Which equation is equivalent to log5x3 - logx2 = 2?.

There are 1,814,400 ways to choose and arrange 8 people in a straight line from a group of 10 people.

To determine the number of ways 8 people can be chosen and arranged in a straight line from a group of 10 people, we can use the concept of permutations.

The formula for permutations is given by:

P(n, r) = n! / (n - r)!

Where n is the total number of objects and r is the number of objects to be selected and arranged.

In this case, we have 10 people to choose from (n = 10) and we want to select and arrange 8 people (r = 8). Therefore, the formula becomes:

P(10, 8) = 10! / (10 - 8)!

Simplifying the expression:

P(10, 8) = 10! / 2!

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

= 3,628,800

2! = 2 x 1

= 2

P(10, 8) = 3,628,800 / 2

= 1,814,400

Therefore, when there are 10 people to choose from, there are 1,814,400 ways to select and arrange 8 people in a straight line. This is calculated using the permutation formula.

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Answer:

Step-by-step explanation:

where is the question?

Answer:

2/15

Step-by-step explanation:

Step one:

given data

sample space

1 elephant,

4 bears,

3 cats, and

2 dogs.

sample size= 1+4+3+2= 10

Required:

By selecting without replacement, the probability that she chooses a bear both times

Step two:

the first event= Pr(bear)= 4/10= 2/5

the second event, the sample size is now 9 and the number of bears is now 3

Pr(bear)= 3/9= 1/3

Hence, the probability that she chooses a bear both times

= 2/5*1/3

=2/15

Answer:

it's a answer!!

Step-by-step explanation:

ITS AN ANSWER BECAUSE IT CAN BE! THATS WHY! BLAH BLAH BLAH! I do not say blah blah blah

Answer:

C. -1 is less than x

Step-by-step explanation:

-3 < 4x + 1

-3-1 < 4x +(1 -1)

-4 < 4x

-4/4 < 4x/4

-1 < x

Answer:

height of the waste is 20.0 inches.

Step-by-step explanation:

given data

volume = 5, 667.7cubic inches

radius = 9.5 inches

solution

we use here volume of a cylinder is express as

V = πr²h     .................1

put here value

5667.7 = (3.14) × (9.5²) × h

solve it we get

h = 20 inch

so height of the waste is 20.0 inches.

Answer:

29x – 29 = 29x – 11

Step-by-step explanation:

29x-29 = 29x-11

29x-29x = 29-11

0x = 18

Answer:y= -5

X=-6

-5/6

Step-by-step explanation:

The correct interpretation of the 90% confidence interval provided is that the manufacturer can be 90% confident that the true mean difference in fuel economy for cars of this make and model driven with underinflated tires versus properly inflated tires is between -3.339 mpg to -0.585 mpg.

This means that if the study were to be repeated multiple times, the true mean difference in fuel economy would fall within this interval 90% of the time. It does not imply that a randomly selected car or group of cars with underinflated tires will get between 3.339 and 0.585 fewer miles per gallon than a randomly selected car or group of cars with properly inflated tires, as the interval is about the difference in means, not individual car performance.

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The fraction which represent the number of sweaters Maggie knits in 8 days is 2/1 sweaters

Total number of sweaters Maggie knits = Sweaters Maggie knits per day × Number of days

= 1/4 × 8

= (1 × 8) / 4

= 8/4

= 2/1 sweaters

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Answer:  It's "The linear equations have the same slope but different y-intercepts."

Step-by-step explanation:

When 2 equations have the same slope they will be parallel unless they have the same y-intercept than that means they overlap since they are the same.

good luck lol

Answer: 10 kg

Step-by-step explanation:

3% = 0.03

First, take 20 times 0.03 = 0.6kg of salt

We know that the 2% solution of seawater

So, we take 100 times 0.6, then divide by 2 = 30kg

Then take 30 - 20 = 10kg

So, to make a solution from 3% to 2%, we have to add  10 kg of water with a 20 kg solution.

Answer:

101.58 in

Step-by-step explanation:

The ramp r is the hypotenuse of a right triangle with the ground and 28 in height being the legs.

The angle of elevation 16° is the angle inside the triangle opposite the 28 in height.

Using the sine ratio in the right triangle, then

sin16° = \(\frac{opposite}{hypotenuse}\) = \(\frac{28}{r}\) ( multiply both sides by r )

r × sin16° = 28 ( divide both sides by sin16° )

r = \(\frac{28}{sin16}\) ≈ 101.58 in

Answer:

The 3rd answer

Step-by-step explanation:

Step-by-step explanation:

Dividing the shape into two:

The area of the rectangle is

A= 13.5*4.8= 64.8km2

the area of the triangle

A = [( 5.7-4.8) *13.5 ]/ 2= 6.075km2

Therefore the total area is

At = 64.8 + 6.075 = 70.875km2

Answer:

= 3z4 - 2z2 -5z

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

The slope equation for this problem is

y2-y1

--------

x2-x1

So the y2=4, y1=3, x2=8, and x1=0

4-3      =1

-----       --

8-0     =8

Which is 1/8

Answer: 1/8

Step-by-step explanation:

Use the slope formula and slope-intercept form

y = mx + b to find the equation.

y = 1/8x + 3

Using the mid-point concept, we have that:

The mid-point between two points is the halfway point between them, and is found using the mean of the coordinates.

The center of the circle is the mid-point of the coordinates of the diameter, hence:

The radius is the distance between the center and the end-points of the diameter, hence, applying the formula for the distance between two points:

\(r = \sqrt{(5 - 2)^2 + (8 - 7)^2} = \sqrt{10} = 3.16\)

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The general solution to the differential equation is y(x) = (5/2)x^3 - (4/3)x^2 + (1/2)x + C1e^(-x) + C2e^(-2x).

To solve this initial value problem, we need to find the general solution to the differential equation and then use the initial conditions to find the particular solution.

The characteristic equation is r^2 + 3r - 2 = 0, which has two distinct real roots of r1 = -2 and r2 = -1.

The general solution to the differential equation is y(x) = (5/2)x^3 - (4/3)x^2 + (1/2)x + C1e^(-x) + C2e^(-2x)

Now we can use the initial conditions y(0) = 0 and y'(0) = 0 to find the values of C1 and C2.

y(0) = 0 = (5/2) * 0^3 - (4/3) * 0^2 + (1/2) * 0 + C1e^(0) + C2e^(0)

y'(0) = 0 = 5x^2 - (8/3)x + (1/2) + C1e^(-x) - C2e^(-2x)

Solving these equations, we find that C1 = 0 and C2 = 0, so the particular solution to the initial value problem is y(x) = (5/2)x^3 - (4/3)x^2 + (1/2)x.

This method is the standard way to solve Initial value problems for linear homogeneous differential equations with constant coefficients. It relies on finding the characteristic equation, and the general solution of the differential equation. Then we use the initial conditions to find the particular solution.

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Step-by-step explanation:

Please find the attached pics for answers.

Answer:

9/14

Step-by-step explanation:

3/7  divided by 2/3?

Division of fractions is equivalent to multiplication by the reciprocal of the second fraction:  3/7 divided by 2/3 = 3/7 multiplied by 3/2

Once rearranged, multiply all of the numerators by each other. Do the same with the denominators and form a new fraction with these values:

3/7 x 2/3 = 9/14

Answer:

9/14

Step-by-step explanation:

3/7 × 3/2

top part of fractions

3×3 = 9

bottom part of fractions

2×7 = 14

9/14 cannot be simplified so final answer is

9/14

Answer:

The answer is C

Step-by-step explanation:

Need explanation??

Answer:

y=-3x+6

Slope:-3

y-intercept:6

The radius and height of a real soda can with a double thickness in the top and bottom surfaces that minimize its surface area are approximately 2.89 cm and 13.15 cm, respectively. These dimensions are closer to the dimensions of a real soda can compared to the dimensions obtained in part (a).

a. To minimize the surface area of a cylindrical soda can, we need to find the values of radius and height that minimize the surface area equation.

Let's denote the radius of the can as r and the height as h. The volume of the can is given as 354 cm^3, so we have:

πr^2h = 354

Solving for h, we get:

h = 354 / (π\(r^2\))

The surface area of the can can be calculated as follows:

A = 2πr^2 + 2πrh

Substituting the expression for h in terms of r, we get:

A = 2πr^2 + 2πr(354 / πr^2)

Simplifying:

A = 2πr^2 + 708 / r

To minimize the surface area, we need to find the value of r that makes the derivative of A with respect to r equal to zero:

dA/dr = 4πr - 708 / r^2

Setting dA/dr = 0, we get:

4πr = 708 / r^2

Multiplying both sides by r^2, we get:

4πr^3 = 708

Solving for r, we get:

r = (708 / 4π)^(1/3) ≈ 3.64 cm

Substituting this value of r back into the expression for h, we get:

h = 354 / (π(3.64)^2) ≈ 9.29 cm

Therefore, the radius and height of the cylindrical soda can with minimum surface area and volume of 354 cm^3 are approximately 3.64 cm and 9.29 cm, respectively.

b. Real soda cans do not seem to have an optimal design because their dimensions are not the same as the ones obtained in part (a). The radius of a real soda can is 3.1 cm and the height is 12.0 cm. However, real soda cans have a double thickness in their top and bottom surfaces, which means that their dimensions are not directly comparable to the dimensions of the cylindrical can we calculated in part (a).

To find the dimensions of a real soda can with a double thickness in the top and bottom surfaces that minimize its surface area, we can use the same approach as in part (a), but with the appropriate modification to the surface area equation:

A = 4πr^2 + 708 / r

Setting dA/dr = 0, we get:

8πr^3 = 708

Solving for r, we get:

r = (708 / 8π)^(1/3) ≈ 2.89 cm

Substituting this value of r back into the expression for h, we get:

h = 354 / (π(2.89)^2) ≈ 13.15 cm

Therefore, the radius and height of a real soda can with a double thickness in the top and bottom surfaces that minimize its surface area are approximately 2.89 cm and 13.15 cm, respectively. These dimensions are closer to the dimensions of a real soda can compared to the dimensions obtained in part (a).

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Answer:

264 remainder 19

Step-by-step explanation:

Answer:

P

Step-by-step explanation:

Answer:

P is the independant variable.

Step-by-step explanation:

Since B is dependent on P, being B=P6, P is the independent variable.

Answer: Stella would earn $184 in 23 hours.

Step-by-step explanation: First we need to find the unit rate so start by dividing by 9

\(\frac{72}{9} =8\\\frac{9}{9}=1\)

Now we know every hour Stella will earn $8. We can now multiply the amount for 1 hour by 23 to get the amount for 23 hours.

8x23=184

1*23=23

Now we can see that Stella would earn $184 for working 23 hours.

Answer: C) 8.1 x 105

The price per T-shirt should be at least $15 to achieve a profit of $250.

To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.

Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.

Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.

Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.

Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.

By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.

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Range of the value of the game played:To get the range of the value of the game played, we have to find the minimum and maximum possible scores. Minimum score of the game: The minimum score is when both teams play their strongest defense strategy.

For Letran, their strongest defense strategy is the Man-to-man defense and for Mapua, their strongest defense strategy is the Half-court Press defense.Using these defense strategies, Letran can get a score of 45 and Mapua can get a score of 30.Thus, the minimum possible score is 45 + 30 = 75.Maximum score of the game: The maximum score is when both teams play their weakest defense strategy.

For Letran, their weakest defense strategy is the Press defense and for Mapua, their weakest defense strategy is the Man-to-man defense.Using these defense strategies, Letran can get a score of 55 and Mapua can get a score of 40.Thus, the maximum possible score is 55 + 40 = 95.Therefore, the range of the value of the game played is 75 to 95.b) To find the defense strategy in which Letran is weak, we have to see which defense strategy allows Mapua to get the highest score.

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