Suppose there are 9 freshman, 13 sophomores, 13 juniors, and 16 seniors running for the offices of president, vice president, and secretary. If no person can hold more than one office, in how many different ways could these people be elected to these positions?

The graph of the  parent function Y = 2²⁻ ˣ +1 is presented below.

The parent function of a function is the simplest form of the function, which satisfies all the conditions of the given function.

The given function is,

Y= 4×2⁻ˣ+1

To find the parent function, simplify the given function,

Y = 2²ˣ2⁻ˣ+1

Y = 2²⁻ ˣ +1

Function Y = 2²⁻ ˣ +1  is the parent form of the given function Y= 4×2⁻ˣ+1.

The graph of the  Y = 2²⁻ ˣ +1 is presented below.

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The monthly deposit required to save up to $625,357.24 (future value) in 40 years at a 7.2% APR is $225.20.

The monthly deposits are the periodic savings that the investor must make to achieve future value.

The monthly deposit is compounded at the monthly annual percentage rate (APR).

We can compute the required monthly deposits using an online finance calculator as follows:

N (# of periods) = 480 months (40 years x 12)

I/Y (Interest per year) = 7.2%

PV (Present Value) = $0

FV (Future Value) = $625,357.24

Results:

Monthly Deposits (PMT) = $225.20

Sum of all periodic payments = $108,096 ($225.20 x 480)

Total Interest = $517,261.24

Thus, to save $625,357.24 in 40 years, you need to deposit $225.20 monthly.

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The transformation of the graphs is

1st graph is (x,y)→(x-4,y+2)

2nd graph is (x,y)→(x+6,y+0)

Given that,

There are two graphs with 2 triangles in each graph.

We have to find the transformation of the graphs.

Take the 1st graph,

We have 2 triangles ABC and A'B'C'.

The points are,

A=(0,0), B=(3,-4) and C=(-1,-2)

A'=(-4,2), B'=(1,-2) and C'=(-5,0)

We get the transformation as

(x,y)→(x-4,y+2)

Check the A and A' points

The A terms goes left for 4 times to A' so we take x-4 and the A terms goes up for 2 times to A' so we take y+2.

Similarly,

The B terms goes left for 4 times to B' so we take x-4 and the B terms goes up for 2 times to B' so we take y+2.

Similarly,

The C terms goes left for 4 times to C' so we take x-4 and the C terms goes up for 2 times to C' so we take y+2.

Now the 2nd graph,

We have triangle FCP and F'C'P'

The points are,

F=(-5,5), C=(-2,5) and P=(-3,0)

F'=(1,5), C'=(4,5) and P'=(3,0)

We get the transformation as

(x,y)→(x+6,y+0)

Check the F and F' points

The F terms goes right for 6 times to F' so we take x+6 and the F terms remain same so we take y+0

Similarly,

The C terms goes right for 6 times to C' so we take x+6 and the C terms remain same so we take y+0

Similarly,

The P terms goes right for 6 times to P' so we take x+6 and the P terms remain same so we take y+0

Therefore, The transformation of the graphs is

1st graph is (x,y)→(x-4,y+2)

2nd graph is (x,y)→(x+6,y+0)

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Answer:1 is (x,y)>(x-4,y+2)

2nd is (x,y)>(x+6,y+0)

Step-by-step explanation:

(> = an arrow)

I talked to my professional tutor about this, she didn’t happen to explain the answer though. She’s been working as a teacher for 20 years.

Answer:

0.00075757575.

Step-by-step explanation:

I looked it up.

me too. did you know that animals that lay eggs don't have belly buttons?

Answer: x=2πn (n=0, 1, 2, 3,...)

Step-by-step explanation:

2sin²x-cosx+1=0

2(1-cos²x)-cosx+1=0

2(1)-2(cos²x)-cosx+1=0

2-2cos²x-cosx+1=0

-2cos²x-cosx+3=0

Multiply both parts of the equation by -1:

2cos²x+cosx-3=0

Let cosx=t

Domain:

-1≤cosx≤1

Hence, -1≤t≤1

2t²+t-3=0

D=b²-4ac

a=2    b=1    c=-3

D=1²-4(2)(-3)

D=1+24

D=25

√D=√25

√D=5

[tex]\displaystyle\\t=\frac{-bб\sqrt{D} }{2a} \\\\t=\frac{-1б5}{2(2)}\\\\t=\frac{-1б5}{4}\\\\t=-1.5\notin domain\\\\t=1\in domain\\\\cosx=1\\\\x=2\pi n\ where\ n=0, \ 1,\ 2,\ 3,\ ...[/tex]

The slope of equation is 3x + y = 3 is -3

The standard from of Slope - intercept form of equation is y = mx +b

where , m is slope of line

b is y-intercept

and x and y are the variables

Slope of line represents steepness of a line and also termed as gradient .

Y- intercept represents the y- coordinate of the point where the line intersect the y-axis.

In the given question ,

The equation of the line is given as : 3x + 1y = 3

bring 3x to right side,

y = -3x + 3

comparing the equation to standard from

slope of line : m = -3

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Answer:

Step-by-step explanation:

In the following equation: 4x -3=8, x represents a variable

4x - 3  = 8

4x = 11

x = 11/4

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

check

4 x 11/4 - 3 = 8

11 - 3 = 8

8 = 8

the answer is good

Answer: 3: 4^21/5^6

Step-by-step explanation:

Remember when you are raising you need to multiple the powers.

Answer:

Y= 20x + 35

Step-by-step explanation: I have the same test.

The scale Alexander is using for his map is 1 inch : 300 feet

The height of Alexander's triangle in inches is 4 inches

The scale of the map is gotten by comparing the first dimensions Alexander drew

He made 10 inches to represent 3000 feet, this is equivalent to 1 inch to 300 feet hence the scale is 1 inch : 300 feet

Using the scale, a height of 1200 feet would be

1 inch = 300 feet

? inch = 1200 feet

cross multiplying

? * 300 = 1200 * 1

? = 1200 / 300

? = 4 inches

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The answer of 11/3*7/3*5/3 after multiplication is 385/27.

According to the question,

We have the following expression:

11/3*7/3*5/3

We know that when we multiply two more than two fractions then numerator is multiplied into the numerator and the denominator is multiplied into the denominator of another fraction.

So, we have the following expression after multiplying first two fractions:

77/9*5/3

Now, again repeating the above step:

385/27

(This can not be further classified into the simplest form because the numerator and denominator of this fraction can not be divided by one number.)

Hence, the answer of 11/3*7/3*5/3 after multiplication is 385/27.

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The value of t from the given derivative is 7.38.... or −7.38....

The given second order derivative is r''(t)=2/t².

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

Here, r''(t)=2/t²

The anti-derivative is

Set the function up in integral form and evaluate to find the integral.

r'(t) = -2/t

Now, 3=-2/t

⇒ t=-2/3

Set the function up in integral form and evaluate to find the integral.

r(t)=-2ln(|t|)

So, -4=-2ln(|t|)

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form :t=e²,−e²

Decimal Form:

t=7.38905609…,−7.38905609…

Therefore, the value of t from the given derivative is 7.38.... or −7.38....

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Answer:

Take a look at the attachment...

Hope this helps! :)

The cost of each binder is $3.

Given,

In the question:

Angel spends $29 to order binders online.

They buy 8 binders and pay a flat fee of $5 for shipping.

To find the what is x, the cost of each binder?

Now, According to the question;

Based on the given conditions:

Formulate:

Angel spends = $29 to order binders online.

Buy the = 8 binders

Paying = $5 for shipping .

5 + 8 × x = 29

Solve the equation:

5 + 8x = 29

Rearrange the terms;

8x = 29 - 5

8x = 24

x = 24/8

x = 3

Hence, The cost of each binder is $3.

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1133.98 grams of rice is required for the preparation of the recipe which calls for 40 ounces of rice.

Given that:

A recipe requires 40 ounces of rice for its preparation.

We know that,

1 ounce = 28.3495 grams

We also know that,

1 gram = .035274 ounces.

To find the value of 40 ounces multiplies both sides by 40.

40 ounce = 28.3495 grams x 40

40 ounce = 1133.98 grams

Hence, for the preparation of the recipe which calls for 40 ounces of rice, 1133.98 grams of rice is required.

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The sum of interior angles of a tray that is of pentagon shape is 540°

Given,

There is a tray which is of pentagon shape.

We have to find the sum of interior angles of the tray.

We have to find the sum of interior angles of pentagon.

That is,

Sum of interior angle of polygon formula = (n - 2) × 180°

Where, n is the number of sides in a polygon.

Here,

Pentagon has 5 sides.

Then,

Sum of interior angles = (5 - 2) × 180° = 3 × 180° = 540°

That is,

The sum of interior angles of a tray that is of pentagon shape is 540°

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The question is incomplete. Completed question is given below;

Suppose is Jeanine is building a tray for a floral table centerpiece in the shape of a pentagon. The sum of the interior angles of the tray will be

Answer: $194.25

Step-by-step explanation:

Given data

Principal=  $7400

Rate=  10.5%

time= 1/4 years

The simple interest formula is given as

SI= PRT/100

substitute

SI= 7400*10.5* 0.25/100

SI= 19425/100

SI= $194.25

Hence Mark will pay  $194.25

Answer:

x = 3

Step-by-step explanation:

15x + 8 and 9x + 26 are corresponding angles and are congruent , then

15x + 8 = 9x + 26 ( subtract 9x from both sides )

6x + 8 = 26 ( subtract 8 from both sides )

6x = 18 ( divide both sides by 6 )

x = 3

(a) The information remembered by the person in starting is 100%.

(b) The information remembered by the person after 1 week is 66.67%.

(c) The information remembered by the person after 12 weeks is 12.46%.

(d) The information remembered by the person after 52 weeks is 10%

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given function is,

f(x) = [tex]90e^{-0.3x}+10[/tex]              (1)

(a)

Substitute x=0 in the equation (1)

f(0) = 90 e⁰ +10

Since, e⁰ = 1

f(0) = 90 +10

f(0) = 100

The information remembered by the person is 100.

(b)

Substitute x=1 in the equation (1)

f(1) = 90 [tex]e^{-0.3}[/tex]  +10

f(1) = 66.67 + 10

f(1) = 76.67

The information remembered by the person is 66.67%.

(c)

Substitute x=12 in the equation (1)

f(12) = 90[tex]e^{-3.6}[/tex] +10

f(12) = 2.46 + 10

f(12) = 12.46

The information remembered by the person is 12.46%.

(d)

Substitute x=52 in the equation (1)

f(52) = 90[tex]e^{-15.6}[/tex] +10

f(52) = 0.00015 + 10

f(52) = 10(approx)

The information remembered by the person is 10%.

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Answer: its D

Step-by-step explanation

Long Term Capital Gains Taxes tend to be lower than short term

Answer: D by providing a lower tax rate for long-term gains

The probability that exactly 3 automobiles fail the test is 0.01733.

The probability that fewer than 3 of the automobiles fail the test is

0.9803.

Complete question:

Car inspection of all the registered automobiles in Colorado, 5% fail the state emissions test. Twelve Automobiles are selected at random to undergo an emissions test. Round the answers to at least four decimal places

(a) Find the probability that exactly three of them fail the test.

(b) Find the probability that fewer than three of them fail the test.

What is Binomial Distribution?

The probability of success is said to follow a binomial distribution when many similar and independent Bernoulli trials are conducted. The likelihood of success and the quantity of tries are its dimensions. For every trial, the chance of success is the same.

State emission test failure probability is 0.05.

12 vehicles total are present.

Let's look at failing the test as a victory. If success is represented by p, then p = 0.05.

Considering that n represents the number of cars, n equals 12.

Let X represent how many vehicles fail the test.

So, X ∼ Bin (8,0.05)

P(X=x)= [tex]^{n}C_{x}p^{x}(1-p)^{n-x}[/tex]

         = [tex]^{12}C_{x}0.05^{x}(0.95)^{12-x}[/tex]

a) Probability that exactly 3 automobiles fail the test is given by,

  P(X=3)= [tex]^{12}C_{3}0.05^{3}(0.95)^{12-3}[/tex]

             =0.01733

So, the probability that exactly 3 automobiles fail the test is 0.01733.

b) Probability that fewer of them than 3 fail the test is given by,

P(X<3)= P(X≤2)

         = P(X=0)+P(X=1)+P(X=2)

         =  [tex]^{12}C_{0}(0.05)^{0}(0.95)^{12}[/tex] + [tex]^{12}C_{1}(0.05)^{1}(0.95)^{11}[/tex]+[tex]^{12}C_{2}(0.05)^{2}(0.95)^{10}[/tex]

         = 0.9803

Hence, the probability that fewer than 3 of the automobiles fail the test is

0.9803.

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Equation of line will be y = x/3 - 2

A line's equation can be written in many forms in which one is slope-intercept form.

Equation in slope-intercept form is written as y = mx + c where

m = slope

c = y intercept

Slope shows the steepness of the line. It can be given by change in y axis by change in x axis.

y intercept is the point where the line cuts the y axis that is x = 0 at this point.

Points given to us are (6 , 0) and (9 , 1)

slope = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

m = (1 - 0) / (9-6)

m = 1/3

For c put values of either point in the equation as they both are on the line so they both will satisfy the equation.

y = mx + c

0 = (1/3)*6 + c

0 = 2 + c

c = -2

now put values of m and c in the equation and get a general equation.

Therefore of equation of line will be y = x/3 - 2

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Answer:

y = (-1/2)x - 4

Step-by-step explanation:

y = 2x + 6

Perpendicular: y = (-1/2)x + 6

m = (-1/2); (2, -5)

                 (x₁, y₁)

y - y₁ = m(x - x₁)

y - (-5) = (-1/2)(x - 2)

y + 5 = (-1/2)x + 1

    -5               -5

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

y = (-1/2)x - 4

I hope this helps!

Step-by-step explanation:

the slope-intercept form is

y = ax + b

"a" being the slope, "b" being the y-intercept (the y- value when x = 0).

the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.

a perpendicular slope simply turns the original slope upside-down with x and y, and it flips the sign.

the slope of the origins line is 2 = 2/1.

the perpendicular slope is -1/2.

so, the equation looks like

y = -1/2 x + b

to get b we use the point coordinates :

-5 = -1/2 × 2 + b = -1 + b

-4 = b

so, the full equation is

y = -1/2 x - 4

Answer: honestly the only thing i know is that mean is another way of saying expected value

Step-by-step explanation:

Answer:

x = 27

Step-by-step explanation:

Cross-multiply. Wrap some parenthesis around the x+6 to keep it together. Use distributive property. See image.

Answer:

y=-2x

Step-by-step explanation:

2=-2(-1)

2=2

Sorry for late response

The values -3 , -6 , 3 , 8 are in the solution set of the compound inequality 4(x + 3) ≤ 0 and x + 1 > 3

Given, a compound inequality

4(x + 3) ≤ 0 and x + 1 > 3

Now, on solving the first inequality, we get

4(x + 3) ≤ 0

4x + 12 ≤ 0

On subtracting both the sides by 12, we get

4x + 12 - 12 ≤ 0 - 12

4x  ≤ -12

On dividing both the sides by 4, we get

4x/4  ≤ -12/4

x ≤ -3

So, the solution set of the 4(x + 3) ≤ 0 inequality be, x ≤ -3 i.e. all the real numbers less than -3.

Now, on solving the second inequality, we get

x + 1 > 3

On subtracting both the sides by 1, we get

x + 1 - 1 > 3 - 1

x > 2

So, the solution set of the x + 1 > 3 inequality be, x > 2 i.e. all the real number greater than 2.

Now, the values in the solution set of the compound inequality

4(x + 3) ≤ 0 and x + 1 > 3 be,

x ≤ -3 and  x > 2.

As, we can see -3 , -6 , 3 , 8 are satisfying the condition.

Hence, -3 , -6 , 3 , 8 are the values in the solution set of the compound inequality 4(x + 3) ≤ 0 and x + 1 > 3.

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