Answer:
Step-by-step explanation:
From the question; we are given the following inclusive frequency distribution information
Class Frequency f
1.1-1.5 18
1.6-2.0 27
2.1-2.5 31
2.6-3.0 40
3.1-3.5 56
3.6-4.0 55
4.1-4.5 23
Convert the above inclusive frequency distribution to exclusive frequency distribution with respect of the upper and lower class limit ; we have:
Class Frequency f
1.05 - 1.55 18
1.55 - 2.05 27
2.05 - 2.55 31
2.55 - 3.05 40
3.05 - 3.55 56
3.55 - 4.05 55
4.05 - 4.55 23
Class Frequency f cf
1.05 - 1.55 18 18
1.55 - 2.05 27 45
2.05 - 2.55 31 76
2.55 - 3.05 40 116
3.05 - 3.55 56 172
3.55 - 4.05 55 227
4.05 - 4.55 23 250
n = 250
To determine the daily sales; we can derive that from estimated Mode by using the relation :
Estimated Mode = L + fm − fm-1(fm − fm-1) + (fm − fm+1) × w
here:
L = the lower class boundary of the modal group
fm-1 = the frequency of the group before the modal group
fm = the frequency of the modal group
fm+1 = the frequency of the group after the modal group
w = the group width
However;
It is easier now to determine the modal group (i.e the group with the highest frequency), which is 3.05 -3.55
L = 3.05
fm-1 =40
fm =56
fm+1 = 55
w = 0.5
∴[tex]mode = 3.05 + \dfrac{56 - 40 }{(56 - 40) + (56 -55)} * 0.5 \\ \\ mode = 3.05 + 0.4705 \\ \\ mode = 3.5205[/tex]
To find Median Class ; we use the formula;
Median Class = value of (n / 2)th observation
Median Class = value of (250 / 2)th observation
Median Class = value of 125th observation
From the column of cumulative frequency cf,
we will see that the 125th observation lies in the class 3.05-3.55.
∴ The median class is 3.05-3.55.
Thus;,
L=lower boundary point of median class =3.05
n=Total frequency =250
cf=Cumulative frequency of the class preceding the median class =116
f=Frequency of the median class =56
c=class length of median class =0.5
[tex]Median M=L+n2-cff- c \\ \\ =3.05+125-11656⋅0.5 \\ \\=3.05+0.08036 \\ \\ =3.13036[/tex]
hence median sales = $3130.36
Question 1 Muit Choice Worth 1 points)
(08.01 LC)
The school principal wants to know whether the students in the entire school prefer football or basketball. The principal draws a random sample from the following groups:
• All school teachers
. All girls in each grade
. All students in each grade
• All students on the basketball team
Which of the following groups best represents the population she should take a random sample from to get the best results for her survey?
All school teachers
All girls in each grade
All students in each grade
All students on the basketball team
Answer:
I think its C. All students in each grade
Step-by-step explanation:
because it should be the students choice.
The probability of drawing a pearl bead out of a bag of mixed beads is 2/3. What is the probability of drawing a bead which is not a pearl?
Answer:
[tex]\frac{1}{3}[/tex] probability of drawing a bead which is not a pearl
Step-by-step explanation:
For each bead that you draw, there are only two possible outcomes. Either it is a pearl bead, or it is not. The sum of these probabilities = 100% = 1.
So
2/3 probability of drawing a pearl bead.
p probability of drawing a non pearl bead.
What is the probability of drawing a bead which is not a pearl?
[tex]p + \frac{2}{3} = 1[/tex]
[tex]p = 1 - \frac{2}{3}[/tex]
[tex]p = \frac{3*1 - 2}{3}[/tex]
[tex]p = \frac{1}{3}[/tex]
[tex]\frac{1}{3}[/tex] probability of drawing a bead which is not a pearl
If log10y=2, what does y equal?
Answer:
[tex]y=100[/tex]
Step-by-step explanation:
I don't know if by the 10 you mean the base is 10 or it's being logged with the y, but I'm assuming the base is 10. If that's not right, message me and I'll fix my answer. If,
[tex]log_an=x\\a^x=n[/tex]
Then,
[tex]log_1_0y=2\\10^2=y\\100=y[/tex]
The percent, X, of shrinkage on drying for a certain type of plastic clay has an average shrinkage percentage :, where parameter : is unknown. A random sample of 45 specimens from this clay showed an average shrinking percentage of 18.4 and a standard deviation of 2.2. est at 5% level of significance whether the true average shrinkage percentage : is greater than 17.5 and write your conclusion. Report the p-value.
Answer:
[tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]
The degrees of freedom are given by:
[tex]df=n-1=45-1=44[/tex]
The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4
[tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]
We see that the p value is lower than the significance level so then we can reject the null hypothesis in favor of the alternative.
Step-by-step explanation:
Information given
[tex]\bar X=18.4[/tex] represent the sample mean
[tex]s=2.2[/tex] represent the sample standard deviation
[tex]n=45[/tex] sample size
[tex]\mu_o =17.5[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
We want to test if the true mean is higher than 17.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 17.5[/tex]
Alternative hypothesis:[tex]\mu > 17.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]
The degrees of freedom are given by:
[tex]df=n-1=45-1=44[/tex]
The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4
The p value would be given by:
[tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]
We see that the p value is lower than the significance level so then we can reject the null hypothesis in favor of the alternative.
A firm produces a commodity and receives $100 for each unit sold. The cost of producing and selling x units is 20x 0.25x 2 dollars. Find the number of units the company should produce in order to maximize profit, and find the maximum profit.
Answer:
160 units and $6400
Step-by-step explanation:
We have that the cost per x unit is: 20 * x + 0.25 * x ^ 2
the price per unit is 100, therefore revenue for each unit would be 100 * x
However:
profit = revenue - cost
p (x) = 100 * x - 20 * x - 0.25 * x ^ 2
for the maximum value profit we must derive and equal 0:
p '(x) = 100 - 20 - 0.5 * x
0 = 80 - 0.5 * x
0.5 * x = 80
x = 80 / 0.5
x = 160
Therefore, the maximum profit occurs when there are 160 units, replacing we have:
p (x) = 100 * 160 - 20 * 160 - 0.25 * 160 ^ 2
p (x) = 6400
that is to say that the $ 6400 is the maximum profit.
simplify (51/3)^3
i will give brainlist
Answer: D. 5
Step-by-step explanation:
Typically when you have exponents in a form like this, you would multiply 1/3 with 3 to get 1/3 * 3/1. The threes cancel out and you're left with an exponent of 1. And 5 to the 1 power is 5.
On a coordinate plane, triangle A B C has points (negative 9, 3), (negative 9, 6), (0, 3) and triangle A double-prime B double-prime C double-prime has points (3, negative 1), (3, negative 2), and (0, negative 1).
Which transformations could be performed to show that △ABC is similar to △A"B"C"?
a reflection over the x-axis, then a dilation by a scale factor of 3
a reflection over the x-axis, then a dilation by a scale factor of One-third
a 180° rotation about the origin, then a dilation by a scale factor of 3
a 180° rotation about the origin, then a dilation by a scale factor of One-third
Answer: D 180 degrees rotation about the origin.then a dilation by a scale factor of one-third.
Step-by-step explanation:
A( -9,3) B(-9,6) C (0,3)
After a rotation of 180 degrees you will have the new points as
A (9,-3) B( 9,-6) C (0, -3)
The you after dilating it by a scale factor of 1/3
you will get the coordinates
A ( 3,-1) B( 3,-2) C(0,-1)
which match is what was given in the question.
Answer:
a 180° rotation about the origin, then a dilation by a scale factor of One-third
Step-by-step explanation:
took the test
A spinner has 10 equally sized sections, 8 of which are gray and 2 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue ? Write your answer as a fraction in simplest form.
Answer:
4/25
Step-by-step explanation:
The probability the first spin lands on gray is 8/10 = 4/5.
The probability the second spin lands on blue is 2/10 = 1/5.
The probability of both events is 4/5 × 1/5 = 4/25.
Grandmother bought enough cat food for her four cats to last for 12 days. On her way home she brought back two stray cats. If she gives each cat the same amount of food every day, how many days will the cat food last
Answer:
The number of days the cat food will last is 8 days.
Step-by-step explanation:
In this case, it it provided that Grandmother bought enough cat food for her four cats to last for 12 days.
Assume that each cat consumes x portions of food each day.
Then the four cats will consume, 4x portions of food each day.
Then in 12 days the amount of food consumed by the 4 cats will be:
Total amount of cat food = 12 × 4x
= 48x.
Now, it is provided that she on her way home she brought back two stray cats.
Then the six cats will consume, 6x portions of food each day.
Compute the number of days the cat food will last as follows:
[tex]\text{Number of days the cat food will last}=\frac{\text{Total amount of cat food}}{\text{Amount of food consumed each day}}[/tex]
[tex]=\frac{48x}{6x}\\\\=\frac{48}{6}\\\\=8[/tex]
Thus, the number of days the cat food will last is 8 days.
