Find the inverse of the function.
g(x) = -2x-10

Answer:

Less Than or Equal to

Step-by-step explanation:

In mathematics and computer science, the floor and ceiling functions map a real number to the greatest preceding or the least succeeding integer, respectively. floor(x) : Returns the largest integer that is smaller than or equal to x (i.e : rounds downs the nearest integer).

The dimensions of the garden that minimize the cost is 3.83 and 5.74.

Lets assume the garden has length L and width W and one Length has the brick wall.

L*W = 22 (area constraint)

C = 40 * L + 20 * L + 20 * W + 20 * W

= 60 * L + 40 * W

We need the equation in terms of just one variable, lets use L. We can use the area constraint to do this

W = 22/L (plug this into the C equation)

C(L) = 60*L + 40*(22/L)

= 60*L + 880/L

C(L) = 60*L + 880/L

now take the derivative and get

C'(L) = 60 - 880/L^2

now set that derivative = 0 to find the key L value where the min/max occurs (min in this case)

0 = 60 - 880/L^2

Solve for L,

L = ± (2 sqrt(11/3))

We only need the positive answer as negative length makes no sense here,

L = 3.83 (approximate)

We can now solve for W as well

W = 22/3.83 = 5.74

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Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

The diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.

To convert the diameter of Earth from miles to kilometers, we can multiply the given diameter in miles by the conversion factor of 1.6 kilometers per mile.

Given that Earth's diameter is 7,926 miles, we can calculate its diameter in kilometers as follows:

Diameter in kilometers = Diameter in miles × Conversion factor

Diameter in kilometers = 7,926 miles × 1.6 kilometers/mile

Diameter in kilometers = 12,681.6 kilometers

Rounding this value to the nearest whole number, we get 12,682 kilometers.

Therefore, the correct answer is option D: 12,682 km.

Option A: 49,553 km is not the correct answer. It is not consistent with the given diameter of Earth.

Option B: 120,586 km is also not the correct answer. It is not consistent with the given diameter of Earth.

Option C: 1,392,650 km is significantly larger than the actual diameter of Earth and is not a plausible value.

In conclusion, the diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.

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Answer:

1260

Step-by-step explanation:

Subtract 21 from 8,to get 13.Multiply 13 to the 20 dollars,when you do that you get 260.You add the 260 and the 1000 dollars together.

Answer:

55 YRS

Step-by-step explanation:

T=INTEREST X 100%/PRINCIPAL X RATE

T=4400X100%=440000%/4000 X 2%

T=440000%/8000%

T=55 YRS

Answer:

(x + 2, y - 4)

Step-by-step explanation:

The translation is 2 units right and 4 units down from the original image.

(x + 2, y - 4)

Answer:

The slope is -8 :)

Step-by-step explanation:

trust me

Answer:

V= 270m³

Step-by-step explanation:

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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The expressions (3√-5 + 2)(4√-12 - 1) and (4i - 3)² have values of -24√5 - 2 + 16i√3 - 3i√5 and  -7 - 24i respectively.

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.

In the first expression;

(3√-5 + 2)(4√-12 - 1) will give us -24√5 - 2 + 16i√3 - 3i√5

In the second expression, we have (4i - 3)² which will give us -7 - 24i

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Thus, there is a very high probability (99.93%) that the sample mean would differ from the true mean by less than 3.273 liters, given a sample size of 109 people and a population mean of 152 liters with a variance of 484.

To answer this question, we need to use the Central Limit Theorem, which states that the sampling distribution of the sample means will be approximately normal, regardless of the distribution of the population, as long as the sample size is large enough.

First, we need to calculate the standard error of the mean, which is the standard deviation of the sampling distribution of the sample means. We can use the formula:

standard error of the mean = standard deviation / square root of sample size

Plugging in the values given, we get:

standard error of the mean = √484 / √109
standard error of the mean = 2 / 109
standard error of the mean = 0.018

Next, we need to calculate the z-score, which tells us how many standard errors the sample mean is from the true mean. We can use the formula:

z-score = (sample mean - true mean) / standard error of the mean

Plugging in the values given, we get:

z-score = (sample mean - true mean) / 0.018
3.273 = (sample mean - 152) / 0.018
(sample mean - 152) = 0.018 * 3.273
sample mean = 152 + 0.059
sample mean = 152.059

So the sample mean is 152.059 liters.

Now we can use the standard normal distribution table to find the probability that the z-score is less than 3.273. Looking up the value in the table, we get:

P(z < 3.273) = 0.9993

Therefore, the probability that the sample mean would differ from the true mean by less than 3.273 liters is approximately 0.9993, or 99.93%.

In conclusion, there is a very high probability (99.93%) that the sample mean would differ from the true mean by less than 3.273 liters, given a sample size of 109 people and a population mean of 152 liters with a variance of 484. This probability is based on the Central Limit Theorem and the standard normal distribution table.

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The answers are explained in the solution.

Given that, a bus and a car have speed of 100km/hr and 120km/hr.

They are covering a distance of 340 km, they started travelling at 7:00 am,

Speed = distance / time

A) Bus travelled in 30 minutes = 100 × 0.5 = 20 km

After 30 minutes = 100 × 0.5 = 20 km

Total distance by bus in 1 hour = 40 km

Car covered in 30 minutes = 120 × 0.5 = 60 km

Distance between them = 60-40 = 20 km

Relative speed = 120-100 = 20 km/h

Time to catch up = 20/20 = 1 hour

Distance from Nairobi = 60 + (1 × 120) = 180 km

Therefore, the car catches up with the bus 180 km from Nairobi,

B) Time taken = 30 + 30 + 1 = 2 hours.

7:00am + 2 hours = 9:00 am

C) Time taken by bus to reach the destination = 340 / 100

= 3.4 hours

Hence, bus took 3.4 hours to reach the destination.

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Answer:

im pretty sure this is correct

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer: Ok

Step-by-step explanation:

Answer:

A scatter plot can show a positive relationship, a negative relationship, or no relationship. If the points on the scatter plot seem to form a line that slants up from left to right, there is a positive relationship or positive correlation between the variables.

To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50
Using this recursive rule and the initial population, you can find the population at any given term n.

We are given a population growth model with a recursive rule and an initial population. Let's break down the information and find the population at any given term n.

Recursive rule: Pₙ = Pₙ₋₁ + 50
Initial population: P₀ = 30

Now let's find the population at any term n, using the recursive rule:

Step 1: Determine the base case, which is the initial population.
P₀ = 30

Step 2: Apply the recursive rule to find the next few terms.
P₁ = P₀ + 50 = 30 + 50 = 80
P₂ = P₁ + 50 = 80 + 50 = 130
P₃ = P₂ + 50 = 130 + 50 = 180

Step 3: To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50

Using this recursive rule and the initial population, you can find the population at any given term n.

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Answer:

solution,

radius=7 in

Slant height=25 in

\(h = \sqrt{ {(slant \: height}^{2} - {(radius)}^{2} } \\ = \sqrt{ {(25)}^{2} - {(7)}^{2} } \\ = \sqrt{625 - 49} \\ = \sqrt{576} \\ = \sqrt{ {(24)}^{2} } \\ = 24 \: in\)

Volume of cone:

\( \frac{1}{3} \pi \: {r}^{2} h \\ = \frac{1}{3} \times \pi \times {(7)}^{2} \times 24 \\ = \frac{1}{3} \times \pi \times 49 \times 24 \\ = 392\pi \: {in}^{3} \)

hope this helps...

Good luck on your assignment...

Answer:

392 (pi) in^3

Answer:

i) around 41.7 kg

ii) 72 books

Step-by-step explanation:

i) if 108 books are 30 kg then how much is the mass for 150? You cross multiply so 150 multiply by 30 and 108 multiply by x (the unknown mass). you will get 4500=108x and then 4500/108 is the unknown mass.

ii) use the same way as above.

Answer: -36

Step-by-step explanation:

an = a1 + f × (n-1)

an = 18 - 9 × (n-1)

a7 = 18 - 9 × (7-1)

a7 = 18 - 9 × (6)

a7 = 18 - 54

a7 = -36

Answer:

\(24\pi \: cm {}^{2} \)

Step-by-step explanation:

The area of a cone is

\(\pi \times r {}^{2} + \pi \times r \times \sqrt{ {r }^{2} + {h}^{2} } \)

The volume of the conical paper cup will be option (D) 24π

The steps are as follow:

r = base radius = 3 cm

h = height of cone = 8 cm

V = volume of cone = (1/3)πr²h.

V = (1/3)π*3²*8.

V = 24π

So, the volume of the conical paper cup will be option (D) 24π

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The exact values of all angles in the interval [0, 360°) that satisfy the given equations are:

data = 45°, 135°, 315°.

To solve the given trigonometric equations, we will consider each equation separately.

tan²(data) - 1 = 0:

First, let's rewrite tan²(data) as (sin(data)/cos(data))²:

(sin(data)/cos(data))² - 1 = 0

Now, we can factor the equation:

(sin²(data) - cos²(data)) / cos²(data) = 0

Using the Pythagorean identity sin²(data) + cos²(data) = 1, we can substitute sin²(data) with 1 - cos²(data):

((1 - cos²(data)) - cos²(data)) / cos²(data) = 0

Simplifying further:

1 - 2cos²(data) = 0

Rearranging the equation:

2cos²(data) - 1 = 0

Now, we solve for cos(data):

cos²(data) = 1/2

cos(data) = ± √(1/2)

cos(data) = ± 1/√2

cos(data) = ± 1/√2 * √2/√2

cos(data) = ± √2/2

From the unit circle, we know that cos(data) = √2/2 corresponds to angles 45° and 315° in the interval [0, 360°). Therefore, the solutions for data are:

data = 45° and data = 315°.

cos(data)sin(data) = 1:

Since cos(data) ≠ 0 (otherwise the equation wouldn't hold), we can divide both sides by cos(data):

sin(data) = 1/cos(data)

sin(data) = 1/√2

From the unit circle, we know that sin(data) = 1/√2 corresponds to angles 45° and 135° in the interval [0, 360°). Therefore, the solutions for data are:

data = 45° and data = 135°.

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The exact value for the tangent of 240° is -0.422618261740699.  The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side of a right triangle. In order to calculate the tangent of 240°, first, find the ratio of the length of the opposite side to the length of the adjacent side. Then, use a calculator to convert the ratio into a decimal. To do this, simply divide the length of the opposite side by the length of the adjacent side. The decimal that is produced is the exact value for the tangent of 240°. In this case, the value is -0.422618261740699.

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Given the shown Venn diagram

We will find (A∩ B)'

The answer will be all the elements that are not in both A and B

So, the answer will be option A

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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The inequality to find the possible numbers of tickets Noah can purchase is 6 + 2x ≤ 30

6 + 2x ≤ 30

2x ≤ 30 - 6

2x ≤ 24

x ≤ 24/2

x ≤ 12

The possible number of ride tickets Noah can purchase is x ≤ 12

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Answer:

48

Step-by-step explanation:

I do not have one sorry!

The value of the missing length in the triangle is b. 100

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

The triangle

The height is calculated using the Pythagoras theorem as

h²= 60² - 36²

So, we have

h²= 2304

Evaluate

h = 48

Next, we have

(x -36) * 36 = 48 * 48

When evaluated, we have

x -36 = 64

So, we have

x = 64 + 36

Evaluate

x = 100

Hence, the value of x is 100

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The values of all sub-parts have been obtained.

(1). The option B is correct answer which is 65.

(2). The option A is correct answer which is $1315.

What is EOQ model?

Economic order quantity (EOQ) refers to the optimal number of units that a business should buy to satisfy demand while reducing inventory costs including holding costs, shortage costs, and order costs.

(1). Evaluate the safety stock:

As given,

Demand during lead time = 90 units, and standard deviation = 40 units.

Service level = 95%, and its value is 1.64.

Safety stock = Service level × standard deviation

                     = 1.64 × 40

                     = 65.

Hence, the option B is correct.

(2). Evaluate the Annual carrying cost:

As given,

Co = $120, Cc = $15, Cs = $40, and demand (D) = 5000 units.

φopt = √ [(2CoD/Cc) {(Cs + Cc) /Cs}]

Substitute values,

φopt = √ [(2*120*5000/15) {(40 + 15) /40}]

φopt = 331.66

φopt ≈ 332 units.

Now,

Sopt = φopt {Cc/(Cc + Cs)}

Substitute values,

Sopt = 332 {15/(15 + 40)}

Sopt = 90.5454

Sopt ≈ 91 units.

Now calculate Annual carrying cost,

Annual carrying cost = (Cc/2φopt)*(φopt - Sopt)²

Substitute values,

Annual carrying cost = [15/(2 × 332)]*[332 - 91]²

Annual carrying cost = (15/664)*(241)²

Annual carrying cost ≈ 1315 units.

Hence, the Annual carrying cost is $1315.

Hence, the values of all sub-parts have been obtained.

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The dimensions of the box that maximize the volume are x = √700 and h = 100 / √700.

To find the largest possible volume of the box, we need to optimize the dimensions of the box. Let's denote the length of each side of the square base as x and the height of the box as h.

The surface area of the box consists of the area of the square base (x^2) and the four sides of the box (4xh). Since the box has an open top, we do not consider the top surface. The total surface area is given as 2100 square centimeters, so we have:

x^2 + 4xh = 2100

To maximize the volume, we need to express the volume of the box (V) in terms of a single variable. The volume of a rectangular prism is given by V = x^2h.

We can rewrite the equation for the surface area to solve for h:

h = (2100 - x^2) / (4x)

Now we can substitute this expression for h in the volume equation:

V = x^2 * [(2100 - x^2) / (4x)]

Simplifying, we have:

V = (1/4) * (2100x - x^3)

To find the maximum volume, we need to find the critical points of this function. We take the derivative of V with respect to x and set it equal to zero:

dV/dx = 2100/4 - (3/4)x^2 = 0

Solving this equation, we find:

2100/4 = (3/4)x^2

x^2 = 700

x = √700

Substituting this value back into the equation for h, we find:

h = (2100 - 700) / (4 * √700) = 1400 / (4 * √700) = 100 / √700

Therefore, the largest possible volume of the box is:

V = (1/4) * (2100 * √700 - 700 * √700) = 350√700 cubic centimeters.

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Answer:

Step-by-step explanation:

We know that:

Work:

        6D + 4C = 76

        7(6D + 4C = 76)

        42D + 28C = 532

Now, let's substitute the value of D into the first equation.

Hence, the cost of 1 dozen doughnut is $6 and the cost of a dozen croissant is $10.

Hoped this helped.

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