A normal distribution has a mean of 101 and a standard Deviation of 12. find the probability that a value selected at random is in the following interval.at most 13

Answer:

  0.5

Step-by-step explanation:

The sides opposite and adjacent to the given angle are shown in this right triangle. The relation between them is given by the tangent trig function:

  Tan = Opposite/Adjacent

  tan(63°) = 1/x

We can multiply this equation by x/tan(63°) to find the value of x:

  x = 1/tan(63°) ≈ 1/1.96261 ≈ 0.509525

The length x is about 0.5 units.

Given:

The equation of a parabola is:

\(y=(x+2)^2-1\)

To find:

The coordinates of the vertex of the given equation.

Solution:

The vertex form of a quadratic function is:

\(y=a(x-h)^2+k\)               ...(i)

Where, a is a constant and (h,k) is the vertex.

We have,

\(y=(x+2)^2-1\)                 ...(ii)

On comparing (i) and (ii), we get

\(a=1\)

\(h=-2\)

\(k=-1\)

We know that the vertex of the parabola is (h,k).

Therefore, the vertex of the given equation is (-2,-1).

Answer: I think it is false...

Answer:

\(\sqrt{13}\)

Step-by-step explanation:

we can solve this using the distance formula: \(\sqrt{(x_{2}-x_1)^{2} + (y_{2}-y_1)^{2}}\)

\(x_1, y_1\) is (3, 1)

\(x_2, y_2\) is (-1, -2)

\(\sqrt{(1-3)^2 + (-2-1)^2}\)

which simplifies to: \(\sqrt{(-2)^2 + (-3)^2}\)

then: \(\sqrt{2^2 + 3^2}\) or: \(\sqrt{4+9}\)

your final answer is: \(\sqrt{13}\) or about 3.61

The difference between their yearly incomes is $31,304.

To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:

For the student who drops out of high school:

Yearly Income = Weekly Income x Number of Weeks

= 451 x 52

= 23,452

For someone with a bachelor's degree:

Yearly Income = Weekly Income x Number of Weeks

= 1053 x 52

= 54,756

The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:

Difference = Bachelor's Yearly Income - Student's Yearly Income

= 54,756 - 23,452

= 31,304

Therefore, the difference between their yearly incomes is $31,304.

It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.

Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.

For more such answers on incomes

https://brainly.com/question/28414951

#SPJ8

Answer:

Step-by-step explanation:

from the figure and the measurements it is a square, the diagonals are perpendicular and form 4 angles of 90°, so 90° is your answer.

9514 1404 393

Answer:

  c. 11

Step-by-step explanation:

The sum of all 6 numbers is ...

  6 × average of 6 = total of 6

  6 × 6 = 36 = total of 6

Then the remaining number is ...

  total of 5 + sixth number = total of 6

  25 + sixth number = 36

  sixth number = 36 -25 = 11

The total area of the garden is given as follows:

52 ft².

The area of a rectangle of length l and width w is given by the multiplication of these dimensions, as follows:

A = lw.

For the new rectangle, the dimensions are given as follows:

Hence the area of the new part is of:

A = 4 x 8

A = 32 ft².

Considering the previous part of 20 ft², the total area is given as follows:

32 + 20 = 52 ft².

More can be learned about the area of a rectangle at https://brainly.com/question/25292087

#SPJ1

Answer:

the angle between u=(8, -2) and v=(9,3) is 32.5°

Step-by-step explanation:

u=(8,-2)=(u1,u2)→u1=8, u2=-2

v=(9,3)=(v1,v2)→v1=9, v2=3

We can find the angle between two vectors using the formula of dot product:

u . v =║u║║v║cos α   (1)

And the dot product is:

u . v = u1 v1 + u2 v2

u . v = (8)(9)+(-2)(3)

u . v = 72-6

u . v = 66

║u║=√(u1²+u2²)

║u║=√((8)²+(-2)²)

║u║=√(64+4)

║u║=√(68)

║u║=√((4)(17))

║u║=√(4)√(17)

║u║=2√(17)

║v║=√(v1²+v2²)

║v║=√((9)²+(3)²)

║v║=√(81+9)

║v║=√(90)

║v║=√((9)(10))

║v║=√(9)√(10)

║v║=3√(10)

Replacing the known values in the formula of dot product (1):

u . v =║u║║v║cos α

66 = 2√(17) 3√(10) cos α

Multiplying:

66 = 6√((17)(10)) cos α

66 = 6√(170) cos α

Solving first for cos α: Dividing both sides of the equation by 6√(170):

Simplifying: Dividing the numerator and denominator on the left side of the equation by 6:

(66/6)/(6√170/6)=cosα→11/√170=cosα→cosα=11/√170

cosα=11/13.03840481→cosα=0.84366149

]

Answer:

Log 8 (5) + 6 log 8 (x) - Log 8 (y)

Step-by-step explanation

expand 5x^6 =  Log 8(5) + 6log

if its multiplication, its +

if its division its -

Answer:

Step-by-step explanation:

shaded area=6×1=6 sq. units

whole area=10×10=100 sq. units

reqd. =6/100 ×100=6 %

Answer:

