The number of chairs in a row at an opera house follows the arithmetic series: tn = 25 + (n - 1)4. if there are going to be 50 rows. how many chairs does the opera house have?

Answer:

it lies on 4 faces hope it helps

Answer:

The answer is four.

Step-by-step explanation:

Answer:

B. 11

Step-by-step explanation:

We can try it for each

10*2+5=25

25-10=15❌

11*2+5=27

27-11=16 ✔

12*2+5=29

29-12=17❌

6*2+5=17

16-6=11❌

So it's B

The five equivalent fractions of 4/5 are:

4 × 2/5 × 2 = 8/10

4 × 3/5 × 3 = 12/15

4 × 4/5 × 4 = 16/20

4 × 5/5 × 5 = 20/25

4 × 6/5 × 6 = 24/30

8 : 10

12 : 15

16 : 20

20 : 25

24 : 30

Answer:

Yes, because it passes through the center of the data points

Step-by-step explanation:

its true

Answer:

what he said

Step-by-step explanation:

Answer:

Lines  C and D

Step-by-step explanation:

For a pair of lines to be perpendicular ,

    the product of their slope must be - 1 .

Slope of A:

\(2x - 3y = 6\\\\-3y = -2x + 6\\\\y = \frac{-2x}{-3} + \frac{6}{-3}\\\\\)

\(y = \frac{2}{3}x - 2\\\\slope_A = \frac{2}{3}\)

Slope of B:

\(3x - 2y = - 9\\\\-2y = - 3x - 9\\\\y = \frac{-3x}{-2} - \frac{9}{-2}\\\\y =\frac{3x}{2} + \frac{9}{2}\\\\slope_B = \frac{3}{2}\)

Slope of C:

\(y = - \frac{3}{2}x - 5 \\\\slope_C = -\frac{3}{2}\)

Slope of D:

\(y = \frac{2}{3}x + 2\\\\slope_D = \frac{2}{3}\)

Product of the slopes = - 1

\(slope_A \times slope_B = \frac{2}{3} \times \frac{3}{2} = 1 \neq - 1 \\\\Therefore, not\ perpendicular.\\\\Slope_B \times slope_C = \frac{3}{2} \times \frac{-3}{2} = \frac{-9}{4} \neq -1\\\\Therefore , not \ perpendiucalr.\\\\Slope_C \times slope_D = -\frac{3}{2} \times \frac{2}{3} = - 1\\\\Therefore , perpendicular\\\\\\Slope_A \times slope_D = \frac{2}{3} \times \frac{2}{3} = \frac{4}{9} \neq 1\\\\therefore , not \ perpendicular.\)

The required statements "The rate of change of f(x) and g(x) must be opposites" and "The y-intercepts of f(x) and g(x) must be opposites." describe f(x) and g(x) as the original functions.

From the given information, we know that h(x) is the sum of f(x) and g(x), and j(x) is the product of f(x) and g(x).

Therefore, f(x) and g(x) are likely to be linear functions, as the sum of linear functions is linear and the product of linear functions is quadratic.

Additionally, the y-intercepts of f(x) and g(x) could be zero, as this would result in the y-intercept of h(x) being zero as well. The rate of change of f(x) and g(x) must be opposites since the product of two linear functions with the same slope will always result in a quadratic with a negative leading coefficient.

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(a) Construct confidence intervals are : 90%: [428.95, 444.05], 95%: [427.13, 445.87], 99%: [423.67, 449.33].

(b) The 99% confidence interval has the widest interval.

(a) To construct confidence intervals for the mean breaking strength of the wool fibers, we shall use the given formula:

Confidence interval = sample mean ± (critical value * standard error)

The critical value here will depends on the level of confidence. For a 90% confidence level, the critical value is 1.645 (from the standard normal distribution). For a 95% confidence level, the critical value is 1.96, and for a 99% confidence level, the critical value is 2.576.

Standard error is obtained by dividing the sample standard deviation by the square root of the sample size.

Plugging in the values, we can calculate the confidence intervals:

90% confidence interval:

Lower bound = 436.5 - (1.645 * (11.9 / √20))

Upper bound = 436.5 + (1.645 * (11.9 / √20))

95% confidence interval:

Lower bound = 436.5 - (1.96 * (11.9 / √20))

Upper bound = 436.5 + (1.96 * (11.9 / √20))

99% confidence interval:

Lower bound = 436.5 - (2.576 * (11.9 / √20))

Upper bound = 436.5 + (2.576 * (11.9 / √20))

(b) The width of a confidence interval depends on both the critical value and the standard error. When aiming for a higher level of confidence, the interval becomes wider as it requires a larger critical value. Consequently, it can be concluded that among the given confidence intervals, the one with a 99% confidence level will have the broadest range.

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Answer:

I think is 8.787e+6 cubic inches.

Answer:

A) y=1500+150x

Step-by-step explanation:

The y-intercept (0,1500) matches up with the first equation.

Each time x increases by one, y increases by 150. Example- (1, 650) and (2, 1800)

Please give brainliest if I helped! :)

Answer:

y= 150 + 1500x

Step-by-step explanation:

the yintercept is 1500. each point on the y axis is 100 and each point on the y axis is 1

so i go up 3 which is 300 and to the right 2 points which is 2 to get to the next point.

300/2 is 150

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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The Polynesian Triangle is a vast region of the Pacific Ocean that encompasses Hawaii, New Zealand, and Easter Island. The Polynesians were skilled navigators who traveled across this vast expanse of water using only the stars, winds, and currents to guide them. They developed a sophisticated system of navigation that allowed them to travel thousands of miles across the open ocean with remarkable accuracy.

One of the primary methods used by the Polynesians to navigate the Polynesian Triangle was celestial navigation. They used the stars, moon, and planets to determine their position and direction. They had an intimate knowledge of the night sky and could identify hundreds of stars and constellations. They used these celestial bodies to create mental maps of the sky that they could use to navigate by. They also used the position of the sun during the day to determine their direction.

Another method used by the Polynesians was wayfinding. Wayfinding is a complex system of navigation that involves observing the natural environment, such as waves, clouds, and birds, to determine one's position and direction. The Polynesians had an intimate knowledge of the ocean currents and wind patterns in their region. They could read the waves and clouds to determine their direction and could even detect land from great distances by observing the behavior of birds.

The Polynesians also used navigational instruments such as the kamalae and the kapele. The kamalae was a wooden board with a small hole in it that was used to measure the angle between two stars. The kapele was a cord with knots tied in it that was used to measure distance traveled.

It is important to note that Indigenous knowledge is often passed down through oral traditions and cultural practices. When interpreting this knowledge, it is essential to do so with respect for its origins and context. Adding interpretations or misrepresenting Indigenous knowledge can dilute its meaning and significance.

In conclusion, the Polynesians used a variety of methods to navigate the Polynesian Triangle, including celestial navigation, wayfinding, and navigational instruments. Their knowledge of the natural environment and their ability to read the stars and currents allowed them to travel vast distances across the open ocean with remarkable accuracy. When interpreting Indigenous knowledge, it is essential to do so with respect for its origins and context.

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The probability of randomly selecting a red six or a black king from a 52-card deck is 1/13.

To find the probability of selecting a red six or a black king from a 52-card deck, we need to determine the number of favorable outcomes (red six or black king) and divide it by the total number of possible outcomes (52 cards).

There are 2 red sixes (hearts and diamonds) and 2 black kings (spades and clubs) in a deck.

Since we want to select either a red six or a black king, we can add these numbers together to get a total of 4 favorable outcomes.

Since there are 52 cards in a deck, the total number of possible outcomes is 52.

Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: Probability = Number of favorable outcomes / Total number of possible outcomes Probability = 4 / 52 Probability = 1 / 13

Therefore, the probability of randomly selecting a red six or a black king from a 52-card deck is 1/13.

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Traingle DEF is isosceles

So

Hence

There are 7 people in Mr. Wilson's class, as Zach is the second person and Mary is the seventh person.

To calculate the total number of people in the class, we can use the formula 2x = 7, where x is the total number of people. Solving for x, we get x = 7.

To determine the number of people in Mr. Wilson's class, we can use the formula for the number of people in a circle, which is N = 2(n-1), where n is the number of people standing opposite each other in the circle. In this case, n is 2 (Zach and Mary). Therefore, N = 2(2-1) = 2 people. However, since there are 7 people in total in the circle, we can conclude that the number of people in Mr. Wilson's class is 7. To explain further, based on the given information, we can say that Zach is the second person, which means there are 2 people before him in the circle. Therefore, there are 7 people in Mr. Wilson's class. To further explain, we can break down the equation as follows: The person opposite of Zach is the seventh person, or 7th, so we can say that 7 is equal to the number of people in the class multiplied by 2, or 2x. Then, solving for x, we get x = 7. This means that the total number of people in the class is 7.

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If the end plan changed the length of each side by 9 feet , then the scale factor comparing your original garden to your final result is  0.70 .

in the question ,

it is given that

the length of square garden in original plan = 13 feet .

and

in the end plan the length of the square garden is = 9 feet

So , the scale factor can be calculated using the formula

scale factor = (length of side in end plan) / (length of side in original plan)

On substituting , the values ,

we get ,

scale factor = 9/13

= 0.6923

rounding to the nearest hundredth

we get ,

≈ 0.70

Therefore , If the end plan changed the length of each side by 9 feet , then the scale factor comparing your original garden to your final result is  0.70 .

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Answer:

\(y=3x\)

Step-by-step explanation:

\(Ax+By+C\) ⇒ \(y=mx+b\)

\(3x+y=0\)

Since there are no coefficients on the \(y\), you can convert the equation in one step.

Subtract \(3x\) from both sides

\(y=3x+0\) \(or\) \(y=3x\)

plz mark me brainliest. :)

A) H0: μ = 8mg, Ha: μ ≠ 8mg.

B) \(t = (x̄ - μ) / (s / sqrt(n)) = (10.3 - 8) / (2 / sqrt(25)) = 5.5\).

C) Degrees of freedom = n - 1 = 24, two-tailed t-test, α = 0.01, critical values are  ±2.492. p-value < 0.01.

D) We reject the null hypothesis and conclude that there is strong evidence that the mean amount of active ingredient in all dosages produced is different from 8 mg. The sample mean is significantly higher than 8 mg, indicating that the production process needs improvement.

(A) The null hypothesis is that the population mean of the active ingredient is equal to 8 mg, while the alternative hypothesis is that it is different from 8 mg. In symbols, H0: μ = 8 vs. Ha: μ ≠ 8.

(B) We apply the t-test formula to determine the value for the test statistic:

\(t = (xbar - μ) / (s / sqrt(n))\)

where Î14 is the estimated population mean, n is the number of samples size, x bar represents the sample mean, and s is the standard deviation of the sample. Plugging in the values from the problem, we get:

\(t = (10.3 - 8) / (2 / sqrt(25)) = 3.25\)

(C) To determine the critical value or the p-value, we look up the t-distribution with 24 degrees of freedom ( df = n - 1) and a two-tailed significance level of 0.01. The critical values are  ±2.492, while the p-value is less than 0.01.

(D) Based on the results, we reject the null hypothesis and conclude that the mean amount of active ingredient in all dosages produced is different from 8 mg at the 1% significance level. In practical terms, this means that the drug production process needs to be investigated and improved to ensure that the correct amount of active ingredient is consistently delivered in each dosage.

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Prove of the given theorem is shown below by using definition of LU decomposition.

Now, For the given theorem, we need to show that the cost of computing the LU-decomposition of A is p³/3 - p/3 multiplications/divisions, and p/3 - p²/2 + p/6 additions/subtractions.

Since, in the LU-decomposition, we express A as the product of a permutation matrix P, a lower-triangular matrix L, and an upper-triangular matrix U.

That is, A = PLU.

The cost of computing the LU-decomposition involves the cost of computing P, L, and U, which we will consider separately.

Computing P:

Since P is a permutation matrix, computing P involves at most p(p-1)/2 row interchanges (swapping two rows of A).

Each row interchange requires p multiplications/divisions and p-1 additions/subtractions.

Therefore, the total cost of computing P is at most p(p-1)/2 × (p multiplications/divisions + (p-1) additions/subtractions).

Computing L:

Computing L involves computing p(p-1)/2 entries, which involve p-1 multiplications/divisions and p-1 additions/subtractions each.

This gives a total cost of p(p-1)/2 × (p-1 multiplications/divisions + (p-1) additions/subtractions).

Computing U:

Computing U involves computing p² entries, which involve p-1 multiplications/divisions and p-1 additions/subtractions each. This gives a total cost of p² × (p-1 multiplications/divisions + (p-1) additions/subtractions).

Adding up the costs of computing P, L, and U, we get:

p(p-1)/2 (p multiplications/divisions + (p-1) additions/subtractions) + p(p-1)/2 (p-1 multiplications/divisions + (p-1) additions/subtractions) + p²(p-1 multiplications/divisions + (p-1) additions/subtractions)

Simplifying this expression, we get:

p³/3 - p/3 multiplications/divisions + p/3 - p²/2 + p/6 additions/subtractions

which is the desired result.

To obtain the expressions 1 + 2 + ... + n = n(n+1)/2 and

1² + 2²+ ... + n² = n(n+1)(2n+1)/6, w

e can use the formulas for the sum of an arithmetic series and the sum of a series of squares, respectively.

These formulas are well-known and can be proved by induction or other methods.

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First, we need to determine the number of coins.

10+16+17+12 =55

Notice that she replaces the coin after each draw so the number of coins does not change.

(a) What is the probability that Marissa obtains a quarter on the first draw?

P(quarter) = number of quarters/ total number of coins = 10/55 = 2/11

b) What is the probability that Marissa obtains a penny or a dime on the second draw?

P(penny or dime) = (number of pennies or dimes) / total = (12+17)/55 = 29/55

(c) What is the probability that Marissa obtains at most 10 cents worth of money on the third draw?

At most 10 cents means she can have a penny, a nickel or a dime

P(penny, nickel, or dime) = ((number of pennies, nickels or dimes)/ total = ( 16+17+12) /total = 45/55 = 9/11

(d) What is the probability that Marissa does not get a nickel on the fourth draw?

She can have a quarter, a dime or a penny, ( no nickels)

P( no nickel) = (number of quarters, dimes or pennies) /total = ( 10+17+12)/ total = 39/55

(e) What is the probability that Marissa obtains at least 10 cents worth of money on the fifth draw?

She must get at least 10 cents, which is a dime or a quarter

P(dime or quarter) = (number of dimes or quarters) / total = (10+17)/55 = 27/55

Going from top left to right then bottom left to right

Answers:

1st. answer: 94

2nd. answer: 82

3rd. answer: 142

4th answer: 88.2

5th. answer: 130

6th. answer: 178

(also I relearned how to do triangles)

(I'm going to follow you so if you have any more questions I can help)

Answer:

0.75 I think but I'm sure that it's right

Answer:

\({7}^{3} \)

Step-by-step explanation:

simplify numerator to get

\( {7}^{7} \)

simplify denominator to get

\( { ({7}^{2} )}^{2} \)

which simplifies to

\( {7}^{4} \)

now that it's

\( \frac{ {7}^{7} }{ {7}^{4} } \)

the exponents subtract to get our final answer

Answer:

Step-by-step explanation:

(16-9)^7

[(5+2)^2]^2

(16-9)^7

823543

[(5+2)^2]^2

(49)^2

2401

823543/2401 = 343

Answer:

x + 6 y - 4

Step-by-step explanation:

A moved 6 units to the right so plus 6 then moved 4 units down so minus 4

Answer:

40 cm square

Step-by-step explanation:

Area of rectangle formula is :- L*B

Answer:

..............................

To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.

Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.

Let's assume the square footage of office 143 is 800 square feet.

Number of gallons needed = Square footage / Coverage rate per gallon

Number of gallons needed = 800 square feet / 50 square feet per gallon

Number of gallons needed = 16 gallons

Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.

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Universal Foods has a debt-to-value ratio of 40%, its debt is currently selling on a yield of 6%, and its cost of equity is 12%. The corporate tax rate is 40%. The company is now evaluating a new venture into home computer systems. The internal rate of return on this venture is estimated at 13.4%. WACCs of firms in the personal computer industry tend to average around 14%

What is Universal's WACC?

b. Will Universal make the correct decision if it discounts cash flows on the proposed venture at the firm's WACC?

c. Should the new project be pursued

Answer:

A.) 8.64%

B.) No

C.) No

Step-by-step explanation:

Given the following :

DEBT-TO-VALUE ratio (D/V) = 40% = 0.4

Debt rate (rD) = 6% = 0.06

Corporate tax( tC) = 40% = 0.4

Cost of Equity (rEquity) = 12% = 0.12

EQUITY-TO-VALUE ratio (E/V) = (1 - 0.4) =0.6

rEquity = (D / V) × (1 - Tc)rDebt + (E / V) × rEquity

= 0.40 × (1 - 0.4)(0.06) + (0.6) × 0.12

= 0.0144 + 0.072

= 0.0864

= 8.64%

B) No, The IRR is above the company WACC

C.) No, NPV will be negative as IRR is less than 14%

a. Universal Foods' Weighted Average Cost of Capital (WACC) = 8.16% (7.2% + 0.96%)

b. Universal Foods will make the correct decision by discounting the cash flows on this venture at the firm's WACC because it is always lower than the estimated internal rate of return (IRR).

c. Universal Foods should pursue the project since the internal rate of return is estimated at 13.4%, and Universal Foods' WACC is lower than the industry average.

Data and Calculations:

Debt-to-value ratio = 40%

Debt's yield rate = 6%

Corporate tax rate = 40%

Weighted cost of debt = 0.96% (6% x (1 -60%) x 40%)

Cost of equity = 12%

Weighted cost of equity = 7.2% (12% x (1 -40%)

Industry Average WACC = 14%

Internal rate of return = 13.4%

Question Completion:

a. What is Universal's WACC?

b. Will Universal make the correct decision if it discounts cash flows on the proposed venture at the firm's WACC?

c. Should the new project be pursued?

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