Consider a deck of 52 cards with 4 suits and 13 cards (2-10,J,K,Q,A) in each suit. Jack takes one such deck and arranges them in a line in a completely random order. Now he wants to find the number ofPower Trios in this line of cards. APower Trio is a set of 3 consecutive cards where all cards are either a Jack, Queen or King (J,Q or K). APerfect Power Trio is a set of 3 consecutive cards with exactly 1 Jack, 1 Queen and 1 King (in any order).a) Find the expected number of Power Trios that Jack will find.
b) Find the expected number of Perfect Power Trios that Jack will find.

Answer:

first blank would be 5,-2 and the second blank would be 58/9,-4

Answer:

c

Step-by-step explanation:

volume is the correct answer

Answer:

16 - x = -2

16 + 2 = x

x = 18

hope it helps!

The reason a congressperson could give for opposing a tax plan that produces an average tax cut of $4,000 based on concerns around equity, fiscal responsibility, and economic impact.

A congressperson could oppose a tax plan that produces an average tax cut of $4,000 for various reasons, such as:

In this case, the congressperson may argue that the tax plan exacerbates income inequality and is not equitable.

The congressperson may argue that the tax plan is fiscally irresponsible and does not prioritize the needs of the American people.

The congressperson may argue that the tax plan does not have the desired effect of boosting economic activity and creating jobs, and therefore is not an effective policy.

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The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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Once you have followed these steps, you should be able to help the virologist conclusively decide what quantities a and b model by analyzing the given differential equations.

It seems that the specific functions a and b, as well as the differential equations, are not provided in your question. However, I can guide you on how to approach this problem using the given terms and general concepts.

A virologist studies the dynamics of infectious disease using mathematical models. The three quantities of interest are infected people (I), susceptible people (S), and immune people (R). Functions a and b will represent two of these three quantities. To determine which quantities a and b model, we can analyze the given differential equations and follow these steps:

Step 1: Identify the variables and their relationships
Look for the variables (S, I, and R) in the differential equations and analyze how they are related to each other. Determine if there are any rate constants or parameters that link the variables.

Step 2: Analyze the equations' behavior
Study the differential equations' behavior over time, considering different initial conditions. Observe if the equations exhibit any trends, such as an increase or decrease in the quantities.

Step 3: Compare the equations with known epidemic models
Compare the given differential equations with known epidemic models, such as the SIR model or the SEIR model. These models have well-defined equations that describe the rates of change for susceptible, infected, and immune individuals.

Step 4: Rule out alternatives
Based on your analysis, eliminate the alternatives that don't match the behavior exhibited by the differential equations. Ensure that your conclusion is supported by a logical argument.

Once you have followed these steps, you should be able to help the virologist conclusively decide what quantities a and b model by analyzing the given differential equations.

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The first term will be 0, and the limit of e^-1 = 0.368, so the second term will be 0. The integral converges, the series also converges.

To verify whether the following infinite series converges using the integral test \[\sum_{k=1}^{\infty} k^{2} e^{-2 k}\], we first need to define the integral test.Integral TestLet f be a continuous, positive, decreasing function over [1,∞) such that f(n) = a_n for all n∈N, then the following series is convergent if and only if the integral is convergent:∑n=1∞a_n≡∫1∞f(x)dxTo prove that the given series is convergent, we must verify that the corresponding integral converges. Therefore, let's define the following integral:∫1∞ x^2 e^(-2x)dx = [-1/2(x^2+(1/2)x) e^(-2x)]∞1After applying limits, we obtain:[(-1/2(e^-∞(∞^2+(1/2)∞)))-(-1/2(e^-1(1^2+(1/2)1)))]The limit of e^-∞ = 0, so the first term will be 0, and the limit of e^-1 = 0.368, so the second term will be 0. The integral converges.

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Answer:418 and heres why

Step-by-step explanation:

2(14.5 times 7 = 101.5 times 2 = 203

next

2(14.5 times 5 =72.5 times 2=145

then last

2(7 times 5= 35 times 2=70  add them all together then get  418

hope this help (:

The surface area of the shoe box is,

⇒ SA = 418 square inches

We have to given that,

A shoe box has a length of 14.5 inches, a width of 7 inches, and a height of 5 inches.

Since, We know that,

Surface area of cuboid is,

SA = 2 (lw + lh + hw)

Here, we have;

Length = 14,5

Width = 7 inches

Height = 5 inches

Hence, We get;

The surface area of the shoe box is,

SA = 2 (14.5 x 7 + 14.5 x 5 + 5 x 7)

SA = 2 (101.5 + 72.5 + 35)

SA = 2 (209)

SA = 418 square inches

Thus, The surface area of the shoe box is,

⇒ SA = 418 square inches

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The area of the shaded regions is: 44π

Area of a circle where "r" is the radius is determined using the formula: πr².

The figure given has three circles, namely:

The area of the shaded regions = Area of circle A - Area of Circle B + Area of Circle C

Area of Circle A = (π)(8)² = 64π

Area of Circle B = (π)(4)² = 16π

Area of Circle C = (π)(2)² = 4π

Thus:

The area of the shaded regions = 64π - 16π + 4π

The area of the shaded regions = 44π

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Mason's friends do not play video games are 4.

Mason asked some classmates whether they play video games.

The ratio of friends who play video games to everyone he asked is given as some fraction or decimal value.
Let's assume that the ratio is in the form of "x:y",

"x" represents the number of friends who play video games, and "y" represents the total number of friends that Mason asked.
To find out how many of his friends do not play video games,

To subtract the number of friends who play video games from the total number of friends that Mason asked.

This is because the remaining friends who were not counted in the "x" value of the ratio must be those who do not play video games.
So, the number of friends who do not play video games can be calculated as:
Total number of friends - Number of friends who play video games = y - x
The ratio of friends who play video games to everyone he asked is 3:7,

It means that out of 7 friends, 3 play video games, and 4 do not play video games.

The number of friends who do not play video games can be calculated as:
y - x = 7 - 3 = 4  

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Anwer

$8 per yard

Step-by-step explanation:

2 3/4=11/4

11/4=2.75

22/2.75=8

I hope this helps I inserted images of each of inequality of you need more please ask me in the comments. (:

Answer:

-59

Step-by-step explanation:

2 is the first digit right after the decimal point. The digit after it is 3, Both digits would round down, therefore meaning that the whole number would still be -59

Answer:

20% increase good luckkkkk

The inequality 6x > 2y-5 is rearranged into slope-intercept form y < 3x + 2.5, which requires a dashed boundary line with a slope of 3 and a y-intercept of 2.5.

What type of boundary line would be used and where to shade

6x > 2y-5​?

To arrange the inequality 6x > 2y - 5 into slope-intercept form, we first isolate y on one side of the inequality:

2y - 5 < 6x

2y < 6x + 5

y < 3x + 2.5

So the slope-intercept form of the inequality is y < 3x + 2.5.

To graph this inequality, we would use a dashed boundary line since the inequality is strict (y < rather than y ≤). To find the slope and y-intercept of the boundary line, we can compare the inequality to the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

In this case, we can see that the slope of the boundary line is 3, and the y-intercept is 2.5. So we would draw a dashed line with a slope of 3 and a y-intercept of 2.5.

To determine which side of the boundary line to shade, we can pick a point on one side of the line and see if it satisfies the inequality. One convenient point to use is the origin (0, 0).

6(0) > 2(0) - 5

0 > -5

Since 0 is indeed greater than -5, the point (0, 0) satisfies the inequality. Therefore, we want to shade the side of the boundary line that contains the origin. In other words, we shade the area below the dashed line y = 3x + 2.5.

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Answer:

14 years Will give you 1036 members

Step-by-step explanation:

Set it up as an equation

x/350 = 14/100

100x = 4900

100x/100 = 4900/100

x = 49

49 x 14 = 686

686 + 350 =1036

Using the quadratic formula The coordinates of the midpoint of points A and B are (-2k, 22 + k²).

The equation of the locus of the moving point P equidistant from the two given lines is 12x - 16y - 1 = 0.

For the line kx + y = 1 to intersect the curve y = x^2, we substitute y = x^2 into the equation of the line:

kx + x^2 = 1

Rearranging the equation, we have x² + kx - 1 = 0.

Using the quadratic formula, we find the x-coordinates of the intersection points A and B:

x = (-k ± √(k² + 4)) / 2

Let's denote the x-coordinates of A and B as x1 and x2, respectively.

The y-coordinate of point A is obtained by substituting x1 into the equation y = x²

y1 = (x1)²

Similarly, the y-coordinate of point B is obtained by substituting x2 into the equation y = x²:

y2 = (x2)²

The coordinates of the midpoint of A and B can be found by taking the average of their x and y coordinates:

Midpoint_x = (x1 + x2) / 2

Midpoint_y = (y1 + y2) / 2

Substituting the values of x1, x2, y1, and y2, we get:

Midpoint_x = (-k + √(k² + 4)) / 2

Midpoint_y = (x1² + x2²) / 2

Simplifying the expression for Midpoint_y:

Midpoint_y = (x1² + x2² ) / 2

Midpoint_y = [(x1 + x2)²  - 2x1x2] / 2

Midpoint_y = [(x1 + x2)²  - 2(x1)(x2)] / 2

Midpoint_y = [(x1 + x2)²  - 2(-k)(k + √(k²  + 4))] / 2

Midpoint_y = (k²  + 2k(√(k²  + 4)) + k² ) / 2

Midpoint_y = (2k^2 + 2k(sqrt(k^2 + 4))) / 2

Midpoint_y = k²  + k(√(k²  + 4))

Hence, the coordinates of the midpoint of A and B are (-2k, 22 + k² ).

For the second part of the question, the equation of the locus of P can be found by determining the line that is equidistant from the lines 3x - 4y + 3 = 0 and 6x - 8y - 7 = 0.

Using the formula for the distance between a point (x, y) and a line Ax + By + C = 0:

Distance = |Ax + By + C| / √(A²  + B² )

Let P(x, y) be equidistant from the given lines. Then we have:

|3x - 4y + 3| / √(3²  + (-4)² ) = |6x - 8y - 7| / √(6²  + (-8)² )

Simplifying this equation:

|3x - 4y + 3| = 2|6x - 8y - 7|

This leads to the equation:

12x - 16y - 1 = 0

Hence, the equation of the locus of P is 12x - 16y - 1 = 0.

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Complete question:

If a straight line kx+y=1 cuts the curve y=x 2at A and B, find the coordinates of mid-point of A and B in terms of k. A. (− 2k​ , 22+k 2​ ) B. (− 2k, 4k 2​ ) C. (0,1) D. (− 2k​ ,1) 22. The equation of two lines are 3x−4y+3=0 and 6x−8y−7=0. Let P be a moving point in the rectangular coordinate plane such that it is always equidistant from the two lines. Find o. equation of the locus of P. A. 12x−16y−1=0 B. 16x+12y−1=0 C. 3x−4y−8=0 D. 4x+3y−8=0

Answer:

y = -15

Step-by-step explanation:

All you have to do is 51 divided by -3.4 and it equals -15. Inverse operations in short terms. And if you substitute -15 for y it will fir.

Answer:

-3.4y = 51

y = 51/-3.4

y = 510/-34

y = -15

if it has a diameter of 28, its radius is half that or 14.

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=14\\ h=7.5 \end{cases}\implies V=\pi (14)^2(7.5) \\\\\\ V=1470\pi \implies V=1470(\frac{22}{7})\implies V=4620~m^3\)

Answer: x = -2/9

The correct answer is x = -2/9

Step-by-step explanation:

First, you want to distribute:

4(3x - 3) = -2(76/9 + 5x)

12x - 12 = -2(76/9 + 5x)

The you want to rearrange the terms:

12x - 12 = -2(76/9 + 5x)

12x - 12 = -2(5x + 76/9)

Then you want to distribute again:

12x - 12 = -2(5x + 76/9)

12x - 12 = -10x - 152/9

Then solve:

x = -2/9

Final result:

x = -2/9

Hope this helps =)

Answer:

x=-2/9

Step-by-step explanation:

Hope this helps! Pls give brainliest!

It is essential to encourage and support these girls to continue pursuing their interests and talents in math and science, as excelling in these fields can lead to successful careers and personal growth.

It is unfortunate that some girls may fear focusing on math and science during puberty due to concerns about popularity or attractiveness. However, it is important to remember that excelling in these subjects can lead to numerous opportunities and career paths in the future. It is also important to note that intelligence and academic achievement should be celebrated and valued regardless of gender stereotypes. Schools can play a role in promoting the importance of STEM subjects and encouraging girls to pursue their interests in these areas.

It has been observed that some girls who excelled in math and science during elementary school may develop concerns during puberty that focusing on these subjects might limit their popularity or attractiveness as girls. This could be due to societal stereotypes or peer pressure, which might influence their academic choices and priorities. It is essential to encourage and support these girls to continue pursuing their interests and talents in math and science, as excelling in these fields can lead to successful careers and personal growth.

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It is essential to encourage and support these girls to continue pursuing their interests and talents in math and science, as excelling in these fields can lead to successful careers and personal growth.

It is unfortunate that some girls may fear focusing on math and science during puberty due to concerns about popularity or attractiveness. However, it is important to remember that excelling in these subjects can lead to  and career paths in the future. It is also important to note that intelligence and academic achievement should be celebrated and valued regardless of gender stereotypes. Schools can play a role in promoting the importance of STEM subjects and encouraging girls to pursue their interests in these areas.

It has been observed that some girls who excelled in math and science during elementary school may develop concerns during puberty that focusing on these subjects might limit their popularity or attractiveness as girls.

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Answer:

27 is your answer.

11.5 and 15 are the values that are part of the solution set of the inequality.

Inequality is defined as relationship between non-equal numbers or expressions. The solution of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

-4x + 24 < -2x + 2

-4x + 2x < -24 + 2

-2x < -22

22 < 2x

11 < x

Hence, the solution set of the given inequality is the set of numbers greater than 11. Among the given choices, 11.5 and 15 are both greater than 11.

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Answer:

78% of 100.

Step-by-step explanation:

78 out of 100 is 78/100, in other words 78%.

78 is 78% of 100.

All you need to do is add a percent sign and your set!

If this helped may i have brainliest?

Answer:

R

Step-by-step explanation:

If you count the tiks by 10 instead of ones, Q is less than 50, and S and T are both larger than 60. Therefore, R is the only possible answer.

Hope this helped <3 Brainliest please :)

Answer:

(4;0)

Step-by-step explanation:

y=0

2x-3×0=8

2x=8

x=4

The minimum number of choices in a scoring procedure that the student must eliminate before it is advantageous to guess among the rest is 4. Option E is the correct option.

Suppose that there are n choices remaining for a particular question.

The probability of answering this question correctly is 1/n if the student guesses and the probability of leaving the question unanswered is (n-1)/n.

The expected score for guessing is therefore (7/n) × (1/n) + (2/n) × ((n-1)/n) = (7 + 2(n-1))/n² = (9 - 2/n)/n.

The expected score for leaving the question unanswered is 2/n.

The student should guess if and only if the expected score for guessing is greater than the expected score for leaving the question unanswered.

That is, we must have (9 - 2/n)/n > 2/n, or equivalently 9 > 2n, or n < 4.5.

Thus, if the number of choices remaining is 4 or more, the student should not guess; if the number of choices remaining is 3 or fewer, the student should guess.

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Given:

\(\Delta LMN\sim \Delta LRS\)

To find:

The value of x.

Solution:

We have,

\(\Delta LMN\sim \Delta LRS\)

We know that the corresponding sides of similar triangles are proportional. So,

\(\dfrac{LM}{LR}=\dfrac{LN}{LS}\)

\(\dfrac{18}{2x-18}=\dfrac{30}{10}\)

\(\dfrac{18}{2x-18}=3\)

\(18=3(2x-18)\)

Using distributive property, we get

\(18=3(2x)-3(18)\)

\(18=6x-54\)

\(18+54=6x\)

\(72=6x\)

Divide both sides by 6.

\(\dfrac{72}{6}=x\)

\(12=x\)

Therefore, the correct option is A.

Answer:

x =6

Step-by-step explanation:

8(x - 4) = 16

8x-32=16

8x=32+16

8x=48

x=6

☁️ Answer ☁️

8(x + -4) = 16

8(-4 + x) = 16

(-4 * 8 + x * 8) = 16

(-32 + 8x) = 16

-32 + 8x = 16

Add '32' to each side of the equation.

-32 + 32 + 8x = 16 + 32

-32 + 32 = 0

0 + 8x = 16 + 32

8x = 16 + 32

(Combine like terms) 16 + 32 = 48

8x = 48

And Divide each side by eight

x = 6

Hope it helps.

Have a nice day noona/hyung.