A carpenter wants to cut a 6 foot board into pieces 2/3 foot long . How many pieces can the carpenter make

Answer:

b=22

Step-by-step explanation:

11/4 divided by 1/4 equals 11. 11*2 =22

Answer:

The answer is actually 10

Step-by-step explanation:

b = 10

The solution is x = 6

Step-by-step explanation:

Let us revise some rules of the exponents

∵ [tex]9^{(x+15)}=3^{7x}[/tex]

∵ 9 = 3 × 3

∴ 9 = 3²

- Substitute 9 by 3² in the equation above

∴ [tex](3^{2})^{(x+15)}=3^{7x}[/tex]

- Use the second rule above for the left hand side

∵ [tex](3^{2})^{(x+15)}=3^{2(x+15)}[/tex]

∴ [tex](3^{2})^{(x+15)}=3^{2x+30}[/tex]

∴ [tex]3^{2x+30}=3^{7x}[/tex]

- By using the first rule above

∴ 2x + 30 = 7x

- Subtract 2x from both sides

∴ 30 = 5x

- Divide both sides by 5

∴ 6 = x

The solution is x = 6

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Answer:

90°

Step-by-step explanation:

5, 12 and 13 are the sides of a right triangle ( Pythagorean triple )

13 is the measure of the hypotenuse whose opposite angle is 90°

Answer:

90°

Step-by-step explanation:

5^2+ 12^2 = 13^2

25 + 144 = 169

The Converse Pythagorean Theorem (Egyptian triangle) states that if the length of the sides of a triangle, say a, b, and c, satisfy a^2 + b^2 = c^2, then this is a right triangle with a right angle opposite to side c.

And since 5^2 + 12^2 = 13^2 satisfies the statement a^2 + b^2 = c^2, c (which is 13) is opposite to a 90° angle.

Answer:

6 + 8 + 10 = 24

Answer: 6, 8, and 10

Step-by-step explanation:

x-first number

x+2-second

x+4-third

x+x+2+x+4=24

3x=18

x=6

6, 8, and 10

Answer:

798

Step-by-step explanation:

hsushshxhuxvshsjsvs

The area of a rectangle is given as:

Area = Length x width

Length = 38

Width = 21

The value of 38 x 21 as an area model is 798.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

38 x 21 as an area model.

This can be considered as,

Length = 38

Width = 21

Now,

The area of a rectangle.

= 38 x 21

= 798

Thus,

The value of 38 x 21 as an area model is 798.

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It would take 13 buses to get everyone to the zoo

It would take 26 vans to get everyone to the zoo

It would be cheaper to rent buses

Step-by-step explanation:

The given is:

We need to find how many buses it would take to get everyone to the zoo, how many vans it would take to get everyone to the zoo, and would it be cheaper to rent

∵ The number of students is 388

∵ Each bus can hold 30 students

- Divide the number of students by 30 to find the number of buses

∴ The number of buses = 388 ÷ 30 = 12.92

- They must to rent 13 bus to hold all the students

∴ The number of buses is 13

It would take 13 buses to get everyone to the zoo

∵ The number of students is 388

∵ Each van can hold 15 students

- Divide the number of students by 15 to find the number of vans

∴ The number of vans = 388 ÷ 15 = 25.87

- They must to rent 26 vans to hold all the students

∴ The number of vans is 26

It would take 26 vans to get everyone to the zoo

Let us find the cost of rent of the buses and vans to find which of them is cheaper

∵ The cost of rent of each bus = $895

∵ The number of buses = 13

∴ The cost of rent the buses = 13 × 895 = $11635

∵ The cost of rent of each van = $450

∵ The number of vans = 26

∴ The cost of rent the buses = 26 × 450 = $11700

∵ $11635 < $11700

∴ The cost of rent the buses < the cost of rent the vans

∴ The buses is cheaper than the vans

It would be cheaper to rent buses

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Answer:

[tex]a_{n} = a_{1} + (n-1)[/tex]this is the required representation for showing the position of a term in the sequence.

Step-by-step explanation:

Given:

The sequence is as follow:

0, 1, 2, 3, .......

