please answer correctly 50 points

1. The simple interest rate is 80%

2. The interest earned on the account after 10 years is $75

Simple interest can be defined as a mathematical or arithmetic method of calculating the charge of interest on a given loan.

The formula for simple interest is expressed as;

I = PRT/100

Where;

From the information given, we are to determine the interest rate, R

Substitute the values into the formula, we have;

320 = 200 × R × 2/100

Now, cross multiply, we have;

320(100) = 400R

Find the product of the values

400R = 32000

Divide both sides by the coefficient of the interest rate, we get

R = 32000/400

Find the quotient

R = 80%

If the interest for 2 years is $15

Then in 10 years = $x

cross multiply

x = 150/2

Find the quotient

x = $75

Hence, the rate is 80%

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For the given function f(x) = 7 , the value of x is 5.

We have a linear function in the figure, and linear functions have the same slope for all values of. We can determine the value of f using the secant line equation:

(yB -yA) / (xB - xA) = (yC - yA) / (xC - xA)

Where:

(xA , yA) , (xB , yB)  given

to find ,  (xC , yC)

(xA , yA) = (2,0) , (xB , yB) = (5,7)  and yC = 7

to find xC ,

xC - xA = (yC - yA) / (yB - yA) . (xB - xA)

xC =  xA + (yC - yA) / (yB - yA) . (xB - xA)

xC = 2 + (7-0)/(7-0) x (5 - 2)

xC = 2 + (5 - 2)

xC = 2 + 3

xC = 5

so the value of x in given function f(x) = 7 is 5.

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Answer:

Equation of the parabola:

The height of the arch 18 meters from the center is 6.75m

Explanation:

The arch feet are 72m apart and the origin half way between them. This means that the axis of symmetry (or the x.coordinate of the vertex) is x = 0

Since it's an arch, the parabola is concave down, with it's maximum at the vertex, y = 9. This means that the vertex is at (0, 9). Also, we can see that the y-intercept is y = 9

Finally, we know the two roots of the parabola: x = -36 and x = 36. This is because the points x = -36 and x = 36 are 72m apart, with the center at the original, as the problem says. SInce x = 36 is a root, this means that at that point the y value is 0.

With all this, we can try to find the general form of a parabola. The general form is:

c is the y-intercept. We know that c = 9

We can find the value of b, because we know the coordinates of the vertex. The x-coordinate of the vertex is:

SInce the x-coordinate of the vertex is x = 0

If we solve:

So far we have:

Finally, to find a, we can use the point (36, 0) (one of the roots)

And solve:

Thus, the equation of the arch is:

Evaluating this equation for x = 18, we can find the height of the arch:

The result of the indicated operations are:

(a) -4.324.

(b)  4.324.

(c) 0.9

(a) -1.424-2.9

Calculate the sum of the decimals,

The result is -4.324.

(b) 1.424-(-2.9)

Remove the bracket and change the sign in the middle and add the decimals to get the sum,

1.424 + 2.9 = 4.324.

(c) -1.424-(-2.9) -0.576

Remove the parentheses and change the sign,

-1.424 + 2.9 - 0.576

Add the negative decimal numbers and subtract them from the positive decimal number.

-2 + 2.9 = 0.9

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For given function f,

domain = (-3, -1) ∪ (2, 5]

range = (0, 3) ∪ (1, 5]

In this question, we have been given the graph of the function f.

We need to write the domain and range of f.

From the graph of function f we can observe that, function f is a piecewise function.

For first part x takes vales which are greater than -3 and less than -1

And y takes values between 0 to 3

For first curve the domain is (-3, -1) and the rage of function f is (0, 3)

For the second part, x takes value which are greater than 2 and less than or equal to 5.

And y has values between 1 to 4.

So, for the second part the domain is (2, 5] and the range is (1, 5]

Therefore, for given function f,

domain = (-3, -1) ∪ (2, 5]

range = (0, 3) ∪ (1, 5]

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Answer: (-9/2,-53/4)

Step-by-step explanation:

Answer:

[tex]y=\left(x+\dfrac{9}{2}\right)^2-\dfrac{53}{4}[/tex]

Step-by-step explanation:

Vertex form of a quadratic equation:  

[tex]\boxed{y=a(x-h)^2+k}[/tex]

where:

To find the vertex form of a quadratic equation, complete the square.

Given quadratic equation:

[tex]y=x^2+9x+7[/tex]

Add and subtract the square of half the coefficient of the term in x to the right side of the equation:

[tex]\implies y=x^2+9x+\left(\dfrac{9}{2}\right)^2+7-\left(\dfrac{9}{2}\right)^2[/tex]

[tex]\implies y=x^2+9x+\dfrac{81}{4}+7-\dfrac{81}{4}[/tex]

[tex]\implies y=x^2+9x+\dfrac{81}{4}-\dfrac{53}{4}[/tex]

Factor the perfect square trinomial formed by the first 3 terms:

[tex]\implies y=\left(x+\dfrac{9}{2}\right)^2-\dfrac{53}{4}[/tex]

The absolute value function as piecewise function of y = -3(x + 24)/4 and y = 3(x - 38)/4

The absolute value function is commonly understood as a function providing the distance the number is from zero on a number line.

y = 3/4|x-6|-8

y = 3/4(-(x-6))-8

y= 3/4( -x + 6) -8

y = 3(-x + 6 - 32)/4

4y = -3x - 24

y = -3(x + 24)/4

For another function of y

y = 3/4|x-6|-8

y= 3/4( x - 6) -8

y = 3(x - 6 - 32)/4

4y = 3(x - 38)

y = 3(x - 38)/4

The absolute value function as piecewise function of y = -3(x + 24)/4 and y = 3(x - 38)/4

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The value of the limit will be equal to -2.

A function may be defined as the one in which for one input variable x there is only one output variable y. The input variable is called independent variable and the output variable is called dependent variable. Limit on a function may be defined as the value of input variable reaches a certain specified value the output of function also reaches a certain specified value. The function [tex]\lim_{x \to-2}[/tex] (x²)/(2x + 4) can be solved by using the rule [tex]\lim_{x \to a}[/tex] f(x)/g(x) = [tex]\lim_{x \to a}[/tex] f'(x)/g'(x).

Here f(x) = x², f'(x) = 2x

g(x) = 2x + 4, g'(x) = 2

Now, [tex]\lim_{x \to-2}[/tex] (x²)/(2x + 4) = [tex]\lim_{x \to-2}[/tex] (2x/2)

[tex]\lim_{x \to-2}[/tex] (x) = -2 which is the required value.

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4 gallons of paint will be used to paint the inside of the barn.

In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.

Given Data

Jay needs 19 quarts more paint for the outside of his barn than for the inside.

he uses 107 quarts in all

Paint needed for Inside = x

Paint needed for outside =  x + 19

So,

Total paint = Paint for outside + Paint for inside

107 = x + x+ 19

107 = 2x + 19

2x = 88

x = 44

Number of gallon = [tex]\frac{44}{4}[/tex]

Number of gallon = 4

4 gallons of paint will be used to paint the inside of the barn.

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Answer:

x=5

Step-by-step explanation:

If the slope is undefined, it is a vertical line. Since the slope-intercept equation is y=mx+b, but the slope is undefined, the equation would have to be the x coordinate, because that is the unchanging variable in a vertical line. So, the answer is x=5.

The probability that the average person has a time faster than Usain Bolt’s record of 9.58 seconds

P(x>9.58)=1

This is further explained below.

Mean[tex](\mu)[/tex]=14 seconds

Standard deviation[tex](\sigma)[/tex]=0.8 seconds

To determine the likelihood that the average individual will beat Usain Bolt's record of 9.58

To express the statement "the probability that the average person has a time faster than Usain Bolt’s record of 9.58 seconds" in a mathematical equation we have:

[tex]&P(x > 9.58)=P\left(\frac{x-\mu}{\sigma} > \frac{9.58-14}{0.8}\right) \\\\&P(x > 9.58)=P\left(z > -\frac{4.42}{0.8}\right) \\\\ &P(x > 9.58)=P(z > -5.525)[/tex]

P(x>9.58)=1

Note: we would make use of the normal table in reading z>-5.525

In conclusion, By using standard normal distribution we get

P(x>9.58)=1

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Answer:

3/16

We assume that the marbles are drawn without replacement.

P(blue and yellow)

= P(b1 and y2) + P(y1 and b2)

= P(b1) P(y2) + P(y1) P(b2)

= (1/4)(1/2) + (1/4)(1/4)

= 1/8 + 1/16 = 2/16 + 1/16 = 3/16

Answer:

x = 0

Step-by-step explanation:

A line that has undefined slope is a vertical line. A vertical line has an equation in the form "x = anumber"

In the given information, (0,5), x is 0 and y is 5. What we need is the information on x.

x is 0.

x = 0 is the equation of the line.

Answer:

x=0.

Step-by-step explanation:

undefined slope is a vertical line. if it passes through (0,5) it means its on the y line

Answer:

length is 28,breadth is 29

Step-by-step explanation:

firstly we need to know the definition of consecutive integers:-Consecutive integers are those numbers that follow each other . They follow in a sequence or in order.

let the length and breadth be represented by n and n+1

since we are given in perimeter

perimeter of a rectangle =2(length+breadth)

114=2(n+n+1)

114=2n+2n+2

114=4n+2

114-2=4n

112=4n

n=28

:-n=28,(n+1)=28+1=29

:-the length is 28 and the breadth is 29

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The value of the average price per square foot in 2002 is  $101. 5

A function can simply be defined as a rule, a law, an equation or an expression that is made up of two variables and shows or explains the relationship between them.

The variables are;

Given the function;

P(t) = 0. 018t³ - 0. 294t² + 3. 065t + 55. 190

Where;

For the year 2002 , the value of t would be 10

Substitute the value into the formula

P(10) = 0. 018(10)³ - 0. 0294(10)² + 3. 05(10) + 55. 190

expand the bracket, we have

P(10) = 0. 018(1000) - 0. 0294(100) + 30. 5 + 55. 90

multiply through

P(10) = 18 - 2.  + 30. 5 + 55. 90

Add the values

P(10) = $101. 5

Hence, the value is  $101. 5

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Given:

Required:

Find (fg)(4)

Explanation:

Given functions are

Final answer:

The value of (fg)(4) = 4

The other endpoint of the segment is (7, 14)

From the question, we have:

On the segment, we have the following endpoints

Endpoint 1, A = (-3,-2)

Midpoint, M = (2,6)

The midpoint of the segment is calculated using

Midpoint (x, y) = 1/2 * (x1 + x2, y1 + y2)

Where

(x1, y1) = (-3,-2)

(x, y) = (2,6)

Substitute the known values in the above equation

So, we have

(2, 6) = 1/2 * (-3 + x, -2 + y)

Multiply both sides of the equation by 2

So, we have

(4, 12) = (-3 + x, -2 + y)

By comparison, we have

-3 + x = 4

-2 + y = 12

Evaluate the like terms in the above equation

So, we have

x = 7

y = 14

When the above solution is represented as a coordinate, we have the following

(x, y) = (7, 14)

Hence, the other endpoint of the segment where the segment has the endpoint (-3,-2) and midpoint (2,6) is (7, 14)

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Answer: the andwer to that is C

Step-by-step explanation:

1) If  A = {U, S, T, A, C}, then the Subsets of  {U, S, T, A, C} are;

as detailed below

2) If B = {red, blue, yellow}. then the Subsets of {red, blue, yellow} are;

as detailed below

Subsets are a part of one of the mathematical concepts called Sets. For example If a set A is a collection of odd numbers and set B consists of {1,3,5}, then B is said to be a subset of A.

Thus;

1) Subsets of  {U, S, T, A, C} are;

{U}, {S}, {T}, {A}, {C},

{U, S}, {U, T}, {S, T}, {U, A}, {S, A}, {T, A}, {U, C}, {S, C}, {T, C}, {A, C},

{U, S, T}, {U, S, A}, {U, T, A}, {S, T, A}, {U, S, C}, {U, T, C}, {S, T, C}, {U, A, C}, {S, A, C}, {T, A, C},

{U, S, T, A}, {U, S, T, C}, {U, S, A, C}, {U, T, A, C}, {S, T, A, C},

{U, S, T, A, C}

2) Subsets of {red, blue, yellow} are;

{Red}, {Yellow}, {Blue},

{Red, Yellow}, {Red, Blue}, {Yellow, Blue},

{Red, Yellow, Blue}

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Answer:

13 correct me if i am wrong

Step-by-step explanation:

Each deck has 52 cards in it. If Linda has c decks of cards, then the expression for the total number of cards that she has is

52 x c

= 52c

Answer:

17

Step-by-step explanation:

To find k, we use

∫∞−∞∫∞−∞fXY(x,y)dxdy=1.

Thus, we have

1=∫∞−∞∫∞−∞fXY(x,y)dxdy=∫10∫10x+cy2dxdy=∫10[12x2+cy2x]x=1x=0dy=∫1012+cy2dy=[12y+13cy3]y=1y=0=12+13c.

Therefore, we obtain c=32.

To find P(0≤X≤12,0≤Y≤12), we can write

P((X,Y)∈A)=∬AfXY(x,y)dxdy,for A={(x,y)|0≤x,y≤1}.

Thus,

P(0≤X≤12,0≤Y≤12)=∫120∫120(x+32y2)dxdy=∫120[12x2+32y2x]120dy=∫120(18+34y2)dy=332.

We can find marginal PDFs of X and Y from their joint PDF. This is exactly analogous to what we saw in the discrete case. In particular, by integrating over all y's, we obtain fX(x). We have

Marginal PDFs

fX(x)=∫∞−∞fXY(x,y)dy, for all x,fY(y)=∫∞−∞fXY(x,y)dx, for all y.

Example

In Example 5.15 find the marginal PDFs fX(x) and fY(y).

Answer:

17

Step-by-step explanation:

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Answer

When x = 12, y = 180

Explanation

We are told that y varies directly as x, which can be written as

y ∝ x

Introducing the constant of variation, k, we have

y ∝ x

y = kx

We can then solve for k knowing that

y = 90 when x = 6

y = kx

90 = (k) (6)

90 = 6k

Divide both sides by 6

(90/6) = (6k/6)

15 = k

k = 15

We can then write the relationship between y and x as

y = kx

y = 15x

when x = 12, y = ?

y = 15x

y = 15 (12) = 180

Hope this Helps!!!

Answer:

1 is to 3

Find the lowest common factor of both numbers, which is 3. Then divide it into both numbers

The given statement can be written as an algebraic expression as: 2/(x + 2).

A mathematical statement that expresses phrases or words using numbers, variables, and operation signs can be referred to as an algebraic expression.

To translates a given statement in to algebraic expression, we can use "x" as a variable to represent the unknown number in the given word problem.

For example, the number that is added to 2, in the above given scenario, can be represented as "x" in order to translate the given statement into an algebraic expression.

The word "sum" will be represented with the operation sign, "+". Therefore, "the sum of 2 and a number" will be translated as an algebraic expression as, (x + 2).

Therefore, the whole statement, "2 divided by the sum of 2 and a number" will then be expressed in algebraic expression as: 2/(x + 2).

In conclusion, the statement, "2 divided by the sum of 2 and a number", can be written as an algebraic expression as: 2/(x + 2).

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The two pairs of conjugates are ([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]).

In mathematics, a pair of binomials with identical phrases that part opposite arithmetic operators in the midst of these similar terms are referred to as conjugates. Below are a few more instances of conjugate pairs: p + q, p - q. 3 + 1, 3 - 1. 4 - 3i, 4 + 3i.

Let the two pair of conjugates is

([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex])

Use the formula,

(a+b) and (a-b) = [tex]a^{2}-b^{2}[/tex]

Then,

([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) = [tex]\sqrt{2} ^{2}-i^{2}[/tex]

We know that,

[tex]i^{2}=-1[/tex]

([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) = 2-(-1)

 ([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) =  3

Hence, The two pairs of conjugates are ([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) with a product 3 .

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According to the solving the  two pairs of conjugates with a product of 3:

(√2 - i ) & (√2 + i ).

When two binomials are identical except for the signs separating the terms, they are said to be conjugates. You only need to rephrase a binomial and alter the sign of the second term to create its conjugate.

given number = 3.

lets the two pair of conjugates is:

(√2 - i ) & (√2 + i )

Use the formula:

a² - b² = (a + b) and  (a - b)

So,

(√2 - i ) & (√2 + i ) = (√2)² -( i )²

We know that,

i² = -1

So,

(√2 - i ) & (√2 + i ) = 2 - (-1)

(√2 - i ) & (√2 + i ) = 3

According to the solving the  two pairs of conjugates with a product of 3:

(√2 - i ) & (√2 + i ).

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Han is therefore mistaken in what he claims. The area is 8640 [tex]feet^{2}[/tex]

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given Data

Let "x" represent the restaurant's actual space.

You are aware that the map's scale is 1 inch to 12 feet. As a fraction, this is written as follows:

[tex]\frac{1inch}{12feet}[/tex]

Calculate the restaurant's scale drawing area. Such is:

([tex]\frac{1inch}{12feet}[/tex]) ² = [tex]\frac{1inch^{2} }{144feet^{2} } }[/tex]

We can set up this percentage and then solve for "x" to determine the precise location of the restaurant because the restaurant's location is indicated on the map.

Such is:

[tex]\frac{144}{1}[/tex] = [tex]\frac{x}{60}[/tex]

60 (144) = x

x = 8640 [tex]feet^{2}[/tex]

Han is therefore mistaken in what he claims.

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Answer:

an = -4n +12

Step-by-step explanation:

the nth term in this arithmetic sequence is : an = a1 + (n -1 )d

a1 = 8 d = a2-a1 = 4-8 = -4 ( common difrence)

an = 8 + (n -1 )(-4) = 8 - 4n +4

an = -4n +12