Jose created a ball pit for his little sister to play in. he put 40 red balls, 55 purple balls, 45 yellow balls, and 60 green balls into the ball pit. while his sister is playing, one ball rolls out of the pit. what is the probability that the ball is red? 0.17 0.17 0.20 0.20 0.25 0.25 0.40

The points on each linear function are given as follows:

The slope-intercept representation of a linear function is given as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

In the context of this problem, the points on segment AB are given as follows:

A(-7,-4), B(5,4).

Hence the slope is:

m = (4 - (-4))/(5 - (-7)) = 8/12 = 2/3.

The coordinates of point C are given as follows:

C(-2,6).

When two lines are parallel, they have the same slope, hence:

y = 2/3x + b

When x = -2, y = 6, hence the intercept b is calculated as follows:

6 = 2/3(-2) + b

b = 6 + 4/3

b = 22/3.

Hence the parallel line is:

y = 2/3x + 22/3.

Another point on the line is found when x = 1, hence:

y = 2/3(1) + 22/3 = 24/3 = 8.

Hence point (1,8).

When two lines are perpendicular, the multiplication of their slopes is of -1, hence:

2/3m = -1

m= -3/2.

Hence:

y = -3/2x + b

When x = -2, y = 6, hence the intercept b is calculated as follows:

6 = -3/2(-2) + b

6 = 3 + b

b = 3.

Hence the perpendicular line is:

y = -3/2x + 2.

Another point is when x = 2, hence:

y = -3/2(2) + 2

y = -1.

Point (2,-1).

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Answer:

1) Small-Cherry-Green, 2) Small-Cherry-Purple, 3) Small-Cherry-Red, 4) Small-Vanilla-Green, 5) Small-Vanilla-Purple, 6) Small-Vanilla-Red, 7) Small-Strawberry-Green, 8) Small-Strawberry-Purple, 9) Small-Strawberry-Red, 10) Small-bubble gum-Green, 11) Small-Bubble gum-Purple, 12) Small-Bubble gum-Red , 13) Huge-Cherry-Green, 14) Huge-Cherry-Purple, 15) Huge-Cherry-Red, 16) Huge-Vanilla-Green, 17) Huge-Vanilla-Purple, 18) Huge-Vanilla-Red, 19) Huge-Strawberry-Green, 20) Huge-Strawberry-Purple, 21) Huge-Strawberry-Red, 22) Huge-Bubble gum-Green, 23) Huge-Bubble gum-Purple, 24) Huge-Bubble gum-Red

b) 24

2) Tree diagram method

b) Each unique snow cone has an element of each category

3) 2

i) By counting

ii) By finding out the possible combinations

Step-by-step explanation:

The details of the options at Tia's Snow Xpress includes;

2 (different) sizes; Small or huge size

4 (different) flavors; Cherry, vanilla, strawberry, bubble gum

3 glow-in-the-dark spoon choices; Green, purple, red

1) Let the 'a' represent the small size let 'b' represent the huge size, let 'c' represent cherry, let 'v' represent vanilla, let 's' represent strawberry, let 'b' represent bubble gum, let '1' represent green, let '2' represent purple and let '3' represent red, we have;

The possible outcomes are;

ac1, ac2, ac3, av1, av2, av3, as1, as2, as3, ab1, ab2, ab3

bc1, bc2, bc3, bv1, bv2, bv3, bs1, bs2, bs3, bb1, bb2, bb3

With the use of MS Word, we have;

1) Small-Cherry-Green, 2) Small-Cherry-Purple, 3) Small-Cherry-Red, 4) Small-Vanilla-Green, 5) Small-Vanilla-Purple, 6) Small-Vanilla-Red, 7) Small-Strawberry-Green, 8) Small-Strawberry-Purple, 9) Small-Strawberry-Red, 10) Small-bubble gum-Green, 11) Small-Bubble gum-Purple, 12) Small-Bubble gum-Red

13) Huge-Cherry-Green, 14) Huge-Cherry-Purple, 15) Huge-Cherry-Red, 16) Huge-Vanilla-Green, 17) Huge-Vanilla-Purple, 18) Huge-Vanilla-Red, 19) Huge-Strawberry-Green, 20) Huge-Strawberry-Purple, 21) Huge-Strawberry-Red, 22) Huge-Bubble gum-Green, 23) Huge-Bubble gum-Purple, 24) Huge-Bubble gum-Red

Therefore;

b) There are 24 different combinations in total

2) The method used to find the combinations is a tree diagram with branches extending from, the size of the Snow Cone Xpress to the choices for the glow-in-the-dark spoons

b) The method was used because of there are more than two categories each with different number of items and each unique Snow Cone Xpress option comprises of an element of each category

3) The number of Snow Cones that includes the cherry flavor and a green spoon = 2 different Snow cones

b) The answer can be arrived at by either;

i) Counting from the listed snow cone options

ii) Noting that a setting the only options for flavor as cherry and the only option for the glow-in-the-dark spoon as green and then combining both categories into one category option with the connection 'and' we have the possible combination as 3 items taking 2 at a time less the combination of the small and huge snow cones as follows;

Combinations = ₃C₂ - 1 = 2

The solution to the inequality 6m + 2 > -27 is  m > -4.33

The solution to the inequality 8(p-6)>4(p-4) is  p > 8

The given inequality is:

6m  +  2  >  - 27

Subtract 2 to both sides of the inequality

6m  +  2 - 2  >  -27  -  2

6m   >  -29

Divide both sides by 6

\(\frac{6m}{6}> \frac{-29}{6} \\m > \frac{-29}{6}\\m > -4.83\)

For the inequality  8(p-6)>4(p-4)

Expand the inequality using the distributive rule

8p  -  48   >  4p  -  16

Collect like terms

8p  -  4p  >  -16  +  48

4p    >  32

Divide both sides of the inequality 4

\(\frac{4p}{4} > \frac{32}{4}\\p > 8\)

The solution to the inequality 6m + 2 > -27 is m > -4.33

The solution to the inequality 8(p-6)>4(p-4) is p > 8

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Answer:

6

Step-by-step explanation:

1 1 /2    ÷  1/ 4

=    3/2  ÷  1/4

= 6

Answer: x² + 4x +3=0

Step-by-step explanation:

Add 4x to both sides.

To calculate the perimeter, add the lengths of sides AB, BC, and AC. The area can be found using Heron's formula. To find the angles, use the law of cosines.

1. **Perimeter and area of triangle ABC**

To find the perimeter and area of triangle ABC, we need to use the given information about its sides and angles.

Let's assume that side AB has a length of "a", side BC has a length of "b", and side AC has a length of "c". The given angles are angle A, angle B, and angle C.

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the perimeter P of triangle ABC is given by: P = a + b + c.

To find the area of triangle ABC, we can use Heron's formula, which states that the area A of a triangle with side lengths "a", "b", and "c" is given by: A = √(s(s - a)(s - b)(s - c)), where s is the semi-perimeter of the triangle, given by: s = (a + b + c) / 2.

Once we have calculated the area, we can use the law of cosines to find the measures of the angles. The law of cosines states that for a triangle with side lengths "a", "b", and "c", and opposite angles A, B, and C, the following relationships hold:

cos(A) = (b^2 + c^2 - a^2) / (2bc)

cos(B) = (a^2 + c^2 - b^2) / (2ac)

cos(C) = (a^2 + b^2 - c^2) / (2ab)

Using these formulas, we can calculate the measures of the angles A, B, and C.

To find the exact values of the perimeter, area, and angles, we would need the specific lengths of the sides and the measures of the angles. Please provide those values, and I can assist you with the calculations.

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The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .

In the question ,

it is given that ,

The random variable X is said to be normally distributed  ,

the mean is given as , μ = 70 , and

standard deviation of normal distribution is  (σ) = 10

probability that X is between 72 and 84 is written as P(72 < X < 84)

= P((72 - 70)/10 \(<\) Z \(<\) (84 - 70)/10)

= P(0.2 < Z < 1.4)

= P(0 \(<\) Z \(<\) 1.4) – P(0 \(<\) Z \(<\) 0.2)

From the z table , we get the values as

= 0.4192 – 0.0793

= 0.3399

≈ 0.340

Therefore , The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .

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Answer:

0.32653061224

Step-by-step explanation:

To write 0.32653061224 as a fraction you have to write 0.32653061224 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

0.32653061224 = 0.32653061224/1 = 3.2653061224/10 = 32.653061224/100 = 326.53061224/1000 = 3265.3061224/10000 = 32653.061224/100000 = 326530.61224/1000000 = 3265306.1224/10000000 = 32653061.224/100000000 = 326530612.24/1000000000 = 3265306122.4/10000000000 = 32653061224/100000000000

And finally we have:

0.32653061224 as a fraction equals 32653061224/100000000000

The value of a comic book in dollars has been found to be 0.20y + 1.50, where y is the number of years since it was released. is  

(a)  \(0.2$\)

(b) \(1.5$\)

\(0.2 y+1.5 \longleftarrow \text { initial value }\)

\(when $y$ increase one. the value increase $\$ 0.2$\)

Travelling to movies and television programmes. An element of a comic book being in a popular film or television programme is a major factor in its value rising. Characters' comic book appearances have become far more valuable as they are integrated into the Marvel Cinematic Universe.

