Evaluate these questions 27(1/3)2

Answer:

The volume is decreasing at a rate of about 118.8 cubic feet per minute.

Step-by-step explanation:

Recall that the volume of a cylinder is given by:

[tex]\displaystyle V=\pi r^2h[/tex]

Take the derivative of the equation with respect to t. V, r, and h are all functions of t:

[tex]\displaystyle \frac{dV}{dt}=\pi\frac{d}{dt}\left[r^2h\right][/tex]

Use the product rule and implicitly differentiate. Hence:

[tex]\displaystyle \frac{dV}{dt}=\pi\left(2rh\frac{dr}{dt}+r^2\frac{dh}{dt}\right)[/tex]

We want to find the rate at which the volume of the cylinder is changing when the radius if 4 feet and the volume is 32 cubic feet given that the radius is growing at a rate of 2ft/min and the height is shrinking at a rate of 3ft/min.

In other words, we want to find dV/dt when r = 4, V = 32, dr/dt = 2, and dh/dt = -3.

Since V = 32 and r = 4, solve for the height:

[tex]\displaystyle \begin{aligned} V&=\pi r^2h \\32&=\pi(4)^2h\\32&=16\pi h \\h&=\frac{2}{\pi}\end{aligned}[/tex]

Substitute:

[tex]\displaystyle\begin{aligned} \frac{dV}{dt}&=\pi\left(2rh\frac{dr}{dt}+r^2\frac{dh}{dt}\right)\\ \\ &=\pi\left(2(4)\left(\frac{2}{\pi}\right)\left(2\right)+(4)^2\left(-3\right)\right)\\\\&=\pi\left(\frac{32}{\pi}-48\right)\\&=32-48\pi\approx -118.80\frac{\text{ ft}^3}{\text{min}}\end{aligned}[/tex]

Therefore, the volume is decreasing at a rate of about 118.8 cubic feet per minute.

Answer:

I cant see the whole image

Step-by-step explanation:

please show it.

Answer:

y/x

Step-by-step explanation:

Since x=cos(e) and y=sin(e) and tan(e)=sin(e)/cos(e), then tan(e)=y/x.

Answer/Step-by-step explanation:

2. a. 5y - 3 = -18

Add 3 to both sides

5y - 3 + 3 = -18 + 3

5y = -15

Divide both sides by 5

5y/5 = -15/5

y = -3

b. -3x - 9 = 0

Add 9 to both sides

-3x - 9 + 9 = 0 + 9

-3x = 9

Divide both sides by -3

-3x/-3 = 9/-3

x = -3

c. 4 + 3(z - 8) = -23

Apply the distributive property to open the bracket

4 + 3z - 24 = -23

Add like terms

3z - 20 = -23

Add 20 to both sides

3z - 20 + 20 = - 23 + 20

3z = -3

Divide both sides by 3

3z/3 = -3/3

z = -1

d. 1 - 2(y - 4) = 5

1 - 2y + 8 = 5

-2y + 9 = 5

-2y + 9 - 9 = 5 - 9

-2y = -4

-2y/-2 = -4/-2

y = 2

3. First, find the sum of 3pq + 5p²q² + p³ and p³ - pq

(3pq + 5p²q² + p³) + (p³ - pq)

3pq + 5p²q² + p³ + p³ - pq

Add like terms

= 3pq - pq + 5p²q² + p³ + p³

= 2pq + 5p²q² + 2p³

Next, subtract 2pq + 5p²q² + 2p³ from 3p³ - 2p²q² + 4pq

(3p³ - 2p²q² + 4pq) - (2pq + 5p²q² + 2p³)

Apply distributive property to open the bracket

3p³ - 2p²q² + 4pq - 2pq - 5p²q² - 2p³

Add like terms

3p³ - 2p³ - 2p²q² - 5p²q² + 4pq - 2pq

= p³ - 7p²q² + 2pq

4. Perimeter of the rectangle = sum of all its sides

Perimeter = 2(L + B)

L = (5x - y)

B = 2(x + y)

Perimeter = 2[(5x - y) + 2(x + y)]

Perimeter = 2[5x - y + 2x + 2y]

Add like terms

Perimeter = 2(7x + y)

Substitute x = 1 and y = 2 into the equation

Perimeter = 2(7(1) + 2)

Perimeter = 2(7 + 2)

Perimeter = 2(9)

Perimeter = 18 units

5. First let's find the quotient to justify if the value we get is greater than or less than 2.25

7⅙ ÷ 3⅛

Convert to improper fraction

43/6 ÷ 25/8

Change the operation sign to multiplication and turn the fraction by the left upside down.

