if you got 8 out of 17 questions right and they are worth 2 points each what did you make on the test

really? you can do that?

\(f^(-1)(2) = 6\), which is consistent with our earlier result.

A function that "undoes" another function is known as an inverse function. If f(x) is a function, then f(x inverse, )'s indicated by f-1(x), is a function that accepts f(x output )'s as an input and outputs f(x initial )'s input.

Given the function f(x) = √(2x - 8), if f^(-1)(x) is the inverse function of f(x), what is \(f^(-1)(2)\)?

Solution:

To find f^(-1)(2), we need to find the value of x such that  \(f(x) = 2\) . We can set up an equation:

\(f(x) = \sqrt(2x - 8) = 2\)

Squaring both sides, we get:

\(2x - 8 = 4\)

\(2x = 12\)

\(x = 6\)

Therefore, \(f^(-1)(2) = 6.\)

We can also verify this result by using the definition of an inverse function. If f^(-1)(x) is the inverse function of f(x), then by definition:

\(f(f^(-1)(x)) = x\)

We can substitute x = 2 and solve for f^(-1)(2):

\(f(f^(-1)(2)) = 2\)

\(f^(-1)(2) = (f(6))^(-1)\)

f(6) = √(2(6) - 8) = √4 = 2

Therefore,\(f^(-1)(2) = 6\), which is consistent with our earlier result.

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Answer:

they're both acute im 100% sure

Step-by-step explanation:

Check the picture below.

\(\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+56}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)\)

\(\left(-\cfrac{ 56}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (56)^2}{4(-16)}\right) \implies \left( - \cfrac{ 56 }{ -32 }~~,~~0 - \cfrac{ 3136 }{ -64 } \right) \\\\\\ \left( \cfrac{7}{4}~~,~~49 \right)\implies \stackrel{seconds\qquad feet}{\left(1\frac{3}{4} ~~ ~~,~ ~~ ~49 \right)}\)

Answer:

37.5%

Step-by-step explanation:

An absolute value equation to find the minimum and maximum acceptable nail length is; 31/32 ≤ X ≤  1 ¹/₃₂

We are told that the company manufactures 2 nails that are 1 inch in length. The actual length is allowed to vary by up to 1/32 inch. Thus;

Actual Length of nail = 1 inch

Allowable variation = 1/32 inches

The minimum allowable length is expressed as:

minimum allowable length = actual length - allowable variation

minimum allowable length = 1 - (1/32) = 31/32

The maximum allowable length is expressed as:

Maximum allowable length = Actual length + allowable variation

Maximum allowable length = 1 + (1/32) = 1 ¹/₃₂

The length of X, of the nail must be follow the equation :

Minimum ≤ X ≤ maximum

Thus, an absolute value equation to find the minimum and maximum acceptable nail length is; 31/32 ≤ X ≤  1 ¹/₃₂

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Answer:

6

Step-by-step explanation:

The notation 3! means to find the factorial of 3. The factorial of an integer n = n * (n-1) * (n-2) *... all the way down to 1. So in this case, 3 factorial is:

3 * 2 * 1 = 6

It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.

Time = Distance / Speed

Time = 389 miles / 65 mph

Time ≈ 5.98 hours

Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.

To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.

Number of gallons = Distance / Mileage

Number of gallons = 389 miles / 29 miles per gallon

Number of gallons ≈ 13.41 gallons

The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.

Cost = Number of gallons * Cost per gallon

Cost ≈ 13.41 gallons * $3.89/gallon

Cost ≈ $52.18

Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

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Answer:

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Answer:

This is a guess but I think it's 5 min per table.

Step-by-step explanation:

The reason being:

if we know that she has 9 tables to get to and each table can seat 4 people, we would have to multiply both numbers to find how many TOTAL people are in the restaurant during the first few hours.

9x4 = 36 people in total

then, we need to convert 3hrs into minutes to get a more accurate rep as to how much time she would spend at each table (she isn't going to spend the entire 3 hrs with only one table now, is she?)

so for this, we convert 3hrs into minutes

1 min = 60 secs

1 hr = 60 minutes

3hrs -> 60 x 3 = 180 minutes

now, to understand how many time she spends at each table, we need to figure out by dividing the # of people by the amount of minutes.

180 minutes/36 people = 5 mins per table.

Answer:

0 or 0.62921348314 (if done by the calculator)

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 89 on the left side and the dividend 56 on the right side like this:

8 9 ⟌ 5 6

Step 2:

The divisor (89) goes into the first digit of the dividend (5), 0 time(s). Therefore, put 0 on top:

0

8 9 ⟌ 5 6

Step 3:

Multiply the divisor by the result in the previous step (89 x 0 = 0) and write that answer below the dividend.

0

8 9 ⟌ 5 6

0

Step 4:

Subtract the result in the previous step from the first digit of the dividend (5 - 0 = 5) and write the answer below.

0

8 9 ⟌ 5 6

- 0

5

Step 5:

Move down the 2nd digit of the dividend (6) like this:

0

8 9 ⟌ 5 6

- 0

5 6

Step 6:

The divisor (89) goes into the bottom number (56), 0 time(s). Therefore, put 0 on top:

0 0

8 9 ⟌ 5 6

- 0

5 6

Step 7:

Multiply the divisor by the result in the previous step (89 x 0 = 0) and write that answer at the bottom:

0 0

8 9 ⟌ 5 6

- 0

5 6

0

Step 8:

Subtract the result in the previous step from the number written above it. (56 - 0 = 56) and write the answer at the bottom.

0 0

8 9 ⟌ 5 6

- 0

5 6

- 0

5 6

Answer:

f, x, 7, -2

Step-by-step explanation:

Using the normal distribution, there is a 0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The proportion estimate and the sample size are given as follows:

p = 0.45, n = 437.

Hence the mean and the standard error are:

The probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3% is 2 multiplied by the p-value of Z when X = 0.45 - 0.03 = 0.42.

Hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{X - \mu}{s}\)

Z = (0.42 - 0.45)/0.0238

Z = -1.26

Z = -1.26 has a p-value of 0.1038.

2 x 0.1038 = 0.2076.

0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.

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Answer:

6.8333333333 or 41/6

Step-by-step explanation:

Answer:

~ 0.375 centimeters of the snowflake in real life ~

Step-by-step explanation:

Let us plan out our steps, and solve for each:

1. Given the information, let us create a proportionality as such:

      48       =           1      ⇒   x - centimeters of the snowflake in real life

       18                    x

2. Now let us cross multiply, and solve through simple algebra for x:

48 * x = 18,

x = 0.375 centimeters of the snowflake in real ife

Answer:

Around 0.40

Step-by-step explanation

If she doubles the gift every year, do 18x2=36, 36 rounds to 40 or 0.40.

The total of all the gifts on the girl's 18th birthday given from her grandma for this considered case is  evaluated as 2621.43 dollars

Lets suppose the geometric sequence has its initial term is \(a\), multiplication factor is  r, then, its sum is given as:

\(S_n = \dfrac{a(r^n-1)}{r-1}\)

(sum till nth term)

The sequence would look like \(a, ar, \cdots, ar^{n-1},\cdots\)

For this case, we are specified that:

That shows that the gift amounts each year will form a geometric sequence where a = 1, and r = 2 (as amounts are doubled).

The gift amounts would look like:

\(\\1, 2, 4, \cdots\\or\\1, 2\times 1, 2^2 \times 1, \cdots\)

We have to find these terms' sum till 18th term(18th term is the gift of her 18th birthday).

Thus, we have: n = 18, a = 1, and r = 2.

The sum will be:

\(S_n = \dfrac{a(r^n-1)}{r-1} = \dfrac{1(2^{18}-1)}{2-1} = 2^{18} - 1 = 262143 \: \rm cents\)

There are 100 cents in 1 dollars,

Thus, 1 cent = 0.01 dollars,

and thus, 262143 cents form 2621.43 dollars.

Thus, the total of all the gifts on the girl's 18th birthday given from her grandma for this considered case is  evaluated as 2621.43 dollars

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The unknown angle measures are 51.5° and 51.5° respectively.

What is an isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides.

Given, side DE = side EF

Then, ∠D = ∠F

So, the sum of all angles of the triangle = 180°

or, ∠D + ∠E + ∠F = 180°

or, ∠F + 77° + ∠F = 180°

or, 2∠F = 180° - 77°

or, ∠F = 103/2 = 51.5°

And, ∠D = 51.5°

Hence, the unknown angle measures are 51.5° and 51.5° respectively.

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The height of the tree is 186 inches if Shadow of tree is 523 inch shadow of human is 180 inch height of human is 64 inch.

Cross multiplication occurs when the numerator of the first fraction is multiplied by the denominator of the second fraction, and the numerator of the second fraction is multiplied by the denominator of the first fraction.

We have given information that

Shadow of tree = 523 inch

Shadow of human = 180 inch

Height of human = 64 inch

height of tree = x

Lets solve this with cross multiplication

⇒ \(\frac{64}{180} = \frac{x}{523}\)

⇒ 180 × x = 64 × 523

⇒ x = (64 × 523)/180

⇒ x = 185.95

       = 186 approx.

