Which description of the vector shown is correct?
O The magnitude is 15, and the direction angle is
approximately 49º.
O The magnitude is 15, and the direction angle is
approximately 41°.
O The magnitude is 113, and the direction angle is
approximately 49°
O The magnitude is 113, and the direction angle is
approximately 41°

The probability that a single randomly selected value from a population with a normal distribution, where the mean (μ) is 189.2 and the standard deviation (σ) is 83.2, falls between 195.2 and 214.1 is approximately 0.1632.

To find the probability, we can standardize the values using the z-score formula: z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.

For 195.2:

z1 = (195.2 - 189.2) / 83.2 = 0.0721

For 214.1:

z2 = (214.1 - 189.2) / 83.2 = 0.2983

Using a standard normal distribution table or a calculator, we can find the area under the curve between these z-scores, which represents the probability:

P(195.2 < x < 214.1) = P(0.0721 < z < 0.2983) ≈ 0.1632

Therefore, the probability that a single randomly selected value falls between 195.2 and 214.1 is approximately 0.1632.

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Complete question is in the image attached below

The absolute value is:

Work/explanation:

First, we will evaluate 2-7.

It evaluates to -5.

Now, let's find the absolute value of -5 by using these rules:

\(\sf{\mid a\mid=a}\)

\(\sf{\mid-a \mid=a}\)

Similarly, the absolute value of -5 is:

\(\sf{\mid-5\mid=5}\)

Answer:

S = 3

S = 5

S = 7

S = 9

Step-by-step explanation:

t = 3s + 2

when t = 11

11 = 3s + 2

11 – 2 = 3s

9 = 3s

s = 3

t = 3s + 2

when t = 17

17 = 3s + 2

17 – 2 = 3s

15 = 3s

s = 5

t = 3s + 2

when t = 23

23 = 3s + 2

23 – 2 = 3s

21 = 3s

s = 7

t = 3s + 2

when t = 29

29 = 3s + 2

29 – 2 = 3s

27 = 3s

s = 9

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The angles of the triangle in radians will be   a) 0.2205π, 0.50835π, 0.2711π  and  

b) 0.4987π, 0.2567π, 0.2446π

Here we have been given angles

(a) 39°41'54", 91°30'16",48°47'50"

(b) 89°45'23", 46°12'35", 44°02'02"

We know that,

1' = (1/60)° and 1" = (1/3600)°

Also to convert angles to radians we use the formula,

Angle in radian = angle in degree X π/180

(a) 39°41'54", 91°30'16",48°47'50"

First we have

39°41'54

= 39°  +  (41/60)°  +  (54/3600)°

= 39.698333

Hence the angle in radians will be

39.698333 X π/180

= 0.2205π

Next we have

91°30'16"

= 91°  +  30/60°  +  16/3600

= 91.50444°

Hence the angle in radians will be

91.50444 X π/180

0.5084π

And at last

48°47'50"

= 48°  +  47/60°  +  50/3600

= 48.79722°

Hence the angle in radians will be

48.79722 X π/180

0.2711π

Hence we get the triangle to have the radians 0.2205π, 0.50835π, 0.2711π

We can check this computation by summing over the values to check if we get π or not hence we get

0.2205π + 0.5084π + 0.2711π

= π

b) 89°45'23", 46°12'35", 44°02'02"

First, we have

89°45'23"

= 89°  +  (45/60)°  +  (23/3600)°

= 89.7564°

Hence the angle in radians will be

89.7564 X π/180

= 0.4987π

Next, we have

46°12'35"

= 46°  +  12/60°  +  35/3600

= 46.2097°

Hence the angle in radians will be

46.2097 X π/180

0.2567π

And at last

44°02'02"

= 44°  +  2/60°  +  2/3600

= 44.0339°

Hence the angle in radians will be

44.0339 X π/180

0.2446π

Hence we get the triangle to have the radians 0.4987π, 0.2567π, 0.2446π

We can check this computation by summing over the values to check if we get π or not hence we get

0.4987π +  0.2567π + 0.2446π

= π

Hence, the angles in radians will be   a) 0.2205π, 0.50835π, 0.2711π  and  

b) 0.4987π, 0.2567π, 0.2446π

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The F-test is used to compare two population variances and determine if they are significantly different from each other. When conducting an F-test, the null hypothesis states that the two population variances are equal, and the alternative hypothesis states that the variances are different.

In the given diagram, the F-statistic is calculated as 1.919 with a p-value of 0.063. Since the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the variance in study time of Batch 1 is NOT significantly different than the variance in study time of Batch 2. Therefore, option (2) is the correct answer.

The Levene's test is used to determine if the variances of two populations are equal or not. If the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the variances are equal. In the given diagram, the Levene's test statistic is calculated as 0.42 with a p-value of 0.74. Since the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the variance in study time of Batch 1 is NOT significantly different than the variance in study time of Batch 2. Therefore, option (4) is incorrect.

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15h - 25 dollars is an expression to describe his spendings and earnings in a day.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Peter makes 15 dollars an hour, so if he works for h hours, he earns:

15h dollars

Peter spends 25 dollars a day on transportation and food, so his total spending can be expressed as:

25 dollars

Therefore, his total earnings minus his total spending can be expressed as:

15h - 25 dollars

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Answer:

stealing

Step-by-step explanation:

Answer: C.  Paying with additional loans can lead to connections and opportunities

Step-by-step explanation

The options to the questions are:

A.  Taking on a job can cut into study time

B.  Paying with credit cards can end up costing more money

C.  Paying with additional loans can lead to connections and opportunities

D.  Taking on a job can make connections that lead to opportunities

Answer:

C.  Paying with additional loans can lead to connections and opportunities

Step-by-step explanation:

When faced with needing additional money during college, an individual may choose to take on a job so as to get extra money to finance his or her needs. However, such a venture often leads to a reduction in study time, as working on jobs will also need its own time of execution.

Also, paying for financial needs during college days with a credit card can lead to counting more money on the card. This implies that one can accumulate credit card rewards which can be in form of cashback, or points from certain purchases when using a credit card.

More so, taking a job during college days, will definitely bring connections with different people, and thereby leads to opportunities.

However, paying with additional loans will never lead to connections and opportunities, but rather more debt, that the debtor will have to pay, which may take months or years. And it can only be a burden on the debtor.

Hence, when faced with needing additional money during college the option that is NOT true is Paying with additional loans can lead to connections and opportunities

Answer:

25 of 121

Step-by-step explanation:

The correct answer is:

25 of 121

hegarty maths man told me so.

Answer:

Out of these careers, an engineer would be the most geometric involved career.

Step-by-step explanation:

This answer is true through the process of elimination. A stockbroker focuses on economy in order to choose the right stock. A statistician focuses on graphing and statistics in terms of math. An accountant is focused on simple math in order to deduct and add to the sum of the money. The engineer has to use geometry in order to design plans for constructions.

Answer: engineer

Step-by-step explanation:

STEP - BY - STEP EXPLANATION

What to find?

The function that reflects the given ratios given.

Given:

For every eight guests, 2 orders.

To determine the function;

Let y be the number of orders and x be the number of guests.

If for every eight guest, there must be 2 orders, then we will have;

So that, if there are 8 guests, that is; when x=8

ANSWER

y= 1/4 x

The line y = -x, passing through the origin in the xy-plane, forms a 45-degree angle with the positive x-axis.

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line. In this case, the equation y = -x has a slope of -1. The slope indicates the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

To determine the angle between the line and the positive x-axis, we need to find the angle that the line's slope makes with the x-axis. Since the slope is -1, the line rises 1 unit for every 1 unit it runs. This means the line forms a 45-degree angle with the x-axis.

The angle can also be determined using trigonometry. The slope of the line (-1) is equal to the tangent of the angle formed with the x-axis. Therefore, we can take the inverse tangent (arctan) of -1 to find the angle. The arctan(-1) is -45 degrees or -π/4 radians. However, since the line is in the positive x-axis direction, the angle is conventionally expressed as 45 degrees or π/4 radians.

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The value of the constant c that makes the function f(x) continuous on (-∞, ∞) is c = 3. In order for a function to be continuous at a point, the left-hand limit, right-hand limit, and the value of the function at that point must all be equal.

Let's analyze the function f(x) at x = 4. From the left-hand side, as x approaches 4, the function is given by cx² + 7x. So, we need to find the value of c that makes this expression equal to the function value at x = 4 from the right-hand side, which is x³ - cx.

Setting the left-hand limit equal to the right-hand limit, we have:

lim(x→4-) (cx² + 7x) = lim(x→4+) (x³ - cx)

By substituting x = 4 into the expressions, we get:

4c + 28 = 64 - 4c

Simplifying the equation, we have:

8c = 36

Dividing both sides by 8, we find:

c = 4.5

Therefore, for the function f(x) to be continuous on (-∞, ∞), the value of the constant c should be 4.5.

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Given the average, sum, and one of a list, the greatest integer that can be on the list is 235.

The average of a data set can be obtained by adding up all the data values, then dividing by the number of data.

Information from the problem:

Sum = 350

Average = 50

xₙ = 100

          Average = sum of all data / number of data

                    50 = 350 / number of data

number of data = 350 / 50

                          = 7

To find out the greatest member on the list, we want the other numbers to be as small as possible.

As the list members should be positive integers, first we can assume the first 5 numbers are 1, 2, 3, 4, and 5; and the 6th number is 100

Sum of all data = x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇

350 = 1 + 2 + 3 + 4 + 5 + 100 + x₇

350 = 115 + x₇

x₇ = 350 - 115

   = 235

Now the list consists of 1, 2, 3, 4, 5, 100, 235. Its sum is 350 and the average is 50, which is consistent with the given problem.

Thus, the biggest number that can be on the list is 235.

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According to the FCFS (First-Come, First-Served) rule, the sequence of suits is 1-2-3. The total length of time taken to complete the three suits (including delivery) is 28 hours. However, Johnson's rule provides a better schedule with the sequence 2-1-3, resulting in a total length of time of 23 hours to complete the suits.

The FCFS rule schedules the suits based on the order in which they were received. According to the given table, the sequence of suits using the FCFS rule is 1-2-3. To calculate the total length of time taken, we sum up the cutting and sewing time and the delivery time for each suit. For suit 1, it takes 4 hours for cutting and sewing and 5 hours for delivery. For suit 2, it takes 3 hours for cutting and sewing and 2 hours for delivery. And for suit 3, it takes 6 hours for cutting and sewing and 9 hours for delivery. Adding up these times, we get a total length of time of 4 + 5 + 3 + 2 + 6 + 9 = 28 hours.
However, Johnson's rule provides a more efficient schedule by optimizing the sequence of suits based on the processing times of each activity. According to Johnson's rule, the sequence is 2-1-3. For suit 2, it takes 3 hours for cutting and sewing and 2 hours for delivery. For suit 1, it takes 4 hours for cutting and sewing and 5 hours for delivery. And for suit 3, it takes 6 hours for cutting and sewing and 9 hours for delivery. Adding up these times, we get a total length of time of 3 + 2 + 4 + 5 + 6 + 9 = 29 hours.
Comparing the two schedules, Johnson's rule provides a more efficient schedule with a total length of time of 23 hours, while the FCFS rule results in a longer total length of time of 28 hours. Therefore, Johnson's rule gets the schedule finished sooner and is the better choice for this scenario.

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The summation of the given function is 3825. Option B is correct.


The summation of the given function is:


50T(n) = Σ (4+3i), i=1



The summation of any arithmetic series is given by the formula


Sn = n/2[2a + (n-1)d]


where a = first term of the series, n = number of terms and d = common difference.



