Find the solution set of this inequality. Select
the correct graph.
18x + 161 > 16
Click on the correct answer.

Answer:

[tex]3a^4[/tex]

Step-by-step explanation:

Given expression is [tex]27a^{12}[/tex].

Now we need to find the cube root of given expression [tex]27a^{12}[/tex].

[tex]\sqrt[3]{27a^{12}}[/tex]

[tex]=\sqrt[3]{3*3*3a^{4*3}}[/tex]

[tex]=\sqrt[3]{3^3\left(a^4\right)^3}[/tex]

[tex]=\sqrt[3]{\left(3a^4\right)^3}[/tex]

Since cube root and cube are opposite operations of each other. So they will cancel each other.

[tex]=3a^4[/tex]

Hence correct choice is the last choice [tex]3a^4[/tex].

Answer:

Step-by-step explanation:

Start with the distance squared.

The distance from the center to the point on the circle is found from

Formula

d^2 = r^2 = (x2 - x1)^2 + (y2 - y1)^2

Givens

x2 = 2

x1 = - 5

y2 = -8

y1 = - 8

Center= (-5,-8)

Solution

r^2 = (2 - - 5)^2 + (-8 - - 8)^2

r^2 = 49 + 0

r^2 = 49

equation

(x + 5)^2 + (y + 8)^ = 49

Answer:

The size of Harry's loan is $9000.

Step-by-step explanation:

D(t) models Harry's remaining debt, in dollars, as a function of time t, in months  that is given by :

[tex]D(t) =-200t+ 9000[/tex]

We can see 200 is in negative that means it is getting deducted from the function. So, Harry must be paying this each month against his loan.

Lets put t = 0, that shows no payments have been made.

This will get the amount of loan, before any payments.

[tex]D(t)=-200(0)+9000[/tex]

So,[tex]D(t) =9000[/tex]

Hence, the size of Harry's loan is $9000.

Answer:

$200

Step-by-step explanation:

I got $9000 wrong on Khan and $200 right

Answer:

4:15, 4 to 15, 4/15

Answer:

64/3 cc or 64/3 cm³

Step-by-step explanation:

The formula for the volume of a triangular pyramid is

V = (1/3)(area of base)(height)

Here we have a square prism (actually, a cube), whose square base is 4 cm by 4 cm (4 cm is the cube root of 64 cc).  The height of this cube is also 4 cm.

The volume of a triangular pyramid of base area (4 cm)² and height 4 cm is

V = (1/3)(base area)(height)

   = (1/3)(16 cm²)(4 cm) = 64/3 cc

Answer:

64/3 cc or 64/3 cm³

Step-by-step explanation:

Percent error = |(Measured - Actual) / Actual| × 100. For Measured 68, Actual 60: [tex]\( \frac{|68 - 60|}{60} \times 100 ≈ 13.3\% \).[/tex]

To find the percent error, you can use the formula:

[tex]\[ \text{Percent Error} = \left| \frac{\text{Measured Value} - \text{Actual Value}}{\text{Actual Value}} \right| \times 100 \]\\[/tex]

Given:

- Measured Value = 68

- Actual Value = 60

Substitute these values into the formula:

[tex]\[ \text{Percent Error} = \left| \frac{68 - 60}{60} \right| \times 100 \]\[ \text{Percent Error} = \left| \frac{8}{60} \right| \times 100 \]\[ \text{Percent Error} = \left| 0.1333... \right| \times 100 \]Now, rounding to the nearest tenth:\[ \text{Percent Error} ≈ 13.3\% \]\\[/tex]

So, the percent error is about 13.3%. This indicates that the measured value is approximately 13.3% higher than the actual value.

The percent error, rounded to the nearest tenth, is about 13.3%.

To find the percent error, you can use the following formula:

[tex]\[\text{Percent Error} = \frac{{|\text{Estimated Value} - \text{Actual Value}|}}{{\text{Actual Value}}} \times 100.\][/tex]

Here, the estimated value is 68 marbles, and the actual value is 60 marbles.

