Use the circle to answer the questions.

A circle with radius 5.4 centimeters.

The diameter is
cm.



The circumference in terms of Pi is

Using 3.14 for Pi, the approximate circumference of the circle is
cm.

The smallest three-digit number divisible by the first three prime numbers (2, 3, and 5) and the first three composite numbers (4, 6, and 8) is 120.

The first three prime numbers are 2, 3, and 5. The first three composite numbers are 4, 6, and 8. In order for a number to be divisible by all six of these numbers, it must be divisible by their least common multiple (LCM).

The LCM of 2, 3, 5, 4, 6, and 8 is 120. Therefore, the smallest three-digit number divisible by the first three prime numbers and the first three composite numbers is 120.

Here is a more detailed explanation of how to calculate the LCM:

Find the prime factorization of each number.

Find the highest power of each prime factor.

Multiply the prime factors together, using the highest power for each factor.

The highest power of 2 that appears in any of the prime factorizations is 2^3.

The highest power of 3 that appears in any of the prime factorizations is 3^1.

The highest power of 5 that appears in any of the prime factorizations is 5^1.

Therefore, the LCM of 2, 3, 5, 4, 6, and 8 is 2^3 * 3^1 * 5^1 = 120.

To know more about number click here

brainly.com/question/28210925

#SPJ11

Answer:

2:10 or 1:5

Step-by-step explanation:

Answer: 4 squares to 1 triangle

Step-by-step explanation: both can be divided by two and that is the largest number they can be divided into

We would reject the null hypothesis in favor of the alternative hypothesis.

The null hypothesis (H0) is that the average number of classes per quarter for students is 2 or less. The alternative hypothesis (Ha) is that the average number of classes per quarter for students is greater than 2. We can express this as:

H0: μ ≤ 2 (mean number of classes per quarter)

Ha: μ > 2

Where μ represents the population mean. This hypothesis is based on the instructor's belief that students take more than 2 classes on average.

The significance level (alpha) is given as 0.01, which means that if the p-value of the test is less than 0.01, we would reject the null hypothesis in favor of the alternative hypothesis.

Learn more about hypothesis

brainly.com/question/29106378

#SPJ11

a. The probability that the selected student will be female According to the given problem, the total number of associate degrees awarded by US community colleges was 788,325 and 488,142 of these degrees were awarded to women.

Hence, the probability that a selected student will be female is:  P(Female) = Number of females awarded associate degree / Total number of associate degrees awarded= 488,142 / 788,325 `= 0.619 (rounded to three decimal places) Thus, the probability that a selected student will be female is 0.619.b. The probability that the selected student will be male Since the total number of associate degrees awarded is 788,325, we can find the probability that a selected student will be male by subtracting the probability that a selected student will be female from 1 (because there are only two genders).Therefore, `P(Male) = 1 - P(Female) = 1 - 0.619 = 0.381 (rounded to three decimal places)`The main answer to part (a) is 0.619 while the main answer to part (b) is 0.381.The problem gives the total number of associate degrees awarded by US community colleges in a certain academic year. A total of 488,142 of these degrees were awarded to women. Using this information, we can find the probability that a selected student will be female (part a) and the probability that a selected student will be male (part b).

The probability that a selected student will be female is 0.619 while the probability that a selected student will be male is 0.381.

To know more about decimal visit:

https://brainly.com/question/30958821

#SPJ11

Answer:

27

Step-by-step explanation:

Since pink dots is the highest(30) and Purple is second highest so purple must be close to 30.

The requried, height of the purple bar on the relative frequency bar graph is 22, and the answer is (D) 22.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
Since the vertical axis of the bar graph is marked off in percentages, we can determine the height of each bar by multiplying its frequency by 2, since 50 students were surveyed (i.e., 100% of the sample size).

The frequency of the purple color pattern is 11, so its height on the bar graph is 11*2 = 22.

Therefore, the height of the purple bar on the relative frequency bar graph is 22, and the answer is (D) 22.

Learn more about Statistics here:
https://brainly.com/question/23091366

#SPJ7

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 100000\\ P=\textit{original amount deposited}\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &12 \end{cases}\)

\(100000 = P\left(1+\frac{0.08}{12}\right)^{12\cdot 12}\implies 100000=P\left( \frac{151}{150} \right)^{144} \\\\\\ \cfrac{100000}{\left( \frac{151}{150} \right)^{144}}=P\implies \boxed{38411.47\approx P}\)

The correct answer is (a) event. An event is a subset of outcomes from the sample space. It represents a specific outcome or set of outcomes that we are interested in. Events can be simple, consisting of a single outcome, or they can be compound, consisting of multiple outcomes.

For example, consider rolling a fair six-sided die. The sample space is {1, 2, 3, 4, 5, 6}. Let's say we are interested in the event of rolling an even number. The event in this case would be {2, 4, 6}, which is a subset of the sample space.

Events can also be mutually exclusive, meaning they cannot occur at the same time, or they can be independent, meaning the occurrence of one event does not affect the probability of the other event occurring.

In summary, an event is a subset of outcomes from the sample space and represents a specific outcome or set of outcomes that we are interested in. It is an important concept in probability theory.

To learn more about probability here:

brainly.com/question/30924040

#SPJ11

The value of the given integral by converting it into polar coordinates is [a⁴ / 4] (1 - (-1)) = [a⁴ / 2].Hence, the correct option is (d) [a⁴ / 2].

To evaluate the iterated integral by converting to polar coordinates,

we need to change the limits of the integral into polar coordinates.

So the given integral in polar form is ∫(from θ = 0 to θ = π/2) ∫(from r = a to r = 0)\(4r^3cos(θ)sin(θ)dr dθ.\)

The polar coordinate conversion is given by x = r cos(θ) and y = r sin(θ).Given integral ∫a0∫0−√a2−y24x2y dx dy can be expressed in the form of polar coordinates as follows:

∫(from θ = 0 to θ = π/2) ∫(from r = a to r = 0) 4r³cos(θ)sin(θ) dr dθ

Where, x = r cos(θ) and y = r sin(θ)

Now, we can evaluate this integral using the polar coordinate conversion.

∫(from θ = 0 to θ = π/2)

∫(from r = a to r = 0) 4r³cos(θ)sin(θ) dr

dθ=∫(from θ = 0 to θ = π/2) [cos(θ)sin(θ) ∫(from r = a to r = 0) 4r³ dr ]

dθ= ∫(from θ = 0 to θ = π/2) [ cos(θ) sin(θ) (r⁴) / 4] (from r = a to r = 0)

dθ=∫(from θ = 0 to θ = π/2) [cos(θ) sin(θ) (a⁴) / 4]

dθ= [a⁴ / 4] ∫(from θ = 0 to θ = π/2) sin(2θ)

dθ= [a⁴ / 4] ([- cos(2θ)] from θ = 0 to θ = π/2)

for such more question on polar coordinates

https://brainly.com/question/4522672

#SPJ11

Answer:

Step-by-step explanation:

If XY bisects DF at point E, then DE = EF.

Given DE = 2y and EF = 8y-3

2y = 8y-3

subtract 8y from both sides

2y-8y = 8y-8y-3

-6y = -3

y = 3/6

y = 1/2

y = 0.5

DF = DE+EF

DF= 2y+8y-3

DF = 10y - 3

DF = 10(0.5)-3

DF = 5-3

DF = 2

By using the concept of bell shaped curve of normal distribution, it can be concluded that

The histogram would not look like a bell shaped curve because occurance of fire may not be constant in  all the case.

What is normal distribution?

Normal distribution is a continuous type probability distribution whose probability density function is given by

f(x) = \(\frac{1}{\sigma \sqrt{2\pi}}e^-{\frac{z^2}{2}\)

Where z = \(\frac{x - \mu}{\sigma}}\) where \(\mu\) is the mean and \(\sigma\) is the standard deviation

A fire department in a small town keeps track of the number of fires it has to fight each day for a year and records the 365 values central limit theorem.

Here, in this case it is not confident that the histogram would not look like a bell shaped curve because occurance of fire may not be constant in  all the case.

To learn more about normal distribution, refer to the link-

https://brainly.com/question/4079902

#SPJ4

Answer:

14 m/s²

Step-by-step explanation:

From the question

a ∝ F/m.............. Equation 1

Where a = aceleration, m = mass, F = force

make F the subject of the equation

F = ma............ equation 2

Given: m = 7 kg, a = 4 m/s²

Therefore,

F = 7(4)

F = 28 N

For another object whose mass is 2 kg,

Make a the subject of equation 2

a = F/m

a = 28/2

a = 14 m/s²

Answer:

There can be no answer, as you did not provide the box plot to compare the data.

ANSWER: 68 CM PO YAN ANS. KO

Answer:

D. y=2x-1 (I got B wrong)

the factors and prime factorization of 14 and 28. (The biggest common factor number is the GCF number) So the greatest common factor 14 and 28 is 14.Jul

Answer:

y = 1/8x + 25/8

Step-by-step explanation:

Answer:

The movement of matter through the living and nonliving parts of an ecosystem is a continuous process, a cycle. A is a series of events that happens over and over again. Matter in an ecosystem may change form, but it never leaves the ecosystem, so the matter is said to cycle through the ecosystem

Step-by-step explanation:

Answer:

Biogeochemical cycle.

Step-by-step explanation:

Answer:

y=2/3x+4

Step-by-step explanation:

4 is y-intercept

2/3 is  the slope (rise/run)

Answer: y = \(\frac{2}{3}\)x + 4

Step-by-step explanation:

    This is in slope-intercept form. We are missing the m and the b value. See attached for more information.

[m aka the slope]

   Starting from point (-6, 0), counting up 2 units, then right 3 units to point (-3, 2), gives us a slope of \(\frac{2}{3}\) via rise-over-run

[b aka the y-intercept]

   The line intersects the y-axis at positive 4.

-> This value is "4"

Answer:

B) 65 sq in

Step-by-step explanation:

SA = area of base + 1/2(perimeter of base)(slant height)

= 5² + 1/2(20)(4)

= 25 + 40

Answer: 2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

8 × .75 = 6lbs

she'd need 6lbs so she'd buy two bags of 5lbs

Answer:

Step-by-step explanation:

This is because,

As,

Negative integers are -1, -2, -3, -4, -5 .......

Also,

0 is neither negative integer nor positive integer,

And,

Positive integers are 1, 2, 3, 4, 5 .........

Therefore here ,

We get two sets of NON - POSITIVE INTEGERS,

That is 0 ( neither negative nor positive) and -1, -2, -3, -4, -5 ........ (Negative integers)

So,

Set of ( .......... -5, -4, -3, -2, -1, 0 ) is non - positive integers.

Answer:

C

Step-by-step explanation:

We are given 5 negative values plus 0. Keep in mind that 0 is not positive or negative. A non-positive integer is any negative number plus zero which the set follows. C is the only logical answer. A is incorrect because a negative number cannot be a whole number. B is incorrect because while we have negative values, we also have 0 and as stated previously, its not a negative or positive value. D is also incorrect because a non-negative integer is any positive value and zero but again, we don't have any positive values.

Best of Luck!

Answer: 16 meters in total, even tho it seems they didn’t move at all

Step-by-step explanation:

Answer:

16 meters

Step-by-step explanation:

Down 8 meters is a distance of 8m

Up 8 meters is a distance of 8m

8m+8m = 16 meters total

Based on the number of members and the ratio in which they chose the types of film, the number who chose Action in the second week more than the first week is 6 people.

Assuming that the number of members is 99 members, the number who chose Action on the second week were:

= (7 / (5 + 7 + 6)) x 99

= 39 people

The number who chose Action in the first week:

= (5 / (2 + 5 + 8)) x 99

= 33

The difference is:

= 39 - 33

= 6 people

Find out more on ratios at https://brainly.com/question/12024093

#SPJ1

First image -Right triangle(One angle is 90 degrees)

Second image-Isosceles triangle(Two equal sides and two equal angles).

Answer: 131.39

Step-by-step explanation:

Answer:  A.  X=4

Step-by-step explanation:

Since the line is on the X axis you can see its touching x,4 y,0

We are not truly independent because we are sampling more than 10% of the population.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Here,

3/15 = .2,

meaning that we are sampling more than 10% of the population hence violating independence.

Because we are sampling over 10% of the population, we are not acting independently.

To know more about probability,

https://brainly.com/question/11234923

#SPJ4

Answer:

x = 3

Step-by-step explanation:

4(x - 11) + 8x + 8 = 0

Distribute the 4.

4x - 44 + 8x + 8 = 0

Combine like terms.

4x + 8x - 44 + 8 = 0

12x - 36 = 0

Add 36 to both sides.

12x = 36

Divide both sides by 12.

x = 3

Proof:

4(x - 11) + 8x + 8 = 0

Substitute value.

4(3 - 11) + 8(3) + 8 = 0

Subtract inside the parenthesis.

4(-8) + 8(3) + 8 = 0

Multiply.

-32 + 24 + 8 = 0

Add.

-8 + 8 = 0

0 = 0.

The minimum sample size needed to guarantee a given margin of error increases , the correct option is (b) .

What is Margin Of Error ?

The term margin of error is defined as an estimate of a small sample that is drawn from a relatively large population data.

the margin of error is usually governed by the parameters such as the standard deviation , sample size and desired confidence level.

to find missing term in the given statement , let us consider the values ,

where σ ⇒ Standard deviation for population

and m as "Margin of error"  and Z as "Empirical value of Z-score" at a given confidence level .

So , minimum sample size for given confidence level is given by

⇒ (Z×σ)²/m²

from above formula we can conclude that minimum sample size is directly related to population's standard deviation.

Therefore, the minimum sample size required would "increase" with the increase in population "standard deviation" .

Learn more about Margin Of Error here

https://brainly.com/question/29982243

#SPJ4

Graph the line.

y=-4x+4

Graph the line.

y=-4x+4Graph the line.

y=-4x+4Graph the line.

y=-4x+4Graph the line.

y=-4x+4Graph the line.

y=-4x+4