How to find exponential function?

The surface area of the given two rectangular prism is given as follows:

498 cm².

The surface area of a rectangular prism of length l, width w and height h is given as follows:

S = 2(lw + wh + hl).

For this problem, there are two prisms, with dimensions given as follows:

Hence the surface area of the figure is the combined surface area of each figure, hence:

S = 2(7 x 7 + 12 x 7 + 12 x 7) + 2(2 x 7 + 2 x 2 + 7 x 2) = 498 cm².

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Answer:

  f(x) = x³ -12x² +46x +148

Step-by-step explanation:

When p is a root of polynomial function f(x), (x -p) is a factor. When the coefficients are real, any complex roots come in conjugate pairs.

Given the two roots of f(x), we know the third root is the conjugate of the given complex root. The factored form will be ...

  f(x) = (x -(-2))(x -(7 +5i))(x -(7 -5i))

Rearranging a bit, this is ...

  f(x) = (x +2)((x -7) -5i)((x -7) +5i)

The latter two factors are recognizable as the factors of the difference of squares, so this is ...

  f(x) = (x +2)((x -7)² -(5i)²) = (x +2)((x -7)² +25)

Multiplying the factors, we have ...

  f(x) = (x +2)(x² -14x +49 +25) = (x +2)(x² -14x +74)

  f(x) = x³ -14x² +74x +2x² -28x +148 . . . . . use the distributive property

  f(x) = x³ -12x² +46x +148 . . . . . . . . . . collect terms

Answer:

B

Step-by-step explanation:

Cos is the adjacent side over the hypotenuse.  The adjacent side to <E is side ED.  The hypotenuse is side EF.  ED/EF.  They do not go right out and give you this choice, but you see that B says the same thing.

The ODE is separable.

[tex]\dfrac{dy}{dx} = xy \iff \dfrac{dy}y = x\,dx[/tex]

Integrate both sides to get

[tex]\displaystyle \int\frac{dy}y = \int x\,dx[/tex]

[tex]\boxed{\ln|y| = \dfrac12 x^2 + C}[/tex]

But notice that replacing the constant [tex]C[/tex] with [tex]-C[/tex] doesn't affect the solution, since its derivative would recover the same ODE as before.

[tex]\ln|y| = \dfrac12 x^2 - C \implies \dfrac1y \dfrac{dy}{dx} = x \implies \dfrac{dy}{dx} = xy[/tex]

so either of the first two answers are technically correct.

Answer:370 play football and 20 play hockey

Step-by-step explanation: because 400 - 130 equals 370 for football

then hockey 150-130 equals 20

Then the total students are 420

150+400-130 equals 420

Based on the requirements for FICA and Medicare tax, the amount to be withheld in March for FiCA is $685.10 and for Medicare is $160.23.

The amount to be withheld in December of FICA is $523.90 and for Medicare is $160.23.

In March, the amount to be withheld is:

= 11,050 x 6.2%

= $685.10

To find out the amount withheld in December, find out the earnings up to that point:

= 11,050 x 12

= $132,600

FICA can only be withheld on the first $130,000 so the amount of FICA In December is:

= 6.2% x ( 11,050 - (132,600 - 130,000))

= $523.90

The amount will be the same for both March and December as Medicare is for all earnings:

= 11,050 x 1.45%

= $160.23

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The probability that exactly 7 are men out of 10 sports car owners who are randomly selected is 0.215 given that 60% of people who purchase sports cars are men. This can be obtained by using binomial distribution formula.

This question can be solved using binomial distribution formula.

The formula for binomial distribution is the following,

P(X) = ⁿCₓ pˣ qⁿ⁻ˣ

where,

n = number of trials(or the number being sampled)

x = number of success desired

p = probability of getting a success in one trial

q = 1 - p = probability of getting a failure in one trial

Here in the question it is given that,

⇒ 60% of people who purchase sports cars are men

This statements clearly means that probability of men purchase sports cars is 60%.

⇒ P(men purchasers) = p = 60% = 0.6

From this we can find the probability of women who purchase sports cars,

⇒ P(women purchasers) = q = 1 - p = 1 - 0.6 = 0.4

So we can find the probability that exactly 7 are men out of 10 sports car owners who are randomly selected

It is a binomial case with n = 10

By using the  formula for binomial distribution we get,

P(X = 7) = ¹⁰C₇ × 0.6⁷ × 0.4³

P(X = 7) = 120 × 0.0279936 × 0.064

P(X = 7) = 0.21499

P(X = 7) = 0.215

Hence the probability that exactly 7 are men out of 10 sports car owners who are randomly selected is 0.215 given that 60% of people who purchase sports cars are men.

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Answer:

answer

Step-by-step explanation:

To see whether or not two lines are parallel, we must compare their slopes. Two lines are parallel if and only if their slopes are equal. The line 2x – 3y = 4 is in standard form. In general, a line in the form Ax + By = C has a slope of –A/B; therefore, the slope of line q must be –2/–3 = 2/3.

Using the permutation formula, there are 157,410 ways for the medals to be distributed.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 3 athletes are chosen from a set of 55, hence the number of ways is given by:

P(55,3) = 55!/52! = 157,410

157,410 ways for the medals to be distributed.

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The distance that he has traveled exists 73km 500m.

Distance exists described as the amount of space between two items or the condition of existing far apart. The distance of an object can be described as the complete path traveled by an object.

Given: A motorist travels from town A to town B, which exists 84km apart. He has finished 7/8 of his journey.

To estimate the distance that he has traveled

He covered 7/8 out of 84 km

So, 7/8 × 84 = 73.5 km

The distance he has traveled = 73 km 500 m

Therefore, the distance that he has traveled exists 73km 500m.

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1. By de Moivre's theorem,

[tex]\left(4\left(\cos\left(\dfrac{7\pi}9\right) + i \sin\left(\dfrac{7\pi}9\right)\right)\right)^3 = 4^3 \left(\cos\left(\dfrac{21\pi}9\right) + i \sin\left(\dfrac{21\pi}9\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac{7\pi}3\right) + i \sin\left(\dfrac{7\pi}3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac\pi3\right) + i \sin\left(\dfrac\pi3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\dfrac12 + i\dfrac{\sqrt3}2\right) \\\\ ~~~~~~~~ = \boxed{32 + 32\sqrt3\,i}[/tex]

2. First write the given number in exponential/trigonometric form.

[tex]z = 5-5\sqrt3\,i[/tex]

has modulus

[tex]|z| = \sqrt{5^2 + \left(-5\sqrt3\right)^2} = \sqrt{100} = 10[/tex]

and since it lies in the second quadrant of the complex plane, its argument is

[tex]\arg(z) = \pi + \tan^{-1}\left(-\dfrac{5\sqrt3}5\right) = \pi + \tan^{-1}\left(-\sqrt3\right) = \pi - \dfrac\pi3 = \dfrac{2\pi}3[/tex]

So, we have

[tex]z = 5 - 5\sqrt3\,i = 10 e^{i2\pi/3} = 10 \left(\cos\left(\dfrac{2\pi}3\right) + i \sin\left(\dfrac{2\pi}3\right)\right)[/tex]

Now we apply de Moivre's theorem again, and make sure to account for the multivalued-ness of the exponential function. For [tex]k\in\{0,1,2,3,4\}[/tex], the fifth roots of [tex]z[/tex] are

[tex]z^{1/5} = 10^{1/5} e^{i(2\pi/3 + 2\pi k)/5}[/tex]

[tex]k=0 \implies z^{1/5} = 10^{1/5} e^{i2\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{2\pi}{15}\right) + i \sin\left(\dfrac{2\pi}{15}\right)\right)}[/tex]

[tex]k=1 \implies z^{1/5} = 10^{1/5} e^{i8\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{8\pi}{15}\right) + i \sin\left(\dfrac{8\pi}{15}\right)\right)}[/tex]

[tex]k=2 \implies z^{1/5} = 10^{1/5} e^{i14\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{14\pi}{15}\right) + i \sin\left(\dfrac{14\pi}{15}\right)\right)}[/tex]

[tex]k=3 \implies z^{1/5} = 10^{1/5} e^{i20\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{4\pi}3\right) + i \sin\left(\dfrac{4\pi}3\right)\right)}[/tex] [tex]k=4 \implies z^{1/5} = 10^{1/5} e^{i26\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{26\pi}{15}\right) + i \sin\left(\dfrac{26\pi}{15}\right)\right)}[/tex]

Answer:

simplification of the original equation is below/

Step-by-step explanation:

9+4t=-3(1-2t) can be simplified into

9+4t=-3+6t because of distributing the -3 to both the 1 and -2t.

however, this can simplified to

4t-6t=-3-9

and this can simplify to

-2t=-12

which can simplify to

t = 6

give brainliest please!

hope this helps :)

The answer is 4) 140.

If we closely examine the pattern of the series, we see that after a number is subtracted by a value, it is multiplied by the same value, and then it moves on to the next natural number.

The next step, according to the pattern, would be to multiply 4.

The probability that the project will be completed before the graduation time is 0.6873.

It should be noted that probability simply means the likelihood of the occurence of an event.

From the table attached, it can be seen that the probability that the project will be completed before the graduation time is 0.6873.

Also, the probability that the project will be completed before the end of week 15 will be 0.3983.

Lastly, the probability that the project will be completed before the end of week 13 will be 0.0203.

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The surface area of the figure illustrated will be 286 yards²

The surface area of a solid object simply implies the measure of the total area which the surface of an object occupies. This is typically done by adding all the areas on the surface of the object.

It should be noted that the surface area of a cuboid will be:

= 2(lw + lh + wh)

w = width = 7

l = length = 9

h = height = 5

Surface area = 2(lw + lh + wh)

= 2(7 × 9) + 2(9 × 5) + 2(7 × 5)

= 126 + 90 + 70

= 286 yards²

Therefore, the surface area of the solid will be 286 yards².

Complete question:

Find the surface area of the solid given that the length is 9 yards, the width is 7 yards, and the height is 5 yards.

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Comparing g(x) with f(x), you can see that the function f(x) is translated to the right by 6 units to produce g(x) which is equivalent to (x-6)²

Transformation is a techniques use to change the position of an object on an xy-plane.

Given the parent function f(x) = x² and the function g(x) = x²-12x +36

Factorize g(x);

g(x) = x²-6x-6x+36

g(x)=x(x-6)-6(x-6)

Group the terms to have;

g(x) = (x-6)²

Comparing g(x) with f(x), you can see that the function f(x) is translated to the right by 6 units to produce g(x) which is equivalent to (x-6)²

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Use the quotient and chain rules. If

[tex]y = \dfrac{\cos(2x)}{\tan(2x)}[/tex]

then the derivative is

[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) \frac d{dx}\cos(2x) - \cos(2x) \frac d{dx}\tan(2x)}{\tan^2(2x)}[/tex]

[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) (-\sin(2x)) \frac d{dx}(2x) - \cos(2x)\sec^2(2x) \frac d{dx}(2x)}{\tan^2(2x)}[/tex]

[tex]\dfrac{dy}{dx} = \dfrac{-2\sin(2x)\tan(2x) - 2 \sec(2x) }{\tan^2(2x)}[/tex]

and we can rewrite this by

• multiplying by [tex]\frac{\cos^2(2x)}{\cos^2(2x)}[/tex],

[tex]\dfrac{dy}{dx} = \dfrac{-2\sin^2(2x)\cos(2x) - 2 \cos(2x) }{\sin^2(2x)}[/tex]

• factorizing,

[tex]\dfrac{dy}{dx} = -\dfrac{2\cos(2x) \left(\sin^2(2x) + 1\right)}{\sin^2(2x)}[/tex]

etc

Landon's finance charge is $613.2

Landon's monthly payment is; $80.22

It is convenient to compute the monthly payment first, then figure the total amount repaid and the finance charge.

The amortization formula is:

 A = Pr/(1 - (1 + r)⁻ⁿ)

where;

A is the monthly payment

P is the loan amount

r is the monthly interest rate

n is the number of months

b) Using the above formula, we can get the monthly payment as;

A = $4200(0.055/12)/(1 - (1 +0.055/12)⁻⁶⁰) = $19.708333/0.23995049

A = $80.22

The monthly payment amount is $80.22

a) 60 monthly payments add up to;

$80.22 × 60 = $4813.2

Since $4200 of that amount is principal, the finance charge is;

$4813.2 - $4200.00 = $613.2

Landon's finance charge is $613.2

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The height of the ladder on the building is 19.77 feet

Represent the height of the ladder on the building with h

So, the given parameters are:

Angle, x = 64 degrees

Length of ladder, l = 22 feet

The height of the ladder on the building is calculated using

sin(x) = h/l

Substitute the known values in the above equation

sin(64) = h/22

Multiply both sides by 22

h = 22 * sin(64)

Evaluate the product

h = 19.77

Hence, the height of the ladder on the building is 19.77 feet

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Answer:

Step-by-step explanation:

Answer:

The shortest piece is the first piece and it is 14 cm long.

