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Algebra 1
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Answer:

y = 15.4

Step-by-step explanation:

the outer and inner triangles are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{y}{11}\) = \(\frac{8+3.2}{8}\) = \(\frac{11.2}{8}\) ( cross- multiply )

8y = 11 × 11.2 = 123.2 ( divide both sides by 8 )

y = 15.4

Answer:

\(-10x + 4 y + 27\)

Step-by-step explanation:

Answer: -10x+4y+27

Step-by-step explanation: first, combine the like terms

20 + 7= 27

-9x-x=-10x

4y stays the same so, if simplified this equals

-10x+2y+27

Answer: 1.5

Step-by-step explanation:

Step-by-step explanation:

A. x^2-9x+18

B. x^2-8x+16

C. 2x^2-5x-12

D. 12x^2-31x+7

In a wheel game with eight equally spaced sectors, Keisha's chances of winning a reward on both spins are 1/16.

Probability—the possibility that an occurrence will happen—is calculated by dividing here the same number of favorable outcomes by the total number of possible outcomes. A coin toss serves as the most simple instance. If you flip a coin, there are only two possible outcomes: heads or tails.

The spinners will get a reward each everytime she lands on white. She will spin the wheel twice.

Here, there are two instances of such color white in the wheel, and there are a total of eight sectors. the likelihood that white will appear in the spin for the first time is,

P = 2/8

P = 1/4

The second case's circumstances are the same. In this instance, the outcomes including both wheel revolutions are independent of one another.

According to the product rule, the likelihood that a white sector will both spin and emerge is,

P = 1/4 * 1/4

P = 1/16

In a wheel game with eight equally spaced sectors, Keisha has a 1/16 chance of winning a reward on both spins.

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The complete question is-

Keisha is playing a game using a wheel divided into eight equal sectors, as shown in the diagram. Each time the spinner lands on white, she will win a prize. If she spins this wheel twice, what is the probability she will win a prize on both spins? Please show all steps!

Answer:

Since the only even prime number is 2, we can say that its reciprocal is 1 2 \dfrac{ 1 }{ 2 } 21​. By checking, we get 2 × 1 2 = 1 2 \times \dfrac{ 1 }{ 2 } = 1 2×21​=1.

Step-by-step explanation:

Using the normal approximation to the binomial, there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.

This problem is incomplete, but researching it on a search engine, it asks the probability that the sum of these Bernoulli variables is of less than 60.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The binomial distribution is a series of n Bernoulli trials with p probability of a success on each trial, hence the parameters for the binomial distribution are given as follows:

n = 100, p = 0.5.

The mean and the standard deviation are given by:

Using continuity correction, the probability that the sum is less than 60 is P(X < 59.5), which is the p-value of Z when X = 59.5, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (59.5 - 50)/5

Z = 1.9

Z = 1.9 has a p-value of 0.9713.

Hence there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.

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Answer:

11.7

Step-by-step explanation:

I just solved and added them all-

You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:

Calculate the accumulated balance after 15 years of regular deposits:

We can use the formula for the future value of a regular deposit:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV is the future value (accumulated balance)

P is the regular deposit amount

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

P = $125.00 (regular deposit amount)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 15 (number of years)

Plugging the values into the formula:

FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)

Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.

Calculate the balance after an additional 5 years of accumulation:

To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:

FV = P * (1 + r/n)^(nt)

where:

FV is the future value (balance after accumulation)

P is the initial principal (accumulated balance after 15 years)

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:

P = (accumulated balance after 15 years)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 5 (number of years)

Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.

By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

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To evaluate the triple integral, E xyzdV, we must integrate with respect to each of the three variables: x, y, and z. Let's begin by finding the limits of integration for each of these three variables.

The integral can now be written as:

E xyzd

V = ∫₀¹ ∫₀¹ ∫₀¹ xyz dzdydx

By evaluating the integral, we get:

E xyzdV = 1/6.

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The a = 0.Substituting the values of a, b, and c in the general equation, we get:y = 0x² + 2x + 3The quadratic function is:y = 2x + 3Answer: The quadratic function is y = 2x + 3.

The given table illustrates the values of a quadratic function. Here is how you can find the quadratic function:Step 1: Write the general form of a quadratic function y = ax² + bx + c, where y is the dependent variable and x is the independent variable. a, b, and c are constants that affect the shape and position of the parabola.Step 2: Substitute the values from the table for x and y to form a system of equations.Step 3: Solve the system of equations to find the values of a, b, and c. Once you have found these values, substitute them into the quadratic equation to get the quadratic function.

The given table is as follows:x   |  0   |  2   |  4  |   6y   |  3   |  1   |  -1  |   -3Step 2:Form a system of equations using the values in the table. Here are the equations:y = a(0)² + b(0) + cy = a(2)² + b(2) + cy = a(4)² + b(4) + cy = a(6)² + b(6) + cStep 3:Solve the system of equations.Using the first equation, y = c. Hence, we have:y = 0²a + 0b + c3 = cThe value of c is 3.Using the second equation, we have:y = 2²a + 2b + 3y = 4a + 2b + 3Subtracting the two equations, we get:- 2a - b = - 2a + b = 2b = 4Therefore, b = 2.Substituting the values of b and c into the first equation, we get:3 = a(0)² + 2(0) + 3

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Answer

:2.12$

Step-by-step explanation:

Answer:

She can make 15 scarves with 5 yards of fabric

For each yard of fabric,3 scarves can be made

Step-by-step explanation:

5 yards  = 5/1 yards

5/1 divided into 1/3     is the same as

5/1 multiplied by 3/1

5X3 = 15

The solutions to the given equation are x = π/6, x = 5π/6, x = π/4, and x = 7π/4 in the interval 0 < x < 2π.

To solve this equation, we need to find all the values of x that satisfy the equation:

(2 sin x -1) (2 cos^2 x-1)=0

This equation is satisfied if either of the factors is equal to zero. So we have two cases:

Case 1: 2 sin x -1 = 0

Adding 1 to both sides and then dividing by 2, we get:

sin x = 1/2

The solutions to this equation are x = π/6 and x = 5π/6 in the interval 0 < x < 2π.

Case 2: 2 cos^2 x-1 = 0

Adding 1 to both sides and then dividing by 2, we get:

cos^2 x = 1/2

Taking the square root of both sides, we get:

cos x = ±√(1/2) = ±1/√2

The solutions to this equation are x = π/4 and x = 7π/4 in the interval 0 < x < 2π.

Therefore, the solutions to the given equation are x = π/6, x = 5π/6, x = π/4, and x = 7π/4 in the interval 0 < x < 2π.

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The cost of safely disposing of the toxic chemicals is approximately five times what the company paid to purchase it.(Option D)

Sentence correction or sentence improvement is a type of grammatical practice where a sentence is given with a word or a phrase that requires grammatical changes or improvement.

Now,

Hence, the correction needs to be made at Option D; the correction would be: "paid to purchase them."

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With the help of Chebyshev's theorem, the percentage of data between 5 to 45 is 89%.

The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem.

Numerous other probability distributions can be applied to this theorem.

Chebyshev's Inequality is another name for Chebyshev's Theorem.

One of many theorems established by Russian mathematician Pafnuty Chebyshev is known as Chebyshev's theorem.

According to Bertrand's postulate, there is a prime between n and 2n for every n.

So, the percentage of data within 15 to 45 is:

In this instance, we're looking for numbers between 15 and 45.

Since 30 -3*5 = 20 and 30 + 3*5 = 45, we are therefore within 3 deviations of the mean. So, since k = 3, we can find the percent as follows:

% = (1 - 1/3²) × 100 = 88.88% = 89%

Therefore, with the help of Chebyshev's theorem, the percentage of data between 5 to 45 is 89%.

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Answer:

11. A) 12

12. D)11

Step-by-step explanation:

11. We substitute x with 12 in 3(x)-11.

3(12)-11=

36-11= 25

We substitute x with 12 for the second equation (x+13).

12+13=25

Both answers match so the answer for #11 is 12.

12.We substitute x with 11 in 4(x)-4.

4(11)-4=

44-4=40

We substitute x with 11 for the second equation (2(x)+18)

2(11)+18=

22+18=40

Both answers match so the answer for #12 is 11.

Answer:

\(6\sqrt{3}\)

Step-by-step explanation:

In a 30-60-90 triangle, the side opposite to the right angle is \(2x\) , the side opposite to the 30 degrees is x and the side opposite to the 60 degrees is \(x\sqrt3\). Since 12 is on the side with \(2x\), we can use reasoning to deduce that the unknown side is \(6\sqrt3\).

The average value of \(f(x) = -3x^2 - 4x + 4\) over the interval [0, 3] is -11/3.

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the average value of a function f(x) over an interval [a, b], we can use the formula:

Average value = (1 / (b - a)) * ∫[a, b] f(x) dx

In this case, we want to find the average value of \(f(x) = -3x^2 - 4x + 4\)over the interval [0, 3].

Average value = (1 / (3 - 0)) * ∫\([0, 3] (-3x^2 - 4x + 4) dx\)

Simplifying:

Average value = (1/3) * ∫[0, 3] \((-3x^2 - 4x + 4) dx\)

          \(= (1/3) * [-x^3 - 2x^2 + 4x] from 0 to 3\)

          \(= (1/3) * (-(3^3) - 2(3^2) + 4(3)) - (1/3) * (0 - 2(0^2) + 4(0))\)

             = (1/3) * (-27 - 18 + 12) - (1/3) * 0

             = (1/3) * (-33)

             = -11/3

Therefore, the average value of \(f(x) = -3x^2 - 4x + 4\) over the interval [0, 3] is -11/3.

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the answer is b. x =7

steps

176=(3x+5)+(21x+3)

176=24x+8

168=24x

x=7

An inequality is a mathematical statement that represents a comparison between two values or expressions using symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). It indicates that one value is not necessarily equal to the other.

To write the inequality that represents the sentence "The product of a number and 8 is at least 25," we can use the following steps:

1. Let's assume the number in the sentence as "x".

2. The product of the number "x" and 8 can be written as 8x.

3. The phrase "at least" indicates that the value on the left side of the inequality should be greater than or equal to the value on the right side.

4. Thus, the inequality representing the sentence is: 8x ≥ 25.

In summary, the inequality that represents the given sentence is 8x ≥ 25.

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To make iced tea using 8 cups of water, Marie will need an appropriate amount of drink mix.

The amount of drink mix needed depends on the desired strength or concentration of the iced tea. Generally, for a standard iced tea recipe, a ratio of 1 teaspoon of drink mix per 8 ounces (1 cup) of water is used.

In this case, since Marie is using 8 cups of water, she will need 8 teaspoons of drink mix.

This assumes that Marie wants to maintain a standard strength for her iced tea. However, individual preferences may vary, and adjustments can be made based on personal taste preferences for a stronger or weaker tea.

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In the equation y = $7.20x + $790, "y" represents the total cost. An equation is a mathematical statement that shows the relationship between two or more variables. In this equation, there are two variables - "x" and "y". The variable "x" represents the number of units produced or sold, while "y" represents the total cost.

The coefficient of "x" in the equation, which is 7.20, represents the variable cost per unit. This means that for each unit produced or sold, there is an additional cost of $7.20. The constant term, which is $790, represents the total fixed costs. Fixed costs are those costs that do not vary with the number of units produced or sold.To find the total cost of producing or selling a certain number of units, we can plug in the value of "x" into the equation and solve for "y". For example, if we want to find the total cost of producing 100 units, we can substitute x=100 into the equation:
y = $7.20(100) + $790
y = $720 + $790
y = $1510
Therefore, the total cost of producing 100 units is $1510. In summary, "y" represents the total cost in the given equation, which is determined by both fixed and variable costs.
In the equation y = $7.20x + $790, "y" represents option C: total costs. This equation has two components: "$7.20x" represents the variable costs per unit, where x is the number of units, and "$790" represents the total fixed costs. By adding these two components together, you get the total costs (y) for producing x units.

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Answer: 12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Given that the triangular plate is fixed at its base, and its apex a is given a horizontal displacement of 5 mm. suppose that a = 600 mm.In order to find the deflection, consider the right triangle OAB where O is the origin,

A (0,600) and B (x,y).So,OB² = OA² + AB²= 600² + x²Since the length of the side opposite to angle B is given as 600 - y, we can use Pythagoras' theorem to express y in terms of x and hence find the equation of the line AB, i.e. y = f(x).Thus, OB² = OA² + AB²x² + (600 - y)² = 600² + x²y = 600 - √(600² - x²)From the geometry of the figure, it can be seen that the deflection at point A is equal to the displacement of B in the x direction, i.e.5 mm. Therefore, the deflection at point A is 5 mm.Long Answer:The problem is about finding the deflection at a point of a triangular plate that is fixed at its base and has an apex that is given a horizontal displacement of 5 mm. It is also given that a = 600 mm. In order to solve the problem,

we need to consider the geometry of the situation and use some elementary trigonometry.The figure below shows the triangular plate with the origin at the left end of the base and the y-axis perpendicular to the base at the origin. The apex of the triangle is at point A with coordinates (0,600).Let B (x,y) be a point on the plate such that OB is perpendicular to the base. Then, OB = x and AB = y. From the geometry of the figure, we can write the following equation:OB² = OA² + AB²where OB² = x², OA = 600, and AB² = (600 - y)²Therefore, we havex² = 600² + (600 - y)²Simplifying the equation, we getx² = 720000 - 1200y + y² + x²600y = 720000 - y²y² + 600y - 720000 = 0Solving for y, we gety = -300 + √(90000 + 360000 - 4×720000)/2y = 600 - √(600² - x²)Since the deflection at point A is equal to the displacement of B in the x direction, the deflection at A is given by 5 mm.Answer: The deflection at point A is 5 mm.

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Answer: 240

Step-by-step explanation:

1. 12,000×.04=240

2. 12,000+240= 12,240

Answer:

$12,240

Step-by-step explanation:

$12,000 = 100%

$12,000 / 100 = $120

$120 = 1%

$120x 2 = %240.

$240 = 2%

$12,000+ 240 = $12,240

Answer:

\(4(3 + x) + x = x + 4\)

\(12 + 4x + x = x + 4\)

\(12 + 5x = x + 4\)

\(5x - x = 4 - 12\)

\(4x = - 8\)

\( \large \: x = \frac{ - 8}{4} \)

\(x = - 2\)

Answer:

The answer would be F(x)= 3

Step-by-step explanation:

you just substitute the 0 for all the x's in this case the x next to the 2.

f(x)= 3-2(0)

Then you multiply the 2 to the 0 which will give you 0.

f(x)= 3-0

And lastly you would subtract the 3 from the 0 and your answer will be

F(x)=3

Hope this helped!!!

Answer:

3.5×10^4=35000

Step-by-step explanation:

Consider the value

3.5

we are saying that we are counting in units (1's) in that we have

3

1

2

of 1's

'.....................................................................................

Consider the value

3.5

×

10

. Now we are saying we have

3

1

2

of tens. That is; 3 lots of 10 is 30 and

1

2

of 10 is 5 so we have

30

+

5

=

35

'.................................................................................

Note that

10

2

is 100

Consider the value

3.5

×

10

2

. Now we are saying we have

3

1

2

of

100

'

s

So if we are counting in 100's then the decimal point stays where

it is and we move the number of 3.5 to the left until the

3 becomes hundreds.

Note that we have to insert a place holder of 0 just to the left of the decimal point to make sure the three is viewed as in the hundreds.

3.5

×

10

2

−−−−−−−−−−−−−−−−−−→

slide to the left 2 places

350.0