43/6 × 8/25

= (43 × 8)/(6 × 25)

= (43 × 4)/(3 × 25)

= 172/75

≈ 2.29

Therefore, the quotient of 7⅙ ÷ 3⅛ is greater than 2.25

Answer:

hi, option C is correct because it has a right angel. please give brainliest

Answer:

x P(x)

0 0.4167

1 0.5

2 0.0833

3 0

Step-by-step explanation:

The speedometers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this question:

7 + 2 = 9 speedometers, which means that [tex]N = 9[/tex]

2 are not correctly calibrated, which means that [tex]k = 2[/tex]

3 are chosen, which means that [tex]n = 3[/tex]

Complete the probability distribution table.

Probability of each outcome.

So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,9,3,2) = \frac{C_{2,0}*C_{7,3}}{C_{9,3}} = 0.4167[/tex]

[tex]P(X = 1) = h(1,9,3,2) = \frac{C_{2,1}*C_{7,2}}{C_{9,3}} = 0.5[/tex]

[tex]P(X = 2) = h(2,9,3,2) = \frac{C_{2,2}*C_{7,1}}{C_{9,3}} = 0.0833[/tex]

Only 2 defective, so [tex]P(X = 3) = 0[/tex]

Probability distribution table:

x P(x)

0 0.4167

1 0.5

2 0.0833

3 0

Answer:

[tex]25 \times 2 = 50 \\ you \: are \: idiot \: [/tex]

really?! :|

Answer:

No, the sum of all the probabilities is not equal to 1.

Step-by-step explanation:

Given

[tex]\begin{array}{ccccc}x & {0} & {1} & {2} & {3} & {P(x)} & {0.001} & {0.007} & {0.033} & {0.059} \ \end{array}[/tex]

Required

Determine if the given parameter is a probability distribution

For a probability distribution to exist, the following must be true;

[tex]\sum P(x)=1[/tex]

So, we have:

[tex]\sum P(x) = 0.001 + 0.007 + 0.033 + 0.059[/tex]

[tex]\sum P(x) = 0.1[/tex]

Hence, it is not a probability distribution because the sum of all probabilities is not 1

Answer:

$40,000

Step-by-step explanation:

this the workings above

Answer:

C

Step-by-step explanation:

200 x 5 = 1,000

100 x 10 = 1,000

C - 5 to 10 days

Answer:

C. 5 to 10 days

Step-by-step explanation:

If she drove 100 miles per day, then

1000/100 = 10

it took her 10 days.

If she drove 200 miles per day, then

1000/200 = 5

it took her 5 days.

Since she drove between 100 miles and 200 miles per days,

it took her from 5 to 10 days.

Answer: C. 5 to 10 days

Answer:

-15.875

Step-by-step explanation:

First, we can sum up the first 5 terms.

-8 + (-4) = -12

-12 + (-2) = -14

-14 + (-1) = -15

-15 + (-1/2) = -15.5

Next, we can find a pattern in the data. We can tell that the next number is one half of the current number. For example, -4 is one half of -8. To find the next number, we simply multiply our current number by one half. Thus, the sixth number is -1/4 and the seventh is -1/8. Adding these to our current total, we have

-15.5 - 1/4 = -15.75

-15.5 - 1/8 = -15.875 as our answer

Answer:

Step-by-step explanation:

Interesting question

They form at right angles. The reason is the highways meet at right angles is that the United States does something really interesting and well thought out with its highway system.

The odd numbers run North and South

The even numbers run East and West.

So I-75 runs North and South

I-80 runs East and West.

They will, when they meet, form a right angle. This works for the interstates, but there a system for the intrastates as well.

I wish Canada would do something like that.

Answer:

20 + 2x = 4x

Step-by-step explanation:

So you are setting the two expressions equal to each other.

buying a membership card  and paying each time looks like this: 20 + 2x where x is the number of times you go to the gym.  20 dollars base then 2 each time you go.

4 each time you go is just 4x

so just set the two equal to each other.

20 + 2x = 4x

If you solve it you will get x = something, which would be the number of times to make the two equal.  

Answer:

<2 and <13 are alternate exterior angles.

In simple form, alternate exterior angles are the opposite angle on the opposing parallel line. So, to make you understand better, <4 and <15 are alternate exterior angles.

Hope this helps :D

Answer:

annualy=$3689.62

semiannually=$3695.27

monthly=$3700.06

weekly=$3700.81

daily=$3701.00

Continuously=$3701.03

Step-by-step explanation:

Given:

P=3000

r=3%

t=7 years

Formula used:

Where,

A represents Accumulated amount

P represents (or) invested amount

r represents interest rate

t represents time in years

n represents accumulated or compounded number of times per year

Solution:

(i)annually

n=1 time per year

[tex]A=3000[1+\frac{0.03}{1} ]^1^(^7^)\\ =3000(1.03)^7\\ =3689.621596\\[/tex]

On approximating the values,

A=$3689.62

(ii)semiannually

n=2 times per year

[tex]A=3000[1+\frac{0.03}{2}^{2(4)} ]\\ =3000[1+0.815]^14\\ =3695.267192[/tex]

On approximating the values,

A=$3695.27

(iii)monthly

n=12 times per year

[tex]A=3000[1+\frac{0.03}{12}^{12(7)} \\ =3000[1+0.0025]^84\\ =3700.0644[/tex]

On approximating,

A=$3700.06

(iv) weekly

n=52 times per year

[tex]A=3000[1+\frac{0.03}{52}]^3^6 \\ =3000(1.23360336)\\ =3700.81003[/tex]

On approximating,

A=$3700.81

(v) daily

n=365 time per year

[tex]A=3000[1+\frac{0.03}{365}]^{365(7)} \\ =3000[1.000082192]^{2555}\\ =3701.002234[/tex]

On approximating the values,

A=$3701.00

(vi) Continuously

[tex]A=Pe^r^t\\ =3000e^{\frac{0.03}{1}(7) }\\ =3000e^{0.21} \\ =3000(1.23367806)\\ =3701.03418\\[/tex]

On approximating the value,

A=$3701.03

Answer:

B

Step-by-step explanation:

When we reflect something across the y axis, the y axis stays the same but the x values change by a factor of -1.

B is the Answer

Answer:

c. switch the x-values and y-values in the table

Step-by-step explanation:

For any table or graph reflection over the line y=x

The rule is (x,y) ----> (y,x)

f(x) is reflected over the line y=x, so the coordinates of f(x) becomes

(-2,-31) becomes (-31,-2)

(-1,0) becomes (0,-1)

(1,2) becomes (2,1)

(2,33) becomes (33,2)

As per the rule, we switch the x-values and y-values in the table

For reflection over the line y=x , the coordinate becomes

(-31,-2)

(0,-1)

(2,1)

(33,2)

Answer:

0.913716

Step-by-step explanation:

Given a normal distribution :

Mean, x = 1050

Standard deviation, σ = 375

The Zscore = (x - mean) / σ

Zscore = (675 - 1050) / 275

Zscore = - 1.364

The probability :

P(Z > - 1.364)

P(Z > - 1.364) = 1 - P(Z < - 1.364) = 1 - 0.086284

P(Z > - 1.364) = 0.913716

Answer:

5√2

Step-by-step explanation:

Given √10*√5

Using surd, the expression can be evaluated further as :

√10*√5 = √50

√50 can be expressed as :

√50 = √25*2 = √25 * √2

√25 = 5

Hence,

√50 = √25 * √2 = 5√2

Hence, √10*√5 = 5√2

For now, I'll focus on the figure in the bottom left.

Mark the point E at the base of the dashed line. So point E is on segment AB.

If you apply the pythagorean theorem for triangle ABC, you'll find that the hypotenuse is

a^2+b^2 = c^2

c = sqrt(a^2+b^2)

c = sqrt((8.4)^2+(8.4)^2)

c = 11.879393923934

which is approximate. Squaring both sides gets us to

c^2 = 141.12

So we know that AB = 11.879393923934 approximately which leads to (AB)^2 = 141.12

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

Now focus on triangle CEB. This is a right triangle with legs CE and EB, and hypotenuse CB.

EB is half that of AB, so EB is roughly AB/2 = (11.879393923934)/2 = 5.939696961967 units long. This squares to 35.28

In short, (EB)^2 = 35.28 exactly. Also, (CB)^2 = (8.4)^2 = 70.56

Applying another round of pythagorean theorem gets us

a^2+b^2 = c^2

b = sqrt(c^2 - a^2)

CE = sqrt( (CB)^2 - (EB)^2 )

CE = sqrt( 70.56 - 35.28 )

CE = 5.939696961967

It turns out that CE and EB are the same length, ie triangle CEB is isosceles. This is because triangle ABC isosceles as well.

Notice how CB = CE*sqrt(2) and how CB = EB*sqrt(2)

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

Now let's focus on triangle CED

We just found that CE = 5.939696961967 is one of the legs. We know that CD = 8.4 based on what the diagram says.

We'll use the pythagorean theorem once more

c = sqrt(a^2 + b^2)

ED = sqrt( (CE)^2 + (CD)^2 )

ED = sqrt( 35.28 + 70.56 )

ED = 10.2878569196893

This rounds to 10.3 when rounding to one decimal place (aka nearest tenth).

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

Now I'm moving onto the figure in the bottom right corner.

Draw a segment connecting B to D. Focus on triangle BCD.

We have the two legs BC = 3.7 and CD = 3.7, and we need to find the length of the hypotenuse BD.

Like before, we'll turn to the pythagorean theorem.

a^2 + b^2 = c^2

c = sqrt( a^2 + b^2 )

BD = sqrt( (BC)^2 + (CD)^2 )

BD = sqrt( (3.7)^2 + (3.7)^2 )

BD = 5.23259018078046

Which is approximate. If we squared both sides, then we would get (BD)^2 = 27.38 which will be useful in the next round of pythagorean theorem as discussed below. This time however, we'll focus on triangle BDE

a^2 + b^2 = c^2

b = sqrt( c^2 - a^2 )

ED = sqrt( (EB)^2 - (BD)^2 )

x = sqrt( (5.9)^2 - (5.23259018078046)^2 )

x = sqrt( 34.81 - 27.38 )

x = sqrt( 7.43 )

x = 2.7258026340878

x = 2.7

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

As an alternative, we could use the 3D version of the pythagorean theorem (similar to what you did in the first problem in the upper left corner)

The 3D version of the pythagorean theorem is

a^2 + b^2 + c^2 = d^2

where a,b,c are the sides of the 3D block and d is the length of the diagonal. In this case, a = 3.7, b = 3.7, c = x, d = 5.9

So we get the following

a^2 + b^2 + c^2 = d^2

c = sqrt( d^2 - a^2 - b^2 )

x = sqrt( (5.9)^2 - (3.7)^2 - (3.7)^2 )

x = 2.7258026340878

x = 2.7

Either way, we get the same result as before. While this method is shorter, I think it's not as convincing to see why it works compared to breaking it down as done in the previous section.

Answer:

Qu 2    =  10.3 cm

Qu 3.   = 2.7cm

Step-by-step explanation:

Qu 2. Shape corner of a cube

We naturally look at sides for slant, but with corner f cubes we also need the base of x and same answer is found as it is the same multiple of 8.4^2+8/4^2 for hypotenuse.

8.4 ^2 + 8.4^2 = sq rt 141.42 = 11.8920141 = 11.9cm

BD = AB =  11.9 cm  Base of cube.

To find height x we split into right angles

formula slant (base/2 )^2 x slope^2  = 11.8920141^2 - 5.94600705^2 =  sq rt 106.065

= 10.2987863

height therefore is x = 10.3 cm

EB = 5.9cm

BC = 3.7cm

CE^2  = 5.9^2 - 3.7^2  = sqrt 21.12 = 4.59565012 = 4.6cm

2nd triangle ED = EC- CD

= 4.59565012^2- 3.7^2 = sq rt 7.43000003 =2.72580264

ED = 2.7cm

x = 2.7cm

Step-by-step explanation:

i would love to say 2 but the word had shows that he does not have 3 apples anymore so the answer is either

0 or -1

The number of apples left after taking the 1 apple from 3 apples by a person is 2 apples.

Subtraction stands for the resultant number, which exists acquired by taking the difference of a number from another number.

Let a number be subtracted from the number b. Then the consequent number after subtracting b from a will be,

d = b - a

Here, (a, b) exists the real numbers.

It exists given that there exist 3 apples. 1 apple stand was taken. Let's assume after taking the 3 apples, that there exist x apples remaining.

As there exist a total of 3 apples and 1 apple stand taken, then to estimate the number of apples left, we must subtract 1 apple from 3 apples.

Therefore, the total apples left exist,

x = 3 - 1

x = 2

To learn more about subtraction operation

https://brainly.com/question/26883387

#SPJ2

Answer:

11x-8x+8y

3x+8y SEEESH IN DEEZ NU                           TS

Step-by-step explanation:

Answer:

10x-5

Step-by-step explanation:

f(x)=5x

g(x)=2x-1

To create a composite function, replace x in f(x) with g(x)

f(g(x)) = 5(g(x) = 5(2x-1) = 10x-5

compute is an electronic devices

Answer:

80 students

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

60% of 500 = 300

72% of 500 = 360

40% of 500 = 200

28% of 500 = 140

300+360 = 660

660 - 2x = 500

660 - 500 = 2x

160 = 2x

2x = 160

x = 80

9514 1404 393

Answer:

  325°

Step-by-step explanation:

The bearing in the reverse direction is 180° more (or less) than the bearing in the forward direction.

  145° +180° = 325°

The bearing of Q from P is 325°.

If the bearing of P and

Q is 145°

Soo,

the bearing of Q from P is 145+180=325°

Because it is reserve in the forward direction

[tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex]

Answer:

11/12 cups

Step-by-step explanation:

2/3+1/4 = ( 2x4 + 3x1 )/( 3x4 ) = ( 8+3 )/12 = 11/12

Answer:

option d is correct one in which value of T lies

Answer:

hi

Step-by-step explanation: