Determine the distance across the lake, d.

Answer:

:< :< :< :< :< :< :< ?

Step-by-step explanation:

Answer:

The best way to decompose the composite figure to determine its area is as a semicircle, a trapezoid, and two rectangles. This way, we can use the following formulas to find the area of each part:

Area of a semicircle = 21​πr2, where r is the radius of the circle.

Area of a trapezoid = 21​(b1​+b2​)h, where b1​ and b2​ are the bases and h is the height of the trapezoid.

Area of a rectangle = l×w, where l is the length and w is the width of the rectangle.

Then, we can add up the areas of each part to find the total area of the composite figure. The other options are not as convenient because they either involve more parts or more complicated shapes. For example, option A would require finding the area of a triangle, which involves using trigonometry or the Pythagorean theorem. Option B would require finding the area of four triangles, which is more tedious than finding the area of two rectangles. Option C would require finding the area of a square, which is redundant because a square is a special case of a rectangle.

Step-by-step explanation:

The composite figure can be decomposed into a semicircle, a trapezoid, and two rectangles.

Option D is the correct answer.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as: 1/2 x sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

The given figure can be decomposed into the following figure.

- Semicircle

- Trapezoid

- Two rectangles

Thus,

A semicircle, a trapezoid, and two rectangles.

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Answer:

Her mom's candle has more citrus in it. Peppermint isn't a citrus scent.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

7^2 is 49-8x2 what is 16-16you get 49-16-16 what equals 17  so ur answer is D

Answer:

Step-by-step explanation:

Let x - be the number of sweets in small packs

y - be the number of sweets in big packs

Therefore, we have:

4x + 3y = 175 (1)

5x + 2y = 154 (2)

Now, we find the difference between (1) & (2) is:

y-x = 21. Thus, y = 21+x

Now we substitute the value of y = 21+x to any of the two statements, we have 4x + 3(21+x) = 175 => 4x + 63 + 3x = 175.

Hence, 7x = 175 - 63 = 112 or simply, x=16.

Now, finding the value of y:

5(16) + 2y = 154

80 + 2y = 154

2y = 154-80

2y = 74

y = 37.

Therefore, there are 16 sweets in each small pack and 37 sweets in each big pack.

The idea of the Laffer Curve, named after economist Arthur Laffer, is expressed mathematically as a relationship between tax rates and government revenue.

The concept suggests that at a certain point, increasing tax rates will actually lead to a decrease in government revenue, as people will be discouraged from working or investing. The Laffer Curve is typically illustrated as a bell curve, with revenue on the y-axis and tax rate on the x-axis.

At lower tax rates, increasing the rate leads to an increase in revenue. However, at a certain point, increasing the rate further leads to a decrease in revenue. The optimal tax rate, where revenue is maximized, is different for each economy and can vary over time.

The Laffer Curve is often cited by those advocating for lower tax rates and fewer government regulations on businesses as a way to stimulate economic growth and increase revenue.

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Answer:

This is a little late but it's D. ​1.15h+3=1.75h

Step-by-step explanation:

I took this test

The height of a rider on the London Eye Ferris wheel in London can be modeled by the function h(t) = A * cos(B * t), where t represents time in minutes. The Ferris wheel stands 135 meters tall with a diameter of 120 meters. It takes half an hour (30 minutes) to complete one revolution.

1. At t = 0 minutes, the rider is not at the bottom of the wheel but at the midpoint of the wheel's diameter, so the rider's height is equal to the radius of the wheel, which is half of its diameter. Therefore, the rider's height at t = 0 minutes is 120/2 = 60 meters.

2. To determine the time it takes for the rider to reach the top, we need to find the period of the cosine function. The period (T) is the time it takes for one complete cycle of the function. In this case, the period is equal to the time it takes for the Ferris wheel to make a full revolution, which is 30 minutes. So, the rider reaches the top after half of the period, which is T/2 = 30/2 = 15 minutes. At that time, the rider's height is equal to the sum of the radius of the wheel and its height, which is 60 + 135 = 195 meters.

