The teacher gave a true and false quiz where P(true) = 0.5 for each question. Interpret the likelihood that the first question will be true.

Likely.
Unlikely.
Equally likely and unlikely.
This value is not possible to represent probability of a chance event.

Answer:

  A.  P

Step-by-step explanation:

You want to identify the point that represents a striking deviation in the given box plot.

The interquartile range for this box plot is the difference between the upper and lower quartiles:

  29 -26 = 3

The "fence" that is 1.5 times the IQR below the lower quartile is ...

  26 -3·1.5 = 21.5

Point P lies beyond this fence, so is considered an outlier in the data set.

Point P represents a striking deviation, choice A.

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The type of pay modeled in the given image is c. Commission pay.

Commission pay is a form of variable pay where the employee is paid based on the percentage of sales that they make. In this case, the y-axis represents the pay earned and the x-axis represents the sales made.

The straight line represents the commission rate, which is constant at 15%. The more sales the employee makes, the more pay they will earn.

Therefore the correct option is C.

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The ratio of the two arc lengths is equal to a / b. (Correct choice: B)

In this problem we must determine the ratio of two arc lengths, that is, the ratio between two circular arcs. The length of a circular arc is described by the following expression:

s = θ · r

Where:

s - Arc length

θ - Angle, in radians.

r - Radius

And the ratio of the length JK to the length MN is:

JK / MN = (θ · a) / (θ · b)

JK / MN = a / b

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As a result, the right response is s(23), which can be written as [tex]8s^3[/tex] as to calculate a shipping box's volume is based on the box's dimensions.

A tri object's volume is a measurement of how much space it takes up. The usual measurement tool is a cubic unit, such as a cubic metre (m3) or cubic foot (ft3). The formula used to determine a solid item's volume depends on the shape of the object. For instance, the volume of a cube is determined by multiplying the length of a single of its sides by six, whereas the capacity of a cylinder is determined by dividing the area of its base by the diameter. Engineering, mathematics, and architecture are just a few of the disciplines where the idea of volume is crucial.

given

The formula used to calculate a shipping box's volume is based on the box's dimensions.

The box's volume can be expressed as follows if its side length is s:

[tex]V = s^3[/tex]

As a result, the right response is s(23), which can be written as [tex]8s^3[/tex] as to calculate a shipping box's volume is based on the box's dimensions.

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A principal of $1,380.89 will earn $55.99 interest at 9.75% from February 4, 2021, to July 6, 2021.

To calculate the interest earned by a principal at a given interest rate over a certain period of time, we use the following formula:

Interest = Principal x Rate x Time

In this case, we need to find the principal, so we can rearrange the formula as follows:

Principal = Interest / (Rate x Time)

First, we need to calculate the time period in years between February 4, 2021, and July 6, 2021.

February 4, 2021 to July 6, 2021 is 152 days or approximately 0.416 years (calculated as (July 6, 2021 - February 4, 2021) / 365).

Principal = 55.99 / (0.0975 x 0.416) = $1,380.89 (rounded to the nearest cent)

Therefore, a principal of $1,380.89 will earn $55.99 interest at 9.75% from February 4, 2021, to July 6, 2021.

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Answer:w = 74.66 mph

d = 19.92 degrees

Step-by-step explanation:

Let's call the speed of the wind "w" and the direction angle of the wind "d". We can use vector addition to solve for these unknowns.

First, let's find the direction of the plane. The bearing of N * 65 deg * E can be represented as a vector with an initial point at the North pole and a terminal point 65 degrees east of due north. Since the plane is flying on this bearing, its direction vector is the same as the bearing vector. We can find the components of this vector as follows:

cos(65) = x / 1

x = cos(65)

y = sin(65)

So the direction vector of the plane is <cos(65), sin(65)>.

Next, let's find the ground speed vector. We can represent this vector as the sum of the plane's airspeed vector and the wind vector:

ground speed = airspeed + wind speed

We know that the magnitude of the ground speed vector is 390 mph, and we know the direction angle of the ground speed vector is 30 degrees. We can use this information to set up two equations:

|airspeed + wind speed| = 390

tan(d) = (wind speed)_y / (wind speed)_x

Since we know the direction vector of the plane, we can express the airspeed vector in terms of this vector as follows:

airspeed = 360 <cos(65), sin(65)>

Now we can substitute the airspeed vector and the wind speed vector into the equation for the ground speed vector, and use the fact that the magnitude of the ground speed vector is 390 to solve for the components of the wind speed vector:

|360 <cos(65), sin(65)> + <(wind speed)_x, (wind speed)_y>| = 390

Squaring both sides and using the fact that cos^2(x) + sin^2(x) = 1, we get:

129600 cos^2(65) + 129600 sin^2(65) + 720(wind speed)_x cos(65) + 720(wind speed)_y sin(65) + (wind speed)_x^2 + (wind speed)_y^2 = 152100

Simplifying, we get:

51840 + 720(wind speed)_x cos(65) + 720(wind speed)_y sin(65) + (wind speed)_x^2 + (wind speed)_y^2 = 152100

Substituting the equation for the direction angle of the wind and simplifying, we get:

51840 + 720w cos(65 - d) + w^2 = 152100 tan^2(d)

We now have two equations and two unknowns: w and d. We can solve for them using algebra or a numerical solver. Using a numerical solver, we find:

w = 74.66 mph

d = 19.92 degrees

Therefore, the speed of the wind is 74.66 mph, and its direction angle is 19.92 degrees.

Answer:

5%

Step-by-step explanation:

Percent error equation is:

(Absolute value of experimental value - actual value / actual value) * 100

Experimental Value: 315

Actual Value: 300

315 - 300 / 300 = 0.05

0.05*100 = 5

Percent error is 5%

Answer: the percent error is 5%

Step-by-step explanation:

Answer:

surface area=bh+2ls+lb

Step-by-step explanation:

If you think it is too long to remember, just find the area of each of the shapes on it and add them together.

Hope this helps :)

Answer:

9ft

Step-by-step explanation:

From the left side, you know one length is 4ft abd the one below is 5ft, when you add them together its the answer of 9ft, which is the missing side.

it's 9ft

its 9ft because when you add 4 +5 you get 9. two rectangles a present in the diagram. the 4ft and 5ft are apart of the rectangle where the missing side is, adding those two together would give you 9 and in a rectangle sides facing each other are epual therefore the missing side is 9

Answer:

x = 3,

y = -2

Step-by-step explanation:

Let's write the given equations into a system:

{2x - y = 8,

{3x + 2y = 5;

Let's make y the subject from the 1st equation:

-y = 8 - 2x / × (-1)

y = 2x - 8

Replace y in the 2nd equation with its value from the 1st one:

3x + 2(2x - 8) = 5

Expand the brackets:

3x + 4x - 16 = 5

Collect like-terms:

7x = 5 + 16

7x = 21 / : 7

x = 3

y = 2 × 3 - 8 = -2

Answer:

x2+10x+25

Step-by-step explanation:

It goes like this:

X2+2*1x*5+5*5

If local supermarket offers a pack of 12 sodas for $3.48 on sale, and the local discount warehouse offers the soda in a 36-can case for $11.52, In terms of price per soda, the supermarket pack is the better value.

To determine which is the better value between the supermarket pack of 12 sodas for $3.48 and the discount warehouse 36-can case for $11.52, we need to calculate the price per soda for each option.

For the supermarket pack, the price per soda can be found by dividing the total cost by the number of sodas in the pack:

Price per soda = $3.48 / 12 = $0.29

For the discount warehouse case, the price per soda can be found by dividing the total cost by the number of sodas in the case:

Price per soda = $11.52 / 36 = $0.32

From these calculations, we can see that the price per soda is lower for the supermarket pack at $0.29 compared to $0.32 for the discount warehouse case. Therefore, in terms of price per soda, the supermarket pack is the better value.

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Ilana ran a total distance of 23.725 miles during her first week of training for a half marathon.

Distance refers to the amount of space or physical separation between two points or objects. It is a measure of how far apart two objects or points are from each other.

Ilana will run 4.125 miles each day for the first three days, which gives a total distance of:

4.125 miles/day × 3 days = 12.375 miles

For the next two days, she will run 5.675 miles per day, which gives a total distance of:

5.675 miles/day × 2 days = 11.35 miles

To find the total distance that Ilana ran during her first training week, we simply add the distances from the first three days and the next two days:

12.375 miles + 11.35 miles = 23.725 miles

Therefore, Ilana ran a total of 23.725 miles during her first week of training.

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A linear function would best fit the data because as x increases, the y values change by an approximate constant. The rate of change of this function is approximately 8950 people a year.

To determine which type of function best fits the data, we can analyze the difference in the y values (Estimated Population) as x increases.

Differences between consecutive y values:

58,207 - 49,372 = 8,835

66,998 - 58,207 = 8,791

75,798 - 66,998 = 8,800

The differences between consecutive y values are relatively constant as x increases. This suggests that a linear function would be more appropriate than an exponential function

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The simplified expression based on tej values given is 3a⁴b + 4a³b³.

An expression is a combination of variables, constants, and operators that can be evaluated to produce a single value. In programming languages, expressions are used to represent computations and are often used to assign values to variables, compare values, or perform mathematical operations. Expressions can be simple, such as a single variable or constant, or complex, involving multiple operations and variables.

It should be noted that to simplify the expression a²b(3a² +4ab²), we can distribute the a²b term to the terms inside the parentheses using the distributive property of multiplication:

a²b(3a² +4ab²) = 3a⁴b + 4a³b³

Therefore, the simplified expression is 3a⁴b + 4a³b³.

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If the number 48700 is written in scientific notation, it will be in form 4.87×10ⁿ, and the value of n is 4.

Scientific notation describes the shorthand way of writing very large or very small numbers in standard forms.

Writing in scientific notation, a number between 1 and 10 is multiplied by a power of 10.

48700 = 4.87×10ⁿ = 4.87×10⁴

Thus, the n represents the exponent of power 10 to which the number is reduced.

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The proof that angles D and E are congruent is added below

From the question, we have the following parameters that can be used in our computation:

∠CDB and ∠CEB are inscribed in a circle A.

The general rule is that angles that are inscribed in the same arc are congruent.

So, we have the following two column proof

Statements                                     Reasons

∠CDB = ∠CEB                                Given

Segments BD = CE                         CPCTC

Segments BE = CD                         CPCTC

Arcs BE = CD                                   Corresponding arcs

∠D = ∠E                                           Corresponding angles

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Based on the image, we can infer that the router cannot cover the kitchen area.

To calculate if the router covers the living room and kitchen area, we must identify the area that the router can cover. In this case, the router covers an area of 850 square feet. However, we must take into account that this area is counted around the router.

From the above, we can infer that the router has signal coverage of 14 meters around it, so it would only cover the living room area.

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The probability of Caleb selecting a 5 on the first selection and then selecting a 5 on the second selection after returning the card to the deck and shuffling is 1/9.

There are a total of 12 cards, out of which 4 are 5s. Since Caleb returns the card to the deck and shuffles it, the selection of the first card does not affect the probability of selecting a 5 on the second selection.

Therefore, the probability of selecting a 5 on the first selection is 4/12 = 1/3, and the probability of selecting a 5 on the second selection is also 4/12 = 1/3.

