Type in only your numerical answer to the given problem if G(x)=x^2-5, then g(3)=?

There are 28 which is 256. That means there are 256 different values you can store in a byte, since a byte is eight bits. There are 256 eight-bit ASCII codes, for instance.

1 byte = 8 bits

Number of bits = [tex]2^{8}[/tex]

= 2*2*2*2*2*2*2*2

= 4*2*2*2*2*2*2

= 8*2*2*2*2*2

= 16*2*2*2*2

= 32*2*2*2

= 64*2*2

= 128*2

= 256 bits.

Therefore that means there are 256 different values you can store in a byte, since a byte is eight bits.

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The radius of the bigger sphere is 30cm.

Two spherical solids have masses of 15g and 405kg respectively

Mass is directly proportional to volume for same metal (Density)

Let Mass of Solid 1 be M₁ and Volume be V₁

Mass of Solid 2 be M₂ and Volume be V₂

Now  M₁/M₂ =  V₁/V₂

Volume of sphere is directly proportional to R³

So,  M₁/M₂ = V₁/V₂ = R₁³/R₂³​

15/405000 = 10³/x³

∛15/∛405000 = 10/x

2.466/73.986 = 10/x

2.466x = 73.986 x 10

x = 739.86/2.466

x = 30

Therefore, the radius of the bigger sphere is 30cm.

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Answer:

[tex]f^{-1}(x)=\dfrac{3-x}{5-x}, \quad \{x|x\neq 5\}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=\dfrac{5x-3}{x-1}[/tex]

As the given function is a rational function, the domain and range are restricted.

f⁻¹(x) is the notation for the inverse of the function.  

The inverse of a function is a reflection in the line y = x.

To find the inverse of the given function, swap f(x) for y:

[tex]\implies y=\dfrac{5x-3}{x-1}[/tex]

Rearrange the equation to isolate x:

[tex]\implies y(x-1)=5x-3[/tex]

[tex]\implies xy-y=5x-3[/tex]

[tex]\implies 3-y=5x-xy[/tex]

[tex]\implies 3-y=x(5-y)[/tex]

[tex]\implies x=\dfrac{3-y}{5-y}[/tex]

Swap the x for f⁻¹(x) and the y for x:

[tex]\implies f^{-1}(x)=\dfrac{3-x}{5-x}[/tex]

The range of the function is the domain of the inverse function.

Therefore, the domain of the inverse function is restricted:

Answer:

- 90

Step-by-step explanation:

substitute x = - 2 into f(x)

f(- 2) = 3[tex](-2)^{5}[/tex] - [tex](-2)^{4}[/tex] - 6(- 2) + 10

        = 3(- 32) - (16) + 12 + 10

        = - 96 - 16 + 22

        = - 112 + 22

        = - 90

[tex]{ \boxed{ \sf{f( - 2) = - 90}}}[/tex]

Step-by-step explanation:

[tex]{ \red{ \tt{f(x) = {3x}^{5} - {x}^{4} - 6x + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = 3( { - 2})^{5} - ( { - 2})^{4} - 6( - 2) + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = 3( - 32) - 16 + 12 + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = - 96 - 16 + 12 + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = - 112 + 22}}}[/tex]

[tex]{ \green{ \boxed{ \bold{f( - 2) = - 90}}}}[/tex]

The total cost of the hooded sweatshirts will be 29 × 31 = $899.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.

Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.

As per the given,

Number of hooded sweatshirts = 29

Cost of one hooded sweatshirt = $31

Total cost = 29 × 31 = $899.

Hence "The total cost of the hooded sweatshirts will be 29 × 31 = $899".

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Answer:

A, C, D, E

Step-by-step explanation:

17 is a positive whole number

All whole numbers are integers and rational

Natural numbers are numbers that are positive whole numbers

It is real since you don't have any negative roots

The structure's length is 93 feet long and its width is 62 feet.

acc to our question -

Let W stand for the rectangle's flower garden's width and L for its length.

A rectangle flower garden with a width that is precisely two thirds of its length is created by an architect.

The following can be written:

W=2/3L

Given that the fence is 310 feet long, the rectangle's perimeter must also be 310 feet.

Perimeter = 2 (L + W)

The perimeter surrounding it)

2w + 2h = 310

2((2/3) * h) + 2h = 310

4h/3 + 2h = 310

10h/3 = 310

10h = 930

h = 93 feet

w = (2/3) * 93

w = 62 feet

Hence, The structure's length is 93 feet long and its width is 62 feet.

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Answer:

$420

Step-by-step explanation:

multiple 10.50 by 40 to get 420

The required pounds of peanut that can make one pound of peanut butter is given as 5 1/3

If  2/3 pounds of peanut = 1/8 pounds of peanut butter

? quantity of peanut = one pound of peanut butter

This would be better expressed in numbers as

2/3 = 1/8

? = 1

To solve for this , we would have to cross multiply

such that we would have

2/3 = 1/8?

to get the unknown, we have to divide through by 1/8

2/3 ÷ 1/8 = unknown

2/3 x 8/1

= 16/3

= 5 1/3

Hence the required pound that would be needed to make the peanut butter is given as 5 1/3

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In  linear equation, No of marker is 5 and no of pencil is 3 .

What is a linear equation example?

Myles has 12 markers and 20 pencils.

take LCM of 12 and 20  = 60

no of 12 markers = 5

no of 20 pencils = 3

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Answer:

[tex]d=-6[/tex]

[tex]a_9=-49[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]-1[/tex] and the second term is [tex]-7[/tex], then each successive term in the sequence is [tex]6[/tex] less than the previous term. The common difference is [tex]-6[/tex] ( [tex]d=-6[/tex] ).

The formula representing the arithmetic sequence is:

[tex]a_n=-6n+5[/tex]

Therefore, the ninth term in the sequence is:

[tex]a_9=-6(9)+5[/tex]

[tex]a_9=-54+5[/tex]

[tex]a_9=-49[/tex]

The probability that a single lottery has one correct number, using the hypergeometric distribution, is of:

0.4159 = 41.59%.

The probability mass function of the hypergeometric distribution is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

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

The parameters of the function are listed as follows:

In the context of this problem, the values of these parameters are given as follows:

N = 40, k = 7, n = 7.

The probability that a single lottery has one correct number is P(X = 1), hence x = 1 and the calculation is as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 1) = h(1,40,7,7) = \frac{C_{7,1}C_{33,6}}{C_{40,7}} = 0.4159[/tex]

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(A) and (E) are the true statement.

Given,

In the question:

Jake and Liana make and sell wooden birdhouses. Jake spent $150 buying supplies. He sells each birdhouse for $15. The equation P = 12x - 120 represents the profit, P, Liana earns for selling x birdhouses. Jake and Llana each made 50 birdhouses.

To find the which statement is true?

Now, According to the question:

Jake's Profit: J = 15x - 150

Liana's Profit : P = 12x - 120

(A) when x = 0, P = -120, J = -150

then, 150 - 120 = $30

So, Jake spent $30 more than Liana

So, A is true, B is wrong.

(C) when x = 50 , J = 15 x 50 - 150 = $600

P = 12 x 50 - 120 =$480

Since, 600> 480

(D) when J = P

then, 15x - 150 = 12x = 120

3x = 30

x = 10

x = 10 not equal to 20

So, D is wrong

(E)  when P> -0 , and J > 0

then, 12x -120 > 0 and 15x - 150 > 0

=> x > 10

So, the minimum is 11, E is true .

Hence, Above the solution (A) and (E) are the true statement.

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Answer:

A square is an sqaure.

Step-by-step explanation:

circle is a circle. :) happy to help

Step-by-step explanation:

1:

1/5 of 90 = 18 hours which are sold.Means are 72 houses left.

2.

1/3 of 72 =24 houses sold again. Sooo means there are 48 houses left to be sold

The first person to get both integrity ticket and free water bottle is the person who comes 36th. This can be calculated by using L.C.M

What is L.C.M?

The value that's equally divided by 2 provided numbers is that the lowest common multiple of any two. Least common multiple is its full name. Another name for it's the Lowest common divisor (LCD)

Main Body:

According to question,

Every 4th person who walks into the dance gets a free water bottle

Every 9th person who walks in gets an integrity ticket.

so the L.C.M of 4 and 9 should be calculated.

L.C.M of 4 and 9 is 36.

Hence L.C.M is 36

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Using the distance formula, the distance between the point is √130.

In the given question we have to find the distance between given point in the graph.

From the graph the given points are (4,4) and (-3, -5).

The formula for the distance between point is

Distance = √{x(2)-x(1)}^2+{y(2)-y(1)}^2

From the given points; x(1)=4, y(1)=4, x(2)= -3 and y(2)= -5.

Now putting the value:

Distance = √{-3-4}^2+{-5-4}^2

Distance = √{-7}^2+{-9}^2

Distance = √49+81

Distance = √130

The distance between the point is √130.

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Answer:

  (d)  Jamar's ending account balance is higher than Beth's ending balance.

Step-by-step explanation:

You want to know the best description of the relationship between final balances of two ordinary annuities:

The attached calculator display shows the ending balance for Jamar's annuity and for Beth's annuity. We assume the final balance is the balance after the final payment. That is, Beth's balance will be known 15 years before Jamar's balance is known.

Jamar's balance: $274,083.57

Beth's balance: $167,247.33

The best description is ...

Jamar's ending account balance is higher than Beth's ending balance.

__

Additional comment

Jamar makes twice as many payments of half the amount each, so his total contribution is the same as Beth's. His early payments are earning interest for twice as long as Beth's, so his account earns more interest.

Answer:√53 or 7.28010988928

Step-by-step explanation:

The first number is 3 and the second number is -5.

According to the question,

We have the following information:

There are two mystery numbers. The sum of 6 times the first number and 4 times the second number is -2. The sum of 6 times the first number and 2 times the second number is 8.

Now, let's take the first number to be x and the second number to be y.

So, we have the following expressions:

6x+4y = - 2

6x = -2-4y ...(1)

6x+2y = 8

Putting the value of 6x from equation 1:

-2-4y+2y = 8

-2-2y = 8

-2y = 8+2

-2y = 10

y = -10/2

y = -5

Putting this value of y in equation 1:

6x = -2-4y

6x = -2-4*(-5)

6x = -2+20

6x = 18

x = 18/6

x = 3

Hence, the first number is 3 and the second number is -5.

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The family coverage paid by Martha's employer for health care coverage is $2592.

What is a health care coverage?

Health insurance is a sort of insurance that pays for unexpected medical costs brought on by a disease. These expenditures may be associated with the price of hospitalisation, or the cost of medical visits.

Main body:

Let the total biweekly salary of Martha be x.

Therefore according to question :

18% of x =$108

(18/100)*x =108

x= 600

Martha earns $600 biweekly.

monthly earning of Martha be 600*2 =$1200

Therefore total coverage annually = 108*total salary day

                                                          =108*24

                                                          =$2592

Hence the answer is $2592.

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The slope of the line is - 2 with the equation as 2 x + y - 2 = 0

We are given that:

y intercept of the line = 2

Point is (0, 2)

It is parallel to the line 2 x + y = - 5

Slope of line 2 x + y = - 5:

y' = - 2

m = - 2

Slope of parallel lines are equal

m = m'

m' = - 2

Equation of the line:

y - y₁ = m( x - x₁)

y - 2 = - 2( x - 0)

y - 2 = - 2 x

2 x + y - 2 = 0

a) standard form of the equation = 2 x + y - 2 = 0

b) slope of the line = m' = - 2

c) point-slope form = (y - 2) / (x - 0) = - 2

d) Properties of algebra used = cross multiplication and simplification.

Therefore, we get that, the slope of the line is - 2 with the equation as 2 x + y - 2 = 0

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The equivalent equation to the given equation i.e, x = x² - 20  is   x² - x - 20 = 0

What is a Quadratic equation ?

A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.

The given expression is,

x = x² - 20

We have to make the equation in quadratic form i.e, ax² + bx + c = 0

so, first take x to the right side

0 = x² - 20 - x

Now swap the equation,

x² - 20 - x = 0

put 'x' term in middle and constant term at last like this,

x² - x - 20 = 0

Hence, The equivalent equation to the given equation i.e, x = x² - 20 is  x² - x - 20 = 0

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Applying the definition of exterior angle of a triangle, the value of m is: m = 32.

An exterior angle of a triangle can be defined as the angle formed outside the triangle when one of its side is extended.

The exterior angle to an interior angle, is supplementary to the interior angle. That is, they have a sum of 180 degrees when we add their angle measures together.

Given the following:

Measure of angle Z = 4m - 15

Measure of the exterior angle to angle Z = 2m + 3

Therefore:

4m - 15 + 2m + 3 = 180

Combine like terms

6m - 12 = 180

6m = 180 + 12

6m = 192

6m/6 = 192/6

m = 32

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Answer:

  x = 5

Step-by-step explanation:

You want to know what number must be excluded from the domain of f(x) = 15/(x -5).

The domain of a function is the set of numbers for which it is defined. The function f(x) = 15/(x-5) will be undefined when the denominator is zero:

  x -5 = 0

That will be the case when x = 5.

The domain of f must exclude x=5.

 a) the constant of proportionality multiplies every actual linear    dimension

 b)  height of a can of fruit juice is 3.85 inches high

What is Proportionality?

The term proportionality describes any relationship that is always in the same ratio.

Explanation for answer:

Since the desire is to have students look twice as tall, we expect the constant of proportionality to be [tex]\frac{1}{2}[/tex].

Instead, we're told that the stage manager is using a height of 44 inches to represent an 80-inch door.

This means their constant of proportionality is [tex]\frac{40}{80} = 0.55[/tex]

a) Any new props can be scaled by this factor (0.55) to find their height on set.

b) A 7-inch can would be scaled to [tex]7\times 0.55 = 3.85\ inches[/tex]

Question: The school's theater club is building sets that will make ordinary students look like giants. The actors need a door, a table, and a stool that will make them look almost twice as tall!

DOOR: actual height is 80 inches and Height on Set is 44 inches

TABLE: actual height is 28 inches

STOOL: actual height is 18 inches

How can the stage manager use the constant of proportionality to find the dimensions of any new props the director requires?

What should the height of a can of fruit juice used as a prop be if its actual height is 7 inches? Show your work.

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Answer:

[tex]x\leq -7 or x > -2[/tex]

Step-by-step explanation:

-8x+14 ≥ 60 or - 4x + 50 < 58
     -8x ≥ 56 or         - 4x < 8
        [tex]x \leq -7[/tex] or            [tex]x > -2[/tex]