Use either method to simplify the complex fraction. ((1)/(f^(3))-(1)/(a^(3)))/((1)/(f^(2))-(1)/(a^(2)))

The perpendicular distance between the two parallel sides, height h of the trapezium is 8cm

It is important to note the properties of a trapezium;

the formula for area of  trapezium is;

Area = a + b/ 2 ·(h)

Substitute the value

80 = (4 + 16)/ 2  (h)

Add the values

80 = 10h

Divide by the coefficient of h

h = 8cm

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Complete question:

The area of a trapezium is  80cm^2

The lengths of its parallel sides are  4cm and 16cm respectively. Find the perpendicular distance between the two parallel sides.

Answer:

There are 60 seconds in 1 minute, so in 5 1/2 minutes:

5 minutes x 60 seconds/minute = 300 seconds

1/2 minute x 60 seconds/minute = 30 seconds

Adding those together gives:

300 seconds + 30 seconds = 330 seconds

Therefore, there are 330 seconds in 5 1/2 minutes.

There are 330 seconds in 5 and 1/2 minutes. We find this by converting the minutes (both the whole and the half) into seconds and adding these amounts together.

To calculate the number of seconds in 5 and 1/2 minutes, we need to know the basic fact that 1 minute equals 60 seconds. With this, we can easily convert minutes to seconds by multiplying the number of minutes by 60.

First, let's convert the 5 whole minutes into seconds: 5 minutes x 60 seconds/minute = 300 seconds.

Next, let's convert the half minute: 1/2 minute x 60 seconds/minute = 30 seconds.

FInally, add these two amounts together: 300 seconds + 30 seconds = 330 seconds. Therefore, 5 and 1/2 minutes equals 330 seconds.

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Answer:

180

Step-by-step explanation:

Answer: 180.2

Step-by-step explanation: 85% of 212 is 180.2

Answer:

x=16 and y=9

Step-by-step explanation:

(x+19)+(9x+1)=180

Combine Like Terms

10x+20=180

Subtract 20 from both sides

10x=160

Divide 10 by both sides

x=16

Fill in for x in (9x+1) to help find y

9*16+1

145

3y+8+145=180

Combine like terms

3y+153=180

Subtract 153 from both sides

3y=27

Divide 3 by both sides

y=9

The answers are a.(f∘g)(x) = x^2+2x+1 and b. (g∘f)(x) = x^2+1.

Let f(x)=x^2 and g(x)=x+1. We are asked to find a.(f∘g)(x) and b. (g∘f)(x).

a. (f∘g)(x) = f(g(x)) = f(x+1) = (x+1)^2 = x^2+2x+1

b. (g∘f)(x) = g(f(x)) = g(x^2) = x^2+1

Therefore, the answers are a.(f∘g)(x) = x^2+2x+1 and b. (g∘f)(x) = x^2+1.

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Total SUM Sq is 22623.933

To address the research question of whether there were any statistically significant differences on the rated levels of trustworthiness across the three conditions, a one-way ANOVA test was conducted in JAMOVI, using a significance criterion of 5%. The independent variable was the type of face width (narrow, average, wide), and the dependent variable was the trustworthiness rating. The JAMOVI output showed that the one-way ANOVA test was significant, F(2,57) = 11.203, p < 0.001, η2 = 0.281. Post-hoc tests revealed that the difference in the trustworthiness ratings between narrow and wide faces was statistically significant, p = 0.001, d = 1.121, 95% CI [0.579, 1.664], and the difference between average and wide faces was statistically significant, p = 0.025, d = 0.556, 95% CI [0.039, 1.074]. These results indicate that trustworthiness ratings were significantly different between the three face widths, with narrow faces receiving the highest ratings, followed by average faces, and then wide faces.

JAMOVI Output:
One-Way ANOVA
Source df Sum Sq Mean Sq F p
Between 2 6409.933 3204.967 11.203 0.000
Error 57 16214.000 284.532
Total 59 22623.933

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The height of the Eiffel Tower is approximately 311.6 meters.

Yes, we can determine the height of the Eiffel Tower if we are standing 1,721 meters away from it and the angle of elevation is \( 10.37^{\circ} \). We can use the tangent function to find the height of the Eiffel Tower. The tangent function is defined as the opposite side over the adjacent side. In this case, the opposite side is the height of the Eiffel Tower and the adjacent side is the distance from the Eiffel Tower, which is 1,721 meters. The equation for the tangent function is:

tan( \( 10.37^{\circ} \) ) = height / 1,721

We can rearrange the equation to solve for the height of the Eiffel Tower:

height = tan( \( 10.37^{\circ} \) ) * 1,721

Using a calculator, we can find the value of tan( \( 10.37^{\circ} \) ) and multiply it by 1,721 to get the height of the Eiffel Tower:

height = 0.181 * 1,721

height = 311.6 meters

Therefore, the height of the Eiffel Tower is approximately 311.6 meters.

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The solutions to the equation x^2 + 8x +4 = 0 are x1 and X2.

(a) Without solving the equation write down the value of
(i) x1 + x2 = -8 (The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a, so in this case, -8/1 = -8)
(ii) x1x2 = 4 (The product of the roots of a quadratic equation ax^2 + bx + c = 0 is c/a, so in this case, 4/1 = 4)

The solutions to the equation ax^2 + bx+c=0 where a,b,c E Z are 1/x1 and 1/x2

(b) Use part (a) to find the value of
(i) b/a = -(1/x1 + 1/x2) = -(-8) = 8 (The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a, so in this case, -b/a = -8)
(ii) c/a = 1/x1 * 1/x2 = 1/4 (The product of the roots of a quadratic equation ax^2 + bx + c = 0 is c/a, so in this case, c/a = 4)

Find the values of a, b, and c where a is the smallest possible positive value.
Since a is the smallest possible positive value, let a = 1. Then, b = 8 and c = 4. So the values of a, b, and c are 1, 8, and 4, respectively.

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Substituting the values into the formula gives us Angle XZY = 180° - angle XYZ - angle YXZ = 180° - 95° - 50° = 35°. Thus, the measure of angle XZY in triangle XYZ is 35 degrees

We use the knowledge that the total of the angles in any triangle is always 180 degrees to determine the size of angle XZY in triangle XYZ. Angle YXZ is known to measure 50 degrees, while angle XYZ is known to measure 95 degrees. In order to determine the measure of angle XZY, we can subtraction the measurements of these two angles from 180 degrees. We obtain Angle XZY = 180° - angle XYZ - angle YXZ = 180° - 95° - 50° = 35° by substituting the values into the formula. As a result, the angle XZY in triangle XYZ has a measure of 35 degrees.

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The answer to this question is as follows It's vital to keep in mind that the equation x only pertains to the cost of the water and not the cost of the popcorn in the same way that you stated it.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.  

To calculate Theodore's overall spending, use the following expression:

3x + 4.50

This is due to the fact that he also spent $4.50 on a bag of popcorn in addition to the three waters, which each cost x dollars apiece. His whole expenditure may be calculated by adding these two charges.

When we condense the formula 3x + 4.50, we get:

the 7.50x

It's vital to keep in mind that the x only pertains to the cost of the water and not the cost of the popcorn in the same way that you stated it.

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If "n is the positive integer, then n is even if and only if 7n + 4 will be even" is true.

To prove that we need to show the two things:

If n is even, then 7n+4 will be even.

If 7n + 4 is even, then n will be even.

Proof: Suppose that n is even. Then they exists an integer k such that n =2k. We can substitute this expression for n into 7n + 4 to get:

7n + 4 = 7(2k) + 4 = 14k + 4

= 2(7k + 2)

Since 7k + 2 is also an integer, we can see that 7n + 4 is even, since it is equal to twice an integer.

Now suppose that 7n + 4 is even. Then there exists an integer m such that 7n + 4 = 2m. We will rearrange this equation to have:

7n = 2m - 4

= 2(m - 2)

Since m - 2 is also an integer, we can see that 7n is even, since it is equal to twice an integer. Therefore, n must be even as well, since an odd integer multiplied by 7 cannot result in an even number.

Since we have shown both directions of the statement, we can conclude that "n is a positive integer, then n is even if and only if 7n + 4 is even" is true.

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We need to add 225 ml of water to the 90 ml of concentrate to make lemon squash.

The ratio of concentrate to water in the lemon squash is 2:5, which means that for every 2 parts of concentrate, there are 5 parts of water.

If we have 90 ml of concentrate, we can use this ratio to find the amount of water needed.

We can set up a proportion as follows:

2/5 = 90/x

Where x is the amount of water needed.

To solve for x, we can cross-multiply:

2x = 5 * 90

2x = 450

x = 225

Therefore, we need to add 225 ml of water to the 90 ml of concentrate to make lemon squash.

