Which expression is equivalent to one over three p + 15?

A.one over three(p + 45)
B.one over three(p + 5)
C.3(p + 45)
D.3(p + 5)

PQ=11

PS^2+SR^2=QR^2

PS^2+PS^2=PQ^2

9514 1404 393

Answer:

  11 cm

Step-by-step explanation:

The law of cosines can be helpful here. In order to find PQ, we must know the cosine of the angle R. Fortunately, SOH CAH TOA reminds us it is ...

  Cos = Adjacent/Hypotenuse

  cos(R) = 10/14 = 5/7

__

The law of cosines gives us the relation ...

  PQ^2 = PR^2 +QR^2 -2·PR·QR·cos(R)

  PQ^2 = 15^2 +14^2 -2(15)(14)(5/7) = 121

  PQ = √121 = 11

The length of PQ is 11 cm.

_____

Alternate solution

This can be solved using the Pythagorean theorem twice.

  QS^2 = QR^2 -SR^2 = 14^2 -10^2 = 96

  PQ^2 = PS^2 +QS^2 = 5^2 +96 = 121

  PQ = √121 = 11

Answer:

Use Mathpapa to find your answer.

Step-by-step explanation:

It's a good, and powerful program.

Answer:

huh???

Step-by-step explanation:

Answer: the slope of the graph is -1

Step-by-step explanation: because x has a coefficient of negative 1 but if you wanted to graph this line, you have to be careful since you go down 1 unit and right 1unit. The line is descending since it has a negative slope so technically the slope is -1/1 but we can just say it’s -1

The combined balance of both bank accounts at the end of 3 years is closest to $1039.76.

To calculate the combined balance of both bank accounts after 3 years, we'll calculate the balance for each account separately and then add them together.

For Bank A, we can use the compound interest formula:

A =\(P(1 + r/n)^(nt)\)

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount

r = annual interest rate (as a decimal)

n = number of times that interest is compounded per year

t = number of years

In this case, Wanda deposited $370 at a 2.25% interest rate compounded annually, so we have:

P = $370

r = 2.25% = 0.0225 (as a decimal)

n = 1 (compounded annually)

t = 3 years

Using the formula, we can calculate the balance for Bank A:

A_A = \(370(1 + 0.0225/1)^(1*3)\)

=\(370(1.0225)^3\)

= 370(1.0678450625)

= $394.76

For Bank B, we can use the simple interest formula:

A = P(1 + rt)

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount

r = annual interest rate (as a decimal)

t = number of years

In this case, Wanda deposited $600 at a 2.5% simple interest rate, so we have:

P = $600

r = 2.5% = 0.025 (as a decimal)

t = 3 years

Using the formula, we can calculate the balance for Bank B:

A_B = 600(1 + 0.025*3)

= 600(1.075)

= $645

Finally, we can calculate the combined balance of both bank accounts:

Combined Balance = A_A + A_B

= $394.76 + $645

= $1039.76

Therefore, the combined balance of both bank accounts at the end of 3 years is closest to $1039.76.

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9514 1404 393

Answer:

  9.  c. 1

  10.  c. y = 15/x

Step-by-step explanation:

The equation for inverse variation can be written as ...

  y = k/x

The value of k can be determined from given values of x and y. Multiply by x to get ...

  k = xy

Solving for x, you get ...

  x = k/y

___

9. k = (1/7)(49) = 7

  x = k/y = 7/7

  x = 1

__

10. k = (3)(5) = 15

  y = 15/x

Answer:

Step-by-step explanation:

The text is a statistics problem that asks to find the probability of a certain range of values in a normal distribution. A normal distribution is a bell-shaped curve that shows how data values are spread around the mean. The mean is the average of all the data values, and the standard deviation is a measure of how much the data values vary from the mean. To solve this problem, we can use the following steps:

Convert the given range of values to standard scores or z-scores. A z-score tells us how many standard deviations a value is away from the mean. To find the z-score, we use the formula: z=σx−μ​

where x is the value, μ is the mean, and σ is the standard deviation. For example, to find the z-score for 33.5 psi, we plug in the values: z=233.5−35​=−0.75

This means that 33.5 psi is 0.75 standard deviations below the mean. Similarly, to find the z-score for 36 psi, we plug in the values: z=236−35​=0.5

This means that 36 psi is 0.5 standard deviations above the mean.

Use a z-table to find the area under the curve for each z-score. A z-table is a table that shows the probability of getting a z-score less than or equal to a given value. For example, to find the area under the curve for -0.75, we look up the row for -0.7 and the column for 0.05 in the z-table and get 0.2266. This means that there is a 22.66% chance of getting a z-score less than or equal to -0.75. Similarly, to find the area under the curve for 0.5, we look up the row for 0.5 and the column for 0 in the z-table and get 0.6915. This means that there is a 69.15% chance of getting a z-score less than or equal to 0.5.

Subtract the smaller area from the larger area to find the area between the two z-scores. This area represents the probability of getting a value between 33.5 and 36 psi in the normal distribution. For example, to find the area between -0.75 and 0.5, we subtract: 0.6915−0.2266=0.4649

This means that there is a 46.49% chance of getting a value between 33.5 and 36 psi in the normal distribution.

Multiply the area by 100 to convert it to a percentage and write it with the appropriate units: The percentage of tires that are inflated to a pressure between 33.5 and 36 psi is 0.4649×100=46.49%

The loss on selling 50 shares of stock would be 87.50.

To calculate the loss on selling 50 shares of stock originally bought at

\(13\frac{3}{4}\) and sold at 12, we need to determine the difference between the purchase price and the selling price, and then multiply it by the number of shares sold.

First, let's convert the purchase price from a mixed fraction to a decimal. \(13\frac{3}{4}\) can be expressed as 13.75.

Next, we calculate the difference between the purchase price and the selling price:

\(13.75 - 12 = 1.75.\)

Finally, we multiply the difference by the number of shares sold:

\(1.75 \times50 = 87.50.\)

Therefore, the loss on selling 50 shares of stock would be 87.50.

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Answer:

The answer is

B. 8/10

Step-by-step explanation:

To find the composition we need, let's first find the general expression:

Hence:

Now we can evaluate when x=1/2:

Therefore:

Answer: 6 T-shirts

Step-by-step explanation:72/12=6

Step-by-step explanation:

i think it should be

2(8x+3)+10

Answer:

16x+16

Step-by-step explanation:

8x+3+8x+3+5+5

16x+6+10

16x+16

Answer:

B

Step-by-step explanation:

total number of people minus people who prefer soda, iced tea, or lemonade= people who prefer water

450-101-67-108=174

Answer:

D: 276 preferred water

Step-by-step explanation:

Answer:

Cable: 10%  Satellite: 40%  Streaming Service: 50%

Step-by-step explanation:

There are 10 friends  

1 has cable

4 have satellite

5 have streaming service  

Which means:

Cable is 10%

Satellite is 40%

Streaming Service is 50%

Answer:

Cable Television: 10%

Satellite Television: 40%

Streaming Service: 50%

Step-by-step explanation:

Cable television: \(\frac{1}{1+4+5} =\frac{1}{10} =\frac{10}{100}\) or 10%

Satellite television: \(\frac{4}{1+4+5} =\frac{4}{10} =\frac{40}{100}\) or 40%

Streaming service: \(\frac{5}{1+4+5} =\frac{5}{10} =\frac{50}{100}\) or 50%

The first question, it is decreasing because the slope is negative.

Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

(a) The local extrema of the polynomial are: Local maximum at x = -0.68 and Local minimum at x = -0.32

(b) There is no global minimum or maximum.

To find the local extrema and absolute extrema of the given polynomial 10x⁵ + 22x⁴ + 20x³ - 0x² + 6, we need to take the first and second derivatives of the polynomial and find the critical points.

The first derivative is:

50x⁴ + 88x³ + 60x²

The second derivative is:

200x³ + 264x² + 120x

Setting the first derivative to zero, we get:

50x⁴ + 88x³ + 60x² = 0

Factoring out x², we get:

x²(50x² + 88x + 60) = 0

Using the quadratic formula to solve for the roots of the quadratic equation 50x² + 88x + 60 = 0, we get:

x = -0.68 or x = -0.32

These are the critical points of the polynomial. To determine whether they correspond to local extrema or inflection points, we need to look at the sign of the second derivative at each point.

Substituting x = -0.68 into the second derivative, we get:

200(-0.68)³ + 264(-0.68)² + 120(-0.68) = -148.68

Since the second derivative is negative at x = -0.68, this critical point corresponds to a local maximum.

Substituting x = -0.32 into the second derivative, we get:

200(-0.32)³ + 264(-0.32)² + 120(-0.32) = 9.48

Since the second derivative is positive at x = -0.32, this critical point corresponds to a local minimum.

To find the absolute extrema, we also need to evaluate the polynomial at the endpoints of the interval we are interested in. Since the polynomial does not have any real roots, we can assume that the interval of interest is the entire real line.

Taking the limit of the polynomial as x approaches positive or negative infinity, we see that the leading term dominates and the polynomial goes to positive infinity as x approaches infinity and negative infinity.

Therefore, there is no global minimum or maximum.

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A)
i) the inequality to show the number of ballons that the dance committee can buy is: 0.80b + 65 ≤ 125

ii)  solving the inequality above, we arrive at b ≤ 75
B) The graph is attached accordingly.

C) See the description of the solution below.

Let's start by defining our variables. Let b be the number of balloons that the dance committee could buy.

The cost of b balloons is $0.80b. We want to make sure that the cost of the balloons plus the amount already spent on decorations ($65) is less than or equal to the budget of $125. So we can write the following inequality:

0.80b + 65 ≤ 125

Now we can solve for b:

0.80b + 65 ≤ 125

0.80b ≤ 125 - 65

0.80b ≤ 60

b ≤ 75

Therefore, the dance committee can buy up to 75 balloons to stay within their budget.

