A man needed money for college. He borrowed $5,000 at 16% simple interest per year. If he paid $200 interest, what was the duration of the loan?

The probability that not more than 5 graduates plan to pursue a graduate degree is 0.0191.

Given Information

Percentage of college graduates that plan on pursuing a graduate degree=50%

Number of graduates selected=14

Let us consider the event that a college graduate plans on pursuing a graduate degree as a success.

The probability of getting success is p = 0.50

Let X denotes the event of success.

We have, n = 14.

Then,

X∼Bin(14,0.50).

The pmf of X is given as,

\(P(X)= ^nC_xP^x(1-P)^n^-^x\\\\P(X)= ^1^4C_x(0.50)^x(0.50)^1^4^-^x\)

The probability that not more than 5 graduates plan to pursue a graduate degree can be computed as,

P(X≤5)=5∑¹⁴Cₓ(0.50)x(0.50)¹⁴⁻ˣ

=0+0.00001+0.00012+0.00081+0.00396+0.01425

P(X≤5)=0.01914

Hence, the probability that not more than 5 graduates plan to pursue a graduate degree is 0.0191.

The probability that exactly 7 of the college graduates plan to pursue a graduate degree can be computed as,

P(X=7)=¹⁴C₇(0.5)⁷(0.5)⁹

P(X=7)=0.08395

Therefore, the probability that exactly 7 of the college graduates plan to pursue a graduate degree is 0.0840.

The probability that at least 9 but not more than 14 of the college graduates plan to pursue a graduate degree can be computed as,

P(9≤X≤14)=14∑x=9 ¹⁴Cₓ(0.50)x(0.50)¹⁴⁻ˣ

P(9≤X≤14)=0.18889+0.19833+0.16227+0.10142+0.04681+0.01505

P(9≤X≤14)=0.71277

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Answer:

-9u^7v - 6u^5v - 21u^2v

Step-by-step explanation:

The expression equivalent to\(-4x^2 + 2x - 5(1 + x)\)  is \(4x^2 + 8x + 5.\)

This expression matches the form \(x^2 + x + c,\) where c = 5.

To simplify the given expression \(-4x^2 + 2x - 5(1 + x)\) and make it equivalent to the expression \(x^2 + x + c,\) where c is a constant term, we need to perform some algebraic operations.

First, let's distribute the -5 to the terms inside the parentheses:

\(-4x^2 + 2x - 5 - 5x\)

Next, we can combine like terms:

\(-4x^2 + (2x - 5x) - 5 - 5x\)

Simplifying further:

\(-4x^2 - 3x - 5 - 5x\)

Now, let's rearrange the terms to match the form \(x^2 + x + c:\)

\(-4x^2 - 3x - 5x - 5\)

To make the leading coefficient positive, we can multiply the entire expression by -1:

\(4x^2 + 3x + 5x + 5\)

Now, we can combine the x-terms:

\(4x^2 + 8x + 5\)

So, the expression equivalent to \(-4x^2 + 2x - 5(1 + x)\) is \(4x^2 + 8x + 5.\)This expression matches the form \(x^2 + x + c,\) where c = 5.

It's important to note that the original expression and the equivalent expression have different coefficients and constants, but they represent the same mathematical relationship.

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(a) The scale factor from shape A to shape B is 3/4.

(b) The value of w is 21/4 cm.

A scale factor is the ratio of the new object to a given original object.

For example,

The scale factor is A : B.

We have two similar trapezoid as shown in the picture.

Find (a) the scale factor from shape A to shape B, and (b) the value of w!

The scale factor from shape A to shape B can be determined by analyzing one of the side length. We can take the longest side of the trapezoid.

Scale factor = 9/12 = 3/4

The value of w side is correspond to 7. So,

w/7 = 3/4

w = 3/4 × 7

w = 21/4 cm

Hence, the scale factor is 3/4 and the value of w is 21/4 cm.

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Given:

Consider the below figure attached with this question.

To find:

The value of x.

Solution:

We know that, the sum of all exterior angles of a quadrilateral is always 360 degrees.

The below figure represents the four exterior angles of the quadrilateral. So,

\(65^\circ+106^\circ+78^\circ+x^\circ=360^\circ\)

\(249^\circ+x^\circ=360^\circ\)

\(x^\circ=360^\circ -249^\circ\)

\(x^\circ=111^\circ\)

Therefore, the measure of x is \(111^\circ\).

