The data below are the temperatures on randomly chosen days during the summer and the number of employee absences at a local company on those days. Construct a 95% prediction interval for y, the number of days absent,

given x = 95 degrees and y= 0.449x - 30.27

Temperature, x 72 85 91 90 88 98 75 100 80
Number of absences, y 3 7 10 10 8 15 4 15 5

Answer:

0.06944444444 as a fraction equals 6944444444/100000000000

Volume of the solid generated by revolving the plane region about the y-axis is [tex]\frac{6561 \pi}{7}[/tex] .

Given, that y = x3/2, y = 27, x = 0

So, the volume of the solid generated by revolving the region about y axis will be,

[tex]V=\int_0^92\pi(x)(27-y)dx[/tex]

[tex]V=\int_0^92\pi x(27-x^{\frac{3}{2}})dx[/tex]

[tex]V=\left [ 27{\pi}x^2-\frac{4{\pi}x^\frac{7}{2}}{7} \right ]_0^9[/tex]

[tex]V=\left [ \frac{{\pi}\left(189x^2-4x^\frac{7}{2}\right)}{7} \right ]_0^9[/tex]

[tex]V=\frac{6561 \pi}{7}[/tex]

The image of the region bounded by plane is attached below.

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The volume of the solid generated by revolving the plane region about the y-axis is approximately 6863.01 cubic units.

To use the shell method to find the volume of the solid generated by revolving the plane region about the y-axis, we need to express the limits of integration and the height of the infinitesimally thin cylindrical shells.

Given the equations:

y = x^(3/2)

y = 27

x = 0

To determine the limits of integration, we need to find the intersection points between the two curves: y = x^(3/2) and y = 27.

Setting the equations equal to each other:

x^(3/2) = 27

Taking the square root of both sides:

x = 27^(2/3)

x = 9

Therefore, the limits of integration are x = 0 and x = 9.

Now, let's consider an infinitesimally thin cylindrical shell with height "h" and radius "r" at some x value between 0 and 9.

The height of the shell, "h", is the difference between the y-values of the two curves:

h = 27 - x^(3/2)

The radius of the shell, "r", is the x-value.

The volume of the shell can be expressed as:

dV = 2πrh dx

To find the total volume, we integrate this expression from x = 0 to x = 9:

V = ∫[0, 9] 2π(27 - x^(3/2))x dx

Now, let's evaluate this integral:

V = 2π ∫[0, 9] (27x - x^(5/2)) dx

Integrating term by term:

V = 2π [(27/2)x^2 - (2/7)x^(7/2)] evaluated from 0 to 9

Plugging in the limits of integration:

V = 2π [(27/2)(9)^2 - (2/7)(9)^(7/2)] - 2π [(27/2)(0)^2 - (2/7)(0)^(7/2)]

Simplifying and evaluating the expression:

V = 2π [(27/2)(81) - (2/7)(3√(9))] - 0

V = 2π [1093.357] ≈ 6863.01 cubic units

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Answer:

a) P.V  of is OP₁ = [ 1.5i + 0j + 2.6k ],   P.V  of is OP₂ = [ 1.5i + 1.5j + 2.12k ]

b) Vector connecting P₁ to P₂ is [ 0i + 1.5j + 0.48k ]  

c) cylindrical coordinates are (1.5, π/2, 0.48)

Step-by-step explanation:

Given that;

r = 3

P₁ ( 3, 0°, 30° ),   P₂ ( 3, 45°, 45° )

a)

P.V of P₁

x = rcos∅sin∅ = 3(cos0°) ( sin30°) = (3 × 1 × 0.5) = 1.5

y = rsin∅sin∅  = 3(sin0°) (sin30°)   = (3 × 0 × 0.5) = 0

z = rcos∅        = 3(cos30°)             = ( 3 × 0.866)  = 2.6

∴ P.V  of is OP₁ = [ 1.5i + 0j + 2.6k ]