To graph the solution set, we can plot b on the horizontal axis and shade the region to the left of b = 75, since b must be less than or equal to 75.

The solution set represents all possible values of b that satisfy the inequality. In this case, the solution set is b ≤ 75, which means that the dance committee can buy up to 75 balloons and still stay within their budget.

As the number of balloons increases, the cost of the balloons also increases, and the amount of money left in the budget decreases.

Therefore, the more balloons the dance committee buys, the less money they will have left for other decorations or expenses.

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Full Question:


Since the above question is incomplete, it appears you are referring to the question below.


The dance committee has a budget of $125 to decorate the gym for a spring dance. They already spent $65. Some members want to buy helium balloons that cost $0.80 each.

A) Write and solve an inequality to show the number of balloons that the dance committee could buy.

B) Graph the solution set for the inequality.
C) Describe what the solution means and how the number of balloons affects the amount in the budget.

x and y have the values 7 and 7√2, respectively.

The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.

We can use this information to determine the values of x and y because the base is specified as being 7.

Let's give the perpendicular side the value of x, and the hypotenuse the value of y.

The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.

Consequently, x = 7.

We can determine that x:y:2x using the ratio of 1:1:2.

When we enter the value of x, we may calculate y:

7:y:√2(7)

Simplifying even more

7:y:7√2

Given that the hypotenuse (y) equals 72, we can write:

y = 7√2

Thus, x and y have the values 7 and 7√2, respectively.

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Answer:

5/3

Step-by-step explanation:

To find the slope we pick one set of points

2/3,-1/2

Set your equation up like this

y2-y1/x2-x1

Plug in and subtract(notice the negative)

And we get 5/3

Hope this helps

BA=(3),(3),(-1) is the answer

Answer:

Look below

Step-by-step explanation:

Let's start by converting 4 m into cm:

\(4m * \frac{10^{2}cm}{1m} \)\(= 4*10^{2}cm=400cm\)

Since Megan's chain is only 400 cm long, Mason's chain is longer by 79 cm.

Answer:

Masons is longer

Step-by-step explanation:

4m=400 cm

479cm=4.79 m

I'm pretty sure you could answer the rest.

Answer:

Step-by-step explanation:

step 1

100%/the total number = percent for one probability

100/5 = 20%

2 and 4 is even.

total even number * percent for one probability = total percent for even number

20% * 2 = 40%

therefore total even number is 40%

The probability is:

Step-by-step explanation:

Remember the formula for probability:

\(\boxed{\!\!\boxed{\bold{Probability=\frac{Favourable~outcome}{total~outcomes}\quad}}\!\!}\)

In this case, the favourable outcome (an even number) is 2, because there are only 2 even numbers in the set.

As for the total outcomes, there are 5 of them, because we have 5 numbers total.

So the probability of choosing an even number is 2/5.

Answer:

(C) 12

Step-by-step explanation:

To solve this problem, we can use the following steps:

Find half of 80: 80/2 = 40

Add 20 to half of 80: 40 + 20 = 60

Find one fifth of the result: 60/5 = 12

Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.

Answer:

(C) 12

Step-by-step explanation:

What is one fifth of twenty more than half of 80

0.5 × 80 = 40

What is one fifth of twenty more than half of 80

40 + 20 = 60

What is one fifth of twenty more than half of 80

1/5 × 60 = 60/5 = 12

Answer: The expression for the absolute value of x+2 when x is less than 2 is -(x+2).

Step-by-step explanation: When x is less than 2, x+2 is a negative number. The absolute value of a negative number is its opposite with the negative sign, so the absolute value of x+2 is -(x+2). Therefore, when x is less than 2, the expression for the absolute value of x+2 is -(x+2).

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

The length of EB is approximately 14.6 units when rounded to the nearest tenth.

To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.

Using the similarity ratio, we can set up the proportion:

DF / CF = DE / EB

Plugging in the given values, we have:

13.1 / 10.9 = 17.5 / EB

To find EB, we can cross-multiply and solve for EB:

13.1 * EB = 10.9 * 17.5

EB = (10.9 * 17.5) / 13.1

EB ≈ 14.6

Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.

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Answer:

44 miles

Step-by-step explanation:

25-2.95

22.05

22.05/0.5

They can go 44 miles

She can travel 44.1 miles at most.

Inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Let Katie can travel \(x\) miles

\(2.95 + 0.50x\leq 25\)

\(0.50x\leq 25-2.95\)

\(x\leq 44.1\)

She can travel 44.1 miles at most.

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The equation solved for the variable are;

h = S- 2B/p

b = S - hp/2

To determine the equation, we need to know that the subject of formula for  an equation is described as the variable that is made to stand on one end of the equality sign.

It is the variable that is being worked out.

From the information given, we have that;

S= hp + 2B.

To make the height with the variable 'h' the subject, we have;

collect the terms

hp = S - 2B

Divide by the coefficient

h = S- 2B/p

For b, we have;

S - hp = 2b

divide by the coefficient

b = S - hp/2

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