The regular price of an item at a store is $2,000. If the sale price is $1,120, what percent is the discount?

The events E and F are not independent

The given parameters are:

P(E n F) = 0.036

P(E|F) = 0.09

P(F|E) = 0.1

To calculate P(E), we use:

P(F|E) = P(E n F)/P(E)

This gives

P(E) = P(E n F)/P(F|E)

So, we have:

P(E) = 0.036/0.1

Evaluate

P(E) = 0.36

To calculate P(F), we use:

P(E|F) = P(E n F)/P(F)

This gives

P(F) = P(E n F)/P(E|F)

So, we have:

P(F) = 0.036/0.09

Evaluate

P(F) = 0.4

To calculate P(E U F), we use

P(E U F) = P(E) + P(F) - P(E n F)

So, we have:

P(E U F) = 0.36 + 0.4 - 0.036

Evaluate

P(E U F) = 0.724

The events E and F are independent if

P(E n F) = P(E) * P(F)

This gives

0.036 = 0.36 * 0.4

Evaluate

0.036 = 0.144 --- false

Hence, the events E and F are not independent

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It would Julia 0.60 years more to double the initial investment.

What is future value?

Future value means the initial investment multiplied by 2 since the future value is meant to double.

The formula for future value of a continuously interest rate is provided below:

FV=PV*e^(rt)

FV=future value=$4,200*2=$8,400

PV=initial investment=$4,200

e=exponential constant=2.7182818

r=interest rate=9.5%

t=number of years it takes for the investment to double=unknown

$8,400=$4,200*2.7182818^(9.5%*t)

$8,400/$4,200=2.7182818^(0.095t)

2=2.7182818^0.095t

take log of both sides

ln(2)=0.095t* ln(2.7182818)

0.095t=ln(2)/ln(2.7182818)

0.095t=0.69314718781684800

t=0.69314718781684800/0.095

t=7.30 years

The future value when interest is compounded quarterly is shown thus:

FV=PV*(1+r/4)^(N*4)

FV=$8,400

PV=$4,200

r=8 7/8%

r=8.875%

N=the number of years it would take for the initial investment to double=unknown

$8,400=$4,200*(1+8.875%/4)^(N4)

$8,400=$4,200*(1+0.0221875)^(N4)

$8,400/$4,200=(1+0.0221875)^(N4)

2=(1+0.0221875)^(N4)

2=(1.0221875)^(N4)

take log of both sides

ln(2)=N4*ln(1.0221875)

N4=ln(2)/ln(1.0221875)

N4=31.5857423180125

N=31.5857423180125/4

N=7.90

Difference in years=7.90-7.30

difference in years=0.60 years

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Using a system of equations, the amounts of cholesterol in each item are given as follows:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The variables for this problem are given as follows:

By eating 1​ egg, 1​ cupcake, and 1 slice of​ pizza, a child consumes 303 mg of cholesterol, hence:

x + y + z = 303.

3 cupcakes and 4 slices of​ pizza, he or she takes in 90 mg of cholesterol, hence:

3y + 4z = 90

y + 1.33z = 30.

By eating 2 eggs and 1​ cupcake, a child consumes 570 mg of cholesterol, hence:

2x + y = 570.

Then, writing y and z as functions of x:

Then, replacing on the first equation:

x + y + z = 303.

x + 570 - 2x + 1.5x - 406 = 303.

0.5x + 164 = 303.

x = (303 - 164)/0.5

x = 278.

The amounts for the cupcake and the slice of pizza are given as follows:

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The function g(x) is g(x)= (3x)^2

The complete question is in the image

From the graph in the image, we have:

f(x) = x^2

The function f(x) is stretched by a factor of 3 to form g(x).

This means that:

g(x) = f(3x)

So, we have:

g(x)= (3x)^2

Hence, the function g(x) is g(x)= (3x)^2

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Answer:

Yes

Step-by-step explanation:

All sides and angles look equal and appears to be a regular hexagon

Hope this helped and have a good day

Answer:

Yes.

Step-by-step explanation:

Hello!

A regular polygon is a closed shape with sides of equal length, and angles of equal degree. A regular polygon also forms around a general center.

This seems to be a regular polygon as all side lengths and angles seem to be equivalent, and there is a center point to the .

This shape is a hexagon, so the measure of the angles are 120°.