P.V of P₂

x = rcos∅sin∅ = 3(cos45°) ( sin45°) = (3 × 0.7071 × 0.7071) = 1.5

y = rsin∅sin∅  = 3(sin45°) (sin45°)   = (3 × 0.7071 × 0.7071) = 1.5

z = rcos∅        = 3(cos45°)                 = ( 3 × 0.7071)            = 2.12

∴ P.V  of is OP₂ = [ 1.5i + 1.5j + 2.12k ]

b)

Vector connecting P₁ to P₂ is given by

OP₂ - OP₁ = [ 1.5i + 1.5j + 2.12k ] - [ 1.5i + 0j + 2.6k ]

= [ 0i + 1.5j + 0.48k ]  

c)

P₁P₂ → = [ 0i + 1.5j + 0.48k ]  = [ 1.5j + 0.48k ]  

so in a cylindrical coordinate, it should be

r = √(o² + 1.5²) = 1.5

∅ = tan⁻¹[y/π] = π/2

z = 0.48

cylindrical coordinates are (1.5, π/2, 0.48)

Answer:

The answer is D. 3

Step-by-step explanation:

A number refers to the expression of a quantity or a magnitude. In mathematics, a number represents a fixed quantity of something or generally of a number system.

The numbers have a fixed order that determines their value.

The numbers are in order of:

Unit = 8

Ten = 3

Hundred = 5

Unit of thousand = 7

Ten thousand = 2

Hundred thousand = 4

Million unit = 1

10 million = 4

And a hundred million represented by = 3.

Answer:

Positive

Step-by-step explanation:

The product of two negative numbers has a positive sign, whereas the product of a positive and a negative number is negative.

Since -35 and -625 are both negative, they would have a positive sign for their product.

Hope this helps.

Answer: Positive

Step-by-step explanation:

Answer:

358

Step-by-step explanation:

Answer:

358

Step-by-step explanation:

(See below for the picture of how to do it.)

Answer:

  7 < third side < 13

Step-by-step explanation:

The triangle inequality requires the sum of the shortest two side lengths to be more than the longest side length. The effect of that is to limit the third side to values between the sum and difference of the other two sides:

  7 < third side < 13

Answer:

b/4 +b + b-8 =73

2b + b/4 = 81

9b/4 = 81

9b =81 * 4

b = 9* 4

b = 36

The sides of the triangles are 9 inch, 28 inch and 36 inch respectively

Step-by-step explanation:

Answer:

Equation:

LM = (1/2)KM

2x+4 = (1/2)(5x-6)

Hoped I helped

put a brainiest for me pls

The length of KL will be equivalent to 16.

Given is to that  KL = 4x - 8 and KM = 6x − 4

Since [M] is the midpoint, so we can write -

KL = (1/2)KM

(4x - 8) = (1/2)(6x - 4)

4x - 8 = 3x - 2

4x - 3x = 8 - 2

x = 6

So -

KL = (1/2)(6 x 6 - 4)

KL = (1/2) x 32

KL = 16

Therefore, the length of KL will be equivalent to 16.

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Answer:

10.2% chance

Step-by-step explanation:

There are 12 peaches and 8 bananas for a total of 20 pieces of fruit.

So we can write it:

[tex]\frac{12}{20} * \frac{11}{19} * \frac{10}{18} * \frac{9}{17}[/tex] =  [tex]\frac{11880}{116,280}[/tex] = .102 or 10.2% chance

For ease multiply all numerators (top numbers) together, then multiply the denominators (bottom numbers) together, and then divide.

12 * 11 * 10 * 9 = 11880

20 * 19 * 18 * 17 = 116,280

We start with 12 peaches and 20 total fruit, as we select a peach the number of peaches and total fruit goes down by one. We do this 4 times because you draw 4 fruits. If you select 1 fruit your chances of it being a peach are 12/20, each time you select a fruit the chances of it being a peach go down because you have 1 less total fruit, and 1 less peach. This is why you multiply each probability together.

Answer:

10.2% probability

Step-by-step explanation:

12 peaches

8 bananas

Chance of getting a peach the first time is 12/20 the second time is 11/19, third 10/18, and fourth 9/17

11880/116280 = .1022 = 10.2% probability

Step-by-step explanation:

= f (8) - f (-5)

= 3*8-2 -(3*-5-2)

= 22-(-15-2)

= 22+17

= 39

Answer:

60= per hour ....which is 1 hrs

so 120= 2 hrs

60+60

120

2hr is the answer

Answer:

3.5 hours

Step-by-step explanation:

[tex]speed \: = 60 \\ distance = 210 \\ time = \\ speed \: = \frac{distance}{time} [/tex]

[tex]time = \frac{distance}{speed} \\ time = \frac{210}{60} \\ time = \frac{7}{2} [/tex]

[tex]time = 3.5 \: hours[/tex]

Answer:

2208

Step-by-step explanation:

So first we can write this as 4(500+50+2)

Then we distribute it 4*500+4*50+4*2

Multiply to get 2000+200+8

So the answer is 2208

Answer:

[tex]\mathbf{I =2{\sqrt{x+36}} + 6 \ In \begin {vmatrix} \dfrac{{\sqrt{x+36}}-6}{{\sqrt{x+36}}+6}\end {vmatrix}+ C}[/tex]

Step-by-step explanation:

Given that :

[tex]I = \int \dfrac{\sqrt{x+36}}{x} \dx = \int \dfrac{2u^2}{u^2-36} \ du[/tex]

x = u² - 36

Let u = [tex]\sqrt{x+36}[/tex]

Then:

[tex]du =\dfrac{1}{2 \sqrt{x+36}}dx[/tex]

[tex]2 \sqrt{x+36} \ \ du =dx[/tex]

[tex]2 u^2 \ \ du =dx[/tex]

[tex]\dfrac{2u^2}{u^2-36} \\ \\ 2u^2 \\ \\ 2u^2 - 72[/tex]

∴

[tex]I = \int 2 du + \int \dfrac{72}{u^2-36}\ du[/tex]

[tex]I = \int 2 du + 72 \int \dfrac{du}{u^2-6^2}[/tex]

[tex]I =2u+ 72 \times\dfrac{1}{2\times 6} \ In \begin {vmatrix} \dfrac{u-6}{u+6}\end {vmatrix}+ C[/tex]

[tex]I =2u + 6 \ In \begin {vmatrix} \dfrac{u-6}{u+6}\end {vmatrix}+ C[/tex]

substituting the value of u, we have:

[tex]\mathbf{I =2{\sqrt{x+36}} + 6 \ In \begin {vmatrix} \dfrac{{\sqrt{x+36}}-6}{{\sqrt{x+36}}+6}\end {vmatrix}+ C}[/tex]

Answer:

B

Step-by-step explanation:

a. csc x − 1 > 0

csc x > 1

sin x < 1

x = [0, π/2) U (π/2, 2]

b. cos x − 1 > 0

cos x > 1

x = no solution

c. cot x − 1 > 0

cot x > 1

tan x < 1

x = [0, π/4) U (π/2, 2]

d. tan x − 1 > 0

tan x > 1

x = (π/4, π/2) U (π/2, 3π/4)

Of the 4 options, only B has no solution.

The only inequality that does not have a solution with the range is option B;  cos x − 1 > 0.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

A. csc x − 1 > 0

csc x > 1

sin x < 1

x = [0, π/2) U (π/2, 2]

B. cos x − 1 > 0

cos x > 1

x = no solution

C. cot x − 1 > 0

cot x > 1

tan x < 1

x = [0, π/4) U (π/2, 2]

D. tan x − 1 > 0

tan x > 1

x = (π/4, π/2) U (π/2, 3π/4)

Therefore option B is the only inequality that does not have a solution with the range.

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Answer:

32

Step-by-step explanation:

Linear pair means they form a line, or add to 180°.

2x − 5 + 4x − 7 = 180

6x − 12 = 180

6x = 192

x = 32

Answer:

1, 4, 9, 16, 25, 36, 49, 64, 81, and 100

Step-by-step explanation:

Let's pretend that the locker number is represented as a Binary (meaning it's either open or closed).

