During the two hours of the morning rush from 8 a.m. to 10 a.m., 100 customers per hour arrive at the coffee shop. The coffee shop has a capacity of 0.8 minutes per customers. What is the number of customers waiting at 10 a.m.

To solve the question

First, we will represent the unknown number by y

then we can represent the question mathematically as follow:

Solving the above

Next, to get y, we will cross multiply

Dividing both sides by 90

Therefore, the number is 30

Answer:

g = \(\frac{4}{3}\)

Step-by-step explanation:

4 - \(\frac{1}{12}\) g - 2 = \(\frac{3}{2}\) g + 1 - \(\frac{5}{6}\) g

multiply through by 12 ( the LCM of 12, 2 and 6 ) to clear the fractions

48 - g - 24 = 18g + 12 - 10g

- g + 24 = 8g + 12 ( subtract 8g from both sides )

- 9g + 24 = 12 ( subtract 24 from both sides )

- 9g = - 12 ( divide both sides by - 9 )

g = \(\frac{-12}{-9}\) = \(\frac{12}{9}\) = \(\frac{4}{3}\)

For the first part, the number of license plates is: 65,780,800 and for the second part, the number of license plates with 3 consecutive digits is: 16,524,288.

If there are no restrictions on where the digits and letters are placed, the number of 8-place license plates consisting of 5 letters and 3 digits with no repetitions allowed can be found using the permutation formula:

nPr = n! / (n-r)!

where n is the number of available characters (26 letters and 10 digits) and r is the number of characters needed for the license plate (8).

Therefore, the number of license plates is:

(26 P 5) x (10 P 3) = (26!/21!) x (10!/7!) = 65,780,800

If the 3 digits must be consecutive, there are 8 possible positions for the block of digits (either the first 3, second 3, or last 3). Once the position of the block is chosen, the number of license plates can be found by counting the number of ways to arrange the letters and the block of digits. The number of ways to arrange the letters is 26 P 5, and the number of ways to arrange the block of digits is 10 (since there are only 10 possible sets of consecutive digits).

Therefore, the number of license plates with 3 consecutive digits is:

8 x (26 P 5) x 10 = 16,524,288

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The complete question goes thus:

If there are no restrictions on where the digits and letters are placed, how many 8

-place license plates consisting of 5

letters and 3

digits are possible if no repetitions of letters or digits are allowed? What if the 3

digits must be consecutive?

Main Answer: A range of values, that with a certain degree of probability contain the population parameter, is known as a "confidence interval estimate."

Supporting Question and Answer:

What is the purpose of a confidence interval estimate in statistics?

The purpose of a confidence interval estimate in statistics is to provide a range of values that, with a certain degree of probability, contains the population parameter of interest. This range allows for a measure of uncertainty and provides a level of confidence in the estimation process.

Body of the Solution: The correct answer is "confidence interval estimate."

A confidence interval estimate is a range of values that, with a certain degree of probability (often represented by a confidence level), is believed to contain the population parameter of interest. It is used in statistics to provide an estimate of an unknown population parameter based on sample data. The confidence interval provides a range rather than a single point estimate, allowing for a measure of uncertainty in the estimation process.

Final Answer: The correct answer is "confidence interval estimate."

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A range of values, that with a certain degree of probability contain the population parameter, is known as a "confidence interval estimate."

The purpose of a confidence interval estimate in statistics is to provide a range of values that, with a certain degree of probability, contains the population parameter of interest. This range allows for a measure of uncertainty and provides a level of confidence in the estimation process.

The correct answer is "confidence interval estimate."

A confidence interval estimate is a range of values that, with a certain degree of probability (often represented by a confidence level), is believed to contain the population parameter of interest. It is used in statistics to provide an estimate of an unknown population parameter based on sample data. The confidence interval provides a range rather than a single point estimate, allowing for a measure of uncertainty in the estimation process.

The correct answer is "confidence interval estimate."

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Answer: x=2

Step-by-step explanation:

-4x+7=-1

-4x=-8

x=2

The probability that the other child is also a girl, given that one of them is a girl, is 2/3 or approximately 0.6667.

To determine the probability that the other child is also a girl given that one of them is a girl, we need to consider the possibilities of the gender combinations for Alice's two children.

Let's denote the gender of the first child as G (girl) and B (boy), and the gender of the second child as G' and B'.

There are four possible combinations for the gender of the two children: GG, GB, BG, and BB.

However, we are given that one of the children is a girl. This eliminates the BB combination since we know both children cannot be boys.

Thus, we are left with three possible combinations: GG, GB, and BG.

Out of these three combinations, two of them involve at least one girl: GG and GB. This means there is a 2 out of 3 chance that the other child is a girl.

Therefore, the probability that the other child is also a girl, given that one of them is a girl, is 2/3 or approximately 0.6667.

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The unique challenges of lack of baseline data, sample size, and objectivity pose significant obstacles in environmental science. Researchers must work diligently to overcome these challenges through careful data collection, innovative methodologies, and critical analysis.

The challenge of lack of baseline data in environmental science refers to the difficulty in establishing a starting point or reference point to compare future observations or changes. Baseline data provides important information about the current state of the environment, such as air quality, water quality, biodiversity, and ecosystem health. Without this baseline data, it becomes challenging to assess and monitor changes over time accurately.

Sample size is another unique challenge in environmental science. It refers to the number of observations or data points collected for a particular study or analysis. A larger sample size generally provides more reliable and representative results. However, in environmental science, it is often difficult to obtain large sample sizes due to logistical constraints, limited resources, and the complexity of natural systems. This limitation can affect the precision and generalizability of research findings.

Objectivity is a critical aspect of scientific inquiry, including environmental science. It involves conducting research without bias or personal opinion, relying on empirical evidence and logical reasoning. However, achieving complete objectivity is challenging because researchers may have inherent biases, conscious or unconscious. Additionally, interpreting data can be subjective, leading to different conclusions. Environmental scientists strive to minimize subjectivity by using rigorous methodologies, peer review, and transparent reporting.

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The correct phrase commonly used to word conditional probabilities is "given that." This phrase explicitly indicates the condition or event on which the probability calculation is based and emphasizes the dependence between events in the probability calculation.

Let's discuss each option in detail to understand why the correct phrase is "given that" when wording conditional probabilities.

"Dependent": The term "dependent" refers to the relationship between events, indicating that the occurrence of one event affects the probability of another event. While dependence is a characteristic of conditional probabilities, it is not the specific wording used to express the conditionality.

"Given that": This phrase explicitly states that the probability is being calculated based on a specific condition or event being true. It is commonly used to introduce the condition in conditional probabilities. For example, "What is the probability of event A given that event B has already occurred?" The phrase "given that" emphasizes that the probability of event A is being evaluated with the assumption that event B has already happened.

"Either/or": The phrase "either/or" generally refers to situations where only one of the two events can occur, but it does not convey the conditional nature of probabilities. It is often used to express mutually exclusive events, where the occurrence of one event excludes the possibility of the other. However, it does not provide the specific condition on which the probability calculation is based.

"Mutually exclusive": "Mutually exclusive" refers to events that cannot occur simultaneously. While mutually exclusive events are important in probability theory, they do not capture the conditionality aspect of conditional probabilities. The term implies that if one event happens, the other cannot occur, but it does not explicitly indicate the specific condition on which the probability calculation is based.

In summary, the correct phrase commonly used to word conditional probabilities is "given that." It effectively introduces the condition or event on which the probability calculation is based and highlights the dependency between events in the probability calculation.

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The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in

(4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in

(6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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Answer: 4/9

Step-by-step explanation:

Mark as brainliest please ❤️✨

Answer:

4/9ths

Step-by-step explanation:

We first let 0.4 (4 being repeated) be x

Since x is recurring in 1 decimal places, we multiply it by 10.

Next, we subtract them.

Lastly, we divide both sides by 9 to get x as a fraction.

A Type I error occurs when the student incorrectly rejects the null hypothesis and concludes a difference when there isn't one, while a Type II error occurs when the student fails to reject the null hypothesis

In this study, the student is testing the hypothesis that the average age at first childbirth of mothers at community colleges (CBC) is lower than the national average age of 26 years old.

Type I error: A Type I error would be committed if the student decides that the average age at first childbirth of CBC mothers is 26 years old, but in reality, the true mean is NOT 26 years old. In other words, if the student incorrectly rejects the null hypothesis and concludes that the average age at first childbirth for CBC mothers is significantly different from the national average when it is not. Type II error: A Type II error would be committed if the student decides that the average age at first childbirth of CBC mothers is NOT 26 years old, but in reality, the true mean is 26 years old. In other words, if the student fails to reject the null hypothesis and concludes that there is no significant difference in the average age at first childbirth for CBC mothers compared to the national average when there actually is a difference. To summarize, a Type I error occurs when the student incorrectly rejects the null hypothesis and concludes a difference when there isn't one, while a Type II error occurs when the student fails to reject the null hypothesis and concludes no difference when there actually is one.

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Answer:

hanges made to your input should not affect the solution:

(1): Dot was discarded near "4.".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    5*x+7*y-(3914)=0

STEP

1

:

Equation of a Straight Line

1.1     Solve   5x+7y-3914  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  5x+7y-3914  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 3914/7 so this line "cuts" the y axis at y=559.14286

 y-intercept = 3914/7  = 559.14286

Calculate the X-Intercept :

When y = 0 the value of x is 3914/5 Our line therefore "cuts" the x axis at x=782.80000

 x-intercept = 3914/5  = 782.80000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 559.143 and for x=2.000, the value of y is 557.714. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 557.714 - 559.143 = -1.429 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -1.429/2.000 = -0.714

Geometric figure: Straight Line

 Slope = -1.429/2.000 = -0.714

 x-intercept = 3914/5 = 782.80000

 y-intercept = 3914/7 = 559.14286

Step-by-step explanation:

Answer:

y= -5/7x+3914/7

Step-by-step explanation:

Slope form is y=mx+b

5x+7y=3914

7y = -5x+3914 minus the 5x from each side

7y=-5x+3914  divide 7 from each side --> y= -5/7x+3914/7

So, 5x+7y=3914 is in ax+by=c (standard form) the "a" in "ax" can't be negative either.

The value of 'a1' is 0.

Let's denote the first term of the geometric series as 'a' and the common ratio as 'r'. The sum of an infinite geometric series can be calculated using the formula:

Sum = a / (1 - r)

We are given that the sum of the infinite geometric series a1, a2, a3, ... is 7. Therefore, we have:

7 = a / (1 - r) ---- (Equation 1)

Now, let's consider the sum of the infinite geometric series a2, a4, a6, ....

The first term of this series is a2 = ar, the second term is a4 = ar^3, the third term is a6 = ar^5, and so on.

The sum of this series can be calculated as:

Sum = (ar) / (1 - r^2)

We are given that the sum of this series is 3. Therefore, we have:

3 = (ar) / (1 - r^2) ---- (Equation 2)

Now, we can solve these two equations simultaneously to find the values of 'a' and 'r'.

From Equation 2, we can rewrite it as:

3(1 - r^2) = ar

Expanding and rearranging:

3 - 3r^2 = ar

3 = ar + 3r^2 ---- (Equation 3)

Now, substitute the value of 'ar' from Equation 3 into Equation 1:

7 = (ar) / (1 - r)

Multiplying both sides by (1 - r):

7(1 - r) = ar

Expanding:

7 - 7r = ar

7 = ar + 7r ---- (Equation 4)

Now, we have two equations (Equation 3 and Equation 4) with two variables ('a' and 'r'). We can solve these equations simultaneously.

Subtract Equation 4 from Equation 3:

3 = ar + 3r^2 - (ar + 7r)

3 = ar - ar + 3r^2 - 7r

3 = 3r^2 - 7r

Rearranging:

3r^2 - 7r - 3 = 0

This is a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. After solving the quadratic equation, we find two possible values for 'r': r = 1 or r = -3/2.

Now, we can substitute these values of 'r' back into Equation 4 to find the corresponding values of 'a'.

For r = 1:

7 = a(1) + 7(1)

7 = a + 7

a = 0

For r = -3/2:

7 = a(-3/2) + 7(-3/2)

7 = -3a/2 - 21/2

42 = -3a - 21

3a = -63

a = -21

Therefore, the two possible values for 'a' are 0 and -21.

However, since we are looking for the value of 'a1' (the first term of the geometric series), the value of 'a' should be positive. Thus, the value of 'a1' is 0.

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The population of Medway, Ohio, is expected to be approximately 3728 in the year 2020.

From the question, we have the following parameters that can be used in our computation:

Initial, a = 4007

Rate = 0.36% per year

The decay function is represented as

y = a(1 - rate)^x

So, we have

y = 4007 * (1 - 0.36%)^x

This gives

y = 4007 * (0.9964)^x

The year 2020 is 20 years from 2000

So, we have

x = 20

Substitute the known values in the above equation, so, we have the following representation

y = 4007 * (0.9964)^20

Evaluate

y = 3728

Hence, the approximate solution is 3728

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Answer:

5.5

Step-by-step explanation:

The given operation is :

20 - 0.45 x 20 - 1.75 x 2 - 2

In the above algorithm contains more than one operations to be executed. Here we use the BODMAS rule that states that we first calculate the brackets then the orders, following multiplication or division and then at last addition or subtraction. Therefore,

20 - ( 0.45 x 20 ) - ( 1.75 x 2 ) - 2

= 20 - 9 - 3.5 - 2  

= 11 - 3.5 - 2

= 7.5 - 2

= 5.5

Answer:

17

Step-by-step explanation:

well with the order of operations in this case you would do division first so it would be 72/8 = 9 then next you would add the 9+8 and that would leave you with 17

therefore c is the correct answer

hope this helped

have a good day :)

Answer:

D) 39

Step-by-step explanation:

There are a couple of steps to this. First, note that you must plug in the given number that replaces x into the right side's x. After you find the answers, you must then subtract both answers to get your result.

First step, find g(8):

g(x) = 3x - 2

When x = 8,

g(8) = 3(8) - 2

Remember to follow PEMDAS, the order of operations. First, multiply, then subtract:

g(8) = (3 * 8) - 2

g(8) = (24) - 2

g(8) = 22

Next step, find g(-5):

g(x) = 3x - 2

g(-5) = 3(-5) - 2

g(-5) = (3 * -5) - 2

g(-5) = (-15) - 2

g(-5) = -17

Note that you are subtracting both numbers. When there are two negative signs directly next to each other, it becomes a positive:

22 - (-17) = 22 + 17 = 39

D) 39 is your answer.

~

Answer:

Addition

Step-by-step explanation:

x - 3 = -5

Add 3

x = -2

An equivalent system of equations to the given system equations are 5Fx+5Gy=5H and Qx+Ry=S. Therefore, option C is the correct answer.

Equivalent system of equation is that system of equations in which solution does not change. If a constant multiplied on both sides of an equation then solution of equation remain same.

The given system of equations are Fx+Gy=H and Qx+Ry=S.

A) 5Fx+5Gy=5H

First equation is multiplied by 5 but the value remains same as original equation Fx+Gy=H

Second equation Qx−Ry=S is not same as original equation Qx+Ry=S

B) First equation 5Fx+Gy=5H is not same as original equation Fx+Gy=H

Second equation Qx+5Ry=S is not same as original equation Qx+Ry=S

C) First equation 5Fx+5Gy=5H is multiplied by 5 but the value remains same as original equation Fx+Gy=H

Second equation Qx+Ry=S is same as the original equation Qx+Ry=S

D) First equation Fx+5Gy=5H is not same as original equation Fx+Gy=H

Second equation Qx+Ry=S is same as the original equation Qx+Ry=S

An equivalent system of equations to the given system equations are 5Fx+5Gy=5H and Qx+Ry=S. Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Choose an equivalent system of equations to the following system:

Fx+Gy=H

Qx+Ry=S

A. 5Fx+5Gy=5H

Qx−Ry=S

B. 5Fx+Gy=5H

Qx+5Ry=S

C. 5Fx+5Gy=5H

Qx+Ry=S

D. Fx+5Gy=5H

Qx+Ry=S

Answer:

w = 215 degrees

Step-by-step explanation:

A  circle = 360 degrees total. So, 145 + w should equal 360.

145 + w = 360

145 + w -145 = 360 - 145

w = 215

Hope this helps :)

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We need to make 28 pairwise comparisons among the eight means to compare the mean SAT scores for each ethnic group.

To make all pairwise comparisons among the eight means, we need to calculate the number of unique pairs of means. The formula for calculating the number of unique pairs is n(n-1)/2, where n is the number of items.

The SAT is a standardized test widely used for college admissions in the United States. The test measures knowledge and skills in reading, writing, and mathematics. The test is scored on a scale of 400-1600, with separate scores for the reading/writing and math sections, each ranging from 200-800. The College Board publishes mean SAT scores for various groups, including ethnic groups, genders, and geographic regions.

In this case, we have 8 ethnic groups, so the number of unique pairs of means is:

8(8-1)/2 = 28

Therefore, we need to make 28 pairwise comparisons among the eight means to compare the mean for each ethnic group.

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The College Board publishes mean SAT scores for eight ethnic groups. How many tests are required to make all pairwise comparisons among the eight means?

The flattened box of the rectangular prism is represented by the net of the rectangular prism.

What is rectangular prism?

A rectangular prism is a prism with rectangle-shaped bases (the top face and bottom face).

There are three pairs of identical opposing faces on each of its six faces, making a rectangular prism's opposite faces all be the same. Its length, breadth, and height are its three dimensions. Rectangular tissue boxes, school notebooks, laptops, fish tanks, big buildings like freight containers, rooms, storage sheds, etc. are a few instances of rectangular prisms in daily life.

The flattened box of the rectangular prism is represented by the net of the rectangular prism.

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Answer:

70

Step-by-step explanation:

Knowing both values of variables m and n, you could substitute each of the values inside the equation.

=(-(2))-3(-24)

=(-2)+72

=70

Hope it helped! (:

Answer:

13

Step-by-step explanation:

The difference between the x-values is 5.

The difference between the y-values is 12.

These are the non-hypotenuse sides.

12^2 + 5^2 = c^2

144 + 25 = c^2

169 = c^2

c = 13

The distance between the two points is 13.

Answer:

13 units

Step-by-step explanation:

(-1,5) and (4, -7)

To find the distance of two points, we use the distance formula:

\(d = \sqrt{(x_{2}-x_1)^2 + (y_2-y_1)^2 }\)

Let's plug in what we know.

\(d = \sqrt{(4 - (-1))^2 + (-7 - 5)^2 }\)

Evaluate the double negative.

\(d = \sqrt{(4 +1))^2 + (-7 - 5)^2 }\)

Evaluate the parentheses.

\(d = \sqrt{(5)^2 + (-12)^2 }\)

Evaluate the exponents.

\(d = \sqrt{(25) + (144) }\)

Add.

\(d = \sqrt{(169) }\)

Evaluate the square root.

\(d = 13\)

13 units

Hope this helps!

2x + 40 = 180

2x = 140

x= 70

answer is 70

Answer:

Step-by-step explanation:

1). By applying cosine rule in the given triangle,

   cos(x°) = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

   cos(x°) = \(\frac{6}{8}\)

   x = \(\text{cos}^{-1}(\frac{3}{4} )\)

   x = 41.41°

2). By applying cosine rule in the given triangle,

   cos(x°) = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

   cos(x°) = \(\frac{4}{5}\)

   x = \(\text{cos}^{-1}(0.8)\)

   x = 36.87°

3). By applying cosine rule in the given triangle,

   cos(x°) = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

   cos(x°) = \(\frac{51}{85}\)

   x = \(\text{cos}^{-1}(0.6)\)

   x = 53.13°

Answer:

First tale nth term and find relation of a , d, n

Try yourself

Answer:

424.3m³

Step-by-step explanation:

I'm sorry, I don't have any proof because I used the go.ogle calculator, you're just gonna have to trust me on this one

Answer:

48 : 42

Step-by-step explanation:

1. Whatever you do to one side of the ratio you do to the other.

2. If there are 42 forks, then the ratio then looks like this: x : 42

3. One side of the ratio was multiplied by six.

4. Do the same to the other and you get 48 : 42

Hope this helps ~

Answer:

48 knives

Step-by-step explanation:

The original ratio is 8:7

Our ratio now, looks like this k:42 (k is just a variable)

First, divide 42 by 7 and you'll get 6.

Multiply 6 by 8 and you'll get a product of 48.

Our new ratio should look like this 48:42

There are 48 knives.