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3 years ago

13

The entry tickets at a community fair cost $5 for children and $10 for adults. On a certain day 1000 people we entered in the fa

r and $7,100 is collected. How many adults and how many children were at the fair?

1 answer:

Hitman42 [59]3 years ago

6 0

580 kids
420 adults

hope this helps

brainliest plz

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Which fraction is greater than 3/5<br><br> 4/6<br><br> 6/12<br><br> 3/8<br><br> 4/10

Ulleksa [173]

Answer:

a.) 4/6

Step-by-step explanation:

3/5 = .6

<u><em>4/6 = .666666666667</em></u>

6/12= 0.5

3/8= .375

4/10= .4

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3 years ago

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Suppose that a college determines the following distribution for X = number of courses taken by a full-time student this semeste

lidiya [134]

Answer:

$E(X) = \sum_{i=1}^n X_i P(X_i) = 3*0.07 +4*0.4 +5*0.25 +6*0.28= 4.74$ In order to find the variance we need to calculate first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 3^2*0.07 +4^2*0.4 +5^2*0.25 +6^2*0.28= 23.36$ And the variance is given by:

$Var(X) = E(X^2) +[E(X)]^2 = 23.36 -[4.74]^2 = 0.8924$

And the deviation would be:

$Sd(X) =\sqrt{0.8924} =0.9447$

Step-by-step explanation:

Previous concepts

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).

Solution to the problem

For this case we have the following distribution given:

X 3 4 5 6

P(X) 0.07 0.4 0.25 0.28

We can calculate the mean with the following formula:

$E(X) = \sum_{i=1}^n X_i P(X_i) = 3*0.07 +4*0.4 +5*0.25 +6*0.28= 4.74$

In order to find the variance we need to calculate first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 3^2*0.07 +4^2*0.4 +5^2*0.25 +6^2*0.28= 23.36$

And the variance is given by:

$Var(X) = E(X^2) +[E(X)]^2 = 23.36 -[4.74]^2 = 0.8924$

And the deviation would be:

$Sd(X) =\sqrt{0.8924} =0.9447$

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3 years ago

3. What line forms when a plane and a cylinder intersect?

leonid [27]

The answer to this depends on the angle at which they intersect. If it intersects<span> the cylinder perpendicular to the axis then a circle is formed. </span><span>If the plane intersects the cylinder at an angle, it will form an ellipse. This will be true until the plan is parallel with the axis of the cylinder. At that point, the surface will become a rectangle.</span>

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3 years ago

All bags entering a research facility are screened. The screening process is not perfect so that 77% of the bags that contain fo

garik1379 [7]

Answer:

(1) 0.5933

(2) 0.8955

Step-by-step explanation:

We are given that all bags entering a research facility are screened.

Let Probability that bags entering the building contains forbidden material,

P(F) = 0.69

Probability that bags entering the building does not contains forbidden material, P(NF) = 1 - 0.69 = 0.31

Let event A = alarm gets triggered

Probability that alarm gets trigger given the bags contain forbidden material, P(A/F) = 0.77

Probability that alarm gets trigger given the bags does not contain forbidden material, P(A/NF) = 0.20

(1) Probability that a bag triggers the alarm, P(A) ;

P(A) = P(F) * P(A/F) + P(NF) * P(A/NF)

= (0.69 * 0.77) + (0.31 * 0.20) = 0.5313 + 0.062

= 0.5933

Therefore, probability that a bag triggers the alarm is 0.5933 .

(2) Probability that a bag that triggers the alarm will actually contain forbidden material is given by P(F/A) ;

Using Bayes' Theorem;

P(F/A) = $\frac{P(F) * P(A/F)}{P(F) * P(A/F) + P(NF) *P(A/NF)}$ = $\frac{0.69*0.77}{0.69*0.77+0.31*0.20}$ = $\frac{0.5313}{0.5933}$

= 0.8955

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3 years ago

Rajan needs 1 liter of 15% hydrochloric acid solution for an experiment. He checks his storage cabinet, but he only has a 5-lite

Delvig [45]

Answer:

<em>0.75</em><em> liters of 5% hydrochloric acid solution </em>
<em>0.25</em><em> liters of 45% hydrochloric acid solution.</em>

Step-by-step explanation:

Let us assume that, x liters of the 5% hydrochloric acid and y liters of the 45% hydrochloric acid solutions are combined.

As Rajan need total of 1 liter of solution, so

$x+y=1$

i.e $x=1-y$ --------------------1

As Rajan needs 5% hydrochloric acid and 45% hydrochloric acid to make a 1 liter batch of 15% hydrochloric acid, hence acid content of the mixture of two acids will be same as of the final one, so

$0.05x+0.45y=1\times 0.15$

i.e $5x+45y=15$ -------------2

Putting value of x from equation 1 in equation 2,

$\Rightarrow 5(1-y)+45y=15$

$\Rightarrow 5-5y+45y=15$

$\Rightarrow 5+40y=15$

$\Rightarrow 40y=15-5=10$

$\Rightarrow y=0.25$

Putting the value of y in equation 1,

$x=1-0.25=0.75$

Therefore, Rajan must use 0.75 liters of 5% hydrochloric acid solution and 0.25 liters of 45% hydrochloric acid solution.

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3 years ago