Find the 8th term in the
sequence
- 1 / -1, -2, -4,...

Answer:

v(x) = x(22 - 2x)(28 - 2x)

Step-by-step explanation:

The length of the box = 28 - 2x inches,

The width = 22 - 2x inches and the height  = x inches.

v(x) = x * width * length.

The volume of the open top box is [tex]V(x) = (28 - 2x)(22 - 2x)(x)[/tex] cubic inches

The volume of the box is V = (length)(width)(height).

Let the cutout side length be [tex]x[/tex] inch,

We are to cut out [tex]x[/tex] by

So, the length of the box is [tex]28 - 2x[/tex] inch

the width of the box is [tex]22 - 2x[/tex] inch and

the height of the box is [tex]x[/tex] inch

Now, substituting the values in the volume formula, we get

[tex]V(x) = (28 - 2x)(22 - 2x)(x)[/tex] cubic inches

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Answer:

-2/3

Step-by-step explanation:

m=(6-4)/(-2-1)=2/-3=-2/3

Answer:

[tex]\large\boxed{m=-\dfrac{2}{3}}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (1, 4) and (-2, 6).

Substitute:

[tex]m=\dfrac{6-4}{-2-1}=\dfrac{2}{-3}=-\dfrac{2}{3}}[/tex]

Answer:

0

Step-by-step explanation:

In military time format, first two digits are in hours. We know that, on a digital clock, the first two digits always shows between 01 to 24.

So, there is no probability that the first two digits will show more than 25.

As there is no probability, the probability will be zero or 0. Because probability of any incident is whether 0 or 1; where 1 is for certain event.  

Answer:

z = 14

Step-by-step explanation:

Solve for z:

(4 z)/7 - 15 = -7

Put each term in (4 z)/7 - 15 over the common denominator 7: (4 z)/7 - 15 = (4 z)/7 - 105/7:

(4 z)/7 - 105/7 = -7

(4 z)/7 - 105/7 = (4 z - 105)/7:

1/7 (4 z - 105) = -7

Multiply both sides of (4 z - 105)/7 = -7 by 7:

(7 (4 z - 105))/7 = -7×7

(7 (4 z - 105))/7 = 7/7×(4 z - 105) = 4 z - 105:

4 z - 105 = -7×7

7 (-7) = -49:

4 z - 105 = -49

Add 105 to both sides:

4 z + (105 - 105) = 105 - 49

105 - 105 = 0:

4 z = 105 - 49

105 - 49 = 56:

4 z = 56

Divide both sides of 4 z = 56 by 4:

(4 z)/4 = 56/4

4/4 = 1:

z = 56/4

The gcd of 56 and 4 is 4, so 56/4 = (4×14)/(4×1) = 4/4×14 = 14:

Answer:  z = 14

Answer: There are 16 cups in every gallon so we could divide 152 by 16 and get our number of gallons which would give us 9.63 or a little over 9 and a half gallons.

Step-by-step explanation:

Answer:

k = 0.28

Step-by-step explanation:

The price of peaches at Al's supermarket can be determined by the equation P = 0.28n ........... (1)

where P is the price and n is the number of pounds of peaches.

Now, it is clear that the price of peaches is proportional to the number of pounds of peaches.

So, we can write,

P ∝ n

⇒ P = kn ............. (2) where k is the constant which we have to multiply to covert from proportionality to equation form.

Now, comparing equations (1) and (2) we get k = 0.28 which is the value of the constant of proportionality. (Answer)

Final answer:

The constant of proportionality in the equation p = 0.28n is 0.28, representing the price per pound of peaches at Al's supermarket.

Explanation:

The constant of proportionality in the equation p = 0.28n, where P is the price and n is the number of pounds of peaches, is 0.28. This constant represents the price per pound of peaches at Al's supermarket. When you want to compute the amount spent on peaches, you multiply the quantity (in pounds) by this constant of proportionality, which is the price per pound. As an example, if you have 10 pounds of peaches, the total cost would be calculated as 10 pounds × $0.28 per pound, resulting in a total of $2.80 for the peaches.