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Answer:

x=0

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

10(x−2)=−20

(10)(x)+(10)(−2)=−20(Distribute)

10x+−20=−20

10x−20=−20

Step 2: Add 20 to both sides.

10x−20+20=−20+20

10x=0

Step 3: Divide both sides by 10.

10x/10 = 0/10

Answer:

x=0

Step-by-step explanation:

0-2= -2

So

10 x -2= -20

Hope that helped.

Answer:

Step-by-step explanation:

You have everything you need to find the area directly

A = 1/2 * b * h

b = 20

h = 15

Area = 1/2 * 20 * 15

Area = 150 m^2

The equation given in slope-intercept form does not represent the graph because the y-intercept of the graph is equal to 4 while the y-intercept of the equation is equal to 5.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Based on the information provided regarding the equations and graphs, the y-intercept are as follows:

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The symbolic quantified statement is given as:

For all real integers x and y, if x³ = y³, then x = y.

Using quantifiers, this can be written as:

∀x,y∈ℝ, (x³ = y³) → (x = y)

The symbolic quantified statement represents the original sentence using logical symbols and quantifiers.

The universal quantifier (∀) is used to denote "for all," while the implication arrow (→) represents "if... then." The statement asserts that if the cubes of any two real integers x and y are equal, then x and y are equal as well.

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Step-by-step explanation:

the length of the diagonal is calculated out of the length and width by using Pythagoras (after all, one length, one width and the diagonal are creating a right-angled triangle).

25² = length² + width²

length = 2×width + 10

we are using the second in the first equation :

25² = (2×width + 10)² + width²

625 = 4×width² + 40×width + 100 + width²

525 = 5×width² + 40×width

105 = width² + 8×width

width² + 8×width - 105 = 0

a quadratic equation

ax² + bx + c = 0

has the general solutions

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = width

a = 1

b = 8

c = -105

width = (-8 ± sqrt(8² - 4×1×-105))/(2×1) =

= (-8 ± sqrt(64 + 420))/2 =

= (-8 ± sqrt(484))/2 =

= (-8 ± 22)/2 = -4 ± 11

width1 = -4 + 11 = 7

width2 = -4 - 11 = -15

a negative size of the length of a side of a shadow does not make any sense, so, our valid solution is

width = 7 in.

and then

length = 2×width + 10 = 2×7 + 10 = 14 + 10 = 24 in.

The triangles ABC and DBE are similar by the SAS similarity theorem

The measure of the side lengths AC is 16 units

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

The triangles ABC and DBE

These triangles have the following measures

This means that the triangles are similar by the SAS similarity theorem

Using the SAS similarity theorem, we have the following equation

(x + 1)/12 = (x + 5)/15

Cross multiply the equation

15x + 15 = 12x + 60

So, we have

3x = 45

Divide by 3

x = 15

This means that

x + 1 = 15 + 1 = 16

x + 5 = 15 + 5 = 20

Hence, the measure of the side lengths are 16 and 20 units

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The correct statements regarding the domain and the range of the functions are given as follows:

For the square root function, we have that:

Hence if we multiply the function by a negative number, the domain of the function remains constant, but the range is changed.

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Answer:

Infinite Solution!

Step-by-step explanation:

First, We simplify the right side.

Distribute -4, -4x-20=-4x-20

Now we add +4x to both sides, now the equation stands as -20=-20

We know when the solution is same #= same #. We have infinite solution!

Answer:

Calcular las dimensiones de un rectángulo, sabiendo que es 4cm más largo que ancho y ... Área = base•altura ... Encuentra más respuestas.

Step-by-step explanation:

Answer:

how do you translate?

Step-by-step explanation:

y=1/2x-2 is perpendicular to y=2x+3

Answer:

answer is D

Step-by-step explanation:

(2^3)^-2= 2^(3)*(-2)
             = 2^-6
             = 1/2^6
             = 1/64

     

The expressions (a), (d), (e) and (f) have values less 1.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Solving each expression :-

1) 4¹¹ / 4¹⁴        

= 4¹¹ × 4⁻¹⁴

= (4)¹¹⁻¹⁴

= 4⁻³

= 1 / 4³

2) (3⁵)² / 3⁸

= 3¹⁰ / 3⁸

= 3¹⁰⁻⁸

= 3²

= 9

3) 4⁻¹ × 4⁵

= 4⁻¹⁺5

= 4⁴

= 64

4) (2³)⁻²

= 2⁻⁶

= 1 / 2⁶

5) (5⁴)² x 5⁻¹¹

= 5⁸ x 5⁻¹¹

= 5⁻³

= 1 / 5³

6) (6⁻⁴ x 6⁶) / 6³

= 6² / 6³

= 1 / 6

Hence, the expressions (a), (d), (e) and (f) have values less 1.

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