The length of a rectangle is 5 5/3 inches. the width of the rectangle is half of its length. what is the perimeter of the rectangle?
(a) 16.8 inches
(b) 8.4 inches
(c) 2.8 inches
(d) 15.68
(question and answers attached)

Answer: [tex]y-1=\frac{3}{2}(x+1)[/tex]

Step-by-step explanation:

[tex]2x+3y-6=0\\\\3y=-2x+6\\\\y=-\frac{2}{3}x+2[/tex]

So, the slope of the given line is -2/3, meaning the slope of the line we want to find is 3/2.

Substituting into point-slope form, we get the equation of the line is

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

The value of the constant of variation include 8, 3.2, and 1.25

From the information given, when x = -0.5, y = -4.0. The constant will be:

y = kx

-4 = -0.5k

k = -4.0/-0.5

k. = 8

When x = 2.5, y = 8

y = kx

8 = 2.5k

k = 8/2.5

k = 3.2

When x = 4, y = 5

y = kx

5 = 4k

k = 5/4

k = 1.25

Learn more about constant of variation on:

brainly.com/question/12180039

#SPJ1

The experimental probability that the subsequent booth competitor will receive a reward is 3/8.

The possibility of an event occurring is determined by probability.

The probability of the occurrence ranges from 0 to 1.

If the event doesn't happen, it = 0;

otherwise, it = 1.

For instance, the likelihood that it will storm on Sunday ranges from 0 to 1. If it storms, the event is given a value of 1. If it doesn't, the event is given a value of zero.

Depending on the outcome of a study that has been run several times, the experimental probability is calculated.

The number of winners in the games divided by the total number of competitors in those games determines the probability that the following competitor will earn a reward.

So, here the probability = 6/16 = 3/8 (by dividing both the numerator and the denominator by 2).

Therefore, the final solution is P= 3/8 .

Learn more about the experimental probability here:

https://brainly.com/question/15729871

#SPJ4

Answer:

C

Step-by-step explanation:

The temperature rises by 30 degrees, so lets say that it goes from 0 to 30.

The temperature is now 30. But then, it falls by 30 degrees. It is now 0 again. The quantities even out, or make 0.

Answer:

Step-by-step explanation:

The correct answer is D.  If we are multiplying by 10 we would move the decimal place one place to the right to show that the number is now 10 times bigger.  If we multiply by one hundred.  We are getting 100 times bigger, so we would move the decimal place 2 places to the right.

The opposite is true if we are dividing.  Instead of moving the decimal to the right to show that the number is getting bigger, we move to the left to show that the number is getting smaller.  If we are getting smaller by 10, we would move the decimal one place to the left. In this case, we are getting 100 times smaller so we move the decimal two places to the left.

Answer:180 °

Step-by-step explanation:

Answer:

90 degrees

Step-by-step explanation:

The only numbers that are possible to be divided into 180 are these: 30, 45, 60, 90, & 180.

Now to figure out if this figure is symmetrical. It is. Why? Because you can put at least one line through each triangle. 8 in total but 180 cannot be divided by 8. So you could maybe split it in half. 180/4= 45

45x2= 90

Easy: Since there are now, two halves, since it is split up, it could be possible that the answer could be 90. Because 180/2 halves= 90.

The answer is 90

Carpenter remove [tex]3/16[/tex] inches from the top of the plank to the same thickness of wood from the top and bottom of the plank.

How many inches does the carpenter remove from the top of the plank ?

A wooden plank is [tex]5ft[/tex] long and [tex]1\frac{1}{2}[/tex] inches thick

to make the plank [tex]1\frac{1}{8}[/tex] inches thick

Carpenter needs  to cut off

[tex]=1\frac{1}{2} -1\frac{1}{8} \\=\frac{3}{2} -\frac{9}{8} \\=\frac{3}{8}[/tex]

Carpenter cuts each side

[tex]=\frac{3}{8} /2\\=\frac{3}{16} inches[/tex]

Learn more about the thickness of the plank here :

https://brainly.com/question/28045699

#SPJ4

Answer:

25%

Step-by-step explanation:

When you simple 6 out of 24 you get a quarter.

