The area of a trapezoid with bases b₁ and b₂ and height his (b₁
+ b₂)h. Mrs. Barker's
classroom has a table with a trapezoid-shaped top. The trapezoid has bases 4 feet and 2 feet
and height 3 feet.
What is the area of the tabletop?

Answer:

12

Step-by-step explanation:

The figure is a right triangle with hypotenuse = QS

The  base from the graph = 4 units
(or you can just subtract the x-coordinates 2 - (-2) = 4)

The height from the graph is 3 units
(Or you can subtract the y-coordinates: 1 - (-2) = 3)

Since this is a right triangle the square of the hypotenuse = sum of squares of the other two sides

QS² = 3² + 4² = 9 + 16 = 25

QS, the hypotenuse = √25 = 5

The perimeter = sum of the sides = 3 + 4 + 5 = 12 units

The system of inequalities for the graph is

a) y < 3x - 4

b) y = x + 3

Given data ,

Let the inequality equations be represented as A and B

where

Let the first point be P ( 0 , 3 )

Let the second point be Q ( -3 , 0 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 3 - 0 ) / ( 0 + 3 )

m = 1

Now , equation of line is y - y₁ = m ( x - x₁ )

y - 0 = 1 ( x + 3 )

y = x + 3

And , the second equation is

Let the first point be R ( 0 , -4 )

Let the second point be S ( 2 , 2 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( -4 - 2 ) / ( 0 - 2 )

m = -6/-2

m = 3

Now , equation of line is y - y₁ = m ( x - x₁ )

y - 2 = 3 ( x - 2 )

Adding 2 on both sides , we get

y = 3x - 4

Since , it is a dotted line ,

y < 3x - 4

And , the solution to the inequality is point of intersection

where A ( 3.5 , 6.5 ) is the solution

Hence , the inequality equations are solved and A ( 3.5 , 6.5 ) is the solution

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163. The distance between A(-5, 6) and B(5, -5) is: AB ≈ 14.9 units

164. Applying the Pythagorean theorem, we have: Diagonal ≈ 21.2 ft.

165. Marissa's final answer is wrong. It should be, c = √676 = 26 units.

166. Missing side = 29 ft.

The Pythagorean theorem states that c² = a² + b², given that a and b are shorter legs and c is the hypotenuse or longest leg of the right triangle.

163. The distance between A(-5, 6) and B(5, -5):

AB = √[(5−(−5))² + (−5−6)²]

AB = √221

AB ≈ 14.9 units

164. Apply the Pythagorean theorem to find the diagonal:

Diagonal = √(15² + 15²) ≈ 21.2 ft.

165. The answer Marissa got is wrong. The final answer which is the square root of 676 is:

c = √676 = 26 units.

166. Missing side = √(20² + 21²) = 29 ft.

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Answer:

60 ft^2

Step-by-step explanation:

To get the total volume we will need to multiply all the lengths. This means we will have to do 4 x 3x 5.

4 x 3 x 5 = 15x 4 = 60

Answer:

60 ft³

Step-by-step explanation:

V = 4 ft × 3 ft × 5 ft

V = 12 ft² × 5 ft

V = 60 ft³

The length of side A, in centimeters is 12. Option A

To determine the value, we need to know that;

When two sides of a figure are equal in length, that is in (measure).

For example in a square all sides are equal in length so they're all corresponding measurements.

From the information given, we have that;

Side A corresponds to 24 cm

Length 6 cm corresponds to Length 12 cm

The given parameters can be represented mathematically as;

A/24 = 6/12

cross multiply the values, we have;

12A = 6(24)

Multiply the values

12A = 144

Divide by the coefficient, we have;

A = 12 centimeters

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The correct answer is, A (aka 12)

Divide the total number of blocks by the total number of storage containers.

5144/8 = 643 blocks in each storage container.

Tommy and Ruth will meet at a coordinate that is 0.5x km away from Ruth's starting point.

In this problem, Tommy and Ruth are cycling towards each other. We are given that Tommy cycles twice as fast as Ruth and they both start cycling at the same time. Our goal is to determine at which coordinate they will meet.

To solve this problem, we need to use the concept of distance, speed, and time. Let's assume that Ruth cycles at a speed of "x" km/hr. Since Tommy cycles twice as fast as Ruth, his speed will be "2x" km/hr.

Let's say that Tommy and Ruth meet at a distance of "d" km from Ruth's starting point. Now, let's calculate the time taken by both Tommy and Ruth to reach this point.