Answer:

30 km

Step-by-step explanation:

Distance = rate x time

Distance = 20 x 1.5

Distance = 30

[tex]20*1.5=30[/tex] [tex]km[/tex]

Correct answer:-

Avg. speed = [tex]20km/h[/tex]

Time = [tex]1.5 hour[/tex]

Distance traveled in 1.5 hours is Distance = Speed x Time

So,

[tex]D = 20 * 1.5 = 30.[/tex]

reference link-

a cyclist travels at a speed of 20 km per hour how far will he ...https://brainly.in › Math ›

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A function which could represent the graph is: C. f(x) = x⁴(x - a)(x - b)².

The nature of the intercept on a polynomial graph highlights the nature of its multiplicity. Also, the polynomial graph has no single zero (factor) but bounced off the x-axis at three (3) different locations.

This ultimately implies that the polynomial graph has an even multiplicity at these three (3) points:

x⁴

x - a

(x - b)²

In conclusion, a function which could represent the graph is f(x) = x⁴(x - a)(x - b)².

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The fraction computed shows that the total inches the infant grew over the three months is 3 3/4 inches.

First month = 2/4 inches

Second month = 1 inch

Third month = 7/4 inches.

The total inches the infant grew over the three months will be;

= 2/4 + 1 + 7/4

= 3 1/4 inches.

The difference in the infants from the second month to the third month will be:

= 7/4 - 1

= 3/4 inches.

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No pair of lines can be proven to be parallel considering the information given, therefore, the answer is: D. None of the options are correct.

Two lines that are cut across by a transversal can be proven to be parallel to each other if:

Thus, given the following information:

m∠2 = 115°

m∠15 = 115°

With only these two angles given, we can't use any of the theorems to prove that any of the two lines are parallel because angle 2 and angle 15 are located entirely on two different transversals that crosses two lines.

In summary, we can conclude that:

D. None of the options are correct.

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A Ferris wheel with a diameter of 10 m and makes one complete revolution every 80 seconds. Assuming that at time t = 0, the Ferris Wheel is at its lowest height above the ground of 2 m, the cosine equation of the graph drawn is, y = 5 cos [( π/40)(x - (π/2))] + 3.  Here, amplitude of the graph is 5, value of k is  π/40, d is π/2 and c is 3.

Developing the Equation of a Cosine Graph

The given information constitutes the following,

Diameter = 10 m

⇒ Radius, r = 5 m

Time, t = 80 s

Height above the ground, h = 2 m

Thus, we can infer that,

Amplitude, A = 5 m

Period, T = 80 s

Minimum height = 2 m

The cosine function is given as,

a cos [k(x − d)] + c

Here, A is amplitude

B is cycles from 0 to 2π and thus period = 2π/k

d is horizontal shift

c is vertical shift (displacement)

Now, 2π/k = 80

⇒ k = 2π/80 = π/40

The value of c is given as,

c = Amplitude - Minimum height

c = 5 - 2

c = 3

For a shift to the left by π/2 gives, we have,

d = π/2

Thus, the desired equation of the drawn cosine graph is,

y = 5 cos [( π/40)(x - (π/2))] + 3

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The polynomial is quadratic trinomial

The polynomial function is given as:

4x^2+ 8x +16

The highest power in the above polynomial is 2.

This represents quadratic

The number of terms in the above polynomial is 3

This represents trinomial

Hence, the polynomial is quadratic trinomial

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Answer:

1/2

Step-by-step explanation:

This is an independent event.  It does not matter what happened before the chances of getting a tail on one toss will always be what I want/all outcomes.  There are only 2 outcomes:  heads or tails.  I am only looking for one of those outcomes, so 1/2.

All the angles required to complete each sentence are:

In this question we must take advantage of definitions and theorems of Euclidean geometry to complete the three sentences seen in the figure. Now we proceed to present each sentence completed in detail:

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Jeremiah has to sell 5000 dollars worth of computers to get paid $130 on a given day. Using the linear equation, the required value is calculated.

An equation in which if the highest degree of the variable is 1(one), then that equation is said to be a linear equation.

General form: ax + b = c; where the power of the variable x is 1.

It is given that,

Jeremiah makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day.

Consider,

P - as total pay on a day, x - as the number of dollars worth of computers, B - as basic pay, and C - as commission percentage.