To Find:

The expression while using 'n' to represent the position of a term in the sequence where n = 1 for the first term 0, 1, 2, 3, ....

Solution:

n = to represent the position of the term in the sequence.

[tex]a_{1} = \textrm{represent the first term in the sequence.} = 0[/tex]

d = Common difference.,i.e difference between the consecutive term.

d = second term - first term.

or

d = third term - second term.

Here we have d = 1 - 0 = 1

or                     d = 2 - 1 = 1

So, the required expression is

[tex]a_{n} = a_{1} + (n-1)\times d[/tex]

[tex]a_{n} = a_{1} + (n-1)[/tex]

If we require first term put n = 1

[tex]a_{1} = a_{1} + (1-1)[/tex]

[tex]a_{1} = 0[/tex]

If we require second term put n = 2

[tex]a_{2} = a_{1} + (2-1)[/tex]

[tex]a_{2} = 0 + 1[/tex]

[tex]a_{2} = 1[/tex]

If we require third term put n = 3

[tex]a_{3} = a_{1} + (3-1)[/tex]

[tex]a_{3} = 0 + 2[/tex]

[tex]a_{3} = 2[/tex]

and so on.......

Answer: The answer will be C.

Answer:

the process of retting softens the tissue and helps to separate the fibres

Step-by-step explanation:

the process of retting softens the tissue and helps to separate the fibres

Thanks

Answer: 53.2

Step-by-step explanation:

Answer:

0.01879

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

35/100X = 28

35X = 2800

2800/35=80

Answer: 80

Step-by-step explanation: To answer the question 28 is 35% off what number, we translate the question into an equation.

So we have "28 is" which means 28 = 35% which we need to write as a decimal. To write a percent as a decimal, we move the decimal point 2 places to the left so 35% can be written as the decimal .35. Next we have "of what number" which means times X.

Now we have the following equation.

28 = (.35) (x)

Now to solve for x since x is being multiplied by .35, we need to divide by .35 on both sides of the equation.

On the right side of the equation, the .35's cancel and we have x. On the left side of the equation, we have 28 ÷ .35 which is 80.

So 80 = x.

Therefore, 28 is 35% of 80.

Answer:

1

Step-by-step explanation:

Using the rule of exponents

[tex]a^{0}[/tex] = 1

Thus

[tex](75x^2z^12)^{0}[/tex] = 1

Answer:

1

Step-by-step explanation:

any non-zero expression raised to the power of 0 equals 1

Answer:

See explanation

Step-by-step explanation:

Let [tex]F(x)=\left(\dfrac{2}{3}\right)^x.[/tex] Plot the graph of this function. From the graph:

A. The domain of the function is [tex]x\in (-\infty,\infty).[/tex]

B. The range of the function is [tex]y\in (0,\infty).[/tex]

C. The y-intercept of the graph of F(x) is [tex](0,1).[/tex]

D. The horizontal asymptote is x-axis.

E. The graph of the function F(x) is decreasing from left to right.

F. The value [tex]\frac{2}{3}[/tex] determines that the graph of the function is decreasing from the left to the right.

Answer:

what he said above me

Step-by-step explanation:

Answer:

3x^2 + 12x + 4y^2 - 8y = 32

Step-by-step explanation:

3(x^2+4x)+4(y^2-2y)=32

At first we have to break the parenthesis to get the variables in normal position. To break those, we have to multiply each with the help of algebraic expression:

or, (3*x^2) + (3 × 4x) + (4 × y^2) - (4 × 2y) = 32

or, 3x^2 + 12x + 4y^2 - 8y = 32

Since the equation does not have anything to add or deduct, therefore, it is the answer.

Answer:

5n+p>40

n+p<20

Step-by-step explanation:

Since pennies are worth 1 cent and nickels 5, using n as the number of nickels and p as the number of pennies, we can say that 5*n+1*p>40. Then, n+p is less than 20, so n+p<20. Our answer is then

5n+p>40

n+p<20

The currency called the dollar can be split into smaller forms called nickels, pennies, dimes, and quarters.

The system of inequalities that represents how many pennies and nickels that Jada could have is given as:

Let's represent the number of :

pennies = p

nickels = n

It is important to also note that:

1 penny = $0.01

1 nickel = $0.05

40 cents can also be written as: $0.40

Jada has p pennies and n nickels that add up to more than 40 cents.

The word more than means greater than and this can be represented by the inequality sign ">". Hence, our inequality equation is given as:

$0.01 x p + $0.05 x n > $0.40

0.01p + 0.05n > 0.40

She had fewer than 20 coins altogether.

The word fewer means less than and this can be represented by the inequality sign "<". Hence, our inequality equation is given as:

p + n < 20

Therefore, the system of inequalities that represents how many pennies and nickels that Jada could have is given as:

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Answer:

[tex]x=0,x=-4,x=-3[/tex]

Step-by-step explanation:

The given equation is

[tex]x^3 + 7x^2 + 12x = 0[/tex]

Factoring by x:

[tex](x^2 + 7x + 12)x = 0[/tex]

One of the root is x=0. Let's solve the parentheses.

Expanding the trinomial

[tex]x^2 + 4x+3x + 12=0[/tex]

Factoring

[tex]x(x + 4)+3(x + 4)=0[/tex]

Factoring

[tex](x + 4)(x+3)=0[/tex]

This will give us the two remaining roots

[tex]x=-4,x=-3[/tex]

Answer:

4200 tickets of [tex]\$28[/tex] and 1800 tickets of [tex]\$40[/tex] were sold

Step-by-step explanation:

Given:

Tickets are sold at price [tex]\$28[/tex] and [tex]\$40[/tex].

Let Number of tickets sold at price [tex]\$28[/tex] be [tex]x[/tex].

Let Number of tickets sold at price [tex]\$40[/tex] be [tex]y[/tex].

Theater has maximum capacity of 6000 seat.

Hence,

[tex]x+y=6000 \ \ \ \ equation \ 1[/tex]

Total revenue to be generated is [tex]\$189600[/tex]

[tex]\therefore 28x + 40y= 189600 \ \ \ \ equation \  2[/tex]

Now Multiplying equation 1 by 40 we get,

[tex]x+y=6000\\40x+40y=240000\ \ \ \ equation \ 3[/tex]

Now Subtracting equation 2 by equation 3 we get,

[tex](40x+40y=240000)- (28x + 40y= 189600)\\12x=50400\\\\x=\frac{50400}{12}=4200[/tex]

Now substituting value of x in equation 1 we get,

[tex]x+y=6000\\4200+y=6000\\y=6000-4200= 1200[/tex]

Hence a total of 4200 tickets of [tex]\$28[/tex] and 1800 tickets of [tex]\$40[/tex] were sold

To generate a total revenue of $189,600, 4200 tickets should be sold at $28 and 1800 tickets should be sold at $40.

To find the number of tickets to be sold at each price, we can set up a system of equations. Let's assign variables:

       Let x be the number of tickets sold at $28.

The total revenue from selling x tickets at $28 is 28x, and the total revenue from selling y tickets at $40 is 40y. Since the total revenue is $189,600, we can write the equation:

28x + 40y = 189,600

We also know that the total number of tickets sold is x + y = 6000.

We can solve this system of equations to find the values of x and y. One way is to multiply the second equation by 28 and subtract it from the first equation:

28x + 40y - 28x - 28y = 189,600 - 28(6000)

12y = 189,600 - 168,000

12y = 21,600

y = 21,600 / 12 = 1800

Substituting the value of y in the equation x + y = 6000, we get:

x + 1800 = 6000
x = 6000 - 1800 = 4200

Therefore, 4200 tickets should be sold at $28 and 1800 tickets should be sold at $40 to generate a total revenue of $189,600.

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Answer:

6 papayas and 11 pineapples

Step-by-step explanation:

So, we need to find an answer of how many papayas and pineapples she bought, and we only spent $48.

So,  papayas are $2.50 each, and Pineapples are $3.00 each and we only bought 17 fruits total.

lets try 8 papayas, and 9 Pineapples.

$2.50 x 8 = $20.00 total on Papayas

$3.00 x 9 = $27.00 total on Pineapples.

That would only be $47 spent total.

Lets try 10 papayas and 7 pineapples.

$2.50 x 10 = $25.00

$3.00 x 7 = $21.00

That would only be a total of $26 spent.

Lets try 6 papayas and 11 pineapples.

$2.50 x 6 = $15.00

$3.00 x 11 = $33.00

This would be a total of $48 spent.

Answer:

9/2

Step-by-step explanation:

(3/4)/6=(3/4)(6/1)=18/4=9/2

f(18) = 39.50

This gives the monthly cost Kelsey will pay if she streams 18 movies in a month

Step-by-step explanation:

Given function is:

[tex]f(x) = 1.50x+12.50[/tex]

Here x is the number of movies

so for f(18), this means that the total number of movies will be 18

Solving

[tex]f(18) = 1.50(18)+12.50\\f(18) = 27+12.50\\f(18) = 39.50[/tex]

Hence,

f(18) = 39.50

This gives the monthly cost Kelsey will pay if she streams 18 movies in a month

Keywords: functions, Domain,range

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Answer:

there is no mode

Step-by-step explanation:

The mode is the value that appears most frequently in a data set. In this set of numbers none appear more than once. There is no mode.

Answer:

First box: 2

Second box: 30

Third box: 42

Step-by-step explanation:

5 sixes means 5 · 6, which equals 30. An unknown amount of sixes equals 12, which is 2 because 2 · 6 = 12.

30 + 12 = 42

7 · 6 = 42, so 42 is the answer.

I hope this helped! :)

Answer:

No, the correct answer of 4.9+0.03 would be 4.93

Good morning,

Answer:

No

Step-by-step explanation:

4.9+0.03=4.93

and 4,93≠4.093.

:)

Answer: 6.65

Step-by-step explanation:

19-(19×.65)

Answer:

$ 6.65

Step-by-step explanation:

100% - 65% = 35%

Hence, $19 x 35% = $6.65

Answer:

(0, 5 )

Step-by-step explanation:

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

From the table when x = 0, y = 5

Thus (0, 5) is the y- intercept

Answer:

-2x+3y=15

Step-by-step explanation:

y=2/3x+5

y-2/3x=5

-2/3x+y=5

3(-2/3x+y)=3(5)

-2x+3y=15

The average rate of change of d(t) from t = 3 to t = 6 represent: A. The coin travels an average distance of 44.1 meters from 3 seconds to 6 seconds.

In Mathematics and Geometry, the average rate of change (ARoC) of a function f(x) on a closed interval [a, b] can be calculated by using this mathematical equation (formula):

Average rate of change (ARoC) = [tex]\frac{f(b) - f(a)}{(b - a)}[/tex]

Based on the given quadratic function, we can reasonably infer and logically deduce the following:

[tex]d(t)=4.9t^2\\\\d(3)=4.9(3)^2[/tex]

f(a) = d(3) = 44.1

[tex]d(t)=4.9t^2\\\\d(6)=4.9(6)^2[/tex]

f(a) = d(3) = 176.4

Next, we would determine the average rate of change (ARoC) of the function over the interval [3, 6]:

Average rate of change (ARoC) = [tex]\frac{176.4 - 44.1}{(6 - 3)}[/tex]

Average rate of change (ARoC) = 44.1 meters.

In this context, we can logically deduce that the coin travels an average distance of 44.1 meters from 3 seconds to 6 seconds.

Answer:

4.8, 135, 0.2822, 0.024

Step-by-step explanation:

4*1.2=4.8

7.5*18=135

0.34*0.83=0.2822

0.04*0.6=0.024

780 students prefer chocolate milk.

Step-by-step explanation:

Let,

the total percentage = 100%

Students who prefer plain white milk = 35%

Students who prefer chocolate milk = 100 - 35 = 65%

Number of students = 1200

No. of students who prefer chocolate milk = 65% of total students

No. of students who prefer chocolate milk = [tex]\frac{65}{100}*1200[/tex]

No. of students who prefer chocolate milk = [tex]\frac{78000}{100}\\[/tex]

No. of students who prefer chocolate milk = 780

780 students prefer chocolate milk.

Keywords: percentage, subtraction

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