Solve the equation and check your answer. 0.95 t plus 0.05 left parenthesis 100 minus t right parenthesis equals 0.49 left parenthesis 100 right parenthesis

Answer:

129 468  

Step-by-step explanation:

I'm not sure if you're supposed to reuse the same numbers just in a different Three digit number. Or if you're supposed to use the number one time and one time only. But if not here's there's some numbers that you could use

He basically all You have to do Is take the numbers and turning them into three digit numbers Without repetition.

Hope this helps you!

Also it's saying that 664 is not allowed Because it they are reusing the six When there's no Extra six to use. So remind you not to use the same number twice!

Answer: $ 22,466.45

Step-by-step explanation:

Given : Future value : [tex]FV= \$50,000[/tex]

The number of time period : [tex]t=10\text{ years}[/tex]

The rate of interest : [tex]r=8\ %=0.08[/tex]

Let P be the present value.

The formula to calculate the future value is given by :-

[tex]FV=Pe^{rt}[/tex]

[tex]50000=Pe^{0.08\times10}\\\\\Rightarrow\ 50000=P\times2.22554092849\\\\\Rightarrow\ P=\dfrac{50000}{2.22554092849}\\\\\Rightarrow\ P=22466.4482059\approx22,466.45[/tex]

Hence, the present value of asset would be $ 22,466.45.

The present value needed to obtain $50,000 in 10 years at an 8% continuously compounded interest rate is $22,466.48.

To determine the present value of an asset that grows to $50,000 in 10 years with an 8% annual compound interest rate, continuously compounded, we can use the formula for continuous compounding, which is:

A = Pe^rt

where:

A is the future value of the investment/loan, including interest,

P is the principal investment amount (the initial deposit or loan amount),

r is the annual interest rate (decimal),

t is the number of years the money is invested or borrowed for,

e is the base of the natural logarithm (approximately equal to 2.71828).

In this problem, we have A = $50,000, r = 0.08 (8% expressed as a decimal), and t = 10 years. We are solving for P, the present value.

Rearranging the formula to solve for P gives:

P = A / e^rt

P = 50000 / e^(0.08)(10)

Now calculate the value:

P = 50000 / e^0.8

P = 50000 / 2.22554... (using a calculator for e0.8)

P = $22,466.48 (rounded to two decimal places)

Thus, you would need to invest $22,466.48 now to have $50,000 in 10 years at an 8% annual compounded continuously interest rate.

[tex]\displaystyle\int_{C_1}\vec F\cdot\mathrm d\vec s=\int_0^1(t^2+t^4,4t^3)\cdot(1,2t)\,\mathrm dt=\int_0^1(t^2+9t^4)\,\mathrm dt=\boxed{\frac{32}{15}}[/tex]

[tex]\displaystyle\int_{C_2}\vec F\cdot\mathrm d\vec s=\int_0^1(2t^2,4t^2)\cdot(1,1)\,\mathrm dt=\int_0^16t^2\,\mathrm dt=\boxed{2}[/tex]

The value of the line integral depends on the path, so [tex]\vec F[/tex] is not a gradient vector field.

The line integrals ∫c1F⋅ds and ∫c2F⋅ds are computed by replacing x and y with the parametric representations, calculating ds, completing the dot product, and conducting the integration. If the results are identical, F is a gradient vector field.

To compute the line integrals, ∫c1F⋅ds and ∫c2F⋅ds, where c1(t)=(t, t2) and c2(t)=(t,t) for 0≤t≤1 of the vector field F=(x2+y2,4xy), we can reduce each of them to an integral over t, the parameter of the path. In the case of c1(t), replace x and y by t and t² correspondingly, for calculation. Similarly, in the case of c2(t), replace x and y by t in calculations.

Let's consider ∫c1F⋅ds. Here, F = (t²+t⁴,4t³) and ds can be calculated using the Pythagorean theorem leading to sqr(1+4t²). The dot product F.ds is then calculated and integrated from 0 to 1. Repeat the process for ∫c2F⋅ds.