Answer:

a doesn't equal 0

Step-by-step explanation:

State under which condition the original and the simplified expressions are equivalent

Answer: C

Step-by-step explanation:

The answer is C because it says 360 and 300. If you do a problem solve for that one on a peace of paper I think it would be 16.7%

Answer:

Step-by-step explanation:

Change in number = number visited in 1st week - number visited in 2nd week

= 360-300 = 60

So percentage change in number= 60/360×100=16.67

The greatest possible length of each  piece is 16 inches

Latisha has two pieces of ribbon. One piece of ribbon is 48 inches and  the other is 80 inches

Ribbon is to be cut into pieces of equal length

To find the greatest possible length of each piece, we have to find greatest common divisor of 48 and 80

The greatest common factor, or GCF, is the greatest factor that divides two numbers

Steps to find G.C.F of 48 and 80

1) Find the prime factorization of 48

[tex]48 = 2 \times 2 \times 2 \times 2 \times 3[/tex]

2) Find the prime factorization of 80

[tex]80 = 2 \times 2 \times 2 \times 2 \times 5[/tex]

3) To find the GCF, multiply all the prime factors common to both numbers:

Therefore, [tex]GCF = 2 \times 2 \times 2 \times 2 = 16[/tex]

So, 16 inches is the greatest possible length to cut so that every piece is of equal length.

3 x 3 x 3 x 3 x 23 = 1,863. It can also be written in exponential form as 3 to the power of four times 23.

Answer:

Step-by-step explanation:

[tex]\begin{array}{c|cc}1863&3\\621&3\\207&3\\69&3\\23&23\\1\end{array}[/tex]

249 children and 394 adults swam at the public pool.

Step-by-step explanation:

Number of people swam at pool = 643

Receipts = $1161.50

Cost for one child = $1.50

Cost for one adult = $2.00

Let,

x be the number of children

y be the number of adults

According to given statement;

x+y=643    Eqn 1

1.50x+2.00y = 1161.50   Eqn 2

Multiplying Eqn 1 by 2

[tex]2(x+y=643)\\2x+2y=1286\ \ \ Eqn\ 3\\[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](2x+2y)-(1.50x+2.00y)=1286-1161.50\\2x+2y-1.50x-2.00y=124.50\\0.5x=124.50[/tex]

Dividing both sides by 0.5

[tex]\frac{0.5x}{0.5}=\frac{124.50}{0.5}\\x=249[/tex]

Putting x=249 in Eqn 1

[tex]249+y=643\\y=643-249\\y=394[/tex]

249 children and 394 adults swam at the public pool.

Keywords: linear equation, subtraction

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Answer: 28 inches

Step-by-step explanation:

Side1 + side 2 + side 3 =

7 inches + 8 inches + 13 inches =

28 inches

To determine the number of seats left in the basketball arena, the number of tickets sold (5,134) is subtracted from the total arena capacity (7,000), resulting in 1,866 seats remaining available.

A basketball arena can hold approximately 7,000 people.

Fans bought 5,134 tickets before the game.

The number of seats left to fill before the game can be calculated by subtracting the tickets bought from the total arena capacity: 7,000 - 5,134 = 1,866 seats left to fill.

There should be a typo in the question: the correct formula would be

[tex]X\cap(Y\cup Z)=(X\cap Y)\cup (X\cap Z)[/tex]

Let's compute [tex]X\cap (Y\cup Z)[/tex] first. We have

[tex](Y\cup Z)=\{1, 4, 5, 6, 7, 8, 9\}[/tex]

If we intersect this set with X, we have

[tex]X\cap (Y\cup Z) = \{5, 8, 9\}[/tex]

So, that would be the left hand side. For the right hand side, we have

[tex]X\cap Y = \{8\},\quad X\cap Z = \{5,9\}[/tex]

And their union is again [tex]\{5,8,9\}[/tex]

Final answer:

The intersection of two sets can be proven using a membership table for the given sets X, Y, and Z.

Explanation:

The intersection of two sets, written as AnB, is a set consisting of all elements that are both in A and B. We can use a membership table to prove the following equation: X ∩ (Y ∪ Z) = (X ∩ Y) ∪ (Y ∩ Z).

Answer:

3(x - 3)²

Step-by-step explanation:

Given

3x² - 18x + 27 ← factor out 3 from each term

= 3(x² - 6x + 9)

= 3(x - 3)² ← in factored form

Answer:

x=-117/4

Step-by-step explanation:

5x-15+130=x-2

5x-x+115=-2

4x+115=-2

4x=-2-115

4x=-117

x=-117/4

Answer:

6/12

Step-by-step explanation:

A fourth of 8 is 2, so there would be 6/12 of the tub of frosting left.

Answer:

5/12

Step-by-step explanation:

8/12=2/3

2/3-1/4=8/12-3/12=5/12

Answer:

0.41

Step-by-step explanation:

formula;  y = kx (where k is the constant variation)

the standard equation representing direct variation

y = 0.41 x is the equation to find the constant of proportionality

so, K = 0.41

conservation imporoper fraction to mixed number answer

Answer:

a.)  x= 11

d.) -7

g.) -5

Step-by-step explanation:

a.) x+1 = 4*3

x=12-1

d.)3x+1=-4*5

3x+1=-20

x=-7

g.)11x-1=-8*7

11x-1=-56

11x=-56+1

x=-5

Answer:

Step-by-step explanation:

[tex]a)\\\dfrac{x+1}{3}=4\\\\\dfrac{x+1}{3}=\dfrac{4}{1}\qquad\text{cross multiply}\\\\(x+1)(1)=(3)(4)\\\\x+1=12\qquad\text{subtract 1 from both sides}\\\\x+1-1=12-1\\\\\boxed{x=11}[/tex]

[tex]d)\\\\\dfrac{3x+1}{4}=-5\\\\\dfrac{3x+1}{4}=\dfrac{-5}{1}\qquad\text{cross multiply}\\\\(3x+1)(1)=(4)(-5)\\\\3x+1=-20\qquad\text{subtract 1 from both sides}\\\\3x+1-1=-20-1\\\\3x=-21\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}=\dfrac{-21}{3}\\\\\boxed{x=-7}[/tex]

[tex]g)\\\dfrac{11x-1}{8}=-7\\\\\dfrac{11x-1}{8}=\dfrac{-7}{1}\qquad\text{cross multiply}\\\\(11x-1)(1)=(8)(-7)\\\\11x-1=-56\qquad\text{add 1 to both sides}\\\\11x-1+1=-56+1\\\\11x=-55\qquad\text{divide both sides by 11}\\\\\dfrac{11x}{11}=\dfrac{-55}{11}\\\\\boxed{x=-5}[/tex]

Answer:

The answer is b = 1/24.

Step-by-step explanation:

Given:

25+11/12b=47.

Now, to solve the equation to get the value of b:

[tex]25+\frac{11}{12b}=47[/tex]

Subtracting both sides with 25 we get:

[tex]\frac{11}{12b}=22[/tex]

Multiplying both sides by 12b we get:

[tex]11=264b[/tex]

Dividing both sides by 264 we get:

[tex]\frac{1}{24}=b[/tex]

Therefore, the answer is b = 1/24.

Answer:

The factory must produce 6,400 parts  so that there is 1 ton of scrap aluminum for recycling.

Step-by-step explanation:

1 part produced  ⇒ 5 ounces scrap aluminium recycled.

So, the ratio of parts produced : Scrap of aluminium = 1   : 5  .... (a)

Let us assume for m parts produced ,  1 ton of scrap is recycled.

Also, 1 ton = 2, 000 pounds

and 1 pound = 16 ounces

⇒ 1 ton = 2000 x (16 ounces)  = 32,000 ounces

So, for m parts made in the  factory, 32,000 ounces scrap is recycled.

So, the ratio of parts produced : Scrap of aluminium =  m   : 32,000  .... (b)

From both the given ratio, we get

1   : 5  = m   : 32,000

or, [tex]\frac{1}{5}  = \frac{m}{32,000}  \implies m = \frac{32,000}{5}  = 6,400[/tex]

⇒ m = 6,400

Hence, the factory must produce 6,400 parts  so that there is 1 ton of scrap aluminum for recycling.

Answer:

6,400

Step-by-step explanation

if im late then my bad, how ya'll day going? and Byeee, i'm at school ;)

If there is a 30% chance of it raining, then that means there is a 70% chance of it not raining.

100%-30%=70%

Answer: 70%

Step-by-step explanation: In terms of probability, 100% is the maximum which means something is certain. There are some occasions where it can be higher than 100% like dealing with percent increase or decrease, but in this case, we're talking about 100%.

In this problem, we're given that the probability of rain for tomorrow is 30% and we're asked to find the probability that it will not rain.

Since 100% will be the maximum when dealing with probability, we will subtract the chance it will rain tomorrow which is 30% from 100%.

100% - 30% = 70%.

Therefore, the probability/chance it will not rain is 70% which means it's likely it will not rain.

Answer:

This graph does not represent a function.

Step-by-step explanation:

This graph does not pass the vertical line test. The vertical line test states that if a vertical line drawn intersects the graph of the relation more than once, then the relation is a NOT a function.

Answer:

The slope of the given line 1 is  -4/5.

The slope of the given line 2 is  0.

The line 2 has a greater slope then line 1.

Step-by-step explanation:

The slope of a line with points (x1,y1) and (x2,y2) is given as:

[tex]m = \frac{y_2- y_1}{x_2-x_1}[/tex]

Now, Here the, points of the line 1 are A (-2,7) and B (3,3)

So, here, the slope of line AB  is [tex]m = \frac{3 -7}{3-(-2)}  = \frac{-4}{3 +2} =   \frac{-4}{5}[/tex]

Hence, the slope of the given line 1 is  -4/5.

Now, Here the, points of the line 2 are P (5,1) and Q (9,1)

So, here, the slope of line PQ  is [tex]m = \frac{1-1}{9-5}  = \frac{0}{4} =   0[/tex]

Hence, the slope of the given line 2 is  0.

Now, as we can see  0    >  ( -4 / 5)

So, the line 2 has a greater slope then line 1.

Answer:

x=3

Step-by-step explanation:

we move the 1 to the other side so

it goes from -1 to a positive 1 then add it to the 14 then you will have

5x=15

to remove the x divided 5 on both sides and you get x=3

The equivalent value of the equation is x = 3

Given data ,

Let the equation be represented as A

Now , the value of A is

5x - 1 = 14​

So , the left hand side of the equation is equated to the right hand side by the value of ( 14 )

On simplifying the expression , we get

5x - 1 = 14​

Combining the like terms in the expression , we get

Adding 1 on both sides , we get

5x = 15

Divide by 5 on both sides , we get

x = 15/5

x = 3

Therefore , the value of x = 3

Hence , the expression is x = 3

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Answer:

1:3

Step-by-step explanation:

Sugar : Flour

2 : 6  (substitute the numbers of cups)

1 : 3    (simplify by reducing. divide both sides by 2)

The ratio is 1:3.

Answer:

1:3

Step-by-step explanation:

2:6[sugar is to flour]

1:3[to simplify divide both sides by two]

Answer:2

Step-by-step explanation:if she deposits 10 dollars every week she would be adding 10 dollars which means we have to multiply 10 by however many weeks she saves

Sarah's weekly deposits after h weeks can be calculated using the linear equation D = 200 + 10h. This equation includes her starting balance of $200 and adds $10 for each week.

The subject of this question is Mathematics, specifically focusing on the concept of linear equations.

The correct formula to show Sarah's deposits at the end of h weeks would be (3) D = 200 + 10h. This formula works by establishing 200 as her starting amount (her current bank balance), and adding $10 for each week (h).

For instance, if h was 5 weeks, Sarah would have D = 200 + 10 * 5 = 200 + 50 = $250 in her bank account. This demonstrates how the formula allows you to calculate her weekly deposits effectively.

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Answer:

115 yards per minute

Step-by-step explanation:

575/5= 115

Answer:

115 yds per minute

The drawing will help