What’s the correct answer for this?

Answer:

Step-by-step explanation:

The absolute change in game length is ...

  (180 min) -(150 min) = 30 min . . . . change in game length

__

The relative change is expressed as a fraction of the original game length:

  (30 min)/(150 min) × 100% = 20% . . . . relative change in game length

Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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Bertha's dive is 5 times farther than the end of Vernon's dive

A ratio can defined mathematical as an ordered pair of numbers, like variables b and c, when written form b / c with the denominator greater than the value zero.

It explains how many times a particular number is composed of another number in a given proportion.

It is also seen as the comparison of two quantities, elements or numbers having the same unit measure. It goes further to explain how much of one of the element or quantity contains another.

This is done on the basis of  their magnitude or sizes.

Given that;

Bertha's dive ended = -25 m

Vernon's dive ended = -5 m

Divide the values

= -25/-5

= 5 times

Hence, the value is 5 times

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The mean population in the U.S. is 2,068,548.

The median population in the U.S. is 1,565,659.

There is no mode in the dataset.

The standard deviation of the populations for the top twelve largest cities in the U.S. is 2,279,894.12.

To find the mean population, we need to sum up all the populations and divide by the total number of cities.

Mean = EF / n

Mean = 8,336,817 + 979,576 + 2,693,976 + 2,320,268 + 1,680,992 + 1,584,064 + 1,547,253 + 1,423,851 + 1,343,573 + 1,021,795 + 978,908 + 911,507

Mean = 24, 822,580 / 12

Mean =  2068548.33333

Mean =  2,068,548

Arranging populations in ascending order:

\(911,507, 978,908, 1,021,795, 1,343,573, 1,423,851, 1,547,253, \\1,584,064, 1,680,992, 2,320,268, 2,693,976, 8,336,817, 979,576\)

Median population = (1,547,253 + 1,584,064) / 2

Median population = 1,565,658.50.

The mode represents the value(s) that appear most frequently in the dataset. In this case, there is no single mode as each population value occurs only once. Therefore, we can say that there is no mode in the dataset of the top twelve largest cities in the U.S.

Standard Deviation:

\(\sqrt{(8,336,817 - 1,574,232)^2 + (979,576 - 1,574,232)^2 + (911,507 - 1,574,232)^2) / 12}\\\\\)

\(= \sqrt{62,333,273,003,930 / 12}\\= \sqrt{5,194,439,417,828.33} \\\\= 2,279,894.12\)

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Step-by-step explanation:

x-a

The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

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Answer:

3x = 6y

Step-by-step explanation:

8 - 2y = 6y and 3x is by itself so it would be 3x is equal to 6y.

There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

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Step-by-step explanation:

a/b is invalid, when b = 0.

so, F(x) is invalid, if (1 + sin(2x)) = 0.

(1 + sin(2x)) can only be 0, if sin(2x) = -1

sin(angle) = -1

angle = 2x = 270° or 3pi/2

x = 135° or 3pi/4

so,

x <> 135° or 3pi/4

Answer:

27.15 +(21.72 divided by 4) is your answer

The step-by-step explanation

you have to divide 108.60 by 4 and then get 20% of 108.60 and after divide your answer to the % by 4 and add it to 27.72

We can rewrite the sphere's equation in Cartesian coordinates.

\(\rho = 42 \cos(\varphi) \implies \rho^2 = 42 \rho \cos(\varphi) \implies x^2+y^2+z^2 = 42z\)

Complete the square to get

\(x^2 + y^2 + z^2 - 42z = 0 \implies x^2 + y^2 + (z - 21)^2 = 21^2\)

which represents a sphere centered at (0, 0, 21) with radius 21. You can find the sphere's volume easily from here.

But that's not what you're asked to do. You want to find the volume of the intersection of the two spheres. (see attached plot)

The two spheres meet in the plane z = 21/2:

\(x^2+y^2+z^2 = 21^2 \implies x^2+y^2 = 21^2 - z^2\)

\(x^2+y^2+(z-21)^2 = 21^2 \implies 21^2 - z^2 + (z-21)^2 = 21^2 \implies z = \dfrac{21}2\)

and we express this plane in spherical coordinates as

\(z = \rho \cos(\varphi) = \dfrac{21}2 \implies \rho = \dfrac{21}2 \sec(\varphi)\)

We use this plane to cut the region of interest in half; we have to do this to find the volume because the ρ coordinate does not vary uniformly between the two spheres. On the plus side, the region is symmetrical across this plane, so we only need one integral.

Find the angle φ at which the two spheres meet:

\(42\cos(\varphi) = 21 \implies \cos(\varphi) = \dfrac12 \implies \varphi = \cos^{-1}\left(\dfrac12\right) = \dfrac\pi3\)

Putting everything together, the volume of the region is

\(\displaystyle 2 \int_0^{2\pi} \int_0^{\pi/3} \int_{21/2 \, \sec(\varphi)}^{21} \rho^2 \sin(\varphi) \, d\rho \, d\varphi \, d\theta = \boxed{\fraC{15,435\pi}4}\)

I leave the details of computation to you.

