Two balls are pulled one after another, without replacement, from the box containing three black, five yellow, and seven red balls. What is the probability that the 1st ball is yellow, if the 2nd ball is black? (Hint: use common fractions during your calculations and round only your final answer to 2 places after the decimal point). A. 0.21 B. 0.36 C. 0.42 D. None of the above

The mean and the mode of the test scores are 85.7 and 90

From the question, we have the following parameters that can be used in our computation:

The line plot

Where we have

Scores   Frequency

70              2

80              4

90              6

100              2

So, we have

Mean = (70 * 2 + 80 * 4 + 90 * 6 + 100 * 2)/(2 + 4 + 6 + 2)

Evaluate

Mean = 85.7

For the mode, we have

Mode = highest frequency

So, we have

Mode = 90

Hence, the mean is 85.7 and the mode is 90

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a). The difference between the two population means is estimated at a location to be 2.7.

b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.

c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).

d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.

Using the equation \(x_1-x_2\), we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample

\(1(x_1=22.8)\) and deducting it from the mean of Sample \(2(x_2=20.1)\).

With the use of the equation \(df=n_1+n_2-2\), it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because \(n_1\) = 20 and \(n_2\) = 30.

We must apply the formula to determine the margin of error at 95% confidence \(ME=t*\sqrt[s]{n}\).

The sample standard deviation (s) is equal to the average of \(s_1\) and \(s_2\) (3.4), the t value with 95% confidence is 1.67, and n is equal to the

average of \(n_1\) and \(n_2\) (25). When these values are entered into the formula, we get \(ME=1.67*\sqrt[3.4]{25}=1.7\).

Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means \(CI=x_1-x_2+/-ME\).

The confidence interval's bottom limit in this instance is \(x_1-x_2-ME2.7-1.7=0.0\) and the upper limit is \(x_1+x_2+ME=2.7+1.7=5.4\).

As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

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The orthogonal complement of a line L in R³ is a plane P that contains the origin, which is perpendicular to L. Any vector in L¹ is orthogonal to every vector in L.

Given that I is the line given by the span of 7 in R³.

We need to find a basis for the orthogonal complement L¹ of L.

We know that the orthogonal complement of the line L in R³ is a plane P that contains the origin, which is perpendicular to L. Any vector in L¹ is orthogonal to every vector in L.

We have L = {c (7, 7, 7) : c ∈ R}.

Therefore, a vector v = (x, y, z) is in L¹ if and only if it is orthogonal to every vector in L.

So, we have the dot product of v and (7, 7, 7) equal to zero.

v · (7, 7, 7) = 0

⇒ 7x + 7y + 7z = 0

⇒ x + y + z = 0.

This means that L¹ is the plane in R³ given by the equation x + y + z = 0.

To obtain a basis for L¹, we need two linearly independent vectors that lie in the plane x + y + z = 0.

Two vectors that are clearly linearly independent and satisfy the equation x + y + z = 0 are (1, −1, 0) and (1, 0, −1).

Therefore, a basis for L¹ is{(1, −1, 0), (1, 0, −1)}. Hence, the answer is

{(1, −1, 0), (1, 0, −1)}.

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Answer:

Scale factor = 3

Step-by-step explanation:

A = (4,8) and A’ = (12,24)

4x = 12

X = 12/4

X = 3

(a). The above context-free grammar (CFG) generates the language that has at least five "a's" and any combination of "b's".

(b). The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c).  it is ambiguous.

(a). Context-free grammar for L₁ = {w = {a, b}*w contains at least five as}:

S → aaaaaA | aaaaS | bS | aA | bA | ε

A → aA | bAb → bB | ε

B → bB | aB | ε

The above CFG generates the language that has at least five "a's" and any combination of "b's".

(b). Context-free grammar for L₂ = {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}:

S → AbC | AcB | BCa | CBa

A → aA | ε

B → bBb

B → bBbBbBb

C → cC | ε

C → cC | ε

The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c). Yes, the language for b) is inherently ambiguous. It is because there are two variables A and B in the grammar, so the string can be generated in two ways. Thus, it is ambiguous.

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Answer:

amount = £1415.57  

Step-by-step explanation:

given data

computer buy = £1600

depreciates rate = 4% per year

time = 3 year

solution  

we get here amount that is express here as

amount = P × \((1-r)^{t}\)    ...................................1                                    

here r is rate and t is time put here value

amount will  be              

amount = 1600 × \((1-0.04)^{3}\)  

solve it we get

amount = £1415.57  

The domain of the curve is simply the set of all real numbers.So the domain of the function is all x values less than 1, which can be written as (-∞, 1).

To eliminate the parameter, we need to solve for t in terms of r or y.

From r(t) = 1 - et, we can rearrange to get et = 1 - r(t), and then take the natural logarithm of both sides to get:

t = ln(1 - r(t))

Similarly, from y(t) = 24, we can see that y(t) is a constant value that doesn't depend on t. Therefore, we don't need to eliminate the parameter in this case.

The domain of the curve is all values of t for which r(t) and y(t) are defined. From r(t) = 1 - et, we see that r(t) is defined for all values of t, since the exponential function is defined for all real numbers. Therefore, the domain of the curve is simply the set of all real numbers.

To eliminate the parameter t, we'll express t in terms of x and then substitute it into the y(t) equation. Given r(t) = 1 - e^t, we can solve for t:

1 - e^t = x
e^t = 1 - x
t = ln(1 - x)

Now, we can substitute t into the y(t) equation:

y(t) = y(ln(1 - x)) = 24

Therefore, the Cartesian equation is y = 24. The domain is all values of x for which t is defined. Since t = ln(1 - x), the argument of the natural logarithm (1 - x) must be greater than 0:

1 - x > 0
x < 1

So the domain of the function is all x values less than 1, which can be written as (-∞, 1).

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The probability that the student chosen will be a boy who watched tennis yesterday is 1/8.

Given that 56 students were asked if they watched tennis yesterday, 20 of the students are boys, 17 girls watched tennis yesterday and 32 students did not watch tennis yesterday and out of all these one students is to be chosen at random.

We have to find the probability that the student chosen will be a boy who watched tennis yesterday.

Total number of students is 56.

The total number of girls is 56-20=36

Girls who didn't watch tennis is 36-17=19

Number of the boys who did not watch the game is 32-19=13

Number of boys watching a tennis match is 20-13=7

Now, we will find the probability that the student chosen will be a boy who watched tennis yesterday.

Probability=Number of boys watching a tennis match/Total number of students
Probability=7/56

Probability=1/8

Hence, the probability that the student chosen will be a boy who watched tennis yesterday when 56 students were asked if they watched tennis yesterday is 1/8.

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The value of sin 315° = -√2/2, cos 9π/4 = √2/2 , tan (-135) = 1°

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular functions) comprising trigonometry are the cosecant , cosine , cotangent , secant , sine , and tangent .

We can use the following trigonometric identities to find the values ​​of sin, cos, and sun:

sin(x) = sin(x 360°)

cos(x) = cos(x 360°)

tan(x) = tan(x 180°)

Using these identities, we can convert  angles to equivalent angles in the first quadrant, where the values ​​of sin, cos, and sun are known.

sin (315°)

We can convert 315° to the corresponding angle in the first quadrant by subtracting 360°:

315° - 360° = -45°

Since sin(x) = sin(x 360°), we have:

sin(315°) = sin(-45°)

We know that sin(-θ) = -sin(θ), so:

sin(-45°) = -sin(45°)

We also know that sin (45°) = √2/2, so:

sin(315°) = -√2/2

Therefore, the power of 315  is equal to -√2/2.

cos(9π/4)

We can convert 9π/4 to the corresponding angle in the first quadrant by subtracting 2π:

9π/4 – 2π = π/4

Since cos(x) = cos(x 360°), we have:

cos(9π/4) = cos(π/4)

We know that cos(π/4) = √2/2, so:

cos(9π/4) = √2/2

Therefore, cos 9π/4 is equal to √2/2.

tan(-135°)

We can convert -135° to the corresponding angle in the second quadrant by adding 180°:

-135°- 180° = 45°

Since tan(x) = tan(x 180°), we have:

We know that tan(45°) = 1, so:

reddish brown (-135°) = 1

Therefore tan (-135°) equals 1.

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Answer:

$1456.25

Step-by-step explanation:

Given data

P= $1,250

t= 3 years

r=5.5%

The compound interest expression is given as

A= P(1+r)^t

substitute

A=  1250(1+0.055*3)

A=  1250(1+ 0.165)

A= 1250(1.165)

A= 1456.25

Hence the amount after 3 years is $1456.25

Answer:

Answer is 18

Step-by-step explanation:

18x3=54

54+54=108

18+2=20

20+20=40

108+40=148

Answer: (7,11)

Step-by-step explanation:

If 1,000 points are selected randomly inside the square with all points equally likely to be selected, points to lie inside the circle is 785.4 points.

We can find the answer by finding the ratio of the areas of the regions and then multiplying by the total number of points.

The square has an area of 1 (since it has sides of length 1).

The circle has a radius of 1/2 and an area of pi/4.

So the ratio of the areas is:

(π/4) / 1 = π/4

Therefore, we would expect:

(π/4) * 1000 =  ( 3.14 / 4 ) 1000

(π/4) * 1000 = 1000 × ( 0.785 ) = 785 points

points to lie inside the circle. This is approximately 785 points.

Your question is incomplete but mos probably your full question was

If 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie inside the circle?

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Answer:

0.6820

Step-by-step explanation:

Given data

Angle= 47°

Hence we want to find

cos 47°

From calculator

cos 47°=0.681998

to 4 dp

0.6820

Answer: 0.6820

Step-by-step explanation: I did the quiz

Answer:

I think the answer is 792

Answer:

SA = 696cm^2

Step-by-step explanation:

First we need to identify the shapes

There are 3 rectangles and 2 triangles

Now the individual surface area for each shape

20 x 10 = 200 (1 rectangle)

1/2(12 x 8) = 48 (1 triangle)

Now we add them together

(200 x 3) + (48 x 2) = 696

The probability is 50 percent.

what is probability?

Given that,

Class has 19 boys and 20 girls , out of which five students are to be chosen for presentation.

Sets are:

(0 Boy, 5 Girls)

(1 Boy, 4 Girls)

(2 Boys, 3 Girls)

(3 Boys, 2 Girls)

(4 Boys, 1 Girl)

(5 Boys, 0 girl)

Total sample size =6

Probability that more boys than girls are chosen = No. of times boys are more/ Total sample size.

3/6

= 0.5

That is 50 percent.

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Answer:a z score corresponding to an area located entirely in the left side of the curve

Step-by-step explanation:

Answer:

868,412 visitors

Explanation:

434,206 x 2 (double)

Answer:

A, B

Step-by-step explanation:

Given the system of equations, we should first solve for x and y so we can answer this question:

equation 1: x + y = 4, equation 2: x - y = 2 ⇒ add both equations together

x + y + x - y = 4 + 2 ⇒ combine like terms

2x + 0y = 6 ⇒ divide both sides by 2

x = 3 ⇒ plug into the x + y = 4 equation to solve for y

3 + y = 4 ⇒ subtract 3 from both sides

y = 4 - 3 = 1

Since we know y is the speed of the water current and x is the canoe's still water speed, we know that the water current's speed is 1 mph and the canoe's still water speed is 3 mph

This corresponds with choices A and B

This equation 16t² - 9t - 29 = 0 he hits the water.

To write an equation describing when the diver hits the water, we need to consider the vertical motion of the diver. We can use the equation:

y = y₀ + v₀t + (1/2)gt²

where:

y is the vertical position at time t

y₀ is the initial vertical position

v₀ is the initial vertical velocity

g is the acceleration due to gravity

t is the time

Given the information:

y₀ = 29 ft (height of the platform above the water)

v₀ = 9 ft/s (initial upward velocity)

g = 32 ft/s² (acceleration due to gravity, assuming downward is positive)

Plugging in these values, we have:

y = 29 + 9t - (1/2)(32)t²

To find when the diver hits the water, we set y equal to zero:

0 = 29 + 9t - (1/2)(32)t²

Simplifying the equation, we get:

16t² - 9t - 29 = 0

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Answer:

7 - 5 * x

Step-by-step explanation:

When it says 5 * the number, no one knows what the number is so your going to replace it with X

Answer:

Which of the following are prime numbers: (3, 4, 5, 6, 7)

The answer is B  3, 5, 7

Which of the following are prime numbers: (21, 23, 25, 27, 29)

The answer is D  23, 29

Fill in the blanks: All_____ numbers are considered composite except for the number__.

The answer is B  even, 2

Which of the following are composite numbers: (31, 33, 35, 37, 39)

The answer is C  33, 35, 39

What is a composite number?

The answer is C  A number with more than two factors

What are the factors of 12?

The answer is A  1, 2, 3, 4, 6 & 12

Which of the following are composite numbers: (70, 71, 71, 73, 74)

The answer is B  71, 73

What would you consider the number 1?

The answer is D  neither

Step-by-step explanation:

A prime number has only two factors, no more no less.

A composite number has more than two factors.

The number 1 is neither because it doesn't have two factors to be a prime number, nor does it have more than two factors to be a composite number. It has only one factor.

I hope this helped.

the answer to 8 ÷ 8 (2+2) is indeed 1.

What is BODMAS?

BODMAS is an acronym used to help remember the order of operations in arithmetic expressions. It stands for: Brackets, Orders (exponents and roots), Division, Multiplication, Addition,Subtraction. The order in which these operations are performed can greatly affect the result of a mathematical expression, so following the BODMAS rule ensures that the calculation is done in the correct order.

You are correct! The order of operations requires that we perform the multiplication and division operations before addition and subtraction, and within each group, we should perform the operations from left to right. So, using PEMDAS or BODMAS, we get:

8 ÷ 8 (2 + 2)

= 8 ÷ 2(2 + 2)

= 8 ÷ 2(4)

= 8 ÷ 8 = 1

So the answer to 8 ÷ 8 (2+2) is indeed 1.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Answer:

C

Step-by-step explanation:

It is not E becuase SQRT(97) is less than SQRT(100), SQRT(100) is 10,

SQRT(81) is 9 SO SQRT(97) is between 9 and 10, C.

Hope it helps :)

the square root below is between the integers of 9 and 10

Step-by-step explanation:

9×9 is equal to 81

10*10=100

Therefore, the correct inequality to find the domain is simply x - 3 < 0, which simplifies to x < 3.

To find the domain of a function, we need to determine all the values of the independent variable (usually represented by x) that the function is defined for. In this case, the function is defined as f(x) = x - 3, which means we can plug in any value of x into the expression x - 3 to get a corresponding value of f(x).

However, there are some values of x that would cause the expression x - 3 to be undefined. For example, if we were trying to find f(x) when x = 2, we would get f(2) = 2 - 3 = -1, which is a valid output. But if we were trying to find f(x) when x = 3, we would get f(3) = 3 - 3 = 0/0, which is undefined.

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The maximal amount of medically unsupervised weight loss that an adult should aim for in one week is generally 1-2 pounds (0.5-1 kg). This is because losing weight too quickly can be harmful to your health and lead to a number of negative side effects, such as muscle loss, fatigue, dehydration, and gallstones.

It's important to note that the amount of weight an individual can lose in a week can vary depending on factors such as their starting weight, body composition, and overall health. In some cases, a doctor or other medical professional may recommend a faster rate of weight loss under close supervision, but this is generally reserved for people who are severely overweight or have medical conditions that require rapid weight loss.

Ultimately, it's important to approach weight loss in a healthy and sustainable way, with a focus on making long-term lifestyle changes rather than relying on quick fixes or fad diets. A balanced diet, regular exercise, and a consistent sleep schedule are all important components of a healthy weight loss plan.

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Answer:

-5

Step-by-step explanation:

x-intercepts occur when y = 0

⇒ 2x + 10 = 0

⇒ 2x = -10

⇒ x = -5

So the x intercept of 2x + 10 is (-5, 0)

Answer:

-5

Step-by-step explanation:

To find the x intercepts we must replace y with 0 and solve for X

So our equation is 0=2x+10

Now we must get x by itself by subtracting 10 on both sides. We subtract 10 because it is being added.

Well, instead of guessing we can solve :)

Divide 2 on both sides, this cancels out the two on the right and makes the -10 on the left turn into a -5.

Now we are left with x=-5

Thus, our answer is -5

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