How does the graph of g(x) = (x − 8)3 + 3 compare to the parent function f(x) = x3?

Answer:

40

Step-by-step explanation:

Answer:

Step-by-step explanation:

5a + b - 2*a*c

a = 4

b = 12

c = 1

5*4 + 12 - 8

20 + 12 -8

24

The expression "x > 100" is used to determine the range of values that x can take and the range is all positive integers greater than 100.

An expression is a combination of numbers, variables, and operators that can be evaluated to a numerical value. In this case, the expression "x > 100" is used to determine the range of values that the variable x can take.

The expression checks whether x is greater than 100. If x is indeed greater than 100, then the expression evaluates to True and the next decision in the sequence is reached. If x is not greater than 100, then the expression evaluates to False and the next decision is not reached.

Therefore, the range of values that x can take is all the integers greater than 100. For example, x can be 101, 102, 103, and so on. The range of values for x is not limited, meaning it can be any positive integer greater than 100.

In mathematical terms, the expression "x > 100" can be written as:

x ∈ Z, where Z is the set of all integers and x > 100

In other words, x can be any integer that belongs to the set of all integers, as long as it is greater than 100.

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Answer:

y=6x

Step-by-step explanation:

y-y1=m(x-x1)

y-0=6(x-0)

y=6(x)

y=6x

Answer:

$ 71.83  

Step-by-step explanation:

This year's earnings=last year's earnings*(1+growth rate)=$2*(1+20%)=$2.4

This year's dividend=2.4 *payout ratio=2.4 *20%=$0.48

Next year's earnings=$2.4*1.2=$2.88

Next year's dividend=2.88 *0.2=$ 0.58  

Year 3 earnings=$2.88*1.2=$ 3.46  

Year three dividend= 3.46*0.2=$0.69  

year 4 earnings =$3.46*1.08=$ 3.74  

Dividend from year 4 onward= 3.74  *0.5=1.87

From year 4 terminal value=1.87 /(cost of equity-growth rate)=1.87/(10%-8%)=$93.5

Share price is present value of the above dividends amnd terminal value=0.48/(1+0.1)^0+0.58/(1+0.1)^1+0.69/(1+0.1)^2+93.5/(1+0.1)^3=$ 71.83  

Using simultaneous equation, the solution to the system of linear equations are 1223 $10 tickets, 1332 $20 tickets, and 763 $30 tickets were sold.

Let's solve the problem step by step.

Let:

x = number of $10 tickets sold

y = number of $20 tickets sold

z = number of $30 tickets sold

From the given information, we can form the following equations:

Equation 1: x + y + z = 3318 (Total number of tickets sold)

Equation 2: y = x + 109 (109 more $20 tickets than $10 tickets were sold)

Equation 3: 10x + 20y + 30z = 61760 (Total sales from ticket sales)

We can use these three equations to solve for the values of x, y, and z.

First, let's substitute Equation 2 into Equation 1:

x + (x + 109) + z = 3318

2x + 109 + z = 3318

2x + z = 3209 (Equation 4)

Now, let's substitute the value of y from Equation 2 into Equation 3:

10x + 20(x + 109) + 30z = 61760

10x + 20x + 2180 + 30z = 61760

30x + 30z = 59580

x + z = 1986 (Equation 5)

We now have a system of equations (Equations 4 and 5) with two variables (x and z). We can solve this system to find the values of x and z.

Multiplying Equation 4 by 30, and Equation 5 by 2, we get:

60x + 30z = 96270 (Equation 6)

2x + 2z = 3972 (Equation 7)

Now, subtract Equation 7 from Equation 6:

(60x + 30z) - (2x + 2z) = 96270 - 3972

58x + 28z = 92298

Simplifying, we have:

29x + 14z = 46149 (Equation 8)

Now, we can solve Equations 5 and 8 simultaneously:

x + z = 1986 (Equation 5)

29x + 14z = 46149 (Equation 8)

Multiplying Equation 5 by 14, and Equation 8 by 1, we get:

14x + 14z = 27804 (Equation 9)

29x + 14z = 46149 (Equation 8)

Now, subtract Equation 9 from Equation 8:

(29x + 14z) - (14x + 14z) = 46149 - 27804

15x = 18345

Divide both sides of the equation by 15:

x = 18345 / 15

x = 1223

Substituting the value of x into Equation 5, we can find z:

1223 + z = 1986

z = 1986 - 1223

z = 763

Now that we have the values of x and z, we can substitute them back into Equation 1 to find y:

1223 + y + 763 = 3318

y + 1986 = 3318

y = 3318 - 1986

y = 1332

Therefore, the solution to the problem is:

x = 1223 (number of $10 tickets sold)

y = 1332 (number of $20 tickets sold)

z = 763 (number of $30 tickets sold)

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Answer:

Step-by-step explanation:

V = 3.9V

I = 0.12A

Ohm's Law, V = IR

Rearranging Ohm's Law, R = V/I

R = 3.9/0.12 = 32.5Ω

Hey there!

2/3 + 1/4

= 2×4/3×4 + 1×3/4×3

= 8/12 + 3/12

= 8 + 3/12 - 0

= 11/12

Therefore, your answer is: 11/12

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

\(\frac{11}{12}\)

Step-by-step explanation:

\(\frac{2}{3} +\frac{1}{4}\)
First, find the lowest common denominator (LCD):

3*4=12
Next, convert the fractions to a base of 12.
\(\frac{2}{3} * \frac{4}{4} = \frac{8}{12}\)

\(\frac{1}{4} * \frac{3}{3} = \frac{3}{12}\)
Then, add our fractions with the same base (12):

\(\frac{8}{12} + \frac{3}{12} = \frac{11}{12}\)

9514 1404 393

Answer:

  349.0 grams

Step-by-step explanation:

The amount remaining can be modeled by an exponential function of the form ...

  remaining = (initial amount)(1 - decay rate)^t

  q(t) = 640(1 -0.073)^t

  q(8) = 640(0.927^8) ≈ 349.0 . . . grams

The amount remaining after 8 minutes is about 349.0 grams.

Answer:

You could resell it for $240.

Step-by-step explanation:

a. When we have ' ≥ ' means the number is greater than or equal to another number. Similarly when we have ' ≤ ' means the number is less than or equal to another number. These symbols are made up of less than, greater than, and equal to symbols.

≥ is made up of ' > ' and ' = ' impling the number is either greater to or equal to the another number.

≤  is made up of ' < ' and ' = ' impling the number is either greater to or equal to the another number.

b. The inequality ' ≥ ' means the number is greater than or equal to another number.

c. The mathematical sentences where relations symbols such as ≥, ≤, and ≠ are used are called inequalities. Inequality is the relational symbol that is used to compare two entities or numbers.

d. There are five types of inequality symbols and they are as follows -

> greater than

< less than

= equal to

≠ not equal to

≥ greater than equal to

≤ less than equal to

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The complete question is -

a. What symbol you will use if you have ≥ and ≤?

b. What does ≥ mean in an inequality?

c. What do you call a mathematical sentence where relations symbols such as ≥ ≤ and ≠ are used?

d. What are the 5 types of inequality symbols?

Answer: x<4

Step-by-step explanation:

If we break this down as

-2+4x<14 and we add 2 to both sides

4x+<16 and divide by 4

and you get x<4

The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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Answer:

17x+12=12

17x=12-12

17x=0

divide both sides by 17

x=0

rough check

17(0) = 12-12

0=0

I hope this helps

Answer:

It’s probably infinitely many solutions

Step-by-step explanation:

See attached picture

*sorry if that doesn’t help

Step-by-step explanation:

CFB reads as twenty five degrees

complementary angle  will add to it to sum 90 degrees  = sixty five degrees

   angle CFD is sixty five degrees

Answer:

87452

Step-by-step explanation:

not needed

Answer: in 2015 they sold 37,314.  In total they sold 87,452 in all three years combined.

Step-by-step explanation:

Answer:

Step-by-step explanation:

In this question, we need to use the formula of means to solve the. We can set the number of beads Rajiv brings as X, and use the formula of mean to get the total number of beads that the Four(4) children have and the total number of beads that the Five(5) children have.

Four(4) children each have some beads, the mean number of beads is: 8

        4 * 8 = 32

We set the number of beads Rajiv brings as:

x, so the total number of beads that the Five(5) children have is:

32  +  x

The mean number of the Five(5) children is now: 9

      5  *  9   =  45

     32 +  x    =    45

      x  +  32  =    45

           -  32  =   -32

       x            =     13

By solving the above equation, you can get:

x  =  13

       13

Hope this helps!

a. The probability of no insect contaminants in a 225-gram bar from a brand at the mean contamination level can be found using the Poisson probability formula:

\(P(X = 0) = \frac{ (e^{-λ})(λ^0)}{0!} = \frac{(e^{-14.4})(14.4^0)}{0!}= 0.000000831\)

b. If you consume a bar that is one-fifth the size tested (45 grams) from a brand at the mean contamination level, the mean number of insect fragments would be one-fifth of 14.4, or 2.88. The probability of no insect contaminants can be found using the Poisson probability formula:

\(P(X = 0) = \frac{(e^-λ)(λ^0)}{0!} = \frac{(e^-2.88)(2.88^0)}{0!} = 0.056032\)

c. If you consume seven 28.35 gram (one-ounce) bars this week from a brand at the mean contamination level, the mean number of insect fragments would be (7 * 28.35/225) * 14.4 = 5.4336.

The probability of consuming one or more insect fragments in more than one bar can be found using the Poisson probability formula and the complement rule:

\($$\begin{aligned}& P(X>1) \\& =1-P(X \hat{a} 1) \\& =1-\left[\left(e^{-} \hat{I}\right)\left(\hat{I}^0\right) / 0 !+\left(e^{-} \hat{I}\right)\left(\hat{I}^1\right) / 1 !\right] \\& =1-\left[\left(e^{-} 5.4336\right)\left(5.4336^0\right) / 0 !+\left(e^{-} 5.4336\right)\left(5.4336^1\right) / 1 !\right] \\& =0.994784\end{aligned}$$\)

d. The probability of contamination more than twice the mean of 14.4 can be found using the Poisson probability formula and the complement rule:

\(P(X > 28.8) = 1 - P(X ≤ 28.8) \\= 1 - ∑(e^-λ)(λ^x)/x!\\ = 1 - 0.999999999999999 \\= 0.000000000000001\)

This probability is extremely small, so it can be considered unusual and not typical variation.

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Answer:Did you ever get a answer?? I need them badly! And if i dint turn this in my whole life is ruined!! Im sorry that i don’t have answers for you

Step-by-step explanation:

Answer:

part a is 24.3 miles part b is 24 miles part c is 1.3 miles part d is 50 miles part e is 0.65 miles part f is 5 miles

Step-by-step explanation:

HOPE THIS HELPS!

Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

Step-by-step explanation:

1) if m(∠A)∈[0;90°), then

\(cos(A)=\sqrt{1-sin^2A} =\frac{3}{5};\)

\(sin2A=2sinAcosA=2*\frac{3}{5} *\frac{4}{5}=\frac{24}{25};\)

\(cos2A=cos^2A-sin^2A=\frac{9}{25}-\frac{16}{25}=-\frac{7}{25};\)

\(tan2A=\frac{sin2A}{cos2A}=-\frac{\frac{24}{25}}{\frac{7}{25}}=-\frac{24}{7}.\)

2) if m∠A∈[90°;180°), then

cos(A)=-0.6;

sin2A=-0.96;

cos2A=-0.28;

tan2A=-24/7.

Answer:

11 cm

Step-by-step explanation:

r² = 9² + 6.3²

r² = 120.69

r = 10.9859000542

Rounded

r = 11 cm

Answer:

\(\rm 10.9 cm \)

Step-by-step explanation:

Given that :-

And we need to find out the radius of the circle.

\(\text{ Theorem :-}\)

Using Pythagoras Theorem :-

\(\implies \rm OA^2= AB^2+OB^2\\\\\rm\implies OA^2= (6.3 cm)^3+(9cm)^2\\\\\rm\implies OA^2=

120.69 \\\\\implies\boxed{\rm OA = 10.9 cm }\)

Hence the radius is 10.9 cm

Answer:

870

Step-by-step explanation:

The number of elements in the intersection A∩B is 2.

The intersection of two sets A and B, denoted as A∩B, represents the set that contains all the elements that are common to both A and B.

A = {1, 2, 4, 5}

B = {1, 3, 5, 7}

To find the intersection A∩B, we compare the elements of set A with the elements of set B.

Any element that appears in both sets is considered to be part of the intersection.

The elements that are common to both A and B are 1 and 5.

These two elements appear in both sets, so they are included in the intersection.

Thus, the intersection A∩B = {1, 5}.

Hence, the number of elements in the intersection A∩B is 2, as there are two elements in the set {1, 5}.

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Answer:

x = \(\frac{4}{5}\), y = \(\frac{1}{5}\)

Step-by-step explanation:

Express as 2 equations, that is

x + y = 1 → (1)

- x + 9y = 1 → (2)

Add the 2 equations term by term to eliminate x, that is

10y = 2 ( divide both sides by 10 )

y = \(\frac{2}{10}\) = \(\frac{1}{5}\)

Substitute this value into (1) and solve for x

x + \(\frac{1}{5}\) = 1 ( subtract \(\frac{1}{5}\) from both sides )

y = \(\frac{5}{5}\) - \(\frac{1}{5}\) = \(\frac{4}{5}\)

Answer:

The correct answer for this question is A

Answer: i think c

Step-by-step explanation:

Answer:

1) B = 88°, a = 13.1, b = 26.9

2) C = 73°, a = 20.9, b = 12.6

Step-by-step explanation:

To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies B=180^{\circ}-A-C\)

\(\implies B=180^{\circ}-29^{\circ}-63^{\circ}\)

\(\implies B=88^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}\)

\(\implies a=13.0876493...\)

\(\implies a=13.1\)

Solve for b:

\(\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}\)

\(\implies b=26.9194211...\)

\(\implies b=26.9\)

\(\hrulefill\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies C=180^{\circ}-A-B\)

\(\implies C=180^{\circ}-72^{\circ}-35^{\circ}\)

\(\implies C=73^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}\)

\(\implies a=20.8847511...\)

\(\implies a=20.9\)

Solve for b:

\(\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}\)

\(\implies b=12.5954671...\)

\(\implies b=12.6\)

Answer:

81

Step-by-step explanation:

3*3=9

9*3=27

27*3=81

Answer:  90

Step-by-step explanation:

3 to the fourth power =  81

81 + 9 = 90