Find the slope of the line. Write your answer in simplest form.​

Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

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Answer:

The area of the shaded region is 195.84sqft.

Step-by-step explanation:

Area of shaded region= 1/2(sum of parallel side)*height - π\((radius)^{2}\)

Area of shaded region=1/2(20+34)*24 - π\((12)^{2}\)

Area of shaded region=648-452.16

Area of shaded region=195.84 sqft.

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Answer:

greatest because 15.01>15

Answer:

15.01 is greater.

Step-by-step explanation:

Sqare root of 225 is 15.

The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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Answer:

The greatest height the bird reached was 26 feet

At 5 seconds the bird was going down.

Step-by-step explanation:

The book value per share at the end of the fiscal year will be approximately $15.35.

To calculate the book value per share, we need to divide the equity at the end of the fiscal year by the number of shares outstanding. Let's break down the calculation:

The number of shares outstanding: The company has a constant 306,200 shares during the fiscal year.

Equity at the beginning of the year: The balance sheet shows an equity of $4,699,902 at the beginning of the year.

Net income: The income statement indicates a net income of $399,786.

Dividends paid: The company pays out $297,789 in dividends.

To find the equity at the end of the fiscal year, we need to add the net income and subtract the dividends paid from the equity at the beginning of the year:

Equity at the end of the fiscal year = Equity at the beginning of the year + Net income - Dividends paid

= $4,699,902 + $399,786 - $297,789

= $4,801,899

Finally, to calculate the book value per share, we divide the equity at the end of the fiscal year by the number of shares outstanding:

Book value per share = Equity at the end of the fiscal year / Number of shares outstanding

= $4,801,899 / 306,200

≈ $15.65 (rounded to two decimal places)

Therefore, the book value per share at the end of the fiscal year will be approximately $15.35.

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From the chi-square test, the p-value is greater than significance level so, we can't reject the null hypothesis. The distribution of patients in this data set of wards in community hospital has not changed.

We have a community hospital is studying its distribution of patients. Random sample with

number of patients = 317

There is a table present in above figure contains the type of patients, old rate and present rate of occurrence of type of patients.

Level of significance = 0.05

We have to test the claim that the distribution of patients in these ward is same or not.

Now, For testing the claim we will use the chi-square test, null and alternative hypothesis are defined as \(H_0\): the distribution of patients has not Changed

\(H_a\): the distribution of patients has Changed

Patients observed Expected

Maternity ward 65 20% of 317 = 63.4

Cardiac ward 100 32% of 317 = 101.44

burn ward 29 10% of 317 = 31.7

children ward 48 15% of 317 = 47.55

All wards 75 23% of 317 = 72.91

Now, calculate the χ² statistic : \(χ² = \frac{ \sum( O_i - E_i)²} {E_i}\)

where, Oᵢ --> observed value for iᵗʰ

Eᵢ --> excepted value for iᵗʰ

\(χ² = \frac{ \sum( 65 - 63.4)²} {63.4} + \frac{ \sum( 100 - 101.44)²} {101.4} + \frac{ \sum( 29 - 31.7)²} {31.7} + \frac{ \sum( 48 - 47.55)²} {47.55} + \frac{ \sum( 75 - 72.91)²} {72.91} \\ \)

= 0.355

Now, we calculate p-value for χ² > 0.355, from the calculater the critical value for

\(χ² = 0.355\) and degree of freedom = n - 1 = 5 - 1 = 4 , where 5 is number of categorical variables. So, \( P( χ² > 0.355)\) = 0.99

Since, the p-value = 0.99 > 0.05, so we fail to reject the null hypothesis. Hence, from the above test we can accept the claim that the distribution of patients has not changed.

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Complete question:

the community hospital is studying its distribution of patients. a random sample of 317 patients presently in the hospital gave the following information: type of patient, old rate of occurrences of these types of patients and present number of occurrence of type of patients. Using a 5% level of significance, test the claim that the distribution of patients in these wards has not changed.

Answer:

Here is your 2 answers.

Step-by-step explanation:

First question: -2+3y=9

step 1 simplify first so now it's 3y-2

step 2 add both sides by 2 now its 3y=11

step 3 divide both sides by 3 so on the left both sides should cross out leaving only y=11/3 so this is your first answer

Second question:

I attach the link this question acquires a graph to plot I believe so here is the answer for the second one hope I help please mark brainliest if I did! <3

Answer:

Step-by-step explanation:

So first combine like terms so x squared and 6x in the first one. Then subtract or add the term that has a like term on the opposing side I think so in #1 it would be 3 so then you would have 7x squared = -3 then solve from there I think. I'm not sure if I'm right but hopefully this helps you :)

If a red ball is drawn at random from one of the urns, there is a higher probability (2/3) or 0.667 that it came from Urn A rather than Urn B. This suggests that Urn A is more likely to be the source of the red ball.

To calculate the probability that Urn A was chosen given that a red ball was drawn, we can use Bayes' theorem.

Let's denote the events:

A = Urn A was chosen

B = Urn B was chosen

R = A red ball was drawn

We want to find P(A|R), the probability that Urn A was chosen given that a red ball was drawn.

According to Bayes' theorem:

P(A|R) = (P(R|A) * P(A)) / P(R)

P(R|A) is the probability of drawing a red ball given that Urn A was chosen. Since Urn A has four red balls and four black balls, the probability of drawing a red ball from Urn A is 4/8 = 1/2.

P(A) is the prior probability of choosing Urn A, which is 0.5 since there is an equal chance of selecting either Urn A or B.

P(R) is the overall probability of drawing a red ball, which can be calculated by considering all possible scenarios:

P(R) = P(R|A) * P(A) + P(R|B) * P(B)

P(R|B) is the probability of drawing a red ball given that Urn B was chosen. Since Urn B has two red balls and six black balls, the probability of drawing a red ball from Urn B is 2/8 = 1/4.

P(B) is the prior probability of choosing Urn B, which is also 0.5.

Substituting the values into the equation:

P(R) = (1/2) * (1/2) + (1/4) * (1/2) = 3/8

Now we can calculate P(A|R) using Bayes' theorem:

P(A|R) = (P(R|A) * P(A)) / P(R) = (1/2 * 1/2) / (3/8) = 4/6 = 2/3

Therefore, the probability that Urn A was chosen given that a red ball was drawn is 2/3 or approximately 0.667.

In conclusion, if a red ball is drawn at random from one of the urns, there is a higher probability (2/3) that it came from Urn A rather than Urn B. This suggests that Urn A is more likely to be the source of the red ball.

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Answer:

4 units

Step-by-step explanation:

The length of the shorter side is equal to the difference in y-coordinates of two vertically opposite vertices. The y-coordinates of the vertices (-1, -5) and (3, -5) are both -5, so the vertical side between them is not the shorter side. The y-coordinates of the vertices (3, -7) and (-1, -7) are both -7, so the vertical side between them is the shorter side. The difference in the x-coordinates of these two vertices is 3 - (-1) = 4, so the length of the shorter side is 4 units.

Answer: Your answer is 2

Step-by-step explanation: I did the k12 quiz here's proof

Answer:

Step-by-step explanation:

(a) To find the probability that it is raining when you arrive in Oneirabad on a random day, we need to use the law of total probability.

Let A be the event that it is raining, and B be the event that it is the Wet season.

P(A) = P(A|B)P(B) + P(A|B')P(B')

Given that the Wet season lasts for 1/3 of the year, we have P(B) = 1/3. The probability that it is raining during the Wet season is 3/4, so P(A|B) = 3/4.

The Dry season lasts for 2/3 of the year, so P(B') = 2/3. The probability that it is raining during the Dry season is 1/6, so P(A|B') = 1/6.

Now we can calculate the probability that it is raining when you arrive:

P(A) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it is raining when you arrive in Oneirabad on a random day is 13/36.

(b) Given that it is raining when you arrive, we can use Bayes' theorem to calculate the probability that your visit is during the Wet season.

Let C be the event that your visit is during the Wet season.

P(C|A) = (P(A|C)P(C)) / P(A)

We already know that P(A) = 13/36. The probability that it is raining during the Wet season is 3/4, so P(A|C) = 3/4. The Wet season lasts for 1/3 of the year, so P(C) = 1/3.

Now we can calculate the probability that your visit is during the Wet season:

P(C|A) = (3/4)(1/3) / (13/36)

= 1/4 / (13/36)

= 9/52

Therefore, given that it is raining when you arrive, the probability that your visit is during the Wet season is 9/52.

(c) Given that it is raining when you arrive, the probability that it will be raining when you return to Oneirabad in a year's time depends on the season. If you arrived during the Wet season, the probability of rain will be different from if you arrived during the Dry season.

Let D be the event that it is raining when you return.

If you arrived during the Wet season, the probability of rain when you return is the same as the probability of rain during the Wet season, which is 3/4.

If you arrived during the Dry season, the probability of rain when you return is the same as the probability of rain during the Dry season, which is 1/6.

Since the season you arrived in is independent of the weather when you return, we need to consider the probabilities based on the season you arrived.

Let C' be the event that your visit is during the Dry season.

P(D) = P(D|C)P(C) + P(D|C')P(C')

Since P(C) = 1/3 and P(C') = 2/3, we can calculate:

P(D) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it will be raining when you return to Oneirabad in a year's time, given that it is raining when you arrive, is 13/36.

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Answer:(3,2)

Step-by-step explanation:

A: 3,2

y = 2

y = 4x - 10

2 = 4x - 10

2 + 10 = 4x

12 = 4x

12/4 = x

3 = x

solution is : (3,2)

The empirical rule, also known as the 68-95-99.7 rule, is a statistical guideline that applies to data with a normal distribution. It states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

In this case, we are given that the average age of retirement for the entire population in a country is 64 years, with a standard deviation of 3.5 years.

To find the approximate age range in which 95% of people retire, we can use the empirical rule. Since 95% falls within two standard deviations, we need to find the range that is two standard deviations away from the mean.

Step-by-step:

1. Find the range for two standard deviations:
  - Multiply the standard deviation (3.5 years) by 2.
  - 2 * 3.5 = 7 years

2. Determine the lower and upper limits:
  - Subtract the range (7 years) from the mean (64 years) to find the lower limit:
    - 64 - 7 = 57 years
  - Add the range (7 years) to the mean (64 years) to find the upper limit:
    - 64 + 7 = 71 years

Therefore, on the basis of the empirical rule, approximately 95% of people retire between the ages of 57 and 71 years, based on the given average age of retirement (64 years) and standard deviation (3.5 years).

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Answer:

A. Checks and Balances.

Step-by-step explanation:

Checks and balances is a system of government that keeps branches from becoming too powerful. An example of this would be a president or governor vetoing a bill.

I hope this was helpful. If so, please give me 5 stars, send thanks and brainliest. Thank you

Answer:

4/ 3 = 7

Step-by-step explanation:

Answer: x=3

Step-by-step explanation:

first add two to each side

Simplify  7+2 to 9

3x=9

divide both sides by 3.

x=9/3

simplify 9/3 to 3

​

The type of influence on wellness that this represents is given as follows:

A. Social.

An influence on wellness is an activity that improves the morale of certain aspect of our lives.

The aspect improved in this problem is the social aspect, along with the physical aspect, as follows:

Since this is an example of social bonding, option A gives the correct option regarding which type of influence on wellness this is an example of.

For example, reading a book would be intellectual influence, while recycling would be environmental influence.

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The expected value of the sample mean of the values obtained in these 300 tosses is 3.5

Given :

A fair six sided die is tossed 300 times

We have to find the expected value of the sample mean of the values obtained in these 300 tosses.

A dice have six sides:

In a fair dice every side has equal chance of occurrence,

Now the probability of presence of each side = 1/6

Now the expected value of the sample mean of the values obtained in these 300 tosses is given by:

E(x) = Σx P(x =x)

= 1*1/6 + 2*1/6 + 3*1/6 + 4*1/6 + 5*1/6 + 6*1/6

= 1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6

= 1/6 (1+2+3+4+5+6)

= 1/6 (21)

= 21/6

E(x) = 3.5

Hence, the expected value of the sample mean of the values obtained in these 300 tosses is 3.5

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Answer:

48 cups

Step-by-step explanation:

‐-------------------

Answer:

i think it is B

Step-by-step explanation:

because the height and length are going to be that same

Answer:

6.25 lb and 100 oz

Step-by-step explanation:

One lb (Pound) is equal to 16 oz (Ounce). Therefore, 100 oz equals...

100 oz / 16 = 6.25 lb

and

100 oz = 100 oz

Answer:

lol

Step-by-step explanation:

do you go to meridian

Answer:

i gotchuuu

Step-by-step explanation:

the answer is 118w of just 118

if u got What sApp I can explain it more on there if u want but that's the only thing I have so u might wanna get it if u want me to help u

Answer:

√4 and √9

Step-by-step explanation:

√4 and √9 are the two square roots are used to estimate √8.

The overlapping area between the line y = x - 6 and the curve y = 6/x and evaluating the integer coordinates within this region, we find that there are 13 lattice points contained in R.

The region defined by the simultaneous conditions x - y < 6, xy < 6, and x > 0 can be determined by graphing the inequalities.

However, since the question asks for the number of lattice points in the region, we can solve it algebraically.

First, let's consider the condition x - y < 6. If we rearrange this inequality, we get y > x - 6. This represents a region above the line y = x - 6 on the coordinate plane.

Next, let's analyze the condition xy < 6. We can rewrite this inequality as y < 6/x.

This represents a region below the curve y = 6/x.

To find the region that satisfies both conditions, we need to identify the overlapping area between the line y = x - 6 and the curve y = 6/x. This overlapping area is our region of interest, denoted as R.

To determine the lattice points within R, we need to find the integer coordinates (x, y) that satisfy both inequalities.

Since x > 0, we can start by evaluating the integer values of x from 1 to 5. For each x-value, we can calculate the corresponding y-value using the equation y = x - 6. If this y-value is less than 6/x, it satisfies both conditions and is considered a lattice point within R.

For example, when x = 1, y = 1 - 6 = -5, which is less than 6/1. So the lattice point (1, -5) is within R.

By repeating this process for x = 2, 3, 4, and 5, we can determine the other lattice points within R.

After evaluating all possible integer values of x, we find that R contains a total of 13 lattice points.

Therefore, the answer to the question is that the region R contains 13 lattice points.

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Answer:

No

Step-by-step explanation:

4 5/8 = 4.625 because 458=4+(5÷8)=4+0.625=4.625

4.65>4.625 so she has less

The equations obtained from evaluation of the data in the table and the predicted cost of hiring the DJs are as follows;

Part B

The equation representing the cost of hiring Celinda is; c = 36·h + 16

The equation representing the cost of hiring Brian is; c = 38·h + 4

Part C

The cost of hiring Celinda for 5 hours is $196

Cost of hiring Brian for 5 hours is $194

A linear equation is an equation that has an highest index of 1.

Part B

The first difference in the cost of hiring each DJ is presented as follows;

Celinda; 160 - 124 = 124 - 88 = 88 - 52 = 36

Brian; 156 - 118 = 118 - 80 = 80 - 42 = 38

The first difference are constant, therefore, the relationship are linear, which can be represented by linear equations.

The difference between the subsequent values in the number of hours of 1 indicates that we get;

Slope of the equation for Celinda = 36

The equation representing the total cost for Celinda is therefore;

Where c represents the cost and h represents the number of hours, we get;

c - 52 = 36·(h - 1)

c = 36·h - 36 + 52

The equation for Brian, with a slope of 38, is therefore;

c - 42 = 38·(h - 1)

c = 38·h - 38 + 42 = 38·h + 4

Part C

The cost of hiring each DJ for 5 hours is therefore;

h = 5

The cost of hiring Celinda for 5 hours is; c = 36 × 5 + 16 = 196

The cost of hiring Celinda for 5 hours is $196

The cost of hiring Brian for 5 hours can be obtained by plugging in h = 5 in the equation; c = 38·h + 4

Therefore; c = 38 × 5 + 4 = 194

The cost of hiring Brian for 5 hours is $194

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The standard form of a linear equation is expressed as

Ax + By = C

The given points that the line passed through are (6, 4) and (- 4, 9)

The first step is to find the slope of the equation. The formula for finding slope is expressed as

slope, m = (y2 - y1)/(x2 - x1)

From the points given,

x1 = 6, y1 = 4

x2 = - 4, y2 = 9

m = (9 - 4)/(- 4 - 6) = 5/- 10

m = - 1/2

The eqyation of a line in the slope intercept form is expressed as

y = mx + c

m = slope

c = y intercept

To find c, we would substitute m = - 1/2, x = 1 and y = 4 into the slope intercept equation. It becomes

4 = - 1/2 * 1 + c

4 = - 1/2 + c

c = 4 + 1/2 = 9/2

Thus, we have

y = - x/2 + 9/2

Converting it to standard form, the standard form is

x/2 + y = 9/2

- x + 2y = 9

where

A = - 1, B = 2 and C = 9