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There is a unique x∈Hi​ such that f(x)=y. Explanation:

If f is a function, then for any partition (Fi​)i∈I​ of B, (f−1(Fi​))i∈I​ is a partition of S. This is because for any x∈S, there is a unique y∈B such that f(x)=y. Thus, x belongs to exactly one of the sets f−1(Fi​), and so these sets form a partition of S.Conversely, if (f−1(Fi​))i∈I​ is a partition of S for any partition (Fi​)i∈I​ of B, then f is a function. This is because for any x∈S, there is a unique i∈I such that x∈f−1(Fi​), and so there is a unique y∈Fi​ such that f(x)=y.2) If f is bijective, then for any partition (Hi​)i∈J​ of S, (f(Hi​))i∈J​ is a partition of B. This is because for any y∈B, there is a unique x∈S such that f(x)=y. Thus, y belongs to exactly one of the sets f(Hi​), and so these sets form a partition of B.Conversely, if (f(Hi​))i∈J​ is a partition of B for any partition (Hi​)i∈J​ of S, then f is bijective. This is because for any y∈B, there is a unique i∈J such that y∈f(Hi​), and so there is a unique x∈Hi​ such that f(x)=y.Explanation:

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The comparison of the population shows that the correct option is C.

Class A: median = 90, IQR = 12.5

Class B: median = 80, IQR = 10 The variation in the test scores is about the same, but Class A has greater test scores.

The variation in test scores is about the same between Class A and another group, but Class A has greater test scores, it means that Class A as a group performed better on the test than the other group.

It should be the total score for A is 2200 while the score for B is 2110.

Therefore, it should be noted that the correct option is C.

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Answer:

= 1/2

Step-by-step explanation:

the slope or the gradient (m)

[tex] \frac{y1 - y2}{x1 - x2} [/tex]

the points is (6,1) and (-6,-5)

therefore

[tex] \frac{1 - ( - 5)}{6 - ( - 6)} \\ = \frac{1 + 5}{6 + 6} \\ = \frac{6}{12} \\ = \frac{1}{2} [/tex]

therefore the slope of the line is 1/2

Answer:

You need to add 50 gallons of the 3% solution to the 50 gallons of the 7% solution and that will give 100 gallons of a 5% solution.

False, for both statements.

For the first statement, let A be an n x n matrix. If for two vectors y and z of Rⁿ we have Ay = Az, it does not necessarily mean that y=z. It is possible that A is a singular matrix, meaning that it does not have an inverse. In this case, there could be multiple vectors that would give the same result when multiplied by A. Therefore, it is not always true that y=z.

For the second statement, if A is a matrix of size n x n such that A³ = Iⁿ (where Iⁿ is the identity matrix of size n), it does not necessarily mean that A is invertible. It is possible for a matrix to have a power that equals the identity matrix, but not have an inverse. For example, consider the matrix A = [[0,1],[0,0]]. A² = [[0,0],[0,0]], and A³ = [[0,0],[0,0]], which is equal to I². However, A does not have an inverse, as its determinant is 0. Therefore, it is not always true that A is invertible if A³ = Iⁿ.

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The area οf the red band is 1766.3 [tex]cm^2[/tex].

Area is a measure οf the amοunt οf twο-dimensiοnal space taken up by a shape οr surface. It is measured in square units, fοr example square metres (m²) οr square centimetres (cm²). Area can alsο be used tο calculate the perimeter οf a shape, which is the tοtal length οf the οutside οf the shape. Knοwing the area and the perimeter οf a shape can be useful in many calculatiοns and can help tο sοlve a range οf prοblems.

The area οf the target can be calculated with the equatiοn

=>A = [tex]\pi r^2[/tex].

ln this case, the radius (r) is 30.0 cm, so

=> A = [tex]\pi30^2[/tex] = 1766.3 [tex]cm^2[/tex].

The area οf the entire target is 1766.3 [tex]cm^2[/tex], and since the red band takes up a pοrtion of the entire target, the area οf the red band is 1766.3  [tex]cm^2[/tex]

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Answer:

32 meters

Step-by-step explanation:

[tex]\frac{8}{15}[/tex] = [tex]\frac{x}{60}[/tex]  Set up a proportion using corresponding sides

15 x 4 = 60

8 x 4 = 32

Helping in the name of Jesus.

Answer:

Awnser "y = 10x + 60"

Step-by-step explanation:

So, the chart coordinate should looks like this:

(1, 75)

(2, 70)

(3, 80)

(4, 95)

(4, 100)

And there is a line passing (0, 60) and (2, 80)

So we just need to find the y-intercept and the slope by the line:

Slope: [change in x over change in y] = 20 ÷ 2 = 10

y-intercept: [the value of y when x equal 0] = 60 (because the line passed through (0, 60) )

Step-by-step explanation:

Answer; 10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test

Step-by-step explanation:

Answer:

9 [tex]cm^{2}[/tex]

Step-by-step explanation:

All the sides have the same length, so if the perimeter.  The distance around the figure is 24, then each side is 6 (24 divided by 4 is 6)

The area of a triangle is

a = 1/2 bh

a = 1/2(6)(3)

a = 1/2(18)

a = 9

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

The answer is 11.61

The value οf x and y in the shape will be 18/5 mm and 15/2 mm respectively.

An integer is any number including 0, pοsitive numbers, and negative numbers. It shοuld be nοted that an integer can never be a fractiοn, a decimal οr a per cent. Sοme examples οf integers include 1, 3, 4, 8, 99, 108, -43, -556, etc.

Integers are a set οf cοunting numbers (pοsitive and negative), alοng with zerο, that can be written withοut a fractiοnal cοmpοnent. As mentiοned abοve, an integer can be either pοsitive, negative οr zerο.

All natural numbers are alsο integers that start frοm 1 and end at infinity.

All whοle numbers are alsο integers, starting frοm 0 and ending at infinity.

An integer is a whοle number withοut any fractiοn οr decimal part.

Using alternate angles and vertically οppοsite angles we can find their ratiο and prοpοrtiοn in οrder tο get the value οf x and y.

[tex]\frac{x}{9} =\frac{3}{y} =\frac{2}{5}[/tex]

x = 2(9)/5 = 18/5 mm

y = 3(5)/2 = 15/2 mm

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The numbers in the cards are:

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

Cards = 45, 45 and 46

Next, we have

Multiples of 2, 3 and 4

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

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The probability of getting 4 heads is 0.205078125, the probability of getting 6 heads is 0.205078125, the expected number of heads is 5, and the variance of the number of heads is 2.5.

The probability of getting 4 heads or 6 heads in 10 coin tosses can be calculated using the binomial probability distribution formula:

P(X=x) = nCx * p^x * (1-p)^(n-x)

Where:
n = number of trials (10)
x = number of successes (4 or 6)
p = probability of success (0.5)
1-p = probability of failure (0.5)
nCx = combination of n things taken x at a time

For 4 heads:
P(X=4) = 10C4 * 0.5^4 * 0.5^(10-4)
P(X=4) = 210 * 0.0625 * 0.015625
P(X=4) = 0.205078125

For 6 heads:
P(X=6) = 10C6 * 0.5^6 * 0.5^(10-6)
P(X=6) = 210 * 0.015625 * 0.0625
P(X=6) = 0.205078125

The expected number of heads can be calculated using the formula:
E(X) = n * p
E(X) = 10 * 0.5
E(X) = 5

The variance of the number of heads can be calculated using the formula:
Var(X) = n * p * (1-p)
Var(X) = 10 * 0.5 * 0.5
Var(X) = 2.5
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The complete table is

Whose card Length Width Perimeter Area

Sanya          10 cm 8cm               36cm         80 cm²

The perimeter of a shape is the distance around its edges. For a rectangle, like Sanya's greeting card, the perimeter can be found by adding up the lengths of all four sides. In this case, we have:

Perimeter = 2 × Length + 2 × Width

Perimeter = 2 × 10 cm + 2 × 8 cm

Perimeter = 20 cm + 16 cm

Perimeter = 36 cm

So, the perimeter of Sanya's greeting card is 36 centimeters. This means that if you were to walk all the way around the edges of the card, you would cover a distance of 36 centimeters.

The area of a shape is the amount of space it takes up. For a rectangle, the area can be found by multiplying its length by its width. In this case, we have:

Area = Length × Width

Area = 10 cm × 8 cm

Area = 80 cm²

So, the area of Sanya's greeting card is 80 square centimeters. This means that if you were to cover the card completely with paint or ink, you would need 80 square centimeters of paint or ink.

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Complete Question:

Sanya made greeting cards. Complete the table for their cards:

Whose card Length Width Perimeter Area

Sanya          10 cm 8cm              

The side of figure WXYZ corresponds with QR is XY

In mathematics, mirror images are often used in the study of symmetry and geometry. A mirror image, also known as a reflection, is a transformation that flips an object over a line called the mirror line.

An image appears to be reversed from left to right. Therefore, the left side of the object appears to be on the right side of the image, and the right side of the object appears to be on the left side

Here we have

Parallelogram PQRS and WXYZ which are two mirror images

Here the corresponding side of the two figures are

=> PQ and WX

=> QR and XY

=> RS and YZ

=> PS and WZ

Therefore,

The side of figure WXYZ corresponds with QR is XY

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On Saturday evening, there were 520 covers. If the popularity index of the Grilled Salmon is 10%, then the number of portions of the salmon that were served on Saturday is 10% of 520, which is equal to 52 portions.

To calculate this, you can use the following formula:

Number of portions of salmon = popularity index of salmon * number of covers

= 10% * 520

= 0.10 * 520

= 52 portions

Therefore, 52 portions of the Grilled Salmon were served on Saturday.

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