5. (10 points) The fill volume of an automated filling machine used for filling cans of carbonated beverage is normally distributed with a mean of 367 ml and a standard deviation of 3 ml. If all cans less than 358 or greater than 373 ml are scrapped, what proportion of cans is scrapped? Solution:

Answer:

The method that could be used to fairly choose the class president in the given scenario is flipping a fair coin. This is because flipping a fair coin is a random process and both candidates have an equal chance of winning. This ensures fairness in the selection process. Asking a group of senior teachers or letting the two candidates mutually decide who should win may introduce biases and may not be fair to both candidates. Rolling a biased die may also introduce unfairness as the outcome is not random and is predetermined.

Answer:

  y = 4x² -8x +10

Step-by-step explanation:

You want to write the equation y = 4(x -1)² +6 in standard form.

The distributive property is used to eliminate parentheses.

  y = 4(x -1)² +6 . . . . . . given equation

  y = 4(x -1)(x -1) +6 . . . . . the meaning of the exponent of 2

  y = 4((x(x -1) -1(x -1)) +6 . . . . . distributive property applied once

  y = 4(x² -x -x +1) +6 . . . . . . . . . . distributive property applied again

  y = 4(x² -2x +1) +6 . . . . . . collect terms inside parentheses

  y = 4x² -8x +4 +6 . . . . . . . distributive property applied

  y = 4x² -8x +10 . . . . . . . . . collect terms

a) The probability of picking a sweet tea on the first draw is 8/12. Since we did not replace the first tea, the probability of picking another sweet tea on the second draw is 7/11. Similarly, the probability of picking a sweet tea on the third draw is 6/10. Therefore, the probability of picking 3 sweet teas in a row is:

(8/12) * (7/11) * (6/10) = 0.2545 or 127/500

b) There are 3 ways to pick exactly one sweet tea: S U U, U S U, U U S, where S represents a sweet tea and U represents an unsweetened tea. The probability of picking a sweet tea on the first draw is 8/12, and the probability of picking an unsweetened tea is 4/12. Therefore, the probability of picking exactly one sweet tea is:

(8/12) * (4/11) * (3/10) + (4/12) * (8/11) * (3/10) + (4/12) * (3/11) * (8/10) = 0.4364 or 48/110

Null hypothesis: H0: p ≤ 0.56

Alternative hypothesis: H1: p > 0.56

We have,

Let p be the true proportion of people in the population who support stricter gun laws.

The null and alternative hypotheses in symbolic form for the claim that more than 56% of people support stricter gun laws are:

Null hypothesis: H0: p ≤ 0.56

Alternative hypothesis: H1: p > 0.56

Thus,

The null hypothesis states that the proportion of people in the population who support stricter gun laws is less than or equal to 56%, while the alternative hypothesis states that the proportion is greater than 56%.

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Note that where the above events are described, the probablity of A occurring given that B occurrs is 6/25.

We can use Bayes' theorem to find the conditional probability

P  (A| B) = P(A and B ) / P( B)

From the problem statement, we know that P(A) = 1/3,

P(B) = 5/6, and

P (A and B) = 1/5.

Substituting to get .....

P(A | B) =  (1/5) / (5/6)

= 1/5 x (6 /5)

= 6/25

Hence, we are corect to state that the probability of A occurring given that B occurs is 6/25.

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The answer is D :)  )

For a standard normal distribution, the approximate value of

P(-0.41) ≤ z ≤ (0.73) is 43%.

Option A is the correct answer.

We have,

To find the approximate value of P(-0.41) ≤ z ≤ (0.73) for a standard normal distribution, we need to use the standard normal table.

Looking at the table,

The value of P(Z ≤ 0.73) = 0.7673.

The value of P(Z ≤ -0.41) = 0.3409.

To find the value of P(-0.41) ≤ Z ≤ (0.73),

We need to subtract P(Z ≤ -0.41) from P(Z ≤ 0.73):

P(-0.41) ≤ Z ≤ (0.73) = P(Z ≤ 0.73) - P(Z ≤ -0.41)

P(-0.41) ≤ Z ≤ (0.73) = 0.7673 - 0.3409

P(-0.41) ≤ Z ≤ (0.73) = 0.4264

Rounding this value to the nearest whole percent, we get 43%.

Therefore,

For a standard normal distribution, the approximate value of

P(-0.41) ≤ z ≤ (0.73) is 43%.