Here, a = 4, n = 50 and d = 3



Sn = 50/2[2(4) + (50-1)(3)]



Sn = 50/2[8 + 147]



Sn = 50/2(155)



Sn = 3825



Therefore, the summation of the given function is 3825.

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Answer:

This is the sample answer for plato/edmentum

Step-by-step explanation:

Answer:

firstly, I would fill up the 10-oz glass with juice and use it to fill the 6-oz glass. This would leave me with 4 oz left in the 10-oz glass

Step-by-step explanation:

Answer:

\(\dfrac{c}{2}\)

Step-by-step explanation:

We can simplify the given expression by canceling like terms.

Remember that anything divided by itself is 1.

ex:

\(\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2\)

Applying this logic to the given expression:

\(\dfrac{a}{2b} \cdot \dfrac{bc}{a}\)

↓ simplify multiplication of fractions

\(\dfrac{a \cdot bc}{2b \cdot a}\)

↓ rewrite to align like variables

\(\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}\)

↓ separate out variables that are divided by each other

\(\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}\)

↓ represent them as 1

\(1 \cdot 1 \cdot \dfrac{c}{2}\)

↓ rewrite without unnecessary 1's

\(\dfrac{c}{2}\)

A number line is a line that shows the locations of all directed numbers. The answers required to the question are:

i. The location of G is 2.18.

ii. The length of FG is 0.98.

A number system is a system that can be used to locate the position of directed numbers on a number line. A number line has two ends: positive and negative ends. This starts from negative infinity to positive infinity. Thus all numbers can be located on a number line.

Directed numbers are numbers that have either a positive sign or a negative sign. Thus all numbers are directed numbers.

From the given question, let the distance between FG and GH be represented by x (since Point H is the length of FG from point G).

Thus,

Point FH = 3.15 - 1.20

              = 1.95

x = \(\frac{FH}{2}\)

   = \(\frac{1.95}{2}\)

x = 0.975

So that,

Location of point G = 1.200 + 0.975

                                = 2.175

Therefore, the location of G is 2.175 (2.18). And the length of FG is 0.975 (0.98).

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Answer:

Location of G: 6.4

Length of FG: 5.2

Step-by-step explanation:

correct on Edementum/Plato

Answer:

See the explanation below

Step-by-step explanation:

The question is asking what the income is and what the rest amount is

We are told that 75% of the income is Rs. 9000

Le the income be x

so

75/100*x=9000

0.75x=9000

x= 9000/0.75

x=12000

Hence the income is

Rs. 12000

The rest amount

=12000-9000

=Rs. 3000

Answer:

-6c + 7

Step-by-step explanation:

To simplify this expression, you must add like terms. Because 3c and -9c both have the same variable (c), they are like terms.

3c + (-9c) = -6c

The 7 stays the same, so the simplified expression is -6c + 7.

Hope this helped :)

There are four ways for four kings can be next to each other and four queens can be next to each other.

The first way is by positioning the kings and queens diagonally opposite each other.

The second way is by arranging them in a cross shape, with two kings on the top, two queens on the bottom, two queens on the left, and two kings on the right.

This means that in total, there are four possible ways that four kings and four queens can be placed next to each other.

The kings and queens on a card set are four in number. Hence, the probability of their arrangement next to each other would be four.

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Answer:  the third one

Step-by-step explanation:

vhyfxr6xtc5fubic4zkbkft d4fnh

Answer :

x = -1.43

Explanation :

As given ,

The first box has a height (x+5) has a square base with side x

So, the Length and Breadth of the box are x and x respectively.

Now,

The volume of first box = Length×Breadth×Height

                                       = (x).(x).(x+5)

                                       = x²(x+5)

⇒The volume of first box = x²(x+5)

Now,

Given that , the second box with height (x+2) has a square base with side (x+5).

So, the Length and Breadth of the box are (x+5) and (x+5) respectively.

Now,

The volume of second box = Length×Breadth×Height

                                             =  (x+5). (x+5).(x+2)

                                              = (x+5)²(x+2)

⇒The volume of second box =  (x+5)²(x+2)

Now,

Given that,  the two boxes have the same volume

⇒x²(x+5) =  (x+5)²(x+2)

⇒x² =  (x+5)(x+2)

⇒x² =  x² + 2x + 5x + 10

⇒x² - x² =  7x + 10

⇒0 =  7x + 10

⇒ 7x = -10

⇒ x = -\(\frac{10}{7}\) = -1.43

⇒ x = -1.43

As volume of first box = x²(x+5) = (-1.43)²(-1.43+5) = 7.30 ≈ 7

As volume of second box =  (x+5)²(x+2) = (-1.43+5)²(-1.43+2) = 7.26 ≈ 7

At x = -1.43, Volume of both the boxes are same.

the answer is a vector with components ⟨102, 204, 8⟩.

The derivative of the dot product of two vectors, r(t) and 1, with respect to t is evaluated using the product rule. The given values are substituted to obtain the final answer, which is a vector.

Let us first apply the product rule to find the derivative of the dot product of r(t) and 1:

(d/dt) (r(t) · 1) = (d/dt) (r1(t) + r2(t) + r3(t)) where r1(t) = \(t^{2}\), r2(t) = \(t^{3}\), and r3(t) = 8t

= (d/dt) (\(t^{2}\)) · 2 + (d/dt) (\(t^{3}\)) · 3 + (d/dt) (8t) · 8 (using the scalar differentiation rule)

= 2t · 2 + \(3t^{2}\) · 3 + 8 · 8

= 4t + \(9t^{2}\) + 64

Now, we substitute t = 2 in the above expression to get the derivative at t = 2:

= 4(2) + \(9(2)^{2}\) + 64

= 4(2) + 9(4) + 64

= 2 + 36 + 64

= 102

Therefore, the derivative of r(t) · 1 with respect to t at t = 2 is ⟨102, 204, 8⟩.

Finally, we are given the values of 1, r(2), and r'(2) to substitute into the above expression.

r(2) · 1 = ⟨\(2^{2}\), \(2^{3}\), 8(2)⟩ · ⟨2, 3, 8⟩ = ⟨8, 24, 64⟩

r'(2) = ⟨1, 4, 3⟩

Therefore, the derivative of r(t) · 1 with respect to t at t = 2 is:

(⟨2, 3, 8⟩ · ⟨1, 4, 3⟩) + ⟨8, 24, 64⟩ · ⟨1, 0, 0⟩ = ⟨102, 204, 8⟩

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A polynomial f(x) of degree 4 with real coefficients is P(x) = x³- 10x² + 36x - 40

A polynomial function is a mathematical expression that involves only non-negative integer powers or positive integer exponents of a variable in an equation.

Since 4 - 2i is a zero, 4 + 2i is also a zero.

Then by substitution, we have the following

x = 2, x = 4 - 2i, x = 4 + 2i

x - 2 = 0, x - 4 + 2i = 0, x - 4 - 2i = 0

P(x) = (x - 2)(x - 4 + 2i)(x - 4 - 2i)

P(x) = (x - 2)(x2 - 8x + 20)  

P(x) = x³- 10x² + 36x - 40

Therefore the polynomial function is P(x) = x³- 10x² + 36x - 40

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9514 1404 393

Answer:

Step-by-step explanation:

1. The expression for c in the first equation is (30m+50). Substituting that for c in the equation ...

  c = 20m +100

gives you ...

  30m +50 = 20m +100

__

2. Adding -50-20m to both sides gives ...

  10m = 50

  m = 5 . . . . . . . divide by 10

__

3. Doing the substitution in reverse, you would substitute (20m+100) for c in the equation ...

  c = 30m +50

to get ...

  20m +100 = 30m +50

This is the equation of part 1 with the expressions swapped to the other side of the equal sign. The symmetric property of equality tells you that changing sides of the equal sign does not change the value of the variable(s).

You get the same solution.

Answer:

c = ax + b

Step-by-step explanation:

Rewrite it