A construction worker's starting salary is $43,000. Each year she receives a $1100 raise.
A.) Let an be the construction worker's salary in the nth year. Write an explicit formula of the form an = bn + c to model this situation.

an = 41,900 + 1100n

B.) Find a10 = $ 52,900

C.) In what year will her salary be $55,100? ________________

Answers

Answer 1

A) The explicit formula which model this situation will be;

⇒ an = $43,000 + $1,100n

Where, ''an'' be the construction worker's salary in the nth year.

B) The value of a₁₀ = $54,000

C) After 11 years her salary will be $55,100.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A construction worker's starting salary = $43,000.

And, Each year she receives a $1100 raise.

Now,

A) Let ''an'' be the construction worker's salary in the nth year.

So, We can formulate;

⇒ an = $43,000 + $1,100n

B) Since, The construction worker's salary in the nth year is,

⇒ an = $43,000 + $1,100n

Put n = 10, we get;

⇒ a₁₀ = $43,000 + $1,100 × 10

⇒ a₁₀ = $43,000 + $11,000

⇒ a₁₀ = $54,000

C) Let after n year her salary will be $55,100.

So, We can formulate;

⇒ an = $43,000 + $1,100n

⇒ $55,100 = $43,000 + $1,100n

Solve for n as;

⇒ $55,100 - $43,000 = $1,100n

⇒ $12,100 = $1,100n

⇒ n = 12,100 / 1,100

⇒ n = 11

Thus, After 11 years her salary will be $55,100.

Therefore, A) The explicit formula which model this situation will be;

⇒ an = $43,000 + $1,100n

Where, ''an'' be the construction worker's salary in the nth year.

B) The value of a₁₀ = $54,000

C) After 11 years her salary will be $55,100.

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Related Questions

4\5 of a liter of water filled 4\7 of a bucket. how many liters of water can the bucket hold?

Answers

The liters of water that the bucket hold is 5/7 liters of water.

What is a fraction?

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, 4/5 of a liter of water filled 4/7 of a bucket. The liters that it can hold will be:

= 4/7 ÷ 4/5

= 4/7 × 5/4

= 20 / 28

= 5/7

It can hold 5/7 liters.

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Pleaseeee helppp fastest and accurate answer will get the most points

Answers

Answer for a) is 15/2 gotten by multiplying 7•2 and adding 1.
b) is 11/3 gotten by multiplying 3•3 and adding 2.
c) is 27 and 1/2 gotten by changing the mixed numbers into the fractions above and multiplying then changing back into a fraction by dividing 165/6.
d) is 2 and 1/22 which is gotten by again changing the mixed numbers into fractions dividing by flipping 11/3 into 3/11 and multiplying which gives 45/22 which when divided gives you 2 and 1/22.

Please help me answer this question

Answers

The double angle results are;

sin 2x = 62/64

cos 2x = 14/64

tan 2x = 384/83

What is double angle?

We can see that it is possible for an angle to be given in the double angle format and we need to obtain the angles from it.

We know that sin x = 5/8

Using the Pythagoras theorem;

c^2 = a^2 + b^2

c = 8

a= 5

b= √c^2 - a^2

b = √ 8^2 - 5^2

b = √ 64 -25

b= 6.2

cos x = 6.2/8

Tan x = 5/6.2

Then;

sin2x = 2 sinxcosx

sin 2x = 2(5/8 × 6.2/8)

sin2x = 2(31/64)

sin2x = 62/64

cos 2x = 1 - 2sin^2x

cos 2x = 1 - 2(5/8)^2

cos 2x = 1 - 2(25/64)

cos 2x = 1 - 50/64

cos 2x = 14/64

Tan 2x = 2tan x/1 - tan^2 x

tan 2x = 2 (5/6.2)/1 - (5/6.2)^2

tan 2x = 10/6.2/1 - 25/38.4

tan2x = 10/6.2/13.4/38.4

tan2x = 10/6.2 * 38.4/13.4

tan 2x = 384/83

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What is the factored form of 16x^2 - 16x - 12?

Answers

Answer:

4(2x +1)(2x-3)

Step-by-step explanation:

What number is the abscissa of the point ( 8,7 )

Answers

In coordinate system, the number that is the abscissa of the point ( 8,7 ) is 8.

coordinate geometry:

It establishes a connection between geometry and algebra using curves and line graphs.

A point's x and y coordinates are also referred to as abscissa and ordinate, respectively.

The abscissa and ordinate all together are called coordinates.It is for a point in the Cartesian plane, an ordered pair is used as the symbol.

the abscissa is the x–coordinate of any point A(x, y).

so,

abscissa of the point ( 8,7 ) is 8.

In coordinate system, the number that is the abscissa of the point ( 8,7 ) is 8.

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8:24=26:X

Help me find the missing term.

Answers

Answer:

x = 78

Step-by-step explanation:

[tex]\frac{8}{24} =\frac{26}{x}[/tex]

==> cross multiply

26 x 24 = 8 x "x"

==> simplify

624 = 8x

==> divide both sides by 8

78 = x

Answer: x = 78

Step-by-step explanation:

It is 78 because if you cross-multiply, you get 624 = 8x. Then if you divide by 8 on both sides, you get x = 78.

b) If a-b=5 and a² + b² = 37, find the value of ab

Answers

The value of ab=6.

What is [tex](a-b)^2[/tex] formula ?

    To find the square of a binomial, use the [tex](a-b)^2[/tex] formula. One of the most common algebraic identities is the a minus b Whole Square Formula. This formula is also known as the difference between two terms squared formula. To factorise some special types of trinomials, the [tex](a-b)^2[/tex] formula is used.

Here [tex](a-b)^2 = a^2+b^2-2ab[/tex] then,

=> [tex](a-b)^2 = a^2+b^2-2ab[/tex]

Here a-b=5 and [tex]a^2+b^2[/tex] = 37.

=> [tex]5^2[/tex] = 37-2ab

=> 25 = 37-2ab

=> 2ab=37-25

=> 2ab = 12

=> ab=6.

Hence the value of ab=6.

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A farmer has 70 acres of land available for planting either soybeans or wheat. The
preparation cost per acre of land is $60 for soybeans and $30 for wheat. Soybeans
require 3 workdays per acre, while wheat requires 4 days. The farmer can make a
profit of $180 per acre of soybeans and $100 per acre of wheat. He cannot spend more
than $1800 in preparation costs and cannot use a total of more than 120 workdays.
How many acres of each crop should be planted to maximize the profit? What is the
maximum profit he can make off of these 70 acres?

Answers

The maximum profit for soybeans is 30 acres and the maximum profit for wheat is 60 acres.

The maximum profit from these 70 acres is $12600

What is profit?

Mathematically profit is considered the amount of gain from any business activity. Whenever a shopkeeper sells a product, his motive is to take advantage of the buyer in the name of profit. .

Given,

Total land = 70 acres

For soyabeans,

1 acre = $60 for 3days

⇒Profit=$180

Foe wheat,

1 acre = $30 for 4days

⇒Profit=$100

Working days must ≤ 120

Preparation cost ≤ 1800

For soyabeans,

60$ for 3 days

1800$ for ?

x = (1800×3)/60

x = 90 days

1 acre = 3 days

? = 90 days

x = 90/3

x = 30 acres

For wheat,

30$ for 4 days

1800$ for ?

x = (4×1800)/30

x = 240 days

1 acre for 4 days

? for 240 days

x = 240/4

x = 60 acres

The maximum profit for soybeans is 30 acres and the maximum profit for wheat is 60 acres.

Maximum profit is:

1 acre for 180$

70 acres for ?

x = (180×70)/1

x = $12600

The maximum profit from these 70 acres is $12600

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AP STATISTICS MATH
(Image above) PLEASE HELP THANK YOU (brainlist answer)

Answers

The probabilities are given as follows:

3. P(rides bus|owns a car) = 1/3.

4. P(red|organic) = 3/5.

How to calculate a probability?

The probability of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

For item 3, the outcomes are given as follows:

Desired outcomes: rides bus and owns a car -> 8 people.Total outcomes: owns a car -> 24 people.

Hence the probability is:

P(rides bus|owns a car) = 8/24 = 1/3.

For item 4, the outcomes are given as follows:

Desired outcomes: red and organic -> 18%Total outcomes: organic -> 30%.

The error was in identifying the total outcomes, and the probability is:

P(red|organic) = 18/30 = 3/5.

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PLEASE HELP will give brainly and 10 points Which inequality is represented by the number line graph?

