If Bob deposits $5,000 at the beginning of each year for 10 years in an account paying 12% interest compounded annually, find the amount he will have at the end of the 10 years.
a.
$98,272.92
c.
$94,625.32
b.
$98,828.28
d.
$95,876.82

Using the concept of simple interest and compound interest, the first equation is \(S = 200(1.1)^t\), while the second is S = 250 + 20t

c. It will take over 7 years for the accounts to be equal.

The similarities between simple interest and compound interest is that both deals with saving of money over certain period of time with a fixed rate. While the difference between both is that in compound interest, the interest are compounded while in simple interest it is not. This implies that compound interest is an exponential function while simple interest is a linear function.

Simple interest = P(1 + rt)

Compound interest = P(1 + r/n)ⁿˣ

To solve this, we can write equations;

For the first scenario;

\(S = 200(1.1)^t\)

For the second scenario;

S = 250 + 20t

NB: The first case is a compound interest while the second is a simple interest.

c. To determine when the two accounts will be equal;

\(250 + 20t = 200(1.1)^t\)

Solving for t;

t = 7.01 ≈ 7 years

Therefore, it will take over 7 years for the accounts to be equal

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Answer:

A=1024 yd.^2

Step-by-step explanation:

A=s^2

Substitute,

A=32^2

So,

A=1024 yd.^2

Answer:

1024 yd²

Step-by-step explanation:

Since it's a square, the side lengths will all be the same length. Due to this, you can square the given value to find the area.

A(Square) = 32² = 1024

Given: The equation x² = 5x + 4

We have to draw the the graph for the given equation.

Consider the given equation,

x^2 - 5x - 4 = 0  

The vertex of the parabola of the form f(x) = ax^2 + bx + c   is given by x = -b/2a

Here,

a= 1

b= -5

c= -4

vertex = x = 5/2= 2.5

Also, the y coordinate at x = 2.5 is,

y = (2.5)^2 -5(2.5)-4

y = -10.25

Thus the vertex of parabola is (2.5 , -10.25)

y - intercept is the point where x = 0

put x = 0 in given equation

f(x) = 0 - 0 -4

f(x) = -4

hence y intercept is at (0, -4).

Now, we calculate x- intercept

x- intercept is where y is equal to 0.

Put f(x) = 0

We have,

x^2 - 5x - 4 = 0

by using quadratic formula,

x = -b ±√b² - 4ac/2a

x=5 ±√-5² - 4 (1)(-4)/2

x= 5±√41/2.

Hence with the obtained values the graph of the equation is obtained.

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It is important the order we write the vertices of a triangle in a congruent statement as

B. The order tells us what sides are congruent.

D. The order tells us what angles are congruent.

A vertex (plural vertices) in geometry is the intersection of two straight lines. Three line segments come together to form a triangle. The ends of a triangle's three sides meet at three separate points in a plane to form the triangle, which has three sides with two endpoints each. The vertices of a triangle are the three distinct intersecting points or corners.

Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.

The vertices of a triangle in a congruent statement are important for the ordering. In conclusion, the correct options are B and D.

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Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Caludia needs to pay 2917.6128 as a payment of compound interest capital+interest.

What is compound interest?

compound interest is interest on principal + interest and this denotes to the addition of interest to the principal amount of a loan or deposit.

Capital(p) = $6400

Rate of interest(r) = 11%

Years(n) = 3

The general formula of compound interest is \(A= p(1+\frac{r}{100}})^n\).

Now

\(A= 6400(1+\frac{11}{100}})^3\\A=6400 \times \frac{111}{100} \times \frac{111}{100} \times \frac{111}{100}\\A= 8752.8384\)

The entire amount (Capital+interest) is equal to $8752.8384.

If we take 1 year as a period then Claudia needs to pay \(\frac{8752.8384}{3}\\=2917.6128\)

Therefore, Claudia needs to pay 2917.6128 as a payment of compound interest capital+interest.

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Answer: the first thing is your answer :)

thx for the points

Step-by-step explanation:

g

(

x

)

=

x

2

−

3

The parent function is the simplest form of the type of function given.

f

(

x

)

=

x

2

The transformation being described is from

f

(

x

)

=

x

2

to

g

(

x

)

=

x

2

−

3

.

f

(

x

)

=

x

2

→

g

(

x

)

=

x

2

−

3

The horizontal shift depends on the value of

h

. The horizontal shift is described as:

g

(

x

)

=

f

(

x

+

h

)

- The graph is shifted to the left

h

units.

g

(

x

)

=

f

(

x

−

h

)

- The graph is shifted to the right

h

units.

In this case,

h

=

0

which means that the graph is not shifted to the left or right.

Horizontal Shift: None

The vertical shift depends on the value of

k

. The vertical shift is described as:

g

(

x

)

=

f

(

x

)

+

k

- The graph is shifted up

k

units.

g

(

x

)

=

f

(

x

)

−

k

- The graph is shifted down

k

units.

Vertical Shift: Down

3

Units

The graph is reflected about the x-axis when

g

(

x

)

=

−

f

(

x

)

.

Reflection about the x-axis: None

The graph is reflected about the y-axis when

g

(

x

)

=

f

(

−

x

)

.

Reflection about the y-axis: None

Compressing and stretching depends on the value of

a

.

When

a

is greater than

1

: Vertically stretched

When

a

is between

0

and

1

: Vertically compressed

Vertical Compression or Stretch: None

Compare and list the transformations.

Parent Function:

f

(

x

)

=

x

2

Horizontal Shift: None

Vertical Shift: Down

3

Units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

image of graph

Answer:

approximately 6.7

Step-by-step explanation:

I'm assuming this is a triangle, but since there's no picture that's just my guess

We can use The Pythagorean Theorem

3•3=9

6•6=36

9+36=45

square root of 45 is approximately 6.7

Answer:

18 cm for area or perimeter, or just multiplying if y= 3cm*6cm

Step-by-step explanation:

For Perimeter:

multiply 3 by 2, and get 6, then multiply 6 by 2 and get 12 then you will add 6 and 12 together to get 18

For Area:

multiply 6 by 3 or do 6+6+6 and get 18 either way

For Multipling to find y:

do the same that you would do for finding the area

Answer:

5-4=12x+x

1=13x

1/13=×

Answer:

d) 189.3 in²

Step-by-step explanation:

Area of rectangle is,

→ w × l

→ 10 × 15

→ 150 in²

Area of semi circle is,

→ (1/2)πr²

→ (1/2) × 3.14 × (5)²

→ 1.57 × 25

→ 39.3 in²

Now the total area will be,

→ 150 + 39

→ 189.3 in²

Thus, total area is 189.3 in².

Answer:

The numerical value of the circumference is greater than the numerical value of the area.

Step-by-step explanation:

Diameter = 3 meters

The radius is half of diameter so,

Radius = 3 ÷ 2 = 1.5 meters

Circumference = 2πr (r is the radius)

= 2 x π x 1.5 = 9.42 meters (rounded to 3 significant figures)

Area of a circle = π\(r^{2}\)

= π x \(1.5^{2}\)

= π x 2.25 = 7.06 meters

The true statement is

The numerical value of the circumference is greater than the numerical value of the area.

The space a circle takes up in a two-dimensional plane is known as the area of the circle.

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area.

we have,

Diameter = 3 m

Radius= D/2 = 3/2 m

So, Area of Circle

= πr²

= 3.14 x 3/2 x 3/2

= 7.065 m²

and, Circumference of circle

= 2πr

= 2 x 3.14 x 3/2

= 9.42 m

Thus, The numerical value of the circumference is greater than the numerical value of the area.

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The standard deviation of the number of restaurants that failed within a year is 3.46.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

Given that the probability that an independent restaurant will fail in the first year is 48%. Therefore, the probability can be written as,

p = 48% = 0.48

q = 1-p = 1-0.48 = 0.52

Also, Kristen obtains a random sample of 66 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. Therefore, the sample size is 53.

n = 53

Now, the standard deviation can be calculated as,

Standard deviation, σ = √(npq)

                                    = √(53 × 0.48 × 0.52)

                                    = √11.9808

                                    = 3.46

Hence, the standard deviation is 3.46.

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Answer:

6417

Step-by-step explanation:

if A = b*h then when we substitute b for 93 and h for 69

A=93*69 = 6417

Your deposit must be returned by the landlord within 30 days, less any sum subtracted for damages.

To maximize their earnings, landlords set the rent on rental properties at market rates. Should they... Your reported income plays a big part in how much rent you will have to pay.

3% of the existing rent or the local Consumer Price Index (CPI), whichever is higher, is the maximum increase in rent that the landlord is permitted to make once every 12 months. The requirements of California Tenant Protection Act (AB1482) are expressly applicable to rent hikes.

A renter may be evicted even without a lease. Considering that there isn't a lease or rental agreement, a landlord or property management is free to evict a renter for any reason. The sole need under law would be that the renter being evicted receive a formal notice before being removed.

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Answer:

Step-by-step explanation:

1 Wanderer

2 moves on its own orbits the sun

3 Saturn

4 saturn

Answer:

Solved below.

Step-by-step explanation:

The data is provided for the starting salary (in $1,000) at some company and years of prior working experience in the same field for randomly selected 10 employees.

(a)

The formula to compute the correlation coefficient is:

\(r=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\\)

The required values are computed in the Excel sheet below.

\(\begin{aligned}r~&=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\r~&=~\frac{ 10 \cdot 7252 - 97 \cdot 661 } {\sqrt{\left[ 10 \cdot 1335 - 97^2 \right] \cdot \left[ 10 \cdot 45537 - 661^2 \right] }} \approx 0.9855\end{aligned}\)

Thus, the sample correlation coefficient r is 0.9855.

(b)

The slope of the regression line is:

\(b_{1} &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\\= \frac{ 10 \cdot 7252 - 97 \cdot 661 }{ 10 \cdot 1335 - \left( 97 \right)^2} \\\\\approx 2.132\)

Thus, the slope of the regression line is 2.132.

(c)

The y-intercept of the line is:

\(b_{0} &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\\= \frac{ 661 \cdot 1335 - 97 \cdot 7252}{ 10 \cdot 1335 - 97^2} \\\\\approx 45.418\)

Thus, the y-intercept of the line is 45.418.

(d)

The equation of the sample regression line is:

\(y=45.418+2.132x\)

(e)

Compute the predicted starting salary for a person who spent 15 years working in the same field as follows:

\(y=45.418+2.132x\\\\=45.418+(2.132\times15)\\\\=45.418+31.98\\\\=77.398\\\\\approx 77.4\)

Thus, the predicted starting salary for a person who spent 15 years working in the same field is $77.4 K.

Answer:

Yes correct

Step-by-step explanation:

I think this is correct becase: 2 50

5 55

7 62

etc

these are all correct

Answer:

the correct answer is 17

First triangle x = 30

Second triangle N = 55

There are 540 men living in the mini city.

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

Therefore, there are 540 men living in the mini city.

To check our answer, we can substitute x = 540 into our original equation:

540 + (540 + 150) = 1230

690 = 1230

This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.

We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

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The surface area of the right rectangular prism is given as follows:

358 m².

The surface area of a prism is obtained with the sum of the areas of each part of the prism.

The parts that compose the prism are given as follows:

The area of a rectangle is given by the multiplication of each of the dimensions of the rectangle.

Hence the surface area of the prism is calculated as follows:

S = 2 x (7 x 12 + 5 x 12 + 5 x 7) = 358 m².

(multiplication by two due to the two rectangles with each of the dimensions).

The prism is given by the image shown at the end of the answer.

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Answer:

Jingle bells swing and jingle bells ring

Snowing and blowing up bushels of fun

Now the jingle hop has begun

Jingle bell, jingle bell, jingle bell rock

Jingle bells chime in jingle bell time

Dancing and prancing in Jingle Bell Square

In the frosty air

What a bright time, it's the right time

To rock the night away

Jingle bell time is a swell time

To go gliding in a one-horse sleigh

Giddy-up jingle horse, pick up your feet

Jingle around the clock

Mix and a-mingle in the jingling feet

That's the jingle bell rock

Jingle bell, jingle bell, jingle bell rock

Jingle bell chime in jingle bell time

Dancing and prancing in Jingle Bell Square

In the frosty air

Jingle bell, jingle bell, jingle bell rock

Jingle bell chime in jingle bell time

Snowing and blowing up bushels of fun

Now the jingle hop has begun

Jingle bell, jingle bell, jingle bell rock

Jingle bells chime in jingle bell time

Dancing and prancing in Jingle Bell Square

In the frosty air

What a bright time, it's the right time

To rock the night away (rock the night away)

Jingle bell time is a swell time

To go gliding in a one-horse sleigh

Giddy-up jingle horse, pick up your feet

Jingle around the clock

Mix and a-mingle in the jingling beat

That's the jingle bell

That's the jingle bell

That's the jingle bell rock

Jingle bell, jingle bell, jingle bell rock

Jingle bell, jingle bell, jingle bell rock

Jingle bell, jingle bell, jingle bell rock

Wooo

Step-by-step explanation:

Amazing

jingle bell jingle bell jingle bell rock​

Answer:

Step-by-step explanation:

We will use the combination rule to solve this questions since it bothers selection. Combination has to do with selection.

If r objects are to be selected from n pool of objects, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

If there are Eight committee members meeting in a room that has twelve chairs, the number of ways they can sit in the chair can be done in 12C8 number of ways.

12C8 = 12!/(12-8)!8!

12C8 = 12!/4!8!

12C8 = 12*11*10*9*8!/4*3*2*8!

12C8 =  12*11*10*9/4*3*2

12C8 = 11*10*9/2

12C8 = 11*5*9

12C8 = 495

Hence the committee can sit in the chairs in 495 different ways

The equation is 3y / 3 = 2y / y. And the value of 'y' will be 2.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The equation is given as,

3y / 3 = 2y / y

Simplify the equation, then we have

3y / 3 = 2y / y

3y / 3 = 2

y = 2

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Answer:

  96°

Step-by-step explanation:

You want the value of angle C in the diagram with two parallel lines and a triangle between them.

The sum of angles in a triangle is 180°, so the missing angle in the triangle is ...

  180° -60° -24° = 96°

Angle C and the one we just found are alternate interior angles with respect to the parallel lines and the transversal that forms those angles. As such, they are congruent:

  C = 96°

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Answer:

14 students have to retake the test

Step-by-step explanation:

to calculate the mean mark as

sum of ( product of mark and frequency ) ÷ total

mean = \(\frac{14(2)+15(10)+16(2)+17(3)+18(13)}{30}\)

        = \(\frac{28+150+32+51+234}{30}\)

       = \(\frac{495}{30}\)

      = 16.5

students who score less than 16.5 will retake the test , that is

2 scored 16 , 10 scored 15 , 2 scored 14

number who have to retake test = 2 + 10 + 2 = 14

The utility maximization point is the location at which an indifference curve and the budget constraint line Tangent to one another

The maximization point is the location at we know that the budget line shows the combinations of goods consumer can buy at market price with his income.

Indifference curve shows combination of goods giving equal satisfaction to a consumer.

So for higher level of utility or utility maximization, it is the point where indifference curve and budget constraint line are tangent to one another.

The budget constraint line are tangent to one another.

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The utility maximization point is the location at which an indifference curve and the budget constraint line ________

Select one:

a. intersect each other

b. completely overlap

c. are tangent to one another

d. parallel each other

Answer:

Step-by-step explanation:

From the given information:

Let:

\(\mu_1\) represent the population mean no. for DH group.

\(\mu_2\) represent the population mean no. for no DH group  

\(n_1\) represent the sample sizes of DH

\(n_2\) represent the sample sizes of  no DH

Sample size: \(n_1 = n_2 = 20\)

For both groups, the population standard deviation of runs scored = 2.54  

i.e

\(\sigma^2_1 = \sigma_2^2 = 2.54\)

The null & alternative hypothesis;

\(H_o : \mu_1 \le \mu_2 \\ \\ H_a: \mu_1 > \mu_2\)

Level of significance:

The test statistics is:

\(z = \dfrac{\bar x_1 - \bar x_2}{\sqrt{\dfrac{\sigma^2_1}{n_1} + \dfrac{\sigma_2^2}{n_2} }}\)

where;

\(\bar x_1\) = sample mean for DH group

\(\implies \dfrac{1}{n_1} \sum \limit ^{n_1}_{i=1} x_1 \\ \\ = \dfrac{1}{20}(0+6+8+2+2+4+7+7+6+5+1+1+5+4+4+5+7+11+10+0) \\ \\ = \dfrac{92}{20}\)

= 4.6

\(\bar x_2\) = sample mean for no DH group

\(\implies \dfrac{1}{n_2} \sum \limit ^{n_1}_{i=1} x_1 \\ \\ = \dfrac{1}{20}(3+6+2+4+0+5+7+6+1+8+12+4+6+3+4+0+5+2+1+4) \\ \\ = \dfrac{83}{20}\)

= 4.15

Now:

\(z = \dfrac{4.60- 4.15}{\sqrt{\dfrac{2.54^2}{20} + \dfrac{2.54^2}{20} }} \\ \\ = \dfrac{0.45}{\sqrt{0.32258 +0.32258 }} \\ \\ = \dfrac{0.45}{0.803219} \\ \\\)

= 0.5602

Since the test is one-tailed by looking at that \(H_a:\)

The P-value = \(P(Z > z)\)

\(\implies 1 - P(Z \le z) \\ \\ = 1 - P(Z \le 0.5602)\)

Using Excel Function " =normdist(z)"; we have":

\(= 1- 0.7123\)

P-value = 0.2877

Decision rule: To reject \(H_o\), if \(p-value < \alpha \ at \ 0.10\)

Conclusion: SInce P = 0.2877 which is \(> \ \alpha \ at \ 0.10.\)

We fail to reject the \(H_o\) and conclude that there is insufficient evidence to support the given claim that: \(\text{more runs are scored in games for which DH is used.}\)

Answer:

1. d. Two sided t-test

2. b. 0.000193

3. a. Since p- value is very small we can conclude that the more soda the student drink the heavier they get.

4.  c. Test in inconclusive; thus we cannot claim that there is a correlation between drinking soda and weight.

Step-by-step explanation:

The hypothesis testing is used to test the claim against the alternative hypothesis. The p value is determined in order to conclude the result for the test as whether to accept or reject the null hypothesis. The null hypothesis can be accepted when the p value is greater than the critical value of the t-test.

The simplified expression involving complex numbers is given as follows:

5 + 5i.

Complex numbers are number that have a real and an imaginary part, and are defined as follows:

z = a + bi.

In which:

The basic relation of complex numbers is given as follows:

i² = -1.

The fraction for this problem is given as follows:

(2 + i)(4 - 2i)/(1 + i).

The numerator is simplified as follows:

(2 + i)(4 - 2i) = 8 - 4i + 4i - 2i² = 8 + 2 = 10.

Hence the fraction is of:

10/(1 + i).

To remove the complex number from the denominator, the entire fraction is multiplied by the conjugate of the denominator, hence:

10/(1 + i) x (1 - i)/(1 - i) = 10(1 + i)/(1 - i²) = 10(i + 1)/2 = 5 + 5i.

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Answer: it would help if you added an image

Step-by-step explanation:

Answer:

Where is the cylinder?

Step-by-step explanation: