A right triangle is shown. The length of the hypotenuse is 4 centimeters and the lengths of the other 2 sides are congruent.
The hypotenuse of a 45°-45°-90° triangle measures 4 cm. What is the length of one leg of the triangle?

2 cm
2 StartRoot 2 EndRoot cm
4 cm
4 StartRoot 2 EndRoot cm

This means that in the population represented by the formula, someone with a femur length of 27.4 centimeters would be expected to have a height of 128 centimeters

When h is 128, we can use the formula h = 2.46f + 60.6 to solve for the corresponding value of f.

128 = 2.46f + 60.6

Subtracting 60.6 from both sides:

67.4 = 2.46f

Dividing both sides by 2.46:

f ≈ 27.4

Therefore, when h is 128, the f-value (length of the femur) is approximately 27.4 centimeters. This means that in the population represented by the formula, someone with a femur length of 27.4 centimeters would be expected to have a height of 128 centimeters.

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The angle θ lies in Quadrant I given that cos(θ) > 0 and sin(θ) > 0.

Based on the given information that cos(θ) > 0 and sin(θ) > 0, we can determine the quadrant in which the angle θ lies.

Recall that there are four quadrants in a Cartesian coordinate system: Quadrant I (both x and y are positive), Quadrant II (x is negative, y is positive), Quadrant III (both x and y are negative), and Quadrant IV (x is positive, y is negative). The cosine function, cos(θ), represents the x-coordinate of a point on the unit circle, while the sine function, sin(θ), represents the y-coordinate.

Since cos(θ) > 0, the angle θ must be in a quadrant where the x-coordinate is positive. This means that θ can lie in either Quadrant I or Quadrant IV. Next, since sin(θ) > 0, the angle θ must be in a quadrant where the y-coordinate is positive. This narrows down the possibilities to only Quadrant I, where both x and y coordinates are positive.

Therefore, the angle θ lies in Quadrant I given that cos(θ) > 0 and sin(θ) > 0.

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The value of the algebraic expression from the given parameters is:

x³ + 1/x³ = 0

The given problem is simply based on the expansion.

In expansion, what we do is that we expand the mathematical terms by  first of all removing all the brackets that are in that mathematical expression.

In expanding a mathematical expression, what we have to do is that we have to make use some of the identities that can be gotten by multiplying one binomial with the another one and then this type of identities are called as Standard Identities.

For example:  

(x + a)(x + b) = x² + (a + b)x + ab

Thus:

(x + 1/x)² = 3

x + 1/x = √3

(x+1/x)³ = x³ + (1/x)³ + 3(x)(1/x) (x + 1/x)

√3³ = x³ + 1/x³ + 3(√3)

x³ + 1/x³ = 3√3 - 3√3

x³ + 1/x³ = 0

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Answer:

The unit  in a volume are always cubic meter

Step-by-step explanation:

Chain of Thought Reasoning: Volume is a three dimensional space, which is measured in three dimensions (length, width, and depth). The SI unit for length is meters, so the SI unit for volume is cubic meters (m^3).                        I hope this helps you

Hi! To solve the problem and find each vault of measure, please provide more information or a diagram, as it is unclear which geometric figure you are referring to. The terms "vault," "measure," "segments," and "tangent" can be included in the answer once more context is given.

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Angle WXY is vertical to angle WXZ, they are equal, therefore, angle WXY is also 141 degrees.

To find the angle WXY, we need to use the properties of angles formed by intersecting chords in a circle. The angles formed by intersecting chords are related to the arcs intercepted by those chords.

Given that the arc WVX is equal to (13x + 9) and the angle WXZ is equal to (5x + 36), we can set up an equation:

Angle WXZ = [tex]\frac{1}{2}[/tex] * Arc WVX

(5x + 36) = [tex]\frac{1}{2}[/tex] * (13x + 9)

To solve for x, we'll multiply both sides of the equation by 2 to eliminate the fraction:

2(5x + 36) = 13x + 9

10x + 72 = 13x + 9

Subtracting 10x and 9 from both sides, we get:

72 - 9 = 13x - 10x

63 = 3x

Dividing both sides by 3, we find:

x = 21

Now that we have the value of x, we can substitute it back into the equation for the angle WXZ to find its value:

Angle WXZ = 5x + 36 = 5(21) + 36 = 105 + 36 = 141 degrees

Since angle WXY is vertical to angle WXZ, they are equal. Therefore, the angle WXY is also 141 degrees.

