Answer:
The price before tip was 35
Step-by-step explanation:
Let x = original amount
x * 20% = 7
Change to decimal form
x * .20 = 7
Divide each side by .20
x*.20/.20 = 7/.20
x =35
-2x(x+3)-(x+1)(x-2)=
Answer:
-3x^2 -5x +2
Step-by-step explanation:
-2x(x+3)-(x+1)(x-2)=
Distribute
-2x^2 -6x -(x+1)(x-2)
Foil
-2x^2 -6x -(x^2 -2x +x -2)
Combine like terms
-2x^2 -6x -(x^2 -x -2)
Distribute the minus sign
-2x^2 -6x -x^2 +x +2
Combine like terms
-2x^2 -x^2 -6x +x +2
-3x^2 -5x +2
Answer:
[tex]\huge\boxed{-2x(x+3)-(x+1)(x-2)=-3x^2-5x+2}[/tex]
Step-by-step explanation:
[tex]-2x(x+3)-(x+1)(x-2)[/tex]
Use the distributive property: a(b + c) = ab + ac
and FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex]=(-2x)(x)+(-2x)(3)-\bigg[(x)(x)+(x)(-2)+(1)(x)+(1)(-2)\bigg]\\\\=-2x^2-6x-\bigg(x^2-2x+x-2\bigg)=-2x^2-6x-x^2-(-2x)-x-(-2)\\\\=-2x^2-6x-x^2+2x-x+2[/tex]
Combine like terms:
[tex]=(-2x^2-x^2)+(-6x+2x-x)+2=-3x^2+(-5x)+2\\\\=-3x^2-5x+2[/tex]
Which of the following functions best describes this graph ?
Answer:
answer D
Step-by-step explanation:
Lets have a look to the graph and to the each of given functions.
As we can see in graph it intersects X in points (-3;0) and (-6;0) that means the function has the roots x1=-3 and x2=-6
Function A has the roots x1=+3 and x2=+6 => doesn' t fit
Function B has only 1 root x=2 , so can be factorized y=(x-2)^2 => doesn' t fit
Function C has 2 roots x1=4 and x2=-5 => doesn' t fit
Function D can be factotized as y=(x+6)*(x+3) so has 2 roots x1=-6 x2=-3 => exactly what we need!!!
We can also notice that the coefficient near x² is equal to 1 and is positive.
That means the legs of the graph directed up,- this is exactly like in our graph. It gives us extra argument why we choose D.
Six identical coins are tossed. How many possible arrangements of the coins include three heads and three tails?
Answer:
The possible arrangement= 18 ways
Step-by-step explanation:
Six identical coin are tossed.
Coin has only a tail and a head.
In how many possible ways can the arrangement be 3 head and 3 tail.
The possible arrangement= (3! * 3!)/2
The reason for dividing by two because coin has two face.
The possible arrangement= (3! * 3!)/2
The possible arrangement=( 6*6)/2
The possible arrangement= 36/2
The possible arrangement= 18 ways
Which of the following is equivalent to4−(−5∗9−1)÷2+(5)2−7?
Answer:
-20
Step-by-step explanation:
Follow the PEDMAS order (from top to bottom):
Parentheses
Exponents
Division and Multiplication
Addition and Subtraction
(-5 × 9 - 1) ÷ 2 + (5)2 - 7
(-45 - 1) ÷ 2 + 10 - 7
-46 ÷ 2 + 10 - 7
-23 + 10 - 7
-13 - 7
-20
Answer:
-20
Step-by-step explanation:
=> [tex](-5 * 9-1)/2+(5)2-7[/tex]
Expanding parenthesis
=> [tex](-45-1)/2+10-7[/tex]
=> [tex]-46/2 + 3[/tex]
=> -23 + 3
=> -20
Find the unknown side length, x. Write your answer in simplest radical form.
Answer:
Correct option: D
Step-by-step explanation:
In the figure we have a right triangle, that is, one of the angles is a 90° angle. Therefore, we can use the Pythagoras' theorem to find the relation between the sides of the triangle:
[tex]a^2 = b^2 + c^2[/tex]
Where b and c are cathetus of the triangle (sides adjacent to the 90° angle) and a is the hypotenuse (opposite side to the 90° angle).
So in our case, we have that x is the hypotenuse, and 40 and 42 are cathetus, so we have:
[tex]x^2 = 40^2 + 42^2[/tex]
[tex]x^2 = 1600 + 1764[/tex]
[tex]x^2 = 3364[/tex]
[tex]x = 58[/tex]
So the correct option is D.
I really need help on this question
Answer:
d. 38
Step-by-step explanation:
AB = AD - BD = 54 - 36 = 18
AC = AB + BC = 18 + 20 = 38
1). f(x) = 3x + 15 then what's f^-1(x)?
Answer:
Step-by-step explanation:
f(x)=3x+15
let f(x)=y
y=3x+15
flip x and y
x=3y+15
3y=x-15
y=1/3 x-5
or f^{-1}x=1/3 x-5
what is the 20th term of the arithmetic sequence a(n)=-5+(n-1)3
Answer:
52
Step-by-step explanation:
a(n)=-5+(n-1)3
a(20)=-5+(20-1)3
a(20)=52
The 20th term of the arithmetic sequence is 52.
What is Arithmetic sequence?An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
For example,
In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 ... is arithmetic because the difference between consecutive terms is always two.
The nth term of an arithmetic sequence is given by an = a + (n – 1)d.
Given:
a(n)=-5+(n-1)3
First term,
a(1)= -5 + 0
a(1)= -5
second, a(2)= -5 + 1*3
a(2)= -2
Third, a(3)= -5+6
a(3)= 1
d= 3
So, the 20th term
a(20)= -5+ (20-1)3
a(20)= -5 + 57
a(20)= 52
Hence, the 20th term is 52.
Learn more about Arithmetic Sequence here:
https://brainly.com/question/10396151
#SPJ2
Assume that y varies directly with
x, then solve.
If y=6 when x=2/3 find x when y=12.
Х=? (It’s a fraction)
Answer:
x = 4/3
Step-by-step explanation:
Direct variation:
y = kx
We use the given x-y point to find k.
6 = k * 2/3
k = 6 * 3/2
k = 9
The equation is
y = 9x
For y = 12,
12 = 9x
x = 12/9
x = 4/3
Gena wants to estimate the quotient of –21.87 divided by 4.79. Which expression shows the best expression to estimate the quotient using front-end estimation? Negative 21 divided by 4 Negative 21 divided by 5 Negative 20 divided by 4 Negative 20 divided by 5
Answer:
-21/5 = -4.2
Step-by-step explanation:
-21.87 / 4.79 = -4.5657.....
So, the quotients is -4
Now, Let's see who's quotient is equal to think one:
-21/4 = -5.25
-21/5 = -4.2
-40/4 = -5
-20/5 = 4
Answer:
-21/5 = -4.2
Step-by-step explanation:
please please please help me. i need to pass, will do anything. ANYTHING!
Answer:
[tex]d \approx 5.8[/tex]
Step-by-step explanation:
Just use the distance formula.
[tex]d=\sqrt{(x_2-x_{1})^2+(y_2-y_{1})^2}[/tex]
[tex]d=\sqrt{(3-0)^2+(5-0)^2}}[/tex]
[tex]d=\sqrt{(3)^2+(5)^2}}[/tex]
[tex]d=\sqrt{9+25}[/tex]
[tex]d=\sqrt{34[/tex]
[tex]d \approx 5.8[/tex]
what is the constant of proportionality for 4y=16
Answer:
Step-by-step explanation:
y=4x
Letters a, b, c, and d are angles measures. Lines m and n are cut by transversal p. At the intersection of lines p and m, labeled clockwise, from uppercase left, the angles are: a, b, c, blank. At the intersection of lines p and n, labeled clockwise, from uppercase left, the angles are: blank, blank, d, blank. Which equation is enough information to prove that lines m and n are parallel lines cut by transversal p? Select three options. a = c a = d c = d b + c = 180° b + d = 180°
Answer:
b, c, e
Step-by-step explanation:
the reasons have to include an angle from both of the parallel lines. by using process of elimination it is b, c, e. I also got it right
Answer:
B. a=d
C. c=d
E. b + d=180°
Step-by-step explanation:
Got Correct On MyPath.
Yesterday at 1:00 P.M., Maria’s train was 42 miles north of Gull’s Beach, traveling north at an average speed of 90 mph. At the same time on the adjacent track, Elena’s train was 6 miles north of Gull’s Beach, traveling north at an average speed of 101 mph. To the nearest hundredth of an hour, after how much time will the trains meet up? 0.23 hours 0.31 hours 3.27 hours 4.36 hours
Answer:
3.27 hours
Step-by-step explanation:
Calculate the difference in speed and distance between the trains.
The relative speed:
101 - 90 = 11 mph
Difference in distance:
42 - 6 = 36 miles
[tex]time=\frac{distance}{speed}[/tex]
[tex]t=\frac{36}{11}[/tex]
[tex]t = 3.27[/tex]
Answer:
yeah she is correct
Step-by-step explanation:
helpppppppppppppppppppppp i will give star thanks bralienst
Answer:
90/x=70/100 that's my answer
[tex]90 \x = 70 \100[/tex]
Answer:
90/x = 70/100
Step-by-step explanation:
Is means equals and of means multiply
90 = 70% *x
Changing to decimal form
90 = .70x
Changing to fraction form
90 = 70/100 *x
Divide each side by x
90/x = 70/100
The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume there are 360 days in a year. P = $7000, r = 0.2%, t = 6months
Answer:
$7
Step-by-step explanation:
Simple interest formula:
I = Prt
6 months = 6 * 30 days = 180 days
1 year = 360 days
t = (180 days)/(360 days) = 0.5
I = $7000 * 0.002 * 0.5
I = $7
Answer:
$7
Step-by-step explanation:
Recall that simple interest is given by
I = Prt,
Where :
I = interest (we are asked to find this)
P = principal amount = given as $7000
r = rate = given as 0.2% = 0.002
t = time in years = given as 6 months = 0.5 years
SImply substitute the known values into the equation above:
I = Prt
= (7000)(0.002)(0.5)
= $7
A bag of marbles contains 4 green marbles, 3 blue marbles, 2 red marbles, and 5 yellow marbles. How many total possible outcomes are there when choosing a marble from the bag?
Answer:
its 14/C
Step-by-step explanation:
i got i right on edg U^U
Answer:
16
Step-by-step explanation:
i did edge test yea dont be imma fake :***
Part A Each time you press F9 on your keyboard, you see an alternate life for Jacob, with his status for each age range shown as either alive or dead. If the dead were first to appear for the age range of 75 to 76, for example, this would mean that Jacob died between the ages of 75 and 76, or that he lived to be 75 years old. Press F9 on your keyboard five times and see how long Jacob lives in each of his alternate lives. How long did Jacob live each time? Part B The rest of the potential clients are similar to Jacob, but since they’ve already lived parts of their lives, their status will always be alive for the age ranges that they’ve already lived. For example, Carol is 44 years old, so no matter how many times you press F9 on your keyboard, Carol’s status will always be alive for all the age ranges up to 43–44. Starting with the age range of 44–45, however, there is the possibility that Carol’s status will be dead. Press F9 on your keyboard five more times and see how long Carol lives in each of her alternate lives. Remember that she will always live to be at least 44 years old, since she is already 44 years old. How long did Carol live each time? Part C Now you will find the percent survival of each of your eight clients to the end of his or her policy using the simulation in the spreadsheet. For each potential client, you will see whether he or she would be alive at the end of his or her policy. The cells in the spreadsheet that you should look at to determine this are highlighted in yellow. Next, go to the worksheet labeled Task 2b and record either alive or dead for the first trial. Once you do this, the All column will say yes if all the clients were alive at the end of their policies or no if all the clients were not alive at the end of their policies. Were all the clients alive at the end of their policies in the first trial? Part D Next, go back to the Task 2a worksheet, press F9, and repeat this process until you have recorded 20 trials in the Task 2b worksheet. In the Percent Survived row at the bottom of the table on the Task 2b worksheet, it will show the percentage of times each client survived to the end of his or her policy, and it will also show the percentage of times that all of the clients survived to the end of their respective policies. Check to see whether these percentages are in line with the probabilities that you calculated in questions 1 through 9 in Task 1. Now save your spreadsheet and submit it to your teacher using the drop box. Are your probabilities from the simulation close to the probabilities you originally calculated?
Step-by-step explanation:
brain list me please......
Answer:
Jacob:
Alive 69-70
alive 79-80
alive 62-63
alive 73-74
alive 78-Died 79
Carol:
alive 88-89
alive 67-68
alive 99-100
alive 73-74
alive 94- Died 95
Step-by-step explanation:
Translate and solve: 3x less than two times the sum of 2X and one is equal to the sum of 2 and 5
Answer:
The answer is x = 5Step-by-step explanation:
The statement
3x less than two times the sum of 2X and one is written as
2( 2x + 1) - 3x
the sum of 2 and 5 is written as
2 + 5
Equate the two statements
We have
2( 2x + 1) - 3x = 2+5
Expand
4x + 2 - 3x = 7
Simplify
4x - 3x = 7 - 2
We have the final answer as
x = 5Hope this helps you
Safegate Foods, Inc., is redesigning the checkout lanes in its supermarkets throughout the country and is considering two designs. Tests on customer checkout times conducted at two stores where the two new systems have been installed result in the following summary of the data.
System System B
n1=120 n2=100
x1=4.1 minutes x2=3.4 minutes
σ1=2.2minutes σ2= 1.5 minutes
Test at the 0.05 level of significance to determinewhether the population mean checkout times of the two newsystems differ. Which system is preferred?
Answer:
We conclude that the population means checkout times of the two new systems differ.
Step-by-step explanation:
We are given the result in the following summary of the data;
System System B
n1=120 n2=100
x1=4.1 min x2=3.4 min
σ1=2.2 min σ2= 1.5 min
Let [tex]\mu_1[/tex] = population mean checkout time of the first new system
[tex]\mu_2[/tex] = population mean checkout time of the second new system
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex] {means that the population mean checkout times of the two new systems are equal}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex] {means that the population mean checkout times of the two new systems differ}
The test statistics that will be used here is Two-sample z-test statistics because we know about population standard deviations;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1} + \frac{\sigma_2^{2} }{n_2}} }[/tex] ~ N(0,1)
where, [tex]\bar X_1[/tex] = sample mean checkout time of the first new systems = 4.1 min
[tex]\bar X_2[/tex] = sample mean checkout time of the second new systems = 3.4 min
[tex]\sigma_1[/tex] = population standard deviation of the first new systems = 2.2 min
[tex]\sigma_2[/tex] = population standard deviation of the second new systems = 1.5 min
[tex]n_1[/tex] = sample of the first new systems = 120
[tex]n_2[/tex] = sample of the second new systems = 100
So, the test statistics = [tex]\frac{(4.1-3.4)-(0)}{\sqrt{\frac{2.2^{2} }{120} + \frac{1.5^{2} }{100}} }[/tex]
= 2.792
The value of z-test statistics is 2.792.
Now, at 0.05 level of significance, the z table gives a critical value of -1.96 and 1.96 for the two-tailed test.
Since the value of our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the population mean checkout times of the two new systems differ.
a lottery game has balls numbered 1 through 19. what is the probability selected ball is an even numbered ball or a 4 g
Answer:
Probability ball is an even numbered ball or a 4 [P(A or B)] = 9 / 19
Step-by-step explanation:
Given:
Number of balls = 1 to 19
Find:
Probability ball is an even numbered ball or a 4
Computation:
Total even number = 2, 4, 6, 8, 10, 12, 14, 16, 18
Probability to get even number P(A) = 9 / 19
Probability to get 4 number P(B) = 1 / 19
P(A and B) = 1 / 19 (4 common)
Probability ball is an even numbered ball or a 4 [P(A or B)]
P(A or B) = P(A) + P(B) -P(A and B)
P(A or B) = [9 / 19] + [1 / 19] - [1 / 19]
Probability ball is an even numbered ball or a 4 [P(A or B)] = 9 / 19
Please do either 40 or 39
Answer:
y = 1.8
Step-by-step explanation:
Question 39).
Let the operation which defines the relation between a and b is O.
Relation between a and b has been given as,
a O b = [tex]\frac{(a+b)}{(a-b)}[/tex]
Following the same operation, relation between 3 and y will be,
3 O y = [tex]\frac{3+y}{3-y}[/tex]
Since 3 O y = 4,
[tex]\frac{3+y}{3-y}=4[/tex]
3 + y = 12 - 4y
3 + y + 4y = 12 - 4y + 4y
3 + 5y = 12
3 + 5y - 3 = 12 - 3
5y = 9
[tex]\frac{5y}{5}=\frac{9}{5}[/tex]
y = 1.8
Therefore, y = 1.8 will be the answer.
Factories A, B and C produce computers. Factory A produces 4 times as manycomputers as factory C, and factory B produces 7 times as many computers asfactory C. The probability that a computer produced by factory A is defective is0.04, the probability that a computer produced by factory B is defective is 0.02,and the probability that a computer produced by factory C is defective is 0.03. Acomputer is selected at random and found to be defective. What is the probabilityit came from factory A?
Answer:
The probability is [tex]P(A') = 0.485[/tex]
Step-by-step explanation:
Let assume that the number of computer produced by factory C is k = 1
So From the question we are told that
The number produced by factory A is 4k = 4
The number produced by factory B is 7k = 7
The probability of defective computers from A is [tex]P(A) = 0.04[/tex]
The probability of defective computers from B is [tex]P(B) = 0.02[/tex]
The probability of defective computers from C is [tex]P(C) = 0.03[/tex]
Now the probability of factory A producing a defective computer out of the 4 computers produced is
[tex]P(a) = 4 * P(A)[/tex]
substituting values
[tex]P(a) = 4 * 0.04[/tex]
[tex]P(a) = 0.16[/tex]
The probability of factory B producing a defective computer out of the 7 computers produced is
[tex]P(b) = 7 * P(B)[/tex]
substituting values
[tex]P(b) = 7 * 0.02[/tex]
[tex]P(b) = 0.14[/tex]
The probability of factory C producing a defective computer out of the 1 computer produced is
[tex]P(c) = 1 * P(C)[/tex]
substituting values
[tex]P(c) = 1 * 0.03[/tex]
[tex]P(b) = 0.03[/tex]
So the probability that the a computer produced from the three factory will be defective is
[tex]P(t) = P(a) + P(b) + P(c)[/tex]
substituting values
[tex]P(t) = 0.16 + 0.14 + 0.03[/tex]
[tex]P(t) = 0.33[/tex]
Now the probability that the defective computer is produced from factory A is
[tex]P(A') = \frac{P(a)}{P(t)}[/tex]
[tex]P(A') = \frac{ 0.16}{0.33}[/tex]
[tex]P(A') = 0.485[/tex]
A firm just paid an annual dividend of $1.40 and increases that dividend by 2 percent each year. How do you find the price if the firm's stock at year 4 if the discount rate is 13 percent?
Answer:
14.05
Step-by-step explanation:
We have the following:
Current Dividend = D0 = $ 1.40
g = growth rate = 2%
r = discount rate = 13%
Dividend in Year 5
= D5 = D0 * (1 + g) ^ 5
= $ 1.40 * (1 + 2%) ^ 5
= $ 1.40 * (1.02) ^ 5
Firm Stock Price at the end of year 4 = Dividend in Year 5 / (r - g)
= $ 1.40 * (1.02) ^ 5 / (13% -2%)
= $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02)
Therefore, firm stock at the end of year 4 is
P4 = $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02) = 14.05
and click Submit
By visual inspection, determine the best fitting regression model for the
scatterplot.
O A Quadratic
O B. Linear
OC Exponential
OD. No pattern
Answer:
quadratic
Step-by-step explanation:
This graph has a parabola form wich is a propertie for qaudratic functions
Answer:
A
Step-by-step explanation:
A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 min for the angle of elevation to change from 45° to 60°. After how much more time will this car reach the base of the tower? Options: a. 5( √3+ 1 ) b. 6 (√3 +√2) c. 7 (√3- 1) d. 8 (√3-2)
Answer:
The correct answer is option a.
a. 5( √3+ 1 )
Step-by-step explanation:
Given that the angle changes from 45° to 60° in 10 minutes.
This situation can be represented as right angled triangles [tex]\triangle[/tex]ABC (in the starting when angle is 45°)and [tex]\triangle[/tex]ABD (after 10 minutes when the angle is 60°).
AB is the tower (A be its top and B be its base).
Now, we need to find the time to be taken to cover the distance D to B.
First of all, let us consider [tex]\triangle[/tex]ABC.
Using tangent property:
[tex]tan\theta =\dfrac{Perpendicular}{Base}\\\Rightarrow tan 45=\dfrac{AB}{BC}\\\Rightarrow 1=\dfrac{h}{BC}\\\Rightarrow h = BC[/tex]
Using tangent property in [tex]\triangle[/tex]ABD:
[tex]\Rightarrow tan 60=\dfrac{AB}{BD}\\\Rightarrow \sqrt3=\dfrac{h}{BD}\\\Rightarrow BD = \dfrac{h}{ \sqrt3}\ units[/tex]
Now distance traveled in 10 minutes, CD = BC - BD
[tex]\Rightarrow h - \dfrac{h}{\sqrt3}\\\Rightarrow \dfrac{(\sqrt3-1)h}{\sqrt3}[/tex]
[tex]Speed =\dfrac{Distance }{Time}[/tex]
[tex]\Rightarrow \dfrac{(\sqrt3-1)h}{10\sqrt3}[/tex]
Now, we can say that more distance to be traveled to reach the base of tower is BD i.e. '[tex]\bold{\dfrac{h}{\sqrt3}}[/tex]'
So, more time required = Distance left divided by Speed
[tex]\Rightarrow \dfrac{\dfrac{h}{\sqrt3}}{\dfrac{(\sqrt3-1)h}{10\sqrt3}}\\\Rightarrow \dfrac{h\times 10\sqrt3}{\sqrt3(\sqrt3-1)h}\\\Rightarrow \dfrac{10 (\sqrt3+1)}{(\sqrt3-1)(\sqrt3+1)} (\text{Rationalizing the denominator})\\\Rightarrow \dfrac{10 (\sqrt3+1)}{3-1}\\\Rightarrow \dfrac{10 (\sqrt3+1)}{2}\\\Rightarrow 5(\sqrt3+1)}[/tex]
So, The correct answer is option a.
a. 5( √3+ 1 )
PLEASE HELP!! Write the proportion. 120 feet is to 150 feet as 8 feet is to 10 feet. (18 points!!)
Answer:
4 : 5
Step-by-step explanation:
you can divide 120 and 150 by 30 and 8 and 10 by 2.
120/30 = 4
150/30 = 5
8/2 = 4
10/2=5
Answer: 4:5
Step-by-step explanation:
Suppose that Vera wants to test the hypothesis that women make less money than men doing the same job. According to the Bureau of Labor Statistics (BLS), the median weekly earnings for men in the professional and related occupation sector in 2015 was $1343. Vera collected median weekly earnings data for women in 2015 from a random subset of 18 positions in the professional and related occupation sector. The following is the sample data. $1811, $728, $1234, $966, $953, $1031, $990, $633, $796, $1325, $1448, $1125, $1144, $1082, $1145, $1256, $1415, $1170 Vera assumes that the women's median weekly earnings data is normally distributed, so she decides to perform a t-test at a significance level of α = 0.05 to test the null hypothesis, H0:µ=1343H0:μ=1343 against the alternative hypothesis, H1:µ<1343H1:μ<1343 , where µμ is the population mean. If the requirements for performing a t-test have not been met, only answer the final question. Otherwise, answer all five of the following questions. First, compute the mean, x⎯⎯⎯x¯ , of Vera's sample. Report your answer with two decimals of precision.
Answer:
There is sufficient evidence to conclude that women make less money than men doing the same job.
Step-by-step explanation:
The hypothesis for the test can be explained as follows:
H₀: Women does not make less money than men doing the same job, i.e. [tex]\mu\geq \$1343[/tex].
Hₐ: Women make less money than men doing the same job, i.e. [tex]\mu<\$1343[/tex].
From the provided data compute the sample mean and standard deviation:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{18}[1811+728+...+1170]=1125.11\\\\s=\sqrt{\frac{1}{n-1}\sum (X-\bar x)^{2}}=\sqrt{\frac{1}{18-1}\times 1322541.86}=278.92[/tex]
Compute the test statistic as follows:
[tex]t=\frac{\bar x-\mu}[\s/\sqrt{n}}=\frac{1125.11-1343}{278.92/\sqrt{18}}=-3.143[/tex]
The test statistic value is -3.143.
Compute the p-value as follows:
[tex]p-value=P(t_{n-1}<-3.143)=P(t_{17}<-3.143)=0.003[/tex]
*Use a t-table.
The p-value of the test is 0.003.
The p-value of the test is very small for all the commonly used significance level. The null hypothesis will be rejected.
Conclusion:
There is sufficient evidence to conclude that women make less money than men doing the same job.
Explain the connection between the chain rule for differentiation and the method of u-substitution for integration.
Answer:
Chain rule: [tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex], u-Substitution: [tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]
Step-by-step explanation:
Differentiation and integration are reciprocal to each other. The chain rule indicate that a composite function must be differentiated, describing an inductive approach, whereas u-substitution allows integration by simplifying the expression in a deductive manner. That is:
[tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex]
Let integrate both sides in terms of x:
[tex]f[u(x)] = \int {\frac{df}{du} \frac{du}{dx} } \, dx[/tex]
[tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]
This result indicates that f must be rewritten in terms of u and after that first derivative needs to be found before integration.
Imagine working in a freelance developer earning 80 USD per hour how many weeks you will have to take a 12 hour flight on a weekday you can either book a flight for ticket for 11 AM for 900 USD or 11 PM flight or 11 USD there is no Internet boards if you take the day off like you will lose a day of work what would you do
Answer:
pay the 11 AM ticket
Step-by-step explanation:
Note that the flight last for 12 hours, and assuming the freelance developer can still work (have access to the internet) on the airplane throughout the flight, he stand to earn $960 ($80*12), which will still cover the cost of the flight with a profit of $60 ($960-900).
However, if he decides to pay the $11 flight ticket and there is no Internet on boards; there by losing a day of work, he stand to have lost working time which would earn with $900.
Therefore, the best choice is to pay the 11 AM ticket.