As seen in the diagram below, Joseph is building a walkway with a width of x feet to go around a swimming pool that measures 15 feet by 9 feet. If the total area of the pool and the walkway will be 567 square feet, how wide should the walkway be?

Answer:

C.  The number 5/11 is a rational number because it is a repeating decimal.

Step-by-step explanation:

The importance of this question is to distinguish a rational number from an irrational number.

A rational number can be written as a ratio or a set of repeating decimals.

An irrational number cannot be written as a ratio and cannot be represented by repeating decimals.

So out of the four options you have, the first two, A and B, are false, C is true, and D is false since rationality doesn't have anything to do with signs.

Cheers.

Answer:

The slope is -5/2 as a fraction

or -2.5 as a decimal.

Step-by-step explanation:

First we have to get it into this format y = mx + b

5x + 2y = 6 (subtract 5x on both sides)

2y = -5x + 6 (divide by 2 on both sides)

y = -5/2x + 3

The slope is -5/2 or -2.5

Hope this helps ya!!

On solving the question, Since r = 10 and the center is (0, 0), the standard form equation of this circle is (\((x - 0)^2 + (y - 0)^2 = 10^2\)or just\(x^2 + y^2 = 100.\)

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a straightforward circular form without edges or parts. a curved form with a closed geometry.

As standard form for a circle=  \((x - h)^2 + (y - k)^2 = r^2,\) and here (h, k) is the center and r is the radius.

\((6 - 0)2 + (8 - 0)2 = r2 -- > 62 + 82 = r2 -- > 100 = r2 -- > 10 = r.\)

Since r = 10 and the center is (0, 0), the standard form equation of this circle is (\((x - 0)^2 + (y - 0)^2 = 10^2\)or just\(x^2 + y^2 = 100.\)

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Answer:

Step-by-step explanation:

A. BECAUSE THERE IS 2 BARS WITH NUMBER OF STUDENTS AS 4

Answer:

Step-by-step explanation:

Answer:

area=21 cm^2

Step-by-step explanation:

split the shape into a triangle and rectangle and count the squares to find the length of the sides

area of the rectangle=3×5

area of rectangle=15

area of triangle= 4×3

area of triangle=12

area of triangle=12÷2

area of triangle=6

area of shape=15+6

area of shape=21

Explanation

To solve the question, we will be aware that

There are 3 hours between 6PM and 9PM ,

The main pump's emptying rate is 1/4 tanker per hour. It will be open

the entire 3 hours, so it will empty 3/4 of the tank.

this means that the auxiliary pump must empty the remaining 1/4

Thus

Thus, we will have

Therefore

The auxiliary pump should start by 6pm + 45 minutes = 6:45pm

There are 6 subgroups of order 7 in Z/28Z. To find them, you need to identify which elements of Z/28Z generate a group of order 7.

These elements are 1, 7, 13, 19, 25, and 27. Each element creates a subgroup of order 7. These subgroups are:

1) {1, 7, 13, 19, 25, 27, 28}
2) {1, 7, 13, 19, 25, 27}
3) {1, 7, 13, 19, 25}
4) {1, 7, 13, 19}
5) {1, 7, 13}
6) {1, 7}

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in general, to perform a hypothesis test comparing the means of two independent samples using the critical value method, you would follow these steps:

State the null and alternative hypotheses. For example, the null hypothesis could be that there is no difference in means between the two populations (i.e., H0: µ1 - µ2 = 0), and the alternative hypothesis could be that there is a significant difference in means (i.e., Ha: µ1 - µ2 ≠ 0).

Determine the level of significance, α, which represents the probability of rejecting the null hypothesis when it is actually true. For example, if α = 0.05, then there is a 5% chance of making a Type I error (rejecting the null hypothesis when it is true).

Calculate the test statistic. The most common test statistic for comparing the means of two independent samples is the t-test. The formula for the t-test is:

t = (x1 - x2) / [s^2pooled/n1 + s^2pooled/n2]^0.5

where x1 and x2 are the sample means, s^2pooled is the pooled variance (calculated using the two sample variances and sample sizes), and n1 and n2 are the sample sizes.

Determine the critical value(s) from the t-distribution table based on the degrees of freedom (df) and level of significance (α). The degrees of freedom for a two-sample t-test is calculated as:

df = n1 + n2 - 2

Compare the test statistic to the critical value(s). If the absolute value of the test statistic is greater than the critical value(s), then reject the null hypothesis; otherwise, fail to reject the null hypothesis.

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The lengths JL and PM are the lengths that make up the triangle JMP

The side length JL is twice the side length PN.

So, we have:

JL = 2 * PN

This gives

JL = 2 * 39

JL = 78

Hence, the length of JL is 78 units

The side length PM is half the side length KL.

So, we have:

PM = 0.5 * KL

This gives

PM = 0.5 * 95

PM = 47.5

Hence, the length of PM is 47.5 units

The angle MLK is congruent to the angle JMP.

So, we have:

MLK = JMP

This gives

MLK = 105 degrees

Hence, the measure of angle MLK is 105 degrees

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Answer:

S=(-2,5) T=(-3,4) U=(-4,0)

The equation of the straight line passing through Q and the midpoint of the line segment PR is 12x + 13y = 71.

To solve this question, we use the principles of 2-D coordinate geometry, which is the plane consisting of all points (x,y).

The midpoint  C between two points A(x₁,y₁) and B(x₂,y₂) is defined as

C(x,y) = [(x₁+x₂)/2 , (y₁+y₂)/2]

Thus, the midpoint of the points P(2,4) and R(-1,6), labelled as M, will be

M = [(2-1)/2 , (4+6)/2]

M = [ (1/2) , 5]

Now, the equation of the line segment between two points A and B is defined as

(y-y₁)/(x-x₁) = (y₂-y₁)/(x₂-x₁)

*This is called the two-point form of a line.

Using the two points M and R through which we need the required line segment to pass, we apply the above formula to arrive at the answer.

Thus by simplifying,

(y - 5)/(x-0.5) = (-1 - 5)/(7-0.5)

(y - 5)/(x-0.5) = (-6/6.5) = [-12/13]

(y - 5) = (-12/13)(x-0.5)

(y - 5) = -12x/13 + 6/13

13y - 65 = -12x + 6

13y + 12x = 71

Hence, we can say that the equation of the line passing through the midpoint of P and R, and through Q is 12x + 13y = 71

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Answer:

P =3Q +21

Step-by-step explanation:

Given: Rahim was asked to make p the subject of this formula

Q = p/3 - 7

He started his answer as follows

3Q = p - 21 hence p =

To Find, Complete Rahim's final answer.

Solution:

Q = p/3 - 7

Multiply both sides by 3

3Q = 3(p/3 - 7)

3Q = 3 × p/3 - 3 × 7

3Q = p - 21

Adding 21 both sides

3Q + 21 = p -21 +21

3Q + 21 = p

interchange sides

p = 3Q + 21

hence p =3Q +21

The line cross the Y axis in y=-2

The equation of a line is Y=ax+b where a is the slope and b the y intercept of the line

we know that for x=3 => y=4 then we plug the values we know in the equation of the line:

now we use the point we know:

then solve for b

The the y intercept of the line is y=-2

Answer:

Independent = time intervals

Dependant = how far the leaves travel

Step-by-step explanation:

independent = what you change

dependent = what you measure

Answer

a tape measure

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

MARK BRAINLIEST plz

Answer:

Step-by-step explanation:

g(-3) = 4(-3) - 1 = -12 - 1 = -13

f(-13) = 2(-13) + 3 = -26 + 3 = -23

Answer:

8 feets

Step-by-step explanation:

Given that:

Area of rectangular board = 100 ft²

Length if identical rectangular chart = 12.5ft

The are of a rectangle is obtained thus :

Area = Length * breadth

100 = 12.5feets * breath

The breadth = 100 ft² / 12.5 ft

The breadth of the chart = 8 feets

To solve a differential equation with exponential equations, start by isolating the dependent variable and any coefficients that may exist on either side of the equation. Next, take the natural logarithm of both sides of the equation and use the properties of logarithms to simplify the equation. Solve for the dependent variable. Finally, take the exponential of both sides of the equation and simplify it to get the solution.

For example, consider the differential equation dy/dx = 2y.

Isolate the dependent variable to get y = dx/2.

Then, take the natural logarithm of both sides to get ln(y) = ln(dx/2).

Use the property ln(a/b) = ln(a) - ln(b) to get ln(y) = ln(dx) - ln(2).

Solve for ln(y) to get ln(y) = ln(dx) - ln(2).

Then, take the exponential of both sides to get \(y = e^{ln(dx) - ln(2)}\) and simplify to get the solution \(y = (dx/2) e^{ln(dx)}\).

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The slope is 3. After 1 second, the car's distance increases by 7 feet.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided, we have the following equation that represents the relationship between distance and time;

y = 3x + 4

At x = 1 second, the distance is given by;

y = 3(1) + 4

y = 3 + 4

y = 7 feet.

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Answer: Thx, Listen to some JuiceWRLD

Step-by-step explanation:

There are 720 ways the Grandview high school band can manage the order of their performance of six pieces of music

To determine the number of ways the Grandview high school band can manage the order of their performance of six pieces of music, we need to find the number of permutations of six objects taken six at a time.

The following is the formula for the number of permutations of n objects taken r at a time:

P(n, r) = n! / (n - r)!

In this case, we need to find P(6, 6), which is:

P(6, 6) = 6! / (6 - 6)!

= 6! / 0!

= 6 x 5 x 4 x 3 x 2 x 1

= 720

Therefore, there are 720 ways the Grandview high school band can manage the order of their performance of six pieces of music.

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Answer:

2.5 kilograms

Step-by-step explanation:

3 x 5/6 = 2.5

The Poisson distribution is applied to events where the probability of occurrence of a certain number of events in a fixed interval of time, space, or distance is small but not necessarily "very small". False.

The Poisson distribution is used to model events that occur randomly and independently over a continuous or discrete interval of time, space, or distance, such as the number of phone calls received at a call center in an hour, the number of cars passing through a toll booth in a given time period, or the number of emails received per day. The Poisson distribution is characterized by a discrete probability mass function that describes the probability of a certain number of events occurring in a given interval, and it is widely used in probability theory and statistics for modeling events with low to moderate occurrence rates.

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The poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is very small.

Given statement is False.

Because, The Poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is not necessarily very small, but rather where the events occur randomly and independently at a constant average rate.

The Poisson distribution models the number of events that occur in a fixed time interval or within a certain area or volume of space, assuming that the events occur independently of each other and at a constant average rate. It is used in many fields, such as biology, physics, economics, and engineering, to model the occurrence of rare or common events.

The Poisson distribution has several important properties, including:

Its mean is equal to λ, and its variance is also equal to λ.

It is a discrete distribution, meaning that it models only whole numbers of events.

It is often used to model rare or unusual events, but can also be used for events that occur frequently, as long as they occur independently at a constant average rate.

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The simplified form of the expression (m - 3n)(m + 2n) - m(m - n) is - 6n².

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).

Therefore, let's simplify the expression as follows:

(m - 3n)(m + 2n) - m(m - n)

Let's open the first two bracket

(m - 3n)(m + 2n) = m² + 2mn - 3mn - 6n²

m² + 2mn - 3mn - 6n² = m² - mn - 6n²

Therefore,

m² - mn - 6n² - m(m - n)

m² - mn - 6n² - m² + mn

combine like terms

m² - m² - mn + mn - 6n² = - 6n²

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Answer:

2 = (2/3)*(6)+b

2 = 4+b

b= -2

so slope intercept form is y = (2/3)x -2

To find the point slope form, simply plug in m and the point given.

y-2 = (2/3)*(x-6)

Step-by-step explanation:

Answer:

It is B and D

Answer:

Aiden would have $67 more than Autumn.

Step-by-step explanation:

Aiden compounded continuously, which uses the formula: \(P(t)=P_oe^r^t\)

Plugging in what we know about Aiden's investment: \(P(11)=98000e^0^.^0^2^*^1^1\)

That gives us: 122115.5196

Autumn invested using regular compound interest, which has the formula: \(A=P(1+\frac{r}{t})^n^t\)

Since Autumn's investment is getting compounded quarterly, n=4 because it gets compounded 4 times a year.

Plug in Autumn's investment: \(A=98000(1+\frac{0.02}{4})^4^*^1^1\)

That gives us: 122048.5974

Now just subtract the two and round to the nearest dollar:

\(122115.5196-122048.5974=66.92215187\)

OR

$67. Aiden would have $67 more than Autumn after 11 years.

Answer:

x^2 + 10x + 25; (x + 5)^2.

Step-by-step explanation:

When we're talking about line segments, we just have to find the sum of the two parts of the line segment to find the value of the whole. In this case, we have x^2 + 25, and 10x. So, we add them together.

x^2 + 25 + 10x

= x^2 + 10x + 25

Since this can be immediately factored into (x + 5)^2, you have your answer.

Hope this helps!