2. Metcalf School has two third-grade rooms (A and B) and two fourth-grade rooms
(C and D). Together, rooms C and D have 46 students. Room A has 6 more students
than room D. Room B has 2 fewer students than room C. Room D has 22 students.
How many students are there altogether in rooms A and B?

Answer:

Total cost of x students tuition = $2,800x

Step-by-step explanation:

Total cost of x students tuition

= Amount of tuition × number of students

Amount of tuition= $2,800

Number of students = x

Total cost of x students tuition

= Amount of tuition × number of students

= $2,800 * x

= $2,800x

Total cost of x students tuition = $2,800x

For example, if there are 2 students in total

Total cost of x students tuition = $2,800x

When x= 2

= $2,800 × 2

= $5,600

Total Cost of students paying tuition of $2,800 each is $5,600

Answer:

-7, |-2|, 3, |4.5|

Step-by-step explanation:

-7 is the lowest number, since it is a negative. The absolute value of -2, or |-2|, is 2 making it the second lowest. 3 comes next. The absolute value of 4.5 is 4.5, being the greatest number.

Answer:

-7, |-2|, 3, |4.5|

Step-by-step explanation:

First, let's find -2 and |4.5| .

Absolute value of a number is its distance from 0. Remember, absolute value is always zero or positive.

Now, let's use a number line to order the numbers. Numbers to the left are less than numbers to the right.

The values in order from least to greatest is as follows: -7, |-2|, 3, |4.5|.

Answer:

C. 2.937

Step-by-step explanation:

Given the following :

H0 : p = 0.25

H1 : p > 0.25

Number of observations (n) = 647

p' = 30% = 0.3

SD = sqrt[(p(1 - p) / n)]

1 - p = 1 - 0.25 = 0.75

SD = sqrt[(0.25 * 0.75) / 647]

SD = sqrt[0.0002897]

SD = 0.0170234

Z = (p' - p) / SD

Z = (0.3 - 0.25) / 0.0170234

Z = 0.05 / 0.0170234

Z = 2.9371187 = 2.937

Answer:

65x and 32 that your answer

65x and 32 is your answer to the question.

i hop ....

i hope

ihope

solution

Answer:

B. [tex]5*\frac{1}{7}[/tex]

Step-by-step explanation:

5÷7 is also [tex]\frac{5}{7}[/tex]--that divided sign is what the fractional bar represents in a fraction.

now multiply [tex]5*\frac{1}{7}=\frac{5}{1}*\frac{1}{7}=\frac{5*1}{1*7}=\frac{5}{7}[/tex]

both are the same result, so your answer is Choice B.

I hope this helps you

a.

   x   -  the length of the shorter piece

b.

   twice as large means:

   2x  -  the length of the loger piece  

   so:

      x + 2x  - the sum of length of pieces {total of rope}

the equation:   x + 2x = 36

c.

  x + 2x = 36

     3x = 36

    ÷3     ÷3

     x = 12 ft

2x = 2×12 = 24 ft

The length of the shorter piece is 12 ft

The length of the loger piece is 24 ft

Answer:

The correct option is b.

Step-by-step explanation:

Standard deviation is one of the measure of dispersion or spread of a dataset from the average value of the dataset. The standard deviation measures the absolute variability of the distribution of values.

The higher the spread or variability in the data set, the greater is the standard deviation value and thus greater will be the magnitude of the deviance of the value from their average.

It is provided that the  standard deviation of the distribution of house age is about 16 years.

The standard deviation of 16 years imply that the age for all the houses in the sample is 16 years from the mean.

Thus, the correct option is b.

Answer:

The confidence interval = ($47.41, $53.39)

Step-by-step explanation:

Confidence Interval formula

= Mean ± z × Standard deviation/√n

Mean = $50.40

Standard deviation = $12.30

z score for a 95% confidence interval = 1.96

n = 65

Confidence Interval = $50.40 ± 1.96 × $12.30/√65

= $50.40 ± 2.9902293815

Confidence Interval =

$50.40 - 2.9902293815 =

47.409770618

≈$47.41

$50.40 + 2.9902293815 = 53.390229381

≈$53.39

Therefore, the confidence interval = ($47.41, $53.39)

Answer:

864

Step-by-step explanation:

let's take side of the cube as C. then volume of the cube will be C^3. we know that C^3 is 1728 inches. so C = 12. total surface area of a cube is 6*C*^2. so that is equal to 6×12×12 = 864

Answer:

D) $18,000

Step-by-step explanation:

A company has found that its expenditure rate per day (in hundreds of dollars) on a certain type of job is given by

E'(x) = 10x + 11,

where x is the number of days since the start of the job.

Find the expenditure if the job takes 5 days.

Step 1

We Integrate

E(x) =∫E'(x) dx

=∫[10(x) + 11] in hundreds of dollars

(5x² + 11x + c) in hundreds of dollars

Step 2

(5x² + 11x + c) in hundreds of dollars

x is the number of days since the start of the job.

x = 5

5x² + 11x

[5(5)² + 11(5)] in hundred of dollars

= [5 × 25 + 55] in hundreds of dollars

=[ 125 + 55] in hundreds of dollars

=[180] in hundreds of dollars

Hence the expenditure is 180 in hundreds of dollars

This means, 180 × $100

= $18000

Therefore, the expenditure costs $18,000

Answer:

B.) translation and rotation

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

a.   Since a line doesn't have endpoint, it doesn't matter which

two points we use to name a line so we could call this line DC.

b.   A ray is a figure that starts at and endpoint and continues

forever in one single direction. So a ray here would be ray AB.

c.   Opposite rays are two rays that share a common endpoint,

have no other points of intersection, and all points are collinear.

So ray EC and ray ED would be opposite rays.

A) Line names are made using two letters, since line CD passes through E, line CD could be renamed CE

B) a Ray has one end point and goes in one direction. If A is the endpoint, the line goes through point B

The Ray would be AB with an arrow pointing to the right above the letters.

C) Opposite rays create a straight line and have the same point.

Ray ED is opposite EC

Answer:

[tex]y = 7x - 175[/tex]

Step-by-step explanation:

Given

Initial temperature= 25ºC

Rise = 1ºC

Rate  = 7 joules

Required

Determine the equation of the system

Let the final temperature be represented with x and the heat required be represented with y

This question will be solved using the following heat formula

[tex]Heat\ Required = Rate * Change\ in\ Temperature[/tex]

[tex]Heat\ Required = Rate * (Final\ Temperature - Initial\ Temperature)[/tex]

Substitute y for Heat Required; 7 for Rate; x for Final Temperature and 25 for Initial Temperature

[tex]y = 7(x - 25)[/tex]

Open the bracket

[tex]y = 7x - 7 * 25[/tex]

[tex]y = 7x - 175[/tex]

Hence, the equation of the system is

[tex]y = 7x - 175[/tex]

Answer:

The square root of 4 is 2(not irrational)

The square root of 100 is 10(not irrational

Step-by-step explanation:

Answer:

E.

Step-by-step explanation:

6^2=x^2+3^2

X^2=36-9

X=

[tex] \sqrt{27} [/tex]

Answer:

5x - 2 = 8

5x = 8 + 2

5x = 10

x = 10/5

x = 2

Answer: A

Step-by-step explanation:

For this problem, we would distribute the outer exponent to each exponent inside. Once we distribute, we multiply the exponents together.

[tex]2^\frac{12}{5} *9^\frac{4}{5}[/tex]

Answer:

When we have exponents (being multiplied) in a parenthesis which also has an exponent, the exponent of the parenthesis gets multiplied by each one of the others. We have to distribute the outer exponent to each exponent inside, like:

[tex](a^n*b^m)^p = a^{n*p}*b^{m*p}[/tex]

If there are numbers but no exponents (inside), it also happens the same, but as the exponent of the parenthesis gets multiplied by 1, we can just put the exponent, like:

[tex](a*b)^p=a^p+b^p[/tex]

So, in our case we have what we have explained: two numbers, one of them with an exponent and the other without it in a parenthesis which also has an exponent, so we multiply that exponent by the ones of the numbers inside the parenthesis.

[tex](2^3*9)^\frac{4}{5}[/tex] = [tex]2^{3*\frac{4}{5}}*9^\frac{4}{5}[/tex] = [tex]2^\frac{12}{5}*9^\frac{4}{5}[/tex]

So the answer is [tex]2^\frac{12}{5}*9^\frac{4}{5}[/tex]

Answer:

20+2=22

Step-by-step explanation:

When you go down by 2, then use the Inverse Operation to add it up.

Step-by-step explanation:

5x+3x=12+4

8x=16

x=16÷8

x=2

Answer:

[tex] \boxed{ \bold{ \huge{\boxed{ \sf{x = 2}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{5x - 4 = - 3x + 12}[/tex]

Move 3x to left hand side and change it's sign

⇒[tex] \sf{5x + 3x - 4 = 12}[/tex]

Move 4 to right hand side and change it's sign

⇒[tex] \sf{5x + 3x = 12 + 4}[/tex]

Collect like terms

⇒[tex] \sf{8x = 12 + 4}[/tex]

Add the numbers

⇒[tex] \sf{8x = 16}[/tex]

Divide both sides of the equation by 8

⇒[tex] \sf{ \frac{8x}{8} = \frac{16}{8} }[/tex]

Calculate

⇒[tex] \sf{x = 2}[/tex]

Hope I helped!

Best regards!!

Answer:

(If they were talking about 3,335, then) 100 times greater

(If they were talking about 3,335 then) 10 times greater

Step-by-step explanation:

When you visualize it, ignore the other numbers and think of only the threes.

Count how many spaces/places they are from each other, and that's how many 0s you should put after a 1 as your answer.

Same as decimal moving and multiplying by 10's.

Answer:1760

Step-by-step explanation:

Some integers are irrational is false

Answer:

A.) Some integers are irrational

Step-by-step explanation:

Integers are natural numbers, their opposites, and zero. (-2,-1,0,1,2)

Natural numbers, whole numbers, and integers are all rational numbers.

Irrational numbers cannot be written as quotients of integers, and they have decimal representations that do not repeat or terminate ([tex]\sqrt{2},\pi[/tex]).

The other statements are true

Answer:

24 square cm

Step-by-step explanation:

[tex]area \: of \: \triangle = \frac{1}{2} \times base \times height \\ = \frac{1}{2} \times 12 \times 4 \\ = 6 \times 4 \\ = 24 \: {cm}^{2} \\ [/tex]

Answer:

  C: real number

Step-by-step explanation:

The set of real numbers includes rational and irrational numbers. It would be difficult (impossible) to draw a number line consisting of only rational numbers or only irrational numbers.* So, the number lines we draw represent all real numbers.

_____

* There are an infinite number of rational numbers between any pair of irrational numbers. Similarly, there are an infinite number of irrational numbers between any pair of rational numbers

Answer:

The answer to this question can be defined as follows:

The Lower sum ="0.659"

The Upper sum ="0.859"

Step-by-step explanation:

In the given equation there is some mistype error, so the correct equation and its solution can be defined as follows:

Equation:

[tex]y= \sqrt{1-x^2}[/tex]

calculating the Δx:

[tex]=\frac{(1 - 0)}{5}\\\\=\frac{1}{5}[/tex]

calculating the Upper sum value:

[tex]=\bigtriangleup x \times (f(0) + f(\frac{1}{5}) + f(\frac{2}{5}) + f(\frac{3}{5}) + f(\frac{4}{5})) \\\\= \frac{1}{5} \times (1 + \sqrt{(\frac{24}{25})} + \sqrt{\frac{21}{25}} + \frac{4}{5} + \frac{3}{5})\\\\= 0.859[/tex]

calculating the Lower sum value:

Answer:

The upper sum value is 0.8592

The lower sum value is 0.6592.

Step-by-step explanation:

Given information:

The equation [tex]y=\sqrt{1-x^2}[/tex]

And [tex]n=5[/tex]

now, first find derivative of the above equation:

As, [tex]\Delta x=(1/5)\\\Delta x=0.2[/tex]

Now calculate the upper sum value as :

[tex]U=0.2[\sqrt{1-0}+\sqrt{1-0.2^2}+\sqrt{1-0.4^2}+\sqrt{1-0.6^2}]+ \sqrt{1-0.8^2}\\U=0.2\times 4.296\\U=0.8592\\[/tex]

Hence, the upper sum value is 0.8592

Now ,calculate the lower sum value as:

[tex]L=0.2[\sqrt{1-0.2^2}+\sqrt{1-0.4^2}+\sqrt{1-0.6^2}+\sqrt{1-0.8^2}+\sqrt{1-1^2}]\\L= 0.2\times 3.296\\L=0.6592\\[/tex]

Hence, the lower sum value is 0.6592.

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