Looking at this, we can see that each locker is only acted upon if the student number is a factor of it. This is why the 3rd person changes the state of every 3 lockers, the 4th student changes the state of every 4 lockers, etc.

The factors of a number are the numbers that the original number is evenly divisible by. When we divide these, we also receive a factor. With this information, we can conclude that unless one of the factors is the square root of the number, then the "second divided by" factor is itself. For every other number, there will be a "second divided by" factor, so an even number of them. Because an even number + 1 = odd number, then only perfect squares will have an odd number of factors.

Hope this helped!

Answer:

The open lockers are:

1,4,9,16,25,36,49,64,81,100

Step-by-step explanation:

Note that locker 1 is opened by only the first student. So it stays open throughout.

Locker 2 is first opened by student 1, then closed by student 2. Other students don't touch it. So it stays closed.

Locker 3 is first opened by student 1, then closed by student 3. Other students don't touch it. So it stays closed.

Since 4 is a multiple of 1, 2, and 4, it is changed by the 1st, 2nd, and 4th students. Since there is an odd number (3) of changes, locker 4 stays open.

Observe that a locker at position n is opened by students with factors of n.

Every number can be written as the product of a pair of distinct numbers except perfect squares. For example, 6 can be written as 1 × 6 and 2 × 3. Hence, it has 4 factors, which means it is touched an even number of times, making it stay locked.

A number like 9 is written as 1 × 9 and 3 × 3. Hence, it has 3 factors, which is odd, making it stay open.

Since the perfect squares from 1 to 100 are 1,4,9,16,25,36,49,64,81,100, then the open lockers are:

1,4,9,16,25,36,49,64,81,100

Answer:

I'd say that it's a good start, but he is assuming that his rate of growth will remain the same.

Since there are relatively few people 6'10" tall, it's likely that his extrapolation is too high.

Maybe if he could study the growth rates and heights at various ages of people who did achieve 6'10" height, he would have a sounder basis for his theory.

Answer: p^2 = 25 ^2 = 625

Answer:

Step-by-step explanation:

5x - 9 < 21

5x < 30

x < 6

Answer:

a)Amount of money left on Keith's card in dollars = $90 - $15x

= $(90 - 15)

b) Amount of money left on Mary's card in dollars= $110 - $20x

= $(110 - 20x)

c) Write an equation to show that the two cards have the same amount of money left on them [don't know how to do this part.

$90 - 15x = $110 - 20x

Step-by-step explanation:

Let x be the number of pizzas purchased. For each card, write an expression for the amount of money left on the card after purchasing x pizzas.

For Keith

Keith received a gift card of $90 for a pizza restaurant. The restaurant charges $15 per pizza.

x numbers of pizza costs = $15x

Hence, the amount of money left on Keith's card after purchasing x pizzas =

$90 - $15x

For Mary,

Mary received a gift card of $110 for a different pizza restaurant. The restaurant charges $20 per pizza.

Hence, x number of pizzas cost =$20 × x

= $20x

Therefore, the amount of money left on Mary's card after she buys x pizzas =

$110 - $20x

Amount of money left on Keith's card in dollars = __________

Amount of money left on Mary's card in dollars=____________

Write an equation to show that the two cards have the same amount of money left on them [don't know how to do this part.

To find the equation that shows that the two cards have the same amount of money =

Equation 1 = Equation 2

$90 - 15x = $110 - 20x

Collect like terms

-15x + 20x = $110 - $90

5x = 20

x = 20/5

x = 4

Hence, anytime Keith and Mary buys 4 pizzas their gift card will have the same amount of money left on them.

Answer:

Let x the number Mr John thinks

He double it so 2×x=2x ( double = multiplying by 2 )

The result is 58

So 2x=58

We solve the equation

2x=58

So x =58/2

x=19

So it's 19 the number Mr John thinks

Answer:

4 cups of flour

Step-by-step explanation:

We just need to double 2. The phrase "double" means to multiply by 2 so the answer is 2 * 2 = 4 cups of flour.

Answer:

-7/10 >= 2k - 4

Step-by-step explanation:

For this problem, we can simply follow the wording to write the inequality.

-7/10 is at least twice a number k minus 4

-7/10 >= 2k - 4

We use >= since is says at least, meaning it could be equal or greater than

We multiply k by 2 since it states the number is twice k

And we subtract 4 from the 2k since the number is "minus 4" from the twice k.

Thus, we have our inequality, -7/10 >= 2k - 4.

Cheers.

Answer:

125 cm and 75 cm

125:75 = 5:3

Step-by-step explanation:

Let the number be 5x and 3x

we are taking these value because in ratio

a:b = ax:bx

that is if we multiply both part of ratio by a same number ratio remains same.

____________________________________________________

Since we have divided 200 cm in two parts with value 5x and 3x

Thus,

sum of 5x and 3x will be equal to 200 cm

5x+3x = 200cm

8x = 200cm

x = 25 cm

Thus,

first part = 5x = 5*25 = 125 cm

other part = 3x = 3*25 = 75cm

Answer:

Equation 1

Step-by-step explanation:

It does not have an x value with an exponent of 2 or greater.

Answer: I would think that equation 1 represents a linear function as it fllows the y= mx +b formula.

Step-by-step explanation: Linear functions sometimes use slope intercept form which is y = mx + b in this equation 2x would be your slope and 1 would be your y intercept.

Answer:

[tex] \boxed{ \bold{ \huge \boxed{ \sf{x = 18.5}}}}[/tex]

Step-by-step explanation:

[tex] \sf{3(22 + 2) = 18 + 4(x - 5)}[/tex]

Add the numbers : 22 and 2

⇒[tex] \sf{3 \times 24 = 18 + 4(x - 5)}[/tex]

Multiply the numbers : 3 and 24

⇒[tex] \sf{72 = 18 + 4(x - 5) }[/tex]

Distribute 4 through the parentheses

⇒[tex] \sf{72 = 18 + 4x - 20}[/tex]

Calculate the difference

⇒[tex] \sf{72 = - 2 + 4x}[/tex]

Swap the sides of the equation

⇒[tex] \sf{ - 2 + 4x = 72}[/tex]

Move 2 to right hand side and change it's sign

⇒[tex] \sf{4x = 72 + 2}[/tex]

Add the numbers : 72 and 2

⇒[tex] \sf{4x = 74}[/tex]

Divide both sides of the equation by 4

⇒[tex] \sf{ \frac{4x}{4} = \frac{74}{4} }[/tex]

Calculate

⇒[tex] \sf{x = 18.5}[/tex]

Hope I helped!

Best regards!!

Answer:

x=18.5

Step-by-step explanation:

3(22+2) =18 + 4(x-5)

3(24) = 18 + 4(x-5)

72=18+4(x-5)

4(x-5)+18=72

4x-20+18=72

4x= 72-18+20

4x=72+2

4x=74

x=74/4

x=18.5

Answer: P = 6 miles

Step-by-step explanation: A rectangle is a quadrilateral with opposite sides with the same measure. As Central Park is one, its parallel sides has the same measurement.

Distance of points gives the measurement of the sides of the rectangle. It is calculated as:

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

For the first two points, (-1.25,-0.25) and (-1.25,0.25), note that x-components is the same, so, only y-component is relevant to the distance:

[tex]d=\sqrt{(-1.25+1.25)^{2}+(0.25+0.25)^{2} }[/tex]

[tex]d=\sqrt{(0.5)^{2} }[/tex]

d = 0.5

Two sides of the rectangle are 0.5 miles.

For points (-1.25,0.25) and (1.25,0.25), y-component will add 0 to the formula. Then,

[tex]d=\sqrt{(1.25+1.25)^{2}+(0.25-0.25)^{2} }[/tex]

[tex]d=\sqrt{(2.5)^{2}}[/tex]

d = 2.5

Two sides of the park are 2.5 miles.

Perimeter is the sum of all the sides of a geometric figure.

Perimeter of central Park is

P = 0.5+0.5+2.5+2.5

P = 6

Central Park has perimeter of 6 miles.