A bag contains 10 black chips and 5 white chips. dexter and thanh play the following game. dexter randomly selects one chip from the bag. if the chip is​ black, dexter gives thanh ​$7. if the chip is​ white, thanh gives dexter ​$10.

Answer:

n = 12

Step-by-step explanation:

Rewrite it as \(\frac{(n+3)}{5} = 3\)

Multiply both sides by 5

(n+3) = 15

You can drop the parenthesis now.

n + 3 = 15

n = 12

Answer:

12/5

Step-by-step explanation: 12/5 + 3 ÷ 5 = 3

The percentages of observations within 1, 2, and 3 standard deviations from the mean are important for understanding the spread of a normal distribution.

For a normal distribution, we can estimate the percentage of observations that are within a certain number of standard deviations from the mean.

The percentages for 1, 2, and 3 standard deviations are commonly referred to as the "68-95-99.7 rule" or the "empirical rule". Here are the percentages:Within 1 standard deviation of the mean: Approximately 68% of observations are expected to be within 1 standard deviation of the mean.

This includes approximately 34% of observations on either side of the mean.Within 2 standard deviations of the mean: Approximately 95% of observations are expected to be within 2 standard deviations of the mean. This includes approximately 47.5% of observations on either side of the mean.

Within 3 standard deviations of the mean: Approximately 99.7% of observations are expected to be within 3 standard deviations of the mean. This includes approximately 49.85% of observations on either side of the mean.The percentages of observations within 1, 2, and 3 standard deviations from the mean are important for understanding the spread of a normal distribution. They are commonly used in statistical analysis to identify outliers or unusual observations.

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Answer:

Step-by-step explanation:

Given two points

(

x

1

,

y

1

)

and

(

x

2

,

y

2

)

, the slope is defined as

XXX

m

=

Δ

y

Δ

x

=

y

2

−

y

1

x

2

−

x

1

Given statement solution is :-  P(5) = 1/6.

The probability of rolling a 5 is 1/6 or approximately 0.1667.

The probability of getting any side of the die is 1/6. The probability of obtaining a 1 is 1/6, the probability of obtaining a 2 is 1/6, and so on. The number of total possible outcomes is equal to the total numbers of the first die (6) multiplied by the total numbers of the second die (6), which is 36.

A standard die has six sides printed with little dots numbering 1, 2, 3, 4, 5, and 6. If the die is fair (and we will assume that all of them are), then each of these outcomes is equally likely. Since there are six possible outcomes, the probability of obtaining any side of the die is 1/6.

Since a standard die has six sides numbered from 1 to 6, the probability of rolling a specific number, such as 5, is equal to the probability of getting that number out of the total possible outcomes.

The total number of possible outcomes when rolling a die is 6 (one for each side). Since each side has an equal chance of landing face-up, the probability of rolling a 5 is 1 out of 6.

Therefore, P(5) = 1/6.

The probability of rolling a 5 is 1/6 or approximately 0.1667.

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The constant k is equal to 11/6.

The range of the joint density function f(x, y) is 0 < x < 1 and 0 < y < 1.

The joint density function f(x, y) is f(x, y) = (11/6) + xy, 0 < x < 1, 0 < y < 1

We have,

To determine the value of the constant k and the range of the joint density function f(x, y), we need to integrate the joint density function over its entire range and set the result equal to 1, as the joint density function must integrate to 1 over the feasible region.

The joint density function f(x, y) is defined as:

f(x, y) = k + xy, 0 < x < 1, 0 < y < 1

To find the value of k, we integrate f(x, y) over its feasible region:

∫∫ f(x, y) dxdy = 1

∫∫ (k + xy) dxdy = 1

Integrating with respect to x first:

∫ [kx + (1/2)xy²] dx = 1

(k/2)x² + (1/4)xy² |[0,1] = 1

Substituting the limits of integration:

\((k/2)(1)^2 + (1/4)(1)y^2 - (k/2)(0)^2 - (1/4)(0)y^2 = 1\)

(k/2) + (1/4)y² = 1

Now, integrating with respect to y:

(k/2)y + (1/12)y³ |[0,1] = 1

Substituting the limits of integration:

(k/2)(1) + (1/12)(1)³ - (k/2)(0) - (1/12)(0)³ = 1

(k/2) + (1/12) = 1

Simplifying the equation:

k/2 + 1/12 = 1

k/2 = 11/12

k = 22/12

k = 11/6

Therefore,

The constant k is equal to 11/6.

The range of the joint density function f(x, y) is 0 < x < 1 and 0 < y < 1.

