5.) $28,000 invested at a rate of 4% compounded annually
a.) Write a compound interest function to model the situation.

Answer:

sin∅ = 12/13

Step-by-step explanation:

use pythagorean theorem to find the missing side

a² + 5² = 13²

a² = 13² - 5²

a² = 169 - 25

a² = 144

a = 12

-----------------------------

Sin∅ = opp/hyp

sin∅ = 12/13

Answer:

The answer is below

Step-by-step explanation:

Given that mean (μ) = $32500, standard deviation (σ) = $2500.

a) The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

For x < 36000:

[tex]z=\frac{36000-32500}{2500}=1.4[/tex]

From the normal distribution table, P(x < 36000) = P(z < 1.4) = 0.9192 = 91.92%

b) One standard deviation of mean = μ ± σ = (32500 ± 2500) = (30000, 35000)

Two standard deviation of mean = μ ± 2σ = (32500 ± 2*2500) = (27500, 37500)

Empirical rule states that 68% of data falls within one standard deviation from the mean, 95% falls within two standard deviation from the mean and 99.7% falls within one standard deviation from the mean.

Hence 95% of salaries is between $27,500 and $37,500.

c) 95% of salaries is between $27,500 and $37,500.

P(x < 27500) = (100% - 95%) / 2 = 2.5%

d) If the z score is less than -3 or greater than 3, it is considered an outlier.

For x < 42000:

[tex]z=\frac{42000-32500}{2500}=3.8[/tex]

Hence $42000 is an outlier

Answer:

4/5

Step-by-step explanation:

y =4/5x-3

The equation is in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

The slope is 4/5

Answer:

4/5

Step-by-step explanation:

The slope will be in front of the x in slope intercept form.

Answer:

The letters M, N, A , E appear twice and G, T appear once.

So, the first case was where all the letters were different, thus, the number of words formed were:

6C5 . 5!(further permutation) = 720

the second case was where there were two groups of two alike letters and one different letter. Thus, the number of words formed were:

2C1 . 4C2 . 3! = 72

the third case was where there were one group of two alike letters and three different letters.

Thus, the number of words formed were:

4C1 . 5C3 . 4!= 960

thus, the total number of words were:

720 + 72 + 960 = 1752

but this answer is wrong as the Real answer is 1824.

Step-by-step explanation:

Answer:

Result:

{0, 3/7}

Decimal approximation:

{0, 0.428571}

Step-by-step explanation:

Find the norm...

and you know I wanna speedrun

Answer:

598.16

Step-by-step explanation:

Eh you should have the formula if not I can't really type it but ,trust, the answer is 598.16 in²

Answer:

261.3 in.

Step-by-step explanation:

Answer:

ASA

Step-by-step explanation:

Both triangles contains two angles which indicate that it can only be the top 2 options.

The daughter will take 6 hours to complete the housework if working alone.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

A woman when working with her takes 2 hours to complete the housework and takes 3 hours when working alone.

Let's suppose y minutes taken by the daughter to complete the housework:

Rate for daughter = 1/x

1/3 + 1/x = 1/2

2x + 6 = 3x

x = 6 hours

Thus, the daughter will take 6 hours to complete the housework if working alone.

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I think the 4th one but Im not too sure please forgive me if I'm wrong.

(a) ft/s

(b) 1ft/s

Given equation;

y = (- 16x² + 50x + 3)ft       -------------(i)

Where;

y is measured in feet(ft)

x is measured in seconds(s).

(a) The rate of change of y with respect to x is found by dividing the total change in y by the total change in x. i.e

Δy / Δx

Where;

Δy = y₂ - y₁  

Δx = x₂ - x₁

∴ Δy / Δx = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]              --------------(ii)

Since y is measured in feet, Δy will also be measured in feet.

Also, since x is measured in seconds, Δx will also be measured in seconds.

Therefore, the rate of change of y with respect to x (Δy / Δx) will be measured in feet per second (ft/s)

(b) The rate of change of y between x  = 0 and x = 2 can be found by using equation (ii)

Where;

y₂ is the value of y at x = 2 found by substituting x = 2 into equation (i)

y₁ is the value of y at x = 0 found by substituting x = 0 into equation (i)

=> y₂ =  - 16(2)² + 50(2) + 3 = 39

=> y₁ =  - 16(1)² + 50(1) + 3 = 37

Now, substitute the values of y₂, y₁, x₂ and x₁  into equation (ii)

Δy / Δx = [tex]\frac{39 - 37}{2 - 0}[/tex]  

Δy / Δx = [tex]\frac{2}{2}[/tex]

Δy / Δx = 1

Therefore, the rate of change of y is 1 ft/s

Answer:

Step-by-step explanation:

no of sides (n)=11

sum=(n-2)180

=(11-2)180

=9*180

=1620

therefore sum of the interior angles of a polygon having 11 sides id 1620°.

Answer:

n= 1620

Step-by-step explanation:

I know the answer is correct I got the exact same question during the lessons.

Answer:

H0 : μd = 0

H1 : μd > 0

Step-by-step explanation:

The scenario described above can be compared statistically using a paired test mean as the mean if the two groups are dependent, the two restaurants, Albuquerque and Santa Fe are both restaurant locations of a single restaurant company. Hence, to test the mean difference, we use the paired test statistic. Defined thus `

Null hypothesis ; H0 : μd = 0 and the Alternative hypothesis ; H1 : μd > 0

Answer:

Two Sample T test with Ha = Albernuque>Santa Fe

Step-by-step explanation:

Khan

Answer:

Kelvin’s error is that when he got the final result, that was the amount that was marked down. He still needed to find the price after the original price was marked down by that number wich in this case is $18.39. So using one of his steps, 30.65(0.6)=18.39. We can subtract 30.65 (original price) and 18.39 (mark down price). You’d get 11.26 dollars as the final price.

Answer:

A = $3,101.09

A = P + I where

P (principal) = $2,600.00

I (interest) = $501.09

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 3.53/100

r = 0.0353 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 2,600.00(1 + 0.0353/12)(12)(5)

A = 2,600.00(1 + 0.002941667)(60)

A = $3,101.09

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $2,600.00 at a rate of 3.53% per year compounded 12 times per year over 5 years is $3,101.09.

Answer:

{x|x rx>-2}

Step-by-step explanation:

hope helpful answer

Answer:

13, I believe :)

Step-by-step explanation:

3(4)-5(5)

multiply by the coefficient

=12-25

=-13

Two formulas:

Compound interest - A = P(1 + r/n)^nt

Simple interest = A = P(1 + rt)

A - final amount

P - initial principal balance

r - interest rate

n - number of times interest applied per time period

t - number of time periods elapsed

Suri --

A = 4,000(1+0.03/1)^5

A = $4,637.09

Carter --

A = 4,000(1+0.03*5)

A = $4,600

In 5 years, Suri makes $37.09 more than Carter

Answer:

[tex]3 * f(-8) - 3 * g(-2) = 6[/tex]

Step-by-step explanation:

Given

This question has a missing graph (See online)

Required

[tex]3 * f(-8) - 3 * g(-2)[/tex]

From the graph:

[tex]f(-8) = -2[/tex]

and

[tex]g(-2) = -4[/tex]

So, we have:

[tex]3 * f(-8) - 3 * g(-2) = 3 * -2 -3 * -4[/tex]

[tex]3 * f(-8) - 3 * g(-2) = 6[/tex]

Answer: Mean(Mia)=34.33 Mean(Sophia)=35.667

Sophia's phone calls on average, are longer in length than Mia's phone calls.

Step-by-step explanation:

Answer:

B on edge

Step-by-step explanation:

Answer:

Tn = -13n +37

ordered list is 24, 11 , -2 , -15, -28 ,-41

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

Explanation:

The diagram is shown below. We know the vertical part of the triangle is 13 inches, which is the side opposite the reference angle 13 degrees. The adjacent side is unknown. We'll call it x. This is how long the base of the ramp is, which is the horizontal distance along the entire ramp. This distance is on the ground. The ramp itself is the hypotenuse but it seems like your teacher isn't wanting to know this value. So we'll ignore the hypotenuse.

We'll use the tangent rule to connect the opposite and adjacent sides.

tan(angle) = opposite/adjacent

tan(13) = 13/x

x*tan(13) = 13

x = 13/tan(13)

x = 56.309186365694

x = 56 inches is the approximate horizontal distance underneath the ramp

The base of the ramp is 57 inches long.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The tangent function relates the opposite side (height) and adjacent side (base) of a right triangle to the angle of elevation.

We know the opposite side is the height of the ramp, which is 13 inches, and the angle of elevation is 13 degrees.

Let the adjacent side (the base of the ramp) be "x".

The tangent of 13 degrees is equal to the opposite side divided by the adjacent side:

tan(13) = 13/x

To solve for x, we can multiply both sides by x:

x × tan(13) = 13

Then, we can divide both sides by tan(13):

x = 13 / tan(13)

x = 13 / 0.228

x= 56.99

Therefore, the base of the ramp is 57 inches long.

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Answer:

23 nickels and 16 dimes

Step-by-step explanation:

16 dimes = 1.60

23 nickels = 1.15

1.60 + 1.15 = 2.75

This question is incomplete, the complete question is;

Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x4 = t and x2 = s and solve for x1 and x3 in terms of t and s.)

[1 0 0 1]

[0 0 1 0]

[0 0 0 0]

(x1, x2, x3, x4) =________

Answer:

the solution for the given system is; ( x₁, x₂, x₃, x₄ ) = ( -t, s, 0, t )

Step-by-step explanation:

Given the data in the question;

coefficient matrix

[tex]\left[\begin{array}{cccc} 1&0&0&1 \\ 0&0&1&0 \\ 0&0&0&0 \end{array}\right][/tex]

Now, from linear system;

[tex]\left[\begin{array}{cccc} 1&0&0&1 \\ 0&0&1&0 \\ 0&0&0&0 \end{array}\right] \left[\begin{array}{ccc}x_1\\x_2\\x_3\\x_4\end{array}\right] = \left[\begin{array}{ccc}0\\0\\0\\0\end{array}\right][/tex]

So, with the matrix, the associated equation is;

x₁ + x₄ = 0, x₃ = 0

Number of variables is 4 and ranked of the matrix is 2,

Hence, there are infinite solutions,

There are also two free variables;

from the question,

Let x₄ = t and x₂ = s be the free variables

so

x₁ + x₄ = 0

x₁ + t = 0

x₁ = -t

Therefore, the solution for the given system is;

( x₁, x₂, x₃, x₄ ) = ( -t, s, 0, t )

Answer:

its c

Step-by-step explanation: