Answer this easy geometry question

To determine the percentage of times the machine will dispense more than 7.1 oz of coffee, we need to calculate the z-score and find the corresponding area under the normal distribution curve.

The z-score is calculated using the formula:

z = (x - μ) / σ

where x is the value we're interested in (7.1 oz), μ is the mean (7.6 oz), and σ is the standard deviation (0.5 oz).

Let's calculate the z-score:

z = (7.1 - 7.6) / 0.5

z = -0.5 / 0.5

z = -1

Now we need to find the area under the normal distribution curve for a z-score of -1. We can use a standard normal distribution table or a statistical calculator to find this area.

The area corresponds to the probability that the machine will dispense more than 7.1 oz.

Using a standard normal distribution table, we can find that the area to the left of z = -1 is approximately 0.1587. Since we're interested in the area to the right (more than 7.1 oz), we subtract this value from 1:

P(X > 7.1) = 1 - 0.1587

P(X > 7.1) ≈ 0.8413

Therefore, the vending machine will dispense more than 7.1 oz approximately 84.13% of the time.

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The inequality that can be used to represent the number of miles, x, Jaime could bicycle on the 4th week to meet his goal is 240 + 310 + 320 + x ≥ 4 (280).

What is inequality?

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other.

For the next four weeks, Jaime wants to log at least 280 miles per week on average. Jamie's objective can be graphically expressed by the inequality: T4, or alternatively T 4 if T is the total number of miles he will pedal his bicycle for four weeks (280).

The sum of the distances Jamie has covered and has yet to cover is the total number of miles Jamie will cycle during this time. Hence,  T = 240 + 310 + 320 + x. Replacing this term into the inequality T ≥ 4(280) gives 240 + 310 + 320 + x ≥ 4(280). Therefore, choice D is the correct answer.

Thus, the correct answer is  240 + 310 + 320 + x ≥ 4 (280).

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To maximize the expected value (E[W]) in the given game, the optimal strategy is to stop rolling the die and accept the value of X if X is greater than the expected value of Y.

Otherwise, roll the die again for the second time and accept the value of Y. The maximum E[W] achievable using this strategy is the maximum between the expected value of X and the expected value of Y.

To determine the optimal strategy, we need to compare the expected values of X and Y. Since the die is fair, each face has an equal probability of 1/6. Thus, the expected value of X is E[X] = (1+2+3+4+5+6)/6 = 3.5.

If we choose to roll the die for the second time, we have to consider all possible outcomes. The expected value of Y can be calculated by averaging the values from 1 to 6 with each having a probability of 1/6. Therefore, E[Y] = (1+2+3+4+5+6)/6 = 3.5.

Now, to maximize E[W], we compare E[X] and E[Y]. If E[X] > E[Y], then it is optimal to stop the game and accept the value of X. If E[X] ≤ E[Y], then it is optimal to roll the die for the second time and accept the value of Y.

Since E[X] = E[Y] = 3.5, the strategy is indifferent between stopping the game or rolling the die again. Thus, the maximum E[W] achievable is 3.5, which is obtained by either accepting X or rolling for Y.

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The probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute is 0.4582.

Given that the population mean, \(\mu\) = 90 wpm

The standard deviation of the population ,\(\sigma\) = 10

Sample size, n = 12

Sample mean, \(\bar x\) = 95

The reading rate of students follows the normal distribution.

Let z = \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt n} }\)

        = \(\frac{95 - 90}{\frac{10}{\sqrt 12} }\)

        = 1.732

Probability that the mean reading exceeds 95 wpm = P(\(\bar x\) >95)

                                                                                       = P(z>1.732)

                                                                                       = 1- P(z<1.732)

                                                                                       = 0.4582

[The value 0.4582 found from the area under the normal curve using tables].

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Answer:

AB=QR

BC=RS

CD=ST

AD=QT

Step-by-step explanation: trus

1) The amplitude c+ is c+l

2) The expectation value is 0

3) The uncertainty ΔSX is √(3/7) c+.

