The area of the trapezium, pqrs is

The corresponding angles and sides that show that the triangles are similar are: <A ≅ <R; <K ≅ <T; <M ≅ <L

RL/AM = RT/AK = TL/KM = 1.5.

Similar triangles are triangles that look alike but might be bigger or smaller than each other. This means that their matching or corresponding angles are the same and their matching sides have the same proportional length.

Therefore, from the image, we have corresponding pairs of angles that are congruent as follows:

Angles A and R

Angles K and T

Angles M and L

The corresponding sides that are proportional are:

AM and RL, which is RL/AM = 6/4 = 1.5

AK and RT, which is RT/AK = 7.5/5 = 1.5

KM and TL, which is TL/KM = 9/6 = 1.5

Therefore, the triangles are similar.

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The value of total area of the shape is,

⇒ 82 cm²

We have to given that;

Figure of shape is shown.

Since, Figure is made by three rectangles.

And, Area of rectangle is,

A = length x width

Hence, The area of upper rectangle is,

A = 3 x 8

A = 24 cm²

Area of middle rectangle is,

A = (11 - (3 + 5)) x (8 - 2)

A = 3 × 6

A = 18 cm²

Area of lower rectangle is,

A = 5 x 8

A = 40 cm²

Thus, The value of total area of the shape is,

⇒ 24 + 18 + 40 cm²

⇒ 82 cm²

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An expression that can be used to find the volume of the figure include the following: B. (2 cm × 8 cm × 7 cm) + (1 cm × 6 cm × 8 cm).

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of figure = (2 cm × 8 cm × 7 cm) + (1 cm × 6 cm × 8 cm)

Volume of figure = 112 cm³ + 48 cm³

Volume of figure = 160 cm³

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The surface area of the rectangular prism is 1476 square units

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

30 mm by 12 mm by 9 mm

The surface area of the rectangular prism is calculated as

Surface area = 2 * (Length * Width + Length * Height + Width * Height)

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

Area = 2 * (30 * 12 + 30 * 9 + 12 * 9)

Evaluate

Area = 1476

Hence, the area is 1476 square units

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The mass of the 405 cm³ milk is 417.15 grams.

Density is simply  the mass of a substance per unit volume.

It is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that:

Density of the milk p =  1.03g/cm³

Volume of the milk v = 405 cm³

Mass m = ?

Plug the values into the above formula and solve for mass m.

p = m / v

m = pv

m = 1.03g/cm³ × 405 cm³

m = 417.15 g

Therefore, the value of the mass is 417.15 grams.

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The profit as a percentage of the cost price​ is 20%

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

The profit is the difference beyween the selling price and the coste price

So, we have

Profit = 540000 - 450000

Evaluate

Profit = 90000

Next, we have

Percentage = Profit/Cost price * 100

This gives

Percentage = 90000/450000* 100

Evaluate

Percentage = 20%

Hence, teh percentage is 20%

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Answer:

Step-by-step explanation:

To find the profit as a percentage of the cost price, we need to calculate the profit first.

Profit = Selling price - Cost price

Profit = #540,000 - #450,000

Profit = #90,000

Now we can calculate the profit percentage as follows:

Profit percentage = (Profit / Cost price) x 100

Profit percentage = (#90,000 / #450,000) x 100

Profit percentage = 20%

Therefore, the profit as a percentage of the cost price is 20%.

The tax deduction is explained below.

We need to take into account a few things in order to establish how much, if any, of the $1,000,000 loss Ethan may deduct in the current year.

We need to know Ethan's basis in his ELS shares, or shareholder basis. Shareholder basis, which is changed yearly based on numerous criteria such as income, losses, donations, and payouts, symbolizes the investment a shareholder has in the S corporation.

Ethan might be entitled to deduct the loss up to the amount of his basis if his basis is positive.

We must assess if Ethan is covered by the at-risk regulations. The shareholder's amount at risk in the S corporation is the only amount that can be deducted for losses under the at-risk regulations.

If Ethan is subject to these rules, his loss deduction could be limited based on his at-risk amount.

A few tax provisions were temporarily changed as a result of the CARES Act. The CARES Act specifically altered the exclusions for business losses for non-corporate taxpayers, including individual S company shareholders. Ethan might not be able to deduct the $1,000,000 loss because of restrictions on company losses that existed prior to the CARES Act.

The excess business loss limitation for non-corporate taxpayers was temporarily suspended under the CARES Act.

This meant that Ethan and other individual shareholders could write off business losses without being constrained by the prior cap of $250,000 ($500,000 for married taxpayers filing jointly).

Therefore, regardless of any restrictions that could have existed before to the passage of the CARES Act, Ethan would be permitted to deduct the entire $1,000,000 loss in the current year if the CARES Act is applicable.

Taxpayers were temporarily helped by being able to deduct losses from other income. It's crucial to remember that the CARES Act was passed in reaction to the COVID-19 outbreak and that some of its requirements could not be in force at the moment.

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Answer:

62.25

Step-by-step explanation:

this quadrilateral is a trapizoid

A = (a+b)/2 * h

a = x

b = 2.4+4.2+x

h = 7.5

we know x is 5 so we just plug it in

after doing that we get 62.25

The average weight of a sample of objects is 94.83 pounds and the spread of the weights around the mean is measured by the sample standard deviation, which is 31.16 pounds.

The given data shows the weights (in pounds) of adult wild mountain lions captured and released for the first time in the San Andres Mountains.

(a) Using a calculator with mean and sample standard deviation keys, we can find the sample mean weight x and sample standard deviation s.

[tex]x = (70 + 107 + 130 + 128 + 60 + 64) / 6 = 94.83 \pounds\\\\s = \sqrt{\frac{(70 - 94.83)^2 + (107 - 94.83)^2 + ... + (64 - 94.83)^2} {5}}[/tex]

= 31.16 pounds

Therefore, the sample mean weight x is 94.83 pounds and the sample standard deviation s is 31.16 pounds.

(b) To find a 75% confidence interval for the population average weight u of all adult mountain lions in the specified region, we can use the formula:

CI = x ± t*(s/√n)

where CI is the confidence interval, x is the sample mean weight, t is the t-score for the desired confidence level (75% in this case), s is the sample standard deviation, and n is the sample size (6 in this case).

From the t-table, the t-score for a 75% confidence level with 5 degrees of freedom is 2.015.

Plugging in the values, we get:

CI = 94.83 ± 2.015*(31.16/√6) = (63.6 pounds, 126.1 pounds)

Therefore, we can be 75% confident that the true population average weight of all adult mountain lions in the specified region is between 63.6 pounds and 126.1 pounds.

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Answer:

0.0909

Step-by-step explanation:

4 blue + 5 red + 3 black = 12 chips in total.

p=probability

1st draw:

p (blue) = 4/12

there are now 11 chips in the bag, 4-1 =3 are blue.

2nd draw?

p (blue) = 3/11

probability of pulling one blue chip followed by another blue chip is:

(4/12) X (3/11) = (4X3)/12X11)

= (12)/(132)

= 1/11

0.0909

Step-by-step explanation:

7!  =  7 P 7 = 5040 ways

7 choices for first

6 choices for 2nd

5 choices for 3rd

4 chouces for 4th

3

2

1

           7 x 6 x 5 x 4 x 3 x 2 x 1 = 7!

An equation relating to P to N include the following: P(N) = 16.75N - 650.

In Mathematics, profit is a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.

Mathematically, the amount of profit made from selling x number of books can be calculated by using the following function:

Profit made = Revenue earned – Cost of production (cost price)

P(N) = R(N) - C(N)

P(N) = 33.70N - (650 + 16.95N)

P(N) = 33.70N - 650 - 16.95N

P(N) = 16.75N - 650

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The fraction of the wall that is concrete is 12/19

A fraction is a mathematical representation of a part of a whole or a division of one quantity by another. It consists of two parts: a numerator and a denominator, separated by a horizontal line called a fraction bar or a division slash.

The numerator represents the number of parts or the quantity being considered, while the denominator represents the total number of equal parts or the divisor. The numerator and denominator are both whole numbers or integers.

In this problem, to determine the fraction that is concrete, we have to know the total length of the wall.

length of wall = 24 + 5 + 9 = 38 inches

The fraction of the wall that is concrete = 24 / 38 = 12/19

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Answer:

[tex]20x+240y/y[/tex]

Step-by-step explanation:

1. Subtract the numbers

2. Evaluate the exponents

3. Subtract the numbers, again

4. Have a great day and thx for your inquiry :)

The total angle measurement of a triangle sum above is 180°. So yes,  it is possible to only make a right angle triangle but  impossible to draw a triangle

To check if a triangle can be drawn with 25°, 65°, and 90° angles, we use the Triangle Angle Sum Theorem stating that all triangle angles add up to 180 degrees.

If you add all the angles together (25 + 65 + 90 = 180°),  We can draw a triangle based on this sum, but we only consider the angles' nature. The triangle has angles of 25°, 65°, and 90°, making it a right triangle. It only applies to right triangle and not others triangle .

Note that based on the given angle measures of 25°, 65°, and 90°, it is impossible to draw a triangle as it does not follow the triangle inequality property.

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The probability that the spinner on the left will land on a 6 and the spinner on the right will land on a shaded area will be 1/9. The correct option is A.

Probability is a branch of mathematics that deals with the measurement and analysis of uncertainty. In other words, probability is the measure of the likelihood or chance that a particular event will occur.

The probability that the spinner on the left will land on a 6 is calculated as,

P₁ = 2 / 12

The spinner on the right will land in a shaded area is,

P₂ = 8 / 12

The total probability will be,

P =  ( 2 / 12 ) x ( 8 / 12 )

P = 1 / 9

Therefore, the probability that the spinner on the left will land on a 6 and the spinner on the right will land on a shaded area will be 1/9. The correct option is A.

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Answer: $89 for one day and 70 miles

Step-by-step explanation:

Friday has a 60% chance of rain. This indicates a relatively high Probability of rainfall, making it more likely to experience wet conditions on Friday.

The weather table provides information on the chance of rain for five consecutive days, starting from Monday to Friday. Here are the details:

Day of the Week | Chance of Rain

----------------|---------------

Monday          | 70%

Tuesday         | 10%

Wednesday    | 40%

Thursday        | 50%

Friday             | 60%

According to the table, Monday has the highest chance of rain with a probability of 70%. This indicates that there is a relatively high likelihood of rain occurring on Monday. However, it does not guarantee that it will rain, as there is still a 30% chance of a dry day.

On Tuesday, the chance of rain drops significantly to 10%. This suggests that it is highly unlikely for rain to occur on Tuesday, with a higher probability of dry weather.

Wednesday shows a moderate chance of rain at 40%. This indicates a somewhat higher possibility of precipitation compared to Tuesday but not as high as Monday.

Thursday follows with a 50% chance of rain. This suggests an even chance of rain or no rain, making it relatively uncertain.

Finally, Friday has a 60% chance of rain. This indicates a relatively high probability of rainfall, making it more likely to experience wet conditions on Friday.

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Answer:

$690

Step-by-step explanation:

To find the interest earned in three years, we can use the interest formula

Interest = Principal x Rate x Time

- Principal = $600 (the amount John deposited)

- Rate = 5% per year (as a decimal, this is 0.05)

- Time = 3 years

Interest = $600 x 0.05 x 3 = $90

Therefore, John will earn $90 in interest over 3 years.

To find his account balance, including interest, after 3 years, we can simply add the interest earned to the original principal:

Account balance = Principal + Interest

Account balance = $600 + $90 = $690

Therefore, John's account balance, including interest, after 3 years will be $690.

Answer:

Simple interest: 690, compound interest: 694.5

Step-by-step explanation:

Simple interest  = PRT/100 = 600*5*3/100 = 90 = 600+90 = 690

compound interest = P(1+r/100)^n = 600(1+5/100)^3 = 694.5

Your answer depends on if its simple or compound interest if not said so either of the answers I have given to you is right :)

The measure of angle RST is 90°.

option D.

The measure of angle RST is calculated by applying the principle of a right angle triangle as shown below;

A right-angled triangle, also known as a right triangle, is a triangle in which one of the angles measures exactly 90 degrees. The side opposite the right angle is called the hypotenuse, while the other two sides are known as the legs.

From the given diagram, the measure of angle RST is calculated as follows;

∠S = 90 (since this angle has a symbol of right angle)

So the other two angles, R and T are complementary.

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The error in solving the system of equations is given as follows:

Application of the negative signal, the distributive property must be applied instead of simply changing the signal of the first term.

The correct solution is:

(-10, -38).

The system of equations for this problem is defined as follows:

Replacing the second equation into the first, we have that:

2x - (4x + 2) = 18.

The negative sign changes the sign of all the terms inside the parenthesis, hence the value of x is obtained as follows:

2x - 4x - 2 = 18

-2x = 20

2x = -20

x = -10.

Then the value of y is given as follows:

y = 4(-10) + 2

y = -38.

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Answer:

Yes it can be negative

Step-by-step explanation:

For example, in a vacuum, there is no atmospheric pressure and the pressure is zero. If we introduce a sealed container into the vacuum and pump out the air, the pressure inside the container will be negative compared to the pressure outside the container.

the unit rate is 4 meters per second, meaning that for every second that passes, the distance increases by 4 meters.

The table shows the relationship between time and distance time is measured in seconds and distance is measured in meters.

The table provides us with the data points of time and distance allows us to examine the relationship between these two variables.

The table as time increases the distance also increases.

This suggests that there is a positive relationship between time and distance.

The unit rate of the relationship tells us how much distance changes for every unit of time.

The unit rate is 4 meters per second meaning that for every second that passes, the distance increases by 4 meters.

The relationship shown in the table is not necessarily a linear relationship.

A linear relationship would mean that the distance changes by the same amount for each unit of time.

The increase in distance is not constant over time.

From 5 seconds to 10 seconds the distance increases by 20 meters but from 10 seconds to 15 seconds the distance increases by 20 meters again and from 15 seconds to 20 seconds the distance increases by 20 meters yet again.

The table provides us with a snapshot of the relationship between time and distance and by examining the data we can identify patterns and relationships that can help us understand the behavior of these variables.

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The given function is tan (0+24°) and its cofunction can be expressed as ;tan (0+24°)=  tan (66⁰-0)

Therefore tan (0+24°) in terms of its cofunctions, we need to use the formulas for sin and cos of complementary angles.

The complementary angle of 24° is 66° because 24° + 66° = 90°.

Using the formula for the sum of two angles, we can then substitute these values to get:

tan (0+24°)=  tan (66⁰-0)

Therefore, expression of tan (0+24°)in terms of its cofunctions is tan (0+24°) =  tan (66⁰-0)

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The solution of the system of equations is the point (-4, 0)

Here we have the system of equations:

y = -x - 4

4y - 2x = 8

To find the solutions graphically, what we need to do is graph both equations on the same coordinate axis, and then find the points where the graphs of the equations intercept. These points are the solutions of the system.

On the image at the end, you can see the graph of the system of equations, there we can see that the lines intercept at the point (-4, 0), so that is the solution.

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The correct answer is option C: [tex]\(k + 4 = 16\).[/tex] This linear equation represents the relationship between Tina and Kai's volunteer times.

To represent the given situation, the equation that correctly represents the relationship between Tina's volunteer times (Tina = 16) and Kai's volunteer times (Kai = k) is:

[tex]\[Tina = Kai + 4\][/tex]

In this equation, Tina's volunteer times are represented by "Tina," and Kai's volunteer times are represented by "Kai." Since Tina has volunteered 4 more times than Kai, we add 4 to Kai's volunteer times to get the total number of times Tina has volunteered.

Substituting the given values, we have:

[tex]\[16 = k + 4\][/tex]

This equation represents the fact that Tina has volunteered [tex]16[/tex] times, which is equal to Kai's volunteer times (k) plus the additional 4 times that Tina volunteered.

Simplifying the equation:

[tex]\[k + 4 = 16\][/tex]

This equation is equivalent to the original equation and represents the relationship between Tina and Kai's volunteer times. Hence, the correct answer is option C: [tex]\(k + 4 = 16\).[/tex]

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the measure of the angle that is supplementary to angle RST is 90 degrees

To determine the value of the angle, we need to know the following;

From the information given, we have that;

Angle RST is its own complement

Then, angle RST =90 degrees

The supplementary angle should be y

Then,

RST + y= 180

substitute the values

y = 180 - 90

subtract the values

y= 90 degrees

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The number of unique preference orders that are represented in the table would be B. Five.

An individualized preference order is one way to assign a hierarchal ranking to an assortment of options. This ordering is recognized as "unique" because each item is assigned its own rank, with no two elements sharing the same level of priority.

From what is shown on the table, we have Voters 2, 4, 5 and 7 having a unique order. From these four voters, we therefore have four unique preference orders.

However, there is another unique preference order which is the shared preference order of Voters 1. 3 and 6 because this is unique preference order shared by three people.

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