Calculate the absolute error :

  [tex]\[ |\text{68 - 60}| = 8. \][/tex]

Calculate the relative error :

[tex]\[ \frac{{8}}{{60}}. \][/tex]

Convert to percentage :

[tex]\[ \frac{{8}}{{60}} \times 100 = 13.333. \][/tex]

Round to the nearest tenth :

[tex]\[ \approx 13.3.[/tex]

Thus, the percent error, rounded to the nearest tenth, is about 13.3%.

Question :

You estimate that a jar contains 68 marbles. The actual number of marbles is 60. Find the percent error. Round your answer to the nearest tenth. The percent error is about %.

I am pretty sure it’s step one

The volume of the foam is  : 8[tex]r^{3}[/tex]

A cube is a three dimensional shape made of 6 squares.

it has 8 corners and 12 edges.

Analysis:

Given that the sphere fits snugly in the cube the length of each face of the cube would be twice the radius of the sphere.

therefore:

L = 2r

where r = radius of sphere,

L = length of each face of cubic foam

volume of cubic foam = [tex]L^{3}[/tex]

= [tex](2r)^{3}[/tex]

= [tex]8r^{3}[/tex]

In conclusion, the volume of the cubic foam is  [tex]8r^{3}[/tex]

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Answer:

(2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)

Step-by-step explanation:

For this case we must factor the following expression:

[tex]8x^{24} -27y ^ 6[/tex]

So:

We rewrite [tex]8x^{24}\ as\ (2x ^ 8) ^ 3[/tex]

We rewrite[tex]27y ^ 6\ as\ (3y ^ 2) ^ 3[/tex]

(2x ^ 8) ^ 3- (3y ^ 2) ^ 3

Since both terms are perfect cubes, factor using the cube difference formula:

[tex]a ^ 3-b ^ 3 = (a-b) (a ^ 2 + ab + b ^ 2)[/tex]

Where:

[tex]a = 2x ^ 8\\b = 3y ^ 2[/tex]

Rewriting:

[tex](2x ^ 8-3y ^ 2) ((2x ^ 8) ^ 2 + (2x ^ 8) (3y ^ 2) + (3y ^ 2) ^ 2) =\\(2x ^ 8-3y ^ 2) (4x ^{16} + 6x ^ 8y ^ 2 + 9y ^ 4)[/tex]

ANswer:

Option C

Answer:

Area: pir^2

r=4

4pi^2

if pi=3.14

then the area is 50.24ft^2

Circumference: pi x d

d=8

8pi

if pi=3.14

then the circumference is 25.12ft.

ANSWER

Circumference=8πft

Area=16π ft²

EXPLANATION

The circumference of a circle calculated using the formula:

C=πd

The diameter of the circle is 8ft.

The circumference is

C=8π ft.

The area of a circle is given by:

A = πr²

Where r=8/2=4 ft is the radius of the circle.

Therefore the area is

A = π×4²

A=16π ft²

Answer:

B

Step-by-step explanation:

Given the 2 equations

x³ + y = 0 → (1)

11x² - y = 0 → (2)

Add (1) and (2) term by term to eliminate the term in y

x³ + 11x² = 0 ← factor out x² from each term

x²(x + 11) = 0

Equate each factor to zero and solve for x

x² = 0 ⇒ x = 0

x + 11 = 0 ⇒ x = - 11

Substitute these values into (1) for corresponding values of y

(1) y = - x³

x = 0 ⇒ y = 0 ⇒ (0, 0) is a solution

x = - 11 ⇒ y = - (- 11)³ = 1331 ⇒ (- 11, 1331) is a solution

Answer:

y = ln( x + 6 ) - 11

h = 6

k = -11

h + k = -5

Step-by-step explanation:

Horizontal shift changes whats inside the brackets, in other words, changes just the x-value.If the shift is right, the number should be subtracted, if the shift is left, the number should be added.

Vertical shift changes the equation as a whole.if the shift is up, the number of should be added.If the shift is down, the number should be subtracted.

