find the volume of this triangular prism

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given exponential function

STEP 2: Compare with the standard exponential function to determine whether it shows growth or decay.

If a is positive and b is greater than 1 , then it is exponential growth.

If a is positive and b is less than 1 but greater than 0 , then it is exponential decay.

Hence, the given function shows an exponential decay.

STEP 3: Graph the values by using a table of values

We generate a table of values first

STEP 4: Plot the graph of the data values

Answer: Multiply 102 by 8.82 = 899.64x

Answer:

y = -1/2x + 6.

Step-by-step explanation:

The line perpendicular to y = 2x + 3 has slope of - 1/2 so we can write it as

y = -1/2x + c

When x = -4, y = 8 so we substitute:

8 = -1/2 (-4) + c

8 = 2 + c

c = 8-2 = 6

So, the answer is

y = -1/2x + 6.

Answer:

y = -1/2x + 6.

Step-by-step explanation:

Problem

Juanita wants to buy a computer. She needs to earn at least 400 dollars. If she makes 9 dollars an hour and has already saved 40 dollars, how many hours does she need to work?

Solution

Let x the number of hours required we can set up the following inequality:

40 + 9x > 400

And now we can solve for x we can subtract 40 and we got:

9x > 360

And then we got:

x> 40

So then Juanita needs to work at least 40 hours

And the graph of the inequality is given by:

The club has to send 57 coupons to existing members.

Given,

The number of coupons sent out by a new club to boost sales for next year's membership = 152

They provide 3 times as many to potential members than to existing members

We have to find the number of coupons they send to existing members;

Here,

x be the number of coupons to existing members.

Then,

3x = 152

Now,

x = 152/3 = 50.66 ≈ 57

That is,

The club has to send 57 coupons to existing members.

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Class rings are sold by a nearby jewelry store, which buys them for $60 each. The amount of markup is y=204.

Given that,

Class rings are sold by a nearby jewelry store, which buys them for $60 each. The ring has a name and date engraved on it, and the retailer markup it up by 340% before selling it.

We have to find the equation that can be used to find the amount of markup y.

So,

We can write the equation as

Amount of markup=340% of the purchases amount

Taking amount of the markup as y and purchases amount is $60.

y=340%×60

y=340/100×(60)

y=34×6

y=204

Therefore, The amount of markup is y=204.

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Answer:

[tex]\sf 12-5x+6x=4[/tex]  (Given)

[tex]\sf 12+x=4[/tex]  (Combine like terms)

[tex]\sf x=-8[/tex]  (Subtraction property of equality)

--------------------------------------------------

Hope this is what you're looking for!

Answer:

1. given

2. combine like terms,

3. subtraction property of equality

Step-by-step explanation:

Answer:

3 5/14 (second choice)

Step-by-step explanation:

c = -3 1/7

d = 6.5 (6 1/2 as fraction)

-3 1/7 as improper fraction: -22/7

6 1/2 as improper fraction: 13/2

Now put both fractions into a common denominator

-22/7 = -44/14

13/2 = 91/14

Now add:

-44/14 + 91/14 = 47/14

Change 47/14 back to fraction

47/14 = 3 5/14

In an observational study, we measure or survey members of a sample without trying to affect them. In an experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.

This is clearly an observational study

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The cost for a year is cheaper in the Gym A than Gym B. The value of k for the cheaper membership would be; $10.

An equation is an expression that shows the relationship between two or more numbers and variables. A linear equation is an equation that increases at a constant rate.

An equation in the form y = kx is called a linear equation.

In the equation of form y = kx

y = dependent variable which is the total cost

x = number of months

k = constant of proportion / cost per month

Thus k = y/x

The Cost per month at Gym A = $50 / 5 = $10

The Cost per month at Gym B = $40 / 3 = $13.33

The Membership cost at Gym A for a year = $10 x 12 = $120

The Membership cost at Gym B for a year = $13.33 x 12 = $160

Hence, The cost for a year is cheaper in the Gym A than Gym B. The value of k for the cheaper membership would be; $10.

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Answer: the measure of H is 39 the measure of G is 51

Step-by-step explanation:

6x-15+3x+6=90

9x-9=90

9x=99

x=11

6(11)-15=51

3(11)+6=39

The unknown angles are as follows:

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, linear angles, alternate angles etc.

Therefore,

∠1 = 110 degrees

∠2 = 180 - 110 (sum of angles on a straight line)

∠2 = 70°

∠3 = ∠1 (vertically opposite angles)

Vertically opposite angles are congruent. vertically opposite angles share the same vertex

Therefore,

∠3 = 110°

∠2 = ∠4 (vertically opposite angles)

∠4 = 70°

∠1 = ∠5 (corresponding angles)

Corresponding angles are congruent

∠5 = 110°

∠6 = ∠4(alternate angles)

Alternate angles are congruent.

∠6 = 70°

∠1 = ∠7 (alternate exterior angles)

∠7 = 110°

∠2 = ∠8(alternate exterior angles)

∠8 = 70°

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The blue ribbon is 2.2 times longer than the orange ribbon

From the information given, we have that;

Now, lets convert the mixed fractions to improper fractions;

Length of orange ribbon = 95/12

Length of blue ribbon = 209/12

The ratio is expressed as;

Length of blue ribbon/length of orange ribbon

Substitute the values, we have;

= 209/12 ÷ 95/12

Take the inverse of the divisor and multiply

= 209/ 12 × 12/95

= 2. 2 times

Hence, it is 2.2 times longer.

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Step-by-step explanation:

[tex] \frac{5}{6} (a) - 3 = \frac{5}{8} \\ lcd = 48 \\ \\ \frac{5}{6} (a)(48) - 3(48) = \frac{5}{8} (48) \\ 40a - 144 = 30 \\ 40a = 30 + 144 \\ 40a = 174 \\ \frac{40a}{40} = \frac{174}{40} \\ a = 4\frac{14}{40} \\ a = 4 \frac{7}{20} [/tex]

I FIRST FOUND THE LCD AFTER THAT MULTIPLY EACH AND EVERY TERM IN THE EQUATION BY IT TO HET RID OF THE FRACTIONS AND SOLVE FOR a.

Answer:

The answer to your question is: 6 units

Step-by-step explanation:

Data

A (-4, 0)

B (-3,1)

C (0,-2)

D (-1,-3)

Formula

d = √((x2 - x1)² + (y2 - y1)²)

Process

dAB = √((x2 - x1)² + (y2 - y1)²)                 dAC = √((0 + 4)² + (-2 + 0)²)

      = √((-3 + 4)² + (1 - 0)²)                      dAC = √((4)² + (-2)²)

      = √((1)² + (1)²)                                    dAC = √(16 + 4)

      = √1 + 1                                             dAC = √20

dAB = √2  = dCD

dAD = √((-1 + 4)² + (-3 - 0)²)                    

dAD = √((3)² + (-3)²)

dAD = √9 + 9

dAD = √18 = dBC

reactangle's area = base x height = √18 x √2 = √18 x 2 = √36

                                                       = 6 units

Our strategy to win $200 is to use $100 in just one chance. It is the best bet for winning $200.

Given that we start with $100 at a casino and can bet any amount of that particular money to play a game to any amount of times where we have a 40% chance of winning in each game. If we win, we will gain the amount we bet and return the amount that we bet. If we lose, we will lose our bet.

It has been asked that what should be our strategy to win get $200.

We can write from the given information that:

Probability of wining = 40 % = 0.4

Probability of losing = 1 - 0.4 = 0.6

The best bet to win $200 is to bet $100 in one go itself.

For the above bet chance of winning $100 is 0.4

But let us assume that we are betting $50 two times,

Then L-Lose and W-Win

There will be 4 rational possible cases (WW,WL,LW,LL)

Probability of all the 4 above given cases will be as follows:

Probability of (WW) = 0.4 X 0.4 = 0.16

Probaility of (WL) = 0.4 X 0.6 = 0.24

Probability of (LW) = 0.6 X 0.4 = 0.24

Probability of (LL) = 0.6 X 0.6 = 0.36

Now for winning $100 we need to win both the bets of $50.

But the probability of winning both the bets = 0.16 ( very less than 0.4)

Hence the best bet would be to use $100 in one chance itself.

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Our strategy to win $200 is to use $100 in just one chance. It is the best bet for winning $200.

It has been asked that what should be our strategy to win get $200.

We can write from the given information that:

Probability of wining = 40 % = 0.4

Probability of losing = 1 - 0.4 = 0.6

The best bet to win $200 is to bet $100 in one go itself.

For the above bet chance of winning $100 is 0.4

But let us assume that we are betting $50 two times,

Then L-Lose and W-Win

There will be 4 rational possible cases (WW,WL,LW,LL)

Probability of all the 4 above given cases will be as follows:

Probability of (WW) = 0.4 X 0.4 = 0.16

Probability of (WL) = 0.4 X 0.6 = 0.24

Probability of (LW) = 0.6 X 0.4 = 0.24

Probability of (LL) = 0.6 X 0.6 = 0.36

Now for winning $100 we need to win both the bets of $50.

But the probability of winning both the bets = 0.16 ( very less than 0.4)

Hence the best bet would be to use $100 in one chance itself.

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The distance between the two points is 10 units and the slope of the line is -78/25

To find the distance between two points, we can simply use the formula of distance between two which is given as

[tex]d=\sqrt{(y_2-y_1)^2 + (x_2 - x_1)^2}[/tex]

Let's substitute the values and solve for the distance.

[tex]d=\sqrt{(y_2-y_1)^2 + (x_2 - x_1)^2}\\d = \sqrt{(1-7)^2 + (-3 - 5)^2} \\d = 10[/tex]

2)

The slope of the line can be found using the two points given.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\[/tex]

let's substitute the values and solve.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\\\m = -\frac{78}{25}[/tex]

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It is a completely randomized design.

What is completely randomized design ?

Completely randomized designs are used in experiment design to explore the effects of a single primary factor without taking additional nuisance variables into account. This article describes single-factor, entirely randomized designs. On the basis of the various levels of that primary factor, the experiment compares the values of a response variable. The levels of the main factor are given at random to the experimental units in fully randomized designs.

Objects or subjects are assigned to groups in a completely random design at random. Labeling each subject before choosing from the labeled participants in a table of random numbers is one common practice for allocating subjects to treatment groups. Computers can be used to accomplish this as well.

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The measure of the acute angles in the triangle are 7.5 and 82.5

From the question, we have the following parameters:

One acute angle is 11 times the measure of the other acute angle.

Let the acute angles be x and y

Such that

y = 11x

The sum of the acute angles in a right triangle is 90

So, we have

x + y = 90

This gives

x + 11x = 90

So, we have

12x = 90

Divide by 12

x = 7.5

Recall that y = 11x

So, we have

y = 11 x 7.5

Evaluate

y = 82.5

Hence, the acute angles are 7.5 and 82.5

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Answer:

it would be 89

Step-by-step explanation:

The number of hours ago was the temperature 0 degrees is 6 hours.

Temperature simply means the degree if hotness and coldness in a body.

In this case, the temperature has been dropping 2 1/2 degrees every hour. Let the number of hours be h.

This will be illustrated as:

-15 = -2.5h

where h = number of hours

Divide

h = -15 / -2.5

h = 6

Therefore, the correct option is 6 hours.

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Answer:

5;3

Step-by-step explanation:

The total pounds of apples that Chris must pick before Pam’s orchard is cheaper that David's is 14.

The first step is to determine the total cost of picking apples from both orchards.

Cost of picking apples from David's Orchard : (10 x $2) + [(x - 10) x $1]

$20 + $x - $10

= $10 + $x

Cost of picking apples from Pam's Orchard : $10 + ($10 x $1.5) + [(x - 10) x 0.75]

$10 + $15 + 0.75x - 7.5

= $17.50 + 0.75x

When  Pam's Orchard is cheaper, the equation becomes :

$10 + $x  > $17.50 + 0.75x

$x - 0.75x > $17.50 - $10

0.25x > $7.50

x > $7.50 / 2.5

x > 3

Total pounds should be greater than 3, so it can be 4.

Total pounds = 10 + 3 = 14

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Answer:

6.5°

Step-by-step explanation:

We know that both XYZ and LMN are complementary angles.

Complementary angles add up to 90°.

So,

we can simply add both of the expressions and set it equal to 90 (degrees).

(3x+14) + (5x+24) = 90

-> add the variables and constants

8x+38=90

-> subtract the 38 from both sides (90-38)

8x=52

-> divide out the coefficient to isolate the variable

x=6.5

So, the answer is 6.5 degrees.

Hope this helped :)

The equation that represents the value of d is d = b + kc

The graph that completes the question is added as an attachment

The equation of the graph is given as

y = kx

Because the graph shows a direct variation, the equation can be illustrated as

y = mx

Where m represents the slope of the line

By comparing the equation y = mx and y = kx, we can conclude that

m = k

This means that the slope of the equation y = kx is k

From the graph, we have the points

(x, y) = (a, b) and (a + c, d)

The slope of a line is calculated using

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

Slope = k

(x₁, y₁) = (a, b) and (x₂, y₂) = (a + c, d)

So, we have

k = (d - b)/(a + c - a)

Evaluate the like terms

k = (d - b)/(c)

Multiply both sides by c

d - b = kc

Add b to both sides

d = b + kc

Hence, the value of d is d = b + kc

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Answer: 25 + 12.5v ≥ 170

Step-by-step explanation:

We already have the 25 reward points; it also gives the information that she gets 12.5 points for each visit. Because we don't know the amount she has gone to the theater or will go we have to use a variable; 12.5v. When we add them, we get 25 + 12.5v. The inequality we use is ≥ because it says "at least". When this is used that means it has to be equal to or greater and that is why use that sign and get the full equation;

5 + 12.5v ≥ 170

Answer:

55

Step-by-step explanation:

The cost of each ticket is 8.9 dollars.

What is cost price?

In mathematics, the term cost price can be explained with the help of profit which states, as the amount which is on the commodity and in the form of standard price called cost price. For the profit, the amount of the commodity can be designed by the shopkeeper which is bigger amount as per the cost price.

According to the question, the Jason bought 4 tickets for basket ball game. He paid a total cost of $42.10 for the tickets and for parking as $6.50

The paid amount for the 4 tickets is: $42.10.

And the parking cost is: $6.50

Total cost price without parking is: $42.10 - $6.50 = $35.60

Therefore, to calculate the cost of each ticket is: 35.60/4 = 8.9 dollars

Hence, the cost of each ticket is 8.9 dollars.

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Two day growth factor for the height of the sun flower is 1.1449

Take the current number and subtract it from the prior value to determine the growth rate. The growth rate is then expressed as a percentage by multiplying the difference by the previous number and dividing by 100.

A height increases by 7% per day

So the growth factor for height of sun flower is  107/100 =1.07

For 2.7 days - 12 inch

3.74 days increase by 7% by day

⇒ 12 + 7/100 x 12

⇒ 12 ( 107/100 )

⇒ 12.84 inches

3.74 days 12.84 inches

4.74 days increase by 7 % by day

⇒ 12.84 + 7/100 x 12.84

⇒ 12.84 x 107/100

⇒ 13.73 inches

Two days growth factor

⇒ 107/100 x 100/107

⇒ 1.1449

Hence Two day growth factor for the height of the sun flower is 1.1449

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