A sphere has a diameter of 10 in. What is the volume of the sphere?
V = StartFraction 125 Over 3 EndFraction inches cubed
V = StartFraction 500 Over 3 EndFraction inches cubed
V = StartFraction 500 Over 3 EndFraction pi inches cubed
V = StartFraction 4,000 Over 3 EndFraction pi inches cubed

Answer:

When new, the scooter cost $900

Step-by-step explanation:

The complete question in the attached figure

we have

[tex]A(t)=900(0.85)^t[/tex]

This is a exponential function of the form

[tex]A(t)=a(b)^t[/tex]

where

A(t) ----> represent the value of a motor scooter

t ----> the number of years after it was purchased

a ---> represent the initial value or y-intercept

b is the base of the exponential function

r is the percent rate of change

b=(1+r)

In this problem we have

[tex]a=\$900\\b=0.85[/tex]

The base b is less than 1

That means ----> is a exponential decay function (is a decreasing function)

Find the percent rate of change

[tex]b=(1+r)\\0.85=1+r\\r=0.85-1\\r=-0.15[/tex]

Convert to percentage (multiply by 100)

[tex]r=-15\%[/tex] ---> negative means is a decreasing function

Verify each statements

case A) When new, the scooter cost $765.

The statement is false

Because the original value of the scooter was $900

case B) When new, the scooter cost $900

The statement is true (see the explanation)

case C) The scooter’s value is decreasing at a rate of 85%  each year

The statement is false

Because the scooter’s value is decreasing at a rate of 15%  each year (see the explanation)

case D) The scooter’s value is decreasing at a rate of  0.15% each year

The statement is false

Because the scooter’s value is decreasing at a rate of 15%  each year (see the explanation)

Answer:

coupon b offers $10.50 off whereas the other is only for $10 off

Step-by-step explanation:

25%*42=10.5

Answer:

Are you VSCO??

Step-by-step explanation:

The greatest common factor is simply which factors of each number are shared between them. Factors are numbers that multiply together to get a certain number.

For example, a) 2x, 4

The factors of 2x are 2 and x

The factors of 4 are 2 and 2

The factors that are shared between them is 2, so the greatest common factor is 2 in this case.

For 2x^2, 4x it's easier to write it out:

The factors of 2x^2 are 2, x, x

The factors of 4x are 2, 2, x

Because they both have 2 and x, the greatest common factor is 2x in this case.

Answer:

Yes, they are congruent

Step-by-step explanation:

Yes, they are congruent because all the side and angle lengths are congruent.

Answer:

Yes

Step-by-step explanation:

Answer:

x = - 3

Step-by-step explanation:

Given

7 + x - 3 = x - 5 - 3x ( simplify both sides )

4 + x = - 2x - 5 ( add 2x to both sides )

4 + 3x = - 5 ( subtract 4 from both sides )

3x = - 9 ( divide both sides by 3 )

x = - 3

Answer:

56 is the other number

Step-by-step explanation:

let the first number be a

the other number is 5/14 from the question

a x 5/14 = 20

5a/14 = 20

5a = 14  x 20 = 280

a = 280/5 = 56

Answer:

the slope is 4/5

Step-by-step explanation:

because i learn that

Answer:

The average would be 0.5

Step-by-step explanation:

Answer: 0.5

Step-by-step explanation: To find the average, we begin by adding the numbers so we have -3 + 0 + 7 + -2 which is 2.

Now we divide 2 by the number of numbers in the data set which is 4.

2 divided by 4 is 0.5 so the average of these numbers is 0.5.

Answer:

720°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6 ( number of sides of a hexagon ), thus

sum = 180° × 4 = 720°

The sum of the measures of the interior angles of a hexagon is [tex]720^{\circ}[/tex]

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain. The bounded plane region, the bounding circuit, or the two together, may be called a polygon. A hexagon is a six-sided polygon or [tex]6-[/tex]gon. Interior angles are those that lie inside a polygon.

The total of the internal angles of any simple hexagon is [tex]\boldsymbol{720^{\circ}}[/tex]

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Answer:

Step-by-step explanation:

to find the x intercept, sub in 0 for y and solve for x

-6x + 4y = 96

-6x + 4(0) = 96

-6x = 96

x = -96/6

x = -16.....ur x intercept is -16 or (-16,0) <===

to find the y intercept, sub in 0 for x and solve for y

-6x + 4y = 96

-6(0) + 4y = 96

4y = 96

y = 96/4

y = 24....so ur y int is 24 or (0,24) <===

[tex]\text{Find the x and y intercepts:}\\\\\text{x intercepts:}\\\\\text{Plug in 0 to y}\\\\-6x+4(0)=96\\\\\text{Solve:}\\\\-6x+4(0)=96\\\\-6x=96\\\\\text{Divide both sides by -6}\\\\\boxed{x=(-16,0)}\\\\\text{y intercept:}\\\\\text{Plug in 0 to x}\\\\-6(0)+4y=96[/tex]

[tex]\text{Solve:}\\\\-6(0)+4y=96\\\\4y=96\\\\\text{Divide both sides by 4}\\\\\boxed{y=(0,24)}[/tex]

1. Geometric Sequence

2. [tex]a_n = a_{n-1} * 3[/tex]

3. [tex]a_n = 6 * (3)^{n-1}[/tex]

Step-by-step explanation:

Given sequence is:

6, 18, 54, 162,....

Here

[tex]a_1 =6\\a_2 = 18\\a_3 = 54[/tex]

(a) Is this an arithmetic or geometric sequence?

We can see that the difference between the terms is not same so it cannot be an arithmetic sequence.

We have to check for common ratio (ratio between consecutive terms of a sequence) denoted by r

[tex]r = \frac{a_2}{a_1} = \frac{18}{6}= 3\\r = \frac{a_3}{a_2} = \frac{54}{18} = 3[/tex]

As the common ratio is same, the given sequence is a geometric sequence.

(b) How can you find the next number in the sequence?

Recursive formulas are used to find the next number in sequence using previous term

Recursive formula for a geometric sequence is given by:

[tex]a_n = a_{n-1} * r[/tex]

In case of given sequence,

[tex]a_n = a_{n-1} * 3[/tex]

So to find the 5th term

[tex]a_5 = a_4*3\\a_5 = 162*3\\a_5 = 486[/tex]

(c) Give the rule you would use to find the 20th week.

In order to find the pushups for 20th week, explicit formul for sequence will be used.

The general form of explicit formula is given by:

[tex]a_n = a_1 * r^{n-1}[/tex]

Putting the values of a_1 and r

[tex]a_n = 6 * (3)^{n-1}[/tex]

Hence,

1. Geometric Sequence

2. [tex]a_n = a_{n-1} * 3[/tex]

3. [tex]a_n = 6 * (3)^{n-1}[/tex]

Keywords: Geometric sequence, common ratio

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Answer: time = 3.15 hrs

Step-by-step explanation:

distance = 63km

speed = 20km/hr

time = ?

speed = distance / time

therefore :

time = distance / speed

time = 63/20

time = 3.15 hours

Answer: 3 for whole numbers, but if you want to be exact, 3 and 3/20 (three and three twentieths)

Step-by-step explanation:

20 times 3 is 60, and there is 3 left so you would make it a fraction since it won't divide into 20.

Answer:

a=$1.75 per candy bar

b=$1.74 per candy bar

c=$1.71 per candy bar

d=$1.73 per candy bar

Option C is the better buy.

Hope this helps!

Well, what is the story?

sure, what. you will have to do is to fomulate the links between the human brain and what a computer does, i prefer a mind map, then find the common procedures and use it in your answer

Answer:

the answer is 4x-3

Step-by-step explanation:

To simplify the expression 3x + 4(x - 6) - 3(x - 7), distribute the multiplication across the parentheses, combine like terms, and simplify to get the final result: 4x - 3.

To simplify the expression 3x + 4(x - 6) - 3(x - 7), follow these steps:

Distribute the 4 into the second parenthesis: 4  imes x - 4  imes 6 which gives 4x - 24.

Distribute the -3 into the third parenthesis: -3  imes x + (-3)  imes (-7) which gives -3x + 21.

Combine like terms with the rest of the expression: 3x + (4x - 24) + (-3x + 21).

Add/subtract the x terms and constant terms: 3x + 4x - 3x (which simplifies to 4x) and -24 + 21 (which simplifies to -3).

The simplified form of the expression is 4x - 3.

Answer:

domain: {0, 5, 9, 32} range: {2,3,4,7}

Step-by-step explanation:

we know that

For a set of ordered pairs, the first elements of each ordered pair represents the domain of the function and second elements of each ordered pair represents the range of the function.  

