In Ms. Block's class 8 students share a box of cherries equally. Each of them receives 9 cherries. There are
then 6 cherries left over. How many cherries were there altogether in the box?

Given the subset A, the complement of A, A' is  {6}

Given the complement of C, C is {5, 7, 9}

The universal set contains all the elements of the subsets. '  means complement = it means elements that are not in the subset but in the universal set.

To write a set in a roster form, the elements in the set are written in a row within curly brackets - { }. The elements in the set are then separated by commas.

A' = {6}

C = {5, 7, 9}

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Answer:

  (x, y, z) = (-4, -5, 2)

Step-by-step explanation:

You want the solution to the 3×3 system of equations ...

There are many tools available for solving a system of equations. A typical hand-held graphing calculator offers at least two methods. An online graphing calculator solution is shown in the attachment.

For the attached solution, we defined z in terms of x and y using the second equation. This effectively reduces the system to a 2×2 system, which is easily solved. The same "substitution" method can be used when solving the system by hand.

The graph shows the solution to be (x, y, z) = (-4, -5, 2).

Using z = -4x -4y -34 from the second equation, the system reduces to ...

  3x -y -4(-4x -4y -34) = -15

  19x +15y = -151

and

  2x +3y +5(-4x -4y -34) = -13

  -18x -17y = 157

Writing these equations in general form, we have ...

The "cross multiplication method" gives the solution for x and y as ...

  D = (19)(17) -(18)(15) = 53

  x = (15(157) -17(151))/D = -212/53 = -4

  y = (151(18) -157(19))/D = -265/53 = -5

Then z is ...

  z = -4(-4) -4(-5) -34 = 16 +20 -34 = 2

The solution is (x, y, z) = (-4, -5, 2).

__

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Over a year, a prison's population dropped by 312 inmates. We know that 1 Year = 12 Months.

Additionally, considering that each of the 12 months declined at the same rate.

the Monthly decrease  in members = 312 / 12 = 26

Therefore, the expression used to calculate the monthly drop in prisoner population = Number of prisoners decreased per year / Number of months

Note: If the monthly drop rate is the same, the aforementioned equation is correct ( for all months in that year)

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Answer:

4

Step-by-step explanation:

g(x) is the graph of f(x) shifted up 4 units.

The expression, in terms of s and t, for the number of seats on the airplane is given by 24 s + 9 t.

We are given that there are 2 types of seating in an airplane which are economy and first class seating.

Also,

We are given that:

There are s seats in economy in each row and there are t seats in first class in each row.

Now, there are 24 rows in economy class seating.

So, number of seats in economy class = 24 × s = 24 s

And, there are 9 rows in first class seating.

So, number of seats in first class = 9 × t = 9 t

The total number of seats then will be = 24 s + 9 t

Therefore the expression, in terms of s and t, for the number of seats on the airplane is given by 24 s + 9 t.

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Answer:

John

Step-by-step explanation:

it says Lizzy had which means we don’t know how much she has now. It says Fifi will have so we don’t know how much they have right now. But it says John has so we know what he has so therefore he has the most as of right now

Answer:$49.50

Step-by-step explanation:

First you have to find what 10% of 55 is. So if you times 10% by 55 you come out with $5.5. So after that you must subtract 5.5 from 55 which comes out to $49.50.

Answer:

9/8 mile or 1 and 1/8 mile

Step-by-step explanation:

Add 3/8 + 3/4

LCD is 8 so it would be 3/8 + 6/8 which is 9/8 (which can be converted to the mixed number 1 and 1/8)

hi

5(x+4) =1/2 *(12)* (2X-6)

5x+20 =  6 * ( 2x-6)

5x+20 = 12x-36

5x-12x = -36-20

-7x =  -56

  x = -56/-7

 x = 8

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{9 {}^{(x + 1)} - 3 {}^{2x} }{4 \times 3 {}^{(2x - 1)} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{3{}^{2(x + 1)} - 3 {}^{2x} }{4 \times 3 {}^{(2x - 1)} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{3{}^{(2x + 2)} - 3 {}^{2x} }{4 \times 3 {}^{(2x - 1)} } [/tex]

here :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{3{}^{(2x - 1)}(3 {}^{3} - 3 {}^{1}) }{4 \times 3 {}^{(2x - 1)} } [/tex]

[ taking [tex]{ \sf {3}^{(2x - 1)} } [/tex]common here ]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{27 {}^{} - 3 {}^{}}{4 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{24{}^{} {}^{}}{4 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: 6[/tex]

Answer:7:15 pm

Step-by-step explanation:

We know he went to bed at 9:00 PM and spent 1 hr and 45 minutes playing games. Start by subtracting one hour away, so we get 8:00 PM. subtract 45 minutes from that and he would have started playing at 7:15 PM.

The correct option is C, if f(x) has a domain only with positive values, the graph will be on the first and fourth quadrant.

We know that the domain of f(x) is only the set of positive real numbers. Now remember that the domain of a function is the set of the inputs of that function (the inputs are on the horizontal axis).

Then the graph of f(x) will only be on the positive side of the horizontal axis.  We know that the two quadrants that are on that region are the first quadrant and the fourth quadrant.

Then if f(x) has a domain only with positive values, the graph will be on the first and fourth quadrant, this means that the correct option is C.

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The systolic pressure, to the nearest tenth of a millimeter, for a person of age 41 years is; 133.6 mm Hg

We are given the equation that gives a person's blood pressure, p at the age y year is;

p = 0.007y² - 0.003y + 122

To find the systolic pressure for a person of age 41 years, just plug in y = 41 into the given quadratic equation to get;

p(41) = 0.007(41)² - 0.003(41) + 122

p(41) = 11.767 - 0.123 + 122

p(41) = 133.6

Thus, the systolic pressure, to the nearest tenth of a millimeter, for a person of age 41 years is; 133.6

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Answer: option D

Step-by-step explanation:

Given equation:

P = 6 w + 8 [eq1]

l=2w+4 [where l is length]

using eq1 we have:

6w=P-8

w=(P-8)/6

hence  option D

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Answer: 0.275

Step-by-step explanation:

a. To express 11/40 as a decimal, you need to divide 11 by 40. (Steps shown in image)

b. Sorry, I can't figure out the answer to this. I don't recommend making the denominator a 4 as the numerator would become 1.1.

Step-by-step explanation:

[tex] = ( \frac{3}{5} {)}^{2} [/tex]

[tex] = \frac{ {3}^{2} = 3 × 3 }{ {5}^{2} = 5 × 5 } \\ [/tex]

[tex] = \frac{9}{25} \\ [/tex]

☘️☘️☘️...

Answer:

[tex] \frac{9}{25} [/tex]

Step-by-step explanation:

[tex] { ( \frac{3}{5} )}^{2} \\ = ( \frac{ {3}^{2} }{ {5}^{2} } ) \\ = \frac{9}{25} [/tex]

Answer: 4-3b

Step-by-step explanation:

10-0.5(12+8b)+b    First, distribute -0.5 into 12 and 8b

10-6-4b+b              Then combine like terms

4-3b                        Done!

Answer:

D

Step-by-step explanation:

Acute angle are angles less than 90°.And 43° is less than 90° and the inverse is not less than 90°.

The energy required is 30 watts second.

In order to accomplish work and to produce heat and light, energy must be transferred to a body or to a physical system. Energy is the quantitative attribute that does this. Energy is a preserved resource; according to the rule of conservation of energy, energy can only be transformed from one form to another and cannot be created or eliminated.

The voltage of a battery is 12 V and;

The charge is 2.5C.

Now, energy can be defined as the product of voltage and charge.

Therefore,

E = V × C

E = 12 × 2.5

E = 30 watt second

Hence, the energy needed by the 12 V battery to move 2.5 C through the electrical circuit is 30 watts second.

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Answer:

(i)

Step-by-step explanation:

express the ratio as a fraction, that is

4 : 5 = [tex]\frac{4}{5}[/tex]

to convert the fraction to a percentage multiply it by 100%

[tex]\frac{4}{5}[/tex] × 100% = 4 × 20% = 80%

The first flight is 2 hours and second flight is 2 hours and 48 minutes

The two distances are the same (out and back),

so set them equal.

That distance is cover by having one is (rate)(time) equal to other is (rate)(time).

Let,

One time is “x” and the other is “4.8-x.”

One average rate  is 460 per hour

and the other average rate is 500 per hour.

we know , Speed = [tex]\frac{distance}{time}[/tex]

so , distance = speed × time

put in this formula we get the value of X

⇒460 x = 500 (4.8 -x)

⇒460 x = 2400 - 500x

⇒900 x = 2400

⇒x = 2.5 hours for the slower plane.

⇒4.8- x = 2.3 hours for the faster plane.

The formula speed = distance ÷ time can be rearranged, just like any other equation.

Here detail explanation about relation between speed distance and time :

The formula can be rearranged in three ways:

speed = distance ÷ time

distance = speed × time

time = distance ÷ speed

To calculate one of the variables (speed, distance or time) we need the other two.

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50% of women who said ‘no’ out of the total survey population if 15 men and 75 women were asked if they had seen the company’s latest TV advertisement.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Market research was undertaken to determine whether an ad campaign was successful for the software company.

Total number of people = 15 + 75 = 90

The number of people who said yes = (2/5)90 = 36

The number of people who said no = 90 - 36 = 54

The number of men said yes = (6/15)x15 = 6

The number of men said No = 15 - 6 = 9

The number of women who said no = 54 - 9 = 45

Percentage = (45/90)x100

The percentage of women who said ‘no’ out of the total survey population:

= 50%

Thus, 50% of women who said ‘no’ out of the total survey population if 15 men and 75 women were asked if they had seen the company’s latest TV advertisement.

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The value of the function is [tex]5^t-5[/tex] .

A function is defined as a expression containing one or more variables.

A function, in technical terms, is a mechanism to connect a collection of inputs to a set of outputs.

A function of a single variable (say x) is defined mathematically as g(x).

Let us consider a function of a variable x such that it is defined as:

g(x)=x+1

Here the output are calculated for all values of x . At x=1 the value of the function is denoted as g(1)=1+1=2.

Mathematically to calculate the value of the function f(x) for any particular value of x we substitute the value of x into the value of f(x).

Now the given function is given as:

[tex]f(x)=5^x-5[/tex]

Therefore at x=t,

[tex]f(t)=5^t-5[/tex]

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We need to mix 15 ml of 28 % of solution to get the resulting mixture as a 13 % sugar mixture.

Let the amount of 28 % sugar solution be x ml.

We are given that:

10 % sugar solution = 75 ml

Total solution = 75 ml + x ml

We need the solution to be 13 % sugar solution.

So, we get that:

28 % x + 10 % ( 75 ) = 13 % ( 75 + x )

28 x + 750 = 13 ( 75 + x )

28 x + 750 = 975 + 13 x

28 x - 13 x = 975 - 750

15 x = 225

x = 225 / 15

x = 15

Therefore, we need to mix 15 ml of 28 % of solution to get the resulting mixture as a 13 % sugar mixture.

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Answer: 6.47 hours

Step-by-step explanation:

First, you need to change your seconds into terms of minutes.

16 seconds / 60 s in a min = .266 min

Add that to your minutes:

28+.266 = 28.266 minutes

Now convert your minutes into hours

28.266 min/60 min in an hour=.47

Add that to your hours:

6+.47= 6.47 hours total

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

The prices from 5 gas stations surveyed are given as:

$2.79, $2.99, $2.69, $2.89, and $2.69.

There are no outliers in the dataset

So, the dataset can be summarized by the mean

The mean is

Mean = Sum/Count

So, we have

Mean = ($2.79+ $2.99+ $2.69+ $2.89+$2.69)/5

Evaluate

Mean = 2.81

The article quoted $2.69 as the typical price

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

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