Question 8 of 10
What
transformation was not done to the linear parent function, f(x) = x, to
get the function g(x) = -1/(x+5)+7?
A. Shifted up 7 units
B. Shifted right 5 units
C. Vertically compressed by a factor of 2
D. Reflected over the x-axis

Answer:

volume = 33.5 in³

Step-by-step explanation:

Formula:

\(\sf volume \ of \ a \ cone=\dfrac13\pi r^2h\)

Given:

Substituting the given values into the formula:

\(\sf \implies volume=\dfrac13 \times 3.14 \times 2^2 \times 8\)

                  \(=\dfrac13 \times 3.14 \times 4 \times 8\)

                  \(\sf =33.49333333...\)

                  \(\sf =33.5 \ in^3 \ (nearest \ tenth)\)

There are 4 hundred billions in the number 432,845,979,484.

To determine how many hundred billions are in the number 432,845,979,484, we need to consider the place value of the hundred billions digit.

The number 432,845,979,484 has 12 digits, and we count the digits from right to left, starting with the units place. The digit in the hundred billions place is the seventh digit from the right.

Let's break down the number:

4 hundred billions (4 x 100,000,000,000)

3 ten billions (3 x 10,000,000,000)

2 billions (2 x 1,000,000,000)

8 hundred millions (8 x 100,000,000)

4 ten millions (4 x 10,000,000)

5 millions (5 x 1,000,000)

9 hundred thousands (9 x 100,000)

7 ten thousands (7 x 10,000)

9 thousands (9 x 1,000)

4 hundreds (4 x 100)

8 tens (8 x 10)

4 units (4 x 1)

As we can see, there are 4 hundred billions in the number 432,845,979,484.

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Based on Kendall's interests and lack of skill playing baseball, a good career choice for him would be a football coach. So correct option is A.

Baseball is a bat-and-ball game that is played between two teams of nine players each. The objective of the game is to score runs by hitting a ball thrown by the opposing team and running around a series of four bases on a diamond-shaped field.

The game is typically played in nine innings, with each team taking turns at bat and in the field. The team in the field tries to prevent the other team from scoring by catching the ball and getting the opposing players out, while the team at bat tries to score runs by hitting the ball and running around the bases.

Baseball is a popular sport in many countries, particularly in the United States, where it is often referred to as "America's pastime." It has a rich history and culture, with many famous players, teams, and moments that have become part of popular culture.

Based on Kendall's interests and lack of skill playing baseball, a good career choice for him would be a football coach. Coaching allows him to be involved in the sport he enjoys and make a career out of it, without requiring him to have exceptional athletic ability. As a coach, he can use his knowledge of the sport to teach and train players, develop strategies, and lead a team to success.

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Answer:

225 stickers

Step-by-step explanation:

(900+450)/2 = 1,350/2= 675

so, Carla shared with Justin :

900-675 = 225 stickers

Answer:

  maybe

Step-by-step explanation:

It depends on your strategy for determining ordered pairs.

A straightforward interpretation of the problem would say 1 roll gives an x-value, and the next roll gives the corresponding y-value. If that is the strategy, in 10 rolls, there will be repeats of the x-value. So, the pairs cannot represent a function.

__

If you adopt a different strategy, such as using the rolled number as the tens digit of the x-value, and sequentially assigning the numbers 0 to 9 to the units digit of the x-value, then all of the x-values will be different. Regardless of how you arrive at the y-values, the result will always be a function when graphed.

__

Basically, any strategy that makes it likely that the x-values will be different makes it likely that the relation will be a function. Otherwise, it is unlikely (or impossible) that the relation will be a function.

In summary, days of the month can be considered as an example of categorical data, specifically ordinal data, since they have a natural ordering but the differences between categories are not necessarily equal.

Categorical data is a type of data that represents characteristics or qualities of a group of individuals or objects. It is a type of data that is divided into categories or groups based on specific characteristics or attributes. Categorical data is sometimes also referred to as qualitative data. Categorical data can be further divided into two subtypes: nominal and ordinal data. Nominal data is characterized by categories that have no natural order or ranking, such as colors, names, or categories of a variable. For example, the color of a car (red, blue, green) is nominal data. Ordinal data, on the other hand, is characterized by categories that have a natural order or ranking, such as rankings, levels, or scores. For example, a student's grade level (freshman, sophomore, junior, senior) is ordinal data.

Here,

In the case of days of the month, each day can be classified into a specific category or group, which is the corresponding day number. For example, we can classify January 1st, 2023 as day 1, January 2nd, 2023 as day 2, and so on.

Categorical data is typically divided into two types: nominal and ordinal. Nominal data is characterized by categories that have no natural order or ranking, while ordinal data is characterized by categories that have a natural order or ranking.

Days of the month can be considered as ordinal data since they have a natural ordering from 1 to 31 (or 28/29/30 in the case of February). However, it is important to note that the difference between the days is not necessarily equal, meaning that the distance between, for example, day 1 and day 2 is not the same as the distance between day 15 and day 16.

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Answer:

(1) 0.125

(2) 0.125

Step-by-step explanation:

The total number of possible outcomes is:

N = 8

(1)

Compute the probability that the number picked is between 3 and 5 as follows:

Number of Favorable outcomes = 1

The probability is:

P (Number picked is between 3 and 5) = 1/8 = 0.125

Thus, the probability that the number picked is between 3 and 5 is 0.125.

(2)

The number usually picked appears to be in in the range [3,5], i.e. the numbers could be, {3, 4 or 5}.

Number of Favorable outcomes = n (Number < 4 and within [3, 5]) = 1

P (less than 4 ∩ within [3, 5]) = 1/8 = 0.125

Thus, the probability that the number picked is less than 4 knowing that the number usually picked appears to be in in the range [3,5] is 0.125.

A. The distributions of the periods is that using the five number summary is that

B. The box and whisker plot of the periods is attached

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

7th Period

66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96

3rd Period

52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97

The distributions of the periods will be compared using the five-number summaries

Using a graphing tool, the five-number summaries are:

7th Period

3rd Period

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

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Answer:

45

Step-by-step explanation:

The simplified form of 7 log3x + 4 log3z - 6 log3y is log3(x^7 z^4 / y^6).

We can simplify the expression using the following logarithmic rule:

log a + log b = log ab (product rule)

log a - log b = log(a/b) (quotient rule)

c log a = log a^c (power rule)

Using these rules, we can simplify 7 log3x + 4 log3z - 6 log3y as follows:

7 log3x + 4 log3z - 6 log3y

= log3x^7 + log3z^4 - log3y^6 (using the power rule)

= log3(x^7 z^4 / y^6) (using the quotient rule)

Therefore, the simplified form of 7 log3x + 4 log3z - 6 log3y is log3(x^7 z^4 / y^6).

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Answer:

3  3/8

Step-by-step explanation:

3.5/8 - 1/4 =  3   5/ 8 - 2/8  = 3  3/8

Answer:

1 * 10^16 or 10000000000000000

Step-by-step explanation:

Answer: 1e+16 or 10000000000000000

Step-by-step explanation: Just multiply it

Answer:

0.66 melones por niño o 2/3

Step-by-step explanation:

10/15=2/3=0.66

The solution of the given system of equations is (4, 7).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are y=3x-5 -------(I) and y=1/2 x+5 -------(II)

Substitute equation (I) in (II), we get

3x-5=1/2 x+5

3x-1/2 x=5+5

2.5x=10

x=4

Substitute x=4 in equation (I), we get

y=3(4)-5

y=7

So, solution is (4, 7)

Therefore, the solution of the given system of equations is (4, 7).

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Answer:

2^12

Step-by-step explanation:

Answer:

Converting the equation \(x^2-20x+13=0\) into completing the square method we get: \(\mathbf{(x-10)^2=87}\)

Step-by-step explanation:

we are given quadratic equation: \(x^2-20x+13=0\)

And we need to convert it into completing the square method.

Completing the square method is of form: \(a^2-2ab+b^2=(a-b)^2\)

Looking at the given equation \(x^2-20x+13=0\)

We have a = x

then we have middle term 20x that can be written in form of 2ab So, we have a=x and b=? Multiplying 10 with 2 we get 20 so, we can say that b = 20

So, 20x in form of 2ab can be written as:  2(x)(10)

So, we need to add and subtract (10)^2 on both sides

\(x^2-20x+13=0\\x^2-2(x)(10)+(10)^2-(10)^2+13=0\\(x^2-2(x)(10)+(10)^2) \:can\: be\: written\: as\: (x-10)^2 \\(x-10)^2-100+13=0\\(x-10)^2-87=0\\(x-10)^2=87\)

So, converting the equation \(x^2-20x+13=0\) into completing the square method we get: \(\mathbf{(x-10)^2=87}\)

Answer:

Answer:

3.5

Step-by-step explanation:

42/12=3.5

The table with the correct values for A, B and C is given as follows:

Black 9 36 63 90

White 13 52 91 130

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The input and output variables for this problem are given as follows:

Then the constant k is obtained as follows:

91 = 63k

k = 91/63

k = 13/9.

Hence the equation is:

y = 13x/9.

Hence the values are given as follows:

Hence the first table is correct.

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

The best assessment of the linearity of the relationship between the day of the month and account balance would be "Because the residual plot has no obvious pattern, and the scatterplot appears linear, it is appropriate to use the line of best fit to predict the account balance based on the day of the month."The correct answer is option C.

When assessing linearity, it is important to examine both the scatterplot and the residual plot. The scatterplot is used to visualize the relationship between the variables, while the residual plot helps us assess the appropriateness of a linear model by examining the pattern of the residuals (the differences between observed and predicted values).

If the scatterplot appears reasonably linear, it suggests that there is a linear relationship between the variables. In this case, since the scatterplot appears linear, it supports the use of a linear model to predict the account balance based on the day of the month.

Furthermore, the residual plot is used to check for any patterns or systematic deviations from the line of best fit. If the residual plot exhibits no obvious pattern and the residuals appear randomly distributed around zero, it indicates that the linear model captures the relationship adequately.

Therefore, if the residual plot shows no obvious pattern, it provides further evidence in favor of using the line of best fit to predict the account balance based on the day of the month.

In conclusion, when the scatterplot appears linear and the residual plot shows no obvious pattern, it is appropriate to use the line of best fit to predict the account balance based on the day of the month.

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Answer:

person above

Step-by-step explanation:

the obvious

Looking at the given diagram,

PQ is parallel to RS

This means that

Triangle PQT is similar to triangle RST

We can say that

PT/RT = QT/ST

Given that

PT = 30 cm, QT = 60 cm

RP = 5 cm

RT = RP + PT = 5 + 30

RT = 35 cm

ST = QT + SQ = 60 + SQ

Therefore,

30/35 = 60/(60 + SQ)

By cross multiplying, it becomes

30(60 + SQ) = 35 * 60

1800 + 30SQ = 2100

30SQ = 2100 - 1800

30SQ = 300

SQ = 300/30

SQ = 10 cm

OPtion A is Correct

Keegan's error is assuming that the product of the slopes of any two sides of a triangle should be -1 for the triangle to be a right triangle.

To determine if the triangle LMN is a right triangle, Keegan should instead calculate the lengths of the three sides of the triangle and check if they satisfy the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

To correct his approach, Keegan should calculate the lengths of sides LM, MN, and NL using the coordinates of the vertices and then check if the Pythagorean theorem holds true.

If the squared length of one side is equal to the sum of the squares of the other two sides, then the triangle LMN is a right triangle.

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the equations are

y = x -14

y = x + 12

now we will evaluate the slope of both the line

for

y = x - 14

compare it with standard form of line

y = mx + C

here m is the slope of line

so for y = x - 14 the slope is coefficient of x

that is m = 1

now for

y = x + 12

m = 1

both the slopes are equal

so the both lines will be parallel to each other.

The simplified expression of 32/5 x 3(-7/5) is  -672/25

The mathematical expression is given as:

32/5 x 3(-7/5)

Evaluate the product of 3 and -7/5

32/5 x 3(-7/5) =  32/5 x -21/5

Evaluate the product of 32 and -21

32/5 x 3(-7/5) =  672/5 x -1/5

Evaluate the product of 5 and 5

32/5 x 3(-7/5) =  672/25 x -1

So, we have:

32/5 x 3(-7/5) =  -672/25

Hence, the simplified expression of 32/5 x 3(-7/5) is  -672/25

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The equation of the perpendicular bisector of the line segment with endpoints (-7, 2) and (-1, -6) is y = (3/4)x + 1.

To find the equation of the perpendicular bisector of a line segment, we need to determine the midpoint of the line segment and the slope of the line segment. The perpendicular bisector will have a negative reciprocal slope compared to the line segment and will pass through the midpoint.

Given the endpoints (-7, 2) and (-1, -6), we can find the midpoint using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Midpoint = ((-7 + (-1))/2, (2 + (-6))/2)

= (-8/2, -4/2)

= (-4, -2)

The midpoint of the line segment is (-4, -2).

Next, we need to find the slope of the line segment using the slope formula:

Slope = (y2 - y1)/(x2 - x1)

Slope = (-6 - 2)/(-1 - (-7))

= (-6 - 2)/(-1 + 7)

= (-8)/(6)

= -4/3

The slope of the line segment is -4/3.

Since the perpendicular bisector has a negative reciprocal slope, the slope of the perpendicular bisector will be 3/4.

Now, we can use the midpoint (-4, -2) and the slope 3/4 in the point-slope form of a line to find the equation of the perpendicular bisector:

y - y1 = m(x - x1)

y - (-2) = (3/4)(x - (-4))

y + 2 = (3/4)(x + 4)

y + 2 = (3/4)x + 3

y = (3/4)x + 1.

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The missing fourth vertex needed to create a rectangle is (25, 3) option D.

Vertices (singular: vertex) are the corners or points where two or more lines, edges, or curves intersect and form an angle.

Here, the width of one side of the rectangle;

⇒ +3 - (-6) = 9 unit                (left side y-coordinates)

Similarly the length of the rectangle;

⇒ 25 - (-15) = 40 unit             (up-side x-coordinates)

Since a rectangular shape has two sets of equal sides of equivalent width (y-coordinates) and length (x-coordinates), we realize that the missing fourth vertex should be 9 units and 40 units over the point (25, -6). and (-15, 3)

So, we add 9 to the y-coordinate of (25, -6) and add 40 to the x-coordinate of (-15, 3) to get the missing vertex:

⇒ (25, -6+9) = (25, 3)

⇒ (-15+40, 3) = (25, 3)

Therefore, the missing fourth vertex is (25, 3)

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