Answer:
Linda has $15Reuben has $25Manuel has $30Step-by-step explanation:
Together, they have 4 times what Linda has, plus $10. So, Linda has 1/4 of $60 = $15.
Linda has $15
Reuben has $25 . . . . . . $10 more than Linda
Manuel has $30 . . . . . . twice what Linda has
In Sparrowtown, the use of landlines has been declining at a rate of 5% every year. If there are 20,000 landlines this year, how many will there be in 15 years? If necessary, round your answer to the nearest whole number.
Answer:
5,000
Step-by-step explanation:
If it decreases by 5% a year, it'll decrease by 75% in 15 years
i.e 1 year = 5%
15 years = x
Cross multiply
x = 75%
Therefore, since it decreases by 75%
100 - 75 x 20,000 = 5,000
100
what are the coordinates of point b on ac such that ab=2/5ac
Answer:
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
Step-by-step explanation:
Coordinates of points A and C are (-8, 6) and (2, 5).
If a point B intersects the segment AB in the ratio of 2 : 5
Then coordinates of the point B will be,
x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]
where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.
For the coordinates of point B,
x = [tex]\frac{2\times 2+(-8)\times 5}{2+5}[/tex]
= [tex]-\frac{36}{7}[/tex]
y = [tex]\frac{2\times 5+5\times 6}{2+5}[/tex]
= [tex]\frac{40}{7}[/tex]
Therefore, coordinates of pint B will be,
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
Translate the phrase into a variable expression. Use the letter sto name the
variable. If necessary, use the asterisk (*) for multiplication and the slash
(1) for division.
the product of 60 and the number of seconds...
Answer:
The statement
the product of 60 and the number of seconds is written as
60 * s
Hope this helps you
How does the frequency of f(x) = cos(2x) relate to the frequency of the parent function cos x?
Answer:
The frequency of f(x) is two times the frequency of the parent function.
Step-by-step explanation:
We can say that the number that is beside the x is equal to [tex]2\pi *f[/tex], where f is the frequency.
Then, for the parent function, we get:
[tex]1 = 2\pi f_1[/tex]
or solving for [tex]f_1[/tex]:
[tex]f_1=\frac{1}{2\pi }[/tex]
At the same way, for f(x), we get:
[tex]2=2\pi f_2\\f_2=2(\frac{1}{2\pi })[/tex]
But [tex]\frac{1}{2\pi }[/tex] is equal to [tex]f_1[/tex], so we can write the last equation as:
[tex]f_2=2f_1[/tex]
It means that the frequency of f(x) is two times the frequency of the parent function.
heLpPppPPpppPPpppppPPpppPPpppPPpppPPPpppPPPpppPPPPppppp
Answer:
Triangle D is your answer.
Answer:
Hey there!
Triangle C is unique, as one side and two angles determine a unique triangle.
Hope this helps :)
Find the solution(s) of the quadratic equation 2x2 – 3x – 35 = 0
Answer: x = 5, x = -7/2
Step-by-step explanation:
2x² - 3x - 35 = 0
Step 1: Find two values whose product = 2(-35) and sum = -3: -10 & 7
Step 2: Replace the b-value of -3x with -10x + 7x:
2x² - 10x + 7x - 35 = 0
Step 3: Factor the first two terms and the second two terms:
2x(x - 5) +7(x - 5) = 0
Step 4: Write the factored form:
Notice that the parenthesis are identical. This is one of the factors. The outside values are the other factor:
Parenthesis: (x - 5)
Outside: (2x + 7)
Factored form: (x - 5)(2x + 7) = 0
Step 5: Set each factor each to zero and solve for x:
x - 5 = 0 2x + 7 = 0
x - 5 [tex]x=-\dfrac{7}{2}[/tex]
The solutions of the quadratic equation given as 2x² - 3x - 35 = 0 are x=5 and x =-3.5.
Given that:
2x² - 3x - 35 = 0
This is a quadratic equation.
It is required to find the solutions of this equation.
The solution of the quadratic equation of the form ax² + bx + c = 0 can be found using the quadratic formula:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
From the given equation:
a = 2
b = -3
c = -35
Substitute to the quadratic formula.
[tex]x=\frac{-(-3)\pm \sqrt{(-3)^2-4(2)(-35)}}{2(2)}[/tex]
[tex]=\frac{3\pm \sqrt{9+280}}{4}[/tex]
[tex]=\frac{3\pm \sqrt{289}}{4}[/tex]
[tex]=\frac{3\pm 17}{4}[/tex]
So, the solutions are:
[tex]x=\frac{3+ 17}{4}=5[/tex], and [tex]x=\frac{3-17}{4}=-3.5[/tex]
Hence, the solutions are x =5, -3.5.
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What is the value of x in the equation 5 (4 x minus 10) + 10 x = 4 (2 x minus 3) + 2 (x minus 4)?
Answer:
x = 1.5
Step-by-step explanation:
5(4x-10)+10x=4(2x-3)+2(x-4)
Distribute(5)
20x-50+10x=4(2x-3)+2(x-4)
Distribute(4)
20x-50+10x=8x-12+2(x-4)
Distribute(2)
20x-50+10x=8x-12+2x-8
Combine like terms
30x-50=10x-20
Subtract(10x)
20x-50=-20
Add(50)
20x=30
Divide(20)
x = 1.5
Hope it helps <3
Answer:
x = 3/2Step-by-step explanation:
5 ( 4x - 10) + 10x = 4(2x - 3) + 2(x - 4)
Expand the terms
That's
20x - 50 + 10x = 8x - 12 + 2x - 8
Simplify
30x - 50 = 10x - 20
Group the constants at the right side of the equation
That's
30x - 10x = - 20 + 50
20x = 30
Divide both sides by 20
x = 3/2
Hope this helps you
Find three consecutive even integers such that the square of the third is 60 more that the square of the second
Answer:
-4,4,16
Step-by-step explanation:
They are all even integers.
-4^2=16
4^2=16
16^2=256
the square of the third,16 is 256 which is more than the square of the second,4=16
The three consecutive even integers such that the square of the third is 60 more than the square of the second are -18, -16 and -14.
What are integers?Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given:
Let the three even consecutive integers are 2n-2, 2n and 2n + 2.
According to the question,
So,
(2n + 2)² = (2n)² - 60
4n² + 4 + 8n = 4n² -60
8n = -64
n = -8
That means, the integers are -18, -16 and -14.
Therefore, the required even integers are -18, -16 and -14.
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905,238 In a word form
Answer:
nine hundred five thousand two hundred thirty-eight
Zoey wants to use her iPad throughout a 6-hour flight. Upon takeoff, she uses the iPad for 2 hoursand notices that the battery dropped by 25%, from 100% to 75%. How many total hours can Zoeyexpect from the iPad on a full battery charge?
Answer:
8 hours
Step-by-step explanation:
25%= 2 hrs
100%=8 hrs
brainliest plsssssssssssssssssssss
-zylynn
PLEASE HELP!!! Select the three statements that give benefits of having a savings account. A. When I withdraw money from my savings account too many times, I can be charged a fee. B. When I put money in a savings account, the bank will pay me interest. C. If there were an emergency, I would have the money to cover expenses. D.When I use a savings account, my money is insured by the FDIC up to $250,000.
Answer:
answer is B
Step-by-step explanation:
Eighty percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 63% have an emergency locator, whereas 89% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. (Round your answers to three decimal places.) (a) If it has an emergency locator, what is the probability that it will not be discovered? (b) If it does not have an emergency locator, what is the probability that it will be discovered?
Answer:
a) P(B'|A) = 0.042
b) P(B|A') = 0.625
Step-by-step explanation:
Given that:
80% of the light aircraft that disappear while in flight in a certain country are subsequently discovered
Of the aircraft that are discovered, 63% have an emergency locator,
whereas 89% of the aircraft not discovered do not have such a locator.
From the given information; it is suitable we define the events in order to calculate the probabilities.
So, Let :
A = Locator
B = Discovered
A' = No Locator
B' = No Discovered
So; P(B) = 0.8
P(B') = 1 - P(B)
P(B') = 1- 0.8
P(B') = 0.2
P(A|B) = 0.63
P(A'|B) = 1 - P(A|B)
P(A'|B) = 1- 0.63
P(A'|B) = 0.37
P(A'|B') = 0.89
P(A|B') = 1 - P(A'|B')
P(A|B') = 1 - 0.89
P(A|B') = 0.11
Also;
P(B ∩ A) = P(A|B) P(B)
P(B ∩ A) = 0.63 × 0.8
P(B ∩ A) = 0.504
P(B ∩ A') = P(A'|B) P(B)
P(B ∩ A') = 0.37 × 0.8
P(B ∩ A') = 0.296
P(B' ∩ A) = P(A|B') P(B')
P(B' ∩ A) = 0.11 × 0.2
P(B' ∩ A) = 0.022
P(B' ∩ A') = P(A'|B') P(B')
P(B' ∩ A') = 0.89 × 0.2
P(B' ∩ A') = 0.178
Similarly:
P(A) = P(B ∩ A ) + P(B' ∩ A)
P(A) = 0.504 + 0.022
P(A) = 0.526
P(A') = 1 - P(A)
P(A') = 1 - 0.526
P(A') = 0.474
The probability that it will not be discovered given that it has an emergency locator is,
P(B'|A) = P(B' ∩ A)/P(A)
P(B'|A) = 0.022/0.526
P(B'|A) = 0.042
(b) If it does not have an emergency locator, what is the probability that it will be discovered?
The probability that it will be discovered given that it does not have an emergency locator is:
P(B|A') = P(B ∩ A')/P(A')
P(B|A') = 0.296/0.474
P(B|A') = 0.625
What is 25÷5what is 25 / 5
Answer:
5
Step-by-step explanation:
25/5
=5✖️5=25
=5/1
Answer:
25÷5 = 5 and 25/5 = 125
Step-by-step explanation:
hope this helps!
please answer me question 3 solving part
Answer:
1. D
2. B
3. A
Step-by-step explanation:
Question 1:
The pair of <JKL and <LKM can be referred to as linear pairs. They are two adjacent angles that are formed from the intersecting of two lines.
Question 2:
Given that <KLM = x°
<KML = 50°
<JKL = (2x - 15)°
According to the exterior angle theorem, exterior ∠ JKL = <KLM + KML.
2x - 15 = x + 50
Solve for x
2x - x = 15 + 50
x = 65
Therefore, <KLM = 65°
QUESTION 3:
<JKL = 2x - 15
Plug in the value of x
<JKL = 2(65) - 15
= 130 - 15
<JKL = 115°
solve the nonlinear system of equations. State the number of solutions.
Answer:
Step-by-step explanation:
Hello,
Question 15
We can search x such that:
[tex]x^2-4x+4=2x-5\\\\\text{*** subtract 2x-5 from both sides ***}\\ \\x^2-4x-2x+4+5=0\\ \\\text{*** simplify ***}\\ \\x^2-6x+9=0 \\ \\\text{*** we can notice a perfect square ***}\\ \\x^2 -2\cdot x \cdot 3 + 3^2=(x-3)^2=0\\\\\text{*** taking the root ***}\\\\x-3=0\\\\\large \boxed{\sf \ \ x=3 \ \ }[/tex]
There is 1 solution.
Question 16
Again, we search x such that:
[tex]x^2-8x+15=2x-6\\\\\text{*** subtract 2x-6 from both sides ***}\\\\x^2-8x-2x+15+6=0\\\\\text{*** simplify ***}\\\\x^2-10x+21=0 \\ \\\text{*** we are looking for two roots where the sum is 10 and the product is 21 = 7 x 3 ***} \\\\x^2-7x-3x+21=x(x-7)-3(x-7)=(x-3)(x-7)=0\\\\\large \boxed{\sf \ \ x= 3 \ or \ x =7 \ \ }[/tex]There are two solutions.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
This function to calculate the area of a rectangle is not very readable. Can you refactor it, and then call the function to calculate the area with base of 5 and height of 6? Tip: a function that calculates the area of a rectangle should probably be called rectangle_area, and if it's receiving base and height, that's what the parameters should be called.
Answer:
Here is the refactored function:
def rectangle_area(base, height):
area = base * height
return area
print("The area is ", rectangle_area(5,6))
Step-by-step explanation:
The above program has a function rectangle_area that takes two variables base and height as parameters. The function then computes the area of rectangle by multiplying the values of base and height. The result of the multiplication is assigned to the variable area. Then the function returns the resultant area.
print("The area is ", rectangle_area(5,6)) statement calls rectangle_area() method by passing values of base and height i.e. 5 and 6 to compute the area. The output of this program is:
The area is 30
Note that the use of rectangle_area function name describes what the function does i.e. it computes the area of rectangle. By naming the parameters as base and height that clearly depicts that in order to compute rectangle are we need the base and height of rectangle. So this makes the code readable.
Solve the simultaneous equations 2x-y=7 3x+y=3
Answer:
( 2 , - 3 )Step-by-step explanation:
Using elimination method:
2x - y = 7
3x + y = 3
--------------
5x = 10
Divide both sides of the equation by 5
[tex] \frac{5x}{5} = \frac{10}{5} [/tex]
Calculate
[tex]x = 2[/tex]
Now, substitute the given value of X in the equation
3x + y = 3
[tex]3 \times 2 + y = 3[/tex]
Multiply the numbers
[tex]6 + y = 3[/tex]
Move constant to R.H.S and change it's sign
[tex]y = 3 - 6[/tex]
Calculate
[tex]y = - 3[/tex]
The possible solution of this system is the ordered pair ( x , y )
( x , y ) = ( 2 , -3 )---------------------------------------------------------------------
Check if the given ordered pair is the solution of the system of equation
[tex]2 \times 2 - ( - 3) = 7[/tex]
[tex]3 \times 2 - 3 = 3[/tex]
Simplify the equalities
[tex]7 = 7[/tex]
[tex]3 = 3[/tex]
Since all of the equalities are true, the ordered pair is the solution of the system
( x , y ) = ( 2 , - 3 )Hope this helps..
Best regards!!
magazine provided results from a poll of adults who were asked to identify their favorite pie. Among the respondents, % chose chocolate pie, and the margin of error was given as percentage points. What values do , , n, E, and p represent? If the confidence level is %, what is the value of ?
Complete Question
A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 12 % chose chocolate pie, and the margin of error was given as plus or minus 5 percentage points.What values do [tex]\r p , \ \r q[/tex], n, E, and p represent? If the confidence level is 90%, what is the value of [tex]\alpha[/tex] ?
Answer:
a
[tex]\r p[/tex] is the sample proportion [tex]\r p = 0.12[/tex]
[tex]n[/tex] is the sample size is [tex]n = 500[/tex]
[tex]E[/tex] is the margin of error is [tex]E = 0.05[/tex]
[tex]\r q[/tex] represents the proportion of those that did not chose chocolate pie i.e [tex]\r q = 1- \r p[/tex]
b
[tex]\alpha = 10\%[/tex]
Step-by-step explanation:
Here
[tex]\r p[/tex] is the sample proportion [tex]\r p = 0.12[/tex]
[tex]n[/tex] is the sample size is [tex]n = 500[/tex]
[tex]\r q[/tex] represents the proportion of those that did not chose chocolate pie i.e
[tex]\r q = 1- \r p[/tex]
[tex]\r q = 1- 0.12[/tex]
[tex]\r q = 0.88[/tex]
[tex]E[/tex] is the margin of error is [tex]E = 0.05[/tex]
Generally [tex]\alpha[/tex] is the level of significance and it value is mathematically evaluated as
[tex]\alpha = ( 100 - C )\%[/tex]
Where [tex]C[/tex] is the confidence level which is given in this question as [tex]C = 90 \%[/tex]
So
[tex]\alpha = ( 100 - 90 )\%[/tex]
[tex]\alpha = 10\%[/tex]
Select the correct answer. Brad is planting flowers in a grid-like pattern in his garden. He is trying to determine the possible numbers of rows and columns in which he can plant his flowers. He determines that two possibilities are 8 rows and 25 columns or 10 rows and 20 columns. What is the constant of proportionality in this inverse variation?
Answer:
[tex]C.\ 200[/tex]
Step-by-step explanation:
Given
Let R represents rows and C represents Columns
When R = 8, C = 25
When R = 10, C = 20
Required
Given that there exist an inverse variation, determine the constant of proportionality;
We start by representing the variation;
[tex]R\ \alpha \ \frac{1}{C}[/tex]
Convert proportion to an equation
[tex]R\ = \ \frac{k}{C}[/tex]
Where k is the constant of proportion;
[tex]R * C\ = \ \frac{k}{C} * C[/tex]
Multiply both sides by C
[tex]R * C\ = k[/tex]
Reorder
[tex]k = R * C[/tex]
When R = 8, C = 25;
The equation [tex]k = R * C[/tex] becomes
[tex]k = 8 * 25[/tex]
[tex]k = 200[/tex]
When R = 10, C = 20;
The equation [tex]k = R * C[/tex] becomes
[tex]k = 10 * 20[/tex]
[tex]k = 200[/tex]
Hence, the concept of proportionality is 200
PLEASEEEEE HELPPOO
For Individual or Group Explorations
Maximizing the Total Profit
Payles at The Christmas Store very periodically with a high ef 550.000 in December
the Christmas Stove also comes the Powe, where profits reach a high of $80,000
in Aurust and a few of $20,000 in February Assume that the profit function for
Crm Store
Save
40
20
10
1 2 3 4 5 6 7 8 9 10 11 12
Month
a) Write the profit function for The Christmas Store as a function of the month
and sketch its graph
b)
Write the profit function for The Pool Store as a function of the month and
sketch its graph.
are are length
Write the total profit as a function of the month and sketch its graph. What is
the period?
are inside the
est enth of a
Use the maximum feature of a graphing calculator to find the owner's maxi-
mum total profit and the month in which it occurs.
Find the owner's minimum total profit and the month in which it occurs.
We know that y -a sin x + bcos x is a sine function. However, the sum of
two arbitrary sine or cosine functions is not necessarily a sine function. Find an
example in which the graph of the sum of two sine functions does not look like
a sine curve.
Explain.
is tangent to one
Answer:
what
Step-by-step explanation:
Which parent function is represented by the graph?
A. The quadratic parent function
B. The absolute value parent function
C. An exponential parent function
D. The linear parent function
Answer:
D. The linear parent function
Step-by-step explanation:
Linear functions are always characterized by a straight line graph with or without an intercept on the vertical or horizontal axis. A linear function usually has an independent variable and a dependent variable. The independent variable is commonly depicted as x while the dependent variable is y.
Thus a linear equation is an equation of the type y=ax where a is a constant term. The equation of a straight line graph his y=mx +c, where;
m= gradient of the straight line graph
x= the independent variable
y= the dependent variable
c= the vertical intercept
Answer:
The linear parent function :)
Step-by-step explanation:
Does the mean represent the center of the data? A. The mean represents the center. B. The mean does not represent the center because it is the smallest data value. C. The mean does not represent the center because it is the largest data value. D. The mean does not represent the center because it is not a data value. E. There is no mean age.
Answer:
A. The mean represents the center.
A. The median represents the center.
B. The mode does not represent the center because it is the smallest data value.
Step-by-step explanation:
Mean
(9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11)/13 = 120/13 = 9.2
The mean 9.2 and it represents the center of data.
Median
By arranging the set of data, the median, the median is the center number
8,8,8,8,8,8,(9),9,9,10,11,12,12
The median is 9 and it represents the center of data.
Mode
The mode is the number that appears most in the set of data.
The number that appears most in the set of data is 8 and does not represent the set of data.
Given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:
the mean is: 9.2the median is: 9the mode is: 8A. The mean does represents the center of the data set
Given the following data set:
9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8, 11
Let's find the mean, median, and mode.
Mean of the data set:
Mean = sum of all values / number of values
Mean = [tex]\frac{9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11}{13}[/tex]
Mean = [tex]\frac{120}{13} = 9.2[/tex]
Median of the data set:
Order the data from the least to the greatest then find the middle value.
Thus:8, 8, 8, 8, 8, 8, (9,) 9, 9, 10, 11, 12, 12
The middle value is 9.
The median = 9Mode of the data set:
The mode = the data value that appears most
8 appeared the most, therefore, the mode = 8
If you observe, you will note that the mean and median of the data set are similar. We can as well conclude that the mean represents the center of the data set.
In summary, given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:
the mean is: 9.2the median is: 9the mode is: 8A. The mean does represents the center of the data set
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What value of x is I the solution set of 3(x-4)>5x+2
Answer:
-7 > x
Step-by-step explanation:
3(x-4)>5x+2
Distribute
3x-12>5x+2
Subtract 3x from each side
3x-12-3x>5x-3x+2
-12 > 2x+2
Subtract 2 from each side
-12-2>2x+2-2
-14 > 2x
Divide by 2
-14/2 > 2x/2
-7 > x
Answer:
[tex]\boxed{x<-7}[/tex]
Step-by-step explanation:
3(x-4)>5x+2
Expand brackets.
3x - 12 > 5x+2
Subtract 3x and 2 on both sides.
-12 - 2 > 5x - 3x
-14 > 2x
Divide both sides by 2.
-7 > x
Switch sides.
x < -7
Enter a range of values of x
Answer:
[tex]-5<x<26[/tex].
Step-by-step explanation:
We know that if two corresponding sides of two triangles are equal, then third sides of the triangles depend on angle between equal sides.
Angle opposite to larger side is larger.
Since, 14 < 15, therefore
[tex]2x+10<62[/tex]
[tex]2x<62-10[/tex]
[tex]2x<52[/tex]
[tex]x<26[/tex] ...(1)
We know that, angle can not not negative.
[tex]2x+10>0[/tex]
[tex]2x>-10[/tex]
[tex]x>-5[/tex] ...(2)
From (1) and (2), we get
[tex]-5<x<26[/tex]
Therefore, the range of values of x is [tex]-5<x<26[/tex].
The probability of a potential employee passing a drug test is 91%. If you selected 15 potential employees and gave them a drug test, how many would you expect to pass the test
Answer:
The number expected to pass that test is [tex]k = 14 \ employees[/tex]
Step-by-step explanation:
From the question we are told that
The probability of success is p = 0.91
The sample size is n = 15
The number of employee that will pass the test is mathematically represented as
[tex]k = n * p[/tex]
substituting values
[tex]k = 15 * 0.91[/tex]
[tex]k = 14 \ employees[/tex]
What is x? The degree of the angle of x
Answer:
x = 60°
Step-by-step explanation:
All the angles in a triangle add up to 180°. So, you have this equation.
87° + 33° + x = 180°
120° + x = 180°
x = 60°
The measure of angle x is 60°.
Hope that helps.
What is a3 if an=64(12)n−1
Answer:
[tex]\huge\boxed{a_3=9,216}[/tex]
Step-by-step explanation:
[tex]a_n=64(12)^{n-1}\\\\\text{substitute}\ n=3:\\\\a_3=64(12)^{3-1}=64(12)^2=64(144)=9,216[/tex]
Write 3 expressions containing exponents so that each expression equals 81
Answer:
9x9= 81
3x3x3x3=81
81 to the first power.
Step-by-step explanation:
I hope this helps in any way:)
Identify the P-VALUE used in a hypothesis test of the following claim and sample data:
Claim: "The proportion of defective tablets manufactured in this factory is less than 6%."
A random sample of 500 tablets from this factory is selected, and it is found that 20 of them were defective. Test the claim at the 0.05 significance level.
Answer:
The calculated value Z = 2 > 1.96 at 0.05 level of significance
Alternative Hypothesis is accepted
The proportion of defective tablets manufactured in this factory is less than 6%."
Step-by-step explanation:
Step(i):-
Given Population proportion P = 0.06
Sample size 'n' = 500
A random sample of 500 tablets from this factory is selected, and it is found that 20 of them were defective.
Sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{20}{500} =0.04[/tex]
Null hypothesis :H₀: P = 0.06
Alternative Hypothesis :H₁:P<0.06
Level of significance = 0.05
Z₀.₀₅ = 1.96
Step(ii):-
Test statistic
[tex]Z = \frac{p^{-} -P}{\sqrt{\frac{P Q}{n} } }[/tex]
[tex]Z = \frac{0.04 -0.06}{\sqrt{\frac{0.06 X 0.94}{500} } }[/tex]
Z = - 2
|Z|= |-2| = 2
Step(iii):-
The calculated value Z = 2 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
Alternative Hypothesis is accepted
The proportion of defective tablets manufactured in this factory is less than 6%."
For each function, determine if it intersects or is parallel to the line y=−1.5x. If it intersects the line, find the intersection point. y=0.5x−6
Answer: the intersection point is (2.4, -4.8)
Step-by-step explanation:
A) we have the function:
y = 0.5*x - 6.
First we want to know if this function intersects the line y´ = -1.5*x
Now, first we can recall that two lines are parallel only if the slope is the same for both lines, here we can see that the slopes are different, so the lines are not parallel, which means that the lines must intersect at some point.
Now, to find the intersection point we asumme y = y´ and want to find the value of x.
0.5*x - 6 = -1.5*x
(0.5 + 1.5)*x - 6 = 0
2.5*x = 6
x = 6/2.5 = 2.4
Now, we evaluate one of the functions in this value of x.
y = 0.5*2.4 - 6 = -4.8
So the intersection point is (2.4, -4.8)