Martha’s video game rental plan costs $18 per month .which table shows the sum of the amounts that Martha will pay for her video game rental plan over the next 5 months

It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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Answer:

22.6%.

Step-by-step explanation:

To calculate the percent error of a measurement, you can use the following formula:

Percent Error = (|measured value - actual value| / actual value) x 100%

Plugging in the values from the problem:

Percent Error = (|4.1 inches - 5.3 inches| / 5.3 inches) x 100% = (1.2 inches / 5.3 inches) x 100% = 0.226 x 100% = 22.6%

To the nearest tenth of a percent, the percent error is 22.6%.

The height of the ceiling at the center of the hall will be approximately 19.9 feet.

To design a hall 110 feet in length as a whispering gallery, the height of the ceiling at the center should be 19.9 feet. This is calculated as follows:

Given that the hall has a length of 110 feet and is designed as a whispering gallery.

Also, the foci are located 30 feet from the center. We are to determine the height of the ceiling at the center.

To solve the problem, we will use the formula for a whispering gallery which is given as:

1 / b2 = 1 / a2 - 1 / c2where a, b, and c are the semi-axes of the ellipse and are related by the equation:

a2 = b2 + c2Using the given information, we can find the value of a as follows:

a = 55 feet (half the length of the hall) and

c = 30 feet (distance of the foci from the center of the hall)

Substituting these values in the equation for a above, we have:

b2 = a2 - c2= 55² - 30²= 3025 - 900= 2125 feet²Therefore, b = √2125 = 46.1

feetNow we can calculate the height of the ceiling at the center using the formula for the height of an ellipse at its center, which is given as:

height = b2 / a= (46.1)2 / 55= 19.9 feet (rounded to one decimal place)

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The first one is the the correct answer because the angles have a sum of 180 degrees.

Hope that helps you!!

The value of  x of chord = 5

By definition of circle,

The chord of a circle is defined as the line segment connecting any two locations on the circle's perimeter; nevertheless, the diameter is the longest chord of a circle that goes through the centre of the circle.

The chord is one of the several line segments that may be made in a circle, and its endpoints are on the circumference.

⇒ 6 (6 + x) = 7 (7 + 11)

Solve for x;

⇒ 36 + 6x = 7 × 18

⇒ 36 + 6x = 126

⇒ 6x = 126 - 36

⇒ 6x = 90

⇒ x = 15

Thus, The value of x = 5

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Answer:

all real numbers

Step-by-step explanation:

The domain are the values of the input values x that makes the given function exist

Given the function:

y= x^2+4x

Since x^2 is a perfect square, the value of x can exist on all real numbers

Hence the domain of the function is all real numbers

Using a system of equations, it is found that Charlie won $270.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Linda won $10 less than three times as much as Charlie, hence:

x = 3y - 10

Linda won $800, hence the amount won by Charlie is found as follows:

800 = 3y - 10

3y = 810

y = 810/3

y = 270

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Answer:

answer: 12

Step-by-step explanation:

You get 12 by doing base × height. So our base in this problem is 2.5 and our height is 4.8 so

2.5 × 4.8 = 12 Hope this helps!

The sampling error or sampling variability is the discrepancy between the sample and group norms.

Among the most frequent kinds of sampling mistakes is sampling prejudice. When the sample's participants are not indicative of the general community, it happens. A poll has sampling bias if it only includes respondents from one region of the nation and does not include respondents from the other regions.

For instance, the mother, kids, or the complete family could be the populace in a poll on breakfast cereals. Selection Error: Occurs when respondents self-select their involvement in the poll, suggesting that only the people who are eager are participating.

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Answer:

1/72

Step-by-step explanation:

multiple the numerators and denominators by each other so 1*1 = 1 and 8*9 = 72

False. If E and F are independent events, then Pr(E|F) is not necessarily equal to Pr(E).

The probability of an event E given event F, denoted as Pr(E|F), represents the probability of event E occurring given that event F has already occurred. In the case of independent events, the occurrence of one event does not affect the probability of the other event occurring.

By definition, two events E and F are independent if and only if Pr(E ∩ F) = Pr(E) × Pr(F), where Pr(E ∩ F) represents the probability of both events E and F occurring.

Now, let's consider the statement that Pr(E|F) = Pr(E) when E and F are independent events. This implies that the probability of event E occurring given that event F has occurred is the same as the probability of event E occurring without any knowledge of event F.

However, this is not necessarily true. The conditional probability Pr(E|F) takes into account the occurrence of event F, which may affect the probability of event E. Even if events E and F are independent, the value of Pr(E|F) may differ from Pr(E) if the occurrence of event F provides additional information or changes the probability distribution of event E.

The statement "Pr(E|F) = Pr(E)" when E and F are independent events is false. While independence between events E and F ensures that the occurrence of one event does not affect the probability of the other event, it does not guarantee that the conditional probability Pr(E|F) will be equal to the unconditional probability Pr(E).

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Answer:

I put it in a calculator and got 51.5

Step-by-step explanation:

Answer:

If I'm understanding the question right it's -.05

Step-by-step explanation:

(2x - 3) = 2

There is no more simplifying to be done in the parentheses.

2x - 3 = 2

Subtract 3 on each side to get the x value by itself.

2x = -1

Divide each side by 2 so the x is by itself.

x = -.05

And that's it, hope I helped :)

The given integral expression is \(3(x - 4)\sqrt{x}\). We are required to integrate it using the substitution u = √x. Let's begin by using the chain rule of differentiation to find dx in terms of du.\(dx/dx = 1 => dx = du / (2\sqrt{x} )\)Substituting the value of dx in the integral expression,

we get:\(3(x - 4)\sqrt{x} dx = 3(x - 4)\sqrt{x}  (du / 2\sqrt{x} ) = 3/2 (x - 4)\)duUsing the substitution u = √x, we can write x in terms of u: \(u = \sqrt{x}  \\=> x = u^2\)Substituting the value of x in terms of u in the integral expression, we get:3/2 (x - 4) du = 3/2 (u^2 - 4) duNow we can integrate this expression with respect to u:\(\int3/2 (u^2 - 4) du = (3/2) * \int(u^2 - 4) du= (3/2) * ((u^3/3) - 4u) + C= (u^3/2) - 6u + C,\) where C is the constant of integration.

Substituting the value of u = √x, we get:\(\int3(x - 4)\sqrt{x}  dx = (u^3/2) - 6u + C= (\sqrt{x} ^3/2) - 6\sqrt{x}  + C\)This is the final answer in terms of x, obtained by substituting the value of u back in the integral.

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Answer:

a = 27

perimeter = 3a

= 3 * 27

= 81

Answer:

\( \frac{2}{3} n - 11 \geqslant 17\)

\(n \geqslant 42\)

Explanation:

difference equals -

two-thirds equals 2/3

a number n equals variable of n

and 11 equals 11

at least equals _> (but like those together)

For solving equations just use photomath

The solution to the expression is n ≥ 42

An equation, statement of equality between two expressions consisting of variables and/or numbers

An equation is a mathematical expression that contains an equals symbol.

Equations often contain algebra.

Algebra is used in maths when you do not know the exact number in a calculation.

Translating the equation

\(\rm \dfrac{2}{3} \;n-11 \geq 17\)

\(\rm \;n \geq (17 + 11)\times\dfrac{3}{2}\\\\\\ n \geq 42\)

Therefore the solution to the expression is n ≥ 42

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The product of a real number and its multiplicative inverse is always equal to 1.

The equation that shows the product of a real number and its multiplicative inverse is:

a * (1/a) = 1

In this equation, 'a' represents a real number, and '1/a' represents its multiplicative inverse. The multiplicative inverse of a real number is the reciprocal of that number, which when multiplied together with the original number results in the identity element for multiplication, which is 1. Therefore, the product of a real number and its multiplicative inverse is always equal to 1.

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The polynomial expression when expressed in standard form is; A: n6 + 7mn5 + 14m2n4 – 5m3n3 – 6m6

The polynomial expression to be simplified is expressed as;

8mn⁵ - 2m⁶ + 5m²n⁴ - m³n³ + n⁶ - 4m⁶ + 9m²n⁴ - mn⁵ - 4m³n³

Grouping like terms gives;

8mn⁵ - mn⁵ - m³n³ - 4m³n³ - 2m⁶ - 4m⁶ + 5m²n⁴ + 9m²n⁴ + n⁶

This would be simplified to get;

7mn⁵ - 5m³n³ - 6m⁶ + 14m²n⁴ + n⁶

Looking at the given options, we can conclude that the only correct one is option A because it is well arranged according to their powers.

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Answer:

5.04

Step-by-step explanation:

The independent variable in this study is the place of residence, specifically whether the participants live in Florida or Pennsylvania.

The researcher is interested in examining the relationship between the location of residence and the amount of money spent on clothes. By selecting participants from both Florida and Pennsylvania, the researcher can compare the spending habits of individuals from these two locations and determine if there is a significant difference. Thus, the independent variable is the categorical variable that defines the groups being compared, which in this case is the place of residence.

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Answer:

3rd option

Step-by-step explanation:

∠ 1 and 75° are corresponding angles and are congruent , so

∠ 1 = 75°

Answer:

Yul I can't help u I don't understand it

The absolute value model |x - 30| = 10 represents the time required for Jack to fold his laundry. (Correct choice: D)

Absolute values are functions used in mathematics that represents the magnitude of a number, whose definition is summarized below:

In this case, we must determine an absolute value model that contains the maximum and minimum times required by Jack to fold his laundry, This is represented by the following model:

|x - a| = b

Where:

If we know that a = 30 min and b = 10 min, then the absolute value model is:

|x - 30| = 10

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Answer:

It will take them 7.89 days

Recall that the terms in an expression are the individual parts of an expression that do not share the same variables with the same exponents, in other words, the number of different terms in a given expression is equal to the number of terms that cannot be added together.

Example:

The expression

has 3 terms.

Answer: The expression

has 2 terms.

Answer:

0

3

Step-by-step explanation:

Answer:

dunno

Step-by-step explanation:

Answer:2.25

Step-by-step explanation:

3/4 is equal to 0.75 and 0.75*3=2.25

The centroid of the region bounded by the curves y = 12x and y = √x is (72,1.88).

To find the centroid of the region bounded by the given curves y = 12x and y = √x, the following steps should be followed.

Step 1: Sketch the region bounded by the two curves to have an idea of what the region looks like.

Step 2: Determine the area of the region bounded by the two curves. The area A can be computed by evaluating the definite integral of the difference between the two functions. \(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx\]\)  We solve for this integral below.\(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = 64 - 1728 + \frac{2}{3}\sqrt{6}\] \[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = -1663.30\]\)

Step 3: To find the centroid of the region, we need to determine the x and y coordinates of the centroid. The x-coordinate of the centroid is given by the formula below.

\(\[x = \frac{1}{A}\int\limits_{a}^{b} \frac{1}{2}(y_1^2-y_2^2)dx\]\)

where A is the area of the region, and y1 and y2 are the upper and lower functions, respectively. Substituting values, we obtain

\(\[x = \frac{1}{-1663.30}\int\limits_{0}^{144} \frac{1}{2}((\sqrt{x})^2-(12x)^2)dx\]  \[x = 72\]\)

 The y-coordinate of the centroid is given by the formula below.

\(\[y = \frac{1}{2A}\int\limits_{a}^{b}(y_1+y_2)\sqrt{(y_1-y_2)^2+4dx}\]\)

 Substituting values, we obtain \(\[y = \frac{1}{2(-1663.30)}\int\limits_{0}^{144}(12x+\sqrt{x})\sqrt{(\sqrt{x}-12x)^2+4dx}\]  \[y = 1.88\]\)

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The function that represents the volume is as follows:

V(x) = x³ - 4x

The length, width, and height of the ottoman if the volume is 5,760 in³ are as follows:

length = 18 inches

width = 18 - 2 = 16 inches

height = 18 + 2 = 20 inches

where

l = length

w = width

h = height

Therefore,

The length is as follows:

The width two inches shorter than the length:

The height two inches taller than the length:

Therefore,

volume = x (x - 2)(x + 2)

volume = x(x² + 2x - 2x - 4)

volume = x(x² - 4)

volume = x³ - 4x

If the volume is 5760 in³, the length, height and width can be found as follows:

5760 = x³ - 4x

x³ - 4x - 5760 = 0

By trying a few value of x, x = 18.

Therefore,

length = 18 inches

width = 18 - 2 = 16 inches

height = 18 + 2 = 20 inches

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