Given that f(x) = x2 +3x – 40 and g(x) = x +5, find (f +g)(x) and express

Answer:

Check the steps shown in the picture : Hope it helps.

The probability that their pizza will be a thin crust and have ham or bacon on it is 0.25, or 25%.

It is a number between 0 and 1, where 0 denotes the impossibility of the event and 1 denotes its certainty.

Part A: The sample space for their pizza, with one of the two crust options and one of their four favorite toppings, can be organized as follows:

Thin crust with ham

Thin crust with bacon

Thin crust with pepperoni

Thin crust with mushroom

Deep dish with ham

Deep dish with bacon

Deep dish with pepperoni

Deep dish with mushroom

Part B: There are two options for the crust, and two options for the toppings that Pattie likes. So there are a total of 2 x 2 = 4 possible pizzas that Pattie would like.

Therefore, the probability that their pizza will be a thin crust and have ham or bacon on it is 2/8 = 1/4 = 0.25, or 25%.

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It will take 382 months for the remaining material to fall below half of its original 115 quantity.

We must solve the equation where m is equal to 115/2 (half of the starting amount) to determine the number of months it will take for the remaining material to fall below half of its starting amount of 115.

Subsequently, we made the condition:

We ought to settle it one small step at a time: 115/2 = 115 - 10log(t-1).

Divide the situation's two sides by 115: Since (115 - 10log(t-1)) / 115 1/2 is the same as (115 - 115/2) / 115, subtract 1 from each side of the equation: 115/2 = 115 - 10log(t-1).

1/2 - 1 equals - (10log(t-1)/115) 1/2 - 1 equals - (10log(t-1)/115)

1 = (10log(t-1)/115) Divide by 115 on both sides:

115 = 10log(t-1)

Section the various sides by 10:

115/10 = log(t-1) Ascertain the different sides' antilogarithm utilizing base 10:

On each side of the equation, add one: 10(115/10) is equal to t minus 1 t minus 1 = 10.

The value is: t = 10(115/10) + 1.

As a result, it will take 382 months for the remaining material to fall below half of its original 115 quantity.

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Sorry I couldn't really do the equation, but I found this! Hope this helps! Have a nice day. Also I can send you the link, but only if you want.

Answer:

2\(\sqrt{17}\)

Step-by-step explanation:

Use the distance formula to determine the distance between the two points.

Distance = \(\sqrt{(7-(-1))^{2} + (4-2)^{2} }\)

Simplify, and you will get the answer

2\(\sqrt{17}\)

Answer:

-18

Step-by-step explanation:

-8 + 70/-7

-8 - 10

-18

Answer:

21

Step-by-step explanation:

a= μ-3.16*σ , b= μ+3.16*σ if each fish caught is equally likely to be any one of these 4 distinct types.

Chebyshev's inequality is a probability theory that ensures that, over a vast range of probability distributions, no more than a particular proportion of values would be present within a selected limits or range as from mean. In other words, only a certain fish caught will be discovered within a given range of the distribution's mean.

The formula for which no more than a particular number of values can exceed is 1/K2; in other words, 1/K2 of a distribution's values can be more than or equal to K standard deviations away from the distribution's mean. Furthermore, it asserts that 1-(1/K2) of a distribution's values must be within, but not include, K standard deviations of the distribution's mean.

How to solve?

from Chebyshev's inequality for Y

P(| Y - μ|≤ k*σ ) ≥ 1-1/k²

where

Y =  the number of fish that need be caught to obtain at least one of each type

μ = expected value of Y

σ = standard deviation of Y

P(| Y - μ|≤ k*σ ) = probability that Y is within k standard deviations from the mean

k= parameter

thus for

P(| Y - μ|≤ k*σ ) ≥ 1-1/k²

P{a≤Y≤b} ≥ 0.90 →  1-1/k² = 0.90 → k = 3.16

then

P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90

using one-sided Chebyshev inequality (Cantelli's inequality)

P(Y- μ≥ λ) ≥ 1- σ²/(σ²+λ²)

P{Y≥b} ≥ 0.90  →  1- σ²/(σ²+λ²)=  1- 1/(1+(λ/σ)²)=0.90 → 3= λ/σ → λ= 3*σ

then for

P(Y≥ μ+3*σ ) ≥ 0.90

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Answer:

295

Step-by-step explanation:

360-65=295

circle=360 degrees

Answer:

j=6

Step-by-step explanation:

2=5j-28

+28  +28

30=5j

/5    /5

j=6  

Answer:

See Explanation

Step-by-step explanation:

Let the number of cookies be x and the number of cupcakes be y.

If the total is 280, then

\(5x + 2y = 280\)

Subtract 5x from both sides

\(5x - 5x + 2y = 280 - 5x\)

\(2y = 280 - 5x\)

Make y the subject

\(y = 140 - \frac{5}{2}x\)

See attachment for graph

Any of the following equation can be plotted on the graph (they literally represent the same thing)

\(5x + 2y = 280\)

\(2y = 280 - 5x\)

\(y = 140 - \frac{5}{2}x\)

Answer:

its 200 cookies and 80 cupcakes

Step-by-step explanation:

my explanation is the kid right next to me told me the answer and the teacher said his was right

Answer:

Step-by-step explanation:

Ratio of corresponding sides are same in similar figures:

Find OP:

The approximate value of x(t), which indicates the location of coordinate the ladder's foot at time t seconds, is 6.85. 7

Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematicses, scientists, and engineers frequently employ a variety of coordinate systems.

The location in the cartesian plane will be determined by the coordinate points. A point's distance from the y axis is known as the x-coordinate, also known as the abscissa, and its distance from the x-axis is known as the y-coordinate, also known as the ordinate.

based on the information provided,

x = the distance between the wall and the bottom of the ladder

y = distance of the top of the ladder from the ground

x² + y² = 25²

x² + 7² = 25²

x² = 625 -49 = 429

y = √576

Differentiating the equation with respect to time t gives

2x dx/dt + 2y dy/dt = 0

dx/dt = -y dy/dt / x

 = -√576 * (2) / 7

= 6.85 feet per second approximately.

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Answer:

c

Step-by-step explanation:

The property justified by step 4 is after substitution in the equation you get the desired result.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the data in the question,

In step 3 substitution of value is taking place.

In step 4 when values are substituted the final result is obtained, so step 4 is the result step.

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The net outward flux across the boundary of the tetrahedron is: 5, using the concept of gradient of function.

The gradient of a function is related to a vector field and it is derived by using the vector operator ∇ to the scalar function f(x, y, z).

Given vector field:

F = ( -x, 3y, 2 z )

Δ . F = (i δ/δx + j δ/δy + k δ/δz) (-x, 3y, 2 z )

Δ . F = [δ/δx(-x)] + δ/δy (3y) + δ/δz (2z)]

Δ . F = - 1 + 3 + 2

Δ . F = 4

According to divergence theorem;

Flux =  ∫∫∫ Δ . (F) dv

x+y+z = 1; so, 1st octant

∫₀¹∫₀¹⁻ˣ∫₀¹⁻ˣ⁻y (4) dz dy dx

= 4 ∫₀¹∫₀¹⁻ˣ (1 - x - y) dy dx

= 5

Therefore, we can conclude that the net outward flux across the boundary of the tetrahedron is: 5

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Answer:

y=1.5x+12.75

Step-by-step explanation:

Answer:

19.5 in.

Step-by-step explanation:

Let the width = x.

The length is 3 more than the width, so the length is x + 3.

perimeter = 2 * length + 2 * width

perimeter = 2(x + 3) + 2x

perimeter = 72

2(x + 3) + 2x = 72

2x + 6 + 2x = 72

4x + 6 = 72

4x = 66

x = 16.5

x + 3 = 16.5 + 3 = 19.5

Answer: 19.5 in.

Answer:

i did it wrong but i dont know how to delete my answer now

Step-by-step explanation:

The linear function is y = (-1/2)x + 4.

What is a linear function?

A linear function whose graph is a straight line and which is represented by an equation of the form y = ax + b where a and b are constants, a does not equal zero, and x is any real number.

Here, we have

Given,

A linear function has an x-intercept of 8 and a y-intercept of 4.

So, The two points on the line are (8, 0) and (0, 4).

Now, slope(m) = (4 - 0)/(0 - 8).

slope(m) = -4/8.

slope(m) = -1/2.

As it has a y-intercept of 4 it is the value of b, In y = mx + b.

Hence, the linear function is y = (-1/2)x + 4.

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Each bird feeder received 1/6 pound of birdseed.

To determine the amount of birdseed in each bird feeder, we divide the total amount of birdseed (1/2 pound) by the number of bird feeders (3):

Amount of birdseed in each bird feeder By using division method = 1/2 pound ÷ 3 = 1/6 pound

Therefore, each bird feeder received 1/6 pound of birdseed. By dividing the total amount of birdseed (1/2 pound) equally among the 3 bird feeders, each feeder received 1/6 pound of birdseed. This ensures an even distribution of birdseed among all the feeders.

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the claim aligns with the null hypothesis, as both assert the absence of an effect, difference, or relationship between variables.

The claim and the null hypothesis are the same when the claim being made is that there is no significant difference or relationship between variables or that there is no effect or impact of a particular factor. In other words, the claim asserts that the null hypothesis is true.

For example, if the null hypothesis (H₀) states that there is no difference between the means of two groups, the corresponding claim would be that the means are indeed equal. Similarly, if the null hypothesis states that there is no correlation between two variables, the claim would be that there is indeed no significant correlation.

In such cases, the claim aligns with the null hypothesis, as both assert the absence of an effect, difference, or relationship between variables.

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The cartons hold 1305 blocks.

What are Comparing quantities?

- Finding an unknown quantity that has a relationship with a certain condition associated to it is the process of comparing quantities.

- One or more quantities with their units will be provided to us, and we will   be required to determine the value of the same quantity in other units (i.e.  in higher values or in lower values).

We given that,

A carton holds 87 blocks.

It means, 1 carton holds = 87 blocks

So find 15 cartons holds how much of blocks.

15 cartons holds = 15 * 87

                            = 1305 blocks

Hence, we can say that the cartons hold 1305 blocks.

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when the cake is cut into \(2\) ounce pieces instead of \(3\) pieces it yields \(180\) pieces.

How to find large cake pieces ?

Given in the question when cake cuts into piece that each weight is \(3\) ounce it yields \(120\)

So original large cake weight is

\(w=120*3\\\\w=360\)

So we can find cake pieces when cake cuts into weight \(2\) each piece

\(pieces=\frac{360}{2}\\=180\)

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The Expression for the Area a of the rectangle as a function of length L is given by A(L) = 12L - L^2 .

Let,

length, L, and the width, W, are components that help determine the area, A, and the perimeter, P of the rectangle. These are given by the following equations

 A=LW

 P=2L+2W

Given,

Perimeter of the Rectangle = 24m.

We are asked to express the perimeter of the rectangle as a function of the length, L, of one of its sides.

We will first set up the equation of the Perimeter of the rectangle. We can let the width of the rectangle be W.

P = 2L+2W

24 = 2L+2W

12 = L+W

W = 12-L

Since we want to express the Area as a function of L, we have to find the value of W in terms of L. This is so we can eliminate the width in the equation for the Area. The Area as a function of L is as follows.

A(L, W) = LW

A(L) = L(12-L)

A(L) = 12L-L^2

Therefore, the Area as a function of L is given by A(L) = 12L-L^2.

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Answer:

4

Step-by-step explanation:

To solve for x in the equation:

√(2x - 7) = 1

We can start by isolating the square root by squaring both sides of the equation:

(√(2x - 7))^2 = 1^2

2x - 7 = 1

Next, we can isolate the variable by adding 7 to both sides of the equation:

2x = 8

Finally, we can solve for x by dividing both sides by 2:

x = 4

Therefore, the solution to the equation √(2x - 7) = 1 is x = 4.

Answer:

its y = 3x + 4

Step-by-step explanation:

it is because the y intercept is 4 and the slope is 3/1

The correct option is D. Translated 3 units left and 1 unit up; vertically stretched.

To determine the correct transformation from the graph of the standard absolute value function f(x) to the graph of g(x) = 12 |x + 3| - 1, let's analyze the given options.

A. Translated 3 units right and 1 unit down; vertically stretched:

This transformation involves shifting the graph of f(x) to the right by 3 units and down by 1 unit. However, it does not mention any vertical stretching or compression.

Therefore, option A does not match the transformation required for g(x).

B. Translated 3 units left and 1 unit down; vertically compressed:

This transformation involves shifting the graph of f(x) to the left by 3 units and down by 1 unit.

Again, it does not mention any vertical stretching or compression.

Therefore, option B does not match the transformation required for g(x).

C. Translated 3 units right and 1 unit up; vertically compressed:

This transformation involves shifting the graph of f(x) to the right by 3 units and up by 1 unit. It also states that the graph is vertically compressed.

This option includes both the horizontal shift and the vertical compression, but it does not match the vertical stretch present in g(x).

Therefore, option C does not match the transformation required for g(x).

D. Translated 3 units left and 1 unit up; vertically stretched:

This transformation involves shifting the graph of f(x) to the left by 3 units and up by 1 unit. It also states that the graph is vertically stretched. This option includes both the horizontal shift and the vertical stretch, matching the transformations in g(x).

Therefore, option D matches the transformation required for g(x) = 12 |x + 3| - 1.

Thus, the correct option is D. Translated 3 units left and 1 unit up; vertically stretched.

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The bias displayed by investors who consider the $60 price a bargain relative to the recent $100 price is: b) Anchoring

Anchoring bias refers to the tendency to rely heavily on the first piece of information encountered (the anchor) when making decisions or judgments. In this case, the initial anchor is the high price of $100, and investors are using that as a reference point to evaluate the $60 price as a bargain. They are "anchored" to the previous high price and are influenced by it when assessing the current value.

Anchoring bias is a cognitive bias that affects decision-making processes by giving disproportionate weight to the initial information or reference point. Once an anchor is established, subsequent judgments or decisions are made by adjusting away from that anchor, rather than starting from scratch or considering other relevant factors independently.

In the given scenario, the initial anchor is the high price of $100 per share for Walmart. When the price falls to $60 per share, some investors consider it a bargain relative to the previous high price. They are influenced by the anchor of $100 and perceive the $60 price as a significant discount or opportunity to buy.

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