write (10^2)^-3 as a power of 10 with a single exponent

Answers

Answer 1

To write (10^2)^-3 as a power of 10 with a single exponent, we can use the property of exponents that states that when we raise a power to another power, we multiply the exponents. So:

(10^2)^-3 = 10^(2*-3) = 10^(-6)

Therefore, (10^2)^-3 can be written as 10^-6 with a single exponent of -6.

Answer 2

Answer:

10^-6 as a power of 10 with a single exponent.

Step-by-step explanation:

To write (10^2)^-3 as a power of 10 with a single exponent, we can simplify the expression by using the rule that states that when we raise a power to another power, we multiply the exponents.

Therefore:

(10^2)^-3 = 10^(2*-3) = 10^(-6)

Therefore, (10^2)^-3 is equivalent to 10^-6 as a power of 10 with a single exponent.


Related Questions

0.2w – 5 = 13
Solve pleaseeee I'm struggling

Answers

Answer:

90

Step-by-step explanation:

A marketing research firm wishes to study the relationship between wine consumption and whether a person likes to watch professional tennis on television. One hundred randomly selected people are asked whether they drink wine and whether they watch tennis. The following results are obtained:

Answers

Based on the results obtained, the firm can analyze the data and determine if there is a significant correlation between the two variables. This information can be used to develop marketing strategies for wine and tennis-related products and services.

A marketing research firm is conducting a study to understand the relationship between wine consumption and an interest in watching professional tennis on television. They randomly select 100 people and gather data on their wine-drinking habits and whether they watch tennis or not.

To analyze the data, the marketing research firm can create a cross-tabulation, also known as a contingency table, with two rows representing the categories of wine consumption (wine drinkers and non-wine drinkers) and two columns representing the categories of watching tennis (tennis watchers and non-tennis watchers).

From the data collected, the firm can calculate the percentages of people in each category (e.g., percentage of wine drinkers who watch tennis, percentage of non-wine drinkers who watch tennis, etc.) to determine if there is a relationship between wine consumption and an interest in watching professional tennis on television.

The marketing research firm can then use statistical tests, such as the chi-square test, to assess if the observed relationship between wine consumption and tennis watching is statistically significant or if it could have occurred by chance.

In conclusion, the marketing research firm is using a systematic approach to study the relationship between wine consumption and an interest in watching professional tennis on television. This research can provide valuable insights for businesses in the wine and sports industries to better target their marketing efforts.

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April is filling six identical cones for her piñata. Each cone has a radius of 1.5 inches and height of 9 inches.

What is the total volume of the cones?

Answers

Formula for the volume of a cone = 1/3h(pi)r^2

1.5(which is r or the radius) squared is equal to 2.25.

Multiply by the height (9) and you get 20.25.

Multiply by 1/3, and get 6.75.


Finally, multiply 6.75 with pi.


6.75pi is equal to the volume of one cone.

Then, multiply by 6.

40.5in^2

P( factor of 72 and even) please answer in decimal

Answers

The probability of having factor of 72 and even will be 0.75.

How to calculate the probability

The prime factorization of 72 is 2^3 * 3^2. It should be noted that to find the number of factors of 72, one must add 1 to each exponent in the prime factorization and multiply accordingly: (3+1) * (2+1) = 12.

Therefore the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

Evidently, 9 of these 12 factors will be even since they contain at least one factor of 2; thus, 6 of the factors of 72 are even.

The probability will be:

= 9/12

= 0.75

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tres veces la diferencia de 15 y 13​

Answers

tres veces la diferencia de 15 y 13 es 6.

find the area of the triangle

Answers

The area of the triangle in this problem is given as follows:

A = 479.3 m².

How to obtain the area of the triangle?

First we must use the law of sines to obtain the measure of angle A as follows:

sin(A)/31 = sin(105º)/50

Hence:

sin(A) = 31 x sine of 105 degrees/50

sin(A) = 0.5989

A = arcsin(0.5989)

A = 36.8º.

Considering that the sum of the measures of the internal angles of a triangle is of 180º, the measure of angle B is given as follows:

36.8º + <B + 105º = 180º

<B = 180 - (36.8 + 105)

<B = 38.2º.

We have two sides of 50m and 31m, with an angle between them of 38.2º, hence the area of the triangle is given as follows:

A = 0.5 x 50 x 31 x sine of 38.2 degrees

A = 479.3 m².

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A coin is tossed nine times. Find the probability of getting exactly six heads.

Answers

Answer:

When a coin is tossed 9 times the probability of getting exactly six heads is obtained with the help of Bernoulli trials. The probability of getting exactly six heads is 21/128.

A certain test preparation course is designed to help students improve their scores on the GRE exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 7 students' scores on the exam after completing the course:
24,6,21,8,16,10,18
Using these data, construct a 80% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal
Step 1:Calculate the sample mean for the given sample data. Round your answer to one decimal place.
Step 2:Calculate the sample standard deviation for the given sample data. Round your answer to one decimal place.
Step 3:Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Step 4:Construct the 80% confidence interval. Round your answer to one decimal place (Lower endpoint, Upper endpoint)

Answers

Step 1: The sample mean is (24+6+21+8+16+10+18)/7 = 15.7 (rounded to one decimal place)

Step 2: The sample standard deviation is calculated using the formula:

s = sqrt[(Σ(x - mean of x)^2) / (n - 1)]

where Σ is the sum of the squared deviations from the mean, mean of x is the sample mean, and n is the sample size.

Using the given data, we get:

s = sqrt[((24-15.7)^2 + (6-15.7)^2 + (21-15.7)^2 + (8-15.7)^2 + (16-15.7)^2 + (10-15.7)^2 + (18-15.7)^2) / (7-1)]

s = 6.679 (rounded to one decimal place)

Step 3: To find the critical value, we use a t-distribution with n-1 degrees of freedom and a confidence level of 80%. From a t-distribution table or using a calculator, we find the critical value to be 1.397 (rounded to three decimal places).

Step 4: Using the formula for the confidence interval:

CI = mean of x ± t*(s / sqrt(n))

where mean of x is the sample mean, t is the critical value, s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

CI = 15.7 ± 1.397*(6.679 / sqrt(7))

CI = (9.47, 21.93)

So the 80% confidence interval for the average net change in a student's score after completing the course is (9.47, 21.93).

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Jean invested $380 in stocks. Over the next 5 years the value of her investment grew as shown in the accompanying table. Find the equation that best models the data

Answers

An equation that best models the data is [tex]y = 380(1.04)^x[/tex]

How to write and determine an exponential function?

In Mathematics and Geometry, an exponential function is typically represented by the following mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

x represent time.a represent the base value, vertical intercept, or y-intercept.b is the growth rate, common ratio, and rate of change.

Based on the table, we would calculate the value of a and b as follows;

[tex]f(x) = a(b)^x[/tex]

380 = a(b)⁰

a = 380

Next, we would determine value of b as follows;

395 = 380(b)¹

395 = 380b

b = 395/380

b = 1.04

Therefore, the required exponential function is given by;

[tex]f(x) = y = 380(1.04)^x[/tex]

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

the diameter of a cylinder is 7yrds. the height is 12 yards. what is the volume, in terms of 3.14 and the nearest cubic yard, of the cylinder

Answers

Step-by-step explanation:

Area of the circular end  x height = volume

pi r^2  * h    = volume        r = 1/2 * 7 = 3.5 yds

pi * (3.5^2) * 12 =~ 462 yd^3

2 tubs of ice cream cost £5.90 how much would 5 of these tubs cost?

Answers

Answer:

£14.75.

Step-by-step explanation:

1. Find how much 1 tub of ice cream cost. We can find this by dividing the cost of the 2 tubs in half:

5.90 / 2 = 2.95 = 1 tub ice cream

2. Multiply the cost of 1 tub of ice cream (2.95) by 5 to know the price of the 5 tubs:

2.95 x 5 = 14.75

Hence, 5 tubs of ice cream cost £14.75.

The following table provides a probability distribution for the random variable y.y f(y) 2 0.10 4 0.40 7 0.20 8 0.30(a) Compute E(Y).(b) Compute Var(y) and o.

Answers

The expected value E(Y) = 5.6, Var(Y) = 326.64 and σ ≈ 18.07.

(a) To compute the expected value E(Y), we need to multiply each value of y with its corresponding probability and sum them up. Here's the calculation:
E(Y) = (2 * 0.10) + (4 * 0.40) + (7 * 0.20) + (8 * 0.30) = 0.2 + 1.6 + 1.4 + 2.4 = 5.6
(b) To compute the variance Var(Y) and standard deviation σ, we first need to find E(Y^2) and then use the formula Var(Y) = E(Y^2) - (E(Y))^2.
E(Y^2) = (2^2 * 0.10) + (4^2 * 0.40) + (7^2 * 0.20) + (8^2 * 0.30) = 4 + 64 + 98 + 192 = 358
Now, we can compute Var(Y):
Var(Y) = E(Y^2) - (E(Y))^2 = 358 - (5.6)^2 = 358 - 31.36 = 326.64
Finally, we can compute the standard deviation σ:
σ = sqrt(Var(Y)) = sqrt(326.64) ≈ 18.07

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a polynomial of degree four with leading coefficient 1 and integer coefficients has two real zeros, both of which are integers. which of the following can also be a zero of the polynomial? A. 1+i√11/2B. 1+i/2C. 1/2+iD. 1+i/2E. 1+i√13/2

Answers

If we let a = 0, b = 1, and c = 1, then the polynomial

[tex]x(x-1)(x^2 +[/tex]

Since the polynomial has integer coefficients, if one of the roots is a complex number, then its conjugate must also be a root. Therefore, options A and E cannot be roots of the polynomial, since they have non-real conjugates.

We know that the polynomial has degree 4, so it has four roots in total (counting multiplicities). We also know that two of the roots are integers, so let's call them a and b. Then the polynomial can be written as:

[tex](x - a)(x - b)(cx^2 + dx + e)[/tex]

where c, d, and e are integers (because they are the coefficients of the quadratic factor). We know that the leading coefficient is 1, so c must be nonzero.

Since the polynomial has two real roots, its discriminant must be nonnegative:

[tex]d^2 - 4ce > = 0[/tex]

We can use this inequality to rule out some of the answer choices. For example, option C cannot be a root, because if we substitute x = 1/2 + i into the polynomial, we get:

([tex](1/2 + i) - a)((1/2 + i) - b)(c((1/2 + i)^2) + d(1/2 + i) + e)[/tex]

The real part of this expression is:

(1/4 - a + 1/4 - b)(c(1/4 - 1) + d/2 + e) = -(a + b - 1/2)(3c/4 + d/2 + e)

If we assume that a and b are integers, then this expression is an integer multiple of 3c/4 + d/2 + e. However, we can choose values of c, d, and e such that 3c/4 + d/2 + e is not an integer (for example, if c = 4, d = 1, and e = 0, then 3c/4 + d/2 + e = 4.5). Therefore, the real part of the expression cannot be zero, and option C cannot be a root.

We can also rule out option D using the same argument. If we substitute x = 1 + i/2, then the real part of the expression is:

((1 + i/2) - a)((1 + i/2) - b)(c((1 + i/2)^2) + d(1 + i/2) + e)

(1 - a + i/2)(1 - b + i/2)(c(5/4 + i) + d(3/2 + i/2) + e)

The real part of this expression is an integer multiple of c(5/4) + d(3/2) + e, which can be non-integer for some choices of c, d, and e.

Therefore, the only possible answer choices are A and B. To determine whether they are roots of the polynomial, we can use the fact that the sum and product of the roots are given by:

a + b + (complex roots) = -d/c

ab(complex roots) = e/c

We know that a and b are integers, so if we can find a polynomial with integer coefficients that has roots a, b, and either A or B, then that root is also a root of the original polynomial.

For option A, we have:

1 + i√11/2 = 2(cos(75°) + i sin(75°))

Therefore, if we let a = 0, b = 1, and c = 1, then the polynomial

[tex]x(x-1)(x^2 +[/tex]

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Out of all the readers who visit a blog, 11% click on an advertisement. Predict how many readers will click on an advertisement if 500 people visit the blog in one day.

Answers

Answer ( I think ):

55

Explanation:

If 500 people visit the blog in one day, and 11% of people click on the advertisement, then you find 11% of 500 by dividing 500 by .11 to get 55.


Hope this helps! :)

PLEASE HELP ME
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.


Sport Baseball Basketball Tennis Soccer
Number of Students 17 12 27 44


Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44

Answers

Answer:

D: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44

Step-by-step explanation:

Because the categories are unrelated to each other it would be unlikely that you would use a histogram in this situation. Histograms are often only used for change or continuous data about a particular group or sample.

D is correct becuase it makes use of a bar graph and the number of players per section are correctly allocated unlike answer choice C which switches some sports and the number of players they should have.

Answer: histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44

Step-by-step explanation:

URGENT PLEASE HELP I’M TRYING TO GET MY GRADE TO A C OR B!!!
Solve for c.

(c+9)^2=64


Responses

c=−17, c=−1
c equals negative 17, , , c equals negative 1

​c=−73−−√, c=73−−√​
​, c equals negative square root of 73 , c equals square root of 73 ​

c=−55−−√, c=55−−√
c equals negative square root of 55, , , c equals square root of 55

c = 1, c = 17

Answers

Answer:

√(c+9)² =√64

c+9 =8

c=8-9

c=-1

How many repeating digits are in the smallest group of repeating digits in the decimal equivalent
of 2/9?
A. 1
C. 3
B. 2
D. 4

Answers

The number of repeating digits in the group is 1

How many repeating digits are in the group

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

Number = 2/9

When evaluated, we have

Number = 0.222.....

The above nummber has repeating digits

When approximated, we have

Number = 0.2

In the above number, the number of repeating digits is 1

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The Beta [a, b] density has the form: f(x) = {[(a+b)/([(a) r()) } Xa-1 (1 - X)B-1 + - where a and ß are constants and 0 SX S1. You can check Blitzstein's book to get more details for this distribution (p. 380, or table C on p. 605).

Answers

The Beta distribution is a continuous probability distribution with support on the interval [0,1], and is often used to model random variables that have limited range, such as probabilities or proportions.

The Beta [a, b] density has the form f(x) = {[(a+b)/([(a) r()) } Xa-1 (1 - X)B-1 +, where a and b are constants and 0 <= x <= 1. This density function describes the probability of observing a value x from a Beta [a, b] distribution.

The parameters a and b are often referred to as shape parameters, and they control the shape of the distribution. Specifically, the larger the values of a and b, the more peaked the distribution will be, while smaller values of a and b will lead to flatter distributions.

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Pls i need this !!!!

Answers

Answer:

$80

Step-by-step explanation:

please mark brainliest answer

Problem 6: (12 pts] Give an example of the requested vector or vector-valued function for each statement below, or state that no such vector exists. In order to receive full credit, you must show that your vector meets the requested criteria or explain why no such vector exists. Answers with no justification will receive a score of 0. 1. [4 pts) Suppose that ū = (1, 2). Find a vector ū so u + = vor explain why no such vector exists. II. [4 pts) Suppose that u = (2,1,3). Find a nonzero vector v so u xv = u + v or explain why no such vector exists. = 4 or explain why no such III. [4 pts) A vector-valued function r(t) = (x(t), y(t)) for which vector-valued function exists.

Answers

There is no such vector-valued function r(t) that satisfies the given condition.

I. There is no such vector ū that satisfies u + ū = (1, 2) because if we add any vector to u, we change its direction and magnitude, but the vector ū should have the same magnitude and opposite direction to u.

II. Let v = (1, 3, -1). Then u + v = (2+1, 1+3, 3-1) = (3, 4, 2) and u x v = (-5, 7, -1). So u x v = u + v. Therefore, v satisfies the given condition.

III. There is no such vector-valued function r(t) because if r(t) = (x(t), y(t)) satisfies the condition that r'(t) = 2r(t), then we have:

x'(t) = 2x(t) and y'(t) = 2y(t)

These are two separate first-order differential equations, which have general solutions of the form:

x(t) = c1e^(2t) and y(t) = c2e^(2t)

where c1 and c2 are constants determined by the initial conditions. However, the vector-valued function r(t) = (x(t), y(t)) cannot have a constant magnitude because its components are functions of t that grow exponentially with time. Therefore, there is no such vector-valued function r(t) that satisfies the given condition.

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Find a₁ for the geometric series described.
Sn = -26,240, n = 8, r = -3

Answers

The first term of the geometric series is 16.

How to find the  a₁ for the geometric series

Using the formula for the sum of a geometric series to solve for the first term (a₁):

Sn = a₁(1 - rⁿ)/(1 - r)

Substituting the given values, we get:

-26,240 = a₁(1 - (-3)⁸)/(1 - (-3))

Simplifying the exponent and denominator, we get:

-26,240 = a₁(1 - 6,561)/(4)

-26,240 = a₁(-6,560/4)

-26,240 = a₁(-1,640)

Dividing both sides by -1,640, we get:

a₁ = 16

Therefore, the first term of the geometric series is 16.

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21 kg of bannanas cost 147. How much would 9 kg cost

Answers

Answer:

$63

Step-by-step explanation:

First find the cost of bananas per kilogram. To find that, divide $147 by 21

147/21=7

One kilogram of bananas costs $7

Now that you know the cost per kilogram, multiply $7 by the number of kilograms asked in the question, which in this case is 9

7*9=$63

9 kilograms of bananas costs $63

Answer: 63

Step-by-step explanation:

You can set up a proportion cost/weight=cost/weight

[tex]\frac{147}{21} = \frac{x}{9}[/tex]        Costs go on the top so x is cost for 9 kg

[tex]x=\frac{147*9}{21}[/tex]

x=63

How do we classify the critical point if both eigenvalues are real and equal???

Answers

They may require more advanced techniques from dynamical systems theory to fully understand the behavior of the system.

What is the eigenvalues of a critical point of a linear system?

If both eigenvalues of a critical point of a linear system of differential equations in two dimensions are real and equal, the critical point is a degenerate node.

The behavior of the solutions near a degenerate node depends on the higher-order terms in the Taylor series expansion of the vector field around the critical point. Specifically, the critical point is asymptotically stable if the higher-order terms in the Taylor series expansion satisfy certain conditions, and unstable otherwise.

If the higher-order terms in the Taylor series expansion satisfy the so-called "center manifold" conditions, then the critical point is a center, and the solutions near the critical point exhibit periodic behavior.

In general, the classification of a critical point with real and equal eigenvalues can be more complicated than the case where the eigenvalues have different signs, and may require more advanced techniques from dynamical systems theory to fully understand the behavior of the system.

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Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) provides a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.
Formulate null and alternative hypotheses to test the analyst's claim.

Answers

Null hypothesis: The percentage of stocks traded on the NYSE that went up on January 31, 2006, is not 30%.

Alternative hypothesis: The percentage of stocks traded on the NYSE that went up on January 31, 2006, is 30%.
To test the financial analyst's claim that 30% of the stocks traded on the NYSE went up on the same day, we can formulate the null and alternative hypotheses using the information about the DJIA stock market performance. Here are the hypotheses:
Null Hypothesis (H0): The proportion of stocks that increased in price on the NYSE is 30% (p = 0.30).
Alternative Hypothesis (H1): The proportion of stocks that increased in price on the NYSE is not 30% (p ≠ 0.30).
These hypotheses will help determine whether the analyst's claim about the overall stock market performance is accurate or not.

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Mr.Simon has 20 containers of soup.3 containers of soup feeds 4 people.At this rate,how many people can he serve with 20 containers

Answers

Mr. Simon can serve 26 people with 20 containers of soup.

How many people can Mr.Simon serve with 20 containers?

Given that: Mr.Simon has 20 containers of soup. 3 containers of soup feeds 4 people.

Frst, we need to know how many people can be fed by one container of soup.

We are given that 3 containers of soup can feed 4 people.

Hence, we can calculate how many people one container of soup can feed by dividing 4 people by 3 containers

One person ⇒  4/3

Next, we multiply the number of people per container by the total number of containers, which is 20 in this case.

This gives us:

= 20 × (4/3)

= 80/3

= 26.667

≈ 26

Mr. Simon can feed 80/3 people with 20 containers of soup. However, since we cannot serve a fractional part of a person, we should round the answer to a whole number. In this case, rounding down gives us 26.

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Find a 99% confidence interval for the average number of hours a student spends studying for a statistics exam if o is known to be 6.25 hours and a sample of 50 students has x=4 (3.176.4.824)(1.941, 6.059)(3.307, 4.693) (3.090,4.910(3.650.4.350) (1.724,6 276)

Answers

The 99% confidence interval for the average number of hours a student spends studying for a statistics exam is (2.059, 5.941) hours.

To find a 99% confidence interval for the average number of hours a student spends studying for a statistics exam, we can use the formula:

CI = x ± z*(o/sqrt(n))

where CI is the confidence interval, x is the sample mean, z is the z-score for the desired confidence level (in this case, 99%), o is the population standard deviation, and n is the sample size.

Plugging in the given values, we get: CI = 4 ± 2.576*(6.25/sqrt(50)) CI = 4 ± 1.941 CI = (2.059, 5.941)

Therefore, the 99% confidence interval for the average number of hours a student spends studying for a statistics exam is (2.059, 5.941) hours.

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Xion baked 9 brownies for his friends. He wants to share them equally among his 4 friends so that everyone gets the same amount. If he wants to use all the brownies, how many brownies will each child get?

Answers

Answer:

(Excluding Xion) Each person will get 2 1/4 brownies

Step-by-step explanation:

9 brownies distributed equally to 4 friends.  If each person gets two brownies, there is one left over.  Divide 1 by 4 and you get 1/4.  1/4 in decimal form is 0.25.  2+0.25=2.25

Or you could just use a calculator to divide 9 by 4 and it would come up with 2.25

Please help me solve this problem! I need help. where to start?

Answers

Answer:

150

Step-by-step explanation:

An equilateral triangle has 3 congruent angles.

Each angle of an equilateral triangle measures 60°.

A square has 4 right angles.

Each angle of a square measures 90°.

The measures of the 2 angles of equilateral triangle and one right angle of the square have a total measure of

60° + 60° + 90° = 210°

A full circle has a degree measure of 360°.

x° = 360° - 210°

x = 150

what will the the measures of the interior be?

Answers

The sum of the measures all the interior angles of a polygon having 14 sides is 2160°.

How to calculate the sum

The formula we use for this is

Sum of interior angles of a polygon

= ( n-2)*180

Where “n” is the number of sides of the polygon.

Here n=14

So, sum = (14–2)*180 = 2160 degrees

Therefore, the sum of the measures all the interior angles of a polygon having 14 sides is 2160°.

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What will be the sum of the measures all the interior angles of a polygon having 14 sides?

one hundred sixty people who suffer from painful diabetic neuropathy have volunteered to participate in a study. eighty are selected at random and are given the drug gabapentin, while the remaining participants are given a placebo. a neurologist evaluates the symptoms of all volunteers after two months to determine if there has been substantial improvement in the severity of the symptoms. does the use of volunteers make this study invalid?

Answers

Overall, while the use of volunteers does not automatically make the study invalid, it is important to carefully consider probability of bias and take steps to minimize them in the study design and analysis.

The use of volunteers in this study does not necessarily make it invalid, but it could introduce potential sources of bias. Volunteers may not be representative of the larger population of individuals with painful diabetic neuropathy, as they may be more willing to participate in the study or may have different levels of disease severity or other factors that could affect their response to treatment.

Additionally, the random assignment of participants to the gabapentin or placebo group helps to minimize bias, but there is still a possibility of confounding variables that could influence the results. For example, if individuals who were assigned to the gabapentin group were more likely to adhere to the treatment regimen or had more social support, this could influence the outcome of the study independent of the drug's effectiveness.

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