Graph the line by plotting any two ordered pairs with integer value coordinates that satisfy the equation.- 21 = 0AnswerKeypadKeyboard ShortcutsPoints can be moved by dragging or using the arrow keys. Any lines or curves will be drawn once allrequired points are plotted and will update whenever a point is moved.10SI10310101

Both containers hold the same amount of water.

Given are two solid figures, we need to compare which of them holds more water,

The container one has a base dimension of 3 ft × 180 in with height 90 in. and the second container has base dimension of 3 ft × 180 in with height 90 in.

To compare which container holds more water, we can calculate the volume of each container.

For consistency, let's convert all measurements to a single unit.

1 foot is equal to 12 inches, so the base dimensions of both containers can be expressed as

3 ft × (180 in + 3 ft × 12 in/ft) = 3 ft × 216 in

= 648 in × 648 in.

The volume of a container is calculated by multiplying the base area by the height.

Therefore, the volume of each container can be determined as follows:

Container 1:

Volume = Base area × Height

Volume = (648 in × 648 in) × 90 in

Container 2:

Volume = Base area × Height

Volume = (648 in × 648 in) × 90 in

Since the base dimensions and the height are identical for both containers, their volumes will also be the same.

Therefore, both containers hold the same amount of water.

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The product and the quotient of the functions are as follows:

(rs)(4) =8

(r / s)(3) = 2

A function relates input and output. It relates an independent variable with a dependent variable.

Therefore, let's solve the function as follows:

r(x) = 2√x

s(x) = √x

Therefore, let's find

(rs)(4) = r(4) × s(4) = 2√4 × √4 = 4 × 2 = 8

Let's find

(r / s)(3) = r(3) / s(3) = 2√3 / √3 = 2

Therefore,

(rs)(4) =8

(r / s)(3) = 2

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Answer:

a. y = 2x + 1: Not from x to y

b.1 = 2y – 4x: Not from x to y

c. y^2 – 1 = x: This is a function from x to y

Step-by-step explanation:

We are to determine whether or not the equations are function from x to y

Given the function y = f(x)

y is a dependent variable while the input variable is an independent variable. So we can say y is a function from y to x.

Also x = f(y) can be expressed as equation of a function from x to y i.e x is dependent and the input variable is independent

From tthe following options, the equation that is a function from x to y is

y² – 1 = x

This can also be written as x = y² – 1 where f(y) is y² – 1

The rest are not a function of x to y but otherwise unless re-written

Answer:

2,500 grams

Step-by-step explanation:

2.5 kilograms = 2,500

Therefore, the laptop is 2,500 kilograms.

hope i helped

The difference (faculty-student) in the sample proportions of those who think that students should have five minutes to switch classes usually varies by roughly 0.096 from the actual difference in proportions.

A low standard deviation shows that the values tend to be close to the mean (also known as the expected value) of the set, whereas a high standard deviation suggests that the values are spread out over a broader range.

The standard deviation is a measure of variance or dispersion in statistics.

So, the sampling distribution's standard deviation is calculated as follows:

\(\begin{aligned}& \sigma_{\mathrm{F}}-\sigma_{\mathrm{s}}=\sqrt{\frac{0.37 \times(1-0.37)}{28}+\frac{0.89 \times(1-0.89)}{100}} \\& \sigma_{\mathrm{F}}-\sigma_{\mathrm{s}}=0.096\end{aligned}\)

The actual proportional difference between those who believe five minutes is not enough time for pupils to switch courses and those who believe this is generally 0.096.

Therefore, the difference (faculty-student) in the sample proportions of those who think that students should have five minutes to switch classes usually varies by roughly 0.096 from the actual difference in proportions.

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Correct question:

n a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let p hat Subscript Upper F and p hat Subscript Upper S be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class. Which of the following is the correct shape and justification of the sampling distribution of p hat Subscript Upper F Baseline minus p hat Subscript s ?

This equation has infinitely many solutions.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given: 3x+4y = -10...(1),

y = -3/4x - 5/2....(2)

We solve this linear equation and we get

We multiply equation (2) by 4 and we get

4y + 3x = -5(2)

4y + 3x = -10

Hence, this equation has infinitely many solutions.

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Dot plots are used for continuous, quantitative, and univariate data, because they are helpful in identifying clusters and gaps, in addition to outliers, which is one of their primary functions.

This is further explained below.

Generally, Dot plots are used for continuous, quantitative, univariate data. It could be possible to identify the data points if there are just a few of them.

Dot plots are one of the most fundamental forms of statistical plots, and they are most beneficial when used in the presentation of data from collections ranging from extremely tiny to relatively large.

In conclusion, In addition to performing one of their core purposes, which is spotting outliers, they also do a good job of locating clusters and gaps in the data.

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The joint relative frequency for school children who plan to attend camp and have swimming lesson is 44%.

The correct option to the given question is option d.

We are required to find the joint relative frequency for school children who plan to attend camp and have swimming lessons, rounded to the nearest percent.

To find the joint relative frequency, we use the formula as follows:

Joint relative frequency = frequency of interest / total frequency

Joint relative frequency for school children who plan to attend camp and have swimming lessons = 42 / 96

(As we are looking for the students who plan to attend camp and have swimming lessons, we are interested in the first column of the table and the entry at the intersection of the first row and second column.)

Joint relative frequency for school children who plan to attend camp and have swimming lessons = 0.4375

Joint relative frequency for school children who plan to attend camp and have swimming lessons (rounded to the nearest percent) = 44%(option d).

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Answer:

5

Step-by-step explanation:

first you have to subtract x for example 0-5 square and use it on y and then square root both of them you will got the answer

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

Answer:

Step-by-step explanation:

Given that:

Let the others be = b

One of the bottom edge is five times longer than the others

i.e. L= 5b

The Volume of a box = L × b × h

V  =  5b²h

where; V is constant

Differentiating  with respect to t

\(2bh \bigg ( \dfrac{db}{dt} \bigg) + b^2\bigg(\dfrac{dh}{dt} \bigg) = 0\)

2h(db) = -b(dh)

Therefore, the surface area = lb + 2bh + 2lh ; since there is no top.  

A = 5b² + 2bh + 10bh

A = 5b² + 12bh

When A is minimum, \(\dfrac{dA}{dt}\) = 0

10b(db) + 12b(dh) + 12h(db) = 0

\(10b(db) + 12b[\dfrac{-2h(db)}{b}] + 12h(db) = 0\)

10b(db) + 12h(db) = 24h(db)

10b = 12h

5b = 6h

Recall that

l = 5b     and   L × b × h = V

Thus;

5b × b × \(\dfrac{5b}{6}\) = V

\(b = 3\sqrt{\dfrac{6V}{25}}\)

L = 5b

h = \(\dfrac{5b}{6}\)

Answer:

e

Step-by-step explanation:

1. Write as an algebraic equation

e-2=15

2. Isolate e

add 2 on both sides to cancel put the -2

e=17

Answer:

Part A:  $45, Part B:  $8

Step-by-step explanation:

Part A: 60 - 10 = 50

50 * 0.30 = 15

60 - 15 = $45

Part B:  60 * 0.30 = 18

18 - 10 = $8

Answer: part a: $35

part b $32

Step-by-step explanation:

By rearranging the equation, we get the equation of the line parallel to 5x + 4y = 24 that passes through the point (8, -5) as y = (-5/4)x + 5.To find the equation of a line parallel to another line, we need to determine the slope of the given line.

The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope.

To determine the slope of the given line 5x + 4y = 24, we need to rearrange the equation in slope-intercept form. First, subtract 5x from both sides: 4y = -5x + 24. Next, divide all terms by 4: y = (-5/4)x + 6. Therefore, the slope of the given line is -5/4.

Since the line we are looking for is parallel to this line, it will also have a slope of -5/4. Now we can use the point-slope form of a line to find the equation. The point-slope form is given as y - y1 = m(x - x1), where (x1, y1) represents the given point (8, -5) and m is the slope.

Substituting the values into the equation, we have y - (-5) = (-5/4)(x - 8). Simplifying further, y + 5 = (-5/4)x + 10.

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Answer:

Second and third option.

Step-by-step explanation:

The initial cost is $20 with an additional $3 per class, so:

20 + 3 * each class

In equation for this is:

20 + 3x

This means that the second and third option are both correct.

Hope this helps!

The equation represents the relationship is y = 3x +20

The amount that Lucy paid to join the fitness class represents her fixed cost. Fixed cost is the cost that does not change with he number of classes she takes.

The amount Lucy pays per class is her variable cost. Variable cost increases with the number of classes she attends.

Her variable cost can be presented with the expression : $3 × x. Where x represents the number of classes she takes.

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Lucy's total cost = fixed cost + Variable cost

y = 3x +20

The population after 68 years from now is 160, 000.

A relation of the form y = \(a^x\), with the independent variable x ranging over the entire real number line as the exponent of a positive number a.

Given:

10000 is the initial population

2 is the rate at which the population grows

68/17 is the number of periods that the population grows

Now, using Exponential function the population can be represented as

= 10000 x \(2^{(68/17)}\)

= 10000 x \(2^{(4)}\)

= 10000 x 16

= 160, 000

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1. The offer price of the 800 shares of a mutual fund with a NAV of $14.10 that Bill Roundy bought is $11,280.

2. For this investment, Bill paid $11,618.40, including the load charge of 3%.

A load charge is a sales commission that investors pay when they buy (front-end load) or redeem (back-end load) shares in a mutual fund.

NAV means net asset value.

NAV refers to the difference between the investee company's total assets and its total liabilities.

The total number of mutual fund shares bought by Bill = 800

The net asset value of the shares = $14.10

Load charge = 3%

Offer price = $11,280 (800 x $14.10)

Amount Bill paid for the investment = $11,618.40 ($11,280 x 1.03)

Thus, with an offer price of $11,280 for the mutual fund, Bill Roundy paid a total of $11,618.40, including the load charge.

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Answer:

120 miles

Step-by-step explanation:

if you represent 2 1/2 hours in 5 sections of 30 minute and devide 150 by 5 you get 30 so the train is traviling 1 mile per minute so just subtract 30 and you get 120

Answer:

A

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

Here m = - 13 and (a, b ) = (5, 7 ) , then

y - 7 = - 13(x - 5) → A

Step-by-step explanation:

\( \hookrightarrow \: b =4\: and \: p =6\)

Now,

\( \hookrightarrow \: h = \sqrt{ {p}^{2} + {b}^{2} } \\ \hookrightarrow \: h = \sqrt{ {6}^{2} + {4}^{2} } \\ \hookrightarrow \: h = \sqrt{52} \\ \hookrightarrow h = 2 \sqrt{13} \)

The constants and coefficients of the given equations are as follows:

3x + 7y =18: The constant ⇒ 18

3x + 7y =18: The coefficients ⇒ 3, 7

2x - 4y = 9: The constant ⇒ 9

2x - 4y = 9: The coefficients ⇒ 2, -4

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression.

It is typically a number, but it can also be any expression.

They may also be referred to as parameters if the coefficients are variables in and of themselves.

The term "constant" has several meanings in mathematics.

When used as a noun, it can have any of the following two meanings: a constant, a well-defined number, or another immutable mathematical entity.

So, we have the equation:

3x + 7y =18

2x - 4y = 9

Then,

3x + 7y =18: The constant ⇒ 18

3x + 7y =18: The coefficients ⇒ 3, 7

Similarly,

2x - 4y = 9: The constant ⇒ 9

2x - 4y = 9: The coefficients ⇒ 2, -4

Therefore, the constants and coefficients of the given equations are as follows:

3x + 7y =18: The constant ⇒ 18

3x + 7y =18: The coefficients ⇒ 3, 7

2x - 4y = 9: The constant ⇒ 9

2x - 4y = 9: The coefficients ⇒ 2, -4

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The solution to the operation in this problem is given as follows:

9.

First we solve the integrals inside the floor operation.

At the numerator, the integral is given as follows:

\(\int_0^1 (\sum_{n = 3}^{n = 5} 5n \sqrt{25}) dx\)

Applying the square root of 25 = 5, we have that:

\(\int_0^1 (\sum_{n = 3}^{n = 5} 25n) dx\)

The sum can be applied as follows:

\(\sum_{n = 3}^{n = 5} 25n = 25(3) + 25(4) + 25(5) = 300\)

Thus the integral is given as follows:

\(\int_0^1 300 dx\)

N = 300x, from x = 0 to x = 1.

Applying the Fundamental Theorem of Calculus, the numerator for the floor operation is given as follows:

N = 300(1) - 300(0) = 300.

The sum in the denominator is given as follows:

\(\sum_{n = 2}^{n = 5} 2 + 6 = \sum_{n = 2}^{n = 5} 8 = 4 \times 8 = 32\)

Thus the integral is given as follows:

\(\int_0^1 32 dx\)

D = 32x, from x = 0 to x = 1.

Meaning that the denominator has a value of 32.

Then the whole operation can be resumed as follows:

floor(300/32).

The quotient of 300 and 32 is given as follows:

300/32 = 9.375.

Then the floor operation gives the highest integer that is less than the decimal number, as follows:

floor(9.375) = 9.

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Answer:

Here you go: When a linear function is expressed in different forms, its slope and y-intercept remain the same. The slope from the equation is -1, and the y-intercept from the equation is 3. The slope from the table is -1, and the y-intercept from the table is −3. These are not the same functions.

Step-by-step explanation:

Answer:

A) x, y turns into -x, -y

B) x, y turns into -y, x

Therefore, the result of the synthetic division of 4x³ - 14x² + 17x - 10 by x - 2 is: 4x² - 6x + 5

Division is a mathematical operation that involves splitting a quantity into equal parts. It is the inverse or opposite of multiplication. Division is used to find out how many times one quantity is contained within another quantity, or to distribute a quantity evenly among a given number of groups. In division, the quantity being divided is called the dividend, the quantity by which the dividend is divided is called the divisor, and the result is called the quotient. The dividend is divided by the divisor to obtain the quotient.

Here,

To perform synthetic division of 4x³ - 14x² + 17x - 10 by x - 2, we need to set up the division table as follows:

  2 | 4  -14   17  -10

    |    8  -12   10

    |--------------

    | 4  -6    5    0

        2 | 4  -14   17  -10

          |    8  -12   10

          |--------------

          | 4

        2 | 4  -14   17  -10

          |    8  -12   10

          |--------------

          | 4  -6

        2 | 4  -14   17  -10

          |    8  -12   10

          |--------------

          | 4  -6   5

        2 | 4  -14   17  -10

          |    8  -12   10

          |--------------

          | 4  -6   5    0

The first row of the table contains the coefficients of the dividend, 4x³ - 14x² + 17x - 10, written in descending order of powers of x. The divisor, x - 2, is written to the left of the table.

To perform the division, we bring down the first coefficient, which is 4, and multiply it by the divisor, x - 2, to obtain 4x. We write this result under the second coefficient, -14, and add the two values to get 4x - 28, which we then repeat the process, multiplying it by the divisor to obtain 4x - 8.

We continue this process until we reach the last row, which contains the coefficients of the quotient. The last term, 0, indicates that there is no remainder.

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Answer:

Its the bottom left one :)

Step-by-step explanation:

hi

let's remind us that  1 hour  = 60 minutes.

9 miles in  45 minutes means  :

9 = 45

? = 60

so  ?  =   9*60 /45  

         =   3*3 *20*3  / 3*3 *5

         =   3*3 *5*4 *3 / 3*3 *5

           =    4*3

          = 12  

So  9 miles in 45 minutes is  12 miles an hour.  

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Answer:

9/3

Step-by-step explanation:

could also be simplified to 3, but just the reciprocal is 9/3

Answer:  9/3

Step-by-step explanation: