Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.

A 5:1 mixture of Vaseline and 1 mg of hydrocortisone ung contains 833.33 mg of Vaseline. This can be found by dividing the weight of the mixture by the sum of the ratio parts.

A 5:1 mixture of Vaseline and 1 mg of hydrocortisone ung (ointment) means that there are 5 parts of Vaseline for every 1 part of hydrocortisone.

To find how many mg of Vaseline is in the mixture, we need to know the total weight of the mixture. Let's assume that the weight of the mixture is 1 gram (1000 mg) for simplicity.

Since the mixture is 5:1 Vaseline to hydrocortisone, we can divide the total weight of the mixture by the sum of the ratio parts (5+1=6) to get the weight of 1 part of the mixture:

Weight of 1 part of the mixture = 1000mg / 6 = 166.67 mg

Therefore, the weight of 5 parts of the mixture (which is the amount of Vaseline in the mixture) is:

5 x 166.67 mg = 833.33 mg

So, a 5:1 mixture of Vaseline and 1 mg of hydrocortisone ung contains 833.33 mg of Vaseline.

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Given the expression:

At y = 3, it means that we substitute all the y variables in the expression into 3.

We get,

Therefore, the answer is -4.

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The nutritionist should perform hypothesis testing followed by Independent T-test to see if coffee and tea differ in mean caffeine content .

We need to Know about Hypothesis testing and independent t test to answer this-

Hypothesis testing is a type of statistical test that is used to comapare data and drawing conclusion from them.

An independent t-test is a statistical test that determines whether the means of two unrelated groups are significantly different from each other.

We can find the difference caffeine content following these steps -

1)H0=Null hypothesis=tea and coffee has same caffeine level

HA=tea and coffee has different caffeine level

2)The independent samples t-test is utilized to determine whether two different sample means come from the same population or whether they come from two distinct populations with different mean values. Two populations can be considered independent when the data in one group is not connected to the data in the other group.

The t value obtained should be then performed under hypothesis testing.

3)And the calculated T value should be comaperd with the desired significance level (generally =0.05) and if the t value comes in between the critical values the nutritionist can assume that both tea and coffee has same caffeine level in this null hypothesis will be accepted.

Whereas if the calculated t value doesn't falls in between the critical value then the nutritionist can assume that tea and coffee has different caffeine level.

Hence null hypothesis will be rejected.

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If the staysail is 10.5 feet and height is 30 feet then the area of the staysail is 157.5 feet²

To find the area of the staysail, we can use the formula for the area of a triangle:

Area of triangle = 1/2 x base x height

In this case, the base of the staysail is given as 10.5 feet and the height is given as 30 feet.

Substituting these values into the formula, we get:

Area of staysail = 1/2 x 10.5 feet x 30 feet

Simplifying the expression, we get:

Area of staysail = 0.5 x 10.5 feet x 30 feet

Area of staysail = 157.5 square feet

Therefore, the area of the staysail is 157.5 square feet. This means that if the staysail were to be laid flat, it would cover an area of 157.5 square feet.

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Answer:

1,687.5 square millimeters

Step-by-step explanation:

There are six faces of a cuboid:

1. Top and bottom face: length x width

- Top face area = Length x Width = 15mm x 7.5mm = 112.5 square mm

- Bottom face area = Top face area = 112.5 square mm

2. Front and back face: height x width

- Front face area = Height x Width = 45mm x 7.5mm = 337.5 square mm

- Back face area = Front face area = 337.5 square mm

3. Left and right face: height x length

- Left face area = Height x Length = 45mm x 15mm = 675 square mm

- Right face area = Left face area = 675 square mm

Therefore, the total surface area of the cuboid is the sum of all six faces:

Total Surface Area = 2(Top face area + Front face area + Left face area)

= 2(112.5 square mm + 337.5 square mm + 675 square mm)

= 2(1125 square mm)

= 2250 square mm

Therefore, the surface area of the given cuboid is 2250 square mm.

Answer:

4w-8

Step-by-step explanation:

4(w-2)

(4*w)-(4*2)

4w-8

Answer:

4w-8

Step-by-step explanation:

4(w - 2)

Distribute

4*w - 4*2

4w-8

Answer: 61 degrees

Step-by-step explanation:

Therefore, option A is the correct: the probability cannot be determined since the standard deviation has not been determined specifically as left or right skewed.

The probability that the next Sunday customer will spend at least $40 cannot be determined without additional information about the distribution of customer purchases.

The given information indicates that the distribution is skewed, but does not specify the direction of the skewness. Additionally, the distribution may not necessarily follow a Normal model, which means that we cannot rely on the empirical rule to estimate probabilities based on standard deviations away from the mean.

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1. x + 4 = 0 or x + 7 = 0

x = -4 or x = -7

2. 3x - 7 = 0 or 2x + 5 = 0

x = 7/ 3 or x = -5/ 2

3. x + 5 = 0 or x -8 = 0

x = -5 or x = 8

4. (x - 6) = 0 or (3x + 7) = 0

x = 6 or x = -7/ 3

5. 5x + 2 = 0 or 2x + 1 = 0

x = -2/ 5 or x = -1/ 2

1. (x+4)(x+7)=0

We have that;

Zero product property;

x + 4 = 0 or x + 7 = 0

x = -4 or x = -7

2.  (3x-7)(2x+5)=0

We have that;

Zero product property ;

3x - 7 = 0 or 2x + 5 = 0

x = 7/ 3 or x = -5/ 2

3. x² -3x - 40=0

x² -8x + 5x - 40 = 0

factorize the common multipliers

x(x - 8) + 5(x - 8) = 0

Zero product property;

x + 5 = 0 or x -8 = 0

x = -5 or x = 8

4. 3x² - 11x - 42=0

3x² +7x - 18x - 42 = 0

Factorize further

x(3x + 7) - 6(3x + 7) = 0

Zero product property;

(x - 6) = 0 or (3x + 7) = 0

x = 6 or x = -7/ 3

5. 10x² + 9x + 2 = 0

10x² + 5x + 4x + 2 = 0

Factorize

5x( 2x + 1) + 2 (2x + 1) = 0

Zero product property;

5x + 2 = 0 or 2x + 1 = 0

x = -2/ 5 or x = -1/ 2

Thus, the zero product property states that the product of two non-zero elements is not zero

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Answer:

ad bc

Step-by-step explanation:

Answer: for part a the answer is aed and bec.

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

We have the algebraic expression 3x + 16 = 7x and are asked to solve.

When we need to solve for x, we need to get x alone always.

So 3x + 16 = 7x.

Subtract 3x from both sides :

16 = 4x

Divide 4 from both sides :

x = 4

Answer:

\( \large \boxed{x = 4}\)

Step-by-step explanation:

Goal

Given

\(3x + 16 = 7x\)

Step 1

\(16 = 7x - 3x \\ 16 = 4x\)

Step 2

\( \frac{16}{4} = x \\ 4 = x\)

Step 3

\(3x + 16 = 7x \longrightarrow 3(4) + 16 = 7(4) \\ 12 + 16 = 28 \\ 28 = 28\)

The equation is true for x = 4. Hence, the solution is x = 4

Answer:

negative. the slope is proceeding down

Answer: x=8

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

4(2x + 1) + 2 = 5(x + 6)

8x + 4 +2 = 5x + 30

Collect like terms

8x - 5x = 30 - 4 - 2

3x = 24

Divide both side by 3

x = 8

There are 2,520 ways to arrange the word "PARVAMONSTRA" such that it begins and ends with consonants.

To arrive at this number, we need to consider the arrangement of the consonants at the beginning and end, as well as the arrangement of the remaining letters in the middle.

To determine the arrangement of the consonants at the beginning and end, we have 7 consonants to choose from.

Since the first and last letters must be consonants, we have 7 choices for the first letter and 6 choices for the last letter.

For the middle letters, we have 10 letters in total (including the remaining consonants and vowels). However, since some of these letters are repeated, we need to account for the repeated letters.

In "PARVAMONSTRA," the letters A and R are repeated twice. Therefore, we have 10!/(2!2!) ways to arrange the middle letters.

Multiplying the choices for the first and last letters (7 * 6) and the number of ways to arrange the middle letters (10!/(2!2!)), we get a total of 2,520 ways to arrange the word "PARVAMONSTRA" with consonants at both the beginning and end.

Therefore, there are 2,520 different ways to arrange the word "PARVAMONSTRA" such that it starts and ends with consonants, taking into account the repetition of the letters A and R.

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Answer:

24 (whatever units you're using)

Step-by-step explanation:

distance can never be negative so from 16 to 0 is 16. it then goes down 8 which is another 8 units

Therefore, the probability that exactly 4 out of 20 randomly chosen college students are near-sighted is closest to 0.7988 or approximately 0.80.

To find the probability that exactly 4 out of 20 randomly chosen college students are near-sighted, we can use the binomial probability formula.

The formula for the probability of k successes in n trials, with a probability of success p in each trial, is given by:

\(P(X = k) = (n choose k) * p^k * (1 - p)^{(n - k)\)

In this case, n = 20, k = 4, and p = 0.28 (probability of a student being near-sighted).

Plugging in these values into the formula, we get:

\(P(X = 4) = (20 choose 4) * (0.28)^4 * (1 - 0.28)^{(20 - 4)\)

Calculating the values:

(20 choose 4) = 4845

\((0.28)^4\) ≈ 0.006859

\((1 - 0.28)^{(20 - 4)\) ≈ 0.19224

P(X = 4) ≈ 4845 * 0.006859 * 0.19224

≈ 0.7988

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Answer:

65 cm squared

Step-by-step explanation:

\(\it tan60^o=\dfrac{AB}{BC} \Rightarrow \sqrt3=\dfrac{AB}{50} \Rightarrow AB=50\sqrt3\approx50\cdot1,732\approx87\ m\)

The difference between the depths in February and July is 19 feet.

To find the difference between the depths in February and July, we need to subtract the depth in February from the depth in July.

The depth in February is given as |−6|, which is 6 feet, and the depth in July is given as |−25|, which is 25 feet.

Difference = Depth in July - Depth in February

Difference = 25 feet - 6 feet

Difference = 19 feet

Therefore, the difference between the depths in February and July is 19 feet.In February, the depth of the lake is given as |−6|, which represents the absolute value of -6. The absolute value of a number disregards its sign, so |−6| is equal to 6 feet.

In July, the depth of the lake is given as |−25|, which represents the absolute value of -25. Again, disregarding the sign, |−25| is equal to 25 feet.

To find the difference between the depths in February and July, we subtract the depth in February from the depth in July:

Difference = Depth in July - Depth in February

Difference = 25 feet - 6 feet

Difference = 19 feet

Therefore, the difference between the depths in February and July is 19 feet. This means that the lake experienced a change of 19 feet in depth between those two time points.

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Answer:

if i have 19

Step-by-step explanation:

Correct question :

There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 7 9 . There are 28 red marbles in the bag and each is equally likely to be chosen. Work out how many marbles in total there must be.

Answer:

Total number of marbles = 36

Step-by-step explanation:

Marbles in bag: Red and Blue only

Probability of randomly choosing a red marble = 7/9

Number of red marbles = 28

Total number of marbles in the bag =?

Probability = required outcome / Total possible outcomes

P(red marble) = required outcome (number of red marbles) / Total possible outcomes(total number of marbles

7/9 = 28 / total number of marbles

Total number of marbles * 7/9 = 28

Total number of marbles = 28 ÷ 7/9

Total number of marbles = 28 * (9/7)

= 252 / 7

Total number of marbles = 36

The RACI matrix is the Responsible, Accountable, Consult & Inform matrix. It is a tool used in project management to clearly define the roles and responsibilities of team members in relation to a project.

c. Responsible, Accountable, Consult & Inform matrix

The RACI matrix is a tool used in project management to clearly define roles and responsibilities. It stands for Responsible, Accountable, Consulted, and Informed. Assigning these roles to individuals or teams, it ensures efficient allocation of resources and effective communication throughout the project.

The matrix identifies who is Responsible for a task, who is Accountable for its completion, who needs to be Consulted before decisions are made, and who needs to be Informed about progress. This helps to avoid confusion and ensure that resources are allocated appropriately, which can ultimately impact the cost of the project.

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The mulch will cost the homeowner $49.

To find the cost of the mulch, we need to first find the volume of mulch required to cover the garden.

Using the formula for a circle:

Area of a half circle = (1/2) * π * r^2

Plugging in the values, we get:

Area of half circle = (1/2) * π * 6^2 = 56.55 square feet

We need to find the volume of mulch required to cover the garden with a 3 inch layer.

Volume of mulch = Area of half circle * Height of mulch

Volume of mulch = 56.55 * 0.25 = 14.14 cubic feet (rounded to two decimal places)

Finally, we can find the cost of the mulch by multiplying the volume by the cost per cubic foot:

Cost of mulch = Volume of mulch * Cost per cubic foot

Cost of mulch = 14.14 * 3.50 = $49 (rounded to the nearest dollar)

Therefore, the mulch will cost the homeowner $49.

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Answer:

The answer would have to be B

Step-by-step explanation:

explains itself

Answer:it’s B

Step-by-step explanation:

A) Approx. 1067 is the required sample size to ensure 95% confidence that the sample proportion will not differ from the true proportion by more than 3%.

B) When the previous estimate is 65%, approx. 971 is the sample size needed to achieve 95% confidence that the sample proportion will not differ by more than 3% from the true proportion.

To determine the sample size needed for estimating the proportion of drivers exceeding the speed limit, we can use the formula for sample size calculation for proportions:

n = (Z² * p * (1 - p)) / E²

where:

n = the sample size.

Z = the Z-value associated with the confidence level of 95%.

p = the estimated proportion or previous estimate.

E = the maximum allowable error, which is 3% or 0.03.

We calculate as follows:

A. No previous estimate for p is available:

Here, we will assume p = 0.5 (maximum variance) since we don't have any prior information about the proportion. So, adding the values into the formula:

n = (Z² * p * (1 - p)) / E²

n = ((1.96)² * 0.5 * (1 - 0.5)) / 0.03²

n= (3.842 * 0.5 * (0.5))/0.03²

n = (1.9208*0.5)/0.0009

n ≈ 1067.11

Thus, to be 95% confident that the sample proportion will not differ from the true proportion by more than 3%, a sample size of approximately 1067 is required.

B. Supposing previous studies found that the sample percentage of drivers who exceeded the speed limit is 65%:

Here, we have a previous estimate of p = 0.65:

Putting the values into the formula:

n = (Z²* p * (1 - p)) / E²

n = ((1.96)² * 0.65 * (1 - 0.65)) / 0.03²

n= (3.842 * 0.65 *(0.35))/0.0009

n ≈ 971

Hence, with the previous estimate of 65%, a sample size of approximately 971 is necessary to be 95% confident that the sample proportion will not differ from the true proportion by more than 3%.

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