The joint density function f(x, y) is given by:

f(x, y) = (11/6) + xy, 0 < x < 1, 0 < y < 1

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Answer:

d= -1/8

Step-by-step explanation:

8d+d+3d+2+4d= 16d+2

16d= -2

d= -1/8

The Solution:

We want to find the equation of a line S, which passes through point (6,2).

Let the required equation of line S be

Where m = the slope of line S, and

We are told that line S is parallel to line r, which is, y = 56x + 1. This implies that both lines have the same slope (m).

So, to find the slope (m) of line S, we shall compare y=56x+1 to the general form of equation of a line as given below:

Comparing both equations below:

Substituting 56 for m, and the given point (6,2) in the formula above, we get

Clearing the bracket, we get

Thus, the equation of line r is: y = 56x - 334

Answer:

(x + 4)^2 + (y - 1)^2 = 61.

Step-by-step explanation:

We need to find the square of the radius and the coordinates of the center.

Center = (-10 + 2)/2 , (-4 + 6)/2

= (-4, 1).

Length of the diameter

=  √((-10-2)^2 + (-4-6)^2)

= √(144 + 100)

=√244

So the radius = √244/2

and r^2 = 244/4 = 61,

So the equation of this circle is:

(x - (-4)^2 + (y - 1)^2 = 61

(x + 4)^2 + (y - 1)^2 = 61.

(x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given coordinates of the diameter of circle are  (-10,-4) and (2,6)

Diameter=√(x₂-x₁)²+(y₂-y₁)²

x₂=2,x₁=-10, y₁=-4, y₂=6

Diameter=√(2-(-10))²+(6-(-4))²

=√(12)²+(10)²

=√144+100

=√244

We know that Radius=Diameter/2

R=√244/2

Squaring both sides

R²=244/4

R²=61

So the equation of this circle is:

(x - (-4)² + (y - 1)² = 61

(x + 4)²+ (y - 1)² = 61.

Hence (x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)

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Answer:

3 minutes

Step-by-step explanation:

30÷1.5=20

1h=60mins

60÷20=3minutes

We need to find the angle (rounded to the nearest whole degree) of a circle that would represent the percent of students taking mathematics.

Since a complete turn around the circle has 360º, we have the following proportion:

Number of students Angle

734 360º

442 x

Then, cross multiplying the above values, we obtain:

Answer: 217º

Answer:

217°

Step-by-step explanation:

The fraction of students taking math is   442/734

 we need this same fraction of the 360 degrees in a circle

442/734 * 360 = 217°

Answer:

can u take pic again?

Step-by-step explanation:

Answer:

x = 7, x = -3

Step-by-step explanation:

We can find the zeros by factoring the equation using the zero product property.

x^2-4x-21 = 0

(x-7)(x+3) = 0

x-7 = 0

x = 7

x+3 = 0

x = -3

Zeros are x=7 and x= -3.

Answer:

Step-by-step explanation:

If

τ

1

and

τ

2

are two typologies on non-empty set

X

, then ………………. is topological space.

The expression that shows the number 8 in one's place will be 72.35 + 45.81 and 9.56 + 9.41. Then the correct options are B and C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The expression that shows the number 8 in one's place.

Let's check all the options, then we have

A) 34.56 + 24.89 = 59.45

In the number 59.45, the one's place is 9. So, it is incorrect.

B) 72.35 + 45.81 = 118.16

In the number 118.16, the one's place is 8. So, it is correct.

C) 9.56 + 9.41 = 18.97

In the number 18.97, the one's place is 8. So, it is correct.

D) 12.34 + 15.42 = 27.76

In the number 27.76, the one's place is 7. So, it is incorrect.

The expression that shows the number 8 in one's place will be 72.35 + 45.81 and 9.56 + 9.41. Then the correct options are B and C.

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Answer:

58

Step-by-step explanation:

Put the numbers in chronological order and find the middle number

0, 0, 38, 47, 58, 65, 78, 99, 227

Helping in the name of Jesus.

Answer:

a. 1.2 minutes

b. 0.83 lap

Step-by-step explanation:

a. We take 6 divided by 5 = 1.2 minutes per lap.

b. We take 5 divided by 6 = 0.83 lap in 1 minute

Answer:

It looks like there aren't many great matches for your search

Step-by-step explanation:

Answer:

£196 and 400cm

Step-by-step explanation:

3.5^2 = 12.25 will give the whole floor

12.25 × 16 = 196

20^2= 400cm is the front cover of the book

Answer: 15 - 6i

Step-by-step explanation:

3(5-2i)

3×5+3×(−2i)

Do the multiplications.

15−6i

The length of the side labeled x is 75.3 when rounded to the nearest tenth which can be determined by using Pythagorean theorem.

The Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

To find the length of the side labeled x, we will first need to calculate the length of the other two sides.

For the first triangle, the hypotenuse is equal to the side labeled x, so the length of the side labeled x can be calculated using the formula:

x = √(35² + 42²) = 50.1

For the second triangle, the hypotenuse is the side opposite the right angle, which is equal to the side labeled x. We can calculate the length of the side labeled x using the formula:

x = √(60² + 50²) = 75.3

For the third triangle, the hypotenuse is the side opposite the right angle, which is equal to the side labeled x. We can calculate the length of the side labeled x using the formula:

x = √(28² + 34²) = 39.6

Therefore, the length of the side labeled x is 75.3 when rounded to the nearest tenth.

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The rounded value of x in the triangles is:

25) x ≈ 76

27) x ≈ 21

29) x ≈ 104

All trigonometric identities are based on six trigonometric ratios. Sine, cosine, tangent, cosecant, secant, and cotangent. All these trigonometric ratios are defined using the sides of a right triangle as follows: Adjacent side, opposite side, and hypotenuse side.

25) Since, Sinθ = Opposite side/hypotenuse

Sin35° = 39/hypotenuse

hypotenuse = 39/Sin35°

Sin35° = 0.57

hypotenuse = 39/0.57

hypotenuse = 68.42

Now, using Pythagoras theorem:

hypotenuse² = base² + perpendicular²

68.42² = 39² + perpendicular²

4681.29 - 1521 = perpendicular²

4681.29 - 1521 = perpendicular²

3160.29 = perpendicular²

√3160.29 = perpendicular

56.21 = perpendicular

For the calculation of x:

Cosθ = Adjacent side/hypotenuse

Cos42° = 56.21/x

0.74 = 56.21/x

x = 56.21/0.74

x = 75.95

x ≈ 76

27) Cosθ = Adjacent side/hypotenuse

Cos60° = 14/hypotenuse

0.5 = 14/hypotenuse

hypotenuse = 14/0.5

hypotenuse = 28

Now, using Pythagoras theorem:

hypotenuse² = base² + perpendicular²

28² = 14² + perpendicular²

784 - 196 = perpendicular²

588 = perpendicular²

√588 = 24.24

perpendicular = 24.24

For the calculation of x:

Sinθ = Opposite side/hypotenuse

Sin50 = 24.24/hypotenuse

0.76 = 24.24/hypotenuse

hypotenuse = 24.24/0.76

hypotenuse = 31.89

Using Pythagoras theorem:

hypotenuse² = base² + perpendicular²

31.89² = x² + 24.24²

1016.97 = x² + 587.57

x² = 1016.97 - 587.57

x² = 429.4

x = √429.4

x = 20.72

x ≈ 21

29) Sinθ = Opposite side/hypotenuse

Sin28° = 44/hypotenuse

0.46 = 44/hypotenuse

hypotenuse = 44/0.46

hypotenuse = 95.65

Using Pythagoras theorem:

hypotenuse² = base² + perpendicular²

95.65² = 44² + perpendicular²

perpendicular² = 9148.92 - 1936

perpendicular² = 7212.92

perpendicular = √7212.92

perpendicular = 84.92

For the calculation of x:

Cosθ = Adjacent side/hypotenuse

Cos34 = 84.92/x

x = 84.92/0.82

x = 103.56

x ≈ 104

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Answer:

x = 45

Step-by-step explanation:

\(540 + 6x = 810\)

Step 1 : Collect like terms

\(6x = 810 - 540\)

Step 2 : Simplify

\(6x = 270\)

Divide both sides of the equation by 6

\( \frac{6x}{6} = \frac{270}{6} \)

Step 4 : Simplify

\(x = 45\)

I hope it helps :)

Answer:

Well...X=45

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation:540+6*x-(810)=0

Pull out like factors :-270 + 6x  =   6 • (x - 45)

Solve  :    x-45 = 0::

Add  45  to both sides of the equation:  x = 45

Answer: 0.9

Step-by-step explanation:

i) The probability density function for the number of non-defective items in a sample of ten items picked at random is: P(X=x) =10Cx × 0.9ˣ × 0.1¹⁰⁻ˣ

ii) The probability of having none or all the ten items being non-defective

is: 0.3487.

Here, we have,

Probability that item is non defective (P)=0.90

q=1-0.90=0.1

n=10

i) let X be the number of non defective iteam

Probability function of this given by the binomial distribution formula

P(X=x)

=10Cx × 0.9ˣ × 0.1¹⁰⁻ˣ

ii)P( X=0 or X=10)=P(X=0)+P(X=10)

P(X=0)=10C0×0.9^0×0.1^10

=0.0000000001

P(X=10)=10C10×0.9^10×0.1^0

=0.3487

P(X=0 or X=10)=0.3487+0.0000000001

=0.3487

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The area of the sector is A = π cm² and amplitude is a = 0.75 cm

Given data ,

The area of a sector is given by the formula:

A = (1/2) x r² x θ

where r is the radius of the sector and θ is the central angle in radians.

On simplifying , we get

A = π cm²

r = 1.5 cm

Substituting these values into the formula, we get:

π = (1/2) x (1.5)² x θ

π = (3/4) x θ

Solving for θ, we get:

θ = (4/3) x π

The amplitude of the sector is half of the radius, so:

amplitude = (1/2) x 1.5 cm = 0.75 cm

Hence , the amplitude of the sector is 0.75 cm

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Answer:

D. Yes, because it passes the vertical line test

Yes, the graph represent a function because it passes the vertical line test, option D is correct.

The vertical line test is a criterion used to determine if a graph represents a function.

According to the vertical line test, if any vertical line intersects the graph in more than one point, then the graph does not represent a function.

In other words, for a graph to represent a function, every input (x-value) must correspond to exactly one output (y-value).

If the graph fails the vertical line test, it means that there is at least one x-value that has multiple corresponding y-values, which violates the definition of a function.

As we observe the graph every x value has a unique y value, so it represents a function.

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a. The probability that both balls are red is (25/40) * (24/39) = 0.385, the probability that the first ball is red and the second is not is (25/40) * (15/39) = 0.288, the probability that the first ball is not red and the second is red is (15/40) * (25/39) = 0.288, and the probability that neither ball is red is (15/40) * (14/39) = 0.163.

b. The probability that the second ball is red is calculated as the sum of the probabilities that the first ball is blue and the second ball is red, and the probability that the first ball is red and the second ball is red. Therefore, the probability that the second ball is red is (15/40) * (25/39) + (25/40) * (24/39) = 0.538.

c. The probability that at least one of the balls is red is the complement of the probability that neither ball is red. Therefore, the probability that at least one of the balls is red is 1 - 0.163 = 0.837.

The problem involves calculating the probabilities of drawing two balls from an urn without replacement. To calculate the probabilities, a tree diagram can be used to visualize the different possible outcomes. The probabilities of each event can be calculated by multiplying the probabilities of each individual step.

Part a provides the probability of different events, including the probability that both balls are red, the probability that the first ball is red and the second is not, the probability that the first ball is not red and the second is red, and the probability that neither ball is red. Part b involves finding the probability that the second ball is red, which can be calculated by summing the probabilities of the different possible outcomes that result in a red second ball.

Finally, part c asks for the probability that at least one of the balls is red, which can be found by subtracting the probability that neither ball is red from 1.

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The logistic function to model this situation is P(t) = 20(1 + e^(-1.8(t - 2.734))).

(a) The logistic function that models this situation can be written as:

P(t) = L / (1 + e^(-k(t - t0)))

Given that 20 people initially have the virus (P(0) = 20), and in the long run, approximately 6250 people become infected (P(∞) = 6250), we can determine the values of L and t0 in the logistic function.

At t = 0, we have P(0) = L / (1 + e^(-k(0 - t0))) = 20.

Solving for L, we get:

20 = L / (1 + e^(kt0))

L = 20(1 + e^(kt0)).

In the long run, we have P(∞) = L / (1 + e^(-k(∞ - t0))) = L / (1 + e^(kt0)) = 6250.

Substituting the value of L, we get:

6250 = 20(1 + e^(kt0)) / (1 + e^(kt0)).

6250 = 20.

Solving this equation, we find that e^(kt0) = 311.25.

Taking the natural logarithm of both sides, we get:

kt0 = ln(311.25).

t0 = ln(311.25) / k.

Substituting the given value of k = 1.8, we can calculate t0:

t0 = ln(311.25) / 1.8 ≈ 2.734.

Therefore, the logistic function to model this situation is:

P(t) = 20(1 + e^(-1.8(t - 2.734))).

(b) The graph of the logistic function P(t) will start at 20, increase rapidly initially, and then gradually approach the asymptote of 6250 as t increases. The vertical coordinate at the point where the rate of infection starts to decrease can be estimated from the graph.

The logistic function to model this situation is P(t) = 20(1 + e^(-1.8(t - 2.734))). The graph of the function will provide insights into the length of time until the rate at which people are becoming infected starts to decrease and the corresponding vertical coordinate at that point.

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The price that Maura sell each scarf would be =$33. Maura sells each scarf for $33. That is option A.

To calculate the amount of money that Maura spends on each scarf the following is carried out.

The amount of money that she spends on the scarf material = $5.50

The percentage selling price of each scarf = 600% of $5.50

That is ;

= 600/100 × 5.50/1

= 3300/100

= $33.

Therefore, each price that is sold by Maura would probably cost a total of $33.

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