if the simple interest on $2,000 for 2 year is $320 then what is the interest rate

Answer:

Total = Principal * (1 + rate) ^ years

We have to solve this for years:

Years = {log(total) -log(Principal)} ÷ log(1 + rate)

Jocelyn: Years = {log(total) -log(1,600)} ÷ log(1.025)

Marcus: Years =  {log(total) -log(400)} ÷ log(1.054)

We know the years must be equal but we won't know the total so we'll call that "x".

[log(x) -log(1,600)] ÷ log(1.025) = [log(x) -log(400)] ÷ log(1.054)

EDITED TO ADD

Time is about 49 Years 8 Months and total is about 5,454.00

We know the years must be equal

Step-by-step explanation:

Answer:

[tex]\large\boxed{(x,\ y)\to (x+3,\ y-2)}[/tex]

Step-by-step explanation:

[tex](4,\ -8)\to(7,\ -10)\\\\4\to7\Rightarrow4+3=7\\\\-8\to-10\Rightarrow-8-2=-10\\\\\text{Conclusion}\\\\(x,\ y)\to (x+3,\ y-2)[/tex]

Answer:

first choice: (x, y) ------> (x + 3, y - 2)

Step-by-step explanation:

The x-coordinate started as 4. Then it became 7. To change from 4 to 7, you add 3. The rule for x is to add 3.

The y-coordinate started as -8. Then it became -10. To go from -8 to -10, you subtract 2. The rule for y is to subtract 2.

Look at the choices, and pick the one that adds 3 to x and subtract 2 from y.

The answer is the first choice: (x, y) ------> (x + 3, y - 2)

Answer:

2 fluid ounces

Step-by-step explanation:

8 is a lot of mouthwash to use and anything aove that is a just alot...

Answer:

The cost of  chair is [tex]\$260[/tex]

The cost of  a lamp is [tex]\$65[/tex]

The cost of  a table is [tex]\$237[/tex]

Step-by-step explanation:

Let

x----> the cost of  chair

y----> the cost of  lamp

z----> the cost of table

we know that

[tex]x+y+z=562[/tex] ----> equation A

[tex]x=4y[/tex] -----> [tex]y=x/4[/tex] -----> equation B

[tex]z=x-23[/tex] ------> equation C

substitute equation C and equation B in equation A and solve for x

[tex]x+(x/4)+(x-23)=562[/tex]

[tex](9/4)x=562+23[/tex]

[tex](9/4)x=585[/tex]

[tex]x=585*4/9=\$260[/tex]

Find the value of y

[tex]y=260/4=\$65[/tex]

Find the value of z

[tex]z=260-23=\$237[/tex]

therefore

The cost of  chair is [tex]\$260[/tex]

The cost of  a lamp is [tex]\$65[/tex]

The cost of  a table is [tex]\$237[/tex]

Known: 12 bags in 3 hours

Question: X bags in 8 hours

1) Find the amount of bags made in 1 hour

12/3 = 4 bags per hour

2) If each hour makes 4 bags, and the factory is running for 8 hours then multiply the rate of bag production by the time running

8*4=32

Final Answer = 32 bags

I tried to personal message you but it didn't work. I have a question about your question it says "making both at the same rate". My question is both what?

If a random student has a 33% probability of belonging to a minority, then there is a 67% chance that they do not. In a sample of 10 students, the probability that exactly 4 do not belong to a minority is

[tex]\dbinom{10}40.67^4(1-0.67)^{10-4}\approx0.0547[/tex]

For this case we have that by definition, to move from Celsius to Fahrenheit we must apply the following formula:

[tex]F = \frac {9} {5} C + 32[/tex]

Example, we want to convert 45 degrees Celsius to Fahrenheit:

[tex]F = \frac {9} {5} (45) +32\\F = 9 * 9 + 32\\F = 81 + 32\\F = 113[/tex]

Thus, 45 degrees Celsius equals 113 degrees Fahrenheit.

ANswer:[tex]F = \frac {9} {5} C + 32[/tex]

For anyone who still needs this:

1. Multiply your Celsius measurement by 9/5 (or 1.8)

2. Add 32 to the result

Formula: F = (9/5)°C + 32

Answer:

Is it a decimal?

Step-by-step explanation:

Answer:

-240°, -600°

Step-by-step explanation:

Coterminal angles are angles that land in the same spot around a circle.

So, that means they do full turns of the circle to reach each other.

To find coterminal angles of a given angle (here 120 degrees), you add or subtract 360 (the number of degrees in a full circle).  That can go in both positive or negative directions.

So, from 120 degrees, let's find the coterminal angle that is 1 rotation above and one rotation below:

120 + 360 = 480

120 - 360 = -240

You see that 480 isn't among the possible answers, so one part of the answer is -240.  If you subtract another 360 degrees, you end up with -600 degrees... so the answer is -240°, -600°

Answer:

[tex]\lim_{x \to \pi } e^x=e^\pi[/tex]

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I would say that the owner wants people to believe that dance classes are a good form of exercise.

Answer:

15 is the answer

Step-by-step explanation:

The length of the suspension line from the harness to the edge of the open chute is approximately 10.97 ft.

To find the length of the suspension line, we can use the Pythagorean theorem. The distance from the parachute to the center of the diameter is the radius of the parachute, which is half the diameter. Therefore, the radius is 15 ft / 2 = 7.5 ft. The suspension line is the hypotenuse of a right triangle with one leg being the radius and the other leg being the distance from the parachute to the edge of the open chute. Using the Pythagorean theorem, we can calculate the length of the suspension line as follows:

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Answer:

This is just a guess so I'm sorry if its wrong but I'd guess that it's A

Answer:

It is A

Step-by-step explanation:

You can use the Pythagorean Theorem a^2+b^2=c^2

3^2+5^2=c^2

9+25=c^2

34=c^2

square root of 34=c

Answer:

Finding the mean is very simple, add them all together and divide that sum by the number of data points you have; in this case there are 45

Step-by-step explanation:

[tex]\frac{74+67+74.25+64+72+...}{45}[/tex] = mean

Answer:

Option B.

Step-by-step explanation:

If a quadratic equation is defined as

[tex]ax^2+bx+c=0[/tex]         .... (1)

then the quadratic formula is

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

The given equation is

[tex]10x^2=6+9x[/tex]

It can rewritten as

[tex]10x^2-9x-6=0[/tex]            .... (2)

On comparing (1) and (2) we get

[tex]a=10,b=-9,c=-6[/tex]

Using quadratic formula we get

[tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(10)(-6)}}{2(10)}[/tex]

[tex]x=\dfrac{9\pm \sqrt{81+240}}{20}[/tex]

[tex]x=\dfrac{9\pm \sqrt{321}}{20}[/tex]

Therefore, the correct option is B.

Answer:

B

Step-by-step explanation:

I got it right

Answer: Last option.

Step-by-step explanation:

The total amount of concrete in the ramp ([tex]V_t[/tex]) will be the sum of the volume of the  rectangular prism ([tex]V_{rp}[/tex]) and the volume of the triangular prism ([tex]V_{tp}[/tex])

[tex]V_t=V_{rp}+V_{tp}[/tex]

The formulas are:

[tex]V_{rp}=lwh[/tex]

Where "l" is the lenght, "w" is the width and "h" is the height.

 [tex]V_{tp}=\frac{bhl}{2}[/tex]

Where "l" is the lenght, "b" is the base and "h" is the height.

Substituting, we get:

[tex]V_t=V_{rp}+V_{tp}\\\\V_t=lwh+\frac{bhl}{2}\\\\V_t=(18in)(6in)(6in)+\frac{(8in)(6in)(18in)}{2}\\\\V_t=1,080in^3[/tex]

Answer:

The guy above me is correct lol

Step-by-step explanation:

Answer:

1, 3, 9, 27

Step-by-step explanation:

[tex] a_n = 3^{n - 1} [/tex]

You need the first 4 terms, so let n = 1, and evaluate the expression. Then do the same for n = 2, n = 3, and finally n = 4.

n = 1

[tex] a_1 = 3^{1 - 1} = 3^0 = 1 [/tex]

n = 2

[tex] a_2 = 3^{2 - 1} = 3^1 = 3 [/tex]

n = 3

[tex] a_3 = 3^{3 - 1} = 3^2 = 9 [/tex]

n = 4

[tex] a_4 = 3^{4 - 1} = 3^3 = 27 [/tex]

Answer:

Step-by-step explanation:

Notice that the greatest number of dots is over the '70,' indicating that 70% of the students in the town enjoy playing video games.

This problem has to do as much with your ability to interpret graphs as to apply statistics concepts correctly.

Answer:

Step-by-step explanation:

The angle you can get right away is z.

z + 93 = 180

z + 93 - 93 = 180 - 93

z = 87

===============

The next step is to solve for y. You need to draw a line from  y to the center and another one from z to the center.

The triangle containing part of y and part of z has a central angle of 106 degrees.

Part of y + partz + 106 = 180

part of y + partz = 74

part of y = partz = 37                The triangle is isosceles because 2 of the legs are radii.

Do the same thing from 93 to the center and the other part of y to the center.

The central angle is 58

The two other angles are equal

part of y + part of 93 + 58 = 180

partofy + partof93 = 180 - 58

partofy + partof93 = 122

partofy = part93 = 61

So

y = 61 + 37 = 98

========================

x + y = 180 (opposite angles in a quadrillateral that fits in a circle = 180)

x + 98 = 180

x = 82

====================

x = 82

y = 98

z = 87

Answer:

[tex]7\frac{1}{2}\ plates[/tex]

Step-by-step explanation:

we know that

The recipe calls for 2/3 cups of cheese for each plate of nachos

so

using proportion

Find out how many plates can she make with five cups of cheese

let

x ----> the number of plates

[tex]\frac{1}{(2/3)}\frac{plate}{cups} =\frac{x}{5} \frac{plates}{cups}\\ \\x=5/(2/3)\\ \\x=7.5\ plates[/tex]

Convert to mixed number

[tex]7.5=\frac{14}{2}+\frac{1}{2}=7\frac{1}{2}\ plates[/tex]

She can make 7.5plates with 5 cups of cheese

According to the question, we are told that the recipe calls for 2/3 cups of cheese for each plate of nachos. This is expressed as:

2/3 cups of cheese = 1 plate of nachos

In order to calculate the number of plates she can make with  five cups of cheese

5 cups  = x

Cross multiply

2/3x = 5

2x = 15

x = 7.5 plates

Hence she can make 7.5plates with 5 cups of cheese

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Answer:

[tex]y=-2x-1[/tex]

Step-by-step explanation:

Let the first coordinate point be (x_1,y_1) and the second coordinate point be (x_2,y_2)

So

x_1 = -2

y_1 = 3

x_2 = -4

y_2 = 7

Now we can use the formula for equation of line to figure it our.

Equation of line formula is  [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Plugging in the known values and arranging in slope-intercept form, we have:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y-3=\frac{7-3}{-4-(-2)}(x-(-2))\\y-3=\frac{4}{-2}(x+2)\\y-3=-2(x+2)\\y-3=-2x-4\\y=-2x-4+3\\y=-2x-1[/tex]

This is the equation of the line passing through the points ( -2, 3) and ( -4, 7)

Final answer:

To find the equation of the line, the slope is calculated as -2, using the point-slope form with one of the points yields y - 3 = -2(x + 2). Simplifying this, the equation of the line is y = -2x - 1.

Explanation:

To find the equation of a line passing through two points, first, determine the slope (m) of the line. The slope is calculated as the change in y (vertical) divided by the change in x (horizontal). For the points (-2, 3) and (-4, 7), the slope is:

m = (y2 - y1) / (x2 - x1) = (7 - 3) / (-4 + 2) = 4 / (-2) = -2.

Next, use the point-slope form:

y - y1 = m(x - x1),

where (x1, y1) is a point the line passes through. Using point (-2, 3) and the slope -2:

y - 3 = -2(x + 2).

Rewrite this equation in slope-intercept form (y = mx + b) by simplifying and solving for y:

y = -2x - 4 + 3,

y = -2x - 1.

Therefore, the equation of the line passing through the points ( -2, 3) and ( -4, 7) is y = -2x - 1.

Answer:

sinθ = 12/15 -> 4/5

cosθ = 9/15 -> 3/5

tanθ = 12/9 -> 4/3

cscθ = 15/12 -> 5/4

secθ = 15/9 -> 5/3

cotθ = 9/12 -> 3/4

Step-by-step explanation:

The theta is where you would use to identify the numbers for the trig functions. The adjacent side is the one closest to the theta (but not the diagonal line, that is the hypotenuse), and the opposite line is the line next to the adjacent line.

For the first three trig functions, would use the method Soh Cah Toa.

Sin = opp/hypotenus, Cosine = adjacent/hypotenuse, and Tangent = opposite/adjacent. Then, there is cosecant(csc) = hyp/opp, secant = hyp/adj, and cotangent = adj/opp.

Answer:

A

Step-by-step explanation:

There are calculators online that you can use to answer this, some even show you the work step by step

Answer:

Final answer is [tex]\frac{21x-7}{3x^2-2}[/tex]

Step-by-step explanation:

We have been given two terms [tex]\frac{21x}{3x^2-2}[/tex]

and [tex]\frac{7}{3x^2-2}[/tex]

Now we need to find their difference. So let's subtract them

[tex]\frac{21x}{3x^2-2}-\frac{7}{3x^2-2}[/tex]

Denominators are equal so we can easily subtract numerators

[tex]=\frac{21x-7}{3x^2-2}[/tex]

We may factor the numerator but we won't get any factor in denominator that can be cancelled with numerator.

Hence final answer is [tex]\frac{21x-7}{3x^2-2}[/tex]

Answer:

49.999999999999974312306505198184 V

Step-by-step explanation:

Step 1: you see 45°, which gives you a easy conversion [tex]\frac \pi 4[/tex]).

Now, [tex]t = 392.7 \mu s = 392.7* 10^{-6} s[/tex], start replacing.

[tex]V= 50 cos ( 2* 10^3 * 392.7 *10^{-6} -\frac \pi 4) = 50 cos (0.7854 - \frac \pi 4) =\\ 49.999999999999974312306505198184 V[/tex]

Answer:

68.2 feet

Step-by-step explanation:

The angle of elevation, the one from the ground up, is given as 33 degrees.  If Kari is 105 feet from the tree, that serves as the measure of the base of the right triangle.  We are looking for the height of the tree, which is the side opposite the angle.  What we have, then, is the angle (33 degrees), the side adjacent to the angle (105 ft), and we are looking for the side opposite the angle (x).  What we need to use is the tangent ratio, which relates the side opposite the angle to the side adjacent to the angle, as follows:

[tex]tan33=\frac{x}{105}[/tex]

To solve for x we multiply both sides of the equation by 105 to get 105tan33°=x.  Plug that into your calculator in degree mode to get 68.18779729.  Round from there to get 68.2 feet.

Answer:

A

Step-by-step explanation:

The line passes through the points (-3,-7) and (9,1).

The slope of the line can be calculted using formula

[tex]\dfrac{y_2-y_1}{x_2-x_1}.[/tex]

Thus, the slope of the given line is

[tex]\dfrac{1-(-7)}{9-(-3)}=\dfrac{8}{12}=\dfrac{2}{3}.[/tex]

Answer:

A

Step-by-step explanation:

slope is given by the formula:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

We need 2 points to find a line's slope.

Plugging these into the slope formula, we will get the slope:

[tex]\frac{1--7}{9--3}\\=\frac{1+7}{9+3}\\=\frac{8}{12}\\=\frac{2}{3}[/tex]

correct answer is A

Answer:

Step-by-step explanation:

One

Since you are asked to solve this using a graphing tool, here is the results as graphed by Desmos.

The point you want is (3,2)

The answer is 2.

Two

Multiply the second equation by 2

2[0.5x - y = 10]

x - 2y = 20              Add the first equation

x + 2y = 16      

2x = 36                   Divide by 2

x = 36/2

x = 18

Since this is all you are asked for, x = 18 is the answer.

Three

y is an exterior angle.

It is the sum of the two (given) remote interior angles.

y = 35 + 105

y = 140

x and y are supplementary (they add up to 180o

x + y = 180

x + 140 = 180

x = 180 - 140

x = 40

y - x = 140 - 40

y - x = 100        

Answer:

y = 1/2

Step-by-step explanation:

If two variables x and y vary inversely, then:

xy = k

where k is the constant variation.

In this case:

xy = 6

When x = 12:

12y = 6

y = 1/2

The value of y when x is 12 is 2 (option C)

Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases. Example is the price of a commodity and the quantity acquired, the higher the price, the lower of commodity bought and vice- versa.

here, we have,

Inverse relationship between two quantities x and y is expressed as:

x= ky

where k is the constant

k = 6

when x = 12

12 = 6y

divide both sides by 6

y = 12/6

y = 2

therefore the value of y when x is 12 is 2

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