Solve for x. Show your work, and give exact answers where possible. Otherwise, round to the nearest hundredth.

The Sales of the electronic store in 1 year is 66,776.88    

Applications of Compound interest:

Compound interest is an interest that is calculated on the principal and the interest accumulated over the previous period. The concept of compound interest can be used in different types of situations like an Increase in population or a decrease in population, Depreciation, or increasing the value of an item, etc.

The formula for compound interest is given by

Total amount, A = P(1 + r/n)^nt  

where  P = initial amount

r = rate of increase              

n = number of compounds in year

t = time period in years

Here we have,

The rate of increase in sales r = 2.7% (per monthly)  

=> r = 2.7/100 = 0.027

Here sales are increased monthly

then the number of compounds per year = 12

Sales in this month, P = 65000  

From above formula

Sales in 1 year, A = 65000(1 + 0.027/12)¹²

= 65,000(1 + 0.00225)¹²

= 66,776.88    

Therefore,

Sales of the electronic store in 1 year =  66,776.88      

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The descending order to the list is 1, 4/5, 41%, -1.3, -7/4.

What us descending order?

When numbers are arranged from greatest to smallest or highest to lowest it is said to be in descending order.

Main Body:

To solve this question we need to convert all numbers into decimal system.

calculate:

1 can be written as 1.00

4/5 can be written as 0.8

-7/4 = -1.75

41% = 41/100 = 0.41

-1.3 can remain as it is because it itself is in decimal form.

Hence the order from greatest to smallest is as

1 > 0.8 > 0.41 > -1.3 > -1.75

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The expected value of the proposition is -$1007.41

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]

In which [tex]C_{x},x[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{x},x= \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Suppose a basketball player has made 215 out of 322 free throws.

This means that p = 215/322 = 0.6677

2 free throws:

This means that

Probability of making two free throws.

This is P(X = 2).

P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]

P(X = 2) = [tex]C_{2},2.(0.6677)^2.(0.3323)^0[/tex] = 0.29629

Expected value:

If he makes both free throws, you earn $24. So 0.29629 probability of you earning $24.

Otherwise, you have to pay $32. 1 - 0.29629 = 31.70371 probability of you losing $32.

E = 0.29629*24 - 31.70371*32 = -1007.41

Hence, The expected value of the proposition is -$1007.41

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The slope of the line tangent to f(x) at x = 1 is -8

The instantaneous rate of change of f(x) at x = 1 is -8

The equation of line tangent to f(x) at x = 1 is y  = -8x + 9

The tangent line to a curve at a given point is the line which intersects the curve at the point and has the same instantaneous slope as the curve at the point.

so the slope of a line at that point is the slope of the curve at that point.

f(x) = -4[tex]x^{2}[/tex] + 5

To find the slope, we differentiate f(x) with respect to x

dy/dx  = d/dx( -4[tex]x^{2}[/tex]) + d/dx(5)

           = -8x + 0

dy/dx = -8x

The slope = -8x

at x = 1,

the slope becomes, -8(1) = -8

The instantaneous rate of change of f(x) at x = 1 is the same as the slope of the line tangent to f(x) = -8

The slope of the line is -8

to find the equation of the tangent line, we need to find the coordinates of the point the line touches the curve.

one of the coordinates x = 1, to find y, we substitute x into f(x)

f(x) = -4[tex](1)^{2}[/tex] + 5

f(x) = 1

so the point is (1, 1)

so equation of straight line

[tex]\frac{y - y_{1} }{x - x_{1} }[/tex] = m

y - 1/x - 1 = -8

by cross multiplying

y - 1 = -8(x - 1)

y - 1 = -8x +8

y = -8x + 9

In conclusion,

The slope o the line tangent to f(x) at x = 1 is -8

The instantaneous rate off change of f(x) at x = 1 is -8

The equation of line tangent to f(x) at x = 1 is y  = -8x + 9

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Step-by-step explanation:

first put 4 3/4 into a improper fraction ---> 19/4

you get 19/4 because  4 is equal to 16/3 plus the 3/4

then you will do keep, flip change so it becomes multiplication

so instead of 1/3 divided by 19/4 it will be 1/3 x 4/19 then

multiply it out to get 19/12

The area of the piece of land with coordinates (0, 0), (-100, 300) and (200, -200) is as measured by the surveyor is 4000 square meter

The given coordinates being plotted as

A (0, 0)

B (-100, 300)

C (200, -200)

Area of triangle is solved by 0.5 * base * height

dimensions from attached plot, BC = 316.2, Aa = 253

= 0.5 * BC * Aa

= 0.5 * 253 * 316.2

= 39 999.3 approximately 40 000

The plot gave an area of 40 000 square units on paper converting using the given scale which is: One unit in the coordinate plane represents 1m

1 unit = 1 m

1 square unit = 1 square meter

4000 square units = ?

cross multiplying

? = 4000 square units

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By using concept of ratio, it can be calculated that

100 boys attended the camp

What is ratio?

Ratio between two numbers determines how much one number is greater than the other.

The first part of the ratio is called antecedent and the second part of the ratio is called consequent.

Here, concept of ratio will be used

Let the number of boys be 4x and the number of girls be 6x

There were 50 more girls than boys

By the problem,

6x - 4x = 50

2x = 50

[tex]x = \frac{50}{2}[/tex]

x = 25

Number of boys who attended the camp = 4 [tex]\times[/tex] 25 = 100

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Answer:

40-20= 20

Step-by-step explanation:

8(5)- 4(5)= 4(5)

40-20=20

Differentiation of the function [tex]f(x) = (-x^{2} - 4)x^{5}[/tex] with respect to [tex]x[/tex] is [tex]f'(x) = -7x^{6} - 20x^{4}[/tex].

What is the differentiation of the function?

A function differentiation is a method of displaying the rate of change of a function at a given moment. It is the slope of the tangent line at a point on a graph for real-valued functions.

We have,

                                     [tex]f(x) = (-x^{2} - 4)x^{5}[/tex]

By simplifying the given function, we get

                                      [tex]f(x) = -x^{7} - 4x^{5}[/tex]

Now, we will differentiate the given function with respect to [tex]x[/tex].

                                    [tex]\frac{d}{dx} f(x) = \frac{d}{dx} (-x^{7} - 4x^{5})[/tex]

                                    [tex]f'(x) = \frac{d}{dx} (-x^{7}) - \frac{d}{dx} (4x^{5}))[/tex]

                                     [tex]f'(x) = -7x^{6} - 20x^{4}[/tex]

Hence, differentiation of the given function with respect to [tex]x[/tex] is [tex]f'(x) = -7x^{6} - 20x^{4}[/tex].

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If traveling with the current certain boat went 9 mph against the same boat it only went 1 mph the speed of the current  is 4km/h  and no current is 5km/h.

Let b represent  the speed of the boat

Let c represent  the speed of the current

Downstream:

b + c = 9

Upstream:

b - c = 1

Subtraction

2c = 9-1

2c = 8

Divide both side by 2c

c = 8/2

c = 4 km/h (current)

No current

b = 9 - 4

b = 5 km/h

Therefore the speed is 4km/h and no current is 5km/h.

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The area of the plot is 193 sq.yd.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, A developer buys an empty lot to build a small house.

To find the area, we need to be divided the figure into triangles and rectangles

Area of the first triangle = (1/2) * base * height

base = 17 unit and height = 10 unit

= (1/2) * 17 * 10

= 17*5=85 sq. unit

Area of the second triangle = (1/2)* 9* 8

=36 sq. unit

Area of the rectangle = base * height

base = 9 unit and height = 7 unit

Area = 9*7= 63 sq. unit

Area of the last triangle = (1/2) * 2*9

= 9 unit

Adding all the areas to get the area of the plot = 85+36+63+9

Hence, Area of the plot = 193 sq.yd.

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Answer:

R = 19 yr old; T = 7 yr old

Step-by-step explanation:

From the information given, we can create a system of equations to find both Richard and Teo's ages, letting R represent Richard's age and T represent Teo's age.

Thus we have:

[tex]R +T=26\\2T+5=R\\\\2T+5+T=26\\3T+5=26\\3T=21\\T=7\\\\R+7=26\\R=19[/tex]

When you plug in the numbers, you find that twice Teo's age is 14 as 7*2 = 14.  5 more than 14 is 19 as 14 + 5 = 19.

1. Her Average would be 80

2. Yes, there are more dots around points 80.

Answer:

5x-9=26

Step-by-step explanation:

5x=35

5 5

x = 7

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Answer:

x = 7

Step-by-step explanation:

When five times a number is decreased by 9 ​, the result is 26 . What is the​ number?

5x - 9 = 26

add 9 to both sides:

5x - 9 + 9 = 26 + 9

5x =35

divide both sides by 5:

5x/5 =35/5

x = 7

The number of minutes is 195 minutes when the customer spends $267.00. The correct option is B.

From the information, the total cost of a plane ride, C, is given as a function

C = $33.00 + $1.20m

where n = number of minute

Since the customer spends $267.00 on a plane ride, this will be:

C = = 33.00 + $1.20m

33 + 1.2m = 267

Collect like terms

1.2m = 267 - 33

1.2m = 234

Divide

m = 234 / 1.2

m = 195

Minutes used is 195 minutes

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Answer:

$12,312

Step-by-step explanation:

$2,052 * 6 = $12,312

Answer:

Hello there! While I didn't have this assignment, I found the assignment on Coursehero and took the liberty of downloading the pdf.

BE SURE TO USE QUILLBOT FOR PARAPHRASING AND PREPOSTSEO FOR PLAGIARISM CHECKING

Step-by-step explanation:

The function f(x) = -3(x + 2)² + 1 has it's vertex as (-2, 1) and an axis of symmetry x = -2

The graph of a quadratic function is called a parabola and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph. You can think of like an endpoint of a parabola.

In the given function;

f(x) = -3(x + 2)² + 1

Kindly find the attached graph of the function below

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Therefore the required polynomial is [tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

What is an leading coefficient?

The numbers placed in front of the variable with the biggest exponent are known as leading coefficients. They can be whole numbers, fractions, or decimals, as well as positive, negative, real, or imaginary, just like conventional coefficients.

According to fundamental theorem of algebra , if a + bi be a zero of a polynomial with real coefficients then a-bi is also a zero

Now given that f(x) be a polynomial with degree 5 and with zeros -7,-i,-3+i

and f(x) be a polynomial with real coefficients.

therefore by fundamental theorem of algebra

+i and -3-i are also zeros of f(x)

so zeros of f(x) are 7, -i, -3 + i, i, -3 -i

Degree is 5, so there is at most 5 zeros therefore the required polynomial will be

f(x) = a(x + 7)(x + i )(x - i)(x +3- i)(x +3 +i)

= a[(x +7)(x² + 1)(x² +6x + 10)]

[tex]= a\left[x^5+ 13x^4 + 53x^3 +83x^2 + 52x + 70]\right[/tex]

[tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

Therefore the required polynomial is [tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

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Answer:

In the first one you should write: 6, because the test tells you that in 6 minutes she runs 3/4miles.

So in 12 minutes she runs (3/4miles)*2. (basically 3/4 miles in the first 6 minutes, and other 3/4 miles in the remaining 6munutes).

So in the second space you can write 12, and on the right 2*(3/4), which is... (3/2).

