Guys pls help me with 1 and 2

We require both to ascertain whether the findings are independent, this criterion is applied.

Statistics frequently employs the binomial distribution as a discrete distribution. When compared to a binomial distribution, the normal distribution is continuous. The chance for 'x' success of an investigation in 'n' trials is represented by the binomial distribution.

As per the given information in the question,

The normal distribution can be used to approximate the binomial distribution. The situation when performing a normal approximation is as follows:

np ≥ 10 and,

np(1 - p) ≥ 10

This criterion is used to determine whether the results are independent.

We are aware that when n and p are combined, the results are independent.

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We checked the equation of lines are not parallel to each other.

The two lines when located at the same plane and equidistance from each other are called parallel lines. The properties of parallel lines as shown in equation is that both have same slope but different y intercept.

Two parallel lines never intersect.

equation of line passes through the point (- 3, -3) and (3, 9)

is given by the formula [ y - y₁] = [(y₂- y₁) / (x₂- x₁)] [x - x₁}

                                      [ y- (-3)] = [9 - (-3) / 3- (-3)] [x - (-3)]

                                 (y +3) = [(9+3)/ (3+3)] (x+3)

                                  y+ 3 = 12/ 6 (x+3)

                                  y+3 = 2 (x+3)

                                   y+3 = 2x+6

                                   y = 2x+3 this is the first line.

equation of line passes through (-5, 12) and (1, 0)

                          [y - 12] = [(0 - 12) / 1 - (-5)] [x - (-5)]

                       y -12 = -12/ 6 (x+5)

                         y - 12 = -2 x - 10

                        y = - 2x + 2

the above is the equation of second line.

the above two equation have same slope but different sign. Hence, the lines are not parallel to each other.

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You will be able to withdraw approximately $3,076.32 at the end of 5 years.

To calculate the amount you will be able to withdraw at the end of 5 years, we can use the future value formula for compound interest.

The formula for calculating the future value (FV) of a present value (PV) invested at an annual interest rate (r) for a certain number of years (t) is:

\(FV = PV * (1 + r)^t\)

Given:

PV = $2,300

r = 6% = 0.06 (decimal representation)

t = 5 years

Substituting these values into the formula, we get:

FV = $2,300 * \((1 + 0.06)^5\)

Calculating the expression inside the parentheses:

\((1 + 0.06)^5 = 1.338225\)

Multiplying the present value by this factor:

FV = $2,300 * 1.338225

FV ≈ $3,076.32

Therefore, you will be able to withdraw approximately $3,076.32 at the end of 5 years.

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You deposit $2,300 into an account that pays 6% per year. Your plan is to withdraw this amount at the end of 5 years to use for a down payment on a new car. How much will you be able to withdraw at the end of 5 years? Do not round intermediate calculations. Round your answer to the nearest cent

False. The term "undisturbed" refers to the state of the soil or sediment sample before it is collected.

An undisturbed sample is one that has not been altered or disturbed in any way during the sampling process.

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Answer:

Step-by-step explanation:

The most appropriate choice for expectation will be given by-

Expected value for someone who buys the ticket = $\((-1591.2)\)

What is expectation?

At first it is important to know about probability of an event.

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Suppose x is a random variable with the probability function f(x). suppose

\(x_1. x_2,........,x_n\) are the values corrosponding to the actual occurance of the event and \(p_1, p_2.,,,, p_n\) be the corrosponding probabilities.

Expectation is given by the formula \(p_1x_1+p_2x_2+...+p_nx_n\)

Here,

Total number of tickets = 832

Number of prized tickets = 1

Probability of winning a ticket = \(\frac{1}{832}\)

Probability of losing a ticket = \(\frac{831}{832}\)

Gain of winning = $(1600 - 5) = $1595

Loss of losing = $(5 - 1600) = -$1595

Expected value for someone who buys the ticket

\(1595 \times \frac{1}{832} + (-1595)\times \frac{831}{832}\)

\(1595\times(\frac{1-831}{832})\\-1595\times \frac{830}{832}\\\)

$\((-1591.2)\)

Expected value for someone who buys the ticket = $\((-1591.2)\)

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Answer:

I don't even know what those last 2 words are. Good Luck though.

Triangles FGH and ABC are congruent because of the: AAS congruence theorem.

The AAS congruence theorem states that when two angles and one non-included side in one triangle are congruent to corresponding two angles and one non-included side in another triangle, then both triangles are congruent.

In the proof given, it is established that both triangles have two corresponding congruent angles, and also, BC ≅ GH which are non-included sides.

Therefore, both triangles are congruent because of the AAS congruence theorem.

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Answer: x= -4

Step-by-step explanation: slope = (y2-y1)/(x2-x1).

(4-7)/(-7-x)

-3/-7-x=1

Multiply both sides by -7-x

-3=-7-x

Add 7 to both sides

4=-x so x = -4

Answer:

A intersection B = {12,18,24,30}

Step-by-step explanation:

A ={3,6,9,12,15,18,21,24,27,30,33,36,39}

B ={10,12,14,16,18,20,22,24,26,28,30}

As a result, the quartile's value will be 52.5.

Data in math refers to numerical facts and values that are collected and organized for analysis. Data helps to answer questions, solve problems, and gain insights. It is used to perform calculations, draw conclusions, and make predictions. Data can be presented as tables, graphs, diagrams, and charts, and can be used to identify trends, compare different sets of information, and study cause-and-effect relationships.

Given information is:
56 32 48 52 51 53 48 38 35 42 40 46 54 50

If you organise the given data in ascending fashion first, you can retrieve the value of the top quartile.

32, 35, 38, 40, 42, 46, 48, 48, 50, 52, 53, 54, 56

48, 50, 52, 53, 54, and 56 are in the upper quartile.

The upper quartile value is expressed as:

=53+52/2

=105/2

=52.2

As a result, the upper quartile's value will be 52.5.

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Heidi earned $30 in commission.

The amount of money that the store made from Heidi's sales is equal to $720.

In this exercise, you're required to determine the amount of money earned by the salesperson as commission based on the price at which she sold a jewelry.

Mathematically, the amount of commission earned on the sales of a product can be calculated by using this mathematical expression:

Commission = Percent commission × Sales price

Given the following data:

Percent commission = 4%

Sales price = $750.

Substituting the given parameters into the formula, we have;

Commission = 4/100 × 750

Commission = 0.04 × 750

Commission = $30.

Next, we would determine the amount of money that the store made from her sales:

Sales = $750 - $30.

Sales = $720.

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The required area under the whole probability density curve is given by option C. 1.

The area under the entire probability density curve is equal to,

As the probability density function (pdf) represents the probability of a continuous random variable.

And continuous random variable taking on a specific value within a certain range.

Since the total probability of all possible outcomes must be equal to 1.

This implies that the area under the entire probability density function (pdf) curve must also be equal to 1.

Therefore, the area under the entire probability density curve function is equal to option c. 1.

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Answer:

The first option

The probability of a type i error for a sample of size 10 depends on the significance level (α) chosen for the hypothesis test. Assuming a standard significance level of 0.05, the probability of a type i error for a sample of size 10 can be calculated using a t-distribution table or a statistical software.

A type i error occurs when a null hypothesis is rejected when it is actually true. In hypothesis testing, the significance level (α) is the probability of rejecting the null hypothesis when it is actually true. A common significance level used in statistical analysis is 0.05, which means that there is a 5% chance of rejecting the null hypothesis when it is actually true.

The probability of a type i error for a sample of size 10 can be calculated using a t-distribution table or a statistical software. The calculation involves finding the critical value of t at the chosen significance level and degrees of freedom (df), which is equal to the sample size minus 1 (n-1). For a sample size of 10 and a significance level of 0.05, the critical value of t is approximately 2.306 (from a t-distribution table with 9 degrees of freedom).

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The system of three equations and three unknowns to write the equation are: 5t²+80t+6990.

Given:

Elevation              Travel time

6990 feet                    0 hours

8290 feet                    10 hours

10875 feet                   21 hours

Using this formula

y(t)=at²+bt+c

Where:

At:

t=0; y=6990

6990=a(0)²+b(0)+c

c=6990 Equation 1

At:

t=10; y=8290

8290=a(10)²+b(10)+6990

1300=100a+10b Equation 2

At:
t=21; y=10,875

10875=a(21)²+b(21)+6990

3885=441a+21b Equation 3

Using equation 2 and 3 to solve for a and bc

1300=100a+10b

1300-10b/100=a

13-0.1b=a

Plug into equation 3

3885=441(13-0.1b)+21b

3885=5733-14.1b+21b

b=80

a=13-0.1(80)

a=13-8

a=5

Hence:

Write the Equation by plugging a,b and c

y(t)=5t²+80t+6990

Therefore the system of three equations and three unknowns to write the equation are: 5t²+80t+6990.

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Answer:

C. Zero

Step-by-step explanation:

The solution of the system of equations would be the point where they intersect, but since these lines are parallel, they will never intersect, so therefore there are zero solutions.

Answer:

2.52

Step-by-step explanation:

21*.12=

2.52

The expression that represents the fee for signing up the day of the activity is x + 0.20x. This means that fee for signing up the day of the activity is original fee (x) plus an additional 20% of original fee (0.20x).

For example, if the community center charges $50 for signing up before the day of the activity, then the fee for signing up the day of the activity would be:

$50 + ($50 x 0.20) = $50 + $10 = $60

So, individuals who sign up the day of the activity are charged a higher fee than those who sign up before the day of the activity, because they are charged the original fee plus an extra 20% of the original fee. This is often used as an incentive for individuals to sign up early and to help the community center plan and prepare for the activity accordingly.

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The surface area of a square pyramid with base length of 3 ft. and height of 6 ft. is 45 square ft. (option A)

The formula for the surface area of a square pyramid is given by:

A = a² + a  √(a² + 4h²)

Where:

A = surface area

a = base length

h = height of the pyramid

In the given problem, the side length of the base = W = L = 3 ft.

Hence,

a = 3 ft.

h = 6 ft.

Plug these parameters into the formula:

A = 3² + 3 x √(3² + 4x6²)

A = 9 + 3 x √153

A = 45 ft². (option (A)

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Answer:

6.934

Step-by-step explanation:

6,934 milliliters is equal to 6.934 liters.

Unit conversion is defined as expressing the same quantity by different measurement units.

For example, a distance of 20 meter can be also expressed as 2000 cm. The distance is same.

Given a volume in milliliters, that is 6,934 milliliters.

We have to convert this to liters.

We have the conversion that,

1 liter = 1000 milliliters

1000 milliliters = 1 liter

1 milliliter = 1/1000 liter

6,934 milliliters = 6,934 × (1/1000) liter

                          = 6.934 liters

Hence the correct unit is 6.934 liters.

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The number of different ways the prizes can be awarded is 161700

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

The number of different ways the prizes can be awarded is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 100 and r = 3

Substitute the known values in the above equation

Total = ¹⁰⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 100!/97!3!

Evaluate

Total = 161700

Hence, the number of ways is 161700

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Answer:

Step-by-step explanation:

Do you have a picture of the problem?

Answer:

The answer is: 720

Step-by-step explanation:

V=B x H

in this case you have 2 heights. So your gonna multiply 6 x 8.

Which makes 48. Then your gonna multiply 48 x 15. Which equals to 720.

The total floor-space area of two rooms whose dimensions (width and length) of room1 have been read into two variables width1 and length1 and the dimensions of room2 have been read into two other variables width2 and length2 can be calculated by using the following expression: `(width1 * length1) + (width2 * length2)`

In this expression, `(width1 * length1)` calculates the floor space of the room1 and `(width2 * length2)` calculates the floor space of room2.

When both of these floor spaces are added using the "+" operator, the result is the total floor-space area of the two rooms.

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Answer:

Step-by-step explanation:

\(x^2 - 7x + 9 = 0\quad\implies\quad a=1\,,\ b = -7\,,\ c=9\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-7)\pm\sqrt{(-7)^2-4\cdot1\cdot9}}{2\cdot1}=\dfrac{7\pm\sqrt{49-36}}2\\\\x_1=\dfrac{7+\sqrt{13}}2\,,\quad x_2=\dfrac{7-\sqrt{13}}2\)