Answer:
2.37 ; 1.6731
Step-by-step explanation:
Given the data:
X:___0____1____2____3____4____5
P(x):_0.10_0.15_0.26__0.30_0.15__0.04
the expected frequency of floods per town per summer
Σ(flood per Town per summer) * probability
Σ(X)*p(x)
Σ(0*0.10) + (1*0.15) + (2*0.26) + (3*0.30) + (4*0.15) + (5*0.04)
= (0 + 0.15 + 0.52 + 0.90 + 0.60 + 0.2)
= 2.37
Variance (s²) :
Σ[x². P(x)] - u²
Using an online variance calculator to save computation time :
s² = 16731 / 10000
s² = 1.6731
Prove that if r is any rational number, then 3r2 − 2r + 4 is rational. The following properties may be used in your proof. Property 1: Every integer is a rational number. Property 2: The sum of any two rational numbers is rational. Property 3: The product of any two rational numbers is rational. Note: Property 1 is Theorem 4.3.1, Property 2 is Theorem 4.3.2, and Property 3 is Exercise 15 in Section 4.3. Using these properties, choose explanations for each step in the given proof.
Given:
Expression is
[tex]3r^2-2r+4[/tex]
To prove:
If r is any rational number, then [tex]3r^2-2r+4[/tex] is rational.
Step-by-step explanation:
Property 1: Every integer is a rational number. It is Theorem 4.3.1.
Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.
Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.
Let r be any rational number.
We have,
[tex]3r^2-2r+4[/tex]
It can be written as
[tex]3(r\times r)-2r+4[/tex]
Now,
3, -2 and 4 are rational numbers by property 1.
[tex]r^2=r\times r[/tex] is rational by Property 3.
[tex]3r^2\text{ and }-2r[/tex] are rational by Property 3.
[tex]3r^2+(-2r)+4[/tex] is rational by property 2.
So, [tex]3r^2-2r+4[/tex] is rational.
Hence proved.
We want to prove that if r is rational, then:
[tex]3*r^2 - 2r + 4[/tex] Is also rational.
The proof is below:
Remember that a rational number is any number that can be written as a quotient of two integer numbers.
Then we have:
[tex]r = \frac{a}{b}[/tex]
Where a and b are integers.
If we replace that in our equation, we get:
[tex]3*(\frac{a}{b}) ^2 - 2*(\frac{a}{b}) + 4\\\\\frac{3a^2}{b^2} - \frac{2a}{b} + \frac{4}{1}[/tex]
Note that if a is an integer, then 3*a^2 is also an integer.
If b is an integer, then b^2 is also an integer.
Now we can perform the sum of these fractions to get:
[tex]\frac{3a^2}{b^2} - \frac{2a}{b} + \frac{4}{1}\\\\\frac{3a^2 - 2ab + 4b^2}{b^2}[/tex]
And because integers are closed under the addition, then the numerator of that fraction is also an integer, then we have that the given expression can be written as a quotient of two integers, thus, it is a rational number.
If you want to learn more, you can read:
https://brainly.com/question/15815501
2х - Зу= 2
х= бу - 5
X=
Y=
Answer:
2x-3y=2
x=6y-5
2(6y-5)-3y=2
use the distributive property.
2*6y=12y
2*-5=-10
12y-10-3y=2
combine like terms
12y-3y=9y
9y-10=2
add 10 to both sides.
9y-10+10=9y
2+10=12
9y=12
divide both sides by 9
9y/9=y
y=about 1.33
plug in the value of y in the expression equal to the value of x.
x=6(1.33)-5
solve
6*1.33=7.98
x=7.98-5
7.98-5=2.98
Step-by-step explanation:
x=2.98
y=1.33
Work out 2 1/3 divided by 1/4
Answer:
9.3333333
Step-by-step explanation:
Answer:
[tex] \frac{9}{4} \div \frac{1}{4}
\frac{9}{4} \times \frac{4}{1}
= \frac{34}{4} \\ \\ \\ \\ = 9[/tex]
How do you know if a sum or product will result in a rational or irrational number?
What is the size of a terabyte?
A bacteria population increases exponentially at a rate of r% each day. After
32 days, the population has increased by 309%. Find the value of r.
Answer:
r=4.5% daily
Step-by-step explanation:
Exponential Growth
The natural growth of some magnitudes can be modeled by the equation:
[tex]P=P_o(1+r)^t[/tex]
Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
We know after t=32 days, the population has increased by 309%. Being the original population P the 100%, then the population reached 309+100= 409%.
Substitute the given values into the model function:
[tex]409\%P_o=100\%P_o(1+r)^{32}[/tex]
Simplifying:
[tex]4.09=(1+r)^{32}[/tex]
We need to solve for r. Taking the 32nd root:
[tex]\sqrt[32]{4.09}=\sqrt[32]{(1+r)^{32}}[/tex]
Simplifying:
[tex]1+r=\sqrt[32]{4.09}=1.045[/tex]
Solving:
[tex]r=1.045-1\Rightarrow r=0.045[/tex]
r=4.5% daily
I"LL MARK YOU BRANLIEST IF YOU ANSWER CORRECT! Ayana's favorite brownie recipe calls for 1/2 of a cup of flour for every 1/3 of a cup of cocoa powder. For a bake sale, she plans to make a larger batch with 1 cup of cocoa powder. How much flour should she use?
Answer:
either a full cup or 1 1/2
are fractions with the same denominator?
Answer:
To solve fractions, you MUST HAVE THE SAME DENOMINATORS WHEN DEALING WITH ADDITION AND SUBTRACTION.
Step-by-step explanation:
For example, 2/3 + 3/6
The denominators in this case have a common denominator which is 6.
All you have to do is multiply the 2/3 by 2 in the numerator and the denominator. Once you do, you'll get 4/6 which you could then add to 3/6 to get 7/6 which would equal 1 1/6 or 7/6 either is fine.
Hope this helps! :)
Answer:
To solve fractions, you MUST HAVE THE SAME DENOMINATORS WHEN DEALING WITH ADDITION AND SUBTRACTION.
Step-by-step explanation:
Multiply the following binomials:
(x + 10)(x - 5)
Answer:
X^2+5x-50
Step-by-step explanation:
X^2-5x+10x-50
Answer:
X² - 5x + 10x - 50
Step-by-step explanation:
Use the FOIL method!
On a map, 1 inch equals 5 miles. If two cities are 7 inches apart on the map, how far are they actually apart
Answer:
35
Step-by-step explanation:
7 * 5 = 35
2 and square root of 2 + square root of 8 - 4 and square root of 1 over 2
Answer:
2.828427125, 2.82 or just round it to 3 if you want
Step-by-step explanation:
All you have to do is type it into the Desmos Scientific Calculator exactly how you see it.
[tex](x - 2) { }^{2} = 0[/tex]
How many solutions does this equation have?
Which is greater, 9 x 10^-2 or 3 x 10^-4? How many times greater is the number you chose than the other number? Explain your reasoning.
Answer:
The solution to 9x10^-2 is 0.09 or (3/10)^2. The solution to 3x10^-4 is 0.0003 or 3/10000. Based on that, 9x10^-2 fits into 3x10^-4 three-hundred (300) times.
Is 5 x n - 3 the correct algebraic expression for five times the difference of a number and three
Answer:
5(n-3)
Step-by-step explanation:
There would be parenthesis because you'd subtract three from the number first.
PLZ, HELP WILL GET BRAINLIEST AND A LOT OF POINTS.
What is the exponential function rule for the following points
x f(x)
1 8
2 32
3 128
4 512
Answer:
y=2(4^x)
Step-by-step explanation:
if you notice, all the y-values are multiplied by 4 for each x-value. this means 4 is raised to the power of x. however, when you plug this in, you realize that the value produced is only half the actual y-values, so you multiply this whole thing by 2.
y=2(4^x)
Answer:
f(x) = 2^(2x+1)
Step-by-step explanation:
You can tell that each of the outputs of f(x) are powers of 2, so all you have to do is figure out the pattern of the exponents.
2^3 = 8
2^5 = 32
2^7 = 128
2^9 = 512
the relationship between the sequence
3,5,7,9
when you start on 1 is
2x+1
2(1)+1 = 3
2(2)+1 = 5
etc.
Every morning for the past 12 days Beth used 2/3 of a cup of milk on her cereal to determine how much milk she used in total she set up the equation 2/3x12
Answer:
8
Step-by-step explanation:
2/3*12=24/3=8
easy way:
2/3*12/1=24/3=8
HELP NEEDED ASAP MATHS PLEASE!!!
Need help with this one please show it step by step.
Thank you!
Answer:
which class you are plz say dude
An instructor gives his class a set of 18 problems with the information that the next quiz will consist of a random selection of 9 of them. If a student has figured out how to do 13 of the problems, what is the probability the he or she will answer correctly
all 9 questions? =.0147
atleast 8 questions ?
Answer:
The probability the he or she will answer correctly is 1.5%
Step-by-step explanation:
What is the minimum number of x-intercepts that a polynomial of degree 10 can have?
Jim Kosla earns $156,200 annually as a plant manager. He is married and supports 3 children. The state tax rate in his state
is 3.55% of taxable income. What amount is withheld yearly for
state income tax?
Answer:
$5545.10
Step-by-step explanation:
3.55% of $156,200 = $5545.10
jamie and her 2 friends decide to buy a pizza pie and split the cost. The pizza pie cost $12.78. If Jamie has $5, how much does she have left over after they buy the pizza pie?
Answer:
she has no more money
Step-by-step explanation:
Answer:
7.78 if u subtract
but no more money i guess
Types of Data
Numbers
Yes/No
Longer response
What is the campus like?Is there on-campus housing?Is financial aid available?Are engineering scholarships offered?What majors are available?How much is the tuition?How many students are enrolled?What is the average class size?What percentage of those who apply are accepted?What dining options are offered on campus?
jfjkejkiydtmhfsngdjfs
There is a meeting in Conference Room A.
The ratio of women to men is 3 to 4. If there
are 18 women at the meeting, how many men are there?
A) 21 men
B) 54 men
C) 24 men
D) 72 men
Answer:
I think 21 is it right ...
Divide:
−54 ÷ −9 =
pls help llllllllllllllll
Answer:
Step-by-step explanation:
When you divide two negative numbers, the negative sign cancels. So you just get an answer of 6.
Answer:
6
Step-by-step explanation:
-54 / -9
ok so first of all we can just change them to positive
54 / 9
this is what goes on in my head
the 2 digits equal 9
a number times 9 is just that number less then that number times 10
54 / 9 = 6
-54 / -9 = 6
Translation is a congruency transformation. True or false
Answer:
True
Step-by-step explanation:
In a translation, the figures face the same direction and are congruent.
Jamie has a sprinkler than covers a circular area with diameter 16 feet. What is the area of lawn that the
sprinkler covers?
Answer:
64π or 201.0619298297
Step-by-step explanation:
Area of a circle: πr²
To find r, the radius of the circle, take the diameter (16) and halve it to get 8. You can now place 8 into the equation to get π8². Square 8 to get 64. You now now have π64, or 201.0619298297.
I need help on this ASAPPPPPPP
Which expression shows how to convert 60 hours into days?
Answer: so, 60 hours = 60/24 days = 2 days 12 hrs
Step-by-step explanation:
Given m||n, find the value of x.
t
>m
(3x+14)
(7x-4)
Answer:
(3x+14°) + (7x-4)° = 180°
=> 10x + 10 = 180
=> 10x = 180 – 10
=> x = 170/10
=> x = 17
The value of x is 17