Answer:
Consider the following identity:
a³ - b³ = (a + b)(a² - ab + b²)Let a = 2, b = 1/2
(2 + 1/2)(2² - 2*1/2 + 1/2²) = 2³ - (1/2)³ =8 - 1/8Use the algebraic identity given below
[tex]\boxed{\sf a^3-b^3=(a+b)(a^2-ab+b^2)}[/tex]
[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-1+\dfrac{1}{4})[/tex]
[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-2\times \dfrac{1}{2}+\dfrac{1}{2}^2)[/tex]
Here a =2 and b=1/2[tex]\\ \sf\longmapsto 2^3-\dfrac{1}{2}^3[/tex]
[tex]\\ \sf\longmapsto 8-\dfrac{1}{8}[/tex]
A researcher is interested in finding a 90% confidence interval for the mean number of times per
day that college students text. The study included 147 students who averaged 44.7 texts per
day. The standard deviation was 17.9 texts. Round answers to 3 decimal places where possible.
a. To compute the confidence interval use a tv distribution.
b. With 90% confidence the population mean number of texts per day is between
and
texts.
Answer:
90% confidence the Population mean number of texts per day
(42.2561 ,47.1439)
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 147
mean of the sample size x⁻ = 44.7
standard deviation of the sample 'S' = 17.9
90% confidence the Population mean number of texts per day
[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,(x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })[/tex]
Step(ii):-
Degrees of freedom
ν=n-1=147-1=146
t₀.₁₀ = 1.6554
[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,(x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })[/tex]
[tex](44.7 - 1.6554 \frac{17.9}{\sqrt{147} } ,(44.7 + 1.6554 \frac{17.9}{\sqrt{147} })[/tex]
(44.7 - 2.4439 ,44.7 + 2.4439 )
(42.2561 ,47.1439)
Conclusion:-
90% confidence the Population mean number of texts per day
(42.2561 ,47.1439)
find out what's wrong with this graph
Answer:
The y-axis is upside down, meaning that instead of the values increasing as they go up, they decrease.
Find the distance between (8,4) and (8,8).
Answer:
From the given points above, the distance between them is 4 units.
Step-by-step explanation:
In order to find the distance between the two points, we must know the distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Now, we plug in our numbers from the coordinate points that we are given to their respectful places.
[tex]d=\sqrt{(8-8)^2+(8-4)^2}[/tex]
Now, we solve. First, simplify the terms in parentheses. So, subtract 8 from 8 and subtract 4 from 8.
[tex]d=\sqrt{(0)^2+(4)^2}[/tex]
Next, solve for the exponents.
[tex]d=\sqrt{0+16}[/tex]
Add the numbers in the radical.
[tex]d=\sqrt{16}[/tex]
Solve the radical.
[tex]d=4[/tex]
So, the distance between the two given points is 4 units.
Refer to △ABC. Find the length of side AB .
Step-by-step explanation:
Hello, there!!!!
It's simple lets get started with simple solution.....
Given,
AC= 7cm
BC= 25cm
let AB be x.
Now, As it is a Right angled triangle, taking angle B as a refrence angle. we get,
h= BC= 25cm
p= AC= 7cm
b= AB= x
now, by Pythagoras relation we get,
[tex]b = \sqrt{ {h}^{2} - {p}^{2} } [/tex]
[tex]or \: b = \sqrt{ {25}^{2} - {7}^{2} } [/tex]
By simplifying it we get,
b= 24cm
Therefore, the value of AB is 24 cm.
Hope it helps...
Solve for x: −3|2x + 6| = −12.
Answer:
x = -1 or x = -5
Step-by-step explanation:
−3 * |2x + 6| = −12 / -3
|2x + 6| = 4
because this is an absolute value equation there are 2 solutions:
2x + 6 = 4 or 2x + 6 = -4
2x = -2 or 2x = -10
x = -1 or x = -5
Answer:
x = -1 or x = -5
Step-by-step explanation:
cuz it is
The cost in dollars y of producing x computer
desks is given by y = 40x + 4000
X
100
200
300
a. Complete the table
y
b. Find the number of computer desks that can be produced for $6200. (Hint: Find x when y = 6200.)
a. Complete the table.
х
100
200
300
y
b. For $6200,_ computer desks can be produced
Answer:
a.
y= 40x +4000
x= 100 --> y= 40(100)+4000= 4000+4000=8000
x=200 --> y= 40(200)+4000= 6000+4000= 10000
x=300 --> y= 40(300)+4000= 12000+4000= 16000
(in $)
b.
y= 40x+4000
6200= 40x+4000
6200-4000= 40x
2200= 40x
2200/40= x
55= x
(in unit)
Step-by-step explanation:
I hope this helps
if u have question let me know in comments ^_^
What is the inverse of the function a(x)=1/x-2
Answer:
x = 1/x - 2
Step-by-step explanation:
find the value of X from the given picture
Answer:
x = 108
Step-by-step explanation:
The sum of a circle is 360
90 + x/2 + x+x = 360
Combine like terms
90 + 2x+x/2 = 360
90 + 5/2 x = 360
Subtract 90 from each side
5/2x = 270
Multiply each side by 2/5
5/2x * 2/5 = 270*2/5
x =108
The equation 8(y-3)= -40 is solved in several steps below. For each step, choose the reason that best justifies it.
Addition property of Equality
Subtraction Property of Equality
Multiplication property of equality
Division property of equality
simplifying
distributive property
Answer:
Step-by-step explanation:
The steps and their reasons for the equation 8(y - 3) = - 40 are given below.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equation is given below.
8(y - 3) = - 40
Steps Reason
8(y - 3) = - 40 Given
8y - 24 = - 40 Distributive property
8y - 24 + 24 = - 24 + 24 Addition Property of Equality
8y = - 16 Simplifying
8y / 8 = - 16/8 Division property of equality
y = - 2 Simplifying
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
Find the product of the roots of the equation
xl-5x - 36 = 0
Answer:
Step-by-step explanation:
Hello, I assume that you mean
[tex]x^2-5x-36[/tex]
The product is -36.
[tex]x_1 \text{ and } x_2 \text{ are the two roots, we can write}\\\\(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1\cdot x_2[/tex]
So in this example, it means that the sum is 5 and the product is -36.
Thank you
List the stem numbers below!!
Answer:
see below
Step-by-step explanation:
The stems are in the middle and the leaves are on the left and right
Stems are 0,1,2,3,4,5
f(x) = 3x + 2
What is f(5)?
Answer:
17
Step-by-step explanation:
f(x) = 3x + 2
f(5) = 3(5) + 2
f(5) = 15 + 2
f(5) = 17
Answer:
17
Step-by-step explanation:
f(x) = 3x + 2
Plug in:
3(5) + 2
15 + 2 = 17
Hope this helped.
What is the slope? Please Help
Answer:
-1
Step-by-step explanation:
Pick two points on the line
(0,2) and (2,0)
Using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 0-2)/(2-0)
= -2/2
= -1
Answer:
-1
Step-by-step explanation:
Use two points on the line to find the slope, using rise over run.
We can use the points (0, 2) and (2, 0).
From the first point to the other, the y value decreases by 2 and the x value increases by 2.
Use rise (change in y value) over run (change in x value):
-2 / 2
= -1
So, the slope is -1.
It used to take 20 hours to get to Los Angeles, now it takes 12 hours, how much shorter was it?
Step-by-step explanation:
It takes 20 Hours to get to Los Angeles
Now it takes 12 hours....
Therefore we subtract 20 from 12
which becomes
20 - 12= 8.
So it's 8 hours shorter
_____, as a defense mechanism, is the unconscious act of keeping threatening or disturbingthoughts, feelings, or impulses out of consciousness.
a. Sublimation
b. Projection
c. Reaction formation
d. Repression
represent -√2.3 and +√2.3 on number line
Answer:
-√2.3 on left of number line and zero and +√2.3 on right side of number line and zero
Step-by-step explanation:
Natalie's team needs to make a decision on how to handle a big product recall. People on the team have a lot of strong opinions. Management wants everyone to come to a consensus and to find a solution that everyone can support. What's the best way to get to a consensus?
a) Everyone on the team talks until the entire team agrees on one decision. O b) Everyone on the team discusses options and then votes. Oc) The team passes the decision-making responsibility to an outside person. O di The team leader makes a decision without input from the other members.
Answer:
a) Everyone on the team talks until the entire team agrees on one decision.
Step-by-step explanation:
Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense
I need help on this question ASAP please?
Answer:
B.
Step-by-step explanation:
10c + 5 ≤ 45
10c ≤ 40
c ≤ 4
Since the inequality uses the less than or equal to sign, we use a shaded circle on the number line. Since c is less than or equal to 4, your answer will be B, since the line extends infinitely to the left of 4.
Hope this helps!
Answer:
B
Step-by-step explanation:
To get the answer, you need to simplify or re-write the equation given:
10c + 5 ≤ 45 = 10 × c + 5 - (45) ≤ 0Next, group the like terms together:
10c - 40Now, we can apply algebra to simplify the equation further:
(10c ÷ 10) ≤ (40 ÷ 10)c ≤ 4Now, look at your options. Only option B matches our equations. Therefore, B is the correct answer.
What is the area of the regular polygon shown below?
Answer:
shown below..I can't see..
Answer:
93.5 for area
Step-by-step explanation:
there is no picture so that's a simple guess
Compare –3.5 and . Use <, >, or =.
–3.5 >
–3.5 <
–3.5 =
Answer:
-3.5 > -4.5-3.5 < -1.5-3.5 = -3.5Step-by-step explanation:
Give any integer that suits the expression:-3.5 > -4.5-3.5 < -1.5-3.5 = -3.5• The farther a negative integer from 0, the smaller its value.[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
A ball is released at a height of 16 inches to roll inside a half-cylinder. It rolls
to a height of 8 inches on the other side of the cylinder on roll 1. Each time it
rolls up a side of the cylinder, the ball reaches a point that is as high as it
had reached on the other side.
-lo
This explicit formula models the height of the ball, in inches, the nth time it
rolls up a side of the cylinder.
How high does the ball roll on its 5th time up the cylinder's side?
Answer:
Step-by-step explanation:
Using the given formula, we put n = 5
[tex]h = 8* {(\frac{1}{2}) ^{n-1}[/tex]
h = 8 / 16
h = 1 / 2 inches
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
a^2-2a-224=0
Answer:
{-14, 16}
Step-by-step explanation:
The coefficients of this quadratic are a = 1, b = -2 and c = -224.
Thus, the discriminant is b^2 - 4ac, or (-2)^2 - 4(1)(-224), or 900, whose square root is 30.
Thus, the roots (solutions) are
-(-2) ± 30
x = ----------------- = {-14, 16}
2
trigonometric identities
1/tan x = cot x
Cot x + tan x = 1/ sin x cos x
The answer is D.
Write an equation for a line perpendicular to y = − 5 x + 5 and passing through the point (5,5)
Answer:
The answer is
[tex]y = \frac{1}{5} x + 4[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the line perpendicular to
y = -5x + 5 we must first find the slope of
Comparing with the general equation above
Slope = - 5
The slope of the perpendicular line is the negative inverse of the slope of the original line
Slope of perpendicular line = 1/5
Equation of the line using point (5,5) and slope 1/5 is
[tex]y - 5 = \frac{1}{5} (x - 5)[/tex][tex]y - 5 = \frac{1}{5} x - 1[/tex][tex]y = \frac{1}{5} x - 1 + 5[/tex]We have the final answer as
[tex]y = \frac{1}{5} x + 4[/tex]Hope this helps you
Answer:
y=0.2x+4 or y=1/5 x+4.
Step-by-step explanation:
When one line is perpendicular to another, you have to find the opposite reciprocal for the slope of the given equation.
For instance, if you have the number 5, the reciprocal of 5 is 1/5 or 0.2. The opposite of positive is negative. Therefore, it is -0.2.
Therefore, if the slope of the first equation is -5, the slope for the next equation is 1/5. Reciprocal of -5 is -1/5. The opposite of -1/5 is positive 1/5. Or, the opposite of negative is positive. Therefore, it would be 1/5x.
However, we are not done.
Since we are given that the line passes through the point (5,5), we need to find the y-intercept of this equation.
The formula for slope-intercept is y=mx+b.
M is your slope
B is your y-intercept.
We can find the y-intercept by actually plugging in the point (5,5) into the new equation.
5=0.2(5)+b.
5 is x and 5 is also y.
(x,y).
Simplify the equation by multiplying 0.2 times 5. That is equal to 1.
We now have 5=1+b.
Isolate for the letter "b" by subtracting 1 from both sides.
1-1 is 0.
5-1 is 4.
Therefore, b=4.
Finally, we can plug in the y-intercept into the new equation.
y=0.2 or 1/5x+4.
I hope this helps! I also hope you have a great rest of your day!
The joint density function for a pair of random variables X and Y is given. f(x, y) = Cx(1 + y) if 0 ≤ x ≤ 4, 0 ≤ y ≤ 4 0 otherwise f(x,y) = 0
A) Find the value of the constant C. I already have 1/24.
B) Find P(X < = 1, Y < = 1)
C) Find P(X + Y < = 1).
Answer:
A) C = 1/96
B) P(x<=1, y<=1) = 1/128 or 0.0078125 to 7 places
C) P(x+y<=1) = 5/2305, or 0.0021701 to 7 places
Step-by-step explanation:
f(x,y) = C x (1+y)
A)
To find C, we need to integrate the volume under region bound by
0 <= x <= 4, and
0 <= y <= 4
This volume equals 1.0.
Find integral,
int( int(f(x,y),x=0,4), y = 0,4) = 96C
therefore C = 1/96
or
F(x,y) = x (1+y) / 96 ............................(1)
B)
P(x<=1, y<=1)
Repeat the integral, substitute the appropriate limits,
P = int( int(F(x,y),x=0,1), y = 0,1)
= 1/128 or 0.0078125
P(x<=1, y<=1) = 1/128 or 0.0078125 to 7 places
C)
P(x+y<=1)
From the function, we know that this is going to be less than one half of the probability in (B), closer to 1/4 of the previous.
It will be again a double integral, as follows:
P = int( int(F(x,y),x=0,1-y), y = 0,1)
= 5/2304
= 0.0021701 (to 7 decimals)
P(x+y<=1) = 5/2305, or 0.0021701 to 7 places
One time Maria took 27 minutes to walk 1.8km to school. She left home at 07:48 . Write down the time Maria arrived at school
Answer:
8:15
Step-by-step explanation:
Can some body write a word problem using these numbers
Answer:
Mr Singh was travelling from England to Punjab, India. He arrived 5 hours after 0:00. When he was on the plane, there was a delay which caused the whole flight to be pushed 4 hours ahead. This would mean that he would arrive 9 hours after 0:00. Mr Singh was also with his son and he had some homework to do. He had to order the numbers [tex]-4,-2\frac{1}{3} ,0, \frac{3}{4} ,\sqrt{5},5[/tex] from lowest to highest.
Describe the following sequence using an algebraic expression as a rule 0; 2,4; 6
Answer:
Step-by-step explanation:
I assume the sequence is 0, 2, 4, 6
nth term = 2(n-1)
The general manager, marketing director, and 3 other employees of CompanyAare hosting a visitby the vice president and 2 other employees of CompanyB. The eight people line up in a randomorder to take a photo. Every way of lining up the people is equally likely.Required:a. What is the probability that the bride is next to the groom?b. What is the probability that the maid of honor is in the leftmost position?c. Determine whether the two events are independent. Prove your answer by showing that one of the conditions for independence is either true or false.
Answer:
Following are the answer to this question:
Step-by-step explanation:
Let, In the Bth place there are 8 values.
In point a:
There is no case, where it generally manages its next groom is = 7 and it will be arranged in the 2, that can be arranged in 2! ways. So, the total number of ways are: [tex]\to 7 \times 2= 14\\\\ \{(1,2),(2,1),(2,3),(3,2),(3,4),(4,3),(4,5),(5,4),(5,6),(6,5),(6,7),(7,8),(8,7),(7,6)\}\\[/tex][tex]\therefore[/tex] required probability:
[tex]= \frac{14}{8!}\\\\= \frac{14}{8\times7 \times6 \times 5 \times 4 \times 3\times 2 \times 1 }\\\\= \frac{1}{8\times6 \times5 \times 4 \times 3}\\\\= \frac{1}{8\times6 \times5 \times 4 \times 3}\\\\=\frac{1}{2880}\\\\=0.00034[/tex]
In point b:
Calculating the leftmost position:
[tex]\to \frac{7!}{8!}\\\\\to \frac{7!}{8 \times 7!}\\\\\to \frac{1}{8}\\\\\to 0.125[/tex]
In point c:
This option is false because
[tex]\to P(A \cap B) \neq P(A) \times P(B)\\\\\to \frac{12}{8!} \neq \frac{14}{8!}\times \frac{1}{8}\\\\\to \frac{12}{8!} \neq \frac{7}{8!}\times \frac{1}{4}\\\\[/tex]
A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 80 indicated they like the taste. At 95% confidence, test to determine if at least 22% of the population will like the new soft drink.
Required:
Determine the p-value.
Answer: p-value of the test = 0.167
Step-by-step explanation:
Given that,
sample size n = 400
sample success X = 80
confidence = 95%
significance level = 1 - (95/100) = 0.05
This is the left tailed test .
The null and alternative hypothesis is
H₀ : p = 0.22
Hₐ : p < 0.22
P = x/n = 80/400 = 0.2
Standard deviation of proportion α = √{ (p ( 1 - p ) / n }
α = √ { ( 0.22 ( 1 - 0.22 ) / 400 }
α = √ { 0.1716 / 400 }
α = √0.000429
α = 0.0207
Test statistic
z = (p - p₀) / α
z = ( 0.2 - 0.22 ) / 0.0207
z = - 0.02 / 0.0207
z = - 0.9661
fail to reject null hypothesis.
P-value Approach
P-value = 0.167
As P-value >= 0.05, fail to reject null hypothesis.
Since test is left tailed so p-value of the test is 0.167. Since p-value is greater than 0.05 so we fail to reject the null hypothesis.