the weight of written reports produced in a certain department has a normal distribution with mean 60 grams and standard deviation 12 grams. what is the probability that the next report will weigh less than 45 grams?

Answer:

Step-by-step explanation:

Before comparison can take place, these three measurements must be expressed in the same unit of measurement:

130 inches becomes 130/12 feet, or 10.83 ft;

4 yards becomes 4*3 feet, or 12 feet; qne

10 feet stays as is.  

It becomes obvious that the greatest measurement is 12 feet, followed by 10.83 feet, followed by 10 feet.

The ordered list from greatest to least is 4 yards, 130 inches, 10 feet.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

First, we need to convert all the units to a common unit before we can compare them.

Let's convert them all to inches:

4 yards = 12 feet × 4 = 48 feet = 48× 12 inches = 576 inches

10 feet = 10 × 12 inches = 120 inches

Now we have: 130 inches, 576 inches, 120 inches

Ordering from greatest to least, we get:

576 inches, 130 inches, 120 inches

4 yards, 130 inches, 10 feet

Therefore, the ordered list from greatest to least is 4 yards, 130 inches, 10 feet.

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9) Diagonals of a parallelogram bisect each other, so KN=NM. Thus, KM=13.5+13.5=27 cm

10) Opposite sides of a parallelogram are congruent, so LM=KJ=17 cm

11) Based on Question 9, MN=13.5 cm

Based on the t-test assuming equal variances a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal."

It is vital to establish whether or not the variances of the two groups being compared are indeed identical before performing a t-test under the assumption of equal variances. This is significant since the t-calculation statistic depends on the assumption that variances are equal.

One can look at the ratio of the variances between the two groups to evaluate the assumption of equal variances. Typically, it is acceptable to infer that the variances are not equal if the ratio of the variances is more than two or lower than half. One can presume that the variances are equal in the absence of such proof. Since the variances are not equal, it is not logical to infer that they are.

Complete and correct Question:

Based on the t-test assuming equal variances on the T-Test Equal worksheet, is it reasonable to assume that the variances are equal?
a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal.
b. Whether the variances are equal or not is not relevant for this situation.
c. Examining the ratio of the variances, it is reasonable to conclude that the variances are equal.
d. It is impossible to determine if the variances are equal given the data we have.

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The probability that Jack will win is 0.00015. The result is obtained by dividing the number of tickets that Jack has by the total number of events.

Probability of an event is calculated by dividing the number of favorable outcomes by the total number of events in the sample space.

In a certain lottery are 100 balls numbered from 1 - 100 in a large basket. Three numbered balls are randomly drawn without replacement. To win the lottery, a player's ticket must have each of the numbers drawn in no particular order.

If jack buys 21 tickets, find the probability that he will win!

In any the order, the different triples of tickets that a player can have can be found by a combination.

The total number of events would be

\(= \: _{100}C_{3}\)

\(= \frac{100!}{3! \:97!} }\)

\(= \frac{98 \times 99 \times 100}{2 \times 3}\)

= 161700 different triples

Jack has 21 tickets. So, the probability that Jack will win is

P = 21/161700

P = 0.00013

Hence, Jack will win with the probability of 0.00013.

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Arithmetic expressions can be used as control expressions in programming languages when a control structure, such as an if statement or a loop, expects a condition to determine the flow of execution

Arithmetic expressions can be used as control expressions in certain programming languages or contexts where a control structure expects a conditional expression to determine the flow of execution.

Typically, control expressions are used in decision-making structures such as if statements, while loops, for loops, and switch statements.

In most programming languages, the control expression must evaluate to a boolean value (true or false) in order to determine the execution path. However, some languages allow arithmetic expressions to be used in control structures, considering a value of zero as false and any non-zero value as true.

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The equation of the quadratic function that models the data is y = x^2 + 3x + 4

A quadratic function is represented as:

y = ax^2  +bx + c

Next, we enter the data values on the table to a graphing calculator.

From the graphing calculator, we have:

a = 1, b = 3 and c = 4

Substitute these values in y = ax^2  +bx + c

So, we have

y  = x^2 + 3x + 4

Hence, the equation of the quadratic function that models the data is y = x^2 + 3x + 4 and the scatter plot is (a)

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From the given diagram, we can identify two right-angled triangles. The triangles are shown below:

Using trigonometric ratios, we can find x as follows

We can equate the expressions for DF as follows:

Solving for x:

Answer:

x = 5

Answer: False

Step-by-step explanation:

All the 100 students engaged in the experiment were picked on the basis that all the students of the university have a chance of being selected. The selected participants must have represented the whole university well.

So, having a 95% confidence interval that the experiment might have atmost 5% error prone is statistically enough and not too wide to give an accurate estimate.

Round to the closest whole percent, 23% of the participants in the event are under the age of 20.

For the stated question-

Total number of people = 30 + 50 + 40 + 10

Total number of people = 130

Number of participants are under the age of 20 = 30.

Let 'x' be the % of the participants are under the age of 20.

Thus,

x% of 130 = 30

x = 30 x 100 / 130

x = 23.07

x = 23%

Thus, round to the closest whole percent, 23% of the participants in the event are under age of 20.

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Answer:

-9

Step-by-step explanation:

16-25=-9

Answer: -9

Step-by-step explanation:

Answer:

Answer vary :

0.25884

Step-by-step explanation:

honestly in my opinion that’s the answer.

1. 21.57 times 0.12 = 2.5884

then divide 2.5884 by the power of ten, wich is moving the decimal to left with how many zeros their are.

-0.25884

since in 10 their is only one 0 we moved the decimal only one time to the left.

and that’s how I came to that solution.

Answer:

bearing of A from C is - 65.24°

the distance |BC| is 187.84 m

Step-by-step explanation:

given data

girl walks AB = 285 m (side c)

bearing angle B = 78°

girl walks AC = 307 m (side a)

solution

we use here the Cosine Law for getting side b that is

ac² = ab² + bc² - 2 × ab × cos(B)     ...............1

307² = 285² + x²  - 2 × 285 cos(78)

x = 187.84 m

and

now we get here angle θ , the bearing from A to C get by law of sines

sin (θ) = \(\frac{187.84}{307} \times sin(78)\)

sin (θ) =  0.5985  

θ = 36.76°

and as we get here angle BAC that is

angle BCA = 180 - ( 36.76° + 78° )

angle BCA = 65.24°

and here  negative bearing of A from C so - 65.24°

Answer:

the answe is X= 14/ A :)

explanation: I took the exam review good luck!

Answer:

It is A

Step-by-step explanation:

edge 2022

Answer:

For the function f(x) = 3(x − 1)2 + 2, identify the vertex, domain, and range

Step-by-step explanation:

The vertex is (1, 2), the domain is all real numbers, and the range is y ≥ 2.

The vertex is (1, 2), the domain is all real numbers, and the range is y ≤ 2.

The vertex is (–1, 2), the domain is all real numbers, and the range is y ≥ 2.

Answer:

see explanation

Step-by-step explanation:

the equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

f(x) = 3(x - 1)² + 2 ← is in vertex form

with vertex = (1, 2 )

The domain of a parabola exists for all real values of x

domain : x ∈ R

the range of the parabola are the values of y from the y- coordinate of the vertex, upwards.

range : y ≥ 2

Answer:

1.   d

2 c

3  a

4   g

5  h

6  e

7  b

8  f

9 i

10   j

Step-by-step explanation:

The set of algebra tiles represents the polynomial expression 3x + x^3.

To determine the expression represented by the given set of algebra tiles, we need to understand the values assigned to each tile. In this case, the tiles provided are:

1 1 1 111 1 1 1

From this arrangement, we can interpret the tiles as follows:

1 = x

111 = x^3

Thus, the set of algebra tiles can be translated into the following polynomial expression:

x + x + x + x^3 + x + x + x

Simplifying this expression, we can combine like terms:

3x + x^3

Therefore, the set of algebra tiles represents the polynomial expression 3x + x^3.

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Step-by-step explanation:

Parallel lines cut by a transversal coloring activity is an activity that helps students understand the pattern of angles when parallel lines are cut by a transversal. The activity involves coloring the angles formed by the parallel lines and the transversal in different colors. This helps students identify the different types of angles formed and their relationships with each other.

The shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

What is a normal distribution?

A normal distribution is a function on some random variables, which represent the set of all those random variables in a symmetrical bell shape about the mean value.

It shows that the probability of occurrence of some data which is distributed over a function is more at or around the mean.

It is also known as probability distribution curve.

The normal distribution has two parameters:

What is the shape of the normal distribution?

The normal distribution curve is at it's peak at the mean value. This shows that the probability of occurrence of the data or value is more concentrated or distributed about the mean. It is also symmetric about the mean. As we more further from the mean, we see that the normal distribution curve gradually decreases showing that the probability of occurrence of the data or the values decreases. The shape that this curve forms is like a bell-shaped. So the shape of normal distribution is bell shape.

Hence, the shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

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Answer:

B

Step-by-step explanation:

9+(−2)^3

=9+ −8

=1

Answer:

b is your answer

Answer: 3/8

Step-by-step explanation:

\(\text{Let boy be: $ A$} \\$$\text {Let girl be } B \\\\$$\mathrm{$A A B B \ \ A B A B \ \ A B B A \ \ B A A B \ \ B A B A \ \ B B A A} \\\\=$\frac{6}{16} = \bf{\frac{3}{8}}\)

The probability of a defect is 0.0013.

Given that the process standard deviation is 15, we can assume the process average is 9 (which is the mean of the given defect range).

Therefore, the defect range can be written as:

P(weight < 8.85) = P(X < 8.85 - 9) = P(X < -0.15)

and

P(weight > 9.15) = P(X > 9.15 - 9) = P(X > 0.15)

Since the standard deviation is 15, and the process control is at plus or minus 1 standard deviation, the range of values for defects can be written as:

P(-1×15 < X < 1×15) = P(-15 < X < 15)

Now, using the Normal distribution, we can calculate the probability of defects by finding the area under the distribution curve, outside of the process control. This is certainly outside the scope of this question, but the answer (to 4 decimals) is 0.0013.

Therefore, the probability of a defect is 0.0013.

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The best option for the daughter would be  receiving $8,000 every year for 10 years.

To determine the present value of each option, we need to calculate the present value of the cash flows associated with each option using the discount rate of 7%.

Option A: $55,000 today (present value of a lump sum)

The present value of Option A can be calculated as the initial amount itself since it is received today:

Present Value (Option A) = $55,000

Option B: $8,000 every year for 10 years (present value of an annuity)

The present value of Option B can be calculated using the formula for the present value of an ordinary annuity:

PV (Option B) = C  [(1 - (1 + r)⁻ⁿ / r]

Where:

C = Cash flow per period = $8,000

r = Discount rate = 7% = 0.07

n = Number of periods = 10

Plugging in the values, we get:

PV (Option B) = $8,000 [(1 - (1 + 0.07)⁻¹⁰ / 0.07] ≈ $57,999.49

Option C: $90,000 in 10 years (present value of a future sum)

The present value of Option C can be calculated using the formula for the present value of a future sum:

PV (Option C) = F / (1 + r)^n

Where:

F = $90,000

r =  7% = 0.07

n = 10

Plugging in the values, we get:

PV (Option C) = $90,000 / (1 + 0.07)¹⁰ ≈ $48,667.38

Now, let's compare the present values of the options:

PV (Option A) = $55,000

PV (Option B) = $57,999.49

PV (Option C) = $48,667.38

Based on the present values, the best option for the daughter would be  receiving $8,000 every year for 10 years.

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There are 6 possible arrangements of four children on a 4-animal merry-go-round if Andy is seated on the giraffe.

If Andy is seated on the giraffe in a 4-animal merry-go-round, the arrangement of four children on the merry-go-round can be determined as follows:

Since Andy is already seated on the giraffe, only three children are left to be seated on three other animals. The first child can be seated on any of the three remaining animals. The second child can be seated on either of the two remaining animals since one has already been occupied.

Finally, the third child can be seated on the only remaining animal. Therefore, there are three options for the first child, two options for the second child, and one option for the third child, resulting in 3*2*1 = 6 possible arrangements of four children on a 4-animal merry-go-round if Andy is seated on the giraffe.Answer:6.

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Answer: 5.7 slices

Step-by-step explanation:

7x=40. x represents number of slices per day, 7 is because you eat pizza every day and there's 7 days in a week.

Divide both sides by 7:

7x/7 = 40/7

x= 5.7

Answer:

b = 12000p

Step-by-step explanation:

Given the equation:

b = 1500p

Where ;

b = number of bytes of information

p = number of packets of data

Each byte 'b' of information contains 8 bits of information :

Hence, equation which shows relationship between packet data and bit of information:

Since ;

1 packet = 1500 byte of information

1 byte of information = 8 bits of information

Hence, 1 packet will contain (1500 * 8 = 12000 bits) of information

Hence, the equation between packet data and bit of information becomes :

b = 12000p

Where ;

b = number of bits of information

p = number of packets of data

Answer:

6. a) The coordinate of the y-intercept is (0, 4)

b) The y-intercept represent the initial distance before she started hiking

7. The domain of the function is 0 ≤ c ≤ ∞

8. The correct option is;

b. all real numbers from 2.6 to 13"

9. Please find attached the required graph of the function created with Microsoft Excel

Step-by-step explanation:

6. From the given graph, we have;

The coordinate of the y-intercept = (0, 4)

The y-intercept represent the initial distance before she started hiking

7. The given function that models the number of cans Luis will have after his purchase is f(c) = 24·c + 5

The domain of the function is the possible values of "c", which is 0 ≤ c ≤ ∞

∴ The domain of the function = 0 ≤ c ≤ ∞

8. The number of hours Roger plays video games, t is 2 ≤ t ≤ 5

The number of games Roger plays on average within an hour = 2.6 games

The function f(t) = 2.6·t gives the number of games Roger plays in "t" hours

Therefore, we have;

The range = f(2) ≤ f(t) ≤ f(5) = 2.6 × 2 ≤ f(t) ≤ 2.6 × 5 = 5.2 ≤ f(t) ≤ 13

The range of the function = 5.2 ≤ f(t) ≤ 13

The correct option is "b" " all real numbers from 2.6 to 13"

9. Please find the required graph of the function \(f(x) = -\left | x - 2 \right | + 3\), created with Microsoft Excel.

Another possible vertex of the square is determined as (2, 1).

option B is the correct answer.

The vertex of a figure is the point of intersection of two sides of the shape.

The perimeter of the square is given as 12 units, the length of each side of the square is calculated as follows;

P = 12 units

a side length = 12 units / 4 = 3 units

To determine another possible vertex of the square, the length between the points must be equal to 3.

Let's consider point A;

A = (1, 2)

given vertex = (-1, 1)

distance between the points = √ (-1 -1)² + (1 - 2)² = √5

Let's consider point B;

B = (2, 1)

given vertex = (-1, 1)

distance between the points = √ (-1 -2)² + (1 - 1)² = √9 = 3

Thus, point B is another possible vertex of the square.

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