The following stem-and-leaf plot represents the times in minutes required for 26 co-workers to commute to work. Use the data provided to find the quartiles. Commute Times in Minutes Stem Leaves 2 1 3 5 5 5 8 3 1 5 6 7 8 9 4 2 3 4 6 6 6 8 5 2 2 4 5 7 7 8 Key: 2|1
Answer:
Q1 = 30.25 minutes
Q2 = 42.5 minutes
Q3 = 40 minutes
Step-by-step explanation:
Given, In Question
The stem and leaf diagram (key 2 I 1)Stem | Leaves
2 | 1 3 5 5 5 8
3 | 1 5 6 7 8 9
4 | 2 3 4 6 6 6 8
5 | 2 2 4 5 7 7 8
We need to find the quartiles Q1, Q2 and Q3. We know that,Q1 = (1/4)*(n+1)th value
Q2 = (1/2)*(n+1)th value
Q3 = (3/4)*(n+1)th value
where n is the total number of co-workers 26.
So, Q1 = (1/4)*(26+1)th valueQ1 = 6.75th value
we need to count the leaves in the plot starting from the first one until we reach the 6.75th value. So, by counting, we conclude that the 6.75th value lies between the 6th and 7th value i.e. 28 and 31.
Q1 = 28 + (31-28)*0.75
= 28 + 2.25
Q1 = 30.25 minutes
Now, Q2 = (1/2) * (26+1)th value
= 13.5th value.
From the plot, we find that the 13.5th value lies in the middle of the 13th and 14th values i.e. 42 and 43. So,
Q2 = (42+43)/2
= 85/2
Q2 = 42.5 minutes
And, Q3 = (3/4)*(26+1)th value
= 20.25th value
From the plot. we find that the 20.25th value lies somewhere between the 20th and 21st value i.e. 52 and 52. So,
Q3 = 40 + (52-52)*0.25
= 40 + 0
Q3 = 40 minutes
Find the area of the composite/irregular figure. Use 3.14 for pi.
PLEASE SHOW WORK/EXPLANATION FOR BRAINLIEST
Answer:
151.25cm
Step-by-step explanation:
First split the the shape into two, a rectangle and a semicircle.
Let's begin with the rectangle. The formula for the area of a rectangle is
A = l × w
A = 16 × 7
A = 112
Now we move onto the semicircle. We know that the length of the long side of the rectangle is 16. Because of the markings, we know that the missing portion of the 6cm line is 16 as well. That means that we would do 16 - 6 to find that small missing length. It gives us 10cm which will act as the diameter for the semicircle.
The formula for the area of a semicircle is
A = [tex]\frac{\pi r^{2} }{2}[/tex] (fill in what you know)
A = [tex]\frac{3.14 (5^{2} )}{2}[/tex] (The radius is half the diameter. So 10 ÷ 2 = 5)
A = [tex]\frac{3.14(25)}{2}[/tex] (Solve what's in the parentheses first)
A = [tex]\frac{78.5}{2}[/tex] (multiply pi and 25)
A = 39.25
Now all we have to do is add the two areas to get the combined area of the whole.
A = 112 + 39.25
A = 151.25
If a1 = 4 and an = (an-1)2 + 3 then find the value of a4.
Answer:
pay more
Step-by-step explanation:
Write the equation of a straight line that passes through the point (3,1) and is parallel to the line y=2x-1
Answer:
Step-by-step explanation:The new line will be parallel to the line represented by y =2x +2
The equation y = 2x + 2 is written in slope- intercept form (i.e. y=mx + b) where m represents the slope. So the slope of this line is 2. A line parallel to y = 2x + 2 will have the same slope. This means the slope of the new line will also be 2.
To determine the equation of the new line, we can use the given point to find the y intercept of the new line:
y = 2x + b
Use x = -1 and y =3 to find b (or the y intercept ) of the new line:
3 = 2 * (-1) + b
3= -2 + b
b=5
Therefore, the equation of the line passing thru (-1,3) with the same slope as that of y = 2x + 2 will be:
y = 2x + 5
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1
Please help . Stuck
Answer:
[tex] - \frac{9}{2} [/tex]
Step-by-step explanation:
Rate of change of y with respect to x
[tex] = \frac{60 - 96}{ - 12 - ( - 20)} \\ \\ = \frac{ - 36}{ - 12 + 20} \\ \\ = \frac{ - 36}{ 8} \\ \\ = - \frac{9}{2} [/tex]
what number must you add to complete the square? x^2+28x=11
To complete 2ab of (a+b)²
2ab=28x2x(b)=28xb=28x/2xb=14b²=196196 must be added on both sides to get complete square as (x+14)²
Answer:
196
Step-by-step explanation:
Given equation:
[tex]x^2+28x=11[/tex]
Step 1
When completing the square for an equation in the form ax²+bx+c=0, the first step is to move the constant to the right side of the equation.
This has already been done in the given equation:
[tex]x^2+28x=11[/tex]
Step 2
Add the square of half the coefficient of x to both sides.
This forms a perfect square trinomial on the left side:
[tex]\implies x^2+28x+\left(\dfrac{28}{2}\right)^2=11+\left(\dfrac{28}{2}\right)^2[/tex]
Simplify:
[tex]\implies x^2+28x+14^2=11+14^2[/tex]
[tex]\implies x^2+28x+196=11+196[/tex]
[tex]\implies x^2+28x+196=207[/tex]
Step 3
Factor the perfect square trinomial on the left side:
[tex]\implies (x+14)^2=207[/tex]
We have now completed the square and can go onto solving the equation.
Therefore, 196 must be added to both sides of the equation to complete the square.
A boat heading out to sea starts out at Point A, at a horizontal distance of 819 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 14∘ . At some later time, the crew measures the angle of elevation from point B to be 7∘ . Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Answer:
[tex]844\:\text{ft}[/tex]
Step-by-step explanation:
I've created a diagram and added steps on GeoGebra for reference. Please refer to the diagram below:
In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side (o/a).
Therefore, we have the two equations:
[tex]\begin{cases}\tan 14^{\circ}=\frac{h}{819}\\\tan 7^{\circ}=\frac{h}{819+x}\end{cases}[/tex]
Because [tex]h=h[/tex] (reflexive property), we have:
[tex]819\tan 14^{\circ}=\tan 7^{\circ}(819+x)[/tex]
Isolating and solving for [tex]x[/tex]:
[tex]\frac{819+x}{819}=\frac{\tan 14^{\circ}}{\tan 7^{\circ}},\\\\1+\frac{x}{819}=\frac{\tan 14^{\circ}}{\tan 7^{\circ}},\\\\\frac{x}{819}=\frac{\tan 14^{\circ}}{\tan 7^{\circ}}-1,\\\\x=819(\tan 14^{\circ}\cot 7^{\circ}-1),\\\\x=844.07256243\approx \boxed{844\text{ ft}}[/tex]
Solve for the value of X pleassee
Answer:
188
Step-by-step explanation:
SR and ST are equal in length so the arc SR and arc ST also have same measurement
since the perimeter of the circle is equal to 360 and arc RT is given as 64
x = (360 - 64) / 2
x = 188
Use law of sines or law of cosines to find the length of side AB Please show work !!
Answer:
[tex]AB = 11.3[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
Length AB
To do this, we make use of sine law which is represented as:
[tex]\frac{a}{\sin(a)} = \frac{b}{\sin(b)} = \frac{c}{\sin(c)}[/tex]
So, we have:
[tex]\frac{15}{\sin(70)} = \frac{AB}{\sin(45)}[/tex]
Make AB the subject
[tex]AB = \frac{15}{\sin(70)} * \sin(45)[/tex]
[tex]AB = \frac{15}{0.9397} *0.7071[/tex]
[tex]AB = 11.3[/tex]
the ratio equivalent to 3:4.
Answer:
33:44
Step-by-step explanation:
4*11=44
3*11=33
The ___ is the center of mass of the triangle.
A. median
B. midpoint
C. orthocenter
D. centroid
Answer:D.CENTROID
Step-by-step explanation: THE ONLY CORRECT ANSWER IS CENTROID
Rent me $250 washing cars with his mobile car wash company he charges $70 per car and earn $50 in tips write an equation to represent the situation
Answer:
Try 250 = 70x + 50, or y = 70x + 50.
Step-by-step explanation:
He made 250 total. The variable is how many cars he washes. The y-intercept is 50. Therefore, either 250 = 70x + 50, or y = 70x + 50.
Answer:
250 = 70x + 50
Step-by-step explanation:
this is the equation if you are looking for the profit
Ex.
You washed 2 cars
250 = 70 (2) + 50
250 = 190
-190 -190
60
you are still $60 away from making a profit
Function limits:
Exercise approximation method
9514 1404 393
Answer:
A. 2
B. 6
Step-by-step explanation:
The attachment shows the table of values for exercises A and B.
A spreadsheet is also a useful tool for repeated function evaluation. Most spreadsheets carry about 16 significant digits, so can give good approximations down to very small differences from the limit value.
__
Additional comment
Here, the function simplifies to ...
f(x) = (2x)(x -1)/(x -1) = 2x
The simplified function can be evaluated directly at the limit value of x, with no approximation needed.
Determine the radius of a cone that has a volume of 155.521 cubic inches and a height of 9 inches.
Answer:The answer is 4.06
Step-by-step explanation:
Okay I am 98% sure my math could be wrong since I don’t know what the possible answers to the question are but this is what I got.
write the number sentence as an inequality: a number n is greater than 1
ill give brainlyiest
Answer:
n > 1
Step-by-step explanation:
7,35,175, 875,... find the 10th term
Which function of x has a y-intercept of -5?
Answer:
[tex]y = - 3x - 5 \\ c = - 5[/tex]
PLEASE HELP!!!
In 1994, the city of Amuel had a population of 1,256 people. That same year a factory opened near the town, and many people moved into the city limits. The population grew to 1,381 people in 1995, and in 1996 the population of Amuel reached 1,519 people. Assume this rate of growth continued until the factory closed in 2007. How many people were living in Amuel when the factory closed? Explain. Round to the nearest whole number, if needed.
Answer:
Step-by-step explanation:
so if in 1994 it was = 1,256
1995 = 1256 + x = 1,381 {x is 125}
1996 = 1381 + x = 1,519 {x is 138}
2007 = it is eleven years from 1996 to 2007 so take the average of the both digits which we will find through adding both the x quantities and dividing it with 2 the answer is 131.5. back to 2007, so multiply 11 with 131.5 which is 1,446.5. now add 1,446.5 to 1519
and the answer is 2,965.5.
hope it helps
Which lists all the factors of 78?
A. 1, 2, 3, 6, 13, 26, 39, 78
B. 1, 2, 4, 19, 39, 78
C. 1, 2, 6, 13, 39, 78
D. 2, 3, 6, 13, 26, 39
Answer:
1, 2, 3, 6, 13, 26, 39, 78
Answer:
Factors of 78: 1, 2, 3, 6, 13, 26, 39, and 78.
Step-by-step explanation:
I hope this helps!!!!!
LAST ONE, ON A TIMER. Find the zeros of the function and write in a + bi form.
-(x+1)^2-4=0
Answer:
Option DStep-by-step explanation:
-(x+1)²- 4 = 0(x+1)² = - 4 x + 1 = ± √-4x = -1 ± 2iCorrect choice is D
Answer:
D
Step-by-step explanation:
Given
- (x + 1)² - 4 = 0 ( add 4 to both sides )
- (x + 1)² = 4 ( multiply both sides by - 1 )
(x + 1)² = - 4 ( take the square root of both sides )
x + 1 = ± [tex]\sqrt{-4}[/tex] = ± 2i ( subtract 1 from both sides )
x = - 1 ± 2i , then
x = - 1 + 2i, x = - 1 - 2i → D
Write the product in standard form. (2 + 3i)(2 - i)
9514 1404 393
Answer:
7 +4i
Step-by-step explanation:
(2 +3i)(2 -i) = 2(2 -i) +3i(2 -i) = 4 -2i +6i +3 = 7 +4i
_____
i = √-1, so i^2 = -1. Otherwise the product is identical to what you would get if "i" were a variable.
Zoey bought a new skateboard that cost 36.79. How much change should she get if she paid for the skateboard with two 20 bills
Answer:
4 dollars and something back
Step-by-step explanation:
Hi there!
»»————- ★ ————-««
I believe your answer is:
$3.21
»»————- ★ ————-««
Here’s why:
Zoey bought a $36.79 skateboard and paid for it with two $20 bills. This means that Zoey paid $40 in total.⸻⸻⸻⸻
[tex]40.00-36.79=\boxed{3.21}[/tex]
⸻⸻⸻⸻
She should get $3.21 as her change.
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
solve for y in y/4 =-7
Answer:
y = -28
Step-by-step explanation:
y/4 =-7
Multiply each side by 4
y/4 *4 =-7*4
y = -28
Answer:
-28
Step-by-step explanation:
y/4=-7
multiply by 4 on but sides
y = -7(4)
y = -28
A T-shirt stand on the boardwalk recently sold 6 purple shirts and 9 shirts in other colors. What is the experimental probability that the next shirt sold will be purple?
Answer:
2/5.
Step-by-step explanation:
To find the denominator, you add all of the times the experiment has been done.
6 + 9 = 15.
Then, since they're asking about purple shirts, you put that as the numerator.
Making it 6/15.
To simplify, divide both sides by 3, making it 2/5 simplified.
The solution is, 2/5 is the experimental probability that the next shirt sold will be purple.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
To find the denominator, you add all of the times the experiment has been done.
6 + 9 = 15.
Then, since they're asking about purple shirts, you put that as the numerator.
Making it 6/15.
To simplify, divide both sides by 3, making it 2/5 simplified.
Hence, The solution is, 2/5 is the experimental probability that the next shirt sold will be purple.
To learn more on probability click:
brainly.com/question/11234923
#SPJ3
The manager of the dairy section of a large supermarket chose a random sample of 250 egg cartons and found that 30 cartons had at least one broken egg. let p denote the proportion of all cartons which have at least one broken egg. Find a point estimate for p and also construct a 90% confidence interval for p.
Answer:
The point estimate for p is of 0.12.
The 90% confidence interval for p is 0.0862 < p < 0.1538.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The manager of the dairy section of a large supermarket chose a random sample of 250 egg cartons and found that 30 cartons had at least one broken egg.
This means that [tex]n = 250, \pi = \frac{30}{250} = 0.12[/tex]
The point estimate for p is of 0.12.
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 - 1.645\sqrt{\frac{0.12*0.88}{250}} = 0.0862[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 + 1.645\sqrt{\frac{0.12*0.88}{250}} = 0.1538[/tex]
The 90% confidence interval for p is 0.0862 < p < 0.1538.
Each observation indicates the primary position played by the Hall of Famers: pitcher (P), catcher (H), 1st base (1), 2nd base (2), 3rd base (3), shortstop (S), left field (L), center field (C), and right field (R). a. Construct frequency and percent frequency distributions to summarize the data. Position Frequency Percent Frequency (to one decimal) Pitcher % Catcher % 1st base % 2nd base % 3rd base % Shortstop % Left field % Center field % Right field % b. What position provides the most Hall of Famers
Answer:
a. See below for the Frequency and Relative frequency Table.
b. Pitcher (P) is the position provides the most Hall of Famers.
c. 3rd base (3) is the position that provides the fewest Hall of Famers.
d. R is the outfield position that provides the most Hall of Famers.
e. Th number of Hall of Famers of Infielders which is 16 is less than the 18 Hall of Famers of those of outfielders.
Step-by-step explanation:
Note: This question not complete. The complete question is therefore provided before answering the question as follows:
Data for a sample of 55 members of the Baseball Hall of Fame in Cooperstown, New York, are shown here. Each observation indicates the primary position played by the Hall of Famers: pitcher (P), catcher (H), 1st base (1), 2nd base (2), 3rd base (3), shortstop (S), left field (L), center field (C), and right field (R).
L P C H 2 P R 1 S S 1 L P R P
P P P R C S L R P C C P P R P
2 3 P H L P 1 C P P P S 1 L R
R 1 2 H S 3 H 2 L P
a. Use frequency and relative frequency distributions to summarize the data.
b. What position provides the most Hall of Famers?
c. What position provides the fewest Hall of Famers?
d. What outfield position (L, C, or R) provides the most Hall of Famers?
e. Compare infielders (1, 2, 3, and S) to outfielders (L, C, and R).
The explanation of the answers is now provided as follows:
a. Use frequency and relative frequency distributions to summarize the data.
The frequency is the number of times a position occurs in the sample, while the relative frequency is calculated as the frequency of each position divided by the sample size multiplied by 100.
Therefore, we have:
Frequency and Relative frequency Table
Position Frequency Relative frequency (%)
P 17 30.91%
H 4 7.27%
1 5 9.09%
2 4 7.27%
3 2 3.64%
S 5 9.09%
L 6 10.91%
C 5 9.09%
R 7 12.73%
Total 55 100%
b. What position provides the most Hall of Famers?
As it can be seen from the frequency table in part a, Pitcher (P) has the highest frequency which is 17. Therefore, Pitcher (P) is the position provides the most Hall of Famers.
c. What position provides the fewest Hall of Famers?
As it can be seen from the frequency table in part a, 3rd base (3) has the lowest frequency which is 2. Therefore, 3rd base (3) is the position that provides the fewest Hall of Famers.
d. What outfield position (L, C, or R) provides the most Hall of Famers?
As it can be seen from the frequency table in part a, we have:
Frequency of L = 6
Frequency of C = 5
Frequency of R = 7
Since R has the highest frequency which is 7 among the outfield position (L, C, or R), it implies that R is the outfield position that provides the most Hall of Famers.
e. Compare infielders (1, 2, 3, and S) to outfielders (L, C, and R).
Total frequency of infielders = Frequency of 1 + Frequency of 2 + Frequency of 3 + Frequency of S = 5 + 4 + 2 + 5 = 16
Total frequency of outfielders = Frequency of L + Frequency of C + Frequency of R = 6 + 5 + 7 = 18
The calculated total frequencies above imply that number of Hall of Famers of Infielders which is 16 is less than the 18 Hall of Famers of those of outfielders.
How many small squares in this rectangle should be shaded to represent
5 of
I
Answer:
Where's the picture
Step-by-step explanation:
The picture...
What is the value of x?
Answer:
80°
Step-by-step explanation:
Central Angles and the Arc they create are equal
In which function is x = 2 mapped to 32 ?
Answer:
Option 2 is the correct answer
[tex]g(x) = 4 {(x + 3)}^{2} - 68 [/tex]
Step-by-step explanation:
[tex]g(x) = 4 {(x + 3)}^{2} - 68 \\ \\ \because \: g(2) = 4 {(2 + 3)}^{2} - 68 \\ = 4 {(5)}^{2} - 68 \\ = 4(25) - 68 \\ = 100 - 68 \\ = 32[/tex]
Answer:
option b
Step-by-step explanation:
See image below:)
FYI you can use the app photo math, you just take a pic of the problem and it gives you the answer and explains the steps and it is free.
Please help me in this question.
Answer:
a) 24
b) 63
c) 2
d) -2
Step-by-step explanation:
you are supposed to try different numbers, but...
X-9 = 15 add 9 to both sides
X = 24
7x/9 = 49 multiply both sides by 9
7x = 441 divide by 7
x = 63
3(x + 6) = 24 divide both sides by 3
(x + 6) = 8 subtract 6 from both sides
X = 2
11x + 2 = -20 subtract 2 from both sides
11x = -22 divide both sides by 11
X = -2
