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The area of a circle is 16.71cm2.
Find the length of the radius rounded to 2 DP.

There are 5040 different committees that can be formed from a class of 10 students where each member is assigned a unique position in the committee.

In this problem, we are asked to find the number of possible committees that can be formed from a class of 10 students, where each committee has 4 members who are assigned unique positions. This means that the order in which the students are selected and assigned positions matters. Therefore, we need to use the permutation formula to solve this problem.

To find the number of possible committees, we need to calculate the number of ways we can select 4 students from a class of 10 and assign each of them a unique position. We can do this in two steps:

Step 1: Selecting 4 students from a class of 10
The number of ways we can select 4 students from a class of 10 is given by the combination formula:

C(10,4) = 10!/(4!6!) = 210

Step 2: Assigning unique positions to the selected students
Once we have selected the 4 students, we need to assign each of them a unique position. The first student can be assigned any of the 4 positions (President, Vice President, etc.). The second student can then be assigned any of the remaining 3 positions, the third student can be assigned any of the remaining 2 positions, and the fourth student will be assigned the last remaining position. Therefore, the number of ways we can assign unique positions to the selected students is given by:

4 x 3 x 2 x 1 = 24

Putting these two steps together, we get the total number of possible committees as:

210 x 24 = 5040

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Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

According to the statement seen in this question, the line segments RT and  ST are collinear to each other. Mathematically speaking, the length of the line segment ST can be found by using the following formula:

RT = RS + ST

ST = RT - RS

ST = 19 - 6

ST = 13

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

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Answer:

2 is ur answer.

hope it helps you.

The discriminant of this equation is 261

It has two solutions are they are -0.76 and 0.86

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

5n^2-n=13

Rewrite as

5n^2-n - 13 = 0

The discriminant is

D = b^2 - 4ac

So, we have

D = (-1)^2 - 4 * 5 * -13

Evaluate

D = 261

In (a), we have the discriminant to be greater than 1

This means that it has two solutions

We have

5n^2-n - 13 = 0

Using the quadratic formula, the solution is

x = (-b ± √D)/4a

So, we have

x = (1 ± √261)/4 * 5

x = (1 ± 16.2)/20

So, we have

x = (1 - 16.2)/20 and (1 + 16.2)/20

Evaluate

x = -0.76 and 0.86

Hence, the solutions are -0.76 and 0.86

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Answer:

1. Slope = -3/5

  Y-intercept = (0, -3)

2. Slope = -2/3

   Y-intercept = (0, -2)

The set of integers for which p(k) is true is all even integers for which p(k) is proved true if we also prove that p(k)^p(k 2)=> p(k-2).

Considering that p(- 2) and p(0) are valid and expecting that p(k)^p(k+2) => p(k-2), we can decide the arrangement of numbers k for which p(k) is valid by acceptance. In particular, we can show that p(k) is valid for all even numbers k by enlistment, as follows.

To begin with, since p(- 2) and p(0) are valid, the base instance of k = - 2 is valid.

Then, expect that p(k) is valid for some even number k. Then, at that point, utilizing the given ramifications, we have p(k+2) is valid.

At long last, utilizing a similar ramifications once more, we have that p(k-2) is valid. Accordingly, by acceptance, we have shown that p(k) is valid for all even numbers k.

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Answer: option 3 is correct

Step-by-step explanation: Simplify the expression.−8m^5z^6

The dependent variable in the given graph is; Total Cost

A dependent variable is defined as the variable that changes in an experiment.

Now, a dependent variable depends on other factors. For example, a test score could be classified as a dependent variable because it could change depending on several factors like how much the student studied, how much sleep the student got the night before taking the test, or even how hungry the student was when he took the test.

The domain of a function is simply defined as the set of all possible input values that we are allowed to plug into a particular function. Meanwhile the range of a function is defined as the set of all possible output  values that the particular function assumes.

Now, in this question, we see that days is the domain because it is the set of all input values while total cost depends on the number of days and as such is the range and dependent variable.

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Answer:

enlargement ; 2

Step-by-step explanation:

dilation is change in the size of the figure.

in the given scenario, figure's size is increasing so dilation is called enlargement and scale factor must be greater than 1.

scale factor = dimension of new shape / dimension of original shape

let's calculate the difference in terms of boxes of both figures to calculate the scale factor,

scale factor = 6/3

thus, in the given dilation we have enlargement of 2

Answer:

The ratio of apples to peaches is 2 to 9.

Step-by-step explanation:

For every 1 apple, there are 3 bananas.

For every 3 peaches, there are 2 bananas.

To compare apples to peaches, we need to make the bananas in each of the proportions equal.

(1 apple = 3 bananas ) x 2    --> 2 apples= 6 bananas

(3 peaches = 2 bananas) x 3 --> 9 peaches= 6 bananas

Now that the bananas are equal and the other fruits are proportionate to the number of bananas, we can see that for every 2 apples there are 9 peaches.

Answer:

∠ QPR = 56°

Step-by-step explanation:

Δ RST is isosceles ( 2 congruent sides ) , then base angles are congruent

∠ SRT = \(\frac{180-44}{2}\) = \(\frac{136}{2}\) = 68°

∠ PRQ and ∠ SRT are vertically opposite angles and are congruent , so

∠ PRQ = 68°

Δ PRQ is isosceles ( 2 congruent sides ), then base angles are congruent , so

∠ QPR = \(\frac{180-68}{2}\) = \(\frac{112}{2}\) = 56°

=====================================================

Explanation:

Triangle TRS is isosceles due to the sides TR and TS being congruent.

Let x be the measure of angle R of triangle TRS. It's also the measure of angle S. The base angles of any isosceles triangle are the same.

Add up the three angles of triangle TRS. Set the sum equal to 180. Solve for x.

T+R+S = 180

44+x+x = 180

44+2x = 180

2x = 180-44

2x = 136

x = 136/2

x = 68

This means angle TRS is 68 degrees.

Subsequently, it also means angle QRP is 68 degrees as well. These two angles are congruent vertical angles.

----------------------

Now focus on triangle PQR. This triangle is also isosceles.

We have the following interior angles

So,

P+Q+R = 180

y+y+68 = 180

2y+68 = 180

2y = 180-68

2y = 112

y = 112/2

y = 56 is the measure of angle QPR

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Answer:

5cm

Step-by-step explanation:

Convert 1.5m into cm to make it easier to solve.

1.5m --> 150cm (*100)

The real bike length is 30 times larger than the scale. So to undo this we need to divide by 30.

150cm / 30 = 5cm

Answer: "C"

roots would make the function "0"

so just plug in the numbers...

with a + 12 you need minuses to cancel out...

B & C can not be the answer...

A is -i -3 + 4i - 12 which also is not 0

C is :  8i -12 -8i +12 WHICH DOES = 0

Step-by-step explanation:

Answer:

0.67

Step-by-step explanation:

2/3= to 0.66 which means 0.67 would be technally larger than 0.66

An effective sampling method is not cast doubt on the usefulness of the sample

The effective sample is a calculation of the approximate sample size needed to obtain the same degree of accuracy as a simple random sample. It is denoted mathematically by the formula n/D, where n represents the sample size and D denotes the design effect. It is employed as a means of condensing the volume of data.

Effective sample size calculations are mostly used for qualitative analyses of the sample size. The sample size calculates the total number of measurements or observations made during an experiment or survey. The effective sample size—rather than the actual sample size—is utilized in this assessment since it is thought that a sample size of 30 is necessary for an analysis to be valid.

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There are 25 students in the class and 3 students are undecided about the type of party they want.

We know that 20% (percent)of the students want an ice cream party. Let's call the total number of students in the class "x." Then we can set up an equation:

0.2x = 5

Solving for x, we get:

x = 5 / 0.2

x = 25

So there are 25 students in the class. We also know that 5 want an ice cream party, 7 want a movie party, and 10 want a costume party. That adds up to 22 students. So the rest of the students must be undecided:

25 - 22 = 3

Therefore, 3 students are undecided about the type of party they want.

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Complete Question

Mrs. Conley asks her class what kind of party they want to have to celebrate their excellent behavior. Out of all the students in the class, 5 want an ice cream party, 7 want a movie party, 10 want a costume party, and the rest are undecided. If 20%, percent want an ice cream party, how many students are in the class?

Based on the information provided, the archaeological sample's estimated age is = 0.214136  years

Half life given is 5730

t₆.₅ = Ln2/k

k= ln 2/ 5730

The rate constant ,

k = 0.00012 year⁻¹

Given that 23 % of the 14C remains

then |A1|/|A2|  = 0.23

As we know ,

|A1|/|A2| = e ⁻₍kt₎

Hence, on solving the equation we get ,

ln(0.23)= -1.46967

t = -0.31471/ --1.46967

= 0.214136 years

The amount of time needed for a quantity (of substance) to decrease to half of its initial value is known as the half-life (symbol t12). In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long stable atoms last. The phrase is also used more broadly to describe any kind of exponential decay (or, very infrequently, nonexponential decay).

The biological half-life of medications and other compounds in the human body, for instance, is a term used in the medical sciences. Half-opposite life's in exponential growth is time's doubling.

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Answer:

You need the minimum cost for renting the meeting room given the following info

Reservation Fee = $18

Hourly Rate = $5

The renter wants to keep the cost below $58

So the cost will vary with the time, t you use the inequality below

5t + 18 ≤ 58

You can solve this to get that minimum

You can check you answer by graphing it.

I hope this helps!<3

Answer:

19

Step-by-step explanation:

Answer:

6xy + 18x + 6y

Hope this helps!

Answer:

i dont know the answer to this

Step-by-step explanation:

Because i just dont

Answer:

It depends on what shape your talking about, like: a rectangle - Length  multiplied by Width

Step-by-step explanation:

Hope this helped, plz mark as brainiest :)

The simplest form by adding two number is \(3\sqrt{5}+2\sqrt{2}\)  and it is irrational number.

The square root of any number is equal to a number, which when squared gives the original number. Let us say n is a positive integer, such that  \(\sqrt{n.n}=\sqrt{(n)}^2=n\)

Given that, the two numbers,

3 square root of 5= \(3\sqrt{5 }\)

2 square root of 2 = \(2\sqrt{2}\)

Sum of these two numbers = \(3\sqrt{5}+2\sqrt{2}\)

We cannot simplify this term further.

The simplest form by adding two numbers is \(3\sqrt{5}+2\sqrt{2}\)

As it is clear, it is a irrational number.

Because, \(\sqrt{2}\) and \(\sqrt{5}\) is a irrational number.

Hence, the simplest form by adding two number is \(3\sqrt{5}+2\sqrt{2}\)  and it is irrational number.

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Using binary search to find the key 60 in the given list, the elements compared in order are: 38, 76, 60.

1. We start by comparing the key (60) to the middle element of the list, which is 38. Since 60 is greater than 38, we know that the key must be in the second half of the list.
2. Next, we compare the key to the middle element of the second half of the list, which is 76. Since 60 is less than 76, we know that the key must be in the first half of the second half of the list.
3. We then compare the key to the middle element of the first half of the second half of the list, which is 50. Since 60 is greater than 50, we know that the key must be in the second half of the first half of the second half of the list.
4. Next, we compare the key to the middle element of the second half of the first half of the second half of the list, which is 72. Since 60 is less than 72, we know that the key must be in the first half of the second half of the first half of the second half of the list.
5. Finally, we compare the key to the middle element of the first half of the second half of the first half of the second half of the list, which is 60. Since 60 is equal to 60, we have found the position of the key in the list.


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Answer:

5530

Step-by-step explanation:

Answer:

Step-by-step explanation:

50 times 9 equals 450

then add the 5050 and 30 to get 5080

then add up 5080 and450 and get your answer of 5530

Answer:

10.7 cm

Step-by-step explanation:

V = (4/3)πr³

5128.8467 = (4/3)(3.14)r³

1225.043 = r³

r = 10.7

The standard deviation of x for scores on the Critical Reading part of the test is approximately 18.26.

To find the standard deviation of x for scores on the Critical Reading part of the test, we can use the formula:

\(σ(x) = σ / √n\)

where σ is the population standard deviation and n is the sample size.

Plugging in the values given in the question:

\(σ(x) = 100 / √30\)

≈ 18.26

Therefore, the standard deviation of x for scores on the Critical Reading part of the test is approximately 18.26.

(b) Using the same formula, we can find the standard deviation of x for scores on the Mathematics part of the test:

\(σ(x) = 100 / √60\)

≈ 12.91

So, the standard deviation of x for scores on the Mathematics part of the test is approximately 12.91.

(c) Again, using the same formula, we can find the standard deviation of x for scores on the Writing part of the test:

\(σ(x) = 100 / √90\)

≈ 10.58

Hence, the standard deviation of x for scores on the Writing part of the test is approximately 10.58.

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Answer:

D

Step-by-step explanation:

Because you have to multipy 6 · 3 when you divide  you subract the exponents. therefore it will be m.

The answer is $25.5!

Answer: -2m2 -m - 10

Step-by-step explanation:

(-5m2 - 8) - (-3m2 + m + 2)

Everything is behind the (-) when you have a parenthesis chang the sign so and let the () so will be

-5m2-8 +3m2 - m -2

Now you are going to add or subtract numbers for the one the same letter ( base) and for the one that don't have a other letter (base) you will let it like this so will be

-5m2 + 3m2 = -2m2

-8 -2 = -10

-2m2 - m - 10

Hope helps