Marvel's first comic book just sold for $1.26m. Movies have contributed to the enduring popularity of superheroes, bringing in new audiences. The printed comic is still big business, worth over $1bn in North America alone.

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Answer:

x = -113

y = 30

Step-by-step explanation:

110+10+2y=180

2y=180-110-10

=60

y=60/2

y=60/2 =30

-3x-10-2x+15+110+120+95=540

-3x-2x =540+10-15-110-120-95

-5x=210

x=210/-5

x=210/-5 = - 42

Step-by-step explanation:

Here,

110+2y+10=180°(being sum of angles in

a straight line)

y=180-120

y=60°,,

now,

to find the value of X,

120+95+110+3x-10+2x+15=540°(being sum of all angle of pentagon)

330+5x=540°

5x=540-330

5x=210

X=210/5

x=42°,,

To solve the problem we must know about Like Terms.

like terms are those terms that are having the same variables, also the variables are of the same order as well.

for example, 25x and 5x are like terms; 30xy and 7xy are like terms, 9x³ and 4x² are not like terms, etc.

The polynomial can be written as \(x ^3 + 5x^2+5x - 2\).

Given to us

We will simplify the given polynomial, therefore, bring the like terms together,

\(x ^3 + 3x^2 - x + 2x^2 + 6x - 2\\\\=x ^3 + (3x^2 + 2x^2)+(- x + 6x) - 2\\\\=x ^3 + 5x^2+5x - 2\)

Hence, the polynomial can be written as \(x ^3 + 5x^2+5x - 2\).

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False. The columns of matrix P are not necessarily eigenvectors of matrix A. While the diagonal matrix D contains the eigenvalues of A, the eigenvectors are not explicitly determined by the columns of P.

False. The columns of matrix P are not guaranteed to be eigenvectors of the transpose of matrix A (A.T).

In the given equation, \(a = PDP^(-1),\)

where D is a diagonal matrix and P is an invertible matrix.

The diagonal elements of D represent the eigenvalues of matrix A, while the columns of P correspond to the eigenvectors of A.

When considering the transpose of matrix A (A.T), we have \((A.T) = (PDP^(-1)).T = (P^{(-1)})^T D^T P^T.\)

Taking the transpose of a product involves reversing the order of the matrices and transposing each matrix individually.

Therefore, we have \((A.T) = P^T D^T (P^{(-1)})^T.\)

Since P is an invertible matrix, its transpose \(P^T\) is also invertible. Similarly, the transpose of the inverse of \(P, (P^{(-1)} )^T,\) is also invertible.

However, the key point is that the diagonal matrix\(D^T\) is not guaranteed to have the same eigenvalues as matrix A.

The eigenvalues of A are present in D, but they may not remain on the main diagonal after transposing.

Thus, the columns of matrix P, which correspond to the eigenvectors of A, may not necessarily be the eigenvectors of A.T.

In conclusion, the statement is false.

The columns of matrix P do not have to be eigenvectors of the transpose of matrix A (A.T).

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Answer:it’s A

Step-by-step explanation: I did it on edg

The textbook b has the highest median review score of 7, it is the most popular textbook among the three.

To find the most popular textbook among the three, we will find the median review score of each textbook and then compare them. Since each textbook has a different number of reviews, we will find the median using the following steps:

Put all the reviews in numerical order.

Find the middle value. If there is an odd number of reviews, this is the median score. If there is an even number of reviews, take the average of the two middle scores.

To find the median review score of textbook a:

2, 6, 6, 7, 7, 8, 9

Putting the scores in order: 2, 6, 6, 7, 7, 8, 9

The median is the fourth score, which is 7. Therefore, the median review score of textbook a is 7.

To find the median review score of textbook b:

4, 4, 6, 8, 8, 9, 10

Putting the scores in order: 4, 4, 6, 8, 8, 9, 10

The middle two scores are 6 and 8, so we take their average: (6 + 8) / 2 = 7

Therefore, the median review score of textbook b is 7.

