1. Adrian invests $10,000 in an account that increases by 8% each year. What is the balance in the account after 15 years?

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Reason:

If the linear scale factor is 5, then the volume scale factor is 5^3 = 125

Meaning we'll multiply the old volume by 125 to get the new volume

new volume = 125*(old volume)

new volume = 125*(24)

new volume = 3000

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A more in-depth look:

Consider a 2 by 2 by 2 block. Its volume is 2*2*2 = 8

Now multiply each dimension by 5, so we now have a 10 by 10 by 10 block. The new larger volume is 10*10*10 = 1000

The volume ratio is 1000/8 = 125, which matches with the value found earlier.

Since we multiplied each piece by 5, and did so three times, we're really multiplying the volume by 5*5*5 = 125.

Answer:

Yes

Step-by-step explanation:

So we know the second child was a boy however if the first child was a boy, the probability of getting a second boy would be 7/17 since one boy is missing and one person is missing from the total.

However, if a girl was chosen as the first child, the probability of getting a boy second would be 8/17 since no boys would be missing but one person would be missing from the original total.

According to Heron's formula, the area of a triangle whose vertices are R(x, y) = (3, 4), S(x, y) = (6, 2) and T(x, y) = (7, 10) has a value of approximately 14.525 units.

In this question we must determine the lengths of the three sides of the triangle by Pythagorean theorem and then the area is determined by Heron's formula.

First, we determine the length of each side:

[tex]RS = \sqrt{(6-3)^{2}+(2-4)^{2}}[/tex]

[tex]RS = \sqrt{3^{2}+(-2)^{2}}[/tex]

[tex]RS = \sqrt{13}[/tex]

[tex]ST = \sqrt{(7-6)^{2}+(10-2)^{2}}[/tex]

[tex]ST = \sqrt{1^{2}+8^{2}}[/tex]

[tex]ST = \sqrt{65}[/tex]

[tex]RT = \sqrt{(7-3)^{2}+(10-4)^{2}}[/tex]

[tex]RT = \sqrt{4^{2}+6^{2}}[/tex]

[tex]RT = \sqrt{80}[/tex]

Now we calculate the area of the triangle by Heron's formula:

[tex]s = \frac{\sqrt{13}+\sqrt{65}+ \sqrt{80}}{2}[/tex]

s ≈ 10.306

[tex]A = \sqrt{10.306 \cdot (10.306 - \sqrt{13})\cdot (10.306 - \sqrt{65})\cdot (10.306 - \sqrt{80})}[/tex]

A ≈ 14.525

According to Heron's formula, the area of a triangle whose vertices are R(x, y) = (3, 4), S(x, y) = (6, 2) and T(x, y) = (7, 10) has a value of approximately 14.525 units.

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Answer:

2y = x - 1

Step-by-step explanation:

y = 2y

mx = x

c = -1

Answer:

The mean is greater than median

Step-by-step explanation:

Option D

Answer:

-1 - 4 i

Step-by-step explanation:

5 - (2 * i) - (2 * (3 + i)) =

-1 - 4 i

Answer:

P(A) = 13/18

P(B) = 7/18

Step-by-step explanation:

A) Sum greater than 5

If the sum needs to be >5, then it can be 6, 7, 8, 9, 10, 11, and 12.

There are 26 out of 36 events where the sum is >5, thus P(A) = 26/36 = 13/18.

B) Sum divisible by 4 or 6

The sum ranges from 2 to 12, there are two methods to calculate this:

B1) Method 1: Calculate the frequency one by one

The sums divisible by 4 or 6 are S = {4, 6, 8, 12}. There are 9 of them, n(S) = 14. Thus P(B) = 14/36 = 7/18.

B2) Method 2: Use the rule of not mutually exclusive events

Not mutually exclusive events (might also be called mutually inclusive) happens when two events can happen together at the same time. In this problem, the sum might be divisible by 4 and 6 at the same time, i.e. the number 12.

