There are 644 boys and 520 girls in a school. The probability that a boy is chosen at random studies French is 3/7. The probability that a girl is chosen at random studies French is 5/8.
a) Work out the number of students in the school who study french
b) What is the probability, as a fraction, that a student chosen at random from the whole school does NOT study French

Answer:

x =6.0

The base is 6x  = 35.8

The side is 3x =  17.9

Step-by-step explanation:

We can use the pythagorean theorem

a^2 + b^2 = c^2

(6x)^2 +(3x)^2 = 40^2

36x^2 + 9x^2 = 1600

Combine like terms

45x^2 = 1600

Divide each side by 45

45x^2 /45 =1600/45

x^2 =35.555555555

Take the square root of each side

sqrt(x^2) = sqrt(35.555555555)

x =5.96284794 = 6.0

The base is 6x = 6*5.9628479 =35.77708 = 35.8

The side is 3x = 3*5.9628479 =17.88854382= 17.9

Answer:

x = 6.0

3x = 17.9

6x = 35.8

Step-by-step explanation:

Using pythagoras theorem

40² = (3x)² + (6x)²

1600 = 9x² + 36x²

1600 = 45x²

x² = 320/9

x = 5.96284794

3x = 17.88854382

6x = 35.77708764

Answer:

x²/9 − (y + 1)²/81 = 1

Step-by-step explanation:

-2y − 82 + 9x² = y²

9x² = y² + 2y + 82

9x² = y² + 2y + 1 + 81

9x² = (y + 1)² + 81

9x² − (y + 1)² = 81

x²/9 − (y + 1)²/81 = 1

Answer:

166 legos are required

Step-by-step explanation:

In this case, let's analyze the data. We need 3 trophies, using at most 324 legos in total. The big trophy requires 220 legos, the smallest requires 135, so we need to know how much will be used in the medium trophy. This number should be 135 < X < 220

Now, if we know that the total legos to be used are 324, then, we can make a difference and sum for all the legos, and then, calculate the number of legos used.

Total legos = A + B + C

324 = 220 + 135 + C

324 = 355 + C

C = -31

This means that there is difference of 31 legos between the smallest and biggest trophy, therefore, this difference should be used and added to the smallest trophy and see how much Tristen use in the final trophy:

135 + 31

= 166 legos

So we need to use 166 legos to build the final trophy.

Answer:

he already used 355 so 166

Step-by-step explanation:

Answer:

102, 78

Step-by-step explanation:

angle 1= x

angle 2= x-24

x+x-24=180

x=102

x-24=78

102+78=180

The measure of the angles are 102 and 78 degrees

If the difference of two supplementary angles is 24 degrees, then;

x - y = 24

y = x - 24

Taking the sum of the angles and equating to 180 degrees since they are supplementary

x + y = 180

x + x - 24 = 180

2x = 180 + 24

2x = 204

x = 102

Since y = 180 - x

y = 180 - 102

y = 78 degrees

Hence the measure of the angles are 102 and 78 degrees

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Answer:4

Step-by-step explanation:

464565=753

Answer:

1/3

Step-by-step explanation:

Probability 2/6 = 1/3

Answer - 1/3

Probability is 1/3

Answer:

5x -20

Step-by-step explanation:

p(x) = r(x) - c(x)

      = 11x - (6x+20)

Distribute the minus sign

     = 11x -6x -20

Combine like terms

     = 5x -20

Answer:

[tex] p =\frac{Possible}{Total}[/tex]

Where possible represent the possible cases on this case 5 since we have 5 balls and the total is the size of the sample space on this case 12. And replacing we got:

[tex] p =\frac{5}{12}= 0.417[/tex]

And rounded to the tenths place we got:

[tex] p=0.4[/tex]

And the best answer is:

B. 0.4

Step-by-step explanation:

For this case the size of the sampel space is 5+4+3= 12 representing the total of balls used.

We select a random ball from the total and we want to find the probability of selecting a blue ball. And for this case the can use the empirical definition of probability from Laplace given by:

[tex] p =\frac{Possible}{Total}[/tex]

Where possible represent the possible cases on this case 5 since we have 5 balls and the total is the size of the sample space on this case 12. And replacing we got:

[tex] p =\frac{5}{12}= 0.417[/tex]

And rounded to the tenths place we got:

[tex] p=0.4[/tex]

And the best answer is:

B. 0.4

Answer:

y = x^4 - 2x^2 + 3​

y' = 4x^3 - 4x

y'' = 12x^2 - 4

To find local minimum and local maximum, we find solution of y' = 0

=>  4x^3 - 4x = 0

<=>4x(x - 1)(x + 1) = 0

<=> x = 0,  

substitute into y  => y(0) = 0 - 0 + 3 = 3 => A(0, 3)

substitute into y'' => y''(0) = 0 - 4 = -4 < 0 => A(0, 3) is a maximal

<=> x = 1,  

substitute into y => y(1) = 1 - 2 + 3 = 2 => B(1, 2)

substitute into y'' => y''(1) = 12 - 4 = 8 > 0 => B(1, 2) is a minimal

<=> x = -1,  

substitute into y => y(-1) = 1 - 2 + 3 = 2 => C(-1, 2)

substitute into y'' => y''(-1) = 12 - 4 = 8 > 0 => C(-1, 2) is a minimal

Hope this helps!

:)

Answer:

5 hours

Step-by-step explanation:

5.6 all you have to use is .6 times 5hours to make 3kmapart

Step-by-step explanation:

We can express 3/11 as odds by saying "3 in 11". Therefore, you have a 3 in 11 chance of winning. Hope this helps!

Answer:-8

Step-by-step explanation: you add -1+ -1, to get -2, then -2+-2, to get -4 and so forth.

The missing term is -8.

The complete sequence is –1, –2, –4, -8, –16, –32.

A unique kind of sequence called a geometric sequence has a constant ratio between every two succeeding terms. This ratio is regarded as one of the geometric sequence's common ratios.

aₙ=a₁(r)ⁿ⁻¹

Given:

–1, –2, –4, ?, –16, –32.

The sequence is a geometric sequence.

So, we will find the common ratio,

r = -2/-1 = 2

The general formula of geometric sequence,

aₙ = a₁(r)ⁿ⁻¹

a₄ = (-1)(2)⁴⁻¹

a₄ = (-1)(8)

a₄ = -8

Therefore, the missing term is -8.

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Answer:

48 and 132 degrees

Step-by-step explanation:

supplement=s

one angle=2s+36

2s+36+s=180

3s+36=180

3s=144

s=48

2(48)+36=132

Therefore, 48 and 132 degrees

I hope this helped and have a good rest of your day!

Answer:

The mode is gymnastics

Step-by-step explanation:

The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!

hope his helps!!!!!!!!!!!!

Answer:

Radius, r = 10.64 m

Step-by-step explanation:

The formula of a spherical shaped object is given by :

[tex]V=\dfrac{4}{3}\pi r^3[/tex]

r is radius of a sphere

[tex]r=(\dfrac{3V}{4\pi })^{1/3} \\\\r=(\dfrac{3\times 5044}{4\times 3.14 })^{1/3} \\\\r=10.64\ m[/tex]

So, the radius of a sphere is 10.64 m.

Answer:

30 for the other two sides

Step-by-step explanation:

180-120=60

Divide 60 in half to get 30

Answer:

The overall expected grade point average for the semester is 3.16/3.1 or 3.2 if you round it up.

Step-by-step explanation:

To get the average, you need to add up all the numbers then divide the sum by how many numbers you added.

3.5 + 3.0 + 3.0 = 9.5

9.5 / 3 = 3.16

Given Information:

expected grade in two-credit course = 3.5

expected  grade in three-credit course = 3.0

expected grade in four-credit course = 3.0

Required Information:

Expected overall grade point average = ?

Answer:

The expected overall grade point average of this college student is 3.11

Step-by-step explanation:

The overall expected grade point average is given by

E(X) = Sum of grades/Total number of credit hours

Sum of grades = ∑ weightage*expected grades

Sum of grades = 2*3.50 + 3*3.0 + 4*3.0 = 28

Total number of credit hours = 2 + 3 + 4 = 9

E(X) = Sum of grades/Total number of credit hours

E(X) = 28/9

E(X) = 3.11

Therefore, the expected overall grade point average of this college student is 3.11 .

Answer: I think the answer is 3.

Step-by-step explanation:

Kim's team scored the same number of innings to win the game and Kim's team already had 6 points so four times a number has to be greater than 17.

4* 3 + 6= 18

which means the minimum number can't be less than three so they may have scored three or more points in  each of the four innings that was left.

Answer:

The roles can be assigned in 15120 ways.

Step-by-step explanation:

The parts, which means that the order in which the people are selected is important. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this question:

5 people chosen from a set of 9. So

[tex]P_{(9,5)} = \frac{9!}{(9-5)!} = 15120[/tex]

The roles can be assigned in 15120 ways.

Answer:

A. 64/125

B. 124/125.

Step-by-step explanation:

A).  As the events ( germinate or not germinate) are independent we multiply the probabilities.

Prob(All seeds germinate) = 4/5*4/5*4/5 =  64/125.

B). Probability of at least one germinating =  1 - probability that none germinate

Probability of  1 seed not germinating = 1 -45 = 1/5.

So Prob(at least one germinating)

= 1 - (1/5 * 1/5 * 1/5)

= 1 - 1/125

= 124/125.

The probability that all 3 seeds will germinate is 64/125 and the probability that at least one of the seeds will germinate is 124/125.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

(A)

The probability of all seeds will germinate will be the product of individual probability since all events are independent.

4/5 × 4/5 × 4/5 =  64/125.

B)

Probability of at least one germinating =  1 - the probability that none germinate

The probability of  1 seed not germinating will be given as,

1 -4/5 = 1/5

Thus, the probability of all three seeds not germinating = 1/5 ×  1/5 ×  1/5

Thus, the probability that at least 1 of the seeds will germinate.

⇒ 1 - (1/5 × 1/5 × 1/5)

⇒ 1 - 1/125

⇒ 124/125

Hence "The probability that all 3 seeds will germinate is 64/125 and the probability that at least one of the seeds will germinate is 124/125".

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Step-by-step explanation:

the length s of the arc AC is given as :

s = r. 0

where

r = 10 is radius

0 = 90°

= π/2 rad is angle

s = 10. π/2

= 5π

= 5.3.14

= 15.7 ~ 16

Answer:

162

Step-by-step explanation:

54 * 3 = 162

hope it's helpful

Answer:

162

Step-by-step explanation:

54 x 3 = 162

54+ 54+ 54= 162

Answer:

0.1 probability of Matt picking a red fish

6 of the fish are red.

Step-by-step explanation:

We have these following probabilities:

70% = 0.7 probability that the fish is blue.

20% = 0.2 probability that the fish is green.

p probability that the fish is red.

The sum of all these probabilities is 100% = 1. So

0.7 + 0.2 + p = 1.

p = 0.1

0.1 probability of Matt picking a red fish

There are 60 fish in the fish bowl. How many of the fish are red?

n trials with p probability of sucess. The expected value is

[tex]E(X) = np[/tex]

Here we have [tex]n = 60, p = 0.1[/tex]. So

[tex]E(X) = np = 60*0.1 = 6[/tex]

6 of the fish are red.

The probability of Matt at the time of picking a red fish is 0.1.

And, The number of fish that should be red is 6.

Since

There is a 70% probability when the fish is blue

And, 20% probability when the fish is green.

Now

Here we assume p be the probability in the case when the fish is red.

So,

Here the sum of probabilities should be 100% i.e. equal to 1.

Now

The following calculation is to be done

0.7 + 0.2 + p = 1

0.9 + p = 1

So,

p = 0.1

Now for the red one it should be

= 60 (0.1)

= 6

Hence, The probability of Matt at the time of picking a red fish is 0.1.

And, The number of fish that should be red is 6.

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Answer:

Isosceles

Step-by-step explanation:

An isosceles triangle is a triangle in which the length of at least two sides are same.

The triangle which Seth has two sides of same length that is 20 inches.

Third side is different.

Hence. the triangle which Seth has is  isosceles.

Answer:A reta é um objeto unidimensional, isto é, possui apenas uma dimensão. Observando bem uma reta, é possível notar que qualquer medida feita sobre ela representará apenas um comprimento. Dessa maneira, pode-se afirmar que retas não possuem largura, apenas comprimento.

Step-by-step explanation:

Answer:

See I don't know the answer but I did another one like this if it doesn't help you can report it no problem

Step-by-step explanation:

There are 2 different ways you can solve this problem and you'll get the same answer.

To help you visualize what you have to do, it might be easiest to translate your problem to a unit that easier to use.

Since you only have a ribbon 5 feet long, but you must cut it into 6 pieces, you know it won't even be 1 foot long.

One way to solve the problem would be to translate your 5-foot ribbon into a ribbon divided into inches.

1 foot = 12 inches

To find out how many inches long your ribbon is, you'll need to multiply the number of feet by 12.

Once you know that, then you can more easily divide it by 6. This will tell you how many inches each ribbon is.

Careful! the answer is to be put into feet so once you know how many inches long the ribbon is, you must then divide by 12 to get the correct answer in feet. Don't forget to round to the nearest tenth.

Another way to solve the problem is to simply divide the 5 feet by the number 6 and then round your number to the nearest tenth. It may be harder to visualize the answer this way, but you will get the same answer as if you translated your ribbon into inches and then divided by 12.

Good luck! I hope this helps!

32 inches of ribbon does she have left.

Unit conversion is a multi-step process that includes rounding, selecting the appropriate number of significant digits, and multiplying or dividing by a numerical factor.

We have,

Total length of Ribbon = 12 feet

After using 7 feet the remaining left

= 12 - 7

= 5 feet

Now, She gave 28 inches to her sister then the ribbon left

= 5 feet - 28 inches

= 60 inches - 28 inches

=  32 inches

= 2.66667 feet

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Answer: 20 quarts of peanut oil worth 19 cents a quart must be mixed.

Step-by-step explanation:

Let x represent the number of quarts of peanut oil worth 19 cents a quart that would be in the mixture.

The total number of quarts in the mixture would be x + 100

The cost of the x quarts would be x × 19 = 19x cents

The cost of 100 quarts of the other peanut oil would be 25 × 100 = 2500 cents

The cost of the mixture would be

24(x + 100) = 24x + 2400

Therefore, the equation would be

19x + 2500 = 24x + 2400

24x - 19x = 2500 - 2400

5x = 100

x = 100/5

x = 20

Answer:

20 quarts

Step-by-step explanation:

Answer:

Median = 18

This is the middle line in the box.

Range = 6

This is the difference between the highest and lowest values, 21 - 15.

25th percentile = 17

This is the Q1 value, which is the left side of the box.

75th percentile = 20

This is the Q3 value, which is the right side of the box.

Interquartile range = 3

This is Q3-Q1, which is 20 - 17. This is another way to measure spread.

To begin, you must plug all the values you have into a formula, and also putting them in the right form.

The formula for the volume of a cylinder is: πr²h

FINDING RADIUS: With this in mind, now we know that, our diameter must be converted to a radius. To do this, you divide your diameter by two. This gives you, 4 as your radius.

FINDING HEIGHT: In the question you sent, you can tell they've given you, your height, so all you need to do is plug it into the equation.

PLUGGING IT IN:

Your pi, stays the same when using a calculator, just press your pi symbol depending on the calculator you are using. Your radius is 4, therefore it wants you to square it, which is 4x4, which equals 16. Next, you want to multiply it by the height, so just multiply it with your height, 5.5

YOUR ANSWER:

276.46m

Answer:

2.5% of drivers have a reaction time more than 2.14 seconds

16% of drivers have a reaction time less than 1.78 seconds

84% of drivers have a reaction time less than 2.02 seconds

Step-by-step explanation:

The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

In this problem, we have that:

Mean = 1.9s

Standard deviation = 0.12

What percentage of drivers have a reaction time more than 2.14 seconds?

2.14 = 1.9 + 2*0.12

So 2.14 is two standard deviations above the mean.

Of the 50% of the measures above the mean, 95% are within 2 standard deviations of the mean, so, below 2.14. The other 5% is above.

0.05*0.5 = 0.025

2.5% of drivers have a reaction time more than 2.14 seconds

What percentage of drivers have a reaction time less than 1.78 seconds?

1.78 = 1.9 - 0.12

So 1.78 is one standard deviation below the mean.

Of the 50% of the measures that are below the mean, 68% are within one standard deviation of the mean, that is, greater than 1.78.

100 - 68 = 32

0.32*50 = 0.16

16% of drivers have a reaction time less than 1.78 seconds

What percentage of drivers have a reaction time less than 2.02 seconds?

2.02 = 1.9 + 0.12

So 2.02 is one standard deviation above the mean.

Of the measures that are below the mean, all are below 2.02.

Of those that are above, 68% are below 2.02.

0.5 + 0.68*0.5 = 0.84

84% of drivers have a reaction time less than 2.02 seconds

The percentage of drivers have a reaction is :

-2.5% of drivers have a reaction time more than 2.14 seconds

-16% of drivers have a reaction time less than 1.78 seconds

-84% of drivers have a reaction time less than 2.02 seconds

Answer 1:

2.14 = 1.9 + 2*0.12

2.5% of drivers have a reaction time more than 2.14 seconds

Answer 2:

1.78 = 1.9 - 0.12

16% of drivers have a reaction time less than 1.78 seconds.

Answer 3:

2.02 = 1.9 + 0.12

84% of drivers have a reaction time less than 2.02 seconds

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