We have that the distance traveled by the football ball is the hypotenuse of a right triangle whose other legs are 25 yards (40 yard line - 15 yard line) and 35 (45 yard line - 10 yard line), so the distance ir traveled was:

Which means he traveled around 43 yards

Answer:

5/12

Step-by-step explanation:

Probability of getting either heads or tails of a coin : 1/2

Probability of getting 1,2,3,4, or 6 on a dice: 5/6

Multiply those two probabilities : 1/2 * 5/6 = 5/12

You have a 5 out of 12 chances of getting heads on a coin AND any number but a 5 on a dice.

Hope this helps!

Answer:ok

Step-by-step explanation:

Check the picture below.

we have three sides, let's look at the two smaller sides first.

if we move the sides closer and ever closer to each other, to the extent that one is right on top of the other, what is the length of the red side?  Well, assuming the two smaller sides are one pancaked on top of the other, the red side will be as long as 7 - 6 = 1.  However, the sides can't be on top of each other, because if that's so, we have a flat-line, and thus we wouldn't have a triangle.  So whatever the third side may be, it must be greater than 1.

Now, if we move the sides away from each other, farther and farther to the extent that one is parallel to the other, then the third side will just be as long as 6 + 7 = 13.  However, we can't do that, because if that were to happen, we again will have a flat-line and not a triangle.  So whatever the third side may be, it must be less than 13.

now, 14 inches is out of that range, so no dice.

Answer:

38 pills

Step-by-step explanation:

To find the number of pills, you need to divide the weight of each pill by the total weight needed.

0.76 grams / 0.02 grams = 38 pills

Answer:

length= 24cm

Step-by-step explanation:

interpreting the question

L=3w

perimeter=2(l+w)

64=2(3w+w)

64=2(4w)

64=8w, Divide both sides by 8

w= 8cm

since w= 8

L=3w

L=3×8

L=24cm

Answer:

-3x+6y+5

Step-by-step explanation:

The equation- -2x-y+10-x+7y-5

Next, combine all the x, y, and real numbers.

X's: (-2x)+(-x)= -3x

Y's: (-y)+(7y)=6y

Real Numbers: (10)+(-5)=5

insert back into an equation

-3x+6y+5

:-) hope this helps

Answer:

1550 miles

Step-by-step explanation:

Every day, he has to drive his car 7 miles to work and 7 miles back, making a total of 14 miles. Adding this to the 296 mile delivery route, that is a total of 310 miles a day. Multiplying this by the 5 days in his workweek, you get a total of 1550 miles. Hope this helps!

Answer:

\(a(9 {a}^{2} b + ba)\)

hope it's helpful ❤❤❤❤❤❤❤

THANK YOU.

An equation of the lines that pass through this pair of points (3,-5) and (2, -1) is equal to y = -4x + 7.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-1 + 5)/(2 - 3)

Slope (m) = 4/-1

Slope (m) = -4.

At data point (2, -1) and a slope of -4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-1) = -4(x - 2)  

y + 1 = -4x + 8

y = -4x + 7

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Answer:

All are equivalent.

Step-by-step explanation:

Step-by-step explanation:

1. Given: a = 4t + 4

We know that

\( a = \frac{dv}{dt} \: \: or \: dv = adt\)

By definition, the integral of a power function x^n is

\( \int {x}^{n} dx = \frac{ {x}^{n + 1} }{n + 1} + k\)

Integrating the acceleration a, we get

\(v = \int adt = \int(4t + 4)dt = 2 {t}^{2} + 4t + k\)

where k = constant of integration. We know that v = 10 when t = 0 so when we do the substitution, we get k = 10 therefore, the final expression for v is

\(v = 2 {t}^{2} + 4t + 10\)

To find s, we need to integrate v. Knowing that

\(v = \frac{ds}{dt} \: \: or \: s = \int v \: dt\)

\(s = \int(2 {t}^{2} + 4t + 10)dt\)

\( = \frac{2}{3} {t}^{3} + 2 {t}^{2} + 10t + k\)

where k once again is the constant of integration. We know that s = 2 when t = 0, which gives us k = 2. Therefore, the final expression for s is

\(s = \frac{2}{3} {t}^{3} + 2 {t}^{2} + 10t + 2\)

2. The potential difference V between two boundaries a and b is given by

\(V = \frac{q}{2\pi \epsilon_0 \epsilon_r} \int_{b}^{a} \frac{dr}{r} \)

Note that the integral in the expression above can be rewritten and the integrated as

\( \int_{b}^{a} \frac{dr}{r} =\int_{b}^{a} {r}^{ - 1} dr = \ln |a| - \ln |b| \)

so the potential difference V is then J

\(V = \frac{q}{2\pi \epsilon_0 \epsilon_r} \int_{b}^{a} \frac{dr}{r}\)

\( = \frac{2 \times {10}^{ - 6} }{2\pi (8.85\times {10}^{ - 12}) (2.77)}( \ln |20| - \ln |10| )\)

\( = 9000 \: V\)

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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SOLUTION

Write out the expression

Then we substitute k=1 into the expression and obatin the value

Similarly,

Then we also substitute the last value of k

finally, we take the sum of the result

Therefore the summation of the expression from 1 to 3 for the values of k is 2

The right option is E (2).

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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