Which is the graph of the function f(x) = -√x

The expected number of hours she will need to work to earn $90 is 8 hours.

a) To earn $90, the driver needs to make $15 deliveries (since $6/delivery * 15 deliveries = $90). The time it takes to make 15 deliveries follows a Poisson distribution with a mean of 1.875 deliveries per hour * t hours = 1.875t deliveries. Therefore, we can set up the following equation to solve for t:

$15 = 1.875t

t = $15/1.875 = 8

So the expected number of hours she will need to work to earn $90 is 8 hours.

b) We are given that the proportion of orders to a Fast Food restaurant follows a Beta distribution with parameters α = 2 and β = 3. We want to find the probability that tomorrow the proportion of orders to a Fast Food restaurant is less than 30%, or equivalently, the probability that the proportion is less than 0.3. Using the Beta distribution, we can calculate this probability as follows:

P(proportion < 0.3) = P(Beta(2,3) < 0.3) ≈ 0.1464

c) To earn $60, the driver needs to make $10 deliveries (since $6/delivery * 10 deliveries = $60). The time it takes to make 10 deliveries follows a Poisson distribution with a mean of 1.875t deliveries. Therefore, we can use the Poisson distribution to calculate the probability that it takes more than 10/1.875 = 5.33 hours to make 10 deliveries:

P(time > 5.33) = 1 - P(time ≤ 5.33)

= 1 - P(X ≤ 10)

= 1 - Poisson(1.875*5.33, 10)

≈ 0.0813

So the probability that the driver will need to work more than 4 hours to earn $60 dollars is approximately 0.0813.

d) The time between deliveries follows an exponential distribution with a mean of 1/1.875 hours = 32 minutes. Therefore, the time until the first delivery of the day follows an exponential distribution with the same mean. The probability that the time until the first delivery is less than 35 minutes is:

P(time < 35) = 1 - e^(-35/32)

≈ 0.6233

So the probability that it will take less than 35 minutes for the first delivery of the day to occur is approximately 0.6233.

e) The time it takes to complete 4 deliveries follows a Gamma distribution with parameters α = 4 (since we want to complete 4 deliveries) and β = 1/1.875 (since the time between deliveries follows an exponential distribution with mean 1/1.875).

The variance of a Gamma distribution with parameters α and β is α/β^2, so the standard deviation of the time to complete 4 deliveries is:

SD = sqrt(4/(1/1.875)^2) ≈ 6.34 minutes

Therefore, the standard deviation of the number of minutes it takes to complete 4 deliveries is approximately 6.34 minutes.

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Answer:

Step-by-step explanation:

1. T

2. F

3. F

4. T

5. F

6. T

Answer:

15 students

Step-by-step explanation:

495/33 = 15

Answer:

Just getting points

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The distance of the student from the foot of the tower is 25.63m the nearest 1/2 is 25.5m.

Given that From the top of a tower 14m high

The angle of depression of a student is 32°

we can use trigonometry to find the distance from the foot of the tower to the student:

tan(32°) = opposite/adjacent = 14/distance

Rearranging this equation gives:

distance = 14/tan(32°)

= 25.63m

Therefore, the distance of the student from the foot of the tower is approximately 25.63m nearest 1/2, this is 25.5m.

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Answer:

(5, -1)

Step-by-step explanation:

Answer:

Jo started decelerating at the 10th minute

His average speed for the last 30 minutes of the journey is 4/30 km/minute

Step-by-step explanation:

To get what Jo did at 10 minute, we look at the graph.

At the 10th minute, we can see that we have a sharp turn from the top to the zero position at the 20th minute

so we can say that Jo started deceleration at the 10th minute

For the last 30 minutes of the journey, he travelled a distance of 4km

So, mathematically, his average speed will be;

Distance/ time = 4km/30 minutes = 4/30 km/minute

The slope of a straight portion of the given distance time graph gives Jo's

speed in the region where the slope is calculated.

Reasons:

(a) From the distance time graph which gives the distance from the starting point, we have;

At minute 5, Jo's distance from the starting point is 0.5 km.

At minute 10, Jo's distance from the starting point is 1 km.

At minute 15, Jo's distance from the starting point is 0.5 km.

Therefore;

Jo turned round and started a journey back to his starting point at minute 10

(b) Jo's speed in the last 30 minutes of the journey is given by the ratio of

the rise and run of the graph as follows;

60 minutes = 1 hour

30 minutes = 0.5 hour

\(Speed = \dfrac{4 \, km - 0 \, km}{60 \, min - 30 \, min} = \dfrac{4 \, km - 0 \, km}{1 \, hr - 0.5 \, hr} = \dfrac{4 \, km}{0.5 \, hr} = 8 \, km/hr\)

Jo's speed the last 30 minutes of the journey = 8 km/hr.

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Answer:

3.2 units

Step-by-step explanation:

Use the law of sines

z/sin 76 = 2.6/sin 51

z = 2.6 sin 76/sin 51 = 3.2

A. Using the distance formula, we can state that the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.

B. The diagonals are equal, AC = BD = √50 units.

C. Based on the slopes of each side, there are 4 right angles on the rectangle.

The distance formula is used to find the distance that exist between tow points that are on a coordinate plane. The formula is: d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

What is the Slope of a Line?

Slope = change in y / change in x.

A. The coordinates of each of the vertices of the rectangle are:

A(1, 2)

B(7, 4)

C(8, 1)

D(2, -1)

Use the distance formula to find AB, CD, BC, and AD.

AB = √[(7−1)² + (4−2)²]

AB = √40

CD = √[(2−8)² + (−1−1)²]

CD = √40

BC = √[(8−7)² + (1−4)²]

BC = √10

AD = √[(2−1)² + (−1−2)²]

AD = √10

Therefore, the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.

B. The diagonals are AC and BD. Find their lengths using the distance formula:

AC = √(8−1)² + (1−2)²]

AC = √50 units

BD = √[(2−7)² + (−1−4)²]

BD = √50 units

Therefore, the diagonals are equal, AC = BD = √50 units.

C. Find the slope of AB, CD, BC, and AD:

Slope of AB = change in y / change in x = rise/run = 2/6 = 1/3

Slope of CD = 2/6 = 1/3

Slope of BC = -3/1 = -3

Slope of AD = -3/1 = -3

-3 is the negative reciprocal to 1/3, this means that, if the two lines that meet at a corner have these two slope, then they will form a right angle because they are perpendicular to each other.

Therefore, there are 4 right angles on the rectangle.

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Answer:

b42rtgv13rgknv1w3nf123ofho2decqwck sorry

Step-by-step explanation:

The matrix I - A(A^T) is the projection matrix that projects vectors onto the orthogonal complement of the range of matrix A, effectively removing any components lying within the range of A.

To prove this, let's consider a vector x in the column space (range) of matrix A. Then there exists a vector y such that Ax = Ay. The projection matrix onto the orthogonal complement of the range of A, denoted Pᵤ, is defined as Pᵤ = I - A(A^T).

Now, let's apply the projection matrix Pᵤ to vector x. We have Pᵤx = (I - A(A^T))x. Using matrix multiplication, this simplifies to Pᵤx = x - A(A^T)x.

Since Ax = Ay, we can substitute Ay for Ax in the equation above, resulting in Pᵤx = x - Ay. Rearranging, we have Pᵤx = x - Ax, which is the definition of the orthogonal complement.

Therefore, Pᵤx is equal to the projection of vector x onto the orthogonal complement of the range of A, proving that I - A(A^T) is the projection matrix onto the orthogonal complement of range A.

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Answer:-12x

Step-by-step explanation:

just trust me on this

Answer:

12 untis

Step-by-step explanation:

12 units becaause on a graph you count from -9,6 to 3,6 which is 12 units.

The critical values occur at x = -8, -10, and -146/13.

To find the critical values of f(x), we need to first take the derivative and find where it is equal to zero or undefined. Using the product rule and simplifying, we get:

f'(x) = 7(x + 8)^6 (x + 10)^6 + 6(x + 8)^7 (x + 10)^5

Next, we set this expression equal to zero and solve for x:

0 = 7(x + 8)^6 (x + 10)^6 + 6(x + 8)^7 (x + 10)^5

0 = (x + 8)^6 (x + 10)^5 [7(x + 10) + 6(x + 8)]

0 = (x + 8)^6 (x + 10)^5 (13x + 146)

Therefore, the critical values occur at x = -8, -10, and -146/13.

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Answer:

I think it's the 3rd one 61 hope this helps

Answer:

(7,12)

Step-by-step explanation:

We are add 1 to the x value each time and 3 to the y value

1st: (3,0)

2nd: (4,3)

3rd: (5,6)

4th: (6,9)

5th: (7,12)

Answer:

19

Step-by-step explanation:

A' represents everything out A

B' represents everything out B

C' represents everything out C

So only the outside is left hope this helps

Student A has the highest shares for both Day 3 and Day 10. Student B has the lowest shares for both Day 3 and Day 10. This is because the growth rate of the function of student A is the highest (1.4 > 1.3 > 1.2)

4. The functions for each student to predict how many shares each student's post will be received on Day 3 and then on Day 10 are: For Student A: f(x) = 100(1.4)^x

On Day 3, the function for student A can be written as f(3) = 100(1.4)^3 = 274 shares. On Day 10, the function for student A can be written as f(10) = 100(1.4)^10 = 2,745 shares.

On Day 3, the function for student B can be written as f(3) = 100(1.2)^3 = 172 shares. On Day 10, the function for student B can be written as f(10) = 100(1.2)^10 = 619 shares.

The function for student C is:f(x) = 200(1.3)^xOn Day 3, the function for student C can be written as f(3) = 200(1.3)^3 = 878 shares. On Day 10, the function for student C can be written as f(10) = 200(1.3)^10 = 19,202 shares.

Student A has the highest shares for both Day 3 and Day 10. Student B has the lowest shares for both Day 3 and Day 10. This is because the growth rate of the function of student A is the highest (1.4 > 1.3 > 1.2), while the growth rate of the function of student B is the lowest.5. The new function representing Amber's photo shares is:f(x) = 3(4)x + 45

This function represents the photo shares of Amber after she decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility. The new function is an upward shift of the original function by 45 units.

The new function representing Amber's photo shares has a y-intercept of 45, which means that Amber's photo will be shared by 45 people even if she does not share her photo with anyone.6. The student whose post travels the fastest is student A.

This is because the growth rate of student A's function is the highest, which means that the rate at which shares increase is the fastest. The function for student A is f(x) = 100(1.4)x

The growth rate of the function for student A is 1.4, which is greater than the growth rate of the functions for students B and C.7. If I had to choose, I would prefer a post with fewer friends initially but more shares, like Amber. This is because the value of the function f(x) = 3(4)x + 45 is greater than the value of the function for students B and C.

Although student A has the highest shares, the initial number of friends is lower compared to Amber.

On Day 3, the function representing Amber's photo shares can be written as f(3) = 3(4)3 + 45 = 57 shares. On Day 10, the function representing Amber's photo shares can be written as f(10) = 3(4)10 + 45 = 333 shares.

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Answer:

Option 4,  8 1/3

Step-by-step explanation:

-2.5 * - 3 1/3 = 8.3 repeating

8.3 repeating = 75/9

75/9 = 8 1/3

if \($a \neq b$\),\($f(n)$\)and \($g(n)$\) will not have the same growth rate. It is not true that \($\forall a, b \in \mathbb{N}, f(n) = a^n, g(n) = b^n$ implies $f \in \Theta(g)$\).

To determine whether $f(n) = a^n$ and $g(n) = b^n$ satisfy $f \in \Theta(g)$, we need to evaluate their growth rates and see if there exist constants $c_1$, $c_2$, and $n_0$ such that $c_1 \cdot g(n) \leq f(n) \leq c_2 \cdot g(n)$ for all $n \geq n_0$.

Let's analyze the growth rates of $f(n)$ and $g(n)$ separately:

1. $f(n) = a^n$:

  - When $a > 1$, $f(n)$ grows exponentially with $n$. For example, if $a = 2$, $f(n)$ doubles with each increment of $n$.

  - When $a = 1$, $f(n)$ is constant and does not grow with $n$.

  - When $0 < a < 1$, $f(n)$ converges to 0 as $n$ increases. For example, if $a = 0.5$, $f(n)$ halves with each increment of $n$.

2. $g(n) = b^n$:

  - When $b > 1$, $g(n)$ also grows exponentially with $n$.

  - When $b = 1$, $g(n)$ is constant.

  - When $0 < b < 1$, $g(n)$ converges to 0 as $n$ increases.

In general, if $a \neq b$, $f(n)$ and $g(n)$ will not have the same growth rate. Therefore, we cannot conclude that $f \in \Theta(g)$ for arbitrary $a$ and $b$.

Thus, it is not true that $\forall a, b \in \mathbb{N}, f(n) = a^n, g(n) = b^n$ implies $f \in \Theta(g)$.

