Write an equation of a line with the given slope and y-intercept.
m = -2,b=4

x=-8 All the values less than 7 are included in the number line. The graph on number line is shown in figure attached. In the options given

Answer:

Elena made 10 batches.

Step-by-step explanation:

1 batch uses 2/3 cup

Elena used 6 2/3 cup

The number of batches is the quotient of 6 2/3 and 2/3.

We need to divide 6 2/3 by 2/3. First, we convert 6 2/3 into a fraction.

6 2/3 ÷ 2/3 = 20/3 ÷ 2/3 = 20/3 × 3/2 = 10

Answer: Elena made 10 batches.

Answer:

10

Step-by-step explanation:

2/3 for 1 cup if he used 6 2/3 of sugar then its 10.

if you times 2/3 by 10 its 6.66 and 6.66 is 2/3

1/3=33

2/3=66

3/3=100

For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.

A right triangle, right-angled triangle, or more formally an orthogonal triangle—previously known as a rectangled triangle—is a triangle with one angle that is a right angle (i.e., a 90-degree angle), meaning that two of its sides are perpendicular. The foundation of trigonometry is the relationship between the sides and other angles of a right triangle.

The hypotenuse is the side that faces the right angle (side c in the figure). Legs are the sides that are next to the right angle (or catheti, singular: cathetus). Side a can be thought of as the side that is adjacent to angle B and opposite to (or opposite) angle A, whereas side b is the side that is adjacent to angle A and opposite to angle B.

Given a right triangle with base = 8 and an angle = 24°

Using angle sum property of triangle

24 + 90 + angle L = 180

L = 66°

Using Sohcahtoa

Tangent: tan(θ) = Opposite / Adjacent

tan(24°) = LK/8

0.445 = LK/8

LH = 8 × 0.445

LK = 3.56

LM = \(\sqrt{MK^2 + LK^2}\)

LM = \(\sqrt{8^2 + 3.56^2}\)

LM = 8.75

Thus, For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.

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Answer: $258.40

Step-by-step explanation:

The formula to calculate the simple interest will be:.

= Principal × Rate × Time

where,

Principal = $3400

Rate = 1.9%

Time = 4

Interest = $3400 × 1.9% × 4

= $3400 × 0.019 × 4

= $258.40

Anna has $540 to spend at the bicycle shop → this means that she can spend the $540 or less, you can symbolize this as ≤ $540

Her costs include:

• A bicycle for ,$402.87

• 3 bicycle reflectors for $10.97/each, the total will be 3*10.97=,$32.91

• A pair of bike gloves for ,$14.42

• With the remaining money, she wants to buy as many biking outfits as possible. Let "o" represent the number of outfits she can buy, considering each one costs $44.90, then the total cost for the outfits can be symbolized as ,$44.90o

The calculation for her total expenses is the sum of everything she buys:

"Bicycle"+"Reflectors"+"Gloves"+"Outfits"≤$540

Using the costs listed above the expression is

Simplify the like terms, i.e. add the alone numbers together

Answer:

3.14

Step-by-step explanation:

110/35=3.14

Answer:

$11

Step-by-step explanation:

44 x 0.25 = 11

The Lotka integral equation and the McKendrick-von Foerster model are distinct mathematical models for studying population dynamics.

The Lotka integral equation describes the growth of a single-species population and incorporates an integral term to represent the accumulated growth.

The McKendrick-von Foerster model focuses on age-structured populations and does not explicitly contain an integral term but can incorporate it for age-dependent processes.

The Lotka integral equation and the McKendrick-von Foerster model are both mathematical models used in population dynamics. While they share similarities, they are based on different assumptions and have distinct characteristics. In this explanation, we will explore the relationship between these two models and highlight their similarities and differences.

The Lotka integral equation considers a single-species population and assumes exponential growth with a declining growth rate as resources become limited. It explicitly incorporates an integral term, representing accumulated growth over time.

On the other hand, the McKendrick-von Foerster model focuses on age-structured populations, considering the transitions between different age classes. While it does not explicitly contain an integral term, it can accommodate integral components if age-dependent processes are included.

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The size for a TV is determined as the diagonal length of the Television.

The Televisions that we see in our daily life are mostly of the rectangular shape.

A rectangular shape is a shape that has 4 sides in it, the opposite sides of the rectangular are parallel and equal. Two pairs of equal sides are formed in this type of shape.

If we connect the vertices that are directly opposite to each other than it is known as the diagonal of the rectangle . Often we see that the TV is of 32'' or 64''. This only means that the diagonal length of the TV is 32'' or 64''. This is how we measure the size of the TV.

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Answer:

its B

Step-by-step explanation:

The graph of exponential function, is described below.

What is an exponential function?

The mathematical formula f(x) = e^x stands for the exponential function. The term, unless specifically stated otherwise, generally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.

The formula for an exponential growth function is y = ab^x, where a > 0 and b > 1. As can be seen in the example of f(x) = 2x below, the graph will ascend. The numbers get smaller as x gets closer to negative infinity, as you can see.

If b > 1 , then the graph's slope is positive and exponential growth is depicted. The value of y approaches infinity as x rises. The value of y approaches zero as x falls.

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Answer:

4 tickets

Step-by-step explanation:

3.25 x 4 = 13

She can afford 4 tickets and have 1.75 $ left over.

hopefully this helps you :)

pls mark brainlest ;)

To find the probability that 5 randomly selected American pet owners will have a photograph of their pet in their wallet, we can use the binomial probability formula.

The binomial probability formula is given by:

\(P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)\)

Where:

P(X = k) is the probability of exactly k successes,

n is the number of trials,

k is the number of successful outcomes,

p is the probability of success on a single trial.

In this case:

n = 5 (5 randomly selected pet owners)

k = 5 (the number of pet owners with a photograph of their pet)

p = 0.43 (the probability of a pet owner having a photograph)

Using the formula:

\(P(X = 5) = C(5, 5) * 0.43^5 * (1 - 0.43)^(5 - 5)\)

C(5, 5) = 1 (since there is only one way to choose 5 out of 5)

\(P(X = 5) = 1 * 0.43^5 * (1 - 0.43)^(5 - 5)\)

\(P(X = 5) = 0.43^5 * 0.57^0\)

\(P(X = 5) = 0.43^5\)

Calculating this value:

P(X = 5) ≈ 0.0434

Therefore, the probability that 5 randomly selected American pet owners will have a photograph of their pet in their wallet is approximately 0.0434, rounded to 3 decimal places.

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Answer:

830

Step-by-step explanation:

Just divide the number by 7

Answer:

Y = 2

Step-by-step explanation:

Use the formula below to find the slope. Plug 0 in for X to find the y intercept. In this case there is no slope. Make sure next time to use commas , instead of periods . when writing coordinates.

Answer:

i dont know

good luck

Step-by-step explanation:

Answer:

7.5

Step-by-step explanation:

triangle ABC and XBY are similar so the sides are in proportion

BX /BY = BA /BC

4/6 = 5/BC; cross multiply

4*BC = 5*6 ; divide both sides by 4

BC= 5*6/ 4 = 30 /4 = 7.5

Ans:- To determine the percentage of toy sales that were helicopters, we needed to determine the total number of toys sold and then calculate the proportion of that totally made up by helicopters.

step-1

Answer:

Step-by-step explanation:

\(m\angle BHD=180^o-x^o\)

\(m\angle DBH+m\angle BHD+m\angle HDB=180^o\\\\47^o+180^o-x^o+31^o=180^o\\\\78^o-x^o=0\\\\x^o=78^o\)

Answer:

-0.03

Step-by-step explanation:

\(3^{-3}=\frac{1}{3^3}\\=-\frac{1}{3^3}\\3^3=27\\=-\frac{1}{27}\\= -0.03\)

Step-by-step explanation:

For a+b, it's a−b. A conjugate is a binomial where the second term is the opposite of the second term of another binomial. In other words, if I have the expression a+b, the conjugate of my expression is a−b. If I were to add the second terms of these two expressions, I would get 0.

the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

To write the system of ordinary differential equations (ODEs) for the transition probabilities Pᵢⱼ(t) of the given continuous-time Markov chain, we need to consider the rate at which the system transitions between different states.