The domain of a function is the set of all possible values of x

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

In this problem we have

values of x ----> [tex]\{0,5,9,32\}[/tex]

values of y ----> [tex]\{2,3,4,7\}[/tex]

therefore

domain: {0, 5, 9, 32} range: {2,3,4,7}

The value of function f (x) at x = 3 is,

⇒ f (3) = - 22

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = - 2x² - 4

Now, Put x = 3 in above function we get;

⇒ f (x) = - 2x² - 4

Put x = 3;

⇒ f (3) = - 2 (3)² - 4

⇒ f (3) = - 2 x 9 - 4

⇒ f (3) = - 18 - 4

⇒ f (3) = - 22

Thus, The value of function f (x) at x = 3 is,

⇒ f (3) = - 22

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Mechanic A worked for 15 hours and mechanic B worked for 5 hours.

Step-by-step explanation:

Given,

Per hour charges of mechanic A = $95

Per hour charges of mechanic B = $75

Total hours worked = 20

Total amount charged = $1800

Let,

x represent the number of hours of mechanic A

y represent the number of hours of mechanic B

According to given statement;

x+y=20          Eqn 1

95x+75y=1800   Eqn 2

Multiplying Eqn 1 by 95

[tex]95(x+y=20)\\95x+95y=1900\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](95x+95y)-(95x+75y)=1900-1800\\95x+95y-95x-75y=100\\20y=100[/tex]

Dividing both sides by 20

[tex]\frac{20y}{20}=\frac{100}{20}\\y=5[/tex]

Putting y=5 in Eqn 1

[tex]x+5=20\\x=20-5\\x=15[/tex]

Mechanic A worked for 15 hours and mechanic B worked for 5 hours.

Keywords: linear equation, elimination method

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The first mechanic worked for 15 hours while the second mechanic worked for 5 hours.

Let's denote the number of hours worked by the first mechanic as x and the number of hours worked by the second mechanic as y.

We know two things:

⇒ x + y = 20

⇒ 95x + 75y = 1800

⇒ y = 20 - x

⇒ 95x + 75(20 - x) = 1800

⇒ 95x + 1500 - 75x = 1800

⇒ 20x + 1500 = 1800

⇒ 20x = 300

⇒ x = 15

⇒ y = 20 - 15 = 5

Thus, the second mechanic worked for 5 hours.

Complete question:

Two mechanics worked on a car. The first mechanic charged $95 per hour, and the second mechanic charged $75  per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1800. How long did each mechanic work?

Answer:

Cash assets is the answer

Incomplete Question the complete question with the figure is below

The triangles shown are similar.

What is the value of x?  

A.  12

B. 15

C. 20  

D. 13

Answer:

The correct option is B. 15

Therefore the value of x is

[tex]x=15\ unit[/tex]

Step-by-step explanation:

Given:

AB = 5

BC = 3

AC = 4

PQ = x

QR = 9

RP  = 12

ΔABC ~ ΔPQR

To Find:

x = ?

Solution:

ΔABC ~ ΔPQR       .................Given

If two triangles are similar then their sides are in proportion.  

[tex]\dfrac{AB}{PQ} =\dfrac{BC}{QR}=\dfrac{AC}{PR} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]  

Substituting the values we get

[tex]\dfrac{5}{x} =\dfrac{3}{9}\\\\x=\dfrac{45}{3}=15\ unit[/tex]

Therefore the value of x is

[tex]x=15\ unit[/tex]

Answer:

At least 33 number of tickets can be sold in order to make a profit.

Step-by-step explanation:

Given:

A theater rents there space for $300 per night.

The company charges $9 per ticket.

Now, to find the least number of tickets that can be sold in order to make a profit.

Amount of rent per night = $300.

Charges of per ticket = $9.

So, to get the least number of tickets sold to get the profit we divide amount of rent per night by charges per ticket:

[tex]300\div9[/tex]

[tex]=33.33[/tex]

Thus, 33 tickets price is 33 × 9 = $297.

Therefore, at least 33 tickets can be sold in order to make a profit.

Convert the fraction to a decimal:

1/25 = 0.04

Multiply by 100 to get the percent:

0.04 x 100 = 4%

The fraction of 1/25 is equivalent to the 4% option (A) 4 % is correct.

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.

We have a fraction:

= 1/25

In decimal:

= 0.04

In percent:

= 0.04×100

= 4%

Thus, the fraction of 1/25 is equivalent to the 4% option (A) 4 % is correct.

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Answer:

Step-by-step explanation:

so he needs to collect at least 120 cans....and he already has 64

c + 64 > = 120 (thats a greater then or equal sign)

c > = 120 - 64

c > = 56....he needs to collect at least 56 more

To represent the number of cans that Xander must still collect to reach at least 120 cans, use the inequality c >= 120 - 64. The solution to the inequality is c >= 56.

To represent the number of cans that Xander must still collect to reach at least 120 cans, we can use the inequality:

c >= 120 - 64

This inequality represents that Xander must collect a number of cans that is greater than or equal to the difference between the desired total (120) and the number of cans he has already collected (64).

The solution to the inequality is:

c >= 56

This means that Xander must still collect at least 56 more cans to reach his goal.

The larger number is 97 and smaller number is 22.

Step-by-step explanation:

Let,

The two numbers are x and y.

According to given statement;

x+y=119      Eqn 1

y-4x=9       Eqn 2

Subtracting Eqn 2 from Eqn 1

[tex](x+y)-(y-4x)=119-9\\x+y-y+4x=110\\5x=110[/tex]

Dividing both sides by 5

[tex]\frac{5x}{5}=\frac{110}{5}\\x=22[/tex]

Putting x=22 in Eqn 1

[tex]22+y=119\\y=119-22\\y=97[/tex]

The larger number is 97 and smaller number is 22.

Keywords: linear equation, elimination method

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Answer:

21 percent of their monthly income is budgeted for food.

Step-by-step explanation:

Given:

The Gonzalez family has a combined monthly income of $1850.

Their food budget is $380 per month.

Now, to find the percent of their monthly income is budgeted for food.

Total income = $1850.

Food budget = $380.

Now, to get the percent of the food budget:

[tex]\frac{380}{1850} \times 100[/tex]

[tex]=\frac{38000}{1850}[/tex]

[tex]=20.54\%.[/tex]

Thus, the percent nearest to whole = 21%.

Therefore, 21 percent of their monthly income is budgeted for food.

Final answer:

Each carrot cost $2.10, found by dividing the total cost of $10.50 by the number of carrots, which is 5.

Explanation:

The student’s question relates to the basic concept of unit price in mathematics. Joe bought 5 carrots for a total of $10.50. To find out how much each carrot cost, we divide the total cost by the number of carrots.

Here’s the calculation step-by-step:

Determine the total cost of the carrots, which is $10.50.

Determine the number of carrots bought, which is 5 carrots.

Divide the total cost by the number of carrots: $10.50 / 5 = $2.10.

So, each carrot costs $2.10 when expressed as a decimal to the nearest hundredth.

Answer:

The number of viruses was 2 times greater than bacteria.

Step-by-step explanation:

The number of viruses was [tex]2*10^9[/tex], and the number of bacteria was [tex]1*10^9[/tex].

To find how many times was the virus number greater than the bacteria number, we just divide the virus number by bacteria number:

[tex]\frac{ virus\:number }{bacteria\:number} =\frac{2*10^9 }{1*10^9} = 2*\frac{10^9}{10^9} =2[/tex]

Viruses are 2 times greater.

Answer:

Viruses are 2 times of the bacteria.

Step-by-step explanation:

Given:

Number of viruses = [tex]2\times 10^9[/tex]

Number of bacteria = [tex]1\times 10^9[/tex]

We have to found how many times viruses are greater than the bacteria.

To find how many times,we can divide both the numbers to compare its values.

Lets

Numerator = Number of viruses

Denominator = Number of bacteria

Dividing both we have,

⇒ [tex]\frac{2\times 10^9}{1\times 10^9}[/tex]

⇒ [tex]2\times 10^(^9^-^9)[/tex] ...[tex]\frac{ab^x}{cb^y}=\frac{ab^x^-^y}{c}[/tex]

⇒ [tex]2\times 10^0[/tex]       ...[tex]a^0=1[/tex]

⇒ [tex]2[/tex]

So the viruses are 2 times of the bacteria.

Answer:

q = 177/13

Step-by-step explanation:

3q - 16q = 7 + 2(-89 – 3)

-13q = 7 + 2(-92)

-13q = 7 - 184

-13q = -177

q = (-177)/(-13)

q = 177/13