The formula for the circumference of a circle (or a sphere) is [tex]2\pi r\\[/tex].
The formula the volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex].
Assuming 43.4 includes the pi, we can do the equation [tex]43.4=2\pi r[/tex]
Solving the equation, we get [tex]\frac{43.4}{2\pi } =r[/tex]
Substituting r into the formua for the volume of a sphere, we get [tex]\frac{4}{3} *\pi *(\frac{43.4}{2\pi } )^3[/tex]
Solving the cube (probably with a calculator), we get [tex]\frac{4}{3} *\pi *\frac{81746.504}{8\pi ^3}[/tex]
It is a bit messy, but we can simplify further by cancelling out the pi's, which leaves us with [tex]\frac{4}{3} *\frac{81746.504}{8\pi ^2}[/tex].
With the butterfly method (or whatever you may call it), we can cancel out the 4 in the numerator and the 8 in the denominator, and multiply the 3 in the denominators.
Which gets us this: [tex]\frac{81746.504}{6\pi ^2}[/tex]
Using a calculator, we get our final answer of (about) 1380.44cm^3
This was very messy, I apologize if I did make any mistakes.
y=|x-3|+|x+2|-|x-5| if x < -2
what does y equal
Answer:
y= |x-3|+ |x+2|-|x-5|; x<-2
y=-2
What is a necessary step for constructing perpendicular lines through a point on a line?
O Draw a line that intersects the first line at an acute angle using a straightedge.
O Draw a ray that intersects the first line at an acute angle using a straightedge.
Draw arcs on either side of a given point on the line,
Draw ares on either sig, of a given point of the line
A necessary step for constructing perpendicular lines through a point on a line is D. Draw arcs on either side of a given point of the line.
What is a perpendicular line?A perpendicular line simply means the lines that intersect at 90 degrees.
In this case, a necessary step for constructing perpendicular lines through a point on a line is to draw arcs on either side of a given point of the line. This can be done by opening the compass bans marking two points of intersection between the arcs in a given line.
Learn more about perpendicular lines on:
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Answer:nj
Step-by-step explanation:
j
Angelina wins money in a competition. She is given the choice as to how she is paid.
Choice 1: Get $1 the 1st day, 2$ the 2nd day, $4 the 3rd day, 8$ the 4th day, and so on
Choice 2: Get 1,000,000 today.
a) With which method of payment will angelina get more money?
c) After how many days will the money Angelina gets from Choice 1 be approximately $1, 000, 000?
Answer:
Choice 120 daysStep-by-step explanation:
You are being asked to compare the value of a growing infinite geometric series to a fixed constant. Such a series will always eventually have a sum that exceeds any given fixed constant.
__
a)Angelina will get more money from the Choice 1 method of payment. The sequence of payments is a (growing) geometric sequence, so the payments and their sum will eventually exceed the alternative.
__
c)For a first term of 1 and a common ratio of 2, the sum of n terms of the geometric series is given by ...
Sn = a1×(r^n -1)/(r -1) . . . . . . . . . . series with first term a1, common ratio r
We want to find n such that ...
Sn ≥ 1,000,000
1 × (2^n -1)/(2 -1) ≥ 1,000,000
2^n ≥ 1,000,001 . . . . add 1
n ≥ log(1,000,001)/log(2) . . . . . take the base-2 logarithm
n ≥ 19.93
The total Angelina receives from Choice 1 will exceed $1,000,000 after 20 days.
What is the coordinate of the midpoint of AB?
Answer:
(5,4)
Step-by-step explanation:
that is directly between the two points
A farmer has some cows and horses. All the animals are either brown or black. The table shows how many of each
animal is on the farm.
one animal is selected randomly. what is the probability of chowing a horse given that they are brown? round answer to nearest hundredth.
Answer:
P = 1/5 = 0.20 = (20%)
Step-by-step explanation:
there are 12 horses and 8 cows, in total there are 20 animals
of which 4 horses are brown
Then
[tex]P=\frac{4}{20} =\frac{1}{5}[/tex]
Hope this helps
Luke drove 150 miles in 3 hours. at this rate how long will it take him to drive 250 mmiles
Answer: 4 1/2 hours
Step-by-step explanation:
if it takes luke 3 hours to drive 150 miles that means in 6 hours he would have driven 300 miles.
he drives 50 miles per hour
so 250 miles is 4 1/2
Help!!! 8. Determine whether each pair of functions f and g are inverses. Explain your reasoning.
Answer:
(b) is inverse while (a) is not inverse.
