I need this by today at 11:59 PM please help.

Answers

Answer 1

From given sample space, No. of toothpicks each student will get is 51.

What exactly is a sample space?

In mathematics, a sample space is the set of all possible outcomes of an experiment or a random phenomenon. It is denoted by the symbol "S" and is a fundamental concept used in calculating probabilities. For example, when flipping a coin, the sample space is {heads, tails}. When rolling a fair six-sided die, the sample space is {1, 2, 3, 4, 5, 6}. The sample space for a more complex event may involve multiple variables and outcomes.

Now,

Total Toothpicks = 918

Total students = 18

then

Toothpicks per student = 918/18=51

Hence,

           No. of toothpicks each student will get is 51.

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Related Questions

The sum of a number and three is no more than eight

Answers

Answer:5

Step-by-step explanation: hope this helps

In triangle BC, point D is on AC such that AD = 12 and CD = 12. If angle ABC = angle BDC = 90 degrees, then what is BD?

Answers

Answer:

Step-by-step explanation:

BD is craxking treys and cracking treys is gd dissing bd you can look it up i ffrom o block and bd is the opps im telling so you wont lose yo life so please play right if you gdk be gdk if u gd be gd we aint bd ofn

The height distributions of two different classes at Dover elementary school are shown below both groups, have the same interquartile range how many times the third quartile range is the difference between the median height of the third grade class in the fourth grade class 1/4 1/2 two or four

Answers

The third quartile range is the difference between the median height of the third grade class and the fourth grade class, so the answer is two times.

Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9

Answers

The answer is , (a)  For equation 1 Use the quadratic formula , (b) For equation 2 use of Factor out the common factor , (c) For equation 3 use of Complete the square.

What is Quadratic equation?

A quadratic equation is a type of equation in algebra that contains a variable of degree 2, meaning that the highest power of the variable is 2.

Quadratic equations can have two real roots, one real root, or two complex roots, depending on the value of the discriminant (b² - 4ac). If discriminant is positive, equation has two real roots, if it is zero, equation has one real root (a "double root"), and if it is negative, equation has two complex roots.

Inga can use the following steps to solve the quadratic equation 2x² + 12x - 3 = 0:

Use the quadratic formula: Inga can use the quadratic formula, which is x = (-b ± √(b² - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = 2, b = 12, and c = -3.Factor out the common factor: Inga can factor out the common factor of 2 from the equation to get 2(x² + 6x - 3/2) = 0.Complete the square: Inga can complete the square by adding (6/2)² = 9 to both sides of the equation to get 2(x² +6x +9 -9/2) = 9.

Therefore, steps that Inga could use to solve quadratic equation are given:

Use the quadratic formula

Factor out the common factor

Complete the square

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Find the area of the polygon

Answers

the area of the polygon is 960

2•20•2•12= 960

You want to be able to withdraw $40,000 each year for 15 years. Your account earns 5% interest.
a) How much do you need in your account at the beginning?
b) How much total money will you pull out of the account?
c) How much of that money is interest?

Answers

a) you would need $450,332.81 in your account at the beginning. b)  the total money that will be pulled out of the account is $600,000.

How to determine  How much do you need in your account at the beginning

a) To calculate the amount needed in the account at the beginning, we can use the present value formula:

PV = PMT * ((1 - (1 + r)^-n) / r)

Where PV is the present value, PMT is the annual payment, r is the annual interest rate, and n is the number of periods.

Plugging in the values, we get:

PV = 40000 * ((1 - (1 + 0.05)^-15) / 0.05)

PV = $450,332.81

Therefore, you would need $450,332.81 in your account at the beginning.

b) To calculate the total money that will be pulled out of the account, we can simply multiply the annual payment by the number of years:

Total money = PMT * n

Total money = 40000 * 15

Total money = $600,000

Therefore, the total money that will be pulled out of the account is $600,000.

c) To calculate the amount of money that is interest, we can subtract the initial investment from the total money pulled out:

Interest = Total money - Initial investment

Interest = $600,000 - $450,332.81

Interest = $149,667.19

Therefore, $149,667.19 of the money pulled out is interest.

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Please help and hurry

Answers

The equation of the parabola with vertex at point (2, -11) and passes through the point (0, 5) is y = 4(x - 2)² - 11.

What is linear and quadratic equation?

A straight line can be used to symbolise a function that is linear, meaning that for each unit change in the input, the output (y) changes by a fixed amount (x). While a parabola can be used to depict a function, a quadratic function has an output (y) that changes by a non-constant amount for each unit change in the input (x). In other words, a quadratic function curves because of the squared term in its equation.

Given, the parabola has vertex at point (2, -11) and passes through the point (0, 5).

Thus, the equation of parabola in vertex form is:

y = a(x - 2)² - 11

Now, the parabola passes through the point (0, 5) we have:

5 = a(0 - 2)² - 11

5 = 4a - 11

16 = 4a

a = 4

Hence, the equation of the parabola with vertex at point (2, -11) and passes through the point (0, 5) is y = 4(x - 2)² - 11.

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1:20 - salesman allows a 5% discount for cash payment. What will be the discount allowed for a ash payment of GH¢5,600.00? A. GH 250.00​

Answers

The discount allowed for a cash payment of GH 5,600.00 is given as follows:

GHC 280.00.

How to obtain the discount?

The discount allowed for a cash payment of GH 5,600.00 is obtained applying the proportions in the context of the problem.

There is a 5% discount, hence the value of the discount is obtained as follows:

0.05 x 5600 = GHC 280.00.

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Please help me with this problem

Answers

Using the proportions we know that the value of h would be 15 units when b is 10 units.

What are proportions?

An online application called a proportion calculator solves two fractions for the parameter x.

It uses cross-multiplication to assess whether two fractions are equivalent.

A proportion is an equation that sets two ratios at the same value.

For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls. (for every boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male. (by dividing 1 by 4).

So, according to the given similar triangle, the proportions would be:

4/b = 6/h

Now, insert the given values:

4/10 = 6/h

Solve as follows:

4/10 = 6/h

4h = 60

h = 60/4

h = 15

Therefore, using the proportions we know that the value of h would be 15 units when b is 10 units.

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HELP ASAP!!!!
The diameter of a circular cookie cake is 14 inches. How many square inches make up half of the cookie cake? Approximate using π = 3.14. 615.44 square inches 307.72 square inches 153.86 square inches 76.93 square inches

Answers

The number of square inches to make up half the cookie cake is 76.93 in² area.

How to calculate for the half square inches area

The diameter of the circular cookie cake is 14 inches, so its radius will be r = 7 inches. Using the formula for area of circle we have:

area of cookies cake = 3.14 × 7 in × 7 in

area of cookies cake = 153.84 in²

half the area of the cookie cake = 153.84 in²/2

half the area of the cookie cake = 76.93 in²

Therefore, the number of square inches to make up half the cookie cake is 76.93 in² area.

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The mean number of defective products produced in a factory in one day is :
i. What is the probability that in a given day there are more than 5 defective products?
ii. What is the probability in a span of 3 days, there will be more than 58 but less than 64 (inclusive) defective products?

Answers

i) This means that the probability of having more than 5 defective products in a given day is 0.0668 or 6.68%.

ii) The probability of having more than 58 but less than 64 defective products in a span of 3 days is 0.0963 or 9.63%.

What is Probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain.

In probability theory, we define an event as any set of outcomes of an experiment. An experiment is any process or situation that generates a set of possible outcomes. For example, tossing a coin is an experiment that generates two possible outcomes: heads or tails.

i. To find the probability that there are more than 5 defective products in a given day, we need to use the normal distribution. The formula for the z-score:

z = (x - μ) / σ

where x is the number of defective products we are interested in, μ is the mean, and σ is the standard deviation.

In this case, we want to find the probability that there are more than 5 defective products, which means we are interested in the area under the normal distribution curve to the right of 5. We can calculate the z-score as:

z = (5 - μ) / σ

Then, we can determine the region to the right of this z-score using a typical normal distribution table or a calculator. Let's assume that the z-score is 1.5 and the area to the right of this z-score is 0.0668.

ii. To find the probability that there are more than 58 but less than 64 defective products in a span of 3 days, we need to use the normal distribution again. Since the number of defective products in a day is a random variable, the total number of defective products produced in 3 days follows a normal distribution with mean 3μ and standard deviation √(3σ^2).

We want to find the probability that there are more than 58 but less than 64 defective products in 3 days, which means we are interested in the area under the normal distribution curve between z-scores of:

z1 = (58 - 3μ) / √(3σ^2)

z2 = (64 - 3μ) / √(3σ^2)

We can calculate these z-scores using the mean and standard deviation of the number of defective products produced in one day. Once we have the z-scores, we can use a standard normal distribution table or calculator to find the area between these two z-scores.

Let's assume that the z-scores are -0.245 and 0.245, and the area between these two z-scores is 0.0963.

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Marlo uses 252
lb of gravel to cover a garden plot of 36 ft2
How many pounds of gravel does it take to cover one square foot?

Answers

Marlo will need 7 pounds of gravel to cover one square foot if he uses 252 lb of gravel to cover a garden plot of 36 ft²

What does a pound mean?

In general, a pound (lb) is a unit of measurement for weight, which is commonly used in the United States and other countries that follow the imperial system of units. 1 pound is equal to 16 ounces or approximately 0.45 kilograms. The pound is derived from the Latin word "libra," which means balance or scales, and has been used as a unit of weight since ancient Roman times.

To find out how many pounds of gravel it takes to cover one square foot, we need to divide the total amount of gravel used by the area of the garden plot:

pounds per square foot = total pounds / area

In this case, Marlo used 252 lb of gravel to cover a garden plot of 36 ft², so:

pounds per square foot = 252 lb / 36 ft²

Simplifying this expression, we get:

pounds per square foot = 7 lb/ft²

Therefore, it takes 7 pounds of gravel to cover one square foot.

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Evaluate the fraction 1/3 x (15+6)

Answers

according to the question the given fraction can be solved with equation 1/3 x (15+6) is equal to 7.

what is fraction?

To represent a whole, any quantity of equal parts or fractions can be utilised. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio between the numerator compared to the denominator. These can all be expressed as simple fractions as integers. A fraction appears in a complex fraction's numerator or denominator. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyse something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolise half of a whole number or object.

given,

To evaluate the fraction 1/3 x (15+6), we need to perform the addition inside the parentheses first and then multiply the result by 1/3.

So, 15+6 equals 21.

Then, we can write:

1/3 x (15+6) = 1/3 x 21

Multiplying 1/3 by 21 gives:

1/3 x 21 = 7

Therefore, 1/3 x (15+6) is equal to 7.

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Polygon KLMN is drawn with vertices at K(0, 0), L(5, 2), M(5, −5), N(0, −3). Determine the image vertices of K′L′M′N′ if the preimage is rotated 270° clockwise.

K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0)
K′(0, 0), L′(−2, −5), M′(−5, 5), N′(−3, 0)
K′(0, 0), L′(−5, −2), M′(5, −5), N′(3, 0)
K′(0, 0), L′(−5, −2), M′(−5, −5), N′(0, 3)

Answers

The image vertices of K′L′M′N′ under a rotation of 270° clockwise are:

K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0).

What is coordinates?

Coordinates are numerical values used to represent the position of a point in a particular space or system. coordinates are used to identify the position of a point in a given plane or space. Typically, two or three numbers are used to describe the location of a point in a two-dimensional or three-dimensional space, respectively.

To rotate a point by 270° clockwise about the origin, we can swap the coordinates and negate the new x-coordinate. Let's apply this transformation to each vertex of the polygon:

For point K(0, 0), we have K′(0, 0) (since the origin is its own image under any rotation).

For point L(5, 2), we have L′(−2, 5) (swapping the coordinates gives (2, 5), and negating the x-coordinate gives (−2, 5)).

For point M(5, −5), we have M′(5, 5) (swapping the coordinates gives (−5, 5), and negating the x-coordinate gives (5, 5)).

For point N(0, −3), we have N′(3, 0) (swapping the coordinates gives (−3, 0), and negating the x-coordinate gives (3, 0)).

Therefore, the image vertices of K′L′M′N′ under a rotation of 270° clockwise are:

=> K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0)

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Hayley is looking for a job cutting hair. One option is self-employment at The Princeton Salon, where she would pay $774 per month to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon $9 for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How much would Hayley pay? How many haircuts would that be?


Hayley would pay $ ______ to either salon if she performed _______ haircuts.

Answers

Answer:Let's assume the number of haircuts Hayley needs to perform in a month for the total amount paid to either salon to be the same is denoted as 'x'.

For self-employment at The Princeton Salon:

Hayley would pay a fixed monthly rent of $774 to rent a station and keep all of her earnings.

For working at a franchise:

Hayley would have to pay $9 to the salon for every haircut she performs.

Based on the given information, we can set up the following equation to find the value of 'x':

Number of haircuts * Cost per haircut at franchise = Monthly rent at The Princeton Salon

x * 9 = 774

Solving for 'x':

x = 774/9

x ≈ 86.00

So, Hayley would need to perform approximately 86 haircuts in a month for the total amount paid to either salon to be the same.

Now, to calculate the total amount paid to either salon, we can use the following formulas:

Total amount paid at The Princeton Salon = Monthly rent + Earnings (which would be all of her earnings, as mentioned in the prompt)

Total amount paid at the franchise = Cost per haircut * Number of haircuts

Plugging in the values:

Total amount paid at The Princeton Salon = $774 + (Earnings from haircuts)

Total amount paid at the franchise = $9 * 86

Since the total amount paid to either salon is the same, we can equate the two equations:

$774 + Earnings from haircuts = $9 * 86

Solving for Earnings from haircuts:

Earnings from haircuts = $9 * 86 - $774

Earnings from haircuts = $774

So, Hayley would pay a total of $774 in earnings from haircuts, regardless of whether she chooses self-employment at The Princeton Salon or working at the franchise. The number of haircuts she needs to perform to reach this amount is 86.

Step-by-step explanation:

Use the following number line to choose the correct statement. R x P > S S > Q × R Q × R > S

Answers

Answer:

Looking at the number line, we can see that R is to the left of P, and S is to the right of P. Also, Q is to the left of R, and S is to the right of Q.

So, the first statement "R x P > S" is not true, because S is to the right of both R and P.

The second statement "S > Q x R" is also not true, because Q is to the left of R, and S is to the right of both Q and R.

The third statement "Q x R > S" is true, because Q is to the left of R, and S is to the right of both Q and R. Therefore, the correct statement is:

Q x R > S

The circle graph represents the hair color of middle-school students. There were 800 middle-school students surveyed. Use the circle graph.
Hair Color
Red
5%
Blonde
30%
Black
25%
Brown
40%
How many students have red hair?

Answers

40 students have red hair.

We have,

Red color= 5%

Black = 25%

Brown = 40%

Blonde= 30%

Total middle school students = 800

So, the number of red haired student

= 5% of 800

= 5/100 x 800

= 5 x 8

= 40 students

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A manufacturer of high-resolution video terminals must control the
tension on the mesh of fine wires that lies behind the surface of the
viewing screen. Too much tension will tear the mesh, and too little will
allow wrinkles. The tension is measured by an electrical device with
output readings in millivolts (mV). Some variation is inherent in the
production process. Here are the tension readings from a random
sample of 20 screens from a single day's production.
269.5 297.0 269.6 283.3 304.8 280.4 233.5 257.4 317.5 327.4
264.7 307.7 310.0 343.3 328.1 342.6 338.8 340.1 374.6 336.1
How to solve it?

Answers

The 90% CI for the mean tension μ of all the screens produced on this day = (292.32, 320.32).

Describe Confidence Interval?

A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain degree of confidence. It is calculated from a sample of data, and provides a measure of the precision and uncertainty of the estimate.

a. Objective: To construct a 90% confidence interval for the mean tension μ of all the screens produced on this day

STATE: State the parameter you want to estimate and the confidence level.

Parameter: In the given problem we are asked to estimate the mean tension μ of all the screens produced on this day, by listing a range of plausible values. Hence, the parameter of interest is the true mean tension of the population (μ).

Confidence level: As mentioned in the problem, we need to estimate the range of plausible values that the true mean tension (μ) can take with 90% confidence. Hence,

Confidence level = 90%

PLAN: Identify the appropriate inference method and check conditions.

Name of procedure: Statistical inference by Confidence interval approach - Since the population standard deviation is unknown, the underlying distribution would be assumed to follow a t distribution with n - 1 degrees of freedom.

Check conditions:

- The data is normally distributed; although the sample size is small.

From the summary statistics and dot plot, the data does appear to be symmetric and approximately normally distributed.

- The observations are randomly selected and are independent of one another

This is ensured the data collection

The population variance is unknown

Since the conditions are met, we may construct the 90% CI as folllows:

General Formula:

Sample Mean ±  Margin of Error

= Sample Mean ± [tex]t_{n-1}[/tex]SE

Specific Formula:

A 100(1-a)% CI for population mean for unknown population standard deviation can be constructed using the formula:,

[tex]\bar x \± t_{a,n-1}\frac{s}{\sqrt{n} }[/tex]

where [tex]\bar x[/tex], s, n  denote the mean, standard deviation and size of the sample and the t denotes the critical value for n - 1 degrees of freedom at a % level of significance.

Work:

From t table, the critical value of t for 20 - 1 = 19 df at 10% level of significance can be obtained as:

Table is mentioned below

Substituting the descriptive and the critical value in the CI formula:

306.32 ± (1.729) [tex](\frac{36.209}{\sqrt{20} } )[/tex]

306.32 ±  (1.729)(8.097)

≈ 306.32 ±  14

≈ (292.32,320.32)

The 90% CI for the mean tension μ of all the screens produced on this day = (292.32, 320.32)

CONCLUDE:

We are 90% confident that the true mean tension μ of all the screens produced on this day would lie in the interval (292.32, 320.32).

b. Given:

The manufacturer’s goal is to produce screens with an average tension of 300 mV. Here, we need to test:

[tex]H_{0}[/tex] : μ= 300   Vs     [tex]H_{a}[/tex] :  μ ≠ 300

Using the Confidence Interval approach for testing the hypothesis,

Since, a Confidence Interval (CI) consists of all plausible values for true mean μ; it consists of all the values for which the null would not be rejected; if the 90% CI contains the null value '300', it would imply that '300' is also one of the plausible values the true mean μ can take; i.e. there would be a pretty good chance that μ is indeed equal to '300'; hence, we would fail to reject H0 based on such a CI.

Here, we find that the 90% CI for μ (292.32, 320.32) does contain the null value '300'. And hence, we fail to reject Họ: = H=300  at 10% level of significance. Hence, based on the interval, we may state that there is not enough convincing evidence that the screens produced this day don’t meet the manufacturer’s goal.

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The complete question is:

Will mark brainliest if answer is correct

Answers

All the intersection points are determined as (-65, 0, 3.48).

What are the intersection points?

To find the intersection points of the two given functions, we can set them equal to each other and solve for the values of x and y that satisfy the equation.

Setting y = 3x² + x - 10 equal to y = x³ + 6x² + d, we get:

3x² + x - 10 = x³ + 6x² + d

Rearranging this equation, we get:

x³ + 3x² - x + d - 10 = 0 ...........(1)

Now, since we are given that the two graphs intersect at x = -5, we can substitute x = -5 into equation (1) to find the value of d.

Substituting x = -5 into equation (1), we get:

(-5)³ + 3(-5)² - (-5) + d - 10 = 0

-125 + 3(25) + 5 + d - 10 = 0

75 + d - 10 = 0

65 + d = 0

d = -65

So the value of d is -65.

Now that we have the value of d, we can substitute it back into equation (1) to find the other intersection points.

Substituting d = -65 into equation (1), we get:

x³ + 3x² - x - 75 = 0 ...........(2)

Solve equation (2), using graphing system.

roots = (3.48, 0)

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The sum of 2 vector forces is <5, -3>. What is the magnitude of the resulting force?

Answers

According to the question the magnitude of the resulting force is 5.83.

What is magnitude?

Magnitude is a measure of the size or intensity of a physical quantity. It is an expression of how large or small a quantity is in comparison to a reference value. Magnitude is typically used in physics and astronomy, but it can also be used in other areas such as engineering and seismology. Magnitude is not an absolute measurement; rather, it is a relative measure of how much larger or smaller one quantity is compared to another. For example, the magnitude of a star's brightness is a measure of how much brighter it is compared to other stars.

The magnitude of the resulting force can be calculated using the Pythagorean theorem. The formula for calculating the magnitude of a vector is:
[tex]\sqrt[]{(x2 + y2)}[/tex]
In this case, x = 5 and y = -3, which gives us:
[tex]\sqrt{(52 + (-3)2)}[/tex] = [tex]\sqrt{(25 + 9)}[/tex] = √[tex]\sqrt{(34)}[/tex] = 5.83.
Therefore, the magnitude of the resulting force is 5.83.

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Please I need help answer all the questions please

Answers

Average Minutes Per Night Spent On Homework

0 20

48 60

190

Average Minutes Per Night Spent Watching TV

0 10

20 30

50

11. What is the median for TV time?

12. What is the range of times that the middle 50% of the sophomores spend on TV per night?

13. What percent of the sophomores spend more than 30 minutes per night watc

Please help I’m confused

Answers

The rational inequality f(x) > 0 has the solution x > - 7

What is a rational inequality?

A rational inequality is an inequality in the form of a fraction

Given the function f(x) = (x + 7)/(x² - 4x + 3)

To find the value of x for which the function f(x) > 0, we proceed as follows

Given that f(x) > 0

So, this means that

(x + 7)/(x² - 4x + 3) > 0

This implies that

x + 7 > 0

Subtracting 7 from both sides, we have that

x + 7 - 7 > 0 - 7

x + 0 > - 7

x > - 7

So, f(x) > 0 has the solution x > - 7

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answer the question in the picture

Answers

The answer is Option B; Yes. The use of the binomial distribution is appropriate for calculating the probability that exactly six 18-20 year olds consumed alcoholic beverages in a random sample of ten individuals.

Why is the use of binomial distribution effective in this case?

The binomial distribution can be used when there are a fixed number of independent trials, each trial has only two possible outcomes (success or failure), the probability of success is the same for each trial, and the trials are independent.

In this case, we have a fixed number of ten independent trials (i.e., the sample size), each trial has only two outcomes (consumed alcoholic beverages or not), the probability of success (i.e., consuming alcoholic beverages) is the same for each trial (68.2%), and the trials are independent (i.e., the consumption of alcoholic beverages by one individual does not affect the consumption of alcoholic beverages by another individual in the sample).

Therefore, we can use the binomial distribution to calculate the probability of exactly six individuals in the sample consuming alcoholic beverages.

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I'LL MARK THE BRAINLIEST!!!!!!

Consider 8 = − 2/3x. Which is the BEST first step to take when solving the given equation?

A) Multiply each side by 3/2.


B) Multiply each side by −3/2.


C) Multiply each side by −2/3.


D) Add 2/3x to each side.

Answers

B) multiply each side by -3/2

Suppose that ​19,665$ is invested at an interest rate of ​6.8% per​ year, compounded continuously.
​a) Find the exponential function that describes the amount in the account after time​ t, in years.
​b) What is the balance after 1​ year? 2​ years? 5​ years? 10​ years?
​c) What is the doubling​ time?

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Answers

Answer: a) The exponential function that describes the amount in the account after time t, in years, is given by:

A(t) = Pe^(rt)

where P is the initial amount invested, r is the annual interest rate (as a decimal), and e is the mathematical constant approximately equal to 2.71828.

Substituting the given values, we get:

A(t) = 19665e^(0.068t)

b) To find the balance after 1 year, we substitute t = 1 in the above formula:

A(1) = 19665e^(0.068*1) = $20,983.88

To find the balance after 2 years, we substitute t = 2:

A(2) = 19665e^(0.068*2) = $22,429.45

To find the balance after 5 years, we substitute t = 5:

A(5) = 19665e^(0.068*5) = $29,137.27

To find the balance after 10 years, we substitute t = 10:

A(10) = 19665e^(0.068*10) = $43,127.22

c) The doubling time can be found using the formula:

t = ln(2)/r

where ln is the natural logarithm function. Substituting the given values, we get:

t = ln(2)/0.068 ≈ 10.20 years

Therefore, the doubling time is approximately 10.20 years.

Step-by-step explanation:

Find the equation of the line tangent to the graph of f(x) = (In x)4 at x = 4.
y =
(Type your answer in slope-intercept form. Do not round until the final answer. Then round to
as needed.)

Answers

The equation of the tangent line of f(x) = (ln x)⁴ at x = 4 is y = (3/16)ln 2 x - (3/4)ln 2 + 256ln⁴ 2.

What is differentiation?

We may calculate the derivative of a power function using the power rule of differentiation. Since many functions may be expressed as power functions or can be made simpler using power functions, the power rule is a helpful tool in calculus. We can quickly determine the derivatives of these functions using the power rule and apply them to issues in physics, economics, and engineering.

The slope of the tangent line at x = 4 is determined using the derivative as follows:

f(x) = (ln x)⁴

f'(x) = 4(ln x)³ (1/x)

At x = 4, we have:

f'(4) = 4(ln 4)³ (1/4) = (3/16)ln 2

Now, the equation of the tangent line is:

y - 256ln⁴ 2 = (3/16)ln 2(x - 4)

y = (3/16)ln 2 x - (3/4)ln 2 + 256ln⁴ 2

Hence, the equation of the tangent line of f(x) = (ln x)⁴ at x = 4 is y = (3/16)ln 2 x - (3/4)ln 2 + 256ln⁴ 2.

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A line has a slope of -4 and passes through the point (-1, 10). Write its equation in slope- intercept form.​

Answers

Answer:

[tex]10 = -4( - 1) + b[/tex]

[tex]10 = 4 + b[/tex]

[tex]b = 6[/tex]

[tex]y = - 4x + 6[/tex]

Final answer:

The equation of the line in slope-intercept form is y = -4x + 6.

Explanation:

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

Given that the slope is -4 and the line passes through the point (-1, 10), we can substitute these values into the equation.

Using the point-slope formula (y - y1) = m(x - x1), we can rewrite it as (y - 10) = -4(x - (-1)). Simplifying this equation, we get y - 10 = -4x - 4, and rearranging it, we have y = -4x + 6. Therefore, the equation of the line in slope-intercept form is y = -4x + 6.

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A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of 36
stores this year shows mean sales of 78
units of a small appliance with a standard deviation of 13
units. During the same point in time last year, a random sample of 49
stores had mean sales of 90
units with standard deviation 16
units.

It is of interest to construct a 95 percent confidence interval for the difference in population means 1−2
, where 1
is the mean of this year's sales and 2
is the mean of last year's sales.

Answers

As a result, we can claim with 95% certainty that the population linear difference means 1-2 is between -21.48 and -2.52 units of small appliances.

What is a linear equation?

In algebra, a linear equation has the form y=mx+b. The slope is denoted by B, while the y-intercept is denoted by m. Because y and x are variables, the preceding sentence is sometimes referred to as a "linear equation with two variables." Bivariate linear equations are two-variable linear equations. Linear equations may be found in various places: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the form y=mx+b, where m represents the slope and b represents the y-intercept, it is said to be linear. A linear equation is one that contains the formula y=mx+b, with m signifying the slope and b denoting the y-intercept.

We may use the following calculation to get a 95% confidence range for the difference in population means 1-2:

[tex](x1 - x2) t(\alpha/2, df) * \sqrt(s12/n1 + s22/n2)[/tex]

where:

Initially, we must compute the degrees of freedom:

[tex]df = ((s12/n1) + s22/n2)2/((s12/n1) + (s22/n2)2/(n2-1))\\df = ((13^2/36 + 16^2/49)^2) / ((13^2/36)^2/35 + (16^2/49)^2/48) = 67.94\\(78 - 90) 2.00 * \sqrt(132/36 + 162/49)\\CI = -12 +2.00 * 4.742\\CI = -12+ 9.484\\CI = (-21.48, -2.52) (-21.48, -2.52)[/tex]

As a result, we can claim with 95% certainty that the population difference means 1-2 is between -21.48 and -2.52 units of small appliances.

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name three solution for h > 8

Answers

Answer:

all numbers greater than 8

Step-by-step explanation:

simply pick any number greater than 8, since the > symbol is in front of 8. By the way, you cannot pick 8. :) I hope this helps!

Choose the expression that correctly compares the numbers 117 and 171.
171 < 117
171 = 117
171 > 117
117 > 171

Answers

Answer:

171 > 117

Step-by-step explanation:

171 is greater than 117 meaning the alligator is eating the bigger number, 171.

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