Since the events are independent, we can multiply the probabilities to find the probability of both events occurring:

P(selecting a 5 on first selection and selecting a 5 on second selection) = P(selecting a 5 on first selection) x P(selecting a 5 on second selection)

= (1/3) x (1/3)

= 1/9

Therefore, the probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the cards, and then draws a 5 on the second selection is 1/9.

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a. The slopes of the lines are:

Slope of line 1 = -5/2

Slope of line 2 = 7/5

Slope of line 3 = -5/2

b.

Line 1 and Line 2 : Neither

Line 1 and Line 3 : Parallel

Line 2 and Line 3 : Neither

From the question, we are to determine the slope of each of the given lines:

Using the formula,

m = (y₂ - y₁) / (x₂ - x₁)

Where m is the slope

m = (2 - 7) / (-2 - (-4))

m = (-5) / (2)

m = -5/2

m = (-8 - (-1)) / (-5 - 0)

m = (-7) / (-5)

m = 7/5

m = (-2 - 8) / (2 - (-2))

m = (-10) / (4)

m = -5/2

b.

NOTE: Two lines are said to be parallel if they have equal slopes; and they are said to be perpendicular if the slope of one is the negative reciprocal of the other.

Thus,

Line 1 and Line 2 : Neither

Line 1 and Line 3 : Parallel

Line 2 and Line 3 : Neither

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Answer: If you are trying to find the third derivative

It would be f'''(x)=159720(11x+3y)^3

Step-by-step explanation:

The third term of the given expression [tex](11x+3y)^6[/tex] is 135[tex]x^4y^2[/tex].

The binomial theorem states that [tex](a+b)^n[/tex] can be expanded as follows:

[tex](a+b)^n[/tex] = nC0*[tex]a^n[/tex] + nC1*[tex]a^{n-1[/tex]*b + nC2*[tex]a^{n-2[/tex]*[tex]b^2[/tex] + ... + nCn*[tex]b^n[/tex]

where nCk is the binomial coefficient, which is defined as n! / k!(n-k)!.

In this case, we have [tex](11x+3y)^6[/tex], so n = 6.

The third term of the expansion is given by nC2[tex]a^{n-2[/tex][tex]b^2[/tex], which is equal to 6C211[tex]x^4[/tex]3[tex]y^2[/tex].

6C2 is equal to 6! / 2!4! = 15, so the third term is equal to 1511[tex]x^4[/tex]3[tex]y^2[/tex] = 135[tex]x^4y^2[/tex].

Therefore, the third term of [tex](11x+3y)^6[/tex] is 135[tex]x^4y^2[/tex].

Here is a breakdown of the steps:

Find the binomial coefficient nC2.

Multiply nC2 by 11[tex]x^4[/tex] and 3[tex]y^2[/tex].

Simplify the expression.

The answer is 135[tex]x^4y^2[/tex].

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Using the continuously compounded interest formula, the amount of debt owed after 5 years is $ 8988.18

The continuous compounding interest formula is given by P = Peⁿˣ where

Since Edgar accumulated $7,000 in credit card debt. If the interest rate is 50% per year and he does not make any payments for 5 years, how much will he owe on this debt in 5 years by compounding continuously? To determine that, we use the continuously compounded interest formula.

Given that

Substituting the values of the variables into the equation, we have that

P = Peⁿˣ

P = $7000e⁰°⁵ ˣ ⁵

P = $7000e⁰°²⁵

P = $7000(1.28)

P = $ 8988.18

So, the amount of debt owed is $ 8988.18

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Based on the data in the table, if Colin draws a marble 336 times, he predicts a yellow marble will be drawn roughly 63 times,  but probably not exactly 63 times.

Based on the data in the table, if Colin draws a marble 216 times, he predicts a white marble will be drawn roughly 2 times that a purple marble will be drawn.

If Colin draws a marble x times, he predicts a yellow marble will be drawn roughly 63 times.

The number of times = 63 / 3/16)

The number of times = 336 times.

If Colin draws a marble 216 times,

Number of times he can draw a white marble = 216 * 1/4

Number of times he can draw a white marble = 54 times

Number of times he can draw a purple marble = 216 * 1/6

Number of times he can draw a purple marble = 36 times

The number of times a white marble can be drawn more than a purple marble = 54/36 or 1.5 times more

The number of times a white marble can be drawn more than a purple marble is approximately two times.

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Answer:

Yes, it's a parallelogram bcz the opposite sides are parallel and equal.

You would need an additional $3.88 to buy the skateboard.

We need to calculate the total cost, including sales tax.

The sales tax rate is 6%, so the tax on a skateboard costing $98 would be as follows:

tax = 0.06 x $98 = $5.88

Consequently, the skateboard would have a total cost of:

total cost = $98 + $5.88 = $103.88

Since you have $100 to spend, you do not have enough money to buy the skateboard. You would need:

additional money = $103.88 - $100 = $3.88

Therefore, you would need an additional $3.88 to buy the skateboard.

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the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.

a) The events are dependent because the selection of the first number affects the probability of selecting a number less than 6 on the second draw.

b) To calculate the probability of selecting a number less than 6 both times, we need to first find the probability of selecting a number less than 6 on the first draw and then the probability of selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw.

The probability of selecting a number less than 6 on the first draw is 5/20, or 1/4, since there are 5 numbers less than 6 (1, 2, 3, 4, and 5) out of 20 total numbers.

Given that a number less than 6 was selected on the first draw, there are only 4 numbers less than 6 left in the box out of a total of 19 remaining numbers. So, the probability of selecting a number less than 6 on the second draw is 4/19.

To find the probability of both events occurring, we multiply the probabilities:

P(selecting a number less than 6 both times) = P(selecting a number less than 6 on the first draw) × P(selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw)

P(selecting a number less than 6 both times) = (1/4) × (4/19) = 1/19

Therefore, the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.

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The equation is true based on the model is B) (-3) + 5 = 2.

If we consider the circles on the left as negative units and the circles on the right as positive units.

Then we can see that there are 5 positive units and 3 negative units, so the sum is

= 5 - 3

= 2.

Therefore, the correct equation is: B) (-3) + 5 = 2.

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The system of linear equations that can be solved from the matrices is given as follows:

Considering that the row [3, -6] is common to matrices Ax and Ay, the matrix A is given as follows:

A = [-5 4; -8 1]

Hence the multiplication of matrices representing the system is given as follows:

[-5 4; -8 1][x; y] = [3; -6]

Applying the multiplication of matrices, the system of equations is given as follows:

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The probability that both events A and B will occur is 1/3 or approximately 0.3333.

To find the probability of both events A and B occurring, we need to calculate the individual probabilities of each event and then multiply them together.

Event A: The first die is a 4 or less.

In a standard six-sided die, there are four outcomes (1, 2, 3, 4) that satisfy this condition. Out of the six possible outcomes, four are favorable, so the probability of event A is 4/6 or 2/3.

Event B: The second die is even.

In a standard six-sided die, there are three even outcomes (2, 4, 6) out of the six possible outcomes.

Therefore, the probability of event B is 3/6 or 1/2.

To find the probability of both events occurring, we multiply the probabilities of each event:

[tex]P(A and B) = P(A) \times P(B) = (2/3) \times (1/2) = 1/3[/tex]

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From the graph attached below, the solution to the system of linear inequalities are (1, 4)

A system of linear inequalities is a collection of linear inequalities in the same variables. The solution is any ordered pair that satisfies each of the inequalities.

In the problem given;

y < - x + 5 ...eq(i)

y ≥ 3x + 1 ...eq(ii)

To determine the solution to the system of linear inequalities, it is easier for us to use graphical method. This is simply done by plotting the points and determine the coordinate at which both inequalities intersect.

From the graph of the system of linear inequalities, the solution to this is (1, 4) which is option E

Kindly find attached graph below

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