 1 and  2 are supplementary angles. The m  2 = 142°, what is the m  1?

Answers

Answer 1

Answer:

They are supplementary > They sum up to 180

Angle 1 + Angle 2 = 180

Angle 1 + 142 = 180

Angle 1 = 38

Step-by-step explanation:


Related Questions

one corner is grounded (v = 0). the current is 5 a counterclockwise. what is the ""absolute voltage"" (v) at point c (upper left-hand corner)?

Answers

Answer: This tells us that the voltage at point C is 5 volts higher than the voltage at point A. However, we still don't know the absolute voltage at either point A or point C.

Step-by-step explanation:

To determine the absolute voltage at point C, we need to know the voltage values at either point A or point B. With only the information given about the current and the grounding of one corner, we cannot determine the absolute voltage at point C.

However, we can determine the voltage difference between two points in the circuit using Kirchhoff's voltage law (KVL), which states that the sum of the voltage drops around any closed loop in a circuit must be equal to zero.

Assuming the circuit is a simple loop, we can apply KVL to find the voltage drop across the resistor between points A and C. Let's call this voltage drop V_AC:

V_AC - 5 = 0 (since the current is counterclockwise and the resistor has a resistance of 1 ohm)

V_AC = 5

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At Store A, a game system sells for $150.The same system sells for $175 at Store B.Use a ratio to compare the price at Store A to the price at Store B.

Answers

Answer:

6:7

Step-by-step explanation:

=store A:store B

=150:175

=6:7

need this answered quick, please provide explanation for answer thanks :p

need this answered quick, please provide explanation for answer thanks :p

Answers

about 45 weeks. subtract 20.2 from 121.5 and then divide by 2.25

Jared also gathered data from a competing real estate broker's office. The competitor's sales were equal to the average
number of sales 8 months before Jared began gathering data and again 2 and 6 months after he began gathering data.
The relative minimum number of sales was lower than the relative minimum number of sales of Jared's office.
Use the sliders for a, b, c, and d to create a graph that could model the competitor's number of sales.

Jared also gathered data from a competing real estate broker's office. The competitor's sales were equal

Answers

Real estate is any immovable property of this kind that has a stake in a piece of land, a building, or housing in general. It also includes the natural resources on the land, such as water, crops, minerals, and minerals.

How does this occur?

from a company real estate broker's office. The competitor's sales were equal to the average number of sales 8 months before jured began gathering data and again 2 and 6 months after he began gathering data. The relative minimum number of sales was lower than the relative minimum number of sales of Jared's office.

Use the sliders for a, b, c, and d to create a graph that could model the competitor's number of sales.

Graph is given below in Image.

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Jared also gathered data from a competing real estate broker's office. The competitor's sales were equal

calculate the angular area of the hst’s field of view in square degrees.

Answers

The angular area of the HST's field of view is 25 square degrees.

The field of view is the extent of the sky that the Hubble Space Telescope (HST) can observe at a given time. It is usually measured in degrees.

To calculate the angular area, we can use the formula for the area of a circle:

Area = π * (angular size/2)^2

Where π is a mathematical constant approximately equal to 3.14, and the angular size is in degrees.

Let's say the angular size of the HST's field of view is 10 degrees.

First, we divide the angular size by 2:

10 degrees / 2 = 5 degrees

Next, we square the result:

5 degrees * 5 degrees = 25 square degrees

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Write an equation of the line that passes through (-1, – 4) and is perpendicular to the line y = (3/4)x -2

Answers

Step-by-step explanation:

The equation of the line is given above

Write an equation of the line that passes through (-1, 4) and is perpendicular to the line y = (3/4)x

As gamers progress through a video game, they earn a higher rank. In an online gaming network, gamers can see what fraction of the way they
are to the next rank. The line plot displays the fraction of the way to the next rank for all the gamers in the network. What fraction of gamers
have bof the way to go to the next rank?
Gamers Progress to Next Rank
Number
of
Gamers
Fraction of Progress to Next Level
A
A.
c.)

Answers

Question isn't well formatted, a picture if the question is attached below.

Answer:

1 / 4

Step-by-step explanation:

From the plot, each dot represent a gamer ; therefore, the total number of gamers will be counting all the dots ;

Total number of gamers = 24

Fraction of gamers that have 7 / 8 of the way to go ;

This means that they have 7/8 of the way left to proceed to next level ;

The fraction is : 1 - 7/8 = 1 /8

This means the number of of people whose progress are on 1/8 ; this is 6

Hence, fraction of gamers that have 7/8 of the way to go :

6 / 24 = 1 / 4

As gamers progress through a video game, they earn a higher rank. In an online gaming network, gamers

Rohan was planning a party and needed to provide 35 lunches. the cost for each plate 5$ and each plate was 6$. how many of each could he buy and spend $198 total?

Answers

for 5 bucks a plate its 39 for 6 bucks its 33

Step-by-step explanation:

pls help :))))))))) uhhhhhhhhh​

pls help :))))))))) uhhhhhhhhh

Answers

The answers are 3 and -13

You need to plug 3 and -5 into x

By doing this, you get :

12 - 3^2       and

12 - (-5)^2

those expressions equal

12 - 9

12 - 25

So you get

3

-13

Seventh gra
Solve for d.
2d + 1 = 7
d
Submit

Answers

Answer:

d = 3

Step-by-step explanation:

2d + 1 = 7

7 -1

2d = 6

2 divided by 2(cancels out), 6 divided by 2 is 3.

d = 3

The answer is: 3

d=3


The VERY short explanation is that 2(3)= 6

So 6 + 1 = 7

Hope this helps!

I don’t understand how to do the problem at all

I dont understand how to do the problem at all

Answers

Answer:

Hahahahahahahahahahaha Sorry

3. Evan works at McDonalds and works 15-20 hours each week. What is the domain and
range if he gets paid 8 dollars per hour?

Answers

Answer:

RANGE: 120 - 160

Step-by-step explanation:

15*8 = 120

20*8 = 160

RANGE: 120 - 160

Question 3 of 12Which algebraic expression represents this mathematical statement?The product7 and a numberO A. n-7O B. 7.nO C. 7 + nO D, n+7SUBMIT

Answers

DEFINITIONS

Algebraic word problems are questions that require translating sentences to equations. The equations we need to write will only involve basic arithmetic operations and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.

SOLUTION STEPS

Step 1: Name the variable.

The variable, in this case, is n.

Step 2: Identify the mathematical operation in this mathematical statement.

Product refers to multiplication. Therefore, we will be using the multiplication operation for the question.

Step 3: Write out the algebraic expression for the statement: "The product of 7 and a number".

Since we are representing the number with n, the product of n and 7 will be given to be:

\(\Rightarrow7\cdot n\)

ANSWER:

The correct option is OPTION B.

[3 + 3 + 3 pts] Let (Xn)n≥1 be a sequence of independent Bernoulli random variables with success probability p. Denote by S₁ the number of failures until the first success, by S₂ the number of failures between the first and second sucess, and, in general, by Sk the number of failures between the (k-1)th and the kth success. (a) Compute the joint probability mass function of S₁,..., Sn. (b) Are the random variables S₁,..., Sn independent? Prove or disprove. (c) Compute the cdf of U = max {S₁,..., Sn}.

Answers

(a)  The joint PMF of S₁, S₂, ..., Sn is: P(S₁ = s₁, S₂ = s₂, ..., Sₙ = sₙ) =\((1 - p)^{(s_1 + s_2 + ... + s_n) } \times p^n\)

(b)  The random variables S₁,..., Sn are  independent.

(c)  the cumulative distribution function (CDF) of U is:

\(F(u) = (1 - \sum (1 - p)^{(k)} \timesp)^n\)

To compute the joint probability mass function (PMF) of S₁, S₂, ..., Sn, we need to consider the number of failures before each success.

(a) Joint probability mass function (PMF) of S₁, S₂, ..., Sn:

Let's first define the random variable S as the sequence of failures until the first success:

S = (S₁, S₂, ..., Sn)

Now, let's calculate the PMF of S:

P(S = (s₁, s₂, ..., sₙ))

Since the random variables X₁, X₂, ..., Xₙ are independent Bernoulli random variables with success probability p.

