Need help with this one please show it step by step.
Thank you!

well, the interest is going to be the increase factor on both cases, so we can simply check how much each will accumulate to in those 4 years

\(~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}\)

\(A = 4000\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies A=4000(1.0125)^{16}\implies \boxed{A \approx 4879.56} \\\\[-0.35em] ~\dotfill\)

\(~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}\)

\(A = 4000\left(1+\frac{0.055}{2}\right)^{2\cdot 4} \implies A=4000(1.0275)^8\implies \boxed{A \approx 4969.52} ~~ \textit{\LARGE \checkmark}\)

The population of the country will be 796 million approximately in the year 2022.

To find when the population of the country will be 796 million, we can set the equation equal to 796 and solve for t:

\(A = 433.4e^{(0.032t)}\\796 = 433.4e^{(0.032t)}\)

Divide both sides by 433.4:

\(e^{(0.032t)} = 1.836\)

Take the natural logarithm of both sides:

\(ln(e^{(0.032t)}) = ln(1.836)\)

0.032t = 0.605

Divide both sides by 0.032:

t = 18.91

Therefore, the population of the country will be 796 million approximately 19 years after 2003. To find the year, we add 19 to 2003:

2003 + 19 = 2022

Therefore, the population of the country will be 796 million approximately in the year 2022.

Learn more about Population of the country  at

brainly.com/question/26835559

#SPJ1

Answer:

you need 90 ounces

Step-by-step explanation:

7.5×12 = 90

The number of routes that Paula can take using graph theory is; E: 4

We will observe that out of the 12 cities, 6 of them possess 3 edges going in/out of them.

The 6 cities are such that there are 2 at the top, 2 at the bottom, and 1 on each side.

In graph theory terms, we can say that they are of degree 3.

Thus, at least 1 edge connecting to each of these cities cannot therefore be used. Furthermore, the same concept applies to the start and end points, due to the fact that we don't want to return to them.

There are 6 + 2 = 8 vertices that we can tell have 1 unused edge, and then we have 17 - 13 = 4 unused edges to work with due to the fact that we have 17 edges in total, and as such must use exactly 13 of them).

Finally, we notice that at each of the 2 cities marked with an O on a path in the image attached, that there are 2 possibilities such that it's either we continue straight and cross back over that same path later, or we will make a left turn, and then turn rightward when we approach the junction again.

This gives us a total of;

2 * 2 = 4 possible different routes

Read more about Number of routes at; https://brainly.com/question/13209100

#SPJ1

Answer:

A line that is parallel to y = 3x - 9 will have the same slope as the given line. The slope of y = 3x - 9 is 3. Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (1, 2)

Substituting the values we get:

y - 2 = 3(x - 1)

Simplifying the equation we get:

y - 2 = 3x - 3

y = 3x - 1

Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is y = 3x - 1 .

;>

Answer:

y=5x

Step-by-step explanation:

because it has only one term which is called monomial.

thank you

Answer:

by ASA rule

they are congruent

There are 3,125 different places to sit if they don't mind sharing s desk sometimes and there are 120 different places to sit, if they all sit on separate tables.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that there are five different tables in the class and five students

Each table can be occupied by only one student

There are 200 days of studying years.

As a small prank on their teacher students would like to sit in a new way every day, so there are no two days during their studying year such that all students are occupying the same tables.

5×4×3×2×1 = 120

There are 120 different places to sit, if they all sit on separate tables.

5×5×5×5×5 = 3,125

There are 3,125 different places to sit if they don't mind sharing s desk sometimes.

Hence, there are 120 different places to sit, if they all sit on separate tables and there are 3,125 different places to sit if they don't mind sharing s desk sometimes.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ1

Answer:

Respond to the post by acknowledging the person’s argument and explaining why he disagrees.

Step-by-step explanation:

did this on edge

have a good day!!

Answer:

The correct answer is C.) Respond to the post by acknowledging the person’s argument and explaining why he disagrees.

Step-by-step explanation:

I just did the assignment on edge 2020 and got it right

Answer:

To calculate the book value of the building, we need to calculate the annual depreciation amount and multiply it by the number of years elapsed since the building was completed.

