Which of the values in the following data set would have a relative frequency of 30%? 10, 20, 20, 50, 30, 20, 10, 50, 60, 70

Answer:

1c       12
1d       4x - 3

2c      10x + 20
2d      60x² + 160x + 100

3c  
Domain is -3 ≤ x ≤ 3
Range is -2 ≤  g(x) ≤ 2

Step-by-step explanation:

Question 1 : f(x) = 2x - 3

Question 2: f(x) = 8x + 10, g(x) = 2x

The probability of getting no 1 and no 6 is 0.01%

There are six possible outcomes in a role. Since no 1 and 6 are to be rolled. There would only be 4 possible outcomes.

So, the chance of rolling no 1 and 6 is  

Since we have 5 rolls. Then we have:  1/6×1/6×1/6×1/6×1/6 =  =0.00013

Therefore, the probability of rolling no 1 and 6 is approximately 0.01%.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it's  that a proposition is true.

he probability of an occasion is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.[note 1]]  the upper the probability of an event, the more likely it's that the event will occur.  an easy example is the tossing of a fair (unbiased) coin. Since the coin is fair,  the 2  outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could even be written as 0.5 or 50%).

These concepts are given an axiomatic mathematical formalization in probability theory, which is employed widely in areas of study such as statistics, mathematics, science, finance, gambling,  AI, machine learning,  computing,  theory of games, and philosophy,  for instance, draw inferences about the expected frequency of events.  applied mathematics is also used to describe the underlying mechanics and regularities of complex systems.

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Answer:

282 [in²].

Step-by-step explanation:

all the details are in the attachment.

Answer:

37+69=106

180/106= 74

Step-by-step explanation:

its 74

Answer: 74°

Step-by-step explanation:

the two angles are first added

the sum of a triangle is 180° so the third angle equal 180- sum of angles.

37+69=106

180-106= 74°

The closing entries to record the given transaction is:  Debit Fees earned $75,000, Credit Income summary $75,000.

Adventure Travel journal entries

1. Debit Fees earned $75,000  

Credit Income summary  $75,000

2. Debit Income summary $60,360  

Credit Salaries expense  $32,800

Credit Rent expense  $16,800

Credit Depreciation expense-Office equipment  $3,960

Credit Advertising expense  $4,000

Credit Office supplies expense  $2,800

3. Debit  Income summary $14,640  

($75,000 - $60,360)

Credit A. Garcia, Capital  $14,640

4. Debit  A. Garcia, Capital $1,000  

Credit A. Garcia, Withdrawals $1,000

Therefore the closing entries to record the given transaction is:  Debit Fees earned $75,000, Credit Income summary $75,000.

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From the given diagram, the pair of angles that are non-adjacent and supplementary are given as follows:

5. FGH

6. LJM

Hence, we need one angle among vertices E, F, G and H, and other with vertices K, J, L, M, N, P, to guarantee the non-adjacency. The angles are:

5. FGH

6. LJM

As:

124 + 56 = 180º, meaning that they are supplementary.

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The claimed made by Lawrence Summers that the women have a lower standards deviation IQ than men is not correct since only 0.15% population has IQ score more than 145

IQ, or intelligence quotient, is a measure of your ability to reason and solve problems. It reflects how well you did on a specific test compared to other people of your age group. While tests may vary, the average IQ on many tests is 100, and 68% of scores lie between 85 and 115.

Given that, suppose an IQ of 145 or higher is required to be a researcher at a top notch research institution

Use the idea of standard deviation, the Empirical Rule, and the fact that the mean and standard deviation IQ of  humans is 100 and 15, respectively, to explain summer's argument.

Approximately 99.7% of the data will lie within 3 standard deviations of the mean. That is, approximately 99.7% of the data lie between α-3β and

IQ scores between = α-3β and α+3β

IQ scores = 100-3x15 and 100+3x15

                = 55 and 145

We can see that approximately 99.7% of the population has IQ scores between 55 and 145

only 0.15% population has IQ score more than 145

Hence the claimed made by Lawrence Summers that the women have a lower standards deviation IQ than men is not correct since only 0.15% population has IQ score more than 145.

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Answer:

Lawrence Summers' assertion that women have a lower IQ standard deviation than men is untrue because only 0.15% of the population has an IQ higher than 145.

Step-by-step explanation:

Lawrence Summers' assertion that women have a lower IQ standard deviation than men is untrue because only 0.15% of the population has an IQ higher than 145.

Your capacity for reasoning and problem-solving is measured by your IQ, or intelligence quotient. It displays how well you performed on a certain test in comparison to other individuals in your age group. The average IQ on several tests is 100, and 68% of scores fall between 85 and 115, notwithstanding test variations.

Given that, let's assume that a prestigious research institute requires researchers to have an IQ of at least 145.

Explain summer's contention using the concept of standard deviation, the Empirical Rule, and the facts that human IQ has a mean of 100 and a standard deviation of 15, respectively.

The data will be within 3 standard deviations of the mean in about 99.7% of the cases. In other words, 99.7% of the values fall between -3 and

IQ scores ranging from -3 to +3

IQ scores are 100 x 3 x 15 and 100 x 3 x 15.

= 55 and 145

We can observe that between 55 and 145 is the range in which 99.7% of the population falls.

Only 0.15 percent of people have an IQ higher than 145.

Since just 0.15% of the population has an IQ score higher than 145, Lawrence Summers' claim that women have a lower standard deviation IQ than men is untrue.

In 6A, 10.5 coulomb of charge is moved through the filament in 1.75 seconds.

The electrical current that flows across conducting wires is carried by electrons, which are tiny particles. Negatively charged particles are electrons.

Charge is expressed in coulombs, or C.

The charge of an electron is 1.6 x[tex]10^{-19}[/tex]C.

The connection between current I and charge amount Q

Charged particle flow is what makes up an electric current.

One ampere of current flows when one coulomb of charge passes through a certain place in a circuit once every second.

The magnitude of an electric current affects how quickly charges flow.

I =[tex]\frac{quantity of charge(Q)}{Time taken (t)}[/tex]

Given: current I= 6A at time t=1.75s,

I = Q / t

Q = I x t

Q = 6 x 1.75

Q =  10.5 coulomb

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Answer:

x=2

Step-by-step explanation:

All of the dimensions on the Left (hex) = all of the dimensions summed on the Right (tri)

6 (5x) =    x+14      +     x+17      + 8x+9

30x = 10x + 40

20x=40

x = 2

Answer:

x = 2

Step-by-step explanation:

6(5x) = x + 14+ x +17 + 8x +9

30x = (10x + 40)

Substrate 10x from both sides.

30x-10x = 30x-10x+40

20x = 40

Divide both sides by 20

x = 2

Therefore x = 2

To check out your work

the both sides are equal.

Substitute x for 2.

6(5x) = x + 14+ x +17 + 8x +9

60 = 60

Answer:

[tex] 5x + 3y = 15 [/tex]

Step-by-step explanation:

The x-intercept is 3, so the ordered pair of that point is (3, 0).

The y-intercept is 5, so the ordered pair of that point is (0, 5).

We need the equation of the line that passes through points (3, 0) and (0, 5). Also, from the y-intercept, we know that b = 5 in the slope-intercept form of the equation of a line,

y = mx + b

b = 5

We now have:

y = mx + 5

We can find the slope using the two given points.

[tex] m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{5 - 0}{0 - 3} = -\dfrac{5}{3} [/tex]

[tex] y = -\dfrac{5}{3}x + 5 [/tex]

Now we change the equation into standard form,

ax + by = c

[tex] y = -\dfrac{5}{3}x + 5 [/tex]

Multiply both sides by 3.

[tex] 3y = -5x + 15 [/tex]

Rearrange terms.