The probability of getting s failures before the first success is given by:

\(P(S_1 = s_1) = (1 - p)^{s_1} \times p\)

The probability of getting s₂ additional failures before the second success is:

\(P(S_2 = s_2) = (1 - p)^{s_2} \times p\)

\(P(S_3 = s_3) = (1 - p)^{s_3} \times p\)

And so on, until the probability of getting sₙ additional failures before the nth success:

\(P(S= s) = (1 - p)^{s} \times p\)

Now, since the random variables S₁, S₂, ..., Sn are independent, the joint PMF is the product of the individual probabilities:

P(S = (s₁, s₂, ..., sₙ)) = P(S₁ = s₁) × P(S₂ = s₂)×... × P(Sₙ = sₙ)

Therefore, the joint PMF of S₁, S₂, ..., Sn is:

P(S₁ = s₁, S₂ = s₂, ..., Sₙ = sₙ) =\((1 - p)^{(s_1 + s_2 + ... + s_n) } \times p^n\)

(b)

To determine whether the random variables S₁, S₂, ..., Sn are independent, we need to check if the joint PMF factorizes into the product of the individual PMFs.

Let's consider three random variables, S₁, S₂, and S₃:

P(S₁ = s₁, S₂ = s₂, S₃ = s₃) = P(S₁ = s₁) ×P(S₂ = s₂) × P(S₃ = s₃)

Using the joint PMF calculated in part (a), we can rewrite this as:

\((1 - p)^{(s_1 + s_2 + s_3)} p^3 = (1 - p)^{(s_1)} \times p \times (1 - p)^{(s_2)} \times p \times (1 - p)^{(s_3)}\times p\)

Simplifying, we have:

\((1 - p)^{(s_1 + s_2 + s_3)} p^3 = (1 - p)^{(s_1 + s_2 + s_3)} p^3\)

Since the equation holds true for any values of s₁, s₂, and s₃, we can conclude that the random variables S₁, S₂, and S₃ are indeed independent.

(c)

To compute the CDF of U, we need to determine the probability that U is less than or equal to a given value u.

CDF of U:

F(u) = P(U ≤ u) = 1 - P(U > u)

Since U represents the maximum value among S₁, S₂, ..., Sn, we have:

P(U > u) = P(S₁ > u, S₂ > u, ..., Sn > u)

Using the independence of S₁, S₂, ..., Sn, we can express this probability as:

P(U > u) = P(S₁ > u)×P(S₂ > u) × ...× P(Sn > u)

The probability that a single random variable Si is greater than u (where Si represents the number of failures between the (i-1)th and the ith success) is:

P(Si > u) = 1 - P(Si ≤ u) = 1 - ∑(k=0 to u) P(Si = k)

Using the PMF derived in part (a), we can calculate this probability:

\(P(Si > u) = 1 - \sum (1 - p)^(^k^) \times p\) (k=0 to u)

Finally, substituting this back into the expression for P(U > u), we have:

\(P(U > u) = (1 - \sum (1 - p)^{(k)} \timesp)^n\) (k=0 to u)

Therefore, the cumulative distribution function (CDF) of U is:

\(F(u) = (1 - \sum (1 - p)^{(k)} \timesp)^n\)

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a circle garden has an area 25 pi if the radius is increase by 2 metters and fencing a soldonly in one merner selection, how much fencing is needed to keep our rabbits

Answers

The fencing needed to keep our rabbits is approximately 44 meters

Given that a circle garden has an area of 25π and the radius is increased by 2 meters and fencing is sold only in one meter section. We need to find how much fencing is needed to keep our rabbits.

Step 1: Area of a circle is given by:

A = πr²

where

r is the radius of the circle garden.

So, the area of circle garden with radius r is given by:

25π = πr²

Dividing both sides by π,

we get:

r² = 25r = ± 5

The radius cannot be negative.

So, r = 5 m

Step 2: When the radius is increased by 2 m, the new radius is:

r + 2 = 5 + 2

= 7 m

Step 3: The length of fencing required will be equal to the circumference of the new circle with radius 7 m.

Circumference of the new circle with radius 7 m is given by:

C = 2πr

= 2π(7)

≈ 43.98 m

Therefore, the fencing needed to keep our rabbits is approximately 44 meters.

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PLEASE TELL ME WHAT ONES TO PUT INSIDE THE BOXES
Eric is adding water to a 60
-gallons pool.
The pool already has 12
gallons of water, and he wants to fill it to at least 27
gallons. The water flows at a rate of 6
gallons per minute.
How many minutes, x
, will it take for Eric to fill the pool with at least 27
gallons of water?

Inequality that represents this situation:
27≤12+6x


To solve the inequality, you can begin by solving the equation as shown.

Drag a diagram to each row of the table to show which number line represents all of the solutions for the inequality and which number line represents all of the solutions for the problem situation.

PLEASE TELL ME WHAT ONES TO PUT INSIDE THE BOXESEric is adding water to a 60-gallons pool.The pool already

Answers

All possible solutions for the inequalities are from 2.5 to infinity.

Option F is the correct answer.

All possible solutions for the problem situation are 2.5 to 8.

Option D is the correct answer.

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

27 ≤ 12 + 6x

Solve for x.

27 - 12 ≤ 6x

15 ≤ 6x

x ≥ 15/6

x ≥ 5/2

x ≥ 2.5

This means,

x values can be 2.5 and more.

Now,
For x = 8,

12 + 6 x 8

= 12 + 48

= 60 gallons (possible)

For x = 9,

12 + 6 x 9

= 12 + 54

= 66 gallons (not possible)

Since the maximum gallon the pool can contain is 60 gallons.

Thus,

All possible solutions for the inequalities are from 2.5 to infinity.

All possible solutions for the problem situation are 2.5 to 8.

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PLEASE TELL ME WHAT ONES TO PUT INSIDE THE BOXESEric is adding water to a 60-gallons pool.The pool already
PLEASE TELL ME WHAT ONES TO PUT INSIDE THE BOXESEric is adding water to a 60-gallons pool.The pool already

? Question
Each set of ordered pairs represents two points on a line. Match each set of ordered pairs with the description of the line
they are on.
Tiles
(-5,-3) and (-5,3) (-7,-1) and (-1,-7)
(-6,-2) and (6,-2)

Answers

The correct matching of the ordered pairs and the line they are on are:

(-5,-3) and (-5,3) - No slope. (-7,-1) and (-1,-7) - Slope = -1(-6,-2) and (6,-2) - No slope

What lines do the ordered pairs belong to?

The slope of the first pair is:

= (3 - (-3)) / (-5 - (-5))

= No slope as slope is 0

The slope of the second pair is:

= (-7 - (-1)) / (-1 - (-7))

= -1

The slope for the third pair is:

= (-2 - (-2)) / (6 - (-6))

= 0 or No slope

Rest of the question is:

slope = -1

No slope

No slope

slope = 2

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Answer: vertical line- (-5,-3) and (-5,3)

neither- (-7,1) and (-1,-7)

horizontal line- (-6,-2) and (6,-2)

hopefully this helps

Step-by-step explanation:

Rectangular prisms have 8 corners and 6 faces. What is the ratio of corners to faces in rectangular prisms?

Answers

4:3

xkjjsdajadsLHSFsdLuhf

Simple probabilityLeslie is a biologist. She is going to randomly select one animal from her lab to study. There are 5 salamanders, 3 crayfish, and 12 minnows in her lab.If necessary, round your answer to 2 decimal places.

Simple probabilityLeslie is a biologist. She is going to randomly select one animal from her lab to study.

Answers

Answer: \(P(salamanders)\text{ = 0.25 }\)

Explanation:

Given:

number of salamanders = 5

number of crayfish = 3

number of minnows = 12

To find:

the probability of salamanders

To determine the P(salamanders), we will divide the number of salamanders by total animals

Total animals = 5 + 3 + 12

Total animals = 20

\(\begin{gathered} P(salamanders)\text{ = }\frac{5}{20} \\ \\ P(salamanders)\text{ = }\frac{1}{4} \end{gathered}\)

In decimal place:

\(P(salamanders)\text{ = 0.25 \lparen2 dp\rparen}\)

Point N is on line segment MO. Given MO = 3x - 10, NO = x, and M N = 8,
determine the numerical length of MO.

Answers

Answer:

MO = 17

Step-by-step explanation:

First, you need to define what if the unknown x.

segment MN and NO are equal to MO.

thus, your equation for the combination is x +8

Now set the values equal to each other

x + 8 = 3x - 10 (subtract x from both sides)

8 = 2x - 10 ( get your x value alone, add 10 to both sides)

18 = 2x (simplfy)

x = 9

Now plug x value into MO

3 (9) - 10 = 17

Check with opposing equation:

9 + 8 = 17 √

Montrer que : Si "n" la somme de deux carrées, alors le reste de division euclidienne de "n" par 4 est toujours différent à 3

Answers

Answer:

Montrer que a ≡ b (mod n) si et seulement si a et b laissent le même reste quand ... 7k + 3 ou la forme x = 7k + 4, alors x2 − 2 est un multiple entier de 7.

Step-by-step explanation:

which of the following factors is a factor of the expression x^2+5x-6
(x-2)
(x+6)
(x+3)
(x+1)

Answers

Answer:

HOLA MATE HERE IS YOUR ANSWER....

{x}^{2} - 5x - 6x

2

−5x−6

WE WILL SOLVE IT BY MIDDLE TERM SPLITTING

product = {6x}^{2}product=6x

2

Sum = 5x

{6x}^{2} \times {1x}^{2} = {6x}^{2}6x

2

×1x

2

=6x

2

-6x + 1x = 5x

ANSWER :

{x}^{2} - 6x + 1x - 6x

2

−6x+1x−6

NOW WE CAN FURTHER CONTINUE IT BY TAKING COMMON

SO,

x(x - 6) + 1 (x - 6)

Answer :

(X+1)(X-6)

PLEASE MARK AS BRAINLIEST

Find the value of Za/2 to construct a confidence interval with level 95%. Round the answer to two decimal places.

Answers

The value of Za/2 to construct a confidence interval with a level of 95% is approximately 1.96.

To construct a confidence interval with a level of 95%, we need to find the critical value Za/2. This value corresponds to the z-score that represents the area under the standard normal distribution curve outside the confidence interval.

The confidence level of 95% indicates that we want to capture the middle 95% of the distribution and leave 5% (2.5% on each tail) in the tails. Therefore, we need to find the z-score that leaves 2.5% in each tail.

To determine the value of Za/2, we can use a standard normal distribution table or statistical software. The value represents the z-score at the critical point, where the area to the right of the z-score is a/2.

For a level of 95%, a is equal to 1 - confidence level = 1 - 0.95 = 0.05. Dividing a by 2, we get a/2 = 0.05 / 2 = 0.025.

Using a standard normal distribution table or statistical software, we find that the z-score corresponding to an area of 0.025 in the right tail is approximately 1.96. Therefore, the critical value Za/2 for a 95% confidence interval is approximately 1.96.

In summary, the value of Za/2 to construct a confidence interval with a level of 95% is approximately 1.96.

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Which product is irrational?
A. 2x50
B. 64x4
C. 9x49
D. 10x8

Answers

Answer:

i don't see in product in here that is irrational

Step-by-step explanation:

the temperature has been dropping 2 1/2 degrees every hour and the current tempter is -15 degrees Ferin height how many hours ago was the temperature 0 degrees Ferin height

Answers

The number of hours ago was the temperature 0 degrees is 6 hours.

What is temperature?

Temperature simply means the degree if hotness and coldness in a body.

In this case, the temperature has been dropping 2 1/2 degrees every hour. Let the number of hours be h.

This will be illustrated as:

-15 = -2.5h

where h = number of hours

Divide

h = -15 / -2.5

h = 6

Therefore, the correct option is 6 hours.

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is anyone expert here in data forecasting methods? I need some help in some topics like time series(holts, holts winter), naive method, regression, acf, pacf, arima, stl method and multivariate time series. please reply if you can help me with these topics

Answers

Yes, there are experts here in data forecasting methods who can help you with the topics you've mentioned including time series (holts, holts winter), naive method, regression, acf, pacf, arima, stl method and multivariate time series.

Below are brief explanations of each of these terms:

Time Series: A time series is a sequence of observations of a particular quantity measured over time. Holts Method: The Holt’s method is a forecasting method that forecasts the data by taking into account the trend component along with the level component. Holts Winter Method: Holt's winter model is used to forecast seasonal univariate time series.Naive Method: The naive method is a forecasting method that uses the most recent observation as a forecast for the next time period.Regression: Regression is a statistical method used to estimate the strength and direction of the relationship between two or more variables.ACF & PACF: Autocorrelation function (ACF) and partial autocorrelation function (PACF) are statistical tools used to determine the nature of the correlation between a variable and its lag.ARIMA: ARIMA stands for AutoRegressive Integrated Moving Average. ARIMA is a forecasting technique that uses past data points to predict future values.STL Method: STL is a time series decomposition method that separates a time series into three components: trend, seasonality, and random.Multivariate Time Series: Multivariate time series analysis deals with the analysis of time series data that involves more than one variable.Based on the topics you've mentioned, you may want to ask specific questions regarding these topics to get more detailed answers.

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Round...
1. 24.263 to the nearest tenth.

Answers

Answer: 24.3

Step-by-step explanation:

A tenth would be the first decimal place.

Since the digit after the digit we need to round is above 5, then we need to round up.

The two turns into a 3.

I would really appreciate if you give brainliest.

Salaries of entry-level computer engineers have Normal distribution with unknown mean and variance. Three randomly selected computer engineers have salaries (in $1000s): 30, 50, 70 (a) Construct a 90% confidence interval for the average salary of an entry-level computer engineer. 302 Probability and Statistics for Computer Scientists (b) Does this sample provide a significant evidence, at a 10% level of significance, that the average salary of all entry-level computer engineers is different from $80,000? Explain. (c) Looking at this sample, one may think that the starting salaries have a great deal of variability. Construct a 90% confidence interval for the standard deviation of entrylevel salaries.

Answers

a) The 90% confidence interval for the average salary of an entry-level computer engineer is of: (16.28, 83.72).

b) The sample contains the value 80, hence it does not give sufficient evidence that the average salary of all entry-level computer engineers is different from $80,000.

c) The 90% confidence interval for the standard deviation of entry level salaries is of: (6.67, 389.86).

What is the confidence interval for the population mean?

The bounds of the confidence interval are given according to the following rule:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

In which the variables of the equation are presented as follows:

\(\overline{x}\) is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.

The sample in this problem is given as follows:

30, 50, 70.

Hence the values of the parameters are given as follows:

\(\overline{x} = 50, s = 20, n = 3\)

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 3 - 1 = 2 df, is t = 2.92.

Then the lower bound of the interval is of:

\(\overline{x} - t\frac{s}{\sqrt{n}} = 50 - 2.92\frac{20}{\sqrt{3}} = 16.28\)

The upper bound of the interval is of:

\(\overline{x} + t\frac{s}{\sqrt{n}} = 50 + 2.92\frac{20}{\sqrt{3}} = 83.72\)

What is the confidence interval for the standard deviation?

The bounds of the confidence interval for the standard deviation are given as follows:

\(\frac{(n - 1)s^2}{\chi^2_\frac{\alpha}{2}} \leq \sigma \leq \frac{(n - 1)s^2}{\chi^2_{1 - \frac{\alpha}{2}}}\)

The critical values of the chi-square distribution with a confidence level of 90% and 2 df are given as follows:

\(\chi^2 = 0.1026, \chi^2 = 5.9915\)

Hence the lower bound of the interval is of:

2 x 20/5.9915 = 6.67.

The upper bound of the interval is of:

2 x 20/0.1026 = 389.86.

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Ursula counted 12 tennis rackets and 288 tennis balls in the sports equipment closet. Which rate best represents the relationship between the number of tennis balls to the number of tennis rackets.
Pls Help Anything Helps!

Answers

Answer:

24:1 or 24/1

Step-by-step explanation:

288/12 = 24

This is the unit rate.  There are 24 tennis balls for each racket.

Answer: 24

Step-by-step explanation:

288/12=24

THERE ARE 24 BALLS PER TENNIS RACKET.

q29:a survey was conducted with 900 ohio university students. one of the conclusions fromthis survey was that 55% of the students believed the academics at ohio university were 'verystrong'. based on these sample results, are you convinced that a majority (i.e. over 50%) of allstudents believe the academics are 'very strong'?

Answers

Based on the information provided, we can conduct a hypothesis test to determine if a majority of all students at Ohio University believe the academics are 'very strong'.

Let's set up the null and alternative hypotheses:

Null hypothesis (H₀): The proportion of all students who believe the academics are 'very strong' is equal to 50% or less.

Alternative hypothesis (H₁): The proportion of all students who believe the academics are 'very strong' is greater than 50%.

To test these hypotheses, we can use a one-sample proportion test. We will compare the sample proportion (55%) to the hypothesized proportion (50%) and assess if the difference is statistically significant.

Using appropriate statistical methods, such as calculating the test statistic and obtaining the p-value, we can evaluate the evidence against the null hypothesis. If the p-value is less than the chosen significance level (e.g., 0.05), we would reject the null hypothesis and conclude that a majority of all students at Ohio University believe the academics are 'very strong'. Otherwise, if the p-value is greater than the significance level, we would fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim of a majority belief.

Please note that without the actual test results or the p-value, we cannot make a definitive conclusion in this particular case.

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