Suppose a company's revenue function is given by R(q) = - q^3 + 220q^2 and its cost function is given by C(q) = 500 + 13q, where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars of revenue and cost, respectively.
A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.)
MP(q) =
B) How many items (in hundreds) need to be sold to maximize profits? (Round your answer to two decimal places.)
Answer:
A) MP(q) = -3q² + 440q - 13
B) 146.64 units.
Step-by-step explanation:
The profit function is given by the revenue minus the cost function:
[tex]P(q) = R(q) - C(q)\\P(q) = -q^3+220q^2-500-13q[/tex]
A) The Marginal profit function is the derivate of the profit function as a function of the quantity sold:
[tex]P(q) = -q^3+220q^2-500-13q\\MP(q) = \frac{dP(q)}{dq} \\MP(q)=-3q^2+440q-13[/tex]
B) The value of "q" for which the marginal profit function is zero is the number of items (in hundreds) that maximizes profit:
[tex]MP(q)=0=-3q^2+440q-13\\q=\frac{-440\pm \sqrt{440^2-(4*(-3)*(-13))} }{-6}\\q'=146.64\\q'' = - 0.03[/tex]
Therefore, the only reasonable answer is that 146.64 hundred units must be sold in order to maximize profit.
In a college of exactly 2800 students, exactly 55 % are male. What is the number of female students? Express your answer as an integer.
There are nine saxophone players in the band. The number of saxophone players is one less than twice the number of tuba players. Find the number of tuba players.
Answer:
[tex]5[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the number of tuba players.
We are given that the number of saxophone players is one less than twice the number of tuba players.
There are 9 saxophone players.
[tex]9 = 2 x-1[/tex]
[tex]9+1=2x[/tex]
[tex]10=2x[/tex]
[tex]10 \div 2=x[/tex]
[tex]5=x[/tex]
find x.
8
2radius3
8
8radius3
(hurry plz, will give brainliest) -15pts-
Answer:
Answere is X= 8
Step-by-step explanation:
Use sine law
Sin(angle) = Opposite/ Hypotenuse
Sin (30) = 4 /X
X = 4 / sin (30)
X = 8
A circular garden has a diameter of 12 feet. About how much trim is needed to surround the garden by placing trim on the garden's circumference? 38 ft or 48 ft or 144 ft or 432 ft
Answer:
About 38 feet
Step-by-step explanation:
The formula for a circle's circumference is 2 times pi times r, which is the radius.
Since the diameter is 12, the radius is half the diameter, so the radius is 6.
2 times pi times 6 is about 37.7 feet, or 38 feet.
Hope this helped.
What’s the correct answer for this question?
Answer:
B) (1,2,3,4,5,6,7,8)
Step-by-step explanation:
The answer is B because the union of a set represents everything thing that is within the sets.
Chocolate chip cookies have a distribution that is approximately normal with a mean of 23.1 chocolate chips per cookie and a standard deviation of 2.9 chocolate chips per cookie. Find Upper P 10 and Upper P 90. How might those values be helpful to the producer of the chocolate chip cookies?
Answer:
[tex]z=-1.28<\frac{a-23.1}{2.9}[/tex]
And if we solve for a we got
[tex]a=23.1 -1.28*2.9=19.388[/tex]
And for the 90 percentile we can do this:
[tex]z=1.28<\frac{a-23.1}{2.9}[/tex]
And if we solve for a we got
[tex]a=23.1 +1.28*2.9=26.812[/tex]
The P10 would be 19.388 and the P90 26.812
Step-by-step explanation:
Let X the random variable that represent the chocolate chip cookies of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(23.1,2.9)[/tex]
Where [tex]\mu=23.1[/tex] and [tex]\sigma=2.9[/tex]
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.90[/tex] (a)
[tex]P(X<a)=0.10[/tex] (b)
We can find a z score value who that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28.
Using this value we can do this:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.10[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.10[/tex]
And we can solve for the value of interest
[tex]z=-1.28<\frac{a-23.1}{2.9}[/tex]
And if we solve for a we got
[tex]a=23.1 -1.28*2.9=19.388[/tex]
And for the 90 percentile we can do this:
[tex]z=1.28<\frac{a-23.1}{2.9}[/tex]
And if we solve for a we got
[tex]a=23.1 +1.28*2.9=26.812[/tex]
The P10 would be 19.388 and the P90 26.812
A random sample of 18 graduates of a certain secretarial school typed an average of 80.6 words per minute with a standard deviation of 7.2 words per minute. Assuming a normal distribution for the number of words typed per minute, compute the 95% prediction interval for the next observed number of words per minute typed by a graduate of the secretarial school.
Answer: ( 77.27 , 83.93)
Therefore at 95% confidence/prediction interval is
= ( 77.27 , 83.93)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 80.6 words per minute
Standard deviation r = 7.2
Number of samples n = 18
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
80.6+/-1.96(7.2/√18)
80.6+/-1.96(1.697056274847)
80.6 +/- 3.33
= ( 77.27 , 83.93)
Therefore at 95% confidence/prediction interval is
= ( 77.27 , 83.93)
which is the domain of f(x) = 4^x
will give brainlist!
Answer:
all real numbers
Step-by-step explanation:
The domain is the input values
All values for x are valid as inputs to the function
Simplify 6r · s · 4rt. this is the question
Answer=6 . S/R . 4T
This is the answer because u have to simplify so to do this u have to divide all of this by R
A linear function and its inverse are given.
y=4x-3
y=1/4x+3/4
Which tables could be used to verify that the functions are inverses of each other? Select two options.
x:1, 3, 5, 7, 9
y:1, 3, 5, 7, 9
x:-23, -15, -3, 1, 13
y:-5, -3, 0, 1, 4
x:-18, -12, 0, 3, 9
y:-24, -18, -6, -3, 3
x:-5, -3, 0, 1, 4
y:-23, -15, -3, 1, 13
x:-24, -18, -6, -3, 3
y:-18, -12, 0, 3, 9
Answer:
x: -5, -3, 0, 1, 4
y:-23, -15, -3, 1, 13 for the function.
x:-23, -15, -3, 1, 13
y: -5, -3, 0, 1, 4 for the inverse.
Step-by-step explanation:
we know that if we have the function f(x) = y, then the inverse of f(x) (let's call it g(x)) is such that:
g(y) = x.
now we have
y=4x-3
y=(1/4)x+3/4
The only table that works for our first function is:
x: -5, -3, 0, 1, 4
y:-23, -15, -3, 1, 13
You can see this by replacing the values of x and see if the value of y also coincides.
Then, using the fact that the other table must be for the inverse, we should se a table with the same values, but where the values of x and y are interchanged.
The second table is that one:
x:-23, -15, -3, 1, 13
y: -5, -3, 0, 1, 4
Answer: B and D
x:-23, -15, -3, 1, 13
y:-5, -3, 0, 1, 4
x:-5, -3, 0, 1, 4
y:-23, -15, -3, 1, 13
Step-by-step explanation:
What is 9/8 squaredto the power of 2 ?
Answer:
81/64
Step-by-step explanation:
(9/8)²=9²/8²=81/64
Solve the equation.
3(x + 1)-1=3x+2
Answer:
0=0
Step-by-step explanation:Let's solve your equation step-by-step.
3(x+1)−1=3x+2
Step 1: Simplify both sides of the equation.
3(x+1)−1=3x+2
(3)(x)+(3)(1)+−1=3x+2(Distribute)
3x+3+−1=3x+2
(3x)+(3+−1)=3x+2(Combine Like Terms)
3x+2=3x+2
3x+2=3x+2
Step 2: Subtract 3x from both sides.
3x+2−3x=3x+2−3x
2=2
Step 3: Subtract 2 from both sides.
2−2=2−2
0=0
mp
hence of other wise find the radius of a circle when A= 88/63 leave your answer as a fraction in its simplest form
Answer:
Step-by-step explanation:
A=πr^2
But A=88/63
88/63=πr^2
88/63π=r^2
√88/63π=r
The mean of the data set(9,5,y,2,x) is twice the data set(8,x,4,1,3).what is (y-x)
Answer:
[tex]y-x = 16[/tex]
Step-by-step explanation:
Given
Set 1: (9,5,y,2,x)
Set 2: (8,x,4,1,3)
Required
(y - x)
First the mean values of set 1 and set 2 has to be calculated
For set 1
[tex]Mean _1 = \frac{(9+5+y+2+x)}{5}[/tex]
Collect like terms
[tex]Mean _1 = \frac{9+5+2+y+x}{5}[/tex]
[tex]Mean _1 = \frac{16+ y+x}{5}[/tex]
For set 2
[tex]Mean _2 = \frac{(8+x+4+1+3)}{5}[/tex]
Collect like terms
[tex]Mean _2 = \frac{8+4+1+3+x}{5}[/tex]
[tex]Mean _2= \frac{16+ x}{5}[/tex]
Given that the mean of set 1 is twice the mean of set 2;
[tex]Mean_1 = 2Mean_2[/tex]
[tex]\frac{16+ y+x}{5} =2 * \frac{16+x}{5}[/tex]
Multiply both sided by 5
[tex]5 * \frac{16+ y+x}{5} = 5 * 2 * \frac{16+x}{5}[/tex]
[tex]16+ y+x = 2 * (16+x)[/tex]
Open bracket
[tex]16+ y+x = 32 + 2x[/tex]
Subtract 16 from both sides
[tex]16+ y+x- 16 = 32 + 2x - 16[/tex]
[tex]16 - 16 + y+x = 32 - 16 + 2x[/tex]
[tex]y+x = 16 + 2x[/tex]
Subtract 2x from both sides
[tex]y+x-2x = 16 + 2x-2x[/tex]
[tex]y-x = 16[/tex]
3.14 The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution function F(x) = 0, x< 0, 1 − e−8x, x ≥ 0. Find the probability of waiting less than 12 minutes between successive speeders (a) using the cumulative distribution function of X; (b) using the probability density function of X.
Answer:
(a) The probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.
(b) The probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.
Step-by-step explanation:
The cumulative distribution function of the random variable X, the waiting time, in hours, between successive speeders spotted by a radar unit is:
[tex]F(x)=\left \{ {{0;\ x<0} \atop {1-e^{-9x};\ x\geq 0}} \right.[/tex]
(a)
Compute the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function as follows:
[tex]12\ \text{minutes}=\frac{12}{60}=0.20\ \text{hours}[/tex]
The probability is:
[tex]P(X<0.20)=|F (x)|_{x=0.20}[/tex]
[tex]=(1-e^{-8x})|_{x=0.20}\\\\=1-e^{-8\times 0.20}\\\\=0.7981[/tex]
Thus, the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.
(b)
The probability density function of X is:
[tex]f_{X}(x)=\frac{d F (x)}{dx}=\left \{ {{0;\ x<0} \atop {8e^{-8x};\ x\geq 0}} \right.[/tex]
Compute the probability of waiting less than 12 minutes between successive speeders using the probability density function as follows:
[tex]P(X<0.20)=\int\limits^{0.20}_{0} {8e^{-8x}} \, dx[/tex]
[tex]=8\times [\frac{-e^{-8x}}{8}]^{0.20}_{0}\\\\=[-e^{-8x}]^{0.20}_{0}\\\\=(-e^{-8\times 0.20})-(-e^{-8\times 0})\\\\=-0.2019+1\\\\=0.7981[/tex]
Thus, the probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.
Billy's age is twice Joe's age and the sum of their ages is 45. How old is Billy?
Answer:
30 years old
Step-by-step explanation:
Joe's age can be set to x. Since Billy is twice as old as Joe, his age can be set to 2x. They add up to 45. You can set up an equation, 2x+x=45.
Simplify the equation.
3x=45, x=15
Joe is 15. Billy is 2(15)=30.
what is 12/5 as a mixed nunber
Answer:
2 2/5
Step-by-step explanation:
12/5
5 goes into 12 2 times
12 - 5*2
12-10 =2
There is 2 left over. This goes over the denominator
2 2/5
Duke takes a car in for basic service. The service agent says a few extra repairs are needed, so Duke adds the cost of those repairs mentally, rounding to the nearest 10. What is Duke's total estimate for the repairs? The costs are as follows: Wheel alignment: $82 Transmission fluid flush: $157 Cabin air filter: $58 Note: 4 or less rounds down, 5 or more rounds up. For example, 14 becomes 10, while 15 becomes 20.
Answer:
The total repair cost was around $300 .
Step-by-step explanation:
I wasn't sure when you were saying to round, so here are two options.
(For rounding at the end) :
82+157+58 = 297
Rounds to 300.
(For rounding as he's adding everything up) :
80+160+60= 300.
So either way it's 300!
Hope this helped!
Your company made $120,000 in revenue and $50,000 in costs for 2017. What was your profit?
Answer:
$70,000
Step-by-step explanation:
Profit = Revenue - Costs
x = 120,000 - 50,000
x = 70,000
Simplify the number into simplest radical form.
Answer:
4 sqrt(6)
Step-by-step explanation:
sqrt(96)
We know sqrt(ab) =sqrt(a) sqrt(b)
sqrt(16*6)
sqrt(16) sqrt(6)
4 sqrt(6)
