000,000,000

2^6 = 64

7^1 = 7

10^3 = 1,000

10^8 = 100,000,000

0^4 = 0

7^6 = 117,649

Step-by-step explanation:

The exponent multiplies a number by itself by whatever value it is.

Answer:

↓ ↓ ↓

Step-by-step explanation:

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________________________

Hope this helps! :)

Hence the value of x from the given diagram is 4.5

The relationship between the height on the hypotenuse of a right triangle and the two line segments it generates on the hypotenuse is described by the right triangle altitude theorem, also known as the geometric mean theorem, which is a consequence of elementary geometry.

From the diagram shown:

6/8 = x/6

Cross multiply

6*6 = 8x

36 = 8x

x = 36/8

x = 4.5

Hence the value of x from the diagram is 4.5

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The equation for calculating the area of a triangle is:

A = 1/2 * base * height

where A represents the area of the triangle, base represents the length of the base of the triangle, and height represents the height of the triangle measured perpendicularly to the base.

Answer:

15£

Step-by-step explanation:

if 1£=2$

then30$=30/2

15£

Answer:

Let's start by finding out how many muffins were there in total before the ogre stole 20 of them. Let's call that number "x".

If 5/8 of them were left after the ogre stole 20, then 3/8 of them were taken.

So we can set up an equation:

x - 20 = 3/8x

To solve for x, we can start by multiplying both sides by 8 to get rid of the fraction:

8(x - 20) = 3x

8x - 160 = 3x

Now we can solve for x by subtracting 3x from both sides:

5x - 160 = 0

5x = 160

x = 32

So there were originally 32 muffins.

Now we can find out how many are left:

5/8 of 32 = 20

So there are 20 muffins left.

Step-by-step explanation:

From the given options, option 1 depicts a decreasing function. Hence, option 1 is the correct answer for the graph.

Calculus uses a function's derivative to determine whether a function is rising or decreasing at various intervals in a specific domain. Given a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

We observe that the function of f approaches to 0 as it moves towards infinity. Thus, it is a decreasing function.

From the given options, option 1 depicts a decreasing function. Hence, option 1 is the correct answer.

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The measures of the angles are JKN = 27 degrees and JNK = 126

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

The rectangle

On the rectangle, we have

JKN = NJK

Using the above as a guide, we have the following:

JKN = 27 degrees

The sum of angles in a triangle is 180

So, we have

JNK = 180 - 27 * 2

Evaluate

JNK = 126

Hence, teh angle is 126 degrees

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Answer: the image didnt send with this try reposting

Step-by-step explanation:

this is a little funny out of context tho, best of luck be upon you

Using arithmetic operations, The total cost of six sheets will be:

$27.00 + ($9.00 x 4) = $63.00

If each sheet costs $18.00, then the cost of the first sheet will be $18.00, and the cost of the second sheet will be 50% of $18.00, or $9.00.

So, two sheets will cost the cost of the first sheet plus the cost of the second sheet, which is:

Using addition,

$18.00 + $9.00 = $27.00

For six sheets, we can use the same logic: the first two sheets will cost $27.00, and the next four sheets will be half off. So, the cost of the next four sheets will be 50% of $18.00, or $9.00 each.

Hence, the total cost of six sheets will be:

$27.00 + ($9.00 x 4) = $63.00

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Answer:

try 1/2

Step-by-step explanation:

The optimal strategy would be to fit several models to the data using equation mathematical software or tools, and then assess the goodness of fit using statistical metrics like R-squared or Mean Squared Error.

In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilized. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.

The following exponential model could be a good fit for the data in the image:

[tex]f(x) = 7.5 * e^(0.1x) (0.1x)[/tex]

The data is assumed to develop exponentially with a base of e in this model, with a growth rate of 10% for each unit increase in x.

It is crucial to remember that this is only one potential model and that other exponential models with other parameters could also be able to satisfactorily match the data. The optimal strategy would be to fit several models to the data using mathematical software or tools, and then assess the goodness of fit using statistical metrics like R-squared or Mean Squared Error.

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Answer:

When the ball hits the ground, its height will be 0 meters. Therefore, we need to solve the equation:

h(t) = 0

8t - 5t^2 + 4 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula, but in this case, it's easier to use factoring:

(5t - 4)(t - 1) = 0

From this equation, we can see that either 5t - 4 = 0 or t - 1 = 0. Solving for t in each case, we get:

5t - 4 = 0 ==> t = 0.8 seconds

t - 1 = 0 ==> t = 1 second

Therefore, the ball will reach the ground after either 0.8 seconds or 1 second, depending on the initial height of the ball.

The correct statement regarding the inverse function is given as follows:

[tex]f^{-1}(x) = 3 - \sqrt{\frac{x - 4}{2}}[/tex], with a domain of x ≤ 3.

The function for this problem is defined as follows:

f(x) = 2(x - 3)² + 4.

The axis of symmetry of the function is of x = 3, hence the domain of the inverse function is given as follows:

x ≤ 3.

The inverse function is obtained exchanging x and y and then isolating y, hence:

x = 2(y - 3)² + 4

2(y - 3)² = x - 4.

[tex](y - 3)^2 = \frac{x - 4}{2}[/tex]

[tex]y - 3 = \sqrt{\frac{x - 4}{2}}[/tex]

[tex]f^{-1}(x) = 3 - \sqrt{\frac{x - 4}{2}}[/tex]

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The rhyme scheme of the poem is abab cdcd efef gg. The rhyme scheme creates a sense of symmetry and balance in the poem.

A poem's rhyme system is its regular pattern of final rhymes. It is written using alphabetical letters, each of which stands for a particular rhyme sound. A poem with the rhyme scheme ABAB, for instance, follows a pattern where the first and third lines rhyme, and the second and fourth lines rhyme.

The poem's rhyme scheme can be mathematically described by utilising letters to denote the various rhyming sounds. "Abab cdcd efef gg" is the rhyme pattern used in this poem. This can be written as follows using letters to represent the various sounds:

This pattern is repeated throughout the entire poem, creating a consistent and structured rhyme scheme.

Therefore the rhyme scheme is abab cdcd efef gg.

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Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let's assume that an adult manatee eats "r" pounds of food per day on average. Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d

Here, "p" represents the number of pounds of food, "r" represents the average amount of food consumed per day, and "d" represents the number of days. So, if we know the average amount of food consumed by an adult manatee per day, we can use this equation to calculate how much food it will eat in any given number of days.

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Answer:

Step-by-step explanation:

The equation written in slope-intercept form is: y=3x-2.

The location of A ' given the rotation about the origin and the xy coordinate plane is D. In Quadrant IV.

To rotate a point 180° about the origin, we switch the signs of both coordinates. For instance, if you have ( x, y ) rotated, then it becomes ( - x ,  - y ).

So, if A is located at (-4, 3), then A' is located at (4, -3).

The point A' is located in Quadrant IV, because it has a positive x-coordinate and a negative y-coordinate, which is the characteristic of points in this quadrant.

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The p-value for this sample is approximately 0.004655 which is smaller than the significance level of 0.005. This means that we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the population proportions are not equal.

To test the hypothesis Hₐ : p₁ ≠ p₂ at a significance level of α = 0.005, we can use the two-sample z-test for proportions, where the test statistic is given by:

z = (p₁ - p₂) / sqrt{p(1-p)(1/n₁ + 1/n₂)}

where p = (x₁ + x₂) / (n₁ + n₂) is the pooled sample proportion, x₁ and x₂ are the number of successes in the two samples, n₁ and n₂ are the sample sizes for the two samples, and p₁ and p₂ are the sample proportions for the two samples.

Plugging in the given values, we have:

p₁ = 119/687 ≈ 0.1732

p₂ = 137/577 ≈ 0.2374

n₁ = 687

n₂ = 577

p = (119 + 137) / (687 + 577) ≈ 0.202

z = (0.1735 - 0.2376) / √{0.202 * (1 - 0.202) * (1/687 + 1/577)} ≈ -2.83

The test statistic for this sample is approximately -2.83

To find the p-value for this sample, we need to find the probability of observing a test statistic as extreme as -2.83, assuming that the null hypothesis is true. Since this is a two-tailed test, we need to find the area in the tails of the standard normal distribution that corresponds to a significance level of 0.005:

α/2 = 0.005/2 = 0.0025

Using a standard normal table or a calculator, we can find that the z-score corresponding to an area of 0.0025 in the left tail of the standard normal distribution is approximately -2.81. The z-score corresponding to an area of 0.0025 in the right tail is approximately 2.81.

The p-value for this sample is the sum of the areas in the tails beyond the test statistic:

p-value = P(Z ≤ -2.83) + P(Z ≥ 2.83)

P = 0.004655

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The amount of depreciation to be recorded for year 2 using the straight-line method of calculating depreciation is $6,750.

Straight-line depreciation is calculated by dividing a fixed asset's depreciable base by its useful life. The depreciable base is the difference between an asset's all-in costs and the estimated salvage value at the end of its useful life.

By using the straight-line method of calculating depreciation, the annual depreciation expense would be calculated as follows:

= (Purchase Price - Salvage Value) / Useful Life

= ($60,000 - $6,000) / 8 years

= $54,000 / 8 years

= $6,750.

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Answer:

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, we can consider the distance from home to Best Buy as the hypotenuse, and the distance traveled west and south as the other two sides.

Let's call the distance from home to Best Buy "x". Then, using the Pythagorean theorem:

x^2 = (distance south)^2 + (distance west)^2

We know that the distance west is 5 miles, and the distance home is 25 miles. We don't know the distance south, so let's call that "y".

Then we have:

x^2 = y^2 + 5^2

25^2 = y^2 + 5^2

Solving for y, we get:

y^2 = 25^2 - 5^2

y^2 = 600

y = sqrt(600)

y = 24.49 (rounded to two decimal places)

Now we can plug in y to find x:

x^2 = y^2 + 5^2

x^2 = 24.49^2 + 5^2

x^2 = 625.12

x = sqrt(625.12)

x = 25.00 (rounded to two decimal places)

Therefore, the distance from home to Best Buy is approximately 25 miles.

Step-by-step explanation:

The similar triangles are Δ SRQ ~ Δ RPQ  ~ Δ SRP

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Given is right triangle PRQ, a perpendicular line is drawn to the side PQ from angle R

we need to tell the similar triangles,

From the figure we have,

Δ SRQ ~ Δ RPQ  ~ Δ SRP

And, according to the definition of similar triangle,

SP / RP = PR / RQ

PQ / RQ = RQ / SQ

Hence, the similar triangles are Δ SRQ ~ Δ RPQ  ~ Δ SRP

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The solution to the given equation √(2x + 9) = 7 is x = 20.

Any equation that contains a radical symbol is considered a radical equation. To find the square roots, cubic roots, and higher, radical symbols are used.

The equation is given as follows:

√(2x + 9) = 7

Square both sides of the above equation,

2x + 9 = 7²

2x + 9 = 49

Subtract 9 from both sides of the above equation,

2x = 49 - 9

2x = 40

Divide by 2 into both sides of the equation,

x = 40/2

x = 20

Thus, the solution to the given equation is x = 20.

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The two points with an x-coordinate of 2 and a distance of 5 from (-2, -4) are: (2, -4 + 2√13) and (2, -4 - 2√13)

What is distance formula?

Distance is a measurement of how far away two things or locations are, either numerically or occasionally qualitatively.

Distance formula: [tex]distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]

We can solve this problem using the distance formula, which gives us the distance between two points in a plane:

[tex]distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]

Let (x, y) be a point with an x-coordinate of 2. Then we can write the distance from (-2, -4) to (x, y) as:

[tex]distance = \sqrt{((x - (-2))^2 + (y - (-4))^2)}[/tex]

Simplifying this expression, we get:

[tex]distance = \sqrt{((x + 2)^2 + (y + 4)^2)}[/tex]

We know that the distance between (-2, -4) and (x, y) is 5. Therefore, we can write:

[tex]\sqrt{((x + 2)^2 + (y + 4)^2)} = 5[/tex]

Squaring both sides, we get:

[tex](x + 2)^2 + (y + 4)^2 = 25[/tex]

Expanding the left side, we get:

[tex]x^2 + 4x + 4 + y^2 + 8y + 16 = 25[/tex]

Simplifying this expression, we get:

[tex]x^2 + 4x + y^2 + 8y - 5 = 0[/tex]

To find all points with an x-coordinate of 2 that satisfy this equation, we can substitute x = 2 and simplify the resulting equation:

[tex]2^2 + 4(2) + y^2 + 8y - 5 = 0[/tex]

Simplifying this equation, we get:

[tex]y^2 + 8y + 3 = 0[/tex]

We can solve this quadratic equation using the quadratic formula:

y = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 8, and c = 3.

Plugging in these values, we get:

y = (-8 ± sqrt(8^2 - 4(1)(3))) / 2(1)

Simplifying this expression, we get:

y = (-8 ± √52) / 2

y = (-8 ± 2√13) / 2

y = -4 ± √13

Therefore, the two points with an x-coordinate of 2 and a distance of 5 from (-2, -4) are: (2, -4 + 2√13) and (2, -4 - 2√13)

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Answer:

4/3, -3

Step-by-step explanation:

slope is the number in front of the variable x, and y intercept is when x=0

The order of these numbers from least to greatest is 2.7 x 10³, 2.3 x 10¹¹, 6.5 x 10^12, 4.8 x 10^21

Index forms are simple described as the mathematical expressions or models used to represent numbers that are large or small in more appropriate ways.

They are also termed as scientific notations or standard forms.

Examples of index forms are;

2³ = 8

2 ² = 4

3 ³ = 27

From the information given, we have that;

2.7 x 10³

This is represented as; 2.7 × 10 × 10 × 10

Multiply the values

2700

2.3 x 10¹¹

This is represented as 2. 3 multiply by 10 in 11 times

6. 5× 10^12

This is represented by 6.5 multiplied by 10 in 12 places

4.8 × 10^21

This is represented by 4.8 multiplied by 10 in 21 places.

Hence, the exponent shows the greatest number

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