The changes given to us are 3 units left ( horizontal translation ) and 5 units down ( vertical translation )

If we rewrite the equation, we have:

y = ln( x + 3 + 3 ) - 6 - 5

y = ln( x + 6 ) - 11

Answer:

430/5*9 = 774 miles

Step-by-step explanation:

Answer:

The fraction will decrease [tex]33.33\%[/tex]

Step-by-step explanation:

Let

x/y ----> the fraction

we know that

100%-50^=50%=50/100=0.50

100%-25%=75%=75/100=0.75

substitute

[tex]\frac{x}{y}*\frac{0.50}{0.75} =\frac{2}{3}(\frac{x}{y})[/tex]

therefore

The percent that the fraction will decrease is equal to

[tex](1-\frac{2}{3})*100=33.33\%[/tex]

Answer:

B

Step-by-step explanation:

Use the law of sines to create a proportion.

[tex]\frac{18}{sin(90)}=\frac{x}{sin(20)}[/tex]

Solve for [tex]x[/tex].

[tex]x=6.2[/tex]

Answer:

[tex]x=6.2[/tex]

Step-by-step explanation:

Given triangle is right triangle so we can use trigonometric ratios to find the value of x.

[tex]\sin\left(\theta\right)=\frac{opposite}{hypotenuse}[/tex]

[tex]\sin\left(20^o\right)=\frac{x}{18}[/tex]

[tex]\sin\left(20^o\right)(18)=x[/tex]

[tex](0.34202014332566873304409961468226)(18)=x[/tex]

[tex]6.1563625798620371947937930642807=x[/tex]

[tex]x=6.1563625798620371947937930642807[/tex]

[tex]x=6.2[/tex]

Hence final answer is [tex]x=6.2[/tex]

Answer:  B) 1.6

Step-by-step explanation:

[tex]P=100e^{0.70t}\\\\\underline{\text{Substitute P = 300:}}\\300=100e^{0.70t}\\\\\\\underline{\text{Divide both sides by 100:}}\\3=e^{0.70t}\\\\\\\underline{\text{Apply ln to both sides:}}\\ln\ 3=ln\ e^{0.70t}\\\\\\\underline{\text{ln e cancels out:}}\\ln\ 3=0.70t\\\\\\\underline{\text{Divide both sides by 0.70:}}\\\dfrac{ln\ 3}{0.70}=t\\\\\\\underline{\text{Evaluate using a calculator:}}\\1.569=t[/tex]

Answer:

yes; 5

Step-by-step explanation:

To determine if the sequence is arithmetic, take the second term and subtract the first term

-7 - (-12) = -7+12 = 5

This would be the common difference if our sequence is arithmetic

Now take the second term and add the"common difference"

-7+5 = -2  This is our third term

-2+5 = 3  This is our fourth term

The sequence is arithmetic with a common difference of 5

Answer:

  a) 708.00

  b) 108.00

  c) 11

Step-by-step explanation:

a) The cost is $59 for each of 12 months, so the total cost is ...

  12×$59 = $708

__

b) The "carrying charges" are the difference between what is paid and the cash price:

 $708 -600 = $108

__

c) Saving at the rate of $59 per month, it will take ...

  $600/($59/mo) ≈ 10.17 mo

to save the money. The amount saved will be $590, or $10 short of the required amount after 10 months, so it will take 11 months to save enough for the cash purchase.

Answer:

 a) 708.00

 b) 108.00

 c) 11

Step-by-step explanation:

Answer:

Through trial and error:

7 + (16 - 8) / 2 + (2 * 25 / 5)

Calculate the cost per square foot for each size tile.

1 square foot = 144 square inches.

Small tile = 4 x 4 = 16 square inches.

16 / 144 = 1/9 square foot.

Cost per square foot = 3.50 / 1/9 = $31.50 per square foot.

Large tile = 6 x 12 = 72 square inches.

72 / 144 = 1/2 square foot.

Cost per square foot = 4.50 / 1/2 = $9 per square foot.

The minimum area of the mosaic is 3 feet x 5 feet = 15 square feet.

The large tiles are cheaper per square foot.

Total tiles needed = 15 sq. ft.  / 1/2 sq. ft = 30 tiles.

30 tiles x 4.50 each = $135

Vinyl is = 15 in. * 33 in. = 495 in.²

Vinyl is needed 495 inches² to cover both of triangular sides

We have to given that,

Gymnastics incline mat is shaped like a wedge two sides of the matter shaped like right triangles.

Now, We know that,

Area of triangle is,

⇒ A = 1/2 x  base x height

Here, base = 33 inches

Height = 15 inches

Since, Vinyl needed to cover both of the triangular sides.

Hence, Area is,

A = 2 (Area of triangle)

A = 2 (1/2 x  base x height)

A = base x height

A = 15  x 33

A = 495 inches²

Thus, Vinyl is needed 495 inches² to cover both of triangular sides.

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The probability that an item is either Large or Blue, [tex]\( P(\text{Large or Blue}) \)[/tex], is 0.7 after simplification.

To find the probability [tex]\( P(\text{Large or Blue}) \)[/tex], we will use the principle of inclusion-exclusion. The formula for two events A and B is:

[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]

Let's define our events as:

- A = The event that an item is Large.

- B = The event that an item is Blue.

Looking at the table:

- The probability that an item is Large, [tex]\( P(\text{Large}) \)[/tex], is the sum of all Large items divided by the total number of items.

- The probability that an item is Blue, [tex]\( P(\text{Blue}) \)[/tex], is the sum of all Blue items divided by the total number of items.

- The probability that an item is both Large and Blue, [tex]\( P(\text{Large and Blue}) \)[/tex], is the number of items that are both Large and Blue divided by the total number of items.

From the table:

Now we can calculate the probabilities:

[tex]\[ P(\text{Large}) = \frac{25}{40} \][/tex]

[tex]\[ P(\text{Blue}) = \frac{20}{40} \][/tex]

[tex]\[ P(\text{Large and Blue}) = \frac{17}{40} \][/tex]

Using the inclusion-exclusion principle:

[tex]\[ P(\text{Large or Blue}) = P(\text{Large}) + P(\text{Blue}) - P(\text{Large and Blue}) \][/tex]

Let's do the calculations.

The probability of an item being Large or Blue is [tex]\( P(\text{Large or Blue}) = 0.7 \)[/tex], which is already in its simplest form.

Answer:

  sphere, cylinder, (right circular) cone

Step-by-step explanation:

Any cross section of a sphere is a circle.

A cross section parallel to the base of a cylinder or cone will have the same shape as the base. By definition, a cylinder has a circular base. A "right circular" cone will also have a circular base.

___

A torus, ellipsoid, or hyperboloid may also have a circular cross section.

ANSWER

9.6

EXPLANATION

The given trigonometric equation is:

[tex] \cos(21 \degree) = \frac{9}{y} [/tex]

We want to find y, so we multiply both sides by y to get,

[tex]y\cos(21 \degree) = \frac{9}{y} \times y[/tex]

Cancel out the common factors,

.

[tex]y\cos(21 \degree) = 9[/tex]

. Divide both sides by cos(21°)

[tex]y= \frac{9}{\cos(21 \degree)} [/tex]

[tex]y = 9.64[/tex]

To the nearest tenth, y=9.6

It will take them 30 minutes

The faster computer will take approximately 22.5 minutes to do the job on its own.

Let's assume that the faster computer can complete the job on its own in x minutes.

If the slower computer takes 45 minutes to complete the job on its own, it means that in 1 minute it completes 1/45th of the job.

Working together, the two computers can complete the entire job in 15 minutes. So in 1 minute, they can complete 1/15th of the job.

Therefore, 1/45 + 1/x = 1/15

Simplifying the equation, we get 1/x = 1/15 - 1/45

Substituting the numerator values with a common denominator, 1/x = (3/45) - (1/45) = 2/45

Now, solving for x, we get x = 45/2 = 22.5

So, it will take the faster computer approximately 22.5 minutes to do the job on its own.

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Answer:

72,000

Step-by-step explanation:

wth dude i do not know

Answer:

The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is -80 feet per second.

