Which statement BEST describes the relationship between whole numbers and natural numbers shown in the diagram?
A)
B)
The diagram shows that whole numbers are a subset of natural numbers,
because all whole numbers are natural numbers.
The diagram shows that natural numbers are a subset of whole numbers,
because all natural numbers are whole numbers.
The diagram shows that whole numbers are a subset of natural numbers,
because some whole numbers are not natural numbers.
The diagram shows that natural numbers are a subset of whole numbers,
because all whole numbers and natural numbers have no numbers in
C)
D)
common.

Answer: (7, 2.5)

Step-by-step explanation:

Midpoint formula: [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2} )[/tex]

(x1, y1)= (4, 8)

(x2, y2)= (10, -3)

------------------------------------------------------

 [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2} )[/tex]

=[tex](\frac{4+10}{2}, \frac{8-3}{2} )[/tex]

=[tex](\frac{14}{2}, \frac{5}{2} )[/tex]

=[tex](7, 2.5)[/tex]

Hope this helps!! :)

Please let me know if you have any question

Answer:

[tex]q(x)=2x-5,x\neq-2[/tex]

Step-by-step explanation:

So we have:

[tex]a(x)=2x^2-x-10\\b(x)=x+2[/tex]

And we want to find the quotient q(x). Thus:

[tex]q(x)=\frac{a(x)}{b(x)}[/tex]

Substitute:

[tex]q(x)=\frac{2x^2-x-10}{x+2}[/tex]

Factor the numerator:

[tex]2x^2-x-10\\=2x^2+4x-5x-10\\=2x(x+2)-5(x+2)\\=(2x-5)(x+2)[/tex]

Substitute:

[tex]q(x)=\frac{(2x-5)(x+2)}{x+2}[/tex]

The (x+2)s cancel out. Therefore:

[tex]q(x)=2x-5[/tex]

However, we must restrict x such that it cannot equal -2.

In the original equation, if it did, our answer would be undefined. Thus, our final answer is:

[tex]q(x)=2x-5,x\neq-2[/tex]

And we are done :)

Edit: Typo

29/16= 1.8125

as decimal

Answer:

coordinate  value is [-3,4].

Reltive is mio pie x 78.9 :)

hoped this helped :)

Answer:

1 C JUICE , 1 C MILK , 1.5 SLICE OF BREAD  and 1.5 C CEREAL should each be served to obtain the desired amounts.

Step-by-step explanation:

Given that;

                          protein           carbohydrate         fat             calories

1 cup juice              2                        24                    0                   110

1 cup cereal           8                         4                      8                   120

1 slice bread          2                         10                    6                   100

1 cup milk              10                        13                     0                   85

Now let  number of cups of  juice, cereal , bread milk be

j, c, b and m respectively

from the table and information from the given

protein

2j + 8c + 2b + 10m = 27 ------------------equ 1

carbohydrate  

24j + 4c + 10b + 13m = 58 ---------------equ 2

fat

8c + 6b = 21 ----------------------------------equ 3

calories  

110j + 120c + 100b + 85m = 525 ------- equ 4

Now

equ 1 × 12 - equ 11

⇒(24j + 96c + 24b + 120m = 324) - (24j + 4c + 10b + 13m = 58)

= 92j + 14b + 107m =  266 -----------------equ 5

also

equ 1 × 55 - equ 4  

( 110j + 440c + 110b + 550m = 1485) - ( 110j + 120c + 100b + 85m = 525 )

320c + 10b + 465m = 960  

divide through by 5

64c + 2b + 93m = 192 ----------------------- equ 6

then  

equ(5)×93 - equ(6)×107  

(8556j + 1302b + 9951m = 24738) - (6848j + 214b + 9951m = 20544)

1708j + 1088b = 4194

divide through by 2

854j + 544b = 2097 --------------------------- equ 7

Now

equ(3)×854 - equ(7)×8

(6832c + 5124b = 17934) - ( 6832c + 4352b = 16776)

772b = 1158

b = 1158 / 772

b = 1.5

now put (b=1.5) in equation 3

8c + 6(1.5) = 21

8c 9 = 21

8c = 21 - 9

8c = 12

c = 12/8

c = 1.5

now put (b=1.5) and (c=1.5) in equation 6

64(1.5) + 2(1.5) + 93m = 192

96 + 3 + 93m = 192

93m = 192 - 99

93m = 93

m = 93/93

m = 1

now put (b=1.5), (c=1.5) and (m=1) in equation 1

2j + 8(1.5) + 2(1.5) + 10(1) = 27

2j + 12 + 3 + 10 = 27

2j + 25 = 27

2j = 27 -25

2j = 2

j = 2/2

j = 1

Therefore   1 C JUICE , 1 C MILK , 1.5 SLICE OF BREAD  and 1.5 C CEREAL should each be served to obtain the desired amounts.

Answer: go to quizlet it has the answer i got that question aced

Step-by-step explanation:

mark brainly btw

Answer:

1/2

Step-by-step explanation:

Answer:

1st Slot: f(-3)

2nd Slot: -3

3rd Slot: is not

Step-by-step explanation:

Using the Remainder Theorem, we plug in the root of x + 3 (which is x = -3) and see the remainder.

If the remainder = 0, it is a factor

If the remainder ≠ 0, it is NOT a factor

f(-3) = -2(-3)⁴ - 8(-3)³ - 2(-3) - 63

f(-3) = -3

So, x + 3 is NOT a factor.

We then have our 3 answers.

8(n-1)-2(3n+5)

8n-8-6n-10

8n-6n-8-10

2n-18

2(n-9)

let the unknown no.be x

therefore, 76+122+92+x = 360

                 = 198+92+x = 360

                = 290+x = 360

                    x=360-290

                    x= 70degree

hope this is helpful,

^_^

B. (3, -7)

When the equation is graphed, the vertex is at the point (3,-7). I hope this helps!!!

The vertex of the quadratic expression g(x) = 8x² - 48x + 65 is (3, -7).

Quadratic expressions are polynomial expressions of second degree.

The general form of a quadratic expression is ax² + b x + c.

The vertex of a quadratic function f(x) = ax² + b x + c is,

(-b/2a, f(-b/2a)).

Here the function is,

g(x) = 8x² - 48x + 65

b = -48 and a = 8.

Vertex = (-(-48) / 16, g(-(-48) / 16))

           = (3, g(3))

g(3) = 8(3)² - 48(3) + 65 = 0

g(3) = -7

Hence the correct option is B.

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Answer:

[tex]11 {w}^{2}u \sqrt{2w}[/tex]

Step-by-step explanation:

I'm never sure how far to go on these questions but I think what I'e done looks pretty nice. Essentially I simplified each radical, factored out each variable, combined the radicals after more simplification, and then picked the answer you were most likely looking for. I gave some alternatives in my work that are "simple" too, but the answer above is most likely I'd say.

Work is in the attachment, comment with any questions.

Answer:

Option (B)

Step-by-step explanation:

Average waiting time in the month of October = 20 minutes

Average waiting time in the month of November = 30 minutes

Average waiting time in the month of December = 60 minutes

Average waiting time in the month of January = 40 minutes

Average waiting time in the month of February = 10 minutes

Average waiting time in the month of March = 10 minutes

Average waiting time in the month of April = 30 minutes

Average waiting time in the month of May = 40 minutes

Average waiting time in the month of June = 20 minutes

Total waiting period from October to June = 20 + 30 + 60 + 40 + 10 + 10 + 30 + 40 + 20 = 260

Average waiting period = [tex]\frac{260}{9}[/tex]

                                       = 28.89

                                       ≈ 29 minutes

Option (B) is the answer.

B or C (both are correct just choose one)

B or C (both are correct).

Answer:

45.0

Step-by-step explanation:

44.981 = 45.0 (to 3 s.f.)

*important point to note: the 0 must be included as the question asked for 3 significant figures. In this case, 0 is significant.

I hope this helps :)

Rounding 44.981 to three significant figures gives us 44.9.

To round the value 44.981 to three significant figures, we start counting from the leftmost non-zero digit.

The three significant figures in this case are "44.9".

The digit immediately after the third significant figure is 8.

Since 8 is greater than or equal to 5, we round up the last significant figure, which is 9.

Therefore, rounding 44.981 to three significant figures gives us 44.9.

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Answer:

D. |−3 − 8| = 11

Step-by-step explanation:

We have to simplify an absolute value expression to find the distance between -3 and 8 on a number line.

Firstly, as we know that the absolute value means any number inside the mod (whether positive or negative) will come out as a positive value only, that means;

The absolute value of -6 = [tex]|-6|[/tex] = 6

The absolute value of 6 = [tex]|6|[/tex] = 6

Now, the distance between the numbers -3 and 8 on the number line will be the difference of two numbers inside the mod, that means;

Distance = [tex]|-3-8|[/tex]  =  [tex]|-11|[/tex]

As the number inside the mod comes out as a positive value only, so the distance = 11.

Hence, the distance between –3 and 8 on a number line is 11.

Answer:

1 out is six

Step-by-step explanation:

there are six numbers on a dice cube to get four that is a one out of six.

Answer:

3/6, 1/2 or 50%

Step-by-step explanation:

The answer would be 3/6

because there are 3 factors of 4 and there are 6 total sides so the answer would be 3/6 or 1/2 or 50%

Answer:

B. 12 square ft C. 63 square ft

Step-by-step explanation:

Marlena places a square rug on her living room floor, which is also a square.

Now if a square rug is placed in her room, the area of the floor will definitely be the area if the square rug..

And area of a square it = length ²

The result will give s a perfect square for an integer number.

A. 9 square ft = perfect square

B. 12 square ft = not perfect square

C. 63 square ft =not perfect square

D. 81 square ft= perfect square

So the ones that are not perfect squares Is the answer to the question

The  area of her floor is NOT covered by the rug is 12 square ft and  81 square ft.

It is required to find the area of her floor is NOT covered by the rug.

A square is a four-sided polygon, whose all its sides are equal in length and opposite sides are parallel to each other. Also, each vertices of square have angle equal to 90 degrees.

Given:

Marlena places a square rug on her living room floor, which is also a square.

Now if a square rug is placed in her room, the area of the floor will definitely be the area if the square rug..

If the length of each side of the rug is equal to the length of each side of the room, there will be no area not covered.

According to given question we have,

And area of a square it = length ²

The result will give s a perfect square for an integer number.

A. 9 square ft = perfect square

B. 12 square ft = not perfect square

C. 63 square ft =not perfect square

D. 81 square ft= perfect square

Therefore, the  area of her floor is NOT covered by the rug is 12 square ft and  81 square ft.

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Answer:

(a) The degrees of freedom; the relevant t distribution would have = n - 1 = 41 - 1 = 40.

(b) A 95% confidence interval for the mean speed of vehicles crossing the bridge is [79.92 km/hr, 82.78 km/hr] .

(c) We should not reject the hypothesis since 80 km/h is in the interval found in (b).

(d) Decrease the Type I error probability.

Step-by-step explanation:

We are given that the average speed for a sample of 41 vehicles was 81.35 km/h, with the sample standard deviation being 4.52km/h.

(a) Since here we don't know about population standard deviation, so the distribution that will be used here is t-distribution as the data also follows the normal distribution.

The degrees of freedom; the relevant t distribution would have = n - 1 = 41 - 1 = 40.

(b) Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~   [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average speed of vehichles = 81.35 km/h

             s = sample standard deviation = 4.52 km/h

             n = sample of vehicles = 541

            [tex]\mu[/tex] = population mean  

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.021 < [tex]t_4_0[/tex] < 2.021) = 0.95  {As the critical value of t at 40 degrees of

                                               freedom are -2.021 & 2.021 with P = 2.5%}  

P(-2.021 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.021) = 0.95

P( [tex]-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                      = [ [tex]81.35-2.021 \times {\frac{4.52}{\sqrt{41} } }[/tex] , [tex]81.35+2.021 \times {\frac{4.52}{\sqrt{41} } }[/tex] ]  

                                     = [79.92 km/hr, 82.78 km/hr]

Therefore, a 95% confidence interval for the mean speed of vehicles crossing the bridge is [79.92 km/hr, 82.78 km/hr] .

(c) The hypothesis given to us is;

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 80 km/hr    {means that the mean speed of vehicles over the bridge would be the speed limit of 80 km/h}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 80 km/hr    {means that the mean speed of vehicles over the bridge would be the speed limit of different from 80 km/h}

Here, we should not reject the null hypothesis since 80 km/h is in the interval found in (b) which means that we are 95% confident that the mean speed of vehicles over the bridge would be the speed limit of 80 km/h.

(d) Decreasing the significance level of the hypothesis test above would decrease the Type I error probability because Type I error probability is represented by the significance level.

Answer:

x = 5 +/- 4 ([tex]\sqrt{16}[/tex])

so the answer is 1 and 9

Step-by-step explanatio:

The values of x can be 1 or 9.

The correct option is (B) and (C).

A statement of equality between two expressions consisting of variables and/or numbers. In essence, equations are questions, and the development of a mathematics has been driven by attempts to find answers to those questions in a systematic way.

For example

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.

Given:

x= 5 ± √16

Now, taking the root of 16 which is +4 and -4.

So, x= 5 ± 4

We have two values ,

x= 5+4 or x= 5-4

x=9 or 1

Hence, the solution to x= 5 ± √16 is B. 1 and C. 9.

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Answer:

4 feet

Step-by-step explanation:

We know the the area of a triangle can be represented as [tex]\frac{bh}{2}[/tex].

Since the height is twice the base, we can substitute the value [tex]2b[/tex] in as [tex]h[/tex] in the expression, making it [tex]\frac{b\cdot2b}{2}[/tex]. If the area is 16, we can make the equation

[tex]\frac{b\cdot2b}{2} = 16[/tex]

Now to solve for b.

[tex]\frac{2b^2}{2} = 16\\\frac{2b^2}{2}\cdot2 = 16\cdot2\\\\2b^2 = 32\\\\2b^2\div2 = 32\div2\\\\b^2 = 16\\\\b=4[/tex]

Hope this helped!

Answer:

4w + 6

Step-by-step explanation:

Group like terms

7w - 3w + 6 = 4w + 6

Hope this Helps :)

Answer:

(x ; y) ∈ ∅

Step-by-step explanation:

x = 3 - 3y

x + 3y = - 6

replace x

(3 - 3y) + 3y = - 6

3 - 3y + 3y = - 6

3 = - 6

(x ; y) ∈ ∅

Step-by-step explanation:

we have given the value of x is 3 - 3y

[tex]\blue\star[/tex]x+3y = -6. (eq 1)

put the value of x in equation 1 we get

[tex]\blue\star[/tex] x + 3y = -6

[tex]\blue\star[/tex] 3-3y+3y.= -6

[tex]\blue\star[/tex] 3 = -6

Hope it helps.

Answer:

3 and 1/2  minus 2/3  minus 1/3 =

7/2 minus 2/3 minus 1/3 =

21/6 minus 4/6 minus 2/6 =

17/6 - 2/6 =

15/6 =    5/2 = 2 and 1/2

Optionally, you can think of it this way:

He used 2/3 yards for the pillow and 1/3 yard for the scarf.

So he used 1 yard

3 and 1/2 minus 1 = 2 and 1/2 = 5/2

Step-by-step explanation:

Note. The original question with options given on the bottom

Answer:

F - 1, B -2, A - 3, D - 4, C - 5, E - 6

Step-by-step explanation:

F.  Sample

B. Population  

A. Statistic  

D. Parameter  

C. Data  

E. Variable  

========================================================

Question

A bank manager is interested in the average length of time that customers are willing to wait in line before they give up and leave the bank. Match the vocabulary word with its corresponding example.

---------------------

1. The 25 customers that the manager observed leave

2. All of the bank's customers

3. The average length of time that the 25 customers waited before leaving the bank

4. The average length of time that all customers will wait before leaving the bank

5. The list of times for the 25 customers who left the bank

6. The length of time a customer waits before leaving the bank

---------------------

Answer:

Only one solution

Step-by-step explanation:

[tex] |r - 6| = 0 \\ r - 6 = \pm \: 0 \\ r - 6 = 0 \\ r = 6[/tex]

Answer:

The width of the poster will be 17 inches

Step-by-step explanation:

The area = 204  square inches

Note:

- both length and width are whole numbers

- The width of the poster is greater than 11 inches

- The width is a prime

The prime numbers greater than 11 are

13, 17, 19, 23, 29, ...,

all these numbers divide 204 with a remainder except for 17

Therefore, the width will be 17 inches, and the length will be 12

since 17 divides 204 into 12 places

Answer:

9656.064 rounded its 9656

Step-by-step explanation:

multiply the length value by 1.609344

6000*1.609344

Answer:

3^12

Step-by-step explanation:

(3^3/4(2) - 3/8) ^4/9

(3^6/8-3/8)^4/9

(3^3/8)^4/9

3^3/8(4/9)

3^27/72(32/72)

3^864/72

3^12

Sorry if it's hard to read...

Answer: 56x

Step-by-step explanation: Multiply -8 by -7. Be sure to add your x at the end. VERY important.

I hope this helps you out! ♥

Answer:

[tex]56x[/tex]

Step-by-step explanation:

[tex]-7x(-8)[/tex]

The one and only thing you have to do in this question is to simplify.

[tex]-7x)(-8)[/tex]

This equals

[tex]56x[/tex]

Now you got your answer!

Hope this helps!

Answer:

x=-5

Step-by-step explanation:

opening the bracket on the LHS, we have

-8x-40= -3x+x-7-3

-8x-40= -2x-10

collecting like terms

-8x+2x= -10+40

-6x= 30

divide both sides by -6

x= -5