The annual depreciation amount is calculated as: $1 million / 50 years = $20,000

In 2014, the book value of the building was: $1 million - ($20,000 * (2014 - 2010)) = $1 million - ($20,000 * 4) = $960,000

In 2022, the book value of the building will be: $1 million - ($20,000 * (2022 - 2010)) = $1 million - ($20,000 * 12) = $680,000

Answer:

55 degrees

Step-by-step explanation:

It is given that DCB is a right angle. So the angles are complementary angles

It means that, x+35 degrees = 90

that is, x=90-35= 55 degrees

A function modeling the volume of the box can be found, and the values of x for which the volume is greater than 230 in2 are x = [-2.636, 2.636]. The largest volume is 480 in2, which is achieved when x = 5.

A function that models the volume V of the box can be found by subtracting four \(x2\)from both the length and the width, and then multiplying the result to get the volume:

V = \((12 - 4x2)(20 - 4x2)\)

To find the values of x for which the volume is greater than 230 in2, we can solve the equation

V = \((12 - 4x2)(20 - 4x2) = 230\) for x.

This gives x values of ±2.636

Thus, the values of x for which the volume is greater than 230 in2 are x = [\(-2.636, 2.636\)].

The largest volume that such a box can have is 480 in2, which is obtained when x is equal to the length or width divided by two. This occurs when x = 10/2 = 5. Thus, the largest volume that such a box can have is 480 in2.

Learn more about volume here

https://brainly.com/question/16134180

#SPJ4

When dividing two exponential functions with the same base, the second law states that the exponents must be subtracted

f(4) = (6)⁴ = 1296

According to the first law, adding the exponents will multiply two exponential functions with the same base. According to the second law, we must subtract the exponents when dividing two exponential functions with the same base. The third law indicates that we must multiply the exponents in order to increase a power to a new power.

Here,

Given :

=>f(2) = 36

=> f(3) = 216

So,

=> f(x) = (6)ˣ

=>f(4) = (6)⁴ = 1296

If f(x) = , where b > 0 and b 1, is the formula for an exponential function. B is referred to as the base and x is referred to as the exponent, just like in any exponential expression. Bacterial proliferation is an illustration of an exponential function. Some bacteria grow by two folds per hour.

To learn more about exponential function refer to:

brainly.com/question/2456547

#SPJ1

Answer:

2,29

Step-by-step explanation:

17,56 = 29,01 - 5x

5x = 29,01 - 17,56

5x = 11,45|:5

x = 2,29

Answer:

x =2.29

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Step-by-step explanation:

The equation of rectangular coordtion given polar coordinates are

\(x = r \cos( \alpha ) \)

\(y = r \sin( \alpha ) \)

R is 2, and alpha is 5pi/4

So

\(x = 2 \cos( \frac{5\pi}{4} ) = - \sqrt{2} \)

\(y = 2 \sin( \frac{5\pi}{4} ) = - \sqrt{2} \)

So our rectangular coordinates are

\(( - \sqrt{2} , - \sqrt{2} )\)

To convert from rectangular coordinates to polar coordinates

\(r = \sqrt{ {x}^{2} + {y}^{2} } \)

\( \alpha = \tan {}^{ - 1} ( \frac{y}{x} ) \)

Since the point (3,-2), is in the fourth quadrant, our angle should be within (270 and 360 degrees)

\(r = \sqrt{ {3}^{2} + ( - 2) {}^{2} } = \sqrt{13} \)

\( \alpha = \tan {}^{ - 1} ( - \frac{2}{3} ) \)

We about about

\( \alpha = 326.31\)

So our polar coordinates are

\(( \sqrt{13} ,326.31)\)

The second entry is in degrees. If you need to convert to radians, let me know

Answer:

its 1/36th

Step-by-step explanation:

there are 36 total outcomes

Answer:

probability

Step-by-step explanation:

The desired proof of congruence is given below:

In ΔAMD and ΔBMC,

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given that,

ABCD is the ║gm

Diagonals AC and BD with M as the intersection point.

To prove:

AM ≅ CM

Proof:

In ΔAMD and ΔBMC,

∠M = ∠M                   (∵ Common)

AD = BC                       (∵ opposite sides of ║gm are equal)

∠ADM = ∠CBM           (∵ Alternate angle)

∵ ΔAMD ≅ ΔBMC

Thus, AM ≅ CM      (using AAS property).

Read more about parallelograms here:

https://brainly.com/question/3050890

#SPJ1

Here is parallelogram ABCD:

Prove segment is AM congruent to segment CM.

Answer:

Z = 22.5, Y = 81, X = 26.7

Step-by-step explanation:

Using the lengths you do know compare them to the copy, the only two lengths available that are for the same side length are 33 and 22, divide them together and you get 1.5. Thats the scale factor. Everything else you can figure out by multiplying or dividing by this scale factor.

\(Z = (15)(1.5) = 22.5\\Y = (54)(1.5) = 81\\X = (40)/(1.5) = 26.7\)

The constant of proportionality in the equation is 5/4

The constant connecting two given numbers in what is known in a proportional relationship is the constant of proportionality.

The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

In the problem, y = 5/4x

The constant term 5/4 as used in the equation is used t multiply the input x values to get the out put y values

The term helps in relating x to y

Learn more about constant of proportionality at:

https://brainly.com/question/27598477

#SPJ1

The simplest form of the given expression is (- 8n² +n +1)

Simplification is the process of making simple an expression, terms or equations so as to easy for solving or evaluating.

There are some steps for simplification such as removing parenthesis, collecting like terms, addition or subtraction of like terms and so on.

We are given an expression, ( -7n² - 8n -8) + (- n² + 9n +9)

In order to simplify, we first remove the parenthesis and get

- 7n² - 8n -8 - n² + 9n +9

in the next we will collect like terms

- 7n² - n² -8n +9n - 8 +9

We now add or subtract like terms

- 8n² + n+1

this is the simplest form of the given expression.

To learn more about simplification visit:

https://brainly.com/question/18077355

#SPJ1

The laws of cosine and sine and the given parameters can be used to

calculate the measure of angles and distances.

Correct responses:

Question 1: A. m∠C = 76°, a = 7.84, b = 4.37

Question 2: C. 1 triangle

Question 3: D. 31.2 miles

Question 4: A. b = 10.799

Question 5: C. 28.9°

Question 1:

If m∠A = 72°

m∠B = 32°

c = 8

Therefore;

m∠C = 180° - 72° - 32° = 76°

\(\displaystyle \frac{a}{sin(72^{\circ})} = \mathbf{ \frac{8}{sin(76^{\circ})} }\)

\(\displaystyle a = \mathbf{\frac{8}{sin(76^{\circ})} \times sin(72^{\circ})} \approx 7.84\)

\(\displaystyle b = \frac{8}{sin(76^{\circ})} \times sin(32^{\circ}) \approx 4.37\)

The correct option is therefore;

Question 2

The given parameters are;

\(\displaystyle B = \mathbf{ \frac{\pi}{6} }\)

\(\displaystyle \frac{\pi}{6} = 30^{\circ}\)

a = 20

b = 10

Therefore,  by the law of cosine we have;

Which gives;

10² = 20² + c² - 2×20×c×cos(30°)

100 = 400 + c² - 20·c·(√3)

c² - 20·√3 ·c + 300 = 0

\(\displaystyle c = \frac{20 \cdot \sqrt{3} \pm\sqrt{1200-4 \times 1 \times 300} }{2 \times 1} = \mathbf{ 10 \cdot \sqrt{3} }\)

Therefore, given that c has only one value, the three sides of the triangle are known, and the number of triangles unique triangles by Side-Side-Side description is; C. 1 triangle

Question 3

The distance between the weather station = 24 miles

The bearing of the storm from weather station A = N17°W

The bearing of the storm from weather station B = N48°W

The angle formed at point C in ΔABC  is therefore;

108° - 42° - 107° = 31°

By sine rule, we have;

\(\displaystyle \frac{24}{sin(31^{\circ})} =\mathbf{\frac{x}{sin(42^{\circ})} }\)

Where:

x = The distance from weather station A from the storm

Which gives;

\(\displaystyle x = \frac{24}{sin(31^{\circ})} \times sin(42^{\circ}) \approx \mathbf{31.2 \ miles}\)

Question 4

∠A = 52°

∠C = 57°

Side BC = 9

Therefore;

∠B = 180° - 52° - 57° = 71°

∠B = 71°

According to the law of sines, we have;

\(\displaystyle \frac{b}{sin(71^{\circ})}= \mathbf{ \frac{9}{sin(52^{\circ})} }\)

Therefore;

\(\displaystyle b = \frac{9}{sin(52^{\circ})} \times sin(71^{\circ}) \approx \mathbf{ 10.799}\)

Question 5

Given:

Label of the vertex of the triangle formed are; The golfer, spectator, hole

Distance from the golfer to the hole = 200 yards

Distance from the golfer to the spectator = 140 yards

Vertex angle at the spectator = 110°

By using the law of sines, we have;

\(\displaystyle \frac{200}{sin(110^{\circ})} = \frac{140}{sine \ of \ the \ angle \ at \ the \ hole, \ \phi} \)

Therefore;

\(\displaystyle sin(\phi) = \mathbf{ \frac{140}{200} \times sin(110^{\circ})} = 0.7 \times sin(110^{\circ})\)

The angle at the hole, ∅ = arcsin(0.7×sin(110°)) ≈ 41.13°

Therefore;

The angle that the golfer has = 180° - 110° - 41.1° = 28.9°

Learn more about law of cosine and sine here:

https://brainly.com/question/2384846

https://brainly.com/question/16555495

Part (a)

Answer: Constant of proportionality = 5/8

Reason:

The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.

The direct proportion line must pass through the origin. In other words, the y intercept must be zero.

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

Part (b)

Answer: Not Proportional

Reason:

The y intercept isn't zero.

Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.

Answer:

Hi! You have not shown any options, but your graph should look like this

Step-by-step explanation:

The total number of sheets in both boxes is equal to 1.3 × 10² or 1,300 sheets.

An exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as eˣ.

In Mathematics, laws of indices can be defined as the standard principles and rules that are used for simplifying a mathematical equation or expression that involves powers of the same base.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Mathematically, the total number of sheets in both boxes can be calculated by adding the sheets of paper in each box as follows:

Total number of sheets = 3 × 10² + 10³

Total number of sheets = 300 + 1000

Total number of sheets = 1,300

Total number of sheets = 1.3 × 10² sheets.

Read more on exponent here: brainly.com/question/25263760

#SPJ1

Answer:

233

Step-by-step explanation:

585-352

=233

I hope this helps

Given:

Number of balls packed in a box = 500

Number of boxes packed for shipping = 25

Given that the supervisor randomly picked one crate, opened it up, then randomly chose two boxes from the crate.

He then measures all of the ball bearings from the two boxes.

Let's determine the type of sampling method used here.

Here, we can see that the balls were packed in boxes, then into crates.

Since the manger then chooses one crate out of all crates, then picks only two boxes and sampled all balls in the tow boxes, the type of sampling technique used here can be said to be the cluster sampling technique.

Cluster sampling involves a sampling method where by the population is divided into clusters(small groups), then they randomly select select among these clusters to form a sample.

The cluster sampling is used mostly when the population is large.

ANSWER:

Cluster sampling.

Answer:

291

Step-by-step explanation:

2*2*2=8*2=16

16+(11*5*5)=291

Answer:

291cm^3

Step-by-step explanation:

11×5×5=275cm^3

2×2×2=8cm^3

8cm^3 + 8cm^3= 16cm^3

275+16=291cm^3

Answer: r=2

Step-by-step explanation:

We can use the given 2 points to find slope. Since we are given the slope, we can plug it into the formula and solve for r.

\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =2\)                                        [plug in values]

\(\frac{12-r}{-6-(-11)} =2\)                                   [combine like terms]

\(\frac{12-r}{5} =2\)                                          [multiply both sides by 5]

\(12-r=10\)                                      [subtract both sides by 12]

\(-r=-2\)                                          [divide both sides by -1]

\(r=2\)

Answer:

Step-by-step explanation:

Percentage of purebred dogs in shelters: 25% Number cats and dogs adopted from shelters each year: 4 million. Percentage of cats euthanized in shelters: 70% Percentage of total shelter intake comprised of cats: Approximately 50% (but in some regions 2/3 of shelter population is cats)

Answer:

70 puppies

Step-by-step explanation:

Find 10% which is 200÷10=20

20*3=60=30%

20÷2=10=5% so 60+10=70 puppies