Answer:
6√24 or 29.39metres
Step-by-step explanation:
Area of a triangle is bh/2
The perimeter of an equilateral triangle is 3b
This equilateral triangle can be imagined as two adjoining 30-60-90 triangles. Together, their area is the given 24√3 m²
The base of the individual triangle is √24. The height is √24√3. Multiplying those factors, we get the given area, a proof of sorts, but mure importantly, we can calculate the length of the hypotenuse as 2√24.
sin(30°) = 0.5
√24/(0.5) = 2√24
That is the length of the side of the original equilateral triangle.
The perimeter is 3 times the length of the side:
(3)(2√24) = P
6√24 meters is the perimeter.
given each pair of similar triangles find the missing value. of LJK=PQR find x
Answer:
1
Step-by-step explanation:
3(x + 3) − 2 < 4
does anyone know this?
Answer:3 + ? = 7, 3 + n = 7, 3 + x = 1
Step-by-step explanation:
and so on, where the symbols ?, n, and x represent the number we want to find. We call such shorthand versions of stated problems equations, or symbolic sentences. Equations such as x + 3 = 7 are first-degree equations, since the variable has an exponent of 1. The terms to the left of an equals sign make up the left-hand member of the equation; those to the right make up the right-hand member. Thus, in the equation x + 3 = 7, the left-hand member is x + 3 and the right-hand member is 7.
Answer:
Inequality Form: x < −1
Interval Notation: (−∞, −1)
Step-by-step explanation:
3 (x + 3) −2 < 4
Simplify 3 (x + 3) − 2.
Apply the distributive property.
3x + 3 ⋅ 3 − 2 < 4
Multiply 3 by 3.
3x + 9 − 2 < 4
Subtract 2 from 9.
3x + 7 < 4
Move all terms not containing x to the right side of the inequality.
Subtract 7 from both sides of the inequality.
3x < 4 − 7
Subtract 7 from 4.
3x < −3
Divide each term by 3 and simplify.
x < −1
The result can be shown in multiple forms.
Inequality Form: x < −1
Interval Notation: (−∞, −1)
Ms. Davis is doing an activity with her statistics students where she gives them a 202020-question multiple choice test, and they know none of the answers. Students need to guess on every question, and each question has 555 possible choices, 111 of which is correct.
What are the mean and standard deviation of the number of questions that each student gets correct?
You may round your answers to the nearest tenth.
Answer:
The mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively (
Answer: mean: 4
standard deviation: 1.79
Step-by-step explanation:
A box of cereal weighs 12 ounces and costs $2.16. What is the price of the cereal per ounce?
Answer:
0.18 cents an ounce
Step-by-step explanation:
Take 2.16 and divide it by 12.
Which expression simplifies to 8x^5?
Answer:
32768x^5
Step-by-step explanation:
[tex] {8x}^{5} [/tex]
...
Ten little monkeys were jumping on a bed. There is a 35% chance that one will fall off and bump his head. In the bedroom next door, five kangaroos were jumping on a bed. Being more adept at jumping, there is only a 20% that a kangaroo will fall off the bed.
1. What are the chances that a monkey and a kangaroo will fall off the bed?
2. What are the chances that a monkey will not fall off the bed?
3. If the monkeys enjoy this activity every night for an entire week, what are the chances that a monkey falls off the bed every one of the seven nights?
4. What are the chances that if the monkeys jump every day for a week that at least one will fall off of the bed?
5. What are the chances that the kangaroos can get away with jumping on the bed for 4 straight nights until they finally have someone fall off the bed on the night?
6. What are the chances that the kangaroos can jump two nights in a row with no one falling off the bed?
7. The monkeys manage to go a whole week without someone bumping their head. One of the kangaroos insists that they are due for an injury. Another says they must be getting better at their jumping skills. Do you think they're due for a crash?
Answer:
0.07 ; 0.65 ; 0.00064339296875 ; 3.02 * 10^-12
Step-by-step explanation:
Given :
Number of monkeys, n1 = 10
Probability of fall, off ; p(m) = 35% = 0.35
Number of kangaroos, n2 = 5
Probability of fall, off : p(k) = 20% = 0.2
1.) A monkey and kangaroo falls off;
p(m) * p(k) = 0.35 * 0.2 = 0.07
2.) probability that monkey will not fall off;
1 - p(m) = 1 - 0.35 = 0.65
3.) probability that a monkey falls off every one of seven nights :
P(m) = 0.35 ; for 7 nights ;
0.35 *0.35 * 0.35 * 0.35 * 0.35 * 0.35 * 0.35 = 0.35^7 = 0.00064339296875
4.)
P(x ≥ 1) = p(1) + p(2) +... + p(10)
Using binomial probability calculator :
n = 7*10 = 70 ; p = 0.35
P(x ≥ 1) = 70C1 * 0.35^1 * 0.65^69 = 3.02 * 10^-12
The equation of the line
Answer: y = 2
Step-by-step explanation: Horizontal means y =
Answer:
○ [tex]\displaystyle y = 2[/tex]
Step-by-step explanation:
This is a STRAIT HORISONTAL LINEAR EQUATION, therefore sinse every x-coordinate will have the same y-coordinate of [tex]\displaystyle 2,[/tex] this is the option you would pick.
I am joyous to assist you at any time.
Help me with this please worth 40 points!!!
Step-by-step explanation:
Since KQ bisects RS, we have KR = 0.5SR.
=> 2x - 8 = 0.5(x - 1)
=> 2x - 8 = 0.5x - 0.5
=> 1.5x = 7.5, x = 5.
Ted's taxi service has cabs that can seat 4 people and vans that can seat 15 people. The taxi service can transport a maximum of 134 people in its 17 units. How many vans does Ted's Taci Service have in it's fleet?
A. 19
B. 11
C. 9
D. 6
Answer:
D. 6
Step-by-step explanation:
Can someone please help me?
dotted line that is at (0,1) then the dotted line goes up to the right and also down to the left so for going up its 1 up 1 over and then also draw a line on the orgin 0,0 that goes in the opposistedirection so left up one to the left one and do that corner to corner that line is filled in and then to get your anwser shade in the area below your secoundline to the bottom of the first line which is going to be bottom left of your graph step-by-step explanation:
Has 256 and 81 already been squared?
8th grade math
Please answer ASAP (i'm being timed)
PLEASE HELP IT IS 6th GRADE MATH!!!!!
Answer:
19
Step-by-step explanation:
[tex]\frac{17b - a^{2} }{2}[/tex]
Substitute the "a" and "b"
a = 8
b = 6
[tex]\frac{17 * 6 - 8^{2} }{2}[/tex]
[tex]\frac{17 * 6 - 64}{2}[/tex]
[tex]\frac{102 - 64}{2}[/tex]
[tex]\frac{38}{2}[/tex]
[tex]19[/tex]
Hope this helped!
Have a supercalifragilisticexpialidocious day!
There are 7,500 shares of $10 par value participating 9 percent preferred stock outstanding, and 32,500 shares of common stock outstanding. The common stock cash dividend is $.50 per share, and total dividends of $50,000 are distributed. Remaining dividends are shared equally between common and preferred stockholders. Round your answers to two decimal places, if necessary.
Answer:
add the answers then subtract
Step-by-step explanation:
hope this is right
Kyle's doctor told him that in order to lose weight, he needs to eat less than 2,000 calories a day. He eats 875 calories for breakfast and than 3 protein smoothies. How many calories can the protein smoothies have to reach his goal?
Answer:
375 calories each
Step-by-step explanation:
2000-875=1125
1125/3=375
If point C is the circumcenter, find each missing value(picture attached)
Answer:
d
Step-by-step explanation:
??????????????????????
Answer:
f(8)=91 is the answer
answer is 91
Graph the image of the figure after a dilation with a scale factor of 2 centered at (-7, - 2).
Use the Polygon tool to graph the quadrilateral by connecting all its vertices.
Answer:
Sorry this is late!
Step-by-step explanation:
please help me with this
Answer:
[tex] \frac{17}{8} + \frac{5}{3} = \frac{51 + 40}{24} = \frac{91}{24} [/tex]
hope it can help u~~
Jim has ridden 24 miles of a bike course. The course is 40 miles long. What percentage of the course has Jim ridden so far?
Answer:
-
Step-by-step explanation:
Walmart has soft drinks on sale: 4 packs for $20 Kroger has soft drinks on sale : 3 packs for $18 Which store has the better deal? why?
Answer:
Walmart has the better deal.
Step-by-step explanation:
If you divide the amount of money and the packs they sell, Walmart is cheaper.
Walmart: 20/4 = 5
Kroger: 18/3 = 6
Answer:
It is Walmart 4 packs for 20$
Step-by-step explanation:
If s= 6 inches, and the altitude, h, is 21 inches, what is the volume of the pyramid?
Answer: 42 inches
Step-by-step explanation:
To find the volume you multiply 1/3 of the base which is 6 then with 1/3 is 2 them multiply the altitude which is 21. So 2 times 21 is 42 inches
Answer:
The volume of the pyramid is 42 inches³.
Step-by-step explanation:
The formula is V = ⅓ A H. 6x21=126, 126x1/3=42.
Which expression is equivalent to |b| > 6 ?
b 6
b 6
b > –6 or b –6 and b < 6
Answer:
number 3. is the correct answer.
The formula shown can be used to find A the amount of money Raul has in his saving account Raul wants to find r the rate of interest his money earns which equation is correctly solved for r
Answer: r= A-P/ Pt
Step-by-step explanation: ur welcome
The equation [tex]r = \frac{A-P}{pt}[/tex] is correctly solved for r.
Here,
The formula shown can be used to find A the amount of money Raul has in his saving account.
Raul wants to find r the rate of interest his money earns.
We have to find the equation is correctly solved for r.
What is Rate of interest?
The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.
Now,
The formula which shown to find A is;
A = P + Prt
Hence, equation is correctly solved for r is;
[tex]A = P + Prt\\\\A-P = Prt\\\\r = \frac{A-P}{Pt}[/tex]
So, The equation [tex]r = \frac{A-P}{pt}[/tex] is correctly solved for r.
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Use the following definition of absolute value to prove the given statements: If x is a real number, then the absolute value of x , | x | , is defined by: | x | = { x if x ≥ 0 − x if x < 0 For any real number x , | x | ≥ 0 . Moreover, | x | = 0 implies x = 0 . For any two real numbers x and y , | x | ⋅ | y | = | x y | . For any two real numbers x and y , | x + y | ≤ | x | + | y | .
Answer:
Proved all parts below.
Step-by-step explanation:
As given ,
|x| = [tex]\left \{ {{x , x\geq 0} \atop {-x, x< 0}} \right.[/tex]
To prove- a) For any real number x , | x | ≥ 0 . Moreover, | x | = 0 ⇒ x = 0
b) For any two real numbers x and y , | x | ⋅ | y | = | x y | .
c) For any two real numbers x and y , | x + y | ≤ | x | + | y | .
Proof -
a)
As given x is a real number
Also , by definition of absolute value of x , we get
| x | ≥ 0
Now,
if |x| = 0
⇒ x = 0 and -x = 0
⇒ x = 0 and x = 0
⇒ x = 0
∴ we get
| x | = 0 ⇒ x = 0
Hence proved.
b)
To prove - | x | ⋅ | y | = | x y |
As we have,
|x| = [tex]\left \{ {{x , x\geq 0} \atop {-x, x< 0}} \right.[/tex]
|y| = [tex]\left \{ {{y , y\geq 0} \atop {-y, y< 0}} \right.[/tex]
|xy| = [tex]\left \{ {{xy , x,y > 0 and x,y < 0} \atop {-xy, x > 0, y< 0 and x <0 , y > 0}} \right.[/tex]
We have 4 cases : i) when x > 0 , y > 0
ii) when x > 0 , y < 0
iii) when x < 0, y > 0
iv) when x < 0, y < 0
For Case I - when x > 0 , y > 0
⇒ |x| = x, |y| = y
⇒|x|.|y| = xy
For Case Ii - when x > 0 , y < 0
⇒ |x| = x, |y| = -y
⇒|x|.|y| = -xy
For Case Iii - when x < 0 , y > 0
⇒ |x| = -x, |y| = y
⇒|x|.|y| = -xy
For Case IV - when x < 0 , y < 0
⇒ |x| = -x, |y| = -y
⇒|x|.|y| = (-x)(-y) = xy
∴ we get , from all 4 cases
| x | ⋅ | y | = | x y |
Hence Proved.
c)
To prove - | x + y | ≤ | x | + | y |
Let
|x| = |x + y - y|
≥ |x + y| - |y| ( Triangle inequality)
⇒ |x| + |y| ≥ |x + y|
Hence Proved.
The annual amount of rainfall in Ventura County is bounded by 6.3 and 20.5, is continuous and each outcome is equally likely. Use this information to answer the following four questions.
a. Determine P(10.2 < x < 18.7).
b. Determine P(x > 17.1).
c. Determine P(x < 6.3).
d. What is E[x]?
Answer:
a.0.5984
b.0.2394
c.0
d.13.4
Step-by-step explanation:
We are given that
a=6.3,b=20.5
The pdf of uniform distribution
[tex]f(x)=\frac{1}{b-a}=\frac{1}{20.5-6.3}=0.0704[/tex],6.3<x<20.5
0, otherwise
Now,
a.
P(10.2<x<18.7)=[tex]\int_{10.2}^{18.7}f(x) dx[/tex]
[tex]=0.0704[x]^{18.7}_{10.2}[/tex]
[tex]P(10.2<x<18.7)=0.0704(18.7-10.2)=0.5984[/tex]
b.P(x>17.1)
[tex]P(x>17.1)=\int_{17.1}^{20.5}0.0704dx[/tex]
[tex]=0.0704(20.5-17.1)[/tex]
[tex]=0.2394[/tex]
c.P(x<6.3)=0
d.E[x]=[tex]\frac{a+b}{2}=\frac{6.3+20.5}{2}=13.4[/tex]
given the function f(x)=x^3 +x^2-2x+1 what is the resulting function f(x) is shifted to the left one unit
Answer:
The resulting function is [tex]f(x+1) = x^3 + 4x^2 + 3x + 1[/tex]
Step-by-step explanation:
Suppose we have a function f(x). If we want to shift the function 1 unit to the left, we find f(x+1).
In this question, we have:
[tex]f(x) = x^3 + x^2 - 2x + 1[/tex]
Shifting 1 unit to the left:
[tex]f(x+1) = (x+1)^3 + (x+1)^2 - 2(x+1) + 1[/tex]
[tex]f(x+1) = (x^3 + 3x^2 + 3x + 1) + (x^2 + 2x + 1) - 2x - 2 + 1[/tex]
[tex]f(x+1) = x^3 + (3+1)x^2 + (3+2-2)x + 1 + 1 - 2 + 1[/tex]
[tex]f(x+1) = x^3 + 4x^2 + 3x + 1[/tex]
The resulting function is [tex]f(x+1) = x^3 + 4x^2 + 3x + 1[/tex]
I NEED ANSWER ASAP!!! is the mapping a fun or not a function
Answer:
function
Step-by-step explanation:
pls brainly give
Please help me i only have few hours left i need as much as I can ge. ill get you brainliest and send you free mr.beast merch
Answer:
26cm²
Step-by-step explanation:
Perimeter
2x - 4 + 5x - 13 + x + 9 = 40
8x - 8 = 40
8x = 40 - 8
8x = 32
x = 4
Sides of the triangle
Height = 2x - 4 = 2 x 4 - 4 = 4cm
Hypotenuse = 5x - 13 = 5 x 4 - 13 = 7cm
Base = x + 9 = 4 + 9 = 13cm
Area of triangle
= 1/2 x base x height
= 1/2 x 13 x 4
= 26cm²
Hope this helps
Answer:
26 cm
Step-by-step explanation:
Consider a company that has two different divisions. The annual profits from the two divisions are independent and have distributions Profit1 ~ N(5, 3^2) and Profit2 ~ N(7, 4^2) respectively. Both the profits are in $ Million. Assume that $1 = Rs. 45
A. Specify a Rupee range (centered on the mean) such that it contains 95% probability for the annual profit of the company.
B. Specify the 5th percentile of profit (in Rupees) for the company
C. Which of the two divisions has a larger probability of making a loss in a given year?
Answer:
a) Rs 603.68
b) Rs 476.33
c) first division
Step-by-step explanation:
Total profit = profit 1 + profit 2 = P
hence P ~ N(12,74) = [tex]\frac{P-12}{\sqrt{74} } ~ N(0,1)[/tex]
A ) Specifying a Rupee range ( centered on the mean ) that contains 95% probability for annual profit of the company
$13.41 = Rs 603.68
B) specifying the 5th percentile of profit
p = $10.59 ≈ Rs 476.33
C) The division that has a larger probability of making a loss in a given year is the first division
attached below is a detailed solution of the given problem
A): Range containing 95% probability for profit of company is
(Rs. 99M, Rs. 1026M).
B): Rs. 170.1 Million.
C): First division of the company has larger probability of making a loss.
Given that:
$1 = Rs. 45
[tex]Profit_1 \sim N(5, 3^2) \\ Profit_2 \sim N(7, 4^2)[/tex]
Thus,
Company's profit:
[tex]P \sim N( 5+7, 3^2 + 4^2) = N(12, 5^2)[/tex]
A):
95% of the probability lies between 1.96 standard deviations of the mean.
Thus range is:
[tex]= (12 - 1.96\times 5, 12 + 1.96 \times 5)\\\\= (\$2.2M, \$22.8M)\\ \\= (\rm Rs. \: 99M, \rm Rs. \: 1026M)[/tex]
B): Fifth percentile is calculated as:
[tex]P(Z \leq \dfrac{p-12}{5}) = 0.05[/tex]
From p values of z score table, we get:
[tex]\dfrac{p-12}{5} = -1.644\\p = 12 - 8.22 = 3.78\\[/tex]
Thus at $3.78M dollars, or Rs. 170.1M amount, 5th percentile of profit lies.
Or 5th percentile of profit is Rs. 170.1 Million.
C): Loss is when profit < 0
Thus: p < 0
The first division of company, thus have larger probability of making a loss in a given year.
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Which of the following shows a reflection of the triangle over the horizontal axis?
Answer:
I think the first one is the answer