The following expressions are polynomials. What is the sum of the expressions (8x^(5)-5x^(3)+x^(2)) and (4x^(5)+3x^(4)-6x^(2))?

The the exact measurement of the height of the student is 6.279m.

A number can be expressed as a fraction of 100 using a percentage. It is frequently used, particularly in financial and statistical contexts, to depict ratios and proportions in a more practical and intelligible way. For instance, 50% denotes 50 out of 100, or half of a specified amount. It is represented by the letter "%".

Let's start by calculating the absolute error made in the measurement of the height of the pole:

Absolute error = 5% of 5.98m = 0.05 x 5.98m = 0.299m

If the actual height is 0.299m more than the measured value, then the actual height would be:

Actual height = 5.98m + 0.299m

                      = 6.279m

Therefore, the exact height is 6.279m.

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The surface area of the cylinder would be SA = 2π(1.6)² + 3.2π(3.8) square feet.

Option (A) is correct.

What is the surface area of the cylinder?

The surface area of a cylinder can be calculated using the following formula:

SA = 2πr² + 2πrh

where r is the radius of the circular base of the cylinder, h is the height of the cylinder, and π is the mathematical constant pi, approximately equal to 3.14159.

The surface area of a cylinder is the sum of the areas of its top and bottom circles, plus the area of its lateral surface (the curved surface that connects the two circles). The lateral surface area of a cylinder is found by multiplying the height of the cylinder by the circumference of one of its circular bases. Therefore, the correct method to calculate the surface area of the cylinder with diameter labeled 3.2 feet and height labeled 3.8 feet is:

SA = 2π(1.6)² + 3.2π(3.8)

So, the correct answer is:

SA = 2π(1.6)² + 3.2π(3.8) square feet

Hence, the surface area of the cylinder would be SA = 2π(1.6)² + 3.2π(3.8) square feet.

Option (A) is correct.

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Water turning to blood will be the first plague that will be present.

Both humans as well as mammals can contract the plague. The protozoan parasite is the bacterium that causes it. The most common ways for humans to contract the plague are through handling a plague-infected animal or by getting bitten by a rodent bug that is carrying the disease.

The 10 plagues in the correct order are:

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Explanation:

There are 4 white marbles out of 4+10 = 14 total

4/14 = 2/7 is the probability of randomly picking a white marble.

(2/7)*(2/7) = 4/49 is the probability of picking two whites in a row, when the first marble is replaced.

Use a calculator to find that 4/49 = 0.0816 approximately.

That converts to 8.16% after moving the decimal point two spots to the right. This is equivalent to multiplying by 100.

This person has walked a total of 22 miles. The total displacement vector for this walk is 10.06 miles at an angle of 12.58°. If this person walked straight home, they'd have to walk 10.06 miles.

To find the total displacement vector for this walk, we can use the Pythagorean Theorem to find the magnitude of the displacement vector and the direction of the displacement vector.

First, let's find the magnitude of the displacement vector:

d = √((Δx)² + (Δy)²)

Where Δx is the change in the x-direction and Δy is the change in the y-direction.

Δx = 5 + 4cos(45°) + 0 + 3cos(225°) + 4 = 9.83 miles
Δy = 0 + 4sin(45°) + 6 + 3sin(225°) + 0 = 2.17 miles

d = √((9.83)² + (2.17)²) = √(96.58 + 4.71) = √(101.29) = 10.06 miles

So, the magnitude of the displacement vector is 10.06 miles.

Next, let's find the direction of the displacement vector:

θ = tan⁻¹(Δy/Δx) = tan⁻¹(2.17/9.83) = 12.58°

So, the direction of the displacement vector is 12.58°.

Therefore, the total displacement vector for this walk is 10.06 miles at an angle of 12.58°.

If this person walked straight home, they'd have to walk 10.06 miles.

This person has walked a total of 22 miles. The total displacement vector for this walk is 10.06 miles at an angle of 12.58°. If this person walked straight home, they'd have to walk 10.06 miles.

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If Jen has 72 green marbles, then she has 81 purple marbles.

If Jen has 8 green marbles for every 9 purple marbles, then the ratio of green marbles to purple marbles is 8:9.

If Jen has 72 green marbles, we can use this ratio to determine how many purple marbles she has.

Let's set up a proportion

8/9 = 72/x

where x is the number of purple marbles Jen has.

To solve for x, we can cross-multiply:

8x = 9 × 72

Multiply the terms

8x = 648

Move 8 to right hand side

x = 648 / 8

Divide the numbers

x = 81

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Answer:

Hi

Step-by-step explanation:

im pretty sure this the answer

hope this helps

good luck;)

Answer:

y≤7

Step-by-step explanation:

-8y+25≤-31

take away 25 from both sides

-8y≤-56

then divided by -8 on both sides

y≤7

The probability of escape for the guest is approximately 9 - √27/4.

This can be calculated using the principle of inclusion-exclusion. To calculate the probability of escape, we can calculate the probability of the guest being unable to move from Room 0 to any of the other rooms.

This is the probability of all doors from Room 0 being locked, which is equal to 1/3 x 1/3 = 1/9. Therefore, the probability of escape is 1 - 1/9 = 8/9.

Using the inclusion-exclusion principle, we can calculate the probability of the guest being able to move from Room 0 to any of the other rooms. The probability of the guest being able to move from Room 0 to any of the other rooms is equal to 1 - (1/3 + 1/3 - 1/9) = 9 - √27/4.

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The equation of the tangent line of y = sqrt(3x) passing through (3, 3) is y = (1/2)x + 3/2.

To use Descartes' method of slopes, we need to find the derivative of the function first.

Taking the derivative of y = sqrt(3x) gives:

y' = (1/2) * (3x)^(-1/2) * 3 = (3/2√(3x))

Now we can find the slope of the tangent line at (3, 3) by plugging in x = 3 into the derivative:

y' = (3/2√(3*3)) = 3/6 = 1/2

So the slope of the tangent line is 1/2.

Next, we use the point-slope form of a linear equation to find the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (3, 3).

Plugging in the values, we get:

y - 3 = (1/2)(x - 3)

Simplifying, we get:

y = (1/2)x + 3/2

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a. The probability that a randomly sampled individual has two copies of the C allele is 0.0169.
b. The probability that a randomly sampled individuTherefore, the answers are:
al is a homozygote is 0.7074.
c. The probability that a randomly sampled individual is AS is 0.0332.
d. The probability that a randomly sampled individual is AS or AC is 0.1411.

The probability of an individual having two copies of the C allele can be calculated using the formula for the probability of independent events: P(CC) = P(C) x P(C) = 0.13 x 0.13 = 0.0169.

The probability of an individual being a homozygote can be calculated by adding the probabilities of having two copies of each allele: P(AA) + P(SS) + P(CC) = (0.83 x 0.83) + (0.04 x 0.04) + (0.13 x 0.13) = 0.6889 + 0.0016 + 0.0169 = 0.7074.

The probability of an individual being AS can be calculated using the formula for the probability of independent events: P(AS) = P(A) x P(S) = 0.83 x 0.04 = 0.0332.

The probability of an individual being AS or AC can be calculated by adding the probabilities of each event: P(AS) + P(AC) = 0.0332 + (0.83 x 0.13) = 0.0332 + 0.1079 = 0.1411.

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when dividing x^(4)-3x^(3)-7x^(2)-80 by x-5, the remainder will be -5.

The given polynomial equation is x^(4)-3x^(3)-7x^(2)-80 and we have to divide it by x-5 to find the remainder.

Set up the long division as follows:
```
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
```

Divide the first term of the dividend (x^(4)) by the first term of the divisor (x) to get the first term of the quotient (x^(3)):
```
x^(3)
_______
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
```

Multiply the first term of the quotient (x^(3)) by the divisor (x-5) and write the result below the dividend:
```
x^(3)
_______
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
    x^(4) - 5x^(3)
```

Subtract the result from the dividend to get the new dividend:
```
x^(3)
_______
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
    x^(4) - 5x^(3)
    --------------
         2x^(3) - 7x^(2)
```

Repeat the process with the new dividend until the degree of the remainder is less than the degree of the divisor:
```
x^(3) + 2x^(2) + 3x + 15
______________________
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
    x^(4) - 5x^(3)
    --------------
         2x^(3) - 7x^(2)
         2x^(3) - 10x^(2)
         ---------------
               3x^(2) + 0x
               3x^(2) - 15x
               ------------
                    15x - 80
                    15x - 75
                    --------
                         -5
```

The remainder is -5. Therefore, when dividing x^(4)-3x^(3)-7x^(2)-80 by x-5, the remainder will be -5.

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Answer:

If 41 grams of sugar is 14% of the normal daily allowance for sugar, we can set up a proportion to solve for the recommended amount:

41 grams / x = 14% / 100%

where x is the recommended amount of sugar.

To solve for x, we can cross-multiply and simplify:

41 / 0.14 = x / 1

x = 292.86

Rounding to the nearest gram, the recommended amount of sugar in a normal diet is approximately 293 grams.

The trigonometric equation [tex]\frac{2tanx}{1+tan^2x}[/tex] is equivalent to sin2x

An equation is an expression that shows how numbers and variables are related using mathematical operators like exponent, addition, multiplication, subtraction and division.

Trigonometric identity is used to show relationship between trigonometric functions. Some examples are:

1 + tan²x = 1/cos²x; tanx = cosx/sinx; sin2x = 2sinxcosx

Given:

[tex]\frac{2tanx}{1+tan^2x} \\\\but\ 1+tan^2x=\frac{1}{cos^2x};substituting:\\ \\= \frac{2tanx}{\frac{1}{cos^2x} } \\\\=2tanx*cos^2x\\\\=2*\frac{sinx}{cosx}*cos^2x\\ \\=2sinxcosx[/tex]

= sin2x

The trigonometric equation are equivalent.

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The equivalent expression to the given one is:

y⁸*y³*x⁰*x⁻² = y¹¹*x⁻²

We start with the expression:

y⁸*y³*x⁰*x⁻²

Remember the exponent rule for products of powers with the same base, it says that we can write:

xᵃ*xᵇ = xᵃ⁺ᵇ

So we just add the two exponents.

Using exponent rules, we can rewrite the product as

y⁸*y³*x⁰*x⁻² = y³⁺⁸*x⁰⁻² = y¹¹*x⁻²

That is the equivalent expression.

Then we can write:

y⁸*y³*x⁰*x⁻² = y¹¹*x⁻²

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The values of x if the distance between the points (x, 4) & (3, x) be 131/2 are approximately 9.39 and -4.39.

To find the values of x if the distance between the points (x, 4) & (3, x) be 131/2, we can use the distance formula:

D = √((x2 - x1)² + (y2 - y1)²)

Where D is the distance, (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the given values, we get:

131/2 = √((3 - x)² + (x - 4)²)

Squaring both sides and simplifying, we get:

169 = (3 - x)² + (x - 4)²

Expanding and rearranging, we get:

2x² - 14x - 110 = 0

Using the quadratic formula, we can find the values of x:

x = (-(-14) ± √((-14)² - 4(2)(-110))) / (2(2))

x = (14 ± √(196 + 880)) / 4

x = (14 ± √1076) / 4

x ≈ 9.39 or x ≈ -4.39

So the values of x are approximately 9.39 and -4.39.

Therefore, the values of x if the distance between the points (x, 4) & (3, x) be 131/2 are approximately 9.39 and -4.39.

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The end behavior is as x approaches negative infinity, f(x) approaches negative infinity as x approaches positive infinity, f(x) approaches negative infinity The only x-intercept of f(x) is x = 3.

The given function is f(x) = -x³ + 2x² + 3

1. End behavior:

As the leading coefficient of f(x) is negative, -x^3 dominates the behavior of the function as x approaches negative or positive infinity. Therefore, the end behavior of the function is:

2. X-intercepts:

To find the x-intercepts of f(x), we need to solve the equation f(x) = -x^3 + 2x^2 + 3 = 0. We can factor out a common factor of -1 to simplify the equation:

-x^3 + 2x^2 + 3 = 0

x^3 - 2x^2 - 3 = 0

Using synthetic division or long division, we can find that one of the roots of this equation is x = 3. We can then factor out (x - 3) using polynomial division to find the other two roots:

x^3 - 2x^2 - 3 = (x - 3)(x^2 + x + 1)

The quadratic factor x^2 + x + 1 has no real roots, so the only x-intercept of f(x) is x = 3.

3. Positive/negative:

To determine the sign of f(x) for different values of x, we can look at the sign of each factor in the polynomial:

Putting these together, we can make the following sign chart for f(x):

x                         f(x)

x < 0                   -

0 < x < 3                  +

x > 3                  -

4. Multiplicity:

The only root of f(x) is x = 3, which has multiplicity 1. This means that the graph of f(x) crosses the x-axis at x = 3 and changes sign at that point.

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The logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex] can be translated into the equivalent exponential statement [tex]4^(-2)=(1)/(16)[/tex].

The logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex] can be translated into an equivalent exponential statement by using the definition of logarithms. The definition of logarithms states that if [tex]log_(b)(a)=c[/tex], then [tex]b^c=a.[/tex]

Using this definition, we can translate the logarithmic statement[tex]log_(4)(1)/(16)=-2[/tex] into an equivalent exponential statement by rearranging the terms.

The equivalent exponential statement would be[tex]4^(-2)=(1)/(16)[/tex]. This means that 4 raised to the power of -2 is equal to 1/16.

So, the logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex]can be translated into the equivalent exponential statement[tex]4^(-2)=(1)/(16)[/tex].

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The x-intercepts of y=x2+5x−24 can be determined by solving the equation 0=x2+5x−24. Using the quadratic formula, we can find that x = 6 and x = -4 are the two x-intercepts.

The x-intercepts of y=x2−11x+10 can be determined by solving the equation 0=x2−11x+10. Using the quadratic formula, we can find that x = 5 and x = -2 are the two x-intercepts.
To determine the x-intercepts of the given functions, we need to find the values of x that make y equal to 0. We can do this by factoring the equations and setting each factor equal to 0.

2. y = x^2 + 5x - 24
0 = x^2 + 5x - 24
0 = (x + 8)(x - 3)
x + 8 = 0 or x - 3 = 0
x = -8 or x = 3

The x-intercepts are (-8, 0) and (3, 0).
3. y = x^2 - 11x + 10
0 = x^2 - 11x + 10
0 = (x - 1)(x - 10)
x - 1 = 0 or x - 10 = 0
x = 1 or x = 10

The x-intercepts are (1, 0) and (10, 0).
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Answer:

35

Step-by-step explanation:

(7/20) *100=35

This is why because if 20 percent is equal to 7, so 40 % will be 14, 80% 28 and 100% will be 35

Answer: 35 dolls

Step-by-step explanation:

7/x and 20/100

20 times 5 is 100

and 7 times 5 is 35. Therefore 35 dolls are in Anita’s collection

Answer:

if we follow the rule using y=mx+c, we would use rise and run so the distance is 3 up and 4 run.

7 total distance i guess.....i hope this helps.

The transformation applied to the function f(x) is a translation of 4 units up.

Here we can see that:

f(x) = √(x + 3)

and g(x) is a vertical translation of k units:

g(x) = f(x) + k

To get the value of k, just look how many units the graph has been translated up ( remember that each of the smalls squares in the coordinate axis represents a single unit), we can see that it is 4 units up, then k = 4

We have a vertical translation of 4 units up.

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The coefficient a in the factorization [ x²+a x y+b y²=(x+5 y)(x-4 y) ] is -1. The correct answer is C

Terms are the sum of the numbers or variables, factors are the sum of the numbers or variables multiplied, and coefficient is the number multiplied by the variable.

To find the coefficient a, we can expand the right side of the equation and compare it to the left side.

Expanding the right side gives us: [ (x+5 y)(x-4 y)=x²-4 x y+5 x y-20 y² ]

Simplifying the right side gives us: [ x²+x y-20 y² ]

Comparing this to the left side of the equation, we can see that the coefficient a is -1.

Therefore, the correct answer is c. ( -1 ).

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Answer:

y = (4/3)x + 2/3

The y-intercept is the value of y when x is equal to zero. So we can substitute x = 0 into the equation and solve for y:

y = (4/3)(0) + 2/3 = 2/3
The y-intercept of the line y = (4/3)x + 2/3 is 2/3.

Step-by-step explanation:

Answer:

The y-intercept is (2/3)

Step-by-step explanation:

I will assume that the equation is missing the "x," and will rewrite is as:

 y = (4/3)x + (2/3)

This is in standard form of y = mx + b, where m is the slope and b is the y-intercept.

The slope is (4/3) and the y-intercept is (2/3)

According to the information, it can be predicted that the number of missed shots after six weeks of practice is zero (0).

To calculate the number of lost shots after six weeks of practice, we must take into account the function that relates the weeks of practice with lost shots. In this case we must replace the value of X that corresponds to the weeks of practice and we will obtain as a result the amount of lost shots as shown below:

According to this function, we can infer that after six weeks of practice there will be 0 missed shots.

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The value of g(f(x)) is  3x^(2)+23x+44.

To find g(f(x)), we need to substitute the expression for f(x) into the expression for g(x). This means that wherever we see an "x" in the expression for g(x), we will replace it with the expression for f(x).

g(f(x)) = 3(f(x))^(2)-7(f(x))+4

Now we can substitute the expression for f(x) into the equation:

g(f(x)) = 3(x+5)^(2)-7(x+5)+4

Next, we need to simplify the expression by expanding the squared term and distributing the -7:

g(f(x)) = 3(x^(2)+10x+25)-7x-35+4

g(f(x)) = 3x^(2)+30x+75-7x-35+4

Finally, we can combine like terms to get the polynomial in standard form:

g(f(x)) = 3x^(2)+23x+44

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The answer to the question is that \( A_{1} \) is smaller than \( A_{2} \)

To begin, it is important to note that the terms "emalier" and "5PRECALC7" are not relevant to the question and can be ignored. Additionally, there are several typos and extraneous information that can also be ignored. The main focus of the question is to determine the relationship between \( A_{1} \) and \( A_{2} \).

From the information provided, it is clear that \( A_{1} \) is smaller than \( A_{2} \). This is because the value of \( A_{1} \) is given as 2, while the values of \( b \) and \( c \) are 27 and 33, respectively. Since \( A_{2} \) is the sum of \( b \) and \( c \), it is clear that \( A_{2} \) is larger than \( A_{1} \).

Therefore, the answer to the question is that \( A_{1} \) is smaller than \( A_{2} \).

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Jane deposits $1,250 quarterly into a retirement account that pays interest at the rate of 3.25% per year compounded continuously. At the end of 10 years, she will have $60,358.28 in her account. The correct answer is option 4

To solve the problem, we can use the formula for continuous compounding given by:[tex]A = Pe^{rt}[/tex], where,A is the amount at the end of the investment period, P is the principal (the initial amount deposited), e is Euler's number, which is approximately equal to 2.71828, r is the annual interest rate (expressed as a decimal), t is the time period in years

In this problem, P = $1,250, r = 0.0325 (3.25% as a decimal), and t = 10 years. We need to find A, the amount at the end of 10 years. Substituting the values in the formula, we get:

[tex]A = 1250e^{0.0325 × 10} ≈ $60,358.28.[/tex]

Therefore correct answer is option 4

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The effective interest rate for the specified account is 6.70%.

To find the effective interest rate, we can use the following formula:
Effective Interest Rate = (1 + Nominal Yield / Number of Compounding Periods) ^ Number of Compounding Periods - 1

In this case, the nominal yield is 6.5% and the number of compounding periods is 12 (since it is compounded monthly). Plugging these values into the formula, we get:

Effective Interest Rate = (1 + 0.065 / 12) ^ 12 - 1
Effective Interest Rate = (1.0054166666666667) ^ 12 - 1
Effective Interest Rate = 1.0670171619870418 - 1
Effective Interest Rate = 0.0670171619870418

Multiplying by 100 to convert to a percentage, we get:

Effective Interest Rate = 6.70%

Therefore, the effective interest rate for the specified account is 6.70%.

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Answer: First Picture 100:60  = The answer is A. 5:3 | The Second Picture  K/12=8/24 the answer is A. k=4  | Third Picture is A. 4 | Fourth Picture answer is B. 4 teachers for every 64 students | And Final Picture answer is D. 9.33 miles per hour, Wendy Was Faster. | Hope this helps out today!!

Step-by-step explanation: Its simple math its just either x2 or what's it divided off