The test statistic z = 0.84 and P-value is 0.2005 when there is a line of unassembled furniture produced by The Mean Corporation.
Given that,
There is a line of unassembled furniture produced by The Mean Corporation. The customer care manager is aware that 0.63 of customers have had no issues putting together their furniture at home based on past data.
The null and alternative hypotheses are:
H₀: π = 0.63
H₁: π > 0.63
We have to find
(a) Calculate the test statistic (z).
(b) Calculate the P-value.
We know that,
a) z = p - π / √(π(1-π)/n)
= 0.67 - 0.63 / √(0.63×0.37/102)
= 0.04 / 0.0478
= 0.84
b) p value(one tailed) is 0.2005.
Therefore, The test statistic z = 0.84 and P-value is 0.2005 when there is a line of unassembled furniture produced by The Mean Corporation.
To learn more about statistic visit: https://brainly.com/question/11969248
#SPJ4
What is the equation of the line that passes through the point (4,-2)(4,−2) and has a slope of \frac{5}{4}
4
5
The equation of the line that passes through the point (4, -2) and has a slope of 5/4, in point-slope form is: y + 2 = 5/4(x - 4).
How to Find the Equation of a Line? Goes through a Point?If we are given a point (a, b), that a line goes through and we also know the slope (m) of the line, the equation of the line can be written as y - b = m(x - a) in point-slope form
Given that the line has the following:
A point (a, b) = (4, -2)
The slope of the line (m) = 5/4
To write the equation of the line, substitute m = 5/4, a = 4, and b = -2 into y - b = m(x - a):
y - (-2) = 5/4(x - 4)
y + 2 = 5/4(x - 4)
The answer is: y + 2 = 5/4(x - 4).
Learn more about the equation of a line on:
https://brainly.com/question/13763238
#SPJ1
Write two number that multiply to the value on top and add to the value on bottom
Answer: -4, -4
Step-by-step explanation:
-4 x -4 = 16
-4 + -4 = -8
help me ples this is kinda hard ngl
will give brainliest if correct
To beat the school long jump record, John must jump an additional 5 1/4 inches
Calculating the additional distance to beat a long jump recordFrom the given question, we are to determine how farther John must jump in order to break the record
From the given information,
"A high school track team's long jump record is 23 ft 1 3/4 in"
and
"John's best long jump is 22 ft 8 1/2 in"
First, we will convert the distances to inches
NOTE: 1 ft = 12 inches
23 ft 1 3/4 in = 276 + 1 3/4 in = 277 3/4 in
22 ft 8 1/2 in = 264 + 8 1/2 in = 272 1/2 in
Now, to determine how farther John must jump, we will subtract the distances
277 3/4 in - 272 1/2 in = 5 1/4 in
Hence, he must jump 5 1/4 in farther
Learn more on Calculating the additional distance to beat a long jump record here: https://brainly.com/question/20301568
#SPJ1
Determine whether the sequence is arithmetic or not .if it is,find the common difference and the next three terms given
2,5,8,11,...
2,-4,6,8,10,...
-6,-10,-14,-18,...
40,42,44,46,...
1.2,1.8,2.4,...
1,5,9,13,.
Therefore the common difference in this AP series is 4 and the next 3 terms are 1, 5, 9, 13, 13 + 4, 13 + 8, 13 + 12 or 1, 5, 9, 13, 17, 21, 25.
Arithmetic sequences are what?Rows with a defined pattern, in which the difference between two consecutive terms is equal and fixed, are referred to as arithmetic sequences and series, also known as rows and counting series. In other words, by adding a fixed integer to the previous term, each term in the arithmetic arrangement is obtained from the previous term. To put it another way, every term in the arithmetic series (except from the first term) is obtained by adding a specific integer to the term that comes before it.
Here,
This mathematical sequence can be written as follows:
A, A+D, A+2D, A+3D, A+4D, etc. , a+(n-1)d or
where:
First term: a
d stands for common variation.
It is stated that the arithmetic sequence formula is
a = a + (n-1)d
where
First term: a
n = the number of terms
d stands for common variation.
Common Difference
In mathematical terminology, the common difference is the difference between two words.
2, 5, 8, 11, and more problems
Answer: To determine if a row is an arithmetic sequence or not, first identify the similarities between the rows.
d = 5 - 2 d = 8 - 5 d = 11-8
d = 3.
Each of them differs by 3 points.
The following three words are then 2, 5, 8, 11, 11+3, 11+6, 11+9 or 2, 5, 8, 11, 14, 17, and 20.
Issues 2, 4, 6, 8, and 10 exist.
Answer:
d = -4 - 2 = -6
d = 6 - (-4) = 10
It does not contain arithmetic sequences because there is no common difference.
Challenge: -6, -10, -14, -18,...
Answer:
d = -10 - (-6) = -4
d= -14 - (-10) = -4
d= -18 - (-14) = -4
There is a -4 difference between them all.
The following three terms are then 6, 10, 14, 18, -18, -18 + (-4), -18 + (-8), -18 + (-12), or 6, 10, 14, 18, -18, -22, -26, -30.
Issues 40, 42, 44, 46,...
Answer:
d = 42 - 40 = 2
d = 44 - 42 = 2
d = 46 - 44 = 2
All of them differ by 2 points.
The subsequent three words are either 40, 42, 44, 46, 48, 50, 52 or 40, 42, 44, 46, 46 + 2, 46 + 4, 46 + 6.
Issues: 1.2, 1.8, 2.4,...
Answer:
d = 1.8 - 1.2 = 0.6
d = 2.4 - 1.8 = 0.6
They are all separated by 0.6.
1.2, 1.8, 2.4, 2.4 + 0.6, 2.4 + 1.2, 2.4 + 1.8 or 1.2, 1.8, 2.4, 3.0, 3.6, 4.2 are the following three words.
Issues 1, 5, and 9,13
Answer:
d = 5 - 1 = 4
d = 9 - 5 = 4
d = 13 - 9 = 4
They are all divided by 4 in common.
The subsequent three terms are either 1, 5, 9, 13, 17, 21, or 25. These are 1, 5, 9, 13, 13 + 4, 13, 8, 13, and 12.
Therefore the common difference in this AP series is 4 and the next 3 terms are 1, 5, 9, 13, 13 + 4, 13 + 8, 13 + 12 or 1, 5, 9, 13, 17, 21, 25.
To know more about Arithmetic sequences , visit
https://brainly.com/question/23152423
#SPJ4
7. At a point on the ground 20 m from the wall of a house, the elevation of the bottom of the window was 12°. From the same point, the elevation of the top of the window was 14°. Calculate the height of the window.
Answer:
d = h(cot1 - cot2)
d = 100(cot30 - cot45))
d = 100* (1.732 - 1)
d = 100*0.732
d = 73.2 m
suppose that a community contains 15,000 people. at time time, t, the number n (t) of people who have a gene that causes a triangle on their forehead is 5,000 and is increasing at a rate of 500 per day.
The community will contain 15,000 people with the gene that causes a triangle on their forehead after 20 days.
The rate of change of n (t) with respect to time is 500 people per day. This means that the equation for n (t) is given by:
n (t) = 5,000 + 500t
where t is the number of days since time t. At time t, n (t) = 5,000, and as time passes, the number of people with the gene that causes a triangle on their forehead increases. After 20 days, n (t) = 5,000 +500*20 = 15,000, meaning that after 20 days, the community will contain 15,000 people with the gene that causes a triangle on their forehead.
Learn more about rate of change :
https://brainly.com/question/29058864
#SPJ4
A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow.Hours of Sleep Age Group39 or younger 40 or older Fewer than 6 38 366 to 6.9 60 577 to 7.9 79 778 or more 63 90(a) Conduct a test of independence to determine whether hours of sleep are independent of age.State the null and alternative hypotheses.H0: Hours of sleep per night is not independent of age.Ha: Hours of sleep per night is independent of age.H0: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups.Ha: The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups. H0: Hours of sleep per night is independent of age.Ha: Hours of sleep per night is not independent of age.H0: Hours of sleep per night is mutually exclusive from age.Ha: Hours of sleep per night is not mutually exclusive from age.Find the value of the test statistic. (Round your answer to three decimal places.)What is the p-value? (Round your answer to four decimal places.)p-value =Using a 0.05 level of significance, what is your conclusion?Reject H0. We conclude that hours of sleep per night and age are not independent.Do not reject H0. We cannot conclude that hours of sleep per night and age are not independent. Do not reject H0. We conclude that hours of sleep per night and age are independent.Reject H0. We cannot conclude that hours of sleep per night and age are independent.(b) What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night?Fewer than 6 % 6 to 6.9 % 7 to 7.9 % 8 or more %
Sleep hours per night is independent.
