Find the radius of a cylinder whose height is 10 cm and the total surface area is 352 cm².

A polynomial function of degree 3 with real coefficients and given zeros of -3, -1, and 4 is 4(x - 4)(x + 3)(x + 1) for which f(-2) = 24.

Any modifying value connected to a variable through multiplication is referred to as a "coefficient." Any non-imaginary number is a "real" number

How do you locate a degree 3 polynomial with real coefficients?

A polynomial of degree 3 must take the form a(xr1)(xr2)(xr3) since it has three roots. We are provided with the roots 3, 1, and 4. So, all we have to do is change these to r1, r2, and r3. We now get a(x+3)(x+1)(x4).

We must first factor the provided polynomial equation into a linear and quadratic equation in order to obtain the roots of the three-degree polynomial. The zeros of the three-degree polynomial can then be easily found.

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Answer:

$8303.75

Step-by-step explanation:

(6000x1.025^2)+2000=8303.75

Applying synthetic division, the quotient between 8x³ + 26x² + 19x + 3 by 4x + 3 is:

2x² + 5x + 1.

In this context of this problem, the coefficients of the polynomial 8x³ + 26x² + 19x + 3 are given as follows:

8, 26, 19 and 3.

The divisor is found as follows:

4x + 3 = 0

4x = -3

x = -3/4

x = -0.75.

The resulting coefficients of the quotient are given as follows:

8, 20, 4 and remainder of 0.

Hence the quotient is:

8x² + 20x + 4.

Which can be simplified as:

2x² + 5x + 1.

The first coefficient of the polynomial, of 8, was moved down, the multiplied by -0.75 and added to 26, resulting in 20. Then the same procedure was done with 20(multiplied with -0.75 and added with the next coefficient of 19), until the last coefficient of 3.

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Answer:

2a

Step-by-step explanation:

8a² / 4a

8/4 a²-¹

2a

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Answer:

2a

Step-by-step explanation:

8a^2 = 4a x 2a

8a^2 ➗ 4a

= ( 4a x 2a )/4a

= 2a

Answer:

x=9

y=27

Step-by-step explanation:

the scale factor is [tex]\frac{4}{3}[/tex] so 6 × [tex]\frac{4}{3}[/tex] is x - 1

x-1 is 8

so x is 9.

Base on congruency of vertical angles, the value of z is 7.

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

In other words, vertically opposite angles are angles that opposed each other at one specific vertex, and are formed by two straight intersecting line.

Vertically opposite angles are congruent to each other.

Therefore,

7z + 7 = 9z - 7

subtract 9z from both sides of the equation

7z + 7 = 9z - 7

7z - 9z + 7 = 9z - 9z - 7

-2z + 7 = - 7

subtract 7 from both sides of the equation

-2z + 7 = - 7

-2z + 7  - 7 = - 7 - 7

- 2z = - 14

divide both sides by - 2

z = - 14 / -2

Therefore,

z = 7

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Answer:

Step-by-step explanation:

y>3x+1

y≤-2x-4

Answer

Check Explanation

Explanation

a ≡ b (mod n)

This means a and b have the same remainder when they are divided by n

So, to check if this question works out, we divide what is on the left hand side and what is on the right hand side by what is after the mod.

1) 67 × 73 ≡ 1 × 3 (mod 5)

4891 ≡ 3 (mod 5)

So, to check,

(4891/5) = 978 remainder 1

(3/5) = 0 remainder 3

The remainders are different.

So, this equation is wrong and does not work.

This equation is false.

2) 83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)

Noting that it is the units digit that determines the remainder

3 raised to the power of a multiple of 4 gives 81 raised to the power of a positive integer

5 raised to power of a multiple of 4 gives 625 raised to the power of a positive integer

So, using these numbers,

83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)

81 ≡ 625 (mod 17)

(81/17) = 4 remainder 13

(625/17) = 36 remainder 13

The remainders are the same.

So, this equation is correct and it works.

This equation is true.

Hope this Helps!!!

The interval is from 0.9330 to 0.9350

For given condition;

mean = 0.9340

standard deviation = 0.0030

z-score at 98% = 2.33

n = size of sample = 47

Step 1: calculate the standard error of the mean

standard error of mean  =  z-score * standard deviation/sqrt(n)

                                        =  2.33 * 0.0030/[tex]\sqrt{47}[/tex]

                                        = 0.0010

step 2: upper limit  =  mean + standard error

                                =  0.9340 + 0.0010

                                = 0.9350

           lower limit  =  mean - standard error

                              =  0.9340 - 0.0010

                              = 0.9330

Hence, the interval is from 0.9330 to 0.9350

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The room numbers of two adjacent classrooms are 359 and 361.

What is consecutive odd numbers?

Consecutive odd numbers are odd integers that are separated by 2 and come after one another.

Suppose the first odd number is x, then the another consecutive odd number is x + 2.

The sum of these two numbers is 720.

So,

x + (x + 2) = 720

2x + 2 = 720

2x = 718

x = 359

Therefore, the first odd number is 359 and the second add number is 361 which gives the sum 720.

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The least number of distinct values that can occur in the list is 225.

The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. However, occasionally there is either no mode or more than one mode. When every observed value occurs exactly once in a data collection, there is no mode.

The mode appears 10 times. That leaves 2008 numbers.

The least number of distinct values will occur if all but one of the remaining values appears 9 times

= 2008/9

=223 1/9.

So, The list can include a maximum of 225 distinct values, with the mode appearing 10 times, 223 other values nine times, and the last value once.

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Answer:

-4

Step-by-step explanation:

6 + 4x-y = 6 + (4x-y) = 6 + (-10) = -4

step 1

Find the slope of the line represented by the table of values

take the points

(-8,13) and (-4,5)

m=(5-13)/(-4+8)

m=-8/4

m=-2

step 2

Write the equation of the line that contains the point (-8,6) and has the same slope as the line represented by the table

y=mx+b

we have

m=-2 -----> the same slope of the given line

point (-8,6)

substitute in the equation of the line in slope intercepot form

6=-2*(-8)+b

solve for b

6=16+b

b=-10

therefore

teh equatiion of the line is

Answer:

x = 114

Step-by-step explanation:

since the triangles are congruent then corresponding angles are congruent, then

∠ C = ∠ D , that is

x + 18 = 132 ( subtract 18 from both sides )

x = 114

Answer: 160 mg

Step-by-step explanation:

10% of 200 is 20

therefore, every 6 hours, 20 milligrams of medicine filters into your blood.

there are 24 hours in a day, and 48 hours in 2 days.

6 * 4 = 24

20 * 4 = 80

you get 80 mg of medicine every day.

80 * 2 = 160

you get 160 mg of medicine in two days.

The beam of light along the shoreline when it is 1 km from P is moving at 125.66 km/min.

Given that, a lighthouse is located on a small island 4 km away from the nearest point P.

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

[tex]\frac{d\theta}{dt}[/tex] = 6 rev/min

= 6π rad/min

tan θ = x/6

[tex]\frac{d}{dt}tan\theta=\frac{d}{dt}(\frac{x}{6} )[/tex]

[tex]sec^2\frac{d\theta}{dt} = \frac{1}{6}(\frac{dx}{dt} )[/tex]

[tex]\frac{dx}{dt}=6sec^2\theta\frac{d\theta}{dt}[/tex]

At x=1 km; tan θ= x/6 = 1/6

[tex]sec^2 \theta= 1+tan^2 \theta= 1 + (\frac{1}{6})^2[/tex]

[tex]sec^2 \theta = \frac{10}{9}[/tex]

[tex]\frac{dx}{dt} = 6 sec^2\theta \frac{d\theta}{dt}[/tex]

dx/dt = 6 × 10/9 × 6π

dx/dt = 125.66 km/min

Therefore, the beam of light along the shoreline when it is 1 km from P is moving at 125.66 km/min.

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The faster driving rate of Goldie is 20 miles/hour.

Given that, by driving 10 miles per hour faster, Goldie was able to have 2 hours and 30 minutes off her 50-mile trip.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Here, Speed = 10 miles/hour, Time = 2 hours and 30 minutes = 2.5 hours  and Distance = 50 mile.

Now, Distance = Speed × Time

Let the faster driving rate be x.

