1. Which situation would most likely be
represented by a rational number that is
not an integer?
A number of students in a classroom
B score on a math test
C number of keys on a keyboard
D price of a pencil

- 2a = - 20 | x (-)

2a = 20

a = 20 : 2

a = 10

Answer:

a=10

Step-by-step explanation:

-2a=-20

Divide -2 on each side. You should get a=10

Answer:

[tex] - \frac{53}{25} [/tex]

Step-by-step explanation:

Convert to a mixed number by placing the numbers to the right of the decimal over

100

. Reduce the fraction. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number and adding the numerator to get the new numerator. Place this new numerator over the original denominator.

[tex]2-11i \text{ is the standard form of given expression }[/tex]

Solution:

The standard form of complex number is: a + bi

where a is the real part and bi is the imaginary part

Given expression is:

[tex](2-i)^3[/tex]

Expand the above expression using algebraic identity

[tex](a-b)^3=a^3-b^3-3ab(a-b)[/tex]

[tex]\text{For } (2-i)^3 \text{ we get, a = 2 and b = i}[/tex]

Thus on expanding using the above algebraic identity we get,

[tex](2-i)^3=(2)^3-(i)^3-3(2)(i)(2-i)[/tex]

Simplify the above expression

[tex](2-i)^3=8 -i^3-6i(2-i)\\\\(2-i)^3=8 -i^3-12i+6i^2[/tex]

We know that,

[tex]i^2 = -1\\\\i^3 = -i[/tex]

Substituting in above simplified expression, we get,

[tex](2-i)^3=8-(-i)-12i+6(-1)\\\\(2-i)^3=8 + i -12i -6\\\\\text{Combine the like terms }\\\\(2-i)^3=8 - 6 + i -12i\\\\(2-i)^3=2-11i[/tex]

Thus the given expression is expressed in standard form

Answer:

Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is

[tex]\dfrac{b-3a}{bc^{2}-d}=1[/tex]

Step-by-step explanation:

Evaluate:

[tex]\dfrac{b-3a}{bc^{2}-d}[/tex]

When a=-4, b=2, c=-3, and d =4

Solution:

Substitute, a=-4, b=2, c=-3, and d =4 in above expression we get

[tex]\dfrac{b-3a}{bc^{2}-d}=\dfrac{2-3(-4)}{2(-3)^{2}-4}\\\\=\dfrac{2+12}{18-4}\\\\[/tex]

[tex]\dfrac{b-3a}{bc^{2}-d}=\dfrac{14}{14}=1[/tex]

Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is

[tex]\dfrac{b-3a}{bc^{2}-d}=1[/tex]

Step-by-step explanation:

17.

Opposite angles of a parallelogram are equal.

So [tex]3y^{\circ}=123^{\circ}[/tex]

⇒ y= [tex](\frac{123}{3})^ {\circ}[/tex]

and sum of adjacent angle is = [tex]180^{\circ}[/tex]

Therefore, [tex](2x-5)^{\circ} + 123^ {\circ}=180^{\circ}[/tex]

⇒[tex](2x-5)^{\circ} =180^{\circ}-123^ {\circ}[/tex]

⇒[tex]2x^\circ=57^\circ+5^\circ[/tex]

⇒x=[tex]31^\circ[/tex]

Therefore x=[tex]31^\circ[/tex] and y= [tex](\frac{123}{3})^ {\circ}[/tex]

18.

The diagonals  of rectangle bisect each other.

so, 2x=x+9

⇔2x- x=9

⇔x = 9 units

Again opposite sides are congruent.

So,3y -9 =y+12

⇔3y - y =12+9

⇔y [tex]=\frac{21}{2}[/tex] units =10.5 units

Therefore x = 9 units and y = 10.5 units

19.

[tex]3x^\circ=45^\circ[/tex]         [∵ they are transversal angles]

⇔[tex]x=15^\circ[/tex]

And opposite sides are equal

7y = 4y + 21

⇔7y - 4y = 21

⇔3y = 21

⇔y = 7 units

Therefore [tex]x=15^\circ[/tex] and y = 7 units

Answer:

4 units

Step-by-step explanation:

if f to g is 2 units and h to i is one unit you just add thoes together because that is what the outside of the f to i is. And 7-3 is 4

hope this helps luvs

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The distance between the points G and H  on the line that contains points F, G, H, I, and J is 4 units.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

Given that a line contains points F, G, H, I, J. The space between F and G is 2. The space between H and I is 1. The space between F and I is 7. Therefore, the distance between the two points G and H on the given line can be written as,

GH = FI - FG - Hi

= 7 units - 2 units - 1 unit

= 4 units

Hence, the distance between the points G and H  on the line that contains points F, G, H, I, and J is 4 units.

Learn more about Line:

https://brainly.com/question/21511618

#SPJ6

Answer:

3

Step-by-step explanation:

4x+7=19

4x=19-7

4x=12

x=12/4

x=3

Answer:

B)  (8x-3)²

Step-by-step explanation:

64x2 - 48x + 9= (8x)² - 2*8x*3 + 3²

Compare with a² - 2ab +b² = (a-b)²;  a = 8x and b =3

=(8x-3)²

Answer: 5508

Step-by-step explanation:

all the numbers together equal 72 marbles in total.

(6x2)x (3x3)x (3x17)=

  12       9          51              first multiply the easy numbers 12x9 =108 then

108x51= 5508

The present age of father is 35 and daughter is 7.

Step-by-step explanation:

Let,

Age of father = x

Age of daughter = y

According to given statement;

A man is 5 times older than his daughter.

x = 5y      Eqn 1

In 7 years, the man is 3 times as old as his daughter.

x+7 = 3(y+7)

[tex]x+7=3y+21\\x=3y+21-7\\x=3y+14\ \ \ Eqn\ 2[/tex]

Putting value of x from Eqn 2 in Eqn 1

[tex]3y+14=5y\\14=5y-3y\\14=2y\\2y=14[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{14}{2}\\y=7[/tex]

Putting y=7 in Eqn 1

[tex]x=5(7)\\x=35[/tex]

The present age of father is 35 and daughter is 7.

Keywords: linear equation, substitution method

Learn more about substitution method at:

#LearnwithBrainly

Final answer:

The present ages of the man and his daughter are 35 years and 7 years, respectively.

Explanation:

The question asks us to find the current ages of a man and his daughter, given that the man is currently five times older than his daughter and that after 7 years, he will be three times as old as her. To solve this, we can set up two equations based on the information provided:

Now, we solve the equation from step 2 to find the daughter's age:

So, the daughter is currently 7 years old. To find the man's age, we multiply the daughter's age by 5:

Man's age = 5 x 7 = 35 years old

Therefore, the man is currently 35 years old and the daughter is 7 years old.

Answer:

X = 5

Y= 12

Step-by-step explanation:

3x + 2y = 39 —> (1)

5x - y = 13 —> (2)

Multiply (2) with 2

10x - 2y = 26 —> (b)

(1) + (b)

This will eliminate the y factor, leaving:

13x = 65

Therefore, x = 65/14

X= 5. Put this value of 5 in equation 1, which gives;

15 + 2y = 39

2y = 39-25

2y = 24

Y = 12

Answer:

x=5

y = 12

Step-by-step explanation:

3x + 2y = 39

2y = 39 - 3x

y = (39 - 3x) / 2

5x - y = 13

5x - ((39 - 3x) / 2) = 13

5x - 39/2 + 3/2x = 13

5x + 3/2x = 13 + 39/2

13/2x = 65/2

x = 65/2 * 2/13

x = 65/13

x = 5

y = (39 - 3x) / 2

y = (39 - 3*5) / 2

y = (39 - 15) / 2

y = 24/2

y = 12

Answer:x = -7

Step-by-step explanation:

-2x-10=4

-2x=14

-x=7

X=-7

Answer:

Step-by-step explanation:

[tex]-2(x+5)=4\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2\!\!\!\!\diagup(x+5)}{-2\!\!\!\!\diagup}=\dfrac{4\!\!\!\!\diagup^2}{-2\!\!\!\!\diagup_1}\\\\x+5=-2\qquad\text{subtract 5 from both sides}\\\\x+5-5=-2-5\\\\x=-7[/tex]

Answer: M  = ⁹/₅S

Step-by-step explanation:

 M  ∞ S -------------------------------- 1

M  =  KS ------------------------------ 2

K is a constant and need to be calculated

substitute for M and S in 2 to find K

900 = K500

K      =  ⁹⁰⁰/₅₀₀

       = ⁹/₅

Therefore , the equation that connect / relates M to S will be

M   =  KS

M   = ⁹/₅S

Final answer:

The equation that relates M to S is M = kS, where k is the constant of proportionality.

If M is 900 when S is 500, the equation becomes M = 1.8S.

Explanation:

The equation that relates M to S is M = kS, where k is the constant of proportionality.

To find the value of k, we can use the given values of M and S.

If M = 900 when S = 500, we can substitute these values into the equation to get 900 = k(500).

Solving for k, we divide both sides of the equation by 500, getting k = 1.8.

Therefore, the equation that relates M to S is M = 1.8S.

Answer:

D

Step-by-step explanation:

3×16=48

4×12=48

Answer:

(0,-4)

Step-by-step explanation:

see the image for explanation.

Answer:

( [tex]\frac{4}{3}[/tex], 0 )

Step-by-step explanation:

The x- intercept is where the graph crosses the x- axis. At this point the y- coordinate is zero.

Substitute y = 0 into the equation and solve for x, that is

3x - 4 = 0 ( add 4 to both sides )

3x = 4 ( divide both sides by 3 )

x = [tex]\frac{4}{3}[/tex] ← x- intercept

Answer:

170

Step-by-step explanation:

A number which rounds to 170 when it is rounded to the nearest ten is 168.

What is the number line ?

A number line is a picture of a graduated straight line that serves as visual representation of the real number.

Since we are trying to round of a number, which rounds to 170 when it is rounded to the nearest ten. Therefore, it should be in the range of 166 to 174 (both included).

Let take example of 168, as it can be seen that it is closest to 170, therefore, when it is rounded it will be closest to 170.

Hence, 168 is a number which rounds to 170 when it is rounded to the nearest ten.

To know more about number line click on the link below:

https://brainly.in/question/14244499

#SPJ2

Answer:

The probability distribution for which the value of the median is greater than the value of the mean is - negatively skewed probability distribution.

Step-by-step explanation:

The probability distribution for which the value of the median is greater than the value of the mean is - negatively skewed probability distribution.

Answer:

negative skewed  distribution

Step-by-step explanation:

As can be seen in the figure attached,

Using a calculator, 1200/180 = 6.67 approximately

If you use long division, then you'll get what you see in the diagram below

The 6's go on forever after the decimal point, but if you round to two decimal places, then you'll get that approximate value of 6.67

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

If you want a remainder, then 1200/180 = 6 remainder 120

You can think of it like you having 1200 cookies and 180 friends. Each friend will get 6 whole cookies and there will be 120 left over as the remainder.

Final answer:

By using the elimination method to solve the given system of linear equations, we find that x = 18 and y = 15.

Explanation:

We are looking to solve the system of linear equations:

3x – 2y = 24

x + 2y = 48

To find the values of x and y, we can use substitution or elimination methods. In this case, the elimination method is very straightforward since the y coefficients in the two equations are additive inverses. If we add both equations together, the y terms will cancel out:

3x + x = 24 + 48

4x = 72

Dividing both sides by 4 gives us the value of x:

x = 18

To find y, we can substitute x back into either of the original equations. Let's use the second equation:

18 + 2y = 48

Subtracting 18 from both sides:

2y = 30

Dividing by 2:

y = 15

Thus, the solution to the system of equations is x = 18 and y = 15.

Answer:

0.457 for all the apex students

Step-by-step explanation:

b

The expected number of bases for Ichiro Suzuki in a typical at-bat in 2001 is approximately 0.448, which rounds to 0.441 (Option D) to the nearest thousandth. Thus , the correct option is D.

To calculate the expected number of bases for Ichiro Suzuki in a typical at-bat in 2001, we can use the following formula:

E(X) = (0 ×P(Out)) + (1 × P(Single)) + (2 × P(Double)) + (3 × P(Triple)) + (4 ×P(Home Run))

First, we need to calculate the probabilities for each outcome:

P(Out) = (692 - 192 - 34 - 8 - 8) / 692 = 450 / 692 ≈ 0.651

P(Single) = 192 / 692 ≈ 0.278

P(Double) = 34 / 692 ≈ 0.049

P(Triple) = 8 / 692 ≈ 0.012

P(Home Run) = 8 / 692 ≈ 0.012

Now, plug these probabilities into the formula:

E(X) = (0 × 0.651) + (1 ×0.278) + (2 × 0.049) + (3 × 0.012) + (4 × 0.012)

E(X) ≈ 0.278 + 0.098 + 0.036 + 0.036 ≈ 0.448

Rounding to the nearest thousandth, E(X) is approximately 0.448.

So, the answer to the question is D. 0.441, which is the closest option provided.

For more such questions on  number

https://brainly.com/question/30752681

#SPJ3

Answer:

The relationship ⇒ 25x + 40y = 12,250

Step-by-step explanation:

The number of student memberships = x

The number of adult memberships = y

The monthly membership fee for a student = $25

The monthly membership fee for an adult = $40

The total fee = 25x + 40y

Al's Athletic Club receives $12,250 in membership fees for the month of January.

So, the relationship between x and y is:

25x + 40y = 12,250

For every 2 student memberships (2x$25=$50), there were 305 adult memberships.

To represent the relationship between the number of student memberships (2) and the number of adult memberships (y) at Al's Athletic Club for the month of January, we can use an equation based on the given information. Let's assume that there were 2 student memberships and y adult memberships in January. The monthly membership fees for students and adults are $25 and $40, respectively. The total membership fees collected for the month were $12,250.

The total fees can be represented as:

Total Fees = (Number of Student Memberships * Monthly Fee for Student) + (Number of Adult Memberships * Monthly Fee for Adult)

Using the given information, we can write the equation:

$12,250 = (2 * $25) + (y * $40)

Now, we can simplify this equation:

$12,250 = $50 + $40y

To isolate the variable y, we can subtract $50 from both sides of the equation:

$12,250 - $50 = $40y

$12,200 = $40y

Now, divide both sides by $40 to find the relationship:

y = $12,200 / $40

y = 305

So, the relationship between the number of student memberships (2) and the number of adult memberships (y) for the month of January is represented by the equation y = 305. This means there were 305 adult memberships in January for every 2 student memberships.

For more about Membership Fees:

https://brainly.com/question/33538831

#SPJ3

Answer:

no

Step-by-step explanation:

16.28 can also be written 16.280 (you could add as many zeros to the end as you want its still the same number)

280 is bigger than 275

Answer:

The equation of line passes through [tex](4,-1)[/tex] and perpendicular to the graph [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]y=\frac{-2x}{7}+\frac{1}{7}[/tex]

Step-by-step explanation:

Given point is [tex](4,-1)[/tex] and equation of line is [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex]

Let the slope of line that passes through point [tex](4,-1)[/tex] is [tex]m_1[/tex]

And slope of line [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]m_2=\frac{7}{2}[/tex] . As it is in the form of [tex]y=mx+c[/tex]

We know the relation between slope of perpendicular line are given by

[tex]m_1\times m_2=-1\\And\ m_1=\frac{-1}{m_2}[/tex]

So, the slope [tex]m_1=\frac{-1}{\frac{7}{2}}=\frac{-2}{7}[/tex]

Now, we can write the equation of line having point  [tex](4,-1)[/tex] and slope [tex]\frac{-2}{7}[/tex]

[tex](y-y_1)=m(x-x_1)\\\\(y-(-1))=\frac{-2}{7}(x-4)\\\\y+1=\frac{-2x}{7}-(\frac{2\times -4}{7})\\ \\y+1=\frac{-2x}{7}+\frac{8}{7}\\\\y=\frac{-2x}{7}+\frac{8}{7}-1\\\\y=\frac{-2x}{7}+\frac{8-7}{7}\\\\y=\frac{-2x}{7}+\frac{1}{7}[/tex]

So, the equation of line passes through [tex](4,-1)[/tex] and perpendicular to the graph [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]y=\frac{-2x}{7}+\frac{1}{7}[/tex]

Answer:

12

Step-by-step explanation:

This is an example of Addition property between two positive integers (i.e. whole value numbers), which means the result will be positive and larger than the two numbers.

The result of the addition would be:

[tex]5 + 7 = 12[/tex]

Another way to do it if you are struggling a bit you can write the value of [tex]7[/tex] as [tex]7 = 5 +2[/tex] so then you can say:

[tex]5 + (5 + 2) = 5 + 5 + 2 = 10 + 2 = 12[/tex]

Answer:  4 / -15

Step-by-step explanation:

Answer: 26

Step-by-step explanation: In this problem we have 3 consecutive even numbers whose sum is 84 and it asks us to find the smallest number.

Consecutive even numbers can be represented as x, x + 2, and x + 4.

Since the sum of these is 84, our equation reads

x + (x + 2) + (x + 4) = 84.

Simplifying on the left we get 3x + 6 = 84.

Subtract 6 from both sides and we have 3x = 78.

Divide both sides by 3 and x = 26.

So our smallest number is 26.

To find the smallest of three consecutive even numbers that sum up to 84, we set up an equation and solve for 'x', where 'x', 'x+2', and 'x+4' represent the numbers. Solving this gives us the smallest number, which is 26.

If the sum of three consecutive even numbers is 84, we can find the smallest number by setting up an equation. Let's denote the smallest even number as 'x'. The next consecutive even number would be 'x + 2', and the one after that would be 'x + 4'. The sum of these three numbers should equal 84:

x + (x + 2) + (x + 4) = 84

Simplifying this equation, we get:
3x + 6 = 84

Subtracting 6 from both sides, we have:
3x = 78

Now, dividing both sides by 3 gives us:
x = 26

Therefore, the smallest of the three consecutive even numbers is 26.

Answer:

  350

Step-by-step explanation:

We have two points on the demand curve as (10, 450) and (15, 200). Using the two-point form of the equation for the line between them, we can find the "y" value for "x" = 12 as ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (200 -450)/(15 -10)(12 -10) +450

  = (-250/5)(2) +450

  = -100 +450 = 350

We predict the number of tickets sold at $12 will be 350.

_____

Check

The drop in sales of 50 tickets for each $1 increase in price is consistent with other table values.

The equation relates the scale drawing of the sculpture room to its actual dimensions using equivalent ratios. By setting the actual length corresponding to 6 cm on the drawing to 30 m, we can solve for the unknown actual length, which is 6 meters. So, the actual length of the sculpture room in the museum is 6 meters.

Completing the equation:

The equation in the image is missing a part: it should be:

1 cm : 5 m = x cm : 30 m

Explanation of the equation:

1 cm: This represents the length of the sculpture room on the scale drawing, as indicated by the scale 1 cm : 5 m.

5 m: This represents the actual length corresponding to every 1 cm on the scale drawing.

x cm: This is the unknown variable we're trying to solve for. It represents the actual length of the sculpture room in the museum.

30 m: This is a constant value, chosen because we want to find the length corresponding to 6 cm on the scale drawing (since the sculpture room in the drawing is 6 cm long).

What each part represents:

The colon (:) separates the two equivalent ratios.

The first ratio (1 cm : 5 m) represents the scale factor, which is the conversion factor between the scale drawing and the actual museum dimensions. It tells us that every 1 cm on the drawing corresponds to an actual length of 5 m.

The second ratio (x cm : 30 m) represents the unknown ratio we want to solve for. It relates the unknown actual length (x cm) to the desired actual length of 30 m (corresponding to 6 cm on the drawing).

Solving for x:

To solve for x, we can cross-multiply the two ratios:

(1 cm) * (30 m) = (5 m) * (x cm)

Simplifying the equation, we get:

30 m = 5x cm

Finally, dividing both sides by 5, we get:

x = 6 m

Therefore, the actual length of the sculpture room in the museum is 6 meters.

Answer:

20 - 4×(−6) = 20 + 4×6 = 20 + 24 = 44

Answer:

1. Basically, a ratio is a relation between two values, such that the change of one value will result in the same proportional change in the other (if one value increases 6 times, or decreases 4 times, for example, the same will happen with the other value too.

Since Mrs. Jollie will save $60 for every two panels, then the ratio is:

2 panels: $60

Every ratio can be written in a form of fraction, by simply dividing these values:

2/60  

or, as a reduced fraction:

1/30

2. Now we are given several ratios, which we need to use to find price for 9 panels.

First way:

we can set a proportion because we already said that if we change one value, others will change proportionally as well. So, we take any of these ratios and make a proportion:

2 : $3,000 = 9 : $ x

Solving for x, we get:

x = $3,000 • 9 / 2

x = $13,500

Second way:

From the ratio, we can find the price for a single panel. Then, we simply multiply that with 9 and find the price for nine panels:

one panel costs $3,000 / 2 = $1,500

nine panels cost $1,500 • 9 = $13,500

3. Now, we are again given several ratios and we need to find the price per hour for each company. We can do this by simply dividing:

- ABC Co. 5h : $128

so, price per hour is $128/5 = $25.6

- Solar R' Us 6h : $181

so, price per hour is $181/6 = $30.17

- Light in the Sky 8h: $195

so, price per hour is $195/8 = $24.4

So, the best deal means that the price per hour is the lowest, so the best deal is the Light in the Sky company.