Step-by-step explanation:
we can see this since the values of x and y should flip if the function is inverse. we see this in (b) but not in (a).
help pls
tysm in advance
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-We have given some information in the above table To Find :-We have to find the mean, median and mode of the given data. Let's Begin :-For completion of table you should know the basics formulas :-
For calculating x( mid point)[tex]\sf{=}{\sf{\dfrac{Sum \:of\: class \:interval }{ 2}}}[/tex]
That is,
[tex]\sf{=}{\sf{\dfrac{ = 18 + 25}{2}}}[/tex]
[tex]\sf{=}{\sf{\dfrac{ = 43}{2}}}[/tex]
[tex]\sf{= 21.5 }[/tex]
[ For more calculation ,Please refer the attachment ]
For calculating fx Multiply frequency and midpoint[tex]\sf{ fx = frequency {\times} midpoint }[/tex]
[tex]\sf{ fx = 8 {\times} 21.5 }[/tex]
[tex]\sf{ fx = 172 }[/tex]
[ For more calculation please refer the attachment ]
Now,We have to calculate mean, median and mode of the given data
For meanWe know that the,
Mean = Sum of all observation / no. of observation
That is
[tex]\sf{ Mean = }{\sf{\dfrac{ {\sigma}fx}{{\sigma}x}}}[/tex]
Subsitute the required values,
[tex]\sf{ Mean = }{\sf{\dfrac{ 1811 }{ 187.5}}}[/tex]
[tex]\sf{ Mean = 9.65}[/tex]
Hence, The mean of the given data is 9.65
For MedianWe know that, For odd numbers
[tex]\sf{ Median = l + }{\sf{\dfrac{ (n/2 - c)}{ f}}}{\sf{ h }}[/tex]
Here,
[tex]\sf{ n = }{\sf{\dfrac{ 50 + 1}{ 2}}}[/tex]
[tex]\sf{ n = }{\sf{\dfrac{ 50 }{ 2}}}[/tex]
[tex]\sf{ n = 25 }[/tex]
Lower limit = 34c = 20f = 14h = 41 - 34 = 7Subsitute the required values in the above formula :-
[tex]\sf{ Median = 34 + }{\sf{\dfrac{ (25-20)}{ 14}}}{\sf{ 7 }}[/tex]
[tex]\sf{ = 34 + }{\sf{\dfrac{ 5}{ 14}}}{\sf{ {\times}7 }}[/tex]
[tex]\sf{ = 34 + }{\sf{\dfrac{ 35}{ 14}}}[/tex]
[tex]\sf{ = 34 + 2.5}[/tex]
[tex]\sf{ = 36.5 }[/tex]
Hence, The median of the given data is 36.5 .
For ModeWe know that,
[tex]\sf{ M= l }{\sf{\dfrac{ (f1 - fo)}{ 2f1 - fo - f2 }}}{\sf{ {\times} h }}[/tex]
lower limit = 34 f1 = 14fo = 12f2 = 12H = 7Subsitute the required values,
[tex]\sf{ M= 34 }{\sf{\dfrac{ (14 - 12)}{ 2(14)- 12 - 12 }}}{\sf{ {\times} 7 }}[/tex]
[tex]\sf{ M= 34{\times}}{\sf{\dfrac{ 2}{ 28 - 24 }}}{\sf{ {\times} 7 }}[/tex]
[tex]\sf{ M= 34{\times}}{\sf{\dfrac{ 2}{ 4 }}}{\sf{ {\times} 7 }}[/tex]
[tex]\sf{ M= 34{\times}}{\sf{\dfrac{ 1}{ 2 }}}{\sf{ {\times} 7 }}[/tex]
[tex]\sf{ M= 34{\times}}{\sf{\dfrac{ 7}{ 2 }}}[/tex]
[tex]\sf{ M= 34 + 3.5 }[/tex]
[tex]\sf{ M= 37.5 }[/tex]
So,
Mode = 37.5Hence ,The mode of the given data is 37.5 .
Please answer ASAP! I am very confused. Please explain steps if possible.
Answer:
943 exponent 14
Step-by-step explanation:
The question deals with indices(exponents). Therefore,all laws of indices related to the question must be applied to clearly solve and understand the question.
so,(943 exponent 78 · 943 exponent 1)/943 exponent 65
· means multiplication so simply,(943 exponent 78 × 943 exponent 1)/943 exponent 65
The laws of indices clearly state that, when two indices of the same base are multiplying, you add their exponents and when dividing,you subtract their exponents.
As all the indices have the same base which is "943", we can quickly add & subtract the exponents.
(Leaving base out of calculation now to make it easier to directly deal with exponents)
(78+1)-65(From the rules)
79-65=14,which means 943 exponent 14
∴The answer is 943 exponent 14
PYTHAG THEOREM!
Aubrey is building a slide for her kids. If the ladder is 6 feet tall and she wants the bottom of the slide to be 5 feet from the ladder, how long does the slide need to be? If necessary, round to the nearest tenth.
Answer:
sqrt(11)
Step-by-step explanation:
a^2+b^2 = c^2
a = 5
c = 6
b = ?
25 - b^2 = 36
36 - 25 = b^2
b = sqrt(11)
The ladder should be 7.81 feet long.
What is Pythagoras theorem?Pythagoras theorem tell us the relation between the sides of a right-angled triangle, it states, the sum of the squares of the base and perpendicular is equal to the square of the hypotenuse.
Given that, Aubrey is building a slide for her kids. If the ladder is 6 feet tall, and she wants the bottom of the slide to be 5 feet from the ladder,
This slide is in the form of a right triangle, therefore applying the Pythagoras theorem, we have,
a²+b² = c² (refer to the figure attached)
5²+6² = c²
c² = 25+36
c² = 61
c = √61
c ≈ 7.81
Hence, the length of the slide should be 7.81 feet.
For more references on Pythagoras theorem, click;
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25 % of what number is 5.
SHOW YOUR WORK!!!!
Answer:
The answer is 1.25
Step-by-step explanation:
5% of 25 = ?
5/100 × 25
1/20 × 25 = 25/20 = 5/4 = 1.25
Thus, 5% of 25 is 1.25
for what values of A does the acute angle formed by the lines 3x+2y=10 and Ax-2y=3 have measure of 45 degree
Answer:
Step-by-step explanation:
What time will it take to obtain double of the interest on Rs. 2000 for 3 years at the rate of 15% per annum?
Answer:
6 years
Step-by-step explanation:
Given values :
Principal amount = Rs. 2000Time period = 3 yearsRate = 15% per annumTo Find :
Time taken to obtain twice the interestSolving :
First, find the interest.I = PrtI = 2000 x 0.15 x 3I = 6000 x 0.15I = Rs. 900 So twice the interest = Rs. 1800Now using the [I = Prt] formula,t = I/Prt = 1800/(2000 x 0.15)t = 1800 / 300t = 6 yearsThe question is in the image. I really need help, please.
Answer:
(b) 65/27
Step-by-step explanation:
Here, we notice the index for the summation runs from 0 to 3, so there are a total of 4 terms.
The sum represented by the summation symbol is ...
5(-2/3)^0 +5(-2/3)^1 +5(-2/3)^2 +5(-2/3)^3
= 5(1 -2/3 +4/9 -8/27)
= 5/27(27 -18 +12 -8)
= 5(13/27) = 65/27
__
There is a formula for the sum of a geometric series:
Sn = a1×(1 -r^n)/(1 -r)
Here, the first term is a1 = 5(-2/3)^0 = 5. The common ratio is the base of the exponential, r = -2/3. So, the sum of n=4 terms is ...
S4 = 5×(1 -(-2/3)^4)/(1 -(-2/3)) = 5×(1 -16/81)/(5/3) = 65/27
Help please
What is 600 square feet converted to square yards?
Answer:
66.6667
Step-by-step explanation:
100% correct mark brainliest
use the order of operations to simplify the left side of the inequality below. What values of x make the inequality a true statement? -1/2 (3^(2)+7) x>32
Answer:
x<−0.00325153
x> 0.00325153
Step-by-step explanation:
-1/2 (3^(2)+7) x >32
-1/2 (3^(9) x >32
-1/2 (19683) x >32
-9841.5 x >32
x<−0.00325153
x> 0.00325153
A bank is offering 2.5% simple interest on a savings account. if you deposit $5000,how much interest will you earn in one year?
Answer:
$125 you will end up w/ $5125
Step-by-step explanation:
(20 points!) (photo attached for context)
Line segment ST is congruent to which line segment?
Help me with this pls it’s due on Monday :)
Answer:
area of trapezium=1/2 h(length 1+length2)
1/2*5*(13+6)
1/2*5*19
Answer:
Area = 47.5cm^{2}
Step-by-step explanation:
Area = 1/2 (a+b) × height
Area = 1/2 (6 + 13) × 5
Area = 1/2 (19) × 5
Area = 47.5cm^{2}
There are ten balls in a bag. Three balls are black and seven balls are white. a One ball is chosen at random and then replaced. Then a second ball is chosen at random. Here are two events. D: the first ball is black S: the second ball is black Are D and S independent? Show your working.
Answer:
Given:
Total balls = 10Black balls = 3White balls = 7⇒ P(black ball) = 3/10 = 0.3
⇒ P(white ball) = 7/10 = 0.7
If one ball is chosen at random and replaced, the probabilities do not change between the first and second ball.
Let event D = first ball is black
Let event S = second ball is black
P(D) = 0.3
P(S) = 0.3 (since the first ball is replaced)
⇒ P(D ∩ S) = P(D) × P(S)
= 0.3 × 0.3
= 0.09
For Independent Events we know that: P(A ∩ B) = P(A) × P(B)
Therefore, as P(D ∩ S) = P(D) × P(S) the events are independent.
A swimsuit is on sale for $29.75. If the original price of the swimsuit is $35, what is the percent of the discount?
A. 2%
B. 5%
C. 15%
D. 17%
Answer:
C. 15%
Step-by-step explanation:
35 * 0.15 = 5.25
35 - 5.25 = 29.75
A percentage is a way to describe a part of a whole. The percentage of discount on the swimsuit is 15%.
What is the Percentage?A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
We know that the cost of the swimsuit is $29.75, while the original cost of the swimsuit is $35. Now, after the discount the price will be a percentage of the original, therefore, the discounted price can be written as,
Discounted Price = x% of Original Value
[tex]29.75 = \dfrac{x}{100} \times 35\\\\x = 85[/tex]
Now, as we know that the discounted price is 85% of the original price, therefore, the price will have a 15% discount(100%-85%).
Hence, the percentage of discount on the swimsuit is 15%.
Learn more about Percentages:
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Eight times x is less than or equal to 29
Translate the sentence into an inequality
[tex]8x \leqslant 29[/tex]
Answer:
8x ≤ 29
Step-by-step explanation:
The reason why is because, 8 times 'x' also means 8 multiplied by x.
The words less than or equal to mean ≤, this is because the less than sign (<) denotes that the product of 8 and 'x' is below 29 and the line underneath the less than sign (<) means that it is equal to.
What’s 70x56,000+65,000,000
What are the solution(s) for the following quadratic equation?
f(x)=5x^2+2x-7
Please show work!
[tex]\\ \rm\rightarrowtail 5x^2-2x-7=0[/tex]
[tex]\\ \rm\rightarrowtail 5x^2-7x+5x-7=0[/tex]
[tex]\\ \rm\rightarrowtail x(5x-7)+1(5x-7)=0[/tex]
[tex]\\ \rm\rightarrowtail (x-1)(5x-7)=0[/tex]
[tex]\\ \rm\rightarrowtail x=1,7/5[/tex]
please help with word problems.
Answer:
I am sorry but u didn't really ask any question to be answered so next time give a question to be answered
Use the discriminant to find the number of x-intercepts of the graph of the function.
y = x2 + 3x
Answer:
2 x-intercepts
Step-by-step explanation:
Standard form of quadratic equation: [tex]\sf y=ax^2+bx+c[/tex]
Given equation: [tex]\sf y=x^2+3x[/tex]
Therefore:
a = 1b = 3c = 0Discriminant: [tex]\sf b^2-4ac[/tex]
Substituting values into discriminant:
[tex]\sf \implies 3^2-4(1)(0)=9[/tex]
As discriminant > 0 then 2 real roots (2 x-intercepts)
A study was conducted of 351 species of mammals worldwide. The
scientists conducting the study found that 140 species could be
found in Asia and 94 species could be found in Africa, and of those,
22 could be found in both continents.
What is the probability of randomly selecting a species of mammal
that is neither found in Asia nor Africa? Write your answer as a
fraction.
Answer:
95/351
Step-by-step explanation:
the first thing you must do is to add 140 and 94 and 22 together
you get 256
then you subtract 351 with 256 and get 95
and then you do this
95/351
which of the values shown are potential roots of f(x)=3x^3-13x^2-3x+45? Select all that apply
Answer: 3 and 5 (b and g)
Step-by-step explanation:
I got it correct on Edge
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
75, 90, 108, ...
Find the 7th term.
The 7th term of the sequence to the nearest thousandth is 223.949
What are geometric sequences?These are sequence that increases in an exponential form.
The formula for calculating the nth term of a geometric sequence is expressed as:
Tn = ar^n-1
Given the following parameters
a = 75
r = 1.2
n = 7
Substitute the given parameter into the formula
T7 = 75(1.2)^6
T7 = 223.949
Hence the 7th term of the sequence to the nearest thousandth is 223.949
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Alexis bought 50 collectible stamps at a garage sale. Each week, she purchases 30 stamps to add to her
collection. How many weeks will she need to purchase stamps to have more than 500 stamps?
Answer:
14 (exactly 500) or 15 (over 500)
Step-by-step explanation:
We know that Alexis has already bought 50 stamps.
50 + 30 = 80
We need to subtract to see how many stamps she needs.
500 - 80 = 420
We divide by 30 to see about how many weeks it would take.
420 / 30 = 14
We can add 1 more week because she wants to have more than 500 stamps.
hope this helps :)