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The second equation results in n^2 = c^2.

Let's suppose we have two equations:

Equation 1: c^2 = a^2 + b^2

Equation 2: n^2 = a^2 + b^2

Both equations have the term a^2 + b^2. We can treat these equations as a system of equations and substitute the value of a^2 + b^2 from Equation 1 into Equation 2.

Substituting a^2 + b^2 from Equation 1 into Equation 2, we get:

n^2 = c^2

After substituting, we obtain the equation n^2 = c^2. This equation shows that the squares of the lengths of the sides n and c are equal.

It's important to note that this result holds true because both triangles have the same a and b values, leading to the same value of a^2 + b^2. Therefore, substituting that value into the second equation results in n^2 = c^2.

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If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:

b = total_number_of_pears / pears_per_bag

In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.

Given that Natalie has a total of 48 pears, we can substitute the value into the equation:

b = 48 / pears_per_bag

Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.

Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:

b = 48 / 4

Simplifying the equation gives:

b = 12

So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.

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The end of 6 months, Ram should pay Rs. 276250 compounded half-yearly.

Ram borrowed Rs. 250000 from Sit at an interest rate of 21% per annum. To calculate the compound interest, we need to know the compounding period. In this case, the interest is compounded half-yearly, which means it is calculated twice a year.

To find out how much Ram should pay at the end of 6 months, we can use the compound interest formula:

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

Where:
A = the amount to be paid at the end of the time period
P = the principal amount (the initial amount borrowed) = Rs. 250000
r = the interest rate per period (in decimal form) = 21% = 0.21
n = the number of compounding periods per year = 2 (since it's compounded half-yearly)
t = the number of years = 6 months = 6/12 = 0.5 years

Plugging in these values into the formula, we get:

A = 250000(1 + 0.21/2)^(2*0.5)

Simplifying the equation:

A = 250000(1 + 0.105)^(1)

A = 250000(1.105)

A = Rs. 276250

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The built area of 50% of the house on the rectangular piece of land measures 576 cm^2.

To find the built area of 50% of a house on a rectangular piece of land, we need to calculate the area of the rectangular piece of land and then determine 50% of that area.

The rectangular piece of land has dimensions of 64 cm by 18 cm. To calculate the area, we multiply the length by the width:

Area = Length * Width

Area = 64 cm * 18 cm

Area = 1152 cm^2

The total area of the rectangular piece of land is 1152 cm^2.

To find the built area, which is 50% of the total area, we multiply the total area by 50% (or 0.5):

Built Area = Total Area * 50%

Built Area = 1152 cm^2 * 0.5

Built Area = 576 cm^2

Therefore, the built area of 50% of the house on the rectangular piece of land measures 576 cm^2.

It's important to note that this calculation assumes that the built area is uniformly distributed on the land and represents half of the house's total area. The actual shape and distribution of the house may vary, but this calculation provides an estimate of the built area based on the given information.

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Note the translate question is:

On a rectangular piece of land that measures 64 cm by 18 cm, they are going to build 50% of a house. What is the built area?

Answer:

Step-by-step explanation:

waza skibidi domo dom yes yes  insanito free fire

The domain for the time in this context is (0, 7.4)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let h represent the height of the ball after spending t seconds. A ball is thrown straight up from the top of a building that is 168 ft high with an initial velocity of 96 ft/s.

Given the equation:

h(t) = -16t² + 96t + 168

The reasonable domain restriction for t, is when  the height of the rocket is above the ground. Hence the domain for the time in this context is (0, 7.4)

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The correct choice is A. Both the mean and median will decrease, but the mean will decrease by more than the median.

To determine how removing the 24-second time will affect the mean and median, let's first calculate the mean and median of the original set of times.

The original set of times without the 24-second result is a set of 4 values between 11 and 13 seconds.

Let's assume the original set of times (excluding 24 seconds) is {x1, x2, x3, x4}, where x1, x2, x3, and x4 are unique values between 11 and 13 seconds.

Mean: The mean is calculated by summing up all the values and dividing by the number of values.