Step-by-step explanation:

We have three unknowns so we need 3 equations.

Let x = the length of the first piece

Let y = the length of the second piece

Let z = the length of the third piece.

x + y + z = 74            y = 2x          z = y + 4

There are a number of ways to solve this.  I am going to plug in 2x for y into the first and the third equation to get:

x + y + z = 74

x + 2x + z = 74 Combine the x terms

3x + z = 74

Next, I am going to substitute 2x in for y in the third equation above.

z = y + 4

z = 2x + 4  I am going to put both variable on the left side of the equation

z - 2x = 4

I can know take the two bold equations that I have above and solve for the either x or z.  I am going to solve for z.  I need one of the equation to have a z and the other equation to have -z so that they will cancel one another out.  I am going to multiple z - 2x = 4 all the way through by -1 to get:

z - 2x = 4

-1(z - 2x) = 4(-1)

-z +2x = -4  

I am going to rearrange 3x + z = 74 so that the z term is first and add it to -z + 2x = -4

z + 3x = 74

-z + 2x = -4

      5x = 70 divide both sides by 5

x = 14  This is the length of the first piece.

y = 2x

y = 2(14) = 28

y = 28 This is the length of the second piece.

z = y+4

z = 28 + 4 = 32

or

x + y + z = 74

14 + 28 + z = 74

42 + z = 74  Subtract 42 from both sides.

z = 32

Answer:

x₁ = -4

x₂ = 3

Step-by-step explanation:

x²+ x + 12 = 0

x = {-1±√((1²)-(4*1*-12))} / (2*1)

x = {-1±√(1+48)} / 2

x = {-1±√49} / 2

x = {-1±7} / 2

x₁ = {-1-7} / 2 = -8/2 = -4

x₂ = {-1+7} / 2 = 6/2 = 3

Check:

x₁

-4² + (-4) - 12 = 0

16 - 4 - 12 = 0

x₂

3² + 3 - 12 = 0

9 + 3 - 12 = 0

The exponential function that represent the concentration of algae cells per milliliter in d days is [tex]C(d) = 10(2)^d[/tex]

An equation is an expression that shows the relationship between two numbers and variables.

The standard form of an exponential funtion is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

Let C(d) represent the concentration of algae cells per milliliter in d days

At point (1, 20)

20 = ab   (1)

At point (2, 40)

40 = ab²     (2)

From equations 1 and 2:

b = 2, a = 10

The exponential function that represent the concentration of algae cells per milliliter in d days is [tex]C(d) = 10(2)^d[/tex]

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The number of calories per ounce of soda is 10

The given parameters are:

Calories = 50

Ounces = 5

Let the number of calories be y and the ounces be x.

So, we have:

y = kx

Substitute y = 50 and x = 5

50 = 5k

Divide by 5

k = 10

Substitute k = 10 in y = kx

y = 10x

See attachment for the graph of the relationship between the number of calories and the number of ounces

In (a), we have:

k = 10

This means that the number of calories per ounce of soda is 10

The unit rate and the slope represent the same and they have the same value

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Answer:

First angle: 52°

Second angle: 26°

Third angle: 102°

Step-by-step explanation:

Let the measure of the second angle = x.

Measure of the first angle: 2x

Measure of third angle: x + 76

2x + x + x + 76 = 180

4x + 76 = 180

4x = 104

x = 26    second angle

2x = 2 × 26 = 52      first angle

x + 76 = 26 + 76 = 102     third angle

Answer:

57

Step-by-step explanation:

-7a + 4b

Let a = -3  b = 9

Substitute the values in

-7(-3) + 4(9)

Multiply

21 + 36

Add

57

The plot of [tex]\sqrt{25-x^2}[/tex] is that of the top half of a circle with radius 5. The interval [-5, 0] captures the left half of this semicircle.

Adding 5 to this shifts the plot up by 5 units. The area under this curve is then the combined area of a square with side length 5 and the area of a quarter circle with radius 5.

So we have

[tex]\displaystyle \int_{-5}^0 5 + \sqrt{25-x^2} \, dx = 5^2 + \frac\pi4\cdot5^2 = \boxed{25 + \frac{25\pi}4}[/tex]