Based on the given variation, y does not vary directly with x and the constant of variation are 8, 3.2 and 1.25 respectively.

y = k × x

where,

k = constant of proportionality

y = -40

x = -5

y = k × x

-40 = k × -5

-40 = -5k

k = -40/-5

k = 8

when,

y = 8 and x = 2.5

y = k × x

8 = k × 2.5

8 = 2.5k

k = 8/2.5

k = 3.2

when,

y = 5 and x = 4

y = k × x

5 = k × 4

5 = 4k

k = 5/4

k = 1.25

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The equation to determine the number of consecutive free throws Callie must complete is option B: x + 9 = 0.887(x + 15). The equation to find the time it takes for the garage door to close completely is option B: 4.7 - 0.8t = 0.

To determine the equation that could be used to find the number of consecutive free throws Callie must complete to raise her free-throw percentage to 88.7%, we can set up a proportion.

Let's represent the number of consecutive free throws Callie must complete as 'x'.

The equation would be:

(65/100 + x)/(15 + x) = 88.7/100

Simplifying the equation, we get:

(0.65 + x)/(15 + x) = 0.887

To match the available options, let's manipulate this equation:

Option B: x + 9 = 0.887(x + 15)

Comparing this equation with the simplified version of our equation, we see that it matches. Therefore, the correct equation to determine the number of consecutive free throws Callie must complete is option B: x + 9 = 0.887(x + 15).

Moving on to the second question, to find the equation that can be solved to find the time it takes for the garage door to close completely, we need to consider the rate at which the door moves down.

Let's represent the time it takes for the door to close completely as 't'.

The equation would be:

Initial height - rate × time = 0

Given that the initial height is 4.7 meters and the rate at which the door moves down is 0.8 meters per second, we can set up the equation as follows:

Option B: 4.7 - 0.8t = 0

This equation represents the scenario where the door's height decreases at a rate of 0.8 meters per second until it reaches the ground (height 0). Therefore, the correct equation to find the time it takes for the door to close completely is option B: 4.7 - 0.8t = 0.

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It is not possible that the intersection case is P(A B)=0.5 .

The set of all objects that are members of both sets A and B is represented by the intersection of the two sets A and B, abbreviated as A∩B.

If there is any element x that is an element of both A and B, then we can also say that A intersects (meets) B at x. If A∩B is an inhabited set, which means that there must be some x such that x∈A∩B exists, then A intersects B equivalently.

If A does not intersect B, then A and B are said to be disjoint. They share no elements, to put it simply. If the intersection of A and B contains nothing—A∩B=Ф—then A and B are disjoint.

Explanation:

The likelihood of occurring of an event is called probability.

Consider two events A and B are occurred with probabilities P(A) and P(B)  respectively.

The probability that both the events occurs is,

P(A and B)=P(A∩B)

When both the events are independent,

P(A and B)=P(AB) = P(A)x P(B)

The probability that either A or B occurs is,

P(A or B)= P(AUB) = P(A)+P(B)-P(A∩B)

When both the events are mutually exclusive the probability that either A or B occurs is,

P(A or B)=P(AUB) = P(A)+P(B)

The compliment of the probability is,

P(A)=1-P(A)

The conditional probability of occurring of an event A when it is given that B had already occurred is,

P(A|B)=P(A∩B)/P(B)

Let A represent the situation where the chosen person has a Visa credit card and B represent the situation where they have a Master card. The probability of occurring event A is 0.6 and the probability of occurring event B is 0.4 that is, P(A)=0.6, P(B)=0.4 .

It is known that P(A B)∠P(A) and P(A B)∠P(B) . So, it is not possible that the intersection case, P(A B)=0.5 .

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The value of x in the rhombus is - 96.

A rhombus is a quadrilateral with 4 sides equal to each other. The opposite sides of a rhombus are parallel. The opposite angles are congruent. The diagonals are perpendicular and they bisect each other. The adjacent angles are supplementary.

Therefore,

m∠TXU = (-x - 6) degrees

Hence,

-x -6 = 90

add 6 to both sides of the equations

-x -6 = 90

-x -6 + 6 = 90 + 6

-x = 96

Therefore,

x = -96

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The teacher states that four of these roots are correct, while one is incorrect. Out of the given roots, the incorrect root is -11.5.

We are given that Adam found five roots for the fifth-degree polynomial equation with rational coefficients: -11.5, √2, (2i + 6)/2, -√2, and 3-i. The teacher states that four of these roots are correct, while one is incorrect.

To determine the incorrect root, we can analyze the given options: -11.5, √2, (2i + 6)/2, and 3-i.

Among these options, the only one that is not a valid root is -11.5. This is because the problem specifies that the polynomial equation has rational coefficients, meaning that all the roots must also be rational or irrational numbers that can be expressed as the square root of a rational number.

Therefore, the incorrect root is -11.5 (option F).

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Answer: 17

Step-by-step explanation: 2 is an even number and 17 is an odd number, therefore it can't be divisible by 2. 17 does not have a 5 or a 0 in it therefore it is not divisible by 5. Any multiple of 5 will always have a 5 or 0 in it. If it doesn't have a zero in it anywhere it is not divisible by 10. A multiple of 10 will always have a zero in it.

Answer:

1 team = 10 players

7 teams = 7×10 players

= 70 players

drop out players:

1 team = 2 players

7 teams = 2×7

= 14 players

how many left ?

= total players - drop out players

= 70 - 14

= 56 players

Answer:

Its Las sillas son nuestras

Step-by-step explanation:

On Edge 2021

Answer:

nuestras

Step-by-step explanation:

The money Glen must raise to reach his goal will be $440. And the minimum number of weeks it will take him to reach his goal will be 9 weeks.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Glen raised $275 for his softball team's fundraiser. He wants to raise at least $715. Let 'y' be the amount of money Glen must raise to reach his goal. Then the inequality is given as,

y + $275 ≥ $715

y ≥ $440

Let 'x' be the number of weeks, then we have

50x > $440

x > 8.8

x = 9 week

The minimum number of weeks it will take him to reach his goal will be 9 weeks.

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Answer:

-72

Step-by-step explanation:

-0.125x=16-7

-0.125x=

x=-72

Answer:

x = -72

Step-by-step explanation:

Given equation,

→ -0.125x + 7 = 16

Now we have to,

→ Find the required value of x.

Then the value of x will be,

→ -0.125x + 7 = 16

Subtract RHS with the number 7:

→ -0.125x = 16 - 7

→ -0.125x = 9

Divide RHS with the number -0.125:

→ x = 9 ÷ (-0.125)

→ [ x = -72 ]

Hence, the value of x is -72.

This is the standard form equation of the circle is \((x - 7)^{2}\) + \((y - 14)^{2}\) = 10

The standard form equation of a circle is \((x - h)^{2}\) + \((y - k)^{2}\) = \(r^{2}\), where (h, k) is the center of the circle and r is the radius.

Given the center of the circle as (7, 14) and a point on the circle as (4, 15), we can use the distance formula to find the radius:

r = \(\sqrt{(4 - 7)^{2} + (15 - 14)^{2} }\) =  \(\sqrt{(-3)^{2} + (1)^{2} }\)= \(\sqrt{9 + 1}\) = \(\sqrt{10}\)

So the standard form equation of the circle is:

\((x - 7)^{2}\) + \((y - 14)^{2}\) = \(\sqrt{(10)^{2} }\)

Which can be written as:

\((x - 7)^{2}\) + \((y - 14)^{2}\) = 10

So the standard form equation of the circle is \((x - 7)^{2}\) + \((y - 14)^{2}\) = 10

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We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).

We treat both positive and negative disparities equally by squaring the residual values.  We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.

We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.

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The curl of vector field F is -i - j and the divergence of the vector field F is 0.

We have to follow the below steps:

Step 1: Find curl.

Step 2: Find divergence.

Curl :

Curl is the vector operator that defines the cross product of two vectors. It is applied to a vector field to generate another vector field.

Step 1:

Find the curl of vector field

Curl of the vector field F is defined as ,F = (P, Q, R)

Curl F = (Ry - Qz)i + (Pz - Rx)j + (Qx - Py)k

Where, Ry denotes the partial derivative of R with respect to y. Qz denotes the partial derivative of Q with respect to z, Pz denotes the partial derivative of P with respect to z .Rx denotes the partial derivative of R with respect to x, Qx denotes the partial derivative of Q with respect to x. Py denotes the partial derivative of P with respect to y.

Here,P = -x, Q = y, and R = -2.Then

Ry = 0, Qz = 0, Pz = 0, Rx = 0, Qx = 0, and Py = 0

Therefore, the curl of F = (Ry - Qz)i + (Pz - Rx)j + (Qx - Py)k= -i - j + 0k= -i - j

Then, the curl of vector field F is -i - j.

Divergence:

Divergence is a vector operator that operates on a vector field to produce a scalar value. It measures the magnitude of the outward flux of the vector field from an infinitesimal region around a particular point. Divergence is given by,

Divergence of the vector field F = (P, Q, R)div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z

Here, P = -x, Q = y, and R = -2.Then, ∂P/∂x = -1, ∂Q/∂y = 1, and ∂R/∂z = 0

Therefore, the divergence of the vector field F is

div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z= -1 + 1 + 0= 0

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Answer:

2

Step-by-step explanation:

Hey there!

