What is the value of x?

Answer:

5575 cm³

Step-by-step explanation:

The volume of a sphere is V = (4/3)πr³.  If we substitute r = (d/2 where r is the radius and d the diameter), this formula becomes:

                                        πd³

V = (4/3)π·d³/8, or V = -------------

                                           6

and so, if d = 22 cm, the volume is:

        π(22 cm)³

V = ------------------- = 5575 cm³

              6

To determine the equation of the least squares line, we need to find the slope (m) and the y-intercept (b) using the given data. The formula for the least squares line is:

y = mx + b

where:

m is the slope of the line

b is the y-intercept of the line

We can use the following formulas to calculate the slope and y-intercept:

m = (NΣxy - ΣxΣy) / (NΣx² - (Σx)²)

b = (Σy - mΣx) / N

Given the values:

Σx = 68

Σy = 79

Σxy = 1200

Σx² = 600

N = 12

Let's substitute these values into the formulas:

m = (12 * 1200 - 68 * 79) / (12 * 600 - (68)²)

b = (79 - m * 68) / 12

Calculating the values:

m = (14400 - 5372) / (7200 - 4624)

m = 9028 / 2576

m ≈ 3.5039

b = (79 - 3.5039 * 68) / 12

b = (79 - 238.2752) / 12

b ≈ -13.2738

Therefore, the equation of the least squares line is:

y ≈ 3.5039x - 13.2738

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The equation of the least squares line is y = 1.25x + 10.75

To determine the equation of the least squares line, we need to find the slope (b) and y-intercept (a) using the following formulas:

b = (NΣxy - ΣxΣy) / (NΣx² - (Σx)²)

a = (Σy - bΣx) / N

Given the following values:

Σx = 68

Σy = 79

Σxy = 1200

Σx² = 600

N = 12

Let's calculate the slope (b) first:

b = (12 × 1200 - 68×79) / (12×600 - 68²)

b ≈ 1.25

Now we can calculate the y-intercept (a):

a = (79 - 1.25×68) / 12

a = 10.75

Therefore, the equation of the least squares line is: y = 1.25x + 10.75.

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Answer:

The measure of angle CDE is 37 degrees

Step-by-step explanation:

A survey of 150 college students was done to find out what elective course they were taking Lot A the set of those taking ort, B the set of those taking basketweaving, and C - the set of those taking canoeing. The study revealed the following information A-45 IAN B = 12 181 55 ANC-15 C-40 BC-2 Anno 2  

Based on the given information, we can calculate the number of students who were not taking any of the elective courses.

Let's break down the information provided:

A: The set of students taking Art elective = 45

B: The set of students taking Basket weaving elective = 12

C: The set of students taking Canoeing elective = 40

A ∩ B: The set of students taking both Art and Basket weaving electives = 2

A ∩ C: The set of students taking both Art and Canoeing electives = 15

B ∩ C: The set of students taking both Basket weaving and Canoeing electives = 0 (not specified)

A ∩ B ∩ C: The set of students taking all three electives = 2

To find the number of students who were not taking any of these electives, we need to subtract the total number of students taking at least one elective from the total number of students surveyed.

Total students surveyed = 150

Students taking at least one elective = A ∪ B ∪ C

Students taking at least one elective = A + B + C - (A ∩ B) - (A ∩ C) - (B ∩ C) + (A ∩ B ∩ C)

Students taking at least one elective = 45 + 12 + 40 - 2 - 15 - 0 + 2

Students taking at least one elective = 82

Students not taking any of these electives = Total students surveyed - Students taking at least one elective

Students not taking any of these electives = 150 - 82

Students not taking any of these electives = 68

Therefore, there were 68 students who were not taking any of the elective courses using set theory.

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Answer: 15.867 min

Step-by-step explanation:

Given

Ben took [tex]1\ h\ \text{and}\ 23\ min\ 12\ s[/tex] to complete 15 km

While Mike take [tex]1\ hr\ 39\ min\ 4\ s[/tex] to complete the same

converting time into miniutes

Ben time

[tex]\Rightarrow 60+23+\frac{12}{60}=83.2\ min[/tex]

Mike time

[tex]\Rightarrow 60+39+\frac{4}{60}=99.0667\ min[/tex]

So, mike waited for

[tex]\Rightarrow 99.067-83.2=15.867\ min[/tex]

Q1.1.1 The probability of randomly selecting a male respondent from the sample is 0.4. Q.1.1.2 The probability of randomly selecting a respondent who is female and prefers HP is 0.275. Q.1.1.3 The probability of selecting a male respondent, given that the preferred brand is Lenovo is 0.4545. Q.1.1.4 The probability of selecting a respondent who is male or who prefers HP is 0.575. Q.1.1.5 The probability of selecting a respondent who does not prefer Lenovo is 0.725.

Q.1.1.1 What is the probability of randomly selecting a male respondent from the sample?

The probability of randomly selecting a male respondent is given by the number of male respondents divided by the total number of respondents:

Probability = No. of Males / Total = 160 / 400 = 0.4

Q.1.1.2 What is the probability of randomly selecting a respondent who is female and prefers HP?

The probability of randomly selecting a respondent who is female and prefers HP is given by the number of females who prefer HP divided by the total number of respondents:

Probability = No. of Females who prefer HP / Total = 110 / 400 = 0.275

Q.1.1.3 What is the probability of selecting a male respondent, given that the preferred brand is Lenovo?

The probability of selecting a male respondent, given that the preferred brand is Lenovo, is given by the number of males who prefer Lenovo divided by the total number of respondents who prefer Lenovo:

Probability = No. of Males who prefer Lenovo / Total No. of respondents who prefer Lenovo = 50 / 110 = 0.4545

Q.1.1.4 What is the probability of selecting a respondent who is male or who prefers HP?

The probability of selecting a respondent who is male or who prefers HP is given by the sum of the probabilities of selecting a male respondent and selecting a respondent who prefers HP, minus the probability of selecting both (to avoid double counting):

Probability = (No. of Males / Total) + (No. of Females who prefer HP / Total) - (No. of Males who prefer HP / Total)

Probability = (160 / 400) + (110 / 400) - (40 / 400) = 0.4 + 0.275 - 0.1 = 0.575

Q.1.1.5 What is the probability of selecting a respondent who does not prefer Lenovo?

The probability of selecting a respondent who does not prefer Lenovo is given by the number of respondents who do not prefer Lenovo divided by the total number of respondents:

Probability = (Total - No. of respondents who prefer Lenovo) / Total

Probability = (400 - 110) / 400 = 290 / 400 = 0.725

The complete question is:

The following contingency table gives the results of a sample survey of South African male and female respondents with regard to their preferred brand of notebook:

                              HP  Lenovo  Dell  Total

No. of Females        110    60   70    240

No. of Males             40    50   70    160

Total                        150    110  140    400

Q.1.1.1 What is the probability of randomly selecting a male respondent from the sample?

Q.1.1.2 What is the probability of randomly selecting a respondent who is female and prefers HP?

Q.1.1.3 What is the probability of selecting a male respondent, given that the preferred brand is Lenovo?

Q.1.1.4 What is the probability of selecting a respondent who is male or who prefers HP?

Q.1.1.5 What is the probability of selecting a respondent who does not prefer Lenovo?

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Answer:

1. false

2. false

3. true

Step-by-step explanation:

The mathematical relationship between the relative risk (RR) and the odds ratio (OR) is (c) The relative odds approach.

The mathematical relationship between the relative risk (RR) and the odds ratio (OR) is often described as the relative odds approach.

This approach quantifies the relationship between RR and OR and provides insights into the association between exposure and outcome in observational studies.

The rare disease assumption (a) refers to the assumption made in case-control studies that the odds ratio approximates the relative risk when the outcome is rare.

It is not specifically related to the mathematical relationship between RR and OR.

The built-in bias (b) does not directly relate to the mathematical relationship between RR and OR.

It refers to biases inherent in the study design or data collection process.

Effect modification (d) refers to a situation where the association between an exposure and outcome differs depending on the levels of another variable.

While effect modification can influence the relationship between RR and OR, it is not the specific term used to describe their mathematical relationship.

In summary, the mathematical relationship between RR and OR is best described as the relative odds approach (c), while the other options (a, b, d) are not directly related to this specific relationship.

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Answer:

4 2/3 cups

Step-by-step explanation:

Answer:

27.5ft

Step-by-step explanation:

a² + b² = c²

Plug in what you have:

a² + 12² = 30²

Get a by itself:

a² = 30² - 12²

Simplify:

a² = 900 - 144

Simplify:

a² = 756

Simplify:

√a = √756

Then you get 27.49 and when you round you get 27.5

a. The variance of the data set is 279.111 and the standard deviation is 16.707.

b. Adding an expensive cheese increases the mean to 55.9 and the standard deviation to 48.53.

a. To compute the variance and standard deviation for the given data set, we can use the following formulas:

Variance (s²) = [(Σx²) - (Σx)² / n] - 1

Standard Deviation (s) = √(Variance)

Using the given data set: 29, 62, 37, 41, 70, 82, 47, 52, 49

Step 1: Calculate the mean (x) of the data set.

Mean (x) = (Σx) / n

Σx = 29 + 62 + 37 + 41 + 70 + 82 + 47 + 52 + 49 = 409

n = 9 (number of data points)

Mean (x) = 409 / 9 = 45.44 (rounded to two decimal places)

Step 2: Calculate the sum of squares (Σx²) for the data set.

Σx² = 29² + 62² + 37² + 41² + 70² + 82² + 47² + 52² + 49² = 151509

Step 3: Substitute the values into the variance formula and calculate the variance.

Variance (s²) = [(Σx²) - (Σx)² / n] - 1

Variance (s²) = (151509 - (409)² / 9) / (9 - 1) = 279.111 (rounded to three decimal places)

Step 4: Calculate the standard deviation by taking the square root of the variance.

Standard Deviation (s) = √(Variance)

Standard Deviation (s) = √279.111 = 16.707 (rounded to three decimal places)

b. If a very expensive cheese with a cost per slice of 150 cents was added to the data set, the values of the mean and standard deviation would change. To find the new mean and standard deviation, we need to incorporate the additional data point and recalculate.

New Σx = Σx + 150 = 409 + 150 = 559 (updated sum of the data points)

New n = n + 1 = 9 + 1 = 10 (updated number of data points)

New Mean (x) = New Σx / New n = 559 / 10 = 55.9 (rounded to one decimal place)

The addition of the expensive cheese increased the mean.

To calculate the new variance and standard deviation, we follow the same steps as in part a using the updated Σx and n values:

New Σx² = Σx² + (150)² = 151509 + 22500 = 174009

New Variance (s²) = [(New Σx²) - (New Σx)² / New n] - 1 = (174009 - (559)² / 10) / (10 - 1) = 2355 (rounded to three decimal places)

New Standard Deviation (s) = √New Variance = √2355 = 48.53 (rounded to two decimal places)

Therefore, the addition of the expensive cheese increased both the mean and the standard deviation of the data set.

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Answer:

66.6%

Step-by-step explanation:

You have a 1/6 chance to roll any number. That is a 16.6% chance per number.

So, that means you have a 4/6 (2/3 simplified) probability of not rolling a one or two. That is a 66.6% chance.

[NOTE: The '6' at the end of '16.6%' and '66.6%' is a repeating decimal]

Given,A school janitor has mopped 1/3 of a classroom in 5 minutes.We have to find the rate at which he is mopping.Using the concept of unitary method,Rate of mopping 1 classroom in 5 × 3 = 15 minutes= 1/15 of a classroom in 1 minute.Rate of mopping 1/3 classroom in 5 minutes = (1/3) ÷ 5= 1/15 classroom per minuteHence, the required rate at which he is mopping is 1/15 classroom per minute.

Answer: 1/15.

To determine the rate at which the janitor is mopping, we can calculate the fraction of the classroom mopped per minute.

Given that the janitor mopped 1/3 of the classroom in 5 minutes, we can express this as:

(1/3) classroom / 5 minutes

To simplify this fraction, we divide the numerator and denominator by the greatest common divisor, which is 1:

(1/3) classroom / (5/1) minutes = (1/3) classroom × (1/5) minutes

Multiplying the numerators and the denominators gives us:

1 classroom × 1 minute / 3 × 5

Simplifying further:

1 classroom × 1 minute / 15

Therefore, the rate at which the janitor is mopping is 1/15 classrooms per minute.

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The given information is that the janitor mopped 1/3 of a classroom in 5 minutes. We have to find out at what rate is he mopping.

The rate of mopping is 1/15 classrooms per minute.

Let's try to solve the problem below. The given fraction is 1/3 of a classroom that was mopped in 5 minutes. We need to find the rate of mopping which can be calculated by dividing the fraction of the classroom mopped by the time it took to mop it. The rate of mopping can be found by performing the following calculation:

Rate of mopping = Fraction of the classroom mopped/Time taken to mop

= 1/3/5

= 1/15

So the rate of mopping is 1/15 classrooms per minute. This is the simplified answer.

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Answer:

After 8 hrs both candles would've burned out completely, so they'll, more or less, be at the same height.

[tex]sina=\frac{2\sqrt{13} }{13} \\cosa=\frac{3\sqrt{13} }{13}\\tana=\frac{2}{3}[/tex]

Answer:

A.

Step-by-step explanation:

correct on edge2021

Answer:

Variant b

Step-by-step explanation:

If you multiply it should be a+b but if you divided

A+b-c

Answer:

88 inches

Step-by-step explanation:

formula for circumference: 2pir or pi*diameter

22/7*28=88

88 inches

The statement "If p is prime, then there exists a field of order p²" is true. For any prime number p, there exists a finite field of order p².

Yes, it is true that if p is a prime number, then there exists a field of order p². In mathematics, a field is a specific type of algebraic structure with two operations, addition and multiplication, that satisfy certain properties. The order of a field refers to the number of elements in the field. For any prime number p, there exists a unique finite field of order p², often denoted as GF(p²) or Fp². This field consists of p² elements and is crucial in various areas of mathematics, such as number theory, cryptography, and coding theory.

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Answer:

0.5, 0, -1/4, -1

The z-score for a student who received a score of 90 on the entrance exam is 1.6.

The z-score for a student who received a score of 90 on the entrance exam, with a mean of 82 and a standard deviation of 5, can be calculated as follows:

Plugging in the values:

Simplifying:

Calculating:

Therefore, the z-score for the student who received a score of 90 on the exam is 1.6.

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The required solutions are:

a) Yes, the relation R is an equivalence relation.

b)The equivalence class of -17 is {-17, -23, -29, -35, ...}.

a) In order to determine whether R is an equivalence relation or not, we need to check if it satisfies the following three conditions:

We can see that the relation 'R' satisfies all the conditions ( reflexibility, symmetry, and transitivity), so R is an equivalence relation.

b) In order to find the equivalence class of -17, we need to find all integers that are related to -17 under the relation R.

We can rewrite the relation as mRn if and only if m' - n' = 6k for some integer k.

In this case, -17Rn if and only if (-17)' - n' = -17 - n = 6k for some integer k.

To find all integers n that satisfy this equation, we can rearrange it as n = -17 - 6k.

By putting in different values of k, we can find all the integers n that are in the equivalence class of -17.

For example, when k = 0, n = -17 - 6(0) = -17. So, -17 is in the equivalence class of -17.

We can also see that when k = 1, n = -17 - 6(1) = -23. So, -23 is also in the equivalence class of -17.

The equivalence class of -17 consists of all integers that can be obtained by subtracting multiples of 6 from -17. So, the equivalence class of -17 is {-17, -23, -29, -35, ...}.

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Answer:

try (4,5)

Step-by-step explanation:

that is where the points meet I think it is that I am not sure sorry if it is wrong

Answer:

9.02 x 10^6

Step-by-step explanation:

hope this helps!

Answer:

Step-by-step explanation:

Monday: c and p

Tuesday: 2c+p

Wednesday: 2c+p/2

Thursday: 6c+3p/2

Friday: (2c-12)+(p/2+5)

Adding them all up, you get, for Monday-Friday:  (13c-12)+(9p/2+5)

I'm not sure how to explain this to you though, you just follow the directions they gave, to multiply and subtract.

Hope this is helpful!

Answer:

Well first you must do what's in the parenthesis.

10^2 = 100

100^3 = 1000000

Answer:

x=-5

Step-by-step explanation:

Answer:

The answers are in the attachment above

good day mate

Angle ∠B is a right-angle then the measure of angle ∠A is 43.6 degrees and the measure of angle ∠C is 46.4 degrees.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.

The triangle ΔABC is given.

The angle ∠B is a 90°.

Then the value of the angle ∠C will be

[tex]\rm C = \sin ^{-1} \dfrac{21}{29}\\\\C = 46.40^o[/tex]

Then the value of the angle ∠A will be

     ∠A + ∠C = 90°

∠A + 46.40° = 90°

              ∠A = 43.6°

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