Joshua is 5 ft tall and casts an 8-ft shadow. he is standing next to Jason, who casts a 10 shadow. write a proportion that could be used ti determine Jason's height do not solve

The most suspicious set of outcomes of 30 games played between the two computers would be option C: ABBABABABABBABABABABABABABABAA.

In a fair game where player B is supposed to win 4 out of 5 times, we would expect player B to win approximately 24 out of 30 games.  However, option C shows player B winning only 6 out of 30 games, which deviates significantly from the expected outcome.

This set of outcomes suggests a strong bias towards player A winning, as player B's wins are significantly lower than expected.

It is highly unlikely to observe such a low success rate for player B if the game was truly biased in favor of player B winning 4 out of 5 times.

Option C raises suspicions of an unfair advantage given to player A, potentially indicating some manipulation or incorrect implementation in the programming of the game.

Further investigation would be warranted to determine the cause of this biased outcome and to ensure fair play between the two computers in future games.

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Sure, I can help you solve that math problem step by step.

First, we need to find the length of the hypotenuse of the ramp using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides (a^2 + b^2 = c^2).

So, using that formula, we can calculate the length of the ramp's hypotenuse: c^2 = 4.2^2 + 0.7^2

c^2 = 17.64 + 0.49

c^2 = 18.13

c = sqrt(18.13)

c = 4.26m

Now that we have the length of the hypotenuse, we can use the inverse trigonometric function of sine to find the angle of inclination. The sine of an angle is equal to the opposite side (in this case, the rise of the ramp, which is 0.7m) over the hypotenuse (4.26m).

So, sin(theta) = opposite/hypotenuse

sin(theta) = 0.7/4.26

sin(theta) = 0.1643

Now, we need to find theta by taking the inverse sine of 0.1643 (or sin(theta)).

theta = sin^-1(0.1643)

theta = 9.47 degrees

So the angle of inclination of the ramp to the nearest degree is 9 degrees.

Answer:

a. Let X be the length of a wooden pole produced for electricity networks in rural areas. The probability of a pole being rejected because it is too short is 0.02, and the probability of a pole being rejected because it is too long is 0.05. The acceptable range is between 6.3 m and 7.5 m. We can find the mean and standard deviation of X as follows:

First, we need to find the z-score corresponding to the lower bound of the acceptable range:

z1 = (6.3 - μ) / σ

Similarly, we need to find the z-score corresponding to the upper bound of the acceptable range:

z2 = (7.5 - μ) / σ

Using a standard normal table, we can find the values of z1 and z2 that correspond to the probabilities of 0.02 and 0.95, respectively:

z1 = -2.05

z2 = 1.64

Solving for μ and σ, we get:

z1 = (6.3 - μ) / σ => μ = 6.3 + 2.05σ

z2 = (7.5 - μ) / σ => σ = (7.5 - 6.3) / 1.64 = 0.74

Therefore, the mean and standard deviation of X are:

μ = 6.3 + 2.05(0.74) = 7.6 m

σ = 0.74 m

b. Let Y be the number of rejected poles in a sample of 20 poles. Y follows a binomial distribution with parameters n = 20 and p = 0.02 + 0.05 = 0.07. The probability of finding 2 rejected poles in a sample of 20 poles is:

P(Y = 2) = (20 choose 2) * 0.07^2 * 0.93^18 = 0.242

The probability of finding 2 rejected poles in a sample of 20 poles is 0.242.

Answer:

x ≤ 4

Step-by-step explanation:

To solve the inequality x - 3 ≤ 1, we need to isolate x.

Remember that this is a linear inequality, and linear inequalities are solved the same way as a linear equation - the objective is to leave the variable alone on one side (usually the left-hand side or LHS) to find its value −

x - 3 ≤ 1

x ≤ 4

Therefore, x ≤ 4

From the given information, we have:

PC = 10 (length of segment PC)

∠CBD = x°

∠BCD = x + 54°

We can determine the relationship between angles ∠CBD and ∠BCD by recognizing that they are inscribed angles intercepting the same arc CD. In a circle, the measure of an inscribed angle is half the measure of its intercepted arc. Therefore, we have:

∠BCD = 1/2(arc CD)

Since ∠BCD = x + 54° and arc CD is the diameter, which is 180°, we can set up the following equation:

x + 54 = 1/2(180)

Simplifying the equation:

x + 54 = 90

x = 90 - 54

x = 36

So, the measure of ∠CBD (m∠CBD) is 36°.

The equation of the parabola is[tex](y + 6)^2 = 4(x - 13)[/tex], where the vertex is (13, -6) and the distance between the directrix and focus is 14.

To determine the equation of the parabola, we need to use the standard form for a parabola with a horizontal axis:

[tex](x - h)^2 = 4p(y - k)[/tex]

Where (h, k) represents the vertex of the parabola, and p is the distance from the vertex to the focus (and also from the vertex to the directrix).

Given that the parabola opens to the right, the vertex will be on the left side. Let's assume the vertex is (h, k).

We know that the focus of the parabola is at (13, -6), so the distance from the vertex to the focus is p = 13 - h.

We are also given that the focal diameter is 28, which means the distance between the directrix and the focus is twice the distance from the vertex to the focus.

Therefore, the distance from the vertex to the directrix is d = 28/2 = 14.

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Answer:

5

-----

0.4 | 2

- 0

2.0

- 1.6

-----

4

The graph of y = log1/3(x) is a decreasing curve that passes through the points (1, 0) and (3, -1). The horizontal asymptote is y = 0, and the vertical asymptote is x = 0.

The inverse of y = log1/3(x) is x = 3^y, which is equivalent to y = log3(x). The graph of y = log3(x) is an increasing curve that passes through the points (1, 0) and (3, 1). The horizontal asymptote is y = 0, and the vertical asymptote is x = 0.

When both graphs are plotted on the same pair of axis, they intersect at the point (1, 0) and (3, -1) and (3, 1).

Answer:

  (c)  x³·∛x

Step-by-step explanation:

You want the simplified form of ∛(x¹⁰).

The first part of the problem tells you how to get there. After you have that expression, you need to bring the x⁹ term from under the radical.

  [tex]\sqrt[3]{x^{10}}=\sqrt[3]{x^9\cdot x}=\sqrt[3]{x^9}\cdot\sqrt[3]{x}=\boxed{x^3\cdot\sqrt[3]{x}}\qquad\text{matches choice C}[/tex]

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The area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

To find the area of a vertical cross section through the center of the base of the cone-shaped paperweight, we need to determine the radius of the base first.

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, we know the circumference is about 12.56 inches, so we can set up the equation:

12.56 = 2πr

To solve for r, we divide both sides of the equation by 2π:

r = 12.56 / (2π)

Now we can calculate the radius:

r ≈ 12.56 / (2 × 3.14)

r ≈ 12.56 / 6.28

r ≈ 2 inches

The radius of the base is approximately 2 inches.

Since the vertical cross section passes through the center of the base, the shape of the cross section is a circle. The formula for the area of a circle is A = [tex]πr^2[/tex], where A is the area and r is the radius.

Now we can calculate the area of the cross section:

A = [tex]πr^2[/tex]

A ≈ 3.14 × [tex](2^2)[/tex]

A ≈ 3.14 × 4

A ≈ 12.56 square inches

Therefore, the area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

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Answer: 4.5 or A

Step-by-step explanation:

1) Find LCM of 9 and 6, which is 18.

2) Multiply x/9 by 2. (2x/18)

3) Multiply 3/6 by 3. (9/18)

4) Divide by 2 (numberator on both sides)

               x = 4.5

Answer:187 miles

Step-by-step explanation: 155.33-16.95=138.38/74=187

The limit when n approaches infinity for the given expression is the one in option D, 21.

Here we want to take the following limit of n when it tends to infinity in the following rational expression:

[tex]\lim_{n \to \infty} 24 - 3 - \frac{24}{2n} + \frac{40}{n} + \frac{15}{3n^2}[/tex]

Notice that in all the terms where n appears, it is on the denominator. Thus, when n tends slowly to infinity, the denominator will be way larger than the numerator, and thus, all the fractions will tend to zero, then we will get:

[tex]\lim_{n \to \infty} 24 - 3 - \frac{24}{2n} + \frac{40}{n} + \frac{15}{3n^2} = 24 - 3 = 21[/tex]

The correct option is the last one, D.

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The minimum amount one will pay making a deposit of notes and coins is R7.25.

To determine the minimum amount one will pay when making a deposit of notes and coins, we need to consider the costs mentioned in Table 2.

According to Table 2, the cost for notes deposit is R2.25 per R100 (or part thereof) deposited, and the cost for coins deposit is R5 per R100 (or part thereof) deposited.

To calculate the minimum amount, we need to determine the lowest possible value for both the notes and coins deposit costs.

For notes deposit:

The minimum value would be R2.25, as it is the cost for depositing less than R100 worth of notes.

For coins deposit:

The minimum value would be R5, as it is the cost for depositing less than R100 worth of coins.

To calculate the total minimum amount, we sum up the costs for notes and coins deposits:

Minimum amount = R2.25 (notes deposit cost) + R5 (coins deposit cost)

Minimum amount = R7.25

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The equation that represents the direct variation between a and b in this scenario is: b = -a.

The correct option is (A).

We have,

The number b varies directly with the number a.

This equation states that b is equal to the negative value of a, which reflects the condition that b is located in the opposite direction from 0 compared to a and varies directly with a.

So, the equation cab be stated as b = -a.

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Answer:

120c

Step-by-step explanation:

3 for 10c 1 for 10/3c 3*12 for 10/3 *36 =12*10=120c is the cost of 3 dozen of such cards

Answer:

The expression 3+4x2 can be simplified using the order of operations, which is a set of rules used to determine the sequence in which operations are performed in an expression. According to the order of operations, we first perform any calculations inside parentheses, then we perform any multiplications or divisions (from left to right), and finally we perform any additions or subtractions (from left to right).

There are no parentheses in this expression, so we move on to the next step, which is to perform any multiplications or divisions. In this case, we have 4x2, which equals 8. So, we can replace 4x2 with 8, and the expression becomes:

3+8

Finally, we perform the addition, and get the final result:

11

Therefore, 3+4x2 is equal to 11.

Step-by-step explanation:

2.1.1: The basic charge in the given context refers to a fixed monthly fee that is charged by the municipality for the provision of water services, regardless of the amount of water consumed by the user.

2.1.2: To calculate the tariff for a particular consumption level during 2017/2018, you need to find the relevant consumption tier and then apply the corresponding rate. For example, if the consumption level is 10,000 litres per month, then the relevant tier is 7-15 kilolitres, and the rate for this tier is R15.95 per kilolitre. Therefore, the cost of water for this consumption level is:

10 kilolitres x R15.95/kilolitre = R159.50

To this cost, the basic charge needs to be added. According to the table, the basic charge for 2017/2018 is R7.46 per month. Therefore, the total cost of water and basic charge for this consumption level is:

R159.50 + R7.46 = R166.96

Therefore, the tariff for a consumption level of 10,000 litres per month during 2017/2018 is R166.96.

2.1.3: To verify if Mr Morake's statement is correct, we need to check if the basic charge was included in the calculation of his water bill. Assuming that Mr Morake's water usage for the month of August 2018 fell within the 7-15 kilolitre tier, we can calculate his bill as follows:

Water usage: 10 kilolitres

Cost of water: 10 kilolitres x R17.39/kilolitre = R173.90

Based on the above calculation, it appears that the basic charge was included in Mr Morake's water bill, as his total bill of R201.27 exceeds the cost of water alone. Therefore, it seems that Mr Morake's statement is incorrect, and the basic charge was indeed included in his water bill.

Step-by-step explanation:

The equation for this function is y=2x

So 32*2=64

36/2=18

2*x=2x

y/2=y/2

2x*2=4x

(x+3)*2=2x+6

To solve the inequality:

9.5 + 6x ≥ 42.1

We will follow these steps:

Subtract 9.5 from both sides of the inequality:

9.5 + 6x - 9.5 ≥ 42.1 - 9.5

6x ≥ 32.6

Divide both sides of the inequality by 6:

(6x) / 6 ≥ 32.6 / 6

x ≥ 5.433333...

Rounded to two decimal places, the solution to the inequality is:

x ≥ 5.43

Hello !

68/17 = 4

=> yes for 68

84/17 = 4.941...

=> no for 84

357/17 = 21

=> yes for 357

1001/17 = 58.882...

=> no for 1001

Answer:

The probability that at least one of two independent purchases is a Samsung display can be calculated using the complement rule:

P(at least one Samsung) = 1 - P(neither is a Samsung)

The probability that neither of the two purchases is a Samsung display is:

P(neither is a Samsung) = (1 - 0.29) x (1 - 0.29) = 0.51

Therefore, the probability that at least one of the two purchases is a Samsung display is:

P(at least one Samsung) = 1 - 0.51 = 0.49

The probability that in a collection of two independent purchases, at least one is a Samsung is 0.49.

Answer:

30

Step-by-step explanation:

We can move the triangle on the top to the bottom to form a rectangle.

Then, it is 5x6 = 30.

Answer:

a = 8, b = 2

Step-by-step explanation:

[tex]\sqrt[3]{x^{10} }[/tex] ( substitute x = - 2

= [tex]\sqrt[3]{(-2)^{10} }[/tex]

= [tex]\sqrt[3]{1024}[/tex]

= [tex]\sqrt[3]{2^{10} }[/tex]

= [tex]\sqrt[3]{2^{9 (2)} }[/tex]

= 2³ [tex]\sqrt[3]{2}[/tex]

= 8[tex]\sqrt[3]{2}[/tex] ← in the form a[tex]\sqrt[3]{b}[/tex]

with a = 8 and b = 2