Find the value of x in the triangle shown below.
X°
125°
21°

Cos u - cos u sin²u simplifies to cos³(u). We can solve it in the following manner.

Starting with the expression Cos u - cos u sin²u, we can factor out cos(u) to get:

Cos u - cos u sin²u = cos(u) (1 - sin²(u))

Using the identity sin²(u) + cos²(u) = 1, we can substitute cos²(u) for 1 - sin²(u):

cos(u) (1 - sin²(u)) = cos(u) cos²(u) = cos³(u)

Therefore, Cos u - cos u sin²u simplifies to cos³(u).

In mathematics, a factor refers to a number, algebraic expression, or function that divides or multiplies with another number, algebraic expression, or function without leaving a remainder. For example, in the expression 12x, 12 is a factor of the expression because it can be divided evenly by 12.

In algebra, factoring is the process of finding the factors of an algebraic expression, which means breaking it down into simpler parts that can be multiplied together to get the original expression. Factoring is an important skill in algebra, as it allows us to simplify and solve equations, identify common factors, and manipulate expressions more easily.

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After 60 minutes in the refrigeration, the can of soda will be approximately 42°F.

What is refrigeration?

We are given the following information:

[tex]T_{a}[/tex] = 35°F (temperature of the refrigerator)

To = 73°F (initial temperature of the can of soda)

T = 58°F (temperature of the can of soda after 10 minutes)

We can use these values to find the decay constant k:

T = [tex]T_{a}[/tex] + (To - [tex]T_{a}[/tex])[tex]e^{-kt}[/tex]

58 = 35 + (73 - 35)[tex]e^{-10k}[/tex]

23 = 38[tex]e^{(-10k)}[/tex]

ln(23/38) = -10k

k ≈ 0.0725 (rounded to the nearest thousandth)

Now we can use this value of k to find the temperature of the can of soda after 60 minutes:

T = [tex]T_{a}[/tex] + (To - [tex]T_{a}[/tex])[tex]e^{-kt}[/tex]

T = 35 + (73 - 35)[tex]e^{(-0.0725*60x^{2} )}[/tex]

T ≈ 42°F (rounded to the nearest degree)

Therefore, after 60 minutes in the refrigerator, the can of soda will be approximately 42°F.

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To find the surface area of the rectangular prism, we need to calculate the area of each of the six sides and then add them together. The area of each of the four walls is the product of the length and height, which gives us:

16 feet × 11 feet = 176 square feet (for the two longest walls)

14 feet × 11 feet = 154 square feet (for the two shorter walls)

The area of the ceiling and floor is the product of the length and width, which gives us:

16 feet × 14 feet = 224 square feet (for the ceiling)

16 feet × 14 feet = 224 square feet (for the floor)

To find the total surface area, we add up the areas of all six sides:

176 + 176 + 154 + 154 + 224 + 224 = 1104 square feet

Therefore, we need at least 1104/100 = 11.04 pints of paint to cover the walls of the room. Rounding up to the nearest whole pint, we need 12 pints of paint.

The approximate surface area of the cone is equal to 35 ft²

In Mathematics, the surface area (SA) of a cone can be calculated by using this mathematical expression:

Surface area (SA) of a cone = πr(l + r)

Where:

Note: Radius = diameter/2 = 2/2 = 1 feet.

By substituting the given parameters into the formula for the surface area (SA) of a cone, we have the following;

Surface area (SA) of a cone = 3.14 × (1 + 10)

Surface area (SA) of a cone = 3.14 × (11)

Surface area (SA) of a cone = 34.54 ≈ 35 ft²

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Answer:

827.0 cm³

Step-by-step explanation:

The question we are told is to find the volume of water that can fill the paper cup. This means that we have to find the volume of a cylinder (the cup).

1) understand the equation for volume of a cylinder

The formula for the volume of a cylinder is πr²h

The radius would be half the diameter, which is 4.5, and h would be the height which is 13.

2) Solve

This means our working out would be...

3) Round

We have to round this to the nearest tenth which would be 827.0 or 827!

Hope this helps, have a lovely day! :)

Thus, the number of 6-digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is 20.

What is the number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated?There are 1200 6-digit numbers that can be formed using the digits 0, 1, 2, 5, 7, and 9.Using the formula for a 2-digit number, namely A and B, the number must satisfy A - B = 0,11 or -11.

There is a pattern, therefore, there are 100 numbers that satisfy each. It's because the numbers 0, 1, 2, 5, 7, and 9 are such that the sum of the odd digits minus the sum of the even digits is always either 0, 11, or -11. This is only possible if there is an even number of odd digits or an even number of even digits.

There are 6C3 ways to pick 3 odd digits from {1,5,7,9} and 3C3 ways to pick 3 even digits from {0,2}. By taking the product of these values, we can find the total number of possibilities:[tex]6C3 × 3C3 = 20 × 1 = 20[/tex]

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In statistics, the mean is a measure of central tendency that represents the average value of a set of data. It is calculated by adding up all the values in the data set and dividing by the total number of values. The mean is also known as the arithmetic mean or average.

The formula for the mean is:

mean = (sum of all values) / (total number of values)

1.To find the mean of these scores, we add them up and divide by the total number of scores:

Mean = (83 + 97 + 85 + 84 + 96 + 80 + 80 + 87 + 91) / 9 = 86

2.To find the median, we first need to put the scores in order from lowest to highest:

80, 80, 83, 84, 85, 87, 91, 96, 97

The median is the middle score, which in this case is 85.

3.To find the mode, we look for the score that occur most frequently. In this case, there are two modes: 80 and 85, each occurring twice.

4.To find the range, we subtract the lowest score from the highest score:

Range = 97 - 80 = 17

Therefore, the mean is 86, the median is 85, the mode(s) are 80 and 85, and the range is 17.

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Answer: Number 10 is you are a rectangle

Step-by-step explanation:

Answer:

Step-by-step explanation:

-16-5x=-16. please help

-16 - 5x = -16

5x = -16 + 16

5x = 0

x = 0 : 5

x = 0

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

check

-16 - 5  × 0 = -16           (remember PEMDAS)

-16 = -16

the answer is good

Answer:

x = 0

Step-by-step explanation:

- 16- 5x = - 16

+ 16        + 16

   - 5x = 0

x = 0

Answer:

Step-by-step explanation:

6

The ratio of the first term to the common difference is 1 is to 1 (1:1).

Let's say the first term of the arithmetic progression is 'a' and the common difference is 'd'.

Then the sum of the first five terms will be,

S5 = a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 5a + 10d

And the sum of the first ten terms will be,

S10 = a + (a + d) + (a + 2d)+ ... + (a + 9d)

=10a + 45d

We have been given that sum of the first 10 terms is equal to four times the sum of the first 5 terms, i.e

S10 = 4S5

Substituting the expressions for S5 and S10 in terms of a and d, we get,

10a + 45d = 4(5a + 10d)

Simplifying this equation, we get,

10a + 45d = 20a + 40d

10d = 10a

d = a

So the ratio of the first term to the common difference is 1:1 or 1/1.

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To solve the equation × (3 + 8) = 55, we need to simplify the expression inside the parentheses first, which gives us:

× (3 + 8) = × 11

Now we substitute × 11 back into the original equation:

× 11 = 55

To solve for ×, we divide both sides by 11:

× = 5

Therefore, the number that solves the equation × (3 + 8) = 55 is 5.

The area of the given figure is 44 units.

Answer: The material will cost Meghana $95.84 before taxes.

Step-by-step explanation:

a. To find the area of Meghana's kite, we first need to convert the dimensions from feet to yards since the material is sold per square yard:

Length = 18 ft = 6 yards (since 1 yard = 3 feet)

Width = 4 ft = 4/3 yards (since 1 yard = 3 feet)

The area of the kite is the product of its length and width:

Area = Length x Width = 6 x 4/3 = 8 square yards

b. Meghana needs enough material to cover both sides of her kite, so she needs twice the area of the kite:

Area of both sides = 2 x Area of one side = 2 x 8 = 16 square yards

Therefore, Meghana needs 16 square yards of nylon material.

c. The material is sold for $5.99 per square yard, so the total cost of the material before taxes is:

Total cost = Cost per square yard x Number of square yards

Total cost = $5.99 x 16 = $95.84

Therefore, the material will cost Meghana $95.84 before taxes.

Step-by-step explanation: I hope this helps.

Answer:

the 90% confidence interval for the proportion of pain reduction for the vitamin A oil group is (0.275, 0.465) , placebo group is (0.119, 0.301).

Part A: An appropriate design for the new study would be a randomized controlled trial. The treatments used in this study would be vitamin A oil and a placebo. The method of treatment assignment would be randomized, with patients being randomly assigned to receive either vitamin A oil or the placebo. The variables that should be measured include the level of pain reduction after treatment, the age of the patients, the severity of the pinched nerve, and any side effects experienced by the patients.

Part B: If the study consisted of 100 young patients and 100 old patients instead of 200 patients aged 20–40, the study design would need to be modified. Age is an important variable that could affect the results of the study. To control for this variable, the study could be designed to have two separate treatment groups: one group of young patients and one group of old patients. This would allow for the comparison of pain reduction between the two age groups and would provide more accurate results.

Part C: To construct 90% confidence intervals for the proportion of pain reduction for each treatment group, we can use the following formula:

CI = p ± z*(√(p(1-p)/n))

where p is the proportion of patients reporting pain reduction, z is the critical value from the standard normal distribution for a 90% confidence interval (which is 1.645), and n is the total number of patients in the treatment group.

For the vitamin A oil group:

p = 0.37

n = 100

z = 1.645

CI = 0.37 ± 1.645*(√(0.37(1-0.37)/100))

CI = 0.37 ± 0.095

CI = (0.275, 0.465)

Therefore, the 90% confidence interval for the proportion of pain reduction for the vitamin A oil group is (0.275, 0.465).

For the placebo group:

p = 0.21

n = 100

z = 1.645

CI = 0.21 ± 1.645*(√(0.21(1-0.21)/100))

CI = 0.21 ± 0.091

CI = (0.119, 0.301)

Therefore, the 90% confidence interval for the proportion of pain reduction for the placebo group is (0.119, 0.301).

Part D: Based on the data collected, we can conclude that vitamin A oil is effective in reducing pain levels in patients suffering from pinched nerves in the cervical region of the back. The 90% confidence interval for the proportion of pain reduction for the vitamin A oil group (0.275, 0.465) does not overlap with the 90% confidence interval for the proportion of pain reduction for the placebo group (0.119, 0.301), indicating a statistically significant difference between the two groups. However, further research may be needed to confirm these results and to investigate any potential side effects of vitamin A oil treatment.

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Answer: If you add the same number to both sides of an inequality, the inequality remains true. If you subtract the same number from both sides of the inequality, the inequality remains true. If you multiply or divide both sides of an inequality by the same positive number, the inequality remains true.

The degrees of freedom associated with a pooled-variance two-sample t-test or confidence interval in the given case would be 48.

When a pooled-variance two-sample t-test or confidence interval is to be conducted on two groups, the degrees of freedom is calculated using the following formula: df = n1 + n2 - 2, where n1 and n2 are the sample sizes of the two groups being compared.

In the given scenario, data is collected from 20 random luxury hotels in New York and 30 random luxury hotels in Los Angeles. Therefore, the degrees of freedom for a pooled-variance two-sample t-test or confidence interval would be:df = 20 + 30 - 2df = 48. Hence, the degrees of freedom associated with a pooled-variance two-sample t-test or confidence interval are 48.

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Answer:

1/24

Step-by-step explanation:

1 ft = 12 in

8 X 12 = 96

96/4 = 24

1/24 is the scale factor

Answer: 24:1 (The tiger : The tiger model)

Step-by-step explanation:

1 feet =12 inch

so 8 feet=96 inch

The tiger : The tiger model= 96:4= 24:1

Answer:

S = [tex]\sqrt{3}[/tex]

H = 2

It's D

Step-by-step explanation:

Considering the attached picture

h = 1 x 2 = 2

s = 1 x [tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex]

Answer:

the value of x when f(x) = 15 is 3.5.

Step-by-step explanation:

We are given that:

f(x) = 1 + 4x

We need to find the value of x when f(x) = 15.

So we can set up the equation:

1 + 4x = 15

Subtracting 1 from both sides, we get:

4x = 14

Dividing both sides by 4, we get:

x = 14/4

Simplifying, we get:

x = 3.5

Therefore, the value of x when f(x) = 15 is 3.5.

Answer:

x = 10

Step-by-step explanation:

To solve for x, we need to get x by itself.

Whatever we do to one side, we do it to the other side to keep it balanced.

3x + 15 = 45

     - 15 = -15       (Subtract 15 from both sides)

3x        =   30               (Divide both sides by 3)

3          =    3

x = 10

6.61 is the value of x in the circle.

What does the circle's tangent look like?

A line that only has one point of intersection with a circle is said to be tangent to the circle. Point of contact is the term used to describe the location where the circle and the tangent meet. A straight line that touches a circle at point P is said to be tangent to the circle at P. As the radius connects the circle's centre to point P, the tangent is perpendicular to that radius.

 (39x - 4) = 254

     39x = 254 + 4

      39x =  258

         x = 258/39

         x = 6.61

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The measure of central tendency is the most appropriate for this data is median.

There are a few different measures of central tendency to choose from, but the most common ones are the mean, median, and mode.

The mean is the arithmetic average of the data. To find the mean, you would add up all the values and divide by the total number of values. However, the mean can be sensitive to outliers or extreme values, which could skew the results. In this case, there are no extreme values, but the data is not evenly distributed across the three groups, so the mean may not be the best measure of central tendency to use.

The median is the middle value of the data when it is arranged in order from smallest to largest.

This can be a better measure of central tendency when the data is not evenly distributed. In this case, we can find the median by arranging the data in order: 25, 125, 250. The middle value is 125, which means that half of the pet owners surveyed own fewer than 125 pets, and half own more than 125 pets.

So, the median might be a good choice of measure of central tendency in this case.

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The radius of each circle is approximately 3.46 units.

Since the two circles are congruent and tangent to each other, their centers are located on the same line perpendicular to the side of the square.

Let the center of each circle be O and the point where the circles are tangent be T. Then, the radius of each circle is equal to the distance from O to T.

Drawing a line from O to T, we can see that it forms a right triangle with one leg equal to the radius of the circle and the other leg equal to half the side length of the square. Using the Pythagorean theorem, we can solve for the radius:

[tex]r^2 + (2)^2 = (4)^2r^2 = 12\\[/tex]

r ≈ 3.46

Therefore, the radius of each circle is approximately 3.46 units, rounded to the nearest hundredth.

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Answer:

23,381/160 or 146 21/160

Step-by-step explanation:

56 3/4 = 227/4

1 3/8 = 11/8

1 1/5 = 6/5

227/4( 11/8 + 6/5)

227/4(55/40 + 48/40)

227/4( 103/40) = 23,381/160 or 146 21/160

the probability that among the next 8 users from this state who are interviewed, the probability of the first 6 users first took it for psychological problems is 60% is 0.03456.

As per the given information, 60% of the valium users in Massachusetts first took it for psychological problems. Now, we are supposed to find the probability that among the next 8 users from this state who are interviewed, the probability of the first 6 users first took it for psychological problems is: 60%.

What is Valium?

Valium is a prescription medicine that is used to treat the symptoms of anxiety, alcohol withdrawal, and muscle spasm. The use of Valium can lead to addiction, especially if it is not taken as prescribed by the doctor.The probability of the first 6 users first took it for psychological problems is 60%. Hence, the probability that the first user did not take it for psychological problems is: 40%.

Probability of first user did not take Valium for psychological problems = P(A) = 0.40

Probability of first user took Valium for psychological problems = P(B) = 0.60

Now, we are supposed to find the probability that among the next 8 users from this state who are interviewed, the first 6 users first took it for psychological problems is: 60%.Probability of the first 6 users first took it for psychological problems is:

Probability of the next 5 users took it for psychological problems = P(B) × P(B) × P(B) × P(B) × P(B) = (0.60)⁵

Probability of the next 2 users did not take it for psychological problems = P(A) × P(A) = (0.40)²

Thus, the probability that among the next 8 users from this state who are interviewed, the probability of the first 6 users first took it for psychological problems is 60%, is:(0.60)⁵ × (0.40)²= 0.03456 (rounded to five decimal places)

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