Find the measure of angles 1, 2, 3, and 4.
m< 1 = (4y—18)
m< 3= (5x-11)
m< 2 = (y + 14)
m< 4 = (x + 5)

If you plug in n = 1, then you get 3*n+5 = 3*1+5 = 3+5 = 8. So 8 is the first term.

Repeat for n = 2 and you should get 3n+5 = 3*2+5 = 6+5 = 11. Or simply add 3 to the last term 8 to get 3+8 = 11.

Repeat for n = 3 and n = 4 to get the third and fourth terms to be 14 and 17 respectively.

Answer:

-12 / 17

Step-by-step explanation:

x | -1 | 2 | 5 | 8 |

-----------------------

y | 3 | -1 | -5 | -9 |

Piking the poits at the extreme:

x1 = - 1 ; y1 = 3

x2 = 8 ; y2 = - 9

Slope = Rise / Run

Rise = y2 - y1 = - 9 - 3 = - 12

Run = x2 - x1 = 8 - (-9) = 8 + 9 = 17

Hence,

Slope = - 12 / 17

FMECA is a bottom-up hardware approach to risk assessment. It is an inductive, or data-driven, linking elements of a failure chain as follows: Effect of Failure, Failure Mode, and Causes/Mechanisms. To estimate the reliability of software, most software prediction models use the probability density function to predict "Mean Time To Failure."

FMECA is a systematic and structured analytical methodology used to identify potential failures in a system, equipment, process, or product, and to assess the effect and probability of those failures. FMECA stands for Failure Modes, Effects, and Criticality Analysis. FMECA is similar to FMEA (Failure Modes and Effects Analysis) in that it is used to identify failure modes and assess their risk.

However, FMECA goes beyond FMEA by analyzing the criticality of each failure mode. This makes it an effective tool for identifying the most significant failure modes and prioritizing them for corrective action. A Probability Density Function (PDF) is a function that describes the likelihood of a random variable taking on a particular value.

PDF is used in software prediction models to estimate the reliability of software by predicting "Mean Time To Failure" (MTTF). MTTF is the average time between failures of a system, equipment, process, or product.

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In Algebra 2, students typically use a scientific calculator.

A scientific calculator has advanced functions beyond basic arithmetic operations.

Some of the functions commonly used in Algebra 2 include logarithms, exponents, trigonometric functions, and statistical calculations. Therefore, a scientific calculator with these functions would be most useful for Algebra 2.

Examples of calculators that are often used in Algebra 2 include the TI-84 Plus , the TI-Nspire CX, the Casio fx-9750GII, and the HP Prime Graphing Calculator.

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~Shoto Todoroki here~

Answer:

hope this helps :))

Answer:

y/2

Step-by-step explanation:

Answer: y, because ΔABC ~ ΔEDC

Step-by-step explanation:

In the image we can see that angle D is equal to angle B because they are both marked as 65 degrees. Angle BCA is equal to DCE because they are vertical angles and vertical angles are congruent. Know that those are equal to each that must mean CED is equivalent to CAB because that's the last angle that corresponds with another. So, CED is y.

For the quadratic function y = ax² + bx + c , for which graph passes through the points (2, 31), (3 , 45) , (1, 19) is given by y = x² + 9x + 9.

As given in the question,

Standard form of quadratic function,

y = ax² + bx + c

Graph of the quadratic function passes through the points  (2, 31),

(3 , 45) , (1, 19) .

When passes through (2, 31)

31 = 4a + 2b + c __(1)

Passes through (3,45)

45 = 9a + 3b + c  __(2)

Passes through (1, 19)

19 = a + b + c __(3)

Multiply 9 to (3) and subtract (2) from it,

9a + 9b + 9c =171

9a +3b + c = 45

      6b + 8c = 126 ____(4)

Now, Multiply 4 to (3) and subtract (1) from it,

4a + 4b + 4c =76

4a +2b + c = 31

      2b + 3c = 45____(5)

Multiply 3 to (5) and subtract (4) from it,

6b + 9c = 135

6b + 8c =126

       c = 9

Substitute c= 9 in (5) we get,

2b + 3(9) = 45

⇒ b = 9

Now , substitute b = 9, c = 9 in (3) we get,

a + 9 + 9 = 19

⇒ a = 1

Required quadratic function is :

y = x² + 9x + 9  

Therefore, for the quadratic function y = ax² + bx + c , for which graph passes through the points (2, 31), (3 , 45) ,(1, 19) is given by y =x² + 9x + 9.

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Answer:

24 ft^2

Step-by-step explanation:

The small aquarium:

1 * 3 * 2 = 6 ft^2

The large aquarium

(1 + 1) * (3 + 2) * (2 + 1)

2 * 5 * 3 = 30 ft^2

Difference between the larger aquarium and the smaller aquarium:

30 - 6, or 24.

