6abc2 + 6a2bc


A=1
B=2
C= -3

Answer:

  150 m²

Step-by-step explanation:

You want the total area of a figure consisting of a 12 m wide rectangle 5 m high with a triangle above that bringing the total height to 20 m.

The area of the rectangle is the product of its length and width:

  A = LW

  A = (12 m)(5 m) = 60 m²

The area of the triangle is half the product of its base and height.

  A = 1/2bh

  A = 12/(12 m)(20 -5 m) = 90 m²

The area of the whole figure is the sum of the areas of its parts:

  total area = rectangle area + triangle area

  total area = 60 m² +90 m² = 150 m²

The area of the figure is 150 m².

__

Additional comment

Since you know a triangle's area is equivalent to the area of a rectangle that has half the height, the 15 m high triangle can be considered as a rectangle 7.5 m high. Adding that to the 5 m area of the rectangle already there gives the equivalent area as that of a rectangle 12 m wide and 5+7.5 = 12.5 m high: (12 m)(12.5 m) = 150 m².

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Answer:

The worker needs 3.74L of ingredient B

Step-by-step explanation:

Given

\(A:B = 1.3L:2.7L\)

Required

Determine the B equivalent of (1.3L + 0.5L) of A

\(A:B = 1.3L:2.7L\)

Convert to Fraction

\(\frac{A}{B} = \frac{1.3L}{2.7L}\)

\(\frac{A}{B} = \frac{1.3}{2.7}\) ----(1)

For the new mix of A

\(New\ A = 1.3L + 0.5L\)

\(New\ A = 1.8L\)

New A requires New B:

So:

We have:

\(New\ A: New\ B\)

Convert this to fraction;

\(Ratio = \frac{New\ A}{New\ B}\)

Substitut2 1.8L for New A

\(Ratio = \frac{1.8L}{New\ B}\) --- (2)

Equate (1) and (2)

\(\frac{1.8L}{New\ B} = \frac{1.3}{2.7}\)

Cross Multiply:

\(New\ B * 1.3 = 1.8L * 2.7\)

Divide through by 1.3

\(New\ B = \frac{1.8L * 2.7}{1.3}\)

\(New\ B = \frac{4.86L}{1.3}\)

\(New\ B = 3.74\ L\) (Approximated)

Hence;

The worker needs 3.74L of ingredient B

The lower extreme price at Dealer 1 is higher than the median price at Dealer 2.

Price is the value of a product or service that an individual or business is willing to accept in exchange for a good or service. It is typically determined by the market forces of supply and demand. Prices are usually expressed in monetary terms, but can also be expressed in terms of labor time or other resources. Prices can vary widely depending on the availability of a good or service, the amount of competition, and other factors.
This conclusion can be drawn from the box-and-whisker plots of the prices of the sports cars at each of the two dealerships. The lower extreme price of the sports cars at Dealer 1 is represented by the lower whisker of the box-and-whisker plot and is higher than the median price of the cars at Dealer 2, which is represented by the horizontal line in the middle of the box-and-whisker plot. This means that the lower extreme price of the sports cars at Dealer 1 is higher than the median price of the cars at Dealer 2.

The higher prices of the sports cars at Dealer 1 could be due to several factors. It is possible that the cars sold at Dealer 1 are of a higher quality or have more features than those sold at Dealer 2. Additionally, Dealer 1 may simply be charging higher prices due to its location or reputation. Whatever the reason, it is clear that the lower extreme price of the sports cars at Dealer 1 is higher than the median price of the cars at Dealer 2.

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

5/12

Step-by-step explanation:

i took the test :]

Answer:

208 cubic units

Step-by-step explanation:

The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:

The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.

Now, let’s calculate the volume of the rectangular prism:

The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160

Now, add up the volumes of the rectangular and triangular prisms:

160 + 48 = 208 cubic units

For the given figure, we will find the area

The given figure can be divided into two shapes as shown in the following figure:

Shape (1) is a rectangle:

Length = 9 cm

Width = 6 cm

Area of shape (1) = 9 x 6 = 54 cm²

Shape (2) is a triangle:

Base = 6 cm

Height = 14 - 9 = 5 cm

Area of shape (2) = 1/2 x 6 x 5 = 15 cm²

So, the area of the given figure = 54 + 15 = 69 cm²

Answer:

A

Step-by-step explanation: Hope it HELP

a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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Answer:

571.77 is the correct answer because

C=2πr=2·π·91≈571.76986

Answer:

I think it is \(\frac{6x-18}{x^{4} }\)

Step-by-step explanation:

Since AB is parallel to CD, we have alternate interior angles forming when transversal CE intersects the parallel lines. Therefore,

mZDCE = mZECB (Alternate Interior Angles)

(7x + 2) = (x + 8) (Substitute in the given angle measures)

Solving for x, we get:

7x + 2 = x + 8

6x = 6

x = 1

Now, we can use x to find the measure of angle ZDCE:

mZDCE = (7x + 2)

= (7*1 + 2)

= 9

Therefore, the measure of angle ZDCE is 9 degrees.

Answer:

  -8/3

Step-by-step explanation:

You want the slope of the line shown in the graph.

Whether counting grid squares on the graph, or using the slope formula, it is convenient to choose two points on the grid where the line crosses the intersection of grid lines.

It appears, the line passes through grid points (1, 4) and (4, -4). Using the slope formula, we find the slope of the line to be ...

  m = (y2 -y1)/(x2 -x1)

  m = (-4 -4)/(4 -1) = -8/3

The slope of the line is -8/3.

The slope is the ratio of "rise" to "run" for the line. From the two points we see where the line crosses grid intersections, we have a "rise" of -1 from y=4 to y=-4, and a "run" of 3 from x=1 to x=4.

  rise/run = -8/3 = slope of the line

Answer: Ima say 6

Explanation: I don't have an explanation

The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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To describe the center of the data, we can use either the mean or the median.

To describe the variation of the data, we can use either the range or the interquartile range (IQR).

Looking at the dot plot, it seems that the data is somewhat skewed to the right, with a few high-priced outliers. In this case, the median and the IQR may be more appropriate measures of the center and variation, respectively, as they are less sensitive to outliers.

To find the median and IQR:

Arrange the data in order from smallest to largest.

Find the median, which is the middle value. If there are an even number of values, take the average of the two middle values.

Find the first quartile, which is the median of the lower half of the data.

Find the third quartile, which is the median of the upper half of the data.

Calculate the IQR as the difference between the third quartile and the first quartile.

Here are the steps applied to the dot plot:

We can see that the smallest value is about 20 and the largest value is about 120, giving a range of 100 dollars.

The median is approximately 60 dollars, as it is the middle value between the 11th and 12th data points when the data is arranged in order.

The first quartile is approximately 40 dollars, as it isthe median of the lower half of the data points, which are found below the median.

The third quartile is approximately 80 dollars, as it is the median of the upper half of the data points, which are found above the median.

The IQR can be calculated as the difference between the third quartile and the first quartile, which is approximately 40 dollars.

Therefore, the most appropriate measures to describe the center and the variation for this data set are the median and the interquartile range (IQR), respectively. The median is approximately 60 dollars, and the IQR is approximately 40 dollars.

Answer:

9

Step-by-step explanation:

4 * 2 + 3 - 2 =

= 8 + 1 =

= 9

1) To determine the surface area of a right cone, we must know the radius of the circular base and height of the cone.

2) To determine the surface area and volume of a sphere, we must know the radius of the sphere.

3) The volume of the sphere with a great circle of radius 7 cm is 1436.75 cubic centimeters

4) The area of a regular pentagon with radius 5, and each side of length 6 is 45 square units

To determine the surface area of a right cone:

The formula for the surface area of a right cone is,

A = πr[r + √(h² + r²)]

this means, to determine the surface area of a right cone, we must know the radius of the circular base and height of the cone.

To find the surface area and volume of a sphere:

The formula for the surface area of sphere is,

A = 4πr²

and the formula for the volume of sphere is,

V = 4/3 πr³

This means, to determine the surface area and volume of a sphere, we must know the radius of the sphere.

For a sphere with radius r = 7 cm the volume would be,

V = 4/3 * π * 7³

V = 1436.75 cubic centimeters

Now we need to find the area of a regular pentagon with radius 5, and each side of length 6.

The formula for the area of a regular pentagon is:

A = 1/2 × P × a

where 'p' is the perimeter of the pentagon and 'a' is the apothem of a pentagon.

The perimeter of the pentagon is:

P = 5 * side lengths

P = 5 * 6

P = 30 units

We know that an apothem of a regular polygon is a radius of the inscribed circle.

From given dimensions, a = 5 units

so, the area of a regular pentagon would be,

A = 1/2 × 30 × 5

A = 45 square units

Therefore, the area of a regular pentagon is 45 square units

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Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.

The most common symbols used in inequalities are:

">" (greater than): indicates that the value on the left side is larger than the value on the right side.

"<" (less than): indicates that the value on the left side is smaller than the value on the right side.

"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.

"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.

"≠" (not equal to): indicates that the values on both sides are not equal.

Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.

Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

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Answer:

Step-by-step explanation:

-206

when you divide those two numbers you get a negative number and a decimal because you are dividing by a decimal with a negative sign.

Answer:

-21

...

I think, let me know if I'm wrong

A probability tree is a visual representation of the possible outcomes of an event or series of events. In this case, the event takes a marble out of the bag.

The first step in building a probability tree is to create a starting point that represents the first state of the problem. In this case, the starting point is a bag containing 3 green marbles and 5 white marbles.

The next step is to branch from the starting point and show the possible results of the first event. This includes taking out  the marble out of the bag. The probability of getting a green marble is 3/8 and the probability of getting a white marble is 5/8.

After the first event, the issue status changes. In this case, the bag contains 2 green marbles and 4 white marbles.

The next step is to branch out from the state after the first event and show the possible outcomes of his second event involving pulling another marble out of his pocket. The probability of getting a green marble is 2/6 and the probability of getting a white marble is 4/6. The final step is to label the endpoints of the tree with the possible outcomes of the problem and the probabilities of each outcome.

The probability tree starts with an sack of 3 green marbles and 5 white marbles, as shown in the design showing the possible outcomes of selecting a marble, the new state of the sack after each selection, and the probability of each outcome

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384.

1) Gathering the data

24 rows

16 students in each row.

2) Solving it

If there are 24 rows of students, and each and every one has 16 students than we can say that there are 384 students in the choir, since 24x 16= 384. Also in this choir, we have the shape of a rectangle.

Answer: 5/2

To convert 2.5 into a fraction, firstly we will write the number in x/y form, where x and y are positive integers. So, 2.5 can be written as 2.5/1. For the removal of the decimal, we multiply and divide by 10. And we get, 2.5/1 x 10/10 = 25/10 = 5/2.

The associated p-value for this left-tailed t-test is 0.0359 or 3.59%.

Now, The p-value for a one-tailed t-test with a sample size of 18 and a test statistic of 1.9,

Hence, we need to look up the t-distribution table.

So, Using a one-tailed test with,

df = n - 1

= 18 - 1 = 17 degrees of freedom

We find that the area to the left of 1.9 under the curve is 0.0359.

This means that there is a 3.59% probability of observing a t-statistic less than or equal to 1.9 if the null hypothesis is true.

Therefore, the associated p-value for this left-tailed t-test is 0.0359 or 3.59%.

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Answer:

The dimensions that will maximize the enclosed area of the pen is 250 ft by 250 ft

Step-by-step explanation:

we have the perimeter as 1000

So the sum of the lengths will be

1000/2 = 500

The dimensions that will maximize these pens will be such that they will have equal values

Mathematically, that will be 500/2 = 250 by 250

Answer:

The error is between the given and step 1

Step-by-step explanation:

the negative wasnt distributed to the 4x-3.

it would have been 8x-4x+3=5