\(\textsf{C)} \quad -\dfrac{3}{2}\)

Step-by-step explanation:

To find the average rate of change of a function over an interval, we can use the formula:

\(\boxed{\begin{minipage}{6.3 cm}\underline{Average rate of change of function $f(x)$}\\\\$\dfrac{f(b)-f(a)}{b-a}$\\\\over the interval $a \leq x \leq b$\\\end{minipage}}\)

In this case, the interval is [4, 8], so:

From inspection of the given graph:

Substitute the values into the formula to calculate the average rate of change:

\(\begin{aligned}\text{Average rate of change}&=\dfrac{h(8)-h(4)}{8-4}\\\\&=\dfrac{3-9}{8-4}\\\\&=\dfrac{-6}{4}\\\\&=-\dfrac{3}{2}\end{aligned}\)

Therefore, the average rate of change of h(x) over the interval [4, 8] is -3/2.

Answer:

459.54

Step-by-step explanation:

46(9.99)

=459.54

Answer:

$159.89

Step-by-step explanation:

36 hours + 10 hours = 46

14.99 * 10 = 149.9

(36 hours) $9.99 + (overtime pay) $149.9 = (Total money) $159.89

$9.99 + $149.9 = $159.89

$159.89

Answer:

4096 different cakes can be made if flavors can be repeated.

Step-by-step explanation:

Since at Misu's Ice Cream Parlor, their famous 4-layer ice cream cake consists of four layers of ice cream alternating with layers of cake, if there are 8 flavors of ice cream, and we count different cakes based on the order of ice cream Layers from top to bottom, to determine how many different cakes can be made if flavors can be repeated, the following calculation must be performed:

8 x 8 x 8 x 8 = X

64 x 64 = X

4.096 = X

Therefore, 4096 different cakes can be made if flavors can be repeated.

Answer:

65

Step-by-step explanation:

Hi,

Triangles will always add up to 180 degrees. So, 62 + 53 = 115. Subtract it from 180, 180 - 115, and you get 65.

I hope this helps :)

Answer:

65

Step-by-step explanation:

The sum of the three angles of any triangle is equal to 180 degrees

The first derivative of y with respect to x is d(y)/dx = 4t² + 10t, and the second derivative of y with respect to x is d(2y)/dx² = 8t + 10.

Differential equations are mathematical equations that describe how a function changes over time or with respect to its inputs.

Let x = t² + 3 and y = t² + 5t. We want to find the derivatives of y with respect to x, which means we need to use the chain rule.

The chain rule states that if y = f(u) and u = g(x), then the derivative of y with respect to x is given by

=> d(y)/dx = d(y)/du * du/dx.

First, we will find the derivative of y with respect to t, which is given by

=> d(y)/dt = 2t + 5.

Next, we will find the derivative of x with respect to t, which is given by

=> d(x)/dt = 2t.

Finally, we will multiply these two derivatives to find the derivative of y with respect to x, which is given by

=> d(y)/dx = (2t + 5)(2t) = 4t² + 10t.

Next, we will find the second derivative of y with respect to x, which is given by

=> d(2y)/dx² = d((4t² + 10t))/dt = 8t + 10.

To know more about differential equation here.

https://brainly.com/question/30074964

#SPJ4

The appropriate hypotheses for this test are: H0: There is no difference in the distribution of responses. Ha: There is a difference in the distribution of responses.

The chosen hypotheses are based on the objective of the investigation, which is to determine if there is convincing evidence that the distribution of responses about eating the potato salad differs between employees who are sick and those who are not sick.

The null hypothesis (H0) assumes that there is no difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This means that the proportion of employees who ate the potato salad would be the same in both groups, and any observed difference in the distribution of responses is due to random chance or factors unrelated to being sick or not sick.

On the other hand, the alternative hypothesis (Ha) proposes that there is a difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This suggests that the proportion of employees who ate the potato salad would be significantly different in the two groups, indicating a possible association between consuming the potato salad and getting sick.

By formulating these hypotheses, the investigation aims to evaluate whether the data provides convincing evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating a meaningful relationship between eating the potato salad and falling sick.

Therefore, the correct answer is:

H0: There is no difference in the distribution of responses about eating the potato salad among those who are and are not sick.

Ha: There is a difference in the distribution of responses about eating the potato salad among those who are and are not sick.

For more such questions on hypotheses , Visit:

https://brainly.com/question/25263462

#SPJ11

Answer:

show the whole question

Step-by-step explanation:

Therefore, the volume of the composite figure is 105 cubic inches.

In physics and mathematics, volume refers to the amount of space occupied by a three-dimensional object or region. It is a measure of the size of an object in three dimensions, and is typically expressed in cubic units, such as cubic meters, cubic feet, or cubic centimeters. The volume of an object can be calculated using a formula that is specific to the shape of the object. For example, the volume of a cube can be calculated by multiplying the length, width, and height of the cube, while the volume of a sphere can be calculated using the formula 4/3 x π x r^3, where r is the radius of the sphere. The concept of volume is important in many fields, including architecture, engineering, and science, as it is used to calculate the amount of space that an object or substance occupies, and to determine quantities such as mass and density.

Here,

To find the volume of the composite figure, we need to find the volume of each rectangular prism and add them together.

The volume of a rectangular prism is given by the formula V = l*w*h, where l is the length, w is the width, and h is the height.

For Prism A, V = (7)(3)(2) = 42 cubic inches.

For Prism B, V = (3)(3)(7) = 63 cubic inches.

The total volume of the composite figure is the sum of the volumes of the two prisms:

V_total = V_A + V_B

= 42 + 63

= 105 cubic inches

To know more about volume,

https://brainly.com/question/12237641

#SPJ1

Answer:

x ≈ 62°

Step-by-step explanation:

By applying tangent rule in the given right angled triangle,

tan(x) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(x) = \(\frac{15}{8}\)

tan(x) = 1.875

x = \(\text{tan}^{-1}(1.875)\)

x = 61.93

x ≈ 62°

6. 2 x + y = 14

7. 2 y - 3 x = 8

Also ask one question at a time pls

The product of 5 × 5ab × 5, a, b is 125ab5 when written in its most Simple form

The expression 5 × 5ab × 5, a, b is equal to 125ab5. The reasoning is that when we multiply 5 by 5ab, we get 25ab, which we then multiply by 5 to get 125ab. Since a, b are variables, the product 125ab5 is the product of 5 × 5ab × 5, a, b, when written in its most simple form.

The expression 5 × 5ab × 5, a, b is an algebraic expression, which consists of numbers, variables, and operators. Variables are usually represented by letters or other symbols, while operators such as +, -, ×, ÷, ^ are used to indicate mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. In algebra, expressions can be simplified by combining like terms, expanding brackets, and applying other rules of arithmetic.

The most simple form of an expression is the one that cannot be further simplified.In the given expression, 5 × 5ab × 5, a, b, we can see that the number 5 appears three times, so we can simplify the expression by multiplying the numbers together.

Similarly, we can multiply the variables a and b together to get the term ab. Finally, we write the result as 125ab5, which is the product of 5 × 5ab × 5, a, b, in its most simple form.

Therefore, the product of 5 × 5ab × 5, a, b is 125ab5 when written in its most simple form.

For more questions on  Simple form.

https://brainly.com/question/27624273

#SPJ8

Answer:

Step-by-step explanation:

Volume = Bh

Turn the shape so the trapezoid is on the bottom/base

h=18   for overall shape

B = area of base, trapezoid

B = 1/2 (b₁ + b₂) h  

b₁ = 11

b₂ = 25

h = 24   for trapezoid

B = 1/2 (11 + 25)(24)

B = 432

V = Bh

V = (432)(18)

V= 7776 in³

The meaning of the situation involving the camp director and the sack lunches, is D. The number of lunches left over after packing the boxes.

The remainder in this instance, shows the number of lunches that the camp director will not be able to fit in boxes and so will be left over after the boxes have been packed.

There are 85 sack lunches and yet only 3 lunches can go into a single box. The number of boxes would be:

= 85 / 10

= 10 boxes remainder 5 lunches

10 boxes will be filled with lunch sacks and 5 lunches will be leftover.

Find out more on remainders at https://brainly.com/question/29347810

#SPJ1

The full question is:

The camp director is putting 85 sack lunches in boxes for a picnic. She can fit 8 lunches in each box. She does the division problem shown to find out how many boxes she will need. 85 divided 8 = 10 remainder 5

What is the meaning of the remainder in this situation?

A. The number of extra boxes needed.

B. The number of extra lunches needed.

C. The number of boxes left over after packing the lunches.

D. The number of lunches left over after packing the boxes.

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

Learn more about real return and stocks here: https://brainly.com/question/32228847

#SPJ1

Solutions of these equations is y < - x / 140x + 23 / 140x

Graphs present information to you as a picture or visual representation. This knowledge is referred to as "data." Graphs come in a wide variety of forms. You can compare various data sets using bar graphs. Small dots are used in line graphs to represent the data, and a line is drawn between the dots to indicate what happens to the data.

4x . 35y < - x + 23

4x . 35y + (x-23) < (-x+23) + (x-23) (x-23)

4x .35y + x-23 < -x + 23 + x -23

4x .35y + x-23 < -x + x + 23-23

The formula is as follows: 140xy + x-23 0 140xy + x-23 0 (140xy +x-23) + (-x + 23) -x + 23 140xy + x -23 -x +23 +23 < - x +23\s140xy <-x +23

140xy/140x/(-x +23)/140xy/(-1/140x)+23/140xy/(-x)/140xy/(-x)/140x +23/140x

To learn more about graph refer to:

https://brainly.com/question/19040584

#SPJ1

Answer:

d. 1/4

Step-by-step explanation:

comment if u need explanation

Answer:

it's D. 1/4

Step-by-step explanation: hope that helps

Given:

To determine whether the function is even, odd, or neither:

Put x=-x

we get,

Since,

Hence, this given function is neither odd nor even function.

Therefore, the answer is neither.