Answers

Answer: A

Step-by-step explanation: The dot is a filled-in circle, meaning it has to be A, B, or E. Then, B is saying that the arrow is going left, so that's wrong. E is saying that it is just 6 instead of -6, which leaves us with A.

hope this helps!

please give brainliest!

In a two digit number, the ones digit is
twice the tens digit. If the gits are reversed, the new number is 36 more than the original What is the number

Answers

Answer:

I think 48!

Step-by-step explanation:

Translate the sentence into an equation.

The product of 5 and w is the same as w to the
third power.

Answers

Answer: 5w=w^3

Step-by-step explanation:

This is because the product means multiplication and so it would be 5w and then is in math is the same as equals so you have an equal sign and then it would w to the third power.


Choose ALL answers that describe the quadrilateral VWXYVWXY if VW = 15VW=15, WX = 15WX=15, XY = 15XY=15, YV = 15YV=15, and diagonals have equal length: VX = WYVX=WY.

Answers

A description of the quadrilateral VWXY that has equal length sides and equal length diagonals is that the quadrilateral is a square

What is a quadrilateral?

A quadrilateral is a polygon that has four sides and four vertices or corners, such that a quadrilateral ABCD has sides AB, BC, CD, and AD, and interior angles ∠A, ∠B, ∠C, and ∠D

The given description of the quadrilateral VWXY are;

VW = 15, WX = 15, XY = 15, YV = 15

The lengths of the sides of the quadrilateral VWXY are the same

The length the diagonals are the same;

VX = WY = VX = WY

The properties of a square are;

The interior angles are congruent and equal to 90°

The four sides have equal length

Opposite sides of a square are congruent

The length of the diagonals are the same

The the same length diagonals of quadrilateral indicates that the quadrilateral can be either a square or a rectangle

The property of the quadrilateral of equal length sides indicate that the quadrilateral is a square.

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How do you find the margin of error for the difference between means?

Answers

The margin of error can be calculated in two ways, depending on whether you have population parameters or sample statistics:

Margin of error (parameter) = critical value x population standard deviation Margin of error (statistic) = Critical value x Sample standard error

What is a margin of error?

A margin of error is a statistical metric that accounts for the difference between actual and projected survey results in a random sample.

In layman's terms, the margin of error measures the degree of unpredictability in data and research results. The margin of error formula is calculated by multiplying a critical factor. The result is then divided by the square root of the sample's number of observations.

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If you have 6 eggs and 2 bananas for 4 people, how many eggs and bananas would you need for 10 people?

Answers

Answer:

15 eggs

5 bananas

Step-by-step explanation:

6/4=x/10

6(10)=4x

60=4x

/4.  /4

15=x

We need 15 eggs

2/4=x/10

2(10)=4x

20=4x

5=x

We need 5 bananas


Or


6/4=1 1/2

Now we make 1 and 1/2 have a denominator of 10

1 5/10=15/10

Meaning 15 eggs

2/4=1/2=5/10

Meaning 5 bananas

Hopes this helps please mark brainliest

Answer:you would need 15 eggs and 5 bananas for 10 people

Step-by-step explanation:multiply the 6 eggs and 2 bannanas by 2 then add half more of each

sorry if this confuses you im not a good explainer

30. A big candle is made up of a pyramid with a slant height of attached to a cuboid with a square base of sides and a height of . (i) Calculate the volume of the candle. Another candle is made in the shape of a sphere. The volume of this candle is one-tenth the volume of the big candle. (ii) Show that the radius of the spherical candle is , correct to 3 significant figures. The diagram shows the plan view of a box holding two of the spherical candles. The candles just fit into the box in the shape of a cuboid. (iii) Calculate the volume of empty space in the box.30. A big candle is made up of a pyramid with a slant height of attached to a cuboid with a square base of sides and a height of . (i) Calculate the volume of the candle. Another candle is made in the shape of a sphere. The volume of this candle is one-tenth the volume of the big candle. (ii) Show that the radius of the spherical candle is , correct to 3 significant figures. The diagram shows the plan view of a box holding two of the spherical candles. The candles just fit into the box in the shape of a cuboid. (iii) Calculate the volume of empty space in the box.​

Answers

i) The volume of the candle is 48047.96 cubic cm. ii)the radius of the candle is 10.468 cm and iii)Volume of empty spaces in the box is 8749.73 cubic cm.

i) Slant height of the Pyramid = 39cm

Base length = 30 cm

Height of the pyramid part = √(39²-30²) = 24.92 cm

Volume of the pyramid part = 30 × 30 × 24.92 ÷ 3 = 7475.96 cm³

Height of the candle = 70 cm

Height of the cuboid= 70 - 24.92 = 45.08cm

Volume of the cuboid = 30 × 30 × 45.08 = 40572 cubic cm

Total volume of the candle = 7475.96 cm³ + 40572 cm³ = 48047.96 cm³

ii) Volume of the spherical candle = 0.1 × 48047.96 cm³ = 4804.79 cm ³

Now let the radius be r.

Hence 4/3 πr³ = 4804.79

or, r = 10.4679.. cm

or, r ≈ 10.468 cm

iii) Dimensions of the box = 10.468 × 2 = 20.94 cm

Height = 20.94cm

Width = 10.468 × 4 = 41.87 cm

Volume of the box = 41.87 × 20.94 × 20.94 = 18359.31 cubic cm

Volume of the candles = 4804.79 cm ³× 2 = 9609.58 cm³

Empty space in the box = 8749.73 cm³

Hence the empty spaces is 8749.73 cm³

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y=6/7x+11/7 in standard form

Answers

Answer:

6x-

7y

=

-11

6x-7y=-11

A phone company offers two monthly plans. Plan A costs $28 plus an additional $.0.10 for each minute of calls. Plan B has no initial fee but costs $.0.15 for each minute of calls. What amount of calling do the two plans cost the same

Answers

The amount of calling for which the two plans cost the same will be 525 minutes.

The cost when two plans cost the same amount is $68.25.

Write a slope-intercept equation for a line that passes through (-3,1) and (4, -13).

Answers

Answer:

[tex] \huge{ \bold{y = - 2x - 5}}[/tex]

Step-by-step explanation:

The equation of a line in slope-intercept form is represented by

y = mx + c

where

m is the slope

c is the y-intercept

First of all we have to find the slope from the two points given by using the formula

[tex]m = \frac{y_2 -y_ 1}{x_2 -x_1 } \\ [/tex]

where

(x1, y1) and (x2, y2) are the points

From the question the points are (-3,1) and (4, -13)

We have

[tex]m = \frac{ - 13 - 1}{4 - - 3} = \frac{ - 13 - 1}{4 + 3} = - \frac{14}{7} = - 2 \\ [/tex]

Next we find the y-intercept 'c' by placing one of the points and the slope into the slope-intercept form equation

Using point (-3,1) and m = -2

We have

[tex]1 = ( - 2)( - 3) + c \\ 1 = 6 +c \\ c = 1 - 6 = - 5[/tex]

Since we have both m and c we can place it into the main equation to find the equation

Using point and m = -2 c= -5

We have the final answer as

[tex] \bold{y = - 2x - 5}[/tex]

Hope this helps you

Select the correct answer. Which statement best describes the solution set to this inequality? 0 < 8 + x < 17 A. The solution set includes all values of x greater than 8 and less than 25. B. The solution set includes all values of x less than -8 or more than 9. C. The solution set includes all values of x greater than -8 and less than 9. D. The solution set includes all values of x less than 8 or more than 25.

Answers

The correct option is C.

The statement best describes the solution set to the inequality as the solution set includes all values of x greater than -8 and less than 9.

Inequality: An inequality is an expression that shows an unequal comparison of two or more numbers and variables.

Given that:

Inequality

0 < 8 + x < 17

Adding on both sides by -8.

=> 0 - 8 < 8 + x - 8 < 17 - 8

=> -8 < x < 9

The solution set is (-8,9).

Therefore, the solution set includes the value of x greater than -8 and less than 9.

Hence, the correct statement that best describes the solution is option C.

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I’m just really confused

Answers

Answer:

27

Step-by-step explanation:

cancel out the dilation by multiplying it by the reciprocal

18 x 3/2

27

I'm 80% sure

Answer:

12 is the answer

Step-by-step explanation:

you need to multiply the pre-image (the letters without an apostrophe beside it) with the dilation number (2/30)

A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 40 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16t²+40t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at 1.25 second(s) after launch. (Simplify your answer.)
The maximum height reached by the object is _____ feet. (Simplify your answer.)

Answers

The rocket reaches its maximum height at 1.25 second(s) after launch

The maximum height reached by the object is 32 feet.

Time to reach the maximum height

The function is given as

h(t) = -16t² + 40t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 40

Set to 0

-32t + 40 = 0

So, we have

32t = 40

Divide by 32

t = 1.25

Hence, the time is 1.25 seconds

The maximum height

In (a), we have

t = 1.25

Substitute t = 1.25 in h(t) = -16t² + 40t + 7

h(1.25) = -16(1.25)² + 40(1.25) + 7

Evaluate

h(1.25) = 32

Hence, the maximum height is 32 feet

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i need help asap with this question

Answers

Answer:

C

Step-by-step explanation:

to find the unit rate divide miles travelled by petrol used , that is

60 [tex]\frac{2}{3}[/tex] ÷ 4 [tex]\frac{2}{3}[/tex] ← change mixed numbers to improper fractions

= [tex]\frac{182}{3}[/tex] ÷ [tex]\frac{14}{3}[/tex]

• leave first fraction, change ÷ to × , turn second fraction ' upside down'

= [tex]\frac{182}{3}[/tex] × [tex]\frac{3}{14}[/tex] ( cancel 3 on numerator/ denominator )

= 182 × [tex]\frac{1}{14}[/tex]

= [tex]\frac{182}{14}[/tex]

= 13

the car travels 13 miles per gallon of petrol

The difference of the cubes of two consecutive positive even integers is 56. Find the integers.​

Answers

Step-by-step explanation:

(x+2)³ - (x)³ = 56

(x²+4x+4) (x+2) - (x)³ = 56

x³ + 2x² +4x²+ 8x + 4x + 8 -x³ = 56

6x² + 12x + 8 = 56

6x² + 12x - 48 = 0

x² + 2x - 8 = 0

(x+4) (x-2) = 0

x = -4

x = 2

the integers are 2 and 4

The required two consecutive positive even integers are 2, and 4.

What is an integer?

A number which is not a fraction, and it is a whole number.

For example -1,-2,-3,0,1,2 etc. are integers.

Let two consecutive even numbers are x and x+2,

According to given condition, the difference of cube of x and x+2 is 56,

Implies that,

(x+2)³ - (x)³ = 56

x³ + 8 + 3.x².2+ 3.x.2² -x³ = 56

6x² + 12x - 48 = 0

x² + 2x - 8 = 0

x² + 4x - 2x - 8 = 0

x = -4, 2

Both the integers are positive, so the value of x can't be negative.

Therefore, x=2 and x+2 = 4

So the integers are 2 and 4.

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help me out thank you so much

Answers

The pairs of equations and their responses are below

(1/5)^2 + 1 and 2 12/25 No

(1 + 1/4)^2 and 2 - 7/16 Yes

How to know if the expressions will form equations

This is done by solve both sides of the equation. If they have same answer then they can form equation. If otherwise they they cannot form equation

solving the first expressions

left hand side

(1/5)^2 + 1

= 1/25 + 1

= 26/25

right hand side

2 * 12/25

= 24/25

comparing the two sides shows that  the 26/25 ≠ 24/25

solving the second expressions

left hand side

(1 + 1/4)^2

= (5/16)^2

= 25/16

right hand side

2 - 7/16

= 25/16

comparing the two sides shows that  the 25/16 = 25/16solving the first part

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simon had ​$.30 he spent ​$6.97 at the mall ​, ​$11.37 at the dinner ​, and ​$5.50 at the arcade . How much money does have​ left?

Answers

Answer: $6.16

Step-by-step explanation:

Starting Amount: $30

30-6.97=23.03

23.03-11.37=11.66

11.66-5.50=6.16

The front of a brush fire is moving through some dead grass at a rate of 3 miles per hour. Luckily, it is moving directly toward the fire station, which can dispatch a fire truck to fight the blaze. If the fire station is 1 mile away and the truck can travel straight to the fire's front at 44 miles per hour, how long will it be before the fire truck reaches the fire's front?

Answers

The fire truck, a mile away, traveling at 44 miles per hour towards the the bush fire, which is also traveling towards at 3 miles per hour towards it, reaches the fire's front in 1/47 hours or approximately 76.6 seconds

How many minutes are there in one hour?

There are 60 seconds in a minute and 60 minutes in an hour, which makes 60 × 60 = 3600 seconds in one hour.

