A conical container can hold 120π cubic centimeters of water. The diameter of the base of the container is 12 centimeters.
The height of the container is ___ centimeters. If its diameter and height were both doubled, the container's capacity would be _____times its original capacity.

Oops wrong one man I’m sorry

Answer: The function would be,

[tex]P(x)=50000(1.04)^x+35000(1.055)^x[/tex]

The approximate total profit after 4 years is $ 97341.65.

Step-by-step explanation:

Given,

For branch A,

First year profit = $ 50,000,

And, the profit increased by 4% every year.

Thus, the profit of branch A after x years,

[tex]P_1=50000(1+\frac{4}{100})^x[/tex]

[tex]\implies P_1=50000(1.04)^x[/tex]

Also, for branch B,

First year profit = $ 35,000,

And, the profit increased by 5.5% every year.

Thus, the profit of branch B after x years,

[tex]P_2=35000(1+\frac{5.5}{100})^x[/tex]

[tex]\implies P_2=35000(1.055)^x[/tex]

Hence, the total profit,

[tex]P=P_1+P_2[/tex]

[tex]\implies P(x)=50000(1.04)^x+35000(1.055)^x[/tex]

Which is the required function.

After 4 years, x = 3,

Therefore, the total profit after 4 years would be,

[tex]\implies P(3)=50000(1.04)^3+35000(1.055)^3=\$ 97341.648125\approx \$ 97341.65[/tex]

Answer:

3,4,5 are congruent angles

Step-by-step explanation:

Congruent Angles have the same angle (in degrees or radians). That is all. They don't have to point in the same direction. They don't have to be on similar sized lines.

Answer:

#3 is congruent by SAS; #4 is congruent by SSS; #5 is congruent by AAS; #6 is congruent by ASA

Step-by-step explanation:

For #3, there are sides marked in each so we know we have 2 congruent sides, but the angle where the triangles meet are vertical angles.  So that congruency statement is SAS

For #4, there are again two sides marked in each triangle giving us 2 congruent sides, but since the two triangles share that one side, that gives us the third side for SSS

For #5, we have two angles marked congruent between the two triangles and they also share a side, so AAS is the congruency statement for that one

For #6, again 2 congruent angles and a shared side between, so ASA on that one.

You're in geometry now, yes?

Answer:

20.922

Step-by-step explanation:

Evaluate ln 7.2 on a calculator; the correct result is 1.974.

Multiply that by 3, obtaining 5.922.

Finally, add 15 to that result:  y = 15 + 3 In 7.2 = 20.922

Answer:

Step-by-step explanation:

[tex]x^2+11=36\qquad\text{subtract 11 from both sides}\\\\x^2=25\to x=\pm\sqrt{25}\\\\x=-5\ or\ x=5\\============================\\\\\dfrac{x^2-25}{x+5}=0\qquad Domain:\ x+5\neq0\to x\neq-5\\\\\dfrac{x^2-25}{x+5}=0\to x^2-25=0\qquad\text{add 25 to both sides}\\\\x^2=25\to x=-5\notin D\ or\ x=5\in D[/tex]

Final answer:

0.64 is a finite decimal with zero repeating digits as it does not have digits that continue infinitely after the decimal.

Explanation:

The number 0.64 is a decimal that has two digits after the decimal point. These digits (6 and 4) do not repeat infinitely, making them non-repeating decimal digits. Therefore, there are zero repeating digits in 0.64. A repeating decimal would have one or more digits after the decimal point that continue infinitely, often denoted by a bar over the repeating digits. Since 0.64 does not exhibit this pattern, it is a finite decimal.

the x value of point a is 5

The x value of point A is; 5

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line.

We have been given a graph representing the point A.

therefore, we need to find the coordinate of the given point.

So, we can see that the coorddinate of the point A is (5, 5)

The value x in the point A would be 5.