To find the median review score of textbook c:

5, 5, 6, 6, 6, 7, 10

Putting the scores in order: 5, 5, 6, 6, 6, 7, 10

The middle score is 6. Therefore, the median review score of textbook c is 6.

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In the future, please post the full problem with all included instructions. After doing a quick internet search, I found your problem listed somewhere else. It mentions two parts (a) and (b)

Part (a) asked for the equation of the line in y = mx+b form

That would be y = -2x+9

This is because each time y goes down by 2, x goes up by 1. We have slope = rise/run = -2/1 = -2. This indicates that the height of the candle decreases by 2 inches per hour. The slope represents the rate of change.

The initial height of the candle is the y intercept b value. So we have m = -2 and b = 9 lead us from y = mx+b to y = -2x+9

----------------------------------------------------------------

Part (b) then asks you to graph the equation. Because this is a linear equation, it produces a straight line. We only need 2 points at minimum to graph any line. Let's plot (0,9) and (1,7) on the same xy grid. These two points are the first two rows of the table. Plot those two points and draw a straight line through them. The graph is below

Answer: y = -2x+9

Step-by-step explanation:

Answer:

154

Step-by-step explanation:

the perimeter is the summation of all the sides of the plane. so

15 + 14 + 20 + 9 + 15 + 13 + 50 + 18 = 154

i think this is ✅

Using the labelled size of segments, the perimeter of the given figure is 154 units. Hence, the fourth option is true.

Use the concept of perimeter defined as:

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.

According to the figure,

The perimeter of the given building is the sum of the lengths shown in the figure.

18 + 15 + 14 + 20 + 9 + 15 + 13 + 50 = 154.

Hence,

The required perimeter is 154 units, which is option fourth.

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For a standardized normal distribution, Z, the probability that Z is greater than 1.50 is less than the probability that Z is greater than 2.50. False, is the correct statement regarding the given statement.

In statistics, the standardized normal distribution is a normal distribution with a mean of zero and a standard deviation of one. It is also known as the standard normal distribution. The distribution is entirely defined by its mean and standard deviation. For example, any normal distribution can be standardized by subtracting its mean and dividing by its standard deviation.This distribution is a continuous probability distribution.

A continuous probability distribution is a probability distribution that assigns probabilities to an infinite number of possible outcomes that are not countable. These probabilities are expressed as the area under the curve in a continuous probability distribution. The total area under the curve of a continuous probability distribution is always equal to one.

The statement given "For a standardized normal distribution, Z, the probability that Z is greater than 1.50 is less than the probability that Z is greater than 2.50" is false.

This is because the normal distribution curve is a symmetrical curve and the probability of being greater than a value of 1.50 or 2.50 is the same.

Therefore, the probability of Z being greater than 1.50 is the same as the probability of Z being greater than 2.50. The answer is False.

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Answer:

59,000

Step-by-step explanation:

123,456-64,456=59,000

Answer:

Step-by-step explanation:

its 212123s\

Answer:

-\(\sqrt{1}\), \(\sqrt{2}\), \(\frac{π}{2}\)

Step-by-step explanation:

square roots and pie are irrational.

The given problem statement can be solved by using the z-score formula, that is z = (x - μ)/ σ where x is the value, μ is the mean and σ is the standard deviation of the data set.

For the first part of the problem, we are required to find the probability that a randomly selected education major received a starting salary offer greater than $52,350. The formula to solve for the z-score is shown below:

z = (x - μ)/ σ

z = (52,350 - 46,292)/4,320

z = 1.4

The probability of the salary being greater than $52,350 can be found by using the Z-table or by using the formula P(Z > z) = 1 - P(Z < z). Here, P(Z < 1.4) = 0.9192

Therefore, P(Z > 1.4) = 1 - 0.9192 = 0.0808

For the second part of the problem, we are required to find the probability that a randomly selected education major received a starting salary offer between $45,000 and $52,350.

The formula to solve for the z-scores is shown below:

z1 = (45,000 - 46,292)/4,320z1 = -0.3z2 = (52,350 - 46,292)/4,320z2 = 1.4

The probability of the salary being between $45,000 and $52,350 can be found by using the formula

P(z1 < Z < z2) = P(Z < z2) - P(Z < z1).

Here, P(Z < -0.3) = 0.3821 and P(Z < 1.4) = 0.9192

Therefore, P(-0.3 < Z < 1.4) = 0.9192 - 0.3821 = 0.5371

To find the percentage of education majors that received a starting offer between $38,500 and $45,000, we first need to convert the values to z-scores. The formula to solve for the z-scores is shown below:

z1 = (38,500 - 46,292)/4,320

z1 = -1.8z2 = (45,000 - 46,292)/4,320

z2 = -0.3

The probability of the salary being between $38,500 and $45,000 can be found by using the formula P(z1 < Z < z2) = P(Z < z2) - P(Z < z1). Here, P(Z < -1.8) = 0.0359 and P(Z < -0.3) = 0.3821

Therefore, P(-1.8 < Z < -0.3) = 0.3821 - 0.0359 = 0.3462

Converting this probability to a percentage, we get:0.3462 x 100% = 34.62%

Therefore, the answer is d. 34.62%.

Therefore, the probability that a randomly selected education major received a starting salary offer greater than $52,350 is 0.0808. The probability that a randomly selected education major received a starting salary offer between $45,000 and $52,350 is 0.5371. The percentage of education majors that received a starting offer between $38,500 and $45,000 is 34.62%.Twenty percent of education majors were offered a starting salary less than 41,969.2$.

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The length of each side of the square is 7 yards.

The square sides are equal in a square. So, we wuill find the square root of the number to get what make one side length.

To get length of each side of the square, we will divide perimeter by 4 since a square has four equal sides.

The formula is: Perimeter = 4 * Side Length

Plugging the values:

28 yd = 4 * Side Length

Side Length = 28 yd / 4

Side Length = 7 yd.

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X= 54

hope it helps

Answer:

WHEN YOU COMPARE THE TEMPERATURE ON MONDAY TO THE TEMPERATURE ON TUESDAY, THE TEMPERATURE ON TUESDAY IS COLDER.

By formulating and solving a Linear Programming model, Tech Mortgage can make informed investment decisions based on specific objectives and constraints.

To solve this problem using Linear Programming, we need to define decision variables, formulate the objective function, and set up the constraints.

Decision variables:

Let x1 be the amount invested in First Trust Deeds.

Let x2 be the amount invested in Second Trust Deeds.

Let x3 be the amount invested in Third Trust Deeds.

Let x4 be the amount invested in Commercial Trust Deeds.

Let x5 be the amount invested in the Savings Account.

Objective function:

Maximize the yearly return:

Maximize 0.0775 x1 + 0.1125 x2 + 0.1425 x3 + 0.0875 x4 + 0.0445 x5

Constraints:

At least $5 million in the savings account:

x5 ≥ 5,000,000

At least 80% of the money invested in residential properties:

x1 + x2 + x3 ≥ 0.8 * (x1 + x2 + x3 + x4 + x5)

At least 60% of the money invested in residential properties should be in first trust deeds:

x1 ≥ 0.6 * (x1 + x2 + x3)

The portfolio risk should not exceed 5%:

0.04² * 4² * x1 + 0.06² * 11.25² * x2 + 0.09² * 14.25² * x3 + 0.03² * 8.75² * x4 ≤ (0.05 * 68,000,000)²

The objective is to maximize the yearly return, subject to the constraints mentioned above. Solving this Linear Programming model will provide the optimal investment amounts for each loan type and the savings account that satisfy the given conditions.

The resulting solution will provide Tech Mortgage with an investment strategy that maximizes yearly returns while meeting the specified requirements.

In conclusion, by formulating and solving a Linear Programming model, Tech Mortgage can make informed investment decisions based on specific objectives and constraints. This allows them to optimize their investment portfolio and balance returns, risk, and diversification to meet their financial goals and requirements.

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Answer:

23x + 12y + -4xy^2

Step-by-step explanation:

So lets first expand

3y (-4 x(5x - 3y + y^2)

let's ignore 3y for now

Since 5x - 3y + y^2 can't be simplified, we move on to multiplying each number.

note: Capital X = Multiplying symbol

___________________________________

-4 X 5x, -4 X - 3y, -4 X y^2

= -20x + 12y + -4xy^2

now we bring back the 3x

3x - -20x + 12y + -4xy^2

so now we simplify, by finding like terms

= 23x + 12y + -4xy^2

Answer: x = 25 mi

Step-by-step explanation:

Sides QO and TR are corresponding.

Sides QP and TS are corresponding.

Sides OP and RS are corresponding.

Create the proportion to solve for x:

5/x = 6/30

Cross multiply:

6x = 150

Divide both sides by 6:

x = 25 mi

Hope this helps!