X^2+ 14x = -33
Quadratic equation

The probability that exactly two of the sampled individuals have used a discount broker is approximately 0.2217 or 22.17%.

To calculate the probability of exactly two individuals in a random sample of nine having used a discount broker, we can use the binomial probability formula.

The binomial probability formula is given by:

\(P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)x^{2}\)

Where:

- P(X = k) is the probability of exactly k successes,

- n is the total number of trials (sample size),

- p is the probability of success on a single trial (probability of an individual investor using a discount broker), and

- (n choose k) represents the number of combinations of n items taken k at a time.

In this case, n = 9 (sample size) and p = 0.30 (probability of an individual investor using a discount broker).

\(P(X = 2) = (9 choose 2) * (0.30)^2 * (1 - 0.30)^(9 - 2)\)

Using the binomial coefficient formula (n choose k) = n! / (k! * (n - k)!) to calculate (9 choose 2), we can plug in the values:

\(P(X = 2) = (9 choose 2) * (0.30)^2 * (1 - 0.30)^(9 - 2)\)

\(P(X = 2) = (9! / (2! * 7!)) * (0.30)^2 * (0.70)^7\)

\(P(X = 2) = (36 / 2) * (0.30)^2 * (0.70)^7\)

P(X = 2) = 36 * 0.09 * 0.08235456

P(X = 2) ≈ 0.2217

Therefore, the probability that exactly two of the sampled individuals have used a discount broker is approximately 0.2217 or 22.17%.

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81 pages.

Step-by-step explanation:

Tuesday: 3 x 3 = 9

Wednesday: 9 x 3 = 27

Thursday: 27 x 3 = 81

Answer:

81

Step-by-step explanation:

3x3x3x3

5) The measure of arc BC is 1.14π radians and the length of arc BC is 2.86π units.

6) The measure of arc ABC is 1.99π radians and the length of arc ABC is 3.14π units.

An arc is a curved line that is a portion of a circle.

It is formed by connecting two points on the circumference of the circle with a curve.

5) BC: To find the measure of arc BC, we need to find the measure of angle BAC.

angle BAC = angle AOC

angle BAC = 129 degrees

Therefore, the measure of arc BC is:

arc BC = (129/360) x (2π x 4)

arc BC = 1.14π radians

To find the length of arc BC, we need to find the measure of angle BAC.

angle BAC = angle AOC

angle BAC = 129 degrees

Therefore, the length of arc BC is:

arc BC = (129/360) x (2π x 4)

arc BC = 2.86π

6) ABC:  To find the measure of arc ABC, we need to find the measure of angle BOC.

angle BOC = 360 - angle AOB - angle AOC

angle BOC = 360 - 51 - 83

angle BOC = 226 degrees

Therefore, the measure of arc ABC is:

arc ABC = (226/360) x (2π x 4)

arc ABC = 1.99π radians

To find the length of arc ABC, we need to find the measure of angle BOC.

angle BOC = 360 - angle AOB - angle AOC

angle BOC = 360 - 51 - 83

angle BOC = 226 degrees

Therefore, the length of arc ABC is:

arc ABC = (226/360) x (2π x 4)

arc ABC = 3.14π

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The complete question is -

Answer:

c

Step-by-step explanation:

The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of  zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88  OR  Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

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Answer:

All right

6. 7

7. -40

8. -1/6

9.  1

10. 3/5

11. -7

If you have any questions don't hesitate to ask

Answer:

Solve the following equations, and explain its each step.

6. 6x +3= 5x + 10

Solution given:

6x +3= 5x + 10

Subtracting both side by 5x

6x-5x+3=5x-5x+10

x+3=10

subtracting both side by 3

x+3-3=10-3

x=7

7. 6+ 0.10x = 0.15x+8

Subtracting both side by 0.15x

6+0.10x-0.10x=0.15x-0.10x+8

6=0.05x+8

subtracting both side by 8

6-8=0.05x+8-8

-2=0.05x

dividing both side by 0.05

-2/0.05=x

x=-40

8. 5-4x=6+2x

adding 4 on both side

5-4x-4x=6+2x+4x

5=6+6x

subtracting both side by 6

5-6=6-6+6x

-1=6x

dividing both side by 6

-1/6=6x/6

x=-1/6

9. 9-2x=7x

Solution given

adding 2x on both side

9-2x+2x=7x+2x

9=9x

dividing both side by 9

9/9=9x/9

x=1

10. 2(x-4) + 2x = -6x-2

open bracket

2x-8+2x=-6x-2

solve like terms

4x-8=-6x-2

adding 6 on both side

4x+6x-8=-6x+6x-2

10x-8=-2

adding 8 on both side

10x-8+8=-2+8

10x=6

dividing both side by 10

10x/10=6/10

x=3/5

11. ½x-3=3/2 x+4

Subtracting both side by ½x

½x-½x-3=³/2 x-½ x +4

solve like terms

-3=x+4

Subtracting both side by 4

-3-4=x+4-4

x=-7

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

The answer of the given question based on the  mathematical induction is , the base case and the inductive step are both proven, the statement holds true for all n∈N+. . hence proved,

To prove the statement using mathematical induction, we will proceed in two steps:

Step 1: Base case
Let's start with the base case, where n = 1.

For the first part, we have:
I * (M⁽⁻¹⁾ * XM)¹ = M⁽⁻¹⁾ * X¹ * M = M⁽⁻¹⁾ * XM

For the second part, we have:
(λ0 1λ)¹ = (λ¹ 0λ¹) = (λ 0λ)

Thus, the statement holds true for n = 1

Step 2: Inductive step
Assuming that the statement is true for n = k, we need to prove it for n = k+1.

For the first part equation:
\(I * (M^{(-1)} * XM)^{(k+1)} = I * (M^{(-1)} * XM)^k * (M^{(-1)} * XM)\)
                         \(= (M^{(-1)} * XM)^k * (M^{(-1)} * XM)\)
                         \(= M^{(-1)} * XM^{(k+1)} * M\)
                         \(= M^{(-1)} * X^{(k+1)} * M\)

For the second part:
\((\lambda_0 1\lambda)^{(k+1)} = (\lambda_0 1\lambda)^k * (\lambda_0 1\lambda)\)
                  \(= (\lambda^k 0\lambda^k) * (\lambda_0 1\lambda)\)
                  \(= (\lambda^k+1 0 \lambda^k+1 1 \lambda^k+1)\)

Therefore, we have shown that if the statement holds true for n = k, then it also holds true for n = k+1

Since the base case and the inductive step are both proven, the statement holds true for all n∈N+.

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a) The probability that the third card will be the two of clubs is 1/50 since there are 50 cards left in the deck after the first two cards have been drawn, and only one of them is the two of clubs.
b) Your odds are the same for choosing the two of clubs on each draw since the probability of drawing the two of clubs does not change with each draw.
c) This example illustrates the difference between independent and dependent events. In the case of drawing cards without replacement, the events are dependent since the outcome of one draw affects the probability of the next draw.
d) If we drew the cards with replacement, the marginal probabilities would not change since the probability of drawing any particular card is always 1/52. However, the joint probabilities would change since each draw is now independent.

a) To find the probability that the third card will be the two of clubs, we need to calculate the joint probability of not drawing the two of clubs in the first two draws and drawing it in the third. The probability of not drawing the two of clubs in the first draw is 51/52, and in the second draw, it is 50/51. The probability of drawing the two of clubs in the third draw is 1/50. So, the joint probability is (51/52) * (50/51) * (1/50) = 1/52.

b) The odds of choosing the two of clubs are the same for each draw: 1/52 for the first, second, or third draw. This is because the probability is based on the number of favorable outcomes (one card) over the total possible outcomes (52 cards) in a standard deck.

c) This example illustrates the difference between independent and dependent events. In this scenario, the events are dependent because each card drawn affects the remaining cards in the deck. If the events were independent, the probability of drawing the two of clubs would not change after drawing the first or second card.

d) If we draw cards with replacement, the marginal, joint, and conditional probabilities change because the events become independent. With replacement, the probability of drawing the two of clubs remains constant at 1/52 for each draw. The joint probability of not drawing the two of clubs in the first two draws and drawing it in the third becomes (51/52) * (51/52) * (1/52), and conditional probabilities will not be affected by the previous draws.