3. The period of the cosine function is T = 30 minutes.

4. The vertical shift of the function represents the average height of the rider throughout one complete cycle. In this case, the average height is the sum of the radius and the height of the Ferris wheel divided by 2, which is (60 + 135)/2 = 97.5 meters. Therefore, the vertical shift of the function is 97.5 meters. The amplitude of the function is half of the vertical distance between the maximum and minimum values, which is (135 - 60)/2 = 37.5 meters.

5. The equation of the cosine function is h(t) = 97.5 + 37.5 * cos((2π/30) * t). To find the rider's height at t = 21 minutes, we substitute t = 21 into the equation: h(21) = 97.5 + 37.5 * cos((2π/30) * 21) ≈ 185.11 meters.

In summary, the rider's height at t = 0 minutes is 60 meters. It takes 15 minutes for the rider to reach the top, at which point their height is 195 meters. The period of the function is 30 minutes. The vertical shift is 97.5 meters, and the amplitude is 37.5 meters. Using the cosine function, the rider's height at t = 21 minutes is approximately 185.11 meters.

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Answer:

12

Step-by-step explanation:

First, let's calculate both of the medians.

Veronica's Median: 141

James' Median: 129

And now, the only thing left for us to do is complete some simple subtraction.

141 - 129 = 12

Your answer is 12.

Answer:

so first you have to find out the median of both of the people. then you have to subtract both of the medians to find out how much veronicas is higher than the other guy

When the height and volume of the cylinder were doubled, the radius remains unchanged.

We know that the formula for the volume of the cylinder is:

V = πr²h

where r is the radius of the cylinder,

h is the height of the cylinder,

and V is the volume of the cylinder

We write above formula for radius:

r² = V / πh

r = \(\sqrt{\frac{V}{\pi h} }\)                   ...........(1)

If the height and volume were doubled, V → 2V and h → 2h

So equation (1) becomes,

\(r=\sqrt{\frac{2V}{\pi\times 2h} }\\\\ r = \sqrt{\frac{V}{\pi \times h} }\)

This means that the radius of the cylinder remains unchanged.

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The complete qeuestion is:

When the height and volume of the cylinder were doubled, what happed to the radius?

The number of students who knows all the 3 languages is 12

Total number of students = 80

Number of students who knows English = 50

Number of students who knows French = 55

Number of students who knows German = 46

Number of students who knows English and French = 37

Number of students who knows French and German = 28

Number of students who knows English and German = 25

Number of students who knows none of the languages = 7

Here we have to use the equation of the union of set

n(E∪F∪G) = n(E) + n(F) + n(G) - n(E∪F) - n(F∪G) - n(E∪G) + n(E∩F∩G)

80 - 7 = 50 + 55 +46 - 37 - 28 -25 + n(E∩F∩G)

n(E∩F∩G) = 73 - 50 -55 -46 +37 +28 +25

n(E∩F∩G) = 12

Hence, the number of students who knows all the 3 languages is 12

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Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

The number that satisfies the result is a perfect cube but not a perfect square is 32768

The number needs to be both a perfect cube and a perfect square. The only 5-digit number that fulfills this requirement is 32768, which is equal to 2¹⁵.

When this number is divided by 4, the result is 8192 (32768/4), which is a perfect square because it can be expressed as 2¹³. However, it is not a perfect cube since it cannot be expressed as an integer raised to the power of 3.

On the other hand, when the number 32768 is divided by 27, the result is 1216 (32768/27), which is a perfect cube because it can be expressed as 2⁶ * 19³. However, it is not a perfect square since it cannot be expressed as an integer raised to the power of 2.

Therefore, the number that satisfies all the given conditions is 32768.

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The claim that independence (r⊥a) and separation (r⊥a|y) cannot both hold is not universally true when y assumes three distinct values.

To show that the claim does not hold when y assumes three distinct values, let's consider a counterexample.

Assume that y can take three values: y1, y2, and y3. We'll construct a scenario where independence (r⊥a) and separation (r⊥a|y) both hold.
Counterexample:
Suppose we have the following probabilities:
P(r=0|y=y1) = 0.5
P(r=1|y=y1) = 0.5
P(r=0|y=y2) = 0.5
P(r=1|y=y2) = 0.5
P(r=0|y=y3) = 0.5
P(r=1|y=y3) = 0.5

Now, let's consider the probabilities for a:
P(a=0|y=y1) = 0.5
P(a=1|y=y1) = 0.5
P(a=0|y=y2) = 0.5
P(a=1|y=y2) = 0.5
P(a=0|y=y3) = 0.5
P(a=1|y=y3) = 0.5

In this scenario, we can observe that:
Independence holds:

P(r⊥a) = P(r) * P(a)

= 0.5 * 0.5

= 0.25
Separation holds:

P(r⊥a|y) = P(r|y) * P(a|y)

= 0.5 * 0.5

= 0.25

Therefore, in this counterexample, independence (r⊥a) and separation (r⊥a|y) both hold even when y assumes three distinct values.

In conclusion, the claim that independence (r⊥a) and separation (r⊥a|y) cannot both hold is not universally true when y assumes three distinct values.

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Answer:

tht hard

Step-by-step explanation:

so i need points

Let's denote the increase in both the radius and the height of the cylinders as 'x' inches.

The volume of a cylinder can be calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

For the first cylinder (with original radius 8 inches and height 3 inches), the volume is given by V₁ = π(8)²(3) = 192π cubic inches.

For the second cylinder (with increased radius and height), the volume is given by V₂ = π(8 + x)²(3 + x).

Given that the resulting volumes are equal, we can set up the following equation:

V₁ = V₂

192π = π(8 + x)²(3 + x)

Canceling out the π from both sides, we have:

192 = (8 + x)²(3 + x)

Expanding the equation:

192 = (64 + 16x + x²)(3 + x)

192 = 192 + 48x + 16x² + 3x + x²

0 = 16x² + 51x

Simplifying the quadratic equation:

16x² + 51x = 0

x(16x + 51) = 0

Setting each factor equal to zero:

x = 0 (nonzero number of inches)

16x + 51 = 0

16x = -51

x = -51/16

Since we're looking for a nonzero increase, the increase is x = -51/16 inches.

Note: It's important to check the validity of the negative value for 'x' since it represents an increase. In this case, the negative value implies a decrease rather than an increase. Therefore, the increase in both the radius and the height is 0 inches.

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Answer:

x=64

Step-by-step explanation:

0=1/8x-8

8=1/8x

8/1/8=1/8x/1/8

x=64

Answer:

The answer will be 10

Step-by-step explanation:

\(2\frac{1}{2} = \frac{5}{2}\)

\(\frac{5}{2}\) ÷ \(\frac{1}{4} = \frac{5}{2} x \frac{1}{4}\) = \(\frac{20}{2}\)

\(\frac{20}{2} =\) 10 (in its simplest form)

The solution of equation 2 1/2 divided by 1/5 in simplest form is, 5

We have to given that,

To Divide 2 1/2 divided by 1/5 in simplest form.

We can simplify,

⇒ 2 1/2 ÷ 1/4

Change into improper fraction,

⇒ 5/4 ÷ 1/4

⇒ 5/4 × 4/1

⇒ 20/4

⇒ 5

Therefore, The solution of equation 2 1/2 divided by 1/5 in simplest form is, 5

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Answer:

The answer would be the product of the division table 20 1/2  Divided by 2 1/4

20 1/2 / 2 1/4= 9 1/9 or 9.1 mph

Rounded she would go 10 miles per hour

When x is correlated with y, it means that there exists a relationship between the two variables, where a change in one variable (x) is associated with a change in the other variable (y).

This relationship can be either positive or negative.

In a positive correlation, as the value of x increases, the value of y also increases, and as the value of x decreases, the value of y decreases as well. This indicates that both variables move in the same direction. On the other hand, in a negative correlation, as the value of x increases, the value of y decreases, and as the value of x decreases, the value of y increases. This shows that the variables move in opposite directions.

It is essential to note that correlation does not imply causation. Just because two variables are correlated does not mean that one variable causes the other to change. There could be other factors or variables that influence the observed relationship between x and y. Additionally, the strength of the correlation can vary, with values close to 1 or -1 representing a strong relationship and values close to 0 representing a weak relationship or no relationship at all.

In conclusion, when x is correlated with y, it means that there is a relationship between the two variables that can be either positive or negative, but this does not necessarily imply causation. The strength of the relationship can also vary, depending on the correlation coefficient value.

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Answer:69

Step-by-step explanation:

because I said so

The interval of convergence for the power series is the set of all values of x for which the series converges. The table mentioned in your question likely shows the values of x for which the series converges or diverges.

The interval of convergence for a power series is determined by finding the values of x for which the series converges absolutely. The convergence or divergence of a power series can be determined using various tests, such as the ratio test or the root test.
Once the interval of convergence is found, it can be summarized as a range of values for x. For example, if the interval of convergence is (-3, 5], then the series converges for all values of x between -3 and 5, inclusive.

Hence, the interval of convergence for a power series is the set of all values of x for which the series converges, and it can be determined by finding the values of x for which the series converges absolutely.

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Answer: 62cm^2

Step-by-step explanation: 70-8=62

After  solving the equation 5(X - C)  = D , for the given matrices , we get , the unknown matrix X is = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\) .

In the question ,

it is given that , the matrices are

A = \(\left[\begin{array}{ccc}7&3\\4&3\end{array}\right]\)   B = \(\left[\begin{array}{ccc}7&2\\7&2\end{array}\right]\)   C = \(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\)   and D = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) .

and the equation is given as 5(X - C)  = D ,

and we have to find the value of unknown matrix X .

let the matrix X be = \(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\)

Substituting , the given matrices A , B , C and D in the equation 5(X - C)  = D ,

we get ,

5(X - C)  = D ,

5X - 5C = D ,

5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) - 5\(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\) = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\)

5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) - \(\left[\begin{array}{ccc}15&15\\20&0\\0&40\end{array}\right]\)

Simplifying further ,

we get ,

5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}25&45\\50&30\\30&40\end{array}\right]\)

Dividing both sides by 5 ,

we get ,

X = \(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\)

Therefore , the matrix X is = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\) .

The given question is incomplete , the complete question is

Solve the matrix equation for the unknown matrix X.

A = \(\left[\begin{array}{ccc}7&3\\4&3\end{array}\right]\)   B = \(\left[\begin{array}{ccc}7&2\\7&2\end{array}\right]\)   C = \(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\)   and D = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) . the equation is

5(X - C)  = D .

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Answer:

Problem 1:  1/64x^8

Problem 2: y^8/9x^2

Step-by-step explanation:

In the first problem, you first need to multiply the -2 exponent to everything in the parenthesis. This is equal to 1/64x^4*-2, simplified to be 1/64x^-8. Finally you simplify the x to 1/64x^8.

For the second problem, you do the same in the first one, getting x^-2/9y^4*-2. This can be simplified to be 3x^-2/y^-8. Finally you make sure there is no negative exponents, so you do y^8/9x^2.

Answer:

1/64x^8 and y^8/9x^2

Step-by-step explanation:

hope this helps have a good night :)

Answer:

9.1 is the nearest tenth

9.11 to the nearest hundredth

just slightly to the right of 9.1

Step-by-step explanation:

sqrt(83)

sqrt(81) = 9

So we know that it is slightly greater than 9

9.1*9.1 =81.81

9.2*9.2=84.64

9.1 is closer

9.11 * 9.11 =82.9921

9.12 * 9.12 =83.1744

9.11 is closer

Answer:

9.1 is the nearest tenth

9.11 to the nearest hundred

to the right of 9.1

Step-by-step explanation:yi did it on i ready6

Answer:

option 4: 18 700 kg/m3

Step-by-step explanation:

Density is the ratio between mass and volume, so let's grab a calculator and plug 374:0.02 = 18.700. Mass is already in kg, volume is already in m^3, so last answer is correct.

The measure of the missing angle α is 62 degrees.

The sum of angles on the straight line adds up to 180 degrees.

From the diagram;

Since the sum of angles on a straight line adds up to 180 degrees.

Angle 1 + Angle 2 + Angle 3 = 180

Plug in the values

118 + α = 180

Subtract 118 from both sides

118 - 118 + α = 180 - 118

α = 180 - 118

α = 62°

Therefore, the value of angle α is 62 degrees.

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