Mathematics High School

What is the exact area of the base of a circular swimming pool with diameter 16 ft?

Answers

Answer 1
Area of a circle = (pi)r^2
diameter is twice the radius, so radius = 8 ft
Area = (pi)(8)^2
= 64(pi)
= 201.06 ft

Related Questions

What is the difference between -5 squared and -5 parenthesis squared?

Answers

-5 is essentially -1·5

Order of operations says to do exponents first, so without parentheses -5², you would square first then multiply by -1, leaving you with an answer of -25.

However, parentheses comes before exponents in order of operations, so with parenthesis (-5)² would be 25.

There are 105 members of the high school band. Of these members, 1/5 play percussion instruments. How many members play percussion?

Answers

21 percussion players

What's the intuition behind the equation 1+2+3+⋯=−1121+2+3+⋯=−112 ?

Answers

The sum clearly diverges. This is indisputable. The point of the claim above, that

[tex]1+2+3+\cdots=-\dfrac1{12}[/tex]

is to demonstrate that a sum of infinitely many terms can be manipulated in a variety of ways to end up with a contradictory result. It's an artifact of trying to do computations with an infinite number of terms.

The mathematician Srinivasa Ramanujan famously demonstrated the above as follows: Suppose the series converges to some constant, call it [tex]C[/tex]. Then

[tex]\begin{matrix}C&=&1&+2&+3&+4&+5&+6&+\cdots\\4C&=&&+4&&+8&&+12&+\cdots\\-3C&=&1&-2&+3&-4&+5&-6&+\cdots\end{matrix}[/tex]

Now, recall the geometric power series

[tex]\displaystyle\sum_{n\ge0}x^n=1+x+x^2+x^3+\cdots=\dfrac1{1-x}[/tex]

which holds for any [tex]|x|<1[/tex]. It has derivative

[tex]\displaystyle\sum_{n\ge1}nx^{n-1}=1+2x+3x^2+4x^3+\cdots=\dfrac1{(1-x)^2}[/tex]

Taking [tex]x=-1[/tex], we end up with

[tex]1+2(-1)+3(-1)^2+4(-1)^3+\cdots=1-2+3-4+\cdots=\dfrac14[/tex]

and so

[tex]-3C=\dfrac14\implies C=-\dfrac1{12}[/tex]

But as mentioned above, neither power series converges unless [tex]|x|<1[/tex]. What Ramanujan did was to consider the sum [tex]1-2+3-4+\cdots[/tex] as a limit of the power series evaluated at [tex]x=-1[/tex]:

[tex]\displaystyle-3C=\lim_{x\to-1^+}\sum_{n\ge1}nx^{n-1}=\lim_{x\to-1^+}\frac1{(1-x)^2}=\frac14[/tex]

then arrived at the conclusion that [tex]C=-\dfrac1{12}[/tex].

But again, let's emphasize that this result is patently wrong, and only serves to demonstrate that one can't manipulate a sum of infinitely many terms like one would a sum of a finite number of terms.

I don’t understand 9) PLEASE HELP!!! The line y=2.5x-7

Answers

The residual of a line is the observed Y value (the numbers in the table) minus the actual value (the Y value you get when you plug in the X value into the equation)... This question is asking you to find the residuals of all the points, square them, and add them... 

For example, the observed Y value for -4 is -15. When you plug in -4 into the equation, you get this: 

2.5x-7
2.5(-4) -7
-10 -7
=-17

The observed Y val. is -15, while the actual (equation) one is -17. -15 -(-17) is 2. 2^2 = 4

Do this process for all of the points, the add up the squared residuals, and you'll be done! 

Hope this helped!

Brand A cereal contains 10 cups of cereal. How many more cups of cereal are in Brand B cereal? 30% more cereal

Answers

There are 13 cups of  more cereal in Brand B.

Answer:

there are 13 more cups

Step-by-step explanation:

i already did it

Evaluate. 3−1⋅(4⋅6)⋅2−3 Enter your answer in the box.

Answers

The answer to this question is 1

20 point to whoever answers first

What is the MEDIAN of may's temperatures

A. 72

B. 61

C. 71

D. 74

Answers

total the temperatures given

 total = 497

 divide by how many they gave (7)

497 / 7 = 71

 answer is C 71 degrees

Answer:

c

Step-by-step explanation:

497 / 7 = 71

Which postulate or theorem can be used to prove that △ABC≅△ADC? ​ ASA Congruence Postulate ​ ​ SAS Congruence Postulate ​ ​ HL Congruence Theorem ​ ​ SSS Congruence Postulate ​

Answers

  Both the triangles ΔABC and ΔADC are congruent by SSS postulate of congruence.

From the picture attached,

In ΔABC and ΔADC,

AB ≅ AD (Given)

BC ≅ CD (Given)

AC ≅ AC (Reflexive property)

Since, corresponding sides of ΔABC are equal to ΔADC,

Therefore, ΔABC ≅ ΔADC (By S-S-S postulate of congruence)

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Mario fills out an information card. His Zip code is 83628. His area code is 208. What is the value of the 2 in comparison in 83,628 and 208

Answers

83620 the 2 is in the 10s place and on 208 the 2 is in the 100s place so the 2 in 208 is 10 times bigger than the 2 in 83620 I hope i'm right sorry if your not
Final answer:

The value of the digit 2 in both 83,628 and 208 is 200 because it is in the hundreds place in both numbers. The comparison shows that the absolute value of the digit 2 is the same in both cases despite being part of different overall numbers.

Explanation:

The value of the digit 2 in the numbers 83,628 and 208 represents different values because of its position in each number, which is determined by the place value system. In the number 83,628, the digit 2 is in the hundreds place, which means it represents 200. In the number 208, the 2 is in the hundreds place as well, so it also represents 200.

However, to understand the value of the 2 in comparison between the two numbers, you must consider the whole numbers. While the value of 2 as an individual digit is the same in both cases (200), the overall values of the numbers are different. In a more complex mathematical context, when comparing values within different numbers like this, the absolute value of the digits may be the same, but their contributions to the numbers they are part of can vary based on the other digits in the number.

Nonetheless, in this comparison, the two-digit 2s both contribute the same absolute value of 200 to their respective numbers because they are both in the hundreds place.

Two cab rides cost the same amount for the same number of miles, m. Which situation can be represented by the equation 2.50 + 0.50m = 1.00 + 0.75m?

Answers

One cab charges an initial fee of $2.50 and then $0.50 for every mile. The other cab company charges an initial fee of $1.00 and then $0.75 for every mile.

The value of m is 6 in the equation 2.50 + 0.50m = 1.00 + 0.75m.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given that Two cab rides cost the same amount for the same number of miles, m.

The given equation is 2.50 + 0.50m = 1.00 + 0.75m.

Two point five zero plus zero point five zero times m equal to one point zero plus zero point seven five times m.

First cab charges an initial fee of $2.50 and then $0.50 for every mile. The other cab company charges an initial fee of $1.00 and then $0.75 for every mile.

2.50 + 0.50m = 1.00 + 0.75m

2.50-1.00=0.75m-0.50m

1.5=0.25m

Divide both sides by 0.25

m=6

Hence, the value of m is 6 in the equation 2.50 + 0.50m = 1.00 + 0.75m.

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Select the classification of the polynomial using its degree and number of terms. 6x^3 The polynomial is classified as a

-cubic monomial
-quadratic monomial
-cubic trinomial

Answers

This expression has 1 term. Why? A term consists of a set of numbers with or without any basic operations. For example, Terms can be represented as 1x + 6. That is two terms because they are separated with an addition sign. So from that knowledge, let's see our options.

1.) Cubic Monomial. Cubic is any number raised to the third power. Since the x is raised to the third power, you can figure it out easily. This only has one term therefore, it is a Monomial. Monomial has a prefix of "Mono=One"

2.) Quadratic Monomial. There is no value raised to the 2nd power (Quadratic)

3.) This only has one term therefore cannot be a Trinomial (Three terms)


Number 1 is the best choice.

Four students wrote statements about cosecant, secant, and cotangent values as shown below.

Anik

The cosecant, secant, and cotangent of an acute angle may be greater than 1 or less than 1.


Isabella

The cosecant, secant, and cotangent of an acute angle are always greater than 1.


Kayla

The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.


Morris

The cosecant and secant of an acute angle may be greater than or equal to 1, but the cotangent of an acute angle is always less than 1.

Which student is correct?

Answers

Answer:

c Kayla is answer

Step-by-step explanation:

Since sine lies between-1 and +1 we have cosecant, reciprocal of sin lying always outside -1 and 1.

i.e. |cosec x|>1

For acute angle sine, cos , tan are positive

So cosec x >1 and similarly since cos x <1, sec x >1 always

But tanx varies between 0 and infinity for acute angles

Hence cot can take values from 0 to infinity

Hence the correct answer is that of Kayla

The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.

The statement about cosecant, secant, and cotangent values that is correct is Kayla's: The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.

What is the sine of an angle?

In Trigonometry, the sine of an acute angle is a ratio of the length of an opposite side of a right-angled triangle to the length of its hypotenuse.  Also, the sine of an angle generally lies between -1 and 1.

What is the cosecant (cosec) of an angle?

In Trigonometry, the cosecant (cosec) of an acute angle is a ratio of the length of its hypotenuse to the length of an opposite side of a right-angled triangle. Thus, the cosecant of an angle is the reciprocal of the sine function and as such lies outside -1 and 1.

What is the cotangent of an angle?

The cotangent of an acute angle is a ratio of the length of its adjacent side to the length of an opposite side of a right-angled triangle.

In conclusion, Kayla's statement about the values of cosecant, secant, and cotangent is correct.

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2000 geometry question im i correct

Answers

yes you are because I got the same.
Angle F is opposite the segment with one tick mark

Angle B is opposite the corresponding segment with a single tick mark.

This means angle B = angle F = 40 degrees

Side Note: we use SAS to prove the triangles congruent; then use CPCTC to find values of corresponding parts

Suppose you invest $2000 at an annual interest rate of 4.5%. how long will it take for it to earn $495?

Answers

100%:2000$=4.5%:x$, x=90$. After 1st year I earned 90$, now I have 2090$.
100%:2090$=4.5%:x$, x=94.5$. After 2nd year I earned 94.5$ more, now I have 2184.05$.
100%:2184.05$=4.5%:x$, x=98.28$. After 3rd year I have 2282.33$.
100%:2282.33$=4.5%:x$, x=102.71$. After 4th year I have 2385.04$.
100%:2385.04$=4.5%:x$, x=107.33$. After 5th year I have 2492.37$.

So I need 6 years to earn 495$.
Final answer:

To calculate how long it takes for an investment to earn a certain amount in simple interest, use the formula T = I / (PR), where I is the interest, P is the principal, R is the rate of interest, and T is the time. For a $2000 investment at 4.5% interest to earn $495, it would take approximately 5.5 years.

Explanation:

The subject of this question is Simple Interest. The formula for calculating simple interest is I = PRT, where I is the interest, P is the principal (the initial amount of money), R is the rate of interest per time period, and T is the time. In this case, we know the interest ($495), the principal ($2000), and the rate (4.5% or 0.045 as a decimal). We're trying to find out the time, so we rearrange the formula to T = I / (PR).

Substituting our known values, we get T = 495 / (2000 * 0.045). Doing the math, the time it takes for the investment to earn $495 is approximately 5.5 years.

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Round 35.78 to the nearest whole second

Answers

Round 35.78 to the nearest whole second
Answer: It is closer to 36 than it is to 35. So 36

This figure shows the procedure for constructing a
A. Pair of parallel lines
B. Bisector of an angle
C. Perpendicular from a point on a line
D. Perpendicular bisector

Answers

B. is your answer hope this helps.

Answer:

B

Step-by-step explanation:

An employee contributes $75 each month to her 401(k). What will be the value of her 401(k) after the 240th deposit (20 years) if the per annum rate of return is assumed to be 12% compounded monthly?

Answers

The value of her 401(k) will be 2,160 compounded monthly.
Final answer:

To calculate the value of the 401(k) after 240 deposits (20 years), you can use the formula for compound interest. Using the formula A = P(1 + r/n)^(nt), where A is the future value, P is the principal investment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years, you can plug in the values to find the answer.

Explanation:

To calculate the value of the 401(k) after the 240th deposit, we can use the formula for compound interest:

Formula: A = P(1 + r/n)^(nt)

Where:

A is the future value of the investmentP is the principal investment ($75 per month)r is the annual interest rate (12%)n is the number of times the interest is compounded per year (12 times for monthly compounding)t is the number of years (20 years)

Using these values, the formula becomes:

A = 75(1 + 0.12/12)^(12*20)

Calculating this expression will give us the value of the 401(k) after 20 years.

To which place value is the number rounded 6.706 to 6.71

Answers

100th becuz it’s in that spot specifically and might as well look it up too

PLEASE HELP!!!!!!!!!!
Whats the value of a?
a-2=3+6a/3
a=

Answers

Solve for a by simplifying both sides of the equation, then isolating the variable.

a = -5

Answer:

a–2=3 6a/3

So I was told The answer was -5 but all the people r wrong its -3

proof

Given that line bd is both the median and altitude of triangle abc, congruence postulate sas is used to prove that triangle abc is what type of triangle

Answers

isosceles triangle 

hope this helps :)

Answer:

Triangle ABC is an isosceles triangle.

Step-by-step explanation:

Let AD represent both the median and altitude of triangle  ABC.

A median divides the side in two equal parts so BD=BC.

An altitude is a perpendicular drawn .A perpendicular makes an angle of 90°. Hence <ADB=<ADC=90°

AD is the side common to both the triangles ADB and ADC.

Hence Δ ADB≅ΔADC by SAS congruence postulate.

So AB=AC by c.p .c .t.c(congruent parts of congruent triangles are congruent)

Hence by definition of Isosceles triangle ΔABC is an isosceles triangle.


In quadrilateral ABDC, AB ∥ CD. Which additional piece of information is needed to determine that ABDC is a parallelogram?

AB ≅ CD
AC ≅ BD
AB ⊥ BD
CD ⊥ BD

Answers

The answer is B AC ≅ BD Since you already know that ab ll cd, all you need to know is that ac is bd

Answer:

B. AC ≅ BD

Step-by-step explanation:

Since the definition of a parallelogram literally says that it's a quadrilateral with 2 parallel sides, we have AB || CD so the 2 other sides (AC and BD) need to be either similar or parallel (either works, due to that if they're similar we can prove that since AB || CD that they're parallel).

The equation 9.95 + 0.30s=c gives the cost c in dollars that a website charges for downloading songs. The variable s stands for the number of songs downloaded. Find the cost of downloading 35 songs

Answers

9.95 + 0.30s=c

 replaces s with 35

9.95 +0.30(35) =c

9.95 + 10.50 = 20.45

 it will cost $20.45

Select the postulate that is illustrated for the real numbers. 5 + (-5) = 0

The commutative postulate for multiplication
Multiplication by one
The addition inverse postulate
Commutative postulate for addition
The distributive postulate
The addition of zero postulate
The multiplication inverse

Answers

the answer is F.The addition of zero postulate

The addition inverse postulate explains the relationship between numbers like 5 and -5 that add up to zero, crucial for understanding real number properties.

The addition inverse postulate is illustrated by the expression 5 + (-5) = 0 for real numbers. This postulate states that for every number, there exists an additive inverse that when added together results in zero.

For example, in the given expression, 5 and -5 are additive inverses of each other, and when added, they cancel out to give zero, satisfying the addition inverse postulate.

This concept plays a crucial role in understanding the properties and operations of real numbers.

Why do two negatives equal a positive when adding?

Answers

Two negatives do not equal a positive when adding. If you're in debt and you add more debt, does that get you out of debt?

Two negatives do equal a positive when you're multiplying them together though. This makes sense if you imagine multiplication as squishing or stretching a particular number on the number line. For example, imagine multiplying 2 x 1/2 as squishing the number 2 two times closer to 0. When you multiply 2 by a negative number, say, -1, you squish it so far down that you flip it to the negative side of the number line, bringing it to -2. You can imagine a similar thing happening if you multiply a number like -4 by -2. You squish -4 down to zero, and then flip it to the positive side and stretch it by a factor of 2, bringing it to 8.

Mandy divided a 12-pound bag of sand into 5 equal pilss What is the weight of each pile

Answers

Mandy divided a 12 - pound bag of sand into equal piles. Is the weight of each pile. - 6045197.

which graph shows the inequality b≤-7

Answers

B) because a filled circle means the 
b≤-7 mean b is "less than or equal to 7"
the arrow to the left of seven is the "less" part and the filled circle is the "equal to" part.

I need help on this immediately. Please help me.

Answers

Short Answers (Explanation in next section below)

Reason A: Given

Reason B: Angle Addition Postulate

Reason C: Substitution Property

Reason D: Subtraction Property of Equality

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

Further Explanation:

Reason A: At the very top of the problem, it states "given: ..." with the given angle property. All we do for the first line of any proof is repeat what is given to us. It seems silly and redundant, but it is important. Whenever you do a proof you always start with what you're given (some fact or theorem already proven earlier) and you somehow try to connect it to what you are trying to prove. 

Reason B: The angle addition postulate is essentially the idea where we break up an angle into smaller pieces. This is probably better shown in a visual style instead of using words. Have a look at the attached image. Notice how the green angle ABD and the red angle DBE combine to form the purple angle ABE. Hopefully the image is clear enough. If not, then feel free to ask any questions. 

Reason C: We're using the substitution property here. If x = a and x = b, then we can say that a = b. That's what is going on but on a more complicated level. 

Reason D: We subtract the quantity "measure of angle DBE" from both sides. It is like going from x+2 = y+2 to x = y (subtract 2 from both sides). This is the subtraction property of equality in action. In general the rule is if a = b, then a-c = b-c

There are X giraffes at the zoo the number of elephants is 4 Less Than 3 times the number of giraffes and there are more than 23 elephants

Answers

 X   the number  of giraffes
the number of elephants is   3x -4 


3X - 4 > 23

3X > 23 + 4
3X > 27
X > 9
there are  more then 9 giraffes in the zoo.



What is 24 ten thousands in standard form

Answers

We have that the standard form of 24 ten thousands is

240,000

From the Question we are told that

24 ten thousands is given

Where

24 ten thousands=24*10000=240,000

Generally the standard form of 24 ten thousands is

240,000

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An urn contains 3 green balls, 2 blue balls, and 4 red balls. in a random sample of 5 balls, find the probability that at least one blue balls is selected.

Answers

Well, it depends. If you take one, do you leave it out, or put it back?? If you leave the ball in, then the probability would be 0.05419228% or 32/59049 but if you put the ball out of the urn, then the probability would be 0.211640211% or 32/15120. YOU'RE WELCOME :)

Final answer:

To find the probability of at least one blue ball being selected from an urn with green, blue, and red balls in a sample of 5, calculate the probability of not selecting any blue balls and then subtract it from 1.

Explanation:

An urn contains 3 green balls, 2 blue balls, and 4 red balls. In a random sample of 5 balls, find the probability that at least one blue ball is selected.

Calculate the probability of not selecting any blue balls: P(no blue) = (7/9) * (6/8) * (5/7) * (4/6) * (3/5) = 0.167

Find the probability of at least one blue ball: P(at least one blue) = 1 - P(no blue) = 1 - 0.167 = 0.883

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