a rectangular flower garden has area of 32 square feet. if the width of the garden is 4 feet less than the length, what is the perimeter, in feet, of the garden?

The solutions for the disruptive property are,

2f+10 = 2 (f + 5)

20+24g = 4(5 + 6g)

32b - 20 = 8(4b - 5)

The solution to the expressions is,

E = 24h -10hn +11d

E = 16s + 2

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The solution of the equations by using distributive property,

2f+10 = 2 (f + 5)

20+24g = 4(5 + 6g)

32b - 20 = 8(4b - 5)

Simplify the expression

E = 24h + 3d - 10hn+ 8d

E = 24h -10hn +11d

The solution of the second expression is,

E = 12s + 4 + 4s - 2

E = 16s + 2

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There are 32 students in each of the remaining 12 homerooms.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

Total students in a senior class = 412 students.

Total number of students in the smallest homeroom = 28

And, 12 homerooms have the same number of students.

Let number of students in each of 12 homerooms = x

So, Total number of students in each of 12 homerooms = 12x

Then, We can formulate;

12x + 28 = 412

Solve for x as;

12x + 28 = 412

Subtract 28 as;

12x + 28 - 28 = 412 - 28

12x = 384

Divide by 12;

x = 32

Thus, There are 32 students in each of the remaining 12 homerooms.

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The inequality that represents the graph is y < x.

The inequality that represents the graph is y < x. This inequality represents the region below the line that forms the graph. In this case, the line starts at the origin and has a slope of 1, meaning that for every increase of 1 unit on the x-axis, the y-coordinate increases by 1 unit as well.

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Final answer:

To find equal expressions, identify different expressions that have the same value when evaluated. Write true number sentences using these equal expressions.

Explanation:

In order to find equal expressions, we need to identify different expressions that have the same value when evaluated. For example, the expressions 3 + 4 and 7 are equal because both evaluate to 7. We can use these equal expressions to write true number sentences, such as 3 + 4 = 7.

Another example is the expressions 2 * 5 and 10, which are equal because both evaluate to 10. We can write the true number sentence 2 * 5 = 10 using these equal expressions.

It's important to note that we're looking for expressions that are equal in value, not necessarily in form. For example, the expressions x + 2 and 3 + x are equal because they represent the same value for any given value of x. We can write the true number sentence x + 2 = 3 + x using these equal expressions.

Answer:

[tex]y=-\frac{2}{3}x+6[/tex]

Step-by-step explanation:

we have been give  that

slope, m = -2/3

The line passes through the point (-3,8).

Hence, [tex]x_1=-3,y_1=8[/tex]

The point slope form of a line is

[tex]y-y_1=m(x-x_1)[/tex]

Substituting the known values

[tex]y-8=-\frac{2}{3}(x-(-3))[/tex]

On simplifying, we get

[tex]y-8=-\frac{2}{3}x-2\\\\y=-\frac{2}{3}x+6[/tex]

Thus, equation of line is [tex]y=-\frac{2}{3}x+6[/tex]

To find the value of b in the equation 25s = 9b = 4c - s^2, we can substitute the given values and solve using the quadratic equation.

To find the value of b, we can use the given information and substitute the values of a, b, and c into the quadratic equation.

The equation is: c = 25s = 9b = 4c - s^2

Substituting the values:

25s = 9b = 4c - s^2

25s = 9b = 4c - s^2

Now we can solve for b:

9b = 4c - s^2

9b = 4(-0.0211) - (9)^2

9b = -0.0844 - 81

9b = -81.0844

b = -81.0844/9

b = -9.01

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Answer:

Expression  p  - 19 .

Step-by-step explanation:

Given  : A number p minus 19 algebraic expression.

To find : Write expression .

Solution : We have given A number p minus 19 .

A number  =  p .

According to question :

p is minus 19

We can see the number p is less than 19

So , p  - 19 .

Therefore, Expression  p  - 19 .

Answer:

There are 14 $10 bills and 16 $20 bills.

Step-by-step explanation:

Let

x = number of $10 bills

y = number of $20 bills

The sum of the value of x and y is $460.

10 x + 20 y = 460   [1]

The sum of x and y is equal to the total number of bills.

x + y = 30

y = 30 - x   [2]

We replace [2] in [1],

10 x + 20 (30 - x) = 460

10 x + 600 - 20 x = 460

-10 x = -140

x = 14

We can get y if we replace this value of x in [2].

y = 30 - 14 = 16

Answer:

the answer is 357.50

Step-by-step explanation:

Answer:

Total bill =  7 pounds .

Step-by-step explanation:

Given : You buy 3.17 pounds of apples, 1.25 pounds of pears, and 2.56 pounds of oranges.

To find : What is your total bill rounded to the nearest cent.

Solution : We have given

Apple = 3.17 pounds

Peas = 1.25 pounds

Orange = 2.56 pounds.

Total bill =  3.17  + 1.25 +2.56 = 6.98

Total bill = 6 .98 pounds .

We can see number after decimal is greater than 5 so number would be increased b 1.

Total bill =  7 pounds .

Therefore, Total bill =  7 pounds .

Without knowing the price per pound of the fruit, it's impossible to calculate the total bill. However, if you knew the individual prices, like in the example, you could add up these amounts together to find the total cost.

The question you're asking appears to be missing some important information. Specifically, we would need to know the price per pound of the apples, pears, and oranges in order to calculate your total bill. However, let's use an analogous example. Suppose you buy 10 apples at 50 cents each, 12 bananas at 20 cents each, and 2 bunches of grapes at 65 cents each. Your total cost would be $5.00 for apples, $2.40 for bananas, and $1.30 for grape. Altogether, this comes to $8.70.

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Given that a trucker changes his tires every 40,000 miles, if he drives 160,000 miles in a year, he will use a total of 5 sets of tires.

The question is asking us to find out how many sets of tires a trucker will use when he drives 160,000 miles in a year, given that he changes his tires every 40,000 miles. To find out, we need to do some simple division.

First, we need to take the total distance traveled, which is 160,000 miles, and divide it by the distance the trucker can travel on a set of tires, which is 40,000 miles. 160,000 miles divided by 40,000 miles equals 4.

So, if the trucker starts the year with a fresh set of tires, he will need to change his tires 4 times throughout the year, meaning he will use a total of 5 sets of tires.

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Answer:

y = 3 1/13

Step-by-step explanation:

Add 3 and combine like terms:

... (2 3/5)y = 8

Multiply by the reciprocal of the coefficient of y.

... y = 8 · (5/13) = 40/13

... y = 3 1/13

_____

Check

(3/5)(3 1/13) - 3 + 2(3 1/13) = 5

(3/5)(40/13) - 39/13 + 2(40/13) = 5 . . . . express everything with 13 as a denominator

24/13 - 39/13 + 80/13 = 5 . . . . . eliminate parentheses

(24 -39 +80)/13 = 5 . . . . . . . . . . add the fractions

65/13 = 5

5 = 5 . . . . . the answer checks

A paint drying situation, has the standard deviation 1.93. The detailed solution is given below.

Given :

Standard Deviation, [tex]\sigma = 7[/tex]

Mean, [tex]\mu = 75[/tex]

Sample, n = 25

Solution :

A) We know that,

[tex]z = \dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n} }}[/tex]     ---- (1)

Now put the values of [tex]\rm x,\;\mu,\;\sigma \;and \;n[/tex] in equation (1) we get,

[tex]z = \dfrac{72.3-75}{\dfrac{7}{\sqrt{25} }}[/tex]

z = -1.93

Therefore, 72.3 is 1.93 standard deviations below the mean.

B) From the above part we know that z = - 1.93.Therefore p-value is,

P(-1.93) = 0.03

Since [tex]\alpha[/tex] = 0.01 and p-value = 0.03, this means that the p-value is greater than the fail to reject the null hypothesis.

C) The p-value for [tex]z\leq -2.8[/tex]

is 0.00256

Therefore, the [tex]\alpha[/tex] for the test procedure that rejects the null hypothesis when [tex]z\leq -2.8[/tex] is 0.0026.

D) For alternate hypothesis,

[tex]\rm \beta (\mu') = P(X>\mu_0-z_1_-_\alpha \frac{\sigma}{\sqrt{n} }|\mu')[/tex]

[tex]\rm = P(-z_1_-_\alpha +\dfrac{\mu_0-\mu'}{\dfrac{\sigma}{\sqrt{n} }})[/tex]

For [tex]\alpha[/tex] = 0.0026

[tex]\rm \beta (70)=1- P(-z_0_._9_9_7_4 +\dfrac{75-70}{\dfrac{7}{\sqrt{25} }})[/tex]

[tex]\rm \beta (70) = 1-P(-2.7949+3.5714)=1-P(0.7765)[/tex]

[tex]\beta (70)=1-0.78128\approx 0.2187[/tex]

E) Now we want n when

[tex]\beta (70) = 0.01[/tex]

[tex]\rm 0.01=1- P(-z_0_._9_9_7_4 +\dfrac{75-70}{\dfrac{7}{\sqrt{n} }})[/tex]

[tex]P(-2.7949+\dfrac{5}{\dfrac{7}{\sqrt{n} }})=0.99[/tex]

[tex]P(-2.7949+\dfrac{5}{\dfrac{7}{\sqrt{n} }})=P(2.3262)[/tex]

[tex]-2.7949+\dfrac{5}{\dfrac{7}{\sqrt{n} }}=2.3262[/tex]

[tex]\rm \sqrt{n} = 7.1695[/tex]

n = 51.4

Therefore we need n = 52.

F)

[tex]\rm p-value = P(\bar{X}\leq \bar{x})[/tex]

[tex]\rm p-value = P(\bar{X}\leq 72.3)=P(z\leq \dfrac{72.3-76}{\dfrac{7}{5}})[/tex]

[tex]\rm p-value = P(z\leq -2.643)[/tex]

[tex]\rm p-value = 0.00411[/tex]

Since p-value is larger that .01 therefore we fail to reject [tex]\mu[/tex] = 76.

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The total cost of a two-week car rental for a trip of 500 miles, split three ways, is $250 per person.

In this calculation, we'll break down the costs into two parts: the weekly rental cost and the mileage cost. The car rents for $250 per week which, for two weeks, is $250 x 2 = $500. The cost for mileage is $0.50 per mile, hence for 500 miles, it will be $0.50 x 500 = $250. Adding these two gives us the total cost, $500 + $250 = $750 for the trip.

It's also mentioned that there are three people sharing this cost. So, the cost per person would be $750 divided by 3 which gives us $250 per person for the two-week trip of 500 miles.

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Answer:

The sum of measure of angle is 5400

Step-by-step explanation:

Given a 32-gon.

we have to find the sum of the angle measures of a 32-gon

In geometry, 32-gon is a thirty-two-sided polygon i.e polygon of 32 sides

The sum of measure of interior angle of polygon is calculated by the formula

[tex]s=(n-2)180^{\circ}[/tex]

where n is number of sides

[tex]s=(32-2)180=30\times 180=5400[/tex]

Hence, option A is correct.

Answer:

[tex]\sin\dfrac{5\pi}{4}=-\dfrac{1}{\sqrt{2}}[/tex]  

[tex]\cos\dfrac{5\pi}{4}=-\dfrac{1}{\sqrt{2}}[/tex]  

[tex]\tan\dfrac{5\pi}{4}=1[/tex]  

Step-by-step explanation:

Given : [tex]\theta =\dfrac{5\pi}{4}[/tex]

The angle is on radian.

We need to find the sine, cosine and tangent.

[tex]\sin\theta =\sin(\frac{5\pi}{4}[/tex]

[tex]\sin\theta =\sin(\pi+\frac{\pi}{4}[/tex]

[tex]\sin\theta =-\sin(\frac{\pi}{4}[/tex]      [tex]\because \sin(\pi+\theta)=-\sin\theta[/tex]

[tex]\sin\dfrac{5\pi}{4}=-\dfrac{1}{\sqrt{2}}[/tex]  

[tex]\cos\theta =\cos(\frac{5\pi}{4}[/tex]

[tex]\cos\theta =\cos(\pi+\frac{\pi}{4}[/tex]

[tex]\cos\theta =-\cos(\frac{\pi}{4}[/tex]      [tex]\because \cos(\pi+\theta)=-\cos\theta[/tex]

[tex]\cos\dfrac{5\pi}{4}=-\dfrac{1}{\sqrt{2}}[/tex]  

[tex]\tan\theta =\tan(\frac{5\pi}{4}[/tex]

[tex]\tan\theta =\tan(\pi+\frac{\pi}{4}[/tex]

[tex]\tan\theta =\tan(\frac{\pi}{4}[/tex]      [tex]\because \tan(\pi+\theta)=\tan\theta[/tex]

[tex]\tan\dfrac{5\pi}{4}=1[/tex]