A new dam being built has the shape of a trapezoid.
The length of the base at the bottom of the dam is 2 times the height.
The length of the base at the top of the dam is 1/5 times the height
minus 30 feet.

a. Write an expression to find the area of the trapezoidal cross
section of the dam.

b. If the height of the dam is 180 feet, find the area
of this cross section.

The percent of decrease from the original number to the final number is 25%. Percentage is count of a quantity per 100 quantities. The percent of decrease from the original number to the final number is 25%

How to find the percentage from the total value?

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

Suppose that the number in consideration be N

Then, we get:

Increased number = N + 50% of N

Since 50% of N is: ,

thus, the increased number = N + N/2 = 3N/2

Now this result is decreased by 50%

Decreased number = result - 50% of  result

Since 50% of result is:

Thus, Decreased number = 3N/2 - 3N/4 = 3N/4

Let us suppose that the original number N is decreased y% to get 3N/4(the final number)

Then,

3N/4 = N - y% of N

y% of N is calculated as:

Thus, we get:

Thus, the original number N is decreased y% = 25% to get 3N/4(the final number)

Thus, The percent of decrease from the original number to the final number is 25%.

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Answer:

PLEASE MARK BRAINLIEST.

Step-by-step explanation:

Notice how the triangle's side lengths are scaled up by a factor of 2. This means that FH*2=x. Solving for x, we get that x=6*2= 12 units.

Answer:

The rate of change between two points is the difference in the y-coordinates divided by the difference in the x-coordinates.

Let's call the first point (-4, 1/2) Point 1, and the second point (1, -1) Point 2.

The difference in the y-coordinates is:

-1 - 1/2 = -3/2

The difference in the x-coordinates is:

1 - (-4) = 1 + 4 = 5

So, the rate of change between the two points is:

(-3/2) / 5 = -3/10

Therefore, the rate of change between Point 1 and Point 2 is -3/10.

Step-by-step explanation:

espero te ayude

Table 4 shows proportional relationship between x and y.

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional. If equivalent elements in two sequences have a constant product, also known as the coefficient of proportionality, then the two sequences are inversely proportional.

The proportionality is given by the following equation:

y = kx

For table 1 substitute the value of x = 40 and y = 8.

8 = k (40)

k = 1/5

Table 1 does not follow the proportionality for all points hence option 1 is incorrect.

Similarly, table 2 and table 3 do not follow the proportionality for all points.

For table 4, substituting the value we have:

2 = k4

k = 1/2

The proportionality is followed for all the values.

Hence, table 4 shows proportional relationship between x and y.

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200 pounds is approximately equal to 90.7185 kg ( rounded to four decimal places )

To convert 200 pounds to kg, we can use the following formula:

1 pound = 0.453592 kg

The conversion factor is 0.453592

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The mass in kg = conversion factor × The mass in pounds

Substitute the values in the equation

The mass in kg = 0.453592 × 200

Multiply the numbers

= 90.7185 kg  ( rounded to four decimal places )

Therefore, 200 pounds is 90.7185 kg

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Here  is a scatter plot that compares hits to at bats for players on a baseball team, as the number of bats increase, the number of hits increases.

A scatter plot is also known as a scatter chart, scattergram, or XY graph. The scatter diagram plots numerical data pairings, one variable on each axis, to demonstrate their connection. Today everyone is wondering when to utilise a scatter plot.

Scatter plots are used in the following scenarios.

When we have numerical data that is paired

When there are several dependent variable values for a single independent variable value

In some instances, such as finding probable root causes of issues, evaluating if two items that appear to be connected both arise with the same precise reason, and so on.

The points will fall along a line or curve if the variables are correlated. The closer the points are to the line, the better the connection. One of the seven key quality tools is this cause examination tool.

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Answer:

26 Students

Step-by-step explanation:

4% is also 0.04 multiplied by the number of students. 650 * 0.04 = 26

Jade was 416 meters above the ground when she deployed her canopy.

What is kinematics?

kinematics, specifically the equation of motion for constant velocity, to solve the problem of finding the height above the ground when a person deploys their canopy while descending.

We can use the formula:

height = rate x time

To determine how high Jade was above the ground when she deployed her canopy. Let's denote the height she was at when she deployed her canopy as "h".

From the given information, we know that Jade descended at a constant rate of 40 meters every 5 seconds, so her rate of descent is 40/5 = 8 meters per second.

We also know that it took her exactly 57 seconds to reach the ground. Therefore, the time she spent descending with her canopy deployed is 57 - 5 = 52 seconds.

Using the formula, we can write:

h = 8 x 52

Simplifying this equation gives us:

h = 416

Hence, Jade was 416 meters above the ground when she deployed her canopy.

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Solving an equation, the number of textbooks sold by the textbook store, which sold a combined total of 236 in a week is as follows:

An equation is a mathematical statement that two or more algebraic expressions are equal or equivalent.

Equations are differentiated from mathematical expressions by the use of the equal sign (=).

The total number of math and physics textbooks sold in a week = 236

Let the number of physics textbooks sold = x

Let the number of math textbooks sold = x + 52

2x + 52 = 236

2x = 236 - 52

2x = 184

x =92

The number of textbooks sold for the week:

Physics textbooks sold = 92

Math textbooks sold = 144 (92 + 52)

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Answer: $725

Step-by-step explanation:

100%-28%=72%

$522/72=7.25

7.25*100%=$725

To check the answer $725-28% (discount)=$203

$725 (yesterday price) - $203 (discount) = $522 (price today)

The value of the expression 18 - (16 • 12) is -174.

To evaluate the expression 18 - (16 • 12), we need to follow the order of operations, also known as PEMDAS. According to PEMDAS, we first perform any calculations inside parentheses, then evaluate exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.

In this expression, we have the operation of multiplication inside parentheses. So, we start by evaluating 16 • 12, which equals 192.

Now, we can rewrite the expression as 18 - 192.

Next, we perform the subtraction, which gives us -174.

Therefore, the value of the expression 18 - (16 • 12) is -174.

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Answer:

I think the system has infinite solutions.

Step-by-step explanation:

The scale factor of the preimage to the image is 5/2

The length of BC is 10 units

The scale factor is the size by which the shape is enlarged or reduced. It is used to increase the size of shapes like circles, triangles, squares, rectangles, etc.

The scale factor of the preimage to the image can be found by finding the ratio of the corresponding sides of the preimage to the image. That is:

scale factor = DC / D'C'

scale factor = 5/2

Also, the scale factor = BC / B'C' and the scale factor is constant (i.e. 5/2)

scale factor = BC / B'C'

5/2 = BC/4

BC = 5/2 * 4

BC = 10 units

Therefore, the length of BC is 10 units

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To convert milligrams to milliliters for water or a substance with the same density, divide the number of milligrams by 1000.

Converting milligrams (mg) to milliliters (ml) depends on the density of the substance being measured. Density is the amount of mass in a given volume, and different substances have different densities. Therefore, the conversion factor will vary depending on what substance you are trying to convert.

However, if you are working with water or another substance with a density of 1 gram per milliliter, then the conversion is straightforward. One milliliter of water weighs one gram, or 1000 milligrams. So to convert milligrams to milliliters for water or a substance with the same density, you simply divide the number of milligrams by 1000.

However, for other substances with different densities, you need to know the substance's density to convert mg to ml. In this case, you will need to use the formula:

Volume (ml) = Mass (mg) ÷ Density (mg/ml)

It's important to note that for some substances, such as oils or syrups, the density may change depending on the temperature or other factors.

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Answer:

20:00 is 8:00 pm

Step-by-step explanation:

an easy way to remember is subtract 2 from the military timing and the number in the ones value is the time.

Ex.

14:00

14 - 2= 12

So it’s 2: 00 pm

20- 2= 18

So it’s 8:00 pm

The diamond problem solver is a graphical tool used to solve problems involving the addition and multiplication arithmetic operations.

It is frequently used in elementary mathematics to assist students in comprehending the relationship between these operations and their inverse operations of subtraction and division.

The diamond problem solver gets its name from the fact that it is drawn in the shape of a diamond with four sections. The sum or product is represented by the top section, the addends or factors are represented by the two side sections, and the missing value is represented by the bottom section.

We use the diamond problem solver by writing the known values in the diamond's two side sections and filling in the missing value in the bottom section. Then we add or multiply the known values to find the value in the diamond's top section.

For example, to solve the problem:

7 + ___ = 12

We would write 7 in the left section of the diamond and 12 in the top section, leaving the right section blank. We then fill in the bottom section with the missing value by subtracting 7 from 12:

12 - 7 = 5

So, the value in the bottom section of the diamond is 5, and the completed diamond would look like this:

  [tex]07\\+ ?\\-\\ 12[/tex]

[tex]07\\+ 5\\--\\ 12[/tex]

As a result, the problem's missing value is 5. The diamond problem solver can also be used to solve multiplication problems by placing the known values in the side sections and the product in the top section.

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Answer:

The profit per sweater is 29 dollars.

Step-by-step explanation:

First find the total profit.

136 - 20

116 for all 4 sweaters

Now divide by 4 since there are 4 sweaters to find the profit per sweater.

116/4

29

The profit per sweater is 29 dollars.

Stratified Sampling separates the population into nonoverlapping groups. By using specific criteria to split the population, we may use this strategy to draw a proportional random sample from each division.

The population is divided into non-overlapping groups or strata, and a proportional simple random sample is taken from each stratum to create a stratified sample. Each group's members ought to have some things in common. We must choose the number of people to choose from each stratum after the strata have been established. Here, the proportionality of the chosen number is crucial. In order to make the characteristic of interest more homogeneous inside a stratum than between strata, strata are based on information other than the characteristic being measured that is known to or thought to fluctuate with the characteristic of interest. Hence, strata can be defined based on any property that explains variation in the characteristic of interest.

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The converted value of Celsius to Fahrenheit represented as 45 Celsius equals to 113 Fahrenheit.

Temperature is measured by the standard units which is defined as  Celsius and Fahrenheit .

Formula which defines  the relation of  Celsius and Fahrenheit is equal to

(°C × 9/5) + 32 =°F

Now Substitute the given value 45 degree Celsius and convert into Fahrenheit we have,

(45°Celsius × 9/5) + 32

= ( 405 / 5 ) + 32

= ( 81 ) + 32

= 113°Fahrenheit

Therefore, the converted value from Celsius to Fahrenheit for the given temperature 45 Celsius is given by 113 Fahrenheit.

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The customer pays $0.72 for a filled balloon.

Let's denote the cost of the balloon and the helium as x.

According to the problem statement, we know that:

x + 80% of x = $0.50

We can simplify this equation by multiplying both sides by 1.8, which is the same as multiplying the right-hand side by 180%:

1.8x + 1.44x = $0.90

2.24x = $0.90

Dividing both sides by 2.24, we get:

x = $0.40

So the cost of the balloon and helium is $0.40.

The price that the customer pays for the balloon is the cost plus the markup, which is 80% of the cost:

Price = Cost + Markup

Price = $0.40 + 80% of $0.40

Price = $0.40 + $0.32

Price = $0.72

Therefore, the customer pays $0.72 for a filled balloon.

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Answer:

$0.90

Step-by-step explanation:

100%= $0.50

100%+80%= 180%

1%= $0.50/100

   = $0.005

180%= $0.005*180

        = $0.90

The cone’s radius r in terms of x is x + 7

From the question, we have the following parameters that can be used in our computation:

Volume, V = 3πx^2 + 42πx + 147π

Height, h = 9

The volume of a cone is

V = 1/3πr^2h

Substitute the known values in the above equation, so, we have the following representation

1/3πr^2 * 9 = 3πx^2 + 42πx + 147π

So, we have

3πr^2 = 3πx^2 + 42πx + 147π

Divide by 3π

r^2 = x^2 + 14x + 49

So, we have

r = √(x² + 14x + 49)

Evaluate

r = x + 7

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The value of x and y are x=[tex]\sqrt{2}[/tex] and y=2, the correct option is B.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

We are given that;

The side of triangle =[tex]\sqrt{2}[/tex]

Now,

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

Since two sides of an isosceles triangle are equal

By pythagoras theorum

y^2= 2+2

y^2=4

y=2

Therefore, by pythagoras theorum the answer will be 2.

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 To find the x-intercept using the straight-line equation, substitute y=0 and solve for x. To find the y-intercept, substitute x=0 and solve for y.

The equation of a straight line is

y=mx+c

is the gradient and

c

is the height at which the line crosses the y-axis, also known as the y-intercept.

The gradient m is the slope of the line - the amount by which the ycoordinate increases in proportion to the x-coordinate. If you have two points (x1,y1) and (x2,y2) on the line, the gradient ism=y2−y1x2−x1

, we must first work out the gradient using the gradient formula above, and then choose either point to substitute into the straight line equation with this gradient.

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Trigonometry equation solver is used to solve mathematical expression with an equality between two elements containing unknown variables and trigonometric functions.

The relationships between the lengths and angles of triangles' sides are the subject of this area of mathematics. A trigonometric equation is one that has one or more ratios of unknown trigonometric angles. The ratios of sine, cosine, tangent, cotangent, secant, and cosecant angles are used to express it.

A trigonometric equation is cos2 x + 5 sin x = 0, for instance. The term "solutions of the given trigonometric equation" refers to all feasible values that fulfil the given trigonometric equation.

sin²A + cos²A = 1

sec²A – tan²A = 1

cosec²A – cot²A = 1

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When rotated about the x axis, a cone will form a circle and the sphere will remain a sphere. The prism and cylinder will not form any new figures when rotated about the x axis.

Cone generally refers to a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. It is a surface formed by the straight line segments joining a circle or other closed curve at different levels. Cone shapes are commonly seen in nature, such as in pine cones, ice cream cones, and volcanoes. In mathematics, a cone is a solid figure with a circular base and a curved surface that comes to a point at the top.

A sphere is a three-dimensional object consisting of a perfectly round shape. It is the surface of a perfectly round ball and is mathematically defined as the set of points that are all the same distance from a single point, which is the center. It is one of the most common shapes in geometry and is found in many everyday objects, such as balls and marbles.

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In NumPy, you can randomize the order of the columns in a 2-dimensional array using the numpy.random.permutation() function.

Here's an example of how to use this function to randomize the order of the columns in a 2-dimensional array:

import numpy as np

# create a 2-dimensional array with 3 rows and 4 columns

arr = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])

# get the number of columns in the array

num_cols = arr.shape[1]

# create a list of column indices

col_indices = np.arange(num_cols)

# shuffle the column indices randomly

shuffled_col_indices = np.random.permutation(col_indices)

# use the shuffled column indices to reorder the columns in the array

arr_shuffled = arr[:, shuffled_col_indices]

# print the original array and the shuffled array

print("Original array:")

print(arr)

print("Shuffled array:")

print(arr_shuffled)

In this example, we first create a 2-dimensional array with 3 rows and 4 columns. We then use the np.arange() function to create a list of column indices, which we shuffle randomly using the np.random.permutation() function.

Finally, we use the shuffled column indices to reorder the columns in the original array and store the result in a new array called arr_shuffled.

The output of the code will be the original array followed by the shuffled array, with the columns randomly rearranged.

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A = ( θ/360)πr² is used to find area of sector and L = ( θ/360)2πr used to find  length of the arc.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

To find the area of a sector:

Find the fraction of the circle represented by the sector by dividing the central angle  θ by 360 degrees.

Multiply this fraction by the total area of the circle, which is given by πr².

The result is the area of the sector, which can be expressed as A = ( θ/360)πr².

To find the length of an arc:

Find the fraction of the circle represented by the arc by dividing the central angle  θ by 360 degrees.

Multiply this fraction by the circumference of the circle, which is given by 2πr.

The result is the length of the arc, which can be expressed as L = ( θ/360)2πr.

Hence, A = ( θ/360)πr² is used to find area of sector and L = ( θ/360)2πr used to find  length of the arc.

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The solution is, the cost of each ticket is $21.25.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

each of them bought a game ticket and a $16.50 team jersey.

together, they paid a total of $75.50.

now, we get,

total cost of jersey = 16.50 * 2

                               =33

so, total cost of ticket = 75.50 - 33

                                    =42.50

so, we get,

the cost of each ticket = 42.50 / 2

                                     =21.25

Hence, The solution is, the cost of each ticket is $21.25.

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