Step-by-step explanation:

The function that models the height of the ball is:

[tex]f(t)=-16t^2+48t=160[/tex]

At t=3, [tex]f(3)=-16(3)^2+48(3)+160=160[/tex]

At t=5, [tex]f(5)=-16(5)^2+48(5)+160=0[/tex]

The average rate of change is simply the slope of the secant line connecting.

[tex](3,f(3))[/tex] and [tex](5,f(5))[/tex].

The average rate of change

[tex]=\frac{f(3)-f(5)}{3-5}[/tex]

[tex]=\frac{160-0}{-2}[/tex]

[tex]=-80fts^{-1}[/tex]

The 21 compartments will be fully filled and the last compartment will contain 3 towels.

The number of compartments that will be filled =  total number of towels/ capacity of one compartment.

So we have 150 towels / 7 towels per compartment ≈ 21.43.

Since we can't have a fraction of a compartment, this means that 21 compartments will be fully filled.

The remaining towels can be found = the total number of towels - the number of towels that fit into the full compartments

Total no. of towels that fit into all compartments = 21 compartments × 7 towels each = 147 towels.

Therefore, we have 150 - 147 = 3 towels left, which will be in the compartment that is not completely filled.

There are 21 compartments filled with towels, and in the 22nd compartment, there will be 3 towels.

Number of compartments filled: 21 compartments  

Towels in a partially filled compartment: 6 towels  

To calculate the number of compartments filled, we need to divide the total number of towels by the maximum number of towels each compartment can hold:

[tex]\( \text{Number of compartments filled} = \frac{\text{Total number of towels}}{\text{Maximum towels per compartment}} \)[/tex]

[tex]\( \text{Number of compartments filled} = \frac{150}{7} = 21.4285 \)[/tex]

Since we can't have a fraction of a compartment, we round down to the nearest whole number, which is 21.

To find out how many towels will be in a compartment that is not completely filled, we subtract the total number of towels already placed in filled compartments from the total number of towels:

[tex]\( \text{Remaining towels} = \text{Total number of towels} - (\text{Number of compartments filled} \times \text{Maximum towels per compartment}) \)[/tex]

[tex]\( \text{Remaining towels} = 150 - (21 \times 7) = 150 - 147 = 3 \)[/tex]

So, there are 21 compartments filled with towels, and in the 22nd compartment, there will be 3 towels.

Complete question

A storage compartment for a gym locker room can hold up to 7 folded towels. There are 22 compartments for towels. Katie has 150 towels to fold and put away. How many of the compartments will be filled? How many towels will be in a compartment that is not completely filled?

let's recall that on the II Quadrant x/cosine is negative whilst y/sine is positive,

also let's recall that the hypotenuse is simply the radius distance and thus is never negative.

[tex]\bf cot(\theta )=\cfrac{\stackrel{adjacent}{-2}}{\stackrel{opposite}{1}}\impliedby \textit{let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{(-2)^2+1^2}\implies c=\sqrt{5} \\\\[-0.35em] ~\dotfill\\\\ csc(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{5}}}{\stackrel{opposite}{1}}\implies csc(\theta )=\sqrt{5}[/tex]

The exact value of csc theta when the value of cot theta is  -2 and the terminal side of theta lies in quadrant II (2) is √(5).

The terminal side of an angle is the rotated side of the initial side around a point to form an angle. This rotation can be clockwise or counter clock wise.

The exact value of csc theta has to be found out. The value of cot theta is,

cot θ = -2

cot θ =-2/1.

By the property of right angle triangle, the ratio of adjacent side to the opposite side is equal to the cot theta. Thus,

Adjacent side= -2

Opposite side= 1

The value of hypotenuse side is equal to the square root of the sum of the square of adjacent side and opposite side. Thus,

Hypotenuse side=√((-2)²+1²)

Hypotenuse side=√(5)

By the property of right angle triangle, the ratio of hypotenuse side to the opposite side is equal to the coses theta. Thus,

coses θ =√(5)/1

coses θ =√(5)

Hence, the exact value of csc theta when the value of cot theta is  -2 and the terminal side of theta lies in quadrant II (2) is √(5).

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Answer:

3a5b

Step-by-step explanation:

Answer:

3a5b

Step-by-step explanation: