**Answer:2.78**

**Step-by-step explanation:**

the probability of rolling a 5 on a six-sided die and then rolling a 2? The chances of rolling a 5 on the first die is 1 in 6. The chances of rolling a 2 on the second roll in 1 in 6. So the probability of a 5, then a 2, is 1 in 36.

We can see that this gives us the exact same answer as the first method: 1/36 as a percentage is 2.78%.

**Answer:**

**A) **[tex]2.78\%[/tex]

**Step-by-step explanation:**

Assuming that Chris throws two standard dices (meaning 6 sides, with the sides numbered as 1, 2, 3, 4, 5, 6, respectively). There is one chance of the dice landing on a 5 for both dices, and presuming that the dices do not hit each other, would be independent variables. This means that there is a 1/6 chance for both:

[tex]\frac{1}{6} * \frac{1}{6} = \frac{1}{36}[/tex]

Change the fraction to a percentage. Divide and solve for a decimal. Then, move the decimal point to the left two place values, and you will obtain your percentage:

[tex]\frac{1}{3} = 0.02777 = 2.777\%[/tex]

You are rounding to the nearest tenth place value (2nd place value right of the decimal point):

[tex]2.777\% = 2.78\%[/tex]

[tex]2.78\%[/tex] is your answer, or **A)**.

~

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Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 5. 7 parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of 10 samples is 6. 1 ppm with a variance of 0. 25. Does the data support the claim at the 0. 01 level? Assume the population distribution is approximately normal. Step 4 of 5: Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places

If the absolute value of the calculated t-value is greater than or equal to 3.250, reject the **null hypothesis. **

To determine the decision rule for rejecting the null hypothesis, we need to calculate the test statistic.

First, we need to calculate the **standard error** of the mean:

standard error = square root of (variance/sample size)

standard error = square root of (0.25/10)

standard error = 0.158

Next, we can calculate the** t-statistic**:

t = (sample mean - hypothesized mean) / standard error

t = (6.1 - 5.7) / 0.158

t = 2.532

Using a two-tailed test at the 0.01 level of significance and 9 degrees of freedom (10 samples - 1), the critical t-value is ±3.250.

Since our calculated t-value of 2.532 is less than the critical t-value of ±3.250, we fail to **reject **the null hypothesis.

Therefore, the data does not support the claim that the current ozone level is at an excess level at the 0.01 level of significance.

Decision rule for rejecting the null hypothesis:

If the absolute value of the calculated t-value is greater than or equal to 3.250, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

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Find the volume of a hexagonal prism whose base

has area 30. 5 square centimeters and whose height is 6. 5 centimeters

The **volume** of the hexagonal prism is approximately 198.25 cubic centimeters.

To find the **volume** of a hexagonal prism, we need to know the area of the base and the height of the prism. In this case, we are given that the base has an area of 30.5 square centimeters and the height is 6.5 centimeters.

First, let's find the **perimeter **of the base. Since a hexagon has six sides, the perimeter will be six times the length of one side. To find the length of one side, we can use the formula for the area of a regular hexagon, which is:

Area = (3√3 / 2) × s²

where s is the length of one side.

30.5 = (3√3 / 2) × s²

s² = 30.5 × 2 / (3√3)

s² ≈ 11.13

s ≈ 3.34

So the perimeter of the** base** is 6 × 3.34 ≈ 20.04 centimeters.

Now we can use the formula for the volume of a prism, which is:

Volume = Base area × Height

Volume = 30.5 × 6.5 ≈ 198.25 cubic centimeters

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Question is attached.

Please show workings

When **solved**, the **value** of either a or b would be 0 such that we have a = 0 or b = 0. They could also both be zero.

If the **product** of two numbers is **zero**, it necessitates that one or both of the values in question contain a value of zero. Similarly, when calculating the cross product of two given vectors and its resulting answer is equivalent to zero, then such vectors exist parallel with one another.

Alternatively, there is the possibility that only **one vector **holds a value of zero themselves:

( a × b ) = 0

This equation is true if either a = 0 or b = 0, or both a and b are zero.

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The table below shows the number of gold, silver and bronze medals won by some

countries in the 1988 Winter Olympic Games.

Work out the ratio of gold to silver to bronze medals won by Sweden.

Give your answer in its simplest form.

Country

Canada

Finland

Soviet Union

Sweden

Gold

0

4

11

4

Silver

2

1

9

0

Bronze

3

2

9

2

**Step-by-step explanation:**

It looks as though ( from your post) Sweden won 4 golds and 0 silver and 2 bronze medals

4:0:2 simplifies to 2 :0 : 1

its due in a few minuets

**Answer:**

**Step-by-step explanation:**

If I'm wrong, write and I'll correct it. Because I don't know how to proceed

Ella makes a model of a log cabin that is 8 inches long at a scale of 1/2.5 feet. She makes a second model of the same building at a scale of 1/2.5 feet. How much longer is the second model than the first?

**Answer: So the second model is 0.2667 feet longer than the first.**

**Step-by-step explanation: 8 inches * (1/12 feet per inch) * (1/2.5) = 0.1333 feet**

**So the length of the first model is 0.1333 feet. **

**The length of the second model is also at a scale of 1/2.5 feet, so its length can be found directly by multiplying the length of the actual building by the scale factor:**

**Length of second model = 1/2.5 * 1 foot = 0.4 feet **

**to make next step we can use difference between these numbers by their lengths: Length of second model - Length of first model = 0.4 feet - 0.1333 feet = 0.2667 feet**

What is the equation of a circle whose center is at the origin and whose radius is 16?x 2 + y 2 = 256x 2 + y 2 = 4x 2 + y 2 = 16

The equation of the circle with center at the origin and **radius **16 is x^2 + y^2 = 256.

To find the equation of a circle with center at the **origin **and radius 16, we can use the general equation of a circle:

x^2 + y^2 = r^2

where (x, y) are the **coordinates **of any point on the circle, and r is the radius.

In this case, the center is at the origin, so the coordinates (x, y) are both 0. The radius is given as 16. Plugging these values into the **equation**, we have:

0^2 + 0^2 = 16^2

0 + 0 = 256

Thus, the equation of the circle is:

x^2 + y^2 = 256

So, the equation of the circle with **center **at the origin and radius 16 is x^2 + y^2 = 256.

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The radius of a bade if a cone is 8 cm. The height is 15 cm. What is the volume of the cone?

**Answer: 1,004.8 or 320**[tex]\pi[/tex]

**Step-by-step explanation:**

[tex]\frac{1}{3} \pi 8^{2} 15=1,004.8[/tex]

A homeowner borrows $65,000 to remodel their home. The loan is financed at a 2.3% interest rate, compounded quarterly. How much will the homeowner owe after 8 years? Group of answer choices $78,090 $65,023 $78,117 $67,300

A homeowner borrows $65,000 to remodel their home. The loan is financed at a 2.3% interest rate, compounded quarterly.

So we have to find 2.3% of 65,000 which is 1495

Now we have to multiply 1,495 by 8 because it is 8 years which is 11960. Now we add 11,960 to 65,000 and our answer is **Answer : 76960**

**(Choice 1)**

In triangle JK L, cos(K) = 21 and angle J is a right angle. What is the value of cos (L)?

solve in the simplest way possible

21+90-180= 69 because it’s gives you the 2 angles already so u just add them and subtract by 180 cause that’s the whole triangle

Assume that a procedure yields a binomial distribution with n trials and a probability of success of p. use a binomial probability table to find the probability that the number of successes x is exactly .

To find the probability that the number of successes x is exactly a certain value in a binomial distribution with n trials and a probability of success of p, we can use a **binomial** **probability** table. The table will provide us with the probability of getting x successes out of n trials, given a specific value of p.

For example, let's say we want to find the probability of getting exactly 3 **successes** in a binomial distribution with 10 trials and a probability of success of 0.5. We can use a binomial probability table to find the probability of getting exactly 3 successes, which is 0.117.

It is important to note that the probability of getting a specific number of successes in a binomial distribution is **dependent** on both the number of trials and the probability of success. Therefore, if we change either of these values, the probability of getting a certain number of successes will also change.

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What is the measure of ∠ABC?

The measure of ABC is 55.

When Bernard was as old as Hector is now, Bernard's age was 4 times Hector's age then. When Hector will be as old as Bernard is now, the sum of their ages will be 51. How old will Bernard be when Hector turns 18 years old?

Base on the ** word problem**, Bernard is currently 21.25 years old. When Hector turns 18, he will be (18 - 17) = 1 year older than his current age. At that time, Bernard will be (21.25 + 1) = 22.25 years old.

Let's start by assigning variables to represent the current ages of Bernard and Hector. Let B be Bernard's current age and H be Hector's current age. Then we can write two equations based on the given information:

"When Bernard was as old as Hector is now, Bernard's age was 4 times Hector's age then." This means that Bernard is currently (B - H) years older than Hector, and that the age difference between them has remained constant over time. So, we can write: B - (B - H) = 4(H - (B - H)).

Simplifying this equation, we get: B - B + H = 4(2H - B)

Simplifying further, we get: 5H - 4B = 0, or B = (5/4)H.

"When Hector will be as old as Bernard is now, the sum of their ages will be 51." This means that when Hector is (B - H) years older than his current age, their sum of ages will be 51. So, we can write: B + (B - H + (B - H)) = 51.

Simplifying this equation, we get: 3B - 2H = 51.

Now we have two equations with two variables. We can substitute the expression for B from the first equation into the second equation, and solve for H:

3B - 2H = 51

3(5/4)H - 2H = 51

(15/4)H = 51

H = 17

So, Hector is currently 17 years old. To find out how old Bernard will be when Hector turns 18, we can use the expression we found earlier for B in terms of H:

B = (5/4)H

B = (5/4)(17)

B = 21.25

So, Bernard is currently 21.25 years old. When Hector turns 18, he will be (18 - 17) = 1 year older than his current age. At that time, Bernard will be (21.25 + 1) = 22.25 years old.

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Express the function graphed on the axes below as a piecewise function.

**Expressing** this function as a piecewise function, we get;

y = -x + 1 for x< -5

y = -1/2x + 4 for x> 4

According to the question, we can see that the **graph** is a line for x < -5. We will find two points on this line to find out the slope.

( - 5,6) and ( -8,9)

The **slope** is m= ( y2-y1)/(x2-x1)

m = ( 9-6)/(-8 - -5) = 3/ ( -8+5) = 3/-3

The slope is -1

Using point-slope form, we will find the **general equation** of this line

y-y1 = m(x-x1) and the point ( -8,9)

y -9 = -1(x - -8)

y -9 = -1(x +8)

y-9 = -x - 8

y = -x + 1 for x< -5

The graph is a line for x > 4

(4,2) and ( 6,1)

The slope is m= ( y2-y1)/(x2-x1)

m = ( 1 - 2)/(6 - 4) = -1/ (2) = -1/2

The slope is -1/2

Using point-slope form

y-y1 = m(x-x1) and the point (6,1)

y -1 = -1/2(x - 6)

y-1 = -1/2 x + 3

y = -1/2x + 4 for x> 4

Therefore,** expressing** this function as a **piecewise** function, we get;

y = -x + 1 for x< -5

y = -1/2x + 4 for x> 4

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Given the height of the cone is 12 m, find the slant height of the cone

a) 5m

b) 13 m

c) 17m

d) 11m

The slant height of the cone is approximately **5 meters**.

We can use the Pythagorean theorem to find the **slant height** of the cone.

The slant height, denoted by l, the height h and the **radius** r form a right triangle where l is the **hypotenuse**:

[tex]l^2 = h^2 + r^2[/tex]

In this case, we are given the height h as 12 m, but we are not given the radius r.

However, we know that the slant height is the distance from the apex of the cone to any point on its circular base.

So, we can draw a line from the apex of the cone to the center of its circular base, which will be perpendicular to the base, and we can use this line as the height of a right triangle that also includes the radius r of the circular base.

Then, we can use the Pythagorean theorem to find the slant height l.

The radius r is half the diameter of the circular base, so we need to find the diameter of the base.

Since we are not given the diameter directly, we need to find it using the height h and the slant height l.

To do this, we can draw a cross section of the cone that includes its circular base and its height, and then draw a line from the apex of the cone to a point on the base that is perpendicular to the diameter of the base.

This line will be the height of a right triangle that also includes the radius r of the base and half the diameter of the base.

Then, we can use the **Pythagorean theorem** to find the diameter of the base.We have:

[tex]l^2 = h^2 + r^2r = sqrt(l^2 - h^2)d/2 = sqrt(l^2 - r^2)d^2/4 = l^2 - r^2d^2 = 4(l^2 - r^2)[/tex]

Substituting the expression for r that we found above, we get:

[tex]d^2 = 4(l^2 - (l^2 - h^2))d^2 = 4h^2d = 2h[/tex]

Now we can substitute this expression for d into the formula for the volume of a cone:

[tex]V = (1/3) * pi * r^2 * hV = (1/3) * pi * ((2h)/2)^2 * hV = (1/3) * pi * h^2 * 4V = (4/3) * pi * h^3[/tex]

We can solve this formula for h:

[tex]h = (3V)/(4*pi)^(1/3)[/tex]

Substituting the given volume of the cone, which we will assume is in cubic meters:

[tex]V = (1/3) * pi * r^2 * h = (1/3) * pi * r^2 * 12V = 16pih = (3(16pi))/(4*pi)^(1/3)[/tex]

**h = 4.819 m**

Now we can find the slant height using the Pythagorean theorem:

[tex]l^2 = h^2 + r^2l^2 = (4.819)^2 + ((2(4.819))/2)^2l^2 = 23.187l = 4.815[/tex] [tex]m[/tex]

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The Bayview community pool has a snack stand where Juan works part time he tracks his total sales during each shift last month this box plot shows the results what fraction of Juan’s shifts had a total sales of $225 or more

The fraction of Juan's shifts with a** total sales** of $225 or more can be found by looking at the box plot.

We can see that the top line of the box represents the** third quartile** (Q3) which is the value where 75% of the data falls below.

In this case, Q3 is at approximately $250. This means that 75% of Juan's shifts had total sales less than $250. To find the fraction of shifts with sales of $225 or more, we need to determine how many shifts fall within the range of $225 to $250.

Looking at the box plot, we can see that the distance between Q1 and Q3 (the interquartile range) is approximately $100. Therefore, the distance between Q1 and $225 is approximately one-third of the** interquartile range **or $33.33. So, any shift with total sales of $225 or more would fall within one-third of the distance between Q1 and Q3.

Therefore, the fraction of Juan's shifts with total sales of $225 or more is approximately one-third of 75%, which is 25%.

In summary, approximately 25% of Juan's shifts at the** Bayview community** pool had total sales of $225 or more, based on the box plot.

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Ron is seeking a loan wi th a simple in teres t ra te o f 7 % per year . he wan ts to borrow $4,500.

If Ron were to borrow $4,500 at a simple interest rate of 7% per** year**, he would be charged $315 in interest each year.

Ron is seeking a loan with a simple** interest rate **of 7% per year, which means that he will be charged 7% of the loan amount as interest each year. Ron wants to borrow $4,500, so to calculate the amount of interest he will be charged each year, we can use the following formula:

Interest = Principal x Rate x Time

In this formula, "Principal" refers to the loan amount, "Rate" refers to the interest rate as a decimal (so 7% would be 0.07), and "Time" refers to the **length** of time the loan will be outstanding, typically measured in years.

Since Ron is seeking a loan with a simple interest rate, we can assume that the interest will be calculated on an annual basis. So if Ron wants to borrow $4,500 at a simple interest rate of 7% per year, the amount of interest he will be charged each year would be:

Interest = $4,500 x 0.07 x 1

Interest = $315

Therefore, if Ron were to borrow $4,500 at a simple interest rate of 7% per year, he would be charged $315 in interest each year. It's important to note that this calculation assumes that Ron will not be making any payments on the** loan **during the year, and that the interest will be added to the principal amount at the end of the year. In practice, many loans are structured differently and may involve monthly payments or other terms.

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Prove the following two properties of the Huffman encoding scheme. (a) If some character occurs with frequency more than 2=5, then there is guaranteed to be a codeword of length 1. (b) If all characters occur with frequency less than 1=3, then there is guaranteed to be no codeword of length 1

(a) Since the character occurs with a frequency higher than 2=5, it is guaranteed to be merged with another character with the same frequency or a lower **frequency**. Therefore, there is guaranteed to be a codeword of length 1 for this character. (b) Since all symbols occur with a frequency less than 1=3, the root of the tree will have a frequency less than 1=3. Therefore, there is guaranteed to be no codeword of length 1 for any symbol in this case.

(a) Let's assume that some character occurs with **frequency **more than 2=5.

The two **nodes **with the lowest frequency are merged into a single node, with the **sum **of their frequencies as the frequency of the new node.

This process is repeated until all the nodes are merged into a single node, which becomes the **root **of the tree.

Since the character occurs with a frequency higher than 2=5, it is guaranteed to be merged with another **character **with the same frequency or a lower frequency.

Therefore, there is guaranteed to be a **codeword **of length 1 for this character.

(b) Let's assume that all characters occur with frequency less than 1=3.

Consider the binary tree created by the **Huffman algorithm**. The root of the tree corresponds to the least frequent **symbol**, which will be assigned the longest codeword.

Since all symbols occur with a frequency less than 1=3, the root of the tree will have a frequency less than 1=3.

This means that the corresponding codeword for the root will be longer than 1 bit. Therefore, there is guaranteed to be no codeword of length 1 for any symbol in this case.

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Reina’s greenhouse is shaped like a square pyramid with four congruent equilateral triangles for its sides. All of the edges are 6 feet long. What is the total surface area of the greenhouse including the floor? Round your answer to the nearest hundredth.

____ft2

With all of the edges 6 feet long, the total surface **area** of the greenhouse including the floor is approximately 98.39 ft².

To find the total** surface** area of Reina's greenhouse, we'll need to calculate the area of the **equilateral** triangular sides and the square base.

1. Equilateral triangular sides:

There are four congruent equilateral triangles with edges of 6 feet each. To find the area of one triangle, we can use the formula A = (s² * √3) / 4, where A is the area and s is the side length.

A = (6² * √3) / 4 = (36 * √3) / 4 = 9√3 square feet

Since there are four triangles, the total area of the triangular sides is 4 * 9√3 = 36√3 square feet.

2. Square base:

The base is a square with side lengths of 6 feet. To find the area, we can use the formula A = s².

A = 6² = 36 square feet

Now, let's add the area of the triangular sides and the square base

Total surface area = 36√3 + 36 ≈ 98.39 ft² (rounded to the nearest hundredth)

So, the total surface area of the greenhouse including the floor is approximately 98.39 ft².

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2. Mandy is walking in the woods. She completes 70% of her walk in 3 hours. She continues walking at that same rate. How much time, in hours, will Mandy's entire walk take?

A 3 4\5

B. 5

C. 6

D. 6 1\2

**Answer:**

If Mandy completed **70%** of her walk in 3 **hours,** then we can find her **walking rate** as follows:

Let's assume that the entire walk takes **t hours**. Then, 70% of the walk would take **0.7t** hours. We know that **Mandy** completes 70% of her walk in 3 hours, so we can set up the following** equation**:

0.7t = 3

Solving for **t**, we get:

t = 3 ÷ 0.7 ≈ **4.29**

So, the entire walk will take approximately** 4.29 hours**. Since Mandy has already walked for 3 hours, the remaining time she needs to **complete **her walk is:

4.29 - 3 = 1.29 hours

Therefore, the answer is closest to option** A, 3 4/5 hours.**

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Use differentials to estimate the value of ⁴√1.3 . Compare the answer to the exact value of ⁴√1.3 . Round your answers to six decimal places, if required. You can use a calculator, spreadsheet, browser, etc. to calculate the exact value. estimate= exact value=

Therefore, the **estimate **is quite close to the exact value, with an error of about 0.000450.

We can use **differentials** to estimate the value of ⁴√1.3 as follows:

Let y = ⁴√x, then we have:

dy/dx = 1/(4x^(3/4))

We want to estimate the value of y when x = 1.3, so we have:

Δy ≈ dy * Δx

where Δx = 0.3 - 1 = -0.7 (since we are **approximating **1.3 as 1)

**Substituting **the values, we get:

Δy ≈ (1/(4(1)^3/4)) * (-0.7) ≈ -0.219

Hence, the **estimate **for ⁴√1.3 is:

y ≈ ⁴√1 + Δy ≈ 0.780

The exact value of ⁴√1.3 is approximately 0.780450255.

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Given the following triangle, If Sin F = 3/5 , then find the Cos D: A) 4/5 B) 4/3 C) 3/4 D) 3/5

If **Sin **F = 3/5 , then the value of Cos D is **4/5 (option a)**

Let us consider the **triangle **in the given question. Since we are given that Sin F = 3/5, we know that the side opposite angle F is 3 and the hypotenuse is 5. Using **Pythagoras theorem**, we can find the length of the adjacent side as follows:

Opposite² + Adjacent² = Hypotenuse²

3² + Adjacent² = 5²

9 + Adjacent² = 25

Adjacent² = 16

Adjacent = 4

So we have found that the length of the **adjacent **side is 4. Now we can use the definition of cosine to find Cos D.

Cosine is defined as the ratio of the adjacent side to the hypotenuse. Therefore,

Cos D = Adjacent/Hypotenuse = 4/5

Hence, the answer is option A) 4/5.

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Map of the city zoo a triangle with points zebras, monkeys, and lions. the distance from zebras to monkeys is 52 feet and from monkeys to lions is x feet. a triangle with points lions, tigers, elephants. the distance from lions to tigers is 96 feet and from tigers to elephants is 78 feet. the path from the zebras to the monkeys is parallel to the path from the tigers to the elephants. what is the distance between the lions and monkeys? 1. proportion: 52 78 = x 96 2. cross-multiply: 4992 = 78x 3. solve: the distance between the lions and the monkeys is feet.

The **distance** between the lions and the monkeys is 64 feet.

We can set up a proportion to find the **distance **between the lions and monkeys. Here's the step-by-step explanation:

1. **Proportion**: Since the path from zebras to monkeys is parallel to the path from tigers to elephants, we can set up a proportion using the given distances: 52/78 = x/96.

2. Cross-multiply: To solve for x, we can cross-multiply: 52 * 96 = 78 * x, which simplifies to 4992 = 78x.

3. Solve: Now we just need to solve for x. Divide both sides of the equation by 78: x = 4992 / 78. This gives x ≈ 64.

So, the **distance** between the lions and the monkeys is approximately 64 feet.

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Question 17 (5 points) ✓ saved

a patient needs to take 0.5 g po qam and 0.25 g po of a medication before sleeping.

how many 500 mg tablets must be dispensed for a 30-day supply?

90 tablets

75 tablets

25 tablets

45 tablets

The** patient** must be dispensed 45 tablets for a 30-day supply.

To determine how many 500 mg** tablets** must be dispensed for a 30-day supply given that a patient needs to take 0.5 g po and 0.25 g po before sleeping, follow these steps:

1. Convert grams to** milligrams:**

0.5 g = 500 mg (morning dose)

0.25 g = 250 mg (evening dose)

2. Calculate the total daily dosage:

500 mg (morning) + 250 mg (evening) = 750 mg per day

3. Calculate the number of 500 mg tablets needed per day:

750 mg / 500 mg = 1.5 tablets per day

4. Calculate the number of tablets needed for a 30-day **supply:**

1.5 tablets per day * 30 days = 45 tablets

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Jon has 8 packets of soup in his cupboard, but all the labels are missing. he knows that there are 5 packets of tomato soup and 3 packets of mushroom soup. he opens three packets at random. work out the probability that all three packets are the same variety of soup.

**Answer:**

37.5%

**Step-by-step explanation:**

If all were the same from opening 3, it would all have to be mushroom soup. This would look like: desired outcome/total quantity: 3/8 = 0.375 = 37.5%

A lube and oil change business believes that the number of cars that arrive for service is the same each day of the week. If the business is open six days a week (Monday - Saturday) and a random sample of n = 200 customers is selected, the critical value for testing the hypothesis using a goodness-of-fit test is x2 = 9. 2363 if the alpha level for the test is set at. 10

The **hypothesis** to be tested here is that the number of cars arriving for service is the same for each day of the week.

The null hypothesis, denoted as H0, is that the observed frequency distribution of cars is the same as the expected **frequency distribution**.

The alternative hypothesis, denoted as H1, is that the observed frequency distribution of cars is not the same as the expected frequency distribution.

To test this hypothesis, we use a **goodness-of-fit** test with the chi-square distribution. The critical value for a chi-square distribution with 6 - 1 = 5 degrees of freedom (one for each day of the week) and alpha level of 0.10 is 9.2363.

If the computed chi-square statistic is greater than 9.2363, then we reject the null hypothesis and **conclude** that the observed frequency distribution is significantly different from the expected frequency distribution.

Thus, if the computed chi-square statistic is greater than 9.2363, we can conclude that the number of cars arriving for service is not the same for each day of the week, and there is **evidence** to support the alternative hypothesis.

If the computed chi-square statistic is less than or equal to 9.2363, then we fail to reject the null hypothesis, and there is not enough evidence to suggest that the **observed frequency** distribution is different from the expected frequency distribution.

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Need help here guys.....

three similar bars of length 200 cm , 300cm and 360 cm are cut into equal pieces. find

the largest possible

area of square which

can be made from any of the three pieces.(3mks)

The largest possible **area of a square** that can be made from any of the three pieces is [tex](400 cm)^{2}[/tex]

To find the largest possible area of a square that can be made from any of the three similar bars of length 200 cm, 300 cm, and 360 cm, you need to first determine the **greatest common divisor (GCD)** of their lengths.

Step 1: Find the** GCD** of 200, 300, and 360.

The **prime factorization** of 200 is [tex](2^{3})(5^{2})[/tex], of 300 is [tex](2^{2})(3)(5^{2})[/tex], and of 360 is [tex](2^{3})(3^{2})(5)[/tex]. The GCD is the product of the lowest powers of common factors, which is [tex](2^{2})5=20[/tex].

Step 2: Determine the **side length** of the largest square.

Since the bars are cut into equal pieces with a length of 20 cm (the GCD), the largest square will have a side length of 20 cm.

Step 3: Calculate the largest possible area of the square.

The area of the square can be found by multiplying the side length by itself: [tex]Area = (side)^{2}[/tex].

[tex]Area = (20 cm)(20 cm) = (400 cm)^{2}[/tex].

So, the largest possible area of a square that can be made from any of the three pieces is [tex](400 cm)^{2}[/tex].

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Find the value of w. Round to the nearest tenth.

**Answer:**

*w** **≈** **6**8**,**3*

**Step-by-step explanation:**

*U**s**e** **t**r**i**g**o**n**o**m**e**t**r**y**:*

*[tex] \sin(42) = \frac{w}{102} [/tex]*

*C**r**o**s**s**-**m**u**l**t**i**p**l**y** **t**o** **f**i**n**d** **w**:*

*[tex]w = 102 \times \sin(42°) ≈68.3[/tex]*

One can of pumpkin pie mix will make a pie ofdiameter 8 in. if 2 cans 9f pie mix are used to make a larger pie of the same thickness, find the diameter use square root of 2 equals 1. 414

The diameter of the **larger** pie is 8 x sqrt(2) inches.

The area of a circle is proportional to the square of its **diameter**. If the diameter of a pie made with one can of pumpkin pie mix is 8 inches, then its area is (4 inches)^2 x pi = 16 pi square inches.

If two cans of pie mix are used to make a larger pie of the same thickness, the total area of the pie will be twice that of the smaller pie.

So, the **area** of the larger pie is 2 x 16 pi = 32 pi square inches.

To find the diameter of the larger** pie**, we need to solve for d in the equation:

Area of circle = (d/2)^2 x pi

32 pi = (d/2)^2 x pi

32 = (d/2)^2

Taking the square root of both sides, we get:

sqrt(32) = d/2 x sqrt(2)

d/2 = sqrt(32)/sqrt(2)

d/2 = 4 x sqrt(2)

d = 8 x sqrt(2)

Therefore, the diameter of the larger pie is 8 x sqrt(2) inches.

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The table below shows the number of students in Mr. Jang's class that are taking 1, 2, 3, or 4 AP classes. After a new student joined the class (not shown in the table), the average (arithmetic mean) number of AP classes per student became equal to the median. How many AP classes is the new student taking?

A) 2

B) 3

C) 4

D) 5

**Answer:**

2

**Step-by-step explanation:**

To solve this problem, we need to first find the current average and median number of AP classes per student, and then use that information to determine the number of AP classes the new student is taking.

To find the current average number of AP classes per student, we can use the information in the table:

(1 AP class) x 6 students = 6 AP classes

(2 AP classes) x 9 students = 18 AP classes

(3 AP classes) x 5 students = 15 AP classes

(4 AP classes) x 4 students = 16 AP classes

Total number of AP classes = 6 + 18 + 15 + 16 = 55

Total number of students = 6 + 9 + 5 + 4 = 24

Average number of AP classes per student = Total number of AP classes / Total number of students

= 55 / 24

= 2.29 (rounded to two decimal places)

To find the current median number of AP classes per student, we need to order the number of AP classes per student from least to greatest:

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4

The median is the middle value when the data is ordered in this way. Since there are 24 students, the median is the average of the 12th and 13th values:

Median = (2 + 2) / 2

= 2

Since we know that the current average and median are not equal, the new student must be taking a number of AP classes that will bring the average up to 2. We can set up an equation to represent this:

(55 + x) / (24 + 1) = 2

where x is the number of AP classes the new student is taking. Solving for x, we get:

55 + x = 50

x = -5

This is a nonsensical answer, as the number of AP classes taken by the new student cannot be negative. Therefore, our assumption that the new student is taking a number of AP classes greater than the current average is incorrect. Instead, the new student must be taking a number of AP classes less than the current average, which will bring the average down to 2.

Let y be the number of AP classes the new student is taking. We can set up a new equation to represent this:

(55 + y) / (24 + 1) = 2 - ((2.29 - 2) / 2)

where the term on the right-hand side represents the amount by which the average needs to decrease in order to reach 2. Solving for y, we get:

55 + y = 46.5

y = 46.5 - 55

y = 8.5

So the new student is taking 8.5 AP classes. However, since the number of AP classes must be a whole number, we need to round this value to the nearest integer. Since 8.5 is closer to 9 than to 8, we round up to 9. Therefore, the answer is:

The new student is taking 9 AP classes. Answer: None of the above (not given as an option).

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