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The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

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When a confidence interval for the difference of two population means contains 0 (D) the population means may be the same.

When a confidence interval for the difference between the two population means contains 0, it means that there is no significant difference between the two population means.

However, it does not rule out the possibility that the population means are different.

This is because the confidence interval provides a range of values that are likely to contain the true difference between the population means, but it is possible that the true difference falls within this range and is not equal to 0.

Therefore, the conclusion that can be drawn is that the population means may be the same.

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To estimate the volume of a region rotated about the y-axis using the midpoint method, we need to divide the region into small vertical slices perpendicular to the y-axis.

By approximating each slice as a cylinder with a height equal to the width of the slice and a radius equal to the midpoint of the slice, we can calculate the volume of each slice. Summing up the volumes of all the slices will give us an estimate of the total volume.

To use the midpoint method, we first divide the region into small vertical slices along the y-axis. Each slice is perpendicular to the y-axis and has a width equal to the thickness of the slice. The midpoint of each slice represents the radius of the corresponding cylinder.

By considering the height of each slice as the width of the slice, we can approximate each slice as a cylinder. The volume of each cylinder is calculated using the formula V = πr²h, where r is the radius and h is the height. Adding up the volumes of all the cylinders or slices will provide an estimate of the total volume of the region rotated about the y-axis using the midpoint method.

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(a) To sketch a graph of the speed over a 3-second time span, we need to know the equation that describes the relationship between speed and time. Without this information, we cannot create an accurate graph.

(b) To find the volume of blood that passes along the artery in one second, we need to use the formula Q = A * v, where Q is the flow rate, A is the cross-sectional area of the artery, and v is the speed of blood flow. The cross-sectional area of the artery is given by A = pi * r^2, where r is the radius of the artery.

Thus, substituting the given values, we get:

A = pi * (5mm)^2 = 78.54 mm^2

v = 0.2 + 0.1 sin(2pit/0.8) (using the given information)

Q = A * v = 78.54 * (0.2 + 0.1 sin(2pit/0.8))

To find the volume of blood that passes along the artery in one second, we need to evaluate Q at t = 1 second, so we get:

Q = 78.54 * (0.2 + 0.1 sin(2pi1/0.8)) = 31.39 mm^3/s

Therefore, the volume of blood that passes along the artery in one second is approximately 31.39 cubic millimeters.

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Answer:

10^-9

Step-by-step explanation:

The critical value for the goodness-of-fit needed to test the claim is A.11.071

Given:

There are 6 colors.

Df= 6-1=5

Critical chi-square with 5 df at 0.05 level of significance = 11.071

Answer: 11.071

Chi-square serves as a statistical examination that analyzes whether there exists any noteworthy disparity between anticipated and witnessed frequencies present inside a categorical compilation of data.

By assessing the interrelationship between two independent variables, the tool determines the scope of association between them till they become independent.

After scrutinizing the differentiation within the outcome extracted from expected and actual observations, which is then evaluated against predetermined chi-square results, the derived p-value deduces the consequent decision concerning null hypothesis dismissal or affirmation in confirming an absence of interrelation between the two initial variable candidates.

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Answer:

9 teenagers

Step-by-step explanation:

12/20 = x/15

180/20 = x

9 = x

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

9 teenagers would take to finish the large pizza in 15 mins

Answer:

3/7 divided by 3/0

\(math\)

Step-by-step explanation:

Answer:

Firstly, we know 3^3 ÷ 3^-4 =2187. So, we got to check the value for each expression given below.

3x 3^6 = 2187

3^7 ÷ 3^0 = 2187

3^-3 ÷ 3^4 = 1/2187 (odd one out)

3^3 x 3^4 = 2187

Answer is 3^-3 ÷ 3^4

Hope this helps!

Answer:

??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Answer:

Step-by-step explanation:

The area of a triangle is 30cm

this is how I got my answer so 5+12=17+13=30 so that's how I got my answer then put center meters at the end of 30 then you have 30cm

Answer:

19.8

Step-by-step explanation:

Subtract 130.2 by 110.4

Answer:

A and C

Step-by-step explanation:

5) logx+log(x+9)=2

log(x(x+9))=2, log(x^2+9x)=2

6) log(x^2+9x)=2

(x^2+9x)=36 or 6^2

Answer: 3

Step-by-step explanation:

test the numbers

Answer:

3

Step-by-step explanation:

first you divide the given number with 11 the remainder you get substract in order to get 0

Answer:

$19.55

Step-by-step explanation:

17*0.15=2.55

17+2.55=19.55

Answer:

6

Step-by-step explanation:

To find the average rate of change, we must calculate the slope over the interval -3/2 to 0. We can use the formula below.

f(b) - f(a) / b - a

f(0) - f(-3/2) / 0 - -3/2

1 - -8 / 3/2

9 / 3/2

18/3

6

Brainliest, please!

Answer:

Step-by-step explanation: The square is 36+12 cm squared

The square area is 48 cm squared.

A square side is square root of 48.

Answer: 4sqrt(3)

Step-by-step explanation:

Answer:

k/j

Step-by-step explanation:

i just took the test, good luck!

The equation used to solve this problem is x + y + z = 100000,  0.04x + 0.06y + 0.08z = 6700 and y = z

An equation is an expression showing the relationship between two or more numbers and variables.

Let x represent the amount of money invested at 4% (short term), y represent the amount of money invested at 6% (intermediate term) and z represent the amount of money invested at 8% (long term)

Since an investor has $100,000 to invest, hence:

x + y + z = 100000    (1)

Also, the investor wishes to have a return of $6700, hence:

0.04x + 0.06y + 0.08z = 6700   (2)

Equal amounts invested in intermediate and long term bonds. This gives:

y = z     (3)

The third equation used to solve this problem is y = z

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Answer:

table will be 7, 11, 15,19

Order pairs will be (1,7)(2,11)(3,15)(4,19)

the fifth term of the sequence will be 23

Step-by-step explanation:

4 (1)+3=7

4(2)+3=11

4(3)+3=15

4(4)+3= 19

4(5)+3=23

Hope this helps

Answer:

A statistical method to identify cost behavior.

Step-by-step explanation:

Costing is the measurement of the cost of production of goods and services by assessing the fixed costs and variable costs associated with each step of production.

In Financial accounting, the three methods used to classify costs into their fixed and variable components includes high-low method, scatter diagrams and least-squares regression.

A least squares regression line is a standard technique in regression analysis used to make the vertical distance obtained from the data points running to the regression line to become very minimal or as small as possible.

Hence, the least-squares regression method is a statistical method that is typically used for identifying cost behavior.

Generally, the sum of the residuals of a least squares regression line is always equal to zero.

The decimal numbers that have an even number in the tenths place, an odd number in the hundredths place, and a prime number in the thousandths place include 0.237, 0.893, 0.475, and 0.652.

An even number is any number that can be divided exactly by two. Even numbers always have a last digit of 0, 2, 4, 6, or 8. Even numbers include 2, 4, 6, 8, 10, 12, 14, and 16.

Odd numbers are those that cannot be divided evenly by two. It cannot be evenly divided into two separate integers. When we divide an odd number by 2, we get a remainder. Odd numbers include 1, 3, 5, 7, and so on.

A prime number is a natural number greater than one that cannot be calculated as the product of two smaller natural numbers. A composite number is a natural number greater than one that is not prime. 5 is prime, for example, because the only ways to write it as a product, 1 5 or 5 1, involve 5 itself.

A prime number is a whole number greater than one with only the number one and itself as factors. A factor is a whole number that can be divided into other numbers evenly.

In this case, 0.237, 0.893, 0.475, and 0.652 have an even number in the tenths place which is the first place after the decimal point. Also, there's an odd number in the hundredths place, and a prime number in the thousandths place.

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Complete question

Write four decimal numbers that have an even number in the tenths place, an odd number in the hundredths place, and a prime number in the thousandths place