find the HCF by prime factorization method 60 and 75​

Answer:

The volume is increasing at a rate of 27093 cubic inches per second.

Step-by-step explanation:

Volume of a cone:

THe volume of a cone, with radius r and height h, is given by:

[tex]V = \frac{1}{3} \pi r^2h[/tex]

In this question:

We have to differentiate implictly is function of t, so the three variables, V, r and h, are differenciated. So

[tex]\frac{dV}{dt} = \frac{\pi r^2}{3}\frac{dh}{dt} + \frac{2\pi rh}{3}\frac{dr}{dt}[/tex]

The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.4 in/s.

This means that [tex]\frac{dr}{dt} = 1.4, \frac{dh}{dt} = -2.4[/tex]

Radius is 140 in. and the height is 186 in.

This means that [tex]r = 140, h = 186[/tex]

At what rate is the volume of the cone changing?

[tex]\frac{dV}{dt} = \frac{\pi r^2}{3}\frac{dh}{dt} + \frac{2\pi rh}{3}\frac{dr}{dt}[/tex]

[tex]\frac{dV}{dt} = \frac{\pi (140)^2}{3}(-2.4) + \frac{2\pi 140*186}{3}1.4[/tex]

[tex]\frac{dV}{dt} = -0.8\pi(140)^2 + 62*2\pi*1.4*140[/tex]

[tex]\frac{dV}{dt} = 27093[/tex]

Positive, so increasing.

The volume is increasing at a rate of 27093 cubic inches per second.

Answer:

The hypotenuse

Answer:

150 dollars. if I am wrong correct me

Answer:

C and D

Step-by-step explanation:

15 to 30 galons at $9.95 to $21.00

the minimum amount can be found by calculating the minimum amount sold at a minimum price 15*9.95 = $149.25

the maximum amount can be found by calculating the maximum amount sold at a maximum price 30*21 = $630

there are 2 choices that are between 149.25 and 630, C, and D

Answer:

4 over 3

because is in side the bracket is part of inequalities

Answer:

7/4

Step-by-step explanation:

(4/7)^-1

We know a^-b = 1/a^b

1/ (4/7)^1

7/4

Answer:

(4/7)^-1

=1/(4/7)^1

=1÷4/7

=1×7/4

=7/4

Therefore 7/4 is equal to 1.75 as a rational number

Answer:

4

Step-by-step explanation:

The mean is the average of a data set. It can be found by adding up all of the values in a data set and then dividing it by the number of values in the data set.

The values in this data set;

[tex]7,5,5,3,2,2[/tex]

The number of values in this data set,

[tex]6[/tex]

Find the mean;

[tex]\frac{sum\ of\ vlaues}{number\ of\ values}[/tex]

[tex]=\frac{7+5+5+3+2+2}{6}\\\\=\frac{24}{6}\\\\=4[/tex]

Answer:

0.0498

Step-by-step explanation:

In this question,

x~exponential

we have

mean = 1/λ = 8

from here we cross multiply, when we do

such that

λ = 1/8

probability of x functioning in 8 months

= e^-λx

= e^-1/8x12

= e^-1.5

= 0.2231

i got this value through the use of a scientific calculator

then the probability that these two are greater than 12

= 0.2231²

= 0.04977

= approximately 0.0498

therefore the probability that both components are functioning in 12 months is 0.0498

Answer:

B. 9

Step-by-step explanation:

When the line runs( x variation) by 1 , it rises (y variation) by 9

And since unit rate is calculated by Rise/Run, the unit rate is 9/1 or 9

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

A

Step-by-step explanation:

since it's negative so it will get smaller

Answer:

L = 0.16 yd, W = 0.22 yd

Step-by-step explanation:

Dimensions of play ground 23/147 yd x 3/14 yd

reducing factor 2/147

Let the original length is L.

[tex]L - \frac{2L}{147} = \frac{23}{147}\\\\L\frac{143}{147} = \frac{23}{147}\\\\L=\frac{23}{143} yd[/tex]

L = 0.16 yd

Let the width is W.

[tex]W - \frac{2W}{147} = \frac{3}{14}\\\\W\frac{143}{147} = \frac{3}{14}\\\\W=0.22 yd[/tex]

Answer:

A number or number sentence that doesn't change

Step-by-step explanation:

Answer:

the constant of proportionality k, is the constant value of the ratio of two proportional quantities y and x

Step-by-step explanation:

k = y/x or y= kx

example : the cost of 20 books is rs. 180 how much will 15 books cost ?

a. rs. 125

b. rs. 130

c. rs. 135

d. rs. 140

answer is c. rs. 135

Answer:

Step-by-step explanation:

(x+3)(x+1)=1

x²+3x+x+3=1

x²+4x+2=0

x²+4x+4=-2+4

(x+2)²=2

x+2=±√2

x=2+√2

and x=2-√2

so x≠-3

and x≠-1

Answer:

a) [tex]Z = 0.0085[/tex]

b) [tex]Z = 0.0095[/tex]

c)  ii. Amy

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Question a:

Nina took a test in English and earned a 71.8. In the English class had a mean of 71.7 and a standard deviation of 11.7.

This means that [tex]X = 71.8, \mu = 71.7, \sigma = 11.7[/tex]

So

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

[tex]Z = \frac{71.8 - 71.7}{11.7}[/tex]

[tex]Z = 0.0085[/tex]

Question b:

Amy took a test in Social Studies and earned a 60.7. Students' test grades in Social Studies had a mean of 60.6 and a standard deviation of 10.5.

This means that [tex]X = 60.7, \mu = 60.6, \sigma = 10.5[/tex]

So

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

[tex]Z = \frac{60.7 - 60.6}{10.5}[/tex]

[tex]Z = 0.0095[/tex]

c) Which person did relatively better?

Amy had a higher z-score, so she did relatively better.

Answer:

x^2+y^2=r^2 is quation of circle whose centre is (0,0)

Answer:

The average rate of change is 5.

Step-by-step explanation:

First plug in the x values.

y=5x+1

=(0)5+1

=1

y=5x+1

=(4)5+1

=21

Average rate of change = the change in the output divided by the change in the input.

Output change: 21-1=20

Input change: 4-0=4

20/4=5

Answer:

[tex]g(x) = -x^2 + 3[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x^2[/tex]

Required

Determine g(x)

First, shift f(x) down by 3 units

The rule is:

[tex]f'(x) = f(x) - 3[/tex]

So:

[tex]f'(x) = x^2 - 3[/tex]

Next, reflect f'(x) across the x-axis to get g(x)

The rule is:

[tex]g(x) = -f(x)[/tex]

So, we have:

[tex]g(x) = -(x^2 - 3)[/tex]

Open bracket

[tex]g(x) = -x^2 + 3[/tex]

Answer:

D

Step-by-step explanation:

I figured out the hard way

Answer:

We know that for a line:

y = a*x + b

where a is the slope and b is the y-intercept.

Any line with a slope equal to -(1/a) will be perpendicular to the one above.

So here we start with the line:

3x + 4y + 5 = 0

let's rewrite this as:

4y = -3x - 5

y = -(3/4)*x - (5/4)

So a line perpendicular to this one, has a slope equal to:

- (-4/3) = (4/3)

So the perpendicular line will be something like:

y = (4/3)*x + c

We know that this line passes through the point (a, 3)

this means that, when x = a, y must be equal to 3.

Replacing these in the above line equation, we get:

3 = (4/3)*a + c

c = 3 - (4/3)*a

Then the equation for our line is:

y = (4/3)*x + 3 - (4/3)*a

We can rewrite this as:

y = (4/3)*(x -a) + 3

now we need to find the point where this line ( y = -(3/4)*x - (5/4)) and the original line intersect.

We can find this by solving:

(4/3)*(x -a) + 3 =  y = -(3/4)*x - (5/4)

(4/3)*(x -a) + 3  = -(3/4)*x - (5/4)

(4/3)*x - (3/4)*x = -(4/3)*a - 3 - (5/4)

(16/12)*x - (9/12)*x = -(4/3)*a - 12/4 - 5/4

(7/12)*x = -(4/13)*a - 17/4

x = (-(4/13)*a - 17/4)*(12/7) = - (48/91)*a - 51/7

And the y-value is given by inputin this in any of the two lines, for example with the first one we get:

y =  -(3/4)*(- (48/91)*a - 51/7) - (5/4)

  = (36/91)*a + (153/28) - 5/4

Then the intersection point is:

( - (48/91)*a - 51/7,  (36/91)*a + (153/28) - 5/4)

And we want that the distance between this point, and our original point (3, a) to be equal to 4.

Remember that the distance between two points (a, b) and (c, d) is:

distance = √( (a - c)^2 + (b - d)^2)

So here, the distance between (a, 3) and ( - (48/91)*a - 51/7,  (36/91)*a + (153/28) - 5/4) is 4

4 = √( (a + (48/91)*a + 51/7)^2 + (3 -  (36/91)*a + (153/28) - 5/4 )^2)

If we square both sides, we get:

4^2 = 16 =  (a + (48/91)*a + 51/7)^2 + (3 -  (36/91)*a - (153/28) + 5/4 )^2)

Now we need to solve this for a.

16 = (a*(1 + 48/91)  + 51/7)^2 + ( -(36/91)*a  + 3 - 5/4 + (153/28) )^2

16 = ( a*(139/91) + 51/7)^2 + ( -(36/91)*a  - (43/28) )^2

16 = a^2*(139/91)^2 + 2*a*(139/91)*51/7 + (51/7)^2 +  a^2*(36/91)^2 + 2*(36/91)*a*(43/28) + (43/28)^2

16 = a^2*( (139/91)^2 + (36/91)^2) + a*( 2*(139/91)*51/7 + 2*(36/91)*(43/28)) +  (51/7)^2 + (43/28)^2

At this point we can see that this is really messy, so let's start solving these fractions.

16 = (2.49)*a^2 + a*(23.47) + 55.44

0 = (2.49)*a^2 + a*(23.47) + 55.44 - 16

0 = (2.49)*a^2 + a*(23.47) + 39.44

Now we can use the Bhaskara's formula for quadratic equations, the two solutions will be:

[tex]a = \frac{-23.47 \pm \sqrt{23.47^2 - 4*2.49*39.4} }{2*2.49} \\\\a = \frac{-23.47 \pm 12.57 }{4.98}[/tex]

Then the two possible values of a are:

a = (-23.47 + 12.57)/4.98  = -2.19

a = (-23.47 - 12.57)/4.98 = -7.23

9514 1404 393

Answer:

Step-by-step explanation:

We assume ...

The wall area is the wall height times the perimeter of the room.

  wall area = (25')(2(100' +65')) = 8250 ft²

The ceiling area is the product of length and width.

  ceiling area = (100')(65') = 6500 ft²

Then the area to be painted with each coat is ...

  painted area = wall area + ceiling area = (8250 +6500) ft² = 14750 ft²

Then two coats of paint will require sufficient paint to cover ...

  (2 coats)×(14750 ft²/coat) = 29,500 ft²

__

If each can of paint covers 1750 ft², the number of cans required is ...

  (29,500 ft²)/(1750 ft²/can) = 16.86 cans

  17 cans must be purchased

__

The cost of 17 cans of paint with sales tax will be ...

  (17 cans)($151.99/can)(1 +15%) = $2971.40

Answer:

25 goat and 15 chicken

Step-by-step explanation:

Say the number of goats is G, then the number of chickens is 40 - G as there are 40 heads and each chicken and each goat has one head.

The number of feet is 130

So 2(40 - G) + 4G = 130

So 80 - 2G + 4G = 130

2G = 50

G = 25

25 goats and 15 chickens

Answer:

3/14

Step-by-step explanation:

it takes 3 days to construct a porch and 14 days to construct a family room

so porch/family room = 3/14

Brainliest if this was correct

Answer:

Step-by-step explanation:

21,753

at unit place=3 not an even number,not equal to 5 and not equal to 0

so 21,753 is not divisible by 2,5 and 10

again

2+1+7+5+3=18 divisible by 3 and 9.

so 21,753 is divisible by 3 and 9.

Answer:

hello again.. I think you have a problem about figures

Step-by-step explanation:

please be brave when you try to solve..try to draw new lines to get angle and then look at the overall of shape.. the photo helps you good bye

Answer:

6x + y

Step-by-step explanation:

6x + 3y/3​

6x + y

Answer:

6x + y

Step-by-step explanation:

6x + 3y / 3

cancel 3y by 3

6x + y

Answer:

Factoring a perfect square trinomial.

Step-by-step explanation:

The left side was able to be simplified via factoring.

Answer:

[tex]E(x) = 177.130[/tex]

[tex]Var(x) = 484.551[/tex]

[tex]\sigma = 22.013[/tex]

Step-by-step explanation:

Given

The attached table

Solving (a): The mean

This is calculated as:

[tex]E(x) = \sum x * p(x)[/tex]

So, we have:

[tex]E(x) = 182.11 * 13\% + 163.88 * 19\% + 180.30 * 33\% + 216.08 * 17\% + 144.92 * 18\%[/tex]

Using a calculator, we have:

[tex]E(x) = 177.1297[/tex]

[tex]E(x) = 177.130[/tex] --- approximated

The average opening price is $177.130

Solving (b): The Variance

This is calculated as:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

Where:

[tex]E(x^2) = \sum x^2 * p(x)[/tex]

[tex]E(x^2) = 182.11^2 * 13\% + 163.88^2 * 19\% + 180.30^2 * 33\% + 216.08^2 * 17\% + 144.92^2 * 18\%[/tex]

[tex]E(x^2) = 31859.482249[/tex]

So:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

[tex]Var(x) = 31859.482249 - 177.1297^2[/tex]

[tex]Var(x) = 31859.482249 - 31374.9306221[/tex]

[tex]Var(x) = 484.5516269[/tex]

[tex]Var(x) = 484.551[/tex] --- approximated

Solving (c): standard deviation

The standard deviation is:

[tex]\sigma = \sqrt{Var(x)}[/tex]

[tex]\sigma = \sqrt{484.5516269}[/tex]

[tex]\sigma = 22.0125418796[/tex]

Approximate

[tex]\sigma = 22.013[/tex]

Answer:

B.18. 44 miles

Step-by-step explanation:

We are given that

Distance between A and B=8 miles

Angle B=Angle BCQ=40 degree (Alternate interior angles)

Angle ACB=180-Angle ACP-Angle BCQ

Angle ACB=180-40-40=100 degree

In triangle ABC

Angle A+ Angle B +Angle C=180 degree using sum of angles of triangle property

Substitute the values

[tex]\angle A+40+100=180[/tex]

[tex]\angle A+140=180[/tex]

[tex]\angle A=180-140[/tex]

[tex]\angle A=40[/tex] degree

Angle A=Angle B

When two angles are equal of a triangle then the triangle is isosceles triangle.

Therefore, triangle ABC is an isosceles triangle.

[tex]\implies BC=AC [/tex]

Now, Sine law

[tex]\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}[/tex]

Using the sine law

[tex]\frac{BC}{sin 40}=\frac{AB}{sin 100}[/tex]

[tex]\frac{BC}{sin 40}=\frac{8}{sin 100}[/tex]

[tex]BC=\frac{8\times sin40}{sin 100}[/tex]

BC=5.22

AC=BC=5.22 miles

Now, total distance covered by the boat=AB+BC+AC

Total distance covered by the boat=8+5.22+5.22=18.44 miles

Hence, option B is correct.

Answer:

13 miles

Step-by-step explanation:

He hikes 4 mph downhill and it takes 30 minutes or 0.5 hours lesser than the trip uphill at 2 mph.

Thus, if the distance upward is x and we are told the distance downhill is 3 miles longer.

Then, since time = distance/speed, we have;

((x + 3)/4) + 0.5 = x/2

Multiply through by 4 to get;

x + 3 + (0.5 × 4) = 2x

x + 5 = 2x

2x - x = 5

x = 5 miles

Now, it means distance uphill = 5 miles and distance downhill = 5 + 3 = 8 miles

Thus, total distance covered = 8 + 5 = 13 miles

Answer:

-192

Step-by-step explanation:

it is a geometric progression

r=-4