The rate at which the bush fire is moving, v₁ = 3 miles per hour

The direction the bush fire moves = Towards the fire station

Distance of the bush fire from the fire station, d = 1 mile

Speed of the fire truck, v₂ = 44 miles per hour

The equation that gives the time, t, the fire truck reaches the fire front is presented as follows;

v₁·t + v₂·t = d

Which gives; 3 × t + 44 × t = 1

47 × t = 1

[tex]t = \dfrac{1}{47}[/tex]

The time it takes the fire truck to reach the bush fire is 1/47 of an hour, which is approximately 76.6 seconds

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Solve: 12x² +5x-4_122x+6
Ox=2
O x = -5
O x = 2, x = -5
Ono solution

Answers

Assuming the _ is an equal sign and the equation isn’t mistyped, the answer is not listed above! Not sure if it helps!

Solution of the expression are,

⇒ x = - 5, x = 2

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ [tex]12^{x^{2} + 5x - 4} = 12^{2x + 6}[/tex]

Now, We can compare as;

⇒ x² + 5x - 4 = 2x + 6

Solve for x as;

⇒ x² + 3x - 10 = 0

⇒ x² + 5x - 2x - 10= 0

⇒ x (x + 5) - 2 (x + 5) = 0

⇒ (x + 5) (x - 2) = 0

⇒ x = - 5, x = 2

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A statistics student is interested in the relationship
between the number of aunts and uncles a person has
and the number of cousins. She surveys a simple
random sample of 12 people and asks them how many
of each they have. She calculates the least-squares
regression line and finds the equation is ý = 2.6 +
1.64x, where y is the number of cousins and x is the
number of aunts and uncles. The residual plot is
shown.
Based on the residual plot, is the linear model
appropriate?
No, the residuals are relatively large.
No, there is a clear pattern in the residual plot.
Yes, there is no clear pattern in the residual plot.
Yes, about half of the residuals are positive and half
are negative.

Answers

The answer is,

Yes, the residual plot lacks a recognizable pattern.

So, the correct option is c

What is a simple random sampling?

A simple random sample, in which each participant has an equal chance of being chosen, chooses a small, random portion of the whole population to represent the entire data set.

Researchers may produce an uncomplicated random sample by using methods like lotteries or random draws.

A sampling error may have occurred if the sample does not accurately reflect the population it is supposed to represent.

By selecting values at random from a population and giving each item a series of values, simple random samples are produced.

Simple random sampling is a sample design option to systematic, stratified, or cluster sampling.

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Which of the following shows the extraneous solution to the logarithmic equation log7 (3x³ + x)-log7(x)=2?
O x=-16
Ox=-4
Ox=4
O x-16

Answers

Answer: x=16

Step-by-step explanation:

log₇(3x²+x)-log₇x=2

Domian:

1)

3x²+x>0

x(3x+1)>0

-∞__+__-1/3__-__0__+__∞

x∈(-∞,-1/3)U(0,∞)

2)

x>0

Hence, x∈(0,∞)

Thus x∈(0,∞)

In this problem we use the following formula:

                       [tex]\boxed {log_ax-log_ay=log_a\frac{x}{y}}[/tex]

[tex]\displaystyle\\log_7(3x^2+x)-log_7x=2\\\\log_7(x(3x+1))-log_7x=2(1)\\\\log\frac{x(3x+1)}{x} =2(log_77)\\\\log(3x+1)=log_77^2\\\\log_7(3x+1)=log_749\\\\Hence,\\\\3x+1=49\\\\3x+1-1=49-1\\\\3x=48\\\\ Divide\ both\ parts \ of\ the \ equation\ by\ 3:\\\\x=16[/tex]

The extraneous solution to the logarithmic equation log7 (3x³ + x)-log7(x)=2 is x= 4.

What is Logarithm?

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number.

We have Logarithmic expression as

log7 (3x³ + x)-log7(x)=2

we know, [tex]log_ax - log_a y= log_a (x/y)[/tex]

Using the above property as

log7 (3x³ + x)-log7(x)=2

[tex]log_7[/tex] (3x³ + x) - [tex]log_7[/tex] x =2

[tex]log_7[/tex] x(3x² +1) / x = 2

[tex]log_7[/tex] (3x²+1) = 2(1)

[tex]log_7[/tex] (3x²+1) = 2(1)[tex]log_7 (7)[/tex]

[tex]log_7[/tex] (3x²+1) = [tex]log_7[/tex]7²

Now, comparing we get

3x² +1 = 7²

3x² = 48

x² = 16

x = 4

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