Cos (90°-0) / sin (180°- 0) - sin^2 (-0)

68% of IQ scores are found to be between 90 and 120

The empirical rule states that for a normal distribution, about 68% of the data falls within one standard deviation from the mean, 95% of the data falls within two standard deviation from the mean and 99.7% of the data falls within three standard deviation from the mean.

Given mean of 105 and a standard deviation of 15.

68% of data falls within one standard deviation from the mean = mean ± standard deviation = 105 ± 15 = (90, 120)

68% of IQ scores are between 90 and 120

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Answer:

∠ 1 = 50°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

140° is an exterior angle of the triangle, thus

90° + ∠ 1 = 140° ( subtract 90° from both sides )

∠ 1 = 50°

Answer:

50 degrees

Step-by-step explanation:

To find the measure of angle 1, you must first find the other unknown angle in the triangle. You can find this through supplementary angles. The bottom angle as well as 140 must be equal to 180 because they are supplementary, so to find it solve 180-140, which is 40. Now two of the angles in the triangle are known, one is 40 and the other is 90 as shown by the square. You know that every angle equals 180 degrees, so to find angle 1 add the known angles and subtract that from 180. 180-(90+40), which equals 50. So m<1=50.

Answer:

it’s years

Step-by-step explanation:

To sketch the graph of the function f(x) that satisfies the given conditions, we will follow these steps:

1. Determine the behavior of the function at x = 6:

  - Since x = 6 is a vertical asymptote, the function f(x) approaches positive infinity as x approaches 6 from the left, and approaches negative infinity as x approaches 6 from the right.

  - We can denote the vertical asymptote as x = 6.

2. Determine the behavior of the function at x = -2:

  - We know that f(-2) = 1.

  - This point can be plotted on the graph.

3. Determine the behavior of the function as x approaches infinity:

  - The limit of f(x) as x approaches infinity is 1.

  - This means that as x increases without bound, the function approaches a horizontal line at y = 1.

4. By knowing the intervals

  - Since the derivative f'(x) is given as 16(x + 2), we can see that f'(x) is positive for x < -2 and negative for x > -2.

  - This means that the function is increasing for x < -2 and decreasing for x > -2.

5. Determine the intervals of concavity and inflection points:

  - Since the second derivative f''(x) is given as 32(x + 6)(6 - x), we can find the points where f''(x) = 0.

  - Solving 32(x + 6)(6 - x) = 0, we get x = -6 and x = 6 as the critical points.

  - The behavior of the second derivative around these points will help determine the concavity and inflection points.

6. Sketch the graph of the function:

  - Start by drawing the vertical asymptote at x = 6.

  - Plot the point (-2, 1) on the graph.

  - Draw the graph with increasing behavior to the left of x = -2 and decreasing behavior to the right of x = -2.

  - Since the function approaches a horizontal line at y = 1 as x approaches infinity, the graph should level off at y = 1 as x increases.

  - The behavior around the critical points x = -6 and x = 6 will determine the concavity and inflection points.

Please note that without specific values for f(x) at other points or additional information, it is challenging to provide a precise sketch of the graph. However, by following the given conditions and using the given derivatives, you can plot the graph and identify the general behavior based on the provided information.

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Answer:

The correct answer is C.

Step-by-step explanation:

Giving the following information:

Present Value (PV)= 250 million

Future Value (FV)= 500 million

Growth rate (g)= 1% per year

First, we need to calculate the number of years required for the population to double:

n= ln(FV/PV) / ln(1+g)  

n= ln(500/250) / ln(1.01)

n= 69.66 = 70 years

It will take 70 years for the population to double.

The answer is c) 50%. A random sample means that each member has an equal chance of being selected. This means that out of a sample size of any number, the percentage of members selected will always be 50%.

For example, if we have a random sample of 100 members, 50 of them will be selected. This principle applies to any population size, regardless of whether it's 10 or 10,000. It's important to note that this applies only to random samples, as non-random samples can have a biased selection process which affects the percentage of members selected. In summary, the percent of members in a random sample that have an equal chance of being selected is always 50%.

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its 4/1 because 1/4 would make it smaller. Imagine taking a quarter id its size vs. 4 times its size.

Answer:

Step-by-step explanation:

its 4/1 because 1/4 would make it smaller. Imagine taking a quarter id its size vs. 4 times its size.

Answer:

  P = 94°

Step-by-step explanation:

The total of interior angles of a pentagon is 180°(5 -2) = 540°.

  P +Q +R +S +T = 540°

  (4x +2)° +132° +(4x -10)° +(5x -11)° +128° = 540°

  13x = 299 . . . . . . . divide by °, subtract 241, collect terms

  x = 23 . . . . . . . . divide by 13

Then the measure of P is ...

  P = (4(23) +2)°

  P = 94°

_____

Additional comment

R = 82°, S = 104°

__

The total of interior angles of an n-sided convex polygon is 180°(n -2).

Answer:

Step-by-step explanation:

The equation that represents the function shown on the graph is (d) y = 4x

The graph that completes the question is added as an attachment

On the graph, we have the following ordered pairs

Line starts at (0. 0) and through (2, 8), (4, 16), then end at (5, 20)

These ordered pairs are

(x, y) = (0. 0), (2, 8), (4, 16), (5, 20)

The ordered pair (0, 0) implies that the line passes through the origin

This means that the equation can be represented as

y = Y/X * x

Where

(X, Y) = any of (2, 8), (4, 16), (5, 20)

So, we have

y = 8/2 * x

Evaluate the quotient

y = 4 * x

This gives

y = 4x

Hence, the equation is (d) y = 4x

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Answer: d

Step-by-step explanation:

yw

Answer:

best deals for children with the highest number of school meals for Englis were found in colorfit and it was Dawes who was Dawes in the ab of the year and the first of the first three years of the year was Dawes and the first of the year was the first of the year was the first of the year was the first of three books to de mark a year of any of any kind and a great achievement for English and it is not

Answer:

any line can pass through the point (2,2) so there needs to be a second point

Step-by-step explanation:

The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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The value of chi-square statistic (\(X^{2}\)) is 11.26

As per the given question

the sample space of all the four cases are 30

the proportions that land upright are the same when the dropping height is 3, 5, 10, and 20 cm.

the formula of chi-squared test is

\(X^2=\sum\frac{(O_i-E_i)^2}{E}\)

where

\(X^{2}\) is chi-square

\(O_i\) is the observed value

\(E_i\) is the expected value

the upright observed value are 20,23,27,29

the upright expected values are 24.75

now

the chi-square at 3cm height is

\(X^2=\(\frac{(20-24.75)^2}{24.75}\)

=> \(X^2=0.91\)

the chi- square at 5cm height is

\(X^2=\(\frac{(23-24.75)^2}{24.75}\)

=> \(X^2=0.12\)

the value of chi-square at 10cm is

\(X^2=\(\frac{(27-24.75)^2}{24.75}\)

=>\(X^2=0.20\)

the value of chi-square at 20cm is

\(X^2=\(\frac{(29-24.75)^2}{24.75}\)

=> \(X^2=1.97\)

the not upright observed values are

10,7,3,1

the not upright expected values are 5.25

the chi-square test at 3cm height is

\(X^2=\(\frac{(10-5.25)^2}{5.25}\)

=> \(X^2=4.30\)

the chi-square test at 5cm height is

\(X^2=\(\frac{(7-5.25)^2}{5.25}\)

=> \(X^2=0.58\)

the chi-square test at  10cm height is

\(X^2=\(\frac{(3-5.25)^2}{5.25}\)

=> \(X^2=0.96\)

the chi-square test at 20 cm is

\(X^2=\(\frac{(1-5.25)^2}{5.25}\)

=> \(X^2=3.44\)

now,

the total

chi-square value at 3cm height is

=>X^2=0.91+4.30

=> \(X^{2}\)= 5.21

chi-square at 5cm height is

=> \(X^{2}=0.12+0.58\)

=> \(X^2=0.71\)

chi-square at 10cm is

=> \(X^{2}=0.20+096\)

=> \(X^2=1.16\)

chi-square at 20 cm is

=> \(X^{2}=0.73+3.44\)

=> \(X^{2}=4.17\)

now ,

the total chi-square statistic is

=>\(X^{2}=\)5.21+0.71+1.17+4.17

=>\(X^{2}=\) 11.26

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Answer:

x = 5

Step-by-step explanation:

Given

\(\frac{2}{6}\) = \(\frac{x}{15}\) ( cross- multiply )

6x = 30 ( divide both sides by 6 )

x = 5

The angles that are alternate exterior angles with angle 5 are <3 and <13 and <9

Alternate exterior angles are two angles that are on the exterior of and , but on opposite sides of the transversal

Conversely,  if two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel.

According to the theorem above, we can conclude that the angles that are alternate exterior angles with angle 5 are <3 and <13 and <9

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Answer: It was 2n-5=3 The other guy was right

Step-by-step explanation: I took the K12 test.

Answer:

b

Step-by-step explanation:

The symbol in the middle of b means greater than or equal to

Answer:

3

Step-by-step explanation:

105/7hrs

15/1hr

15/60min

0.25/per minute

0.25*12

= 3

Answer:

Solution given:

y+135°=180°[sum of opposite angle of a cyclic quadrilateral is supplementary]

y=180°-135°

y=25°

again

2x-1+3x+1=180°[sum of opposite angle of a cyclic quadrilateral is supplementary]

5x=180

x=180/5.x=36

x=36°,y=25°

Step-by-step explanation:

We know that m<1 = m<2 ( being alternate angels) So,

4+ 12x = 11x +12

12x - 11x = 12 - 4

x = 8

Therefore x = 8

Now

m<1 = 4 + 12 * 8

= 4 + 96

= 100

Hope this helps. :)

The z-score of a car that is 6 years old is  -0.625.

To find the z-score of a car that is 6 years old, we can use the formula:

z = (x - μ) / σ

where x is the value we are interested in (in this case, 6 years old), μ is the mean of the distribution (8 years), and σ is the standard deviation (3.2 years).

Plugging in the values, we get:

z = (6 - 8) / 3.2 = -0.625

Therefore, the z-score of a car that is 6 years old is -0.625. This indicates that the car is 0.625 standard deviations below the mean age of cars driven by employees at the company. Since the distribution is normal, we can use this z-score to find the probability of finding a car with an age of 6 years or less, using a z-table or a calculator.

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thanks, this is a answer (:

Answer: x = 0, Y = 2    

              x = 1, Y = 5

Step-by-step explanation:

Y = −3x^2 + 6x + 2

Y = 3x + 2

We can set the two equations equal to each other, since they both equal Y:

−3x^2 + 6x + 2 = 3x + 2

−3x^2 + 3x = 0

 3x(-x + 1) = 0

This gives us two possible solutions:

x = 0

x = 1

When x = 0, Y = 3(0) + 2 = 2

When x = 1, Y = 3(1) + 2 = 5

Therefore, the solutions to the system of equations are:

x = 0, Y = 2

x = 1, Y = 5

Answer:

D

Step-by-step explanation:

The sum to n terms of an arithmetic series is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 12, d = 4 and n = 30 , then

\(S_{30}\) = \(\frac{30}{2}\) [ (2 × 12) + (29 × 4) ]

     = 15(24 + 116)

     = 15 × 140

     = 2100 → D

The sum of the arithmetic series given a₁ =12, d = 4, and n = 30 is 2100, therefore the correct answer is D.

The sum of n terms of an arithmetic series can be easily found using a simple formula which says that, if we have an arithmetic series whose first term is a and the common difference is d, then the formula of the sum of n terms of the arithmetic series is as follows

Sn = n/2 [2a₁ + (n-1)d].

as given in the problem

a₁ =12, d = 4, and n = 30

Sn = 30/2 [2×12 + (30-1)×4]

    = 2100

The sum of the arithmetic series given a₁ =12, d = 4, and n = 30 is 2100.

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hello

\(\dfrac{-1}{x}\sqrt{2}=\dfrac{-\sqrt{2}}{\sqrt{3}-\sqrt{2}}=\dfrac{-\sqrt{2}(\sqrt{3}+\sqrt{2})}{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})}\\\\=\dfrac{-\sqrt{2}(\sqrt{3}+\sqrt{2})}{3-2}\\\\=-\sqrt{6}-2\)

hope this helps

A prism that has three rectangular faces. its other faces are in the shape of parallelograms.

What is a polygon?

A closed polygonal chain of connected line segments makes up a polygon, which is a plane figure. The edges or sides of a closed polygonal chain are the individual pieces. The polygon's vertices or corners are the places where two edges converge. A solid polygon's body is its inside.

Here, we have

Given: a prism that has three rectangular faces.

We have to find its other faces in the shape of.

We concluded that a prism is three-dimensional.

The faces of a prism are polygons. Two opposite faces, called bases, are equal or congruent.

The other faces are parallelograms.

Hence, a prism that has three rectangular faces. its other faces are in the shape of parallelograms.

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Answer:

i think b

Step-by-step explanation:

Answer: 4. 27x + 18            8. 4x - 5

Step-by-step explanation: should be right