On social issues, _____ think people should be liberated from the ways of the past and able to decide for themselves about how to live

If the cycle time is 2 minutes per customer, 30 customers can be served per hour.

The given cycle time is 2 minutes per customer. To calculate how many customers can be served per hour, we need to calculate the number of minutes in an hour as follows: 60 minutes = 1 hour.

The time taken for each customer is 2 minutes. Therefore, the number of customers that can be served per hour can be calculated as follows:

Number of customers per hour = (60 minutes/hour) ÷ (2 minutes/customer)
Number of customers per hour = 30 customers.

Therefore, the number of customers that can be served per hour is 30, according to the given cycle time of 2 minutes per customer.

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When we write out the system of equations, we will get:

[tex]x+y=18[/tex]

[tex]x-y=-8[/tex]

We can then use elimination to get just one variable.

[tex]x+y=18[/tex]

[tex]x-y= -8[/tex]

Which gives us: [tex]2x=10[/tex]

We then divide by 2 and get: [tex]x=5[/tex]

We next plug that into one of the two equations and solve for the other variable: [tex](5)+y=18[/tex]

We subtract 5 from both sides and get: [tex]y=13[/tex]

So the two numbers are 13 and 5.

The measure of angle ACD is approximately 109.5 degrees.

What are parallel lines ?

Parallel lines can be defined in which the lines which are equidistant to each other and they never intersect.

To solve for m<ACD, we can use the fact that the sum of the angles in a triangle is 180 degrees.

We can start by finding the measure of angle ACD, which is opposite to the known side length of 10 units. Using the Law of Cosines, we have:

cos(ACD) = (AD * AD + CD * CD - 100) / (2 * AD * CD)

We know that AD = 8 units and CD = 6 units, so plugging in these values, we get:

cos(ACD) = (64 + 36 - 100) / (2 * 8 * 6) = -1/3

Since -1/3 is negative, we know that angle ACD is obtuse, meaning it measures between 90 and 180 degrees. Therefore, we can take the inverse cosine of -1/3 to find its measure:

cos(ACD) = (-1/3) ≈ 109.5 degrees

Therefore, the measure of angle ACD is approximately 109.5 degrees.

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Answer:

$10.98

Step-by-step explanation:

$10.98

0.06 x 183 = $10.98

If Kathy had $20 to spend on 3 gifts and she spent $10⁷/₁₀ on Gift A and $6²/₅ on Gift B, the (balance) amount left for Gift C is $3.89.

The balance can be determined using subtraction operation.

Subtraction operation is one of the four basic mathematical operations, including addition, multiplication, and division.

Subtraction operation involves the minuend ($20), the subtrahends ($10.07 and $6.04), giving a difference or balance of $3.89.

The total spending budget that Kathy has = $20

The number of gifts to buy = 3

The amount spent on Gift A = $10.07 ($10⁷/₁₀)

The amount spent on Gift B = $6.04 ($6²/₅)

The amount left for Gift C = $3.89 ($20 - $10.07 - $6.04).

Thus, after spending on Gifts A and B, the amount left for Gift C is determined using subtraction operation as $3.89.

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The twο pοssible values οf ∠R tο the nearest 10th οf a degree are 33.6° and 326.4°.

A triangle is a clοsed twο-dimensiοnal geοmetric shape with three straight sides and three angles. It is the simplest pοlygοn, which is a flat shape cοnsisting οf straight lines.

We can use the Law οf Cοsines tο find the length οf side QR:

[tex]c^2 = a^2 + b^2 - 2ab[/tex] cοs(C)

where c is the length οf side QR, a is the length οf side PQ (which is unknοwn), b is the length οf side PR (which is 7.8 cm), and C is the angle οppοsite side c (which is 30°). Substituting the given values, we get:

[tex]QR^2 = PQ^2 + 7.8^2 - 2(PQ)(7.8)cos(30^\circ )[/tex]

[tex]QR^2 = PQ^2 + 60.84 - 7.8PQ[/tex]

Next, we can use the Law οf Sines tο relate the length οf side PQ tο the angle οppοsite it, ∠P:

PQ/sin(30°) = QR/sin(P)

PQ = QR(sin(30°)/sin(P))

Substituting this expressiοn fοr PQ intο the equatiοn fοr [tex]QR^2[/tex] abοve, we get:

[tex]QR^2 = [QR(sin(30^\circ)/sin(P))]^2 + 60.84 - 7.8[QR(sin(30^\circ)/sin(P))][/tex]

Simplifying and rearranging, we get a quadratic equatiοn in terms οf QR:

[tex]QR^2 - 3.9QR + 28.99 = 0[/tex]

Using the quadratic fοrmula, we find that:

QR ≈ 7.466 cm οr QR ≈ 3.866 cm

Since we knοw that QR < PQ + PR = 6 + 7.8 = 13.8, the οnly valid sοlutiοn is QR ≈ 7.466 cm. Therefοre, we have:

[tex]cos(R) = (PQ^2 + QR^2 - PR^2)/(2PQQR)[/tex]

[tex]cos(R) = (PQ^2 + 7.466^2 - 7.8^2)/(2PQ(7.466))[/tex]

[tex]cos(R) = (PQ^2 - 4.928)/[2PQ(7.466)][/tex]

Since cοs(R) ≤ 1, we have:

[tex]PQ^2 - 4.928 ≤ 2PQ(7.466)[/tex]

Sοlving fοr PQ using the quadratic fοrmula, we get:

PQ ≤ 5.474 cm οr PQ ≥ 20.032 cm

Since PQ < PR, the οnly valid sοlutiοn is:

PQ ≈ 5.474 cm

Nοw we can use the Law οf Cοsines again tο find ∠R:

[tex]cos(R) = (PQ^2 + PR^2 - QR^2)/(2PQPR)[/tex]

[tex]cos(R) = (5.474^2 + 7.8^2 - 7.466^2)/(2(5.474)(7.8))[/tex]

cοs(R) ≈ 0.828

R ≈ 33.6° οr R ≈ 326.4°

Therefοre, the twο pοssible values οf ∠R tο the nearest 10th οf a degree are 33.6° and 326.4°.

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The area of the table top is approximately 28.27 square feet. To find the area of a circular table top with a given circumference, we can use the formula A = πr², where r is the radius.

To find the area of the table top, we need to use the formula for the area of a circle, which is:

A = πr²

We are given the circumference of the table top, which is:

C = 2πr

We can solve for r by dividing both sides by 2π:

r = C / (2π) = 18.84 / (2 * 3.14) = 3

Now we can substitute this value for r into the formula for the area of a circle:

A = π(3)² = 9π

Using 3.14 for π, we get:

A ≈ 28.26

Rounding to the nearest hundredth, the area of the table top is approximately 28.27 square feet.

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Answer:

the area of the photograph when it is put into the frame is 80 square inches, and the area of the frame is 88 square inches.

Step-by-step explanation:

Answer: 36 inches(2)

Step-by-step explanation:

Answer:

In a right triangle, one angle is always 90 degrees (a right angle). The other two angles are acute angles, which means they are less than 90 degrees.

Let's call the acute angle we're interested in "a". We know that sin a = 3/5.

"Sin" is short for "sine", which is a ratio of two sides of the triangle. Specifically, it's the ratio of the length of the side opposite angle a to the length of the hypotenuse (the longest side of the triangle, which is always opposite the right angle).

So, in our triangle, if sin a = 3/5, that means the side opposite angle a is 3 units long and the hypotenuse is 5 units long.

Now, we can use the Pythagorean theorem to find the length of the third side of the triangle (the one adjacent to angle a). The Pythagorean theorem says that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In other words:

a^2 + b^2 = c^2

where a and b are the lengths of the two shorter sides, and c is the length of the hypotenuse.

In our triangle, we know that b is the side adjacent to angle a, so we're trying to find its length. We also know that a = 3 and c = 5, so we can plug those values into the Pythagorean theorem and solve for b:

3^2 + b^2 = 5^2

9 + b^2 = 25

b^2 = 16

b = 4

So the length of the side adjacent to angle a is 4.

Now, we can use the ratios of the trigonometric functions (sine, cosine, and tangent) to find the values of cosine and tangent for angle a.

Cosine (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse. So in our triangle:

cos a = adjacent/hypotenuse = 4/5

Tangent (tan) is the ratio of the length of the opposite side to the length of the adjacent side. So in our triangle:

tan a = opposite/adjacent = 3/4

Therefore, if sin a = 3/5 in a right triangle, where a is an acute angle, then cos a = 4/5 and tan a = 3/4.

Under the null hypothesis, this test statistic follows a t-distribution with (n nap + n coffee - 2) degrees of freedom and the p-value is less than the significance level of 0.05,

To determine if there is sufficient evidence that taking a nap promotes faster reaction time than drinking coffee, we can perform a two-sample t-test assuming equal variances. The null hypothesis is that there is no difference in the mean reaction times between the nap and coffee groups, while the alternative hypothesis is that the mean reaction time for the nap group is less than the mean reaction time for the coffee group.

Let's assume that we have collected data on reaction times for both the nap and coffee groups, and have calculated their sample means ( X nap and X coffee) and sample standard deviations (snap and  s coffee). We can then calculate the pooled standard deviation using the formula:

[tex]Sp = sqrt(((nnap - 1) * snap^2 + (ncoffee - 1) * scoffe^2) / (nnap + ncoffee - 2))[/tex]

where n nap and n coffee are the sample sizes for the nap and coffee groups, respectively. We can then calculate the test statistic using the formula:

t = (X nap - X coffee) / (Sp * sqrt(1/nnap + 1/ncoffee))

Under the null hypothesis, this test statistic follows a t-distribution with (n nap + n coffee - 2) degrees of freedom. We can calculate the p-value for this test statistic using a t-distribution table or a calculator. Alternatively, we can use Python or R to perform the test and calculate the p-value.

If the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence that taking a nap promotes faster reaction time than drinking coffee. Otherwise, we fail to reject the null hypothesis.

After calculating the appropriate test statistic, we would save it into variable p2.C.Stat, rounding the value to two decimal places. We would then calculate the p-value for this test statistic and save it into variable p2.C.P, rounding the value to three decimal places.

It's important to note that the assumptions of the two-sample t-test, such as normality and equal variances, should be checked before performing the test. If these assumptions are not met, alternative tests such as the Wilcoxon rank-sum test may be more appropriate.

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The earnings made in 1 day when charging a device with a power rating of 12 W at a rate of 6 cents per kilowatt hour is 0.01728.

Given, Power rating of charger = 12 W. Charge per kilowatt hour = 6 cents = 0.06/kWh.To calculate the earnings in 1 day, we need to calculate the power consumed by the charger in 1 day first.

P = Power rating of charger = 12 Wt = Time = 1 day = 24 hours. Energy consumed = Power x Time. E = P x t= 12 W x 24 hours= 288 Wh = 0.288 kWh. Therefore, energy consumed by the charger in 1 day = 0.288 kWh.

Now, we can calculate the earnings in 1 day as follows: Charge per unit = 0.06/kWh. Earnings = Energy consumed x Charge per unit. Earnings = 0.288 kWh x 0.06/kWh= 0.01728.

Therefore, the earnings made in 1 day when charging a device with a power rating of 12 W at a rate of 6 cents per kilowatt hour is 0.01728.

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Answer:

(15/4)4^x

Step-by-step explanation:

Substituting the x and y values of the first point, we get:

y = ab

60 = ab^(2)

Substituting the x and y values of the second point, we get:

y = ab

960 = ab^(4)

Now we can solve for a and b by eliminating one of the variables. One way to do this is to divide the second equation by the first equation:

960/60 = (ab^(4))/(ab^(2))

16 = b^(2)

Taking the square root of both sides, we get:

b = ±4

Since an exponential function can only have positive values for b, we choose b = 4. Now we can solve for a by substituting b = 4 into one of the original equations:

60 = a(4^(2))

60 = 16a

a = 60/16

a = 15/4

Therefore, the values of a and b are a = 15/4 and b = 4, and the exponential function is y = (15/4)4^x.

After solving the equation N x 4 = 28 for N, then the solution to the equation is N = 7.

An equation is a mathematical statement that shows the equality of two expressions. It typically contains one or more variables and may involve arithmetic operations such as addition, subtraction, multiplication, or division. Equations can be solved to determine the values of the variables that make the equation true. For example, the equation 2x + 5 = 11 is true when x = 3, since 2(3) + 5 = 11.

To solve the equation N x 4 = 28 for N, we need to isolate N on one side of the equation.

First, we can divide both sides of the equation by 4:

N x 4 ÷ 4 = 28 ÷ 4

Simplifying:

N = 7

Therefore, the solution to the equation is N = 7.

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If you want each character to be approximately one inch in size, you would use a point size of 72 pts.

Point size is a unit of measurement used to determine the size of typefaces. It represents the height of the characters in a font. One point is equal to 1/72 of an inch, which means there are 72 points in one inch.

Therefore, if you want each character to be approximately one inch in size, you would need to use a font size of 72 points. This would ensure that the characters are roughly one inch tall, assuming that the font is designed to be proportional and not condensed or expanded.

Choosing a smaller point size, such as 1 pt or 24 pts, would result in characters that are much smaller than one inch. Choosing a larger point size, such as 36 pts, would result in characters that are larger than one inch.

Therefore the correct answer is option b.) 72 pts.

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Answer:

I attached your answer along with an explanation

Step-by-step explanation:

Please Like me follow me and Give me Crown for more help. :)

The student's original statement has an issue in the way the "not" operator is used. The "not" operator (!) is negating the entire expression, including the variable 'x', rather than just the inequality. This leads to incorrect evaluation.

To correctly determine if x is not greater than 20, you should use the "less than or equal to" (<=) operator instead. Here is the corrected statement:

if (x <= 20)

This statement will be true if x is less than or equal to 20, which is the intended condition.

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The three classifications of fundamental skull shapes are: +

The number of degrees of angulation (formed by the petrous pyramids and the midsagittal plane) for each classification is 45, 30, and 15 degrees, respectively.

The skull is a bony structure that supports the face and protects the brain. There are several different skull shapes, which can be classified into three main categories based on their length and width: brachycephalic, mesocephalic, and dolichocephalic.

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The value 1.106 represents the slope of the regression line or the rate of change of y with respect to x.

In the given regression equation y = 3.915(1.106)x:

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The estimated enrollment of a high school in 2022 is approximately 2775 students.

To calculate the estimated enrollment in 2022, we need to use the formula for compound interest:

A =[tex]P(1 + r)^t[/tex]

where:

A = final amount (enrollment in 2022)

P = initial amount (enrollment in 2012)

r = annual interest rate (increase rate)

t = number of years (10)

We know that P = 1350 and r = 0.09 (9%). We can plug these values into the formula:

A = [tex]1350(1 + 0.09)^{10[/tex]

A = [tex]1350(1.09)^{10[/tex]

A = 2774.92

Therefore, the estimated enrollment in 2022 is approximately 2775 students.

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However, it is important to note that without additional information about the function and the windmill itself, further conclusions about its design and performance cannot be made.

Hi! I'd be happy to help you describe the windmill based on the provided graph.The graph of the function represents the relationship between the height (y) of the tip of a windmill blade and the angle of rotation (Θ) made by the blade. This function is periodic, indicating that the windmill blade follows a repetitive motion as it rotates.

The height of the blade tip varies sinusoidally with respect to the angle of rotation, suggesting that the windmill has a circular or rotational motion. The amplitude of the function gives the length of the windmill blade, while the period of the function represents a full rotation (360 degrees) of the windmill blade.

In summary, the windmill has a rotational motion, with the height of the blade tip following a sinusoidal pattern. The length of the windmill blade and the time it takes to complete a full rotation can be determined by analyzing the amplitude and period of the function.

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Answer:

We can use exponential decay formula to solve this problem:

N(t) = N0 * e^(-kt)

where N(t) is the number of employees with petrol cars at time t, N0 is the initial number of employees with petrol cars (in 2013), k is the decay constant, and e is the base of the natural logarithm.

We need to find N(2019), the number of employees with petrol cars in 2019. We know that N0 = 1536, and we need to find k.

Let's assume that the number of employees with petrol cars decreases by 5% each year. This means that the ratio of the number of employees with petrol cars in two consecutive years is:

0.95

Therefore, we can write:

N(2019) = 1536 * 0.95^(2019-2013)

N(2019) = 1536 * 0.95^6

N(2019) = 1133.76

Rounding to the nearest integer, we get:

N(2019) = 1134

Therefore, we can estimate that about 1134 employees owned a petrol car in 2019, assuming that the number of employees with petrol cars decreases exponentially at a rate of 5% per year.

Answer:

There are different ways to approach this problem, but one possible method is:

Define the event A as "the student owns a trampoline".

Find the probability of A: P(A) = 21/23, because 21 out of 23 students said they owned a trampoline.

Find the probability of the complement of A, which is "the student does not own a trampoline". We can denote this event as A', and it is equivalent to "the student is one of the 2 students who did not say they owned a trampoline". Therefore, P(A') = 2/23.

Check that P(A) + P(A') = 1, because the student either owns a trampoline or does not.

Answer the question: the probability that the student does not own a trampoline is P(A') = 2/23, or approximately 0.087 or 8.7% (rounded to one decimal place).

Therefore, the answer is: the probability that the student does not own a trampoline is 2/23, or approximately 0.087 or 8.7%.

Answer:

Diameter is equal to twice the radius. Given, radius is 4 cm. Diameter = 2(4) = 8 cm. Hence, diameter of the circle with radius as 4 cm is 8 cm.

Step-by-step explanation:

please

give brianliest

Answer: Area = 0

Step-by-step explanation:

((2*2)*3.14)-(4*3.14) = 0

Answer:

8;-2

Step-by-step explanation:

8 is the x axis and -2 is the y axis

Answer:

Step-by-step explanation:

Answer:

£164.50

Step-by-step explanation:

If the discount is 6%, then the discounted price is 94% of the original price.

95% of £175 = 0.94 × £175 = £164.50

Using fraction, the total number of cupcakes is obtained to be 5.

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

If 4 cupcakes represent 80% of the order, then we can use proportional reasoning to find the total number of cupcakes.

Specifically, if x is the total number of cupcakes, then we can write -

4/x = 80/100

where the left-hand side represents the fraction of the order that is Nom-Nom-Nom cupcakes, and the right-hand side represents the percentage of the order that is Nom-Nom-Nom cupcakes.

Solving for x, we get -

x = 4 / (80/100) = 5

So the total number of cupcakes is 5. Since 4 of them are Nom-Nom-Nom cupcakes, the remaining 1 cupcake must be a Wow cupcake.

Therefore, in total there are 5 cupcakes.

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I've been waiting to order your cupcakes all day! I'll have 4 Nom-Nom-Nom cupcakes -- that's 80% of my order. The rest of the order are Wow.
Find the total number of cupcakes.

The probability that at least 67 out of 100 cars stopped at a roadblock will not be given a ticket is 2.37.

Given Probability of giving tickets to cars that are stopped = 0.23

Probability of not giving tickets to cars that are stopped = 1 - 0.23 = 0.77

the probability that at least 67 out of 100 cars stopped at a roadblock will not be given a ticket

Here n = 100, p = 0.77, q = 0.23

mean = np = 100*0.77 = 77

standard deviation = [tex](sigma = \sqrt{(100)*(0.77)*(0.23) } = 4.208[/tex]

[tex]P(X\geq 67) = \frac{67 - 77}{4.208}[/tex] = 2.37

P-VALUE is 0.99126 from z-table

Probability is a fundamental concept in mathematics that helps us quantify the likelihood of events occurring and is applicable to a wide range of fields. It is a measure of the uncertainty of an event, expressed as a number between 0 and 1. An event with probability 0 is impossible, while an event with probability 1 is certain.For example, the probability of rolling a six on a fair six-sided die is 1/6, since there is only one favorable outcome out of six possible outcomes.

Probability theory has wide applications in fields such as statistics, finance, engineering, and physics, among others. It is used to model and analyze various phenomena, including weather patterns, stock prices, quantum mechanics, and more.

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