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The equation r-6=0 is given in the cylindrical coordinates. The shape of this equation is not a sphere; it is a cylindrical shell. This equation is a cylindrical shell rather than a sphere.

Therefore, the given statement, "The shape of this equation is a sphere" is FALSE.

Cylindrical coordinates (r, θ, z) are a coordinate system that defines a point in three-dimensional space. It is similar to the polar coordinate system, except that the z-axis is added, resulting in the use of a cylindrical surface to specify the point location.

Let's find the solution.The cylindrical coordinate system is a three-dimensional coordinate system that is defined by the distance from a point in the xy-plane to a fixed point known as the origin, the angle that the point makes with the x-axis, and the vertical height of the point from the xy-plane, which is referred to as the z-coordinate of the point.

When defining a point in three-dimensional space, cylindrical coordinates are commonly used.

A sphere is a three-dimensional object with a curved surface that is equidistant from a single point in space. A spherical coordinate system is often used to specify the position of a point on a sphere. A cylindrical coordinate system, on the other hand, is commonly used to specify the position of a point on a cylindrical shell.

The equation

r - 6 = 0

is given in cylindrical coordinates. This equation is a cylindrical shell rather than a sphere.

Therefore, the given statement, "The shape of this equation is a sphere" is FALSE.

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ANSWER (1):

The three temperatures in order from least to greatest (from the left of the number line to the right of the number line) are written as;

ANSWER (2):

The month of June had the lowest temperature

ANSWER (3):

The month of January had the highest temperature

ANSWER(4):

The month of June had the coldest of the three temperatures

The volume of the smallest container that holds 370 grams of oil is

400 cm³.

Density is mass per unit volume.

We have,

The density of sunflower oil = 0.925

Mass of sunflower oil = 370 grams

Now,

Density = Mass / Volume

So,

The volume of the smallest container that holds 379 grams of oil.

= Mass of the sunflower oil / Density of the sunflower oil

= 370 / 0.925

= 400 cm³

Thus,

The volume of the container that holds 379 grams of oil is 400 cm³.

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The information that is needed to write the equation of a line in point-slope form is the location of one ordered pair that lies on the line and the line's slope. The correct option is the first option

From the question, we are to determine the information that is needed to write the equation of a line in point-slope form.

The point-slope form of a line is given as

y - y₁ = m(x - x₁)

Where, (x₁, y₁) is a point on the line

and m is the slope of the line

Thus, in order to write the equation of a line in the point-slope form, the information that are needed are:

1. An ordered pair on the line

2. The slope of the line

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Answer:

BOC, since angle B and angle C are bisected, sum of angle OBC and OCB will be half of sum of angles B and C which is 108 degrees.

Therefore, there are three different combinations of cars washed and bikes sold that result in savings of $1200: washing 20 cars and selling 73 bikes, washing 30 cars and selling 70 bikes, or washing 10 cars and selling 77 bikes.

To solve this problem, we need to use algebraic equations to find the values of x and y that satisfy the given equation. We can start by rearranging the equation to solve for one of the variables:
5x + 15y = 1200
Divide both sides by 5:
x + 3y = 240
Now we can use this equation to find the values of x and y that add up to 240 and result in savings of $1200. We can use trial and error to come up with different combinations:
Combination 1:
- Washed 20 cars (x = 20)
- Sold 73 bikes (y = 73)
- 20 + 3(73) = 239 (rounded down)
- Savings = 20($60) + 73($10) = $1,800 + $730 = $2,530
Combination 2:
- Washed 30 cars (x = 30)
- Sold 70 bikes (y = 70)
- 30 + 3(70) = 240
- Savings = 30($60) + 70($10) = $1,800 + $700 = $2,500
Combination 3:
- Washed 10 cars (x = 10)
- Sold 77 bikes (y = 77)
- 10 + 3(77) = 241 (rounded up)
- Savings = 10($60) + 77($10) = $600 + $770 = $1,370
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The height of the trapezoid whose area is 204 cm² is calculated as:

h = 12 cm

Recall the area of a trapezoid, which is expressed as:

Area = 1/2 * (sum of parallel bases) * height of trapezoid.

Given the following:

Area (A) = 204 cm²

Perimeter (P) = 62 cm

h = ?

One of the bases is given as 10 cm. The length of the other base would be calculated as follows:

62 - (10 + 13 + 15) = 24 cm

Sum of the bases = 24 + 10 = 34 cm.

204 = 17 * h

204/17 = h

h = 12 cm

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