A 40 ft board is cut into two pieces so that one piece is 8 ft longer than the other piece. Find the length of the two pieces

Answer:

b=4

Step-by-step explanation:

So, we have the function [tex]f(x)=1/x[/tex]. We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).

f(2) = 1/(2) = 1/2

So, we have the point (2, 1/2)

At point b, f(b) = 1/b.

Let's plug this into the slope formula:

[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b} =-1/8[/tex]

Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).

[tex]\frac{.5b-1}{2b-b^2} =\frac{-1}{8}[/tex]

Now, cross multiply.

[tex]4b-8=b^2-2b[/tex]

[tex]b^2-6b+8=0[/tex]

Solve for b. Factor using the numbers -4 and -2.

[tex]=(b-4)(b-2)=0[/tex]

Thus, b=4 or b=2.

However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.

We want to find an interval such that the given equation, f(x) = 1/x, has an average rate of change of -1/8 in that interval.

We will see that the interval is [2, 4]

-------------------------------

For a function f(x), the average rate of change in the interval [a, b] is given by:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

Here we have:

[tex]f(x) = 1/x[/tex]

And the interval is [2, b] such that r in that interval is -1/8, so we need to solve:

[tex]r = -1/8 = \frac{f(b) - f(2)}{b - 2} = \frac{1/b - 1/2}{b - 2}[/tex]

We can rewrite it to:

[tex]-1/8 *(b - 2)= 1/b - 1/2\\\\-1/8 *(b - 2)= 2/2b - b/2b = (2 - b)/2b = -(b - 2)/2b[/tex]

Now we can remove the term (b - 2) because it appears on both sides, so we get:

[tex]-1/8 = -1/2b\\1/8 = 1/2b\\2/8 = 1/b\\1/4 = 1/b\\b = 4[/tex]

Then we found that b must be equal to 4, so the interval is [2, 4]

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r = radius

h = r+12 = height, 12 more than the radius

[tex]V = \text{Volume of cone (oblique or not)}\\\\V = \frac{1}{3}\pi*r^2*h\\\\V = \frac{1}{3}\pi*r^2*(r+12)\\\\V = \frac{1}{3}\pi*r^2*r+\frac{1}{3}\pi*r^2*12\\\\V = \frac{1}{3}\pi*r^3+\frac{1}{3}*12\pi*r^2\\\\V = \frac{1}{3}\pi r^3+4\pi r^2\\\\[/tex]

ANSWER: SECOND OPTION

Answer:

Step-by-step explanation:

Let the unknown number = x

[tex]x *\frac{-5}{27}=\frac{-10}{9}[/tex]

x = [tex]\frac{-10}{9}[/tex] ÷ [tex]\frac{-5}{27}[/tex]

[tex]x=\frac{-10}{9}*\frac{-27}{5}\\\\\\x=-2* - 3\\x = 6[/tex]

Answer:

45°

Step-by-step explanation:

[tex]tan^{-1}(1)[/tex] = 45°

Answer:

[tex]\huge\boxed{\theta=45^o\ \vee\ \theta=225^o}[/tex]

Step-by-step explanation:

[tex]\tan\theta=1[/tex]

[tex]\bold{METHOD\ 1}\\\\\text{Use the table in the attachment}\\\\\tan45^o=1\to\theta=45^o\ \vee\ \theta=45^o+180^o=225^o\\\\\bold{METHOD\ 2}\\\\\tan\theta=1\to\tan^{-1}1=\theta\to\theta=45^o\ \vee\ \theta=225^o[/tex]

Answer:

y = [tex]\frac{1}{2} x - 3[/tex]

x + y = 18

Step-by-step explanation:

Let the kitten's weight be y and the cat's weight be x

Condition # 1:

y = [tex]\frac{1}{2} x - 3[/tex]

Condition # 2:

x + y = 18

Answer:  No they are not inverses.

Step-by-step explanation:

If they are inverses,  then the inverse of f(x) will equal g(x).

[tex]y=\dfrac{1}{x+4}-9\\\\\\\text{Swap the x's and y's:}\\x=\dfrac{1}{y+4}-9\\\\\\\text{Solve for y:}\\x+9=\dfrac{1}{y+4}\\\\y+4=\dfrac{1}{x+9}\\\\y=\dfrac{1}{x+9}-4[/tex]

f⁻¹(x) ≠ g(x) so they are not inverses

Answer:

A

Step-by-step explanation:

Using ZPP we get x = 0, 2x + 4 = 0, x + 5 = 0. Solving these, we get x = 0, x = -2, x = -5.

Answer:

[tex]x = 17[/tex]

Step-by-step explanation:

According to the two tangent theory, tangent MN and tangent NP, which are both from point N, are congruent.

That is, [tex]x + 4 = 21[/tex]

Solve for x

[tex]x + 4 = 21[/tex]

Subtract 4 from both sides

[tex]x + 4 - 4 = 21 - 4[/tex]

[tex]x = 17[/tex]

Answer:

b-What is the average number of rainbows each year in Honolulu?

c-How many pedestrians would use a walkway built over a busy road?

d-How many police cars are equipped with computers?

this is the answer

Step-by-step explanation:

E D G E N U I T Y

The situations it is appropriate to use a sample:

B. What is the average number of rainbows each year in Honolulu?

C. How many pedestrians would use a walkway built over a busy road?

D. How many police cars are equipped with computers?

Simple random sampling is a sampling technique in which each member of a population has an equal chance of being chosen, through the use of an unbiased selection method.  The sample is chosen by a random method as every subject in the sample is assigned a number.

Sampling saves money by granting researchers to gather the same answers from a sample that they would receive from the population. Non-random sampling is significantly cheaper than random sampling because it lowers the cost associated with searchinh people and collecting data from them.

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The equation 4x – 3y = 24 can be represented in the slope-intercept form will be y = (4/3)x - 8.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

4x – 3y = 24

Convert the equation from standard form to slope-intercept form. Then we have

4x – 3y = 24

3y = 4x - 24

y = (4/3)x - 24 / 3

y = (4/3)x - 8

The equation 4x – 3y = 24 can be represented in the slope-intercept form will be y = (4/3)x - 8.

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Answer:

3/4

Step-by-step explanation:

Explanation:

List out the total number of outcomes = {1,2,3,4,5,6,7,8,9,10,11,12}

We have 12 items in this list.

From this list, highlight the outcomes that are less than 9. So we will have this smaller list of {1,2,3,4,5,6,7,8} which has 8 items in it.

There are 8 ways to get what we want (a number less than 9) out of 12 outcomes total

The probability is therefore 8/12 = 2/3

=======================================================

Explanation:

The distribution is perfectly symmetrical about the center 6. Notice how the left side is a mirror copy of the right side, due to the heights being the same. Because of this, the mean, median and mode are all the same value and that is 6. The mode is equal to 6 as this is the most frequent value.

The longer way to do this problem is to add up each value shown. We have four copies of '2', six copies of '3', and so on. The total sum you would get is 372. Divide this over 62 because there are 62 smaller green squares. The final result is the mean of 6.

The number closest to the mean of the given distribution is 6. Therefore, option A is the correct answer.

In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).

From the given histogram,

Number         Frequency

    2                      4

    3                      6

    4                      7

    5                      9

    6                     10

    7                      9

    8                      7

    9                      6

   10                      4

Here, the mean = [2(4)+3(6)+4(7)+5(9)+6(10)+7(9)+8(7)+9(6)+10(4)]/[4+6+7+9+10+9+7+6+4]

= [8+18+28+45+60+63+56+54+40]/62

= 372/62

= 6

Therefore, option A is the correct answer.

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Answer:

$24 will be the cost of tennis racquet with weight 25 oz.

Step-by-step explanation:

Given that Price of racquet is inversely proportional to its weight.

i.e.

[tex]Price \propto \dfrac{1}{Weight}[/tex]

We can replace the proportional sign with a constant of proportionality.

[tex]Price = \dfrac{C}{Weight}[/tex]

Where C is a constant named as constant of proportionality.

Given that cost of 20 oz. racquet is $30.00

Putting both the values :

[tex]30 = \dfrac{C}{20}\\\Rightarrow C = 600[/tex]

So, the equation becomes:

[tex]Price = \dfrac{600}{Weight}[/tex]

Now, we have to find the price of 25 oz. racquet.

Putting Weight = 25 oz and finding Price:

[tex]Price = \dfrac{600}{25}\\\Rightarrow Price = \$24[/tex]

So, $24 will be the cost of tennis racquet with weight 25 oz.

Answer:

? = 33

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan ? = opp / adj

tan ? = 13/20

Take the inverse tan of each side

tan ^-1 tan ? = tan ^-1 ( 13/20)

? = 33.02386756

To the nearest degree

? = 33

Answer:

33.

Step-by-step explanation:

inverse tan (13/20) = 33.023867579302

Answer:

15 mL of the solution with 20% water will be needed.

Step-by-step explanation:

Use the inverse relationship

10 mL * (18-15)% = x mL * (20-18)%

x = 10 mL * (3/2) = 15 mL

Answer: 15mL

Step-by-step explanation:

Create a table. Multiply across and add down. The bottom row (Mixture) creates the equation.

                   Qty     ×     %             =      Total          

Solution A     10         15% → 0.15          10(0.15) = 1.5

Solution B      x          20% → 0.20        x(0.20) = 0.20x

Mixture      10 + x   ×    18% → 0.18   =    1.5 + 0.20x

                                  (10 + x)(0.18) = 1.5 + 0.20x

                                    1.8 + 0.18x  = 1.5 + 0.20x

                                    1.8               = 1.5 + 0.02x

                                    0.3              =          0.02x

                                                15  =  x

Answer:

Construction II

Step-by-step explanation:

Construct 3 perpendicular bisectors of the triangles sides; where they intersect is the point of concurrency. The distance from the point of concurrency to one of the vertices is the radius.

Answer:

61% is a reasonable choice

Step-by-step explanation:

The probability of a strike is 79% or 0.79

=> Independently, the probability of 2 consecutive strikes:

P = 0.79 x 0.79 = 0.6241 ~ 61%

Answer:

Devi's present age = 15 years

Devi's Mother's present age = 45 years

Step-by-step explanation:

Let the present age of Devi be x years.

Therefore, mother's present age = 3x

Five years ago:

Devi's age = (x - 5) years

Mother's age =( 3x - 5) years

According to the given condition:

Five years ago:

Devi's mother's age = 4 times Devi's age

3x - 5 = 4( x - 5)

3x - 5 = 4x - 20

20 - 5 = 4x - 3x

15 = x

x = 15 years

3x = 3* 15 = 45 years

Hence,

Devi's present age = 15 years

Devi's Mother's present age = 45 years

Answer:

(5, 11) and (2, 2)

Step-by-step explanation:

y = (x-2)² + 2

y + 4 = 3x

(x-2)² + 2 + 4 = 3x

x² - 4x + 4 + 6 = 3x

x² - 7x + 10 = 0

(x - 5)(x - 2) = 0

x - 5 = 0, x = 5

x - 2 = 0, x = 2

y = (5-2)² + 2 = 11

(5, 11)

y = (2-2)² + 2 = 2

(2, 2)

Answer:

[tex]\large \boxed{\sf \bf \ \text{ The solutions are } x=2, y=2 \text{ and } x=5, y=11.} \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We want to solve this system of equations.

[tex]\begin{cases}&y=(x-2)^2+2\\&y+4=3x\end{cases}[/tex]

This is equivalent to (subtract 4 from the second equation).

[tex]\begin{cases}&y=(x-2)^2+2\\&y=3x-4\end{cases}[/tex]

Then, we can write y = y, meaning:

[tex](x-2)^2+2=3x-4\\\\\text{*** We develop the left side. ***}\\\\x^2-4x+4+2=3x-4 \\\\\text{*** We simplify. *** }\\\\x^2-4x+6=3x-4\\\\\text{*** We subtract 3x-4 from both sides. ***}\\\\x^2-4x+6-3x+4=0\\\\\text{*** We simplify. *** }\\\\x^2-7x+10=0[/tex]

[tex]\text{*** The sum of the zeroes is 7 and the product 10 = 5 x 2 ***}\\\\\text{*** We can factorise. ***}\\\\x^2-5x-2x+10=x(x-5)-2(x-5)=(x-2)(x-5)=0\\\\x-2 = 0 \ \ or \ \ x-5 = 0\\\\x= 2 \ \ or \ \ x=5[/tex]

For x = 2, y =0+2=2 (from the first equation) and for x = 5 y=3*5-4=15-4=11 (from the second equation)

So the solutions are (2,2) and (5,11)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

See my explanation

Step-by-step explanation:

-2x + (x - 4) = 18

-x - 4 = 18

-x = 22          <- this is wrong in question writing as x = 22

so, x = -22

Answer:

B

Step-by-step explanation:

C is too little and D is too much

Answer:

23

Step-by-step explanation:

Raise 3 to the power of 3

27 - 4

Subtract 4 from 27

23

Hope this was correct

Answer:

23

Explanation:

step 1 - rewrite the expression with the value of x

[tex]x^3 - 4[/tex]

[tex](3)^3 - 4[/tex]

step 2 - solve the exponent

[tex](3)^3 - 4[/tex]

[tex]27 - 4[/tex]

step 3 - subtract

[tex]27 - 4[/tex]

[tex]23[/tex]

therefore, the value of the expression is 23.

Answer:

1/4

1/2

3/4

Step-by-step explanation:

Given:

Types of colors in the spinner

Yellow 1

Red 2

Blue 1

Total:4

Successful outcome of Yellow:1

Successful outcome of Red:2

Successful outcome of Blue:1

Required:

Probability of the

Formula:

Probability= successful outcome ÷ possible outcome

Solution

Probability=1 ÷ 4

Probability= 2÷4

Probability= 3÷4

Hope this helps ;) ❤❤❤

Answer:

An example of a prism could be a an amazon box to represent a rectangular prism.  As the height, length, or width of the box increases, the volume increases allowing more items to fit within the box.

An example of a cone would be an ice cream cone.  As the height or the radius of the cone increases, the more volume the cone can hold, meaning more ice cream for you.

An example of a cylinder could be a cup.  As the height or the radius of the cup increases, the larger the volume.  More drink for you.

An example of a sphere would be a soccer ball.  As the radius increases, the volume of the ball increases.  Hence, larger soccer balls have a bigger radius than smaller soccer balls.  This allows for different varients of the ball to be created (i.e., youth, highschool, college, pro).

Note, the volume can also be decreased by simply shrinking the measurements instead of increasing them.

Step-by-step explanation:

Let's simply look at the equations of each shape.

Volume of a prism = base * height

Volume of a cone = Pi * r^2 * (height/3)

Volume of a cylinder = Pi * r^2 * height

Volume of a sphere = (4/3) Pi r^3

Notice that the volumes of prisms, cones, and cylinders directly correlate to height.  As height increases, the volume increases.  The sphere is unique in that the height is 2 * radius; however, the volume is related to the cube of the radius.  Consider if you expanded the radius of the sphere, the volume will increase.

Answer:

Increase or decrease the dimensions of objects. See below for an explanation!

Step-by-step explanation:

An amazon box, which is a rectangular prism, is an example of a prism. If you increase the height, length, or width of the box, you can fit more stuff inside.

A cup is an example of a cylinder; by increasing the height or radius of the cup, you can fit more of a drink inside.

An icecream cone is an example of a cone; if the height or radius were increased, you might fit more ice cream inside.

A soccer ball is an example of a sphere; increasing the radius makes it larger, and various sizes are available for different levels.

You may also shrink the dimensions for each of these objects to make them smaller.

Hope this helps!

Answer:

x = 8

or

x = -4

Step-by-step explanation:

3x² - 12x = 96

Divide both sides by 3

x² - 4x = 32

Add 4 to both sides

x² - 4x + 4 = 32 + 4

(x - 2)² = 6²

Find the square root of both sides

√(x - 2)² = √6²

x - 2 = +/- 6

x - 2 = +6 or -6

x - 2=+6

x=6+2

x=8

x - 2=-6

x=-6+2

x=-4

x = 8

or

x = -4

Answer:

73cm²

Step-by-step explanation:

Area of rectangle=½ length×width

=½×18×7

=63cm²

Area of triangle=½b×h

base=18-13= 5cm

height=11-7 =4cm

½×b×h

½×5×4

=10cm²

Area of total=63+10

73cm²

Answer: 73c2

Step-by-step explanation:

Answer:

[tex]\frac{7}{12}[/tex] of the cake

Step-by-step explanation:

add [tex]\frac{1}{8}[/tex] and [tex]\frac{1}{6}[/tex] to see the total amount of cake eaten.

a. find the common denominator: 8 x 3 = 24 and 6 x 4 = 24

b. multiply accordingly to get the correct numerator: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex]

c. add: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex] = [tex]\frac{7}{24}[/tex]

subtract found value from total to find left over cake.

a. 24 - 7 = 14

simplify.

a. [tex]\frac{14}{24}[/tex] = [tex]\frac{7}{12}[/tex]

You are left with [tex]\frac{7}{12}[/tex] of the cake.

Researchers are observing those with mumps to see how it affects hearing loss at all. There may be strong correlation, weak correlation, or no correlation at all.

With an experiment, researchers would break the participants into two groups: control group and treatment group. Those in the control group get the placebo (fake treatment) while the treatment group gets the treatment applied to them. If we were dealing with an experiment for this context, then the treatment group would get exposed to mumps on purpose. Of course, this is unethical and dangerous so an experiment for this type of project is not a good idea. It's better to go with an observational study.

Answer:

Hey I know!

1.10 euro

Answer:

397.5 :)

Step-by-step explanation: