Answer:
[tex]Q_1 = 19[/tex] --- first quartile
[tex]Q_3 = 41.5[/tex] --- third quartile
Step-by-step explanation:
Required:
The first and the third quartile
First, we order the dataset in ascending order[tex]Sorted: 6, 10, 11, 12, 15, 18, 20, 21, 24, 25, 26, 29, 30, 34, 35, 38, 40, 41, 42, 43, 44, 46, 55, 61[/tex]
The count of the dataset is:
[tex]n = 24[/tex]
Calculate the median position
[tex]Median=\frac{n+1}{2}[/tex]
[tex]Median=\frac{24+1}{2}[/tex]
[tex]Median=\frac{25}{2}[/tex]
[tex]Median=12.5th[/tex]
This means that the median is between the 12th and the 13th item
Next;
Split the dataset to two parts: 1 to 12 and 13 to 24
[tex]First: 6, 10, 11, 12, 15, 18, 20, 21, 24, 25, 26, 29[/tex]
[tex]Second: 30, 34, 35, 38, 40, 41, 42, 43, 44, 46, 55, 61[/tex]
The median position is:
[tex]Median = \frac{n + 1}{2}[/tex]
In this case; n = 12
So:
[tex]Median = \frac{12 + 1}{2}[/tex]
[tex]Median = \frac{13}{2}[/tex]
[tex]Median = 6.5th[/tex]
This means that the median is the average of the 6th and 7th item of the sorted dataset
So, we have:
[tex]Q_1 = \frac{18 + 20}{2}[/tex]
[tex]Q_1 = \frac{38}{2}[/tex]
[tex]Q_1 = 19[/tex] --- first quartile
[tex]Q_3 = \frac{41+42}{2}[/tex]
[tex]Q_3 = \frac{83}{2}[/tex]
[tex]Q_3 = 41.5[/tex] --- third quartile
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they charged a total of
$750. What was the rate charged per hour by each mechanic if the sum of the two rates was $105 per hour?
Step-by-step explanation:
let's convert the statement into equation..
let the charge of 1st mechanic be x and second be y..
by the question..
10x+5y=750...(i)
x+y=105..(ii)
from eqn(ii)..
x+y=105
or, x=105-y...(iii)
substituting the value of x in eqn (i)..
10x+5y=750
or, 10(105-y)+5y=750
or, 1050-10y+5y=750
or, 1050-750=5y
or, y=300/5
•°• y=60
substituting the value of y in eqn(iii).
x=105-y
or, x=105-60
•°• x= 45..
the rate charged by two mechanics per hour was 60$ and 45$
What is the length of the diagonal of a rectangle with the base of 4 and an altitude of 3
Answer:
5
Step-by-step explanation:
Use the Pythagorean Theorem
C^2=a^2 + b^2
c^2= 3^2 + 4^2
c^2= 9+16
c^2= 25
The take the square root
c= √25
c = 5
Tom and Jerry had a race. Tom started at 0200 running at 4.5km per hour. Jerry started
later at 6:30am running at 6.5km per hour. After five hours, who was ahead, and by how
much (answer in kilometres)
Answer:
Tom, 10.25
Step-by-step explanation:
Distance covered by Tom=4.5*(4 1/2+5)=81/4=42.75km
Distance covered by Jerry=6.5*(5)=32.5km
Tom is ahead from Jerry by 10.25km
Raj wants to get a tropical fish tank. The pet store owner tells him that he needs a tank that has a total volume equal to 80 ounces plus 4 ounces for each fish.
Which model shows two expressions for the total volume of the tank that will hold f fish?
A. 2(2e + 4f + 10g)
B. 80(e + f + g)
C. 2(2e + 2f + 5g)
D. 2(e + 2f + 5g)
Answer:
A. 2(2e + 4f + 10g)
Step-by-step explanation:
At a large Midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 1997, a simple random sample of 100 entering freshmen found that only 10 finished in the bottom third of their high school class. Let p 1 and p 2 be the proportions of all entering freshmen in 1993 and 1997, respectively, who graduated in the bottom third of their high school class. What is a 90% plus four confidence interval for p 1 – p 2?
Answer:
The 90% confidence interval for the difference of proportions is (0.01775,0.18225).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
p1 -> 1993
20 out of 100, so:
[tex]p_1 = \frac{20}{100} = 0.2[/tex]
[tex]s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]
p2 -> 1997
10 out of 100, so:
[tex]p_2 = \frac{10}{100} = 0.1[/tex]
[tex]s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]
Distribution of p1 – p2:
[tex]p = p_1 - p_2 = 0.2 - 0.1 = 0.1[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05[/tex]
Confidence interval:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
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 bound of the interval is:
[tex]p - zs = 0.1 - 1.645*0.05 = 0.01775 [/tex]
The upper bound of the interval is:
[tex]p + zs = 0.1 + 1.645*0.05 = 0.18225 [/tex]
The 90% confidence interval for the difference of proportions is (0.01775,0.18225).
Please help as quickly as possible.
Answer:
D
Step-by-step explanation:
take a calculator and try a few points.
I used x = 10.3 and x = 22.
and only D is really getting close to 0.4 and 3.5 as functional results.
Fixed costs are $3,000, variable costs are $5 per unit. The company will manufacture 100 units and chart a 50% markup. Using the cost-plus pricing method, what will the selling price be? (2 pts)
Your company has fixed costs of $150,000 per year. The variable costs per unit in 2018 were $3 per unit, and 30,000 units were produced that year. Your company uses cost-based pricing and has a profit margin of $3 per unit. In 2019, production increased and your team had more experience—variable costs went down to $2 per unit because of your team’s higher skill and 65,000 units were produced that year. What is the change in selling price from 2018 to 2019? (2 pts)
Fixed Costs are $500,000. Per unit costs are $75, and the proposed price is $200. How many units must be sold to break even? How many units must be sold to realize a $200,000 target return? (2 pts)
Congratulations! You you just decided to become the proud owner of a new food truck offering traditional Mediterranean cuisine. Kitchen and related equipment costs are $100,000. Other fixed costs include salaries, gas for the truck, and license fees and are estimated to be about $50,000 per year. Variable costs include food and beverages estimated at $6 per platter (meat, rice, vegetable, and pita bread). Meals will be priced at $10.
Answer:
1. Using the cost-plus pricing method, the selling price = $5.25
2. The change in selling price from 2018 to 2019 is $3.69 or 33.5% reduction.
3. To break-even, unit sales = 4,000 units
To realize a target return of $200,000, the unit sales = 5,600 units
4. Units to break-even = 12,500 meals
Sales revenue at break-even point = $125,000
Step-by-step explanation:
a) Data and Calculations:
Fixed costs = $3,000
Variable costs per unit = $5
Units manufactured = 100 units
Total variable costs = $500 ($5 * 100)
Total costs = $3,500 ($500 + $3,000)
Cost per unit = $3.50
Markup percentage = 50%
Using the cost-plus pricing method, the selling price = $5.25 ($3.50 * 1.5)
b) Fixed costs per year = $150,000
Variable costs per unit = $3
Production units = 30,000
Total variable costs = $90,000 ($3 * 30,000)
Cost-based pricing with a profit margin = $3 per unit
Total costs = $240,000 ($90,000 + $150,000)
Cost per unit = $8 ($240,000/30,000)
Selling price per unit = $11 ($8 + $3)
Variable cost = $2 per unit
Production units = 65,000 units
Total costs = ($2 * 65,000 + $150,000)
= $280,000 ($130,000 + $150,000)
Unit cost = $4.31 ($280,000/65,000)
Selling price = $7.31 ($4.31 + $3)
Change in selling = $3.69 ($11 = $7.31) = 33.5%
c) Fixed costs = $500,000
Per unit costs = $75
Proposed price = $200
Contribution margin per unit = $125 ($200 - $75)
To break-even, unit sales = $500,000/$125 = 4,000 units
To realize a target return of $200,000, the unit sales = $700,000/$125 = 5,600 units
d) Kitchen and related equipment costs = $100,000
Other fixed costs per year = $50,000
Variable costs = $6 per platter
Price per meal = $10
Contribution margin per meal = $4 ($10 - $6)
Units to break-even = $50,000/$4 = 12,500 meals
Sales revenue at break-even point = $50,000/40% = $125,000
Find the value of x.
X 9 9 7 x = [?]
What are the coordinates of point K?
A (-2,4)
B (-2,-4)
C (2,-4)
D (2, 4)
Answer:
A
Step-by-step explanation:
I guess that is the answer
Which equation is correct?
1
A. cos x =
sin a
1
B. tan x=
CSC 2
C. sec =
COS
1
D. cot 2 =
sec
SUBMIT
The requried secant function is the reciprocal of the cosine function, i.e., sec x = 1/cos x. Option C is correct.
What are trig ratios?If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
The correct equation is option C: sec x = 1/cos x.
This is because the secant function is the reciprocal of the cosine function, i.e., sec x = 1/cos x.
Learn more about trig ratios here:
https://brainly.com/question/14977354
#SPJ7
In 10 words or fewer, what is the square root of -9?
Type answer here...
What is the square root of -9
Answer:
no solution
Step-by-step explanation:
a negative number cannot be square rooted
Answer:
"not possible". no such thing as a negative squared number
what is the simple definition of realnumbers
Answer:
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line (or alternatively, a quantity that can be represented as an infinite decimal expansion).
Solve the formula for the given variable.
-2x - 6 = 4x
Please helppp
Answer:
s snsnnssjsjjsnsnsjs
es 17 es
Elena drank 3 liters of water yesterday. Jada drank 3/4 times as much water as elena. Link drank twice as much as Jada. Did jada drink more or less then elena? Explain how you know
Answer:
Step-by-step explanation:
3\4 bc on a nuberline it would be 3 3\4
I--I----(etc)
so yeah hope i helped
write the equation of the graph, y=? SOMEBODY PLEASE HELP
Answer:
[tex]y=\left(6\right)^{x}\ -3[/tex]
Step-by-step explanation:
Find the lengths of AD, EF, and BC in the trapezoid below.
We know that,
[tex]EF=\dfrac{AD+BC}{2}[/tex]
which is
[tex]x=\dfrac{x-5+2x-4}{2}[/tex]
Now solve for x,
[tex]x=\dfrac{3x-9}{2}[/tex]
[tex]2x=3x-9[/tex]
[tex]x=9[/tex]
Since x is 9, the lengths are,
[tex]AD=x-5=9-5=\boxed{4}[/tex]
[tex]EF=x=\boxed{9}[/tex]
[tex]BC=2x-4=18-4=\boxed{14}[/tex]
Hope this helps :)
identify an equation in point slope form for the line perpendicular to y=5x=2 that passes through (-6,-1)
Answer:
y=-1/5x-11/5
Step-by-step explanation:
perpendicular, product of both gradients = -1
hence, slope = -1/5
y=-1/5x+c
sub y=-1, x=-6
-1=-1/5(-6)+c
c = -1-6/5=-11/5
y=-1/5x-11/5
Can someone help me simplify this?
Answer:
See attached
Step-by-step explanation:
If one foot is
equivalent to 12
inches, how many
inches are in 3 feet?
*Bonus: What is
another name for that
length?
Answer:
36 am I wright
because in this case we should always multiply
Please help on my hw
Answer:
Base is 3 centimeter and hight is 12 cent.
What is the best point estimate for the population's standard deviation if the sample standard deviation is 37.3
Answer:
The best point estimate for the population's standard deviation is 37.3.
Step-by-step explanation:
Best point estimate:
The best point estimate for the population mean is the sample mean.
The best point estimate for the population standard deviation is the sample standard deviation.
In this question:
Sample standard deviation of 37.3, and thus, the best point estimate for the population's standard deviation is 37.3.
Differentiate the x the function :
(3x² - 9x +5²)
Firstly , before solving the equation , we should know about the chain rule and its formula.
Formula For the Chain rule-
$\rightarrow$ $\sf\dfrac\pink{dy}\pink{dx}$=$\sf\dfrac\pink{dy}\pink{du}$ $\times$ $\sf\dfrac\pink{du}\pink{dx}$ $\leftarrow$
_____________________________
$\sf\huge\underline{\underline{Question:}}$
$\sf\small{Differentiate\: x\: the \:function: (3x² - 9x + 5²)}$
$\sf\huge\underline{\underline{Solution:}}$
$\sf{Let\:y = (3x^2 - 9x + 5)^9}$
$\space$
☆ Differentiating both the sides w.r.t.x using chain rule-
$\mapsto$ [tex]\sf\dfrac{dy}{dx}=[/tex][tex]\sf\dfrac{d}{dx}[/tex][tex]\sf{(3x^2 - 9x + 5)^9}[/tex]
$\space$
$\space$
$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{9(3x^2-9x+5)^8}[/tex] [tex]\times[/tex] [tex]\sf\dfrac{d}{dx}[/tex]$\sf\small{(3x^2-9+5)}$
$\space$
$\space$
$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{9(3x^2-9x+5)^8}[/tex] [tex]\times[/tex][tex]\sf(6x-9)[/tex]
$\space$
$\space$
$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{9(3x^2-9x+5)^8}[/tex] $\times$ [tex]\sf{3(2x-3)}[/tex]
$\space$
$\space$
$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{27(3x^2-9x+5)^8(2x-3)}[/tex]
$\space$
$\space$
$\sf\underline\bold\green{❍ dy:dx=27(3x^2-9x+5)^8(2x-3)}$
______________________________
1 Construct the following triangles. You will need a ruler and a protractor.
a) Triangle ABC, where AB = 5 cm,
Answer:
abcdefghijklmnopqrstuvwxy and z
Step-by-step explanation:
Express 8:28 in its simplest form
How much money will there be in an account at the end of 10 years if $4000 is deposited at 6% compounded quarterly
Answer:
$7,256.07
Step-by-step explanation:
A = p(1+r/n)^nt
A = 4000(1+.06/4)^(10*4)
X,and z are midpoints.find the length of each segment
Answers:
MZ = 10ZO = 10MO = 20XZ = 9YZ = 7===========================================
Explanation:
Side MO is twice as long as the midsegment XY. Note how XY and MO are parallel.
This makes
MO = 2*XY = 2*10 = 20
Side MO breaks into two equal halves MZ and ZO
Each of MZ and ZO are 20/2 = 10 units long.
Put another way: XY, MZ and ZO are all the same length (all 10 units long).
---------------
The diagram shows that segment NO is 18 units long, which cuts in half to 18/2 = 9. This is the length of NY, YO and XZ
Also, MN = 14 which cuts in half to 7. This means MX, XN and YZ are all 7 units each.
What number x gives maximum value for c(12,x)?
Answer:
i will say methods try yourself:
How to Determine Maximum Value
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).The first step is to determine whether your equation gives a maximum or minimum. ...
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).The first step is to determine whether your equation gives a maximum or minimum. ...-x2 + 4x - 2.
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).The first step is to determine whether your equation gives a maximum or minimum. ...-x2 + 4x - 2.Since the term with the x2 is negative, you know there will be a maximum point.
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.
.
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plzz follow and make brainlist
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f(x) = 2/cos 2x
f(x) = 2/sin1x
f(x)=1/cos1/sin3
{x∣x ≠ π/4+πn/2} , for any integer n
Must click thanks and mark brainliest
What is the slope of the line that passes through the points (-7, -4) and
(-11, -2)? Write your answer in simplest form.
Answer:
-1/2
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -2 - -4)/( -11 - -7)
=( -2+4)/( -11+7)
= 2 / -4
= -1/2
State two similarities and one difference between the graphs of f(x)= 3^x and g (x)= (1/3) ^x