Now, we know that any wave function can be written as a linear combination of two spin states (up and down), which can be written as:

Ψ = c+ |+> + c- |->

where c+ and c- are complex constants, and |+> and |-> are the two orthogonal spin states such that Sx|+> = +1/2|+> and Sx|-> = -1/2|->.

Hence, we can write the given wave function as:Ψ = c+|+> + i/√7|->

Now, we know that the given wave function has been defined in Sx basis, and not in the basis of |+> and |->.

Therefore, we need to write |+> and |-> in terms of |l> and |r> (where |l> and |r> are two orthogonal spin states such that Sy|l> = i/2|l> and Sy|r> = -i/2|r>).

Now, |+> can be written as:|+> = 1/√2(|l> + |r>)

Similarly, |-> can be written as:|-> = 1/√2(|l> - |r>)

Therefore, the given wave function can be written as:Ψ = (c+/√2)(|l> + |r>) + i/(√7√2)(|l> - |r>)

Therefore, we can write:c+|l> + i/(√7)|r> = (c+/√2)|+> + i/(√7√2)|->

Comparing the coefficients of |+> and |-> on both sides of the above equation, we get:

c+/√2 = c+l/√2 + i/(√7√2)

Therefore, c+ = c+l

The amplitude c+ is a real number and is equal to c+l

The expectation value of the operator Sx is given by: = <Ψ|Sx|Ψ>

Now, Sx|l> = 1/2|r> and Sx|r> = -1/2|l>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= -i/√7(c+l*) + i/√7(c+l)= 2i/√7 Im(c+)

As c+ is a real number, Im(c+) = 0

Therefore, = 0

The uncertainty ΔSX in the state |Ψ> is given by:

ΔSX = √( - 2)

where = <Ψ|Sx2|Ψ>and2 = (<Ψ|Sx|Ψ>)2

Now, Sx2|l> = 1/4|l> and Sx2|r> = 1/4|r>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= 1/4(c+l* + c+l) + 1/4(c+l + c+l*) + i/(2√7)(c+l* - c+l) - i/(2√7)(c+l - c+l*)= = 1/4(c+l + c+l*)

Now,2 = (2i/√7)2= 4/7ΔSX = √( - 2)= √(1/4(c+l + c+l*) - 4/7)= √(3/14(c+l + c+l*))= √(3/14 * 2c+)= √(3/7) c+

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Answer:

D- 224

Step-by-step explanation:

10% of 140 is 14

So then you multiply 14 by 6 to get 60%

then you add that to 140 to equal 224.

The correct statement is that if the sales of burgers at Nick's Burgers increases by 60%, the total sales per day will be increased to 224 burgers per day from 140 burgers per day.

An increase in sales refers to as the positive shift in the sales of goods as compared to previous sessions during a given period of time, given that other factors vary.

The increase in sales will happen as a result of the strategies that may have been adopted by Nick or increase in the demand due to external factors.

The calculation of increased no. of burgers sold per day can be calculated by using the formula and putting the values given in the example as below,

increased sales  = 224

So, the new sales of burgers per day is calculated as 224 per day.

Hence, an increase in sales of burgers at Nick's by 60% will result in sales of 224 burgers per day from 140 burgers per day.

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Answer:

42

Step-by-step explanation:

138+42=180

and since they are parallel lines 1=2

1 = 42

2 = 42

Step-by-step explanation:

Equation of line form: y = mx + c,

where m = slope, c = y-intercept.

Given m = -5,

c =

\( \frac{17}{2} \)

The equation of line:

\(y = - 5x + \frac{17}{2} \: or \: y = - 5x + 8 \frac{1}{2} \)

Answer:

What you need to do is do 45.3 - 7.05 and you should get your answer. And then add your answer to the subtractio problem to 7.05 to see if you get 45.3

Step-by-step explanation:

Answer:

38. 25 (NOT ROUNDED)

Step-by-step explanation:

x= 45.3 -7.05

x= 38.25

The measure of the sum of the interior angle of the regular polygon is 1620 degrees.

All interior angles in a regular polygon are equal.

For a regular polygon, the sum of the interior angle is expressed as:

Sum of interior angles = ( n - 2 ) × 180°

Where n is the number of sides of the regular polygon.

From the diagram, the polygon has 11 sides.

Number of sides n = 11

Plug n = 11 into the above formula and solve for the sum of the interior angles:

Sum of interior angles = ( n - 2 ) × 180°

Sum of interior angles = ( 11 - 2 ) × 180°

Sum of interior angles = 9 × 180°

Sum of interior angles = 1620°

Therefore, the sum of the interior angles is 1620°

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Each level curve represents the points where the function is equal to a particular constant.

A contour map is a graphical representation of an equation that shows how the value of the equation changes over a two-dimensional plane.

The contours are used to visualize where the equation is equal to a particular constant.

In order to draw the contour map of f(x, y) = (x2 -y2), we first need to set it equal to different constants and solve for y.

That is f(x,y)= (x^2 - y^2) = c (where c is a constant)

Then, we solve for y:y = sqrt(x^2 - c) and y = -sqrt(x^2 - c)

We can now plot the values of x and y on a graph and connect the points to form the level curves.

Each level curve represents the points where the function is equal to a particular constant.

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Would the answer be 6? or 9?

(A) Let's find first the derivative of the function f(x), as follows:

To find the slope of the line tangent to f(x), we just input x = 5 on the f'(x) to solve f'(5), which is:

Hence, the slope of the tangent line is m = -20.

(B) The instantaneous rate of change is also the slope of the tangent line of the given function f(x). This means that it has the same value as part (A), which is f'(5) = -20.

(C) For the equation of the tangent line, let's look first at the tangent point. We can get this by substituting x = 5 on the equation f(x) and calculate:

Our tangent point is (5, -48). We then use the slope-intercept equation y = mx + b to generate the equation of the tangent line.

We already solved m which is equal to -20. The values of x and y are equal to the tangent point. What's left is to compute the value of b. We substitute the values of m, x, and y on y = mx + b to solve b, as follows:

Hence, the equation of the tangent line can now be written as:

Answers:

(A) m = -20

(B) f(5) = -20

(C) y = -20x + 58

The first two numbers in each row of the relative frequency table represent the percentage of cars and trucks of a particular color out of the total number of vehicles in the parking lot.

To create a relative frequency table, we need to divide the frequency of each color by the total number of vehicles (65) and then multiply by 100 to get a percentage.

Relative Frequency Table by Color:

The first two numbers in each row must add up to 100% because we are calculating the relative frequency of each color with respect to the total number of vehicles (65). Therefore, the percentage of cars and trucks of each color must add up to 100% of that color's total frequency. The total row must also add up to 100% because it represents the entire population of vehicles.

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The given question is incomplete, the complete question is:

There are 65 vehicles in a parking lot. The frequency table shows data about the types and colors of the vehicles. Complete a relative frequency table to show the distribution of the data with respect to color. Use pencil and paper. Explain why the first two numbers in each row must add up to 100%. Frequency Table Type of Vehicle Color Car Truck Total Blue 22 14 36 Red 12 17 29 Total 34 31 65

Answer:

  19%

Step-by-step explanation:

You want the probability a student is a senior, given that they are female.

The table indicates that 3 +4 +6 +3 = 16 students are female. Of those, 3 are seniors. The desired probability is ...

  P(senior | female) = N(senior & female)/N(senior) = 3/16 = 0.1875

The probability that a female student is a senior is about 19%.

<95141404393>

Step-by-step explanation:

whole numbers are the numbers Start from 0.

century means hundred

16-8=8

hexagon has six sides

91÷7=13

Answer:

I belive the answer is 10

Step-by-step explanation:

$9.74

$9.63

_____

$0.11 rounded to the nearest thenth of a percent is 10

Answer:= ( -$0.09 / $9.63 )*100%

                      ≅ -0.9 %     (note: -0.9% means 0.9% decrease)

Step-by-step explanation:

Answer:

one solution

Step-by-step explanation:

3x + 9 = 25x + 14

-3x         -3x

9 = 22x + 14

-14         - 14

-5 = 22x

Answer:

780

Step-by-step explanation:

divide 4 from 3120 to find how many pop-its are made per hour/ unit rate

The years when the spending be more than $66 billion is in 4 years time.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The equation is given as y=12.7x+15.2 and the amount is $66 billion. Therefore, the value of x will be:

y=12.7x+15.2

66 = 12.7x + 15.2

Collect like terms

12.7x = 66 - 15.2

12.7x = 50.8

Divide

x = 50.8 / 12.7

x = 4

The number of years is 4.

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Answer:

x = 4

Step-by-step explanation:

perpendicular lines have opposite and reciprocal slopes

the line y = 2 is a horizontal line, which means the slope is zero

also, y = 2 intersects the y-axis at 2

a line perpendicular to a horizontal line is a vertical line and, if it passes through the point (4,5) will intersect the x-axis at 4

therefore, the equation would be x = 4

Answer:

Total fringe needed = 132 inches

Step-by-step explanation:

P.S - The exact question is -

Given - Alejandra plans to sew fringe on a scarf. The scarf is shaped like a rectangle. The length of the scarf is 44 inches. The width is one half the length.

To find - How much fringe does Alejandra need?

Proof -

Total fringe needed = Perimeter of the rectangle.

Now,

We know that,

Perimeter of the Rectangle = 2(Length + Width)

Now,

Given that,

Length = 44 inches

Width = one half the length

          = \(\frac{1}{2}\) × 44 = 22 inches

⇒Width = 22 inches

∴ we get

Perimeter of the Rectangle = 2(44 + 22)

                                             = 2(66) = 132 inches

⇒Perimeter of Rectangle = 132 inches

∴ we get

Total fringe needed = Perimeter of the rectangle = 132 inches

⇒Total fringe needed = 132 inches

Answer:

answer is 6 cm, 7cm, 12 cm

Step-by-step explanation:

the rule is that the sum of any two sides of a triangle must be greater than the 1 one side

Answer:

6 cm, 7 cm, 12 cm

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

x+y=7

y=-x+7

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

Area of circle is ~

\(\qquad \tt \dashrightarrow \: \pi {r}^{2} \)

\(\qquad \tt \dashrightarrow \: \pi \cdot ( 8){}^{2} \)

\(\qquad \tt \dashrightarrow \:64 \pi \: \: in {}^{2} \)

So, option D is correct ~

The variable "middle" in a binary search algorithm represents the index or position of the element that is being compared in each iteration of the search process.

In a binary search, the algorithm repeatedly divides the search space in half by comparing the middle element with the target value. The "middle" variable keeps track of the index or position of the element that is considered as the midpoint of the current search range.

During each iteration, the algorithm compares the target value with the element at the middle position. If the target value is equal to the middle element, the search is successful, and the algorithm returns the index of the middle element. If the target value is less than the middle element, the search continues on the left half of the search range, excluding the middle element. If the target value is greater than the middle element, the search continues on the right half of the search range, again excluding the middle element.

The "middle" variable is crucial in the binary search algorithm as it helps determine the boundaries of the search range for each iteration. By updating the middle position based on the comparison results, the algorithm efficiently reduces the search space in each step, resulting in a significant improvement in the search time compared to linear search algorithms.

Thus, the "middle" variable in a binary search algorithm represents the index or position of the element that serves as the midpoint of the current search range, allowing for efficient and systematic exploration of the search space.

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Using the t-distribution, as we have the standard deviation for the sample, it is found that the test statistic is given by -4.47

What are the hypothesis tested?

At the null hypothesis, it is tested if they spend 7 hours a week answering their email, that is:

H₀ : μ = 7

At the alternative hypothesis, it is tested if they spend less than 7 hours, that is:

H₁ : μ < 7

What is the test statistic?

The test statistic is given by:

\(t = \frac{mean - null value}{\frac{\alpha }{\sqrt{n} } }\)

In this problem, the parameters are given as follows:

sample mean = 6. 02 sample size = 1264. standard deviation = 7.80

Hence, the test statistic is:

\(t = \frac{6.02-7}{\frac{7.80}{\sqrt{1264} } }\)

t = -4.466

t = -4.47

Therefore, the test statistic is  -4.47

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