A pail holds
4 1/4
gallons of water. How much is this in cups?

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:

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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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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Answer:

the answer is 357.50

Step-by-step explanation:

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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Sean Matthews' weekly earnings are subject to payroll taxes, including his tips. The deductions for social security and medicare are split between him and his employer. Understanding how these deductions work can enable him to maximize his total earnings.

The subject of the question pertains to Sean Matthews' earnings at the Duluxe Lounge, which involves payroll taxes on his wages and tips. From his regular wages of $300.00 for 40 hours, "payroll taxes" of 6.2% for Social Security and 1.45% for Medicare are deducted. The same deductions also apply to his reported tips of $500.00. These deductions are shared between Sean and his employer, though, it's possible that the employer's share might effectively be passed onto Sean in the form of lower wages.

Learning and understanding these financial procedures can significantly help individuals like Sean to maximise their total earnings.

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$736 will be his Net take home.

Net pay is the money you have left when your paycheck makes its way to you and all of the required taxes are taken out. To find Sean's net pay, both his earned wages and the reported tips will be considered for tax deductions.

Calculate total earnings for the week:
Wages = $300.00.
Total earnings = Wages + Tips = $300.00 + $500.00 = $800.00.

Assume a tax rate (federal, state, and other taxes) of 2%  
Tax deductions = $800.00 x 2% = $16.00.

Calculate net pay:
Net pay = Total earnings - Tax deductions = $800.00 - $16.00 = $736.00.

complete question:

Sean Matthews is a waiter at the Deluxe Lounge. In his first weekly pay in March, he earned $300.00 for the 40 hours he worked. In addition, he reports his tips for February to his employer ($500.00), and the employer withholds the appropriate taxes for the tips from this first pay in March.Calculate his net take-home pay assuming the employer withheld federal income tax (wage-bracket, married, 2 allowances), social security taxes, and state income tax (2%).

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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Final answer:

The probability that an apartment is on the 2nd floor or has 2 bedrooms is 0.7727 or 77.27%.

Explanation:

To find the probability that an apartment is on the 2nd floor or has 2 bedrooms, we need to determine the total number of apartments that satisfy either of the conditions.

On the 2nd floor, there are 2 apartments with 1 bedroom, 2 apartments with 2 bedrooms, and 2 apartments with 3 bedrooms. This gives us a total of 2 + 2 + 2 = 6 apartments on the 2nd floor.

Out of the total distribution of apartments, there are 3 apartments with 1 bedroom, 4 apartments with 2 bedrooms, and 4 apartments with 3 bedrooms. This gives us a total of 3 + 4 + 4 = 11 apartments with 2 bedrooms.

The probability of an apartment being on the 2nd floor or having 2 bedrooms is given by:

Probability = (Number of apartments on the 2nd floor + Number of apartments with 2 bedrooms) / Total number of apartments

Probability = (6 + 11) / (6 + 1 + 1 + 2 + 2 + 2 + 1 + 2 + 4 + 1) = 17 / 22 = 0.7727 or 77.27%

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

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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Answer:

The value of a=6[/tex]

Step-by-step explanation:

step 1:-

col linearity of three points :-

We know that slopes of two parallel lines are equal.If two lines having the same slope pass through a common point ,then two lines will coincide . Hence ,If A,B,C are three points in the X Y- plane, then they will lie on a line,

that is three points are col linear if and only if Slope of AB= slope of BC

step 2:-

Since the given three points are col-linear, we have

Slope of AB= slope of BC

given points are A(2,-2) ,B(-6,2) and C(a,-4)

Step 3 :-

Slope of AB= slope of BC

[tex]\frac{2-(-2)}{-6-2} =\frac{-4-2}{a+6}[/tex]

[tex]\frac{-1}{2} =\frac{-6}{a+6}

 by cross multiplication

we get \\a+6=12\\

Step 4:-

The value of a=6[/tex]

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]  

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.

The unit rate for 521 miles in 14 hours is 37.2 miles per hour

Given:

Total distance travelled = 521 miles

Total time taken = 14 hours

Unit rate = Total distance travelled ÷ Total time taken

= 521 miles ÷ 14 hours

= 37.214285714285

Approximately, 37.2 miles per hour

Therefore, unit rate for 521 miles in 14 hours is 37.2 miles per hour

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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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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.