Find the value of f (8).

Answer:

1. 12 days

2. more than 200 miles

3. 11 lawns

4. at least 9 hours (about 9.92 hours)

Step-by-step explanation:

1. 20x < 254, so x < 12.7. We need an integer here, so x = 12 days.

2.

[tex]70 + .15x < 50 + .25x[/tex]

[tex]20 < .10x[/tex]

[tex]200 < x[/tex]

[tex]x > 200[/tex]

3. 65x > 699, so x > 10.8. Since fractions of lawns are not accepted here, Mark must mow at least 11 lawns.

4. Assuming that the speed stays constant, 65x = 645, so x = 9.92 hours. The trip will take at least 9 hours, actually close to 10 hours.

Answer:

Yes

Step-by-step explanation:

Winning numbers: 2, 4, 6

Losing numbers:  1, 3, 5

The even numbers are greater.

The average even (winning) number is 4.

The average odd (losing) number is 3.

You can win half a dollar on average.

Equation: (1/6)(-1)+(1/6)(2)+(1/6)(-3)+(1/6)(4)+(1/6)(-5)+1/6(6) = 0.5

Assuming simple interest, the formula to calculate the interest Ms. Paul paid is:

In the problem, here are the given information:

Principal (Money borrowed) = $1,200

Rate = 18% or 0.18 in decimal form

Time = 9 months or 0.75 year.

(Take note that the time in the formula is measured in years.)

Let's plug in the given information to the interest formula above.

Then, solve.

Therefore, Ms. Paul paid interest of $162.

The recursive formula of the function is P(n + 1) = 3 + Pn while the explicit formula  is P(n) = 6 + 3(n -1)

The given parameters are

Po = 6

P1 = 9

From the question, we understand that the number of cars follows a linear model

This means that the common difference is

d = P1 - Po

So, we have

d = 9 - 6

Evaluate

d = 3

The recursive formula  is

P(n + 1) = d + Pn

So, we have

P(n + 1) = 3 + Pn

From the question, we understand that the number of cars follows a linear model

This means that the common difference is

d = 9 - 6

Evaluate

d = 3

The explicit formula  is

P(n) = Po + (n -1) * d

So, we have

P(n) = 6 + (n -1) * 3

Evaluate

P(n) = 6 + 3(n -1)

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The Solution:

Given that the vertices of a quadrilateral are:

We are required to find the coordinate of J' when J(9,5) is reflected in the line x=1.

The new x-coordinate will become:

So, the required coordinate of J' is:

Therefore, the correct answer is J'(-8,5)

Answer:

First option is correct.

Step-by-step explanation:

Normally, Pete's dad deposits $25 into his bank account every week.

Now, he wants to deposit x extra dollars for 8 weeks. So, the total deposits for these 8 weeks will be:

8*(25 + x)

He wants to keep the total deposits above 500. So

8*(25 + x) > 500

Now we solve the inequality similarly to how we would solve an equality.

8*(25 + x) > 500

200 + 8x > 500

8x > 500 - 200

8x > 300

x > 300/8

x > $37.50

So the first option is correct.

By using the method of division,  they can buy 11 stamps.

The procedure or act of dividing the condition of division one of the pieces or groupings into which a whole is divided or is divisible. Distribution can be an act, a process, or an instance of distribution among a number. something that separates, divides, or marks off the act of dividing into portions or the process of being divided. one of the chunks or groups into which a whole can be split up or divided. the action, procedure, or occurrence of distributing among a group. Division is the act or process of splitting something that is already divided.

Given that,

18k stamps can be bought with #2.00

2.00 ÷ 0.18= 11.11

Hence, they can buy 11 stamps.

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Answer:

mean: 86 median: 85 mode: 85

Step-by-step explanation:

If a monument in the form of a marble cylinder has a circular base with a radius 1.5 meters and the altitude of the monument is 3.5 meters. then the quantity of marbles contains in the monument is 24.74 meter cube

The shape of the monument  is cylinder

The base radius of the cylinder = 1.5 meter

The altitude of the monument = 3.5 meters

The volume of the cylinder = [tex]\pi r^{2}h[/tex]

Where r is the radius of the cylinder

h is the height of the cylinder

Substitute the values in the equation

The volume of the cylinder = [tex]\pi (1.5)^{2}(3.5)[/tex]

= 24.74 meter cube

Hence, If a monument in the form of a marble cylinder has a circular base with a radius 1.5 meters and the altitude of the monument is 3.5 meters. then the quantity of marbles contains in the monument is 24.74 meter cube

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Answer:

15th customer

Step-by-step explanation:

to find the answer to this, you have to find the least common multiple(I think that’s what it is called). In this case, in order to find it, you can just multiply 5*3 to get 15 for the answer

The equation that represents the total points on the test, including the 2-point and 4-point problems is 2x + 4y = 100

From the information, the test in math class has problems with 2 points (x) and problems worth 4 points (y) and the test has 100 points. The equation to illustrate this will be:

2x + 4y = 100

When one answers 30 2-point questions and 8 4-point questions correctly, the score will be:

= 2x + 4y

= 2(30) + 4(8)

= 60 + 32

= 92

The score is 92 points.

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The peaches required for every cup of water is 4/3

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

so;

    A.T.Q:-                  

Is there two columns of data and two data points? Like this:

peaches          Water

40                    30

400                  300

If so, then there are two ways to do it.

1) You can set up a ratio like this

40/30 = x

:-Where x is the number  of peaches for every cups of water .

So;

x = 40/30  peaches

x = 4/3  peaches

2) Look at the increase from one to the other.

3 cups of water requires 4 peaches.

∵ Hence by unitary method

1 cup of water requires 4 /3  peaches.

:- so; 4/3 peaches are required for every cup of water.

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Answer: ? = 1/2

Step-by-step explanation:

Your question is a bad example, so let me come up with one.

2/8 = 1/4

This is done by dividing both the numerator and denominator by the same value: 2/8 / 2/2

or

2/2 = 1, 8/2 = 4

We now have 1/4

or 9/36

What can we divide 36 by, 9 by? We need to divide by both for it to work.

9/3 = 3

36/3 = 12

3/12 But we can divide this again

3/3 = 1

12/3 = 4

1/4, we could also have divided 9/36 by 6/6 to get 1/4

For 1/8 to get ?/4, we do

8/? = 4

? = 1/2

, so the answer is 1/2/4 = 1/2*4 = 1/8

In  linear equation, The co - ordinates of these points of intersection are ( -2,0) ( 2, 0) .

What are a definition and an example of a linear equation?

   x² + y² = 4 ..........1

   x²/4 - y²/9 = 1

⇒ 9x² - 4y² = 36 ..........2

multiply equation (1) is multiply by 9

      9 x²  + 9y² = 36  ..............3

equation (3) - (2)

   13y² = 0

 y = 0

put y =0 in equation 1

     x² + 0 = 4

      x = ± 2

The co - ordinates of these points of intersection are ( -2,0) ( 2, 0) .

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Answer:

Step by step explanation:

To solve this situation we can create a system of linear equations, with the given information for the customers:

Let x be the price for each hamburger

Let y be the price for each drink

To solve for x and y. We can use the substitution method, which consists of isolating one variable in one of the equations and substitute it into the other.

Let's isolate y in (1):

Now, substitute it into equation (2).

Solve for x:

With the x-value, we can substitute it into the equation (1) to find the price for each drink:

Therefore, the price for each hamburger is $3.5 and for each drink is $1.5.

Now, if we want to buy 8 drinks and 9 hamburgers:

The quantity of teaspoons of syrup it would take to make just one strawberry milkshake is 1 29/35 teaspoons

This is the number which gives the comparison between two quantities. The ratio of teaspoons of strawberry to make strawberry milkshake is the comparison between the two quantities.

Equate the ratio of teaspoons of strawberry syrup to strawberry milkshakes

Teaspoons of strawberry : make strawberry milkshake

3 1/5 : 1 3/4 = x : 1

16/5 ÷ 7/4 = x/1

cross product

16/5 × 1 = 7/4 × x

16/5 = 7/4x

x = 16/5 ÷ 7/4

x = 16/5 × 4/7

= (16 × 4) / (5 × 7)

= 64 / 35

= 1 29/35 teaspoons

The teaspoons of syrup would it take to make just one strawberry milkshake is 1 29/35 teaspoons

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x = Number of posts

y = samuel's savings

If he order 2 posts with words and pictures:

y = 2(10) + 35 = 55

If he order 2 posts with words only and 2 posts with pictures only.

y = 2(5) + 2(10) + 5 + 25 = 10 + 20 + 5 + 25 = 60

Therefore, he could have save 5 dollars

Therefore the equation is:

y = 5x - 5

We know that:

Above, we use the transitive property

First, let's see the points on the coordinate plane:

Now, let's remember that a function has every element of it's domain related with only one element from it's image.

Therefore, x = 2 would create a set of ordered pairs that is not a function. Let's see it in the plane:

As we can see, x = 2 has two values on the image: f(2) = 6 and f(2) = 7, and this never can happen in a function.