50 = x × 2.5

⇒ x = 50/2.5

⇒ x = 20 miles/hour

Therefore, the faster driving rate of Goldie is 20 miles/hour.

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Answer:

Step-by-step explanation:

I don't agree with the other answer.

You need to you systems of equations

So

d=50     t=t-2.5       x=r+10

d=rt

50=(r+10)(t-2.5) (faster equation)

50=rt (slower equation)

t=[tex]\frac{50}{r}[/tex]   (substitute into faster equation)

50 = (r+10)(50/r -2.5)                mult both sides by r to get rid of fraction

50r = (r+10)(50-2.5r)                 FOIL

50r = 50r -2.5r² + 500 -25r     Simplify

2.5r²+25r-500=0                      divide all by 2.5

r²+10r-200                                 factor

(r-20)(r+10)                                 eliminate negative answer

r=20

x=r+10  =20+10 =30 mph

The graph of the equation -4x = -60 is shown below.

A vertical line is expressed as the equation, x = b. Here, the variable "b" is the point on the x-axis where the line intercepts the horizontal axis.

Thus, to plot the graph for a vertical line with the equation, x = b, we would simply draw a vertical line that crosses the x-axis at point b.

Given the equation, -4x = -60, rewrite the equation in the form x = b, to determine the value of b:

-4x/-4 = -60/-4 [division property of equality]

x = 15

This means that the graph of the equation, -4x = -60, would be a graph that has a vertical line that crosses the x-axis at 15.

the graph is shown below.

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The height is the sum of 39 and 9 times the number of boxes, n. The rule is 9n + 39.

An algebraic expression is defined as the type of expression that is made up of a variable, a coefficient and a constant.

From the given box of nails,

The height of 2 boxes of nails = (9× 2) + 39 = 57 In

The height of 3 boxes of nails = ( 9 × 3) + 39 = 66 In

The height of 4 boxes of nails = ( 9× 4) + 39 = 75 ln

That is to say that the height of the box above the floor can be calculated by the sum of 39 and 9 times the number of boxes, n.

Therefore, the rule of heights is 9n + 39 where n is the number of boxes present.

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Answer:

Tip- $5.16

Total cost- $33.86

Step-by-step explanation:

To find a 18% tip, turn 18% into 0.18.

Multiply 28.67 by 0.18.

28.67x0.18=

5.16

If you add that to the bill, it would be 33.86

The quadratic formula for a polynomial is given by:

Therefore, option (C) is correct.

By central limit theorem ,with a large random sample, the sample histogram will not closely resemble the normal curve but with a large random sample, the probability density function of the sample mean closely resembles the normal curve.

The central limit theorem for samples says that if we keep drawing larger and larger samples and calculating their means, the sample forms their own normal distribution (the sampling distribution). The normal distribution will have the same mean as the original distribution and a variance that equals the original variance divided by the sample size. The variable n is the number of values that are averaged together,and not the number of times the experiment is done.

Hence,with a large random sample, the sample histogram will not resemble the normal curve but with a large random sample, the probability density function of the sample mean will closely resemble the normal curve.

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An integer number is a number that can be written without using a rational component. In other words, if a number can be written without using a fraction, then that number is considered an integer.

For example, let's take the first number:

This number is written as a fraction. But, this is also equivalent to:

Since it can also be written without making use of a fraction then this number is an integer.

Also, there are numbers that are written in decimal form. For example:

These types of numbers are not integers.

The correct option regarding the ratio is given as follows:

For a ratio of 3:2, divide AB into 5 equal parts. Each equal part is 2 units, so the point that divides AB into a 3:2 ratio is 2.

A ratio of an amount a over a total amount a + b is given as follows:

r = a/(a + b) = a:b.

In the context of this problem, the ratio is given as follows:

r = 3:2.

Hence the number of equal parts is given by:

equal parts = 3 + 2 = 5.

The length of the segment is:

B - A = 6 - (-4) = 10 units.

Hence the length of each equal part is:

length equal part = 10/5 = 2.

The point that is 3/5 of the way from point -4 to point 6 is found as follows:

x - (-4) = 3/5(6 - (-4))

x + 4 = 30/5

x + 4 = 6

x = 2.