Time taken by Ruth = Distance/Speed = d/x

Time taken by Tommy = Distance/Speed = d/2x

Since they both start cycling at the same time, we can set these two equations equal to each other:

d/x = d/2x

We can then simplify this equation by multiplying both sides by 2x:

2d/x = d

Now we can solve for "d" by multiplying both sides by "x":

2d = dx

d = 0.5x

This means that Tommy and Ruth will meet at a coordinate that is 0.5x km away from Ruth's starting point. To determine the exact coordinates, we need to know where Ruth started cycling from and in which direction they are cycling. If we assume that Ruth started cycling from the origin (0,0) and they are cycling towards each other on a straight path, then they will meet at the coordinate (0.5x, 0).

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Answer:

he should have subtracted 17 from both sides of the equation

Step-by-step explanation:

x+ 17 = 22

subtract 17 from both sides

X + 17 = 22

-17 -17

x = 5

The probability that the sample's mean length is greater than 6.3 inches is0.8446.

Here, we have,

Given mean of 6.5 inches, standard deviation of 0.5 inches and sample size of 46.

We have to calculate the probability that the sample's mean length is greater than 6.3 inches is 0.8446.

Probability is the likeliness of happening an event.

It lies between 0 and 1.

Probability is the number of items divided by the total number of items.

We have to use z statistic in this question because the sample size is greater than 30.

μ=6.5

σ=0.5

n=46

z=X-μ/σ

where μ is mean and

σ is standard deviation.

First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required probability.

z=6.3-6.5/0.5

=-0.2/0.5

=-0.4

p value from z table is 0.3446

Probability that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.

Hence the probability that the mean length is greater than 6.3 inches is 0.8446.

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Answer:

Step-by-step explanation:

$6.80 x 19 pounds = $129.2

$4.70 x 18 pounds = $84.6

            +___________________

             37 pounds = $213.8

$213.8 divided by 37 pounds = 5.77837......

                                                  = $5.78 per pound

If the population in the year 2007 is 111.3 million, then the population in the year 2044 will be 148.37 million.

In order to find the population in the year 2044, we use the population growth formula; which is : P = P₀ × (1 + r)ⁿ;

where P = future population, P₀ = initial population, r = annual growth rate, and n = number of years;

Substituting the values,

We get;

⇒ P = (111.3 million) × (1 + 0.0078)²⁰⁴⁴⁻²⁰⁰⁷;

Simplifying this expression,

We get;

⇒ P = (111.3 million) × (1.0078)³⁷;

⇒ P ≈ 148.37 million;

Therefore, the population in the year 2044 is estimated to be approximately 148.37 million.

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Answer: 79

Step-by-step explanation:

63+65+73+×/4=79

multiply by 4 on both sides

201+x=280

subtract 201 from both sides

x= 79

Answer:

In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio (r).

In this case, the first term (a₁) is 2, and the common ratio (r) can be found by dividing any term by its preceding term. Let's calculate it:

r = 6 / 2 = 3

Now, to find the 15th term (a₅₊₁₋₅), we can use the formula:

aₙ = a₁ * r^(n-1)

Substituting the values, we have:

a₁ = 2

r = 3

n = 15

a₁₅ = 2 * 3^(15-1)

Calculating the exponent first:

3^(15-1) = 3^14 = 4782969

Now, substituting this value back into the formula:

a₁₅ = 2 * 4782969

a₁₅ = 9565938

Therefore, the 15th term of the geometric sequence 2, 6, 18, ... is 9565938.

Step-by-step explanation:

Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.

Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter

Time taken by Peter = 2PM - 10AM

= 4 hrs

Speed of Peter = 84 km/h

Distance travelled by Peter = speed × time

= 84 × 4

= 336 km

So, the distance between Town A and Town B  = distance travelled by Peter = 336 km.

Now, we will calculate time taken by William.

Speed of William = 70 km / hr

Distance travelled by William = distance between Town A and town B = 336 km

Time taken by William = distance / speed

= 336 / 70 hr

= 4.8 hr

This can b converted into hrs and minutes

4.8 hr = 4 hr + 0.8 × 60

= 4 hr 48 mins

Time William took off = 10 AM - 1hr 25 mins

= 8:35 AM

Now, we will calculate the time William would reach town B.

Time = 8:35 + 4hr 48 mins

= 1:23 PM

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Answer:

Step-by-step explanation:

$314.50

Representation of a number in three different ways:

133: [12 tens and 13 ones], [13 tens and 3 ones], [1 hundred, 3 tens and 3 ones]

678: [67 tens and 8 ones], [60 tens and 78 ones], [6 hundreds, 7 tens and 8 ones]

877: [80 tens and 77 ones], [87 tens and 7 ones], [8 hundred, 7 tens and 7 ones]

543: [54 tens and 3 ones], [50 tens and 43 ones], [5 hundreds, 4 tens and 3 ones]

453: [45 tens and 3 ones], [40 tens and 53 ones], [4 hundreds, 5 tens and 3 ones]

341: [30 tens and 41 ones], [34 tens and one], [3 hundreds,4 tens and one]

555: [50 tens and 55 ones], [55 tens and 5 ones], [5 hundreds, 5 tens and 5 ones]

485: [48 tens and 5 ones], [40 tens and 85 ones], [4 hundreds, 8 tens and 5 ones]

789: [78 tens and 9 ones], [70 tens and 89 ones], [7hundreds, 8 tens and 9 ones]

864: [86 tens and 4 ones], [80 tens and 64 ones], [8 hundreds, 6 tens and 4 ones]

652: [65 tens and 2 ones], [60 tens and 52 ones], [6hundreds, 5 tens and 2 ones]

Here given an example to write a particular number in different representations.

13 tens and 12 ones = 13*10 + 12*1 = 130 + 12 = 142.

14 tens and 2 ones = 14*10 + 2*1 = 140 + 2 = 142.

1 hundred, 4 tens and 2 ones = 1*100 + 4*10 + 2*1 = 100 + 40 + 2 = 142.

So three representations are of number 142.

Rest blanks should be filled in same manner taking different numbers for each rows and three columns of each row should be filled with three different representation of that assumed numbers.

Representations for some numbers:

133: [12 tens and 13 ones], [13 tens and 3 ones], [1 hundred, 3 tens and 3 ones]

678: [67 tens and 8 ones], [60 tens and 78 ones], [6 hundreds, 7 tens and 8 ones]

877: [80 tens and 77 ones], [87 tens and 7 ones], [8 hundred, 7 tens and 7 ones]

543: [54 tens and 3 ones], [50 tens and 43 ones], [5 hundreds, 4 tens and 3 ones]

453: [45 tens and 3 ones], [40 tens and 53 ones], [4 hundreds, 5 tens and 3 ones]

341: [30 tens and 41 ones], [34 tens and one], [3 hundreds,4 tens and one]

555: [50 tens and 55 ones], [55 tens and 5 ones], [5 hundreds, 5 tens and 5 ones]

485: [48 tens and 5 ones], [40 tens and 85 ones], [4 hundreds, 8 tens and 5 ones]

789: [78 tens and 9 ones], [70 tens and 89 ones], [7hundreds, 8 tens and 9 ones]

864: [86 tens and 4 ones], [80 tens and 64 ones], [8 hundreds, 6 tens and 4 ones]

652: [65 tens and 2 ones], [60 tens and 52 ones], [6hundreds, 5 tens and 2 ones]

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If gender did not matter then the number of males who would have survived would be 593 males

If gender would not have mattered, the survival rate would be the same for both genders. So, we would use the survival rate of females (which is 296/402) to calculate the expected number of males that would have survived.

First, calculate the survival rate of the females:

Survival rate = Number of females who survived / Total number of females

= 296 / 402

= 0.737

Expected number of male survivors = Number of males * Female survival rate

= 805 x 0.737

= 593 males

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Answer:

the percentage of red marbles in the bag is 30%.

Step-by-step explanation:

To find the percentage of red marbles in the bag, we need to divide the number of red marbles by the total number of marbles and then multiply by 100:

Percentage of red marbles = (Number of red marbles / Total number of marbles) x 100

Number of red marbles = 12

Total number of marbles = 40

Percentage of red marbles = (12/40) x 100

= 0.3 x 100

= 30%

Therefore, the percentage of red marbles in the bag is 30%.

Okay, let's solve this step-by-step:

X/5-y = m-1

Add y to both sides:

X/5 = m

Multiply both sides by 5:

X = 5m

So in this equation, X = 5m.

To find y, we subtract m-1 from both sides of the original equation:

X/5 = 5m

X/5 - (m-1) = 5m - (m-1)

X/5 - m + 1 = 4m

(X - 5m) / 5 = m - 1

X - 5m = 5(m - 1)

X = 20m - 5

So if we let m = any value, we can calculate y. For example:

If m = 3, then:

X = 20*3 - 5

= 55 - 5 = 50

50/X = 5(m - 1) = 5*2 = 10

y = 10

Does this make sense? Let me know if you have any other questions!

The amount in this statement, 6 is 30% of 20 is 6.

The amount in the statement "6 is 30% of 20" is 6.

This statement means that if we take 30% of 20, we get 6.

In other words, the amount 6 is 30% of 20.

We can also verify this by calculating 30% of 20:

30% of 20

= (30/100) × 20

= 0.3 × 20

= 6

Hence,  the amount in this statement is 6.

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The measurement of DE is 10 inches.

If we know that E is the point where the diagonals of the rectangle intersect, then we know that DE is equal to half the length of the diagonal BD.

Using the Pythagorean theorem, we can relate the length of the diagonal BD to the sides of the rectangle.

Let's assume that the length of the rectangle is L and the width of the rectangle is W. Then, the length of the diagonal BD is given by:

BD = √(L^2 + W^2)

Since we know that the diagonals of a rectangle are equal, we have:

AC = BD

BD = 20

Therefore, DE = 1/2 BD = 1/2 (20) = 10 inches.

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Okay, here are the steps to solve this problem:

Fixed costs per month: $1121

Variable cost per gallon: $7.50

Selling price per gallon: $9.00

Monthly sales (gallons): 1494

Cost of goods sold = Variable cost per gallon * Monthly sales

= $7.50 * 1494 gallons

= $11,105

Gross margin = Revenue - Cost of goods sold

= $9 * 1494 gallons

= $13,446

- $11,105 (Cost of goods sold)

= $2,341

Margin of profit = Gross margin - Fixed costs

= $2,341 - $1121

= $1,220

So the margin of profit if 1494 gallons are produced and sold each month is $1,220.

The answer is:

B $1,220

Answer:

34

Step-by-step explanation:

1. Plug in the week's salary into the formula

S=400+35v

1590=400+35v

2. Solve for v.

1590=400+35v

Subract 400 from both sides. Since the opposite of addition is subraction, soing this cancels out the 400.

1190=35v

Divide each side by 35. Since the opposite of multiplication (35v = 35 times v) is division, this will cancel out the 35.

34=v

The equation that represents the amount of money in Sara's piggy bank is y = 0.6x + 1 and the equation that represents the amount of money in Kim's piggy bank is y = 0.2x + 2.2.

The equation that represents the amount of money in Sara's piggy bank over time can be written as

Y = 0.6x + 1

Where Y represents the total amount of money in Sara's piggy bank and x represents the number of weeks.

Similarly, the equation that represents the amount of money in Kim's piggy bank over time can be written as

Y = 0.2x + 2.2

Where Y represents the total amount of money in Kim's piggy bank and x represents the number of weeks.

To visualize these equations, we can create a graph where the x-axis represents the number of weeks and the y-axis represents the amount of money in the piggy bank. We can plot the points for each week and draw a line connecting them. The resulting graph will show the trend of the amount of money in each piggy bank over time.

Here is a graph that represents the scenario

In the graph, the red line represents the amount of money in Sara's piggy bank and the blue line represents the amount of money in Kim's piggy bank. As we can see, Sara's piggy bank grows faster than Kim's piggy bank due to the higher allowance she receives for doing her chores.

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Answer:

7

Step-by-step explanation:

Finding the common difference of an arithmetic sequence is easy peasy lemon squeezy. All you have to do is take any term and subtract it from the next one. For instance, if you take 1 and subtract it from 8, you get 7. If you take 8 and subtract it from 15, you get 7 again. You can do this for any pair of terms and you will always get 7. That's the common difference of the sequence 1, 8, 15, 22, 29, 36, 43. It means that you just add 7 to each term to get the next one. Isn't that neat?

Answer:

AA sim post

Step-by-step explanation:

They DO have equal (similar) angles.....but they do not have equal sides

Answer:

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

Mass is the product of the volume and density and the volume of the rectangular prism is the product of its three dimensions.

Find the volume first:

Convert volume to cm³, taking 2.54 cm per in:

Find the mass:

The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.

The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.

Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.

Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.

Hence, the correct option is {−4, −2, 0, 3, 5}.

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The total "surface-area" of cone having "slant-height" as 10, and base-radius as 6, is 301.44 square units.

The total surface area of a cone can be calculated by adding the area of the base to the lateral surface area.

Let us first calculate the lateral surface area of the cone:

Lateral surface area = πrl; where r is radius , and 'l" = slant-height,

The radius of base = 6 units and slant height is = 10 units.

So, we have:

Lateral surface area = π × 6 × 10

Lateral surface area = 60π square units

Next, Area of the base = πr²;

Area of the base = π × 6²,

Area of the base = 36π square units,

Total surface area = Lateral surface area + Area of the base

Total surface area = 60π + 36π

Total surface area = 96×3.14 = 301.44 square units.

Therefore, the total surface area of cone is 301.44 square units.

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