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To determine which postulate can be used to prove that triangle CAT and triangle DOG are congruent, we need information about the side lengths and angles of each triangle. Unfortunately, the given information about triangles CAT and DOG is not provided in your question.

However, I can briefly explain each of the mentioned postulates to help you understand how they can be applied to prove congruence:

1. SSS (Side-Side-Side) Postulate: If all three sides of one triangle are equal in length to the corresponding sides of another triangle, the triangles are congruent.

2. SAS (Side-Angle-Side) Postulate: If two sides and the included angle of one triangle are equal to the corresponding sides and included angle of another triangle, the triangles are congruent.

3. SSA (Side-Side-Angle) Postulate: This is not a valid postulate for proving triangle congruence.

4. ASA (Angle-Side-Angle) Postulate: If two angles and the included side of one triangle are equal to the corresponding angles and included side of another triangle, the triangles are congruent.

5. AAS (Angle-Angle-Side) Postulate: If two angles and a non-included side of one triangle are equal to the corresponding angles and non-included side of another triangle, the triangles are congruent.

Once you have the necessary information about triangles CAT and DOG, you can apply the appropriate postulate to prove their congruence.

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The limit of the given function as t approaches 0 is undefined.

To find the limit of the given function,[tex]lim (e^(5t) - 1) / (t × sin(t))[/tex] as t approaches 0, follow these steps:

Observe the given function

[tex]lim (e^(5t) - 1) / (t × sin(t)) as t → 0[/tex]

Apply L'Hopital's Rule, since the limit is of the form 0/0 as t approaches 0.

Differentiate the numerator and denominator with respect to t.

Numerator: [tex]d(e^(5t) - 1)/dt = 5e^(5t)[/tex]

Denominator: [tex]d(t × sin(t))/dt = sin(t) + t × cos(t)[/tex]

Rewrite the function with the new numerator and denominator.

lim [tex](5e^(5t)) / (sin(t) + t × cos(t)) as t → 0[/tex]

Evaluate the limit as t approaches 0.

[tex](5e^(5 × 0)) / (sin(0) + 0 × cos(0)) = 5 / 0[/tex]

Since the denominator is still 0, the limit does not exist.

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The values of a, b, and c in the matrix equation are a = 3, b = 1 and c = 8

To determine the values of a, b, and c in the matrix equation:

4 a  +  3  0    = 7  3

3 4      5  b       c   5

By addition operation, we have

a + 0 = 3

3 + 5 = c

4 + b = 5

When the equations evaluated, we have

a = 3

c = 8

b = 1

The above are the values of a b and c

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Complete question

Determine the values of a, b, and c in the following matrix equation.

4 a  +  3  0    = 7  3

3 4      5  b       c   5

The values that satisfy the inequality -1/2x + 5>7 are -8 and -6.

To determine which values from the set {-8, -6, -4, -1, 0, 2} satisfy the inequality -1/2x + 5 > 7, we first need to isolate the variable x. Start by subtracting 5 from both sides of the inequality:

-1/2x > 2

Now, multiply both sides by -2 to solve for x. Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign:

x < -4

Now we can see that the inequality is asking for all values of x that are less than -4. Looking at the given set {-8, -6, -4, -1, 0, 2}, we can identify the values that satisfy this condition:

-8 and -6 are the values that are less than -4.

Therefore, the values from the set {-8, -6, -4, -1, 0, 2} that satisfy the inequality -1/2x + 5 > 7 are -8 and -6.

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577 square feet is the area of the painted part of the wall.

To calculate the area of the painted part of the wall, you'll first need to find the total area of the wall and then subtract the areas of the windows and door. Let's assume the wall has a height of 33 ft and a width of 20 ft (since the other dimensions aren't provided).

