Which is the graph of f(x) = x² + 4 and the function g, a reflection of f(x) across the x-axis?

By calculating the percentage of earnings, we find out that Gary earns more money in one week as compared to Tara. Gary earns $900 and Tara earns $705 in one week. Therefore, the last option is correct.

It is given to us that -

Gary and Tara work as tutors at two different test prep companies

In a week, Gary earns 45% of the $2000 collected from the pupils

In the same week, Tara earns 20% of the $3,525 collected from the pupils

We have to find out who earns more money in a week.

We know that, in a week, Gary earns 45% of the $2000 collected from the pupils. This implies earning of Gary in a week

= 45% of 2000

= $900

Similarly, we know that, in the same week, Tara earns 20% of the $3,525 collected from the pupils. This implies earning of Tara in  the same week

= 20% of 3,525

= $705

Thus, by calculating the percentage of earnings, we can see that Gary earns more money in one week. Gary earns $900 and Tara earns $705 in one week. Therefore, the last option is correct.

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The equation,  y + x = 45 and 2y + 2x = 6 has No Solution .

In the question ,

it is given that ,

the equations are y + x = 45 and 2y + 2x = 6 .

y = 45 - x

Substituting the value of y = 45 - x in the equation 2y + 2x = 6

we get ,

2(45 - x) + 2x = 6          ...by using associative property

Simplifying further ,

we get

90 - 2x + 2x = 6

90 = 6                   .....because   -2x+2x = 0

we know that 90 ≠ 6 ,

hence , the equations have No Solution .

Therefore , The equation,  y + x = 45 and 2y + 2x = 6 has No Solution .

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Answer:

No, Eduardo made a mistake from Step 1 to Step 2. Eduardo should have subtracted 4 from 6 instead of evaluating the exponent. The order of operations says to perform all operations inside parentheses first.

Answer:

I think you are right.Because im sure

Applying the triangle midsegment theorem:

a. x = 17; y = 2

b. Length of DF = 20 units.

The triangle midsegment theorem states that the midsegment of a triangle is always parallel to the third side, and has a length that is half the length of the third side of the triangle.

GH is said to be the midsegment of triangle DEF, therefore:

a. GH = 1/2(EF) [triangle midsegment theorem]

Substitute

x - 3 = 1/2(28)

2(x - 3) = 28

2x - 6 = 28

2x = 28 + 6

2x = 34

2x/2 = 34/2

x = 17

HF = x - 7

Plug in the value of x

HF = 17 - 7

HF = 10

HF = DH = 10

y + 8 = DH

y + 8 = 10

y = 10 - 8

y = 2

b. Length of DF = HF + DH

Length of DF = 10 + 10 = 20 units.

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The point cannot be included in the function is (7, 2). Therefore, option C is the correct answer.

The given coordinate points are (3, 6), (-5, 7), (13, 1), and (7, 14).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

A) (14, 5)

Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (14, 5) is included in the function.

It is a function as every input has a unique output.

B) (5, 6)

Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (5, 6) is included in the function.

It is a function as every input has a unique output.

C) (7, 2)

Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (7, 2) is not included in the function.

Since the element 7 corresponds to two different images i.e., 14 and 2.

D) (8, 0)

Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (8, 0) is included in the function.

It is a function as every input has a unique output.

The point cannot be included in the function is (7, 2). Therefore, option C is the correct answer.

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The system of equations is x + y = 11 and 2x + 3y = 29 and variables are x and y.

Let us assume the number of two point shots be x and the number of three point shots be y. Forming the equation now -

x + y = 11 : Equation 1

2x + 3y = 29 : Equation 2

Rewriting the equation 1 as per x.

x = 11 - y : Equation 3

Keep the value of x form equation 3 in equation 2

2(11 - y) + 3y = 29

Performing multiplication on Left Hand Side of the equation

22 - 2y + 3y = 29

y = 29 - 22

y = 7

Keep the value of y in equation 3.

x = 11 - 7

x = 4

So, the two point shots are 4 and three points shots are 7. The variables are x and y and system of equations are equation 1 and equation 2.

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Answer: 24

Step-by-step explanation:

You can use proportions to calculate this:

[tex]\frac{6}{2} =\frac{x}{8} \\\\2x=6*8\\\\2x=48\\\\x=\frac{48}{2} =24[/tex]

to get the slope of any straight line, we simply need two points off of it, so let's use those two in the picture below.

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-1)}}} \implies \cfrac{-8}{1 +1} \implies \cfrac{ -8 }{ 2 } \implies - 4[/tex]

In the first function have vertical compression by 1/2, in second function have horizontal compresion by 1/4, in third compression have Vertical reflection and in fourth function have Horizontal reflection and horizontal compression by 1/2.

In the given question we have to find the transformations that map the function y = [tex]8^x[/tex] onto each function.

Since we have to find the transformation, so we know that in a transformation;

The transformation from the first equation to the second one can be found by finding a, h and k for each equation.

[tex]y=ab^{x-h}+k[/tex]

The horizontal is define by the value of h. The horizontal shift is defined as:

g(x)=f(x+h) - The graph is shifted to the left h units.

g(x)=f(x−h) - The graph is shifted to the right h units.

Horizontal Shift: None

The vertical shift define on the value of k. The vertical shift is defined as:

g(x)=f(x)+k - The graph is shifted up k units.

g(x)=f(x)−k - The graph is shifted down k units.

Vertical Shift: None

The value of a describes the vertical stretch or compression of the graph.

a>1 is a vertical stretch

0<a<1 is a vertical compression.

(a) The given first function is [tex](\frac{1}{2})8^{x}[/tex].

y = [tex]8^x[/tex]

Combine [tex]8^x[/tex] and 1/2.

y = [tex]8^x[/tex]/2

Assume that

y = [tex]8^x[/tex]  is f(x)=[tex]8^x[/tex] and y= [tex](\frac{1}{2})8^{x}[/tex] is g(x)= [tex](\frac{1}{2})8^{x}[/tex].

On comparing the equation [tex]y=ab^{x-h}+k[/tex]

The value of a, h, and k for f(x)=[tex]8^x[/tex].

a=1, h=0, k=0

The value of a, h and k for g(x)=[tex](\frac{1}{2})8^{x}[/tex].

a=1/2, h=0, k=0

Since the value of h and k so tnere is no horizontal and vertical shift.

SInce the value of a changes from 1 to 1/2 and 1/2 is greater that 0 but less than 1 so there is vertical compression by 1/2.

(b) The given second function is [tex]8^{4x}[/tex].

y= [tex]8^{4x}[/tex] is g(x)= [tex]8^{4x}[/tex].

On comparing the equation [tex]y=ab^{x-h}+k[/tex]

The value of a, h and k for g(x)=[tex]8^{4x}[/tex].

a=1/4, h=0, k=0

Parent Function: f(x)=8^x

So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: None, Vertical Compression or Stretch: None, horizontal compresion by 1/4.

(c) The given third function is [tex]-8^{x}[/tex].

y= [tex]-8^{x}[/tex] is g(x)= [tex]-8^{x}[/tex].

The value of a, h and k for g(x)=[tex]-8^{x}[/tex].

a=-1, h=0, k=0

Parent Function: f(x)=8^x

So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: Reflected, Vertical Compression or Stretch: None.

Vertical reflection

(d) The given fourth function is [tex]8^{-2x}[/tex].

y= [tex]8^{-2x}[/tex] is g(x)= [tex]8^{-2x}[/tex].

The value of a, h and k for g(x)=[tex]8^{-2x}[/tex].

a=-1/2, h=0, k=0

Parent Function: f(x)=8^x

So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: Reflected, Vertical Compression or Stretch: None.

Horizontal reflection and horizontal compression by 1/2.

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Answer:

16

Step-by-step explanation:

8 x 2 = 16  16 - 8 =2

Answer:

16......................

Quotient is 51.97 by dividing 2,183 by 42. A quotient is the amount that results from dividing two numbers.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction.

Multiply the first fraction by the reciprocal of the second to divide rational expressions. We factor everything and search for common factors after rewriting the division as multiplication of the first statement by the reciprocal of the second. Separate logical expressions.

The number 2183 is called the numerator or dividend, and the number 42 is called the denominator or divisor.

The quotient of 2183 and 42, the ratio of 2183 and 42, as well as the fraction of 2183 and 42 all mean (almost) the same:

2183 divided by 42, often written as 2183/42.

2183/42 = 51.97

The answer that is quotient is 51.97

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The mistake she done is that the acutal quotient is 51.97.

The number 2183 is called the numerator or dividend, and the number 42 is called the denominator or divisor.

The quotient of 2183 and 42, the ratio of 2183 and 42, as well as the fraction of 2183 and 42 all mean (almost) the same:

2183 divided by 42, often written as 2183/42.

2183/42 = 51.97

The answer that is quotient is 51.97

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Answer:

C

Step-by-step explanation:

Prime numbers are only divisible by themselves and 1  ....all even numbers are divisible by '2' ,  so all primes are odd numbers

Answer:

For example, a population with a 2% annual growth would have a doubling time of 35 years.Mar 24, 2015

Step-by-step explanation:

The probability that the mean GPA of a random sample of 20 students selected from this university  is 3.10 or higher is 10.93%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Problems of normally distributed samples are solved using the z-score methods.

We know that, in a set with mean and standard deviation , the z-score of a measure X is given by:

                              Z = X - μ/σ

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean  and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean  and standard deviation .

For a Skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

μ = 3.02 , σ = 0.29 , n = 20 and s = 0.29/√ 20 = 0.0648

Find the probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.

This is 1 subtracted by the p- value of Z when X = 3.10. So

By the Central Limit Theorem:

             Z = X - μ / s

       ⇒  Z = 3.1 - 3.02/ 0.0648

       ⇒ Z = 1.23

The Z = 1.23 has a P- value of 0.8907

∴ 1 - 0.8907 = 0.1093

Now, for  getting the percentage,

0.1093 × 100% = 10.93%

10.93% probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.

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Answer:

the answer should be 6000

The recursive formula of the arithmetic sequence calculator -5, -25, -45, and -65 is an = -20n + 15

The arithmetic sequence is

-5,-25,-45,-65

The initial term = -5

The common difference = The second term - The first term

= -25 - (-5)

= -25 + 5

= -20

The nth term of the arithmetic sequence is

an = a+(n- 1)d

When an is the nth term

a is the initial term

d is the common difference

Substitute the values in the equation

an = -5 +(n-1)( -20)

Apply the distributive property

an = -5 -20n + 20

an = -20n + 15

Hence, the recursive formula of the arithmetic sequence calculator -5,-25,-45,-65 is an = -20n + 15

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Answer:

y = x + 6

Step-by-step explanation:

y = mx + c

2 = -4m + c

-2 = -8m + c

2 + 4m = c

-2 = -8m + 2 + 4m

-2 - 2 = -4m

-4 = -4m

-4/-4 = m

m = 1

2 + 4(1) = c

c = 6

y = x + 6

The 99% confidence interval indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems is (0.571, 0.489).

In the given question we have to find the confidence interval indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems.

Gallup surveyed 1,004 american adults.

So n=1004

The results showed that 53% of respondents blamed barack obama a great deal or a moderate amount.

So p=53% = 0.53

The 99% confidence  interval for the proportion of all american adults who blame barack obama a great deal or a moderate amount for u.s. economic problems is

CI=p±z× √{p(1−p)}/n

Now finding the value of z for 99% confidence interval.

The z critical value at 99% confidence interval is 2.575.

Now putting the value

CI=0.53±2.575× √{0.53(1−0.53)}/1004

CI=0.53±2.575× √(0.53*0.47)/1004

CI=0.53±2.575× √0.2491/1004

CI=0.53±2.575× √0.00025

CI=0.53±2.575× 0.0158

CI=0.53±0.0407

CI=(0.53+0.0407, 0.53−0.0407)

CI=(0.571, 0.489)

Hence, the 99% confidence interval indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems is (0.571, 0.489).

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The order of in which the operation in the expression 9 + 3·2² - 1·4, indicates;

3. (a) The value of the expression, 9 + 3·2² - 1·4 is 17

(b) The left and right side of the grouping symbol (the left side) should be placed between the number 3 and 2 and then (the right side should be placed between 1 and 4, so that we get;

9 + 3 × (2² - 1) × 4 = 45

The order of operations is a rule or guide, that states the sequence in which the operations in an expression are to be performed.

3. The specified expression is; 9 + 3·2² - 1·4

(a) The value of the expression 9 + 3·2² - 1·4 can be found using the order of operation of PEMDAS, which stands for; operations from left to right, items in Parenthesis, then Exponents, followed by Multiplication, and Division first then Addition and Subtraction of the terms from left to right as follows;

Therefore;

9 + 3·2² - 1·4 = 9 + 3 × 4 - 1 × 4 = 9 + 12 - 4 = 17

(b) A grouping symbol is the parenthesis.

The location of the parenthesis in the specified expression so that the value is 45 can be found as follows;

Placing the grouping symbol between 3 and 2 and the right parenthesis between 1 and 4, we get;

9 + 3·2² - 1·4 = 9 + 3·(2² - 1)·4 = 9 + 3 × (2² - 1) × 4

9 + 3 × (2² - 1) × 4 = 9 + 3 × (3) × 4 = 9 + 36 = 45

The location to place the grouping symbol so that the value of the expression is 45 is between 3 and 2 and between 1 and 4.

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Step-by-step explanation:

in that setup they will both explode after traveling the same distance.

A is just going faster and has to launch therefore a little bit later.

so, we need to make an equation based on distance traveled and find in that process the number of seconds needed to travel that distance.

speed is distance/time, so we need to multiply speed by time to get distance.

x = seconds for B

x - 0.25 = seconds for A

A is launched after B but explodes at the same time.

so, A's trip is of shorter time than B's trip.

(x - 0.25)×360 = x×320

360x - 90 = 320x

40x - 90 = 0

40x = 90

4x = 9

x = 9/4 = 2.25 seconds

both fireworks will explode 2.25 seconds after B launches (and 2.25 - 0.25 = 2 seconds after A launches).

the explosion will be at

320×2.25 = 360×2 = 720 feet height.

Answer:

B

Step-by-step explanation:

We can notice that based on the given pattern, the average rate of change from [tex]x=n[/tex] to [tex]x=n+1[/tex], where [tex]n \in \mathbb{Z}[/tex], is [tex]-2n-1[/tex].

So, the average rate of change from [tex]x=8[/tex] to [tex]x=9[/tex] is [tex]-2(8)-1=-17[/tex].

The rate of change for the interval from x = 8 to x = 9 is -17.

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.

The relationship defining how one quantity changes in relation to the change in another quantity is given by the rate of change formula.

We know the standard form of quadratic function

y = a (x - b)² + c with vertex (b, c)

Since the vertex is (0, -1) then b= 0, c= -1.

Then, the quadratic equation is:

y= ax² - 1 passes through (1, 2), (2, -5),.....

So, the rate of change in interval (8, 9) is

= y(9)- y(8)/ (9-8)

= -9² -1 - 8² - 1/ 1

= -17.

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The given polynomial is a binomial and the degree is 2.

In a given expression if we have to know the degree of the polynomial we must look at the HIGHEST degree of the polynomial. This along with the table given below will help us identify the degree of the polynomial.

Degree 0 Constant Polynomial

Degree 1          Linear Polynomial

Degree 2 Quadratic Polynomial

Degree 3 Cubic Polynomial

Degree 4 Quartic Polynomial

The above mentions the various degrees of the polynomial , you may refer to it for future references .

The given expression is [tex]15x^2[/tex]

since the degree of the given polynomial is 2

the given is a binomial polynomial .

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Answer:

? ≈ 5.01

Step-by-step explanation:

using the sine ratio in the right triangle

sin24.3° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2.06}{?}[/tex] ( multiply both sides by ? )

? × sin24.3° = 2.06 ( divide both sides by 24.3° )

? = [tex]\frac{2.06}{sin24.3}[/tex] ≈ 5.01 ( to 3 significant figures )

We can change the base formula by:

                           logₐ b = logₓ a /logₓ b

                                         OR

                           logₓ a, logₓ b = logₓ a

The change of base formula is used to change the base of a logarithm.  We know that "log" stands for a logarithm of base 10 and "ln" stands for a logarithm of base e. But there is no option to calculate the logarithm of a number with any other bases other than 10 and e.

The change of base formula solves this issue of changing base from e to 10, and from base 10 to e. Also, it is used in solving several logarithms problems.

Base Formula: -

The change of base formula is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm. This is a property of logarithms. You can see the change of base formula here.

Change of base formula

                            logₐ b = logₓ a /logₓ b

                                         OR

                            logₓ a, logₓ b = logₓ a

Change of Base Formula

Change of base formula can be represented as follows. Here the base of the given logarithm is also changed to a logarithm with a new base. The basic logarithm with a base is transformed to two logarithms with a new and same base. The change of base formula is:

                          logₐ  b = [logₐ x] / [logₐ y]

In this formula,

Change of Base Formula Derivation

Change of base formula derivation can be understood from the following steps. Let us assume that

log ₐ b = p, logₙ a = q, and logₙ b = r.

By converting each of these into exponential form, we get,

a = [tex]b^{p}[/tex], a = [tex]x^{q}[/tex], and b = [tex]n^{r}[/tex]

From the first two equations,

[tex]x^{q}[/tex] = [tex]n^{r}[/tex]

Substituting b =  [tex]n^{r}[/tex] (which is from third equation) here,

([tex]n^{r}[/tex])[tex]^{p}[/tex] = [tex]x^{q}[/tex]

[tex]n^{r}[/tex])[tex]^{p}[/tex] = [tex]x^{q}[/tex](Using a property of exponents)

p r = q

p = q / r

Substituting the values, we get,

logₐ  b = [logₐ x] / [logₐ y]
For Example:

Evaluate the value of log₆₄ 8 using the change of base formula.

Solution:

We will apply the change of base formula (by changing the base to 10). Note that log₁₀ is same as log.

log₆₄ 8 = [log 8] / [log 64]

            = [log 8] / [log 82]

            = [log 8] / [2 log 8]              [∵ log am = m log a]

            = 1 / 2

Answer: log₆₄ 8 = 1 / 2

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[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-1)}) \implies y -5= -3 (x +1) \\\\\\ y-5=-3x-3\implies {\Large \begin{array}{llll} y=-3x+2 \end{array}}[/tex]

The actual attendance at the baseball game is 7168 fans

A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. The abbreviations "pct," "pct," and occasionally "pc" are also used to represent percentage in addition to the symbol "%". A% has neither a recognized unit of measurement nor any dimensions. Take this as an example: There will be 50 men in the class if there are 100 students total and there are 50 men in the class. There are 250 male students overall, or 250 out of 500.

Given,

The actual attendance at the game=5600 fans

Also given that, the threat of a storm caused many to stay home, and his prediction wound up being 28% higher than the actual attendance.

Then,

28% of 5600

=5600×(28/100)

=1568

Total=5600+1568

Total=7168

Therefore, the actual attendance at the baseball game is 7168 fans.

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Answer:

4,375 fans

Step-by-step explanation:

percent error= amount of error/correct amount

1.28x=5600

1.28x/1.28= 5000/1.28

x=4375

Calculated using unit rates, Steven's birthday party will cost him $ 708 if he were to invite 59 guests.

If the party will cost him $168 for him to invite 14 guests, then we will need to calculate the cost for each guest using unit rates.

if 14 guests = $168,

1 guest = 168/14 = $12

so it will cost him $12 per guest he invites

Knowing that each guest will cost him $12, then if Steven wants to invite 59 guests to his birthday party, he will be spending:

59 × $12 = $708

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Answer: 21

Step-by-step explanation:

70x30/100

= 21

Hope this helps! :)