Mean = (x1 + x2 + x3 + x4) / 4

Median: The median is the middle value when the values are arranged in ascending order.

Since there are four values, the median will be the average of the two middle values.

Median = (x2 + x3) / 2

Now, let's consider the options provided and see how removing the 24-second time affects the mean and median.

A. Both the mean and median will decrease, but the mean will decrease by more than the median.

If we remove the 24-second time, the new set of values will still have the same range (between 11 and 13 seconds), and since the 24-second time is the largest value in the original set, removing it will decrease both the mean and median.

However, since the 24-second time is an outlier (a significantly larger value compared to the others), removing it will have a greater impact on the mean compared to the median. The mean will decrease by more because the sum of the values will decrease more than the difference between x2 and x3, affecting the numerator of the mean calculation.

Therefore, choice A is correct.

In conclusion, removing the 24-second time from the original set of times will decrease both the mean and median, but the mean will decrease by more than the median.

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Question

At track practice, Alexia ran 5 attempts of the 100-meter dash. All of her times were different values between 11 and 13 seconds, except for an attempt when she tripped and finished in 24 seconds.

Alexia's coach said they would remove the 24 result from the set of these practice times.

How will removing this time affect the mean and median?

(Choice A)

A. Both the mean and median will decrease, but the mean will decrease by more than the median.

(Choice B)

B. Both the mean and median will decrease, but the median will decrease by more than the mean.

(Choice C)

C. Both the mean and median will increase, but the mean will increase by more than the median.

(Choice D)

D. Both the mean and median will increase, but the median will increase by more than the mean.

Answer:

7

Step-by-step explanation:

V looking shape has ends at 1 & 8

8 - 1 = 7

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The square root of the expression -36 is DNE

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

[tex](-36)^\frac 12[/tex]

By definition, the square root of negative numbers are complex numbers

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

[tex](-36)^\frac 12[/tex] is not a real number

Hence, the solution is DNE

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Answer:

123°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , then

third angle + 22° + 35° = 180°

third angle + 57° = 180° ( subtract 57° from both sides )

third angle = 123°

Answer: 5/ 16

explanation: total= 4x4=16

red and yellow : (r,y) or (y,r)

n= 5

p= 5 1/1 16

p = 5 over 16

The study described is an experimental study in nature. It follows a randomized double-blind placebo-controlled trial design, where participants were randomly assigned to either a verum (onabotulinumtoxinA) or placebo (saline) group.

The researchers administered the treatment (botulinum toxin injection to the glabellar region) to the verum group while the placebo group received a saline injection. The primary end point was the change in depressive symptoms measured using the Hamilton Depression Rating Scale.

The statistical hypothesis in this study does involve a cause/effect relationship between the explanatory variable (botulinum toxin injection) and the response variable (alleviation of depression symptoms).

Potential confounding variables in this study could include factors such as participants' previous medication history, severity of depression, and other ongoing treatments or therapies for depression.

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The equation of the tangent line at the point (108, 6) on the curve y² = x²/(xy - 324) is: y = 6

The equation is given as:

y² = x²/(xy - 324) at (108, 6)

Differentiating implicitly with respect to x gives:

2y(dy/dx) = (2x(xy - 324) - x²(y - 324)(dy/dx)) / (xy - 324)²

Simplifying further using power rule and chain rule gives us:

[tex]\frac{dy}{dx} = \frac{x^{2}y - 648x }{2y(-324 + xy) +x^{3} }[/tex]

We can find the slope by plugging in x = 108 and y = 6 to get

[tex]\frac{dy}{dx} = \frac{(108^{2}*6) - 648(108) }{2(6)(-324 + (108*6)) + 108^{3} }[/tex]

dy/dx = 0

To find the equation of the tangent line, we use the point-slope form:

y - y₁ = m(x - x₁),

where:

(x₁, y₁) is the given point (108, 6) and m is the slope.

Substituting the values, we have:

y - 6 = 0(x - 108)

y = 6

This is the equation of the tangent line at the point (108, 6) on the curve y² = x²/(xy - 324).

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Answer:

A.

3.25x + 13.50 ≤ 40

Step-by-step explanation:

Answer:

m = -0.204

Step-by-step explanation:

Start by creating points (72, 133) and (24, 235.2+133)

You are relating the charge (as a whole number) to the total distance traveled at a respective percentage. At 72% you traveled 133 miles and at 24% you traveled a total of 368.2 miles.

Thus, you can use the slope formula [tex](y2-y1)/(x2-x1)[/tex]

Thus, (72-24)/(133-368.2) = -0.204 (approx.)

Hope this helps!

Answer:

P ≈ $12,654.89

Step-by-step explanation:

To calculate the amount of money that should be deposited today, we can use the formula for compound interest:

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

Where:

A = the future value of the investment ($15,000 in this case)

P = the principal amount (the amount to be deposited today)

r = the annual interest rate (4.5% or 0.045 as a decimal)

n = the number of times the interest is compounded per year (monthly compounding, so n = 12)

t = the number of years (4 years in this case)

Substituting the given values into the formula, we have:

$15,000 = P(1 + 0.045/12)^(12*4)

Simplifying the equation:

$15,000 = P(1.00375)^(48)

To solve for P, we divide both sides of the equation by (1.00375)^(48):

P = $15,000 / (1.00375)^(48)

Using a calculator, we find:

P ≈ $12,654.89

Therefore, approximately $12,654.89 should be deposited today in order to accumulate to $15,000 in 4 years with a 4.5% annual interest rate compounded monthly.

Let's represent the number with the variable "x". According to the given property, we can write the following equation:

3(x + 4) < 7x

Now, let's solve this inequality to find the range of numbers that satisfy the property.

3x + 12 < 7x

Subtract 3x from both sides:

12 < 4x

Divide both sides by 4 (since the coefficient of x is 4):

3 < x

So, the range of numbers that satisfy the given property is x > 3.

Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:

The sample space for this experiment is the one in the last option.

The sample space is the set of the possible outputs that we can have for selecting two marbles.

For example, if first you get a yellow marble, and then a red one, the output will be:

yellow red,

And that is different to the output:

red yellow

Where in the second one you draw the red one first.

From the options, the one that shows the complete sample space is the last one:

"Yellow Yellow, Yellow Red, Yellow Clear, Yellow Green, Yellow Blue, Yellow

Red Yellow, Red Red, Red Clear, Red Green, Red Blue, Red

Clear Yellow, Clear Red, Clear Clear, Clear Green, Clear Blue, Clear

Green Yellow, Green Red, Green Clear, Green Green, Green Blue, Green

Blue Yellow, Blue Red, Blue Clear, Blue Green, Blue Blue, Blue"

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25 quarter cups in 6 1/4 cups

answer: 61

Answer:

slope = - [tex]\frac{3}{2}[/tex] , y- intercept = 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3x + 2y = 14 ( subtract 3x from both sides )

2y = - 3x + 14 ( divide through by 2 )

y = - [tex]\frac{3}{2}[/tex] x + 7 ← in slope- intercept form

with slope m = - [tex]\frac{3}{2}[/tex] and y- intercept c = 7

It is not accurate to make a blanket statement that the U.S. always has a lower unemployment rate than other countries. The unemployment rates can differ significantly based on specific circumstances, making it important to examine the relevant data and context before drawing conclusions.

The statement "The unemployment rate in the U.S. tends to be lower than in other countries" is subjective and cannot be definitively categorized as true or false without further context and data analysis.

Unemployment rates vary across countries due to a multitude of factors, such as economic conditions, labor market policies, demographics, and government interventions. While it is true that at certain times the unemployment rate in the U.S. may be lower than in some other countries, it is not universally true in all circumstances.

Comparing unemployment rates between countries requires a comprehensive analysis of various factors and data points, including the specific time period, the methodology used for calculating unemployment, and the demographic and socio-economic characteristics of each country. Additionally, economic conditions can fluctuate over time, leading to variations in unemployment rates.

Therefore, it is not accurate to make a blanket statement that the U.S. always has a lower unemployment rate than other countries. The unemployment rates can differ significantly based on specific circumstances, making it important to examine the relevant data and context before drawing conclusions.

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The equation of the line parallel to the line passing through (1, -2) and (-4, 3) and passing through the point (-4, -5) is y = -x - 9 in slope-intercept form.

To find the equation of a line parallel to a given line, we need to determine the slope of the given line and then use it to construct the equation of the parallel line.

First, let's calculate the slope of the given line passing through points (1, -2) and (-4, 3). The slope, denoted as m, can be found using the slope formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates, we have:

m = (3 - (-2)) / (-4 - 1) = 5 / (-5) = -1

Now that we have the slope, we can use it to construct the equation of the parallel line.

We'll use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line.

We'll use the point (-4, -5) on the parallel line:

y - (-5) = -1(x - (-4))

y + 5 = -1(x + 4)

Simplifying further:

y + 5 = -x - 4

y = -x - 9

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The combinations of assembling these rectangles for which it is possible to create a rectangle with the length of 15 and the width 11 with no gaps or overlapping are:

A rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides.

Required

Which group forms a rectangle of

[tex]\text{Length}=15[/tex]

[tex]\text{Width}=11[/tex]

First, calculate the area of the big rectangle

[tex]\text{Area}=\text{Length}\times\text{Width}[/tex]

[tex]\text{A}_{\text{Big}}=15\times11[/tex]

[tex]\text{A}_{\text{Big}}=165[/tex]

Next, calculate the area of each rectangle A to E.

[tex]\text{A}_{\text{A}}=11\times7[/tex]

[tex]\text{A}_{\text{A}}=77[/tex]

[tex]\text{A}_{\text{B}}=2\times11[/tex]

[tex]\text{A}_{\text{B}}=22[/tex]

[tex]\text{A}_{\text{C}}=6\times6[/tex]

[tex]\text{A}_{\text{C}}=36[/tex]

[tex]\text{A}_{\text{D}}=6\times5[/tex]

[tex]\text{A}_{\text{D}}=30[/tex]

[tex]\text{A}_{\text{E}}=13\times4[/tex]

[tex]\text{A}_{\text{E}}=52[/tex]

Then consider each option.

(a) 2C + 2D + 2B

[tex]2\text{C}+2\text{D}+2\text{B}=(2\times36)+(2\times30)+(2\times22)[/tex]

[tex]2\text{C}+2\text{D}+2\text{B}=72+60+44[/tex]

[tex]2\text{C}+2\text{D}+2\text{B}=176[/tex]

(b) A + B + C + D

[tex]\text{A}+\text{B}+\text{C}+\text{D}=77+22+36+30[/tex]

[tex]\text{A}+\text{B}+\text{C}+\text{D}=165[/tex]

(c) A + 4B

[tex]\text{A} + 4\text{B}=77+(4\times22)[/tex]

[tex]\text{A} + 4\text{B}=77+88[/tex]

[tex]\text{A} + 4\text{B}=165[/tex]

(d) 3E + 2B

[tex]3\text{E}+2\text{B}=(3\times52)+(2\times22)[/tex]

[tex]3\text{E}+2\text{B}=156+44[/tex]

[tex]3\text{E}+2\text{B}=200[/tex]

(e) E + C + D + 3B

[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=52+36+30+(3\times22)[/tex]

[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=52+36+30+66[/tex]

[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=184[/tex]

Recall that:

[tex]\text{A}_{\text{Big}}=165[/tex]

Only options (b) and (c) match this value.

[tex]\text{A}+\text{B}+\text{C}+\text{D}=165[/tex]

[tex]\text{A} + 4\text{B}=165[/tex]

Hence, options (b) and (c) are correct.

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Savings accounts and CDs are good options for people who want to save money without taking on a lot of risk.

If Anita and Miguel do not take any money from their accounts, Anita's account will grow faster than Miguel's.

This is because the interest rate for Anita's account is 6%, while Miguel's is 5%.

The interest rate is the percentage of the principal that a bank or other financial institution pays for the use of money.

It can be thought of as a fee charged for borrowing money.

The higher the interest rate, the more money a person can earn on their investment.

