Determine the unknown side of the similar triangle ​

btw ik this isn't college math it was automatically set to it

The number of boys more than girls altogether in the two programs is 6 boys

The number of boys and girls in the sport-studies program is :

= 30 x 60 %

= 18 girls

Boys in sport-studies program are:

= 30 - 18

= 12 boys

Boys in media tic program :

= 30 x 70 %

= 21 boys

Girls in media tic program:

= 30 - 21

= 9 girls

The difference is :

= ( 12 + 21 ) - ( 18 + 7 )

= 6 boys

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When applying the Central Limit Theorem (CLT) to define an interval within which we expect 95% of all sample means to fall, we would use a z-value of 1.96. This is because 95% of the area under a normal distribution curve falls within 1.96 standard deviations of the mean. Therefore, using a z-value of 1.96 will give us an interval that contains 95% of all sample means.

Here is a step-by-step explanation:

In conclusion, the correct answer is 1.96

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The balance at the end of a year is $1051.56.

To find the balance at the end of a year, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the balance after t years

P = the principal (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $1000, r = 0.05, n = 2 (since the interest is compounded semi-annually), and t = 1. Plugging these values into the formula, we get:

A = $1000(1 + 0.05/2)^(2*1)

= $1000(1.025)^2

= $1051.56

Therefore, the balance at the end of a year is $1051.56.

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The measure of EFG in the triangle is 58

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

WE have been given that Angles in a triangle add up to equal 180

So, 65 + 57 + ? must equal 180

Solve for the x;

65 + 57 + x = 180

Combine like terms;

122 + x = 180

Subtract 122 from both sides

122 - 122 + x = 180 - 122

x = 58

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The sum of the first 8 terms in the given geometric series is 65,535.

A geometric series is a sequence of numbers in which each term after the first is obtained by multiplying the previous term by a fixed non-zero constant called the common ratio.

In this case, the common ratio is 4, and the first term is 3. So, the first 8 terms of the series are:

3, 12, 48, 192, 768, 3072, 12288, 49152

To find the sum of the first 8 terms, we can use the formula for the sum of a finite geometric series:

S = a(1 - r^n) / (1 - r)

where S is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

Plugging in the given values, we get:

S = 3(1 - 4^8) / (1 - 4)

Simplifying the expression, we get:

S = 65,535

Therefore, the sum of the first 8 terms in the given geometric series is 65,535.

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--The question is incomplete, answering to the question below--

"The common ratio in a geometric series is 4 and the first term is 3. Find the sum of the first 8 terms in the series."

Answer: So whats the question then

Step-by-step explanation:

Answer: f=756

Step-by-step explanation:

f/28=7

multiply both sides of the equation by 28

28 x f/28=28 x 27

cancel out the greatest common factor 28

f=28 x 27

multiply 28 x 27

f=756

Answer:

310cm

Step-by-step explanation:

The Total surface of cuboid is S=2(lb+bh+lh)  

l=length

b=breadth b means w (width)

h=height

S=2(50+70+35)

S=2(155)

=310cm

Answer:

260 cm²

Step-by-step explanation:

Bottom surface area = 5 x 10 = 50

Surface area of the 2 long sides = 2(10 x 7) = 140

Surface area of the 2 short sides  = 2(5 x 7) = 70

Total surface area = bottom + 4 sides = 50 + 140 + 70 = 260 cm²

The true statement about the figure is not represented in the options

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

The triangle

The value of y can be calculated using the following Pythagoras theorem

y^2 = (3x)^2 + (4x)^2

Evaluate

y^2 = 25x^2

So, we have

y = 5x

The height is given as

Height = 100

This means that

4x = 100

So, we have

x = 25

For y, we have

y = 5x

y = 5 * 25

y = 125

For the area, we have

Area = 1/2 * 4x * 3x

Area = 1/2 * 4 * 25 * 3 * 25

Evaluate

Area = 3750

Hence, none of the options are true

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Giving each guest a room in a hotel is impossible if the group size exceeds the number of available rooms, resulting in some individuals having to share a room with someone else or not having a place to stay.

Logical thinking is a type of thinking that involves reasoning based on a set of premises or assumptions to arrive at a conclusion. It is a rational, systematic, and methodical way of thinking that involves analyzing information, identifying patterns, and drawing valid and sound conclusions.

Logical thinking involves using a combination of critical thinking skills, such as analysis, evaluation, and synthesis, to make reasoned judgments. It requires an ability to break down complex problems into smaller, more manageable parts, and to evaluate evidence in a clear and objective manner.

In logical thinking, conclusions are reached through a process of deduction or induction. Deduction involves starting with a general principle or premise and applying it to a specific situation to arrive at a conclusion. Induction, on the other hand, involves starting with specific observations or evidence and using them to make a general conclusion.

Logical thinking is essential in many fields, including science, mathematics, philosophy, and law, among others. It is also important in everyday life, such as when making decisions, solving problems, or evaluating arguments. By using logical thinking, individuals can make informed and reasoned judgments, and arrive at conclusions that are based on evidence and reason, rather than emotion or bias.

The Hotel Cardinality is a mathematical model that assumes that the hotel has an infinite number of rooms. However, in reality, hotels have a limited number of rooms. Therefore, if the group of people is larger than the number of available rooms, it would be impossible to give each person a room. For example, if the hotel has only 10 rooms and the group consists of 15 people, it is not possible to give each person a room. This is because there are more people than the number of available rooms, and some people will have to share a room or be left without a room. Hence, it is not always possible to accommodate all guests in a hotel, especially during peak seasons or when the hotel has limited capacity.

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Answer:

Step-by-step explanation:

the optimal point is (40,000, 40,000, 20,000), which gives an annual income of $680,000. The slack for the first, second, and fourth constraints is 0, and the slack for the third constraint is also 0.

The length of the apothem of the pentagon is 12.96 meters .

What is apothem ?
In geometry, the apothem of a polygon is the distance from the center of the polygon to the midpoint of one of its sides. For a regular polygon (a polygon with all sides and angles equal), the apothem is the perpendicular distance from the center of the polygon to one of its sides.

Explanation:
The formula for the area of a regular pentagon is:

A = (1/2)P × a

where A is the area, P is the perimeter, and a is the apothem.

To solve for the apothem, we need to rearrange the formula and solve for a:

a = (2A) / P

The perimeter of a regular pentagon is given by:

P = 5s

where s is the length of each side.

Substituting the given values, we get:

P = 5s = 5(9.7) = 48.5

A = 315.25

a = (2A) / P = (2 × 315.25) / 48.5 = 12.96

Therefore, the length of the apothem of the pentagon is 12.96 meters (rounded to two decimal places).

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Answer:

Step-by-step explanation:

its 13

Answer:

15 degrees for the first one

90 degrees for the second one

Step-by-step explanation:

Answer:

x = 6/7, y = 33/7

Step-by-step explanation:

y = 2x + 3 ----eq(1)

3x + 2y = 12 ----eq(2)

Substituting value of "y" from eq(1) into eq(2)

3x + 2(2x + 3) = 12

3x + 4x + 6 = 12

7x = 12-6

x = 6/7 ---eq(3)

Substituting value of x or eq(3) into eq (1)

y = 2(6/7) +3

y = 12/7 + 3

y= 12 + 21/7

y= 33/7

Therefore, x = 6/7 and y = 33/7

The length of b = √36 = 6 cm.

Length is a measurement of size and it can be measured in a variety of waste including inches sentiment of metres feet miles and more. Playing these an important concept in mathematics, science and engineering and many others build it to used to calculate the dimensions of this area. And more it is also used to measure the time it takes to travel.


Triangle ABC is a right triangle with angle B = 90°.

If a = 8 cm and c = 10 cm, we can use the Pythagorean Theorem to find the missing length, b.

The Pythagorean Theorem states that a2 + b2 = c2.

Therefore, b2 = c2 – a2 = 102 – 82 = 100 – 64 = 36.

The length of b = √36 = 6 cm.
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The length of median CP is 48.

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

Since the triangles are congruent, corresponding sides are equal. So, we have:

AB = DE (corresponding sides)

BC = EF (corresponding sides)

Now, we can use the formula for the length of a median of a triangle, which states that the median to a side of a triangle is half the length of the side that it intersects. Thus, we have:

CP = (1/2) AB

FQ = (1/2) DE

Substituting the values we have for AB and DE, we get:

CP = (1/2) AB = (1/2) DE = FQ

So, we can equate the expressions for CP and FQ, and solve for x:

3x - 12 = 2x + 8

x = 20

Now that we know the value of x, we can substitute it back into either expression for CP or FQ to find the length of CP:

CP = 3x - 12 = 3(20) - 12 = 48

Therefore, the length of median CP is 48.

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Answer:

it will take approximately 15.42 years for an investment of $567 at 4.5% continuous compounding to double to $1134.

Step-by-step explanation:

The formula for continuously compounded interest is:

A = Pe^(rt)

where A is the final amount, P is the initial principal, r is the annual interest rate, t is the time in years, and e is the mathematical constant approximately equal to 2.71828.

We want to know how long it will take for an initial investment of $567 to double, so our final amount will be $1134. We know that the interest rate is 4.5% or 0.045 as a decimal. Substituting these values into the formula, we get:

1134 = 567e^(0.045t)

Dividing both sides by 567, we get:

2 = e^(0.045t)

Taking the natural logarithm of both sides, we get:

ln(2) = 0.045t

Solving for t, we get:

t = ln(2)/0.045

Using a calculator, we get:

t ≈ 15.42 years

Therefore, it will take approximately 15.42 years for an investment of $567 at 4.5% continuous compounding to double to $1134.

Answer:

it Will give it 15 years in as much as the previous comment is accurate to my answer

Answer:

a=35

Step-by-step explanation:

5a=25×7

5a=175

5a/5=175/5

a=35

Answer:

A≈50.27in²

Step-by-step explanation:

A=πr2=π·42≈50.26548in²

Answer: $18,000 was invested at 11% profit

$15,000 was invested at 3% loss

Step-by-step explanation:

11x - .03 x (33000-x)=1530

11 x 18000- .03 x (33000 - 18000) =1530

1980-.03 x 15000 = 1530

1980 - 450 =  1530

1530 = 1530

Answer:

Step-by-step explanation:

A frequency distribution is a table or graph that displays the number of times each value or range of values occurs in a dataset, while a probability distribution is a function that describes the likelihood of each possible outcome of a random variable in terms of its probability.

In other words, a frequency distribution describes the actual frequencies or counts of the values in a dataset, while a probability distribution describes the theoretical probabilities of the outcomes of a random variable. Frequency distributions are typically used in descriptive statistics, while probability distributions are used in inferential statistics to make predictions and test hypotheses.

The width of the olen river is 16 yards

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

ABC, ~ EDC

The above means tha the triangles are similar triangles

Using the above as a guide, we have the following:

x : 32 = 20 : 40

Express as fraction

x/32 = 20/40

So, we have

x = 32 * 20/40

Evaluate

x = 16

Hence, the length is 16 yards

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Answer:

the odds of both events happening is 1 in 8 or 0.125.

Step-by-step explanation:

here are the step-by-step calculations to find the odds of both events happening:

The probability of the first event happening is 50%, which can be written as a decimal as 0.5.

The probability of the second event happening is 25%, which can be written as a decimal as 0.25.

To find the probability of both events happening, we multiply these probabilities together:

P(both) = P(first) x P(second)

= 0.5 x 0.25

= 0.125

We can also express this probability as odds by dividing the probability of both events happening by the probability of just one event happening (in this case, either the first or second event happening). The probability of one event happening is 0.5 + 0.25 = 0.75, since these events are mutually exclusive (only one of them can happen at a time). So the odds of both events happening is:

P(both) / P(one) = 0.125 / 0.75

= 1/8

Therefore, the odds of both events happening is 1 in 8 or 0.125.

The terminal point P(x, y) on the unit circle determined by the given value of t = 9π/2 is (0, -1).

A terminal point is a point at which a line or curve ends. An example of a terminal point is the point where the line x=5 ends. This point is 5 on the x-axis and has no y-value because the line does not extend beyond that point.

Another example of a terminal point is the point where the circle x2 + y2 = 25 ends. This point is (5,0), where x=5 and y=0. This means that the circle has a radius of 5 and the point (5,0) is the end of the circle.

The unit circle is centered at the origin (0, 0) and has a radius of 1. To find the terminal point with an angle of 9π/2, use the trigonometric functions sine (sin) and cosine (cos).

By calculating the x-coordinate of the point. This can be done using cosine:

x = cos(9π/2)

Since cosine of an angle of 9π/2 is equal to 0, the x-coordinate of the point is 0.

Calculate the y-coordinate of the point. This can be done using sine:

y = sin(9π/2)

Since sine of an angle of 9π/2 is equal to -1, the y-coordinate of the point is -1.

Therefore, the terminal point P(x, y) on the unit circle determined by the given value of t = 9π/2 is (0, -1).

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After constructing the scatter-plot chart, we can find that the Final and Mid-term have a negative relationship.

Dots are used in a scatter plot, also known as a scatter chart or scatter graph, to represent the values of two different numerical variables. The values of a data point are represented by the position of each dot on the horizontal and vertical axes. To view relationships between variables, utilize scatter plots. Scatter plots are primarily used to evaluate and present correlations between two numerical variables. When the data are viewed as a whole, the patterns shown by the dots in a scatter plot are in addition to the values of the individual data points.

Now in the given question, after drawing the scatter chart we can see a strong downward slope which represents a negative linear relationship.

Therefore, the Final and Mid-term have a negative relationship.

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The complete question is:

The accompanying table shows a portion of mid-term and final grades for 32 students.

Construct a scatterplot of Final against Mid-term. Given the scatterplot, which statement best describes the relationship between the Final and Mid-term?

A. Final and Mid-term have a negative relationship.

B. Final and Mid-term have a positive relationship.

C. Final and Mid-term have no relationship.

D. Final and Mid-term have a U-shaped (nonlinear) relationship.

To find the expression for the nth term of the sequence, we need to first find the common difference.

The common difference is the difference between any two consecutive terms in the sequence. We can see that the difference between each pair of consecutive terms is 6. Therefore, the common difference is 6.

To find the nth term, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

Substituting the values we have:

a1 = 5

d = 6

So the expression for the nth term of the sequence is:

an = 5 + (n - 1)6

Simplifying:

an = 6n - 1

The side length of the cube can be written as:

S = 3*∛5  centimeters.

We know that the cube has a volume of V = 135cm³.

Now, remember that for a cube of side length S, the volume is:

V = S³

Here we can replace the volume in the equation above, we will get:

135cm³ = S³

If we apply the cube root in both sides, we will get:

∛(135 cm³) = S

∛135 cm = S

Now we can rewrite that as:

135 = 9*5

Then we can rewrite the expression:

∛135  = ∛(27*5) = ∛27*∛5 = 3*∛5

That is the sidelength of the cube.

So we have A = 3 and B = 5.

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The annual yield of the bond is 3.50%.

To calculate Mike's profit, we first need to determine the total cost of his investment, including the back-end load. The back-end load is calculated by multiplying the initial investment by the loading rate:

Back-end load = $14,000 * 5.5% = $770

So the total cost of Mike's investment is:

Total cost = $14,000 + $770 = $14,770

To determine the profit, we need to subtract the total cost from the total amount Mike received when he sold his shares:

Profit = ($21.85 - $20.00) * 14,000 - $770 = $2,730

Therefore, Mike made a profit of $2,730.

Note that the problem statement is exactly the same as the previous question. The answer is $2,730.

The annual rental income that Clara Teague needs to receive to achieve an annual yield of 8% can be calculated as follows:

Annual rental income = Total investment * Yield

where Total investment = $115,800 - $25,000 = $90,800

So the annual rental income that Clara Teague needs to receive is:

Annual rental income = $90,800 * 8% = $7,264

To determine the monthly rent, we divide the annual rental income by 12:

Monthly rent = $7,264 / 12 = $605.33

Therefore, Clara should charge a monthly rent of $605.33 to achieve an annual yield of 8%.

The annual yield of the bond can be calculated as follows:

Annual yield = (Annual interest payment / Bond price) * 100%

The annual interest payment is:

Annual interest payment = Bond face value * Annual interest rate = $25,000 * 3.7% = $925

The bond price is quoted at 105.7% of its face value, so the bond price is:

Bond price = Bond face value * 105.7% = $25,000 * 1.057 = $26,425

So the annual yield is:

Annual yield = ($925 / $26,425) * 100% = 3.50%

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Using the loan rates we know that the maximum loan amount Tyresa needs to pay for 4 years which is 48 months is $330.81 for the new car.

The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal or the loaned amount.

Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).

The annual cost of a loan to a borrower is referred to as the interest rate and is indicated as a percentage.

APR represents the total yearly cost of a loan to the borrower, including all fees.

The APR is stated as a percentage, just like an interest rate.

Thus, we discover that using the present value formula:

Pv = C[(1-(1+i)n/i)]

Now, calculate for the new car as follows:

Pv = 350[(1-(1+2.79%/12)2.79%/12)]

Pv = $15879.04

Loan amount each month: 15879.04/48 months = $330.81

Similarly, calculate for the old car as follows:

Pv = 350[(1-(1+3.29%/12)3.29%/12)]

Pv = $15721.34

Loan amount each month: 15721.34/48 months = $327.52

Therefore, using the loan rates we know that the maximum loan amount Tyresa needs to pay for 4 years which is 48 months is $330.81 for the new car.

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