Mathematics College

A vending machine is designed to dispense a mean of 7.6 oz of coffee into an 8 oz cup. If the standard deviation of the amount of coffee dispensed is 0.2 oz, and the amount is normally distributed, find the percent of times the machine will dispense from 7.5 oz to 7.9 oz.

Answers

Answer 1

The percentage of time that the machine will dispense from 7. 5 oz to 7. 9 oz is 62.47% of the time.

How to find the percentage ?

Find the Z-scores for both 7. 5 oz and 7. 9 oz :

Z = ( X - μ ) / σ

For 7. 5 oz :

Z = ( 7.5 - 7.6 ) / 0.2

Z = -0. 1 / 0. 2

Z = -0. 5

For 7.9 oz:

Z = (7. 9 - 7.6 ) / 0.2

Z = 0. 3 / 0. 2

Z = 1. 5

Using the z - values from the table, the percentage of time is:

0.9332 - 0.3085 = 0.6247

= 62. 47 %

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Related Questions

how large a sample should be taken if the population mean is to be estimated with 98 percent confidence to within $100? The population has a standard deviation of $800.

Answers

A sample of at least 433 individuals would need to be taken to estimate the population mean with 98% confidence to within $100.

Understanding Population Estimate

To estimate the sample size needed to estimate the population mean with 98% confidence to within $100, we can use the formula:

n = (z * σ / E)²

where:

n = sample size

z = z-score for the desired level of confidence (98% in this case), which can be found using a standard normal distribution table or calculator. For 98% confidence, the z-score is approximately 2.33.

σ = population standard deviation ($800 in this case)

E = margin of error ($100 in this case)

Plugging in the values, we get:

n = (2.33 * 800 / 100)²

n ≈ 432.64

Rounding up to the nearest whole number, we get a sample size of 433. Therefore, a sample of at least 433 individuals would need to be taken to estimate the population mean with 98% confidence to within $100.

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5.
Andre is playing a new card game. This game uses 4 sets of cards:
green, blue, yellow, and red. Each set has 15 cards numbered from
1 to 15. Select all of the actions that have more than 4 possible
outcomes. 7.SP.8, 7.SP.8b
0
selecting a blue card less than 5
selecting a red card greater than 13
selecting a yellow 12 card
selecting an 8 or 9 card of any color
selecting an even-numbered green card greater than 4
selecting a yellow card greater than 4²
selecting a blue card that is a multiple of 3

Answers

The actions that have more than 4 possible outcomes are:

- Selecting an 8 or 9 card of any color (each set has 2 cards for a total of 8 possible outcomes)

- Selecting a yellow card greater than 4² (there are 7 yellow cards that meet this criteria)

- Selecting a blue card that is a multiple of 3 (there are 5 blue cards that meet this criteria)

Therefore, only three of the given actions have more than 4 possible outcomes.

In the coordinate plane, the point X (-1, 0) is translated to the point X' (3, 1). Under the same translation, the points Y (2, 3) and Z (1, -2) are translated to Y' and Z', respectively. What are the coordinates of Y' and Z'?

Answers

The coordinates of Y' are (6, 4) and the coordinates of Z' are (5, -1).

To find the coordinates of Y' and Z', we need to apply the same translation that maps X to X'.

We know that the vector that connects X to X' is (3 - (-1), 1 - 0) = (4, 1).

So, to translate Y to Y', we add the vector (4, 1) to the coordinates of Y:

Y' = Y + (4, 1)

= (2, 3) + (4, 1)

= (6, 4)

Similarly, to translate Z to Z', we add the vector (4, 1) to the coordinates of Z:

Z' = Z + (4, 1)

= (1, -2) + (4, 1)

= (5, -1)

Therefore, the coordinates of Y' are (6, 4) and the coordinates of Z' are (5, -1).

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Help with solving This graph

Answers

Answer:

r=4

center: (-2,4)

Step-by-step explanation:

The equation of a circle is:

(x-h)²+(y-k)²=r²

(h,k) would be the center of the circle and r would be length of the radius

To find r, we simply take the square root of 16, which would be 4

And the center is given in the equation

Someone please help!! (20 POINTS!)

Answers

Answer: C

Step-by-step explanation: Rise/run so 1/1=1 but it's going down so it negative. -1

2raised to power m-3 = 1

Answers

Answer:

m = 3

Step-by-step explanation:

Given:

[tex]2^{m-3}[/tex] = 1

Take the logarithm of both sides (logarithm of 1 is 0):

m - 3 = 0

Add 3 to both sides:

m - 3 + 3 = 0 + 3

m = 3

Hence, m = 3.

Logarithm is the power to which a number must be raised in order to get some other number. For example:

The base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. Meaning [tex]10^{2}[/tex] = 100.

Suppose that the function h is defined as follows.

Answers

For the given function h(x) the points can be plotted on,

(-1,-1)(0,0)(1,1)(2,2)

The given function h(x) is having four conditions and each condition can be clearly discussed below:

Given that for the first condition, the x-axis is ranging from -1 [tex]\leq[/tex] x < 0, the y-axis point is present exactly at -1. Similarly, for the second condition, the x-axis is ranging from 0 [tex]\leq[/tex] x < 1, and the y-axis point is present at 0. For the third condition, the x-axis is ranging from 1 [tex]\leq[/tex] x < 2, and the y-axis point is at 1.Finally, for the fourth condition, the x-axis is ranging from 2 [tex]\leq[/tex] x < 3, and the y-axis point is at 2.

From, the above analysis we plotted the graph and attaching below.

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Given ∠4≅∠14, which lines, if any, must be parallel based on the given information? Justify your conclusion. Responses a∥b, converse of the same-side interior angles theorem a is parallel to b, , converse of the same-side interior angles theorem a∥b, converse of the alternate interior angles theorem a is parallel to b, , converse of the alternate interior angles theorem a∥b, converse of the corresponding angles theorem a is parallel to b, , converse of the corresponding angles theorem not enough information to make a conclusion not enough information to make a conclusion Two horizontal, parallel lines, line c and line d, where line c is above line d. These lines are intersected by two diagonal parallel lines, line a and line b. Line a is to the left of line b. The angles created by each intersection are numbered. From top left, going clockwise, the angles where line a intersects line c are labeled eleven, ten, nine, and twelve. The angles where line b intersects line c are labeled seven, six, five, and eight. The angles where line a intersects line d are labeled fifteen, fourteen, thirteen and sixteen. The angles where line b intersects line d are labeled three, two, one and four.

Answers

Based on the given information that ∠4 ≅ ∠14, we can conclude that lines a and b are parallel by the converse of the corresponding angles theorem. This theorem states that if two lines are intersected by a transversal and corresponding angles are congruent, then the lines are parallel. Therefore, we can conclude that line a is parallel to line b.

However, we cannot conclude that any other lines are parallel based on the given information.

In a sample of 1000 adults, 150 said they are very confident in the nutritional information on restaurant menus. for us adults are selected at random without replacement.

Find the probability that none of the four adults are very confident in the nutritional information on the restaurant menus.

Answers

The probability that none of the four adults is very confident in the nutritional information on the restaurant menus is 0.208 or approximately 20.8%.

Ready to approach this issue by utilizing the hypergeometric conveyance, since we are examining without substitution from a limited populace of two sorts (those who are exceptionally sure and those who are not exceptionally sure).

Let X be the number of grown-ups in a sample of 4 who are not exceptionally sure about the wholesome data on eatery menus.

At that point, X takes after a hypergeometric dissemination with parameters N = 1000, n = 4, and K = 850 (since 850 grown-ups are not exceptionally certain).

The likelihood that none of the 4 grown-ups are exceptionally certain can be communicated as:

P(X = 4) = (K select 4) / (N select 4)

where (K select 4) speaks to the number of ways to select 4 grown-ups from the population of 850 who are not exceptionally sure,

and (N select 4) speaks to the entire number of ways to select 4 grown-ups from the populace of 1000.

Utilizing the equation for binomial coefficients, ready to disentangle this expression as:

P(X = 4) = [(850*849*848*847) / (4*3*2*1)] / [(1000*999*998*997) / (4*3*2*1)]

= 0.208

Hence, the likelihood that none of the four grown-ups are exceptionally certain within the wholesome data on eatery menus is 0.208 or approximately 20.8%.

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Please help me this is so hard and i really dont get this. if you help me with both parts ill give you 60 points

Answers

1) We can rewrite the function in vertex form to find the time when the ball hits the ground. To do this, we need to complete the square.

h(t) = -5t^2 + 40t

h(t) = -5(t^2 - 8t)

h(t) = -5(t^2 - 8t + 16) + 80 (adding and subtracting 16 inside the parentheses to complete the square)

h(t) = -5(t - 4)^2 + 80 (factoring and simplifying)

So, the function in vertex form is h(t) = -5(t - 4)^2 + 80.

2) To find when the ball hits the ground, we need to find when h(t) = 0, since h(t) represents the height of the ball above the ground.

0 = -5(t - 4)^2 + 80 (substituting h(t) = 0)

5(t - 4)^2 = 80

(t - 4)^2 = 16

t - 4 = ±4

t = 4 ± 4

So, the ball hits the ground at t = 0 or t = 8 seconds after launch. However, we can discard the t = 0 solution because that represents the time when the ball is launched, and we are looking for when it hits the ground. Therefore, the ball hits the ground at t = 8 seconds after launch.

5. Un tanque contiene 9 litros de agua si se abre el grifo que vierte tres litros de agua por minuto y y es la cantidad de agua (en litros), que hay en el tanque después de x minutos

Answers

The equation that models the amount of water in the tank after x minutes is:

y = -3x + 9

How many liters are there after x minutes?

We know that the tank contains 9 liters of water, and it loses water at a constant rate of 3 liters per minute.

Then we can model the amount of water y in the tank after x minutes with a linear equation where the y-intercept is 9 and the rate of change is -3 (the amount it loses per unit of x)

Then the equation is:

y = -3x + 9

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Students in a math class recorded the number of text messages they received the previous day. How many students received at least 10 messages? Number of text messages line plot from 0 to 25 by fives. 5 has 2 marks, 10 has 3 marks, 15 has 2 marks, 20 has 4 marks, and 25 has 5 marks. 14 students 11 students 3 students 2 students

Answers

Answer:

Step-by-step explanation:

same goes 4 him i though he loved me but 10 =5x2

a couple decides to keep having children until they have a girl, at which point they will stop having children. they also agree to having a maximum of 3 children. the table shows the probability distribution of X=the number of children such a couple would have.

Answers

From the discrete distribution given, the standard deviation is of 0.83 children.

How to solve

The distribution is:

P(X=1) =0.5

P(X=2) =0.25

P(X=3) =0.25

The mean is 1.75.

The standard deviation is the square root of the sum of the difference squared between each value and the mean, multiplied by it's respective probability.

Hence:

The standard deviation is 0.83 children.

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The point (3,b) lies on the circle with radius 8 and center (−2,−1). What are the possible values of b

Answers

The point (3,b) can lie on the circle with radius 8 and center (-2,-1) for values of b equal to -1 + √39 and -1 - √39.

We know that the circle with radius 8 and center (-2,-1) has the equation:

(x + 2)² + (y + 1)² = 8²

Substituting x = 3 and y = b, we get:

(3 + 2)² + (b + 1)² = 8²

Simplifying, we get:

25 + (b + 1)² = 64

(b + 1)² = 39

Taking the square root of both sides, we get:

b + 1 = ± √39

Therefore, the possible values of b are:

b = -1 ± √39

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Calculate the area of a circle 4ft ,2in,18ft,5.2in,7.3in,14cm,9m,3m,9.2cm,7m,5m,6m

Answers

Answer:

Step-by-step explanation:

It seems like you have provided multiple measurements for the radius of the circle. I'm sorry, but a circle can only have one radius, so I am not able to calculate its area with the given information.

Please provide the correct measurement for the radius of the circle, and I will be happy to help you calculate its area.

f ( x ) = 12 ( 7 ) x using base e

Answers

The answer is 473m in my perspective

Please need answer 17.

Answers

Answer:

sec(θ) = √10/3tan(θ) = 1/3

Step-by-step explanation:

You want the tangent and secant of the angle θ the line x-3y=0 makes with the negative x-axis.

Trig functions

The relations between the angle and its trig functions are ...

Tan = Opposite/Adjacent

Sec = Hypotenuse/Adjacent

Unit circle

We have shown the angle of interest in a unit circle with the "adjacent" side equal to the radius of the circle (1). Then the values of interest are ...

tan(θ) = opposite side = 1/3 . . . . . . . equal to the slope of the line

sec(θ) = hypotenuse = √(1 +(1/3)²) = √(10/9) = (√10)/3

The tangent is 1/3; the secant is (√10)/3.

Additional comment

A third-quadrant angle measured from the +x axis has a negative secant. The tangent is positive there.

Since this angle is measured from the -x axis, it isn't clear whether it is supposed to be considered a 3rd-quadrant angle or not. For the given acute angle θ shown, the trig functions are both positive. YMMV

A large department store found that it averages 362 customers per hour. Assume that the standard deviation is 29.6 and a random sample of 40 hours was used to determine the average. Which statements about this situation are true?

Answers

The 99% confidence interval of the population mean is (352.32, 371.68).

To find the 99% confidence interval of the population mean, we need to use the following formula:

CI = x; ± zα/2 * (σ/√n)

where:

x' = sample mean (362)

zα/2 = z-score for 99% confidence level (2.576)

σ = population standard deviation (29.6)

n = sample size (40)

Substituting the values, we get:

CI = 362 ± 2.576 * (29.6/√40)

CI = 362 ± 9.68

This means that if we take many random samples of 40 hours from the population, we can be 99% confident that the true population mean of the number of customers per hour falls between 352.32 and 371.68.

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Complete question is:

Sonji went to a sandwich shop for lunch with 8 of her friends. Part of the group ordered only a sandwich for $5, and the
rest of the group ordered à combo for $8. The bill for all 9 people totaled $66.00. Which system of equations represents
the number of meals of each type that Sonji and her friends purchased?

Answers

Answer:

x+y=9

5x+8y=66

Step-by-step explanation:

Someone help I have no idea how to do this, it would help if I could get a step by step

Answers

Answer: x=3

Step-by-step explanation:

shaded part is 5/6 of the full circle, so just make an equation.

5/6 pi r^2(formula to find area)=15/2 pi(area given)

cancel out pi and simplify

r^2=9

r=+-3 but cant be negative so r=3

Which is equivalent to 234 2/5

Answers

234 2/5 is equivalent to 1172/5.

234 2/5 is a mixed number, which means it is a combination of a whole number and a fraction.

To convert it to an improper fraction, we need to multiply the whole number by the denominator of the fraction and add the numerator.

The result becomes the new numerator, and the denominator stays the same.

In this case, we have:

234 2/5 = (234 x 5 + 2) / 5

= 1172/5

Therefore, 234 2/5 is equivalent to 1172/5 as an improper fraction.

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Match the line described on the left with the slope of the line on the right.

x=-3 , 6x-3y=18 , the line through (7,5) and (8,5) , the line through (4,-2) and (1,7)

Undefined -3 , 0 , 2

Answers

The Slope of x = -3 is undefined; 6x-3y=18 is 2; (4,-2) and (1,7) is -3; and (7,5) and (8,5) is 0.

What is the Slope of a Line?

Slope of a line (m) = rise/run = change in y / change in x

Note that the slope of vertical lines are always undefined.

Therefore, we have the following:

x = -3 represents the equation of a vertical line, therefore, the slope is undefined.

6x - 3y = 18 is rewritten as y = 2x - 6 in slope-intercept form. The slope is 2.

For (4,-2) and (1,7):

Slope (m) = (7 -(-2))/(1 - 4) = 9/-3 = -3

For (7,5) and (8,5):

Slope (m) = 5 - 5/8 - 7 = 0/1 = 0

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What is the least common dominator of 4/13 and 4/5?

Answers

Answer:

52 is the least common dominator

Answer:

52/65

Step-by-step explanation:

The same fraction we can express in many different forms. If the numerator and denominator ratio is the same, the fractions represent the same rational number.

The least common denominator of a set of fractions is the least number that is a multiple of all the denominators: their least common multiple

The method of calculating the LCD is the same as the calculation least common multiple of fractions denominators.

The simple method for common computing denominators (not least at all) is to multiply all denominators.

In its second year of operation, a local Internet provider’s profits were $170,500. If this amount was 576% of the company’s first-year profits, find the first- year profits (to the nearest hundred dollars).

Answers

Proportionately, if $170,500 profits in the second year of operation represent 576% of the company's first-year profits, the first-year profits will be $29,600.

What is a proportion?

A proportion describes two ratios equated to each other.

Proportion is a fractional value that compares one value or quantity to another.

The profits for the second year of operation = $170,500

Let the profits for the first year of operation = x

Proportionately, if $170,500 is 576% of x, x = $29,600 ($170,500 ÷ 576%)

Using equations, 5.76x = $170,500

x = $29,600 ($170,500 ÷ 5.76)

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Is AB perpendicular to CD? Explain? pls yall fwm on the answer

Answers

Answer: No

Step-by-step explanation: They are not perpendicular due to the slopes. Perpendicular will have the same slopes value wise, but one is negative and one positive.

A yoga studio sells monthly memberships. The function f(x) = −x^2 + 50x − 264 models the profit in dollars, where x is the number of memberships sold.

Determine the zeros, and explain what these values mean in the context of the problem.
x = 6, x = 44; The zeros represent the number of monthly memberships that produces a maximum profit.
x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.
x = 25, x = 361; The zeros represent the number of monthly memberships where no profit is made.
x = 25, x = 361; The zeros represent the number of monthly memberships that produces a maximum profit.

Answers

The zeros of the quadratic profit function are explained as:

x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made

How to find the zeros of a quadratic function?

The quadratic function is given as:

f(x) = −x² + 50x − 264

The general form of expression of a quadratic function is:

f(x) = ax² + bx + c

The quadratic formula to find the zeros is:

x = [-b ± √(b² - 4ac)]/2a

Thus, we have the zeros as:

x = [-50 ± √((-50)² - 4(-1 * -264))]/2(-1)

x = 6 and x = 44

This represents number of monthly memberships where no profit is made.

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20x^2-7x-6=0 by factoring

Answers

Answer:

x = -2/5

x = 3/4

Step-by-step explanation:

Factoring:

20x²-7x-6=0

20x²+8x - 15x - 6 = 0

4x * (5x + 2) - 3 * (5x + 2) = 0

(5x + 2) * (4x - 3) = 0

Cases:

5x + 2 = 0

4x - 3 = 0

x = -2/5

x = 3/4

Answer:

20x^2 -x(15-8)-6=0 here 6×20=120an by subtracting 15-8 we got seven where the 15×8 is also 120

Step-by-step explanation:

now,

20x^2 -15x+8x -6 =0 (here -×-is equal to +thus we write +8)

5x(4x-3) +2(4x-3)=0

(5x+2) (4x-3)=0

Either 5x=-2

X=-2/5

4x=3

X=3/4

evaluate the expression

Answers

After substituting the values as x=3 and y=7, the value of the expression "2x²-y¹+3x⁰" is 14.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified or evaluated to a numerical value.

To evaluate the expression 2x²-y¹+3x⁰ for x=3 and y=7, we substitute the given values, which are x=3 and y=7 into the expression and simplify:

On substituting the values,

We get,

= 2x² - y¹ + 3x⁰

= 2(3)² - 7¹ + 3(1)

= 2(9) - 7 + 3

= 18 - 7 + 3

= 14

Therefore, when x=3 and y=7, the value of the expression 2x²-y¹+3x⁰ is 14.

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What are the roots of the quadratic equation below?
2x² + 8x+7= 0
O A. x = = 2√2
1
O B. x =
-8+√120
8
O
O D. x =
C. x = = 4+√/²
-2+√120

Answers

Answer:

Step-by-step explanation:

Help pleaseee

Expand the logarithm as much as possible

logy^10

Answers

The expanded form of log y^10 is either 10 log y or 10 ln y

Expanding the logarithm

Assuming that the base of the logarithm is not specified, we can use the change of base formula to expand the logarithm:

log y^10 = log (y^10) / log (base)

Using base 10:

log y^10 = log (y^10) / log 10

= 10 log y / 1

= 10 log y

Using natural logarithm:

log y^10 = log (y^10) / log e

= 10 log y / 1

= 10 ln y

Therefore, the expanded form of log y^10 is either 10 log y or 10 ln y, depending on the base used.