if a rectangle has a height of one foot and a triangle has a height of 2 feet with its base exactly one foot more then the rectangle. when would these two shapes have the same area? plz show your work with a equation. Whoever awnsers first will be brainliest

Answer:

350

Step-by-step explanation:

The difference is 35, she's spending 35 everyday

The unit step response, y(t), for the given LTI system with transfer function H(s) = (s+4)(s+5)′(s+2), and input X(s) = 1/s, is a function of time that can be represented as \(y(t) = (4/3)e^(-2t) - (4/3)e^(-5t) - (1/3)e^(-4t) + (1/3)e^(-2t)\).

The unit step response of a linear time-invariant (LTI) system represents the output of the system when the input is a unit step function. In this case, the transfer function H(s) is given as (s+4)(s+5)′(s+2), where s is the Laplace variable. The prime symbol (') denotes differentiation with respect to s.

To find the unit step response, we first need to determine the inverse Laplace transform of the transfer function H(s). By applying partial fraction decomposition, the transfer function can be expressed as H(s) = A/s + B/(s+2) + C/(s+4) + D/(s+5), where A, B, C, and D are constants.

Taking the inverse Laplace transform of each term using known transforms, we obtain the time-domain representation of H(s) as \(y(t) = (4/3)e^(-2t) - (4/3)e^(-5t) - (1/3)e^(-4t) + (1/3)e^(-2t)\).

In summary, the unit step response y(t) for the given LTI system is a function of time that includes exponential terms with different coefficients and time constants. This response represents the system's output when the input is a unit step function.

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Answer:

0

Step-by-step explanation:

Let p be the probability of an adult over 50 wearing glasses for driving. Since we don't know the value of p, we can't use the binomial distribution directly. However, we can use the normal approximation to the binomial distribution since n is large (assuming n * p >= 10 and n * (1-p) >= 10).

Let X be the number of adults over 50 wearing glasses for driving in a random sample of n adults. Then X ~ Binomial(n, p) can be approximated by a normal distribution with mean µ = n * p and standard deviation σ = sqrt(n * p * (1-p)).

We want to find the probability that at least six adults over 50 in a random sample of n wear glasses for driving. This is equivalent to finding P(X >= 6) = 1 - P(X < 6) using the normal approximation.

To apply the normal approximation, we need to standardize the random variable X:

Z = (X - µ) / σ

Using continuity correction:

P(X >= 6) = P(X > 5.5)

Z = (5.5 - n * p) / sqrt(n * p * (1-p))

We can use the standard normal distribution table or calculator to find the probability:

P(Z >= (5.5 - n * p) / sqrt(n * p * (1-p)))

Since we don't know the value of p, we can use a conservative estimate of p = 0.5 (assuming 50% of adults over 50 wear glasses for driving). Then:

P(Z >= (5.5 - n * 0.5) / sqrt(n * 0.5 * (1-0.5)))

For example, if we sample n = 100 adults over 50, the probability of at least six wearing glasses is:

P(Z >= (5.5 - 100 * 0.5) / sqrt(100 * 0.5 * (1-0.5)))

= P(Z >= 0.5)

Using a standard normal distribution table or calculator, P(Z >= 0.5) = 0.3085.

Therefore, the probability of at least six adults over 50 wearing glasses for driving in a random sample of 100 is approximately 0.3085 or 30.85%.

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Answer:

5x^3+15x^2-35x

Step-by-step explanation:

Firstly, you want to combine the "x"s in the (5x*x^2) and the (5x*3x). Once you have that (you will get 5x^3 and 15x^2), you can move onto the last set of parenthesis. We can get 35x from here. Finally, the last step is to add the correct signs. Our final answer will then be 5x^3+15x^2-35x. I hope this helped and please don't hesitate to reach out with more questions!

Answer: 50

Step-by-step explanation:

Answer: The expression is (c-7) / 3

Step-by-step explanation:

Let's say Adam has c pieces of candy

He took seven pieces for himself which means we can write this as c-7

He then divided this amount between his 3 children (c-7)/3

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

Answer:

I belive the answer is a

correct me if I'm wrong

The slope =2 and y-intercept = -3.

What is slope?

Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line.Any two distinct places along the line can be used to determine the slope of any line.

Here let us take two points \((x_1,y_1)=(1.5,0) , (x_2,y_2)=(0,3)\) .

Now using slope formula then,

Slope m = \(\frac{y_2-y_1}{x_2-x_1}\)

=> m = \(\frac{3-0}{0-1.5} = \frac{3}{-1.5}=2\)

Now using equation formula then,

=> \(y-y_1=m(x-x_1)\)

=> y-0=2(x-1.5)

=> y = 2x-3

Here y=mx+b, where b= y-intercept.

Hence slope =2 and y-intercept = -3.

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The solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.

To simplify the equation 3(x-6) - 1/2(8x+10) = -25, we can start by applying the distributive property and then combining like terms.

First, let's distribute the 3 and the -1/2 to the terms inside the parentheses:

3(x-6) - 1/2(8x+10) = 3x - 18 - (4x + 5)

Now, let's simplify further by combining like terms:

3x - 18 - 4x - 5 = -x - 23

So, the simplified equation is -x - 23 = -25.

To solve for x, we can isolate the variable by adding 23 to both sides of the equation:

-x - 23 + 23 = -25 + 23

This simplifies to:

-x = -2

Finally, we can solve for x by multiplying both sides of the equation by -1:

(-1)(-x) = (-1)(-2)

This gives us:

x = 2

Therefore, the solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.

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The experimental probability that of 5 students, at least 3 will make a C is approximately 0.68256 or 68.256%.

To find the experimental probability that of 5 students, at least 3 will make a C using the given random-number table, we can use:

Count the number of digits that represent students who make a C, which is 6 out of 10 digits.

Determine the probability of a single student making a C, which is 60% or 0.6.

Use the binomial probability formula to calculate the probability of getting at least 3 students who make a C out of 5 students:

P(X ≥ 3) = 1 - P(X < 3)

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = C(5,0) * 0.6^0 * 0.4^5 + C(5,1) * 0.6^1 * 0.4^4 + C(5,2) * 0.6^2 * 0.4^3

P(X < 3) = 0.01024 + 0.07680 + 0.23040

P(X < 3) = 0.31744

P(X ≥ 3) = 1 - P(X < 3)

P(X ≥ 3) = 1 - 0.31744

P(X ≥ 3) = 0.68256

Therefore, the experimental probability that of 5 students, at least 3 will make a C is approximately 0.68256 or 68.256%.

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Answer and Step-by-step explanation:

36 dollars minus 17.85 dollars equals $18.15, or 18 dollars and 15 cents.

All you have to do is subtract 36 by 17.85

36 - 17 = 19

100 - 85 = 15

1 is subtracted from 19 because of the decimal.

18.15

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THE Answer is

x-11=3

??

and the number is 14

Answer:

X - 11 = 3

Step-by-step explanation:

3 is the answer and 11 is the part that is being subtracted. In subtraction the smaller number comes second which is why the question says minus 11.

The expression that is equivalent to 14.5d + 8.5 - 1/2d + 1/2 + 2.5d is 17.5d + 9.5.

To simplify the given expression, we combine like terms. First, we add the terms with the variable "d." We have 14.5d + 2.5d, which gives us 17d. Then, we add the constant terms: 8.5 + 1/2 + 1/2 equals 9.5. Thus, the simplified expression is 17.5d + 9.5.To simplify the given expression, we combine like terms. First, we add the terms with the variable "d." We have 14.5d + 2.5d, which gives us 17d.

By combining like terms and performing the necessary calculations, we can simplify the expression 14.5d + 8.5 - 1/2d + 1/2 + 2.5d to 17.5d + 9.5.

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If the interest is compounded continuously, an investment account with the same initial investment and the same APR will have the highest APY.

APY (Annual Percentage Yield) is the effective annual rate of return after compounding. The higher the APY, the more frequently the interest is compounded.

Compounding yields the highest APY because it effectively provides an infinite number of compounding periods. Compounding daily, monthly, or annually yields lower APYs than compounding continuously.

An investment account is a type of financial product that allows people to save or invest money in the hopes of earning a profit. Individual retirement accounts (IRAs), brokerage accounts, savings accounts, and other types of investment accounts are available.

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The preliminary estimate of the cost of building a 600-MW fossil-fuel plant for the assembly of the new long-distance aircraft is approximately $700 million.

To estimate the cost of building a 600-MW fossil-fuel plant, we can use the cost capacity exponent factor and the cost index.

First, let's calculate the cost capacity ratio (CCR) for the 600-MW plant compared to the 200-MW plant:

CCR = (600/200)^0.79

Next, we need to adjust the cost of the 200-MW plant for inflation using the cost index. The cost index ratio (CIR) is given by:

CIR = (current cost index / base cost index)

Using the given information, the base cost index is 400 and the current cost index is 1200. Therefore:

CIR = 1200 / 400 = 3

Now, we can estimate the cost of the 600-MW plant:

Cost of 600-MW plant = Cost of 200-MW plant * CCR * CIR

Using the information provided, the cost of the 200-MW plant is $100 million. Plugging in the values, we have:

Cost of 600-MW plant = $100 million * CCR * CIR

Calculating CCR:

CCR = (600/200)^0.79 ≈ 2.3367

Calculating the cost of the 600-MW plant:

Cost of 600-MW plant = $100 million * 2.3367 * 3

Cost of 600-MW plant ≈ $700 million

Your question is incomplete but most probably your full question was

Suppose that an aircraft manufacturer desires to make a preliminary estimate of the cost of building a 600-MW fossil-fuel plant for the assembly of its new long- distance aircraft. It is known that a 200-MW plant cost $100 million 20 years ago when the approximate cost index was 400, and that cost index is now 1,200. The cost capacity exponent factor for a fossil-fuel power plant is 0.79. What is he preliminary estimate of the cost of building a 600-MW fossil-fuel plant for the assembly of the new long-distance aircraft?

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The directional derivative is a measure of the rate of change of a function in a particular direction. It quantifies how a function changes along a specific vector direction in a given point.

Answer: \((DA)(0,0,0) = 6\sqrt (14)\)

The given function is \(f(x, y, z) = -2 e^x cos(yz)\).

We need to find the directional derivative of this function at Po in the direction of A,

where Po(0,0,0) and A= - 3i+2j+k.

To find the directional derivative we need the directional derivative formula, which is given by:

DA = ∇f.

P where DA is the directional derivative of f in the direction of A, ∇f is the gradient vector of f, and P is the point where the direction derivative is to be calculated.

Let's find the gradient vector of f using the partial derivatives.

\(\partial f/ \partial x = -2 e^x cos(yz)\)

\(\partial f/\partial y = 2 e^x z sin(yz)\)

\(\partial f/\partial z = 2 e^x y sin(yz)\)

Therefore, the gradient vector of f is

∇f = <∂f/∂x, ∂f/∂y, ∂f/∂z> = <-2 e^x cos(yz),

2 e^x z sin(yz), 2 e^x y sin(yz)>

Now, we can find the directional derivative of f in the direction of A at P0 using the formula.

DA = ∇f.P = ∇f . A/|A|

where ∇f = <-2, 0, 0>, A = <-3, 2, 1>and

|A| = \(=\sqrt(3^2+2^2+1^2) \\= \sqrt(14)\)

Now,∇f . A = (-2)(-3) + (0)(2) + (0)(1)

= 6DA = ∇f . A/|A|

=\(6 \sqrt(14)\)

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Answer:

idk if this is what you wanted or not, but I will tell you the feet per second, because that is what it sounds like you want: The truck travels 18 feet every second

Step-by-step explanation:

all you have to do is divide 108 by 6, and the answer is 18 equation:

108 / 6= 18

The probability that a person will wait for more than 9 minutes is approximately 0.0228, or 2.28% when rounded to four decimal places

To find the probability that a person will wait for more than 9 minutes, we'll use the z-score formula and a standard normal distribution table (Z-table).

First, calculate the z-score using the formula:
z = (X - μ) / σ

Where X is the value we're interested in (9 minutes), μ is the mean (5 minutes), and σ is the standard deviation (2 minutes).

z = (9 - 5) / 2
z = 4 / 2
z = 2

Now, look up the probability for a z-score of 2 in a Z-table. You'll find a value of 0.9772, which represents the probability of waiting less than or equal to 9 minutes. To find the probability of waiting more than 9 minutes, subtract this value from 1:

Probability of waiting more than 9 minutes = 1 - 0.9772 = 0.0228

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.

The probability that exactly 7 of them are 16 to 24 years old is 0.222

In this question we have been given a recent study of minimum wage earners found that 55% of them are 16 to 24 years old.

A random sample of 12 minimum wage earners is selected. we need to find the probability that exactly 7 of them are 16 to 24 years old.

Here, n = 12

p = 0.55

1 - p = 0.45

x = 7

Using binomial distrubution the required probability would be,

P = 12C7 * (0.55)^7 * (0.45)^(12 - 7)

P = 792 * 0.01522 * (0.45)^5

P = 792 * 0.01522 * 0.01845

P = 0.2224

Therefore, the required probability is 0.222

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Answer:

 your answer would be 4.5

Step-by-step explanation:

because if you take the 3/4 from 3 and turn it into a decimal it would be 0.75 so 0.75 + 0.75 is 1.5 and 3 + 1.5 = 4.5

i hope i helped you

Answer:

y = 6x - 6

Step-by-step explanation:

Look at the last two points, (1, 0) and (2, 6).

y = mx + b

m = (6 - 0)/(2 - 1) = 6

y = 6x + b

Now look at point (0, -6). The y-intercept, b, is -6.

y = 6x - 6

Step 1

Rearrange the equation

Step 2

Test all options by rearrangement

Option A

Option B

Option C

Option D

Hence, the equivalent options to the equation are options B and C

Answer:

The first option.... The one with the blue dot I guess you have chosen that

Deondra would need to invest approximately $18,112 (rounded to the nearest hundred dollars) for the value of the account to reach $30,000 in 10 years with an interest rate of 4.7% compounded continuously.

We can use the continuous compound interest formula to solve this problem:

A = \(P \times e^{(r \times t)\)

A is the final amount in the account

P is the principal amount invested

r is the interest rate (as a decimal)

t is the time period (in years)

e is the mathematical constant e (approximately equal to 2.71828)

We want to find the value of P that will result in A = $30,000 after 10 years, with an interest rate of r = 4.7% compounded continuously.

We can rearrange the formula above to solve for P:

P = \(A / e^{(r \times t)\)

Substituting in the values we know:

P = \(30000 / e^{(0.047 \times 10)\)

P ≈ 18111.96

This issue can be resolved using the continuous compound interest formula:

A = \(P \times e^{(r \times t)\)

A represents the account's ultimate balance.

P is the invested principal amount

R stands for interest rate in decimal form, T for time in years, and E for the mathematical constant, which is roughly equivalent to 2.71828.

To get A = $30,000 after 10 years at an interest rate of r = 4.7% that is continually compounded, we need to calculate the value of P.

To find P, we can rearrange the equations above:

P = \(A / e^{(r \times t)\)

Adding the values we are aware of: P = \(30000 / e^{(0.047 \times 10)\)

P ≈ 18111.96

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Therefore, approximately 0.0475 or 4.75% of smoke alarms will have a life span of less than 1 year as the cumulative probability for a Z-score of -1.67 is approximately 0.0475.

To find the proportion of smoke alarms with a life span of less than 1 year, we can use the Z-score formula and the properties of the standard normal distribution.

First, we calculate the Z-score using the formula:

Z = (X - μ) / σ

Where X is the value we are interested in (1 year), μ is the mean (2 years), and σ is the standard deviation (0.6 years).

Z = (1 - 2) / 0.6

= -1.67

Next, we look up the corresponding cumulative probability (proportion) for the Z-score of -1.67 in the standard normal distribution table or by using statistical software. The cumulative probability corresponds to the proportion of values less than the given Z-score.

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