[tex] 5x + 3y = 15 [/tex]

The equation is 2x - 8 + 11 = x + 10

The value of x is 7

The value of RS is 6

The value of RT is 17

From the question, we are to write and solve an equation for x

From the given information,

RS = 2x - 8

ST = 11

RT = x + 10

From above, we can write that

RS + ST = RT

Thus,

2x - 8 + 11 = x + 10

Solve the equation for x

2x - 8 + 11 = x + 10

2x - x = 10 - 11 + 8

x = 7

∴ The value of x is 7

Now,

For the values of RS and RT

RS = 2x - 8

∴ RS = 2(7) - 8

RS = 14 - 8

RS = 6

and

RT = x + 10

RT = 7 + 10

RT = 17

Hence,

The equation is 2x - 8 + 11 = x + 10

The value of x is 7

The value of RS is 6

The value of RT is 17

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Answer: -3

Step-by-step explanation: -33 ➗11= -3

Amplitude and period of y = 1 + cos 0 are amplitude: = 1 and period:  2π respectively.

The cosine function cosx is one of the basic functions encountered in trigonometry

y = 1 + cos 0

Rewrite the expression as

−cos(x)+1.

Use the form

acos(bx−c)+d

To find the variables used to find the amplitude, period, phase shift, and vertical shift.

a =-1

b =1 = d

c=0

Find the amplitude

Let

Amplitude: = 1

Phase Shift:  = 0

List the properties of the trigonometric function.

Amplitude: 1

Period:  2π

Phase Shift: None

Vertical Shift: 1

So the amplitude and period of the equation y = 1 + cos 0 are 1 and 2 correspondingly.

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The amplitude and period of the equation y = 1 + cos 0 are 1 and 2 correspondingly.

The cosine formula One of the fundamental trigonometry functions is cosx.

y = 1 + cos 0

Change the wording to

−cos(x)+1.

Apply the form

acos(bx−c)+d

to identify the parameters used to calculate the vertical shift, phase shift, amplitude, and period.

a =-1

b =1 = d

c=0

Measure the amplitude.

Let

Amplification: 1

0 for phase shift

Describe the trigonometric function's characteristics.

1 amplitude

Duration: 2

No phase shift

Shift Vertically: 1

As a result, y = 1 + cos 0 has an amplitude and period of 1 and 2, respectively.

The elasticity of supply for dog food is 25.71

Price elasticity of supply measures the responsiveness of quantity supplied to changes in price of the good.

Price elasticity of supply = midpoint change in quantity supplied / midpoint change in price  

Midpoint change in quantity supplied = change in quantity supplied / average of both supply

change in quantity supplied= 101 - 35 = 66

average of both supply = (101 + 35 ) / 2 = 68

Midpoint change in quantity supplied = 66 / 68 = 0.97

Midpoint change in price = change in price / average of both price

Change in price = 6.75 - 6.50 = $0.25

Average of both price = (6.75 + 6.50) / 2 = $6.625

Midpoint change in price = 0.25 / 6.625 = 0.03774

Price elasticity of supply =  0.97 / 0.03774 = 25.71

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Answer:

Step-by-step explanation:

The original one is false, with the answer being 84.

(a) The greatest number of boxes she can use so that each box contains the same number of pencils and pens is 48.

(b) There will be 48 pencils and pens in each box.

We have given that Tamika has 48 pencils and 80 pens.

So, the greatest number of boxes is 48, because the total number of pencils is 48, in order to share the same number of pencils and pens, the greatest number of boxes would be 48.

And,

Based on above answer and according to question's statement (each box contains the same number of pencils and each box contains the same number of pens), so, there will be one pencil and one pen in each box.

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The turning point of the function f(x) = |x| + 4 lie on the y - axis and has coordinates (0, 4).

A stationary point is called a turning point if the derivative changes sign (from positive to negative, or negative to positive  ) at that point. There are two types of turning points - local maxima and local minima.

Given in the question is a modulus function -

f(x) = |x| + 4

In order to determine the turning point, we will first have to plot the graph of this function -

f(x) = |x| + 4

Now, we can write f(x) as -

f(x) = { (x + 4)  for x ≥ 0    and       (- x + 4) for x < 0} }

Alternatively, you can plot the graph of |x| and positive shift it by 4 units. Refer to the graph attached with the answer. From the graph you can see that after the coordinate (0, 4) the slope becomes positive. Slope of a line gives the rate of change of y with respect to x. So (0, 4) represents the turning point.

Therefore, the turning point of the function f(x) = |x| + 4 lie on the y - axis and has coordinates (0, 4).

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Answer:

Slope(green box) = -3

Intercept(grey box) = 8

Step-by-step explanation:

To determine the best equation to represent the given pattern, we need to find two things.

First: we need to figure out the slope of the function, or in other words, how much the y value changes by each time the x value changes.

Second: we need to find the y-intercept, which is the value of y when x = 0. This value will be the constant of the function which is added to the equation each time.

To start, let's analyze the pattern to find the slope of the function...

As the x -values go up by 1 each time, the y-values are as follows:

5 --> 2 --> -1 --> -4 --> -7

It looks like the numbers decrease by 3 each time, so we can safely assume our slope is -3.

Now, let's find our intercept. We can do this by going to our lowest x value, and adding 3 (opposite direction of our slope) from its y-value to find the y-value of x = 0.

So...

When x = 1, y = 5

5 + 3 = 8

So when x = 0, y = 8, our intercept!

Answer:

(2,0)

Step-by-step explanation:

Answer:

2,0

Step-by-step explanation:

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The type of reasoning for each statement is as follows:

Deductive reasoning is the type of reasoning that follows a more general statement to reach a specific conclusion. The conclusions of inductive reasoning is most likely true. This is the type of reasoning used in mathematics.

Inductive reasoning uses a more specific statement and arrive to a general conclusion. It is goes from bottom to up. The conclusion here is strongly persuasive to be true but still has false probability

For instance, in the second statement "Every Tuesday that Yolanda's family has visited a specific local restaurant, the kids' meals have been free" This does not logically mean the kids' meal is free but it is assumed to be free as it has been happening. more like taking a specific events that has happened for a while and assume it will always be so.

Abductive reasoning is the type of reasoning that follows an incomplete observation to reach a more likely conclusion. The conclusions of abductive reasoning is more of a probability. This is the type of reasoning used in used in our day to day events.

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Considering the equations of a circle and of a parabola, we have that:

a) Tunnel A is a circle, with it's radius meaning that both the width and the height are of 12.

b) Tunnel B is a parabola, with it's vertex and it's roots meaning that it has a width of 32 feet and a height of 16 feet.

c) The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

For Tunnel A, the equation is given by:

x² + y² + 28x + 52 = 0

Completing the squares:

(x + 14)² + y² = -52 + 14²

(x + 14)² + y² = 144.

Hence:

Tunnel A is a circle, with it's radius meaning that both the width and the height are of 12.

A parabolic(quadratic) equation is modeled by:

y = ax^2 + bx + c

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

For Tunnel B, the equation is given as follows:

x² - 36x + 16y + 68 = 0.

16y = -x² + 36x - 68.

Simplifying by 16:

y = -0.0625x² + 2.25x - 4.25.

Hence the coefficients are a = -0.0625, b = 2.25, c = -4.25, and the maximum height is:

[tex]y_v = -\frac{(2.25)^2 - 4(-0.0625)(-4.25)}{(-0.0625)} = 16[/tex]

The width is the difference between the roots, which, using a calculator, are:

2 and 34, hence the width is of 32 feet, as 34 - 2 = 32.

Hence:

Tunnel B is a parabola, with it's vertex and it's roots meaning that it has a width of 32 feet and a height of 16 feet.

For item c, considering the previous items, we have that:

The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.

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The value of the x-intercept is -6

According to the question we have been the equation which is :

                      2y - 5x = 30  (1)

The general expression of slope intercept form is given as :

                 y = mx + c

  where, m = slope

              c = y-intercept

To find the value of x-intercept we will write equation (1) as an equation for x that is

              -5x =-2y + 30

Dividing both the sides by -5 we get

               x = 2/5y + (-6)

Which is in the form of slope intercept form which is

                x = my + c   and the x- intercept will be c = -6

Hence the x-intercept is -6

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The expression on the table shows that the shelf pace that the books take is 1 inch per book.

Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

It should be noted that from the table, the relationship between the books and the inches is illustrated on the table.

Relationships between two variables that are proportional occur when their ratios are equal. Therefore, this is a proportional relationship and is illustrated as:

= 2/2

= 1

Therefore, there's 1 inch per book.

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Answer:

O If a ray bisects an angle, then it divides it into two congruent angles.

Step-by-step explanation:

Answer:

  y = 16(x +2)

Step-by-step explanation:

The equation of the tangent to a curve at a point can be written using the point-slope form of the equation for a line. The point is (x, f(x)), and the slope is the derivative, f'(x).

The point where you want the tangent line has y-value ...

  y = 2(-2)³ -8(-2) = 2(-8)+2(8) = 0 . . . . . point (x, y) = (-2, 0)

The slope at the point where you want the tangent is ...

  y' = 2·3x² -8 = 6(-2)² -8 = 24 -8 = 16 . . . . . slope m = 16

The point-slope equation of a line is ...

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

  y -0 = 16(x -(-2)) . . . . . line with slope 16 through (-2, 0)

  y = 16(x +2) . . . . . simplified

An equation of the tangent line is ...

  y = 16(x +2)

Answer:

Step-by-step explanation:

You want the perimeter and area of the given composite figure.

You will notice that the sum of vertical lengths on the right side of the figure has the same total as the vertical length on the left side:

  2 + 1 + 1 = 4 . . . . units high

Likewise, the horizontal lengths at the top of the figure have the same total as the horizontal length at the bottom:

  4 + 1 + 4 = 9 . . . . units wide

The perimeter is the sum of all side lengths, so is ...

  P = 2(L+W) = 2(9 +4) = 26

The perimeter of the polygon is 26 units.

The blue lines in the attachment show the area can be divided into rectangles whose area is easily computed. The top rectangle has a width of 4 units and a height of 2 units, so its area is ...

  A = WH = (4)(2) = 8 . . . . square units

The middle rectangle has a width of 5 units and a height of 1 unit, so its area is ...

  A = WH = (5)(1) = 5 . . . . square units

The bottom rectangle has a width of 9 units and a height of 1 unit, so its area is ...

  A = WH = (9)(1) = 9 . . . . square units

The total area of the polygon is the sum of the areas of its parts:

  area = top rectangle + middle rectangle + bottom rectangle

  = (8 + 5 + 9) square units = 22 square units

The area of the polygon is 22 square units.

The horizontal line passing through the point (2/3, 1/2) is represented by the equation y = 1/2.

y=mx+c

where m is the slope.

As stated in the problem the line is horizontal. This means that its slope is zero.

y-y1=m(x-x1)

y-1/2=0(x-2/3)

y-1/2=0

y=1/2.

Mathematically it means that it is a line parallel to the x-axis and passing through y = 1/2.

The horizontal line passing through the point (2/3, 1/2) is represented by the equation y = 1/2.

Therefore  horizontal line passing through the point (2/3, 1/2) is represented by the equation y = 1/2.

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The cost of fencing the garden is 2601 dollars.

The area of the garden is 289 square feet.

The fencing cost 9 dollars per square feet's.

Therefore, the cost to fence a garden with area of 289 square feet can be calculated as follows:

Hence,

1 square feet's = 9 dollars

289 square feet = ?

cross multiply

Hence,

cost of fencing the garden = 9 × 289

cost of fencing the garden = 2601

cost of fencing the garden = 2601 dollars

Therefore, the cost of fencing the garden is 2601 dollars.

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