Answer:
V = (4/3)π·5³ = 500π/3
Step-by-step explanation:
The formula for the volume of any sphere as a function of its radius is ...
V = (4/3)π·r³
When the sphere has a radius of 5, we replace r in the formula with 5. The formula for the volume of a sphere with radius 5 is ...
V = (4/3)π·5³
__
When that is evaluated, the volume is found to be ...
V = 500π/3 ≈ 523.599 . . . cubic units
Regis leans a 10-foot ladder against a wall. The base of the ladder makes a 65 angle with the ground.
(a)
What is the distance, In feet, from the base of the ladder to the base of the wall? Round to the nearest tenth of a foot.
(b) Regis needs to move the ladder so that it reaches a window 9.6 feet above the ground.
How many feet closer to the building does he need to move the base of the ladder?
The distance, In feet, from the base of the ladder to the base of the wall is 4.2 ft.
He needs to move the ladder 0.1 ft closer to the base of the building.
The situation forms a right angle triangle.
Right angle triangleRight angle triangle has one of its angles as 90 degrees. The sides and angle can be found using trigonometric ratios.
The length of the ladder is the hypotenuse of the triangle formed. Therefore, the distance, In feet, from the base of the ladder to the base of the wall can be calculated as follows;
cos 65° = adjacent / hypotenuse
cos 65° = d / 10
d = 10 × 0.42261826174
d = 4.22618261741
d = 4.2 ft
She needs to move the ladder so it reached a window 9.6 feet above the ground. Therefore, the distance from the base of the ladder and the wall is as follows;
cos 65 = d / 9.6
d = 9.6 × 0.42261826174
d = 4.05696
d = 4.1
Therefore, he needs to move the ladder 0.1 ft closer to the building.
learn more on right angle triangle here: https://brainly.com/question/14988069
Help anyonee?? 100 points!!
Answer:
D
Step-by-step explanation:
[tex]4\sqrt{x2[/tex] means [tex](x^{2})^{\frac{1}{4} }[/tex] so then according to indices rule, the powers will be multiplied. Do the same thing for y and z as well, and you will get the answer
The number 28,363,775 rounded to the nearest ten thousand is
Answer:
50,000
Step-by-step explanation:
Just put it in the answer lol :p
Answer:
28,360,000
Step-by-step explanation:
The number after the 6 (the ten thousands is 3, so it rounds down to 28, 360, 000.
please give brainliest!
please help me solve for m<C and m<D
Answer:
Step-by-step explanation:
Use law of cosine to calculate the other side.
c² = a² + b² -2ab Cos C
Here, c is the length of the side which is opposite side to ∠E
a = 29 ; b = 25 and C = 109
c² = 29² + 25² - 2*29*25*Cos 107
= 841 + 625 - 1450* (-0.2923)
= 1466 + 423.835
= 1889.835
c =√1889.835
c = 43.47 ≈ 43
No, find ∠D using again use law of cosine
[tex]Cos \ \beta = \dfra{a^{2}+c^{2}}-b^{2}{2ac}\\\\\\ = \dfrac{29^{2}+43^{2}-25^{2}}{2*29*43}\\\\\\Cos \ \beta =\dfrac{841+1849-625}{2494}=\dfrac{2065}{2494}\\\\Cos \ \beta = 0.828\\\\\beta =Cos^{-1} \ 0.828\\\\[/tex]
β = ∠C = 34°
α = 180 - (34 +107)
α = ∠D = 39
Other angles are
∠C = 34° and ∠D°39
What is the approximate volume of a cone with a height of 9 ft and radius of 3 ft? Use 3.14 to approximate pi, and express your final answer to the nearest hundredth Enter your answer as a decimal in the box. ft3
spherical water tank of radius R = 5m is emptied through a small circular hole of radius r = 0.03 m at the bottom. The top of the tank is open to the atmosphere. The instantaneous water level h in the tank (measured from the bottom of the tank, at the drain) can be determined from the solution of the following ODE:
dh /dt =r²(2gh)^0.5/ 2hR-h²
where g = 9.81 m/s². If the initial (t = 0) water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.
Answer:
water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.
Step-by-step explanation:
water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.
Please help I'll mark brainliest
what is 3.1 converted into a simplified fraction?
Answer:
31/10
Step-by-step explanation:
Please answer this relatively quickly, I'm not in very much of a rush but would like to get this done.
Answer: 6
Step-by-step explanation:
Because you have to multiply then remove the fraction and set equal to 0 and solve for x which I’m pretty sure gives u 6
If my dot plot is not skewed or symmetrical which measure of variability should I use? (15 data points) PLEASE HELP THE ASSIGNMENT IS DUE TONIGHT!
these are the data points: 5,6,7,7,7,8,8,9,9,9,9,9,10,10,11
I also need the best measure of center!
If the data is not skewed, then the mean is the best measure of center.
This then also includes the standard deviation because the standard deviation relies on the mean.
To get the mean, add up the data values:
5+6+7+7+7+8+8+9+9+9+9+9+10+10+11 = 124
Then divide by the sample size n = 15
124/n = 124/15 = 8.267 approximately
Once you determine the mean, you can then determine the standard deviation which involves a bit more complicated steps. The rough outline is:
Subtract each data value from the mean. So right off the bat, we can see how important the mean is when it comes to calculating the standard deviation.Square those differences from step one.Add up the squares to get the Sum of the Squared Errors (SSE)Divide the SSE by n-1 to get the sample variance, or divide by n to get the population variance. It will depend on context which version you go for.Apply the square root to the variance to get the standard deviation.Once again, step 1 shows how critical the mean is to finding the standard deviation. The standard deviation measures how far each value is from the mean on average. In other words, it's like a measure of the average distance from the mean.
Use of spreadsheet software is strongly recommended to keep track of everything. You can also use a standard calculator to compute the standard deviation. There are also tons of free online calculators that can help out with that as well.
-----------------------------------------------------------
If the data was skewed to one side, then the median is the better measure of center because it is not affected by outliers. The IQR (interquartile range) is used instead of the standard deviation for skewed distributions.
After eating a meal at a restaurant, we decided to tip 25%, building a grand total of $87.50. What was the price before the tip?
Answer:
65.62
Step-by-step explanation:
Given:
After eating a meal at a restaurant, we decided to tip 25%, building a grand total of $87.50.
To find:
Price before tip
Solution:
87.50 × 25% = 21.875
~Round~: 21.875 to 21.88
87.50 - 21 .88 = 65.62
Thus the price before the tip is 65.62
Check Answer:
Formula: Higher number - Lower number ÷ original number × 100
Solve:
87.50 - 65.62 = 21.88
21.88 ÷ 87.50=0.25005714285
0.25005714285 × 100 = 25.0057142857
Round - 25%
~lenvy~
At Daniel's Swimwear, there are 76 bikini styles and 4 other types of swimsuit. What percentage of the swimsuit styles are bikinis?
Total swimwear = 76 bikinis + 4 other types = 80 total
divide number of bikinis by total swimwear then multiply by 100:
76/80 = 0.95
0.95 x 100 = 95%
Answer: 95% are bikinis
3/9 and 1/2 common denominator
Given:
[tex]\frac{3}{9}[/tex] and [tex]\frac{1}{2}[/tex]
Finding a common denominator:
9 * 2 = 18
-> If you need to stop here, a common denominator is 18.
Converting [tex]\frac{3}{9}[/tex]:
[tex]\frac{3}{9}[/tex] = [tex]\frac{3*2}{9*2}[/tex] = [tex]\frac{6}{18}[/tex]
Converting [tex]\frac{1}{2}[/tex]:
[tex]\frac{1}{2}[/tex] = [tex]\frac{1*9}{2*9}[/tex] = [tex]\frac{9}{18}[/tex]
-> [tex]\frac{6}{18}[/tex] and [tex]\frac{9}{18}[/tex]
55% of 70 =
I want to know for my hw
Answer:
38.5
Step-by-step explanation:
70*(0.55) = 38.5
Answer:
Step-by-step explanation:
To find 55% of 70, we need to write an equation.
this equation will be 55x70/100
now, the answer to 55x70 / 100 is
38.5
We get this answer, because 55x70=3850
and 3850 divided by 100 is 38.5
please answer the following questions
Answer:
False
Step-by-step explanation:
There are some quadratic equations that cannot be solved using the factoring technique. That is why the quadratic formula exists, to solve equations that cannot be factored.
A 10-inch tire has a diameter of 10 inches. What is the circumference of these tires?
Answer:
31.4
Step-by-step explanation:
diameter (d) = 10
circumference = (3.14)d
= (3.14)10 = 31.4
circumference = 31.4
for each of the figures, write an absolute value equation that has the following solution set 3 and 7
The solution set 3 and 7 are the true values of the absolute value equation
The absolute value equation that has a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]
How to determine the absolute value equation?The solution sets of the absolute value equation are given as:
x = {3, 7}
Calculate the mean of the solutions
[tex]x_1 = \frac{7 +3}{2}[/tex]
[tex]x_1 = 5[/tex]
Calculate the difference of the solutions divided by 2
[tex]x_2 = \frac{7 - 3}{2}[/tex]
[tex]x_2 = 2[/tex]
The absolute value equation is the represented as:
[tex]|x - x_1| - x_2 = 0[/tex]
Substitute known values
[tex]|x - 5| - 2 = 0[/tex]
Add 2 to both sides
[tex]|x - 5| = 2[/tex]
Hence, the absolute value equation that has the a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]
Read more about absolute value equation at:
https://brainly.com/question/2166748
What is the value of n in the equation below?
Answer:
9
Step-by-step explanation:
12ⁿ⁻⁵ = 12⁴
n - 5 = 4
n = 9
what is 0.0981 rounded to the nearest tenth of a percent
Answer:
0.1 percent
Step-by-step explanation:
sorry I don't have an explanation. sorry if it's wrong, at least I tried
Answer:
0.1
Explanation:
It's right
Choose the multiplication problem that correctly shows partial products.
A) A
B) B
C) C
Answer:
B) B
Step-by-step explanation:
2 times 4 is 8, so in this case the option is option b as none of the other options show this.
In total,
2 * 4 = 8
60 * 4 = 240
240 + 8 = 248
Can someone help me out!
Answer:
option c
Step-by-step explanation:
This is the net of square pyramid.
Base of the square pryamid is square and all the other face are triangle.
How many factors do numbers of the form p^n and q^m have if p and q are two different prime numbers and m and n are natural numbers?
The only common factor between these two numbers will be 1.
How many factors do these numbers share?
Remember that any number can be decomposed as a product of prime numbers. For example for 18 we have:
18 = 2*3*3
There 18 is written as a product of its prime factors.
Now, for our case of p^n and q^m we will have:
p^n = P = p*p*p...*p n times.
q^m = Q = q*q*q*...*q m times.
Now, notice that because q and p are primes, there is no common factor in these two decompositions. (and we can't decompose it furthermore). Then we conclude that the only factor that these numbers share is the trivial one, which is 1.
If you want to learn more about prime numbers, you can read:
https://brainly.com/question/145452
Natalie has 112 boxes she left 105 five boxes and she found 20 boxes how much dose she have?
Answer:
27 boxes.
Step-by-step explanation:
This situation can be represented by the equation:
(112 - 105) + 20 = ?
First we subtract 105 from 112:
112 - 105= 7
Now add 20.
7 + 20 = 27
Natalie has 27 boxes now.
Katie ate dinner at a restaurant. The bill came to $77. If she left an 18% tip, how much was the tip?
Can someone pls help me?
Answer:
$13.86
Step-by-step explanation:
Just multiply 77 by 18 percent as a decimal (.18) to get the answer, which is $13.86
Hopefully this helps- let me know if you have any questions!
What is the value of y in the equation 4x +3 y= 23 when x=2 , x=6
Answer:
5, -⅓
Step-by-step explanation:
x = 2:
4x + 3y = 23
3y = 23 - 4(2)
3y = 15
y = 5
x = 6:
4x + 3y = 23
3y = 23 - 4(6)
3y = -1
y = -⅓
if the log↓b(a)=0, what is the value of a?
explain why log↓0 (3) and log↓1 (3) do not exist.
Answer:
1. a = 1
2. See explanation below.
Step-by-step explanation:
First Question
Given:
[tex]\displaystyle \large{\log_b a = 0}[/tex]
Convert to exponential:
[tex]\displaystyle \large{\log_b a = c \to b^c = a}[/tex]
Thus [tex]\displaystyle \large{\log_b a = 0 \to b^0 = a}[/tex]
Evaluate:
[tex]\displaystyle \large{b^0 = a}[/tex]
We know that for every values to power of 0 will always result in 1, excluding 0 to power of 0 itself.
Solution:
[tex]\displaystyle \large{a = 1}[/tex]
__________________________________________________________
Second Question
Given:
[tex]\displaystyle \large{log_0 3}[/tex] and [tex]\displaystyle \large{\log_1 3}[/tex]
Let’s convert to an equation:
[tex]\displaystyle \large{\log_0 3 = x}[/tex] and [tex]\displaystyle \large{\log_1 3 = y}[/tex]
The variables represent unknown values of logarithm.
Convert to exponential:
[tex]\displaystyle \large{0^x = 3}[/tex] and [tex]\displaystyle \large{1^y = 3}[/tex]
Notice that none of x-values and y-values will satisfy the equations. No matter what real numbers you put in, these equations will always be false.
Hence, no solutions for x and y.
The longer leg of a right triangle is 1 cm longer than the shorter leg. The hypotenuse is 9 cm longer than the shorter leg. Find the side lengths of the
triangle.
cm
Length of the shorter leg: 0
Length of the longer leg: 0
Length of the hypotenuse: 0
cm
cm
Answer:
Shorter leg = 20 cm.
Longer leg = 21cm.
Hypotenuse = 29 cm
Step-by-step explanation:
Let the shorter leg be x cm long
Then longer leg = x + 1 and hypotenuse = x + 9 cm long
So by Pythagoras:
x^2 + (x + 1)^2 = (x + 9)^2
0 = x^2 + 18x + 81 - x^2 - (x^2 + 2x + 1)
x^2 + 18x + 81 - x^2 - x^2 - 2x - 1 = 0
-x^2 + 16x + 80 = 0
x^2 - 16x - 80 = 0
(x - 20)(x + 4) = 0
So x = 20 (we ignore the negative root).
So longer leg = 20 + 1 and hypotenuse = 20 + 9.
Kala drove 603 miles in 9 hours at the same rate how many miles would she drive in 12 hours
Answer:
804
Step-by-step explanation:
603/9 x 12
67 x 12
804
Answer:
804 miles in 12 hours
Step-by-step explanation:
603/9 which = 67
67*12 which equal 804
don't forget the unit (mph)
Need help, Brainliest if correct only…. dont answer if you don’t know. Thank u!
Answer:
3/1
Step-by-step explanation:
In triangle ABC, the known side is AC, which is equal to 6. The corresponding side to AC from triangle DEF would be FD, which is equal to 2. You divide 6/2 in order to get 3/1.
A model of Earth is located 7600 meters from the Globe Arena in Sweden’s solar system model. The volume of the model is approximately 3052.08 cubic centimeters. What is the length of the radius of the Earth model?
The length of the radius of the mudel is 9 cm
Step-by-step explanation:[tex]By\ the\ topic[/tex]
[tex]The\ volume\ of\ the\ mudel\primes\ is\ 3052.08{\rm cm}^3[/tex]
[tex]Formula\ for\ the\ volume\ of\ the\ sphere\ is[/tex]
[tex]\frac{4}{3}\pi\ r^3[/tex]
[tex]\frac{4}{3}\pi\ r^3=3052.08[/tex]
[tex]\pi\ r^3=\frac{3}{4}\times3052.08=2289.06[/tex]
[tex]\gamma3=2289.06\div\pi[/tex]
[tex]\gamma=\sqrt{\frac{2289.06}{\pi}}\approx\sqrt{\frac{2289.06}{3.14}}+\sqrt{729}[/tex]
[tex]r=9cm[/tex]
[tex]7hus,\ the\ length\ of\ the\ vadius\ of\ eanth[/tex]
[tex]mudel\ is\ 9\ cm[/tex]
[tex]Application\ of\ the\ volume\ of\ the\ spheve?[/tex]
I hope this helps you
:)