find the 25th, 50th, and 75th percentile from the following list of 32 data. please enter exact answers.

For the given circle the value of cotθ is -√30/√19.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The terminal side of an angle θ.

The standard position intersects the unit circle at (√30/7, -√19/7).

We need to find the value of cotθ.

Suppose that θ is an angle in standard position whose terminal side intersects the unit circle at (√30/7, -√19/7)

cotθ=x/y

=-√30/7/√19/7

=-√30/7×7/√19

=-√30/√19

Hence, the value of cotθ is -√30/√19 for the given circle.

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The value of x in first part = 16

The value of x in second part = 10

Part a

The angle U = angle Z = 54 degrees

Angle V = angle Y = 67 degrees

Therefore angle W = angle X

The sum of the angles in  a triangle is 180 degrees

Then, the equation will be

54 + 67 + a = 180

121 + a = 180

a = 180 - 121

a =  59 degrees

Then

4x - 5 = 59

4x = 59 + 5

4x = 64

x = 64/4

x = 16

Part 2

Similarly the unknown angle as b

Sum of the the angles in a triangle is 180 degrees

58 + 74 + b = 180

132 + b = 180

b = 180 - 132

b = 48 degrees

Then the equation will be

5x - 2 = 48

5x = 48 + 2

5x = 50

x = 50/5

x = 10

Therefore, the value of x in the part a and part b are 16 and 10 respectively

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The volume of the composite solid is 5770.28ft³

The composite solid is made up of a cylinder and a hemisphere

The volume is the addition of the two solids

Volume=[tex]\pi[/tex]r²h +2/3πr²

The given parameters are

π=22/7

h=22 ft

r=9 ft

Input the values to get

(22/7*9*9*22) + (2/3*22/7*9*9)

Simplifying the terms to get

5600.57+169.71

The volume is = 5770.28c

ft³

In conclusion, the volume of the solid is 5,770.28ft³

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Answer:

62 degrees

Step-by-step explanation:

(3x-13)+(2x+4)+(180-116)=180

5x-9+64=180

5x+55=180

   -55.  -55

5x=125

/5. /5

x=25

3(25)-13

75-13

62

hopes this helps

Answer:

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

Let the number be x.

Set equation for x and solve:

Answer:

C and D are correct.

Step-by-step explanation:

In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

The differentiation for the given function is f'(x) = -27x⁸- 48x³. The correct option is (A).

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = (f(x + h) - f(x)) /(x + h - x).

Geometric meaning of it is the slope of the function at a given point.

The given function is f(x) = (-x⁵ - 4). 3x⁴

It is in the form of u.v, the differentiation is given as below,

uv' + vu'

As per the above expression suppose (-x⁵ - 4) = u and 3x⁴ = v.

Now, the differentiation can be done as follows,

f'(x) = d(-x⁵ - 4)/dx × 3x⁴ + (-x⁵ - 4) × d(3x⁴)/dx

      = -5x⁴ × 3x⁴ + (-x⁵ - 4) × 4 × 3x³

      = -15x⁸ + 12x³(-x⁵ - 4)

      = -15x⁸ - 12x⁸ - 48x³

      = -27x⁸- 48x³  

Hence, the differentiation is obtained as f'(x) = -27x⁸- 48x³.

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The rate of change of y with respect to x for this line is 4 / 5 .

Given :

The graph of a line is shown on the grid. The coordinates of both points indicated on the graph of the line are integers.

From the graph :

The marked coordinates are ( 5 , 7 ) and ( -5 , -1 ) .

slope m = rate of change of y / rate of change of x

= y2 - y1  / x2 - x1

= -1 -7 / -5 - 5

= -8 / -10

= 8 / 10

= 4 / 5

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[tex]3x-8=14[/tex]

Add 8 to both sides:

[tex]3x-8+8=14+8[/tex]

[tex]3x=22[/tex]

Divide both sides by 3:

[tex]\dfrac{3x}{3} =\dfrac{22}{3}[/tex]

[tex]\fbox{x = $\dfrac{22}{3} $ or 7.333333}[/tex]

Therefore, the probability that the probability that the difference in the weights of the two oranges exceeds 3 ounces is 0.0385 .

The study of numerical estimates of the likelihood that an event will occur or that a proposition is true is known as probability. The probability of an occurrence is a number between 0 and 1, where 0 often indicates that the event is impossible and 1 typically indicates that it will happen.

Here,

Let X1 and X2  represent the weights of the two oranges.

Let  d=X1 - X2 represent the difference in weight.

We're given that

X1 ~ N(12, 1.2^2)

X2 ~ N(12, 1.2^2)

Then,

Then, d N(12-12, 1.22 +1.22) or N (0, 21.22)

So the standard deviation of this √2.1.22 = 1.6971

Let's find

=> P(d>3)

=> 1-(1891)

=> 1-0.9615 = 0.0385

Therefore the probability that the probability that the difference in the weights of the two oranges exceeds 3 ounces is 0.0385 .

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The p-value of ay distribution given can be calculated using the formula P(Z < X) where X is any sample data.

To find the p-value for a left-tailed test of hypothesis for a mean when the test statistic has been calculated as -1.03, you can use the following formula:

p-value = P(Z < -1.03)

Where Z is the standard normal distribution. You can use a z-table or a calculator to find the probability that a standard normal random variable is less than -1.03. The resulting p-value will be the probability that the test statistic is as extreme or more extreme than the observed value, given that the null hypothesis is true.

To find the p-value for a right-tailed test of hypothesis for a mean when the test statistic has been calculated as 2.58, you can use the following formula:

p-value = P(Z > 2.58)

Where Z is the standard normal distribution. You can use a z-table or a calculator to find the probability that a standard normal random variable is greater than 2.58. The resulting p-value will be the probability that the test statistic is as extreme or more extreme than the observed value, given that the null hypothesis is true.

To find the p-value for a two-tailed test of hypothesis for a proportion when the test statistic has been calculated as 1.91, you can use the following formula:

p-value = 2 * P(Z > 1.91)

Where Z is the standard normal distribution. You can use a z-table or a calculator to find the probability that a standard normal random variable is greater than 1.91. The resulting p-value will be twice this probability, since the test is two-tailed and we need to consider both tails of the distribution.

To find the p-value for a two-tailed test of hypothesis for a proportion when the test statistic has been calculated as -1.16, you can use the following formula:

p-value = 2 * P(Z < -1.16)

Where Z is the standard normal distribution. You can use a z-table or a calculator to find the probability that a standard normal random variable is less than -1.16. The resulting p-value will be twice this probability, since the test is two-tailed and we need to consider both tails of the distribution.

Note that in all of these cases, you need to assume that the population standard deviation is known. If the population standard deviation is not known, you will need to use a different test statistic and a different approach to calculate the p-value.

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Answer:

n = the quantity 4 times c minus 3 all over negative p

Explanation:

Interpretation of answers to equation

n = the quantity 4 times c minus 3 all over negative p = [tex]\frac{4c-3}{-p}[/tex]

n = the quantity 4 times c minus 13 all over negative p = [tex]\frac{4c-13}{-p}[/tex]

n = the quantity 4 times c plus 3 all over p = [tex]\frac{4c+3}{p}[/tex]

n = the quantity 4 times c plus 13 all over p = [tex]\frac{4c+13}{p}[/tex]

Step-by-step:

[tex]-np-5=4(c-2)[/tex]

[tex]-np-5=4c-4(2)[/tex]

[tex]-np-5=4c-8[/tex]

[tex]-np-5+5=4c-8+5[/tex]

[tex]-np=4c-3[/tex]

Divide both side by -p

[tex]n=\frac{4c-3}{-p}[/tex]

n = the quantity 4 times c minus 3 all over negative p

Answer:

The answer is the option A, which is: A.) n ≥ − the quantity 4 times c minus 3 all over p.

Step-by-step explanation:

You have −np − 5 ≤ 4(c − 2)

When you solve for n, you obtain:

-np-5 ≤ 4(c-2)

-np≤4c-8+5

Therefore, you have:

n≤-(4c-3/p)

Hope it helps :) make me as Brainlest! Or Expert-Verified Answer!

Answer:

m∠WYZ = 23°

Step-by-step explanation:

The percentage of students that have grade point averages that are at least 3.48 is of:

2.5%.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

Considering the mean of 2.62 and the standard deviation of 0.43, a grade point average of at least 3.48 is at least two standard deviations above the mean.

100 - 95 = 5% of the measures are at least two standard deviations of the mean. Considering the symmetry of the normal distribution, we have that:

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infinitely many solutions because these 2 lines are exactly the same line. If you multiply the 2nd equation by 2, you will get the 1st one, or if you divide the 1st equation by 2, you will get the 2nd one.

This set {(x, y) | 0 is (a) open, (b) connected, and (c) not simply-connected.

(a) Open: This set is open because all points within the set have a neighborhood that is also within the set.

(b) Connected: This set is connected because there is a path between any two points in the set that does not leave the set.

(c) Not simply-connected: This set is not simply-connected because it contains a hole in the center, which is not a simply-connected space.

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Answer:

approx 17 ft

Step-by-step explanation:

You need to find the 'zeroes' of this equation......where the depth is zero

x^2 - 16x - 8 = 0        You will need to use the Quadratic Formula

                                     with a = 1      b= -16     c = -8

 to find x = 8 +- 6 sqrt 2

     the distance between these zeroes is  12 sqrt2 = 16.97 = ~ 17 feet

Option D is the correct answer. The value of 'c' for the given system of linear equations with infinitely many solutions is - 1.

A linear equation is an equation in which the highest power of the variable is always 1 and the equations are the equations of degree 1. It is the equation for the straight line.

The standard form of the linear equation is ax+by+c =0

where a ≠ 0 and b ≠ 0.

Given a system of linear equations are

1. 3x-9y=-6

⇒ x-3y=-2

Therefore,

a1=1, b1=-3, c1=-2

2. [tex]\frac{x}{2} -\frac{3y}{2} =c\\[/tex]

⇒ x-3y=2c

Therefore,    

a2=1, b2=-3, c2=2

For the system of linear equations with infinitely many solutions,

compare c1=c2

2c=-2

⇒ c=-1

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On solving the provided question we can say that, Number of students jumped greater than 8.5 but less than 11.5 is 7 students.

the frequency or reality that something occurs frequently or a great number of times within a specific time frame. The frequency of buses, for instance, has been the subject of more complaints in recent months.

Number of students jumped greater than 8.5 but less than 11.5= frequency of length of jump greater than 8.5 but less than 11.5

AND,

frequency of length of jump greater than 8.5 but less than 11.5 is -

Number of students jumped greater than  8.5 and less than  9.5 + Number of students jumped greater than 9.5 but less than 10.5 + Number of students jumped greater than 10.5 but less than 11.5=

3+3+1=7 ( since, sum of respective frequencies of the three class)

so, Number of students jumped greater than 8.5 but less than 11.5 is 7 students.

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The expressions representing the length and width of the garden is (5x-1)(2x+7)

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.

Given that, Lillian has a rectangular garden with an area of 10x²+33x-7 square feet.

To find the expressions that would represent the length and width of the garden, we will factorize the expression representing the area of the garden,

10x²+33x-7

= 10x²+35x-2x-7

= 5x(2x+7)-1(2x+7)

= (5x-1)(2x+7)

Hence, The expressions representing the length and width of the garden is (5x-1)(2x+7)

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The operating cost per hour of a plane increases with the number of passengers it carries. More passengers require more fuel, maintenance, and staff, which all increase the overall cost of operating the plane per hour.

Additionally, if the plane is larger and designed to carry more passengers, the operating cost per hour may be higher than for smaller planes.The cost of operating an aircraft per hour is directly related to the number of passengers it carries. As the number of passengers increases, so too does the amount of fuel, maintenance, and personnel needed to safely operate the plane, resulting in a higher operating cost per hour. Additionally, larger planes that can carry more passengers also tend to have higher operating costs per hour than smaller planes.

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The coordinates of A' = (1, 7)

The coordinates of B' = (4, 9)

The coordinates of C' = (3, 6)

There are two ways of translation.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

ΔABC:

Coordinates:

A = (2, 3)

B = (5, 1)

C = (4, 4)

Reflection across y = 5.

So,

A = (2, 5)

There are two units between y = 5 and y = 3.

We add 2 units with the y-coordinate of A = (2, 5)

5 - 3 = 2

So,

A = (2, 5 + 2)

A = (2, 7)

Similarly,

5 - 1 = 4

B = (5, 5 + 4) = (5. 9)

5 - 4 = 1

C = (4, 5 + 1) = (4. 6)

Translation of 1 unit down.

A = (2 - 1, 7) = (1, 7)

B = (5 - 1, 9) = (4, 9)

C = (4 - 1, 6) = (3, 6)

Thus,

The coordinates of ΔA'B'C' are (1, 7), (4, 9), and (3, 6).

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The value of P(A/B) will be = 1/4

As per the question,

As a fair six-sided die is rolled twice

So, the total number of outcomes will be N=6^2=36

A: sum of the two rolls is 5

[tex]$$\begin{aligned}& A=\{(1,4),(2,3),(3,2),(4,1)\} \\& n(A)=4 \\& P(A)=\frac{n(A)}{N}=\frac{4}{36}\end{aligned}$$[/tex]

B: The first roll results in a 2

[tex]B=\{(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\}$ \\$n(B)=6$ \\$P(B)=\frac{n(B)}{N}=\frac{6}{36}$ \\$B \cap A=\{(2,3)\}$ \\$\cap(B \cap A)=1$ \\$P(B \cap A)=\frac{n(B \cap A)}{N}=\frac{1}{36}$\\$P(B \mid A)=\frac{P(B \cap A)}{P(A)}=\frac{1 / 36}{4 / 36}=\frac{1}{36} \times \frac{36}{4}$$P(B \mid A)=\frac{1}{4}$[/tex]

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1/63.

[tex]\frac{\frac{1}{9} }{7}[/tex]

Check the attached image below.

[tex]\frac{1}{9}*\frac{1}{7}[/tex]

[tex]\frac{1}{9}*\frac{1}{7}=\\\\ \frac{1*1}{9*7} =\\\\ \frac{1}{63}[/tex]

[tex]\frac{\frac{1}{9} }{7}=\frac{1}{63}[/tex]

Answer:

The monthly installment amount for this loan is approximately
142956.575 rupees.

Step-by-step explanation:

Total Interest = 850,000 x (1 + 0.12/12)^(12 x 5) - 850,000

= 850,000 x (1 + 0.01)^60 - 850,000

= 850,000 x 1.01^60 - 850,000

= 850,000 x 1.675837 - 850,000

= 850,000 x 0.675837

= 573569.45

= (850000 + 573569.45) / 60

= 142956.575

If you have any question let me know.

Answer:

D = [1,5]

R= [0,4]

.........

Answer:

3/10

Step-by-step explanation:

There are 3 blue sectors out of the total 10.

David ought to keep saving money in his simple interest account regardless of his current age.

He will be able to purchase his 30,000 USD boat at that rate each year. David would need to put at least 5 to 10 percent of his income into a savings account with simple interest.

Your initial investment as well as any interest that has already been accrued will earn interest in a compound interest account. The "compounding" factor is the appreciation of interest based on interest that occurs over time. On the other hand, simple interest accounts only pay interest on the initial principal.

Both guaranteed and non-guaranteed substances benefit from compounding. You might lose all of your money or some of it. Stocks, income trusts, real estate, mutual funds, and gold are all examples.

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The statement that best describes the distribution is C. The data is normally distributed because the majority of the data is in the center.

A histogram is a graphical representation of data points organized into ranges that the user specifies. The histogram, which resembles a bar graph in appearance, condenses a data series into an easily interpreted visual by grouping many data points into logical ranges or bins.

Because the majority of the data is in the center, the data is normally distributed.

Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central region, with values decreasing as one moves away from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are identical.

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