Answer:
bar graphs
Step-by-step explanation:
as in a bar graph, we don't do any calculations to graph on a paper,
so the data values, are taken RAW while graphing.
The height of a cylinder is 9.5 cm. The diameter is 1.5 cm longer than the height. Which is closest to the volume of the cylinder?
Answer:
853.8cm^3
Step-by-step explanation:
[tex]h = 9.5cm\\d = 1.5cm + 9.5 = 10.7\\r =d/2=10.7/2=5.35\\\\V = \pi r^2 h\\V = 3.14 \times (5.35)^2 \times 9.5\\\\V =853.8 cm^3[/tex]
solve for the inequality ᵏ⁄₄ ≥ 6
Answer:
k ≥ 24
Step-by-step explanation:
ᵏ⁄₄ ≥ 6
Multiply each side by 4
ᵏ⁄₄ *4 ≥ 6*4
k ≥ 24
Answer:
k≥24
Step-by-step explanation:
k/4≥6
Use the multiplication property of equality by multiplying both sides by 4 to get
k≥24
If this is wrong or if I did something wrong, please tell me so I can learn the proper way, I am just treating this like a normal problem
Thank you
An appliance company determines that in order to sell x dishwashers, the price per dishwasher must be p = 420 - 0.3x. It also determines that the total cost of producing x dishwashers is given by C(x) = 5000 + 0.3x2. How many dishwashers must the company produce and sell in order to maximize profit? g
The company must produce and sell 350 dishwashers in order to maximize profit.
How to determine the number of dishwashersTo determine the number of dishwashers the company must produce and sell in order to maximize profit, we need to find the value of x that corresponds to the maximum point of the profit function.
The profit (P) is given by the equation:
P(x) = Revenue - Cost
The revenue is calculated by multiplying the price per dishwasher (p) by the number of dishwashers sold (x):
Revenue = p * x
The cost is given by the function C(x):
Cost = C(x)
Therefore, the profit function can be expressed as:
P(x) = p * x - C(x)
Substituting the given expressions for p and C(x):
P(x) = (420 - 0.3x) * x - (5000 + 0.3x²)
Expanding and simplifying the equation:
P(x) = 420x - 0.3x² - 5000 - 0.3x²
Combining like terms:
P(x) = -0.6x² + 420x - 5000
To find the value of x that maximizes profit, we need to find the vertex of the quadratic function. The x-coordinate of the vertex can be determined using the formula:
x = -b / (2a)
In our case, a = -0.6 and b = 420:
x = -420 / (2 * -0.6)
x = -420 / (-1.2)
x = 350
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350 dishwashers must the company produce and sell in order to maximize profit.
Maxima means a point at which the function attains the maximum value.
Given the following information:
Price per dishwasher, p = 420 - 0.3x
Total cost of producing x dishwashers, C(x) = 5000 + 0.3x2
Profit= Total Selling price- Total Cost Price
Total Selling price of x dishwasher, S.P= xp
S.P=x(420 - 0.3x)
S.P=420x - 0.3x²
Profit= 420x - 0.3x² - ( 5000 + 0.3x²)
Profit= 420x - 0.3x² - 5000 - 0.3x²
Profit= -0.6x²+420x-5000
So, profit, f(x)=-0.6x²+420x-5000
To determine the value of x so that maximum profit is possible:
1. Calculate the first derivative of profit function and calculate the value of x by equating it to zero.
2. Select that value of x for which the profit function attains the maximum value, to check the maxima calculate 2nd derivative, if it gives a negative value for the value of x. Then, x is the point of maxima for the given function.
[tex]f(x)=-0.6x^2+420x-5000\\f\prime(x)=-1.2x+420\\f\prime(x)=0\\-1.2x+420=0[/tex]
Calculating the value of x by transposing,
x=420/1.2
x=350
To check maxima, calculating second derivative.
[tex]f\prime(x)=-1.2x+420=0\\f\prime\prime(x)=-1.2[/tex]
2nd derivative is negative, it means that x=350 is the point of maxima.
Thus, a company must produce and sell 350 dishwashers in order to maximize profit.
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What is the range of the function f(x)=3/4|x|-3
Range is [tex]y\in[-3,+\infty)[/tex].
Hope this helps.
01:
Which expression can be used to model the phrase the sum of three and a number?
Answer:
3+x
Step-by-step explanation:
sum= addition
a number= a number
Answer:
3+x
eplanation
The random variable x is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate office. Its probability distribution is as follows:
Houses Sold (x) Probability P(x)
0 0.24
1 0.01
2 0.12
3 0.16
4 0.01
5 0.14
6 0.11
7 0.21
Find the mean of the given probability distribution.
A. μ = 3.35
B. μ = 3.50
C. μ = 3.60
D. μ = 3.40
Answer:
C. μ = 3.60
Step-by-step explanation:
Two tables have been attached to this response.
One of the tables contains the given data and distribution with two columns: Houses Sold and Probability
The other table contains the analysis of the data with additional columns: Frequency and Fx
=> The Frequency(F) column is derived from the product of the probability of each item in the Houses sold column and the total number of houses sold (which is 28). For example,
When the number of houses sold = 0
F = P(0) x Total number of houses sold
F = 0.24 x 28 = 6.72
When the number of houses sold = 1
F = P(1) x Total number of houses sold
F = 0.01 x 28 = 0.28
=> The Fx column is found by multiplying the Frequency column by the Houses Sold column. For example,
When the number of houses sold = 0
Fx = F * x
F = 6.72 x 0 = 0
Now to get the mean, μ we use the relation;
μ = ∑Fx / ∑F
Where;
∑Fx = summation of the items in the Fx column = 100.8
∑F = summation of the items in the Frequency column = 28
μ = 100.8 / 28
μ = 3.60
Therefore, the mean of the given probability distribution is 3.60
The mean of the discrete probability distribution is given by:
C. μ = 3.60
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
In this problem, the table x - P(x) gives each outcome and their respective probabilities, hence, the mean is:
[tex]E(X) = 0(0.24) + 1(0.01) + 2(0.12) + 3(0.16) + 4(0.01) + 5(0.14) + 6(0.11) + 7(0.21) = 3.6[/tex]
Hence option C is correct.
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What is the measure of o?
Answer:
2π radians
Step-by-step explanation:
express 11011 in base two
Answer:
27
Step-by-step explanation:
Hello,
11011 in base 2 is
1 * 16 + 1 * 8 + 0 * 4 + 1 * 2 + 1 in base 10
which is 16 +8+2+1=27
Do not hesitate if you have any question
ANZ Corporation manufactures a product available in two models: ABC, and PQR. Despite the growing popularity of the PQR model, company profits have been declining steadily, and management is beginning to think there might be a problem with their costing system. Material and Labour costs are given below:
ABC PQR
Sales demand 30000 15000
Direct material cost/unit $45 $60
Direct labour cost/unit $30 $40
Production overheads are $600,000 each month.
These are absorbed on a sales demand basis.
Calculate the full production costs for ABC and PQR, using traditional costing method
Answer:
The full production costs are:
ABC = $22,900,000
PQR = $1,700,000
Step-by-step explanation:
Traditional costing method is a costing method that allocates or applies overhead based on a particular metric determined by a company. It therefore add both direct cost of production and production overheads absorbed to obtain the full cost of production.
Since production overheads in this question is absorbed on demand sales basis, the full production costs for ABC and PQR can be computed as follows:
ANZ Corporation
Computation of Full Production Costs
Particulars ABC PQR
Sales demand 30,000 15,000
Cost $ $
Direct cost:
Direct materials cost (w.1) 1,350,000 900,000
Direct labor cost (w.2) 900,000 600,000
Total direct cost 22,500,000 1,500,000
Indirect cost:
Production overhead (w.3) 400,000 200,000
Full production cost 22,900,000 1,700,000
Workings:
w.1: Computation of direct material cost
Direct material cost = Direct material cost per unit * Sales demand
Therefore;
ABC Direct material cost = $45 * 30,000 = $1,350,000
PQR Direct material cost = $60 * 15,000 = $900,000
w.2: Computation of direct labor cost
Direct labor cost = Direct labor cost per unit * Sales demand
Therefore;
ABC Direct material cost = $30 * 30,000 = $900,000
PQR Direct material cost = $40 * 15,000 = $600,000
w.3: Allocation of production overhead
Production overheads allocated to a model = Production overheads * (Model's Sales Demand / Total Sales demand)
Total Sales demand = 30,000 + 15,000 = 45,000
Therefore, we have:
Production overhead allocated to ABC = $600,000 * (30,000 / 45,000) = $400,000
Production overhead allocated to PQR = $600,000 * (15,000 / 45,000) = $200,000
In a survey, 29 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $41 and standard deviation of $8. Construct a confidence interval at a 99% confidence level.
Give your answers to one decimal place.
Answer:
The 99% confidence interval is
[tex]37.167< \= x < 44.833[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 29[/tex]
The sample mean is [tex]\= x =[/tex]$41
The sample standard deviation is [tex]\sigma =[/tex]$8
The level of confidence is [tex]C =[/tex]99%
Given that the confidence level id 99% the level of confidence is evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1[/tex]%
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table which is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
The reason we are obtaining values for is because is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while is the area under the normal distribution curve for just one tail and we need the value for one tail in order to calculate the confidence interval
Next we evaluate the margin of error which is mathematically represented as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 2.58 * \frac{8 }{\sqrt{29} }[/tex]
[tex]MOE = 3.8328[/tex]
The 99% confidence level is constructed as follows
[tex]\= x - MOE < \= x < \= x + MOE[/tex]
substituting values
[tex]41 - 3.8328 < \= x < 41 + 3.8328[/tex]
[tex]37.167< \= x < 44.833[/tex]
Find the perimeter of an equilateral triangle where area is 72cm.
Answer:
38.68 cm
Step-by-step explanation:
Perimeter of an equilateral triangle : P = 3a
Area of an equilateral triangle : A = [tex]\frac{\sqrt{3} }{4}a^2[/tex]
a = side length
The area is given, solve for a.
[tex]72= \frac{\sqrt{3} }{4}a^2[/tex]
[tex]a = 12.894839[/tex]
The side length is 12.894839 centimeters.
Find the perimeter.
P = 3a
P = 3(12.894839)
P = 38.684517 ≈ 38.68
The perimeter is 38.68 centimeters.
Shawn has 25 coins, all nickels and dimes. The total value is $2.00. How many of each coin does he have ?
Answer:
[tex]\boxed{15 \ dime \ and \ 10 \ nickel \ coins}[/tex]
Step-by-step explanation:
1 dime = 10 cents
1 nickel = 5 cents
So,
If there are 15 dimes
=> 15 dimes = 15*10 cents
=> 15 dimes = 150 cents
=> 15 dimes = $1.5
Rest is $0.5
So, for $0.5 we have 10 nickels coins
=> 10 nickels = 10*5
=> 10 nickels = 50 cents
=> 10 nickel coins = $0.5
Together it makes $2.00
The line passing through points
(4,0) and (-2, 1) has a slope of?
A. -6
B. -1/6
C. 1/2
D. 2
E. 1/6
Answer:
b. -1/6
Step-by-step explanation:
slope = (difference in y)/(difference in x)
slope = (1 - 0)/(-2 - 4) = 1/(-6) = -1/6
Answer:
m = -1/6 = B
Step-by-step explanation:
[tex]m = \frac{y_2-y_1}{x_2-x_1} \\ x_1=4\\ y_1=0\\ x_2=-2\\y_2=1.\\m = \frac{1-0}{-2-4} \\m = \frac{1}{-6}[/tex]
What is the focus of the parabola? y=−1/4x2−x+3
Answer: Focus = (-2, 3)
Step-by-step explanation:
[tex]y=-\dfrac{1}{4}x^2-x+3\\\\\rightarrow a=-\dfrac{1}{4},\ b=-1[/tex]
First let's find the vertex. We do that by finding the Axis-Of-Symmetry:
[tex]AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(-1)}{2(\frac{-1}{4})}=\dfrac{1}{-\frac{1}{2}}=-2[/tex]
Then finding the maximum by inputting x = -2 into the given equation:
[tex]y=-\dfrac{1}{4}(-2)^2-(-2)+3\\\\y=-1+2+3\\\\y=4[/tex]
The vertex is: (-2, 4)
Now let's find p, which is the distance from the vertex to the focus:
[tex]a=\dfrac{1}{4p}\\\\\\-\dfrac{1}{4}=\dfrac{1}{4p}\\\\\\p=-1[/tex]
The vertex is (-2, 4) and p = -1
The focus is (-2, 4 + p) = (-2, 4 - 1) = (-2, 3)
What expression be used to add 3/4 + 1/6
Answer:
11 / 12 or 0.9167
Step-by-step explanation:
Given:
3/4 + 1/6
Find:
Value with expression
Computation:
"3/4 added to number 1/6"
3/4 + 1/6
By taking LCM
[9 + 2] / 12
11 / 12 or 0.9167
help i will give you brailenst
Plz help this is an evil question
Answer:
18.9 units of fencing
Step-by-step explanation:
First find the perimeter
P = 2(l+w)
P = 2( 2.5+1.28)
P = 2( 3.78)
P =7.56m
We need 2.5 units of fencing for each meter
Multiply by 2.5
7.56*2.5
18.9 units of fencing
Answer:
Julio needs to purchase 18.9 units of fencing.
Step-by-step explanation:
I meter of the perimeter accounts for 2.5 units of fencing. Respectively 2 meters account for 2 times as much, and 3 meters account for 3 times as much of 2.5 units. Therefore, if we determine the perimeter of this rectangular garden, then we can determine the units of fencing by multiplying by 2.5.
As you can see this is a 2.5 by 1.28 garden. The perimeter would be two times the supposed length, added to two times the width.
2.5 x 2 + 1.28 x 2 = 5 + 2.56 = 7.56 - this is the perimeter. The units of fencing should thus be 7.56 x 2.5 = 18.9 units, or option d.
Please help!! Over several years, Stephon gathered data about his age and the time it took him to run two laps on the school track. The scatter plot shows the data he gathered and the line of best fit. The equation of the line of best fit is y = -2.1x + 565.6. Based on the line of best fit, approximately how long will it take Stephon to run two laps on the track when he is 192 months old?
Answer:
Time taken by Stephen = 162 seconds
Step-by-step explanation:
Stephan gathered data which fits in the line of best fit,
y = -2.1x + 565.6
Where x represents the age (in months)
And y represents the time (in seconds) taken by Stephen to run two laps on the track.
Time taken to run 2 laps at the age of 192 months,
By substituting x = 192 months,
y = -2.1(192) + 565.6
= -403.2 + 565.6
= 162.4 seconds
≈ 162 seconds
Therefore, time taken by Stephen to cover 2 laps was 162 seconds when he was 192 months old.
A casino offers a game wherein a player can roll one six sided die. If the player rolls a 1or 2, they
win. If the player rolls a 3, 4, 5, or 6, they lose. If a player bets $2.00 and wins, they will be paid out
an additional $3.00. If they lose, they lose their initial $2.00. Find the expected value of the $2.00
bet.
Enter your answer rounded to the nearest cent and don't forget, expected values can be negative!
Answer:
Expected Value of $2:
Expected Value of $2:
Win, 0.3333 x $3 = $1
Plus
Loss, 0.6667 x -$2 = -$1.33
Expected value = ($0.33)
Step-by-step explanation:
Probability of a win = 2/6 = 0.3333
Probability of a loss = 4/6 = 0.6667
Expected Value of $2:
Win, 0.3333 x $3 = $1
Plus
Loss, 0.6667 x -$2 = -$1.33
Expected value = ($0.33)
The casino game player's expected value is computed by multiplying each of the possible outcomes by the likelihood (probability) of each outcome and then adding up the values. The sum of the values is the expected value, which amounts to a loss of $0.33.
John needs to produce a scale diagram of a bedroom using a scale of 1:40. The length of the room is 3.4 metres. What is the length on the diagram? _____ cm
Answer:
8.5cm
Step-by-step explanation:
convert 3.4metres to cm that is by multiplying by 100
3.4×100=340cm
1rep 40
?rep 340
that is 340/40
=8.5cm
Answer:
8.5 cm
Step-by-step explanation:
Scale = 1:40
Length of the room = 3.4 meters
3.4 meters =3.4 X 100 =340 cm
Since 1 unit on the diagram represents 40 units
The length of the diagram
[tex]=\dfrac{340}{40}\\\\=8.5$ cm[/tex]
The length of the room on the diagram is 8.5 cm.
6th grade math, help me please.
Answer:
a) [tex]\frac{2}{3} \,\frac{lb}{bread}[/tex]
b) [tex]1\frac{1}{4} \,\frac{in}{domino}[/tex]
Step-by-step explanation:
Part a:
every 4 lbs of flour, she makes 6 loaves of bread. this as a rate in simplest fraction form is:
[tex]\frac{4}{6} \,\frac{lb}{bread} = \frac{2}{3} \,\frac{lb}{bread}[/tex]
Part b:
every 10 inches , 8 dominoes can be placed. then the rate can be written as:
[tex]\frac{10}{8} \,\frac{in}{domino} = \frac{5}{4} \,\frac{in}{domino} =1\frac{1}{4} \,\frac{in}{domino}[/tex]
Tabitha wants to hang a painting in a gallery. The painting and frame must have an area of 58 square feet. The painting is 7 feet wide by 8 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? (5 points)
Answer:
4x² + 30x - 2 = 0
Step-by-step explanation:
Given:
Area = 58 square feet
Width = 7 feet
Length = 8 feet
Since the area is 58, writing the equation, we have:
(8 + 2x)(7 + 2x) = 58
Now expand the equation:
56 + 16x + 14x + 4x² = 58
56 + 30x + 4x² = 58
Collect like terms:
30x + 4x² + 56 - 58 = 0
30x + 4x² - 2 = 0
Rearrange the equation to a proper quadratic equation:
4x² + 30x - 2 = 0
The quadratic equation that can be used to determine the thickness of the frame, x is 4x² + 30x - 2 = 0
f(x)=2x+1 and g(x)=3x2+4, find (f∘g)(−2) and (g∘f)(−2).
Answer:
Step-by-step explanation:
Fog=2(g)+1
2(3x+2+4)+1
2{3x+6)+1
6x+12+1
=6x+13
Fog(-2)=6(-2)+13
-12+13
=1
Gof=3(f)+2+4
=3(2x+1)+6
6x+3+6
=6x+9
Gof(-2)=6(-2)+9
-12+9
=-3
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 8 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 22 feet high
Answer:
(11π/9 )ft/s
Step by step Explanation
Let us denote the height as h ft
But we were told that The diameter of the base of the cone is approximately three times the altitude, then
Let us denote the diameter = 3h ft, and the radius is 3h/2
The volume of the cone is
V = (1/3)π r^2 h
Then if we substitute the values we have
= (1/3)π (9h^2/4)(h) = (3/4)π h^3
dV/dt = (9/4)π h^2 dh/dt
We were given as 22feet and rate of 8 cubic feet per minute
h = 22
dV/dt = 8
8= (9/4)π (22) dh/dt
= 11π/9ft/s
Therefore, the rate is the height of the pile changing when the pile is 22 feet is
11π/9ft/s
Find the sum of the cubes of first three composite numbers.
Answer:
792
Step-by-step explanation:
The first three composite numbers are 4, 6 ,8
so 4^3+6^3+8^3=64+216+512=792
What scenario depicts two independent events
Step-by-step explanation:
A t
eacher is calling on students to present their reports. He calls on Mario first and then chooses the next presenter from the remaining students. The girls’ basketball team is playing against the boys’ basketball team. The coach chooses a captain for the girls’ team and then chooses a captain for the boys’ team. Yasmin is picking flowers from a garden to create a bouquet. She picks a flower, keeps it for the bouquet, and then she picks another. Felipe is making a dentist appointment. First he chooses the day for his appointment, and then he chooses the time from the available openings.
Answer:
A.The school play opens tonight and it is raining.
B.Neva is hungry and she buys a snack from the concession stand.
C. Ari chooses a partner for a group project and then Ezekial chooses a partner from the remaining classmates.
D.Luka paints during school and he stains his shirt.
The owner of a music store gathered data from several schools about the number of students in their concert and marching bands. The scatter plot shows the data she gathered and the line of best fit. The equation of the line of best fit is y = 0.677x + 1.77. Based on the line of best fit, approximately how many students are predicted to be in the marching band at a school with 35 students in the concert band?
Answer:
25 students
Step-by-step explanation:
Given the equation of the best line of fit, [tex] y = 0.677x + 1.77 [/tex] , the number of students predicted to be in the matching band, if we have 35 students in the concert band, can be approximated by plugging in 35 as "x" in the equation of the best line of fit, and solve for "y". y would give us the predicted number of students to expect in the marching band.
[tex] y = 0.677(35) + 1.77 [/tex]
[tex] y = 23.695 + 1.77 [/tex]
[tex] y = 25.465 [/tex]
The approximated number of to be in the marching band, with 35 students in the concert band is roughly 25 students.
Answer:25 students
Step-by-step explanation:
Find the slope of the line passing through the points (-5, 3) and (7,9).
Answer:
[tex]\huge\boxed{slope=\dfrac{1}{2}=0.5}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points
[tex](-5;\ 3)\to x_1=-5;\ y_1=3\\(7;\ 9)\to x_2=7;\ y_2=9[/tex]
Substitute:
[tex]m=\dfrac{9-3}{7-(-5)}=\dfrac{6}{7+5}=\dfrac{6}{12}=\dfrac{6:6}{12:6}=\dfrac{1}{2}[/tex]
Answer:
1/2
Step-by-step explanation:
We can use the slope formula since we have 2 points
m = ( y2-y1)/(x2-x1)
= (9-3)/( 7 - -5)
= (9-3) /( 7+5)
= 6/ 12
= 1/2
Enter the correct answer in the box by replacing the values of a and b. f(x) = a(b)^x
Answer:
f(x)= 8(0.5)^x
Step-by-step explanation:
As you can see on the graph there are two specific points labeled:
(0,8) and (1,4)
The 8 would be the initial value and starting point of the "design"
A is always the initial value so replace that.
Then proceed to divide 4 by 8 to figure out the percentage change its 0.5
leave x as it is
Identify any outlier(s) in the data. {52, 61, 42, 46, 50, 51, 49, 44, 40, 66, 53, 67, 45, 64, 60, 69}
An outlier in statistics is a data point that deviates considerably from other observations. The given data set has no outlier.
What is an outlier?An outlier in statistics is a data point that deviates considerably from other observations. An outlier can be caused by measurement variability or by experimental mistake; the latter is sometimes eliminated from the data set.
To find the outlier for the given data set follow the given steps.
Step one: The first step is to find the quartiles for the data set.
For this data set, the quartiles are:
Q1 = 45.5
Q3 = 62.5
Step Two: Find the Interquartile Range
The interquartile range is the difference between the first and third quartiles.
IQR = Q3 - Q1
IQR = 45.5 - 62.5
IQR = 17
Step Three:
The next step is to set up a fence beyond the first and third quartiles using the interquartile range.
Lower Fence = Q1 - (1.5 × IQR)
Lower Fence = 45.5 - (1.5 × 17)
Lower Fence = 20
Upper Fence = Q3 + (1.5 × IQR)
Upper Fence = 62.5 + (1.5 × 17)
Upper Fence = 88
Step Four: Find the Outliers
Any numbers in the data that are above or below the fences are outliers.
Since there are no numbers outside the two fences. Hence, it can be concluded that the given data set does not have, any outlier.
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