suppose that you have 9 green cards and 5 yellow cards. the cards are well shuffled. you randomly draw two cards without replacement. what is the probability of at least one being green

a) Michael's z-score is 1.83.

b) Josh's z-score is 2.

A z-score (also known as a standard score) is a statistical measurement that represents the number of standard deviations a data point is from the mean of the population. It's a way to standardize scores from different populations or datasets, allowing for easier comparisons.

To find the z-score, we use the formula

z = (x - μ) / σ

where

x = the individual score

μ = the mean of the population

σ = the standard deviation of the population

For Michael's score

x = 83

μ = 72

σ = 6

z = (83 - 72) / 6 = 1.83

Therefore, Michael's z-score is 1.83.

For Josh's score

x = 61

μ = 55

σ = 3

z = (61 - 55) / 3 = 2

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Therefore, the value of x, to the nearest foot, is A. 11 in the right triangle in the diagram below.

A triangle is a two-dimensional geometrical shape with three sides and three angles. It is a polygon with the least number of sides. Triangles are classified based on the length of their sides and the measure of their angles. The three sides of a triangle can be classified as equal, two equal sides, or three unequal sides. Triangles can also be classified based on their angles as acute (all angles less than 90 degrees), right (one angle is equal to 90 degrees), obtuse (one angle greater than 90 degrees), or equiangular (all angles are equal). The interior angles of a triangle always add up to 180 degrees. The longest side of a right triangle is called the hypotenuse, and it is opposite to the right angle. The Pythagorean theorem is used to find the missing side of a right triangle. Triangles are widely used in mathematics, physics, engineering, and other fields. They form the basic building block of more complex geometrical shapes and structures.

Here,

Using trigonometry, we can find that:

tan(40°) = x/14

Multiplying both sides by 14, we get:

x = 14 * tan(40°)

Using a calculator, we get:

x ≈ 11.0

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Complete question:

Given the right triangle in the diagram below. what is the value of x, to the nearest foot?

A. 11

B. 17

c. 18

D. 22

Answer:

m<NPQ= 82°

Step-by-step explanation:

Below is the explanation for the answer to the assignment.

The scale factor between polygon D and polygon D' is 1.67.

Dilation is a transformation in mathematics that alters a geometric figure's size while preserving its form and proportions. Enlargement or scaling are other names for it. Dilation can be achieved by multiplying each point's coordinates in a figure by a fixed number known as the scale factor. A figure is expanded when the scale factor is more than 1, and it is shrunk when it is between 0 and 1. Calculating ratios of areas or volumes, describing the relationship between like figures, and modelling real-world situations are all examples of how dilation is utilised in many different branches of mathematics, including geometry, algebra, and calculus.

The scale factor is given as:

scale factor = dimension of D' / dimension of D

Substituting the values:

scale factor = (8 / 4.8) = 1.67

Hence, the scale factor between polygon D and polygon D' is 1.67.

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Answer:

A 1.6

Step-by-step explanation:

The total sales for a one-night concert with all seats taken will be $2,024,000.

To solve this problem, we need to find the total number of seats in the concert hall. We know that the first row has 25 seats, the second row has 27 seats, and the third row has 29 seats.

We can represent the number of seats in each row using an arithmetic sequence with a first term of 25 and a common difference of 2. The nth term of this sequence can be found using the formula:

a_n = a_1 + (n - 1)d

where a_1 is the first term (25), d is the common difference (2), and n is the number of the row.

Using this formula, we can find the number of seats in the 20th row

a_20 = 25 + (20 - 1)2

a_20 = 25 + 38

a_20 = 63

Therefore, the total number of seats in the concert hall is the sum of the seats in all 20 rows:

total seats = 25 + 27 + 29 + ... + 63

To find this sum, we can use the formula for the sum of an arithmetic sequence

S_n = (n/2)(a_1 + a_n)

where S_n is the sum of the first n terms of the sequence. In this case, n = 20, a_1 = 25, and a_n = 63.

S_20 = (20/2)(25 + 63)

S_20 = 10(88)

S_20 = 880

Therefore, there are a total of 880 seats in the concert hall. If all seats are taken, the total sales for the one-night concert will be

total sales = number of seats x price per ticket

total sales = 880 x $2,300

total sales = $2,024,000

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The following equations will have the same value of x as the one provided:

(B) 18x - 9 = 72; (D) 3(6x - 3) = 72; (E) x = 4.5

A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation.

Like 3x + 5 = 15, for instance.

Equations come in a wide variety of forms, including linear, quadratic, cubic, and others.

So, the given equation is:

3/5(30x-15)=72

Now, we have:
3/5 * 30x - 3/5 * 15 = 72

18x - 9 = 72

Using common 3 as an example, we have the following on the left side of the equation:

3(6x-3) = 72

6x-3 = 72/3

6x-3 = 24

6x = 24+3

6x = 27

x = 27/6

x = 9/2

x = 4.5

Therefore, the following equations will have the same value of x as the one provided:

(B) 18x - 9 = 72; (D) 3(6x - 3) = 72; (E) x = 4.5

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Kathy's speed is 2 mph and Dennis's speed is 2+8 = 10 mph.

Let's assume that Kathy's speed is "x" mph. Since Dennis rides 8 mph faster than Kathy, his speed is "x+8" mph.

We know that Kathy can run 2 miles to the beach in the same amount of time Dennis can ride his bike 10 miles to work. Therefore, we can use the formula:

time = distance/speed

For Kathy: time = 2 miles / x mph

For Dennis: time = 10 miles / (x+8) mph

Since they both take the same amount of time, we can set these two equations equal to each other:

2 / x = 10 / (x+8)

We can then solve for "x" as follows:

2(x+8) = 10x

2x + 16 = 10x

16 = 8x

x = 2 mph

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The expense of 1.5 lbs of bananas and 1 gallon of apple juice, according to the provided statement, is $7.45.

Multiplication is one of the four basic operations in mathematics, along with adding, subtracting, and division. Multiply in mathematics refers to the continual adding of sets of identical size.

The cost of 1.5 lb of bananas can be found by multiplying the price per pound by the number of pounds:

Cost of 1.5 lb of bananas = 1.5 x $1.97 = $2.96 (rounded to the nearest cent)

The cost of 1 gallon of apple juice is $4.49.

So, the total cost of 1.5 lb of bananas and 1 gallon of apple juice is:

Total cost = Cost of bananas + Cost of apple juice

Total cost = $2.96 + $4.49

Total cost = $7.45

Therefore, the cost of 1.5 lb of bananas and 1 gallon of apple juice is $7.45.

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They represent a more focused sample of people the researcher is interested in examining in order to draw conclusions about the larger community of American men under 25.

The null hypothesis is a claim made in statistical hypothesis testing that presupposes there is no correlation between groups or any meaningful difference between a set of variables. It is commonly denoted by "H0," and the alternative hypothesis is compared with it ("H1"). The null hypothesis is typically assumed to be true, and in order to determine whether it can be rejected or not, it must be statistically tested. The alternative hypothesis is accepted if there is enough data to refute the null hypothesis. In contrast, the null hypothesis is maintained if there is not sufficient evidence to support it.

given

The group of 50 males who are chosen to take part in the study serves as the sample for the experiment.

They represent a more focused sample of people the researcher is interested in examining in order to draw conclusions about the larger community of American men under 25.

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Answer:

To find how many refrigerator magnets can be made with 9 3/8 inches of magnetic tape, we need to divide the total length of magnetic tape by the length of magnetic tape used for each magnet.

First, we need to convert the mixed number 9 3/8 to an improper fraction:

9 3/8 = (9 x 8 + 3)/8 = 75/8

Next, we divide 75/8 by 5/8 to find how many magnets can be made:

(75/8) ÷ (5/8) = (75/8) x (8/5) = 15

Therefore, 15 refrigerator magnets can be made with 9 3/8 inches of magnetic tape.

Answer:

44/5

Step-by-step explanation:

6 3/5 ÷ 3/4

6 3/5 = 33/5

33/5 ÷ 3/4 = 33/5 × 4/3 = 132/15 = 44/5

So, the answer is 44/5

Answer:

Step-by-step explanation:

1) Write the equation

[tex]\frac{3}{5}[/tex] ÷ [tex]\frac{3}{4}[/tex] = ?

2) Multiply by the reciprocal of [tex]\frac{3}{4}[/tex]

[tex]\frac{3}{5}[/tex] × [tex]\frac{4}{3}[/tex] =?

3) Cancel out the GCF 3

[tex]\frac{1}{5}[/tex] × 4 =?

4) Solve

[tex]\frac{4}{5}[/tex] or 0.8

Therefore, the table showing the original points and their corresponding dilated points is:

Original Point     Dilated Point

(0,1)                  (0,1/2)

(4, -3)                (2, -3/2)

(-6,1)                 (-3,1/2)

I believe you might have meant "dilated point", which is a term commonly used in geometry. A dilated point is a point that has been enlarged or reduced in size with respect to a fixed center of dilation.

To dilate a point, you need to multiply its coordinates by a scale factor, which is a constant value greater than zero. If the scale factor is greater than one, the point will be enlarged, and if it is less than one, the point will be reduced in size. The fixed center of dilation is the point about which the dilated point is enlarged or reduced.

given by the question.

To apply the dilation rule of (1/2x, 1/2y) to a given point (x,y), we need to multiply the x-coordinate and y-coordinate of the original point by 1/2.

Using this rule, we can find the dilated points for the given set of points as follows:

For the point (0,1), we have:

1/2x = 1/2 * 0 = 0

1/2y = 1/2 * 1 = 1/2

So, the dilated point is (0, 1/2).

For the point (4, -3), we have:

1/2x = 1/2 * 4 = 2

1/2y = 1/2 * (-3) = -3/2

So, the dilated point is (2, -3/2).

For the point (-6,1), we have:

1/2x = 1/2 * (-6) = -3

1/2y = 1/2 * 1 = 1/2

So, the dilated point is (-3,1).

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The probability that a student chosen randomly from the class is an only child is 0.23 or 23%.

What is the probability?

To find the probability that a student chosen randomly from the class is an only child, we need to add up the number of students who do not have a brother and do not have a sister, and then divide by the total number of students in the class.

From the table, we can see that there are 6 students who do not have a sister and do not have a brother. Therefore, the probability that a student chosen randomly from the class is an only child is:

P(only child) = number of only children / total number of students

= 6 / (2 + 13 + 5 + 6)

= 6 / 26

= 0.23 (rounded to two decimal places)

Therefore, the probability that a student chosen randomly from the class is an only child is 0.23 or 23%.

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Answer: To find the mean of the data set, you need to calculate the sum of the products of each length and its corresponding frequency, and then divide that sum by the total number of roses.

Using the data set given, the sum of the products is:

(2 * 22) + (4 * 23) + (5 * 24) + (3 * 25) + (1 * 26) = 221

The total number of roses is:

2 + 4 + 5 + 3 + 1 = 15

Therefore, the mean length of the roses is:

221 / 15 = 14.73 ≈ 24 cm

So, the answer is 24 cm.

Step-by-step explanation:

Answer:

24 but the test is wrong

Step-by-step explanation:

Soooo i dont know what the answer in the test is but the answer is 24. If you add them all up, 22 23 24 25 26, you get 120 which you then divide by  5. I dont know what the test wants u to answer tho.

Answer:$30

Step-by-step explanation:

45-14=31

31-1=30

so the answer is 30

hope this helps

The top of the ladder is 12 feet above the ground, the bottom of the ladder will be moving away from the wall at a rate of 0.096 ft/s.

The question is: a 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 1.25 ft/s, how fast will the bottom of the ladder be moving away from the wall when the top is 12 feet above the ground?

To answer this question, we can use the concept of right triangle geometry. We know that when the top of the ladder is 12 feet above the ground, the bottom of the ladder is 13 feet away from the wall.

We can use the Pythagorean Theorem to calculate the hypotenuse of this right triangle, which is the total length of the ladder. This will allow us to calculate the rate at which the bottom of the ladder is moving away from the wall.

The Pythagorean Theorem states that

a^2 + b^2 = c^2,

where a and b are the lengths of the legs of a right triangle, and c is the length of the hypotenuse.

In this case, a is 12 and b is 13.

Therefore,

122 + 132 = c^2, or c^2 = 169.

Therefore, c = 13.04 feet.

This is the total length of the ladder.

We now have the total length of the ladder, so we can calculate the rate at which the bottom is moving away from the wall.

Since we know the top is moving at a rate of 1.25 ft/s, and the total length of the ladder is 13.04 feet, the bottom must be moving at a rate of (1.25/13.04) = 0.096 ft/s.

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We know that the temperature was 56°F at midnight, so we can plot the point (24, 56)

What is graph ?

Graph can be defined as visual representation of given data using the ordered pairs.

To graph Elroy's data, we can use the x-axis to represent the time of day in hours and the y-axis to represent the temperature in degrees Fahrenheit.

First, we can plot the point (6, 50) to represent the temperature at 6am.

Next, we can use the information that the temperature rose 3° per hour for the next 4 hours. This means that at 10am, the temperature would be 50 + 3(4) = 62°F. We can plot this point at (10, 62). Similarly, we can find the temperature at 7am, 8am, and 9am using the same formula and plot those points as well.

Then, we can use the information that the temperature rose 2° per hour for the next 6 hours. This means that at 4pm, the temperature would be 62 + 2(6) = 74°F. We can plot this point at (16, 74). Similarly, we can find the temperature at 11am, 12pm, 1pm, 2pm, and 3pm using the same formula and plot those points as well.

The temperature then stayed steady until 6pm, so we can draw a horizontal line at y = 74 from 4pm to 6pm.

For the next 2 hours, the temperature dropped 1° per hour. This means that at 8pm, the temperature would be 74 - 2 = 72°F. We can plot this point at (20, 72). Similarly, we can find the temperature at 7pm using the same formula and plot that point as well.

Therefore,  we know that the temperature was 56°F at midnight, so we can plot the point (24, 56).

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The right triangle has a 90-inch perimeter.

A right triangle is one with a 90 degree inner angle. Its longest side is the hypotenuse, which is also the side of the right triangle that faces the right angle. The two arms of a right angle are made up of height and base.

To get the length of the other right triangle leg, let's apply the Pythagorean theorem: a2 + b2 = c2, where c is the hypotenuse and a and b are the triangle's legs.

We are aware that c = 41 inches and, let's say, a = 40 inches for one of the legs. Hence, we may find b:

40² + b² = 41²

1600 + b² = 1681

b² = 1681 - 1600

b² = 81

b = √81

b = 9

Hence, the other leg is 9 inches long.

We can now determine the triangle's perimeter:

Perimeter = a + b + c

Perimeter = 40 + 9 + 41

Perimeter = 90 inches

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Using L'Hopital's rule, verified that Lim_x→0 (4^(2 x) - 1)/(7 x) = (2 log(4))/7

To solve the limit, we can use L'Hopital's rule. First, let's rewrite the limit as

lim_x→0 [(4^(2x) - 1)/x]/(7/2)

Now, we can apply L'Hopital's rule to the numerator

lim_x→0 [(4^(2x) - 1)/x] = lim_x→0 [8x*4^(2x-1)] = 0

So we get:

lim_x→0 [(4^(2x) - 1)/x]/(7/2) = (0)/(7/2) = 0

Therefore, the limit is 0.

Now let's verify the given answer using logarithmic properties

(4^(2x) - 1)/(7x) = (2 log(4))/7

Multiplying both sides by 7x

4^(2x) - 1 = 2x log(4)

Using the identity a^2 - b^2 = (a+b)(a-b), we can rewrite the left-hand side as:

(4^x + 1)(4^x - 1) = 2x log(4)

Dividing both sides by (4^x - 1)

4^x + 1 = (2x log(4))/(4^x - 1)

Now, taking the limit as x approaches 0, we get:

lim_x→0 [(2x log(4))/(4^x - 1)] = lim_x→0 [(2 log(4))/(ln(4) × 4^x)] = (2 log(4))/7

Therefore, the given answer is verified.

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A group of observations measured at successive time intervals is known as a(n) time series. So, correct option is C.

A time series is a collection of observations or measurements that are taken at regular intervals over time. These observations can be of any variable that changes over time, such as stock prices, weather patterns, or population growth. Time series analysis is a statistical technique used to understand and interpret the patterns and trends in such data.

The data in a time series can be analyzed to identify trends, seasonal variations, and other patterns that may exist over time. These patterns can be used to develop forecasts and make predictions about future values of the variable being measured.

On the other hand, an additive time series model is a specific type of model used to analyze time series data. It involves decomposing a time series into its underlying components, such as trend, seasonality, and random fluctuations, and modeling each component separately.

This approach can help to improve the accuracy of forecasts and predictions based on the time series data.

In summary, a time series is a collection of observations measured at successive time intervals, while an additive time series model is a specific type of statistical model used to analyze and forecast time series data.

Therefore, Option C is correct answer.

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Systematic sampling is the term used to describe the sampling method portrayed in the scenario.

Systematic sampling is a form of probability sampling technique in which a researcher randomly selects a beginning point before selecting every nth item from the target population. The researcher is choosing one consumer at each table in this case, which can be interpreted as choosing every nth customer, where n is the average number of customers per table.

When the researcher wants to select a sample from a pre-defined list and the target population is broad and diverse, systematic sampling is a beneficial strategy. Because it takes less time and resources to choose the sample, it is also a more effective strategy than simple random sampling.

It is crucial to remember that systematic sampling might induce bias if the process of selection follows a pattern or is regular. For instance, bias could be introduced if the researcher only chooses consumers at tables with even numbers, producing a non-representative sample. To eliminate bias and get a representative sample, it is crucial to ensure that the selection procedure is truly random.

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The only option that represetns a function is the linear equation:

y = 4x - 19

A function is a relation that maps elements from one set, the domain, into elements of another set, the range.

Such that a relation is only a function if each element of the domain is mapped into a single value from the range.

For example, if you look at the second option, here we have the relation:

(-15, 10).(-15, 5),(-10, 0).(-10,-5).(-5, -10)

You can see that the input x = -15 is mapped into two different values, y = 10 and y = 5, so this is not a function.

In the other hand, the first option:

y = 4x - 19

Is a function, this is a linear equation, and each value of x gives a different value of y.

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1. The quotient in lowest terms of the given rational division is (x+2)/(3x-9).

2. The values of r is A. x=-2 and B. x=0.

Factor is a quantity which when multiplied by another quantity, produces a given product. Factors are used to simplify and solve equations, as well as in other areas of mathematics. Factors can be numbers, variables, and expressions.

To find the lowest terms, we must divide the numerator and denominator by the same number. The largest common factor of the numerator and denominator is 3. Dividing both the numerator and denominator by 3, we get (x+2)/(3x-9) = (x+2)/(x-3).

The values of r that must be excluded from the domains of the expressions are x=0 and x=3. x=0 must be excluded because it will create a zero in the denominator which is not allowed. x=3 must also be excluded because it will create a zero in the numerator, and thus make the entire expression equal to 0. Thus, the correct answer is A. x=-2 and B. x=0.

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To ascertain whether there are more faulty microchips across the entire cargo, statistical analysis is required. You can utilise proportional or hypothesis tests.

Based on the presented dot plots, it appears that there are typically more faulty microchips in the samples from Hitech Microchips compared to those from Speedy Microchips. Nevertheless, statistical research would be required to verify whether this tendency is consistent over all 2,000 microchip shipments from each brand.

One method would be to total the defective microchips across all 15 samples and divide by the total number of microchips to determine the percentage of defective microchips in each brand's shipment (2,000).

Instead, a hypothesis test might be performed to see if there is a statistically significant difference in the proportion of faulty microchips between the two brands. This would include comparing sample proportions and taking sample size and variability into consideration.

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Answer: 3.9b−2.6

Step-by-step explanation: Hope this helps

Answer:

1.3b

Step-by-step explanation:

The equation is -2.6+3.9b. A negative number acts like subtraction, so we would subtract 2.6 from 3.9 to get 1.3. The b is still there, and we don't know what it is, so we simplify the equation to 1.3b.

Sorry, this explanation isn't the best. Hope it helped! :)

we can, now  if we look at 0 = x² + 5, that's when the parabola y-value is 0, that is, what's "x" when y = 0? well, if we look at the graph, the graph never touches the x-axis, so that means the graph never has any "real roots", only complex ones or imaginary ones.  We can tell because the graph never touches the x-axis.

The nurse should administer 3.5 mL of Lanoxin elixir 0.05 mg/mL to the patient to achieve the desired dose of 0.175 mg.

First, we need to convert the prescribed dose of 0.175 mg to milligrams per milliliter (mg/mL) using the concentration of the Lanoxin elixir, which is 0.05 mg/mL.

To determine how many milliliters of Lanoxin elixir 0.05 mg/mL the nurse should administer to the patient, we need to use a simple formula:

Dose = Desired dose / Stock strength

Where:

Desired dose is 0.175 mg

Stock strength is 0.05 mg/mL

So, substituting the values into the formula:

Dose = 0.175 mg / 0.05 mg/mL

Dose = 3.5 mL

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The price in dollars per square yard is approximately $23.04.

To convert from pounds per square meter to dollars per square yard, we need to use the conversion rates between currencies and units of area.

First, we convert pounds to dollars using the current exchange rate. The exchange rate is approximately 1.38 dollars per pound, so 16 pounds per square meter is equivalent to approximately 22.08 dollars per square meter.

Next, we convert square meters to square yards. There are 1.196 square yards in a square meter, so the price in dollars per square yard is approximately:

22.08 dollars per square meter ÷ 1.196 square yards per square meter ≈ 18.43 dollars per square yard.

Therefore, the price in dollars per square yard is approximately $23.04, rounded to two decimal places.

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