Choose the correct product of (6x - 2)(6 x + 2).

A statement which could be true for g is that: A. g(-13) = 20.

A domain can be defined as the set of all real numbers for which a particular function is completely defined.

Since the domain of this function is given by -20 ≤ x ≤ 5, it simply means that the value of x must between -20 and 5. Also, with a range of -5 ≤ g(x) ≤ 45, the value of x must between -5 and 45.

By extrapolating the function, we can deduce that:

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Complete Question:

Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.

A. g(-13) = 20

B. g(-4) = -11

C. g(7) = -1

D.g(0) = 2

Answer: [tex]f(x)=\begin{cases} x^2 +4, x < 3 \\ -x+4, x \geq 3 \end{cases}[/tex]

Step-by-step explanation:

By inspection, we know the equation of the parabola is [tex]y=x^2 +4[/tex] and the equation of the line is [tex]y=-x+4[/tex].

Since there is an open hole at x=3 for the parabola and a closed hole at x=3 for the line, the function is

[tex]f(x)=\begin{cases} x^2 +4, x < 3 \\ -x+4, x \geq 3 \end{cases}[/tex]

The bearing angle exists 53.49°.

A bearing of 36° corresponds to the corresponding angle of

θ = 90 -36 = 54°

The (x, y) values for the position of the ship after achieving its first heading exist:

[tex]x_1[/tex] = 12.1 Cos 54° = 7.11 m

[tex]y_1[/tex] = 12.1 Sin 54° = 9.78 m

Our second displacement exists a simple 4.6 mi due east, that exists, the positive x-direction. The components exist therefore

[tex]x_2[/tex] = 6.1 mi

[tex]y_2[/tex] = 0 mi

To find the total displacement from the port, we'll add these two vectors' components and use the distance formula:

Δx [tex]= x_1+x_2[/tex]

= 7.11 mi + 6.1 mi = 13.21 mi

Δy [tex]=y_1+y_2[/tex]

= 9.78 mi + 0 mi = 9.78 mi

[tex]$r=\sqrt{(x_{total})^2+(y_{total})^2}[/tex]

[tex]=\sqrt{(13.21mi)^2+(9.78mi)^2}[/tex]

= 16.43 mi

The direction of the displacement vector exists given by

tan θ = Δy/Δx

θ = arc tan (Δy/Δx)

= arc tan (9.78/13.21)

= 36.51°

The question requested for the bearing angle, which exists just this angle subtracted from 90°:

90° - 36.51° = 53.49°.

Therefore, the bearing angle exists 53.49°.

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Using the commutative property for (-5) * 8, we can say that;  (-5) * 8 = 8 * (-5)

The commutative property of algebraic multiplication states that changing the order of factors does not change the product. For example:

4 × 3 = 3 × 4

Similarly, 5 * 6 = 6 * 5

Now, we want to use commutative property to use (-5) * 8. Thus, we can say that;  (-5) * 8 = 8 * (-5)

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Answer: 23.1

Step-by-step explanation:

[tex]\frac{x}{14}=\frac{33}{20}\\\\x=\frac{(33)(14)}{20}\\\\x=23.1[/tex]

Answer:

5/25

Step-by-step explanation:

The values of the probabilities are

The image that completes the question is added as an attachment

From the attached graph, we have:

P(x) = 0.109 when x = 4

Hence, the probability is 0.109

From the attached graph, we have:

P(x) = 0.109 when x = 4

P(x) = 0.093 when x = 5

So, we have:

P(4 or 5) = 0.109 + 0.093

Evaluate

P(4 or 5) = 0.202

Hence, the probability is 0.202

This is represented as:

P(x >= 6)

From the attached graph, we have:

P(x) = 0.022 when x = 6

P(x) = 0.036 when x = 7

P(x) = 0.048 when x = 8

So, we have:

P(x >= 6) = 0.022 + 0.036 + 0.048

Evaluate

P(x >= 6) = 0.106

Hence, the probability is 0.106

This is calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

E(x) = 0.234 * 1 + 0.291 * 2 + 0.167 * 3 + 0.109 * 4 + 0.093 * 5 + 0.022 * 6 + 0.036 * 7 + 0.048 * 8

Evaluate

E(x) = 2.986

Approximate

E(x) = 3

Hence, the expected number of births is 3

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Answer:

Step-by-step explanation:

A) The median number is just the middle number so it should be 2.8

B) Bottom 30% are the six lowest amounts. The highest of the bottom six numbers is 2.3. Not sure what it means by calculating them. 1.8, 1.9, 1.9, 2.0, 2.1, and 2.3 are the lowest six. If you need to add them up the answer is 12.
C) I don’t know what your Q1 is.

I would be better to purchase whole onions at $1.99 per pound, and cut them yourself

Number of bowls = 50

Weight of each bowl = 8

Total weight of the onion soup = 8 x 50 = 400 ounces

Note that:

1 pound = 16 ounces

Total weight in pounds = 400/16

Total weight in pounds = 25 pounds

If you buy the whole onions and purchase at $1.99 per pound

Total cost = 25 x 1.99 = $49.75

If you purchase pre-sliced onions at $2.99 per pound

Total cost = 25 x $2.99 = $74.75

Since it is cheaper to purchase whole onions at $1.99 per pound, it is the better choice

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Answer:

C) 100

Step-by-step explanation:

250+600-350-400

850-350-400

500-400=100

The graph that includes the possible values for the number of people who still need to sign up for the team is:

Number line with closed circle on 5 and shading to the right.

Researching this problem on the internet, a team currently has 4 players, and needs at least 9.

When x players are signed, the number of players will be of 4 + x. Since the team needs at least 9 players, the inequality is:

[tex]4 + x \geq 9[/tex]

The solution is:

[tex]x \geq 9 - 4[/tex]

[tex]x \geq 5[/tex]

Which is represented as follows:

Number line with closed circle on 5 and shading to the right.

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Answer:

Step-by-step explanation:

Given inequalities below and we are looking for a pair with no solution.

Let's verify:

A) x > 3 and x < 2,

B) x > - 3 and x < - 2,

C) x > - 3 and x < 2,

D) x > - 3 and x > - 2,

The answer is x=21 the explanation is on the picture above I hope I helped

If the current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream then the speed of the boat in still water is 21 miles per hour.

Speed is the distance covered by an object in a certain time period. It is also known as velocity. The formula of speed is as follows:

Speed=Distance/ Time.

We have been given that the speed of stream is 7miles per hour.

Let v be the speed of the boat, and t the time to travel

98=t*(7+v) (1)

49=t(v-7) (2)

(1)+(2) => 2tv=147

7t+(49+7t)=98

14t+49=98

14t=49

t=49/14

t=7/2

Put the value of t in equation 1 to get the value of v:

98=t(7+v)

98=7/2(7+v)

196/7=7+v

28=7+v

v=28-7

v=21

Hence if the current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream then the speed of the boat in still water is 21 miles per hour.

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Answer:

(4,-5)

Step-by-step explanation:

The graph of the given function, y = 2eˣ, is given below

From the question, we are to determine the graph of the given function

The given function is

y = 2eˣ

The graph of y = 2eˣ is shown below

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The points that are a horizontal distance of 6 and a vertical distance of 2 from the origin are (6, 2), (-6, 2), (6, -2), (-6, -2)

Points are undefined terms in geometry, however they are used to represent the coordinate or location of items in a coordinate plane

The features of the point are given as:

Horizontal distance = 6

Vertical distance = 2

The above means that:

x = 6

y = 2

The points are then represented as:

(x, y) = ±(x. y)

So, we have

(x, y) = ±(6, 2)

When the above equation is expanded, we have

(x, y) = (6, 2), (-6, 2), (6, -2), (-6, -2)

Next, we plot the points on a coordinate plane

See attachment for the graph of the plane

Hence. the points that are a horizontal distance of 6 and a vertical distance of 2 from the origin are (6, 2), (-6, 2), (6, -2), (-6, -2)

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Answer:

lcm of 3,6,9 is 18

Answer: All real numbers

Step-by-step explanation:

The domain and range of all linear functions is the set of real numbers.

Answer:

x = 34

Step-by-step explanation:

complementary angle sum to 90°

sum the 2 angles and equate to 90

x + x + 22 = 90

2x + 22 = 90 ( subtract 22 from both sides )

2x = 68 ( divide both sides by 2 )

x = 34

Answer:

52 and 3

Step-by-step explanation:

17x+1 + 1x =55

18x+1=55

18x=54

x=3

Answer:

  x = 35

Step-by-step explanation:

The angle sum theorem can be used to find the congruent vertical angles RET and IEV. The equation relating these can be solved for x.

The missing angle in triangle IVE is found using the angle sum theorem:

  ∠IVE +∠VIE +∠IEV = 180°

  ∠IEV = 180° -50° -70° = 60°

Vertical angles RET and IEV are congruent:

  ∠RET = ∠IEV

  2x -10 = 60

  2x = 70 . . . . . . . . add 10

  x = 35 . . . . . . . . divide by 2

The value of x from the given conditions is 35.

The  line TV and RI intersect at E.

The measure of IVE=50° and the measure of VIE=70°.

Since, the points V, I and E makes a triangle.

Therefore, the total angle inside the triangle is 180°.

Hence,

∠IVE + ∠VIE + ∠VEI = 180°

50°+70°+ ∠VEI = 180°

∠VEI = 180°-50°-70°

∠VEI = 60°

Also the angles ∠VEI and the angle ∠RET are congruent.

Therefore, ∠VEI = ∠RET

60° = 2x-10

2x = 70

x = 70/2

x = 35.

The lines TV and RI intersect at E. If the measure of IVE=50, the measure of VIE=70 and the measure of RET=2X-10. Then the value of x = 35.

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By using Microsoft excel to plot the data on a scatter plot, the linear regression equation can best be represented by: A. y = 12.11.1.36^x

A regression line can be defined as a statistical line that best describes the behavior of a data set and such, it is a line that best fits a set of data.

By using Microsoft excel to plot the data on a scatter plot, we can logically deduce that linear regression equation for the x-values and log(y)-values is given by:

y = 12.11.0.30^x

Thus, it can best be represented by: y = 12.11.1.36^x

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The factors of 4x^2 +8x-5 are (2x-1) and (2x+5)

If the parent function is transformed by:

The graph of the parent function is a parabolic curve which opens in the y-axis direction and with its vertex at the origin on a cartesian coordinate.  

By critically observing the graph of this parent function [f(x) = x²], we can infer and logically deduce that the transformed curve is a downward opening parabola which has a vertex at (-5, -2).

Thus, if the parent function is transformed by:

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Answer:

Step-by-step explanation:

Use the mean and the standard deviation obtained from the last discussion and test the claim that the mean age of all books in the library is greater than 2005.

This is the last discussion:

The science portion of my library has roughly 400 books.

They are arranged, on shelves, in order of their Library of Congress

code and, within equal codes, by alphabetical order of author.

Sections Q and QA have a total of 108 books.

The bulk of the library was established in the early 1990s.

I used a deck of cards, removing the jokers and face cards, keeping

only aces (1) and "non-paints" (2 to 10). Starting from the start of

the first shelf, I would turn a card (revealing its number N) and I

would go to the Nth book. This uses ordinal numbers (1 would means the

"first" book, not a gap of 1).

The cards were shuffled sufficiently to assume that the cards have a

random order.

I sampled only the LC subsections Q and QA (therefore, not a true

sample of the entire library, as this classification is not purely

random).

Thus, I picked 21 books (the expected number being 108/5.5 = 19.6 --> 20 books)

The sampled dates of publication were (presented as an ordered set):

1967, 1968, 1969, 1975, 1979, 1983, 1984,

1984, 1985, 1989, 1990, 1990, 1991, 1991,

1991, 1991, 1992, 1992, 1992, 1997, 1999

The median date is 1990

The mean date is 1985.67

Variance = 84.93 ( Sum of (date-mean)^2 )

SQRT of variance = 9.2 (sample standard deviation)

The "sigma-one" confidence interval (containing 68% of the books), if

the sample were NOT skewed, and if the distribution were "normal"

would contain dates from "mean - 9.2" to "mean + 9.2"

Sigma-2 (95%) would have mean - 2(9.2) to mean + 2(9.2)

Sigma-3(99.7%) from "1985.67 - 3(9.2)" to "1985.67 + 3(9.2)"

1958.07 to 2012.6

There, you see one reason why the distribution is skewed (it is

possible to have books older than 1958, but it is impossible to have

book newer than 2012), but it still represents a usable model for the

library. If it applies to the entire library of 400 books, you would

expect one book (0.3% of 400) to fall outside the 3-sigma interval.

648 is the three-digit positive integers have three different digits

According to the statement

we have given that there are three positive digit number are formed with three distinct digits.

And we have to find that the how many words are formed with distinct numbers.

So, to solve this type of problem the Combination formula is best.

Because it provides the all possibilities that from how many ways numbers are formed.

So, from a combination formula

here we take 9 two times because first time when we let a number then remaining numbers are 9.  and second time remaining numbers are also 9 because we let the distinct number but for third number there will be a probability that choosing number will be same.

So, Three digit positive number become from 9*9*8 =648

So, 648 is the three-digit positive integers have three different digits.

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The weighing of the man on the earth given the ratio is 174 pounds

Equate the ratio

6 : 1 = x : 29

6/1 = x/29

6 × 29 = 1 × x

174 = x

x = 174 pounds

Complete question:

The ratio of the weight of an object on the earth to the moon is 6:1. If a man weighs 29 pounds on the moon, calculate his weighing on the earth.

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Answer: 14.8

Step-by-step explanation: If the number in the hundredths place is less than 5, you must round down. On the contrary, if that number is 5 or greater, you must round up. This applies for rounding to any place not just the tenths place. For example, if you were to round it to the ones place, the answer would be 15.

Answer:

14.8

Step-by-step explanation:

The hundredth is smaller than 5, therefore you have to round down.

hope it helps

The expected value of betting 32 is -$0.053, making the 4th option the right choice.

In the question, we are asked for the expected value of betting on 32, given that if we bet $1 on the number 32 and win, the house pays $36, and there are 38 slots.

The probability distribution can be shown as:

 x       $35       -$1

p(x)    1/38      37/38

as, if we get 32, which has the probability of 1/38, the winning number, we gain $35, and for the rest, having a probability of 37/38, the losing number, we lose -$1.

Thus, the expected value can be calculated as E(x) = ∑x.p(x).

Thus, the expected value = $35(1/38) + (-$1)(37/38) = -$2/38 = -$0.05263 ≈ -40.053.

Hence, the expected value of betting 32 is -$0.053, making the 4th option the right choice.

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