87th term of 12,0,-12

Final answer:

Mr. Avery can arrange the 30 chairs in 5 rows of 6 chairs each or 3 rows of 10 chairs each to satisfy the conditions of having more than one row and the chairs per row being greater than the number of rows.

Explanation:

Mr. Avery can arrange the 30 chairs in the band room in multiple configurations but must satisfy two conditions: there must be more than one row and the number of chairs in each row must be greater than the number of rows. To find such arrangements, we can look for factors of 30 that adhere to these conditions. One possible arrangement is 5 rows with 6 chairs in each row. This satisfies the conditions because there are more than one row, and the number of chairs per row (6) is greater than the number of rows (5).

Another possible arrangement could be 3 rows with 10 chairs each. Here, the condition is also met since there are more than one row and the number of chairs per row (10) is greater than the number of rows (3). Mr. Avery must ensure there's enough space to move around, so he may need to rearrange the chairs to provide adequate pathways between rows.

First, use distributive property:

5(2r+6)-12r  The original expression; multiply 5 by 2r, and 5 by 6.

10r+30-12r  Keep the -12r, just add it on to the end of the number(s) you found

Next, use communitive property:

10r+30-12r  What we found in the previous step

-2r+30        Combine the like terms; 10r-12r=-2r, then place the 30 at the end

Done! Your answer is -2r+30.

Hope that helps!

Answer:

1/3

Step-by-step explanation:

(8/15)   -   (1/5)

change 1/5 to 3/15 (which is equivalent to 1/5)

(8/15) - (3/15) = (5/15)

Simplify

(5/15) = (1/3)

Answer:

1/3

Step-by-step explanation:

8/15-1/5=8/15-3/15=5/15=1/3

Answer:

Step-by-step explanation:

3 fourteen hr shifts.....that (14 * 3) = 42 hrs....thats 1 day and 18 hrs

first shift starts at 9 AM......

one day later will make it 9 AM the next day....now we have the 18 hrs.....so from 9 AM to 9 PM is 12 hrs.....so we are at 9 PM and have 6 hrs left.....making the last shift end at 3 AM <==

3:00 pm is the  time where  does their third shift end.

Two or more expressions with an Equal sign is called as Equation.

Given that A factory runs nonstop for three 14 - hour shifts.

The first shift starts at 9.00 AM.

We need to find the times does their third shift end.

First shift:

9:00Am to 11:00Pm (14 hours)

second shift:

11:00pm to 1:00 am (14 hours)

Third shift

1:00 am to 3:00 pm (14 hours)

Hence, 3:00 pm is the  times where  does their third shift end.

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Option A

Length of CD is 10 inches

Solution:

The diagram is attached below

Given that, Circle A and circle B are congruent

CD is a cord of both circles

AB = 24 inches

Radius = 13 inches

To find: length of CD

Draw a straight line connecting A and C

AC represents the radius of circle. Also given that radius is 13 inches, So AC = 13 inches

Given in question that AB = 24 inches

Therefore from figure, AO = AB/2 = 24/2 = 12

AO = 12

Let "b" be the length of CO

Therefore, CD = CO + OD = b + b

AOC forms a triangle, so we can use pythogoras theorem

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

By above definition for triangle AOC

[tex]AC^2 = AO^2 + OC^2[/tex]

Substituting AC = 13 and AO = 12 and OC = b

[tex]13^2 = 12^2 + b^2\\\\b^2 = 169 - 144\\\\b^2 = 25\\\\b = 5[/tex]

Thus length of CD is:

CD = b + b = 5 + 5 = 10

Thus length of CD is 10 inches

10 times

tenth

the same

Step-by-step explanation:

K.E is directly proportional to mass thus if the mass increases or decreses "k" times, then so does the K.E

Answer:

1). 10 times more 2). 10 times less 3). the same

Step-by-step explanation:

Answer:

infinite

Step-by-step explanation:

The slope is the amount the line moves in y direction when you go move unit in the x direction. For a vertical line that is infinite...

Benson earned 70 points per game not including the bonus points.

Step-by-step explanation:

Given,

Games of trivia played = 12

Bonus points received per game = 35 points

Bonus points for 12 games = 35*12 = 420 points

Total points earned = 1260 points

Points earned in games = Total points - bonus points

Points earned in games = 1260 - 420 = 840 points

As he scored 840 points in 12 games, therefore,

12 games = 840 points

1 game = [tex]\frac{840}{12} = 70\ points[/tex]

Benson earned 70 points per game not including the bonus points.

Keywords: subtraction, division

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Answer:

The Total number of car is 7 and The Total number of van is 5 .

Step-by-step explanation:

Given as :

The maximum capacity of car = 3 passengers

The maximum capacity of van = 8 passengers

Total number of vehicles = c + v = 12 vehicles

The maximum capacity of vehicles combination = 61 passengers

Let The Total number of car = c

Let The Total number of van = v

Now, According to question

c + v = 12            .........A

3 c + 8 v = 61            ............B

Now, Solving eq A and B

I.e (3 c + 8 v) - 3 × (c + v) = 61 - (3 × 12)

Or, (3 c - 3 c) + (8 v - 3 v) = 61 - 36

Or, 0 + 5 v = 25

∴ v = [tex]\dfrac{25}{5}[/tex]

i.e v = 5

So,The Total number of van = v = 5

Now Put the value of v into eq A

∵ c + v = 12    

So, c + 5 = 12

∴ c = 12 - 5

i.e c = 7

So,The Total number of car = c = 7

Hence,The Total number of car is 7 and The Total number of van is 5 . Answer

The student's question is about determining the number of vans owned by a company using a system of linear equations. By setting up two equations and using the elimination method, we find that the company owns 5 vans and 7 cars.

The question involves solving a system of linear equations to determine how many vans a company owns. We know that the company has a total of 12 vehicles, which are either cars with a capacity of 3 passengers or vans with a capacity of 8 passengers. The total capacity of all 12 vehicles combined is 61 passengers. To solve this problem, we will create two equations based on this information:

Using elimination to solve the equations:

Therefore, the company owns 7 cars and 5 vans.

Answer:

[tex]\large \boxed{\text{19 visitors/mo}}[/tex]

Step-by-step explanation:

The average rate of change is the change in the number of visitors divided by the change in the number of months.

1. Change in number of  visitors  

Change in visitors = 182 -125 = 57 visitors

2. Change in number of weeks

Change in time = 5 - 2 = 3 months

3. Average rate of change

[tex]\begin{array}{rcl}\text{Average rate of change} &= &\dfrac{\text{change in visitors}}{\text{change in months}}\\\\&= &\dfrac{\text{57 visitors}}{\text{3 mo}}\\\\& = & \textbf{19 visitors/mo}\\\end{array}\\\text{The average rate of change is $\large \boxed{\textbf{19 visitors/mo}}$}[/tex]

Answer:

D. implement better procedures at the security gate.

Step-by-step explanation:

did the usa test prep

Answer:

∠CPB is an acute angle.

Step-by-step explanation:

Firstly, lets go over what an acute angle is. An acute angle is any angle that is less than 90°.

In the problem, we are told that ∠APE is a right angle. This means that it is 90°.

As ∠APE and ∠BPD are vertical angles, they must have the same measure. This means that ∠BPD is also 90°

As ∠BPD has the line PC in the middle of it, this angle could be split into ∠CPB and ∠CPD. These two angles must add up to be the same as ∠BPD, which is 90°. As these two angles must add to be 90° they must be less than 90°. This means that both ∠CPB and ∠CPD are acute angles.

As ∠CPD is not one of the options for the question, ∠CPB is the only correct answer.

Acute angles measure less than 90°. Among the options, only C) Angle CPB fulfills this condition. It's the only angle clearly smaller than a right angle in the image.

An acute angle is an angle that measures less than 90 degrees. In the image you sent, only one of the angles measures less than 90 degrees.

-angle APE is a right angle, which measures exactly 90 degrees.

-angle CPE and angle APC are both obtuse angles, which measure more than 90 degrees but less than 180 degrees.

-angle CPB is the only angle that measures less than 90 degrees, so it is the only acute angle.

Therefore, the answer is C) Angle CPB.

Turn both into improper fractions.

6 1/3 = 19/3

4 1/9 = 37/9

Find common denominators

19/3 = 57/9

37/9

Subtract.

57/9 - 37/9 = 20/9

Turn back into a mixed number.

20/9 = 2 2/9

Best of Luck!

Answer:

2 2/9

Step-by-step explanation:

Cuz yeah

Answer:

Step-by-step explanation:

XW II Yz and XY is transversal

∠XYZ +∠ZYX =  180°           {sum of co-interior angle is 180}

2x + 90 + 3x - 5 = 180

5x = 180 - 90 + 5

5x = 95

x = 95 / 5

x = 19

Answer:

A. 8/4=12/w

Step-by-step explanation:

8/4=12/x

8feet long           12 inches

----------------   =    ----------------

4feet wide            X because we dont know exact width

Answer:

A. 8/4=12/w

Step-by-step explanation:

Answer:

A: Its legs are congruent

Step-by-step explanation:

A trapezoid is a quadrilateral with exactly one pair of parallel sides. In a trapezoid the parallel sides are called bases. A pair of angles that share a base as a common side are called a pair of base angles. A trapezoid with the two non-parallel sides the same length is called an isosceles trapezoid.

An isosceles trapezoid is a trapezoid with two congruent sides and congruent base angles.

An isosceles trapezoid is a trapezoid that has two congruent sides. In other words, the two non-parallel sides of an isosceles trapezoid are equal in length. The base angles of an isosceles trapezoid are also congruent. The parallel sides of an isosceles trapezoid are not equal in length.

For example, if a trapezoid has sides AB = 6 cm, BC = 5 cm, CD = 4 cm, and DA = 5 cm, then it is an isosceles trapezoid because sides BC and DA are congruent.

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The percent error is 4.17 %

Solution:

To be labeled as a jumbo egg, the egg is supposed to weight 2.5 oz

When Desmond buys a carton of jumbo eggs, the weight of one is 2.4 oz

To find: percent error

Percent error is the difference between a measured and known value, divided by the known value, multiplied by 100%

[tex]\% \text { error }=\frac{\text {approximate value}-\text {exact value}}{\text {exact value}} \times 100[/tex]

Here approximate value = 2.5 oz and exact value = 2.4 oz

[tex]\% \text { error }=\frac{2.5-2.4}{2.4} \times 100\\\\\% \text { error }= \frac{0.1}{2.4} \times 100 = 4.17[/tex]

Therefore percent error is 4.17 %

Answer:

m∠4= 360-(m∠A+m∠1+m∠3+m∠C+m∠2)

Step-by-step explanation:

In the diagram. check attach image

m∠A + m∠B + m∠C + m∠D = 360º.

Every quadrilateral can be decomposed (cut apart) into two triangles, each of whose angles' measures sum to 180º.

m∠A + m∠1 + m∠ 3 = 180º

m∠C + m∠2 + m∠4 = 180º

m∠A+m∠1+m∠3+m∠C+m∠2+m∠4 = 360º

therefore :

m∠4= 360-(m∠A+m∠1+m∠3+m∠C+m∠2)

I think that the answer is A, because in the range, none of the numbers should be the same, and the numbers are all different in choice A

Answer will be: y=7/3+2x/3

Answer:

y =  2/3x + 7 / 3

Step-by-step explanation:

Step 1: Add 2x to both sides.

−2x+3y+2x=7+2x

3y=2x+7

Step 2: Divide both sides by 3.

3y  / 3 = 2x+7 / 3

y=  2 / 3x  + 7 / 3

Answer:

No value of x makes the equation true.

Step-by-step explanation:

Here are the choices which are missing in the question:

a) Amaya made a mistake because 4 is not equal to 5

b) No value of x make the equation true.

c) All value of x make the equation true.

d) The solution is x= 4 or 5

Given equation is [tex]8x+4=9+4(2x-1)[/tex]

Now, solving the equation:

[tex]8x+4=9+4(2x-1)[/tex]

distributing 4 with both 2x and -1

⇒[tex]8x+4= 9+8x-4[/tex]

⇒[tex]8x+4= 5+8x[/tex]

Subtracting both side by 8x

∴ 4=5

The result indicate that equation has the same result and x has no value.

Answer:

No values of x make the equation true.

Answer:

1,100

Step-by-step explanation:

The total number of ounces that were put in  jars was 1,128 Oz  so your answer would be 1,110 rounded to the nearest hundred.

The answer is;

20 x 30 + 10 x 50 = 1,100

Answer:

C) 2.75x+3.25y ≤ 500

Step-by-step explanation:

Here are the correct options given:

A) 3.25x +2.75y ≤ 500

B)  3.25x + 2.75y ≥ 500

C) 2.75x + 3.25y ≤ 500

D)  2.75x + 3.25y ≥ 500

Given: Nails cost is $2.75 per pound

           Screw cost is $3.25 per pound

           Jerry has only $500 to spend on nails and screws.

           x represent quantity of nail bought and y represent quantity of screw    bought.

As given we know that Jerry has only $500 to spend, so the total cost has to be less than or equal to $500. It cannot go more than $500.

Remember, Total cost= [tex]\textrm{cost of goods per pound}\times quantity[/tex]

Now, Inequality to represent the cost of buying nails and screw.

[tex]\$2.75\times x\ pounds+ \$3.25\times y\ pounds\leq \$ 500[/tex]

∴ [tex]2.75x+3.25y\leq 500[/tex]

Answer. 17<18

The sum of 3x + 14 equals 17x.

The difference between 20 - 2x equals 18x.

Therefore the equation is not equal to each other.

Option A: 3 is the right answer

Step-by-step explanation:

Given

[tex]f(x) = -2x-1[/tex]

In an ordered pair, the x-coordinate is the input to the function and y-coordinate is the output of the function on specified input.

In the given ordered pair,

x-coordinate is -2 so we will put it into the function to get the y-coordinate

So,

[tex]f(-2) = -2(-2)-1\\= 4-1\\=3[/tex]

3 will complete the ordered pair of the point on the graph

Hence,

Option A: 3 is the right answer

Keywords: functions, variables

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Answer:

A

Step-by-step explanation:

(x coodinate, y coodinate) = (x, f(x))

(-2, ___) is saying us x=-2, and question is asking y =?

f(x) = -2x -1

f(-2) = -2.-2 -1

f(-2)= 4 -1

f(-2) = 3

so, y= f(-2) = 2

(x, f(x)) = (-2, f(-2)) = (-2,3)

Hope this helps ^-^

Answer:

x=5

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

what i did was..

41-6 = 30

30/7 = 5

x=5

Answer: Omar can make 14 whole dumplings.

Step-by-step explanation: Make 2 3/4 an improper fraction. To do this, multiply 2 by the denominator, 4. From this, you get 8. Then add 8 to the numerator, which is 3, and you get 11. Keep the denominator and you'll have 11/4.

To divide fractions, you make 3/16 its reciprocal by basically flipping the fraction so that the numerator becomes the denominator and vise versa, making it 16/3. Then multiply 11/4 and 16/3. 11 x 16 is 176; 4 x 3 is 12. The result is 176/12. Simplify by dividing the numerator and denominator by 4. Your resulting answer should be 44/3. Simplify even further by simple division. Your final answer should be 14 2/3. Discard the 2/3 because Omar needs to make whole dumplings. So the answer is 14.