A quarter us equivalent to 25%

I think you mean in terms of [tex]\sin(x)[/tex]?

Recall Euler's identity

[tex]e^{ix} = \cos(x) + i \sin(x)[/tex]

and de Moivre's theorem

[tex]\left(e^{ix}\right)^n = \left(\cos(x) + i \sin(x)\right)^n = \cos(nx) + i \sin(nx) = e^{inx}[/tex]

where [tex]i=\sqrt{-1}[/tex].

It follows that

[tex]\sin(4x) = \mathrm{Im}\left(\cos(x) + i \sin(x)\right)^4[/tex]

By the binomial theorem, expanding the right side gives

[tex]\cos^4(x) + 4i \cos^3(x) \sin(x) - 6\cos^2(x) \sin^2(x) - 4i \cos(x) \sin^3(x) + \sin^4(x)[/tex]

and so

[tex]\sin(4x) = 4\cos^3(x) \sin(x) - 4 \cos(x) \sin^3(x)[/tex]

We can factorize this as

[tex]\sin(4x) = 4 \cos(x) \sin(x) \left(\cos^2(x) - \sin^2(x)\right)[/tex]

and using the Pythagorean identity

[tex]\cos^2(x)+\sin^2(x) = 1 \implies \cos(x) = \pm \sqrt{1-\sin^2(x)}[/tex]

this reduces to

[tex]\sin(4x) = \pm 4 \sqrt{1-\sin^2(x)} \sin(x) (1 - 2 \sin^2(x))[/tex]

Answer:

Perimeter = 36

Area = 81

Step-by-step explanation:

Perimeter of a square is side length * 4.

9*4 = 36

Area of a square is L*L,

9*9 = 81

Answer:

  18π cm² ≈ 56.5 cm²

Step-by-step explanation:

The area of the sector can be found using an appropriate area formula.

When the sector central angle is given in radians, the formula for the area of that sector is ...

  A = 1/2r²θ . . . . . . where θ is the central angle, and r is the radius

When the angle is in degrees, the formula will include a factor to convert it to radians:

  A = 1/2r²θ(π/180) . . . . where angle θ is in degrees

  A = (πθ/360)r² . . . . simplified slightly

The figure shows r=9 cm, and θ=80°. Using these values in the formula gives an area of ...

  A = π(80/360)(9 cm)² = 18π cm² ≈ 56.5 cm²

Answer:

Here's my answer

it's not number but

hope this help

Generally, the equation of a circle is organized like this: [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the centre and r is the radius.

We're given the endpoints of the diameter: [tex](-6,-3)[/tex] and [tex](-6,-8)[/tex].

First, we can find the centre of the circle by finding the midpoint of these two endpoints.

[tex]midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

Plug in the points:

[tex]midpoint=(\dfrac{-6+-6}{2},\dfrac{-3+-8}{2})\\\\midpoint=(-6,\dfrac{-11}{2})[/tex]

Therefore, the centre of the circle is [tex](-6,\dfrac{-11}{2})[/tex]. Plug this into the general equation:

[tex](x-h)^2+(y-k)^2=r^2\\\\(x-(-6))^2+(y-(-\dfrac{11}{2}))^2=r^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=r^2[/tex]

To find the radius of the circle, we can calculate the distance between the centre and one of the given endpoints:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

Plug in the centre and one of the endpoints:

[tex]d=\sqrt{(-6-x_1)^2+(\dfrac{-11}{2}-y_1)^2}\\d=\sqrt{(-6-(-6))^2+(\dfrac{-11}{2}-(-3))^2}\\d=\sqrt{(-6+6)^2+(\dfrac{-11}{2}+3)^2}\\\\d=\sqrt{(0)^2+(-5.5+3)^2}\\\\d=\sqrt{(0)^2+(-2.5)^2}\\\\d=\sqrt{(0)^2+(-\dfrac{5}{2})^2}\\\\d=\sqrt{0+\dfrac{25}{4}}\\d=\sqrt{\dfrac{25}{4}}\\\\d=\dfrac{5}{2}[/tex]

Therefore, the radius of the circle is [tex]\dfrac{5}{2}[/tex]. Plug this into the general equation:

[tex](x+6)^2+(y+\dfrac{11}{2})^2=r^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=(\dfrac{5}{2})^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=\dfrac{25}{4}[/tex]

[tex](x+6)^2+(y+\dfrac{11}{2})^2=\dfrac{25}{4}[/tex]

The possible values for the width is w≥10.

Given that the length of a rectangle is 4 times the width and perimeter is to be less than or equal to 100 meters.

The perimeter of a rectangle is the total distance of its four outer boundaries. The perimeter of the object is twice the length and width of the object. This calculation is made using the formula:

perimeter = 2(length + width).

Here Perimeter=100 and length=4w

Substituting these values in the formula to find width, and we get

100≤2(4w+w)

100≤2(5w)

Divide both sides by 2, and we get

100/2≤(2(5w))/2

50≤5w

Divide both sides by 5, and we get

50/5≤5w/5

10≤w

Hence, the possible value for width when the length of a rectangle is 4 times the width is w≥10.

Learn more about the perimeter of the rectangle from here brainly.com/question/8004702

#SPJ4

The volume of the solid is 900 cubic unit given that the solid lies between planes perpendicular to the x-axis at x = 0 and x = 19, the cross sections perpendicular to the x-axis on the interval 0 ≤ x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x. This can be obtained by finding the area of the square using the length of the diagonal.

Given that, diagonals that run from the parabola y = - 2√x to the parabola   y = 2√x

D = 2√x - (-2√x)

D = 4√x

D² = s² +  s², where s is the side of the square

(4√x)² = 2s²

16x = 2s²

s² = 8x

s² is the area

Thus,

V = [tex]\int\limits^{15}_0 {8x} \, dx[/tex]

V =  [tex]8\int\limits^{15}_0 {x} \, dx[/tex]

V = 4 (15² - 0)

V = 4×225

⇒ V = 900 cubic unit

Hence the volume of the solid is 900 cubic unit given that the solid lies between planes perpendicular to the x-axis at x = 0 and x = 19, the cross sections perpendicular to the x-axis on the interval 0 ≤ x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x.

Learn more about volume of solid between curves:

brainly.com/question/14612324

#SPJ4

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: A solid lies between planes perpendicular to the x-axis at x = 0 and x = 19. The cross sections perpendicular to the x-axis on the interval         0 ≤x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x. Find the volume of the solid.

Using the normal distribution, the value that separates the highest 70% of the scores in a normal distribution from the lowest 30% is:

z = -0.52.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

The value that separates the highest 70% of the scores in a normal distribution from the lowest 30% is is the 30th percentile, which is Z with a p-value of -0.3, hence z = -0.52.

More can be learned about the normal distribution at https://brainly.com/question/4079902

#SPJ1

The probability that at least one of them is a kindergartner; 0.643.

Calculating or estimating how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable."

Probabilities are always expressed in mathematics as fractions, decimals, or percentages with values ranging from 0 to 1.

Calculation for the probability of the one of them is a kindergarden;

The total number of children is 8.

The total number of kindergarden are 3.

The total number of first graders are 5.

Let 'P' be the probability that at least one of them is kindergarden.

P(at least one kindergartner) = 1 - P(no kindergartner) = 1 - P(all first-graders)

The probability that all are first-graders = (5/8)×(4/7)

                                                                  = 5/14

Therefore, P(at least one kindergartner) = 1 - (5/14)

                                                                   = 9/14

                                                                   = 0.643

Therefore, if two children are ill then, the probability that at least one of them is a kindergartner is 0.643.

To know more about probability, here

https://brainly.com/question/13604758

#SPJ4

The correct question is-

A carpool contains three kindergartners and five first-graders. if two children are ill, find the probability that at least one of them is a kindergartner.

[tex]\textbf{Heya !}[/tex]

use the slope-formula:-

[tex]\sf{\cfrac{y2-y1}{x2-x1}}[/tex]

put-in the values

[tex]\sf{\cfrac{-2-1}{1-(-3)}}[/tex]

[tex]\sf{\cfrac{-3}{1+3}}[/tex]

[tex]\sf{\cfrac{-3}{4}[/tex]

[tex]\sf{-\cfrac{3}{4}}[/tex]

`hope it's helpful to u ~

Answer:

x-3

Step-by-step explanation:

Laura's age goes first. You don't know what it is, so you have to leave it as x. You know Jeri is 3 years younger, so you subtract from x.

Answer: -4, 0, 2

Step-by-step explanation:

The graph intersects the x-axis at [tex]x=-4, x=0, x=2[/tex].

The domain and range of the function is D) Domain: (-∞, ∞); Range: (-∞, ∞)

The domain is the input values, or the x values. We can put in any x values for this function.

Domain : (-∞, ∞)

The range is the output values or the y values. We can get any output values for this function

Range: (-∞, ∞)

Learn more about domain on:

https://brainly.com/question/2264373

#SPJ1

Complete question:

What are the domain and range of the function below?

A) Domain: (-∞, -5)

Range: (5, ∞)

B) Domain: (-5, -10)

Range: (5, 10)

C). Domain: (-5, 10)

Range: (-10, 5)

D) Domain: (-∞, ∞)

Range: (-∞, ∞)

The equation of the line that has a slope of 3 and that passes through the point (5,19) is y = 3x + 4

From the question, we are to determine the equation of the line that has a slope of 3 and that passes through the point (5,19)

Using the point-slope form of an equation of a line

y - y₁ = m(x - x₁)

Where m is the slope

and (x₁, y₁) is a point on the line

From the given information

m = 3

x₁ = 5

y₁ = 19

Putting the parameters into the equation, we get

y - 19 = 3(x - 5)

y - 19 = 3x - 15

y = 3x -15 + 19

y = 3x +4

Hence, the equation of the line that has a slope of 3 and that passes through the point (5,19) is y = 3x + 4

Learn more on Equation of a line here: https://brainly.com/question/16875501

#SPJ1

Answer:

B.(x-y)(x+y)

Step-by-step explanation:

The factor of x² - y² can be represented by,

A.(x - y)²

INCORRECT:

Translated to (x - y)(x - y) as the exponent says it multiplied by it self

(x - y)(x - y) = x²- 2xy + y² which doesn't match

B.(x-y)(x+y)

Correct!

x times x =  x²

-y times y = -y²

x² - y²

C.(x+y)(x+y)

INCORRECT

x times x =  x²

y times y = y²

x² + y² which doesn't match as y positive here

D.2(x - y)

INCORRECT

distribute 2 so 2x - 2y which isn't the original

Learn more about Factor here: https://brainly.com/question/11930302

Answer:

10 m

Step-by-step explanation:

If we draw the diagonal of the rectangle, we form a right triangle where the diagonal is the hypotenuse and the legs are 6 and 8.

This is a well-known Pythagorean triple, which gives the diagonal to be 10 m.

Answer:

[tex]100x^2-4\pi x^2[/tex]

Also can be said as:

[tex]4x^2(25-\pi )[/tex]

Step-by-step explanation:

The question is asking you, "how much is left over."

In this scenario, you're going to have to subtract the area of the pool (P) from the total area of the backyard (B), which will leave you with the remaining area of the backyard (x).

This means your equation to solve this question is:

[tex]x=B-P[/tex]

The value of B is the area of the backyard.

We are told that the backyard is a rectangular shape. So, we can use the formula of finding the area of a rectangle.

The formula is [tex]B=L*W[/tex], where L is the length and W is the width.

Both the length and width are 10x, so we must plug that into this equation.

We end up getting:

[tex]B=10x*10x[/tex]

Which can be simplified to:

[tex]B=100x^2[/tex]

The value of P is the area of the pool.

The pool is a circular shape. So, to get the area of it, we must use the formula of finding the area of a circle.

The formula is [tex]P=\pi r^2[/tex], where r is the radius.

Plugging in the radius of 2x, we get:

[tex]P=\pi (2x)^2[/tex]

By solving this out, we end up with:

[tex]P=4\pi x^2[/tex]

From the scenario, we have the equation:
[tex]x=B-P[/tex]

And from steps 1 and 2, we have the values:

[tex]B=100x^2[/tex] and [tex]P=4\pi x^2[/tex]

Now we just plug those values in to get:

[tex]x=100x^2-4\pi x^2[/tex]

And finally, the amount of the backyard remaining is:

[tex]100x^2-4\pi x^2[/tex]

This answer may be simplified to:

[tex]4x^2(25-\pi )[/tex]

The sum of the arithmetic series 19 + 25 + 31 + 37 + … at n = 9 exists 387.

An arithmetic series exists given, 19 + 25 + 31 + 37 + … sum of this series exists to be defined at n = 9.

Arithmetic progression exists the series of numbers that contain a common difference between adjacent values.

The sum of an arithmetic series exists given as

[tex]$S_n = \frac{n}{2}[2a+(n - 1)d][/tex]

Where n be the total terms =9

a be the first term = 19

d be the common difference = 6

Substitute the values in the above equation, we get

[tex]$S_9 = \frac{9}{2}\left[2\cdot 19+\left(9\:-\:1\right)6\right][/tex]

[tex]$ = \frac{9}{2}\left[86\right][/tex]

= 387

Therefore, the sum of the arithmetic series 19 + 25 + 31 + 37 + … at

n = 9 exists 387.

To learn more about the sum of the arithmetic series refer to:

https://brainly.com/question/17140008

#SPJ9

The proofing of the triangle is illustrated below.

Based on the information, the reflexive property of equality states that an angle or shape is always congruent to itself.

The alternate interior angle theorem is that when two parallel lines are cut by a transversal, then the alternate interior angles are the same.

Learn more about triangles on:

brainly.com/question/1058720

#SPJ1

Answer:

answer in picture

Step-by-step explanation:

The function that gives the value of tn for the geometric series is presented as follows;

[tex]t_n = 2 \times 3^{(n - 1)} [/tex]

The given geometric series is presented as follows;

2 + 6 + 18 + 54 +...

From the above series, we have;

The nth term of the geometric series is therefore;

[tex]t_n = a \cdot r^{(n - 1)} [/tex]

Which gives;

[tex]t_n = 2 \times 3^{(n - 1)} [/tex]

Where, tn is the nth term

Learn more about geometric series here:

https://brainly.com/question/2289626

#SPJ1

The correct option is A. hot water moving through a pipe.

Electrical current passing through a metal wire is similar to hot water moving through a pipe.

Electrical charge carriers, often electrons or atoms deficient in electrons, travel as current. The capital letter I is a typical way to represent current. The ampere, denoted by the letter A, is the common unit.

The method of flowing of electrical current in metal wire is-

Comparison of flow of electricity with flow of water in pipe-

To know more about Electric current, here

https://brainly.com/question/1100341

#SPJ4

The complete question is-

which of the following situations would be mist similar to an electrical current passing through a metal wire in a closed circuit?

A. hot water moving through a pipe

B. an automobile traveling through a tunnel

C. an airplane flying through clouds

D. a flying pan heating up on a hot plate

E. a bird building a nest

The properties of a Circle with their definitions are; As highlighted below

1) The distance around a circle is called; Circumference

2) A portion of the circumference of a circle is called; Arc Length

3) The distance from the center to any point on a circle is called; Radius.

4) The distance through the center between points on a circle is called; Diameter

5) The degree measurement of an arc (in reference to its central

angle) is called; Arc Measure

6) An arc which measures less than 180° is called; Minor arc

7) An arc which measures exactly 180° is called; Semi Circle

Read more about Properties of a Circle at; https://brainly.com/question/17072060

#SPJ1