The common formula for not mutually exclusive events is P(A∪B) = P(A) + P(B) - P(A∩B). Nb: P(A) isn't talking about the previous problem, nor does P(B) talk about the second section as a whole; the terms P(A) and P(B) will be utilized next, explained with their uses.

P(A) = probability of the sum being divisible by 4, i.e. the number 4, 8 and 12

P(A) = (3+5+1) / 36 = 9/36 = 1/4

P(B) = probability of the sum being divisible by 6, i.e. the number 6 and 12

P(B) = (5+1) / 36 = 6/36 = 1/6

P(A∩B) = probability of the sum being divisible both by 4 and 6, i.e. the number 12

P(A) = 1 / 36 = 1/36

Here comes the use of formula P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = 1/4 + 1/6 - 1/36 = 7/18

Nb: As you can see, both method B1 and B2 give the same answer. Method B1 is usually easier to use when facing simpler problems like this. I'd recommend using method B2 for more complex and difficult questions, such as when you can't visualize the problem with a table because there are too much sets of variables.

Image of table for reference: https://qph.fs.quoracdn.net/main-qimg-1283a98bd649f522986e2f91a592ffd3

Answer:

greatest to least: cindy, betty, alice

Step-by-step explanation:

multiply each amount by 20- 5 days times 4 weeks

3*20=60 for alice

25*3=75 betty

75*3=225 cindy

Answer:

Step-by-step explanation:

The angles labeled with 2x, 4x, and 3x are on a straight line so their sum is equal to 180

2x + 4x + 3x = 180 add like terms

9x = 180 divide both sides by 9

x = 20

The angle represented with 3x - 30 and the angle represented with 2x + 10 are alternate and their measurement is same

3x - 30 = 2x + 10 export like terms to same side of the equation

3x - 2x = 10 + 30

x = 40

to find the angles replace x with the value found for each.

Answer:

  2973.5 liters

Step-by-step explanation:

You are being asked to find the volume of the largest possible container that has a given surface area. The volume will depend on the shape. If shape is not specified, we know a sphere has the largest volume for a given area.

__

The available area is ...

  ($100) / ($10/m²) = 10 m²

The area of a sphere with diameter d is ...

  A = πd²

Then the diameter for the given area is ...

  10 m² = πd²

  (10/π) m² = d² . . . . . divide by π

  √(10 m²/π) = d ≈ 1.78412 m . . . . . . diameter of the largest sphere

The volume of a sphere is given by ...

  V = 4/3πr³ = (π/6)d³

For the diameter found above, the volume of the sphere will be ...

  V = (π/6)(1.78412 m)³ ≈ 2.97354 m³

There are 1000 liters in a cubic meter, so the largest amount of water that can be contained is ...

  2.97354 m³ × (1000 L/m³) = 2973.54 L

The largest amount of water the container can hold is about 2973.5 liters.

The area of the smallest box that a circular pizza will fit into = 1661 squared cm.

The area of a circle is the amount of space enclosed within the boundary of a circle. The region within the boundary of the circle is the area occupied by the circle.

The circular pizza requires the same amount of dough as the square pizza.

Area of the square pizza =40 cm * 40 cm

                                         = 1600 [tex]cm^{2}[/tex].

Area of circle= [tex]\pi\; r^{2}[/tex]

        1600     = 3.14 *[tex]r^{2}[/tex]

         [tex]r^{2}[/tex] = 510

        r= 22.58

       r = 23 cm approx.

Area of circle= [tex]\pi\; r^{2}[/tex]

                     = [tex]3.14 * (23)^{2}[/tex]

                     = 1661.06 squared cm

The area of the smallest box that a circular pizza will fit into = 1661 squared cm.

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Answer:

m = 60

Step-by-step explanation:

log is another way to write an exponent.

Example:

exponent form:

7^2 = 49

log form:

log_7 (49) = 2



In your question, we need to change to exponent form, from log form.

log_5 (2m+5)=3

5 is the base. 3 is the exponent.

Now it can be solved.

5^3 = 2m+5

125 = 2m + 5

120 = 2m

60 = m

Answer:

3x +18+4x+15=180

7x+33=180

7x=180-33

7x=147

7x÷7=147÷7

x=21

Answer:

[tex]\boxed{\bf x = {21}^{o} }[/tex]

Step-by-step explanation:

We know that the sum of angles of a linear pair is always equal to 180°, they are also known as supplementary angles.

«•••••••••••••••«»•••••••••••••••»

Answer:

Step-by-step explanation:

The problem is concerned with angles 4 and 5, which lie between the lines given as parallel. They are on opposite sides of the line cutting across those parallel lines (the transversal), so they are ...

__

Being congruent angles, their measures are ...

_____

Additional comment

For questions like this, there are many descriptions that are true. It would be helpful to know the possible answer choices.

Answer:

The solution set is {-6, -2}.

Step-by-step explanation:

x^2 + 8x + 15 = 3

x^2 + 8x = -12

Completing the square:

(x + 4)^2 - 16 = -12

(x + 4)^2 = 4

Taking square roots of both sides:

x + 4 =  +/- 2

x = 2 - 4 = -2  or x = -2-4 = -6.

Answer:

2 cm.

Step-by-step explanation:

Volume of the water is the same in the 2 cyinders,

Volume of water in  A = π r^2 * 18.

Volume in B = π (3r)^2 * h.

So 18πr^2 = 9π r^2 h

18 = 9h

h = 18 / 9

= 2

Answer:

[tex]2\sqrt{61\pi }[/tex]

Step-by-step explanation:

Let's find c by using the Pythagorean Theorem: [tex]10^2 + 12^2 = c^2[/tex] so [tex]c = \sqrt{10^2 + 12^2}[/tex]. I'm going to leave c like this so it is easier to multiply by [tex]\sqrt{\pi }[/tex]. [tex]c\sqrt{\pi } = \sqrt{10^2 + 12^2}\sqrt{\pi } = 2\sqrt{61\pi }.[/tex]

Hope this helped! :)

Answer:

last option, x = -1

Step-by-step explanation:

[tex]x^{2} + 2x + 1 = 0\\x_{1} = \frac{-2 + \sqrt{2^{2} - 4(1)(1) } }{2(1)}\\x_{2} = \frac{-2 - \sqrt{2^{2} - 4(1)(1) } }{2(1)}\\x_{1} = \frac{-2 + \sqrt{0} }{2}\\x_{2} = \frac{-2 - \sqrt{0} }{2}\\x = \frac{-2}{2} \\x = -1[/tex]

The value of x by using the Quadratic Formula is,

⇒ x = - 1

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

Equation is,

⇒ x² + 2x + 1

Now, We can use the Quadratic Formula for x as;

⇒ x² + 2x + 1

⇒ x = - 2 ± √2² - 4×1×1 / 2

⇒ x = - 2 ± √4 - 4 / 2

⇒ x = - 2 / 2

⇒ x = - 1

Thus, The value of x by using the Quadratic Formula is,

⇒ x = - 1

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Answer:

D. As the x-values go to positive infinity, the function's values go to positive infinity.

Step-by-step explanation:

the answer on edge 2022

As the x-values go to positive infinity, the function's values go to positive infinity. The correct option is D.

A function is a mathematical formula that describes how the dependent variable and independent variable are related. The dependent variable's value varies in the function together with the independent variable's value.

The correct option is D that as the x-values go to positive infinity, the function's values go to positive infinity.

In mathematics, a function is a rule that gives each input value in a set a distinct output value. A function is, more precisely, a collection of ordered pairs (x, y), where each x-value is matched with precisely one y-value.

The variable x normally represents the input values, also known as the independent variable, while the variable y typically represents the output values, also known as the dependent variable. Typically, a symbol like f(x), where f is the function's name and x is the input variable, is used to represent a function.

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Answer:

(b) 12.459 and (f) 7.65

Step-by-step explanation:

The value of 5 in 13.725 is 0.005 (or 5 in the thousandths place)

We need to find numbers with 10 times that value in the number.

Evaluating the options given :

(a) 5.368

(b) 12.459

(c) 57.31

(d) 6.508

(e) 4.315

(f) 7.65

Hence, the numbers are : (b) 12.459 and (f) 7.65

Answer:

b and f

Step-by-step explanation:

The 5 in 13.725 is in the thousandth place:  0.005

So three places after the decimal point.

If you multiply 0.005 by 10, then it becomes 0.05 (as multiplying by 10 moves the decimal point one place to the right).

Therefore, we are looking for numbers that have a 5 in the hundredth place, so a 5 in the second place after the decimal point.

There are two numbers that have a 5 in the hundredth place:

(b)  12.459

(f)  7.65

Expression 3200(1.06)^t represents the enrollment of a high school t years after 2000 will increase by 6%.

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

The given expression is as follows:-

=  3200 ( 1.06 ) [tex],^t[/tex]

Here when the time has increased the percentage is also increased by 6%.

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Answer:

Length: 18 inches

Width: 6 inches

Step-by-step explanation:

l+w=24

l=3w    w=1w

3w+w=24

       w=6

Length: 3*6=18 inches

Width: 6 inches

Answer: Correct me if I am wrong, but this is how I think you should solve it.

Step-by-step explanation:

1. Simplify 8×5 to 40.

−2×(40+9)−6×7

2. Simplify 40+9 to 49.

−2×49−6×7

3. Simplify −2×49 to −98.

−98−6×7

4. Simplify 6×7 to 42.

−98−42

5. Simplify

−140

Your all done! Hope this helps.

Find Q

Not safe

Apply Pythagorean theorem

PR²=4²+15²=16+225=241

Answer:

a) not safe

b) 15.5 ft (nearest tenth)

Step-by-step explanation:

Tan trig ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

Substituting the given values into the formula and solving for x:

[tex]\implies \sf \tan(x)=\dfrac{4}{15}[/tex]

[tex]\implies \sf x=\tan^{-1}\left(\dfrac{4}{15}\right)[/tex]

[tex]\implies \sf x=14.9^{\circ}\:(nearest\:tenth)[/tex]

As 14.9° is not between 18° and 27°, the roof is not safe.

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Pythagoras’ Theorem

[tex]\sf a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substituting the given values into the formula and solving for PR:

[tex]\implies \sf 15^2+4^2=PR^2[/tex]

[tex]\implies \sf 225+16=PR^2[/tex]

[tex]\implies \sf PR^2=241[/tex]

[tex]\implies \sf PR=\sqrt{241}[/tex]

[tex]\implies \sf PR=15.5\:ft\:(nearest\:tenth)[/tex]

Answer:

The first job pays more

Step-by-step explanation:

950 x 3 = One month pay = 2,850

2,859 x 12 = One year = 34,308 Per Year

Comparing them both

$45,000 One Year, First Job

$34,308 One Year, Second Job

Answer:

answer is a

Step-by-step explanation:

u just look at 6 and 6.60 thats 1 and 10 every eraser but for 3 its 1.30

Answer:

[tex]\frac{93458}{19435}[/tex] ≈ 4.81

Step-by-step explanation:

[tex]\frac{93458}{19435}[/tex] can not be simplified

[tex]8.92 ~ \text{cm}^2\\\\=8.92 \times \left( 1 ~ \text{cm} \right)^2\\\\=8.92 \times \left(10^{-2}~ \text{m} \right)^2~~~~~~;\left[1~ \text{cm} = \dfrac{1}{100}~ \text m} = 10^{-2}~ \text{ m} \right]\\\\=8.92 \times 10^{-4}~ \text{m}^2\\\\=0.000892~ \text{m}^2[/tex]