The reason why we used plus or minus when taking the square root is because; The square root of terms separated by addition and subtraction cannot be calculated individually.
How to use the quadratic formula?
The general formula for a quadratic equation is;
ax² + bx + c = 0
Now, the steps to derive quadratic formula to find the roots of this equation are as follows;
Step 1; Divide both sides of the equation by a to get;
x² + (b/a)x + c/a = 0
Step 2; Transpose the quantity c/a to the right side of the equation to get; x² + (b/a)x = -c/a
Step 3; Complete the square by adding b²/4a² to both sides of the equation to get; x² + (b/a)x + b²/4a² = -c/a + b²/4a²
Step 4; Factor the left side and combine the right side to get;
(x + (b/2a))² = (b² - 4ac)/(4a²)
Step 5: Extract the square-root of both sides of the equation to get;
x + (b/2a) = ±(√(b² - 4ac))/2a
The reason why we used plus or minus when taking the square root is because The square root of terms separated by addition and subtraction cannot be calculated individually.
Read more about Quadratic Formula at; https://brainly.com/question/8649555
#SPJ1
Find the value of 8!
Hey there!
8!
= 8(7)(6)(5)(4)(3)(2)(1)
= 56(6)(5)(4)(3)(2)(1)
= 336(5)(4)(3)(2)(1)
= 1,680(4)(3)(2)(1)
= 6,720(3)(2)(1)
= 20,160(2)(1)
= 40,320(1)
= 40,320
Therefore, your answer should be:
40,320
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Please help, type your answers in order .
Step-by-step explanation:
we know from the laws of motion that in the equation
h = 20t - 1.86t²
the gravitational acceleration is in the factor of the t² term.
h = v0t + 1/2 × g × t²
v0 being the initial velocity (20 m/s).
and we can therefore see, that the gravitational acceleration "a" on Mars is 2×1.86 = 3.72 m/s²
(a)
the velocity v after 2 seconds is (first law of motion)
v = v0 + at = 20 - 3.72×2 = 12.56 m/s
gravity pulling down, so negative acceleration.
(b)
first we need the time when the rock is at 25 m.
25 = 20t - 1.86t²
0 = -1.86t² + 20t - 25
the solution to a quadratic equation is always
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = t
a = -1.86
b = 20
c = -25
t = (-20 ± sqrt(400 - 4×-1.86×-25))/(2×-1.86) =
= (-20 ± sqrt(214))/-3.72
t1 = (-20 + 14.62873884...)/-3.72 =
= 1.443887409... s ≈ 1.44 s
t2 = (-20 - 14.62873884...)/-3.72 =
= 9.308800763... s ≈ 9.31 s
that means, on its way up the rock reached 25m after
1.44 s.
on its way down the rock reached 25 m after
9.31 s.
velocity 0 (the rock came to a stop before falling back down) was after
0 = 20 - 3.72t
3.72t = 20
t = 20/3.72 = 5.376344086... s
that means the rock was falling after this point back to the ground and was gaining speed again.
that accelerating phase until the rock was again at 25 m was
9.308800763... - 5.376344086... = 3.932456677... s
long
the velocity at these points was
v-up = 20 - 3.72×1.443887409... = 14.62873884... m/s ≈
≈ 14.63 m/s
v-down = 0 + 3.72×3.932456677... = 14.62873884... m/s ≈
≈ 14.63 m/s
as expected : the rock did a perfectly symmetric flight path between the two 25 m marks.
so time and speed on both sides had to be identical.
but we have proven it.
Answer:
a) 12.56 m/s
b) up: 14.63 m/s (2 d.p.)
down: -14.63 m/s (2 d.p.)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{The Constant Acceleration Equations (SUVAT)}\\\\s = displacement in m (meters)\\u = initial velocity in m s$^{-1}$ (meters per second)\\v = final velocity in m s$^{-1}$ (meters per second)\\a = acceleration in m s$^{-2}$ (meters per second per second)\\t = time in s (seconds)\\\\When using SUVAT, assume the object is modeled\\ as a particle and that acceleration is constant.\end{minipage}}[/tex]
The average gravitational acceleration on Mars is 3.721 m/s² (about 38% of that of Earth). The fact that the rock is thrown from the surface of Mars rather than the surface of Earth is of no consequence when using the equations of constant acceleration (SUVAT equations) as long as acceleration is not used in the calculations.
Part (a)Given:
[tex]s=20t-1.86t^2, \quad u=20, \quad t=2[/tex]
[tex]\begin{aligned}\textsf{Using }\: s&=\dfrac{1}{2}(u+v)t\\\\\implies 20(2)-1.86(2)^2 & = \dfrac{1}{2}(20+v)(2)\\\\32.56 & = 20+v\\\\v & = 32.56-20\\\\v & = 12.56\:\: \sf m/s\end{aligned}[/tex]
Therefore, the velocity of the rock after 2 s is 12.56 m/s.
Part (b)Find the time when the height of the rock is 25 m:
[tex]\begin{aligned}20t-1.86t^2 & = s\\\implies 20t-1.86t^2 & = 25\\1.86t^2-20t+25 & = 0\end{aligned}[/tex]
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=1.86, \quad b=-20, \quad c=25[/tex]
[tex]\implies t=\dfrac{-(-20) \pm \sqrt{(-20)^2-4(1.86)(25)} }{2(1.86)}[/tex]
[tex]\implies t=\dfrac{20 \pm \sqrt{214}}{3.72}[/tex]
[tex]\implies t=9.308800763..., 1.443887409...[/tex]
Therefore, the height of the rock is 25 m when:
t = 9.31 s (2 d.p.)t = 1.44 s (2 d.p.)To find the velocity (v) of the rock at these times, substitute the found values of t into the equation, along with s = 25 and u 20 m/s:
[tex]\begin{aligned}\textsf{Using }\: s&=\dfrac{1}{2}(u+v)t\\\\\implies v & = \dfrac{2s}{t}-u\\\\v & = \dfrac{2(25)}{t}-20\\\\v & = \dfrac{50}{t}-20\\\\\end{aligned}[/tex]
When t = 1.443887409...s
[tex]\implies v=\dfrac{50}{1.443887409...}-20=14.63\:\: \sf m/s \: \:(2\:d.p.)[/tex]
When t = 9.308800763...s
[tex]\implies v=\dfrac{50}{9.308800763...}-20=-14.63\:\: \sf m/s \: \:(2\:d.p.)[/tex]
Therefore, the velocity of the rock when its height is 25 m is:
up: 14.63 m/s (2 d.p.)down: -14.63 m/s (2 d.p.)Learn more about constant acceleration equations here:
https://brainly.com/question/28211552
https://brainly.com/question/28202782
Briana received a 10-year subsidized student loan of $26,000 at an annual interest rate of 4.125%. Determine her monthly payment (in dollars) on the loan after she graduates in 2 years. (Round your answer to the nearest cent.)
Answer:
$264.78
Step-by-step explanation:
The government pays the interest on Briana's loan while she is in school. Her monthly payments will be for a loan of $26,000. The amount of the payment can be found from the amortization formula, or using a calculator or spreadsheet.
Payment amountFor a loan of principal amount P at annual rate r for t years, the monthly payment is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t)) = $26000(0.04125/12)/(1 -(1 +0.04125/12)^(-120)) = $264.78
Briana's monthly payment after she graduates is $264.78.
A teacher records the number of students present in her 1st period class each day. This count is a ___________ random variable.
A. Discrete
B. Countable
C. Continuous
D. Finite
This count is a discrete random variable (option A).
What is a discrete random variable?A discrete random variable is a variable that contains integers that can only be a limited number of possible values. A discrete random variable is can contain only a finite set of numbers .
An example of discrete random variable is the number of students in the first period class. It is impossible for the number of students in the class to go on indefinitely.
Discrete random variable has the following properties:
It is finiteIt is numericIt is countableIt contains non-negative integers.A continous random variable is a variable that has an infinite number.
To learn more about discrete data, please check: https://brainly.com/question/22916429
#SPJ1
Which of the following is the solution to the inequality below? 9 - 3x >= 2(x - 3) A . x <= 15 B. x >= 15 C. x >= 3 D. x <= 3
Answer: [tex]x \leq 3[/tex]
Step-by-step explanation:
[tex]9-3x \geq 2(x-3)\\\\9-3x \geq 2x-6\\\\15-3x \geq 2x\\\\15 \geq 5x\\\\3 \geq x\\\\x \leq 3[/tex]
He wants to earn 481$ By mowing lawns and he charge $22 for each long what is the maximum number of lungs that he needs to mow to reach his goal of $481
[tex]\stackrel{\stackrel{total~amount}{goal}}{481}~~ = ~~22(lawn)\implies \cfrac{481}{22}=lawn\implies \stackrel{rounded}{22}\approx lawn[/tex]
NO LINKS!! Please help me with this problem
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The given figure shows a vertical hyperbola with its centre at origin, and as we observe the figure, we can conclude that :
Length of transverse axis is :
[tex]\qquad \sf \dashrightarrow \: 2b = 12[/tex]
[tex]\qquad \sf \dashrightarrow \: b = 6[/tex]
length of conjugate axis is :
[tex]\qquad \sf \dashrightarrow \: 2a = 8[/tex]
[tex]\qquad \sf \dashrightarrow \: a = 4[/tex]
Equation of hyperbola ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {y}^{2} }{ {b}^{2} } - \cfrac{ {x}^{2} }{ {a}^{2} } = 1[/tex]
plug in the values ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {y}^{2} }{ {6}^{2} } - \cfrac{ {x}^{2} }{ {4}^{2} } = 1[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {y}^{2} }{ {36}^{} } - \cfrac{ {x}^{2} }{ {16}^{} } = 1[/tex]
Answer:
[tex]\dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]
Step-by-step explanation:
Standard form equation of a vertical hyperbola
[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex]
where:
center = (h, k)vertices = (h, k±a)co-vertices = (h±b, k)foci = (h, k±c) where c² = a² + b²[tex]\textsf{asymptotes}: \quad y =k \pm \left(\dfrac{a}{b}\right)(x-h)[/tex]Transverse axis: x = hConjugate axis: y = kFrom inspection of the graph:
center = (0, 0) ⇒ h = 0, k = 0vertices = (0, 6) and (0, -6) ⇒ a = 6co-vertices = (4, 0) and (-4, 0) ⇒ b = 4Substitute the found values into the formula:
[tex]\implies \dfrac{(y-0)^2}{6^2}-\dfrac{(x-0)^2}{4^2}=1[/tex]
[tex]\implies \dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]
1) La suma de dos números es 58. Si uno de los números es 12 más que el otro
número,
cuáles son los números?
Answer:
Los números son 23 y 35.
Step-by-step explanation:
Q: The sum of two numbers is 58. If one of the numbers is 12 more than the other number, what are the numbers?
Set the numbers as x and y. Using the given information, we have two equations:
x+y=58
x=y+12
Solving using substitution, we have:
y+y+12=58 -> y=23
Substituting, x=23+12=35
The numbers are 23 and 35.
Which choice is equivalent to the expression below?
√6 +2√√3+√27-√12
A. 53-6
OB. 2√3-√21
OC. 3√3+√6
OD. 5√3
The Evaluating expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.
According to the statement
We have given that one evaluating expression which is √6 +√6+√27-√12
And we have to simplify this expression by evaluating it.
So, Given expression is:
√6 +√6+√27-√12
√6 +√6+√(9*3)-√(4*3)
√6 +√6+3√(3)-2√(3)
√6 +√6+√3( 3-2)
After evaluating the expression it become
√6 +√6+√3(1)
√(3*2) +√(3*2) +(1)√3
Take common from above expression then
√3(√2 +√2 ) +√3
√3(2√2) +√3
√3(2√2+ 1)
Now the expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.
So, The Evaluating expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Which choice is equivalent to the expression below?
√6 +√6+√27-√12
A. √3(2√2+ 1)
B. 2√3-√21
C. 3√3+√6
D. 5√3
Learn more about Evaluating expression here https://brainly.com/question/4344214
#SPJ1
Set W consists of the even whole numbers from 2 to 20, inclusive. If a number is selected at random from set W, then what is the probability that the number is a
multiple of 4 and also a multiple of 6?
Answer:
1/19
Step-by-step explanation:
The number in the set that are a multiple of both 4 and 6 is 12.
This is one number out of the 19 numbers in the set, so the probability is 1/19.
Which equation is correct?
O sin gº =z/x
O sin gº=x/z
O tan gº =z/x
O tan gº = x/z
SUPER URGENT PLEASE ANSWER ASAP
Answer:
shown below
Step-by-step explanation:
Look at the white squares, count them. 1, 2, 3. the next will be 4 and 5. draw 4 white squares, then house it in black squares like the others. to know if u did it right, count the black squares, there should be 8, then 9.
If one angle in a parallelogram is a right angle prove the other are the same.
Answer: If one angle of a parallelogram is a right angle, then all other angles would also be right angles and the parallelogram would be a rectangle.
If u spend $25 per day. How many days will it take you to spend $1,000
Answer:
4days atlases in the week
Quantity day
25------------------1
1000---------------x
We solve
[tex]\boldsymbol{\sf{x=\dfrac{1000\times1}{25}=\dfrac{1000}{25}=40 }}[/tex]
Answer: To spend $1,000 it will take 40 days.
ヘ( ^o^)ノ＼(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:
https://brainly.com/question/28182944
The distance from TJ's house to school and back is 0.4 km. In one week TJ travelled 2 km. How many times did TJ go to school?
$$
Answer: 5 times
Step-by-step explanation: The distance from his house to school and back is 0.4 km. Since he traveled 2km in a week, we have to divide 2 by0.4. 0.4x5 = 2 so he went to school 5 times a week.
If 7 and 9 are the remainders when 98 and 165
respectively, are divided by a positive integer a, then a =
Answer:
Step-by-step explanation:
98-7=91
165-9=156
(91/156)/13=7/12
Answer = 13
It is divided by a positive integer a, which will equal the number 13.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the data provided by the question,
The number are 98 and 165.
The remainders are 7 and 9.
So, the actual number is,
98 - 7 = 91 and,
165 - 9 = 156
They are divided by the number 13, so the value of a will be equal to 13.
To know more about arithmetic operations:
https://brainly.com/question/13585407
#SPJ2
The value of your stock investment in a certain company decreased 10 % over the last year. If the value of your stock investment is $7000
today, then what was the value of your stock investment a year ago
The value of the stock a year ago is $7778
How to determine the value of the stock a year ago?The given parameters are:
Depreciation rate, r = 10%
Value of investment today, V(t) = $7000
The value of the stock a year ago is then calculated as:
Value of investment today = Value of investment last year * (1 - Depreciation rate)
Substitute the known values in the above equation
7000 = Last year * (1 - 10%)
Evaluate the difference of 1 and 10%
7000 = Last year * (90%)
Divide both sides by 90%
Last year = 7778
Hence, the value of the stock a year ago is $7778
Read more about depreciation at:
https://brainly.com/question/25297296
#SPJ1
what’s the approximate value of tan 1
Answer: tan 1 radians = 1.557, tan 1 degrees = 0.017
1) The following scatterplot shows the percentage of the vote a candidate received in the 2016 senatorial elections
according to the voter's income level based on an exit poll of voters conducted by a news agency. The income
levels 1-8 correspond to the following income classes:
1 = Under $15,000; 2 = $15-30,000; 3 = $30-50,000; 4 = $50-75,000; 5 = $75-100,000;
6 = $100-150,000; 7 = $150-200,000; 8 = $200,000 or more.
Use the election scatterplot to determine whether there is a correlation between percentage of vote and income
level at the 0.01 significance level with a null hypothesis of ρs = 0.
A) The test statistic is between the critical values, so we fail to reject the null hypothesis. There is no
evidence to support a claim of correlation between percentage of vote and income level.
B) The test statistic is not between the critical values, so we fail to reject the null hypothesis. There is no
evidence to support a claim of correlation between percentage of vote and income level.
C) The test statistic is between the critical values, so we reject the null hypothesis. There is sufficient
evidence to support a claim of correlation between percentage of vote and income level.
D) The test statistic is not between the critical values, so we reject the null hypothesis. There is sufficient
evidence to support a claim of correlation between percentage of vote and income level
The answer to the question is B. The test statistic is not between the critical values, so we reject the null hypothesis. There is sufficient evidence to support a claim of correlation between percentage of vote and income level.
What is the scatter plot?This is the plot that shows the relationship between two different variables along a straight line. All of the points that are known to have a relationship between these variables would fall under this line. Other parts that fall outside the line are regarded as the outliers in the plot.
In this particular question, the outlier is seen to be outside of the critical values so we have to conclude that the solution is B. We fail to reject the null hypothesis.
Read more on scatter plot here: https://brainly.com/question/6592115
#SPJ1
If the lengths of a triangle are 8, 12, and 18 can it be a right triangle?
Hello,
The triangle be right only if : 18² = 8² + 12²
We have : 18² = 18 × 18 = 324
and 8² + 12² = 8 × 8 + 12 × 12 = 208
324 ≠ 208 → the triangle can not be a right triangle
the first term of a geometric sequence is 400 and the common ratio is 0.5. what is the 5th term of the sequence.
Answer:
25
Step-by-step explanation:
Geometric sequence
General form of a geometric sequence:
[tex]a_n=ar^{n-1}[/tex]
where:
a = first termr = common ratio[tex]a_n[/tex] = nth termGiven values:
a = 400r = 0.5n = 5Substitute the given values into the formula and solve:
[tex]\implies a_5=400(0.5)^{5-1}[/tex]
[tex]\implies a_5=400(0.5)^{4}[/tex]
[tex]\implies a_5=400(0.0625)[/tex]
[tex]\implies a_5=25[/tex]
Learn more about geometric sequences here:
https://brainly.com/question/27783194
https://brainly.com/question/25398220
You are currently evaluating your business and trying to decide how much you need to sell to make a profit. Choose one of the following options for your cost and revenue functions. The variable, x, represents the number of units sold.
c(x)=300+260x
r(x)=300x-xsquared
For the option you chose, find the value(s) of x (the number of units sold) to break-even. Show all your work by typing it in or uploading a picture of your handwritten work. What is your profit function, P(x)? What is your profit when you sell 10 more than a break-even point? Is that what you expected? Show all your work
From the given functions, of the cost, c(x) = 300 + 260•x, and revenue, r(x) = 300•x - x², we have;
First part;
The values of x to break-even are;
x = 30, or x = 10
Second part;
The profit function, P(x) is presented as follows;
P(x) = x•(40 - x) - 300
Third part;
The profit (loss) when 10 more units is sold than the break-even point, x = 30 is -($300) unexpected The profit when 10 more units is sold than the break-even point, x = 10 is $100How can the given functions be used to find the profit made?The cost is c(x) = 300 + 260•x
Revenue is r(x) = 300•x - x²
First part;
At the break even point, we have;
c(x) = r(x)Which gives;
300 + 260•x = 300•x - x²
x² + 260•x - 300•x + 300 = 0
x² - 40•x + 300 = 0Factoring the above quadratic equation gives;
x² - 40•x + 300 = (x - 30)•(x - 10) = 0
At the break even point, x = 30, or x = 10
The values of x at the break even point are;
x = 30 units soldx = 10 units soldSecond part;
Profit = Revenue - Cost
The profit function, P(x), is therefore;
P(x) = r(x) - c(x)
Which gives;
P(x) = (300•x - x²) - (300 + 260•x)
P(x) = 300•x - x² - 300 - 260•x
P(x) = 300•x - 260•x - x² - 300
P(x) = 40•x - x² - 300
The profit function is therefore;
P(x) = x•(40 - x) - 300Third part;
When 10 more units are sold than the break even point, we have;
x = 30 + 10 = 40 or x = 10 + 10 = 20
The profit at x = 40 or x = 20 are;
P(40) = 40•(40 - 40) - 300 = -300
P(40) = -($300)When the number of units sold, x = 40, the profit is, P(40) = -($300) unexpected loss
The profit (loss) when the number of units sold increases to 40, of -($300) is unexpected.At x = 20, we have;
P(20) = 20•(40 - 20) - 300 = 100
P(20) = $100When the number of units sold, x = 20, the profit is, P(20) = $100Learn more about functions here:
https://brainly.com/question/88581
#SPJ1
In a unit circle, 0 = 90°. Identify the terminal point and sin 0.
A. Terminal point: (0, 1); sin 0 = 1
B. Terminal point: (1, 0); sin 0 = 0
C. Terminal point: (1, 0); sin 0 = 1
OD. Terminal point: (0, 1); sin 0 = 0
SUBMI
Terminal point: (0, 1); sinФ = 1 ⇒ A
How do you find the terminal point?P(a, b) is the terminal point indicated by t, and the signs are selected based on the quadrant in which this terminal point is located. For each actual number t that is given.The terminal point on the positive x-axis is (1, 0), which denotes that cos(x) = 1, sin(x) = 0 and = 0° or 360°.The terminal point (0, 1) on the positive y-axis indicates that = 90° and cos = 0, sin = 1.The x-terminal axis's point on the negative side is (-1, 0), which indicates that the angle is 180 degrees, cos is -1, and sin is 0.(0, -1), which denotes the terminal point on the negative y-axis, indicates that = 270° and cos = 0, sin = -1.On a unit circle Ф = 90°
Using the second rule listed above
The terminal point is (0, 1)
sinФ = 1
Terminal point: (0, 1); sinФ = 1
To learn more about Terminal point, refer to:
https://brainly.com/question/1982296
#SPJ9
create a pattern of 6 numbers by multiplying a number by 5 to get the next number.starts with 4
Answer:
45 405 415 425 435 445
Step-by-step explanation:
this are the pattern of 6 numbers multiplying by number 5 to get the number starts with 4
Answer:
4,20,100,500,1500,8500.
Step-by-step explanation:
Find the simple interest earned after 4 years on $2,250 invested at an interest rate of 5%.
simple interest= principal x time x rate/100
A store is having a 20% off sale. The sale price of an item with price p is p - 0.2p. What is an equivalent expression.
Which of the following is not irrational? (a) (2-√3)2 (b)(√2+√3)2 (c) (√2-√3)(√2+√3) (d)27√7
Answer: (c)
(√2-√3)(√2+√3)
Step-by-step explanation:
An irrational number is one that cannot be expressed as the ratio of two integers. In other words it cannot be expressed as [tex]\frac{x}{y}[/tex] where x and y are integers
[tex]\sqrt{2}[/tex] is irrational
[tex]\sqrt{3}[/tex] is irrational
In fact the square root of any prime number is irrational. So [tex]\sqrt{5}[/tex], [tex]\sqrt{7}[/tex] etc are irrational. But [tex]\sqrt{9}[/tex] is not irrational since it evaluates to 3 which can be expressed as [tex]\frac{3}{1}[/tex]
Any expression that contains the square root of a prime number is also irrational
Looking at the choices we see that choices (a), (b) and (d) all evaluate to expressions containing square roots of primes
(a) (2-√3)2 = 4 - 2√3 . Hence irrational
(b) √2+√3)2 = 2√2+2√3. Hence irrational
(d) 27√7 is irrational
Let's look at choice (c)
(√2-√3)(√2+√3)
An expression [tex](a+b)(a-b)[/tex] can be evaluated as [tex]a^{2} - b^{2}[/tex]
Here a = √2, [tex]a^{2}[/tex] =[tex]a = \sqrt{2}\\ a^2 = (\sqrt{2} )^2 = 2\\\\b = \sqrt{3} \\b^2 = (\sqrt{3} )^2 = 3\\\\a^2 - b^2 = 2-3 = -1\\[/tex]
This is a whole number(integer) and all integers are rational numbers
Hence correct answer is (c)
In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 5.2 and a standard deviation of 2.5. Answer parts (a)–(d) below.
The probability that a randomly selected study's participant was less than 4 is 0.2266.
How to compute the probability?Given that:
mean = 5.8
standard deviation = 2.4
a) P(x < 4) = P[(x - mean ) /sd < (4 - 5.8) / 2.4]
= P(z < -0.75)
Using z table,
= 0.2266
b) P(4 < x < 6) = P[(4 - 5.8)/ 2.4) < (x - \m ) /sd < (6 - 5.8) / 2.4) ]
= P(-0.75 < z < 0.08)
= P(z < 0.08) - P(z < -0.75 )
Using z table,
= 0.5319 - 0.2266
= 0.3053
c) P(x > 8) = 1 - p( x< 8)
=1- p P[(x - \m ) / sd< (8 - 5.8) / 2.4]
=1- P(z < 0.92)
Using z table,
= 1 - 0.8212
= 0.1788
Lastly, there are no unusual events because all the probabilities are greater than 0.05.
Learn more about probability on:
https://brainly.com/question/24756209
#SPJ1
Amanda rented a bike from Ted's Bikes.
It costs $10 for the helmet plus $4.25 per hour.
If Amanda paid about $33.38, how many hours did she rent the bike?
a) Let h = the number of hours she rented the bike. Write the equation you would use to solve this problem.
Answer:
5.5 hours
Step-by-step explanation:
I am going to assume that a helmet is necessary prerequisite for renting the bike.
I also am assuming that the hourly rate can be turned into a sub hourly rate if the full hour isn’t used.
10+4.25h=33.38
4.25h=23.38
h=23.38/4.25
h=5.5
one of the angles of a triangle is 106° and the other two angles are equal find each of the equal angles
Answer:
37°
Step-by-step explanation:
• recall that the sum of the interior angles of a triangle
is equal to 180°
Then
The measure of the two other angles :
= 180 - 106
= 74°
The measure of each of the equal angles :
= 74 ÷ 2
= 37°
Answer:
the 2 angles r 37
Step-by-step explanation:
the angles of triangle sums up to 180, and lets call the unknown angle x, since they're both equal, x+x=2x
so when 3 angles of triangle adds up, we get 180
106+2x=180
2x=180-106
2x=74, divide both sides by 2 to get x
x=74/2
x=37
PLEASE MARK ME BRAINLIEST OF IT HELPED :)