To find the equation:

3/4 = 6

(3/4)*2= 6*2

so we know that in 1 minute we do 1/8miles, and now we have our formula. (1/8)*6=1*6

the formula is: y(miles) =(1/8)*x

in fact is x=6 minutes, y= (1/8)*6, so y=3/4.

From the given equation y = A(x-h)² +k it is identified that this quadratic function represents the parabola with vertex (h, k).

As given in the question,

Given equation is :

y = A(x-h)² +k

Standard basic parabola equation is y = x² where parabola pass through (0, 0) .

In the given quadratic function y = A(x-h)² +k , it represent equation of parabola which is U shaped .

Value of A > 0 then it open in upward direction .

Value of A <0 then it is open in downward direction.

Vertex of the given parabola y = A(x-h)² +k  is (h, k).

Line of symmetry is given by vertical line x =h.

Therefore, from the given equation y = A(x-h)² +k it is identified that this quadratic function represents the parabola with vertex (h, k).

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Answer: -52

Step-by-step explanation: multiply by breaking apart a factor (-13) x 4

Answer:

28561

Step-by-step explanation:

Find the Exact Value:

Raise -13 to the power of 4.

28561 is the answer.

Answer:

-5/7, 10/7

Step-by-step explanation:

The slope of an equation in standard form is -a/b

so -5/7

Set x to 0 to find the vertical intercept

5(0)+7y=10

7y=10

y=10/7

Answer:  7 4/10 + 2/10 = 38/5 = 7 3/5 = 7.6

Answer Overall : 38/5

Step-by-step explanation:  Conversion a mixed number 7 4/10 to a improper fraction: 7 4/10 = 7 4/10 = 7 · 10 + 4/10= 70 + 4/10= 74/10

To find a new numerator:

a) Multiply the whole number 7 by the denominator 10. Whole number 7 equally 7 * 10/10 = 70/10

b) Add the answer from previous step 70 to the numerator 4. New numerator is 70 + 4 = 74

c) Write a previous answer (new numerator 74) over the denominator 10.

Seven and four tenths is seventy-four tenths

Add: 74/10 + 2/10 = 74 + 2/10 = 76/10 = 2 · 38/2 · 5 = 38/5

The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 10) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 38/5.

In other words - seventy-four tenths plus two tenths is thirty-eight fifths.

First convert the mixed number to a fraction by multiplying 7 by 10 and adding 4

add them together but DONT add the denominators

These numbers can be simplified by 2 so the final answer is:

Answer:

A semicircle has 1 line of symmetry.

Step-by-step explanation:

The decrease in price in dollars of the next model of the car is $5712 and the price of next model is $36288.

According to the question,

We have the following information:

The next model of a sports car will cost 13.6% less than the current model. The current model costs $42,000.

We will find the 13.6% of 42,000 to find the decrease in the price of the next model:

(13.6*42000)/100

$5712

Now, the price of next model will be:

42000-5712

$36288

Hence, the decrease in price in dollars of the next model of the car is $5712 and the price of next model is $36288.

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The probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 97 words per minute is; 0.012676.

This z-score is used to tell us the number of standard errors that exists between the sample mean and the population mean.

The formula for z-score here is;

z = (x' - μ)/(σ/√n)

where;

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

We are given;

Sample mean; x' = 97

Population mean; μ = 91

Standard deviation; σ = 10

Sample size; n = 20

Thus;

z = (x' - μ)/(σ/√n)

z = (97 - 91)/(10/√20)

z = 2.236

From online p-value from z-score calculator, we have;

p = 0.012676

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Complete question is;

The reading speed of second grade students in a large city is approximately​ normal, with a mean of 91 words per minute​ (wpm) and a standard deviation of 10 wpm.

what is the probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 97 words per minute

Answer:

7 hours.

Step-by-step explanation:

Use a clock and count forward.

84 i think?

im not sure if i did my math properly

Answer:

80

Step-by-step explanation:

40 ÷ 6 = 6.66666667 x 12 = 80