2(x+6)/4=3x-2


I’m not sure how to get the answer

Answer:

Both B and C, but I am not sure about just one answer.

Step-by-step explanation:

a) The chance of drawing no court cards (J, Q, K, A) in a hand of 13 cards randomly drawn from a pack of 52 is approximately 0.294. b) The chance of drawing at least one ace but no other court cards in a hand of 13 cards is approximately 0.089. c) The chance of drawing at most one kind of court card (J, Q, K, A) in a hand of 13 cards is approximately 0.633.

a) To find the chance of drawing no court cards, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. In this case, there are 36 non-court cards (52 cards - 16 court cards), and we want to draw 13 cards without any court cards. The probability can be calculated using the formula:

Probability = (number of favorable outcomes) / (total number of possible outcomes)

The number of favorable outcomes is the number of ways to choose 13 cards from the 36 non-court cards, which can be calculated using combinations. Thus, the probability is:

Probability = C(36, 13) / C(52, 13) ≈ 0.2936

b) To find the chance of drawing at least one ace but no other court cards, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. There are 4 aces in the deck, and we want to draw at least one of them along with 12 non-court cards (36 non-court cards - 4 aces).

The probability can be calculated using the formula:

Probability = (number of favorable outcomes) / (total number of possible outcomes)

For drawing two aces, there are C(4, 2) ways to choose two aces and C(36, 11) ways to choose the remaining non-court cards.

Thus, the probability is:

Probability = [C(4, 1) * C(36, 12) + C(4, 2) * C(36, 11)] / C(52, 13) ≈ 0.0892

c) To find the chance of drawing at most one kind of court card, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. There are 4 court cards of each kind (J, Q, K, A), and we want to draw at most one kind of court card.

The probability can be calculated using the formula:

Probability = (number of favorable outcomes) / (total number of possible outcomes)

The number of favorable outcomes is the sum of three cases: drawing no court cards, drawing only one kind of court card, and drawing one court card of each kind. We have already calculated the probability of drawing no court cards in part (a).

Thus, the probability is:

Probability = [C(36, 13) + 4 * C(36, 13) + 4 * C(36, 12)] / C

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To find the chances in a hand of 13 cards drawn randomly from a pack of 52, we can use probability. The chance of no court cards can be calculated using combinations. The probability of at least one ace but no other court cards can be found by subtracting the probability of no aces from the probability of no court cards. The probability of at most one kind of court card can be calculated by finding the probability of having zero court cards and one court card.

To find the chances in a hand of 13 cards drawn randomly from a pack of 52, we can use probability.

There are 12 court cards (J, Q, K, A) in a deck of 52 cards. So, to have no court cards in a hand, we need to select all 13 cards from the remaining 40 non-court cards. The probability can be calculated as 40C13/52C13.

To find this probability, we need to subtract the probability of having no aces from the probability of having no court cards. The probability of having no aces is 48C13/52C13, and the probability of having no court cards is 40C13/52C13. The result is the difference between these two probabilities.

To find the probability of having at most one kind of court card, we can calculate the probability of having zero court cards or one court card. The probability of having zero court cards can be calculated as 40C13/52C13, and the probability of having one court card can be calculated as 12C1 * 40C12/52C13. The sum of these two probabilities gives the probability of having at most one kind of court card.

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Answer:

It's 8

Step-by-step explanation:

\( 16 ^{ \frac{3}{4} } = \sqrt[4]{16 ^{3} } = \sqrt[4]{2 ^{4 \times 3} } = 2^{ \frac{12}{4} } = 2^{3} = 8\)

Answer:

8

Step-by-step explanation:

Step-by-step on how to solve it is in the image below.

Happy to help! :)

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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Total surface area is 124 square feet.

To calculate the total surface area that Zoe paints, we need to find the sum of the surface areas of the rectangular prism and the triangular pyramid.

Surface area of the rectangular prism:

The rectangular prism has six faces, and each face is a rectangle. The length, width, and height of the rectangular prism are given as 4 feet, 4 feet, and 3 feet, respectively.

The surface area of each face is the product of its length and width.

Since there are four sides with dimensions 4 feet by 4 feet, and two sides with dimensions 4 feet by 3 feet, the total surface area of the rectangular prism is:

Surface area of rectangular prism = 4 * (4 * 4) + 2 * (4 * 3)

Surface area of rectangular prism = 64 + 24

Surface area of rectangular prism = 88 square feet

Surface area of the triangular pyramid:

The triangular pyramid has four faces, three of which are triangular and one is the base.

The base of one triangular face is 4 feet, and the height of the face is 6 feet.

To calculate the surface area of each triangular face, we can use the formula: (1/2) * base * height. Since there are three triangular faces, the total surface area of the triangular pyramid is:

Surface area of triangular pyramid = 3 * (1/2) * (4 * 6)

Surface area of triangular pyramid = 3 * 12

Surface area of triangular pyramid = 36 square feet

Total surface area painted by Zoe:

To find the total surface area that Zoe paints, we sum the surface areas of the rectangular prism and the triangular pyramid:

Total surface area = Surface area of rectangular prism + Surface area of triangular pyramid

Total surface area = 88 + 36

Total surface area = 124 square feet

Therefore, Zoe paints a total surface area of 124 square feet.

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Answer:

the middle. because it'sthe intersection of the circles

Answer:

ll

Step-by-step explanation:

the middle intersection point of i  and just took the quiz

Answer:

35

Step-by-step explanation:

if you have 40$ and you want money to have left for the shirt (5$), you subtract 5 from 40 and get 35

The number of people in a restaurant is a discrete random variable with possible values ranging from 0 to 100, while the time it takes for a light bulb to burn out is a continuous random variable with values spanning a non-negative real interval.

Let us now explain each sub-question in a detailed way:

(a) The number of people in a restaurant that has a capacity of 100 is a discrete random variable. This is because the possible values of the random variable are countable and distinct. The number of people in the restaurant can only take on whole number values from 0 to 100, inclusive. The values 0, 1, 2, ..., 100 represent the possible occupancy levels of the restaurant.

(b) The time it takes for a light bulb to burn out is a continuous random variable. This is because the possible values of the random variable form a continuous interval. The time it takes for a light bulb to burn out can theoretically range from a fraction of a second to infinity. It can take on any non-negative real value within this range. Therefore, the possible values of this random variable span a continuum rather than a countable set of distinct values.

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Answer:

Yes

Step-by-step explanation:

y = 110 + 32x

Let x = each value in the table and calculate the corresponding value of y.

You get the following.

x = 0; y = 110

x = 2; y = 174

x = 4; y = 238

x = 6; y = 302

x = 8l y = 366

Since every value from evaluating the function gives the same value as the table, then the answer is yes, the table and the equation represent the same function.

The lengths of the third side of the triangles can be achieved by using the Pythagorean theorem, which says in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.

Three vertices make up the three-sided polygon known as a triangle. There is a point where the three sides are joined end to end.

A triangle's third side must always have a length that falls between (but not exactly equal to) the sum and difference of the other two sides. Consider the examples 2, 6, and 7 as an example. The third side length must therefore be greater than 4 and less than 8.

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Answer:

The choose C. – n – 2

Step-by-step explanation:

3n + 2( -2n-1) = 3n -4n -2 = – n – 2

I hope I helped you^_^

Answer:

Number of miles is either less than 8255.25 or greater than 17255.25.

Step-by-step explanation:

Given that :

Difference in mileage of the sedan and minivan is > 4500

Mikeage of minivan = 12755.25

Possible number of miles on the sedan :

Mileage on minvan ± difference in mileage ;

12755.25 ± 4500

12755.25 + 4500 = 17255.25

12755.25 - 4500 = 8255.25

This means that the possible number of miles on the sedan is either greater than 17255.25 OR less Than 8255.25

Using the areas οf rectangle and semicircle, we fοund the area οf the given cοmpοsite figure as 129.25 sq. units.

Cοmpοsite geοmetric figures are made frοm twο οr mοre geοmetric figures. Finding the area οf a cοmpοsite shape can be dοne using οne οf twο brοad apprοaches.

The tοtal οf the individual areas will represent the cοmpοsite shape's area.

Determine the areas οf the parts οf the larger fοrm that aren't part οf the cοmpοsite shape that are larger than the cοmpοsite shape. The cοmpοsite shape's area will be calculated as the difference between the larger shape's area and the areas οf the larger shape's excluded pοrtiοns.

The given figure can be divided intο a rectangle and a semicircle.

Rectangle

length = 9

width = 10

Area = length * width = 9*10 = 90 sq. units

Semicircle

Diameter = 10

Radius r = Diameter/2 = 10/2 = 5

Area = 1/2 ( πr²) = 0.5 * 3.14 * 5² = 39.25 sq. units

Area οf the cοmpοsite figure = Area οf rectangle + Area οf the semicircle

                                            = 90 + 39.25 = 129.25 sq. units.

Therefοre using the areas οf rectangle and semicircle, we fοund the area οf the given cοmpοsite figure as 129.25 sq. units.

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a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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Answer:

7 feet long

Step-by-step explanation:

This set up will give a right angle triangle where;

Length of the ladder is the hypotenuse = x

The distance of the ladder to the house is the adjacent = 3 feet

Angle of elevation theta = 72 degrees

Using the CAH in trigonometry identity;

cos theta = adjacent/hypotenuse

cos 72 = 3/hyp

hyp = 3/cos72

hyp = 3/0.4258

hyp = 7.05 feet

Hence the ladder is approximately 7 feet long

The given sequence is a arithmetic sequence with the common difference is -6.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is an=a+(n-1)d

The given sequence is 22, 16, 10.

Here,

Common difference = Second term - First term

16-22=-6 and 10-16=-6

Since the common difference between the terms is same, the given sequence is arithmetic sequence.

Hence, 22, 16, 10 is a arithmetic sequence with the common difference is -6.

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The total cost of candy Robert purchases is $46. Hence, we get the second equation: `5x+3y+4z=46`Therefore, the system of equations are : x=2y5x+3y+4z=46 .

Robert purchased three of his favorite types of candy to hand out to trick-or-treaters on Halloween. He purchased 11 pounds of candy, worth $46. Hershey bars cost $5 per pound. Peanut Butter cups cost $4 per pound, and Milky Way bars cost $3 per pound.

The amount of Hershey bars that Robert purchases was equal to double the amount of Miky Way bars. Let the number of Hershey bars Robert purchases be x, number of Milky Way bars be y and number of Peanut butter cups be z.Since Robert purchased 11 pounds of candy, the total number of candies will be x+y+z. We know that the amount of Hershey bars that Robert purchases was equal to double the amount of Miky Way bars.

Hence, we get the first equation:  `x=2y`Next, we need to calculate the total cost of the candies. The total cost of Hershey bars is 5x, the total cost of Milky Way bars is 3y and the total cost of Peanut butter cups is 4z.

We know that the total cost of candy Robert purchases is $46. Hence, we get the second equation: `5x+3y+4z=46`Therefore, the system of equations are: x =2y5x+3y+4z=46 .

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Answer:

\(\huge\boxed{f(8) = 62}\)

Step-by-step explanation:

\(\sf f(x) = 9x-10\\\\Put\ x = 8\\\\f(8) = 9(8) -10\\\\f(8) = 72-10\\\\f(8) = 62\\\\\rule[225]{225}{2}\)

Hope this helped!

Answer:

f(8) = 62

Step-by-step explanation:

To evaluate f(8) substitute x = 8 into f(x) , that is

f(8) = 9(8) - 10 = 72 - 10 = 62

Answer:

30n^15

multiply exponents add reg numbers

The particular solution of the differential equation  y''-5y' 4y=8e^x is A*e^x form.

To find the form of the particular solution for the given differential equation, y'' - 5y' + 4y = 8e^x, we will first identify the terms involved and then determine an appropriate trial function for the particular solution.

Given differential equation: y'' - 5y' + 4y = 8e^x

Here, the left side represents a linear differential equation with constant coefficient and the right side is the non-homogeneous term (8e^x).

To find the form of the particular solution, we'll assume a trial function based on the non-homogeneous term. Since the non-homogeneous term is 8e^x, our trial function will have the form:

Trial function: Y_p(x) = A*e^x

Now, we need to find the derivatives of Y_p(x) and substitute them into the differential equation:

First derivative: Y_p'(x) = A*e^x
Second derivative: Y_p''(x) = A*e^x

Substituting these into the differential equation:

(A*e^x) - 5(A*e^x) + 4(A*e^x) = 8e^x

Simplifying the equation:

(A - 5A + 4A)e^x = 8e^x

Now, we compare the coefficients:

A = 8

So, the form of the particular solution for the given differential equation is Y_p(x) = 8e^x

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The solutions for the systems of inequalities are:

a) (0, -50), (0, -100), (0, -125)

b)  (0, 20), (0, 23) , (0, 24).

When we have a system of inequalities, a solution is a point (x, y) that solves both ienqualities at the same time.

The first one is:

y ≤ x - 8

y < -3x - 9

Here y must be smaller than x, then we can define x like x = 0, and really small values for y, like y = -50, replacing that we will get:

-50  ≤ 0 - 8 = -8

-50 < - 3*0 - 9 = -9

Both of these are true, so (0, -50) is a solution, and trivially, other solutions of the system of inequalities can be things like (0, -100) and (0, -125) are other two solutions.

For the second system:

y > 5x + 1

y > 3

Let's do the same thing, x = 0 and y gets really large values, like y = 20

20 > 5* + 1 = 1  this is true.

20 > 3   this is true.

so (0, 20) is a solution, and also are (0, 23) and (0, 24).

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Answer:

False

Step-by-step explanation:

[If two lines are perpendicular, then the lines intersect to form four right angles] It's true up till here, but a right angle is 90 degrees, not 180 degrees

To yield $26,000 in the future, compounded semiannually at an interest rate of 6%, a lump sum investment needs to be made today. The correct amount to invest can be calculated using the present value formula.

The present value formula can be used to calculate the amount that should be invested today to achieve a specific future value. The formula is given by:

PV = FV / (1 + r/n)^(n*t)

In this case, the future value (FV) is $26,000, the interest rate (r) is 6%, and the compounding is semiannually (n = 2). We need to solve for the present value (PV).

Using the formula and substituting the given values:

PV = 26,000 / \((1 + 0.06/2)^(2*1)\)

PV = 26,000 / \((1.03)^2\)

PV = 26,000 / 1.0609

PV ≈ $24,490.92

Therefore, the correct lump sum to invest today, at 6% compounded semiannually, to yield $26,000 in the future is approximately $24,490.92.

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If the fuselage of the Boeing 777 were made of steel instead of aluminum, the number of passengers it could carry would decrease.

Given that the fuselage of the Boeing 777 is a hollow aluminum cylinder, we can calculate its volume using the dimensions provided: length = 64.0 m, width = 6.2 m, and thickness = 2.5 mm. Using the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height, we can determine the volume of the aluminum fuselage. Since the cylinder has no ends, the height is the same as the length of the fuselage. The radius can be calculated by dividing the width by 2. By substituting these values into the formula, we can find the volume of the aluminum fuselage. Once we have the volume, we can multiply it by the density of aluminum to find the mass of the aluminum fuselage. Dividing the mass by the average passenger mass of 79 kg will give us the approximate number of passengers the Boeing 777 could carry if its fuselage were made of steel. However, we need the specific maximum total mass or engine's lifting capacity to provide an exact answer.

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The value of xy in the given ratio is 12 meters, which suggests that xy is a product of two quantities.

Based on the given information, the ratio between ay and xy is 1:3. We know that ay = 4 meters. Let's find the value of xy. If the ratio between ay and xy is 1:3, it means that ay is one part and xy is three parts. Since ay is 4 meters, we can set up the following proportion:

ay/xy = 1/3

Substituting the known values:

4/xy = 1/3

To solve for xy, we can cross-multiply:

4 * 3 = 1 * xy

12 = xy

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Based on the given information and using the ratio, we have found that xy is equal to 12b, where b represents an unknown value. The exact length of xy cannot be determined without additional information.

The ratio between ayb and xyz is given as 1:3. We know that ay has a length of 4 meters. To find the length of xy, we can set up a proportion using the given ratio.

The ratio 1:3 can be written as (ayb)/(xyz) = 1/3.

Substituting the given values, we have (4b)/(xy) = 1/3.

To solve for xy, we can cross-multiply and solve for xy:

3 * 4b = 1 * xy

12b = xy

Therefore, xy is equal to 12b.

It's important to note that without additional information about the value of b or any other variables, we cannot determine the exact length of xy. The length of xy would depend on the value of b.

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Answer:

y=2x+5

Step-by-step explanation: