Consider a standard deck of playing cards. Suppose we draw five cards at random without replacement. What is the probability of: (a) drawing at least one club

The correct number line that displays the solution `x ≥ 3` would be:

 <------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------>

       -10    -9     -8     -7     -6     -5     -4     -3     -2     -1     0      1      2      3      4      5      6      7      8      9     10

                                   ●------------------------------------------------>

The solution `x ≥ 3` is an inequality that means x is greater than or equal to 3. To graph this inequality on the number line, we mark the point representing the value 3 with a closed circle on the number line and draw an arrow pointing to the right to indicate that all values greater than or equal to 3 satisfy the inequality.

The closed circle at 3 indicates that 3 is included in the solution set, and the arrow to the right indicates that all values greater than 3 also satisfy the inequality. Therefore, any value of x that is equal to or greater than 3 would be considered a solution to the inequality `x ≥ 3`.

It is important to note that if the inequality was `x > 3` (without the equal sign), the closed circle at 3 would be changed to an open circle, indicating that 3 is not included in the solution set, and only values greater than 3 would be considered solutions. In conclusion, the number line provided above correctly displays the solution `x ≥ 3`.

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Answer: 46 ft by 92 ft

Step-by-step explanation:

The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.

Multiple of 11 cant be prime number.

Prime numbers are those that are bigger than 1. Only the number itself and factor 1 are present. This indicates that no number other than 1 and the number itself may be used to divide these numbers without leaving a residue.

Now that multiples of 11 are being questioned, such as 22, 33, and 44, can they be prime numbers?

We know that prime numbers are those that can only be divided by themselves and by one , but since these multiples of 11 are all divisible by 11, they cannot be prime numbers.

The multiple of 11 cannot thus be a prime number.

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The equations can be used to solve for y, the length of the room follows:

B. y² – 5y = 750, C. 750 – y(y – 5) = 0 and E. (y + 25)(y – 30) = 0

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

As per the question, we have

length L = y

width W = y - 5

Since the area of a rectangular room is 750 square feet.

So  L × W = 750

y(y - 5) = 750

y² – 5y = 750 ....(i)

This can be also written as:

750 – y(y – 5) = 0 ....(ii)

Factorizing the equation (i), we get

(y + 25)(y – 30) = 0

Thus, the correct answer would be options (B), (C), and (E).

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Answer:

angle b

Step-by-step explanation:

let's assume the triangle is a right angle triangle . either angle a or c can be equal to 60 degree

Answer:

k=8

Step-by-step explanation:

-5k + 3 = -86/-2

-5k +3 = 43

-5k = 43-3

k = 40/5

k = 8

Answer:  The answer is 30 inches.

Answer:

36

Step-by-step explantion:
1 x 1 = 1 so each cube is 1 square inch

2 x 6= 12

12 x 3 = 36

Answer:

-4

Step-by-step explanation:

6 * 4 = 24

2 * -3 = -6

24 / (-6) = -4

Answer:

75

Step-by-step explanation:

Given:

f(1) = 100

f(n+1) = f(n) - 5

Solve for:

f(6)

Solution:

f(1) = 100

f(2) = f(1) - 5 = 100 - 5 = 100 - 1 x 5 = f(1) - 1 x 5

f(3) = f(2) - 5 = 100 - 5 - 5 = 100 - 2 x 5 = f(1)  - 2 x 5

...

f(n) = f(n - 1) - 5 = 100 - (n-1) x 5 = f(1) - (n-1) x 5

=> f(6) = f(1) - (6-1) x 5 = 100 - 5 x 5 = 100 - 25 = 75

Hope this helps!

Answer:

\(x = 1\) or \(x = -5\)

Step-by-step explanation:

\(4|2x + 4|-7 = 17\\\to4|2x + 4| = 24\\\to |2x + 4| = 6\)

Case 1) 2x + 4 is positive
\(2x + 4 = 6\\\to 2x = 2\\\to x = 1\)

Case 2) 2x + 4 is negative

\(2x + 4 = -6\\\to 2x = -10\\\to x = -5\)

Answer:

6a - 3

Step-by-step explanation:

Dividend: A number/expression that is divided by the divisor.

Divisor: The number/expression that divides the dividend.

Quotient: The result obtained by the division.

Remainder: The number/expression left behind.

Long division method

The solution is the quotient plus the remainder divided by the divisor.

Given dividend:  

Given divisor:  

\(\large \begin{array}{r}2a+1\phantom{)}\\6a-3{\overline{\smash{\big)}\,12a^2\phantom{))..)))}-3\phantom{)}}}\\{-~\phantom{(}\underline{(12a^2-6a)\phantom{)))))}}\\6a-3\phantom{)}\\-~\phantom{()}\underline{(6a-3)\phantom{}}\\0\phantom{)}\\\end{array}\)

Therefore, the quotient is 6a - 3.

Based on the figure, the graph that shows the data on long distance calls on a 10-by-10 grid with appropriate scales is Graph C.

The data is to be shown on a 10-by-10 grid which means that the range of numbers on the x and y axis should be between 0 and 10.

The scales should also be appropriate which means that Time (hours) should represent the x axis and Cost (dollars) should be on the y axis.

Only Graph C has this which makes it the right one.

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Answer: The amount of the mark up is 20$

Step-by-step explanation:

find 50 percent of the 40

50 percent is the same as 0.5

0.5*40=20

Step-by-step explanation:

B^2+8b+7 is a quadratic expression. It can be factored as (b+7)(b+1).

To factor a quadratic expression, you can use the following steps:

1. Find two numbers that add up to the coefficient of the middle term (8) and multiply to the constant term (7).

2. Write the quadratic expression as a product of two binomials, with the two numbers you found in step 1 as the coefficients of the terms in each binomial.

In this case, the two numbers that add up to 8 and multiply to 7 are 7 and 1. So, we can factor B^2+8b+7 as follows:

(b+7)(b+1)

This means that B^2+8b+7 is equal to the product of (b+7) and (b+1).

Here is a step-by-step explanation of how to factor B^2+8b+7:

1. The coefficient of the middle term is 8.

2. The constant term is 7.

3. The two numbers that add up to 8 and multiply to 7 are 7 and 1.

4. Therefore, B^2+8b+7 can be factored as (b+7)(b+1).

Answer:

1 × 4=4,so 4 ÷ 2 1/4=2.0 bracelets.

Step-by-step explanation:

ok in 1 hr to get the number of bracelets,we ought to cross multiply 1 hr multiplied by 4 bracelets and then the answer which is 4, Will be deviided by 9/4 which is the improper fraction from the mixed fraction of 2 1/4 then we get 1.7777 with recurring sevens but because we need number of bracelets,we round off the sevens into one decimal point and thus getting 2.0 bracelets.

Answer:

If Connor makes x dollars in sales, he will make 0.05x + 300 that week.

He makes $408.75 in a week if he makes $2175 in sales.

Step-by-step explanation:

y = 0.05x + 300

y = 0.05(2175) + 300

y = 408.75

The value in the data set varies from 12 by an Average of 4.

The mean of the data set is 12 and the mean absolute deviation is 4.

Option 1: Each value in the data set varies from 12 by exactly 4.

This statement cannot be concluded based on the given information. The mean absolute deviation measures the average distance between each data point and the mean. It does not imply that each value varies by exactly 4 from the mean.

Option 2: Each value in the data set varies from 12 by an average of 4.

This statement is true. The mean absolute deviation of 4 indicates that, on average, each data point deviates from the mean by 4 units. It does not necessarily mean that each value varies by exactly 4, but the average deviation is indeed 4.

Option 3: No values in the data set are less than 8 or greater than 16.

This statement cannot be determined based on the given information. The mean and mean absolute deviation do not provide information about the specific values in the data set. It is possible for some values to be less than 8 or greater than 16 while still maintaining a mean of 12 and a mean absolute deviation of 4.

Option 4: Half of the values in the data set are 8, and half of the values in the data set are 16.

The  value in the data set varies from 12 by an average of 4.

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The outcomes that are contained in the events are

1 - P(X) = 4/5 and 1 - P(X) is the same as P(Not X)

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

X = gray colours

Given that

gray colours = 3 and 10

We have

X = 3 and 10

Not X =1, 2, 4, 5, 6, 7, 8

The probability is then calculated as

P(X) = 2/10 = 1/5

For P(Not X), we have

P(Not X) = 1 - 1/5 = 4/5

In (a), we have

P(Not X) = 1 - 1/5 = 4/5

This means that

P(Not X) = 1 - P(X)

So, the solution is

1 - P(X) = 4/5

Using the above (a) and (b) as a guide, we have the following:

1 - P(X) is the same as P(Not X)

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Answer:

8 1/3

Step-by-step explanation:

9 1/6 = 55/6

55/6 - 5/6 = 50/6 or 8 1/3

The expression tan(arcsec(x/3)) can be written   \(1/3 \sqrt{x^2-9}\)  in algebraic form.

The inverse secant function, or arcsecant, is defined as the inverse of the secant function, which is the ratio of the length of the hypotenuse of a right triangle to the length of the adjacent side. Given x/3 as the length of the adjacent side, arcsec(x/3) is the measure of the angle that has a secant equal to x/3.

The tangent function is the ratio of the length of the opposite side of a right triangle to the length of the adjacent side. By substituting arcsec(x/3) as the measure of the angle in a right triangle, we can use the tangent function to find the ratio of the lengths of the opposite and adjacent sides, which is equal to \(1/3 \sqrt{x^2-9}\).

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The equation for the proportion, p, of consumers who shop with coupons is: p = C/N where C is the number of consumers who use coupons and N is the total number of consumers asked.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

This equation represents the ratio of the number of consumers who use coupons to the total number of consumers. It is commonly used in statistics and market research to measure the prevalence of a certain behavior or preference among a population. By calculating the proportion of consumers who use coupons, businesses can make informed decisions about their pricing strategies, promotions, and advertising campaigns.

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Jeo need to pay $0.4 million to buy Thea’s share.

Given,

Ratio of investment of Joe, Thea, Taylor in the partnership = 1:2:3

Worth of partnership after some years = $1.2 million

Now, we can calculate the share of partners:

Total of investment = 1 + 2 + 3 = 6

1.2 / 6 = 0.2 million, this is the investment.

Now share of partners:

Joe’s share = 0.2 x 1 = $0.2 million

Thea’s share = 0.2 x 2 = $0.4 million

Taylor’s share = 0.2 x 3 = $0.6 million

From the above data’s we can conclude that Joe needs $0.4 million to buy Thea’s share.

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Answer:

1 guest is 6 ounces

40 guests is 240 ounces

240 ounces = 15 pounds of meat

The equation of the tangent line at the point (108, 6) on the curve y² = x²/(xy - 324) is: y = 6

The equation is given as:

y² = x²/(xy - 324) at (108, 6)

Differentiating implicitly with respect to x gives:

2y(dy/dx) = (2x(xy - 324) - x²(y - 324)(dy/dx)) / (xy - 324)²

Simplifying further using power rule and chain rule gives us:

\(\frac{dy}{dx} = \frac{x^{2}y - 648x }{2y(-324 + xy) +x^{3} }\)

We can find the slope by plugging in x = 108 and y = 6 to get

\(\frac{dy}{dx} = \frac{(108^{2}*6) - 648(108) }{2(6)(-324 + (108*6)) + 108^{3} }\)

dy/dx = 0

To find the equation of the tangent line, we use the point-slope form:

y - y₁ = m(x - x₁),

where:

(x₁, y₁) is the given point (108, 6) and m is the slope.

Substituting the values, we have:

y - 6 = 0(x - 108)

y = 6

This is the equation of the tangent line at the point (108, 6) on the curve y² = x²/(xy - 324).

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Answer: D) (-19,-13), see attached picture

Step-by-step explanation:

Answer:

8.09s + 3.79c

Step-by-step explanation:

The $8.09 is pertaining to the satin (s) and the $3.79 is pertaining to the cotton fabric (c).

Answer:

70.77

Step-by-step explanation:

Hope this helps

SOLUTION

In circle geometry, there is a theorem which states that;

The perpendicular bisector of a chord passes through the center of a circle.

GH and KM are the perpendicular bisectors of both chords. They therefore pass through the center of the circle. Also, since they pass through the center of the circle, they are both diameters of the circle. Their point of intersection or where both (GH and KM) meet is the center of the circle.

Looking at the above explanation, the option which satisfies this explanation is option D.

Therefore, option D is the correct answer.

The equation that represents the total number of black and white squares on the chess board is 8 * 2² = 32

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

The chess board

From the chess board, we have

Black squares = 32

White squares = 32

When factorized, we have

Black squares = 32 = 8 * 2²

White squared = 32 = 8 * 2²

Hence, the equation that represents the squares on the chess board is 8 * 2² = 32

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