Last year, Joe had $20,000 to invest. He invested some of it in an account that paid 5% simple interest per year, and he invested the rest in an account that
paid 8% simple interest per year. After one year, he received a total of $1450 in interest. How much did he invest in each account?

Answer:

24/7

Step-by-step explanation:

tan A = opp/adj

For angle Z, the adjacent leg is 14, and the opposite leg is 48.

tan Z = 48/14

tan Z = 24/7

Answer:

their is a 1 in 36 chance that happens

Answer:

y = 8

Step-by-step explanation:

Since the y- coordinates of the points are equal, both 8 , then

This indicates the line is horizontal and parallel to the x- axis with equation

y = c

where c is the value of the y- coordinates the line passes through

The line passes through (- 3, 8 ) and (- 7, 8 ) with y- coordinates 8 , then

y = 8 ← equation of line

Answer:

y = - 3.5x + 53.5

Step-by-step explanation:

Step 1:

7x + 2y = 107       Equation

Step 2:

y = mx + b       Slope Intercet Form

Step 3:

2y = - 7x + 107      Subtract 7x on both sides

Answer:

y = - 3.5x + 53.5       Divide

Hope This Helps :)

Answer:

y=-7/2x+107/2

Step-by-step explanation:

y=mx+b

7x+2y=107

-7x       -7

2y=-7x+107

(divide both sides by 2)

y=-7/2x+107/2

Answer:

None

Step-by-step explanation:

Truly, I'm not sure what type of problem this is, but most people don't favor all the seasons. If there is more to the problem, I would be glad to help further.

Answer:

One possible way to estimate how many people out of 20 would say that they like all seasons is to use a simple random sample. A simple random sample is a subset of a population that is selected in such a way that every member of the population has an equal chance of being included. For example, one could use a random number generator to assign a number from 1 to 20 to each person in the population, and then select the first 20 numbers that appear. The sample would then consist of the people who have those numbers.

Using a simple random sample, one could ask each person in the sample whether they like all seasons or not, and then calculate the proportion of positive responses. This proportion is an estimate of the true proportion of people in the population who like all seasons. However, this estimate is not exact, and it may vary depending on the sample that is selected. To measure the uncertainty of the estimate, one could use a confidence interval. A confidence interval is a range of values that is likely to contain the true proportion with a certain level of confidence. For example, a 95% confidence interval means that if the sampling procedure was repeated many times, 95% of the intervals would contain the true proportion.

One way to construct a confidence interval for a proportion is to use the formula:

p ± z * sqrt(p * (1 - p) / n)

where p is the sample proportion, z is a critical value that depends on the level of confidence, and n is the sample size. For a 95% confidence interval, z is approximately 1.96. For example, if out of 20 people in the sample, 12 said that they like all seasons, then the sample proportion is 0.6, and the confidence interval is:

0.6 ± 1.96 * sqrt(0.6 * (1 - 0.6) / 20)

which simplifies to:

0.6 ± 0.22

or:

(0.38, 0.82)

This means that we are 95% confident that the true proportion of people who like all seasons in the population is between 0.38 and 0.82. Therefore, based on this sample and this confidence interval, we would expect between 8 and 16 people out of 20 to say that they like all seasons in the population.

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(a) The differential equation

\(y' + \dfrac14 y = 3 + 2 \cos(2x)\)

is linear, so we can use the integrating factor method. We have I.F.

\(\mu = \displaystyle \exp\left(\int \frac{dx}4\right) = e^{x/4}\)

so that multiplying both sides by \(\mu\) gives

\(e^{x/4} y' + \dfrac14 e^{x/4} y = 3e^{x/4} + 2 e^{x/4} \cos(2x)\)

\(\left(e^{x/4} y\right)' = 3e^{x/4} + 2 e^{x/4} \cos(2x)\)

Integrate both sides. (Integrate by parts twice on the right side; I'll omit the details.)

\(e^{x/4} y = 12 e^{x/4} + \dfrac8{65} e^{x/4} (8\sin(2x) + \cos(2x)) + C\)

Solve for \(y\).

\(y = 12 + \dfrac8{65} (\sin(2x) + \cos(2x)) + Ce^{-x/4}\)

Given that \(y(0)=0\), we find

\(0 = 12 + \dfrac8{65} (\sin(0) + \cos(0)) + Ce^0 \implies C = -\dfrac{788}{65}\)

and the particular solution to the initial value problem is

\(\boxed{y = 12 + \dfrac8{65} (\sin(2x) + \cos(2x)) - \dfrac{788}{65} e^{-x/4}}\)

As \(x\) gets large, the exponential term will converge to 0. We have

\(\sin(2x) + \cos(2x) = \sqrt2 \sin\left(2x + \dfrac\pi4\right)\)

which means the trigonometric terms will oscillate between \(\pm\sqrt2\). So overall, the solution will oscillate between \(12\pm\sqrt2\) for large \(x\).

(b) We want the smallest \(x\) such that \(y=12\), i.e.

\(0 = \dfrac8{65} (\sin(2x) + \cos(2x)) - \dfrac{788}{65} e^{-x/4}\)

\(\dfrac{788}{65} e^{-x/4} = \dfrac{8\sqrt2}{65} \sin\left(2x + \dfrac\pi4\right)\)

\(\dfrac{197}{\sqrt2} e^{-x/4} = \sin\left(2x + \dfrac\pi4\right)\)

Using a calculator, the smallest solution seems to be around \(\boxed{x\approx21.909}\)

The equation modelling the height of the diver at time of t seconds is expresed as

f(t) = - 4.9t² + 4t + 10

To find the height at t = 1.5, we would substitute t = 1.5 into the function. We have

f(1.5) = - 4.9(1.5)² + 4(1.5) + 10

f(1.5) = - 11.025 + 6 + 10

f(1.5) = 4.975

Her height at 1.5 seconds after diving off the springboard is 4.975 meters

1. Revised Net Operating Income = $66,760

2. Revised Net Operating Income  =$64,640

3. Revised Net Operating Income  =$52,

1. If the sales volume increases by 40 units:

So, New Sales = 8,700 units + 40 units = 8,740 units

and, New Contribution Margin =

= $14.00 x 8,740 units

= 122, 360

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 122360 - 55600

= 66,760.

2. If the sales volume decreases by 40 units:

New Sales = 8,700 units - 40 units = 8,660 units

New Contribution Margin

= 14 x 8660

= 121,240

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 65,640

3. If the sales volume is 7,700 units:

New Sales = 7,700 units

New Contribution Margin

= 14 x 7700

= 107,800

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 52, 200

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Answer:

Population of the 48th generation will be 4469.

Step-by-step explanation:

Recursive formula by which the population is increasing,

\(L_{n+1}=L_n+95\)

L₀ = 4

Common difference 'd' = 95

Recursive formula represents a linear growth in the population.

Therefore, explicit formula for the given sequence will be,

\(L_n\) = L₀ + (n - 1)d [Explicit formula of an Arithmetic sequence]

Here n = Number of terms

L₄₈ = L₀ + (48 - 1)(95)

     = 4 + 4465

     = 4469

Therefore, population of the 48th generation will be 4469.

The zeros of the polynomial function are x = -1 and x = 5

From the question, we have the following parameters that can be used in our computation:

y = x⁴ - 4x³ - 4x² - 4x - 5

To calculate the zeros of the polynomial function, we create a graph of the polynomial

The point where the graph intersect with the x-axis are the zeros of the polynomial function

using the above as a guide, we have the following:

Zeros: x = -1 and x = 5

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BC is tangent to circle A, and the value of r is 10.

Given,

BC=24

CD=16

AD=AB=r

To find the value of r, we can use the fact that a tangent line to a circle is perpendicular to the radius at the point of tangency. So we know that angle ABD is a right angle, and we can use the Pythagorean theorem

The Pythagorean theorem can be used to calculate the value of r:

\(AB^2+BC^2=AC^2\)

\(r^2+24^2=(r+16)^2\)

\(r^2= (r+16)^2-24^2\)

\(r^2\)= \(r^2\)+256+32r-576

\(r^2\)=\(r^2\)+32r-320

\(r^2-r^2\)-32r=-320

-32r=-320

r=320/32

r=10

Therefore the correct answer is r=10.

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The result of the multiplication operation yields 7 7/12

From the question, we are to multiply the given fractions. The given fractions are

1 3/4 and 4 2/6

First, we will convert the fractions to improper fractions

Converting 1 3/4 to an improper fraction

1 3/4 = 7/4

Converting 4 2/6 to an improper fraction

4 2/6 = 26/6

Thus,

The multiplication operation becomes

7/4 × 26/6

= 7/4 × 13/3

= 91/12

= 7 7/12

Hence, the product of the given numbers is 7 1/12

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1. The congruence statements are angle A = angle D, angle B = angle E, angle C = angle F, AB = DE, AC= DF, BC =EF.

3. angle Y = angle N.

5. Angle Z = angle L.

7. The value of x is 7 and the value of y is 8.

What is congruence?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

1. We will compare the number of lines to define the angle and sides.

Since angle A and angle D are denotes by three lines. Thus A = angle D.

In the similar manner angle B = angle E, angle C = angle F, AB = DE, AC= DF, BC =EF.

3.  Since triangle XYZ is congruent with triangle MNL. Thus corresponding angle are equal.

angle Y = angle N

5. Angle Z = angle L

7. Given that the quadrilateral ABCD is congruent  with EFGH.

Thus angle A = angle E

Putting the value of angle A  and angle E:

28 = 4y -4

Add 4 of both sides

32 = 4y

Divide both sides by 4:

y= 8

Again,  

angle B = angle F

Putting the value of angle B  and angle F:

135 = 10x + 65

Subtract 65 from both sides:

70 = 10x

Divide both sides by 10:

x = 7

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Answer:

12.3459 grains

Step-by-step explanation:

Answer:

12.346 grains

Step-by-step explanation:

for an approximate result, multiply the mass value by 15.432

( which is basically 0.8 times 15.432)

Step 1: Isolate the Sin Operator

\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)

Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable

Note that since trig functions have 2 general solutions, this will give us one of our general solutions.

\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)

x₁= 0.48

Solving for x₂

Use the period identity for Sin Functions

\(sin(x)=sin(\pi -x)\)

X in this case is arcsin(0.25)

\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)

So our two general solutions are 0.48 and 5.52

Step 3: Period

Trig Functions have periodic behavior and this function period is

\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)

So our general solutions are

0.48±12k, where k is an integer

5.52±12k, where k is an integer

Let k=1, and we get our next set of solutions:

12.48 and 17.52

So our answer is 0.48,5.52,12.48,17.52

Answer:

43.6 has 3 significant figures.

Answer:

x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

5ab-ab+9a-7a

ab(5-1)+a(9-7)

4ab+2a

a(4b+2)

The value of the function \(\rm f (x) = \frac{18}{6} + 5e^{-0.1x}\) at x = 6 will be 5.744.

Given that:

Function, \(\rm f (x) = \frac{18}{6} + 5e^{-0.1x}\ \ or \ \ f (x) = 3+ 5e^{-0.1x}\\\)

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The value of the function at x = 6 is calculated as,

\(\rm f (x) = 3+ 5e^{-0.1\times 6}\\\\f (x) = 3+ 5e^{-0.6}\)

Simplify the equation further, then we have

f(x) = 3 + 5 · 0.5488

f(x) = 3 + 2.744

f(x) = 5.744

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The similarity ratio of  PQR to VXW is represented as 4 / 1

Similar triangles have the same shape but there sizes may vary. In similar triangles, corresponding sides are always in the same ratio.

The corresponding angles are congruent.

Therefore, the similarity ratio can be found as follows:

PQ / VX = PR / VW = QR / XW

Therefore,

8 / 2 = 4 / 1 = 8 / 2

4 / 1 = 4 / 1 = 4 / 1

Therefore, he similarity ratio of  PQR to VXW is 4 / 1

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Check the picture below.

Answer:

A i think

Step-by-step explanation:

Answer:

u already have the answer

Answer:

For people that can't see the picture it's

C (2,-3/400) third option

Step-by-step explanation:

The probability that the next person will purchase one or more costumes can be found by dividing the number of visitors who purchased one or more costumes by the total number of visitors.

The total number of visitors is 105 + 41 + 8 = 154.

The number of visitors who purchased one or more costumes is 41 + 8 = 49.

So the probability that the next person will purchase one or more costumes is 49/154, which is approximately 0.32 to the nearest hundredth.

Answer:

a. 6276

b. 5590

c. 23128

d. 17325

e. 15090

f. 40419

g. 10496

h. 15000

i. 15648

99% sure

Answer:

6417

Step-by-step explanation:

if A = b*h then when we substitute b for 93 and h for 69

A=93*69 = 6417

Answer:

9

Step-by-step explanation:

You don't need to pass through each edge once.

If we name the top vertex 1 and the bottom vertex 2 then here are the possible combinations:

A-1-B

A-B

A-2-B

A-1-B-A-2-B

A-2-B-A-1-B

A-B-1-A-2-B

A-B-2-A-1-B

A-1-B-2-A-B

A-2-B-1-A-B

Some people say 6 because they think you need to pass through all the edges. But the only restriction with travelling on the edges is you can't pass one twice. The point is read the wording and it becomes easy.

Hope this helps!