Let Pᵢⱼ(t) represent the probability that the Markov chain is in state j at time t, given that it started in state i at time 0.

The ODEs for the transition probabilities can be written as follows:

dP₁₂(t)/dt = q₁₂ * P₁(t) - q₂₁ * P₂(t)

dP₁₃(t)/dt = q₁₃ * P₁(t) - q₃₁ * P₃(t)

dP₂₁(t)/dt = q₂₁ * P₂(t) - q₁₂ * P₁(t)

dP₂₃(t)/dt = q₂₃ * P₂(t) - q₃₂ * P₃(t)

dP₃₁(t)/dt = q₃₁ * P₃(t) - q₁₃ * P₁(t)

dP₃₂(t)/dt = q₃₂ * P₃(t) - q₂₃ * P₂(t)

where P₁(t), P₂(t), and P₃(t) represent the probabilities of being in states 1, 2, and 3 at time t, respectively.

Now, let's consider the second part of the question: Suppose that the initial state is 1. We want to find the probability that after the first transition, the process X(t) enters state 2.

To calculate this probability, we need to find the transition rate from state 1 to state 2 (q₁₂) and normalize it by the total rate of leaving state 1.

The total rate of leaving state 1 can be calculated as the sum of the rates to transition from state 1 to other states:

total_rate = q₁₂ + q₁₃

Therefore, the probability of transitioning from state 1 to state 2 after the first transition can be calculated as:

P(X(t) enters state 2 after the first transition | X(0) = 1) = q₁₂ / total_rate

In this case, the transition rate q₁₂ is 1, and the total rate q₁₂ + q₁₃ is 1 + 2 = 3.

Therefore, the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

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The quantity that is present after 2000 years will be A. 7.851 grams.

From the information given, initially at t = 0, the quantity is 10 grams.

After 2000 years, the appropriate quantity will be:

Q(2000) = 10 (1/2) × (2000/5730)

Q(2000) = 7.851 grams.

In conclusion, the correct option is A.

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Less than 2 units separate the median from the lower quartile for customers making purchases.

The three values known as quartiles divide sorted data into four equal-sized portions, each with an equal number of observations. An example of a quantile is a quantile. First quartile: Also referred to as the lower quartile or Q1. The median or second quartile is also referred to as Q2. Third quartile: Also referred to as the higher quartile or Q3.

Half of the difference between the upper and lower quartiles can be used to define the quartile deviation analytically. Here, the upper quartile (Q3) and lower quartile (Q1) can be used to depict quartile deviation as the letters QD. The term "quartile deviation" is sometimes used to refer to the semi-interquartile range.

The coefficient of quartile deviation serves as a gauge for a collection of data's variability or spread. It is determined by taking the square root of the difference between the upper and lower quartiles, squaring the result, and dividing it by two. Comparing data sets is simple because it is expressed as a percentage.

Therefore, the correct answer is option E. The difference between the median and the lower quartile for the customers making a purchase is less than 2.

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Answer:

distance is 2 units

Step-by-step explanation:

9-7=2

a)  The x-intercepts of the graph of f(x) are x = 2.5 and x = -1.

b) The coordinates of the vertex are (0.75, -5.125).

c) By using the x-intercepts and vertex obtained in Parts A and B, we can accurately depict the shape and positioning of the parabolic graph of f(x).

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

Setting f(x) = 0:

\(2x^2 - 3x - 5 = 0\)

To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring is not straightforward, so let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = -3, and c = -5. Substituting these values into the quadratic formula:

x = (-(-3) ± √((-3)^2 - 4(2)(-5))) / (2(2))

x = (3 ± √(9 + 40)) / 4

x = (3 ± √49) / 4

x = (3 ± 7) / 4

This gives us two possible solutions:

x1 = (3 + 7) / 4 = 10/4 = 2.5

x2 = (3 - 7) / 4 = -4/4 = -1

Therefore, the x-intercepts of the graph of f(x) are x = 2.5 and x = -1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or minimum, we need to consider the coefficient of the x^2 term in the function f(x). In this case, the coefficient is positive (2), which means the parabola opens upward and the vertex represents a minimum point.

To find the coordinates of the vertex, we can use the formula x = -b / (2a). In our equation, a = 2 and b = -3:

x = -(-3) / (2(2))

x = 3 / 4

x = 0.75

To find the corresponding y-coordinate, we substitute x = 0.75 into the function f(x):

f(0.75) = 2(0.75)^2 - 3(0.75) - 5

f(0.75) = 2(0.5625) - 2.25 - 5

f(0.75) = 1.125 - 2.25 - 5

f(0.75) = -5.125

Therefore, the coordinates of the vertex are (0.75, -5.125).

Part C: To graph the function f(x), we can follow these steps:

Plot the x-intercepts obtained in Part A: (2.5, 0) and (-1, 0).

Plot the vertex obtained in Part B: (0.75, -5.125).

Determine if the parabola opens upward (as determined in Part B) and draw a smooth curve passing through the points.

Extend the curve to the left and right of the vertex, ensuring symmetry.

Label the axes and any other relevant points or features.

By using the x-intercepts and vertex obtained in Parts A and B, we can accurately depict the shape and positioning of the parabolic graph of f(x).

The x-intercepts help determine where the graph intersects the x-axis, and the vertex helps establish the lowest point (minimum) of the parabola. The resulting graph should show a U-shaped curve opening upward with the vertex at (0.75, -5.125) and the x-intercepts at (2.5, 0) and (-1, 0).

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The area of the figure is 141.5 units²

The space enclosed by the boundary of a plane figure is called its area. The area is measured in units².

The figure can be sub divided into 3 parts,

The first part is a rectangle,

Area of rectangle = l× w

= 6× 8

= 48units²

The second part is also a rectangle

The area of a rectangle = l×w

= 5 × 11

= 55 unit²

The third part is a triangle

area of a triangle = 1/2 bh

= 1/2 × 11 × 7

= 77/2 = 38.5 units²

therefore the area of the figure = 38.5 + 55+48

= 141.5 units²

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The student's final moment of inertia is 18.18 kgm².

The moment of inertia of an objecr is the property of an object which shows its ability to rotate.

Since a student is standing with her arms outstretched, on a platform that is rotating at 1.6 rev/s. She pulls her arms in and the platform now rotates at 2.2 rev/s. Her original moment of inertia (I0) is 25 kgm². To find the r final moment of inertia, we use the law of conservation of angular momentum.

The law of conservation of angular momentum states that for any rotation, angular momnetum is constant.

So, Iω = constant where

So, Iω = I'ω' where

Making I' subject of the formula, we have that

I' = Iω/ω'

So, substituting the values of the variables into the equation, we have that

I' = Iω/ω'

I' = 25 kgm² × 1.6 rev/s ÷ 2.2 rev/s

= 40 kgm²rev/s ÷ 2.2 rev/s

= 18.18 kgm²

So, the final moment of inertia is 18.18 kgm².

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Answer:

The equations that have one solution are 9=3(5x–2) and 6x–(3x+8)=16

Step-by-step explanation:

To determine which equations have one solution, we will determine the solution(s) to all the equations (that is, find the value of the unknown, x).

1. 8x–3x+5=5x–2

This becomes

5x+5=5x-2

Subtract 5x from both sides

5x-5x+5 = 5x-5x-2

0+5 = 0-2

This equation has no solution

2. 9=3(5x–2)

First, open the bracket by distributing 3

∴ 9 = 15x - 6

Then, add 6 to both sides

9+6 = 15x -6 +6

15 = 15x

Divide both sides by 15

15/15 = 15x/15

1 = x

∴ x = 1

This has one solution.

3. 6x–(3x+8)=16

Open the bracket by distributing –1

6x -3x -8 = 16

3x - 8 = 16

Add 8 to both sides

3x -8 +8 = 16 + 8

3x = 24

Divide both sides by 3

3x/3 = 24/3

x = 8

This has one solution.

4. 9x+4–x=4(2x+1)

This becomes

9x -x +4 = 4(2x+1)

Then, 8x +4 = 4(2x+1)

Open the bracket by distributing 4

8x +4 = 8x +4

This is true for any value of x.

Hence, the equations that have one solution are 9=3(5x–2) and 6x–(3x+8)=16.