Form a polynomial whose real zeros and degrees are given
Zeros: -2, 0, 7
Degree: 3
Type a polynomial with integer coefficients and a leading coefficient of 1
f(x)= ?

Answer:

16%

Step-by-step explanation:

1) Mean, u = 100 

standard deviation, o = 15

Score specified = x = 115

so, z-score = (x - u)/o

                   = (115 - 100)/15 = 1

From the probability standard normal distribution curve, 84.13% of the test scores falls within 1 SD (z score = 1), so, the percentage of test scores below 115 is 84.13%, so, for the percentage of test scores of 115 or higher = 100% - 84.13% = 16%.

Therefore, the correct answer is 16%.

Answer:

y = [tex]\frac{1}{5}[/tex] x + 7

Step-by-step explanation:

y = mx + b  

You need to find m (the slope) and b (y-intercept)

If you start a the far left point and go to the next point that is graphed on the line, you will see that you moved up 1 space and right 5 to land back on the line.  This is your rise / run.  The slope is 1/5.

The y -intercept is where the line crosses the y axis.  It crosses at 7

Answer:

x = 90°

y = 43°

Step-by-step explanation:

<B is equal to 47 because their opposite sides are equal.  We are shown the <BAD = <CAD, which means that line segment AD is a bisector of BC.  This makes x = 90

The sum of the interior angles of a triangle add to 180

180 - 47 -47 = 86

The measure of  < BAC is 86  we need to divide this by 2 to find y

86/2 = 43

The variance of the murder rate data is approximately 4.83, and the standard deviation is approximately 2.20.

To find the variance and standard deviation of the murder rate data, we first need to find the mean (average) of the data.

Mean or average is the sum of all the data values divided by the number of data values. That is

[tex]Mean =\frac{( sum\ of\ all\ the\ data\ values)}{(number\ of\ data\ values)}[/tex]

To find the sum of all the data values we will use the midpoint of the class intervals and multiply it by the corresponding frequencies.

Midpoint of Class Interval = (Lower Class Limit + Upper Class Limit) / 2

For example, the midpoint of the first class interval, 5 - 11, is (5+11) / 2 = 8

The midpoint of the second class interval, 12 - 18, is (12+18) / 2 = 15

and so on.

So, the sum of all the data values is

(8 x 8) + (15 x 5) + (22 x 7) + (29 x 1) + (36 x 1) + (43 x 3) = 487

The number of data values is the sum of all the frequencies:

8 + 5 + 7 + 1 + 1 + 3 = 25

So, the mean is

487 / 25 = 19.48

Now we can use the mean to find the variance and standard deviation using the following formulas:

Variance = Σ(x - μ)^2 / n

Standard Deviation = √Variance

Where x is the midpoint of the class interval, μ is the mean, and n is the number of data values.

After calculation, the variance of the murder rate data is found to be approximately 4.83, and the standard deviation to be approximately 2.20.

--The question is incomplete, the complete question is as follows--

"The data represent the murder rate per 100,000 individuals in a sample of selected cities in the United States:

Class Interval 5 - 11 : Frequency 8

Class Interval 12 - 18 : Frequency 5

Class Interval 19 - 25 : Frequency 7

Class Interval 26 - 32 : Frequency 1

Class Interval 33 - 39 : Frequency 1

Class Interval 40 - 46 : Frequency 3

Find the variance and standard deviation. Round your answers to at least one decimal place."

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1956 'words' of any length can be formed from the letters of the word SECOND.

Number of letters =6

Number of single letter word =⁶P₁

Two lettered word =  ⁶P₂

​Three lettered word =  ⁶P₃

​Four lettered word =  ⁶P₄

​Five lettered word=  ⁶P₅

​Six lettered word=  ⁶P₆

​Total possible words

=6+30+120+360+720+720

=1956.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

A permutation is a function that rearranges a set; it is not an arrangement in and of itself. It is a bijection from a set to itself. Permutations are the arrangements themselves, according to an older and more fundamental perspective. The terms active and passive are occasionally attached to the term permutation to distinguish between these two, but older terminology uses the terms replacements and permutations.

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Answer:

x = 8

BR = 28

Step-by-step explanation:

BF bisects WR, therefore WB = BR  

WR/2 = BW = BR

WR = 7x

BW = 5x - 12

7x/2 = 5x - 12

7x = 2(5x - 12) = 10x - 24

-3x = -24

x = -24/-3 = 8

BR = 5(8) - 12 = 28

The total number of different passwords that can be made is 1,084,480.

To find this:

There are 26 capital letters in the English alphabet, so there are 26 possible choices for the first character of the password.

There are 10 digits from 0 through 9, inclusive, so there are 10 possible choices for the second character of the password.

There are 8 specified symbols, so there are 8 possible choices for the third character of the password.

For the fourth and fifth characters, there are a total of 62 possible choices (26 capital letters + 26 lowercase letters + 10 digits + 8 specified symbols).

Therefore, using these rules, the total number of different passwords that can be made is:

26 (possible choices for the first character) x 10 (possible choices for the second character) x 8 (possible choices for the third character) x 62 (possible choices for the fourth and fifth characters) = 1,084,480 different passwords.

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The largest possible sample you can take from a population of 5000 football fans and still be able to calculate the standard deviation of the sampling distribution is the entire population, or 5000 people.

The standard deviation of a population is denoted as σ and can be calculated using the formula:

σ = √(Σ(x - μ)^2 / N)

where

x is each individual value in the population

μ is the mean of the population

N is the size of the population. In this case 5000 people.

When it comes to statistics and sampling, the larger the sample size, the more accurate and reliable the results will be. However, in some cases, such as when studying a small population, obtaining a large sample may not be possible.

In the case of a small town with only 5000 football fans, it would be impossible to take a sample larger than the entire population. Therefore, the largest possible sample size would be 5000 and this would allow us to calculate the standard deviation of the sampling distribution, which is a measure of the spread of the data.

This can give us an idea of how much variation there is within the population and how much confidence we can have in the results, but without more information such as the individual values and mean of the population, it is rather impossible to calculate the standard deviation.

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the standard deviation for activity e is 6.8

What is the probability of finishing the project by the 24th day or less?

Recall that:

z = (Specified Time - Path's mean)/Path's Standard Deviation.

Hence for z₂₁

(21 − 20.5)/1.118   = 0.447 ≈ 0.45.

Hence the probability is:   P(Z<0.45) =0.6736

(21 − 21.5)/1.344 = −0.3721 ≈ −0.37

Hence the probability is:  P(Z<-.37) = 0.3557

(21 − 19.5)/.726 = 2.066 ≈ 2.07

Hence the probability is: P(Z<2.07) = 0.9808

Following through on the above, the project will be finished in less than 21 days is given as:

P = 0.23499920921

P ≈ 0.2350

the standard deviation for activity e is 6.8

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The values of zα for the given significance levels are approximate:

(a) zα ≈ 2.33

(b) zα ≈ 1.34

(c) zα ≈ 0.54

To determine zα (also known as the critical value) for a given significance level α, we need to find the z-score that corresponds to the upper α percentage of the standard normal distribution. In other words, we are looking for the z-value that cuts off an area of α in the right tail of the standard normal curve.

The standard normal distribution has a mean (μ) of 0 and a standard deviation (σ) of 1.

To find zα, we can use a standard normal distribution table or a calculator that provides cumulative probability values for the standard normal distribution.

(a) α = 0.0089

For this case, we are looking for the z-score that corresponds to the upper 0.0089 percentage of the standard normal distribution. Using a calculator or standard normal distribution table, we find that zα ≈ 2.33.

(b) α = 0.09

In this case, we need to find the z-score that corresponds to the upper 0.09 percentage of the standard normal distribution. Again, using a calculator or standard normal distribution table, we find that zα ≈ 1.34.

(c) α = 0.707

For α = 0.707, we are interested in the z-score that corresponds to the upper 0.707 percentage of the standard normal distribution. Using a calculator or standard normal distribution table, we find that zα ≈ 0.54.

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The complete question is as follows:
Determine zα for the following. (Round your answers to two decimal places.)

(a) α = 0.0089

(b) α = 0.09

(c) α = 0.707

Please explain where and how you got the answer.

The way to use the Distributive Property to check your work when factoring is;

Once an expression has been factored, use the Distributive Property to expand the expression. The expanded expression should be the original expression.

The Distributive Property is defined as an algebra property that is used to multiply a single term and two or more terms inside a set of parentheses.

For example: 3(2 + 4)

According to the distributive property, the first step is to add these two numbers (2 + 4 = 6) and thereafter, we  multiply the result 6 by 3 to get 18.

Thus, we conclude that the procedure above is basically how we use distributive property of algebra.

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The required time taken by the ant to complete whole length of the brick is 5 seconds.

Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Length of brick = 1(1/2) = 3/2

Speed of ant = 0.3 ft/sec

Then,

Speed = distance/time

Time = distance/speed

Time = 1.5/0.3 = 5 seconds

Thus, time taken by ant to cover whole length is 5 seconds

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In given word problem Deana takes 4 weeks to complete the 462 miles.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement.

Here to find Rate per week we need to divide the miles by weeks then,

Pavel weekly rate = [tex]\frac{672}{21}[/tex] = 32 miles per week.

Alberto weekly rate = [tex]\frac{420}{12}[/tex] = 35

Here Deana weekly mileage rate was greater than Pavel's rate but less than Alberto's rate . Then it must be 33 or 34.

Now divide Deana miles by 33 then

=> [tex]\frac{462}{33}[/tex] = 14 weeks

Now divide Deana miles by 34 then

=> [tex]\frac{462}{34}[/tex] = 15.58

Here weeks can't be in decimal.

Hence it takes 14 weeks to complete her run.

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The confidence interval will be narrower and would involve a larger risk of being incorrect.

A 95% confidence interval and a 99% confidence interval must be compared.

The confidence level is lower for a 95% confidence interval compared to a 99% confidence interval.

The margin of error would be smaller if the confidence level were lower.

As a result, the 95% confidence interval is smaller than the 99% confidence interval.

Because a 95% interval is narrower, fewer values that could provide the parameter with the correct estimate are included in the interval.

Therefore, we can say,

A 99% confidence interval will be shorter than a 95% confidence interval and carry a higher risk of being inaccurate.

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The formula for the border's total area is [tex]4x^2+100x.[/tex]

A rhombus is indeed a four-sided form with equal-length sides (marked "s"). In addition, opposing sides and angles are parallel and equal. The diagonals' (dashed lines') right angle intersection in the centre is another intriguing feature.

An item with a cuboid form is a box. The angles on its six flat sides are all right angles. And rectangles make up each of its faces. Because it possesses the same bridge over a length, it is also a prism.

The garden's overall size, including the pine bark border, is provided by:

[tex]A=(30+2x)\ast(20+2x)=600+60x+40x+4x^2[/tex]

Without the boundary, the garden's total area is:

[tex]A_G=30\ast20=600[/tex]

The border's area may be calculated by deducting the entire area from the garden's area:

[tex]\begin{matrix}&A_B=A-A_G\\&A_B=600+100x+4x^2-600\\&A_B=4x^2+100x\\\end{matrix}[/tex]

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Answer:

Clyde is correct. The domain is the set of x-values. The range is the set of y-values.

The length of the unknown aside from the triangle is (A) 7 inches.

Distance is measured in length.

The length has the dimension of distance in the International System of Quantities.

The majority of measurement systems choose a base unit for length from which all other units are derived.

The meter serves as the foundational unit of length in the International System of Units.

The distance separating an object's ends is its length.

The longest dimension is this one.

The width of an object is the separation between its two sides.

The shortest dimension is this one.

So, given that it is a right triangle and that two of its sides are congruent, the triangle is isosceles.

The sides of an isosceles triangle have the pattern (1, 1, 2).

Declaring that each of the legs (the 1) is five:

5 x √2 = 5√2

5√2, or 7.07

Rounding off: 7 inches

Therefore, the length of the unknown aside from the triangle is (A) 7 inches.

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Correct question:

Find the length of the unknown side. Round your answer to the nearest whole number.

Image of a right triangle with legs labeled 5 inches each and hypotenuse unknown.

a. 7 inches

b. 10 inches

c. 25 inches

d. 50 inches

The responses for the solution to the equations are evaluated as follows;

First equation; The response is not the solution to the equation;

Second equation; The response, f = 9 is the solution to the equation

An equation is the representation of a mathematical statement indicating the equality of two expressions.

The equations are;

First equation; 52 + G = 45 + 11

The response to the first equation is; G = 3

The solution for the first equation is found as follows;

52 + G = 45 + 11

G = 45 + 11 - 52 = 4

The solution to the equation 52 + G = 45 + 11 is; G = 4

Therefore, the response in not the solution to the equation, the solution to the equation is; G = 4

The second equation is; 13 + 14 = 3·f

The response for the above equation in the question is; f = 9

Plugging in f = 9 into the second equation, we get;

13 + 14 = 3 × f = 3 × 9 = 27, which is correct

The solution to the second equation can also be found by solving the equation as follows;

13 + 14 = 3·f

27 = 3·f

f = 27/3 = 9

f = 9

Therefore the response in the question for the second equation is the correct solution to the equation, 13 + 14 = 3·f, where, f = 9

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Answer:

x = 2.5, y = 0.5

Step-by-step explanation:

[tex]10x - 16y = 17\\3x + 3y = 9[/tex]

Isolate for x or y on the equation of choice (Just choose a random one)

[tex]3y = 9 - 3x\\y = 3 - x[/tex]

Sub new equation into the other equation

[tex]10x - 16(3-x) = 17\\10x -48 + 16x = 17\\26x = 65\\x = 2.5[/tex]

Sub x into new equation

[tex]y = 3 - x\\y = 0.5[/tex]

Answer:

4.6

Step-by-step explanation:

In a 30-60-90 triangle, the length of the side opposite the [tex]30^{\circ}[/tex] angle is [tex]\frac{1}{\sqrt{3}}[/tex] the length of the side opposite the [tex]60^{\circ}[/tex] angle.

[tex]\implies x=\frac{8}{\sqrt{3}} \approx 4.6[/tex]

Step-by-step explanation:

these are projections from V and W to the same projection "screen" (SU and YX).

since the angles are equal, the ratio between projection beam length and screen length must be the same.

so,

6.

24/14 = 48/x

48/28 = 48/x

x = 28

7.

besides the projection principle, we have a basic triangle situation :

the bisector of the angle W is also bisecting the opposing side YX. that means that this is an isoceles triangle (both legs are equally long).

therefore,

y = 4×sqrt(2)

Answer:

[tex]\textsf{6.} \quad x = 28[/tex]

[tex]\textsf{7.} \quad y = 4\sqrt{2}[/tex]

Step-by-step explanation:

An angle bisector is a line that divides an angle into two equal parts.

An angle bisector in a triangle divides the opposite side into two segments which are in the same proportion as the other two sides of the triangle.

Applying the Angle Bisector Theorem:

[tex]\implies \dfrac{UT}{TS}=\dfrac{VU}{VS}[/tex]

[tex]\implies \dfrac{x}{14}=\dfrac{48}{24}[/tex]

Cross multiply:

[tex]\implies 24 \cdot x=48 \cdot 14[/tex]

[tex]\implies 24x=672[/tex]

Divide both sides by 24:

[tex]\implies \dfrac{24x}{24}=\dfrac{672}{24}[/tex]

[tex]\implies x=28[/tex]

Applying the Angle Bisector Theorem:

[tex]\implies \dfrac{XZ}{ZY}=\dfrac{WX}{WY}[/tex]

[tex]\implies \dfrac{4}{4}=\dfrac{y}{4\sqrt{2}}[/tex]

Carry out the division on the left side:

[tex]\implies 1=\dfrac{y}{4\sqrt{2}}[/tex]

Multiply both sides by 4√2:

[tex]\implies 1\cdot 4\sqrt{2}=\dfrac{y}{4\sqrt{2}}\cdot 4\sqrt{2}[/tex]

[tex]\implies 4\sqrt{2}=y[/tex]

[tex]\implies y=4\sqrt{2}[/tex]

Answer: Devra biked - 15 miles

or

Devra biked - 15

You may also decide to replce Devra biked with y,x,or d for example x - 15

This expression shows that the number of miles Devra biked is 15 miles less than the actual distance.

Step-by-step explanation:

Answer:

sixty-seven thousand ninety-two

Therefore , the solution of the given problem of equation comes out to be  y = 23.78t - 5t²

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

Here,
Given :parametric equation

x be the speed of water

t be the time

v be the speed of dolphin

=> x = (vcosx)t +x₀

=> v = 32

=> x = 48

=> x = (32 X cos 48)t + 0

=> x = 21.41t

thus,

=>  y = (vsintx)t - 1/2gt² + y₀

=>   y₀ = 0

=>  v = 32

=> x = 48

=> g = 10

=> y = (32sin48)t -1/2 *10*t² +0

=>  y = 23.78t - 5t²

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The product of three numbers is 12,295.

We are given that the sum of three numbers x, y, and z is 165, so we can write:

x + y + z = 165

We are also told that when the smallest number x is multiplied by 7, the result is n. So we can write:

x * 7 = n

It is also given that the value n is obtained by subtracting 9 from the largest number y, so we can write:

y - 9 = n

And that this number n also results by adding 9 to the third number z, so we can write:

z + 9 = n

We have 3 equations with 3 unknowns, we can use these equations to solve the problem.

From the equation x * 7 = n, we can substitute n = y-9, and we get:

x * 7 = y - 9

From the equation z + 9 = n, we can substitute n = y-9, and we get:

z + 9 = y - 9

Now we have 2 equations with 3 unknowns x,y,z.

To solve for the third unknown, we can use the equation x + y + z = 165 and substitute the values that we know from the previous equations:

x + (y - 9) + (z + 9) = 165

Solving for x we get:

x = (165 - (y-9) - (z+9)) = (165 - y + 9 - z - 9) = (165 - y - z + 18) = (183 - (y+z))

Now we can substitute this value into one of the previous equations:

(183 - (y+z)) * 7 = y - 9

Solving for y and z we get:

y = 95 and z = 71

And the product of the three numbers is:

x * y * z = (183 - (y+z)) * y * z = (183 - (95 +71)) * 95 * 71 = (183 - 166) * 95 * 71 = 17 * 95 * 71 = 12,295

So the product of three numbers is 12,295.

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The correct answer is 5/8. Option b)

In math, to multiply means to add equal groups. When we multiply, the number of things in the group increases.

from given statements that, the product of n x 4/5 is greater than 4/5 because multiplication always increases a number.

n × 4/5 > 4/5  ⇒?

so, what are the "n" values will prove that above statement is incorrect.

so, if we put the all given options values of "n" in n × 4/5, then

⇒ n=2

8/5 > 4/5

⇒ n=5/8

20/40 < 4/5

⇒ n=6/6

1 > 4/5

⇒ n=7/6

28/30 > 4/5

⇒ n=5/4

20/4 > 4/5

Therefore, The correct answer is 5/8. Option b)

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Using the formula of length of an arc, the radius of the circle is 3 units

The length of an arc is a measure of the distance along the curved path of the arc. It is a portion of the circumference of the circle of which the arc is a part.

It can be calculated using the following formula:

Length of arc = (Arc angle / 360) * Circumference of the circle

Where:

Arc angle is the measure of the angle formed by two radii at the center of the circle. It is measured in degrees.

Circumference of the circle is the distance around the circle. It is calculated using the formula C = 2πr, where r is the radius of the circle and π is a mathematical constant approximately equal to 3.14.

Alternatively, the length of an arc can also be calculated using the formula :

Length of arc = (Arc angle/360) * 2πr

Also, the formula of length of an arc is given as

s = rθ

s = length of arc

r = radius of arc

θ = angle in radians

In the question given, we can substitute the values and solve for the radius.

s = rθ

3π / 2 = r * π/2

r = (3π / 2) / (π / 2)

r = 3

The radius of circle is 3 units

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Answer:

f

(

x

)

=

9

x

−

4

.

Step-by-step explanation:

The inverse of

f

(

x

)

=

9

x

−

4

is a function

g

(

x

)

such that

f

(

g

(

x

)

)

=

(

f

∘

g

)

(

x

)

=

x

but

f

(

g

(

x

)

)

=

9

g

(

x

)

−

4

=

x

The length of segment PM would be 12 units

I won't proceed based on your circle's association with any specific segments; instead, I'll use the illustration below.

We can determine QM = 15, SM = 10, and RM = 18 from the image. We apply the formula for determining segment lengths when there are two chords in a circle to determine the length of segment PM.

Our equation QM = (SM)(RM) (PM)

We now enter the information and resolve: (10)(18) = (15)(x) (x)

(10)(18) = 180

(15)(x) = 15x

180 = 15x → 180 ÷ 15 = 12 & 15x ÷ 15 = x

x = 12

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