A vector field F is said to be a gradient vector field if integral from one point to another remains the same regardless of the path chosen to get from one point to the other. Comparing the obtained results will determine the truth of this statement.

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a. The average value of [tex]f[/tex] on the given interval is

[tex]\displaystyle f_{\rm ave}=\frac1{\pi-0}\int_0^\pi(2\sin x-\sin2x)\,\mathrm dx=\boxed{\frac4\pi}[/tex]

b. Solve for [tex]c[/tex]:

[tex]\dfrac4\pi=2\sin c-\sin2c\implies\boxed{c\approx1.238\text{ or }c\approx2.808}[/tex]

Answer:

The answer is in the attachment.

Step-by-step explanation:

Look at the picture.

The rectangle that has a vertex of C and has one of it's sides on line CD, with the stated lengths is constructed as shown in the image attached below (see attachment).

A rectangle can be described as a 4-sided polygon having all its four interior angles measuring 90 degrees each and has two pairs of opposite equal sides.

Thus, the rectangle that has a vertex of C and has one of it's sides on line CD, with the stated lengths is constructed as shown in the image attached below (see attachment).

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Answer with explanation:

1.

Let a, and b be two numbers between 20 and 5 , which is in geometric progression.

So,the series is as Follows =20 , a, b, 5

Common ratio

          [tex]=\frac{\text{Second term}}{\text{First term}}[/tex]

[tex]\frac{20}{a}=\frac{a}{b}=\frac{b}{5}\\\\b^2=5 a---(1)\\\\a^2=20 b\\\\\frac{b^4}{25}=20 b-----\text{Using 1}\\\\b^3=500\\\\b=(500)^{\frac{1}{3}}\\\\b=5\times (4)^{\frac{1}{3}}\\\\5a=25\times (4)^{\frac{2}{3}}\\\\a=5\times (4)^{\frac{2}{3}}[/tex]

2.

44 -32-3

=12-3

=9

3.

⇒Sin (2.4)=Sin(2+0.4)

⇒Sin 2 ×Cos (0.4)+Cos 2 × Sin (0.4)

⇒Sin (A+B)=Sin A×Cos B+Cos A×Sin B

Answer:

{[tex]z|z<-\frac{1}{2}[/tex]}U{[tex]z|z>\frac{1}{2}[/tex]}

Step-by-step explanation:

Given the inequality [tex]|z| > \frac{1}{2}[/tex] you need to set up two posibilities:

FIRST POSIBILITY : [tex]z>\frac{1}{2}[/tex]

SECOND POSIBILTY: [tex]z<-\frac{1}{2}[/tex]

Therefore, you got that:

[tex]z<-\frac{1}{2}\ or\ z>\frac{1}{2}[/tex]

Knowing this, you can write the solution obtained in Set notation. This is:

Solution: {[tex]z|z<-\frac{1}{2}[/tex]}U{[tex]z|z>\frac{1}{2}[/tex]}

Answer:

{z|z < (-1/2) ∪ z > (1/2)}

Step-by-step explanation:

I got it right. I would explain if I were better at making sense lol

Answer:

After how many years is the fish population 60?

x=2.71 years

Step-by-step explanation:

The fish population increases by a factor of 1.5 each year. We have the equation that represents this situation

[tex]f (x) = 20 (1.5) ^ x[/tex]

Where x represents the number of years elapsed f(x) represents the amount of fish.

Given this situation, the following question could be posed

After how many years is the fish population 60?

So we do [tex]f (x) = 60[/tex] and solve for the variable x

[tex]60 = 20 (1.5) ^ x\\\\\frac{60}{20} = (1.5)^x\\\\3 = (1.5)^x\\\\log_{1.5}(3) = log_{1.5}(1.5)^x\\\\log_{1.5}(3) = x\\\\x =log_{1.5}(3)\\\\x=2.71\ years[/tex]

Observe the solution in the attached graph

Answer:

The last choice is the one you want

Step-by-step explanation:

If you plug in the values of x to our rational function, the y values you get back match those in the last choice.  The limit is -4; we see that as our x value approach 0 (but cannot equal 0!!), the y values get closer and closer to -4.  So that's the limit!

Answer:

There is a 94.52% probability that a randomly selected adult has an IQ less than 132.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 20. This means that [tex]\mu = 100, \sigma = 20[/tex].

The probability that a randomly selected adult has an IQ less than 132 is?

This probability is the pvalue of Z when [tex]X = 132[/tex]. So:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{132 - 100}{20}[/tex]

[tex]Z = 1.6[/tex]

[tex]Z = 1.6[/tex] has a pvalue of 0.9452.

This means that there is a 94.52% probability that a randomly selected adult has an IQ less than 132.

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 20. The probability that a randomly selected adult has an IQ less than 132 is 0.9452 or 94.52%.

Let standardize the IQ value of 132 using the formula for standardization:

Z = (X - μ) / σ

Where:

Z= standardized value (Z-score)

X = IQ value

μ = mean= 100

σ = standard deviation =20

Let's calculate the Z-score for an IQ of 132:

Z = (132 - 100) / 20

Z = 32 / 20

Z = 1.6

Using a standard normal distribution table, the probability is 0.9452.

Therefore, the probability that a randomly selected adult has an IQ less than 132 is 0.9452 or 94.52%.

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Answer:

Step-by-step explanation:

So there is a 3% probability that an athlete is using EPO .

The probability of showing positive on a test when you've used it is 0.99.

3% x 0.99= 2.97%

The probability of a positive result without EPO is 0.1

97% x 0,1 = 9,7 %

My guess is that 2.97% + 9,7% = 12.67% or 0.1267.

I don't know i may be wrong because you've put as an answer 0.0297 but if you like you may take only the first part of the answer.

There is a 0.1267 = 12.67% probability that a randomly selected athlete tests positive for EPO.

A positive test can happen in two cases:

Then, adding these probabilities:

[tex]p = 0.03(0.99) + 0.97(0.1) = 0.1267[/tex]

0.1267 = 12.67% probability that a randomly selected athlete tests positive for EPO.

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Answer:

120/s^6

Step-by-step explanation:

There is an easy formula for this...

L(t^n)=n!/(s^(n+1))

Your n=5 here

L(t^5)=5!/(s^6)

L(t^5)=120/s^6

[tex]\mathcal{L}\{t^n\}=\dfrac{n!}{s^{n+1}}[/tex]

So

[tex]\mathcal{L}\{f(t)\}=\dfrac{5!}{s^{5+1}}=\dfrac{120}{s^6}[/tex]

Answer:

y = 2x − 1

Step-by-step explanation:

By eliminating the parameter, first solve for t:

x = 4 + ln(t)

x − 4 = ln(t)

e^(x − 4) = t

Substitute:

y = t² + 6

y = (e^(x − 4))² + 6

y = e^(2x − 8) + 6

Taking derivative using chain rule:

dy/dx = e^(2x − 8) (2)

dy/dx = 2 e^(2x − 8)

Evaluating at x = 4:

dy/dx = 2 e^(8 − 8)

dy/dx = 2

Writing equation of line using point-slope form:

y − 7 = 2 (x − 4)

y = 2x − 1

Now, without eliminating the parameter, take derivative with respect to t:

x = 4 + ln(t)

dx/dt = 1/t

y = t² + 6

dy/dt = 2t

Finding dy/dx:

dy/dx = (dy/dt) / (dx/dt)

dy/dx = (2t) / (1/t)

dy/dx = 2t²

At the point (4, 7), t = 1.  Evaluating the derivative:

dy/dx = 2(1)²

dy/dx = 2

Writing equation of line using point-slope form:

y − 7 = 2 (x − 4)

y = 2x − 1

To find the tangent to the curve represented by the parametric equations x = 4 + ln(t), y = t² + 6, both methods, eliminating and not eliminating the parameter t, yield the same result. The slope of the tangent line at the point (4, 7) is determined to be 2, thus the equation of the tangent is y - 7 = 2(x - 4).

To find the equation of the tangent to the given curve at the point (4, 7) with the parametric equations x = 4 + ln(t) and y = t² + 6, we can approach the problem in two ways: with and without eliminating the parameter t.

Firstly, without eliminating the parameter, we need to find the derivatives dx/dt and dy/dt, and then use them to find dy/dx which is the slope of the tangent at the given point. Since dx/dt = 1/t and dy/dt = 2t, at the point (4, 7), we have t = 1, making the slope dy/dx = (dy/dt)/(dx/dt) = 2 × 1 / (1/1) = 2. The equation of the tangent line can thus be written as y - y₁ = m(x - x₁), where m is the slope, and (x₁, y₁) is the point of tangency.

This gives us the equation y - 7 = 2(x - 4).

Answer: The answer should be D on edg

Please see the attachment for graph.

For x=1, Put x=1 into equation:

[tex]y = -4\sqrt{1} = - 4[/tex]

For x=4, Put x=4 into equation:

[tex]y = -4\sqrt{4} = - 8[/tex]

For x=9, Put x=9 into equation:

[tex]y = -4\sqrt{9} = - 12[/tex]

     1          -4

     4          -8

     9         -12

Now we plot the points on graph and join the points.

Please see the attachment for graph.

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Answer:

the awnser is a -2.75

Step-by-step explanation:

Answer:

(a) [tex]f'(x)=-\frac{2}{x^3}[/tex]

(b) [tex]y=-0.25x+0.75[/tex]

Step-by-step explanation:

The given function is

[tex]f(x)=\frac{1}{x^2}[/tex]                  .... (1)

According to the first principle of the derivative,

[tex]f'(x)=lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}[/tex]

[tex]f'(x)=lim_{h\rightarrow 0}\frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}[/tex]

[tex]f'(x)=lim_{h\rightarrow 0}\frac{\frac{x^2-(x+h)^2}{x^2(x+h)^2}}{h}[/tex]

[tex]f'(x)=lim_{h\rightarrow 0}\frac{x^2-x^2-2xh-h^2}{hx^2(x+h)^2}[/tex]

[tex]f'(x)=lim_{h\rightarrow 0}\frac{-2xh-h^2}{hx^2(x+h)^2}[/tex]

[tex]f'(x)=lim_{h\rightarrow 0}\frac{-h(2x+h)}{hx^2(x+h)^2}[/tex]

Cancel out common factors.

[tex]f'(x)=lim_{h\rightarrow 0}\frac{-(2x+h)}{x^2(x+h)^2}[/tex]

By applying limit, we get

[tex]f'(x)=\frac{-(2x+0)}{x^2(x+0)^2}[/tex]

[tex]f'(x)=\frac{-2x)}{x^4}[/tex]

[tex]f'(x)=\frac{-2)}{x^3}[/tex]                         .... (2)

Therefore [tex]f'(x)=-\frac{2}{x^3}[/tex].

(b)

Put x=2, to find the y-coordinate of point of tangency.

[tex]f(x)=\frac{1}{2^2}=\frac{1}{4}=0.25[/tex]

The coordinates of point of tangency are (2,0.25).

The slope of tangent at x=2 is

[tex]m=(\frac{dy}{dx})_{x=2}=f'(x)_{x=2}[/tex]

Substitute x=2 in equation 2.

[tex]f'(2)=\frac{-2}{(2)^3}=\frac{-2}{8}=\frac{-1}{4}=-0.25[/tex]

The slope of the tangent line at x=2 is -0.25.

The slope of tangent is -0.25 and the tangent passes through the point (2,0.25).

Using point slope form the equation of tangent is

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-0.25=-0.25(x-2)[/tex]

[tex]y-0.25=-0.25x+0.5[/tex]

[tex]y=-0.25x+0.5+0.25[/tex]

[tex]y=-0.25x+0.75[/tex]

Therefore the equation of the tangent line at x=2 is y=-0.25x+0.75.

Answer:

[tex]k(x)=2^{x}[/tex] ⇒ 1st answer

Step-by-step explanation:

* Lets explain how to solve the problem

∵ [tex]g(x)=3(2^{x})[/tex]

∵ [tex]h(x)=2^{x+1}[/tex]

- Lets revise this rule to use it

# If [tex]a^{n}*a^{m}=a^{n+m}====then==== a^{n+m}=a^{n}*a^{m}[/tex]

- We will use this rule in h(x)

∵ [tex]h(x)=2^{x+1}[/tex]

- Let a = 2 , n = x , m = 1

∴ [tex]h(x)=2^{x}*2^{1}[/tex]

- Now lets find k(x)

∵ k(x) = (g - h)(x)

∵ [tex]g(x)=3(2^{x})[/tex]

∵ [tex]h(x)=2^{x}*2^{1}[/tex]

∴ [tex]k(x)=3(2^{x})-(2^{x}*2^{1})[/tex]

- We have two terms with a common factor [tex]2^{x}[/tex]

∵ [tex]2^{x}[/tex] is a common factor

∵ [tex]\frac{3(2^{x})}{2^{x}}=3[/tex]

∵ [tex]\frac{2^{x}*2^{1}}{2^{x}}=2^{1}=2[/tex]

∴ [tex]k(x) = 2^{x}[3 - 2]=2^{x}(1)=2^{x}[/tex]

* [tex]k(x)=2^{x}[/tex]

Approximately 85.87 mg of Bismuth-210 would remain after 8 days.

To calculate the amount of Bismuth-210 remaining after 8 days, we need to apply the concept of radioactive decay. Bismuth-210 decays by about 13% each day, meaning that 13% of the remaining Bismuth-210 transforms into another atom (Polonium-210) each day.

Let's calculate the amount remaining:

Therefore, after 8 days, approximately 85.87 mg of Bismuth-210 would remain.

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After 8 days, approximately 76.69 mg of Bismuth-210 remains out of the initial 233 mg.

To calculate the amount of Bismuth-210 remaining after 8 days of radioactive decay, follow these steps:

Step 1:

Understand the decay rate.

Each day, 13% of the remaining Bismuth-210 decays into Polonium-210. This means that 87% of the Bismuth-210 remains each day.

Step 2:

Calculate the remaining amount each day.

Start with the initial amount of 233 mg of Bismuth-210.

After the first day: [tex]\( 233 \text{ mg} \times 0.87 = 202.71 \text{ mg} \)[/tex]

After the second day: [tex]\( 202.71 \text{ mg} \times 0.87 = 176.43 \text{ mg} \)[/tex]

Continue this process for 8 days.

Step 3:

Perform the calculations for 8 days.

[tex]\[ \text{Day 1: } 233 \text{ mg} \times 0.87 = 202.71 \text{ mg} \][/tex]

[tex]\[ \text{Day 2: } 202.71 \text{ mg} \times 0.87 = 176.43 \text{ mg} \][/tex]

[tex]\[ \text{Day 3: } 176.43 \text{ mg} \times 0.87 = 153.62 \text{ mg} \][/tex]

[tex]\[ \text{Day 4: } 153.62 \text{ mg} \times 0.87 = 133.67 \text{ mg} \][/tex]

[tex]\[ \text{Day 5: } 133.67 \text{ mg} \times 0.87 = 116.33 \text{ mg} \][/tex]

[tex]\[ \text{Day 6: } 116.33 \text{ mg} \times 0.87 = 101.28 \text{ mg} \][/tex]

[tex]\[ \text{Day 7: } 101.28 \text{ mg} \times 0.87 = 88.10 \text{ mg} \][/tex]

[tex]\[ \text{Day 8: } 88.10 \text{ mg} \times 0.87 = 76.69 \text{ mg} \][/tex]

Step 4:

Interpret the result.

After 8 days, approximately 76.69 mg of Bismuth-210 remains.

So, after 8 days, approximately 76.69 mg of Bismuth-210 remains.

You can use the law sines, which states that in a triangle the ratio between one side length and the sine of the opposite angle is constant.

So, we have

[tex]\dfrac{PR}{\sin(Q)}=\dfrac{QR}{\sin(P)}=\dfrac{PQ}{\sin(R)}[/tex]

In particular, we can use

[tex]\dfrac{PR}{\sin(Q)}=\dfrac{QR}{\sin(P)}[/tex]

to write

[tex]\dfrac{68}{\sin(73)}=\dfrac{47.6}{\sin(P)} \iff \sin(P) = \dfrac{47.6\sin(73)}{68}\approx 0.66[/tex]

Which means

[tex]P\approx \arcsin(0.66)\approx 42[/tex]

Answer:

D.

Step-by-step explanation:

Slope is rise over run by definition, and we are given the values for each in the problem.  The run is 80 and the rise is 15 so

[tex]m=\frac{15}{80}=\frac{3}{16}[/tex]

Answer:

103.62 cm

Step-by-step explanation:

Given : Diameter, D = 33 cm

circumference = πD = 3.14 x 33 = 103.62 cm

Hello, I believe your answer is C.

You can find your answer by plugging in the diameter into the circumference formula: 2πr² (You must divide your diameter in half to get the radius).

Answer:

c

Step-by-step explanation:

i think not 100 percent sure

Answer:

[tex]\large\boxed{(-7x+4)(-7x-4)}[/tex]

Step-by-step explanation:

[tex]\text{The difference of squares:}\ a^2-b^2=(a-b)(a+b)\\\\(-7x+4)(-7x-4)=(-7x)^2-4^2=49x^2-16[/tex]

(-7x + 4) (-7x - 4) can be written as a difference of squares.

Option C is the correct answer.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The difference of squares is a special algebraic form that occurs when we multiply two binomials of the form (a + b)(a - b).

This results in the product of two terms:

The square of the first term minus the square of the second term.

In other words, we have (a + b)(a - b) = a² - b².

In the given options, only (-7x + 4) (-7x - 4) can be written as a difference of squares, by applying the above formula.

We can rewrite it as:

(-7x + 4) (-7x - 4) = (-7x)² - 4² = 49x² - 16

The other options do not follow this pattern and cannot be written as a difference of squares.

Thus,

(-7x + 4)(-7x - 4) = 49x² - 16

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Answer:

573 L is im sure the correct answer

The correct answer is -2 ln|x + 1| + 3 ln|x + 2| + C which corresponds to option (a).

We are asked to evaluate the integral:

∫ (x - 1) ÷ (x² + 3x + 2) dx

First, factor the denominator:

x² + 3x + 2 = (x + 1)(x + 2)

This allows us to use partial fraction decomposition to rewrite the integral :

(x - 1) ÷ [(x + 1)(x + 2)] = A ÷ (x + 1) + B ÷ (x + 2)

Next, solve for A and B:

So, we can write :

(x - 1) ÷ [(x + 1)(x + 2)] = -2 ÷ (x + 1) + 3 ÷ (x + 2)

Integrate both terms separately :

∫ (-2 ÷ (x + 1)) dx + ∫ (3 ÷ (x + 2)) dx

This gives us :

-2 ln|x + 1| + 3 ln|x + 2| + C

Hence, the solution is :

-2 ln|x + 1| + 3 ln|x + 2| + C

The correct answer is option (a).

Complete Question :

Use Partial fraction expansion to evaluate : ∫ (x - 1) ÷ (x² + 3x + 2) dx

a. -2 ln|x + 1| + 3 ln|x + 2| + C   b. [tex]\frac{-2}{x+1}+\frac{3}{x+2}+C - 2 x + 1 + 3 x + 2 + C[/tex]

c. [tex]\frac{2}{\left(x+1\right)^2}+\frac{-3}{\left(x+2\right)^2}+C 2 ( x + 1 ) 2 + - 3 ( x + 2 ) 2 + C[/tex]

d. [tex]\frac{1}{\left(x+3+\frac{2}{x}\right)^2}+C 1 ( x + 3 + 2 x ) 2 + C[/tex]

Answer:

1. A: 0.25; B: 0.03; C: 1.41; D: -0.28

2. A: 0.39; B: 0.06; C: 40.30; D: 21.81

Step-by-step explanation:

For CDF lookups, we used the Excel NORMDIST(x, mean, stdev, TRUE) function. For inverse CDF lookups, we used the NORMINV(x, mean, stdev) function.

Each of these functions works with the area under the curve from -∞ to x, so for cases where we're interested in the upper tail, we subtract the probability from 1, or subtract the x value from twice the mean.

For question 1, we computed the Z values in each case. The NORMDIST function works directly with x, mean, and standard deviation, so does not need the z value.

Answer:

f(x) = 3x² - 12x  -135

Step-by-step explanation:

standard form of a quadratic equation is

y = Ax² + Bx + C

You are given 3 solutions for X and Y, i.e( x=-5, y = 0), (x = 9,y = 0) and  (x = 8,y = -39)

Substitute each of this equations into the quadratic equation  to obtain a system of 3 equations

For ( x=-5, y = 0), 25A - 5B + C = 0 ---------- eq (1)

For ( x= 9, y = 0), 81A + 9B + C = 0 ---------- eq (2)

For ( x= 8, y = -39), 64A + 8B + C = -39 ---------- eq (3)

You have 3 equations and 3 unknowns. Solving this system of 3 equations will give:

A = 3, B = -12, c = -135

Hence the quadratic equation is

y = 3x² - 12x -135

or in function form:

f(x) = 3x² - 12x  -135

Answer:

12 a. 4605 feet 12 b. 1,459,063 square feet

Step-by-step explanation:

For the perimeter, we simply add the lengths of each of the 5 sides together (or multiply 5 times one side length).

P = 5(921)

P = 4605 feet

For the area, we will use composition...add the area of the triangle to the area of the trapezoid.

For the area of the triangle, the formula is

[tex]A=\frac{1}{2}bh[/tex].

Filling in our values gives us

[tex]A=\frac{1}{2}(1490)(541)[/tex] and

A = 403,045 square feet.

Now for the trapezoid.  The formula for a trapezoid is

[tex]A=\frac{1}{2}(b_{1}+b_{2})(h)[/tex]

where the b's represent the bases and the h represents the height.  Filling in our values gives us

[tex]A=\frac{1}{2}(921+1490)(876)[/tex]

Work inside the parenthesis first:

[tex]A=\frac{1}{2}(2411)(876)[/tex] and

A = 1,056,018

Now we add those together to get that area of the Pentagon is 1,459,063 square feet

Answer:

CDI: 1.43/1.24x100= 115 What does this index mean? Good market potential.

Step-by-step explanation:

Answer: CDI: 1.43/1.24x100= 115 What does this index mean? Good market potential.

Step-by-step explanation:

Answer:

0.86 or 86%

Step-by-step explanation:

The data given represent 41% of people in a certain country like to cook and 68% of people in the country like to shop, while 14% enjoy both activities.

The probability that a randomly selected person in the country enjoys cooking or shopping or both.

People who like to cook P(C) = 41% = 0.40

People who like to shopping P(S) = 68% = 0.60

People who like cooking and shopping both P(C∩S) =  14% = 0.14

People who like cooking or shopping or both = P(C∪S)

                        = P(C) + P(S) - P(C∩S)

                        =  0.40 + 0.60 - 0.14

                        = 0.86

The probability that a randomly selected person in the country enjoys cooking or shopping or both is 0.86 or 86%

To calculate the probability that a selected person likes cooking or shopping or both, we add the probabilities of each individual event and subtract the overlapping probability. In this case, it's 94.1%.

You want to find the probability that a randomly selected person in the country enjoys cooking, shopping, or both. To calculate this probability, you can use the principle of inclusion-exclusion for two sets A and B, where:

The formula for the probability that a randomly selected person enjoys either cooking or shopping (or both) is:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Given:

Plug in the values:

P(A ∪ B) = 40.1% + 68% - 14%
= 94.1%

So, the probability that a randomly selected person enjoys cooking or shopping or both is 94.1%.

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