Find the APR, rounded to the nearest tenth of a percent (one decimal place) for the loan. Purchase a living room set for $4,900 at 8% add-on interest for 4 years. Enter only the number without % sign.

Answer:

 x = -2

Step-by-step explanation:

Prime factorize, 27 and 9

27 = 3 *3 * 3 = 3³

  9 = 3*3 = 3²

[tex]\sf \left(\dfrac{1}{27}\right)^{2-x}=9^{3x}\\\\[/tex]

 [tex]\left(\dfrac{1}{3^3}\right)^{2-x}=9^{3x}\\\\(3^{-3})^{2-x}=(3^2)^{3x}\\\\3^{(-3)*(2-x)}=3^{2*3x}\\\\3^{-6+3x} = 3^{6x}[/tex]

Bases are same, so now compare the exponents

     -6 + 3x = 6x

            3x = 6x + 6

       3x - 6x = 6

             -3x = 6

               x  = 6/(-3)

               [tex]\sf \boxed{\bf x = -2}[/tex]

         [tex](x^m)^n=x^{m*n}\\\\\left(\dfrac{1}{a^{m}}\right)=a^{-m}\\[/tex]

Answer:

angle M

Step-by-step explanation:

if you are using side angle side the two sides may be

line LK and NK

and angle M

Answer:

A

Step-by-step explanation:

Inflation decreases the amount of goods and services that can be purchased with a dollar.

The rate of change of the distance from the particle to the origin at this instant is 3 units per second.

The instantaneous rate of change is the rate of change at a particular instant.

A particle is moving along the curve

[tex]y= 4\sqrt{5x+11} .[/tex]

The rate of change of y is given as:

dy / dx = 2

by differentiating both sides,

[tex]\dfrac{dy}{dx} = 4\dfrac{1}{2\sqrt{5x+11} } 5\dfrac{dx}{dt} \\\\\dfrac{dy}{dx} = \dfrac{10}{\sqrt{5x+11} }\dfrac{dx}{dt}\\\\[/tex]

From the question, we have:

(x, y) =  (5,24)

Substitute 5 for x and dy / dx = 2

[tex]\dfrac{dy}{dx} = \dfrac{10}{\sqrt{5x+11} }\dfrac{dx}{dt}\\\\\\5= \dfrac{10}{\sqrt{5(5)+11} }\dfrac{dx}{dt}\\\\\\\sqrt{5(5)+11} = 2\dfrac{dx}{dt}\\\\\\\dfrac{dx}{dt} = 6/ 2 = 3[/tex]

Hence, the rate of change of the distance from the particle to the origin at this instant is 3 units per second.

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Answer:

They both have an infinite number of solutions.

Step-by-step explanation:

Given system of equations:

a) 2x + 4y = 15

b) 6x + 12y = 45

Slope-intercept form: y = mx + b

where:

Rewrite both equations into slope-intercept form:

a) 2x + 4y = 15

⇒ 2x + 4y = 15 [subtract 2x from both sides]

⇒ 2x - 2x + 4y = 15 - 2x

⇒ 4y = - 2x + 15 [divide both sides by 4]

⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

b) 6x + 12y = 45

⇒ 6x + 12y = 45 [subtract 6x from both sides]

⇒ 6x - 6x + 12y = 45 - 6x

⇒ 12y = - 6x + 45 [divide both sides by 12]

⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

New equations:

[tex]\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.

System of equations can have the following:

No Solution: the same slope (both lines will be parallel)

One Solution: different slopes and different y-intercepts

Infinitely Many Solutions: the same slope and y-intercept

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Looking at the given expression, they do not seem to be in the slope-intercept form which is the most common form used for linear expression. Let us convert the equations that were given in the problem statement to follow the slope-intercept form.

Equation #1

Subtract 2x from both sides

Divide both sides by 4

Equation #2

Subtract 6x from both sides

Divide both sides by 12

Since both the first and second equation have the same exact number which means that they will fall exactly on top of each other.  Therefore, there are infinite solutions as they will always continue on top of each other.

Answer:

2/52 so the chance is unlikely.

Step-by-step explanation:

well I think I’m right because sometimes when my family has time we play blackjack in my house for fun or another card game so I should be right.

Answer:

1.6e-7, or .00000016

Step-by-step explanation:

Answer:

A.264

Step-by-step explanation:

((Area Of triangle*height)=Volume

Area of triangle is the base of the triangle multiplied by height of triangle divided by 2

((8*6)/2)*11=264

Answer: Heyaa!~

                  - Write 63 as the product of prime factors -

              - Write the prime factors in ascending order -

         -   what's the highest common factor of 63 and 105   -

             Hopefully this helps you! ^^^

The correct statement is:

"She is not correct because she did not substitute the same number in both expressions in Step 1."

First, let's see if Sophia is correct.

She starts with the expression:

-(4x - 5) + 2*(x - 3) = -2x - 5

Expanding the left side:

-4x + 5 + 2x - 6 = -2x - 5

-2x -1 = -2x - 5

So the constant term is different.

Now, what Sophia does is evaluating in x = 1 and x = -1. You can't do that when finding equivalent expressions. (never evaluate in different numbers).

"She is not correct because she did not substitute the same number in both expressions in Step 1."

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A function assigns the values. The graph of the function f(x) and g(x) can be plotted as shown in the below image.

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function f(x) and g(x) can be plotted as shown in the below image.

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236/100, 59/25, or 2 9/25

Step-by-step explanation:

There are 100 cents in a dollar, so 236/100 is your starting fraction. The simplest improper fraction would be 59/25. But if you're looking for a mixed number, you get 2 9/25.

236 cents is equivalent to 118/50 or 2.36 dollars as a fraction of a dollar.

To solve this problem,

We need to convert 236 cents into dollars.

Since there are 100 cents in one dollar,

we can divide 236 by 100 to get the equivalent dollar value.

⇒ 236 cents ÷ 100 cents per dollar = 2.36 dollars

Now that we know that 236 cents is equivalent to 2.36 dollars,

we can express it as a fraction of a dollar.

To do this, we'll use the fact that one dollar is equivalent to 100 cents, which means that one dollar can be expressed as the fraction 100/100.

To find the fraction of a dollar that 2.36 dollars represents,

we'll divide 2.36 by 1.

⇒ 2.36 ÷ 1 = 2.36/1

To express this as a fraction of a dollar,

Multiply both the numerator and denominator by 100 to get,

⇒ (2.36 x 100) / (1 x 100) = 236/100

Simplifying this fraction, we get,

⇒ 236/100 = 118/50

Therefore,

236 cents is equivalent to 118/50 or 2.36 dollars as a fraction of a dollar.

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no I dont feel like it is the answer

Answer:

A. 65 degrees

Step-by-step explanation:

The required measure of the angle c in the quadrilateral is given as 65°.

As mentioned in the question,
A quadrilateral is inscribed in a circle o. the angle measures the quadrilateral in degrees is given by the expressions shown in the figure.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
In a quadrilateral, the sum of the composite angle is equal to 180°,
∠A + ∠C = 180
130 -x + 95 -2x = 180
-3x = 180 - 225
x = 15

Now,
∠c = 95 - 2x
∠c = 95 - 2×15
∠c = 65

Thus, the required measure of the angle c in the quadrilateral is given as 65°.

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Answer: F = - 2/7

Step-by-step explanation:

[tex]f(x) = x + 9\\f(-7) = -7 + 9\\f(-7) = 2\\f = -\frac{2}{7}[/tex]

Answer:

the answer is 45

see the attachment photo!

The equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The equation made by the given situation is:-

For kyle, there are g students attending 8 classes sp total number of students will be 8g similarly for h students there are 6 classes so the total number of h students will be 6h. The total number of students for both g and h students attending kyle's class is 62. So the equation will be given as:-

8g   +  6h  =  62

Now for Lauren, there are g students attending 5 classes so the total number of students will be 5g similarly for h students there are 10 classes so the total number of h students will be 10h. The total number of students for both g and h students attending Lauren's class is 70. So the equation will be given as:-

5g  +  10h  =  70

Therefore the equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.

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[tex]~~~~~~2I_2 - A\\\\\\=2\begin{bmatrix}1&0\\0&1 \end{bmatrix}-\begin{bmatrix}4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix}2&0\\0&2 \end{bmatrix}-\begin{bmatrix}4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix}2-4&0-2\\0-3&2+3 \end{bmatrix}\\\\\\=\begin{bmatrix}-2&-2\\-3&5 \end{bmatrix}[/tex]

Using the binomial distribution, it is found that approximately 156 cards must be drawn from the deck before players' tokens move forward 50 times.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected number of trials until q successes is:

[tex]E_s(X) = \frac{q}{p}[/tex]

In this problem, the parameters are given as follows:

q = 50, p = 0.32.

Hence:

[tex]E_s(X) = \frac{50}{0.32} = 156[/tex]

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Answer:

It always has an x coord of 0

The first step that we must take before attempting to solve a problem is to understand what it is asking for and what is given to us to help solve the problem.  Looking at the problem statement, we can see that they are asking what is true about the y-intercept.  We are given the information that the y-intercept is the place where a line crosses the y-axis.

Now that we have collected all that information, let us move onto understanding and solving the problem.  So first of all, using the information that was given to us, we know that the y-intercept is the place where a line crosses the y-axis.  The y-axis occurs where the x-coordinate is 0 and the x-axis occurs where the y-coordinate is 0.  Therefore, the option that would best fit the description that we have would be option A, it always has an x coordinate of 0.

Answer:

f(x) = √x + 3

y = √x + 3

√x = y - 3

x = (y - 3)²

Hence inverse of f(x) = (x - 3)² and its domain is x >= 3.

Step-by-step explanation:

hope this helps

The modal class is 70 - 80 and the mean speed is 66.4

The table of values is given as:

Speed    Frequency

40 - 50          10

50 - 60          16

60 - 70          19

70 - 80          23

80 - 90          12

The modal class is the class with the highest frequency

The class 70 - 80 has the highest frequency of 23

Hence, the modal class is 70 - 80

Rewrite the frequency table to include the class midpoints

x             f

45          10

55          16

65          19

75          23

85          12

The estimate of the mean speed is then calculated as:

[tex]\bar x =\frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{45* 10 + 55 * 16 + 65 * 19 + 75 * 23 + 85 * 12}{80}[/tex]

Evaluate

[tex]\bar x = 66.4[/tex]

Hence, the mean speed is 66.4

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Answer:

15.25

Step-by-step explanation:

1/4  is also 0.25 in decimals so add that to your 15 and you get 15.25.

Step-by-step explanation:

the fraction 1/4 is also equivalent to the decimal for of .25 + 15 equals 15.25

Answer:

7 3/5

Step-by-step explanation:

2 x 3 4/5

2 x 19/5

2x19/1x5 = 38/5 = 7 3/5

The triangle is an isosceles right triangle. Then the value of x will be 1.27 cm.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The right-angle triangle is given below.

The given triangle is an isosceles right triangle.

P = B = x

Then we have

1.8² = x² + x²

2x² = 3.24

 x² = 1.62

   x = 1.27 cm

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70d+2-14d= 79+12d-20

70d-14d-12d= 79-20-2

44d= 57

d= 57/44

Answer:

list five solution to the energy crisis of nepal

1d) ↑ (Do the same but turned if that's easier)

1a) 199

1b) 193

1c) 217

1e) Based on the box plot, we can for example, find the lowest and greatest values, the range (largest - smallest), the mean (all values / # values), and the median middle value or q2 given by the second line in the box.

2b) 7

2c) 9.5

2d) ↑

2e) because the data is not ordered, it is difficult to determine the quartile data. Once it is ordered like 6, 7, 7, 7, 8, 8, 9, 10, 10. The data can be visualized alot easier. With the box plot we can determine q3 of the data by looking at the 3rd line, using the whiskers of the box to find the minimum and maximum values.

3)

You need to find the minimum, maximum, the quartile data obtained by having an even amount of data on both sides, order it so that values can be grouped. this includes q1, q2 (or median), and q3.

In this case the ordered data would be: 4,6,8,8,9,11,12,14,14,16.

[4, 6, 8, 8, 9] [] [11, 12, 14, 14, 16]

4 is the minimum, 16 is the maximum, q1 is 8, q3 is 14, and median is 10.

4) ↑

5)

You need to find the minimum, maximum, the quartile data obtained by having an even amount of data on both sides, order it so that values can be grouped. this includes q1, q2 (or median), and q3.

In this case the ordered data would be:

45, 45, 50, 55, 60, 70, 70, 75, 80, 85

[45, 45, 50, 55, 60] [] [70, 70, 75, 80, 85]

45 is the minimum, 85 is the maximum, q1 is 50, q3 is 75, and median is 65.

6) ↑