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Answer:

the answer would be 3.25 meters

Answer:

3 meters and 25 centimeters of ribbon

Step-by-step explanation:

Answer: The number is 8

Step-by-step explanation:

 Let be "x" the certain number. Then "3 times a certain number" means that the number "x" is multiplied by 3. This is:

[tex](3)(x)=3x[/tex]

Now, "3 times a certain number is increased by 4" means that the we must add 4 to [tex]3x[/tex], in other words, this indicate an addition:

 [tex]3x+4[/tex]

And finally "3 times a certain number is increased by 4 the result is 28" means that  [tex]3x+4[/tex] is equal to 28. Then the expression is:

 [tex]3x+4=28[/tex]

To find the number "x", subtract 4 from both sides of the equation:

[tex]3x+4-4=28-4[/tex]

[tex]3x=24[/tex]

Dividing both sides of the equation by 3, you get that the number is:

[tex]\frac{3x}{3}=\frac{24}{3}\\\\x=8[/tex]

Answer: I believe the answer is the second choice.  

81y^4 - 16x^2, the difference of squares.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The shape consists of a cylinder and a hemisphere.

The volume of a cylinder is:

V = πr²h

where r is the radius (half the diameter) and h is the height.

The volume of a hemisphere is:

V = ⅔ πr³

where r is the radius (half the diameter).

The cylinder and hemisphere both have a diameter of 8 cm, or a radius of 4 cm.  The cylinder has a height of 17 cm.

So the total volume is:

V = π(4 cm)²(17 cm) + ⅔ π(4 cm)³

V = π (272 + 128/3) cm³

V ≈ 988.6 cm³

Answer:

444

Step-by-step explanation:

For this case we must find an expression equivalent to:

[tex]log_ {5} (\frac {x} {4}) ^ 2[/tex]

So:

We expanded [tex]log_ {5} ((\frac {x} {4}) ^ 2)[/tex]by moving 2 out of the logarithm:

[tex]2log_ {5} (\frac {x} {4})[/tex]

By definition of logarithm properties we have to:

The logarithm of a product is equal to the sum of the logarithms of each factor:

[tex]log (xy) = log (x) + log (y)[/tex]

The logarithm of a division is equal to the difference of logarithms of the numerator and denominator.

[tex]log (\frac {x} {y}) = log (x) -log (y)[/tex]

Then, rewriting the expression:

[tex]2 (log_ {5} (x) -log_ {5} (4))[/tex]

We apply distributive property:

[tex]2log_ {5} (x) -2log_ {5} (4)[/tex]

Answer:

An equivalent expression is:

[tex]2log_ {5} (x) -2log_ {5} (4)[/tex]

Answer: the answer is c

Step-by-step explanation: 2log5x-2log54

Answer:

A' will be located 10 units from point A along ray PA

Step-by-step explanation:

we know that

The scale factor is equal to 3

To obtain PA', multiply PA by the scale factor

so

PA'=PA*3

PA=5 units

substitute

PA'=(5)*3=15 units

AA'=PA'-PA=15-5=10 units

therefore

A' will be located 10 units from point A along ray PA

Answer:10 units

Step-by-step explanation:

Answer:

V = s^3

V = 729 ft^3 when the side length is 9 ft

Step-by-step explanation:

The volume of a cube is given by

V = s^3  where s is the length of a side

Assuming you mean the side length is 9 ft

V = 9^3

V = 9*9*9

V =729 ft^3

See the attached picture:

Multiply the bracket by 3

3(2f+g+4)

My answer is 6f+3g+12

Answer is true

This is true. You applied the Distributive Property authentically.

Answer:

x = 8

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve for x

The square on the hypotenuse is equal to the sum of the squares on the other two sides, thus

x² + 6² = 10²

x² + 36 = 100 ( subtract 36 from both sides )

x² = 64 ( take the square root of both sides )

x = [tex]\sqrt{64}[/tex] = 8

Answer:

279 ft^2

Step-by-step explanation:

The area of a rectangle of length L and width W is A = LW.

Here, that area is (19.25 ft)(14.5 ft) = 279.125 ft^2, or approx. 279 ft^2

Answer:

x = 75

Marta's jump rope is 75 inches long

Step-by-step explanation:

Hello!! This is how you solve it:

x + ( x - 10 x 3 ) = 120

2x - 10 x 3 = 120

2x - 30 = 120

+ 30. + 30

2x = 150

--- ------

2. 2

x = 75

Final answer:

Marta's jump rope is 87.5 inches long. This was determined by setting up an equation based on the information that Marta's rope is 10 inches shorter than three times Dilbert's rope length, and together they measure 120 inches.

Explanation:

The question involves finding the length of Marta's jump rope when it is known to be 10 inches shorter than three times the length of Dilbert's rope, and when both ropes laid end-to-end measure 120 inches long. Let's denote the length of Dilbert's jump rope as D inches. Therefore, the length of Marta's jump rope can be expressed as 3D - 10 inches. Since the combined length of both ropes is 120 inches, we can write the equation: D + (3D - 10) = 120.

Combining like terms, we get 4D - 10 = 120. Adding 10 to both sides gives 4D = 130, and dividing both sides by 4 yields D = 32.5 inches. Thus, Dilbert's rope is 32.5 inches long, and Marta's rope, being 3(32.5) - 10, calculates to 87.5 inches long.

Step-by-step explanation:

hope it helps you!!!!!!!!!!

Answer:

Hello :))

Step-by-step explanation:

You should set this up as a proportion equation. 8.1kg /1hr =x/7hr You would cross multiply here and end up getting the equation... 1x=8.1*7 (x=56.7 kg)

Hope this helps! :))

By moving the decimal according to the number of places expressed by the exponents, we can see the real value of each answer choice.

A. .0008 lbs not a realistic weight for an 18-wheeler

B. 800 lbs closer but still not enough weight

C. .08 nope not this one either.

D. 80,000 lbs. this is probably in the range we are looking for.

If the exponent is negative, move the decimal that many spaces left. If the exponent is positive, move the decimal that many space right.

The correct answer is D.

Answer:

The reasonable estimate for the weight of an 18-wheeler is [tex]8 * 10^{4} lb[/tex]

Step-by-step explanation:

The average and legally maximum weight of an 18-wheeler is 80,000 pounds.

From option a through d, we check which of the measurement is close or equivalent to 80,000 pounds

By converting this, we have

[tex]= 8 * \frac{1}{10000} lb[/tex]

[tex]= \frac{8}{10000} lb[/tex]

[tex]= 0.0008 lb[/tex]

By converting this, we have

[tex]= 8 * 100 lb[/tex]

[tex]= 800 lb[/tex]

By converting this, we have

[tex]= 8 * \frac{1}{100} lb[/tex]

[tex]= \frac{8}{100} lb[/tex]

[tex]= 0.08 lb[/tex]

By converting this, we have

[tex]= 8 * {10000} lb[/tex]

[tex]= {80000} lb[/tex]

From the 4 conversions, only  [tex]8 * 10^{4} lb[/tex] is equivalent to the average and legally maximum weight of an 18-wheeler, 80,000 pounds.

Hence, the reasonable estimate for the weight of an 18-wheeler is [tex]8 * 10^{4} lb[/tex]

1 = C      2 = I     3 = B  have a good day

I hope to understood my writing

To determine at what time the two lorries will meet, we can use the concept of relative speed. Since the lorries are moving towards each other, their relative speed is the sum of their individual speeds.
The speed of the first lorry is 63 km/h and the speed of the second lorry is 67 km/h. Together their combined speed is:
63 km/h + 67 km/h = 130 km/h
Now we need to calculate how long it will take for them to cover the distance of 520 km between the two towns at their combined speed.
The time taken to cover a distance is equal to the distance divided by the speed, so the time taken \( t \) in hours can be found by:
\( t = \frac{distance}{speed} \)
Substituting the known values into this formula gives us:
\( t = \frac{520 km}{130 km/h} = 4 \) hours
Now we know the lorries will meet after 4 hours of travel.
Given that the lorries start to travel at 7:30 am, we add 4 hours to that time to find the meeting time.
7:30 am + 4 hours = 11:30 am
Therefore, the two lorries will meet at 11:30 am.

Answer: Option E

[tex]0.120\ g[/tex]

Step-by-step explanation:

The exponential decay formula is:

[tex]C (t) = pe^ {-rt}[/tex]

Where p is the initial amount of Ytterbium

r is the rate of decrease

C(t) is the amount of Ytterbium in grams as a function of time

t is the time in days

In this problem:

[tex]p = 80\ g\\\\r=\frac{50\%}{100\%}\\\\r=0.5[/tex]

t is the time in units of 4.2 days

Then

[tex]C(t) = 80e^{-0.5t}[/tex]

We want to calculate the amount of Ytterbium in 54.6 days.

Then as t is the time in units of 4.2 days

[tex]t = \frac{54.6}{4.2} = 13\\\\t = 13[/tex]

Finally

[tex]C(t=13) = 80e^{-0.5*13}[/tex]

[tex]C(t) = 0.120\ g[/tex]

The solution is :the ages of the three are: 12, 15, 6.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

1)

Let x - Kareem's age => Sadie's age - x + 3, Nadra - x/2

We end up with the expression;

x + x + 3 + x/2 = 33

Multiply by 2 to get rid of the fraction;

2x + 2x + 6 + x = 66

5x = 60

x = 12 - Kareem's age;

2) x + 3 = 12 + 3 = 15 - Sadie's age;

3) x / 2 = 12 / 2 = 6 - Nadra's age;

Hence, The solution is :the ages of the three are: 12, 15, 6.

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Final answer:

The student's first error in determining the ages of Sadie, Kareem, and Nadra was in the setup of the equation, incorrectly representing Nadra's age as 2x instead of ½x. Correcting this mistake involves modifying the equation to accurately reflect the relationships between their ages.

Explanation:

The first error made by the student is in the setup of the initial equation for the ages of Sadie, Kareem, and Nadra. The equation (x + 3) + x + 2x = 33 inaccurately represents Nadra's age in relation to Kareem's. Given that Kareem is twice as old as Nadra, Nadra's age should be represented as ½x (half of Kareem's age), not 2x.

Correcting the initial equation should look like this: (x + 3) + x + ½x = 33. This equation accurately represents Sadie being 3 years older than Kareem and Kareem being twice as old as Nadra. To solve this corrected equation, we first combine like terms to simplify: 2½x + 3 = 33. Then, we solve for x to determine each person's age correctly.

Answer:

-4

Step-by-step explanation:

(1/4)*x-(1/8) = (1/2)*x+7/8

First rearrange the numbers

(1/4)*x-((1/2)*x)-(1/8)-(7/8)

1/4*x ((-1/2)*x)-(1/8)-(7/8)

-1/4*x-1 = 0 + 1

-1/4*x = 1  -1/4

x = 1/(-1/4)

x = -4

x = -4

Answer:

z = 24°

Step-by-step explanation:

The 3 angles 48, x and x form a straight angle and sum to 180°, thus

x + x + 48 = 180

2x + 48 = 180 ( subtract 48 from both sides )

2x = 132 ( divide both sides by 2 )

x = 66

The 3 angles in a triangle sum to 180°

sum the 2 known angles and subtract from 180

z = 180° - (66 + 90)° = 180° - 156° = 24°

Answer:

z=24

Step-by-step explanation:

Answer:

Measure B= 121

Measure C=59

Step-by-step explanation:

10x-19=7x+23

3x=42

x=14

plug in x to the problem and you'll find Measure B is 121 so to find Measure C you'll have to subtract 180 and 121 to get 59.

The value of angle B is 121 degree and Angle C is 59 degree, and Angle D has the same measure as the angle B

It is defined as the four-sided polygon in geometry having four edges and four corners and two pairs of congruent sides. It has one pair of opposite congruent angles.

We have a quadrilateral in which angle B and angle D are given.

As we know the opposite angles in the quadrilateral are same in measure.

10x - 19 = 7x + 23

3x = 42

x = 14

Angle B =  10x - 19 = 10(14) - 19 = 121 degree

Angle C =  7x + 23 = 7(14) + 23 = 121 degree

Angle A + Angle C = 360 - 121 -121 = 118

Angle C = 118/2 = 59

Thus, the value of angle B is 121 degree and Angle C is 59 degree, and Angle D has the same measure as the angle B

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Answer:

It is angle 4 because they make 90 degrees together. This is if there are choices for the problem.

It would be ∠4

Angle 4 is the complementary angle of 3 because the sum of these angles is 90 degrees.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have:

From the angle diagram, angle 4 makes the complete right angle.

The sum of the complementary angles is 90 degree

Angle 3 + Angle 4 = 90 degree

Thus, angle 4 is the complementary angle of 3 because the sum of these angles is 90 degrees.

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