In mrs. prosser's class there are 32 students. If 3 out of every 8 prefer to ride their bicycles to school, how many students in the entire class like to ride their bicycles to school?

To find or estimate f(x) for x=0,2,4,6, integrate the given derivative f'(x) with respect to x to find the constant term. Then, add each value of f'(x) in the table to the constant term to obtain the values of f(x) for x=0,2,4,6.

To find or estimate f(x) for x=0,2,4,6, we need to use the values of the derivative f'(x) given in the table. Since f'(x) represents the rate of change of f(x) at different values of x, we can use the derivative to find or estimate the values of f(x). Given that f(0) = 150, we can start by finding the constant term of the function using this initial condition.

Therefore, by integrating f'(x) and adding the constant term, we can find or estimate the values of f(x) for x=0,2,4,6.

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Answer:

<1, 3>, square root of ten

Step-by-step explanation:

To get a 90% acid solution, you should mix 54 gallons of pure acid with the 6 gallons of the 20% acid solution.

To solve this problem, we can use the formula for concentration:

Concentration = (Volume of pure acid) / (Total volume of solution)

Let x represent the volume of pure acid to be added. We know that the total volume of the solution after adding the pure acid is 6 gallons + x gallons. We also know that the concentration of the 20% acid solution is 0.2.

Using the formula, we can set up the equation:

0.9 = x / (6 + x)

Multiplying both sides of the equation by (6 + x), we get:

0.9(6 + x) = x

Simplifying the equation, we have:

5.4 + 0.9x = x

Subtracting 0.9x from both sides of the equation, we get:

5.4 = 0.1x

Dividing both sides of the equation by 0.1, we get:

54 = x

Therefore, you should mix 54 gallons of pure acid with the 6 gallons of the 20% acid solution to get a 90% acid solution.

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The correct answer is:

Total capacity of tank in quarts:

20 gallons = 20 × 4 = 80 quarts

Gasoline used in quarts:

4 gallons 1 quart = (4 × 4) + 1 = 17 quarts

Gasoline left in the tank in quarts:

80 − 17 = 63 quarts

Gasoline left in the tank in gallons and quarts:

63 quarts = 63 ÷ 4 = 15 remainder 3 = 15 gallons 3 quarts

A total of 7 pounds of fruit does the customer buy.

Given that, a customer pays $3.27 for oranges and $4.76 for pears.

The cost of 1 pound orages=$1.09 and the cost of 1 pound pears=$1.19

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.

Now, the number of pounds of oranges =3.27/1.09=3 pounds

The number of pounds of pears =4.76/1.19=4 pounds

Total weight=3+4=7 pounds

Therefore, a total of 7 pounds of fruit does the customer buy.

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Answer:

11

Step-by-step explanation:

The height of the tree when it was transplanted was:

                              4 feet

As we could observe that the given table represents a linear function.

The table is given as follows:

Year since it was      4        4.5        5      

transplanted

Height  (Feet)            12       13          14

We will find the linear function.

Let y denotes height and x denote year since it was transplanted.

We know that any linear function passing through two points (a,b) and (c,d) is given by:

[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]

Here let (a,b)=(4,12) and (c,d)=(5,14)

Hence, the linear function is calculated as follows:

[tex]y-12=\dfrac{14-12}{5-4}\times (x-4)\\\\\\y-12=2(x-4)\\\\\\y-12=2x-8\\\\\\y=2x-8+12\\\\\\y=2x+4[/tex]

Now the height of tree when it was transplanted is the value of y when x=0

Hence, when x=0 we have:

y=4

    Hence, the height was:

               4 feet

The side length of a square whose perimeter is 26.46 inches can be calculated by dividing the given perimeter by 4 (the number of sides in a square), resulting in a side length of approximately 6.615 inches.

The subject of this question is Mathematics, with the specific topic being measurement and geometry. This question is applicable to Middle School grade levels. The student seeks to determine the side length of a square, knowing the perimeter is 26.46 inches.

To find the side length, we need to recall the formula for the perimeter of a square: P = 4s, where P represents the perimeter and s represents the length of a side. The student's square has a perimeter of 26.46 inches, so the equation would be 26.46 = 4s.

To isolate the value of s, we divide both sides of the equation by 4. This gives us: s = 26.46/4. Upon doing the division, we find that each side of the square is approximately 6.615 inches.

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a. The commission from the sale of $ 44,000 worth of​ furnaces is $1,800

b. Commission would double as well.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

We are given that salesperson's commission rate is 5 ​%

Then Commission paid on $36,000 worth of furnaces with a rate of 5% is:

= Amount of sales x commission rate

= 36,000 x 5%

= $1,800

If the sales were to double, the commission would be based on double the amount so it would double;

= 36,000 x 2

= $72,000

Commission = 72,000 x 5%

= $3,600

therefore Commission is doubled.

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To find the flow rate of oil, first calculate the cross-sectional area of the pipe using the formula for the area of a circle, A=πr². Then, multiply the area by the given oil speed to find the volume of oil flowing every second. Multiply this by the number of seconds in a day to find the amount of oil leaving the pipe each day, and remember to convert from cubic inches to cubic feet.

The question is asking us to find the volume of oil leaving the pipe per second and per day. To calculate the flow rate of oil, we first find the cross-sectional area of the pipe by using the formula for the area of a circle A=πr², where r is the radius of the pipe (half the diameter). Since the diameter given is 21 inches, the radius is 10.5 inches.

Next, use the given flow rate of 30 inches/second to calculate the volume of oil flowing every second. This is done by multiplying the area by the oil speed V = A * oil speed.

To find the amount of oil leaving the pipe each day, we multiply the volume per second by the number of seconds in a day .

Note: To convert cubic inches to cubic feet (since the question asks for cubic feet), remember there are 1728 cubic inches in 1 cubic foot.

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Answer:

13 1/2

Step-by-step explanation:

Answer with explanation:

Side of cube = S

Surface Area of Cube = S.A

Relation between Side of a cube and surface area

   [tex]S=\frac{S.A}{6}[/tex]

→If surface area of cube =180 Square meters

Side of cube (S)

                     [tex]S_{1}=\frac{180}{6}\\\\=30[/tex] meters

→  If surface area of cube =120 Square meters

Side of cube (S)

                     [tex]S_{2}=\frac{120}{6}\\\\=20[/tex] meters

[tex]S_{1}-S_{2}=30 -20=10\\\\S_{1}=S_{2}+10[/tex]

Side of cubic having surface area 180 square meters is greater by 10 meters, than a cube with the surface area of 120 square meters.

The minimum value of (m + 2n) is 8.95 and this can be determined by using the arithmetic operations.

Given :

If m and n are two positive real numbers whose product is 10.

Given that m and n are two positive real numbers whose product is 10 that is:

mn = 10

[tex]\rm m= \dfrac{10}{n}[/tex]   ---- (1)

The minimum value of (m + 2n) can be determined by using the following calculation.

Put the value of m in the given expression.

[tex]\rm = \dfrac{10}{n}+2n[/tex]  ---- (2)

Now for minimum value differentiate the above expression with respect to n.

[tex]\rm =-\dfrac{10}{n^2}+2[/tex]  

Now equate the above equation to zero.

[tex]\rm \dfrac{10}{n^2}=2[/tex]

[tex]\rm n = \sqrt{5}[/tex]

Now, put the value of n in equation (2).

[tex]\rm Minimum \;Value = \dfrac{10}{\sqrt{5} }+2\sqrt{5}[/tex]

                          = 8.95

The minimum value of (m + 2n) is 8.95.

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Answer:

Standard form: 600

Unit form: 6 hundreds.

Step-by-step explanation:

We have been given a number [tex]10\times 6[/tex]-tens. We are asked to write our given number in unit form and standard form.  

To write our given number in standard form, we will expand our given number as shown below:

6-tens [tex]6\times 10=60[/tex]

[tex]10\times 6[/tex]-tens would be  [tex]10\times 60=600[/tex]

Therefore, our given number in standard form would be 600.

We know that unit form is writing a number using place value units.

We can see that our given number has 0 ones, 0 tens and 6 hundreds.

Therefore, our given number in unit form would be 6 hundreds.

We have that  the Tens unit form of 10 x 6 and  Standard form is mathematically

[tex]6*10^1[/tex]

6tens

From the question we are told that

10 x 6

10 x 6=60

Standard form is a number, between 1 and 10 multiplied by a power of 10

Generally the equation for the Standard form   is mathematically given as

x*10^y

Therefore

the Standard form  of 10 x 6  is mathematically given as

[tex]6*10^1[/tex]

And

Generally the equation for the Tens unit form of 10 x 6  is mathematically given as

x*tens(10)

Tens-unit form is mathematically given as

6tens

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The maximum height attained by the ball is 25 feet.

The maximum height attained by the ball can be found by determining the vertex of the quadratic equation representing the height of the ball. In the given equation 40t - 16t^2, the coefficient of t^2 is negative, indicating a parabolic shape with a maximum point. The formula for the x-coordinate of the vertex is -b/2a, which in this case is -40/(2*(-16)) = 1.25 seconds. Substituting this value into the equation gives the maximum height: 40(1.25) - 16(1.25^2) = 25 feet.