So, the linear equation that relates x and P is,

P = Cx + B   ...(i)

On substituting the values from the given table we get,

122.5 = C(4500) + B ...(ii)

160 = C(7000) + B ...(iii)

175 = C(8000) + B ...(iv)

By solving equations (iii) and (iv), we get

C = 15/1000 = 0.015

B = 55

Finding x value when P = $130:

We have P = Cx + B. Then for P = 130,

130 = Cx + B

We know C = 0.015 and B = 55

On substituting these values,

130 = (0.015) x + 55

⇒ 0.015x = 130 - 55 = 75

∴ x = 75/0.015 = 5000

Therefore, the required computers are 5000 dollars worth.

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Disclaimer: The given question on the portal was incomplete. Here is the complete question.

Question: Jeremiah is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. Let P represent Jeremiah's total payments on a day on which he sells x dollars worth of computers. The table below has select values showing the linear relationship between x and P. Determine how many dollars worth of computers Jeremiah would have to sell to get paid $130 on a given day.

Table:

x: 4500, 7000, 8000

P: 122.5, 160, 175

respectively.

The  NPV of this investment if the discount rate is 10 percent is: 1.58%.

Year Cash flow  PVIF 10%  Present value

0         ($11.86)     1.000           ($11.86)

1           1.90          0.909           $1.73

2          1.90          0.826           $1.57

3          1.90           0.751           $1.43

4          1.90           0.683          $1.30

5          1.90           0.621           $1.18

6          1.90           0.564          $1.07

7          1.90            0.513          $0.98

8          1.90           0.467          $0.89

9          1.90           0.424          $0.81

10         6.45          0.386         $2.49

NPV                                          $1.58

1.9+5.25-2×35%=6.45

Hence, the NPV is $1.58.

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Answer: (-1, 4)

Step-by-step explanation:

[tex]\left(\frac{-2+0}{2}, \frac{-1+9}{2} \right)=\boxed{(-1, 4)}[/tex]

(-1, 4) is the midpoint of the segment with endpoints at (-2,-1) and (0, 9). This can be obtained by using the formula for finding the midpoint of a line segment.

When the end points of a line segment are known, the mid point of the line segment is calculated using the midpoint formula,

Midpoint formula,

                   [tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex]

(x₁, y₁) and (x₂, y₂) are the endpoints of the line segment.

⇒ This means that, the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is [tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex].

From the question it is given that,

are the endpoints of the line segment.

By using the Midpoint formula we get,

[tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex] = [tex](\frac{-2+0 }{2},\frac{-1+9}{2})[/tex]

[tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex] = [tex](-1, 4)[/tex]

Hence (-1, 4) is the midpoint of the segment with endpoints at (-2,-1) and  (0, 9).

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Answer:

X = 'is the athlete injured' (X in {0,1})

Y = 'the athlete wins' (Y in {0,1})

P(Y=1|X=0) = 0.75

P(Y=1|X=1) = 0.15

P(Y=1) = 0.51

We are looking for P(X=1) - P(Y=1) = P(Y=1|X=0)*(1-P(X=1)) + P(Y=1|X=1)*P(X=1)

The above equation should provide you with the answer 0.4!

Step-by-step explanation:

The inverse variation equation that relates x and y is x = 4032 / y.

if two variables vary inversely, there is a negative relationship between both variables. the increase in one variable leads to a decrease in the other variable

The equation that represents inverse proportion : x = b/y

where b = constant of proportionality

112 = b /36

b = 36 x 112 = 4032

The equation : x = 4032 / y

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The actual roots of f(x) are -4 and 3

The function is given as:

f(x) = 2x^2 + 2x – 24.

Expand the function

f(x) = 2x^2 + 8x- 6x – 24.

Factorize the function

f(x) = 2x(x + 4) - 6(x + 4)

Factor out x + 4

f(x) = (x + 4)(2x - 6)

Set to 0

(x + 4)(2x - 6) = 0

Solve for x

x = -4 and 2x = 6

This gives

x = -4 and x = 3

Hence, the actual roots of f(x) are -4 and 3

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Answer:

A

Step-by-step explanation:

Got 100 on test

The total Stockholders’ Equity  is $4,367,000

Common Stock, $50 par $2,400,000

Paid-In Capital in Excess of Par—Common Stock $576,000

Paid-In Capital from Sale of Treasury Stock $48,000

Total paid in capital $3,024,000

Retained Earnings $1,368,000

Less Treasury stock  $25,000

Total Stockholders’ Equity $4,367,000

Therefore the total Stockholders’ Equity  is $4,367,000.

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Answer:

  see the attached

Step-by-step explanation:

Reflection over a line moves each point so that the segment between it and its image has the reflection line as its perpendicular bisector.

The line of reflection y=x has the effect of swapping the x- and y-coordinates:

  (x, y) ⇒ (y, x) . . . . . reflection in y=x

For example, point C(2, 3) moves to point C'(3, 2).

The attachment shows the reflected figure.

The two solutions to the given quadratic equation are 2i/3, -2i/3 and they are both complex solutions.

Hence, option C is the correct answer.

Given the equation; 9x² + 4 = 0

First, we subtract 4 from both sides.

9x² + 4 = 0

9x² = -4

x² = -4/9

Take the square roots of both sides

x = ±√(-4/9)

Rewrite -4/9 as (2i/3)²

x = ±√(2i/3)²

x = ±(2i/3)

Hence,

x = 2i/3, -2i/3

Therefore the two solutions to the given quadratic equation are 2i/3, -2i/3 and they are both complex solutions.

Hence, option C is the correct answer.

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Answer:

but it says ill get 10 only

Step-by-step explanation:

Hello,

5x² = 90/2

5x² = 45

x² = 45/5

x² = 9

x = √9 or x = -√9

x = 3 or x = -3

The volume within the spherical compression wave increasing in t = 4 seconds is:64000000π cubic ft/sec.

Given:

dr/dt=100 ft/sec

When: t=4 seconds, radius(r)=400ft

Hence:

Volume of a sphere (V)=4/3πr³

dv/dt=4/3π.3r² dr/dt

dv/dt=4πr²dt/dr

When t=4 seconds

dv/dt=4π×(100×4)²×100 cubic ft/sec

dv/dt=4π×(400)²×100 cubic ft/sec

dv/dt=64000000π cubic ft/sec

Therefore the volume within the spherical compression wave increasing in t = 4 seconds is:64000000π cubic ft/sec.

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We know that,

slope = [tex] \rm{\frac{(y2 - y1)}{(x2 - x1)} }[/tex]

Let (0,1)=(x 1 ,y 1 ) and (1,2)=(x 2,y 2 )

So,

Slope of line = [tex] \frac{(2 - 1)}{(1 - 0)} = 1[/tex]

Now,

The required line equaqtion is given by,

==> y−y 1 = m(x-x1)

==> y−1=1(x−0)

==> y−1=x

==> y=x+1

Answer:

5)

rise over run so

5/5 = 1

6)

-2/4 = -0.5

The answers to the questions are:

a. p = { t, v, c, q}

b. {2, 6} ⊂  {2,6,8,12}

c. {0, 3} ⊄ {3,2,4,6}

To represent sets we use

p = { }

Hence

a. p = { t, v, c, q}

b. If 2 and 6 is a proper subset of  [ 2,6,8,12},

This can be represented as

{2, 6} ⊂  {2,6,8,12}

c. the set consisting of the elements 0 and 3 is not a subset of {3,2,4,6} is written as

{0, 3} ⊄ {3,2,4,6}

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Option a. The equation that is used to show the graph of the limacon is given as r = 1 + 3 sin theta.

We have these ppoints [-5,5] by [-5,5]

The limacoin is used to represent a shape that may appear like that of a snail.

This is written in the form of

r = a ± b sin θ

and

r = a ± b cos θ

Given that we have the ± sign, the curve that is at the top of the horizontal; line is the + sign and the one below is the -

If a/b < 1 then a circle is within the circle that was formed as a graph.

Hence from the description that we have given here, the graph has the forms of

r =  a + b sin θ

This is the equation that can be used to suit the form r = 1 + 3 sin theta

Hence option a is right.

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Answer:

x=8   y=2

Step-by-step explanation:

solve for x

1. 4x+4y=40

2. subtract 4y from both sides

3. 4x=40-4y

4. divide both sides by 40

5. [tex]\frac{4x}{4} = \frac{40-4y}{4}[/tex]

6. dividing by four undoes the multiplication by four

7.    [tex]x=\frac{40-4y}{4}[/tex]

8. divide 40 - 4y by 4

9. x=10-y

10. use the last equation to solve the rest