1. How much will it cost to carpet a 25 ft by 13 ft rectangular room if carpeting costs $15.50 per
square foot?
a. $5,037.50
b. 5559.72
c. $419.79
d. $1,679.17

Answer:

8-10 feet

Step-by-step explanation:

If the length of the carpet is two more than the width, the width can be expressed as x and the length can be expressed as x+2. This means that the area(x^2+2x) must be greater than 48 but no less than 80.

Now we can solve for both the maximum and minimum cases:

x^2+2x=48, x^2+2x-48=0, now we can factor, (x+8)(x-6)=0, and now we can use the Zero Product Property to find x=-8;x=6. Since we cant have negative width, x at least has to be equal to 6.

x^2+2x=80,x^2+2x-80=0, now we can factor, (x+10)(x-8), and now using the Zero Product Property to find x=-10;x=8, and since it must be positive, at most x can equal 8.

Now since the length is two more than the width, x, you add two to both of these values and get a range of 8-10 feet.

Answer:

The third option

Step-by-step explanation:

The domain is saying x is greater than or equal to 2, so the third option fits that description.

Hopefully this helps!

Brainliest please?

Answer:

The values of b and a for the logarithmic function in this problem are given as follows:

The logarithmic function in the context of this problem has the format given as follows:

\(y = b\log_3{x + a}\)

The vertical asymptote is at x = -4, hence:

\(y = b\log_3{x - 4}\)

When x = 5, y = -1, hence the parameter b is obtained as follows:

\(-1 = b\log_3{5 - 4}\)

0.477b = -1

b = -1/0.477

b = -2.1.

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Research has shown that when administering a survey, respondents who are asked questions in which they have little or no knowledge are likely to respond with inaccurate or incomplete information.

This can happen due to several reasons, such as the respondents feeling embarrassed or ashamed of admitting their lack of knowledge, or simply guessing the answer to avoid appearing uninformed. Graeff's (2003) study highlights the importance of carefully designing survey questions to ensure that they are clear and easy to understand for all respondents, regardless of their level of knowledge on the topic. It is also important to provide respondents with options such as "I don't know" or "Not applicable" to encourage honest and accurate responses. Administering surveys can be a valuable tool for gathering information, but it is crucial to consider the limitations and potential biases that may arise. Conducting thorough research and using appropriate survey methods can help to ensure that the data collected is reliable and useful for making informed decisions.

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Answer:

Subtract 15 from both sides.

5t > 35

Divide both sides by 5.

t > 7

(Sorry, I can't do the > with the _ under it.)

Please mark me Brainliest; I need it to move onto the next level. =D

Answer:

720

Step-by-step explanation:

16=2^4

30=5*3*2

36=(2^2)*(3^2)

so

(2^4)*5*(3^2)=720

Answer:

7:8

Step-by-step explanation:

First, convert their times to common units. You'll want to put it in seconds:

5 minutes and 50 seconds = 350 seconds

- multiply 5 minutes by 60 to get it into seconds and then add the other 50 seconds to it

- for Elizabeth's time, multiply 6 by 60 seconds and add 40 to it

To get the ratio of their times, divide Alison's time by Elizabeth's time:

350 ÷ 400 = 7:8

Answer:

a) 7:8

Step-by-step explanation:

Alison: 5 minutes and 50 seconds = 355 seconds

Elizabeth: 6 minutes and 40 seconds = 400 seconds

355:400, reduces to 71:80 or 7:8

Two triangles can be congruent if they have the same three angles, according to the Angle-Angle-Angle (AAA) congruence rule.

What are congruent triangles?

Congruent triangles are triangles that have the same size and shape. In other words, if you were to superimpose one triangle on top of the other, the two triangles would fit perfectly together, with all of the sides and angles being equal in measure.

Technically, two triangles can be congruent if they have the same three angles, according to the Angle-Angle-Angle (AAA) congruence rule. However, it is important to note that the AAA congruence rule is not sufficient on its own to prove that two triangles are congruent. This is because two triangles can have the same three angles but still be different in size and shape.

In order to prove congruence, it is necessary to use one of the other congruence rules, such as the Side-Side-Side (SSS) congruence rule, the Side-Angle-Side (SAS) congruence rule, or the Angle-Side-Angle (ASA) congruence rule.

Hence, two triangles can be congruent if they have the same three angles, according to the Angle-Angle-Angle (AAA) congruence rule.

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Answer: 7/5m

Step-by-step explanation:

The initial value of the painting = m

Increase in the painting = 2/5

The final value of the painting will be the addition of the initial value of the painting and the increase. This will be:

= m + (2/5 × m)

= m + 2/5m

= 5/5m + 2/5m

= 7/5m

*see attachment below for the dot plots

Answer:

A. The number of snacks grabbed for Class A has less variability than the number of snacks grabbed for Class B.

Step-by-step explanation:

The extent of variability of the data represented on a dot plot can be determined by the range value.

Range is the difference between maximum value of the data set and the minimum value of the data set.

The larger the range, the more the data has more variability, while the smaller the range, the less the variability of the data.

Range for Class A = 37 - 15 = 22

Range for Class B = 45 - 12 = 33

Therefore, class B has more variability in the number of snacks grabbed compared to Class A.

Correct statement is: "The number of snacks grabbed for Class A has less variability than the number of snacks grabbed for Class B."

Step-by-step explanation & answer:

When a dilation in the coordinate plane has the origin as the center of dilation, we can find points on the dilated image by multiplying the x and y coordinates of the original figure by the scale factor.

For example, if the scale factor is "k", the algebraic representation of the dilation is

(x, y) → (kx, ky)

For enlargements, k > 1 and for reductions, k < 1.

Hope this is what you needed:)

The after the dilation by scale factor of 3, coordinates the point P(x, y) will become P'(3x, 3y).

A dilation is an enlargement or reduction of a figure about a center of dilation by a specified scale factor [k].

Given is a algebraic rule for a dilation with a scale factor of 3.

Suppose that we have a point P(x, y) which is dilated by the

scale factor of 3. Now, after dilation of the coordinate, the final coordinates of that point P(x, y) will become P'(3x, 3y). If the scale factor would have been less than one the point will contract.

Therefore, the after the dilation by scale factor of 3, coordinates the point P(x, y) will become P'(3x, 3y).

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Answer:

Step-by-step explanation:

There are 7+4+1=12 marbles in the bag.  The chances of drawing a green one on the first draw is 7/12.  The chance of drawing a green marble on the second draw is 6/11 (since you didn't replace the first marble you drew).

To find the probability, you just multiply these fractions: 7/12*6/11= 7/22 (reduced fraction).

The scale factor of dilation is 3.

What is Dilation of a circle?

Dilation is the process of altering an object's or shape's size by reducing or enlarging its dimensions by a certain amount of scale. A circle with a radius of 10 units, for instance, is reduced to a circle with a radius of 5 units. This technique is applied in art and craft, photography, and logo design, among other fields.

Given : Radius of original circle A = 3

            Radius of Dilation circle B = 9

We know that, Scale factor of dilation =

Dimension of Dilation shape / Dimension of original shape

So, Scale factor of given dilation = Radius of Circle B / Radius of Circle A

                                                      = 9/3

                                                      = 3.

Hence, Scale factor of dilation of circle B on Circle A is 3.

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Answer:

3,750 cars.

Step-by-step explanation:

We are given that the equation:

\(y=9000-2.4x\)

Models the relationsip between y, the number of unfilled seats in the stadium, and x, the number of cars in the parking lot.

We want to determine the number of cars in the parking lot when there are no unfilled seats in the stadium.

When there are no unfilled seats in the stadium, y = 0. Thus:

\(0=9000-2.4x\)

Solve for x. Subtract 9000 from both sides:

\(-2.4x=-9000\)

Divide both sides by -2.4:

\(x=3750\)

So, there will be 3,750 cars in the parking lot when there are no unfilled seats in the stadium.

The variables examined in the study show the number of hospital visits for cooking-related knife injuries and their frequency during major holidays. The data compiled from emergency departments shows that there is a significant increase in the number of hospital visits for such injuries around major holidays.

This suggests that there may be a correlation between the holidays and the use of knives in cooking, possibly due to increased meal preparation and cooking during these times. Other variables that could be examined in further studies include the types of knives and cooking equipment used, the types of foods being prepared, and the demographics of those who sustain these injuries.

Variables refer to any characteristic, quantity, or attribute that can be measured and that can fluctuate or vary. Variables are of two types:

An independent variable is one that is thought to influence the dependent variable, which is the characteristic or response that is being measured.

The variables examined in the study indicate that the number of hospital visits for cooking-related knife injuries increases around major holidays. This implies that there is a direct relationship between cooking and knife injuries on major holidays. As a result, measures must be put in place to reduce the risk of knife injuries during the holidays. This includes the creation of awareness campaigns and the promotion of safety in the kitchen.

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The required simplified value of the given expression is 32.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
= [∛8]⁵
= [∛2³]⁵
= 2⁵
= 32

Thus, the required simplified value of the given expression is 32.

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Answer:

2(h-8)-h=h-16

2(h-8)=h+h-16

2(h-8)=2h-16

2(h-8)=2(h-8)

h-8=h-8

h-h=8-8

0=0 so their can be infinite value of h.

hence c is correct

we can put in place of anything but answer will be zero.

Answer:

C h= infinitely many solutions

Step-by-step explanation:

when you replace h with any number it is true

say h= 3

2(3-8) - h = h-16

2(-5) - 3 = 3 - 16

-10 - 3 = -13

-13 = -13

using distributive property:

2h-16-h = h-16

combine like terms

h-16=h-16

it is the same expression on both sides of the equal sign

hope that helps!

Answer: parallelograms

Step-by-step explanation:

Answer:

the greatest common factor of 75 and 40 is 5

The area covered by 19, 602 square feet in acres is around 0.45, according to the relation between the two.

As per the known relation between acre and square foot, the two quantities are related through the formula -

1 acre is equal to 43, 560 square feet

Therefore, formula to convert square feet to acre will be -

Amount of area in acres = area covered in square feet/unit equivalent area in square feet

So, rewriting the above mentioned relation.

43, 560 square feet is equal to 1 acre

Thus, 19, 602 square feet will be equal to acres = 19, 602/43, 560

Performing division on Right Hand Side of the equation

The amount of area in acres = 0.45 acres

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Answer:

x > 11

Step-by-step explanation:

15 < 4 + x

Subtracting 4 from both sides (to get rid of the 4 on the right side) gives us:

15 - 4 < 4 + x - 4

11 < x

Answer:

x>11

Step-by-step explanation:

15<4+x

Simplify both sides of the inequality.

15<x+4

Flip the equation.

x+4>15

Subtract 4 from both sides.

x+4−4>15−4

x>11

The first 5-terms of sequence "aₙ = (-1)ⁿ⁻¹/4ⁿ" are : a₁ = 1/4, a₂ = -1/16, a₃ = 1/64, a₄ = -1/256, a₅ = 1/1024.

A sequence is a ordered collection of elements, typically numbers, that are arranged in a specific order. Each element in a sequence is associated with a positive integer index, denoted as n, which represents its position in the sequence.

To find the first 5-terms of the sequence given by the formula aₙ = (-1)ⁿ⁻¹/4ⁿ, we substitute the values of n from 1 to 5:

For n = 1:

a₁ = (-1)¹⁻¹/4¹ = 1/4,

For n = 2:

a₂ = (-1)²⁻¹/4² = -1/16,

For n = 3:

a₃ = (-1)³⁻¹/4³ = 1/64,

For n = 4:

a₄ = (-1)⁴⁻¹/4⁴ = -1/256,

For n = 5:

a₅ = (-1)⁵⁻¹/4⁵ = 1/1024,

Therefore, the first five terms are: 1/4, -1/16, 1/64, -1/256, 1/1024.

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The given question is incomplete, the complete question is

List the first five terms of the sequence. aₙ = (-1)ⁿ⁻¹/4ⁿ.

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Answer:

\( \frac{x}{4} + \frac{1}{2} = \frac{1}{8} \)

\( \frac{x}{4} = - \frac{3}{8} \)

\(x = - \frac{3}{2} = - 1 \frac{1}{2} \)

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.

x/4 + 1/2 = 1/8

Take the 1/2 term on the other side,

x/4=1/8 - 1/2

Taking the LCM on the Right side,

x/4 = (1-4) / 8

x/4 = -3/8

Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,

x = ( -3/8) * 4

x = -3/2

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

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Answer:

Radius of sphere is 3 units.

Step-by-step explanation:

Volume of sphere is given by \(4/3 \pi r^3\)

surface area of sphere is given by \(4 \pi r^2\)

where r is the radius of the sphere.

Given that

The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere.

we equate formula of Volume of sphere  and surface area of sphere

assuming r as the radius.

thus,

\(4/3 \pi r^3 = 4 \pi r^2\\\\4/3 \pi r^3/ 4 \pi r^2 = 1\\=>r/3 = 1\\=> r = 3\)

Thus, radius of sphere is 3 units.

Answer:

just sub in the numbers into the equation to replace the X ..

example for

a) h(7) : 44

Step-by-step explanation:

h(7) : x^2 -5

sub in 7 into the equation to replace X

so you get

(7)^2 - 5

49-5

44