The equation is asking us, c x c = 4

What is c?

Well the only number that is equal to 4 when you square it is 2

James has 60 cars

john has 20 cars

this statement implies that James has 3 times has the number of cars jokhn hax

= 60/ 20

= 3

Answer:

24 codes are possible

Step-by-step explanation:

0 through 4 means we are to select from 0,1, 2 , and 4

That’s a total of 4

The first number has 4 choices, the second 3, the 3rd two and the last 1

The product of the choices are;

4 * 3 * 2 * 1 = 24 codes

Answer

Total Length of Wire = Perimter of Pentagon

= 12 × 5 = 60 cm

Perimeter of Rectangle = 2 (l + b)

Given, l = 3/2 b

Therefore,

2(3/2 b + b) = 60

2 (5b/2) = 60

5b = 60

Breadth b = 12 cm

Length l = 3/2 × 12 = 18 cm

Answer:

i hope its right, im taking the test, i put A

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

******************************************************************************

Kate buys 10 tickets to  a show. She also pays a $5 parking fee. She spent $35 to see the  show.

Each ticket costs x.

10 tickets cost 10x.

Parking is $5.

Total is $35

10x + 5 = 35

******************************************************************************

Ram has 35 gel pens. He gives an equal number of pens to each of his 5 friends and has  10 pens left for himself.

The number of pens he gives each friend is x.

The total number he gives is 5x.

He started with 35 pens ands ended up with 10 pens.

35 - 5x = 10

5x + 10 = 35

******************************************************************************

Yin spends 10 hours on homework this week. She spends 5 hours on science homework  and then answers 35 math problems.

Total time spent on homework is 10 hours.

Science homework is 5 hours.

She spends x time on each of the 35 problems, so the total time spent of the 35 problems is 35x.

35x + 5 = 10

Answer:

A=0, 3, 6, 9, 12, 15

B=25, 20, 15, 10, 5, 0

Step-by-step explanation:

Answer:

The amount left after each friend got $46.

Step-by-step explanation:

Any time you see R1 in bus stop method division, it just means remainder. So dividing 93 dollars between 2 friends gives them both 46 dollars, with one left over!

Hope this helps :)

Answer:

7 is correct.

There are 4 small triangles, 2 medium-sized triangles, and 1 large triangle.

To determine whether the assumption of constant error variance is satisfied for a model with tut, independent variables x, and x₂, you would examine the residual plot where the residuals are plotted against predicted values y.

This plot is also known as the plot of residuals versus fitted values. In this plot, if the residuals are randomly scattered around the horizontal line of zero, then the assumption of constant error variance is satisfied. However, if there is a pattern in the residuals, such as a funnel shape or a curve, then the assumption of constant error variance may not be met. It is important to ensure that the assumption of constant error variance is met, as violation of this assumption can lead to biased and inefficient estimates of the model parameters. Additionally, it can affect the reliability of statistical inferences and lead to incorrect conclusions.
In summary, to determine whether the assumption of constant error variance is satisfied for a model with tut, independent variables x, and x₂, you would examine the residual plot where the residuals are plotted against predicted values y. It is important to check this assumption to ensure the validity of the model and the accuracy of the results.This plot allows you to assess the variance of the residuals and identify any patterns, which could indicate that the assumption of constant error variance may not be met. If the plot shows no discernible pattern and the spread of residuals appears to be uniform across the range of predicted values, the assumption of constant error variance is likely satisfied.

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Answer:

9000 milliliters are in 9 liters

Step-by-step explanation:

multiply the volume value by 1000

Answer:

9 meters , i believe so-

Step-by-step explanation:

2,5,4,6,1,7,3 is the correct order to construct a square.

So looking at the 7 available steps, only the step "Construct horizontal PQ" is possible since that's just a matter of drawing a straight line and labeling the endpoints P and Q. In any case, here are the 7 steps in order. The number in parenthesis after the 1st number is the original scrambled order of that step.  

1. Construct horizontal PQ

2. Construct a circle with point P as the center and a circle with point Q as the center, each circle having a radius PQ

3. Label the point of intersection of the two circles above PQ, point R, and the point of intersection of the two circles below PQ, point S

4. Construct RS, the perpendicular bisector of PQ, intersecting PQ at point T

5. Construct a circle with point T as the center with a radius TQ

6. Label the point of intersection of circles T and RS closest to point R, point U, and the point of intersection of circles T and RS closest to point S, point V.

7. Construct PU, UQ, QV, and VP to complete square PUQV.

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