Answer:
2 /3 +5 = 3
5.666667≠3
False
Step-by-step explanation:
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Lets do this step by step.
~~~~~~~~~~~~~~~~~~~~
Multiply both sides of the equation by [tex]\frac{3}{2}[/tex] .
[tex]\frac{3}{2} . \frac{2}{3} . x = \frac{3}{2} . 5[/tex]
Simplify both sides of the equation.
~~~~
Simplify [tex]\frac{3}{2} . \frac{2}{3} . x .[/tex]
[tex]x = \frac{3}{2} . 5[/tex]
Multiply [tex]\frac{3}{2} . 5[/tex]
[tex]x = \frac{15}{2}[/tex]
The result can be shown in multiple forms.
Exact Form: [tex]x = \frac{15}{2}[/tex]
Decimal Form: [tex]x = 7.5[/tex]
Mixed Number Form: [tex]x = 7\frac{1}{5}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
A 25-foot ladder is placed against a building and the top of the ladder makes a 32° angle with the building. How many feet away from the building is the base of the ladder?
Answer:
since the top of the ladder is making the angle, the of the ladder's base from the building is our opposite and the ladder is the hypotnuse,
sin (32)=opp/hyp, 0.52=opp/25, opp=13 ft
A nut-raisin mix costs $5.26 a pound. Rashid buys 15.5 pounds of the mix for a party. Rashid’s estimated cost of the nut-raisin mix is A.$16 B.$22 C.$61 D.$80
Answer:
D.$80
Step-by-step explanation:
$5.26 x 15.5= $81.53
The closest amount to $81.53 is D.$80
1. find x and y 2. find the measure of each side of LMN
Answer:
X= 3
Y= 18
Each side of the triangle= 10 units
Step-by-step explanation:
LMN is equilateral so
LM = MN
3x+1= 4x-2
3x-4x = -2-1
-x = -3
X= 3
MP is the perpendicular bisector of line LN
so definitely angle lpm =90.
And lpm = 5y = 90
5y = 90
Y= 90/5
Y = 18°
For the side of the triangle
3x+1
But x= 3
3(3)+1
9+1
10
Each side of the triangle= 10 units
Mia agreed to borrow a 3 year loan with 4 percent interest to buy a motorcycle if Mia will pay a total of $444 in interest how much money did she borrow how much interest would Mia pay if the simple interest rate was 5 percent
Answer:
a) $3700
b) $555
Step-by-step explanation:
The length of the loan is 3 years.
The interest after 3 years is $444.
The rate of the Simple Interest is 4%.
Simple Interest is given as:
I = (P * R * T) / 100
where P = principal (amount borrowed)
R = rate
T = length of years
Therefore:
[tex]444 = (P * 3 * 4) / 100\\\\444 = 12P / 100\\\\12P = 444 * 100\\\\12P = 44400\\\\P = 44400 / 12\\[/tex]
P = $3700
She borrowed $3700
b) If the simple interest was 5%, then:
I = (3700 * 5 * 3) / 100 = $555
The interest would be $555.
8. Which statement is always true?
A. 9 times a number is always odd.
B. 9 times a number is always even
C. 10 times a number is always odd.
D. 10 times a number is always even.
Answer:
D
Step-by-step explanation:
Any number multiplied by an even number will always be even. 10 is an even number.
Answer:
d. 10 times a number is always even
Step-by-step explanation:
multiples of 9 contain 81 and 36 which one is even and the other is odd
multiples of 10 ONLY contain even numbers because the unit digit for a multiple of 10 is 0.
So whenever you multiply a number by 10 it will be even
Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter λ = 0.0143. (a) What is the probability that the distance is at most 100 m? What is the probability that the distance is at most 200 m? What is the probability that the distance is between 100 m and 200 m? (b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (c) What is the value of the median distance?
Answer and Step-by-step explanation: For an exponential distribution, the probability distribution function is:
f(x) = λ.[tex]e^{-\lambda.x}[/tex]
and the cumulative distribution function, which describes the probability distribution of a random variable X, is:
F(x) = 1 - [tex]e^{-\lambda.x}[/tex]
(a) Probability of distance at most 100m, with λ = 0.0143:
F(100) = 1 - [tex]e^{-0.0143.100}[/tex]
F(100) = 0.76
Probability of distance at most 200:
F(200) = 1 - [tex]e^{-0.0143.200}[/tex]
F(200) = 0.94
Probability of distance between 100 and 200:
F(100≤X≤200) = F(200) - F(100)
F(100≤X≤200) = 0.94 - 0.76
F(100≤X≤200) = 0.18
(b) The mean, E(X), of a probability distribution is calculated by:
E(X) = [tex]\frac{1}{\lambda}[/tex]
E(X) = [tex]\frac{1}{0.0143}[/tex]
E(X) = 69.93
The standard deviation is the square root of variance,V(X), which is calculated by:
σ = [tex]\sqrt{\frac{1}{\lambda^{2}} }[/tex]
σ = [tex]\sqrt{\frac{1}{0.0143^{2}} }[/tex]
σ = 69.93
Distance exceeds the mean distance by more than 2σ:
P(X > 69.93+2.69.93) = P(X > 209.79)
P(X > 209.79) = 1 - P(X≤209.79)
P(X > 209.79) = 1 - F(209.79)
P(X > 209.79) = 1 - (1 - [tex]e^{-0.0143*209.79}[/tex])
P(X > 209.79) = 0.0503
(c) Median is a point that divides the value in half. For a probability distribution:
P(X≤m) = 0.5
[tex]\int\limits^m_0 f({x}) \, dx[/tex] = 0.5
[tex]\int\limits^m_0 {\lambda.e^{-\lambda.x}} \, dx[/tex] = 0.5
[tex]\lambda.\frac{e^{-\lambda.x}}{-\lambda}[/tex] = [tex]-e^{-\lambda.x} + e^{0}[/tex]
[tex]1 - e^{-\lambda.m}[/tex] = 0.5
[tex]-e^{-\lambda.m}[/tex] = - 0.5
ln([tex]e^{-0.0143.m}[/tex]) = ln(0.5)
-0.0143.m = - 0.0693
m = 48.46
In the given figure, find AB, given thatAC = 14 andBC = 9.
Answer:
Given:
AC = 14 and BC = 9
AB = ?
Solution:
From the fig:
AC = AB + BC
Putting the values
14 = AB + 9
AB = 14 - 9
AB = 5
(you can also take AB = x or any other variable)
Step-by-step explanation:
please what's the solution for 2a²×4a³
Answer:
8a^5
Step-by-step explanation:
Well to start off 2*4=8
So the coefficent will be 8
and when multipling ezponents we add the exponents and 2+3=5 so the exponent will be 5.
So 8a^5 is the answer
−30=5(x+1) solve for x pls help
Answer:
[tex] \boxed{\sf x = -7} [/tex]
Step-by-step explanation:
[tex] \sf Solve \: for \: x: \\ \sf \implies - 30 = 5(x + 1) \\ \\ \sf - 30 =5(x+ 1) \: is \: equivalent \: to \: 5 (x + 1) = - 30: \\ \sf \implies 5(x + 1) = - 30 \\ \\ \sf Divide \: both \: sides \: of \: 5(x+ 1) = - 30 \: by \: 5: \\ \sf \implies \frac{5(x + 1)}{5} = - \frac{30}{5} \\ \\ \sf \frac{5}{5} = 1 : \\ \sf \implies x + 1 = - \frac{30}{5} \\ \\ \sf - \frac{30}{5} = - \frac{6 \times \cancel{5}}{ \cancel{5}} = - 6 : \\ \sf \implies x + 1 = - 6 \\ \\ \sf Subtract \: 1 \: from \: both \: sides: \\ \sf \implies x + (1 - 1) = - 6 - 1 \\ \\ \sf 1 - 1 = 0 : \\ \sf \implies x = - 6 - 1 \\ \\ \sf - 6 - 1 = - 7 : \\ \sf \implies x = - 7[/tex]
Answer:
[tex] \boxed{x = - 7}[/tex]
Step-by-step explanation:
[tex] \mathrm{ - 30 = 5(x + 1)}[/tex]
Distribute 5 through the parentheses
[tex] \mathrm{ - 30 = 5x + 5} [/tex]
Move constant to L.H.S and change its sign
[tex] \mathrm{ - 30 - 5 = 5x}[/tex]
Calculate
[tex] \mathrm{ - 35 = 5x}[/tex]
Swipe the sides of the equation
[tex] \mathrm{5x = - 35}[/tex]
Divide both sides of the equation by 5
[tex] \mathrm{ \frac{5x}{5} = \frac{ - 35}{5} }[/tex]
Calculate
[tex] \mathrm{x = - 7}[/tex]
Hope I helped!
Best regards!!
???????????????????
?
?
?
?
Answer:
It should be 10 for the first box, 1000 for the second box and 100 for the third box.
Step-by-step explanation:
Each extra decimal place value added, u have to multiply it by the next value place such as tenths/hundreths/thousandths
my number is the first multiple of 3,6, and 9 what is my number
Answer:
18 is the first multiple of 3,6, and 9.
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
We need to find the LCM (lowest common multiple) of 3, 6, and 9. Let's count by multiples of 3 to find it.
3 (not a multiple of 6 or 9), 6 (not a multiple of 9), 9 (not a multiple of 6), 12 (not a multiple of 9), 15 (not a multiple of 6 or 9), 18.
Since 18 is the first number that is a multiple of 3, 6, and 9, that is the answer.
What is the range of the function (-1,2) (3,6) (5,8)
Answer:
Range { 2,6,8}
Step-by-step explanation:
The domain is the input and the range is the output
Range { 2,6,8}
Answer:
2, 6, 8
Step-by-step explanation:
The range is the possible values of y, (x, y). So in this case, y could be 2, 6, or 8.
Find the length of the following tangent segments to the circles centered at O and O's whose radii are 5 and 3 respectively and the distance between O and O's is 12. Find segment AB
Answer:
AB = 2 sqrt(35) (or 11.83 to two decimal places)
Step-by-step explanation:
Refer to diagram.
ABO'P is a rectangle (all angles 90)
=>
PO' = AB
AB = PO' = sqrt(12^2-2^2) = sqrt(144-4) = sqrt(140) = 2sqrt(35)
using Pythagoras theorem.
Use the drop-downs to answer the questions about this geometric sequence. –243, 81, –27, 9 … What is the common ratio? What is the fifth term in the sequence? What is the sixth term in the sequence?
Answer:
a= -243
r=81/-243, r= -0.33(common ratio)
to find the 5th term; T5= -243×(0.33)^(5-1)
T5= -243 × (0.33)^4
T5= -3
to find the 6th term; T6= -243 ×(0.33)^(6-1)
T6= -243 ×(-0.33)^5
T6= 1
Answer:
Answer above is correct
Step-by-step explanation:
–243, 81, –27, 9 …
What is the common ratio?
–1/3
What is the fifth term in the sequence?
–3
What is the sixth term in the sequence?
1
What is the solution to the system that is created by the equation y = 2 x + 10 and the graph shown below? On a coordinate plane, a line goes through (negative 2, 0) and (0, 2). (–8, –6) (–4, –2) (0, 2) (2, 4)
Answer:
(–8, –6)
Step-by-step explanation:
The given points represent the x- and y- intercepts of the line, so we can write the equation in intercept form as ...
x/(x-intercept) +y/(y-intercept) = 1
x/(-2) +y/2 = 1 . . . use the given intercepts
x - y = -2 . . . . . multiply by -2
Then the system is ...
y = 2x +10x - y = -2Using the first to substitute into the second, we get ...
x - (2x +10) = -2
-8 = x . . . . . . . . . . . add x+2, simplify
y = 2(-8) +10 = -6
The solution is (x, y) = (-8, -6).
Answer:
(-8,-6)
Step-by-step explanation:
Got it right on edge soooo <3
Find the number of unique permutations of the letters in each word. SIGNATURE RESTAURANT
Answer:
Ok, we have two words:
"Signature"
The letters are: "S I G N A T U R E"
9 different letters.
Now, we can make only words with 9 letters, so we can think on 9 slots, and in each of those slots, we can input a letter of those 9.
For the first slot, we have 9 options.
For the second slot, we have 8 options (because on is already taken)
For the second slot, we have 7 options and so on.
Now, the total number of combinations is equal to the product of the number of options in each selection:
C = 9*8*7*6*5*4*3*2*1 = 362,880.
Now, our second word is Restaurant.
The letters here are " R E S T A U N" such that R, T and A appear two times each, so we have a total of 10 letters and 7 unique letters.
So first we do the same as beffore, 10 slots and we start with 10 options.
The total number of combinations will be:
C = 10*9*8*7*6*5*4*3*2*1 = 3,628,800
A lot of combinations, but we are counting only unique words.
For example, as we have two R, we are counting two times the word:
Restaurant (because we could permutate only the two letters R and get the same word)
So we must divide by two for each letter repeated.
we have 3 letters repeated, we divide 3 times by 2.
C = ( 3,628,800)/(2*2*2) = 453,600
A pharmacist wants to mix a 30% saline solution with a 10% saline solution to get 200 mL of a 12% saline solution. How much of each solution should she use
Answer:
30% constituents=20 mL
10% constituents=180 mL
Step-by-step explanation:
x= 30% volume
y=10% volume
For our first equation, we know the total volume is 200 mL and is the sum
x+y=200
y=200-x (1)
For our second equation, we do a mass balance for 200 mL of final solution.
12% w/v = 0.12 g/mL
This means that in 1 mL of solution, we have 0.12 g of NaCl.
For any solution, concentration multiplied by volume will give the mass of NaCl:
Mass in x mL= C*V (g/mL) (mL)
So in 200 mL, we have
0.12*200 (g/mL) (mL)
=24g of NaCl
Cx*Vx + Cy*Vy=24
0.3x+0.1y=24 (2)
Substitute y=200-x into (2)
0.3x+0.1(200-x)=24
0.3x+20-0.1x=24
0.2x=24-20
0.2x=4
Divide both sides by 0.2
0.2x/0.2=4/0.2
x=20
Substitute x=20 into (1)
y=200-x
y=200-20
y=180
30% constituents=20 mL
10% constituents=180 mL
plzzzzz helpp j + 9 - 3 < 8
Answer:
j < 2
Step-by-step explanation:
Simplify both sides of the inequality and isolating the variable would get you the answer
If the average American sleeps 8 hours a night, with a standard deviation of 1 hour, and I plan on gathering a sample of 12 college students to compare to this population, find the following:
mu =
sigma =
mu_x bar =
sigma_x bar =
Answer:
8 hours
1 hour
8 hours
0.288675
Step-by-step explanation:
We complete the answer as follows;
mu = mean = 8 hours
sigma = standard deviation= 1 hour
Mu_x bar = mu = 8 hours
sigma_x bar = sigma/√(n) = 1/√(12) = 0.288675
Find ZABD if ZABC = 121° in the given figure.
4x+21+3x-5=121
7x+16=121
x=15
angle ABD =4(15)+21=81
Which of the following can be used to find the area of a circle?
A.
B.
C.
D.
Answer:
option B
hope it was useful for you
stay at home stay safe
pls mark me as brain.....
Answer:
[tex]\boxed{Option \ B}[/tex]
Step-by-step explanation:
Area of a circle = [tex]\pi r^2[/tex]
Finding the area of the circle, we need to know what the radius of the circle is. So, We would get the area of the circle.
Smoothing a time series of observations A. is a form of statistical cheating. B. allows statisticians to use less data than would otherwise be required. C. renders the resultant forecast unusable. D. is used to reveal an underlying pattern in the data.
Answer:
D. is used to reveal an underlying pattern in the data.
Step-by-step explanation:
Smoothing a time series is achieved when a computer uses some pre-programmed calculation methods to remove noise from large volumes of data. Smoothing helps a user detect patterns in a set of data, thus making it possible to make future predictions. For example, smoothing can be used in the prediction of the rise and fall of stock prices. This helps the traders to have an idea of what to expect in the cost of trading.
Although smoothing reveals the patterns in a set of data, it provides no explanation as to why it is so. It is left to the researcher to draw conclusions as to the reasons for the patterns.
Heights of women (in inches) are approximately N(64.5,2.5) distributed. Compute the probability that the average height of 25 randomly selected women will be bigger than 66 inches.
Answer:
the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013
Step-by-step explanation:
From the summary of the given statistical dataset
The mean and standard deviation for the sampling distribution of sample mean of 25 randomly selected women can be calculated as follows:
[tex]\mu_{\overline x} = \mu _x[/tex] = 64.5
[tex]\sigma_{\overline x }= \dfrac{\sigma}{\sqrt n}[/tex]
[tex]\sigma_{\overline x }= \dfrac{2.5}{\sqrt {25}}[/tex]
[tex]\sigma_{\overline x }= \dfrac{2.5}{5}[/tex]
[tex]\sigma_{\overline x }[/tex] = 0.5
Thus X [tex]\sim[/tex] N (64.5,0.5)
Therefore, the probability that the average height of 25 randomly selected women will be bigger than 66 inches is:
[tex]P(\overline X > 66) = P ( \dfrac{\overline X - \mu_\overline x}{\sigma \overline x }>\dfrac{66 - 64.5}{0.5} })[/tex]
[tex]P(\overline X > 66) = P ( Z>\dfrac{66 - 64.5}{0.5} })[/tex]
[tex]P(\overline X > 66) = P ( Z>\dfrac{1.5}{0.5} })[/tex]
[tex]P(\overline X > 66) = P ( Z>3 })[/tex]
[tex]P(\overline X > 66) = 1- P ( Z<3 })[/tex]
[tex]P(\overline X > 66) = 1- 0.9987[/tex]
[tex]P(\overline X > 66) =0.0013[/tex]
the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013
PLEASE HELP QUICK!!! In how many ways can you put seven marbles in different colors into two jars? Note that the jars may be empty.
Answer: 14384 ways
Step-by-step explanation:
With 0 identical marbles permitted to be included in any of the jars, An expression can be developed to determine the total of marbles in jar arrangements, which is:
E = [(n+j -1)!]*{1/[(j-1)!]*[(n)!]}, where n = number of identical balls and j =number of distinct jars, the contents of all of which must sum to n for each marbles in j jars arrangement. With n = 7 and j = 4. E = 10!/(3!)(7!) = 120= number of ways 7 identical marbles can be distributed to 4 distinct jars such that up to 3 boxes may be empty and the maximum to any box is 7 balls.
The marble arrangements are: (7,0,0,0) in 4!/3! = 4 ways, (6,1,0,0) in 4!/2! = 12 ways, (5,2,0,0) in 4!/2! = 12 ways, (5,1,1,0) in 4!/2! = 12 ways, (4,3,0,0) in 4!/2! = 12 ways, (4,2,1,0) in 4! = 24 ways, (4,1,1,1) in 4!/3! = 4 ways, (3,3,1,0) in 4!/2! = 12 ways, (3,2,2,0) in 4!/2! = 12 ways, (3,2,1,1) in 4!/2! = 12 ways, (2,2,2,1) in 4!/3! = 4 ways.
Total of ways = 4+12+12+12+12+24+4+12+12+12+4 = 120 as previously determined above for identical marbles and distinct jars.
Taking into account distinct colored marbles, the number of ways of marble distribution into 4 jars becomes as follows:
For (7,0,0,0) = 4*(7!/7!) =4. For (6,1,0,0) = 12*[7!/(6!)(1!)] = 84. For (5,2,0,0) =
12*[7!/(5!)(2!)] = 252. For (5,1,1,0) = 12*[7!/(5!)(1!)(1!)] = 504. For (4,3,0,0) =
12*[7!/(4!)(3!)] = 420. for (4,2,1,0) = 24*[7!/(4!)(2!)(1!)] = 2,520. For (4,1,1,1) =
4*7!/(4!)(1!)(1!)(1!)] = 840. For (3,3,1,0) = 12*]7!/(3!)(3!)(1!) = 1,680. For (3,2,20) = 12*]7!/(3!)(2!)(2!) = 2,520. For (3,2,1,1) = 12*]7!/(3!)(2!)(1!)(1!) = 5,040. For (2,2,2,1) = 4*]7!/(2!)(2!)(2!)(1!) = 2,520.
Total of ways as requested for distinct colored marbles and distinct jars = 4+84+252+504+420+2,520+840+1,680+2,520+5,040+2,520 = 14,384.
A living room is two times as long and one and one-half times as wide as a bedroom. The amount of
carpet needed for the living room is how many times greater than the amount of carpet needed for the
bedroom?
1 1/2
2
3
3 1/2
Answer:
3
Step-by-step explanation:
let's call X the length of the bedroom, Y the wide of the bedroom, A the length of the living room and B the wide of the living room
A living room is two times as long as the bedroom, so:
A = 2X
A living room is one and one-half times as wide as a bedroom, so:
B = 1.5Y
The amount of carpet needed for the living room is A*B and the amount of carpet needed by the bedroom is X*Y
So, AB in terms of XY is:
A*B = (2X)*(1.5Y) = 3(X*Y)
It means that the amount of c arpet needed for the living room is 3 times greater than the amount of carpet needed for the bedroom.
Natalie went to store A and bought 3 4/5 pounds of pistachios for $17. 75. Nicholas went to a store B and brought 4 7/10 pounds of pistachios for $ 19.50. Who got the better deal?
Answer:
Nicholas
Step-by-step explanation:
If you want an explanation I can add one
In right triangle ABC, 2B is a right angle, AB = 48 units, BC = 55 units, and AC = 73 units.
literally please help me
Answer:
73/55
Step-by-step explanation:
The cosecant (csc) is one of the reciprocal functions:
csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)
So, if we can find the sine, we can find the cosecant.
__
The mnemonic SOH CAH TOA reminds you that the sine is ...
Sin = Opposite/Hypotenuse
The above tells you that ...
Csc = 1/Sin = Hypotenuse/Opposite
The hypotenuse of your triangle is AC = 73. The side opposite angle θ is BC = 55. So, the ratio you want is ...
csc(θ) = 73/55
Answer:
[tex]csc (\theta)=\frac{33}{55}[/tex]
Step-by-step explanation:
Hello!
1) The cosecant function is the inverse the sine function. So we can write:
[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]
2) The sine function is the side opposite angle to [tex]\angle \theta[/tex] over the hypotenuse:
[tex]sin(\theta)=\frac{55}{33}[/tex]
3) So, remembering operations with fractions then the cosecant is:
[tex]csc \theta = \frac{1}{\frac{55}{33} } =1 \times \frac{33}{55}[/tex]
[tex]csc (\theta)=\frac{33}{55}[/tex]
4 to the 4th power equals 256. Explain how to use that fact to more quickly evaluate 4 to the 5th power.
Answer: Because 4 is the base of what is being exponentially multiplied, you can multiply 256 by 4 to get 4^5
Hi there! Hopefully this helps!
--------------------------------------------------------------------------------------------------------
So, we know that 4 to the 4th power equals 256.
4 to the 4th power = 4 x 4 x 4 x 4.
So we can add another 4 to the equation to quickly get out answer for 4 to the 5th power.
4 to the 5th power = 4 x 4 x 4 x 4 x 4 = 1024.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Or you could break the equation into parts.
For example, there are FOUR 4s in the equation.
4 x 4 = 16.
4 x 4 = 16.
16 x 16 = 256.
Now since we've added ANOTHER 4, it should look like this:
16 x 16 = 256.
256 x 4 = 1024.
A swimming pool is circular with a 30-ft diameter. The depth is constant along east-west lines and increases linearly from 2 ft at the south end to 7 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.) ft3
Answer:
Volume of water in the pool is 3,182 ft^3
Step-by-step explanation:
In this question, what we want to calculate is the volume of water in the pool.
We proceed as follows;
diameter of pool = 30ft
depth: 2 to 7ft linearly
average depth = (2 + 7)/2 = 9/2 = 4.5 ft
Volume = area * average depth
V = pi * radius^2 * 4.5
where radius = diameter/2 = 30/2 = 15 ft
V = pi * 15^2 * 4.5
V = 22/7 * 225 * 4.5
V = 3,182.14 ft^3
which is 3,182 ft^3 to nearest whole number
The volume of water in the pool is; Volume = 3181 ft³
We are given;
Diameter of swimming Pool; d = 30 ft
Thus; radius; r = d/2 = 30/2 = 15 ft
We are told that the depth is constant along east-west lines and increases linearly from 2 ft at the south end to 7 ft at the north end.
Thus, average depth is;
h_avg = (2 + 7)/2
h_avg = 4.5 ft
Formula for area is; A = πr²
Thus;
A = π × 15²
A = 225π
Formula for volume here is;
Volume = Area × depth
Volume = 225π × 4.5
Volume = 3180.86 ft³
Approximating to a whole number gives;
Volume = 3181 ft³
Read more at; https://brainly.com/question/15276135
Mai invests $20,000 at age 20. She hopes the investment will be worth $500,000 when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.
Answer:
[tex]\approx[/tex] 17.5% per annum
Step-by-step explanation:
Given:
Money invested = $20,000 at the age of 20 years.
Money expected to be $500,000 at the age of 40.
Time = 40 - 20 = 20 years
Interest is compounded annually.
To find:
Rate of growth = ?
Solution:
First of all, let us have a look at the formula for compound interest.
[tex]A = P \times (1+\frac{R}{100})^T[/tex]
Where A is the amount after T years compounding at a rate of R% per annum. P is the principal amount.
Here, We are given:
P = $20,000
A = $500,000
T = 20 years
R = ?
Putting all the values in the formula:
[tex]500000 = 20000 \times (1+\frac{R}{100})^{20}\\\Rightarrow \dfrac{500000}{20000} =(1+\frac{R}{100})^{20}\\\Rightarrow 25 =(1+\frac{R}{100})^{20}\\\Rightarrow \sqrt[20]{25} =1+\frac{R}{100}\\\Rightarrow 1.175 = 1+0.01R\\\Rightarrow R \approx17.5\%[/tex]
So, the correct answer is [tex]\approx[/tex] 17.5% per annum and compounding annually.
Answer:
16.1%
Step-by-step explanation:
(the other person is wrong, trust me)