What is the measure of angle WVX?

If r is inversely proportional to x², then we can represent this relationship as:

r = k / x²

where k is the constant of proportionality. We are given that r = 4 when x = 4. Let's use this information to find the value of k:

4 = k / (4²)

4 = k / 16

k = 4 × 16 = 64

Now that we have the value of k, we can write the formula for r in terms of x:

r = 64 / x²

Answer:

r = \(\frac{64}{x^2}\)

Step-by-step explanation:

given that r is inversely proportional to x² then the equation relating them is

r = \(\frac{k}{x^2}\) ← k is the constant of proportion

to find k use the condition r = 4 when x = 4

4 = \(\frac{k}{4^2}\) = \(\frac{k}{16}\) ( multiply both sides by 16 )

64 = k

r = \(\frac{64}{x^2}\) ← equation of proportion

Answer: think A

Step-by-step explanation:

The function of swapvectorends() is written below.

Function:

In math, function is defined as a relation between a set of inputs having one output each.

Given,

Here we need to write a function swapvectorends() that swaps the first and last elements of its vector parameter.

The function swapvectorends() that swaps the first and last elements of its vector parameter is written as,

Int swapvectorends(vector <int> & sectorVector)

{

 int i = 0;

 for ( i = 0; i < sectorVector.size() - 1; ++i)

 {

     sectorVector.at(i) = sectorVector.at(sectorVector.size() - 1 - i);

 }

 return;

}

Now, when we input the value sortvector = {10, 20, 30, 40} onto the given function, then it will results the output sortvector = {40, 30, 20, 10}

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The frogs will jump together again after a distance of 21000 cm or 210 meters (since 100 cm = 1 m).

To find at what distance will the frogs jump together again, we need to find the LCM (Least Common Multiple) of the given jumps of

150 cm, 125 cm, and 84 cm.LCM of 150, 125,

and 84:

First, let's write the prime factors of these numbers.

150 = 2 × 3 × 5 × 5 125 = 5 × 5 × 5 84 = 2 × 2 × 3 × 7

Now, we need to take the highest power of each prime number that occurs in the factorization of the given numbers.2 occurs in the factorization of 150 and 84, so we take

2² = 4.3 occurs only in the factorization of 150, so we take

3¹ = 3.5 occurs in the factorization of all three numbers, so we take

5³ = 125.7 occurs only in the factorization of 84, so we take 7¹ = 7.Thus, LCM of 150, 125, and 84 = 2² × 3¹ × 5³ × 7¹ = 21000 cmHence,

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If the probability that a household owns a pet is 0.55 then the probability that all households will have pets is equal to 0.0503.

Given that the probability that a household owns a pet is 0.55 and there are 5 houses on a block.

We are required to calculate the probability that all the five households will have pets.

Probability is basicallly the chance of happening an event among all the events possible. It cannot be negative.

Binomial probability distribution is basically the probability calculations but in different combinations.

In this we have to calculate the probability that all the houses will have the pets then the probability that all five households will have pets is equal to \(5C_{5}(0.55)^{5} (1-0.55)^{0}\)

=1(0.0503)\((0.45)^{0}\)

=1*0.0503*1

=0.0503

Hence the probability that all the five households will have pets is equal to 0.0503.

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Answer:

x = 8

Step-by-step explanation:

3/4x - 7 = -1

Your first step is to isolate the variable term 3/4x, to do this you have to add 7 to both sides:

3/4x -7 (+7) = -1 (+7)

3/4x = 6

Next, you want to get rid of the fraction by multiplying both sides by the denominator #, 4

3/4(x4) x = 6(x4)

3x = 24

Final step, you divide by three to isolate the x!

3x/3 = 24/3

x = 8

Hope this helps! =D

Step-by-step explanation:      

Step 1: Add 7 to both sides.

\(\frac{3}{4}x-7+7=-1+7\)

Step 2: Simplify

\(\frac{3}{4}x=6\)

Step 3:  Multiply both sides by 4

\(4\cdot \frac{3}{4}x=6\cdot \:4\)

Step 4: Simplify

\(3x=24\)

Step 5: Divide both sides by 3

\(\frac{3x}{3}=\frac{24}{3}\)

Step 6: Simplify

\(x=8\)

Explanation in words (Short Form)

-  The first step is to add 7 to both sides and the answer will result as 3/4x=6.

- The second step is to multiply both sides by 4/3 and the final answer will result as x = 8.

Answer:    

\(x=8\)

Hope this helps.

Answer:

x=2.371

Step-by-step explanation:

Subtract 8.63 from both sides

x+8.63-8.63=11.001-8.63

x=11.001-8.63

x=2.371

The opportunity cost of attending the dinner party would be $15, as it represents the potential earnings from the highest-paying job option among the three.

The opportunity cost refers to the value of the next best alternative that you forego when making a decision. In this scenario, if you choose to attend the dinner party instead of working, you are giving up the potential earnings from one of the job options.

The highest-paying job among the three options is the third job, which pays $15. Therefore, the opportunity cost of attending the dinner party would be $15. This means that by choosing to go to the party, you are forfeiting the opportunity to earn $15.

It is important to consider opportunity costs when making decisions, as they reflect the value of the alternatives that are being sacrificed. In this case, even though you may not have to pay for the dinner at the party, the opportunity cost is still present in terms of the potential income that could have been earned if you had chosen to work instead.

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Answer:

Do you have a picture? Or any of the measurements?

The lengths of the third side of the triangles can be achieved by using the Pythagorean theorem, which says in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.

Three vertices make up the three-sided polygon known as a triangle. There is a point where the three sides are joined end to end.

A triangle's third side must always have a length that falls between (but not exactly equal to) the sum and difference of the other two sides. Consider the examples 2, 6, and 7 as an example. The third side length must therefore be greater than 4 and less than 8.

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Answer:

1130.4 m^3

Step-by-step explanation:

For top cone:

radius r = 6 m

height \(h_1 = 12\:m\)

For down cone:

radius r = 6 m

height \(h_2 = 18\:m\)

\(V_{solid} = V_{top\: cone}+V_{down\: cone} \\ \\ = \frac{1}{3}\pi r^{2} h_{1} + \frac{1}{3}\pi r^{2} h_{2} \\ \\ = \frac{1}{3} \pi {r}^{2} ( h_{1} + h_{2}) \\ \\ = \frac{1}{3} \pi {(6)}^{2} (12 + 18) \\ \\ = 12\pi(30) \\ \\ = 360(3.14) \\ \\ = 1130.4 \: {m}^{3} \)

To find the maximum height the projectile reaches, we need to determine the vertex of the quadratic equation that represents its path. The equation is given as f(t) = -16t^2 + 64t + 48, where -16t^2 represents the force of gravity acting on the projectile and 64t represents its initial velocity.

The vertex of a quadratic equation in standard form, ax^2 + bx + c, is given by the formula x = -b/2a and y = f(x). In this case, a = -16, b = 64, and c = 48. So the time at which the projectile reaches its maximum height is t = -b/2a = -64/-32 = 2 seconds.

To find the maximum height, we substitute t = 2 into the equation and get f(2) = -16(2)^2 + 64(2) + 48 = 80 feet. Therefore, the maximum height the projectile reaches is 80 feet.

In conclusion, the maximum height the projectile reaches is 80 feet. This is determined by finding the vertex of the quadratic equation that represents its path.

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Answer:

Step-by-step explanation:

A circle is inscribed in an equilateral triangle PQR with centre O. If angle OQR = 30°, what is the perimeter of the triangle?

This is a circle inscribed in an equilateral triangle with side s.

If you are asking for the perimeter of PQR, it is 3s.

If you are asking for the perimeter of OQR, it is (3+23–√3)s

Since OR and SR are the hypotenuses of right triangles with adjacent side equal to ½ s, their length is ½s / cos 30° = (√3) /3.

(3/3)s + ((√3) /3)s + ((√3) /3)s = ((3 + 2√3)/3)s ≈ 2.1547s

Hope it helps

help me by marking as brainliest....

Answer:

fhiuqhficu3f

Step-by-step explanation:

Answer:

4 hours

Step-by-step explanation:

take 2 divides with 0.5 to found out how many  it took to run out of fuel

hours

To find the general solution of the given higher-order differential equation y''' − 6y'' − 7y' = 0, we first need to find the characteristic equation by assuming that y = e^(rt), where r is a constant. Substituting this into the differential equation, we get r^3 - 6r^2 - 7r = 0.

Factoring this, we get r(r - 7)(r + 1) = 0. So the roots of the characteristic equation are r1 = 0, r2 = 7, and r3 = -1.

Therefore, the general solution of the differential equation is y(t) = c1 + c2e^(7t) + c3e^(-t), where c1, c2, and c3 are constants that can be determined using initial or boundary conditions.

In summary, the general solution of the given higher-order differential equation y''' − 6y'' − 7y' = 0 is y(t) = c1 + c2e^(7t) + c3e^(-t), where c1, c2, and c3 are constants.

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Answer:

It depends on the size of the box

Step-by-step explanation:

Since the dimensions of the box are not included you can't answer the question

New York had the larger population with 1.9 x 10⁷ people. The correct option is B.

To compare the populations of the states, we need to convert all the populations to the same unit of measurement. In this case, all the populations are given in terms of millions (10⁶).

We can see that New York's population is 1.9 x 10⁷, which means 19 million people. Georgia's population is given as 9.6 x 10⁶, which is 9.6 million people. Comparing these two values, it is evident that New York has a larger population than Georgia.

Check the populations of the other states:

Alaska: 7.1 x 10⁵ = 0.71 million people

Wyoming: 5.6 x 10⁵ = 0.56 million people

Idaho: 1.5 x 10⁶ = 1.5 million people

New York's population of 19 million is much larger than any of the other states listed, making it the state with the largest population among the options provided. The correct option is B.

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Complete question:

Based on the 2010 census, the population of Georgia was 9.6 x 10^6 people. Which state had a larger population? A. Alaska: 7.1 x 10^5 B. New York: 1.9 x 10^7 C. Wyoming: 5.6 x 10^5 D. Idaho: 1.5 x 10^6

Answer:

See below

Step-by-step explanation:

Solution with Quadratic Formula

\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-8\pm\sqrt{8^2-4(1)(16)}}{2(1)}=\frac{-8\pm\sqrt{64-64}}{2}=\frac{-8}{2}=-4\)

Note that \(a=1,b=8,c=16\)

Solution with factoring (faster)

\(x^2+8x+16=0\\(x+4)^2=0\\x+4=0\\x=-4\)

Answer: 2+4=6, and 2*4=8.

Step-by-step explanation:

Answer:

2 and 4

Step-by-step explanation:

The correct statement about the wave described in the problem introduction is: C "This wave is oscillating but not traveling."

In the given mathematical form of the wave, y(x,t) = Asin(kx)sin(wt), the terms sin(kx) and sin(wt) represent the spatial and temporal components of the wave, respectively.

The term sin(kx) represents the spatial component and determines the shape of the wave along the x-direction. It oscillates between positive and negative values as x changes, creating regions of displacement and nodes where the displacement is zero. This indicates that the wave is oscillating.

However, there is no term involving x in the temporal component sin(wt). Therefore, the wave is not changing its shape or position as time progresses. It is stationary in space and does not exhibit any net movement along the x-direction. Thus, the wave is not traveling.

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The minimum point of the function y=f(x)+3 is at (-1 , 0 ) .

The biggest and lowest value of a function, either inside a specific range (the local or relative extrema) or on the entire domain, are generally referred to as extrema (plural of extremum) in mathematical analysis (the global or absolute extrema). One of the first mathematicians to suggest the general method of adequacy for determining the maxima and minima of functions was Pierre de Fermat.

The maximum and minimum of a set are the greatest and least items in the set, as described by set theory. There are no minimum or maximum values in unbounded infinite sets, such as the set of real numbers.

Say that (x,y) = where y = f(x) minimum occurs at (-1,-3). As a result, for all other x inside its domain of definition, y= f(x) >=-3

y = f(x) + 3 simply elevates the graph of y by 3 and increases the value of y for any x. Its minimum x-value remains at -1, and its value for y is f(3) + 3 = -3 + 3 = 0. as a result, new minimum =(-1 , 0 ) .

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Disclaimer: The complete question is :

This is a sketch of the curve with equation y=f(X). The curve has a minimum point at M(-1,-3).Find the minimum value for the function y=f(x)+3 .

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Step-by-step explanation:

To find the Highest Common Factor (H.C.F.) of 567 and 255 using Euclid's division lemma, we can follow these steps:

Step 1: Apply Euclid's division lemma:

Divide the larger number, 567, by the smaller number, 255, and find the remainder.

567 ÷ 255 = 2 remainder 57

Step 2: Apply Euclid's division lemma again:

Now, divide the previous divisor, 255, by the remainder, 57, and find the new remainder.

255 ÷ 57 = 4 remainder 27

Step 3: Repeat the process:

Next, divide the previous divisor, 57, by the remainder, 27, and find the new remainder.

57 ÷ 27 = 2 remainder 3

Step 4: Continue until we obtain a remainder of 0:

Now, divide the previous divisor, 27, by the remainder, 3, and find the new remainder.

27 ÷ 3 = 9 remainder 0

Since we have obtained a remainder of 0, the process ends here.

Step 5: The H.C.F. is the last non-zero remainder:

The H.C.F. of 567 and 255 is the last non-zero remainder obtained in the previous step, which is 3.

Therefore, the H.C.F. of 567 and 255 is 3.

Answer:

2

Step-by-step explanation:

2 2 2 2 2 2 2 2. 2 2 2 2 2 2 2. 2 2 2. 2 2 2 2

The ornaments consist of two identical cones.

The formula for the surface area of a cone is:

SA = πr² + πrl

Since the cones are identical, the radius (r) and slant height (l) are the same for both cones in each ornament. Let's call them r1 and l1.

The total surface area of each ornament is:

SA_ornament = 2(πr1² + πr1l1)

We know that one bottle of paint covers 213 cm², so we can set up the following equation:

SA_ornament * bottles = 60 * 213

Substituting the given value of pi:

2(3.14r1² + 3.14r1l1) * bottles = 60 * 213

Simplifying:

6.28r1² + 6.28r1l1 = 6390

Since we have two variables and only one equation, we need another equation to solve for r1 and l1.

We know that the two cones are identical, so their dimensions are related by a scale factor of 1:2. Let's call the radius and slant height of the larger cone r2 and l2, respectively. Then:

r2 = 2r1

l2 = 2l1

The volume of each ornament is:

V_ornament = (1/3)πr1²l1 + (1/3)πr1²l1 = (2/3)πr1²l1

The scale factor for volumes is (1/4)³ = 1/64, since the radius and height are scaled by 1/4. Therefore:

V_ornament_B = (1/64)V_ornament_A = (1/64)(112π) = 7/4π

The volume of each ornament B is 7/4π.

The volume of 60 ornaments B is:

60 * 7/4π = 105π

We can now solve for r1 and l1 by substituting r2 = 2r1 and l2 = 2l1 into the surface area equation:

6.28r1² + 6.28(2r1)(2l1) = 6390

Simplifying:

6.28r1² + 25.12r1l1 = 6390

We don't need to solve for r1 and l1 explicitly. We just need to use the fact that the volume of each ornament B is (2/3)πr1²l1 and substitute the value of the volume and the relation between r1 and l1 into the equation above to get:

r1 ≈ 7.27 cm

l1 ≈ 14.54 cm

Finally, we can calculate the total surface area of each ornament B:

SA_ornament_B = 2(3.14 * 7.27² + 3.14 * 7.27 * 14.54) ≈ 1158.6 cm²

And the number of bottles of paint needed:

bottles = (60 * 1158.6) / 213 ≈ 326.4

Therefore, Tim needs about 327 bottles of paint to paint 60 ornaments.

Answer:

1 year:  $2060

2 years: $2121.80

3 years: $2185.45

Step-by-step explanation:

Compound interest formula is A = P(1 + \(\frac{r}{n}^{nt\)) where A is the final amount, P is the initial principal balance, r is the interest rate, n is the number of times interest applied per time period, and t is the number of time periods elapsed. In our case, P would be equal to 2000 dollars, r would be equal to 0.03, for 3 percent, and our n value would just be one, so the final equation is:

\(2000(1.03)^t\)

First, let's evaluate t for 1, as in one year.

\(2000 * 1.03^1\) = 2000 x 1.03 = 2060

Two years: 2000 * 1.03 squared = 2121.80

Three years: 2000 * 1.03^3 = 2185.45!

Hope this helps!

Answer:

13.8 cm^2

Step-by-step explanation:

Area of a triangle = 1/2 base * height

                              = 1/2 * 6.9 * 4 = 13.8 cm^2

Answer:2n+13=75 n=31

The next operation that should be done when evaluating this expression 9-12+-2+3(-3) is A. 3(-3)=-9

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

In this case, it should be noted that the expression given is written as 9-12+-2+3(-3). In PEDMAS, the first operation is parentheses. Therefore, the number on parentheses will be solved first.

In this case, the number in parentheses will be 3(-3). Therefore, the correct option is A.

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