1. Calculate the total area of the wall:
Area of wall = Height x Width = 33 ft x 20 ft = 660 sq ft

2. Calculate the areas of the windows and door:
Window A = 6 ft x 5 ft = 30 sq ft
Window B = 3 ft x 4 ft = 12 sq ft
Window C = 9 sq ft (already provided)
Door D = 4 ft x 8 ft = 32 sq ft

3. Subtract the areas of the windows and door from the total wall area:
Painted area = Wall area - (Window A + Window B + Window C + Door D) = 660 sq ft - (30 sq ft + 12 sq ft + 9 sq ft + 32 sq ft) = 660 sq ft - 83 sq ft = 577 sq ft

The area of the painted part of the wall is 577 square feet.

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Answer:

for that first u should know that how much litres of water that aquarium can contain.

for that first u should know that how much litres of water that aquarium can contain.so that probably depends upon the size length and width of a container

for that first u should know that how much litres of water that aquarium can contain.so that probably depends upon the size length and width of a containera normal container can be filled with approximately 15 containers

The measure of angle M is 20°.

To solve the problem, we need to find the measure of angle M, given the information about Circle K with center O, diameter US, angle MRU = 50°, and angle MUT = 30°.

Step 1: Determine the relationship between angles MRU and MUT.
Since MRU and MUT are both inscribed angles in Circle K, they share the same intercepted arc, which is arc MU.

Step 2: Calculate the measure of arc MU.
The measure of an intercepted arc is twice the measure of the inscribed angle. Since angle MRU = 50°, the measure of arc MU will be 2 * 50° = 100°.

Step 3: Find the measure of angle M.
We know that angle MUT = 30°, and the measure of an intercepted arc is twice the measure of the inscribed angle. Therefore, the measure of arc MT = 2 * 30° = 60°. Now, since arc MU = 100°, we can determine the measure of arc MS (arc MS = arc MU - arc MT) which is 100° - 60° = 40°.

Step 4: Calculate the measure of angle M.
Finally, the measure of angle M can be found using the intercepted arc MS. Since the measure of an intercepted arc is twice the measure of the inscribed angle, angle M = 1/2 * arc MS = 1/2 * 40° = 20°.

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The median is a better center for this data because the data is not normally distributed and clusters on the left.

Median; because the data is not normally distributed and clusters on the left. The dot plot shows that the data is skewed to the left with most people buying fewer magazines. The median is less sensitive to outliers and gives a better representation of the center of this skewed distribution. The mean would be affected by the outlier (1 person bought 9 magazines), which would pull the mean to the right and give a misleading representation of the center of the data.

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Answer:

( 5 , 5½ )

Step-by-step explanation:

It's simple actually, use the midpoint formula,

[tex] \frac{x1 + x2}{2} ... \frac{y1 + y2}{2} = ( \frac{8 + 2}{2} ... \frac{4 + 7}{2} ) = (5..5 \frac{1}{2} )[/tex]

Take the ... as a comma.

So the final answer is ( 5 , 5.5 )

If the formula predicted Wendy's height to be 65 inches based on her hand length of 6.5 inches, the residual would be -2 inches

A residual is the difference between the predicted value of a variable (in this case, height) and the actual value of that variable. Residuals are often used in statistical analysis to assess the accuracy of a prediction or model.

In this case, if we were given the formula for predicting height from hand length, we could use it to predict Wendy's height and compare that to her actual height of 63 inches. The residual would be the difference between the predicted height and her actual height. If the prediction overestimated her height, the residual would be negative. If it underestimated her height, the residual would be positive.

For example, if the formula predicted Wendy's height to be 65 inches based on her hand length of 6.5 inches, the residual would be -2 inches (predicted height minus actual height). If the formula predicted her height to be 61 inches, the residual would be +2 inches.

Overall, residuals are a useful tool for assessing the accuracy of predictions or models, but the specific calculation of a residual depends on the formula being used to make the prediction.

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The height of the real boat is 3 inches and  length of the boat is 45 feet

What is Unit of Measurement?

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

In a scale model of a boat 1 inch represents 5 feet

1 inch =  5 feet

The height of the real boat is 15 feet

We have to find in inches

1/5=x/15

x=3 inches

So height of the real boat is 3 inches

The length of the boat is 9 inches

We have to find in feet

1/5 = 9/x

x=45 feet

Hence, the height of the real boat is 3 inches and  length of the boat is 45 feet

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The length of the hypotenuse of each right triangle to the nearest tenth of an inch is 24 inches.

Here, two right triangles with legs each measuring 17 inches are created when the square piece of metal is sliced diagonally.

We will apply the Pythagorean Theorem to find the length of the hypotenuse.

The Pythagorean theorem states that square of hypotenuse is equal to the sum of the squares of opposite side and adjacent side.

Now,

[tex]Hypotenuse^{2} = 17^{2}+ 17^{2} \\Hypotenuse^{2} =289+289\\Hypotenuse^{2} =578\\Hypotenuse=\sqrt{ 578}\\Hypotenuse=24.04[/tex]

⇒ Hypotenuse ≈ 24 inches (to the nearest tenth of an inch)

Therefore, the length of the hypotenuse of each right triangle to the nearest tenth of an inch is 24 inches.

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a. Sin A = opposite/hypotenuse = √15/4

b.  (Sin A + Cos B) ÷ 2 = (Sin A + Cos B)/2

c.  Tan A  = 1/5

The both angle could be of same size

Since Cos A = adjacent/hypotenuse,

Applying  the Pythagorean theorem,

we can find the opposite side:

opposite^2 + 1^2 = 4^2

opposite^2 = 16 - 1

opposite = √15

Now we can find the value of Sin A:

Sin A = opposite/hypotenuse = √15/4

b.

Sin A + Cos B = (Sin A) + (Cos B)

(Sin A + Cos B) ÷ 2 = (Sin A + Cos B)/2

c. Since Tan B = opposite/adjacent,  

we use  Pythagorean theorem to  find the hypotenuse:

hypotenuse^2 = 5^2 + 1^2

hypotenuse = √26

Tan A = opposite/adjacent = 1/5

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Compared with an SRS of 900 8th-graders, the margin of error for a 95% confidence interval for mu is smaller when using an SRS of 1600 8th-graders.

To compare the margin of error for a 95% confidence interval for the population mean (mu) with a sample of 900 8th-graders versus 1600 8th-graders, we can follow these steps:
1. Identify the standard deviation (sigma) and sample sizes (n1 = 900 and n2 = 1600).
2. Calculate the standard error for each sample size:
SE1 = sigma / sqrt(n1) = 125 / sqrt(900) = 125 / 30
SE2 = sigma / sqrt(n2) = 125 / sqrt(1600) = 125 / 40

3. Determine the critical value (z-score) for a 95% confidence interval. In this case, it is 1.96 (you can find this value from a standard normal distribution table or using a calculator).
4. Calculate the margin of error for each sample size:
ME1 = z-score * SE1 = 1.96 * (125 / 30)
ME2 = z-score * SE2 = 1.96 * (125 / 40)
5. Compare the margin of errors:
ME1 is larger than ME2.

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When Kirill and Max work together, they can complete 11/60 of the puzzle in one hour.

To find out what part of the puzzle Kirill and Max can complete together in one hour, we need to calculate their combined work rate.

Step 1: Find the work rate of Kirill.
Kirill can complete the puzzle in 10 hours, so his work rate is 1/10 of the puzzle per hour.

Step 2: Find the work rate of Max.
Max can complete the puzzle in 12 hours, so his work rate is 1/12 of the puzzle per hour.

Step 3: Add Kirill's and Max's work rates together.
(1/10) + (1/12) = (12 + 10) / (10 * 12) = 22 / 120

Step 4: Simplify the fraction.
The simplified fraction is 11/60.

So, when Kirill and Max work together, they can complete 11/60 of the puzzle in one hour.

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If the triangle is isosceles, then the measure of the third angle could be 42 degrees

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

The sum of angles in a triangle is 180 degrees

If the triangle is isosceles, then we have the following possible sum of angles

Sum 1 = 42 + 96 + 96 = 234 -- false

Sum 1 = 42 + 96 + 42 = 180 -- true

Hence, if the triangle is isosceles, then the measure of the third angle could be 42 degrees

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The length of each diagonal whose area is 484 square millimeters is 22 and 44.

Area of rhombus = 484 square millimeters

Let one diagonal of rhombus = p

other diagonal of rhombus = q

The length of one diagonal of rhombus is one-half as long as the other diagonal of rhombus

p = q/2

Area of diagonal = [tex]\frac{1}{2}d_{1}d_{2}[/tex]

Area of diagonal = [tex]\frac{1}{2}pq[/tex]

Area of diagonal = [tex]\frac{1}{2}\frac{q}{2}q[/tex]

484 = [tex]\frac{1}{4}q^{2}[/tex]

q² = 1936

q = 44 millimeter

p = q/2

p = 44/2

p = 22 millimeter

The length of each diagonal p and q is 22 mm and 44 mm respectively

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Answer:

The total area of the "i" figure is 5.33 square units.

The figure is made up of a square with side length 4 units, a triangle with base 4 units and height 3 units, and a semi-circle with radius 2 units.

The area of the square is 4^2 = 16 square units.

The area of the triangle is (1/2)(4)(3) = 6 square units.

The area of the semi-circle is (1/2)(pi)(2^2) = 2pi square units.

The total area of the figure is 16 + 6 + 2pi = 5.33 square units (to the nearest hundredth of a unit).

Here is a diagram of the figure with the areas of each shape labeled:

[Image of the "i" figure with the areas of each shape labeled]

The situations that can be modeled with an equation include the following:

A. The sale price of a television is $125 off of the original price.

C. Marco spent twice as much as Owen.

E. Ben paid a total of $75 for a shirt and a pair of shoes.

In Mathematics and Geometry, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) expressions that are connected by an equal sign.

Assuming the variable x represent the independent variable and y represents the dependent variable, we have the following equations;

"The sale price of a television is $125 off of the original price."

y = x - 125

"Marco spent twice as much as Owen."

y = 2x

"Ben paid a total of $75 for a shirt and a pair of shoes."

x + y = 75

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Complete Question:

Select all the situations that can be modeled with an equation.

The sale price of a television is $125 off of the original price.

Anna gave away 5 hats.

Marco spent twice as much as Owen.

Susan earns $25 per day for d days.

Ben paid a total of $75 for a shirt and a pair of shoes.

If for "c" tickets, Suzie paid an amount of $324, then the cost of each ticket is represented by "324/c".

The number of tickets that Suzie bought is = c tickets, and

Let "x" be the cost of "each-ticket for "rock-festival".

The total amount spent for "c" tickets is = $324,

Therefore, we can write the cost-equation as;

⇒ c × x = 324,

To find the value of "x", we solve for it by dividing both sides of the equation by "c":

⇒ x = 324/c,

So, the cost of each ticket is $324 divided by the number of tickets "c" that Suzie bought.

Therefore, Each tickets cost is 324/c.

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In a binomial experiment consisting of five trials, the number of different values that x (the number of successes) can assume is 6.

A binomial experiment is a statistical experiment that meets four specific conditions: there are a fixed number of trials, each trial is independent of one another, there are only two possible outcomes (success or failure) in each trial, and the probability of success remains constant throughout the trials.

In this case, the binomial experiment consists of five trials, so the possible outcomes for x (the number of successes) can range from 0 successes to all 5 successes. To find the number of different values x can assume, simply add 1 to the total number of trials, as it includes the case of 0 successes.

Therefore, x can take on the following values: 0, 1, 2, 3, 4, or 5. As there are 6 possible values for x, the number of different values that x can assume in a binomial experiment consisting of five trials is 6.

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Answer:

60

Step-by-step explanation:

Area of a triangle: 1/2(bh)

Base = 12

Height = 10

1/2(12*10)

1/2(120) = 60

The sets (2,6) and [1,5] are not the same mathematically  but they do have some overlap.

The first pair, (2,6), signifies a number line interval that is open and commences at 2, concluding at 6, while excluding the endpoints.

So one can say that the closed interval on the number line between 1 and 5, including both endpoints, is represented by the set [1,5]. any integer that is seen between 1 and 5, inclusive, is included in this set.

Although there is some similarity between the two groups, namely the presence of numbers 2 to 5, they are distinct from each other. The numerical interval (2,6) does not contain the values 2 and 6, whereas those two numbers are part of the range [1,5].

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See transcribed text below

Mathematically these two sets are the same or are they a way of rewriting the other or are they different? (2,6) and [1,5]