This means that the answer to this question is a, 24 ft^2

Answer:

area of the rectangle will be 175 square feet

Comparing the percentages we see that Marco listened to his albums more than Tucker.

A fraction is a number that represents a portion of a whole and is stated as a ratio of two integers, where the denominator is the overall number of equal parts and the numerator is the number of parts. A percentage is a figure that is stated as a fraction of 100 and denotes a portion of a whole. You multiply by 100 to convert a fraction to a percentage. You divide a percentage by 100 and simplify it to get a fraction.

Given that, Tucker listened to 3/8 of his albums.

Converting into percentage we have:

3/8 = 0.375 = 37.5%

For Marco he listened to 39% of his albums.

Thus, comparing the percentages we see that Marco listened to his albums more than Tucker.

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Answer: 19

Step-by-step explanation:

\(g(5)=5-2=3\\\\\impies f(g(5))=f(3)\\\\=3(3)+10=19\)

a) the calculated t-value (2.344) is greater than the critical t-value (1.984), we reject the null hypothesis. b) The p-value associated with a t-value of 2.344 is approximately 0.010 (two-tailed test).

(a) To determine if the differences in average yearly reading growth between Program A and Program B are significant at a 5% level, we can conduct a two-sample t-test.

Let's define our null hypothesis (H0) as "there is no significant difference in average yearly reading growth between Program A and Program B" and the alternative hypothesis (H1) as "Program A leads to higher average yearly reading growth than Program B."

We have the following information:

For Program A:

Sample size (na) = 64

Sample mean (xA) = 1.2

Sample standard deviation (sA) = 0.26

For Program B:

Sample size (nb) = 100

Sample mean (xB) = 1.0

Sample standard deviation (sB) = 0.28

To calculate the test statistic, we use the formula:

t = (xA - xB) / sqrt((sA^2 / na) + (sB^2 / nb))

Substituting the values, we have:

t = (1.2 - 1.0) / sqrt((0.26^2 / 64) + (0.28^2 / 100))

t ≈ 2.344

Next, we determine the critical t-value corresponding to a 5% significance level and degrees of freedom (df) equal to the smaller sample size minus 1 (df = min(na-1, nb-1)). Using a t-table or statistical software, we find the critical t-value for a two-tailed test to be approximately ±1.984.

(b) To calculate the p-value, we compare the calculated t-value to the t-distribution. The p-value is the probability of observing a t-value as extreme as the one calculated, assuming the null hypothesis is true.

From the t-distribution with df = min(na-1, nb-1), we find the probability corresponding to a t-value of 2.344. This probability corresponds to the p-value.

(c) Based on the results of the hypothesis test, where we rejected the null hypothesis, we can conclude that there is evidence to suggest that Program A leads to higher average yearly reading growth compared to Program B.

(d) To calculate the probability of a Type II error (β), we need additional information such as the significance level (α) and the effect size. The effect size is defined as the difference in means divided by the standard deviation. In this case, the effect size is (xA - xB) / sqrt((sA^2 + sB^2) / 2).

Let's assume α = 0.05 and the effect size (xA - xB) / sqrt((sA^2 + sB^2) / 2) = 0.1. Using statistical software or a power calculator, we can calculate the probability of a Type II error (β) given these values.

Without the specific values of α and the effect size, we cannot provide an exact calculation for the probability of a Type II error. However, by increasing the sample size, we can generally reduce the probability of a Type II error.

In summary, the differences in average yearly reading growth between Program A and Program B are significant at a 5% level, suggesting that Program A leads to higher average yearly reading growth. The p-value of the test results is approximately 0.010. Based on these findings, it may be recommended to adopt Program A over Program B. The probability of a Type II error (β) cannot be calculated without specific values of α and the effect size.

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The 95% upper bound represents the value below which 95% of the data falls. In this case, we have X ~ N(70,38), which means that X follows a normal distribution with a mean of 70 and a standard deviation of 38.

To find the 95% upper bound, we need to find the z-score associated with the 95th percentile.

The z-score can be calculated using the formula:
z = (x - μ) / σ

Where:
x is the value we want to find the z-score for,
μ is the mean of the distribution, and
σ is the standard deviation of the distribution.

In this case, we want to find the z-score corresponding to the 95th percentile, which is 1.645. However, the critical value given is 1.69, which is slightly higher than 1.645. Therefore, we will use the critical value of 1.69 instead.

Now, we can rearrange the formula to solve for x:
x = z * σ + μ

Plugging in the values, we have:
x = 1.69 * 38 + 70

Calculating this, we find that the 95% upper bound is approximately 135.1.
Therefore, we can say with 95% confidence that X will be less than approximately 135.1.

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Answer:

D

Step-by-step explanation:

Answer: C

Step-by-step explanation:

C. Y= 3x - 4

Answer:

y = 6

Step-by-step explanation:

Answer: y=6

Step-by-step explanation:

5y=2y+18

3y=18

y=6

Answer:

A'(11, -1)

B'(12, -5)

C'(10, -3)

The formula for Average Fixed Cost (AFC) is: AFC = FC / Q. Where FC represents the total fixed costs incurred by a firm and Q represents the quantity of output produced by the firm.

AFC is a per-unit measure of the fixed cost of production, and represents the amount of fixed cost that is attributed to each unit of output. As the quantity of output increases, the AFC decreases, since the fixed costs are spread out over a larger number of units. AFC is an important concept in economics and business, as it is used to calculate other cost measures such as average total cost and average variable cost.

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The partial derivative of f with respect to s at the point (3,2) is 36.

Use the Chain Rule to find the partial derivatives of f with respect to s and t.

∂f/∂s = ∂f/∂x ∂x/∂s + ∂f/∂y ∂y/∂s ∂f/∂t

         = ∂f/∂x ∂x/∂t + ∂f/∂y ∂y/∂t

Using the given information, we have fx(23,19) = 2 and fy(23,19) = -3.

We need to find ∂x/∂s and ∂y/∂s.

∂x/∂s = 3s² ∂y/∂s = 3t

Now we can substitute these values into the Chain Rule equation for

∂f/∂s.

∂f/∂s = 2(3s²) - 3(3t)

To evaluate this at the point (3,2), we simply plug in s=3 and t=2.

∂f/∂s(3,2) = 2(3(3)²) - 3(3(2))

∂f/∂s(3,2) = 54 - 18

∂f/∂s(3,2) = 36

Therefore, the partial derivative of f with respect to s at the point (3,2) is 36.

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Answer:

cool

Step-by-step explanation:

The perimeter of a rectangle is 2(l+b)

Breadth =" b " is the same thing as width

so if the width is half the length it will be = 1/2w

Final answer = 2(l + 1/2w)

l stands for length

hope u get this right

The critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:  θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.

To find the critical numbers of g(θ) = 4θ - tan(θ) on the interval 0 ≤ θ < 2π, we need to find the values of θ where the derivative of g(θ) is equal to 0 or undefined.

First, we find the derivative of g(θ) using the chain rule and quotient rule:

g'(θ) = 4 - sec²(θ)

To find where g'(θ) is equal to 0, we set the derivative equal to 0 and solve for θ:

4 - sec²(θ) = 0

sec²(θ) = 4

Taking the square root of both sides, we get:

sec(θ) = ±2

Since sec(θ) = 1/cos(θ), we can rewrite this as:

cos(θ) = ±1/2

We know that on the interval 0 ≤ θ < 2π, the cosine function is positive in the first and fourth quadrants and negative in the second and third quadrants.

Therefore, we need to find the values of θ in the first and fourth quadrants where cos(θ) = 1/2, and the values of θ in the second and third quadrants where cos(θ) = -1/2.

For cos(θ) = 1/2, we have:

θ = π/3 or 5π/3 in the first quadrant
θ = 7π/3 or 11π/3 in the fourth quadrant

For cos(θ) = -1/2, we have:

θ = 2π/3 or 4π/3 in the second quadrant
θ = 8π/3 or 10π/3 in the third quadrant

Therefore, the critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:

θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.

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the percent sales tax can be calculated as : sales tax percent =  sales tax  *  100  = $ 527.56 * 100  = 52756

the percent sales tax =  sales tax = list price * sales tax rate

                                                       = $22 * $23. 98

                                                       = $ 527.56

sales tax percent =  sales tax  *  100

                            = $ 527.56 * 100

                            = 52756

Sales tax is a kind of tax that is charged at the time a thing or administration is sold. The purchaser pays the tax to you, and you transmit the tax to the applicable government tax collection body. The taxes that are gathered by every office are then shipped off different divisions at the nearby, region, and state levels to guarantee their continuous activities and capabilities.

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Answer:

i think is (0.5,25)

Step-by-step explanation:

becuse at the time they have the same speed

Answer:

z

Step-by-step explanation:

z

Answer:

a) The piece of pizza she should choose is BE

b) The length of the cheese in her piece of the crust is approximately 20.07 inches

Step-by-step explanation:

The given diameter of the pizza, AE = 20 in.

The measure of the arc AB, \(m\widehat{AB}\) = ∠ACB = 65°

The measure of the arc DE, \(m\widehat{DE}\) = ∠DCE = 110°

Given that AE is the diameter of the circular pizza, we have;

\(m\widehat{BE}\) = ∠BCE = 180° - ∠ACB = 180° - 65° = 115°

Similarly;

∠ACD = 180° - ∠DCE = 180° - 110° = 70°

a) The biggest piece of pizza is the piece with the largest angle which is the  piece formed by arc BE, \(m\widehat{BE}\) = 115°

The piece of pizza she should choose is the piece, BE

b) Arc length = (Arc angle)/360 × (Circumference of the circle)

The circumference of the circular pizza, C = π × Diameter = π × length \(\overline {AE}\)

∴ C = π × 20 in.

The arc length of the arc BE = 115/360 × π × 20 = 115·π/18 ≈ 20.07

The length of the cheese in her piece of the crust, l = The arc length of the arc BE ≈ 20.07 inches.

The expected values of the given functions are:

E(θ) = π/2E(θ - π/2)

= -π/4E(θ²)

=  π²/3E(θⁿ)

=  π^(n+1)/(n+1)E(cosθ)

= 0E(sinθ)

= 0E(|cosθ|)

= 4/πE(cos 2θ)

= 0E(sin 2θ)

= 0E(cos²θ + sin²θ) = 1

We are given a continuous random variable θ that is uniformly distributed between 0 and π. Let us first determine the expression for P(0).We know that the random variable θ is uniformly distributed between 0 and π. Therefore, the probability density function (PDF) of θ is given by:

f(θ) = 1/π for 0 ≤ θ ≤ πP(0) is the probability that the random variable θ takes the value 0.

The probability that θ takes a specific value in a continuous uniform distribution is zero. Therefore, we have:

P(0) = 0Now, let us find the expected values of the given functions using the definition of the expected value.

For a continuous random variable, the expected value of a function g(θ) is given by:

E(g(θ)) = ∫g(θ)f(θ) dθ

Using the PDF we determined earlier,

we can find the expected values of the given functions as follows:

1. E(θ) = ∫θ f(θ) dθ

= ∫θ(1/π) dθ

= [θ²/(2π)]|₀^π

= π²/(2π)

= π/22. E(θ - π/2)

= ∫(θ - π/2) f(θ) dθ

= ∫(θ - π/2)(1/π) dθ

= [(θ²/2 - πθ/2)/π]|₀^π

= -π/4= -0.78543.

E(θ²) = ∫θ² f(θ) dθ

= ∫θ²(1/π) dθ

= [θ³/(3π)]|₀^π

= π²/3= 3.289864.

E(θⁿ) = ∫θⁿ f(θ) dθ

= ∫θⁿ(1/π) dθ

= [θ^(n+1)/(n+1)π]|₀^π

= π^(n+1)/(n+1)5.

E(cosθ) = ∫cosθ f(θ) dθ

= ∫cosθ(1/π) dθ

= [sinθ/π]|₀^π

= 0-0=06.

E(sinθ)= ∫sinθ f(θ) dθ

= ∫sinθ(1/π) dθ

= [-cosθ/π]|₀^π

= 0-0=07.

E(|cosθ|) = ∫|cosθ| f(θ) dθ

= ∫|cosθ|(1/π) dθ

= [2/π]|₀^(π/2)+[-2/π]|^(π/2)_8.

E(cos 2θ) = ∫cos 2θ f(θ) dθ

= ∫cos 2θ(1/π) dθ

= [sin 2θ/2π]|₀^π

= 0-09.

E(sin 2θ) = ∫sin 2θ f(θ) dθ

= ∫sin 2θ(1/π) dθ

= [-cos 2θ/2π]|₀^π

= 0-010. E(cos²θ + sin²θ)

= ∫(cos²θ + sin²θ) f(θ) dθ

= ∫(1/π) dθ= [θ/π]|₀^π

= π/π

= 1

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Ashley sold 180 glasses of lemonade for a total cost of $180, 90 little cups for $1, and 90 large cups for $2.

let x = quantity of sold miniature cups

Let y = the quantity of big cups sold.

She sold 180 cups in total for $180, so:

x + y = 180

1x + 2y = 180

figuring out the equations in a system:

x = 90   y = 90

Small cups of lemonade cost $1, and large cups cost $2, at Ashley's summertime lemonade stand. 180 cups of lemonade in all were sold for $180 by her. We can work up a system of equations to determine how many cups of each variety she sold.

let x = quantity of sold miniature cups

Let y = the quantity of big cups sold.

She sold 180 cups in total for $180, so:

x + y = 180

1x + 2y = 180

We arrive at x = 90 and y = 90 after solving the system of equations. In other words, Ashley sold 180 cups of lemonade for $180 by selling 90 small cups at $1 each and 90 large cups at $2 each.

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Answer:

8yz+xy

like terms and then solve it

The simplified expression is xy + 8yz

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.

For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.

Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

Given:

3xy+5yz-2xy +3yz

Now,

=3xy - 2xy + 5yz+ 3yz

=xy + 8yz

Hence, the simplifies expression is xy + 8yz.

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