Anita and Miguel's accounts are probably savings accounts or CDs, which are low-risk investments that pay a fixed interest rate.

Savings accounts and CDs are good options for people who want to save money without taking on a lot of risk.

Anita and Miguel's accounts are probably savings accounts or CDs, which are low-risk investments that pay a fixed interest rate.

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Answer:

In summary, the faster cyclist cycles at a speed of 18 mi/h since they travel 36 of the 54 miles in 2 hours while cycling twice as fast as the slower cyclist.

Explanationn:

The two cyclists are 54 miles apart and heading toward each other.

One cyclist cycles 2 times as fast as the other. We will call the faster cyclist A and the slower cyclist B.

They meet 2 hours after starting. This means they travel a total distance of 54 miles in 2 hours.

Since cyclist, A cycles 2 times as fast as cyclist B, cyclist A travels 2/3 of the total distance, and cyclist B travels 1/3 of the total distance.

In two hours, cyclist A travels (2/3) * 54 miles = 36 miles.

We need to find the speed of cyclist A in miles per hour.

Speed = Distance / Time

So the speed of cyclist A is:

36 miles / 2 hours = 18 miles per hour

Therefore, the speed of the faster cyclist is 18 mi/h.

The direction and degree of rotation used to create the image include the following: C. 90° clockwise rotation.

In Mathematics and Geometry, a rotation is a type of transformation that moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By applying either a rotation of 90° clockwise or a rotation of 270° counterclockwise to the coordinate of triangle ABC, the coordinate of its image (triangle A′B′C′);

(x, y)                            →            (y, -x)

Point A = (-2, -7)          →     Point A′ (-7, 2)

Point B = (3, -2)          →     Point B′ (-2, -3)

Point C = (2, -10)          →     Point C′ (-10, -2)

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Complete Question:

Determine the direction and degree of rotation used to create the image.

90° counterclockwise rotation

270° clockwise rotation

90° clockwise rotation

180° clockwise rotation

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

Step-by-step explanation:

since we are taking about true halves (I hope), both halves "weigh" the same, and a percentage in one has the same absolute value as in the other.

then the answer is just based on the mean value between both percentages :

x = percentage of the second half

70 = (78 + x)/2

140 = 78 + x

x = 140 - 78 = 62%

she needs at least 62% on the second half to pass the 70% minimum limit of the whole test.

The equation for true airspeed T in terms of altitude and differential pressure p - T = k * (1 + A/50,000) * p

To write the equation for true airspeed T in terms of altitude A and differential pressure p, we need to consider the relationship between indicated airspeed S and differential pressure.The indicated airspeed S is typically measured using a pitot tube, which measures the dynamic pressure of the air flowing around the aircraft. The differential pressure p represents the difference between the dynamic pressure measured by the pitot tube and the static pressure of the surrounding air. In other words, p = dynamic pressure - static pressure.

The equation T = (1 + A/50,000) * S, we can express S in terms of the differential pressure p. Let's assume that S is directly proportional to p:

S = k * p

where k is a constant of proportionality. By substituting this expression for S into the equation for true airspeed, we have:

T = (1 + A/50,000) * (k * p)

Simplifying, we can write the equation for true airspeed T in terms of altitude A and differential pressure p as:

T = k * (1 + A/50,000) * p

where k is the constant of proportionality relating differential pressure to indicated airspeed.

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For the above function describing movie rental expenses, neither the input (6.5) nor the output ($17.50) are possible or reasonable.

The solution (6.5, $17.50) does not make sense for the function g(x) representing the amount of money spent on renting movies, where x is the number of movies.

The reason is that the input value, 6.5, does not make sense in the context of renting movies. The number of movies rented should be a whole number, not a decimal or fractional value. Therefore, the input is not feasible.

In addition, the output value, $17.50, does not make sense either. Typically, the cost of renting movies is given in whole dollar amounts. It is highly unlikely to have a rental cost of $17.50 for a movie marathon involving 6.5 movies. Therefore, the output is not feasible.

In conclusion, neither the input (6.5) nor the output ($17.50) is feasible or realistic for the given function representing movie rental expenses.

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