Let be a random variable with the following probability distribution:
Value (P(X=x)
x of X
10) (0.05)
20) (0.65)
30) (0.05)
40) (0.20
50) (0.05)
Find the expectation E (X) and variance Var (X) of X.

Answers

Answer 1

Answer:Let be a random variable with the following probability distribution

Value x of X / P (X=x)

20 / 0.05

30 / 0.05

40 / 0.35

50 / 0.20

60 / 0.35

Find the expectation of E(X) and variance Var (X) of X.

(A) E (x) = ?

(B) Var (X) =?

Step-by-step explanation:


Related Questions

Prove that sum of measure of three angles of triangle is 180

Answers

Proved that the sum of measure of three angles of triangle is 180 using the Polygon Angle Sum Theorem

To prove that the sum of the measures of three angles of a triangle is 180 degrees, we can use the Polygon Angle Sum Theorem, which states that the sum of the measures of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees.

A triangle is a polygon with three sides, so we can apply the Polygon Angle Sum Theorem to a triangle to find the sum of its interior angles. Using n=3, we have:

Sum of measures of interior angles of triangle = (n-2) × 180 degrees

= (3-2) × 180 degrees [since we are dealing with a triangle]

= 1 × 180 degrees

= 180 degrees

Therefore, the sum of the measures of the interior angles of a triangle is 180 degrees. This means that the sum of the measures of the three angles in a triangle is always 180 degrees, regardless of the size or shape of the triangle.

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Find the value of the the expression x+|x|, if x=7

Answers

x +|x|

= 7 + |7|

= 7 + 7

= 14

because determine of | 7 | is 7

Can someone help me find the elevation of the sun I need the answers that are highlighted in yellow please help image below

Answers

Answer:

Step-by-step explanation:

a.  ∠ACB

b.  AC

c.  AB

d.  BC

e.  tangent, opposite, adjacent

f.  m∠ACB = tan⁻¹(34/45) = 37°

matching question match the sets on the left with a true statement about the cartesian product of those sets on the right. {1, 2} x {3, 4} = {1, 2, 3, 4} x {3, 4, 5, 6} = {4, 5, 6, 7} x {4, 5, 6, 7} = {a, e, i, o, u} x {b, g, t, d} =
{1, 2, 3} x {1, 2, 4} =
Choose:
(5, 5) is a member.
its cardinality is 4. (2, 2) is a member. its cardinality is 20.
(4, 3) is a member.

Answers

The correct answer is: (4, 3) is a member. Its cardinality is 4.

Matching the sets on the left with a true statement about the Cartesian product of those sets on the right:{1, 2} × {3, 4} = {(1, 3), (1, 4), (2, 3), (2, 4)}{1, 2, 3, 4} × {3, 4, 5, 6} = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6), (4, 3), (4, 4), (4, 5), (4, 6)}{4, 5, 6, 7} × {4, 5, 6, 7} = {(4, 4), (4, 5), (4, 6), (4, 7), (5, 4), (5, 5), (5, 6), (5, 7), (6, 4), (6, 5), (6, 6), (6, 7), (7, 4), (7, 5), (7, 6), (7, 7)}{a, e, i, o, u} × {b, g, t, d} = {(a, b), (a, g), (a, t), (a, d), (e, b), (e, g), (e, t), (e, d), (i, b), (i, g), (i, t), (i, d), (o, b), (o, g), (o, t), (o, d), (u, b), (u, g), (u, t), (u, d)}{1, 2, 3} × {1, 2, 4} = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (2, 4), (3, 1), (3, 2), (3, 4)}The following are true statements about the Cartesian product of these sets:its cardinality is 4. (4, 3) is a member.

Therefore, the correct answer is: (4, 3) is a member. Its cardinality is 4.

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Here is a scale drawing of a garden. Tom wants to plant a tree in the garden according to the following rules: It must be 4 m from A and 2 m from CD. Place a cross where Tom can plant the tree. D 2.5 cm A 4 cm C B 1 cm represents 2m​

Answers

Answer:

the cross is the blue color

PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT

Answers

The perimeter of the figure is 16p + 10.

What is perimeter?

The whole length of a two-dimensional or three-dimensional shape's sides or edges is known as its perimeter. It is frequently referred to as the shape's perimeter or circumference. It is possible to determine the perimeter of many geometric forms with accuracy. The perimeter is a key idea in geometry and has several practical uses, such as determining the radius of a circular racetrack or determining the length of fencing required for a certain property.

The perimeter of a figure is the sum of the lengths of all its sides.

Thus,

Perimeter = (p - 9) + (7p + 5) + (p - 9) + (7p + 5)

Perimeter = 2p + 2(7p) + 2(5)

Perimeter = 16p + 10

Hence, the perimeter of the figure is 16p + 10.

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Can someone help me with this

Answers

Solving a system of equations we can see that he cost of a corn dog is $1.25 and the cost of the fries is $3.50

How to find the cost of each item?

We can define two variables here:

x = cost of a corn dog.

y = cost of the fries.

With the information in the question we can write two equations, these two equations form a system of equations that we can solve, the system of equations is the one below:

2x + 3y = 13

4x + y = 8.50

We can isolate y in the second equation to get:

y = 8.50 - 4x

Replace it in the other one:

2x + 3*(8.5 - 4x) = 13

2x + 25.5 - 12x = 13

-10x = 13 - 25.5

x = -12.5/-10 = 1.25

Then:

y = 8.5 - 4*1.25 = 3.5

The cost of a corn dog is 1.25 dollars and the cost of the fries is 3.50 dollars.

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Ryan buys some jumpers to sell on a stall. He spends £190 buying 80 jumpers. He sells 50% of the jumpers for £12 each. He then puts the rest of the jumpers on a Buy one get one half price offer. He manages to sell half the remaining jumpers using this offer. How much profit does Ryan make?

Answers

Ryan makes a profit of £240.  the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.

Ryan spends £190 to buy 80 jumpers. He sells 50% of the jumpers, i.e. 40 jumpers, at £12 each. This brings the total sales to £480. Then, he puts the remaining 40 jumpers on a Buy one get one half price offer. He sells 20 of the remaining jumpers using this offer. Therefore, the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.

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Coordinate matrix for differentiation Let L :P2P be the linear transformation given by L(p(t)) = 5p"(t) + 1p' (t) + 3p(t) + 3tp(t). Let E = (C1, C2, C3) be the basis of P2 given by el(t) = 1, ez(t) = t, ez(t) = ť. and let F = (f1, 82, 83, fa) be the basis of P3 given by fi(t) = 1, fz(t) = t, fz(t) = {2, fa(t) = {'. Find the coordinate matrix LFE of L relative to the ordered bases & and F. LFE = Save & Grade 2 tries left Save only

Answers

The coordinate matrix LFE of L relative to the ordered bases E and F is given by:

LFE=12,3,0,12,3,0,0

LFE =

[[5, 1, 3, 3],

[0, 0, 3, 0],

[0, 0, 0, 0]]

This matrix can be obtained by computing the entries of LFE in terms of the components of L with respect to the basis E and then expressing those components with respect to the basis F. The elements of LFE are computed as follows:

LFE[1,1] = L(e1) = = 5 + 1 + 3 + 3 = 12

LFE[1,2] = L(e2) =  = 0 + 0 + 3 + 0 = 3

LFE[1,3] = L(e3) =  = 0 + 0 + 0 + 0 = 0

LFE[2,1] = L(f1) =  = 5 + 1 + 3 + 3 = 12

LFE[2,2] = L(f2) = = 0 + 0 + 3 + 0 = 3

LFE[2,3] = L(f3) = = 0 + 0 + 0 + 0 = 0

LFE[3,1] = L(f4) =  = 0 + 0 + 0 + 0 = 0

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A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 162 pounds requires 216 milligrams of medicine. What is the weight of a patient who requires 220 milligrams of medicine?

Answers

A patient weighing 220 pounds needs 293 milligrams of medicine.

We have given that,

patient weighing 162

pounds requires 216 milligrams of medicine

We have to calculate the amount of medicine required by a patient weighing 220 pounds

Consider the value of amount of medicine is x.

Set up a proportion.

pounds / milligrams of medicine

What is the proportion we get?

[tex]162/216=220/x[/tex]

So,

[tex]162/216=220/x[/tex]

[tex]162x=216\times220[/tex]

[tex]162x=47,520[/tex]

[tex]x=47,520/162[/tex]

[tex]x=293[/tex]

A patient weighing 220 pounds needs 293 milligrams of medicine.

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Please help me
What is the range of the quadratic function below?

Answers

The range of the quadratic function above is (-∞, 7].

What is the definition of a quadratic function?

In mathematics, a quadratic prοblem is οne that invοlves multiplying a variable by itself, alsο knοwn as squaring. In this language, the area οf a square is equal tο the length οf its side multiplied by itself. The term "quadratic" cοmes frοm the Latin wοrd fοr square, quadratum.

Tο determine the quadratic functiοn's range, we must first determine the functiοn's minimum and maximum pοints. The given functiοn is in vertex fοrm, with the vertex at the pοint (h, k), where h is the vertex's x-cοοrdinate and k is the vertex's y-cοοrdinate.

We can see frοm the given equatiοn that the vertex is at the pοint (1, 7). Because the cοefficient οf the x² term is pοsitive, the parabοla οpens upwards and the vertex is the functiοn's minimum pοint.

Thus, The range of the quadratic function above is (-∞, 7].

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In the figure here, a small block is sent through point A with a speed of 6.8 m/s. Its path is without friction until it reaches the section of length L=14 m, where the coefficient of kinetic friction is 0.78. The indicated height are h1=5.4 m and h2=2.8 m. What are the speeds of the block at (a) point B and (b) point C? (c) Does the block reach point D? (d) If, so what is its speed there; if not, how far through the section of friction does it travel?

Answers

A  small block is sent through point A with a speed of 6.8 m/s. Its path is without friction until it reaches the section of length L=14 m, where the coefficient of kinetic friction is 0.78. The indicated height are h₁ =5.4 m and h₂=2.8 m. The speeds of the block at (a) Point B is 108m/s and (b) Point C is 7.6m/s

The velocity of an object (usually denoted v) is the amount of its position change over time ; therefore it is a scalar quantity. The average speed of an object over a time interval is the distance traveled by the object divided by the duration of the interval; the instantaneous speed remains zero.

(a) At B the speed is :

   V = [tex]\sqrt{V^{2}+2gh_1 }[/tex]

​⇒ V = [tex]\sqrt{(6.8m/s)+ 2(9.8m/s^2) (5.4)}[/tex]

⇒ V = 108.44 m/s

⇒ V = 108 m/s

(b) Here, matters is the difference in heights (between A and C):

   [tex]V = \sqrt{V_0^{2}+2g(h_1+h_2) }[/tex]

⇒  [tex]V = \sqrt{(6.8)+2 (9.8) (5.4- 2.8) }[/tex]

⇒ [tex]V = \sqrt{6.8 +2(9.8)(2.6)}[/tex]      

⇒ √57.76 = 7.6m/s

(c)  Using the results from part (b), we see that its kinetic energy is just at the beginning of its "rough glide" (horizontally to D) is:

1/2 m(7.6m/s)² = 28.88m (with SI units understood).

We note that this kinetic energy will turn entirely into thermal energy

    28.88m =  μₙ mgd

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the equations of motion of a two-degree-of-freedom system can be expressed in terms of the displacement of either of the two masses.true or false

Answers

The statement "the equations of motion of a two-degree-of-freedom system can be expressed in terms of the displacement of either of the two masses" is TRUE.

What are the equations of motion?

The equations of motion refer to a set of mathematical equations that describe the behavior of a physical system over time. These equations define how the position, velocity, and acceleration of an object are related. The equations of motion are applicable to both single and multi-degree-of-freedom systems.

What is a two-degree-of-freedom system?

A two-degree-of-freedom system is a physical system with two independent modes of motion or two degrees of freedom. It is defined by two generalized coordinates that completely define the system's state.

A two-degree-of-freedom system can be either linear or nonlinear, depending on the nature of the force. It is used in the study of structural dynamics, mechanical vibrations, and control engineering.

In a two-degree-of-freedom system, the equations of motion can be expressed in terms of the displacement of either of the two masses. The equations of motion are usually derived using Lagrange's equations, which are a set of equations that describe the dynamics of a mechanical system in terms of its energy. They are given as follows:

Where q₁ and q₂ are the generalized coordinates, m₁ and m₂ are the masses, k₁ and k₂ are the spring constants, and c₁ and c₂ are the damping coefficients.

These equations of motion are nonlinear and can be solved analytically or numerically using various techniques.

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If y varies inversely with x and y is = to 100 x = 25 what is the value of y when x=10

Answers

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=25\\ y=100 \end{cases} \\\\\\ 100=\cfrac{k}{25}\implies 2500=k\hspace{12em}\boxed{y=\cfrac{2500}{x}} \\\\\\ \textit{when x = 10, what's "y"?}\qquad y=\cfrac{2500}{10}\implies y=250[/tex]

Complete the sequence in the grids so that starting
of a 2x2 board turned off by pressing one at a time on each
grid we reach all the lit squares.

Answers

Another strategy is to start by pressing a square in the middle of the grid, and then pressing the squares adjacent to it. This should help you turn off the squares in a cross pattern.

What is sequence?

In mathematics, a sequence is an ordered list of elements, typically numbers, which may be finite or infinite. Each element in the sequence is called a term. For example, the sequence {1, 2, 3, 4, 5} is a finite sequence of integers with five terms. Sequences can be represented in several ways, such as listing out the terms, using a formula to generate the terms, or using recursive rules. For example, the sequence of even numbers can be generated using the formula 2n, where n is a positive integer. So, the first five terms of the sequence are 2, 4, 6, 8, 10. Sequences are used in many areas of mathematics, including number theory, calculus, and statistics. They are also used in real-world applications, such as modeling population growth or predicting stock prices.

Here,

One common strategy is to start by pressing one of the corner squares, and then pressing the squares adjacent to it. Then, move to the adjacent corner square and repeat the process. This should help you turn off the squares in one diagonal line.

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a) Is the value of -42 different from the value of (-4)²? What purpose do the brackets serve? b) Is the value of -23 different from the value of (-2)³? What purpose do the brackets serve?​

Answers

a) The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.

b) The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.

What is exponent?

Exponents are mathematical notation used to indicate that a quantity is being multiplied by itself a certain number of times. The exponent is usually written as a superscript to the right of the base number.For example, in the expression 2³, the base number is 2 and the exponent is 3. This means that 2 is being multiplied by itself three times, resulting in a value of 8. Exponents can also be negative or fractional, indicating that the base number is being divided by itself a certain number of times.

In the given question,

a) The value of -42 is different from the value of (-4)². The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.

b) The value of -23 is different from the value of (-2)³. The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.

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It says to determine whether the following symbolized arguments are valid or invalid by constructing the truth table for each?

Answers

The valid symbolized arguments is HS-valid. (option e).

Now let's focus on the symbolized arguments presented in this question. To determine their validity, we need to identify the form of each argument. In some cases, we may need to rewrite the argument using double negation or commutativity before assigning a name to its form.

The argument form known as Hypothetical Syllogism (HS) is represented as follows:

P⊃Q

Q⊃R

P⊃R

The given argument can be rewritten using double negation as follows:

H⊃~M

M⊃H

H⊃~H

Then, we can see that the argument follows the form of HS, where if H implies not M, and not M implies not H, then we can conclude that H implies not H. This conclusion is always true because it is a contradiction. Therefore, the argument is valid.

Hence the correct option is (e).

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Complete Question:

Determine whether the following symbolized arguments are valid of invalid by identifying the form of each. In some cases the argument must be rewritten using double negation or commutativity before it has a named for. Those arguments without a specific name are valid.

H⊃~M

M

______

~H

a. DA-Invalid.

b. MP-valid.

c. AC-invalid.

d. MT-valid.

e. HS-valid.

Over 9 days Jaison jogged ----- 10m, 6m, 6m, 7m, 5m, 7m, 5m, 8m, 9m
Find the mean distance Jaison jogged

Answers

The mean distance Jaison jogged over 9 days is 7 meters per day. This was calculated by adding up all the distances he jogged and dividing by 9.

To calculate the average distance that Jaison jogged over the 9 days, we used the formula for mean, which involves summing up all the distances he jogged and dividing by the total number of days. After adding up the distances, we found that the total distance Jaison jogged was 63 meters. Dividing this by the 9 days gives us an average distance of 7 meters per day. Therefore, Jaison jogged an average of 7 meters each day over the 9-day period.

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The vertex of the parabola below is at the point (5, -3). Which of the equations
below could be the one for this parabola?-ہے
A. y=-3(x-5)^2-3
B. x=3(y-5)^2-3
C. x=3(y+3)^2+5
D. x=-3(y+3)^2+5

Answers

None of the available options match the parabola's equation.

Which might be the parabola's equation?

To determine the equation of a parabola, we can utilize the vertex form. Assuming we can read the coordinates (h,k) from the graph, the aim is to utilize the coordinates of its vertex (maximum point, or minimum point), to formulate its equation in the form y=a(xh)2+k, and then to determine the value of the coefficient a.

A parabola's vertex form is given by:

[tex]y = a(x-h)^2 + k[/tex]

where (h,k) is the parabola's vertex.

[tex]y = a(x-5)^2 - 3[/tex]

These values are substituted into the equation to produce:

[tex]-15 = a(2-5)^2 - 3[/tex]

[tex]-15 = 9a - 3[/tex]

[tex]-12 = 9a[/tex]

[tex]a = -4/3[/tex]

[tex]y = (-4/3)(x-5)^2 - 3[/tex]

This equation is expanded and simplified to produce:

[tex]y = (-4/3)x^2 + (32/3)x - 53[/tex]

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A sample of size 25 is drawn from a normal population with a population standard deviation of 100. Suppose the mean of the sample is x(bar) = 35. Recall that z0.025=1.96. A 95% confidence interval for the population mean is equal to

Answers

The 95% confidence interval for the population mean is equal to (30.4,39.6).

A confidence interval is a range of values that surrounds the point estimate, such as a sample mean, and provides a sense of the precision of the estimate. The confidence interval (CI) contains the estimated parameter at a given level of confidence, usually 95% or 99%.

The 95% confidence interval for the population mean is given by:

x(bar) ± Zα/2 * σ/√n

Where,

x(bar) = 35σ = 100n = 25Zα/2 = Z0.025 = 1.96

Substituting the values, we get:

CI = 35 ± 1.96 * 100/√25

CI  = (30.4,39.6)

Hence, the 95% confidence interval for the population mean is (30.4,39.6).

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g suppose the acme drug company what is the probability that the percent difference of -.13 or less is seen if the true difference is 0

Answers

To conclude, the probability of the Acme Drug Company seeing a percent difference of -.13 or less if the true difference is 0 is quite low and is equal to 0.0934.

The probability that the Acme Drug Company would see a percent difference of -.13 or less if the true difference is 0 is quite low. This is because a difference of -.13 is a very small percentage in comparison to a true difference of 0.

Mathematically, the probability of this happening would be equal to the area under the standard normal distribution curve for values between -0.13 and 0. In other words, the probability that the Acme Drug Company would see a percent difference of -.13 or less if the true difference is 0 is equal to the area from the left tail of the standard normal distribution curve up to the mean (0) of the curve.

Using a standard normal distribution calculator, we can see that the probability of the Acme Drug Company seeing a percent difference of -.13 or less is 0.0934. This probability is extremely low and it is not likely that the Acme Drug Company would experience such a small percent difference.

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Professor Krugman's economics course, the correlation between the students' total scores prior to the final examination and their final‑examination scores is r=0.5.r=0.5. The pre‑exam totals for all students in the course have mean 280280 and standard deviation 40.40. The final‑exam scores have mean 75 and standard deviation 8.. Professor Krugman has lost Julie's final exam but knows that her total before the exam was 300.300. He decides to predict her final‑exam score from her pre‑exam total.What is the slope of the least-squares regression line of final-exam scores on pre-exam total scores in this course? Give your answer to one decimal place.

Answers

Since only 25% of the variability in y is explained, Julie's actual score could have been much higher than the predicted value.

What is Standard Deviation?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. When the standard deviation is low, the data are concentrated around the mean, and when it is large, the data are widely dispersed.

(a) Slope, b = r*(sy/sx) = 0.5*(8/40) = 0.1

Intercept = y - bx = 75 - 0.1*280 = 47

The regression equation is:

y = 47 + 0.1*x

(b) Put x = 300

y = 47 + 0.1*300

y = 77

(c) r2 = 0.5*0.5 = 0.25

Since only 25% of the variability in y is explained, Julie's actual score could have been much higher than the predicted value.

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expand 5a(a+6)
please help

Answers

5a2 + 30
Here’s the answer , 5a to the power 2 plus 30

4/7+1/8+1/3 prime number​

Answers

Since 7 is the smallest integer that divides 173/168, we can conclude that the sum is not a prime number.

How to solve?

To add the fractions 4/7, 1/8, and 1/3, we need to find a common denominator.

The prime factorization of 7 is 7, the prime factorization of 8 is 2²3, and the prime factorization of 3 is 3. The least common multiple (LCM) of these three numbers is 7× 2²3× 3 = 168.

So, we can rewrite the fractions with the common denominator of 168:

4/7 = 96/168

1/8 = 21/168

1/3 = 56/168

Now we can add these fractions:

96/168 + 21/168 + 56/168 = 173/168

To check if this sum is a prime number, we can use trial division by checking all the integers between 2 and the√ of 173/168 (which is approximately 1.053):

2 does not divide 173/168

3 does not divide 173/168

4 does not divide 173/168

5 does not divide 173/168

6 does not divide 173/168

7 divides 173/168 (24 times)

8 does not divide 173/168

9 does not divide 173/168

...

Since 7 is the smallest integer that divides 173/168, we can conclude that the sum is not a prime number.

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Complete question:

What is the result of adding 4/7, 1/8, and 1/3, and is the sum a prime number?

Graph f(x) = ⌊x⌋ + 1 on the interval [-3,3]

Answers

Substitute the value of x from -3 to 3 in the equation and obtain the value of f(x), and plot the graph for the equation on the give interval.

What is a modulo function?

A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter what input was provided to this function, the output is always favourable.

The function of the graph is given as f(x) = ⌊x⌋ + 1 on the interval [-3,3].

Substitute the value of x from -3 to 3 in the equation and obtain the value of f(x).

Plot the coordinates on the graph to obtain the following.

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y=2x+1
2x-y=3
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

Answers

This is the answer, mark is brainliest

please help
there are 2 possible answers
Let x be the number of boys in a class and y be the number of girls. Which equation represents 2 boys for
every 5 girls? Select all that apply.
A. x=2y-5
B. x=5y-2
C. 5x=2y
D. x=2 1/2y
E. x=2/5y

Answers

Answer:

  C, E

Step-by-step explanation:

You want the equations that represent 2 boys for every 5 girls in a class.

Ratio

The number of boys is represented by x, and the number of girls is represented by y, so you have ...

  x : y = 2 : 5

As fractions, this is ...

  x/y = 2/5

Other representations

Multiplying by 5y gives ...

  5x = 2y . . . . . . matches equation C

Dividing by 5, we have ...

  x = 2/5y . . . . . . matches equation E

2. Two players A and B are competing at a trivia quiz game involving a series of questions. On any individual question, the probabilities that A and B give the correct answer areαandβrespectively, for all questions, with outcomes for different questions being independent. The game finishes when a player wins by answering a question correctly. Compute the probability that A wins if

a) A answers the first question,

b) B answers the first question. ​

Answers

a) The probability that A wins if A answers the first question is α / (α + β).

b) The probability that A wins if B answers the first question is βα+β.

a) If A answers the first question, then the game will be over only if A answers the first question correctly, which has a probability of α. If A answers incorrectly, then B gets to answer the next question, and we are in the same situation but with A's and B's roles reversed. Therefore, the probability that A wins in this case is given by:

P(A wins | A answers first) = α + (1 - α)β P(A wins | B answers first)

b) If B answers the first question, then we are in the same situation as in part a) but with A's and B's roles reversed. Therefore, the probability that A wins in this case is given by:

P(A wins | B answers first) = β P(A wins | A answers first) + (1 - β)β P(A wins | B answers first)

We can solve these equations for P(A wins | A answers first) and P(A wins | B answers first) using algebraic manipulation. For example, we can rearrange the equation in part a) to get:

P(A wins | A answers first) = α / (1 - (1 - α)β)

Similarly, we can rearrange the equation in part b) to get:

P(A wins | B answers first) = β / (1 - (1 - β)α)

Note that these probabilities depend on the values of α and β, which represent the abilities of A and B to answer questions correctly.

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The scatter plot shows the relationship between the test scores of a group of students and the number of hours they study in a week:

On a grid, Label Hours Studying on x axis and Test Scores on y axis. The title of the graph is Test Scores and Hours Studying. The scale on the x axis shows the numbers from 0 to 10 at increments of 1, and the scale on the y axis shows numbers from 0 to 100 at increments of 10. Dots are made at the ordered pairs 1.1, 10 and 2, 25 and 3.1, 10.1 and 4, 30 and 4, 45 and 5, 45 and 6, 25 and 6.5, 60 and 7, 45 and 7.5, 50 and 7.5, 75 and 8, 60 and 8.5, 75 and 9, 60. The ordered pair 1, 100 is circled and labeled as M. All the other points are put in an oval and labeled as N.
Part A: What is the group of points labeled N called? What is the point labeled M called? Give a possible reason for the presence of point M. (5 points)

Part B: Describe the association between students' test scores and the number of hours they study. (5 points)

Answers

Part A: The group of points labeled N is called a scatter plot. The point labeled M is an outlier.

Part B: The association between students' test scores and the number of hours they study is that as the number of hours students study increases, their test scores tend to increase as well.

What is scatter plot?

A scatter plot is a type of graph that displays the relationship between two variables. It is often used to show how one variable is affected by another.

Part A: The presence of point M could be due to an error in recording data, or it could be due to an unusual event or circumstance that is not representative of the population.

Part B: This suggests that the more time students put into studying, the better their test scores will be. However, it is important to note that the graph does not necessarily imply that studying for more hours will necessarily lead to higher test scores, as the scatter plot also shows that there are other factors that could affect test scores.

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Part A: The group of points labeled N is called a scatter plot.

The point labeled M is called an outlier.

The presence of point M is likely due to the fact that the student studied for only one hour, yet achieved a perfect score

Part B: The association between students' test scores and the number of hours they study is that as the number of hours students study increases, their test scores tend to increase as well.

What is scatter plot?

A scatter plot displays the relationship between two variables. It is often used to show how one variable is affected by another.

Part A: The group of points labeled N is called a scatter plot.

The point labeled M is called an outlier.

The presence of point M is likely due to the fact that the student studied for only one hour, yet achieved a perfect score.

Part B: The scatterplot shows a weak positive association between students' test scores and the number of hours they study.

As the number of hours studying increases, the test scores tend to increase, although there is considerable variability in this relationship. The outlier at 1, 100 indicates that there may be other factors other than study time that influence test scores.

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PLEASE HELP I DONT HAVE TIME

Leo has a number of toy soldiers between 27 and 54. If he wants to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?

The answer is 48 but I need step by step explanation

Answers

The number of toy soldiers Leo has is 48.

How to calculate the number of toy soldiers Leo has?

To solve this problem, we need to find a number that satisfies the three given conditions:

The number is between 27 and 54.

When the number is divided by 4, there is no remainder.

When the number is divided by 7, the remainder is 6.

When the number is divided by 5, the remainder is 3.

Let's start by finding a number that satisfies the first two conditions. We can do this by listing the multiples of 4 between 27 and 54:

28, 32, 36, 40, 44, 48, 52

Next, we need to find which of these numbers also satisfies the third condition, that is, leaves a remainder of 6 when divided by 7. We can go through each of these numbers and check:

28 divided by 7 leaves a remainder of 0.

32 divided by 7 leaves a remainder of 4.

36 divided by 7 leaves a remainder of 1.

40 divided by 7 leaves a remainder of 5.

44 divided by 7 leaves a remainder of 2.

48 divided by 7 leaves a remainder of 6.

52 divided by 7 leaves a remainder of 3.

So, the only number that satisfies the first three conditions is 48.

Finally, we need to check if 48 also satisfies the fourth condition, that is, leaves a remainder of 3 when divided by 5. Indeed, 48 divided by 5 leaves a remainder of 3.

Therefore, the number of toy soldiers Leo has is 48.

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