Lesson 2: Data Representations
The dot plot, histogram, and box plot represent the distribution of the same data in 3 different ways.
Battery life in hours

What information can be seen most easily in the dot plot

The present age of Paul is 52 years and the present age of Matt is 10 years.

We are given that two years ago, Paul =  7 times as Matt

Let the current age of Matt be x and of Paul be y

2 years ago, we will have that:

Age of Matt = x - 2

So, we get the equation as:

Age of Paul = 7 ( x - 2) = 7 x - 14

y - 2 = 7 x - 14

y = 7 x - 14 + 2

y = 7 x - 12

Also, we are given that to year from now, Paul = five times Matt

We get that:

y + 2 = 5 ( x + 2)

y + 2 = 5 x + 10

y = 5 x + 10 - 2

y = 5 x + 8

So, we get:

7 x - 12 = 5 x + 8

7 x - 5 x = 8 + 12

2 x = 20

x = 20 / 2

x = 10

y = 5 (10) + 2

y = 50 + 2

y = 52

Therefore, the present age of Paul is 52 years and the present age of Matt is 10 years.

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The HHT is more likely to appear first with a probability of 2/3.

The probability is an estimation of the likelihood that an event will occur. It assesses the event's certainty.

The formula for probability is given as;

P(E) = Number of Favourable Outcomes/Number of total outcomes.

Now according to the given question;

Only the second and third flips in the sequence matter. We understand the first flip is an H, and we're not interested in sequences that begin with T.

Lets start with the given format;

H _ _

If we get an HH_, the game is over and HHT will surely win (regardless of the number of heads we get, the next T is an automatic win). If we get an HTT, the game is over.

If we get an HTH, the game is a tie, and we must restart it.

Thus,

P(HHT) = 1/2

P(HTT) = 1/4

P(Draw) = 1/4

P(HHT wins) = P(HHT) / [1-P(Draw)]

                     = (1/2) / (1-1/4)

P(HHT wins) = 2/3

Thus, the probability of occurrence of HHT has more chances with 2/3.

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The quotient of the given division operation is -343. and The correct option is the first option -343.

According to the statement

We have to find that the value of the quotient.

So, For this purpose, we know that the

Quotient can be defined as the result of the division of a number by any divisor.

In other words, The result of the division is the quotient.

From the given information:

we are to determine the quotient of the given division operation

And

The statement become is:

[tex]\frac{-7^{2} }{-7^{-1} }[/tex]

Then we have to solve this

Then

[tex]\frac{49}{-7^{-1} }[/tex]

Then

49*-7

-343.

the quotient of the given division operation is -343.

So, The quotient of the given division operation is -343. and The correct option is the first option -343.

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Answer:

-343

Step-by-step explanation:

Edge

Answer:

(a) $126

(b) .453333%

Step-by-step explanation:

(a) 476 - 350 = $126

(b)

[tex]si = p \times r\times t \\ 476 = 350 \times r\times 3 \\ 476 = 1050r \\ \frac{476}{1050} = r \\ r = 0.453333\%[/tex]

Based on the shape of the back wall of Joe's bedroom and the dimensions of the rectangle, and the cost per square foot, the paper cost of the wall would be $1,105

First, find the area of the back wall of Joe's bedroom because this is the area that would need to be covered by the wall paper:

Area of rectangle = Length x Width

Solving gives:
= 17 x 13

= 221 square foot

The cost to cover the wall based on the cost in dollars of each square foot is:
= Number of square feet x Cost per square foot

= 221 x 5

= $1,105

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Thus L.H.S = R.H.S that is [tex]\frac{2}{\sqrt{3} cosx + sinx }[/tex]  = [tex]sec(\frac{\pi }{6-x} )[/tex] is proved

According to the question we have been given that

[tex]\frac{2}{\sqrt{3} cosx + sinx }[/tex]  = [tex]sec(\frac{\pi }{6-x} )[/tex]

And we need to prove that left hand side is equal to the right hand side.

To prove this we will solve the right-hand side of the equation first with the help of trigonometry identity. The right hand side of the equation is :

R.H.S = [tex]sec(\frac{\pi }{6-x} )[/tex]

          = [tex]\frac{1}{cos(\frac{\pi }{6-x} )}[/tex]

[As secƟ = 1/cosƟ)

           = [tex]\frac{1}{\frac{cos\pi }{6cosx} + \frac{sin\pi }{6sinx} }[/tex]

[As cos (X-Y) = cosXcosY + sinXsinY , which is a trigonometry identity where X = Π/6 and Y = x]

                   [tex]=\frac{1}{\frac{\sqrt{3} }{2}cosx + \frac{1}{2}sinx } \\= \frac{1}{\frac{\sqrt{3}cosx + sinx }{2} }\\=\frac{2}{\sqrt{3}cosx + sinx}[/tex]          

    R.H.S = L.H.S

or L.H.S = R.H.S

Hence [tex]\frac{2}{\sqrt{3} cosx + sinx } = sec(\frac{\pi }{6-x})[/tex] is proved

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Based on the side-angle-side congruent theorem/postulate, both triangles are congruent. the answers is SAS.

The side-angle-side congruence theorem (SAS) means that two triangles have two pairs of sides that are congruent to each other with a pair of included congruent angles in between the two pairs of congruent sides of both triangles, and thus, both triangles must be congruent to one another.

The diagram shows two triangles that share a common side which is a pair of congruent sides. It also shows a pair of another congruent sides that is marked congruent.

Also, we have a pair of included congruent angles that both triangles have.

Therefore, based on the side-angle-side congruent theorem/postulate, both triangles are congruent. the answers is SAS.

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Answer:B $20 an hour

Step-by-step explanation:

if you look at the graph, in one hour he made $20

The correct options for the linear combinations of the vectors are given by:

A, B, C, D, E and F.

The span between two vectors is the set that contains all linear combinations between these two vectors.

Supposing we have two vectors u1 and u2, as is the case in this problem, the infinitely many linear combinations have the following format:

k1u1 + k2u2

In which k1 and k2 are real numbers.

With k1 = 4 and k2 = -7, we get that option A is correct.

For option B, we have to see if it is possible to solve the following system.

The solution is k1 = k2 = 0, which are real numbers, hence option B is correct.

Both vectors u1 and u2 are part of the span, hence options D and F are correct. The size of the span is of infinity, hence option E is correct while option G is not.

The dimension of the span is of 3, as the vectors have 3 elements, hence option C is correct.

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There are at least two integer points in the line that passes through (5, - 8.5) and (13.8, 6.9).

In this problem we have a line that passes through two points on a Cartesian plane and herein we must check if that line contains at least one point with integer coordinates. First, determine the equation of the line:

Slope

m = [6.9 - (- 8.5)] / (13.8 - 5)

m = 7 / 4

Intercept

b = - 8.5 - (7 / 4) · 5

b = - 69 / 4

The equation of the line is y = (7 / 4) · x - 69 / 4.

Second, evaluate the equation of the line at different integers:

x= 6

y = (7 / 4) · 6 - 69 / 4

y = - 27 / 4

x = 7

y = (7 / 4) · 7 - 69 / 4

y = - 5

x = 8

y = (7 / 4) · 8 - 69 / 4

y = - 13 / 4

x = 9

y = (7 / 4) · 9 - 69 / 4

y = - 3 / 2

x = 10

y = (7 / 4) · 10 - 69 / 4

y = 1 / 4

x = 11

y = (7 / 4) · 11 - 69 / 4

y = 2

x = 12

y = (7 / 4) · 12 - 69 / 4

y = 15 / 4

x = 13

y = (7 / 4) · 13 - 69 / 4

y = 11 / 2

There are at least two integer points in the line that passes through (5, - 8.5) and (13.8, 6.9).

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The 4•x by 5•x inner dimensions of the 53 inches outer perimeter picture frame, the 1 inch wide frame and the 4 × 5 inch picture to be enlarged, gives;

a. The outer perimeter equation is presented as follows;

18•x + 8 = 53 inches

b. The scale factor required for the enlargement of the picture is 2.5

The dimensions of the photo = 4 × 5 inch

Width of the frame = 1 inch

Outer perimeter of the frame = 53 inches

The width of the inside of the picture frame = 4•x

The height of the inside of the picture frame = 5•x

a. The equation for the outer perimeter of the picture frame is therefore;

2 × (4•x + 1 + 1) + 2 × (5•x + 1 + 1) = 53

Which gives;

2 × (4•x + 2) + 2 × (5•x + 2) = 53

8•x + 4 + 10•x + 4 = 53

A simplified equation for the outer perimeter of the picture frame is therefore;

b. Solving the above equation, we have;

18•x + 8 = 53

18•x = 53 - 8 = 45

18•x = 45

Therefore;

x = 45 ÷ 18 = 2.5

x = 2.5

The width and height of the picture frame are therefore;

Width = 4•x = 4 × 2.5 = 10

Height = 5•x = 5 × 2.5 = 12.5

Which gives;

Width = 10 inches

Height = 12.5 inches

The enlargement factor, sf, is given by the ratio of a side of the picture frame to a side of the picture as follows;

sf = 12.5/5 = 2.5

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The distance of the boat from its destination depends on

So with these factors, the distance of the boat from its distance can be calculated.

The distance of the boat from the destination currently is 63 miles

Speed of the boat is 10 miles / hr

Let c be the speed of the river current and

h be the number of hours to reach a particular destination

So, the formula to find the distance of the boat from destination is given by

D = 63 - h(10 - c)

We need to find the formula for boat's distance from its destination after 3 hours

Thus h = 3 hrs

Let us substitute h in above equation, Then

D = 63 - 3(10 - c)

D = 63 - 30 - 3c

D = 33 - 3c

which is the formula for the boat's distance from its destination after 3 hours.

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The addition of the expression (1.38×10⁴) + (8×10³) written in scientific notation is "9 point 3 8 times 10 to the 7th power". option C

(1.38×10⁴) + (8×10³)

= (1.38 + 8) × 10^(4 + 3)

= 9.38 × 10^7

Options:

9.38×10⁴

2.18×10⁴

9.38×10^7

Therefore, the addition of the expression (1.38×10⁴) + (8×10³) written in scientific notation is "9 point 3 8 times 10 to the 7th power".

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Answer:

3/8

change to an improper fraction

1 1/8=9/8

3/4 times 2 equals

6/8

9/8-6/8

3/8

Answer: I think the answer is 3/8 or it can be 5/8.

explanation: I hope this helps.

In this problem, descriptive statistics is used because the survey percentage is used to make inference for all business owners.

Descriptive statistics is used when data from a sample, which is a sub-set of a population, is used to make inferences about the entire population.

In this problem, the data 979 business owners sampled is used to make inference about the population, which is composed by all business owners, hence descriptive statistics is used.

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Answer:

6/5

Step-by-step explanation:

Rise

_____

Run

The slope of parallel line is -6/5

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

given:

Equation: 18x + 15y = 90.

Now, writing the given equation in slope intercept form

15y= 90- 18x

y= 90/15 - 18/15 x

y= 6 - 6/5x

So, the slope of given line is -6/5

Now, the slope of parallel and given is same.

Thus, the slope of parallel line is -6/5

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Answer:

(a) 332

Step-by-step explanation:

Find 40% of 237

94.8, Round to 95

237 + 95 = 332

The value of (f.g) (x) is 2. Option B

A function can be defined as an expression or rule that explains the relationship between an independent and dependent variable.

Given the functions;

To determine (f.g) (x), we need to know that it is a composite function

We substitute the value of g(x)  = 2 as x in f(x)

But we have f(x) = x

Then,

(f.g) (x) = 2

Thus, the value of (f.g) (x) is 2. Option B

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The term or expression 12b represents the number of raffle tickets sold by the members of the band.

Expression: An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

There are b number of members in a jazz band. The jazz band wants to take a tour.

Each of the members sold 12 raffle tickets to raise money for the tour.

Therefore, the number of raffle tickets sold will be the product of the number of jazz members and the number of raffle tickets sold by each member.

So, the expression for the number of raffle tickets sold by the members of the jazz band will be:

= 12 × b

= 12b

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Answer:

(-1, -4)

Step-by-step explanation:

To find the missing endpoint, we can multiply the midpoint coordinates by 2, so we can get 4 and 2. Then we can subtract the coordinates from the endpoint we have, which is A, to those numbers.

4-5 is -1

2-6 is -4

Put them together and we get (-1, -4) as our endpoint B.

Answer:

Step-by-step explanation:

(5+x)/2=2, (6+y)/2=1

for the x value

5+x=4

x=-1

then for the y value

6+y=2

y=-4

then your answer would be (-1,-4)

The equation representing the minimum and maximum scores |x-87| = 1.8

Given that the average score on a lab report is 87 points. All students score within 1.8 points of the average.

Let 'x' be the score of student. The maximum and minimum score of a student lies within 1.8 points of the average.

Then, maximum score of a student, x = 87+1.8

and minimum score of a student, x = 87-1.8

Combining these two equations, we get, x = 87 ±1.8

Or, more conveniently, |x-87| = 1.8 represents the minimum and maximum scores obtained by a student.

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Answer: 8.4261

Step-by-step explanation:

This statement is false. when constructing a congruent line segment to cd the ray needed for the construction it must be not shorter.

Because when constituting a configured line segment to CD the ray never can be shorter. The reason is when we constitute a configured it's Ray line is always increase that mean it's go up Hight and it's must be longer . That's why this statement is false.

Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments. When two lines are the same length, they are said to be congruent. Superimposable figures that entirely enclose each other when stacked one atop the other are congruent segments. The congruent segments continue to be congruent even after being turned, flipped, or rotated.

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Using the monthly payment formula, it is found that the best plan is given by:

The monthly credit card payment would be $238.37, which is lower than the monthly payment on the bank loan.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

For the simple interest payment method, the parameters are given as follows:

r = 0.06, n = 3 x 12 = 36, P = 11000, r/12 = 0.06/12 = 0.005.

Hence:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 11000(0.005)\frac{(1.005)^{36}}{(1.005)^{36} - 1}[/tex]

A = 334.64.

For the credit card payment method, the parameters are given as follows:

r = 0.16, n = 6 x 12 = 72, P = 11000, r/12 = 0.16/12 = 0.0133.

Hence:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 11000(0.0133)\frac{(1.0133)^{72}}{(1.0133)^{72} - 1}[/tex]

A = 238.37.

The monthly credit card payment would be $238.37, which is lower than the monthly payment on the bank loan.

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Answer:

169 squared I think,hope this helps

The solution to the inequality, -5/2(3x - 2) < 6 - 2x is: x > -2/11.

To find the solution to the inequality given, follow the steps explained below:

-5/2(3x - 2) < 6 - 2x [given]

-5/2(3x) -5/2(-2) < 6 - 2x [distribution property]

-15x/2 + 5 < 6 - 2x [simplify]

-15x/2 + 5 - 5 < 6 - 2x - 5 [subtraction property]

-15x/2 < 1 - 2x

-15x/2 + 2x < 1 - 2x + 2x [addition property]

-11x/2 < 1 [simplify]

-11x/2 × 2 < 1 × 2 [multiplication property]

-11x < 2

-11x/-11 > -2/11 [division property]

x > -2/11

Note: the inequality sign would change if we are dividing both sides by a negative number.

Therefore, the solution to the inequality, -5/2(3x - 2) < 6 - 2x is: x > -2/11.

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The reasoning which shows the given statement correctly is [tex]4^{\frac{3}{2}}[/tex].

Given the statement is "4 to the power of 3 over 2 end exponent".

In mathematics, an expression is defined as a set of numbers, variables, and operations that are formed according to context-dependent rules.

In the given statement 3 over 2 means, 3 is divisible by 2 and it can be written as 3/2.

And it is also given that 4 to the power of 3 over 2 that means we have to write 3/2 in the power of 4 and it can be written as

[tex]4^{\frac{3}{2}}[/tex]

Hence, the reasoning which shows the given statement "4 to the power of 3 over 2" correctly is [tex]4^{\frac{3}{2}}[/tex].

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The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be 585.43 + x - 302.05 ≥ 300.

From the information, it was stated that Keisha has $585.43 in her checking account and that she must maintain a balance of $300 to avoid a fee and then she wrote a check for $302.05 today.

The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be:

585.43 + x - 302.05 ≥ 300

Collect like terms

x ≥ 300 - 585.43 + 302.05

x ≥ $16.62

She's needs to deposit at least $16.62.

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