A friend of mine borrowed $800 for 3 years. He claims he paid $968 for the interest and principal. What was the rate on the loan?

Because x is continuous, we should use interval notation, the domain is:

D: [1, ∞)

For a function y = f(x), we define the domain as the set of possible inputs of the function (possible values of x).

To identify the domain, we need to look at the horizontal axis. The minimum value is the one we can see in the left side, and the maximum is the one we could see on the right side.

There we can see that the domain starts at x = 1 and extends to the left, so the notation we can use for the domain is:

D: x ≥ 1

We know that the value x =1 belongs because there is a closed dot there.

The correct option is A, because the domain is continuous (as we can see in the graph), we should use interval notation. In this case the domain can be written as:

D: [1, ∞)

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measure of Angle PRT = 90 degrees

A circle with center T exists -- Given

Point R is on the the circle. -- THIS IS AN ASSUMPTION BASED ON THE PICTURE (if you have more information that makes this not true, the rest of this logic fails).

Line segment TR is the radius of the circle. -- Definition of radius

Line PR is tangent to the circle. -- PR touches at exactly one point: R

Angle PRT has a vertex as point R. -- definition of angle PRT

Since PR is tangent to the circle, TR is perpendicular to PR -- consequence of lines perpendicular to circles

Perpendicular lines form right angles. -- Consequence of two congruent angles that form a straight angle pair.

The measure of a right angle is 90 degrees. -- definition of right angle

Therefore, the measure of angle PRT is 90 degrees.

The probability that the child will also have diabetes is about 1/2500 so the above-given statement is (B) FALSE.

So, if a 30-year-old woman with type-1 diabetes has a child, then the probability that the child will also have diabetes is about 1%:

Now,

Therefore, the probability that the child will also have diabetes is about 1/2500 so the above-given statement is (B) FALSE.

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The correct question is given below:
Risk of diabetes

The American Diabetes Association reports the following information:

In general, if you are a man with type-1 diabetes, the odds of your child getting diabetes are 1 in 17. If

you are a woman with type-1 diabetes and your child was born before you were 25, your child's risk

is 1 in 25; if your child was born after you turned 25, your child's risk is 1 in 100.

For each of the following questions, be prepared to justify your response in class.

A 30-year-old woman with type-1 diabetes has a child. The probability that the child will also have

diabetes is about 1%.

(A) True

(B) False

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Answer:

The last Table

Step-by-step explanation:

After 2 hours of work, you will be charged $80. Add this to the already charged $650 and you will have $730. For each hour add an additional $40 to that cost. The last table matches this.

The equation be showing the relationship between the total cost and the hours is:

c = 40h + 650

A linear equation is given by:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept.

Let c represent the total cost and h represent the hours.

Since the painter charges $40 an hour, hence m = 40. Also he purchased for $650, hence b = 650. The equation be comes:

c = 40h + 650

The table that represent this is the last table and it is attached.

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Answer:

y= -6x-11

If y+2+(6x-9)=0

Step-by-step explanation:

y+2+(6x-9)=0? (I'm assuming)

Subtract 2 from both sides

y+(6x-9)= -2

Subtract (6x-9) from both sides

y= -2-(6x-9)

y= -2-6x-9

y= -6x-11

The numbers are 1 and 8.

We have,

Let's assume the lesser number as "x" and the greater number as "8x".

According to the given information, when the lesser number is subtracted from the greater, the result is 2 more than 5 times the lesser number:

8x - x = 5x + 2

Simplifying the expression:

7x = 5x + 2

Subtracting 5x from both sides:

2x = 2

Dividing both sides by 2:

x = 1

So, the lesser number is 1 and the greater number is 8 times that, which is 8.

Therefore,

The numbers are 1 and 8.

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Answer:

20 m

Step-by-step explanation:

Given that :

Scale of 1 : 50 is used to make a model

If the model has a height of 40 cm ; the height of the house is:

Then, the actual height of the house is (40 * 50) = 2000 cm

Thus the height of the house in metre is :

100cm = 1 meter

2000 cm = 2000 / 100

2000 cm = 20 meter

Height of house in meter = 20 meter

Answer:

Step-by-step explanation:

Hey there,
Here's my reasoning regarding the problem:

Let's assume that the watch at the time it was lost was x years old.
When it was picked it was 3 times as old as it was when it was lost therefore it's currently 3x. The time between when it was lost and when it was found is 38 years. We can break this down into a simple algebraic formula:

3x - x = 38

2x = 38

x = 19

Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Answer:

y=3x+1

Step-by-step explanation:

Use the slope formula and slope-intercept form  y = m x + b  to find the equation.

Answer:

(-4,3),(2,-12)

slope = (-12 - 3) / (2 - (-4) = -15/6

Step-by-step explanation:

y = mx + b

slope(m) = -15/6

use either of ur points...(-4,3)...x = -4 and y = 3

now we sub into the formula and find b, the y int

3 = -15/6(-4) + b

3 = 10 + b

3 - 10 = b

-7 = b

so ur equation is : y = -15/6x - 7....but we need it in standard form

y = -15/6x - 7...add 15/6 to both sides

15/6x + y = -7...multiply both sides by 6

15x + 6y = -42....which reduces to 5x + 2y = - 14 <===

Answer:

It is a right triangle

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

A line that is parallel to y = 3x - 9 will have the same slope as the given line. The slope of y = 3x - 9 is 3. Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (1, 2)

Substituting the values we get:

y - 2 = 3(x - 1)

Simplifying the equation we get:

y - 2 = 3x - 3

y = 3x - 1

Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is y = 3x - 1 .

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Answer:

A.  4

Step-by-step explanation:

Given inequality:

\(x+9 < 4x\)

Rearrange the inequality to isolate x.

Subtract x from both sides of the inequality:

\(\begin{aligned}x+9-x & < 4x-x\\9& < 3x\end{aligned}\)

Divide both sides of the inequality by 3:

\(\begin{aligned}\dfrac{9}{3}& < \dfrac{3x}{3}\\\\3& < x\\\\x& > 3\end{aligned}\)

So the values of x that make the inequality true are:

Therefore, from the given answer options, the value of x that makes the inequality true is x = 4.

To check this, substitute x = 4 into the inequality:

\(\begin{aligned}x+9& < 4x\\x=4\implies 4+9& < 4(4)\\13& < 16\end{aligned}\)

As 13 is less than 16, the inequality is true when x = 4.

Answer:

\(m = 9.5\) -- Unit rate of change

See attachment for graph

Step-by-step explanation:

Given

\(\begin{array}{cccc}Hours & {6} & {9} & {7} \ \\ Amount & {57.00} & {85.50} & {66.50} \ \ \end{array}\)

Solving (a): The unit rate of change.

This implies that we calculate the slope of the table.

This is calculated as:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Where:

\((x_1,y_1) = (6,57.00)\)

\((x_2,y_2) = (9,85.50)\)

\((x_3,y_3) = (7,66.50)\)

The equation becomes

\(m = \frac{85.50 - 57.00}{9 - 6}\)

\(m = \frac{28.5}{3}\)

\(m = 9.5\)

To graph the table, we need to determine the equation.

To do this, we make use of:

\(y = m(x - x_3) + y_3\)

Substitute values for m, x3 and y3

\(y = 9.5(x - 7) + 66.50\)

Open bracket

\(y = 9.5x - 66.50 + 66.50\)

\(y = 9.5x\)

See attachment for graph

Answer:

9.5

Step-by-step explanation:

I hope this helps!

Answer: No it is not.

Step-by-step explanation:

All linear functions can be written in the form y = mx + b, where m is the slope and b is the y-intercept (slope-intercept form). Alternatively, a linear function can be expressed in the form y – y0 = m(x – x0), where m is the slope and (x0, y0) is a point on the line (point-slope form).

Answer:

yes: it has a variable  X

Step-by-step explanation:

Answer:

39 3/8 ft ^2

Step-by-step explanation:

To find the area of a rectangle, multiply the length times the width.

A = l*w

  = 7 1/2  * 5 1/4

Change the mixed numbers to improper fractions.

A = 15/2 * 21/4

    =315/8

Change back to a mixed number.

8 goes into 315 39 times with 3 left over.

 = 39 3/8

Answer:

(you can round to 39.4)

Step-by-step explanation:

Find the area of the rectangle shown

7 1/2 ft

5 1/4ft

7 1/2 = 7.5 ft

5 1/4 = 5.25 ft

Area = L x W

Area = 7.5 x 5.25

Area = 39.375

The domain of the function f(x) = -3x + 2 is (-∞, +∞), representing all real numbers, and the range is (-∞, 2], representing all real numbers less than or equal to 2.

The function f(x) = -3x + 2 is a linear function defined by a straight line. To determine the domain of this function, we need to identify the range of values for which the function is defined.

The domain of a linear function is typically all real numbers unless there are any restrictions. In this case, there is no explicit restriction mentioned, so we can assume that the function is defined for all real numbers.

Therefore, the domain of the function f(x) = -3x + 2 is (-∞, +∞), which represents all real numbers.

Now, let's analyze the range of the function. The range of a linear function can be determined by observing the slope of the line. In this case, the slope of the line is -3, which means that as x increases, the function values will decrease.

Since the slope is negative, the range of the function f(x) = -3x + 2 will be all real numbers less than or equal to the y-intercept, which is 2.

Therefore, the range of the function is (-∞, 2] since the function values cannot exceed 2.

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The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer

You bought 7 paperbacks and 3 hardcovers.

Step-by-step explanation: This doesn't seem college level! Jokes aside, you solve this with a system of equations. Your first equation is 10 = p + h, where p stands for the number of paperbacks and h stands for the number of hardcovers. Your second equation is p = 3h - 2, meaning that the number of paperbacks is triple the number of hardcovers minus 2. Now, you just have to plug in p = 3h - 2 into your first equation, and you get 10 = (3h - 2) + h. 4h = 12, and h = 3, meaning the number of hardcovers must be 3. All you have to do now is subtract 3 from 10, and you have 7, which is the number of paperbacks!

Out of the total number of 10 books bought, there were 3 hardcovers and 7 paperbacks

Paperbacks are two less than three times the hardcovers. Assume the hardcovers are x, the paperbacks would be represented as:

= 3x - 2

Solving would give:

10 = Paperbacks + Hardcovers

10 = 3x - 2 + x

10 = 4x - 2

4x = 10 + 2

x = 12/4

x = 3 hardcovers

Paperbacks:

= 10 - 3

= 7

In conclusion, there are 3 hardcovers and 7 paperbacks.

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Answer:

it's dependent events so multiply each probability

Total marbles = 17+6+12+3=38

P(red) = 17/38

Since without replacement, now total marble is 38-1=37

P(blue)= 6/37

Multiply two probability

(17/38) (6/37) = 0.07

Answer:

A, because for every x value there can only be exactly one y value.  Since 2 pairs with 1 and 4, the relation is not a function.

Step-by-step explanation:

8.75

-1 2/3 × (-5 1/4)

=35/4

= 8 3/4

= 8.75

Answer:

B) 25.5 m²

Step-by-step explanation:

The formula to find the area of a trapezoid: 1/2 x (a + b) x h, where a and b are the parallel lines and h is the height.

1) Input the values into the formula, and solve it.

= 1/2 x (5 + 12) x 3

= 1/2 x 17 x 3

= 1/2 x 51

= 25.5

Answer:

B

Step-by-step explanation:

A = (1/2)(3)(5 + 12)

= (1/2)(3)(17)

= (1/2)(51)

= 25.5 m^2

Answer:

5

Step-by-step explanation:

The proportion of 1040r tax forms completed in less than 77 minutes = 0.06301

How to find the proportion of the tax forms?

The time required to complete a 1040r tax form = normally distributed

Mean = \(\mu\) = 100 minutes

Standard deviation  = \(\sigma\) = 15 minutes

The proportion of 1040r tax forms completed in less than 77 minutes is given by ,

P( X< 77 ) = P ( Z < \(\frac{77-100}{15}\)  )

                = P( Z < - 1.53 )

                =0.06301

Cumulative probability in the normal distribution =0.06301 or 6.301%

What is normal distribution?

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Answer:

The answer is the one at the top left corner.

(y - 12)/(x - 4) = 3/2

Hope this helped!

The solution for the given system of equations is (-2, -2).

What is addition method?

Using the Addition Method to Solve Systems of Equations in Two Variables. The addition method, also known as the elimination method, is a third strategy for resolving linear equation systems. With this approach, we add two terms that share the same variable but have opposing coefficients, resulting in a sum of zero.

Given:

The system of equations,

3x + 7y = -20          ..(1)

-3x + 6y = -6            ..(2)

We have to solve this system of equations using addition method.

Adding equation (1) and (2)

      3x + 7y = -20

 +  -3x + 6y = -6

__________________

       0 + 13y = -26

13y = -26

  y = -2

Plug y = 2 in equation (1), we get

3x + 7(-2) = -20

3x - 14 = -20

3x = -20 + 14

3x = -6

x = -2

Hence, the solution for the given system of equations is (-2, -2).

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If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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Answer:

the 852 is the perfect fit q3

Step-by-step explanation:

The five-number summary of this data set are minimum is 515, maximum value is 986, Q₁ is 686, Q₂ is 852 and Q₃ is 966.

Median of a data set is the element in the middle if the data are arranged in increasing or decreasing order. It is also called second quartile.

Given data set is,

{852, 687, 515, 986, 907, 784, 967, 685, 965}

Arrange this in ascending order first.

{515, 685, 687, 784, 852, 907, 965, 967, 986}

Minimum value = 515

Maximum value = 986

First we have to find the median or the second quartile.

Second quartile, Q₂ = Middle element of the set

Q₂ = 5th element = 852

First quartile = 1/4 (n + 1)th element = 1/4 (9 + 1) = 2.5 th element

Q₁ = (685 + 687) / 2 = 686

Third quartile = 3/4(n + 1)th element = 3/4 (9 + 1) = 7.5th element

Q₃ = (965 + 967) / 2 = 966

Hence the five-number summary of this data set are found.

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