Meaning that the correct option is given by the last one.

The coordinates of A and B are missing, and they are given as follows:

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The correct option regarding the scale and the origin of the graph are as follows:

D.

x-axis scale: 1 unit = 1 week

y-axis scale: 1 unit = 150 minutes

origin: (0 weeks, 0 minutes)

The scale should be chosen focusing on improving the readability of the data-set by the reader, while the origin should be chosen according to the values assumed by the variables.

In the context of this problem, the values of x, in weeks, are:

2, 3, 4, 5, 6, 7, 8.

They increase by one, hence the scale of x should be of 1 unit = 1 week.

The values of y, in minutes are given as follows:

300, 450, 600, 750, 900, 1050, 1200.

They increase by 150, hence the scale of y should be of 1 unit = 150 minutes, which is the rate of change of the problem.

As the measures are both positive values, the origin should be of (0,0), hence the correct option for the scales and the origin is option D.

The table is:

Weeks Minutes

2 300

3 450

4 600

5 750

6 900

7 1,050

8 1,200

The options are:

A. x-axis scale: 1 unit = 2 weeks

y-axis scale: 1 unit = 50 minutes

origin: (0 weeks, 0 minutes)

B. x-axis scale: 1 unit = 2 weeks

y-axis scale: 1 unit = 150 minutes

origin: (2 weeks, 300 minutes)

C. x-axis scale: 1 unit = 1 week

y-axis scale: 1 unit = 50 minutes

origin: (2 weeks, 300 minutes)

D. x-axis scale: 1 unit = 1 week

y-axis scale: 1 unit = 150 minutes

origin: (0 weeks, 0 minutes)

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The parent function of the quadratic function is

∵ x is added by 7

∴ The graph of the function is translated 7 units to the left

∴ The image of the function will be

∵ The function is added by -4

∴ The graph of the function translated 4 units down

∴ The image of the function will be

The transformation is

Shift 7 units left and shift down 4

The answer is D

SOLUTION

We want to solve the equation

cross multiplying, we have

Hence the answer is x = 2, the first option

From the given diagram, let's find the length of the park's boundary.

We can see the side of the park's boundary is a circular arc and the top and bottom are the bases of triangles.

To find the length of the circular sides, apply the length of arc formula:

Where:

Θ = 120 degrees

π = 3.14

radius, r = 50 yards

Hence, we have:

This means the length of one circular side of the boundary is 104.67 yards.

We have two circular sides of the boundary.

The top and bottom sides form equilateral traingles.

Hence, the length of the top and bottom sides are 50 yards each.

To find the total length of the boundary, we have:

Total length = 104.67 + 104.67 + 50 + 50 = 309.34 yards

Rounding off to the nearest yard, the length of the park's boundary is:

309 yards

ANSWER:

D. 309 yards

Devon can have 6 candy bars and 3 sports drinks when he has $15 to spend.

According to the question,

We have the following information:

Devon has $15.

Cost of 1 candy bar = $1

Cost of 1 sports drink = $3

Devon wants to purchase at most 10 items.

It means that the total items should be less than or equal to 10.

Now, we have to spend $15 in such a way that number of items should be less than or equal to 10.

Now, we will look for the number of items for sports drink and change the number of candy bars accordingly.

Let's take 1 sports drink:

$3

We are left with $12. Now, there will be 12 candy bars.

So, this can not satisfy our conditions.

Let's take 2 sports drink:

$6

We are left $9. Now, there will be 9 candy bars. And the number of items is 11.

(This is not satisfying our condition.)

Let's take 3 sports drink:

$9

We are left with $6. Now, there will be 6 candy bars. And the number of items is 9.

This is satisfying all the conditions.

Hence, Devon can have 6 candy bars and 3 sports drinks when he has $15 to spend on snacks.

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Answer:

A

Step-by-step explanation:

ax + by = c  Subtract ax from both sides

by = -ax + c  Divide all the way through by b

[tex]\frac{by}{b}[/tex] = [tex]\frac{-a}{b}[/tex] x + [tex]\frac{c}{b}[/tex]

y = - [tex]\frac{a}{b}[/tex] x +[tex]\frac{c}{b}[/tex]