Given the data:
Hours of Sleep 39 or younger 40 or older
> 6 _____38 36
6 to 6.9 _ 61 58
7 to 7.9 __76 74
8 or more 65 92
The analysis will be conducted using the Chisquare statistic:
The supposition
H0: The amount of sleep each night is independent
H1: The amount of sleep each night is not independent
χ² = (observed - Expected) (observed - Expected)2 / Predicted
to speed up computation. To conduct the analysis, we might utilize a Chisquare calculator:
The evaluation statistic is 4.0061.
Row - 1 * The degree of freedom (column - 1)
Degree of freedom is equal to (4-1)*(2-1)=3*1=3.
Pvalue is 0.261.
Since Pvalue >, we are unable to reject the hypothesis that sleep duration is independent total %
> 6 _____38 36_ 74 _ 14.8
6 to 6.9 61 58 _ 119 23.8
7 to 7.9 __76 74 150 30
8 or higher 65 92 157 31.4
_______240 260 500 100
To learn more about statistics:
https://brainly.com/question/29342780
#SPJ4
find the value of x if triangle abs is an equillateral triangle. pick any two sides and set them equal to eachother
If the triangle ABC is an equilateral triangle having the length as (4x - 3) , and perimeter as 63 in , then the value of x is 6 .
The triangle having all the sides of equal measure is termed as Equilateral triangle.
The triangle ABC is equilateral triangle,
The measure of length of side of triangle ABC is = 4x - 3 ;
The perimeter of the triangle is = 63
So, According to the question,
(4x - 3) + (4x - 3) + (4x - 3) = 63
12x - 9 = 63
12x = 63 + 9
12x = 72
x = 72/12
x = 6
Therefore, the value of x in the given triangle is 6.
-- The given question is incomplete, the complete question is
"Find the value of x, if the triangle ABC is an equilateral triangle with length of each side as (4x - 3), and the perimeter of the equilateral triangle ABC is 63 inches." --
Learn more about Equilateral Triangle here
https://brainly.com/question/22656843
#SPJ4
In addition to the strength and direction of an association between two numerical variables, correlation analyses allow us to predict one variable's value based on the other variable. True False
The given statement is FALSE.
Given info,
In addition to the strength and direction of an association between two numerical variables, correlation analyses allow us to predict one variable's value based on the other variable.
⇒ The statement is FALSE.
Finding the degree and direction of the link between two numerical variables is made easier with the use of correlation analysis.
The value of one variable can be predicted based on the value of another using regression analysis.
To learn more about correlation analysis click here:
brainly.com/question/28541510
#SPJ4
what angle is half of its supplement; the measure of one angle is 15 less than half the measurement of its supplement; complement angle; complementary angles add up to; what are supplementary angles; two angles that add up to 90
So one angle is of measurement 130 degree and the other angle is of measurement 50 degree.
What are angles?When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.
When two lines meet at a point, an angle is created.
An "angle" is the measurement of the "pening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.
Angles are a common occurrence in daily life.
Angles are used by engineers and architects to create highways, structures, and sports venues.
According to our question-
One angle's measurement is 15 less than its supplement's measurement.
Let's say that the supplement angle is measured in degrees.
So the measurement of the other angle is
And the sum of the measurement of supplementary angles is 180.
Multiplying both sides by 2
Therefore, one angle is 130 degrees in length and the other is 50 degrees.
learn more about angles click here:
brainly.com/question/25716982
#SPJ4
Anything helps. Thank you for the help.
Answer: Attached to the post.
Step-by-step explanation:
First, label points A and B--given as (3, -3) and (3, 1) respectively. Now connect the points to form line segment AB.
We need to reflect this line segment over the line y = x. To visualize this easier, let's draw line y = x. Two coordinates on this line is (1, 1) and (0, 0). Plot these points and connect them to form line y = x.
Finally, we need to reflect line segment AB over y = x. Imagine the line y = x is a mirror and reflect the line segment AB over it. In my diagram, line segment A'B' is the answer.
Hi can someone please help me Im struggling with this!!!
The measures of the angles formed by the parallel lines and their common transversal are;
Part A; B. c is equal to b
Part B; c = 60°
Second part; Angle P is 80°
Third part; The missing reason in step 3 is the option D.
Fourth part; Angle B is 72°
What are parallel lines?Parallel lines are lines in the same plane that have the same slope. The perpendicular distance between parallel is constant, such that they do not meet.
D. Vertical angles are congruent
Fourth part; Angle B is
Part A; JK is parallel to LM
Angle ∠c and angle ∠b are corresponding angles, therefore;
∠c and ∠b are congruent
∠c = ∠b
Therefore;
B. c is equal to b
Part B
Angle ∠b and 2·∠b are linear pair angles
Linear pair angles are supplementary, therefore
∠b + 2·∠b = 180°
3·∠b = 180°
∠b = 180°/3 = 60°
∠b = 60°
∠c = ∠b = 60°
B. c = 60°
Second part;
Angle P and the vertical angle to the 100° angle are same side interior angles.
Vertical angles are congruent, therefore;
Angle P and 100° are same side interior angles
Same side interior angles are supplementary, therefore;
m∠P + 100° = 180°
m∠P = 180° - 100° = 80°
Third part;
Angle ∠2 and angle ∠3 are formed by the transversal t and w, therefore, they are vertical angles
Vertical angles theorem states that two sets of linear pair angles, that have congruent angles are formed from the intersection of two lines.
Therefore:
∠2 ≅ ∠3, reason: D. Vertical angles are congruent
Fourth part;
Line A is parallel to line B
The angles, 4·m -24, and 3·m are corresponding angles
Corresponding lines formed by the transversal and two parallel lines are congruent, therefore;
4·m - 24 = 3·m
4·m - 3·m = 24
m = 24 degrees
Taking angle ∠B as the angle formed at the intersection of line B and the transversal, 4·m - 24 we get;
∠B = 4·m - 24
∠B = 4 × 24 = 72°
Angle ∠B = 72°
Learn more about the angle formed between parallel lines that have a common transversal here:
https://brainly.com/question/24607467
#SPJ1
Kala swam 4 kilometers against the current in the same amount of time it took her to swim 12 kilometers with the current. The rate of the current was 2 kilometers per hour. How fast would Kala swim if there were no current?
Against the current he swims 2 km/hours where he swims 4 km in the same 2 hours.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Distance = Rate x Time
Let Kala's swimming speed = X
4 km = (X-2)×Time
12 km = (X+2) × Time
4/x-2 = 12/x+2
Apply cross multiplication
4(x+2)=12(x-2)
4x+8=12x-24
Take all variables on one side
4x-12x=-24-8
-8x=-32
Divide both sides by 8
x=4
Kala swims 4 km/hour
With the current he swims 6 km/hour
Hence, Against the current he swims 2 km/hours where he swims 4 km in the same 2 hours.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
6,000 for six years at 8½% compounded daily will grow to:
Multiple Choice
$9,060.00
$9,788.81
$9,991.15
$9,990.02
Calculating interest on the principal borrowed as well as any prior interest. $6,000 for six years at a daily compounded rate is None of these. No option is correct. The amount is $991.15.
What is compound interest?Annual interest compounding adjective finance. If you borrow $100,000 at 5% interest compounded annually, you would owe $5,250 after the first year on a principal of $105,000. This method involves calculating and adding interest to an investment or loan once a year rather than for a longer period.
The formula to determine how much an investment will grow to overtime when it is placed in an account for years during which it generates dollar-compound interest is:
A = P(1 +r/m) m t
The values for each of these variables are provided as follows, presuming that a year has 365 days: m =365 t=6r 8.5% = 0.085The investment's worth is then computed after six years, as illustrated below.
A =991.15
To learn more about compounded refer to:
brainly.com/question/24274034
#SPJ1
Alex and Lara have $21.00. each to spend at a book fair, where all students receive a 35% discount. They both want to purchase a copy of the same book, which normally sells for $28.50 plus 10% sales tax. To check if he has enough to purchase the book, Alex takes 35% of $28.50 and subtract that amount from the normal price. He takes 10% of the discounted selling price and adds it back to find the purchase amount. Lara takes 65% of the normal purchase price and then computes 110% of the reduced price. Is Alex correct? Is Lara correct? Do they have enough money to purchase the book? explain your answer using complete sentences and show your work.
To begin, let's find how much the book is including tax and the student discount. Once we find this, we can see if Lara or Alex is correct and if they can afford it.
First, we want to compute the student discount. The student discount is 35%. Thus, we can do 0.65 x 28.50 = 18.525. With 10% tax, we have 18.525 x 1.1 = 20.3775. Which will round up to $20.38.
Now, lets see what Alex did and if he got the same answer. First he takes 35% of $28.50 and subtracts it from the normal price.
.35 x 28.50 = 9.975
28.50 - 9.975 = 18.525
Then he takes 10% of this number and adds it back.
.10 x 18.525 = 1.8525
18.525 + 1.8525 = 20.3775
Alex has the correct answer.
Next, we will see if Lara computed it correctly.
First she takes 65% of the normal price.
0.65 x 28.50 = 18.525
Then she computes 110% of the reduced price.
18.525 x 1.10 = 20.3775
Lara also gets the correct answer.
So, do they have enough money to purchase the book?
YES:
$20.38 < $21
Is Alex correct?
YES
Is Lara correct?
YES
Although they used different methods to get the answer, they both got the right one!
Help fsuplnghtssguiinv 1-x=16-4
Answer:
[tex]1 - x = 16 - 4 \\ 1 - x = 12 \\ - x = 1 - 12 \\ - x = - 11 \\ x = 11[/tex]
it's that answer
Need help on this! (Many points!)
Answer:
[tex]\frac{-8}{9}[/tex]
Step-by-step explanation:
Substitute in 7 for x
[tex]\frac{7^{2}-5(7) -6 }{7^{2}-6(7) - 16 }[/tex]
[tex]\frac{49-35-6}{49-42-16}[/tex]
[tex]\frac{-8}{9}[/tex]
find the sum by adding each term together. use the summation capabilities of a graphing utility to verify your result. (round your answer to four decimal places.) 5 1 k2 4 k
The result of the following summation is 114.
We are given the following summation, i = 1 to 6 ∑(4i + 5)
To determine the sum by adding the values, we will substitute the values of i, starting from i = 1 to i = 6, in the expression.
= 4(1) + 5 + 4(2) + 5 + 4(3) + 5 + 4(4) + 5 + 4(5) + 5 + 4(6) + 5
= 4(1) + 4(2) + 4(3) + 4(4) + 4(5) + 4(6) + 30
= 4 + 8 + 12 + 16 + 20 + 24 + 30
= 114
Thus, the result of the sum is 114.
To know more about summation:
https://brainly.com/question/29334900
#SPJ4
Mr and Mrs Jones received their heating bill the details follows
Present meter reading: 2410
Previous meter reading: 2090
Charge per unit: 12p per unit
Service charge: 20p per day for 14 days.
VAT: 5%
Find the total increase of the heating bill.
Answer:
Previous meter reading: 2090
Charge per unit: 12p per unit
Step-by-step explanation:
Answer:
£43.26
Step-by-step explanation:
Given readings:
Present meter reading: 2410Previous meter reading: 2090Calculate the number of units used:
[tex]\begin{aligned} \textsf{Number of units used} &= \textsf{Present meter reading} - \textsf{Previous meter reading}\\&= \sf 2410 - 2090\\&= \sf 320\; units \end{aligned}[/tex]
Given charges:
Charge per unit: 12p per unit.Service charge: 20p per day for 14 days.Calculate the cost excluding VAT:
[tex]\begin{aligned}\textsf{Cost (exc. VAT)}&=\textsf{(\# of units $\times$ charge per unit)}+\textsf{(\# of days $\times$ service charge per day)}\\ & = \sf 320 \times \£0.12 + 14 \times \£0.20\\&= \sf \£38.4+\£2.8\\&= \sf \£41.20\end{aligned}[/tex]
To find the total cost including VAT at 5%, multiply the cost (exc. VAT) by 1.05:
[tex]\begin{aligned}\textsf{Cost (inc. VAT at 5\%)}&= \sf \£41.20 \times 1.05\\&= \sf \£43.26\end{aligned}[/tex]
Mrs. Conrad's art class was painting murals. She had 4 bottles of red paint, 5 bottles of green paint, 4 bottles of yellow paint, 6 bottles of blue paint, and 5 bottles of orange paint. Use the bar diagram to write and evaluate two numerical expressions to represent the total number of bottles of paint.
Answer:
24
Step-by-step explanation:
4+5+6+4+5=24
simple
no big deal
15. Two leaky containers are filling with water. Water enters container A at a rate of 2 cup per 1 • minute and leaks out at 3 2 , 1 3 a rate of 4 cup per a minute. Water enters container B at a rate of 3 cup per 1 5 minute and leaks out at a rate of 1 2 cup per 3 _ minute. Which container needs to be filled faster in order for both containers to gain the same amount of water per minute? By how much more water per minute? Explain.
Container B needs to be filled faster in order for both containers to gain the same amount of water per minute , and by 1/6 water per minute .
What is the rate at which water is filled?Since water enters container A at a rate of 2/3 cup per 1/2 minute, then we can say that;
Rate of Filling container A = (2/3)/(1/2) = 4/3 cups per minute
We are also told that in container A, water leaks out at a rate of 1/4 cup per 3/4 minute. Thus;
Rate of leaking container A = (1/4)/(3/4) = 1/3 cups per minute
Amount of water in Container A in one minute = (4/3) - (1/3)
= 1
Similarly;
Since water enters container B at a rate of 3/4 cup per 1/2 minute, then we can say that;
Rate of Filling container B = (3/4)/(1/2) = 3/2 cups per minute
We are also told that in container B, water leaks out at a rate of 1/2 cup per 3/4 minute. Thus;
Rate of leaking container B = (1/2)/(3/4) = 2/3 cups per minute
Amount of water in Container B in one minute = (3/2) - (2/3) = 5/6
Since amount of water per minute in container A is 1 and the amount of water per minute in container B is 5/6 , then it means that container A fills faster by container B by; 1 - 5/6 = 1/6
Read more about rate of flow at; https://brainly.com/question/19475319
#SPJ1
Complete question is;
two leaky containers are filling with water. water enters container a at a rate of 2/3 cup per 1/2 minute and leaks out at a rate of 1/4 cup per 3/4 minute. water enters container b at a rate of 3/4 cup per 1/2 minute and leaks out at a rate of 1/2 cup per 3/4 minute. which container needs to be filled faster in order for both containers to gain the same amount of water per minute? by how much more water per minute? explain
fy(y)=0.2e^(-0.2y),y>=0
What is the probability that the buyer waits more than 10 minutes?
The probability that the buyer waits more than 10 minutes is 0.0271
How to determine the probability that the buyer waits more than 10 minutes?From the question, we have the following parameters that can be used in our computation:
Probability function:
fy(y)=0.2e^(-0.2y), y ≥ 0
The inequality expression y ≥ 0 means that
The value of y is atleast 0
The probability that the buyer waits more than 10 minutes means that
y = 10
So, we have the following representation
y = 10 in fy(y)=0.2e^(-0.2y)
Substitute the known values in the above equation, so, we have the following representation
fy(10)=0.2e^(-0.2 * 10)
Evaluate the exponents
fy(10)=0.2 * 0.13533528323
Evaluate the products
fy(10) = 0.0271
Hence, the probability is 0.0271
Read more about probability at
https://brainly.com/question/251701
#SPJ1
A researcher wants to know whether the acidity of rain (pH) near Houston, Texas, is significantly different from that near SC Chicago, Illinois. He randomly selects 12 rain dates in Texas and 14 rain dates in Illinois and obtains the following data: Texas 4.69 5.10 5.22 4.46 4.93 4.65 5.22 4.76 4.25 5.14 4.11 4.71 Illinois 4.40 4.22 4.64 4.54 4.35 4.69 4.69 4.75 4.40 4.63 4.45 4.49 4.36 4.52 Source: National Atmospheric Deposition Program (a) Is the sampling method dependent or independent? Why? (b) Because the sample sizes are small, what must be true regarding the populations from which the samples were drawn? (c) Draw side-by-side boxplots of the data. What does the visual evidence imply about the pH of rain in the two states? () Does the evidence suggest that there is a difference in the pH of rain in Chicago and Houston? Use the x = 0.05 level of significance.
Previous question
The sampling method is independent as the rain samples were taken from two different locations. As the sample sizes are small, they can be approximately considered normal distributions and t-test can be used to check the hypothesis.
What is a t-test?Used in inferential statistics, t test can be used when we need to compare two different sets value to check if their is a significant difference between them.
T tests can be paired and dependent, like measuring the weight of a same patient before and after a diet or they can be unpaired an independent. Unpaired datasets might sometime have the same variance or unequal variance. Different formular are used to calculate the t-tests involving different datasets. To prove a null or alternate hypothesis, the t values must be checked with t- test table.
What t-test formula should we use for our problem?As the following datasets measuring rain pH at different cities are indepent and have unequal variances, the following formula should be used for calculating the t-score and the degree of freedom:
T-value= [tex]\frac{Mean1-Mean2}{\sqrt(\frac{var1}{n1})+(\frac{var2}{n2})}[/tex]
Substituing the values of Mean1=4.77; Mean2=4.50, Var1=0.1366, Var2= 0.0242, n1= 12, n2= 14, we get the t value as 2.27
Now calculating degree of freedom, which comes around
Δ=14
At x=0.05, from the table, t value=2.145
Hence as the calculated t vale is more than critical t value, null hypothesis can be rejected and alternate hypothesis can be accepeted proving that their is a significant visible difference in pH in the rain of Chicago and Huston.
To know more about T-tests, follow the link: https://brainly.com/question/29745423
#SPJ4
write a while loop to read integers from input until -1 is read. for each integer read before -1, add the integer to vector numbervect. ex: if the input is 1 6 5 3 -1, then the output is: 1 6 5 3
As per the concept of vector, the while loop for integers is written below.
The term vector refers a quantity or phenomenon that has two independent properties: magnitude and direction.
Here we need to write the a quantity or phenomenon that has two independent properties: magnitude and direction.
While we looking into the given question, we have know that,
Here the input is 1 6 5 3 -1, then
the output is: 1 6 5 3
Then the function for the given statement is written as,
while ((char1 = getchar()) != '-1')
{
if (char1 == ' ')
sp_ct1++;
else if (char1 == '\n')
nl_ct1++;
else
other1++;
}
Therefore, the above function is used to read integers from input until -1 is read.
To know more about function here
https://brainly.com/question/28193995
#SPJ4
1. Given: Cos θ = (3/5), Find: Csc θ
2. Given: Sin θ = (5/6), Find: Cot θ
3. Given: tan θ = (3/4), Find: Cot θ
4. Given: Sec θ = (7/2), Find: Cos θ
5. Given: Sin θ = (2/3), Find: Cosec θ
6. Given: Sin θ = (2/3), Find: Cos θ
7. Given: Cos θ = (3/4), Find: Tan θ
8. Given: Tan θ = (6/4), Find: Sin θ
9. Given: Tan θ = (7/5), Find: Cos θ
10. Given: Tan θ = (7/5), Find: Sec θ
Help please.
the trigonometric function of all the given question is obtained.
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
Given: Cos θ = (3/5), Find: Csc θ = 5/4
Given: Sin θ = (5/6), Find: Cot θ = 11/5
Given: tan θ = (3/4), Find: Cot θ= 4/3
Given: Sec θ = (7/2), Find: Cos θ= 2/7
Given: Sin θ = (2/3), Find: Cosec θ=3/2
Given: Sin θ = (2/3), Find: Cos θ=5/3
Given: Tan θ = (6/4), Find: Sin θ=6/7.21
Given: Tan θ = (7/5), Find: Cos θ=5/8.6
Given: Tan θ = (7/5), Find: Sec θ= 8.6/5
Hence the above trigonometric function of all the given question is obtained.
Learn more about Trigonometric Functions, by the following link.
https://brainly.com/question/25618616
#SPJ1
Edmund is designing his garden. For every yellow tulip, he plans to plant two whites lilies. Using only these two types of flower, he plans to plant 12 flowers in his garden. How many of each type of flower will Edmund plant in his garden?
Solving a system of equations we will see that Edmund will plant 4 yellow tulips and 8 white lilies.
How many of each type of flower will Edmund plant in his garden?Let's define our variables as:
x = number of yellow tulips.y = number of white lilies.We know that for each yellow tulip he will plant two white lilies, then:
y = 2x
And we also know that he wants to plant 12 flowers, so:
x + y = 12
Then we have a system of equations:
x + y = 12
y = 2x
Substituting the second equation into the first one, we will get:
x + 2x = 12
3x = 12
x = 12/3
x = 4
Then the value of y is:
y = 2x
y = 2*4 = 8
Then he will plant 4 yellow tulips and 8 white lilies.
Learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
←+++
-5 -4 -3 -2
5
4+
3
2+
1+
-2
-3
Y
-5
1 2 3 4 5
Find the inequality represented by the graph.
Answer:
i don't know?please tell me in breif i didn't understand?
A television station claims that the amount of advertising per hour of broadcast time has an average of 15 minutes and a standard deviation equal to 1.2 minutes. You watch the station for 1â hour, at a randomly selectedâ time, and carefully observe that the amount of advertising time is equal to 17 minutes. Calculate theâ z-score for this amount of advertising time. A. zequalsnegative 1.05 B. zequals1.05 C. zequals1.67 D. zequalsnegative 1.67
The z-score for the time spent on advertisement as calculated is 1.666 .
According to a television station, there is 15 minutes on average of advertising every hour of broadcast time, with a standard deviation of 1.2 minutes.
i.e.
mean = 15
SD =1.2
Per hour's worth of advertising is represented by the random variable x.
z = x - mean / SD
Since x=17 , we have
z = ( 17 - 15 ) / 1.2
= 2 / 1.2
= 1.666
Consequently, this amount of advertising time has a z-score of -1.666.
A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.
A standard normal table is a mathematical table for the values of, displaying the values of the cumulative distribution function of the normal distribution. It is also known as the unit normal table or the z-score table. The Z-score, commonly referred to as the standard score, expresses how far away from the mean an object is.
To learn more about Z-score
brainly.com/question/28387843
#SPJ4
**WILL MARK BRAINLIEST AND GIVE 30 POINTS**
Tammy and Luke take part in a game in which they earn the same number of points for each catch and lose the same number of points for each miss. Tammy makes 5 catches and misses 1, ending the game with 23 points. Luke earns 8 catches and has 5 misses. Luke ends the game with 30 points.
Part A: Write a system of equations that describes Tammy and Luke's outcomes. Use x to represent the number of points for a catch and y to represent the number of points for a miss.
The system of equations that describes Tammy and Luke's outcomes is written below
5x - y = 238x - 5y = 30How to write the system of equationsIt can be deduced form the question that
x represents the number of points for a catch
y to represent the number of points for a miss
Tammy makes 5 catches and misses 1, ending the game with 23 points
5x - y = 23
Luke earns 8 catches and has 5 misses. Luke ends the game with 30 points
8x - 5y = 30
The system of equations required are
5x - y = 23
8x - 5y = 30
Learn more about linear functions at:
https://brainly.com/question/29225098
#SPJ1
Samantha and Phil wrote equivalent equations to represent the same function, f.
Samantha's equation: f(x)=(x+12)^2−16
Phil's equation: f(x)=(x+16)(x+8)
We can take Samanta's equation and rewrite it in such a way that we get Phil's equation, then the equations are equivalent.
Are the equations equivalent?
Two equations are equivalent if we can rewrite one of them and get the other one.
We know that the equations are:
Samantha's equation: f(x)=(x+12)^2−16
Phil's equation: f(x)=(x+16)(x+8)
We can find the zeros of Samantha's equation by solving the quadratic equation:
(x+12)^2−16 = 0
(x + 12)^2 = 16
(x + 12) = ±√16
x + 12 = ± 4
x = ±4 - 12
Then the two zeros are:
x = (+4 - 12) = -8
x = (-4 - 12) = -16
Then we can factorize the quadratic function of Samantha as:
y = (x - (-8))*(x - (-16))
x = (x + 8)*(x + 16)
That is Phil's equation, then the equations are equivalent.
Learn more about equivalent equations:
https://brainly.com/question/2972832
#SPJ1