Final answer:

Omar can make 14 whole dumplings with 2 3/4 cups of dough when each dumpling requires 3/16 cups of dough.

Explanation:

The student's question asks how many whole dumplings Omar can make with 2 3/4 cups of dough if each dumpling uses 3/16 cups of dough.

Convert 2 3/4 cups to an improper fraction: 11/4 cups.

Divide the total cups of dough (11/4) by the amount needed for one dumpling (3/16) to find the number of dumplings Omar can make.

Perform the division: (11/4) \/ (3/16) = 11/4 \\* 16/3 = 44/3.

Omar can make 44/3 dumplings, which is 14 whole dumplings with some dough left over.

Omar can make 14 whole dumplings with 2 3/4 cups of dough when each dumpling uses 3/16 cups of dough.

Answer:

Step-by-step explanation:

Area= length x width

area=6/7, length=3/5, width=?

6/7=3/5 x width

6/7 divided by 3/5= 6/7 x 5/3 (you have to multiply by the recipricol, or flip the fraction.)

6/7 x 5/3=30/21= 1 3/7=width

The area of a 2D form is the amount of space within its perimeter. The width of the rectangle is 10/7 miles.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The area of a rectangle is the product of its length and its width, therefore, the width of the rectangle can be written as,

Area = Length × Width

Width = Area / Length

Given the area of the rectangle is 6/7 square miles, while the length of the rectangle is 3/5 miles, therefore, the width of the rectangle is,

Width = (6/7)/(3/5)

Width = (6×5)/(7×3) = 10/7

Hence, the width of the rectangle is 10/7 miles.

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Answer:

b. m can be any positive real number.

Step-by-step explanation:

The value of m can be any positive real number. The correct answer is option b) m can be any positive real number.

Step 1

To determine the value of m that makes the ranges of [tex]\( f(x) = m^x \)[/tex] and [tex]\( g(x) = x^m \)[/tex] the same, we need to analyze the ranges of both functions.

Analyzing [tex]\( f(x) = m^x \)[/tex] :

- If [tex]\( m > 0 \)[/tex], [tex]\( m^x \)[/tex] is an exponential function.

 - For [tex]\( m > 1 \)[/tex], [tex]\( f(x) = m^x \)[/tex] increases and its range is [tex]\( (0, \infty) \)[/tex].

 - For [tex]\( 0 < m < 1 \)[/tex], [tex]\( f(x) = m^x \)[/tex] decreases and its range is also [tex]\( (0, \infty) \)[/tex].

Step 2

Analyzing [tex]\( g(x) = x^m \)[/tex] :

- The range of [tex]\( x^m \)[/tex] depends on whether m is positive or negative:

 - For positive m :

   - When [tex]\( m = 1 \)[/tex], [tex]\( g(x) = x \)[/tex], the range is all real numbers, [tex]\( \mathbb{R} \)[/tex].

   - When [tex]\( m > 1 \)[/tex] or [tex]\( 0 < m < 1 \)[/tex], the function is defined for [tex]\( x > 0 \)[/tex] and its range is [tex]\( (0, \infty) \)[/tex] .

 - For negative m :

   - The function [tex]\( x^m \)[/tex] is undefined for [tex]\( x = 0 \)[/tex] and for negative x, and thus its range is [tex]\( (0, \infty) \)[/tex].

Both [tex]\( f(x) = m^x \)[/tex] and [tex]\( g(x) = x^m \)[/tex] have the range [tex]\( (0, \infty) \)[/tex] for any positive [tex]\( m \)[/tex], but for any negative m, [tex]\( g(x) \)[/tex] is undefined at zero and for negative x.

The value of m can be any positive real number (option b).

Complete question : If the range of f(x) = ^mx and the range of g(x) = m ^ x are the same, which statement is true about the value of m?

a) m can only equal 1.

b) m can be any positive real number.

c) m can be any negative real number.

d) m can be any real number.