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Answer:

(4, -3)

(-28,-11)

Step-by-step explanation:

y = [tex]\frac{1}{4}[/tex] x - 4  Substitute 4 for x

y = [tex]\frac{1}{4}[/tex][tex](\frac{4}{1})[/tex] - 4  another name of 4 is [tex]\frac{4}{1}[/tex]

y = 1 - 4

y = -3

(4,-3)

y = [tex]\frac{1}{4}[/tex] x - 4  Substitute -11 for y

-11 = [tex]\frac{1}{4}[/tex] x - 4  Add 4 to both sides

-11 + 4 = [tex]\frac{1}{4}[/tex]x - 4 + 4

-7 = [tex]\frac{1}{4}[/tex]x  Multiply both sides by 4

-7(4) = [tex]\frac{1}{4}[/tex][tex](\frac{4}{1})[/tex]x

-28 = x

(-28,-11)

Helping in the name of Jesus.

the more extreme height was the case for the shortest living man (13.38 standard deviation units below the population's mean) compare with the tallest man that was 9.21 standard deviation units above the population's mean.

To answer this question, we need to use standardized values, and we can obtain them using the formula:

z = (x - μ)σ  ..  [1]  

Where,

x is the raw score we want to standardize.

μ is the population's mean.

σ is the population standard deviation.

A z-score "tells us" the distance from  in standard deviation units, and a positive value indicates that the raw score is above the mean and a negative that the raw score is below the mean.

In a normal distribution, the more extreme values are those with bigger z-scores, above and below the mean. We also need to remember that the normal distribution is symmetrical.

Heights of men at that time had:

μ = 171.59 cm

σ  = 5.47 cm.

Let us see the z-score for each case:

Case 1: The tallest living man at that time

The tallest man had a height of 222 cm.

Using [1], we have (without using units):

z = (x - μ)σ

z = (222 - 171.59)/5.47

z = 50.41 / 5.47

z = 9.21

That is, the tallest living man was 9.21 standard deviation units above the population's mean.

Case 2: The shortest living man at that time

The shortest man had a height of 98.4 cm.

Following the same procedure as before, we have:

z = (x - μ)σ

z = (98.4 - 171.59)/5.47

z = - 13.38

That is, the shortest living man was 13.38 standard deviation units below the population's mean (because of the negative value for the standardized value.)

The normal distribution is symmetrical (as we previously told). The height for the shortest man was at the other extreme of the normal distribution in  standard deviation units more than the tallest man.

Then, the more extreme height was the case for the shortest living man (13.38 standard deviation units below the population's mean) compare with the tallest man that was 9.21 standard deviation units above the population's mean.

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I am pretty sure the answer is b. emplyee 2# but im not 100% sure since your graph is really weird and hard to uunderstand

The volume of the Triangular prism above is 156 cm^3

What is a Triangular Prism?

Triangular Prism is a three-dimensional shape consisting of two triangular ends connected by three rectangles. It has two identical triangles as parallel bases and if it is a right prism all lateral faces are rectangles.

How to determine this

The volume of a Triangular prism is calculated as

Volume = 1/2 * base * height * length

Where the Base = 8 cm

Height = 3 cm

Length = 13 cm

Volume = 1/2 * 8 * 3 *13

Volume = 1/2 *312

Volume = 156 cm^3

Therefore, the volume  of the triangular prism is 156 cm^3

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The quadrilateral ABCD is trapezoid.

What is trapezoid?

A quadrilateral with one set of parallel opposite sides is referred to as a trapezium. It can have congruent sides (isosceles) and right angles (a right trapezium), but neither is necessary.

Here in the given figure ,

[tex]\overline{AD}=\overline{BC}[/tex] are parallel to each other.

We can make right angle using ABC.

Hence the given quadrilateral ABCD is trapezoid.

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Result:

The weight of the pumpkin in November = 71 ounces more than in October.

How to compare the weights?

To compare the weights, we need to convert both weights to the same unit of measurement, either pounds or ounces.

Let's convert the first weight, which is 3 pounds and 11 ounces, to ounces:

3 pounds = 3 x 16 = 48 ounces

11 ounces = 11

So the first weight is 48 + 11 = 59 ounces.

Now, let's convert the second weight, which is 8 pounds and 2 ounces, to ounces:

8 pounds = 8 x 16 = 128 ounces

2 ounces = 2

So the second weight is 128 + 2 = 130 ounces.

To find how many more ounces the pumpkin weighed in November, we subtract the October weight from the November weight:

130 - 59 = 71

Therefore, the pumpkin weighed 71 more ounces in November than it did in October.

Answer:

x = -1

Step-by-step explanation:

You will plug in 8 for y then solve for x:

[tex]\frac{12}{3} = (x-1)^2\\4 = (x-1)^2\\\frac{+}{-}2 = x-1 \\ x= +3, and -1[/tex]

Then the answer is -1 because the graph shows the point in the 2nd quadrant meaning x is negative

The mean is 4746
The median wage is #4618

The wages for the five local government trainees are

#4,166, #4,618, #3,742, #5,838 and #5,366

= 4166+ 4618+ 3742+5838+5366/5

= 23,730/5

Mean = 4,746

The median wage is

Arrange the wages orderly

3,742, 4166, 4618, 5366, 5838

The median wage is #4618

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Step-by-step explanation:

supposedly

A=3

B= -2

C=2

(3-(-2)×2=(3×2)-(-2×2)

5×2=6-(-4)

10=6+4

10=10

Answer: the slope is 6

Step-by-step explanation: the line y=6x-3

To create point R such that a line through points P and R is parallel to line l, Gerald needs to draw a line through points T and N.

We have,

We know that line l is parallel to line m since both lines intersect at point Q and no other point.

The circle centered at Q intersects line m at point S and line l at point N, which means that QS is perpendicular to line l.

Similarly, the circle centered at P intersects line m at point T, which means PT is perpendicular to line l.

To create a line parallel to line l, Gerald needs to find a line perpendicular to line l.

This can be achieved by drawing a line through points T and N. This new line will be parallel to QS and perpendicular to line l.

Finally, Gerald can find the intersection of this new line with the circle centered at P to find point R, which will be equidistant from points P and T. Drawing a line through points P and R will be parallel to line l.

Thus,

To create point R such that a line through points P and R is parallel to line l, Gerald needs to draw a line through points T and N.

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2/7

Assuming I know what standard deviation is, it is there is a 3 ounce "range" that the machine can give, based on that 24 oz mean. So there can be 21,22,23,24,25,26, and 27. Out of those 7, 2 are the numbers we are looking for, so it is 2/7.

The number of cubes needed with an edge length of 1/3  inches is needed to build a cube with an edge length of 1 inch is 27.

We have,

the edge length of smaller cube, a = 1/3 inches

the edge length of the cube to be built, S = 1/3 inches

Now, Volume of cube = a³

= (1/3)³

= 1/27 in³

Volume of the cube to be build =   S³

                                                   =   1³

                                                   =   1 in.³

Thus, Cubes of smaller length are needed for the larger cube

= 1/ (1/27)

= 27

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Step-by-step explanation:

Charlie's monthly pay, P, can be represented as a linear function of the number of items sold, q. The monthly salary of $2,000 represents the y-intercept of the line, and the commission of $100 per item sold represents the slope of the line.

Thus, the model for Charlie's monthly pay, P(q), can be expressed as:

P(q) = 100q + 2000

where q is the number of items sold in a month, and P(q) is Charlie's monthly pay in dollars.

The range of laptops that they should produce per day to make profit is: 1 to 21 laptops

When dealing with inequalities, we could make use of any of the following:

Greater than(>)

Less than (<)

Greater than or equal to (≥)

Less than or equal to (≤)

We are given:

Cost function: C(x) = 4x² - 10x + 150

Revenue function: R(x) = -3x² + 150x + 75

Now, if they want to make profit, then:

R(x) > C(x)

Thus:

4x² - 10x + 150 > -3x² + 150x + 75

Rearranging to get:

7x² - 160x + 75 > 0

Solving using quadratic calculator gives:

x ≈ 1 and 21

Thus the range of laptops that they should produce per day to make profit 1 to 21

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Based ont he the function y = - 2x + 5 + 2x - 5 is given ,

if  x < -2.5, y = 0

i f  x > 2.5, y = 0

if -2.5 ≤  x  ≤ 2.5 = 0

Without the absolute value symbols

y = -2x + 5 + 2x - 5

Where x < - 2.5

y = -2 (-2.5) + 5 + 2 (-2.5 ) - 5

y =  5 + 5 + (-5)-5

y = 0

Where x > 2.5

y = -2 (2.5) + 5 + 2(2.5) - 5

y = 0

Where -2.5 ≤ x ≤ 2.5

y = -2x + 5 + 2x -5

grouping like terms we have

-2x + 2x +5 -5
y = 0

thus, Where -2.5 ≤ x ≤ 2.5

y = 0

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Answer:

x = -16/7 and y = 38/7.

