consider a standard deck of 52 cards. what is the probability of a card being black given it is a queen?

Answer: 3,2

Step-by-step explanation: The degree represents the highest exponent in the function. In this case, there is a cubed term which has an exponent of 3. The leading coeffient represents the number before x that makes that highest exponent and in this case its 2.

Answer: it's less than 6.87...

Answer:

$89 for each payment

Step-by-step explanation:

3,204 / 36 = 89

Answer: Each payment is 89 dollars

Step-by-step explanation:

Divide 3,204 by 36 to get how much each payment will be.

The value of b/a is b/a = 91/3 {(1-b/a)²}.

Cubic equations are polynomials of degree 3. That means the maximum degree of the polynomial is three.

And the standard form of a cubic equation is;

f(x) = ax³ + bx² +cx +d, where a, b, c, and d are constant coefficients a ≠ 0.

Given:

A cubic equation,

a³ - b³ / (a-b)³ = 91 where a and b are real numbers a>b>0.

Simplifying,

(a-b)(a²+b²+ab)/(a-b)³ = 91

(a²+b²+ab)/(a-b)² = 91

(a²+b²+ab-3ab+3ab)/(a-b)³ = 91

3ab/(a-b)² = 91

b/a = 91/3 {(a - b)²/a²}

b/a = 91/3 {(a - b/a)²}

b/a = 91/3 {(1-b/a)²}

Hence, b/a = 91/3 {(1-b/a)²}.

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Another way to write the division expression 34 divided by 8 is 34/8 or 4.25, where 4.25 is the result of the division.

What is a mathematical expression?

A mathematical expression consists of a statement, at least two variables or integers, and one or more arithmetic operations. It is possible to multiply, divide, add, or subtract values with this mathematical operation. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

Another way to write the division expression 34 divided by 8 is 34/8 or 4.25, where 4.25 is the result of the division.

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Answer:

y=4x-1

Explanation:

looking at the x row, as you can see, it goes up by 1 each time. In the y row, it goes up by 4, because -1+4=3, 3+4=7, etc. So your slope is 4, and in the funtion y=mx+b given, that would go in the “m” spot. Then for the “y” spot you need to figure out if x is 0, what is y. Well, that is given to you in the picture. It shows that when x=0, y=-1. So that is you y intercept, going into the b spot. If you put it together, it looks like this: “y=4x-1”.

The two numbers are 3 and 6. We can then solve for y using the quadratic formula:y = [9 ± √(81 - 120)]/2 , y = 3 or 6

The sum of two numbers (x + y) = 9

The product of two numbers (x * y) = 30

We can solve for x and y using the following equations:

x + y = 9

x * y = 30

We can solve for x by dividing both sides of the equation by y:

x = (30/y)

We can then substitute this into the first equation:

(30/y) + y = 9

We can then solve for y by subtracting 30/y from both sides:

y = 9 - (30/y)

We can then solve for y by multiplying both sides by y:

y^2 = 9y - 30

We can then solve for y using the quadratic formula:

y = [9 ± √(81 - 120)]/2

y = 3 or 6

Therefore, the two numbers are 3 and 6.

the complete question is :

What are the two numbers has a sum of 9 and a product of 30 ?

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The closest number to 320 that can be made using these cards is 327.5

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

5 27

FIVE

7 3

TWO

SEVEN

THREE

DECIMAL POINT

To get this number, place the decimal point between the 7 and 5

We also make use of the card with "THREE" and add the number "TWO".

The resulting number is 327.5.

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a) The value of x is 20 cm

b) The area of cones that sought is 680π cm²

a) To find the length of x

Compare the ratio and height of the small cone with the large cone

4/x= 7/35

4.35=7x

x= 20 cm, x is the radius of the large cone

b) To calculate the area of the whole cone

The area you are looking for = (Area of the large cone - Area of the small cone) + area of the circle

The area sought = (π20.35 - π4.7) + 2π4

The area sought = 700π-28π+8π

Area sought = 680π cm²

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The slope is negative three halves for option 2 and the y-intercept is 2. Hence option 2 is the correct answer.

A line's steepness and direction are determined by the line's slope. Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not.

Any two clearly separated points on a line can be used to calculate the slope of any line. Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined.

The y-intercept is obtained when the x coordinate is 0.

From the given options the y-intercept is 2 for option 1 and 2.

The slope is given as:

m = (y2 - y1) / (x2 - x1)

For option 1:

m = (0 - 2) / (3 - 0)

m = -2/3

For option 2:

m = (-1 - 2) / (2 - 0)

m = -3/2

So, the slope is negative three halves for option 2 and the y-intercept is 2. Hence option 2 is the correct answer.

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Answer:

728

Step-by-step explanation:

910/5 = 182 per week

4 weeks = 4*182 =728

We can quickly determine that the person has been moved by 10 miles by logical reasoning.

A mental process called logical reasoning seeks to reach a conclusion in a precise way.

By beginning with a set of premises and reasoning to a conclusion supported by these premises, it takes the shape of inferences or arguments.

Propositions, or true or false statements about the reality of a situation, are what the premises and the conclusion are.

They have a disagreement as a group.

In the sense that it seeks to develop correct arguments that any sane person would find persuasive, logical reasoning is norm-governed.

Logic is the primary academic field that studies logical reasoning.

So, using logical thinking, we can easily tell that the person is displaced by 10 miles.

(refer to the image attached below)

Therefore, we can quickly determine that the person has been moved by 10 miles by logical reasoning.

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So there are ten different combinations of two pupils out of five when there are five kids in my class and I want to choose two to treat to lunch.

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. Permutations and combinations are often mistaken. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.

Here,

To determine the number of ways to pick 2 students out of 5 to treat them to lunch, you can use the combination formula, which is given by nCr, where n is the number of items to choose from, r is the number of items to choose, and nCr is the number of combinations of n items taken r at a time. In this case, n = 5 and r = 2, so the number of ways to pick 2 students out of 5 is:

5C2 = 5! / (2! * (5 - 2)!) = 10

So, there are 10 possible combinations of 2 students out of 5 when there are 5 students in my class and I want to pick 2 to treat them to a lunch.

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The answer is:

A frequency distribution for a collection of data is shown in the accompanying table.

The intervals or ranges of the data are displayed in the left column of the table, and the frequency or number of observations within each interval is displayed in the right column.

For instance, the first row demonstrates that 3 observations fall within the range of 10 to 19, the second demonstrates that 5 observations fall within the range of 20 to 29, and so on.

We only combine the frequencies to determine the total number of observations:

Total observations are equal to 3 + 5 + 7 + 4 + 1 = 20.

By averaging the bottom and upper interval bounds, we can also determine each interval's midpoint. As an illustration, the first interval's midway (10-19) is as follows:

Midpoint: (14.5) (10 + 19) / 2

This may be done for each interval, and to display the midpoints, we can add a third column to the table.

The cumulative frequency, which is the overall frequency as we progress from the shortest interval to the longest interval, can then be calculated. The cumulative frequency can be displayed in the table by using a fourth column.

The finished table is shown here:

Interval Frequency Midpoint Cumulative Frequency

Oct-19 3 14.5 3

20-29 5 24.5 8

30-39 7 34.5 15

40-49 4 44.5 19

50-59 1 54.5 20

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Answer: The equation 63 = 9k is correct.

To solve for k, you can divide both sides of the equation by 9:

63/9 = 9k/9

k = 7

So, k = 7 is the solution to the equation 63 = 9k.

Step-by-step explanation:

The value of k in the equation 63= 9k is 7

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

The equation 63 = 9k is a type of linear equations with one variable.. The variable here is K

To find k;

63 = 9k

divide both sides by 9

63/9 = 9k/9

k = 7

therefore the value of k is 7

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Answer:

The equivalent expression to show another way to represent the new price is b - 0.86b = c .

Step-by-step explanation:

Given that the original price of the purchase is b and the coupon gives a 14% discount, the new price of the purchase is given by:

c = b - 0.14b

To write an equivalent expression, we can multiply both sides of the equation by 100% - 14% to simplify:

c * 100% = b * 100% - 0.14b * 100%

c * 100% = b * (100% - 14%)

c * 100% = b * 86%

c = b * 86%

So, another way to represent the new price of the purchase is c = b * 86%.

For the given equation, we can complete the statements below:

Ariel is correct. For any value of y, the statement -12 = 3 is always true.

The equation has no solutions.

What is an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

The first part of the question is as given below.

Ariel simplifies the equation 3y - 12 = 3(y+1) and says it has no solution.

We are asked to complete the statements based on the above information.

Simplifying the equation,

 3y - 12 = 3(y+1)

3y - 12 = 3y + 3

-12 = 3

Since the y term in the above equation is not present, the given equation has indeed no solution.

Also if we take any value of y, the final answer will always be -12 = 3.

Therefore we can complete the statements as below:

Ariel is correct. For any value of y, the statement -12 = 3 is always true.

The equation has no solutions.

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Answer: Ariel is correct. For any value of y the statement -12=3 is always false and it’s no solution

Step-by-step explanation:

Among the 3 cards the probability of picking an odd number and then picking an odd number is 1/3.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The probability of picking a card with odd number is -

Probability = Favourable outcomes / Total outcomes

Substitute the values in the equation -

P(odd1) = Odd number of cards / Total number of cards

P(odd1) = [tex]\frac{^1C_1}{^3C_1}[/tex]

P(odd1) = 1/3

This is followed by picking up a second card without putting the first card back.

So, out of remaining two cards an odd card needs to be picked.

Probability = Favourable outcomes / Total outcomes

Substitute the values in the equation -

P(odd2) = Remaining odd number of cards / Remaining number of cards

P(odd2) = [tex]\frac{^0C_1}{^1C_1}[/tex]

P(odd2) = 0/1

P(odd2) = 0

The probability of both the events is -

P(odd1) + P(odd2)

1/3 + 0

1/3

Therefore, the probability value is 1/3.

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The probability of the product of the two numbers being a multiple of 5 are 9/36.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

We can approach this problem by listing out all the combinations of two numbers from 1 to 6 and counting the number of combinations for which the product is a multiple of 5.

There are 6 x 6 = 36 possible combinations of two numbers from 1 to 6.

The combinations for which the product is a multiple of 5 are: (1, 5), (5, 1), (2, 5), (5, 2), (3, 5), (5, 3), (4, 5), (5, 4), and (5, 5).

So, there are 9 possible combinations for which the product is a multiple of 5.

The probability that the product of the two numbers is a multiple of 5 is 9/36. Expressing this as a common fraction, we have:

P(product is a multiple of 5) = 9/36 = 1/4

The probability that the product of the two numbers is a multiple of 5 is 9/36.

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In light of the query we've got The circle's radius is equivalent to 3.832 units.

In geometry, the perimeter is the overall area of a shape's boundary. A shape's perimeter is computed by adding the lengths of all of its sides and edges. Linear measurements like cm, metres, inch, and feet are used to express its dimensions.

The answers to our problem is that area

A = (θ/360) * π * r^2

π = 3.14

Perimeter is 24 degree, The formula for circumference is:

C = 2 x πr

Now, we can calculate the radius using the circumference:

r = C / (2 x π)

Substituting the value of C from the equation above, we get:

r = (24 / (2 x π))

Therefore, the radius of the circle is approximately equal to 3.832 units.

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To find the missing  sides of the special right angle,

The ratio for 45°,45°and 90°,   1:1:√2,

and for 60°, 30°, 90°,   1:√3:2.

Special right triangles are right triangles with three defined interior angles and fixed side ratios. If one side is known in these right-angled triangles, we can find the value of the two missing sides. The 45°- 45°- 90° triangle and the 30°- 60°- 90° triangle are additional names for the two exceptional right triangles.

Given finding the  missing sides of the special right angle,

Only right triangles with other internal angles of 30° and 60° or 45°and 45°. are valid according to this criteria. Furthermore, it makes no difference whatever side's length you know in order for the rule to function.

for 45°,45°and 90°.

The 45°,45°,90° theorem states that triangles with these angles will have sides in a ratio 1:1:√2,

where the side opposite 45° equates to 1 in the ratio and the side opposite to 90° equates to √2. To find the missing side, just put the given value in the following ratio and find the value.

For 60°, 30°, 90°

Similar to this, according to the 30°, 60°, 90° theorem, triangles with these angles will have sides in the ratio 1:√3:2,

where the side opposite to 30° equates to 1 in the ratio, the side opposite to 60° equates to √3, and the side opposite to 90° equates to 2 in the ratio. Simply enter the given amount into the following ratio to determine the value to discover the missing side.

Hence the ratios are for 45°,45°and 90°,   1:1:√2,

and for 60°, 30°, 90°,   1:√3:2.

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The first ship with an angle of depression 9° has a 2399.23m distance from the shore. And the first and second ship are on a 1944.19m distance apart.

The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards.

Considering the right triangle formed by the height of the cliff and the distance of the ships from the shore, we shall derive a complementary angle considering their respective angles of depression as:

90° - 9° = 81° for the first ship

90° - 5° = 85° for the second ship

such that;

tan 81° = distance of the first ship from the shore/380m {opposite/adjacent}

distance of the first ship from the shore = 380m × cos 81°

distance of the first ship from the shore = 2399.23m

tan 85° = distance of the second ship from the shore/380m {opposite/adjacent}

distance of the second ship from the shore = 380m × cos 85°

distance of the second ship from the shore = 4343.42

the ships distance apart = 4343.42m - 2399.23m

the ships distance apart = 1944.19m

Therefore, first ship with an angle of depression 9° has a 2399.23m distance from the shore. And the first and second ship are on a 1944.19m distance apart.

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Answer:

Step-by-step explanation:

Mr. Adams will fill 21 plates, and he will have 5 extra cookies.

To find the number of plates filled by Mr. Adams, we need to divide 730 cookies by 35 cookies per plate:

730 ÷ 35 = 21

So, Mr. Adams will fill 21 plates.

To find the number of extra cookies, we use the modulo operator to find the remainder after dividing 730 by 35:

730 % 35 = 5

So, Mr. Adams will have 5 extra cookies.

An expression which does not represent the perimeter of the rug in feet include the following: C. 2(6 7/8) + w.

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W) or P = 2L + 2W

Where:

Substituting the given parameters into the perimeter of a rectangle formula, we have the following expressions;

Perimeter, P = 2(6 7/8 + W)

Perimeter, P = 2(6 7/8) + 2W = 2W + 13 6/8

Perimeter, P = 6 7/8 + W + 6 7/8 + W

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Answer:

the answer is foot/hour

a) The measure of an interior angle is of 135º.

b) The polygon has 8 sides.

An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.

Hence the measure of the interior angle of a polygon with exterior angle of 45º is given as follows:

180 - 45 = 135º.

The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:

S(n) = 180 x (n - 2).

For a regular polygon, all the angles have the same measure, hence:

S(n) = 135n.

Then the value of n, representing the number of sides of the polygon, is obtained as follows:

135n = 180(n - 2)

135n = 180n - 360

45n = 360

n = 360/45

n = 8 sides.

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As the single fraction, we can write the expression as -

k/x.

Given is the expression as follows -

{(kx + k²)/x²} × {x/(x + k)}

The given expression is -

{(kx + k²)/x²} × {x/(x + k)}

{k(x + k)/x²} × {x/(x + k)}

k/x

Therefore, as the single fraction, we can write the expression as -

k/x.

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53.9 degree is the angle of the compass direction of a line connecting your starting point to your final position measured from north of west.

A compass is a tool for orientation and navigation that displays direction in relation to the four cardinal directions of the earth (or points). The directions north, south, east, and west are typically represented on the compass face as initialised abbreviations in a design called a compass rose. The rose can be aligned with the corresponding geographic directions when the compass is employed; for instance, the rose's "N" mark points northward. Compass roses are frequently joined with (or occasionally replaced by) marks indicating angles in degrees. East is 90° degrees, south is 180° degrees, and west is 270° degrees, with north being 0° and the angles increasing clockwise.

Here,

You started by travelling west to north.

Your entire distance from the beginning location is your hypotenuse.

[tex]H^{2}= P^{2}+ B^{2} \\\\H^{2}= 17.5^{2}+ 24^{2}\\\\H^{2}= 306.25+ 576\\\\H=\sqrt{882.25} \\\\=29.7 meters[/tex]

You are moving in the northwest.

Use trigonometry now:

[tex]sin\alpha =\frac{B}{H}\\\\sin\alpha =\frac{24}{29.70} \\\\=0.808\\\\\alpha =53.9 degree[/tex]

That's the angle of the compass direction.

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Solve the following problem using analytical techniques: Suppose you walk 17.5 m straight west and then 24.0 m straight north. How far are you from your starting point, & what is the compass direction of a line connecting your starting point to your final point?

Answer: (1/3, -1)

Step-by-step explanation: substitue 0 for x to find the y

y=-3x-1

y=-3(0)-1

y=-1

then substitue -1 in for y to find the x

3x-y=1

3x-(-1)=1

3x=1

x=1/3