Which right triangle prism has the greatest volume

Answer:

x = 1, y = 60

Step-by-step explanation:

Value of new-releases (x) = $20 each

Value of classic (y) = $8 each

Total budget = $500

Equation : 20x + 8y = 500

The librarian wants to purchase maximum DVDs. She can get more DVDs of classic movies for $8 as they are less costly.

Lets assume the librarian buys at least one new-release DVD.

x=1

20x + 8y = 500

8y + 20(1) = 500

y = 60

Therefore, in a budget of $500, the librarian can purchase 60 classic movies and 1 new-release.

!!

Answer: x=16 y=22

Step-by-step explanation:

Edge test math

Answer:

see explanation

Step-by-step explanation:

Given

6a² - a - 5 = 0

Consider the factors of the product of the a² term and the constant term which sum to give the coefficient of the a- term.

product = 6 × - 5 = - 30 and sum = - 1

The factors are - 6 and + 5

Use these factors to split the a- term

6a² - 6a + 5a - 5 = 0 ( factor the first/second and third/fourth terms )

6a(a - 1) + 5(a - 1) = 0 ← factor out (a - 1) from each term

(a - 1)(6a + 5) = 0

Equate each factor to zero and solve for a

a - 1 = 0 ⇒ a = 1

6a + 5 = 0 ⇒ 6a = - 5 ⇒ a = - [tex]\frac{5}{6}[/tex]

Solution set = { 1, - [tex]\frac{5}{6}[/tex] }

Answer:  The solution set of the given quadratic equation is  [tex]\{1,-\dfrac{5}{6}\}.[/tex]

Step-by-step explanation:  We are given to find the solution set of the following quadratic equation :

[tex]6a^2-a-5=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be solving the given quadratic equation by the method of FACTORIZATION.

To factorize the expression on the L.H.S. of equation (i), we need two integers with sum -1 and product -30. Those two integers are -6 and 5.

The solution of equation (i) is as follows :

[tex]6a^2-a-5=0\\\\\Rightarrow 6a^2-6a+5a-5=0\\\\\Rightarrow 6a(a-1)+5(a-1)=0\\\\\Rightarrow (a-1)(6a+5)=0\\\\\Rightarrow a-1=0,~~~~~~6a+5=0\\\\\Rightarrow a=1,~-\dfrac{5}{6}.[/tex]

Thus, the solution set of the given quadratic equation is  [tex]\{1,-\dfrac{5}{6}\}.[/tex]

Answer:

Coach Johnson will save $1.50

Step-by-step explanation:

1. The first step is to calculate the unit price for each of the packages, ie. how much a single shin guard costs.

If we look at the package of 10 shin guards for $14.50, we can calculate the unit price by dividing the package price ($14.50) by the number of shin guards (10). Thus we get:

14.50/10 = $1.45

Now, if we do the same for the package of 15 shin guards for $22.50, we get:

22.50/15 = $1.50

2. Now we can see that the lowest unit price is $1.45 (package of 10 shin guards) and the highest unit price is $1.50 (package of 15 shin guards).

3. There are two ways to see how much he would save, so I will show both here.

1) First calculate how much the coach will have to pay for a pack of 30 shin guards for each of the packages:

3 packages of 10 shin guards for $14.50 = 3*14.5 = $43.50

2 packages of 15 shin guards for $22.50 = 2*22.5 = $45.00

Now subtract the second value from the first: 45-43.5 = 1.5

Therefor, he will save $1.50.

2) The second method is perhaps what I would personally use as it is a little quicker; so we already know that the unit price for the pack of 10 is $1.45 and the unit price for the pack of 15 is $1.50 - thus, we can say that there is a difference of $0.05 per shin guard in price. Now if we were going to calculate how much the coach would save in buying 30 shin guards, we could simply multiply how much he saves on a single shin guard by 30. Thus, we get:

0.05*30 = 1.5

Therefor, again we get the same answer that Coach Johnson would save $1.50.

Hope that helps :)

Answer:

Let us assume that the pay rate per hour = x

no. of hours worked = n

Gross earnings = x*n

Federal taxes = 18% of gross earnings

= 0.18(x*n)

State taxes = 4% of gross earnings

= 0.04(x*n)

Social security deduction = 7.05% of gross earnings

= 0.0705(x*n)

Total deductions = Federal taxes + State taxes +SSD

= 0.18(x*n) + 0.04(x*n) + 0.0705(x*n)

= 0.2905(x*n)

Net pay = Gross earnings - Total Deduction

Net pay = x*n - 0.2905(x*n)

Net pay = 0.7095(x*n)

The gross earnings are $800. Deductions total $232.40, resulting in a net pay of $567.60 after federal, state taxes, and social security deductions.

Let's calculate various components of a paycheck, starting with the given pay rate and hours worked. Suppose the pay rate is $20 per hour and the employee works 40 hours per week.

1. Gross Earnings:

Gross Earnings = Pay Rate × Hours Worked

Gross Earnings = $20/hour × 40 hours

Gross Earnings = $800

2. Federal Taxes:

Federal Taxes = 18% of Gross Earnings

Federal Taxes = 0.18 × $800

Federal Taxes = $144

3. State Taxes:

State Taxes = 4% of Gross Earnings

State Taxes = 0.04 × $800

State Taxes = $32

4. Social Security Deduction:

Social Security Deduction = 7.05% of Gross Earnings

Social Security Deduction = 0.0705 × $800

Social Security Deduction = $56.40

5. Total Deductions:

Total Deductions = Federal Taxes + State Taxes + Social Security Deduction

Total Deductions = $144 + $32 + $56.40

Total Deductions = $232.40

6. Net Pay:

Net Pay = Gross Earnings - Total Deductions

Net Pay = $800 - $232.40

Net Pay = $567.60

Therefore, the gross earnings are $800, and after accounting for $232.40 in deductions for federal and state taxes along with social security, the net pay is $567.60.

Answer:

Four(4)

Step-by-step explanation:

The given algebraic expression is:

[tex]3x^3y+5x^2+y+9[/tex]

The variables in this expression are [tex]x[/tex] and/or [tex]y[/tex].

The variable terms in this expression are terms containing [tex]x[/tex] and [tex]y[/tex].

These terms are:

[tex]3x^3y[/tex]

[tex]5x^2[/tex]

and

[tex]y[/tex]

Therefore there are 4 variable terms.

Answer:

X=6

Step-by-step explanation:

You need to cross multiply 2 by x+6. this Equals 2x+12. Then you cross multiply 8 by three which is 24. leading to the equation 2x+12=24 . Subtract 12 on both sides to get 2x=12. Divide by two to get 6 as your answer.

Answer:

V=301.59 M^3

Step-by-step explanation:

The volume of a cylinder is 3.14r^2h

3.14(4^2)6=V

3.14(16)6=V

50.24(6)=301.59

Answer:

[tex]\frac{1}{12y}[/tex]

Step-by-step explanation:

This is a multiplication problem.

We want to multiply [tex]\frac{9z^3}{16xy}\cdot \frac{4x}{27z^3}[/tex]

We factor to get:

[tex]\frac{9z^3}{4\times 4xy}\cdot \frac{4x}{9\times 3z^3}[/tex]

We now cancel out the common factors to get:

[tex]\frac{1}{4\times y}\cdot \frac{1}{1\times 3}[/tex]

We now multiply the numerators and the denominators separately to get.

This simplifies to [tex]\frac{1}{12y}[/tex]

Therefore the simplified expression is [tex]\frac{1}{12y}[/tex]

9x-7= 29

9x-7+7= 29+7

9x= 36

Divide by 9 for 9x and 36

9x/9= 36/9

x= 4

Check answer by using substitution method

9x-7= 29

9(4)-7=29

36-7= 29

29= 29

Answer is x=4 (second choice)

Answer:

38/9

Step-by-step explanation:

9x - 7 = 29⁰

9x = 38

x = 38/9

The option that describes the Complement A^c is; D: A^c = {x| x ∈ U and x is an even positive integer}

If the Universal set, U = {all positive integers); and

A = {x|x ∈ U and x is an odd positive integer}.

Thus:

The complement of A is the set of the elements of the universal set which are not in A.

If a set is not odd, then it is even.

Thus:

A^c = {x| x ∈ U and x is an even positive integer}

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Answer:

b. 45deg

Step-by-step explanation:

see attached

Answer:

45

Step-by-step explanation:

We are seen with two lines crossing each other and the angle in which a line has is 180 degrees. Also, the angles labeled 3x and x are supplementary angles, which mean they add up to 180 degrees. Using this information, we can set up an equation.

[tex]x+3x=180[/tex]

[tex]4x=180[/tex]

[tex]x=45[/tex]

Answer:

A

Step-by-step explanation:

Nice problem.

The only way you can get an odd number by multiplying two digits together is if they are both odd.

For example 5*7 = 35 which is odd. You cannot find 2 odd numbers that when multiplied will give an even.

That means that A and B are both odd.

Now if you multiply an odd and an even together, you always get an even.

For example 4 * 9 = 36 which is even.

Since A is known to be odd, C must be even. So the four digit number you want ends in C.

The Answer is A

Answer:

Step-by-step explanation:

The aaaa

Answer:

C. Third option

Step-by-step explanation:

C is the correct answer, because the common ratio is a change from one number into the next in a geometric sequence.

Hope this helps!

Answer:

A) 6 tan θ

Step-by-step explanation:

Given Expression:

6 sin θ sec θ

= 6 sin θ (1/cosθ)

= 6 sin θ/cos θ

= 6 tan θ

In the second step, we substituted 1/cos in place of sec because cos and sec are reciprocals of each other.

In the last step, we know used the formula:

sinθ/cosθ  =  tanθ

Answer:

A.

Step-by-step explanation:

sec(x)=1/cos(x)

So you have 6sin(x)*1/cos(x) which gives you 6*sin(x)/cos(x)

Since sin(x)/cos(x)=tan(x)

then you can rewrite this as 6tan(x)

Answer:

[tex](\frac{x}{9})[/tex]¹²

Step-by-step explanation:

The given function is f(x) = 9x⁻¹²

To find the inverse of f(x) we will write the function in a equation form y = 9x⁻¹²

Now we will replace x from y and y from x

x = 9y⁻¹²

Then we will find the value of y

y⁻¹² = [tex]\frac{x}{9}[/tex]

y = [tex](\frac{x}{9})[/tex]¹²

Now y will be replaced by f⁻¹(x)

f⁻¹(x) = [tex](\frac{x}{9})[/tex]¹²

Therefore inverse of the function f(x) is f⁻¹(x) = [tex](\frac{x}{9})[/tex]¹²

Answer:

A - 108 strips

Step-by-step explanation:

1 yard = 36 inches

3 yards = 108 inches.

If Sara cuts 1-inch strips, she will have 108 strips in total.

Hope this helps!

Answer:

A 108 strips

Step-by-step explanation:

1 yd = 3 ft

3 ft = 3 * 12 inches = 36 inches

3 yds = 3 * 36 = 108

If each strip is 1 inch, we can cut 108 1 inch strips

To solve the equation (−6/11) + m = −9/2, you need to isolate the variable m. The solution to the equation is m = −33/22.

To solve the equation (−6/11) + m = −9/2, we need to isolate the variable m.

First, we can start by subtracting (−6/11) from both sides of the equation: m = −9/2 - (−6/11)

Simplify the equation by finding a common denominator: m = −9/2 + 33/11

Combine the fractions: m = −99/22 + 66/22

Finally, add the numerators and keep the common denominator: m = −33/22

Therefore, the solution to the equation is m = −33/22.

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ANSWER

[tex]\cos B = \frac{ \sqrt{3} }{3} [/tex]

EXPLANATION

The given triangle is a right triangle.

It was given that,

[tex]a = 1[/tex]

and

[tex]b = \sqrt{2} [/tex]

Using the Pythagoras Theorem, we can determine the value of c.

[tex] {c}^{2} = {( \sqrt{2} )}^{2} + {1}^{2} [/tex]

[tex] {c}^{2} = 2 + 1[/tex]

[tex]{c}^{2} = 3[/tex]

[tex]c = \sqrt{3} [/tex]

The ratio is the adjacent over the hypotenuse.

[tex]\cos B = \frac{1 }{ \sqrt{3} } [/tex]

We rationalize to get:

[tex]\cos B = \frac{ \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } = \frac{ \sqrt{3} }{3} [/tex]

Answer:

A survey shows that the probability that an employee gets placed in a suitable job is 0.65.

So, the probability he is in the wrong job is 0.35.

The test has an accuracy rate of 70%.

So, the probability that the test is inaccurate is 0.3. 

Thus, the probability that someone is in the right job and the test predicts it wrong is [tex]0.65\times0.3=0.195[/tex]

The probability that someone is in the wrong job and the test is right is [tex]0.35\times0.7=0.245[/tex]

Answer:

.105

Step-by-step explanation:

The probability that he is in the right job is 0.65, so the probability he is in the wrong job is 0.35, and similarly, the probability that the test is inaccurate is 0.3.  Thus, the probability that someone is in the right job and the test is then wrong is 0.65*0.3=.195, and the probability that someone is in the wrong job and the test is wrong is 0.35*.3=.105.

Answer:

7 & 8

Step-by-step explanation:

For this case we propose a system of equations:

x: Variable representing the plant with pink flowers

y: Variable representing the plant with purple flowers

We have as data that:

[tex]x + y = 15\\8x + 5y = 96[/tex]

From the first equation we have to:

[tex]x = 15-y[/tex]

Substituting in the second equation:

[tex]8 (15-y) + 5y = 96\\120-8y + 5y = 96\\-3y = 96-120\\-3y = -24\\y = \frac {-24} {- 3}\\y = 8[/tex]

Arianna bought 8 purple flowers.

Now we have:

[tex]x = 15-8\\x = 7[/tex]

Arianna bought 7 pink flowers.

Answer:

Arianna bought 7 pink flowers.

The solution to the equation is:

x = -0.8404

How to solve the equation?

The equation is given as:

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

Subtract 8 from both sides to get:

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

Square both sides to get:

[tex]\frac{9}{(x - 2)^{2} }[/tex] - [tex]\frac{12}{(x - 2)}[/tex] = (x - 2)

 [tex]\frac{9 - 12(x - 2)}{(x - 2)^{2} }[/tex] = (x - 2)

Multiply both sides by (x - 2)² to get:

9 - 12x + 24 = (x - 2)³

33 - 12x = x³ - 6x² + 12x - 8

x³ - 6x² + 24x + 25 = 0

Let us try x = -0.8404 to get;

(-0.8404)³ - 6(-0.8404)² + 24(-0.8404) + 25(-0.8404) ≈ 0

Thus, - 0.8404 is a root of the polynomial.

Answer:

Approximately 1130 cubic feet.

Step-by-step explanation:

The volume of a cylinder is the area of its base times its height.

The height of this cylinder is given to be 10 feet. What's the area of its base?

The base of a cylinder is a circle. The area of a circle with radius [tex]r[/tex] is equal to [tex]\pi \cdot r^{2}[/tex]. For the base of this cylinder, [tex]r = 6[/tex] feet. The question also dictates that [tex]\pi = 3.14[/tex]. The area of each circular base will thus be:

[tex]\text{Base} = \pi\cdot r^{2} = 3.14 \times 6^{2} = 113.04[/tex] square feet.

The volume of this cylinder will be

[tex]\text{Volume} = \text{Base}\times \text{Height} = 113.04\times 10 \approx 1130[/tex] cubic feet.