Step-by-step explanation:

To solve the system of equations:

x + 3y - 22 = 0 --- equation (1)

2x - y + 42 = 0 --- equation (2)

x - 11y + 142 = 0 --- equation (3)

We will use the method of substitution to find the values of x and y that satisfy all three equations.

From equation (1), we can express x in terms of y:

x = 22 - 3y --- equation (4)

We can substitute equation (4) into equation (2) and simplify:

2(22 - 3y) - y + 42 = 0

44 - 6y - y + 42 = 0

-7y = -38

y = 38/7

Now, we can substitute the value of y into equation (4) to find x:

x = 22 - 3(38/7)

x = -16/7

Therefore, the solution to the system of equations is:

x = -16/7 and y = 38/7.

The value of the square root 3 6/25 is 1⅘

The square root of a number is a value that can be multiplied by itself to give the original number. For example the square root of 225 is 15.

Another example is the square of 16, which can be gotten by finding the prime product of 16

16 = 2×2×2×2. we can group the 2s into two i.e (2×2) × (2×2) . We can now take one out of 2 .

= 2 × 2 = 4. Therefore the the square root of 16 is 4.

Therefore the square root of 3 6/25 can be found by converting the fraction into improper fraction.

= 81/25

therefore the √81/25 = 9/5 = 1⅘.

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Answer:

The first and second one

Step-by-step explanation:

Since they are one-to-one functions, the first table and the first graph (under the table) are the answers.

Be sure to mark this as brainliest and hope this helps!

Answer: The first one and second one.

Step-by-step explanation:

It's a bit cut-off but for the very first function, each x-value has a corresponding y-value so it is a function. For the second one (the graph), if we do the vertical line test, it will pass it (vertical line touches only one point of the function). The third one (the loop graph) , however, will not pass the vertical line test as there's a point on the graph where if we were to draw a vertical line, it would be touch 2 or 3 points of the function.

Answer:

84 degrees for number 6

Step-by-step explanation:

the area of a circle is 360 degrees, so just subtract the other angles by 360 i think that's how you do it

Answer:

Step-by-step explanation:

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Answer: it will take approximately 14.62 years for the initial investment to double at an interest rate of 4.75% per year, compounded continuously.

Step-by-step explanation: Given an investment of $2000 at a continuously compounded interest rate of 4.75%, the balance in the account can be calculated using the following mathematical expression after t years:

The aforementioned equation, A = P * e^(rt), denotes the relationship between the accrued amount (A) and the principal amount (P), compounded continuously at a fixed annual rate of interest (r) over a specific time period (t), as governed by the mathematical constant "e."

In the context of financial calculations, the symbol 'P' denotes the initial capital investment. The interest rate, represented by the variable 'r', is expressed in the form of a decimal. Additionally, 'e' is the mathematical constant, roughly equivalent to 2.71828. Finally, 't' refers to the duration of the investment, measured in years.

In order to determine the duration of time required for the investment to achieve a twofold increase, it is necessary to solve the corresponding equation:

The equation expressed as 2P = P * e^(rt) can be restated more formally as follows. Given a principal investment amount represented by P and a rate of return indicated by r, compounded over time t, the equation can be expressed as the product of P and the exponential function of e^(rt), yielding twice the initial investment amount.

The variable 2P represents the monetary value acquired through doubling the initial investment.

Upon division of both sides by P, the resulting expression is as follows:

The equation 2 equals the exponential function of the base e raised to the power of the product of r and t.

By applying the natural logarithm function to both expressions, the resultant outcome is:

The natural logarithm of 2 can be represented as rt, where r denotes the logarithmic base and t denotes the logarithm of the argument, in accordance with the conventions of academic mathematical writing.

Upon resolving for the variable t, an outcome is yielded:

The mathematical expression t = ln(2) / r can be written in a formal academic style as follows: The equation determines the relationship between time t and the rate of decay r, where t is equal to the natural logarithm of 2 divided by r.

Upon substitution of the provided values, the resultant output is:

The calculated value of the variable t, representing the length of time in years, is approximately equal to 14.62 years, obtained through the algebraic manipulation of the natural logarithmic function of 2 divided by the constant value of 0.0475.