The composite function F(1) has a value of 2

The definition of the composite function is given as

F(x) = f(xf(xf(x)))

Also, we have

f(1) = 2, f(2) = 5, f '(1) = 4, f '(2) = 5, and f '(5) = 6,

Substitute 1 for x in the equation F(x) = f(xf(xf(x)))

So, we have

F(1) = f(xf(xf(1)))

From the question

f(1) = 2

So, we have

F(1) = f(xf(2))

From the question

f(2) = 5

So, we have

F(1) = f(5)

As a general rule

If f '(2) = 5 then f(5) = 2

So, we have

F(1) = 2

Hence, the value of the function F(1) is 2

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Answer:

160,000

Step-by-step explanation:

Using integrals, the 90th percentile of the given probability distribution is of $53.58.

The amount exceeded only 10% of the time is the 90th percentile of the distribution, which is the value of p for which:

[tex]\int_0^p f(y) dy = 0.9[/tex]

The integral represents the cumulative density function of the distribution, which is the reason why we use it to find the 90th percentile of the distribution.

The function is given by:

f(y) = 3(1 - y)²

Hence the integral is calculated as follows:

[tex]\int_0^p 3(1 - y)^2 dy[/tex]

Applying the integral of the power of y rule, along with the substitution, it is found that:

[tex]\int 3(1 - y)^2 dy = -(1 - y)^3[/tex]

Hence:

[tex]\int_0^p 3(1 - y)^2 dy = -(1 - y)^3|_{y = 0}^{y = p}[/tex]

Applying the Fundamental Theorem of Calculus, considering the value of the definite integral, it is found that:

-(1 - p)³ + 1 = 0.9

-(1 - p)³ = -0.1

(1 - p)³ = 0.1

Applying the cube root to both sides:

1 - p = 0.4642.

p = 1 - 0.4642

p = 0.5358.

This amount is in hundredths of dollars, hence the 90th percentile of the given probability distribution is of $53.58, as 0.5358 x 100 = $53.58.

The problem is missing, and is given by the image at the end of the answer.

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Answer:2.225

Step-by-step explanation:

If you add all the numbers and then divide by the number of numbers given you get the average.

The equation that represents the daily production cost based on the number of pairs of boots manufactured each day is C(x) = 4.75x + 400.

What are linear equations?
Linear equations are a subset of first order equations. Linear equations are defined for lines in the coordinate system. One homogeneous variable of degree one constitutes a linear equation in one variable (i.e., only one variable). A linear equation could contain multiple variables. When a linear equation comprises two variables, for instance, linear equations in two variables are utilized. A mathematical statement known as an equation contains an algebraic expression and the equal symbol (=). It is the equation for a straight line. The equation is shown to be valid when values are substituted for the unknown values in the solutions of linear equations. When there is just one variable, there is just one answer.

Given, the daily production cost (in $) = C(x)
The number of pairs of boots manufactured = x
The cost of making a pair of boots = $ 4.75
The fixed cost of production each day = $ 400
Thus, net cost of making 'x' boots added to the daily fixed production cost will give the  daily production cost.
Therefore, C(x) = 4.75x + 400, is the correct equation.

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Given,

The measure of side YZ is 21.

The measure of side XY is 20.

The measure of side XZ is 29.

Required:

The value of tanX.

The trigonometric ratio is calculated as,

Substituting the values,

ence, the value of tanX is 21/290.

(a),

The common ratio between the terms is

(b).

The common ratio found in (a) tells us that every next number is found by dividing the previous number by 3; therefore, the equation for a_n the nth term will be

(c).

The sixth term will be at n = 6. Putting n = 6 into the equation in (b) gets us

(a) 291/2020

(b) 77/465

(c) 437/1010

(d) 145/376

(e) 32/157

(f) 53/157

(g) 433/465

(h) 335/376

Based on the given task content; the amount of money the customer needs to pay if given a discount of $5 off the second item bought is $38.50

Item 1:

Headphones = $25

Item 2:

CD = $18.50

Amount paid on the second item = original cost - discount

= $18.50 - $5

= $13.50

Total amount the customer needs to pay = cost of item 1 + Amount paid on the second item

= $25 + $13.50

= $38.50

In conclusion, the total amount the customer needs to pay for headphones and CD is $38.50

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From the given histogram, it is found that Class 4 contains the largest number of exam scores.

An histogram of a data-set is a graph that shows the number of times each element of x was observed, or elements in each range of x were observed.

From the histogram in the problem, we have that:

All these number of scores are given at the center of the bars on the graph.

The largest number among these number of scores is of 19 in Class 4, hence Class 4 contains the largest number of exam scores.

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Answer:

I think about 3.4/4=.85 or 85% of acreage was bought.

Step-by-step explanation: