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4 years ago

5

Ms wilson surveyed her class of 36 students about their favorite icecream flavors. Two thirds preferred chocolate. One fourth pr

eferred Strawberry. The rest preferred vanilla. How many students preferred vanilla?

2 answers:

Allisa [31]4 years ago

7 0

24 students prefered chocolate, 3 students prefered strawberry, and 9 students prefered vanilla.

mafiozo [28]4 years ago

3 0

Answer- 9 students preferred vanilla
Hope this Helps! :)

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Let S be the solid beneath z = 12xy^2 and above z = 0, over the rectangle [0, 1] × [0, 1]. Find the value of m > 1 so that th

jonny [76]

Answer:

The answer is $\sqrt{\frac{6}{5}}$

Step-by-step explanation:

To calculate the volumen of the solid we solve the next double integral:

$\int\limits^1_0\int\limits^1_0 {12xy^{2} } \, dxdy$

Solving:

$\int\limits^1_0 {12x} \, dx \int\limits^1_0 {y^{2} } \, dy$

$[6x^{2} ]{{1} \atop {0}} \right. * [\frac{y^{3}}{3}]{{1} \atop {0}} \right.$

Replacing the limits:

$6*\frac{1}{3} =2$

The plane y=mx divides this volume in two equal parts. So volume of one part is 1.

Since m > 1, hence mx ≤ y ≤ 1, 0 ≤ x ≤ $\frac{1}{m}$

Solving the double integral with these new limits we have:

$\int\limits^\frac{1}{m} _0\int\limits^{1}_{mx} {12xy^{2} } \, dxdy$

This part is a little bit tricky so let's solve the integral first for dy:

$\int\limits^\frac{1}{m}_0 [{12x \frac{y^{3}}{3}}]{{1} \atop {mx}} \right.\, dx =\int\limits^\frac{1}{m}_0 [{4x y^{3 }]{{1} \atop {mx}} \right.\, dx$

Replacing the limits:

$\int\limits^\frac{1}{m}_0 {4x(1-(mx)^{3} )\, dx =\int\limits^\frac{1}{m}_0 {4x-4x(m^{3} x^{3} )\, dx =\int\limits^\frac{1}{m}_0 ({4x-4m^{3} x^{4}) \, dx$

Solving now for dx:

$[{\frac{4x^{2}}{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right. = [{2x^{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right.$

Replacing the limits:

$\frac{2}{m^{2} }-\frac{4m^{3}\frac{1}{m^{5}}}{5} =\frac{2}{m^{2} }-\frac{4\frac{1}{m^{2}}}{5} \\ \frac{2}{m^{2} }-\frac{4}{5m^{2} }=\frac{10m^{2}-4m^{2} }{5m^{4}} \\ \frac{6m^{2} }{5m^{4}} =\frac{6}{5m^{2}}$

As I mentioned before, this volume is equal to 1, hence:

$\frac{6}{5m^{2}}=1\\m^{2} =\frac{6}{5} \\m=\sqrt{\frac{6}{5} }$

3 0

3 years ago

What is for number two help

miv72 [106K]

Step 1- turn mixed number into improper fraction.

step 2- multiply 3/2 by 3/1

step 3- turn improper fraction into mixed number

And your done! :)

4 0

3 years ago

At the Olympic Games, a runner won the 26.2 mile marathon race in 2 hr 4 min and 1 second. What was his average speed in mph and

Contact [7]

The average speed of the runner is 12.7 mph and 20.4 km/h

Given that the runner ran 26.2 mile in 2hr and 4 minutes, we start of by converting the time from hours and minutes into minutes and finally hours, since hours is what we need. So, we have

2hr = 120mins

+ 4 mins = 124 mins

124 mins ÷ 60 hour/mins = 2.06 hours.

This means that the runner finished the race in 2.06 hours.

If we are to find the average speed in mile per hour, we have

Average speed = distance ran ÷ time taken

Average speed = 26.2 ÷ 2.06

Average speed = 12.7 mph

From the speed in mph, we can directly convert it to km/hr by saying

1 mph = 1.609 km/h

12.7 mph = 12.7 * 1.609 = 20.4 km/hr

for more, check: brainly.com/question/1989219

4 0

3 years ago

The graph of the function showing the path of a soccer ball thrown by a goalie in a video game, f(x) = –0.05x2 + 2.5x + 5.2, is

Tju [1.3M]

Answer:

The correct option is 4.

Step-by-step explanation:

The given function is

$f(x)=-0.05x^2+2.5x+5.2$

Where f(x) is height of the ball and x is the distance.

It is a polynomial function with degree 2. All polynomial functions are defined for all real numbers, therefore the mathematical domain of the function is all real numbers.

$-\infty$

Factorize the given function.

$f(x)=-0.05(x^2-50x-104)$

$f(x)=-0.05(x^2-50x-104)$

$f(x)=-0.05(x^2-52x+2x-104)$

$f(x)=-0.05(x(x-52)+2(x-52))$

$f(x) = -0.05 (x - 52) (x + 2)$

Put f(x)=0 to find the x intercepts.

$0 = -0.05 (x - 52) (x + 2)$

Equate each factor equal to 0.

$x=52,-2$

Therefore at x=52 and -2, the graph of f(x) intersects x-axis. Before x=-2 and after x=52 the values of f(x) is negative. Height cannot be negative, therefore reasonable domain is lie between -2 to 52.

Distance cannot be negative, therefore the reasonable domain must be positive.

$0\leq x\leq 52$

Therefore the reasonable domain is $0\leq x\leq 52$ and option 4 is correct.

6 0

3 years ago

After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil ide

dimaraw [331]

Answer:

The revised probabilities are;

The probability of finding soil with oil = 0.8

The probability of finding soil with good oil = 0.16

The probability of finding medium quality oil = 0.64

Step-by-step explanation:

The given probability of finding soil with high quality oil, P(QO) = 0.20

The probability of finding soil with medium-quality oil, P(OM) = 0.80

The probability of finding soil with no oil, P(ON) = 0.2

Therefore, given that the probability of finding soil with no oil = 0.2, we have;

The probability of finding soil with oil, P(OP) = 1 - the probability of finding soil with no oil

P(OP) = 1 - 0.2 = 0.8

Which gives;

The probability, P(FG) of finding soil with oil and that the oil is good is given as follows;

P(FG) = P(QO) × P(OP) = 0.2 × 0.8 = 0.16

The probability of finding good oil = 0.16

Similarly;

The probability of finding medium quality oil P(FM) = P(OM) × P(OP) = 0.8 × 0.8 = 0.64

Which gives the revised probability as follows;

The probability of finding soil with oil, P(OP) = 0.8

The probability of finding soil with good oil, P(FG) = 0.16

The probability of finding medium quality oil, P(FM) = 0.64.

3 0

3 years ago