The number 84 can be expressed as the sum of 54 + 30. Which shows how to use the distributive property to rewrite that sum as a multiple of a sum whose addends have no common factors greater than 1?
A. 2(27 + 15)
B. 3(18 + 10)
C. 5(11 + 6)
D. 6(9 + 5)

Answer:

Evelyn can drive 990 miles so her monthly car expenses are no more than $260

Step-by-step explanation:

Set up an equation:

151 + 0.11 ≤ 260

Subtract 151 from both sides.

0.11 ≤ 109

Divide both sides by 0.11.

x ≤ 990.909091

The question said to round your answer down so the budget doesn't exceed, therefore the answer would be 990 miles.

Based on the information given in the advertisement, we can conclude that the sale price of the table is $420.

Here's how we can arrive at this answer:

Let the original price of the table be represented by P.

We know that the sale price of the table is obtained by reducing the original price by 30%. Mathematically, this can be represented as:

Sale price = P - 0.3P

Simplifying this expression, we get:

Sale price = 0.7P

We are also given that the sale saves us $180 on this table. Mathematically, this can be represented as:

0.7P - P = -$180

Simplifying this expression, we get:

-0.3P = -$180

Dividing both sides by -0.3, we get:

P = $600

Therefore, the original price of the table was $600.

Using the equation for sale price that we derived earlier, we can now find the sale price of the table:

Sale price = 0.7P = 0.7 x $600 = $420

Hence, the sale price of the table is $420.

The value of x that makes the relation a function is 3.

Option A is the correct answer.

We have,

A = (5, 3), (4, 9), (7, 2), (x, 6)

Given the points (5, 3), (4, 9), (7, 2), and (x, 6), we need to ensure that x does not repeat in the relation.

If we substitute the given values of x (3, 4, 5, 7) into the relation, we find:

For x = 3: (3, 6)

For x = 4: (4, 6)

For x = 5: (5, 6)

For x = 7: (7, 6)

Now,

A function can not have the same output for the same input.

So,

(4, 6) and (4, 9) are not possible.

(5, 6) and (5, 3) are not possible.

(7, 6) and (7, 2) are not possible.

And,

(3, 6) is possible

Thus,

The value of x that makes a function is 3.

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The given exponential function f(t) = 34000 (1/2)^ (t/12) can be written in the form f(t) = a b^(t) as f(t) = 34000 (0.94387)^t.

Given exponential function is,

f(t) = 34000 (1/2)^ (t/12)3

We have to write this function in the form f(t) = a b^(t).

The given function needs the variable t only in the exponent.

So f(t) can be written as,

f(t) = 34000 [(1/2)^(1/12)]^(t), which has only t in the exponent.

Comparing the given form and the given function, it is clear that,

a = 34,000

b = (1/2)^(1/12) = 0.94387

So the function can be written as,

f(t) = 34000 (0.94387)^t

Hence the function can be written as f(t) = 34000 (0.94387)^t.

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Answer:

Step-by-step explanation:

The answers are:

furthered explained below

A dot plot is a graphical display of data using dots. A good example would be the choice of foods that you and your friends ate for snacks. The illustration below shows a plot for a random sample of integers. Simple plot showing the types of foods a group of friends eats.

(a).

To know the shape of the plots, we will compare the plot with the following figures:

Therefore, for each group, we get:

River otters: Symmetric

Sea otters: Negative skewness

(b).

The river otters have weights that are around 10 and 26 lbs and the majority of the sea otters have weights around 38 and 64 lbs.

Therefore, the plot with the larger center is the plot for the sea otters and it means that the sea otters are heavier than the river otters.

(c).

The outliers are those dots that are too far from the majority of the data. In this case, there are outliers in the plot of the sea otters because we can consider the three dots located at 8, 10, and 12 lbs as outliers.

We can say that these outliers represent the weight of the baby otters. That's why they are smaller than the others.

(d).

We can see the spread as the extension of the dots in the number line. In the first case, the dots go from 10 to 26. However, in the second plot, the dots go from 8 to 64.

Since the difference of 64 and 8 is greater, we can say that the sea otters' plot has a larger spread.

(e).

Since there are outliers in the second plot, the spread is greater because they are too far from the other points. So, the outliers increase the spread of the data.

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The option that shows the inverse's graph (with the correspondent domain and range) is option a.

Remember that for a function:

f(x) = y

The inverse f⁻¹(x) is defined as:

f⁻¹(y) = x

Here the original function is defined by the relation:

x: -1,  1,  3, 5, 7

y: 4, 2, 1, 0, 1

Then for the inverse function, the domain and range are:

x: 4, 2, 1, 0, 1

y: -1, 1, 3, 5, 7

Then the domain is 0 ≤ x ≤ 4

And the range is -1 ≤ y ≤ 7

the option with these two is a, so that is the correct option.

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Answer:

Step-by-step explanation:

The median of the original list is 10. After adding 20, the new median is 15. Thus, the median has increased by 5.

The subject of this question is Mathematics, specifically a concept within statistics known as the median. To find the median of a set of numbers, you first need to sort the numbers from smallest to largest. Once sorted, the median is the middle number. If there is an even number of observations, the median is then calculated as the average of the two middle numbers.

Let's first figure out the median of the original list, which when sorted is 2, 4, 10, 21, 26. The middle number here, the median, is 10.

Then we add 20 to the list, which then is 2, 4, 10, 20, 21, 26. For an even number of observations, we find the average of the two middle numbers, thus, (10+20)/2 = 15.

So, by adding 20 to this list, the median moves from 10 to 15, an increase of 5.

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Answer:

4 cm

Step-by-step explanation:

Step: 1

Consider a circle inscribed in an isosceles triangle with legs of length 13cm and a base length of 10cm.

Step: 2

Draw-in altitude AD will pass through the center  O and bisects the base into two segments each in 5cm length.

So the triangle is isosceles so the segment BD is 6cm.

Draw in radius OB and radius OA  and length of  OD as h.

Refer to the attachment for step 3 and step 4

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a) h(t) = 200 - 4.9t²

b) it takes 6.39 seconds for the stone to reach the ground.

c) The stone strikes the ground with a velocity of -62.62 m/s.

d) It would take 14.37 seconds.

(a) The height of the stone, h(t), at time t can be determined using the formula for the position of an object under constant acceleration:

h(t) = h0 + v0t + (1/2)gt²

Here initial height= 200 m

initial velocity = 0 m/s

g= -9.8 m/s², and t is the time in seconds.

So, the equation becomes:

h(t) = 200 + 0t + (1/2)(-9.8)t²

h(t) = 200 - 4.9t²

(b) To find the time it takes for the stone to reach the ground, we set h(t) = 0 and solve for t:

0 = 200 - 4.9t²

4.9t² = 200

t² = 200/4.9

t² ≈ 40.82

t ≈ √40.82

t ≈ 6.39 seconds

Therefore, it takes 6.39 seconds for the stone to reach the ground.

(c) The velocity of the stone just before it strikes the ground can be found using the formula for final velocity:

v(t) = v0 + gt

In this case, the initial velocity (v0) is 0 m/s and the acceleration due to gravity (g) is -9.8 m/s². So:

v(t) = 0 + (-9.8)t

v(t) = -9.8t

v(6.39) = -9.8 * 6.39

v(6.39) ≈ -62.62 m/s

Therefore, the stone strikes the ground with a velocity of -62.62 m/s (negative sign indicates it is moving downward).

(d) If the stone were thrown downward with a speed of 7 m/s,

the initial velocity (v0) would be -7 m/s (

We can use the same formula as in part (b) to find the time it takes to reach the ground:

0 = 200 - 7t + (1/2)(-9.8)t²

9.8t² - 7t - 200 = 0

t ≈ 14.37 seconds

t ≈ -1.42 seconds (extraneous solution, as time cannot be negative in this context)

Therefore, it would take 14.37 seconds for the stone to reach the ground if thrown downward with a speed of 7 m/s.

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Answer:

The answer for the width of the building is 5m

Step-by-step Explanation:

3cm=1m

15cm=x

cross multiply

x×3=15×1

3x=15

divide both sides by 3

3x/3=15/3

x=5m

The volume of the pyramid is 18069333.33 cubic units

The area of the surface is 313280 square units

The volume of the pyramid is solved using the formula

= 1/2 * base area * height

Where

base area = 440 * 440 = 193600

height = 280

volume of the pyramid = 1/3 * 193600 * 280

volume of the pyramid = 18069333.33 cubic units

The surface area

The surface area is calculated using the formula

= 4 *  area of the triangles

= 4 * 1/2 * 440 * 356

= 313280 square units

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To determine the area of the figure accurately, we need more information or a description of the figure. The measurements provided (4 cm, -3 cm, 8 cm, 6 cm) do not provide enough details to calculate the area. Please provide additional information or a description of the figure so that I can assist you in finding the closest measurement to its area.

The correct option is C. (2, 1).

Given equations:

y = 6x - 11

2x + 3y = 7

We'll start by solving equation 1) for y:

y = 6x - 11

Now, substitute this value of y into equation 2):

2x + 3(6x - 11) = 7

Simplify the equation:

2x + 18x - 33 = 7

20x - 33 = 7

Add 33 to both sides:

20x = 40

Divide both sides by 20:

x = 2

Now, substitute the value of x back into equation 1) to find y:

y = 6(2) - 11

y = 12 - 11

y = 1

Therefore, the solution to the system of equations is (x, y) = (2, 1).

The marginal revenue when 20 units are sold is approximately $24.877.

To find the marginal revenue when 20 units are sold, we need to calculate the derivative of the revenue function with respect to the number of units (x) and then evaluate it at x = 20.

The revenue function is given by R(x) = 25x - 0.003x^2.

The definition of the derivative of a function f(x) is:

f'(x) = lim(h->0) [f(x+h) - f(x)] / h

Let's apply this definition to find the derivative of the revenue function:

R'(x) = lim(h->0) [R(x+h) - R(x)] / h

Substituting the revenue function R(x) = 25x - 0.003x^2:

R'(x) = lim(h->0) [(25(x+h) - 0.003(x+h)^2) - (25x - 0.003x^2)] / h

Expanding and simplifying the expression inside the limit:

R'(x) = lim(h->0) [25x + 25h - 0.003x^2 - 0.003h^2 - 0.006xh - 0.003h] - 25x + 0.003x^2) / h

Canceling out the common terms:

R'(x) = lim(h->0) (25h - 0.003h^2 - 0.006xh - 0.003h) / h

Factoring out h from the numerator:

R'(x) = lim(h->0) h(25 - 0.003h - 0.006x - 0.003) / h

Canceling out h:

R'(x) = lim(h->0) 25 - 0.003h - 0.006x - 0.003

Taking the limit as h approaches 0:

R'(x) = 25 - 0.006x - 0.003

Simplifying:

R'(x) = -0.006x + 24.997

Now, to find the marginal revenue when 20 units are sold, we substitute x = 20 into the derivative:

R'(20) = -0.006(20) + 24.997

Calculating:

R'(20) = -0.12 + 24.997

R'(20) ≈ 24.877

Therefore, the marginal revenue when 20 units are sold is approximately $24.877.

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Randall's conversion is incorrect because centimetre value cannot be less than the meter value for an equivalent measurement.

Both meters and centimeters are used to measure the length of distances or objects. As distances becomes longer, the use of meters would be more preferable as they can represent this distances with smaller values than centimeters.

100 cm = 1 m

Therefore,

40 cm = (40/100) m

40cm = 0.4 m

This shows that centimeters values cannot be greater than equivalent meter values .

Hence, Randall is incorrect .

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Answer:

The formula for radioactive decay is:

N = N₀ * (1/2)^(t/T)

where:

N₀ = initial amount

N = remaining amount

t = time elapsed

T = half-life

Let's plug in the given values:

N₀ = 20 g

N = 15 g

T = 1620 years

15 = 20 * (1/2)^(t/1620)

Dividing both sides by 20:

0.75 = (1/2)^(t/1620)

Taking the logarithm base 1/2 of both sides:

log(0.75) = t/1620 * log(1/2)

Solving for t:

t = log(0.75) / log(1/2) * 1620

t ≈ 623 years

Therefore, it will take approximately 623 years for a 20 g sample of Radium to decay to 15 g.

Step-by-step explanation:

Answer:

B. $750

Step-by-step explanation:

600÷100=6

720÷120=6

840÷140=6

so the difference between all of them is x6

this means we times 125 by 6

125×6=750

Answer: B. $750

Step-by-step explanation:

     If all of the apartments are proportional by the dollar to the area, we will find the constant of proportionality by dividing.

           $600 / 100 m² = 6 $/m²

     Next, we will multiply the area of apartment 3 by this value to find the rent dollar amount.

           125 m² * 6 $/m² = $750

The range of the cost of their family grocery bill is $119.91.

The range of the cost of the Michaels family grocery bill can be calculated by finding the difference between the highest and lowest values.

In this case, the highest value is $176.97, and the lowest value is $57.06.

Range = Highest value - Lowest value

Range = $176.97 - $57.06

Range = $119.91

Therefore, the range of the cost of their family grocery bill is $119.91.

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Answer:

∠ x = 58°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠  BAD is an exterior angle of the triangle , then

x + 56° = 114° ( subtract 56° from both sides )

x = 58°

Answer:

7

Step-by-step explanation:

The probabilities for the size of homes that future buyers will desire are as follows:

2BR: 0.10 or 10%

3BR: 0.35 or 35%

4BR: 0.30 or 30%

5BR: 0.15 or 15%

6BR: 0.10 or 10%

We have,

To determine the probabilities for the size of homes that future buyers will desire, we can use the information provided in the table.

Let's calculate the probabilities for each size of home:

Probability of purchasing a 2BR home: 10%

Probability of purchasing a 3BR home: 35%

Probability of purchasing a 4BR home: 30%

Probability of purchasing a 5BR home: 15%

Probability of purchasing a 6BR home: 10%

To find the probabilities, we divide each percentage by 100:

Probability of purchasing a 2BR home: 10% / 100 = 0.10

Probability of purchasing a 3BR home: 35% / 100 = 0.35

Probability of purchasing a 4BR home: 30% / 100 = 0.30

Probability of purchasing a 5BR home: 15% / 100 = 0.15

Probability of purchasing a 6BR home: 10% / 100 = 0.10

Therefore,

The probabilities for the size of homes that future buyers will desire are as follows:

2BR: 0.10 or 10%

3BR: 0.35 or 35%

4BR: 0.30 or 30%

5BR: 0.15 or 15%

6BR: 0.10 or 10%

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Answer: D (√x < 2)

Explanation: In interval notation, it reads:

0 < x < 4

It goes from 0 to 4.

Answer:

the answer is 60

Step-by-step explanation:

The instantaneous velocity of the coin, from the first derivative of the height function of the coin, is; v(2) = -20 m/s

The derivative of a function is the rate at which the function is changing with regards to the input variable, at a point within the domain of the function.

The height of the tower = 100 m

The function for the height of the coin is; h(t) = 100 - 5·t²

The instantaneous velocity of the coin is the rate of change of the height with respect to time, which is obtained from the derivative of the height function as follows;

The instantaneous velocity; v(t) = h(t)/dt = d(100 - 5·t²)/dt = -10·t

The instantaneous velocity for the coin at t = 2 seconds is therefore;

v(2) = -10 × 2 = -20

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Answer:

y = 36

Step-by-step explanation:

given y varies directly  with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition when x = 5 , y = 15

15 = 5k ( divide both sides by 5 )

3 = k

y = 3x ← equation of variation

when x = 12 , then

y = 3 × 12 = 36

Answer:To find the area of the table in terms of x, we can use the formula for the area of a rectangle: A = length * breadth. Substituting the given values, we get:

A = (√x+6) * (√x+5)

To simplify this expression, we can use the distributive property and the product rule of square roots:

A = √x * √x + √x * 5 + 6 * √x + 6 * 5 A = x + 5√x + 6√x + 30 A = x + 11√x + 30

This is the area of the table in terms of x.

To find the area of the table if x = 1.5, we can substitute x with 1.5 in the simplified expression and evaluate:

A = 1.5 + 11√1.5 + 30 A ≈ 1.5 + 11 * 1.225 + 30 A ≈ 1.5 + 13.475 + 30 A ≈ 44.975

Therefore, the area of the table if x = 1.5 is approximately 44.975 square units.

Step-by-step explanation:

The perimeter of the classroom in feet is 90 feet.

We are given that;

The corners of the classroom are (−12, 15), (−12, −9), (9, 15), and (9, −9).

Now,

Using the given coordinates, we can find the length and width of the rectangle. The length of the rectangle is the difference between the y-coordinates of two opposite corners, which is 15 - (-9) = 24 feet. The width of the rectangle is the difference between the x-coordinates of two opposite corners, which is 9 - (-12) = 21 feet.

P = 2(24 + 21) = 90 feet

Therefore, by the perimeter the answer will be 90 feet.

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