Answer:

y = -1/3x +3

Step-by-step explanation:

First we need to find the slope

m = (y2-y1)/(x2-x1)

   = (2-3)/(3-0)

   -1/3

Then we know the y intercept( where it crosses the y axis)

It crosses at y=3

The slope intercept form is

y= mx+b  where m is the slope and b is the y intercept

y = -1/3x +3

Answer:

[tex]y=\frac{-1}{3} x+3[/tex]

Step-by-step explanation:

Let frame the equation of the line using the points given on the graph

(0,3) and (3,2)

Equation of the line is y=mx+b

where m is the slope and b is the y intercept

To find slope we use formula

[tex]slope =\frac{y_2-y_1}{x_2-x_1} =\frac{2-3}{3-0} =\frac{-1}{3}[/tex]

Y intercept b is the point where the graph crosses y axis

y intercept b = 3

The equation y=mx+b becomes

[tex]y=\frac{-1}{3} x+3[/tex]

Answer:

The tower is approximately 381 feet high.

Step-by-step explanation:

Refer to the sketch attached. The height of the tower can be found in two parts:

Each part can be seen as a leg of a right triangle. The other leg is the distance between the building and the tower and is 300-feet long. The angle opposite to the leg is given.

The height of the tower is the sum of the two parts:

[tex]300\cdot \sin{42^{\circ}} + 300\cdot \sin{37^{\circ}} = 300(\sin{42^{\circ}}+\sin{37^{\circ}}) = 381[/tex] feet.

To calculate the height the radio tower, trigonometry is used. The 'tangent' function is employed twice, once each for the angle of elevation and the angle of depression, to find out the distances to the top and bottom of the tower respectively, which are added together to get the total height.

There are two triangles formed in this problem, one from the observer's line of sight upwards to the top of the radio tower and one downwards to the bottom of the tower. The radio tower is the side that the two triangles share.

We can find the distance to the top and to the bottom of the tower separately using trigonometry, which is based on understanding of angle of elevation and angle of depression.

The height to the top of the tower can be found using the tangent of the angle of elevation (42°), which is the opposite side (height of the tower) divided by the adjacent side (distance from the tower):
height_to_top = tan(42°) * 300 feet.

The height to the bottom of the tower can be found using the tangent of the angle of depression (37°):
height_to_bottom = tan(37°) * 300 feet.

So, the overall height of the radio tower is the sum of these two heights.

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Answer: I think c but I am not sure

Step-by-step explanation: Hope this helps

[tex]\bf -\cfrac{1}{x-9}-\cfrac{-2}{x+7}\implies -\cfrac{1}{x-9}+\cfrac{2}{x+7}\implies \cfrac{2}{x+7}-\cfrac{1}{x-9}\impliedby \stackrel{\textit{our LCD is}}{(x+7)(x-9)} \\\\\\ \cfrac{(x-9)2~~-~~(x+7)1}{(x+7)(x-9)}\implies \cfrac{2x-18~~-~~x-7}{(x+7)(x-9)}\implies \cfrac{x-25}{(x+7)(x-9)}[/tex]

35/14

or

5/2

keep switch flip

Answer:

Step-by-step explanation:

57÷27=?

Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes

57×72=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

5×77×2=3514

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 35 and 14 using

GCF(35,14) = 7

35÷714÷7=52

The fraction

52

is the same as

5÷2

Convert to a mixed number using

long division for 5 ÷ 2 = 2R1, so

52=212

Therefore:

57÷27=21/2

Answer:

Step-by-step explanation:

The volume is increased by a fator of 8.  (unit³)

Then the length of all edges is increased by factor ∛8 = 2. (unit)

Therefore the surface area is increased by a factor 2² = 4. (unit²)

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{-5}{ k})\qquad \qquad radius=\stackrel{4}{ r}\\[2em] [x-3]^2+[y-(-5)]^2=4^2\implies (x-3)^2+(y+5)^2=16[/tex]

Answer: THE ANSWER IS (B)

Step-by-step explanation:

Answer:

b ≠ - 1

Step-by-step explanation:

The denominator of the rational expression cannot be zero as this would make it undefined.

Equating the denominator to zero and solving gives the value that b cannot be.

solve

5b + 5 = 0 ( subtract 5 from both sides )

5b = - 5 ( divide both sides by 5 )

b = - 1 ← excluded value