Find the sum and express it in simplest form.
(8a²+ 6a+ 5) + (-3a² - 2a)
108
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Enter the correct answer.
DOO
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DONE

The answer to this equation using the rule of three is 68.

Let the time taken by the first team to finish the building be T. Since the teams are identical, the time taken by the second team to finish the building would also be T.

After 8 workers move from the second team to the first team, the first team has 16 + 8 = 24 workers and the second team has 25 - 8 = 17 workers.

Let the time taken by the first team after the worker change be T1 and the time taken by the second team after the worker change be T2.

Since both teams finish the construction at the same time, we can say that T1 = T2.

By the rule of three, we know that T/16 = T1/24 and T/25 = T2/17.

Cross multiplying and equating we get, 16T = 24T1 and 25T = 17T2.

So T1 = (24/16)T = 3/2T and T2 = (25/17)T.

The ratio of the time spent working by the teams after the worker change to the time spent working by the original teams is (3/2T + (25/17)T) / T = (3/2 + 25/17) = (317 + 252)/(2*17) = 51/17.

Therefore, p + q = 51 + 17 = 68.

The rule of three is a method used to solve problems involving proportionality. It involves expressing the proportion between two values in terms of a third value. It is a mathematical rule used to find the fourth value when three of the values are known. It's also known as proportionality rule, cross-multiplication rule, and inverse proportionality. The rule of three is a simple way to find the value of an unknown quantity in a proportion. The rule of three is used when three of the four values are known and the fourth is unknown.

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Answer:

B

Step-by-step explanation:

$7 for a child X and $13 for a adult Y

Answer:

  a) 125 different numbers

  b) 60 numbers with different digits

Step-by-step explanation:

You want to know the number of different combinations you can have with three dials, each having numbers 1–5, and you want to know the number of combinations with three different digits.

Any of the three dials may be set to any of the five digits, so there are ...

  5 × 5 × 5 = 125

possible three digit combinations.

The number of different 3-digit numbers is 125.

If the digits are to be different, there can be 5 different first digits, 4 different second digits, and 3 different 3rd digits, for a total of ...

  5 × 4 × 3 = 60

possible combinations with different digits.

The number of 3-digit numbers with different digits is 60.

<95141404393>

a) The list with all the possible outcomes is given as follows:

b) The probabilities are given as follows:

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

Of the 2³ = 8 outcomes, only one result in three heads, hence the probability is given as follows:

p = 1/8.

At least one tail is complementary to three heads, hence it's probability is given as follows:

p = 1 - 1/8 = 8/8 - 1/8 = 7/8.

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Based on the table and average minute per square foot, it would take B. 80 minutes for the home cleaning service to clean 200 square feet.

The average is the mean, which is the constant rate of change.

The average is computed as the quotient of a numerator divided by a denominator.

Square Feet and Cleaning Time

Number of Square Feet,  x          50   80   100   150

Time in Minutes, y                        20   32    40     60

Average square feet per minute = 2.5 ft² (150/60)

Average time per square foot = 0.4 (60/150)

The total time to clean 200 square feet = 80 minutes (200 x 0.4)

Thus, using the average minute per square foot, the total time to clean 200 square feet of space will be 80 minutes.

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The relationship between the slopes of the parallel sides is equal.

The relationship between the lengths of the non-parallel sides is equal.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The parallel sides are DG and EF.

The non-parallel sides are DE and GF.

The slope of DG.

Two points pass through by DG.

(-2, 2) and (1, 2)

Slope = (2 - 2) / (1 + 2) = 0/3 = 0

The slope of EF.

Two points pass through by EF.

(-4, -3) and (3, -3)

Slope = (-3 + 3) / (3 + 4) = 0 / 7 = 0

The length of DE.

D = (-2, 2)

E = (-4, -3)

Length of DE = √(-4 + 2)² + (-3 - 2)² = √(4 + 25) = √29

The length of GF.

G = (1, 2)

F = (3, -3)

Length of GF = √(3 - 1)² + (-3 - 2)² = √(4 + 25) = √29

Thus,

The slope of the parallel sides is equal.

The length of the non-parallel sides is equal.

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Answer:

13 years old.

Step-by-step explanation:

Let x be the age of Jada

Given from the question:

Bobby's Age: 7x + 3 years old

Jada's Age: x years old

7x + 3 = 94

7x = 94 - 3

7x = 91

x = [tex]\frac{91}{7}[/tex]

x = 13

Therefore Jada is 13 years old.

Therefore , the solution of the given problem of speed comes out to be average speed of the aeroplane = 200 km/h.

An object's velocity, as opposed to its speed, describes how quickly it goes in both directions. Velocity in physics is the rate of movement in a specific direction. A car's speed is described when we say it goes at 60 km/h.

Here,

Speed of the aeroplane for 400 km = = (400/2) = 200 km/h (due north)

Speed of the aeroplane = 300 km/h (due east)

Speed is a scalar quantity. So no direction is needed. Just for question, direction is given here, for understanding purpose.

Average speed of the aeroplane = (200 + 300)/2

= 250 km/h

Therefore , the solution of the given problem of speed comes out to be average speed of the aeroplane = 200 km/h.

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Answer:

2000km

Step-by-step explanation:

To find the distance between the two planes at 2:30 pm, we need to determine the positions of each plane at that time.

Since the first plane traveled due south at an average speed of 400 km/h for 4 hours (from 10:30 am to 2:30 pm), it would have covered a distance of 400 km/h * 4 h = 1600 km due south.

Similarly, the second plane traveled due east at an average speed of 300 km/h for 4 hours, covering a distance of 300 km/h * 4 h = 1200 km due east.

To find the distance between the two planes, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the distance between the two planes represents the hypotenuse of a right triangle, with the southward distance traveled by the first plane as one side and the eastward distance traveled by the second plane as the other side.

Using the Pythagorean theorem:

Distance^2 = (1600 km)^2 + (1200 km)^2

Distance^2 = 2,560,000 km^2 + 1,440,000 km^2

Distance^2 = 4,000,000 km^2

Taking the square root of both sides to find the distance:

Distance = √4,000,000 km^2

Distance ≈ 2000 km

Therefore, the two planes are approximately 2000 km apart at 2:30 pm.

The probability that T4 wins is 781.

There are two scenarios in which T4 wins.

The first scenario is where T4 beats T1,73 beats T2, and T4 beats T3, and the second scenario is where T4 beats T1, T2 beats T3, and T4 beats T2.

Considering the first scenario:

The probability of T4 beating t1 is 4/(4+1).

The probability T3 beats T2 is 3/(3+2).

The probability T4 beats T3 is 4/(4+3).

Therefore the first scenario happens with probability 4/(4+1)*3/(3+2)* 4/(4+3)

Considering the second scenario:

The probability of T4 beating t1 is 4/(1+4).

The probability T2 beats T3 is 2/(2+3).

The probability T4 beats T2 is 4/(4+2).

Therefore the second scenario happens with probability 4/(1+4)*2/(2+3)* 4/(4+2)

By summing these two probabilities, the probability that T4 wins is 4/(4+1)*3/(3+2)* 4/(4+3) + 4/(1+4)*2/(2+3)* 4/(4+2) which is equal to 256+525 = 781.

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According to the given sample space the probability that T4 wins is 403/105

Here we have given that there are two scenarios in which T4 wins.

And the first scenario is represents that T4 beats T1, T3 beats T2, and T4 beats T3, then the second scenario is where T4 beats T1, T2 beats T3, and T4 beats T2.

While we considering the first scenario, then we have identified that

T4 beating T1 = 4/5

T3 beats T2 = 3/5.

T4 beats T3 = 4/7.

Then the Probability of first scenario is written as,

=> 4/5 + 3/5 + 4/7

=> 7/5 + 4/7

=> 69/35

Now, we have to take the second scenario, then the probability is written as

T4 beating t1 = 4/5.

T2 beats T3 = 2/5.

T4 beats T2 = 4/6.

Then the probability of the second scenario is calculated as,

=> 4/5 + 2/5 + 4/6

=> 6/5 + 4/6

=> 56/30

When we summing these two probabilities, then the probability that T4 wins is calculated as,

=> 69/35 + 56/30

=> 403/105

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Answer:

y = -x - 10

Step-by-step explanation:

set y as the total money owed

set x as how many days passed

if 0 days are passed, they owed $10, which is "-10" the y-intercept

and owed $1 more everyday which is -1x. We can write it as -x.

The y-intercept of the graph is (0, 10)

This is the point where the graph crosses the y-axis

So, the y-intercept is (0, 10)

To do this, we check the values of x in relation to the values of y

From the graph, we can see that the values of y reduces as the values of x increases to 20

This means that the end behaviour is

As x ⇒ +20, y ⇒ 0 and As x ⇒ -∝, y ⇒ +∝

To do this, we again check the values of x in relation to the values of y

From the graph, we can see that the values of y when x = 0 is 10 and also, we have x = -50 and y = 15

So, the possible values are (0, 10) and (-50, 15)

Here, we make use of the end behaviours

So, we have

The function has no maximum, but it has a minimum at (20, 0)

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Answer:

Group 1 polygons have sides that are the same length. But group 2 polygons do not.

Answer:

B

Step-by-step explanation:

personally it feels like the best fit

Line {m} is the line of reflection for the given geometry.

Given is a pair of heart shaped geometrical figures as shown.

It can be seen clearly that the line {m} forms the line of reflection for the given figure.

Therefore, line {m} is the line of reflection for the given geometry.

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Answer:

[tex]$\boxed{(c) : 11}$[/tex]

Step-by-step explanation:

We can think of this problem as placing $7$ dividers (representing the boys) in $20$ slots (representing the people). Thus, the number of ways to arrange the boys and girls is the number of ways to place the dividers, which is $\binom{20}{7}$.

To find the average value of $S$, we need to find the total number of arrangements where $S = k$ for each possible value of $k$, then divide by the total number of arrangements.

Let's first consider the case where $k=0$. There is only $1$ way to arrange the boys and girls such that there are no boys and girls standing next to each other: BBBBBBBBBBBBBBBBBBBBB.

Next, let's consider the case where $k=1$. There are $\binom{7}{1}\binom{13}{6}$ ways to arrange the boys and girls such that there is exactly $1$ pair of boys and girls standing next to each other. To see this, consider that there are $\binom{7}{1}$ ways to choose the position of the divider that separates a boy and a girl, and $\binom{13}{6}$ ways to arrange the remaining dividers and slots.

We can continue this process to find the total number of arrangements for each possible value of $k$. When we add up all of these arrangements and divide by the total number of arrangements, we get the average value of $S$.

More specifically, the average value of $S$ is equal to

[\frac{1\cdot1+\binom{7}{1}\binom{13}{6}\cdot1+\binom{7}{2}\binom{13}{5}\cdot2+\binom{7}{3}\binom{13}{4}\cdot3+\binom{7}{4}\binom{13}{3}\cdot4+\binom{7}{5}\binom{13}{2}\cdot5+\binom{7}{6}\binom{13}{1}\cdot6+\binom{7}{7}\binom{13}{0}\cdot7}{\binom{20}{7}}.]

Simplifying this expression gives us $\boxed{(c) : 11}$.

Answer:

A.2

Step-by-step explanation:

because 7.21 is twice the number 3.605

Using a system of equations, the unit cost of a charcoal pencil is $3.16.

A system of equations involves two or more equations, also known as simultaneous equations, which are solved concurrently or simultaneously.

The cost of one charcoal pencil is the quotient of the total cost of a charcoal pencil divided by the number.

In this situation, after eliminating brushes, we can determine that the total cost of 5.5 charcoal pencils is $17.39.  After the division operation, the unit cost is computed to be $3.16.

                               Allison     Aubrey

Charcoal pencils       3               2

Brushes                     2               5

Total costs          $17.18          $26.56

Let charcoal pencils = c and brushes = b

3c + 2b = 17.18 ... Equation 1

2c + 5b = 25.56 ... Equation 2

Multiply Equation 1 by 2.5:

7.5c + 5b = 42.95 ... Equation 3

Subtract Equation 2 from Equation 3:

7.5c + 5b = 42.95

-

2c + 5b = 25.56

= 5.5c = 17.39

c = 3.16

Thus, after solving the simultaneous equations, we can determine that the cost of one charcoal pencil is $3.16.

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Answer:

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

Sum of interior angles of a 6-sided polygon is:

Both angles ∠X and ∠Y marked as same, let them be x and ∠W is marked as right angle.

The sum is:

m∠X = m∠Y = 100.5°.

Answer:

m∠X = 100.5°

m∠Y = 100.5°

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3cm}\underline{Sum of the interior angles of a polygon}\\\\$S=(n-2) \times 180^{\circ}$\\\\where:\\ \phantom{ww}$\bullet$ $n$ is the number of sides. \\ \end{minipage}}[/tex]

The given polygon has 6 sides.

Therefore, the sum of its interior angles is:

[tex]\implies S = (6 - 2) \times 180^{\circ} = 720^{\circ}[/tex]

From inspection of the given polygon:

Therefore:

[tex]\implies m \angle U + m \angle V + m \angle W + m \angle X + m \angle Y + m \angle Z = 720^{\circ}[/tex]

[tex]\implies 159^{\circ} + 99^{\circ} + 90^{\circ} + m \angle X + m∠ \angle Y + 171^{\circ} = 720^{\circ}[/tex]

[tex]\implies m \angle X + m \angle Y + 519^{\circ} = 720^{\circ}[/tex]

[tex]\implies m \angle X + m \angle Y = 201^{\circ}[/tex]

As m∠X is equal to m∠Y:

[tex]\implies m \angle X = m \angle Y = 201^{\circ} \div 2 = 100.5^{\circ}[/tex]

The required area of each stained glass section is 1060.71 square centimeters.

Area of a semicircle.

A semicircle is a part of a circle, gotten from the division of a circle into two equal halves. So that halve of a circle is a semicircle. The area of a semicircle can be determined as;

Area of a semicircle = 1/2 [tex]\pi[/tex] r^2

where r is the radius of the circle.

In the given question, we have;

diameter of the church's window = 90 cm

So that its radius is;

r = 90/ 2

 = 45

r = 45 cm

Area of the church's window = 1/2 [tex]\pi[/tex] r^2

                      = 1/2 * 22/7 * 45^2

                      = 3182.143

Area of the church's window is 3182.143 square centimeters

Thus, since the semicircle would be divided into three equal parts;

Area of each stained glass section = 3182.143/ 3

                           = 1060.71 square centimeters

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Answer: 14

Step-by-step explanation:

f(-2) means x is -2, so we can solve for when x = -2 by plugging -2 into the equation.

[tex]f(-2) = 3(-2^{2}) - (-2)\\=3(4) + 2\\=12+2\\=14[/tex]

Answer:

Step-by-step explanation:

So what you start with is the variable "x" in 3 different places. When you are changing the x variable, you need to plug it into every variable in the equation. Start by doing that and the problem will look like: f (-2) = 3 (-2)^2 - (-2) Now you can start with either the 3 (-2)^2 or the - (-2), but it is better to go from left to right.

Your Best

Elina

Note that the percentage of the students in the survey, to the nearest whole number, that prefer outdoor activities given they prefer non-fiction is: 11%.

To get the percentage of those who love outdoor activities as well as non-fiction, we must complete the table.

Given:

Total number of those who love Fiction and Non Fiction but who love indoors = 50

From that list those who love fiction = 24, thus, those who love indoor and non-fiction =

50 - 24 = 26

Total number of those who were served are = 90

If the total number of those who love Fiction and Non-Fiction but who love indoors = 50

Then the total number of those who love Fiction and Non Fiction but who love Outdoors = 90 - 50 = 40

If the total number of those who love outdoor (Fiction and non-fiction) = 40 and those who prefer fiction only from this category is = 30;

Then the total number of those who love Non Fiction but who love Outdoors =

40 -30

= 10

Thus, the percentage of this number against the total number of those surveyed is:

10/90

= 0.1111111111 or 11%

Therefore, the percentage of students in the survey, to the nearest whole number, prefer outdoor activities given they prefer non-fiction is given as 11%. See the full table attached.

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The number of millimeters in each glass is 200ml.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator.

It is important to note that some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

Since Cheetan brought a 2L bottle of milk and used 400 ml from it with the remaining amount of milk he could complely fill 8 glases of the same size and shape. The amount in each will be:

= (2l - 400ml )/8

= (2000 - 400) / 8

= 1600 / 8

= 200ml

Therefore, based on the calculation, there'll be 200 millimeters on each glass.

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Complete question

cheetan brought a 2L bottle of milk and used 400 ml from it with the remaining amount of milk he could complely fill 8 glases of the same size and shape. How many ml will each contain?

After 31 years the population will be the same. Their populations will be 2072 when they are the same.

Growth rates are calculated by dividing the difference between the ending and beginning values for the period under consideration by the starting value. The most common time periods for growth rates are annually, quarterly, monthly, and weekly.

The formula for the growth of the population is:

A = P(1+r)^n

A is the total number population after n years.

P is the initial number of population

r is rate of interest.

For town A,

The initial population is 700. The growth rate is 3.5% = 0.035.

The population of town A after t year is y = 700(1+0.035)^t

For town B,

The initial population is 1400. The growth rate is 1.25% = 0.0125.

The population of town A after t year is y = 1400(1+ 0.0125)^t

The system of equations is:

y = 700(1+0.035)^t

y = 1400(1+ 0.0125)^t

The intersection point is (31.537,2071.432).

After 31 years the populations will be the same.

their populations will be 2072 when they are the same

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Answer:

Rs.2700

Step-by-step explanation:

14% profit means 100% +14% more=114% profit

then to make into decimal 114% divided by 100 to give 1.14

then divide 2850 by 1.14 to find original selling price of bicycle

which will be Rs.2,500

next, a 8% profit means 100%+8% which equals 108% and then make into decimal which is 1.08

then multiply the original selling price (Rs.2,500) by 1.08 to give your final selling price after the 8% profit of ...

Rs.2,700

Answer: they are ripped

Step-by-step explanation:

i guessed

Answer:

3 mi / hr

Step-by-step explanation:

It takes the cyclist 2 hours to go 6 miles further ( 30 -24 mi)

  6 mi / 2 hr = 3 m/hr    

The estimated solution of the system y=3x-6 and y=(2/5)x+5 is (4, 7)

An equation is used to show the relationship between numbers and variables.

The standard form of a linear equation graph is:

y = mx + b

Where m is the slope of the line and b is the y intercept.

Given the linear equation:

y = 3x - 6   (1)

y = (2/5)x + 5     (2)

Subtracting equation 2 from 1 to solve using elimination method gives:

0 = 2.6x - 11

x = 55/13 ≅ 4

put  x = 55/13 in eqn 2:

y = (2/5)(55/13) + 5

y = 87/13 ≅ 7  

The solution is (4, 7)

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Answer:

  6.08 fluid ounces

Step-by-step explanation:

You want the amount of stain required to cover the surface area of the ends and three sides of a beam 6" square and 6 ft long. 128 floz of stain will cover 200 square feet.

The two ends of the beam are 1/2 ft square, so the area of each is ...

  A = s² = (1/2 ft)² = 1/4 ft²

The two ends have a total area of ...

  2 × (1/4 ft²) = 1/2 ft² . . . . end area

Three of the four sides of the beam are to be stained, so their total area is the area of 3 rectangles, each of which is 1/2 ft by 6 ft.

The area of each rectangle is ...

  A = LW

So, the area of the three rectangles is ...

  total side area = 3 × (1/2 ft)(6 ft) = 9 ft²

Then the area to be stained is the sum of the end area and the side area:

  stained area = (1/2 ft²) +(9 ft²) = 9.5 ft²

The amount of stain required is proportional to the area, so we can write the proportion ...

  q/(9.5 ft²) = (128 floz)/(200 ft²)

Multiplying by 9.5 ft² gives ...

  q = (128 floz)(9.5/200) = 6.08 floz

The homeowner needs 6.08 fluid ounces of stain to stain the beam.

Answer:

no

Step-by-step explanation:

Answer:

125 = (15x) + 45
(Sorry if I'm wrong!)