P(A and B)
P(B)
Find P (Junior | Girl) Hint:
Classroom of Students
Boys Girls
Freshman 4 4 8
Sophomore 5
7 12
Junior 2
3 5
Senior 1 4 5
12 18
[?]
Reduce your fraction to lowest terms.
Enter the number that belongs in the green box.

Number of ocicats that [tex]19\frac{1}{2}[/tex] food will last for one week is 4 .

In the question ,

it is given that

the amount of food that the ocicat eats in 1 day = 3/5 pound

So , the amount of food that the ocicat eats in 1 week = (3/5) × 7 = 21/5

we have to find the number of ocicat that can eat [tex]19\frac{1}{2}[/tex] pound of food feed .

So ,

the number of ocicat that can eat  [tex]19\frac{1}{2}[/tex] pound of food feed = [tex]19\frac{1}{2}[/tex] ÷ 21/5

= (19*2+1)/2 ÷ 21/5

= 39/2 × 5/21

= (39 × 5)/(2 × 21)

= 195/42

= 65/14

= [tex]4\frac{9}{14}[/tex]  ocicats

since the number of ocicats cannot be in fraction ,

so number of ocicats = 4

Therefore , Number of ocicats that [tex]19\frac{1}{2}[/tex] food will last for one week is 4 .

The given question is incomplete , the complete question is

An ocicat eats 3/5 of a pound of food daily. How many whole ocicats can a [tex]19\frac{1}{2}[/tex] -pound bag of food feed for one week?

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Step-by-step explanation:

The total weekly profit p, in dollars, from producing and selling x units of a certain product is given by the function p(x) = 225x-(165x+c), where c is a constant. If 75 units were produced and sold last week for a profit of $3,365, what is the value of c?

$3,365 = 225(75) - (165(75) + c)

$3,365 = 16,875 - 165(75) - c

$3,365 = 16,875 - 12,375 - c

$3,365 = 4,500 - c

=1,135 =  - c

c = 1,135

The ratio in simplest form, of the number of tickets jeans sold to the number of tickets jake sold is 12/49.

Given that,

Jake sold 49 tickets while jeans sold 12 for the school.

In simplest form the ratio of the given case will be;

Simplest form:

A fraction is a number that falls between the whole numbers but is not a whole number. It belongs to the entire. A fraction also consists of a denominator and a numerator. We obtain the fraction in its simplest form when both the numerator and denominator can no longer be independently reduced to any smaller integer.

The ratio we get;

→ 12/49

The ratio in simplest form, of the number of tickets jeans sold to the number of tickets jake sold is 12/49.

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Ratio of amount $600 share by Annie and Dermot is 11 : 9, then amount  received by Annie is $330 and Dermot is $270.

As given in the question,

Total amount share by Annie and Dermot is $600.

Ratio of amount share by Annie and Dermot is 11 : 9

Let x be the amount of money.

11x + 9x = $600

⇒ 20x = $600

⇒20x/20 = $600/20

⇒x= $30

Amount received by Annie is equal to

= 11 × 30

= $330

Amount received by Dermot is equal to

= 9 × 30

= $270

Therefore, ratio of amount $600 share by Annie and Dermot is 11 : 9, then amount  received by Annie is $330 and Dermot is $270.

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Answer:

See below.

Step-by-step explanation:

Let the price of drinks be x and the price of candies be y.

9x + 4y = 60 --------------------(1)

10x + 2y = 57.50 --------------(2)

2(10x + 2y) = 57.50*2

20x + 4y = 115 --------------(3)

9x + 4y - 20x - 4y = 60 - 115

9x - 20x = -55

-11x = -55

11x = 55

x = 55/11

Put x = 5 in Eq. (1)

9(5) + 4y = 60

45 + 4y = 60

4y = 60 - 45

4y = 15

y = 15/4

So, the cost of one drink is $5 and the cost of one candy is $3.75.

[tex]\rule[225]{225}{2}[/tex]

Answer:

Clara ate 2/15

Step-by-step explanation:

1/5 equals 3/15

The probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.

What is a binomial distribution?

The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.

Formula to calculate the binomial distribution

P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ

Here, we know that

Solar-heat installations successfully reduce the utility bill 60% of the time.

We have to calculate the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill.

We have 60% = 0.6 = p and n = 10.

We have a binomial distribution: X : (10, 0.6).

We use the binomial distribution formula to calculate the probability

P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ, we get

P(x ≥ 9) = 1 - P(x < 9)

P(x ≥ 9) = 1 - P(x ≤ 8)

P(x ≥ 9) = 1 - ∑⁸₀ P(x = x)

P(X ≥ 9) = 1 - ∑⁸₀¹⁰Cₓ × (0.6)ˣ × (1-0.6)¹⁰⁻ˣ

P(X ≥ 9) = 1 -( 0.00011 + 0.00157 + 0.01062 + 0.04247 + 0.11148 + 0.20066 + 0.25082 + 0.21499 + 0.12093)

P(X ≥ 9) = 1 -0.95365

P(X ≥ 9) = 0.04635

Hence, the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.

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Answer:

6X/X^2-2X+1

Step-by-step explanation:

x

2

−3x+2

9x

2

+18x

​

÷

2x−4

3x

2

+3x−6

​

Divide  

x

2

−3x+2

9x

2

+18x

​

 by  

2x−4

3x

2

+3x−6

​

 by multiplying  

x

2

−3x+2

9x

2

+18x

​

 by the reciprocal of  

2x−4

3x

2

+3x−6

​

.

(x

2

−3x+2)(3x

2

+3x−6)

(9x

2

+18x)(2x−4)

​

Factor the expressions that are not already factored.

3(x−2)(x+2)(x−1)

2

2×9x(x−2)(x+2)

​

Cancel out 3(x−2)(x+2) in both numerator and denominator.

(x−1)

2

2×3x

​

Expand the expression.

x

2

−2x+1

6x

​

Answer:

Hey, hope it helps my friend

Step-by-step explanation:

In the image

Answer:

164 minutes

Step-by-step explanation:

$8 + $0.06m = $17.84

To isolate the m, first bring the eight to the other side

0.06m = 9.84

then divide both sides by 0.06

m = 164

An area 825 by 550 ft gives max area for $6600.

acc to our question-

hence, 3300 + 3300 = $6600

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By using the diagram and the given angle measure we get that:

if, m∠1 = 143°

then, m∠2 = 37°

         m∠3 = 143°

         m∠4 = 37°

What is angles?

An angle is formed when two straight lines or rays meet at a common endpoint.

What is Properties of Congruence?

       For all angles A ,

        ∠A≅∠A .

       An angle is congruent to itself.

        For any angles A  and  B ,

        if ∠A≅∠B , then ∠B≅∠A .

         Order of congruence does not matter.

        For any angles A,B,  and  C ,

        if ∠A≅∠B and ∠B≅∠C , then ∠A≅∠C .

        If two angles are both congruent to a third angle, then the first two        angles are also congruent.

I assume that, this refers to two intersecting lines which form four angles.

         ∠1 + ∠2 = 180°

          143° + ∠2 = 180°

          ∠2 = 180° - 143°

          ∠2 = 37°.

         It means that,  ∠1 = ∠3 =143° (properties of congruency)

         and ∠2 = ∠4 =37° (properties of congruency).

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Answer: 2x^2 -6x

Step-by-step explanation:

First you should distribute the x's as shown:

(x)(x)+(x)(−3)+(3)(x)+(3)(−3)+x2+−6x+9=x2+−3x+3x+−9+x2+−6x+9

Then combine Like terms:

↓x2+−3x+3x+−9+x2+−6x+9=↓

↓(x2+x2)+(−3x+3x+−6x)+(−9+9)↓

2x2+−6x

Hope this helped... :)

Answer:

Step-by-step explanation:

from the area we find the side by taking the square root, having found the side we multiply it by 4 and we have the perimeter, we can solve it with a simple expression that summarizes what I wrote

4√81 =

4 × 9 =

36 mm

answer:

100 text messages.

$50-$40 = $10

$10/$0.1 = 100

100 text messages

The value of the down payment for the car is $345.

From the information, Scott will purchase a new computer on an installment plan and the computer costs $2,300 and requires a 15% down payment.

The value of the down payment will be:

= Down payment percentage × Total cost

= 15% × $2300

= 0.15 × $2300

= $345

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Graph of f(x) = 3x - sin 4x is using method of adding y-coordinates is attached below.

What is graphing method by adding ordinates?

The function y = 3x - sin 4x is actually the sum of two functions, y = 3x and y = - sin 4x.

For every value in the domain, there is a corresponding value in the range so that the point (x, 3x - sin 4x) is on the graph of y = 3x - sin 4x.

According to the given question:

Follow these steps to graphing the function:

1. Open an Excel file. Label the first column "x-coordinates," the second column "y = 3x," the third column "y = -sin 4x," and the fourth column "y = 3x - sin 4x." Set each column to round to four decimal places.

2. Set up the first column to range from -2pi to 2pi by intervals of pi/4.

3. Fill in the second and third columns by utilizing the equations y = 3x and y = - sin 4x, respectively.

4. Fill in the fourth column by simply adding the second and third columns.

5. Graph y = 3x - sin 4x  by using the x-coordinates from column A and the y-coordinates from column D.

Check the attachment below for the required graph obtained after plotting the points.

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Answer:

it should be the first one, if not it’s the third

Step-by-step explanation:

The equation of line with undefined slope and passes through the point

(1/2, 5) will be;

⇒ x = 1/2

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point = (1/2 , 5)

And, The slope = undefined

Now,

Since, We know that;

The equation of line with undefined slope and passes through the point will be;

⇒ x = a

Where, 'a' is the x - intercept.

Here, The point = (1/2 , 5)

The slope = undefined

And, The x - intercept = 1/2

So, The equation of line with undefined slope and passes through the point (1/2, 5) will be;

⇒ x = 1/2

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Answer:

10

Step-by-step explanation:

substitute x = 4 into the expression

3x - 2 = 3(4) - 2 = 12 - 2 = 10

Answer: 10

Step-by-step explanation:

4 × 3 = 12

12 - 2= 19

Hope it helps

An example of experiment is B. Researchers working for a company test their new sneaker design to see if it helps athletes run faster.

An experiment simply means a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. It should be noted that experiments provide insight into cause-and-effect as they demonstrate what outcome occurs when a particular factor is manipulated

Experiments have a vital place in the development of science because experiments are used to test the reality of a thought, an axiom, or a phenomenon with a theoretical basis and to turn it into a law or a theorem.

In this case, testing the new sneakers is an experiment.

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The maximum number of people the lift can safely carry is 8 people.

Given that, the average mass of a man is 84 kg and of a woman is 70 kg.

In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

Now, average = (84+72)/2

= 156/2

= 78

Let the number of people in the left be n.

So, 78n≤620

Divide 78 to both the sides of the inequality

78n/78≤620/78

⇒ n≤7.9

⇒ n≤8

Therefore, the maximum number of people the lift can safely carry is 8 people.

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The proportion of Americans who support federal spending cuts to Medicaid is less than 0.12 leads to Type 1 error.

When we reject a true H₀ it is known as type 1 error. The probability of type 1 errors is inversely proportional to the amount of confidence you choose. There is a 5% possibility of receiving a type 1 error on a test with a 95% confidence level.

When we feel to reject a false H₀ it is known as type 2 error.

H₀:P= 0.12

Hₐ:P= 0.12

The question implies that we actually rejected the null hypothesis, while there is a chance that it is true and we are rejecting a true null hypothesis.

Therefore, it only suggests that there is a possibility that we will make a type 1 error.

Consequently, Type 1 error is the response to our query.

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The required measure of the angle is m∠A=64°.

orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

,

Here,
Angles are represented by an algebraic expression, and the sum of the angle is 180°.
According to the question,
m∠A+m∠B+m∠C=180°
Substitute the value in the equation,
4x+90°+x+10=180°
5x = 180 - 100
5x = 80
x = 16°

Thus, the required measure of the angle is m∠A=64°.

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Answer:

Adult is 10$ and Child is 7$.

Unfortunately for the family, they do not have enough to go to the theater. They do not have that extra dollar.

Hope this helps!

Step-by-step explanation:

2x + 4y = 48

5x + 2y = 64

2x + 4y = 48

10x + 4y = 128

( 10x - 2x ) + ( 4y - 4y ) = ( 128 - 48 )

8x = 80

x = 10

2 ( 10 ) + 4y = 48

20 + 4y = 48

4y = 48 - 20

4y = 28

y = 7

Answer:

10

Step-by-step explanation:

(2w + 4) - (2w - 6)

2w + 4 - 2w + 6

2w - 2w + 4 + 6

10

I hope this helps!