In an indirect proof, it is essential to reach a _____of a known fact.
1. given
2. conclusion
3. contradiction

Answer:

79.77%

Step-by-step explanation:

P(X≥120) = normalcdf(120,1e99,130,12) = 0.7976716754 ≈ 0.7977 = 79.77%

Therefore, about 79.77% of operations last at least 120 minutes

Hey there!

I think the answer is B.

Answer: 7.5 is greater than 7.05 is.

Step-by-step explanation:

Answer:

4.5

Step-by-step explanation:

Since the slope of the equation is 40, we know that for every gallon of gas used, the car travels 40 miles. We know that in total he traveled 180 mi, so if we divide 40 into 180 we can find out how many gallons of gas he used.

180 / 40 = 4.5

so 4.5 gallons of gas were used. To check our work we can just substitute it back into the equation

40 x 4.5 = 180

This equation is true, so now we know that 4.5 gal of gas was used in total. I hope this helps you out :)

The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct

Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.

The formula for calculating YTM is as follows:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

Where:

C = Interest payment

F = Face value

P = Market price

n = Number of coupon payments

Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.

First, let's calculate the semi-annual coupon payment:

Semi-annual coupon rate = 5.2% / 2 = 2.6%

Face value = $1000

Market price = $884

Number of years remaining until maturity = 10 years

Number of semi-annual coupon payments = 2 x 10 = 20

Semi-annual coupon payment = Semi-annual coupon rate x Face value

Semi-annual coupon payment = 2.6% x $1000 = $26

Now, we can calculate the yield to maturity using the formula:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100

YTM = 6.23%

Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.

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The net profit for the year ending December 31, 2021, is £1,000. Therefore, the correct answer is d) £1,000.

To determine the net profit for the year ending December 31, 2021, we need to calculate the total revenue and subtract the total expenses. Let's analyze the transactions provided:

The owners invested £550,000 of their own funds into the business bank account. This does not affect the net profit as it represents an owner's contribution of capital.

The business used £16,000 from the bank account to purchase short features and fashion. This expense reduces the net profit.

The business used £10,000 from the bank account to buy new inventory. This expense also reduces the net profit.

The business bought additional inventory worth £9,000 on credit. This is not an expense for the current year as it represents an increase in assets.

The shop sold £28,000 worth of inventory to customers for cash. This revenue increases the net profit.

The business sold goods costing £6,000 to another business on credit for £8,000. This revenue also increases the net profit.

The business paid £9,000 in rent from the bank account. This expense reduces the net profit.

Depreciation and estimated electricity expenses are not mentioned in the given transactions and cannot be calculated.

The owners withdrew £10,000 in cash for personal use. This is not an expense for the business and does not affect the net profit.

Based on the provided information, we can calculate the net profit as follows:

Total Revenue = £28,000 (from sales to customers) + £8,000 (from sales to another business) = £36,000

Total Expenses = £16,000 (short features and fashion) + £10,000 (new inventory) + £9,000 (rent) = £35,000

Net Profit = Total Revenue - Total Expenses = £36,000 - £35,000 = £1,000

Therefore, the net profit obtained is £1,000.

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Answer:

Step-by-step explanation:

To simplify this equation, we need to assess the parenthesis

we know that 6x5 is 30, but this is a negative

so we can simplify this by turning the 5 positive and the 6 negative

-6x5

Now we multiply!

-6x5= -30

Hope this helps!^^

(a) The object's height at the start of the experiment will be 14 meters.

To find the height at the start of the experiment, we substitute t = 0 into the equation: S(0) = 16 - 2sin(0/5 + 1/3 π) = 16 - 2sin(1/3 π) = 16 - 2sin(π/3) = 16 - 2(√3/2) = 16 - √3 = 14 meters.

(b) The object's greatest height will be 15 meters.

To find the greatest height, we look for the maximum value of the function. Since the sin function oscillates between -1 and 1, the maximum value of -2sin(t/5 + 1/3 π) is 2. Therefore, the maximum height occurs when -2sin(t/5 + 1/3 π) = 2. Solving for t, we have: sin(t/5 + 1/3 π) = -1/2

t/5 + 1/3 π = -π/6 or 11π/6

t/5 = -π/6 - 1/3 π or 11π/6 - 1/3 π

t/5 = -3π/6 or 33π/18

t = -5π/6 or 33π/18

Since t represents time, we discard the negative value -5π/6. Thus, the greatest height occurs at t = 33π/18. Substituting this value into the equation: S(33π/18) = 16 - 2sin(33π/18/5 + 1/3 π) = 16 - 2sin(11π/18 + π/3) = 16 - 2sin(3π/6 + 6π/18) = 16 - 2sin(π/2 + π/3) = 16 - 2sin(5π/6) = 16 - 2(1/2) = 16 - 1 = 15 meters.

(c) The first time the object reaches this greatest height will be at t = 33π/18 seconds after the experiment begins.

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The sample size that gives 99% confidence level and estimate will be within 3 ounces is 0.7386\((standard deviation)^{2}\).

Given  confidence level 99% and margin of error is 3 ounces of true mean.

Margin of error is the difference between the actual values and the calculated value of mean.

Sample size is the number of items taken from the population as a sample for research.

We have to find the sample size.

First we have to find the z value for the corresponding p value of 0.99.

z value=2.58

Margin of error=z*σ/\(\sqrt{n}\)

3=2.58σ/\(\sqrt{n}\)

\(\sqrt{n}\)=2.58/3 σ

Squaring both sides

n=\(2.58^{2}\)σσ

Hence the sample size needed is 2.58 (\((standard deviation)^{2}\).

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19/49 = 0.388

Probability at least two were born on the same day of the week = 1 - probability of all three people were born on different days of the week

Probability of three random people born on different days of the week = 7/7 x 6/7 x 5/7 = 30/49

Probability that at least two were born on the same day of the week = 1 - 30/49 = 19/49 = 0.388

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Time is a continuous data type, meaning it can take any value within a range. For example, the flight time from London to Chicago could range from 6 to 8 hours.

Continuous data is a type of data that can take any value within a range. As opposed to discrete data which can only take certain values, continuous data can take any value within a range. An example of continuous data is time. The flight time from London to Chicago could range from 6 to 8 hours. This time can be measured in any unit, such as seconds, minutes, hours, or days. This type of data is useful in many fields such as mathematics, engineering, and economics. Continuous data provides a more accurate representation of real-world phenomena that often follow a certain pattern or trend. This type of data is also important for analyzing relationships between variables and for making predictions about the future.

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200 x 0.87 = 174

She answered 174 questions correctly.

Answer:

Chloe answered 174 problems correctly.

Explanation:

To find percentage, you would multiply the percentages decimal to the total.

0.87x200=174

The area of the customer's yard is 580π.

The distance formula is given as -

d = √(x₂ - x₁)² + (y₂ - y₁)²

Given is that this grid represents the customer’s yard. The bottom left corner is the origin point  O(0, 0), and the x- and y- axes represent the two fences. The rose bush is at point P(16, 18).

We can write the area of the customer's yard -

A = πr²

Here -

r = d

r² = d²

We can write -

A = πd²

A = π {(x₂ - x₁)² + (y₂ - y₁)²}

A = π{16 x 16 + 18 x 18}

A = 580π

Therefore, the area of the customer's yard is 580π.

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If a negative relation exists between two variables, low scores on one variable will be associated with high scores on the other variable.

In a negative relationship between two variables, a decrease in one variable is accompanied by an increase in the other variable. This means that as scores on one variable decrease (i.e., low scores), the scores on the other variable tend to increase (i.e., high scores). The negative relationship implies an inverse pattern where the variables move in opposite directions.

The exact nature and strength of the negative relationship can vary, but the general trend is that low scores on one variable correspond to high scores on the other variable. This negative association provides insights into the behavior and interactions between the variables being examined.

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Answer:

8:19

Step-by-step explanation:

Ball B:  diameter in mm = 9.5 * 10 = 95 mm

Ratio of Ball A to Ball B = 40 : 95

=  8:19 answer

Answer:

First, we need to factor our denominators:

x^2 - 14x + 49 = (x-7)^2

x^2 - 49 = (x+7)(x-7)

x^2 + 7x = x(x+7)

Now, we can rewrite our original expression as:

[(x+7)(x-7)] / [(x-7)^2]

and

[5(x+7)] / [x(x+7)]

Next, we can simplify by canceling out common factors, such as (x+7) in both the numerator and denominator of the second fraction:

[(x+7)(x-7)] / [(x-7)^2]  *  5 / x

Simplifying further, we get:

5(x+7) / (x-7)^2

This is our final answer.

Step-by-step explanation:

Henry opens a savings account with an annual interest rate of 4.5 percent. After a year, he gets $75,000 in payment. He made a deposit into the savings account of $72,831.68.

Here are the steps on how to calculate the amount Henry invested:

Convert the annual interest rate to a monthly rate.

\(\begin{equation}4.5\% \div 12 = 0.375\%\end{equation}\)

Calculate the number of years.

\(\begin{equation}\frac{18 \text{ months}}{12 \text{ months/year}} = 1.5 \text{ years}\end{equation}\)

Use the compound interest formula to calculate the amount Henry invested.

\(\begin{equation}FV = PV * (1 + r)^t\end{equation}\)

where:

FV is the future value ($75,000)

PV is the present value (unknown)

r is the interest rate (0.375%)

t is the number of years (1.5 years)

\(\begin{equation}\$75,000 = PV \cdot (1 + 0.00375)^{1.5}\end{equation}\)

\$75,000 = PV * 1.0297

\(\begin{equation}PV = \frac{\$75,000}{1.0297}\end{equation}\)

PV = \$72,831.68

Therefore, Henry invested \$72,831.68 in the savings account.

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Answer:

136

Step-by-step explanation:

32*4=128

15=1/4 of a minute

32/4=8

128+8=136

Answer:

136 copies

Step-by-step explanation:

32 copies = 1 minute

128 copies = 4 minutes

15 seconds = 1/4 minute

15 seconds = 1/4 of 32 = 8

128+8 = 136

When calculating a nation’s digital power, the term that is used to refer to the demonstrated capabilities of a nation-state in cyber offense or defense is Cyberwarfare.

Cyberwarfare  can be regarded as the use of cyber attacks against a nation-state so as to produce significant harm.

It should be noted that Cyber Warfare is set of actions  which is been carried out by  nation or organization so as to be able to launch an attack on institutions' computer network systems.

The interests or reasons for cyberwarfares based on the Cybersecurity as well as Infrastructure Security Agency are;

In order to achieve the goals behind the cyberwarfare programs, it is usually designed to focus on spectrum of objectives which will bring harm to national interests.

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The equation that could be used to solve the problem q -22 = 24. The answer is 46. The correct option is D

From the question, we are to determine which equation could be used to solve the given word problem.

The statement is

Twenty-two less than a number is twenty-four

If the number is q, twenty-two less than a number is

q -22

Thus,

Twenty-two less than a number is twenty-four means

q -22 = 24

This is the equation that could be used to solve the problem

Solving the problem

q -22 = 24

Add 22 to both sides

q -22 +22 = 24+22

q = 46

Hence, the equation that could be used to solve the problem q -22 = 24. The answer is 46. The correct option is D

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Answer:

Newton's third law of motion states that every action has an equal and opposite reaction. In softball when the catcher catches the ball the two forces present are the mitt on the ball and the ball on the mitt. The two are equal and in opposite directions.

The resulting equation written in standard form is 16x² - 22x + 6 = 0.

Quadratic Equation in Standard Form: ax² + bx + c = 0

a, b and c are known values. a can't be 0.

"x" is the variable or unknown (we don't know it yet).

The "solutions" to the Quadratic Equation are where it is equal to zero.

They are also called "roots", or sometimes "zeros"

We can Factor the Quadratic (find what to multiply to make the Quadratic Equation)

Calculation for the given equation-

Now, y=-16x²+24x+6

Substitute, y = 12+2x in y = -16x²+24x+6.

=> 12+2x = -16x²+24x+6

=> 16x²-24x-6+12+2x = 0

=> 16x²-22x+6 = 0

Therefore, the quadratic equation given in the standard form is 16x²-22x+6 = 0.

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The complete question is-

The two equations are given below;

Y = 12 + 2x   linear equation

Y = -16x² + 24x + 6  quadratic equation

If you substitute 12 + 2x for y in the second equation how is the resulting equation written in standard form?

The store has 16 board games

What are equivalent ratios?

The ratios that are same when compared are called equivalent ratios. The equivalentity of two or more ratios can be determined by comparing them to one another. For instance, 1:2 and 2:4 have the same ratio.

Let x = number of legos

Let y =  number of board games

Given ratio: 9:6= 9/6

x/y = 9/6

substitute x=24

24/y=9/6

Do cross multiplication

(6*24)/9=y

16=y

or

y=16

So, the store has 16 board games

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KM is equal to JL in trapezoid JKLM, as both KM and JL are the non-parallel sides of the isosceles trapezoid.

To prove that KM is equal to JL in the isosceles trapezoid JKLM, we can use the properties of isosceles trapezoids.

An isosceles trapezoid has two parallel sides (the bases) and two non-parallel sides (the legs) that are congruent.

In trapezoid JKLM, we are given that KL is parallel to JM, which makes JKLM a trapezoid. Additionally, we know that JK and LM are the bases of the trapezoid.

Since JKLM is an isosceles trapezoid, we can conclude that the non-parallel sides KL and JM are congruent.

Therefore, KM is equal to JL in trapezoid JKLM, as both KM and JL are the non-parallel sides of the isosceles trapezoid.

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It is not possible to provide a precise explanation or calculation for constructing a confidence interval or fitting a regression model in this context.

To construct a confidence interval, several key components are needed:

With these components, a confidence interval can be calculated to estimate the true population parameter (e.g., mean, proportion) within a certain range.

The formula for constructing a confidence interval depends on the specific parameter being estimated and the distribution of the data.

In the case of a regression model, additional information is needed, such as the equation or relationship between the dependent variable (Y) and explanatory variable (X).

This equation is used to estimate the fitted values and residuals.

Fitted values are the predicted values of the dependent variable based on the regression model, while residuals are the differences between the observed values and the fitted values.

Without the specific details of the sample size, mean, standard deviation, and the regression equation.

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(a)  The number of ways that at least one of the selected restaurants will serve seafood is 5040 - 2401 = 2639. (b) Subtracting the number of ways that none of the selected restaurants serve seafood (2401) from the total number of ways to select four restaurants (5040).

(a) If the order of selection is important, we can use the concept of permutations. There are three possibilities for each selection: either a seafood restaurant is chosen or a non-seafood restaurant is chosen. Thus, the number of ways that none of the selected restaurants serve seafood is 7 * 7 * 7 * 7 = 2401 (as there are 7 non-seafood restaurants to choose from). The total number of ways to select four restaurants is 10 * 9 * 8 * 7 = 5040. Therefore, the number of ways that at least one of the selected restaurants will serve seafood is 5040 - 2401 = 2639.

(b) if the order of selection is important, there are 2639 ways for Jason to select four restaurants in such a way that at least one of them serves seafood. This is found by subtracting the number of ways that none of the selected restaurants serve seafood (2401) from the total number of ways to select four restaurants (5040).

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Answer:

1. 2/3 or 66.7%

2. 3/5 or 60%

3. 6

4. 1/6 or 16.7%

5. 2/5 or 40%

Step-by-step explanation:

Answer:

1008 \(cm^2\)

Step-by-step explanation:

Given:

Triangular prism with

Base of triangle = 5 + 9 = 14 cm

Height of triangle = 12 cm

Here, we have 3 faces of the prism as a rectangle, all have width = 20 cm

Lengths of faces = 13cm ,14cm and 15 cm respectively

To find:

Total surface area = ?

Solution:

3 faces are rectangular shape and 2 faces are triangular shape.

\(Area\ of\ rectangle = Length \times Width\)

The formula for Total Surface Area of a triangular prism is given as:

\(TSA = 2 \times \text{Area of triangular base}+{\text{Area of rectangular faces}}\\\Rightarrow TSA = 2 \times \dfrac{1}{2}\times Base \times Height+{\text{Area of rectangular faces}}\\\Rightarrow TSA = 14 \times 12 + 15 \times 20+ 13 \times 20+ 14 \times 20\\\Rightarrow TSA = 168 + 840\\\Rightarrow TSA = 1008\ cm^2\)

So, the total surface area of the given triangular prism is 1008 \(cm^2\).