Answer: rental is $415, and the standard deviation is $5.
Step-by-step explanation:
If about 99.7 percent of the monthly rentals fall between 400 and 430, it implies that this range encompasses three standard deviations from the mean.
To calculate the mean, we can find the midpoint of the given range:
Mean = (400 + 430) / 2 = 415
Since the range of three standard deviations covers about 99.7 percent of the data in a normal distribution, we can use this information to estimate the standard deviation (σ).
Standard deviation (σ) = (430 - 415) / 3 = 15 / 3 = 5
Therefore, based on the given information, the mean monthly rental is $415, and the standard deviation is $5.
4+(1/5)[-10*(25-13-3)}÷(-5)]
Answer:
7.6
Step by step explanation
The demand for good X has been estimated by Qxd = 6 − 2Px + 5Py. Suppose that good X sells at $3 per unit and good Y sells for $2 per unit. Calculate the own price elasticity.
The own price elasticity of good X is -0.60, so we can conclude that good X is price inelastic.
What is the price elasticity?The own price elasticity of good X is calculated using the formula:
Elasticity = (% Change in Quantity Demanded) / (% Change in Price)Given the demand function for good X: Qxd = 6 - 2Px + 5Py, we can calculate the initial quantity demanded at a price of $3 per unit:
Qxd1 = 6 - 2(3) + 5(2)
= 6 - 6 + 10
= 10
The new quantity demanded when the price changes to $2.90 per unit:
[tex]Qxd_2[/tex] = 6 - 2(2.90) + 5(2)
[tex]Qxd_2[/tex] = 6 - 5.80 + 10
[tex]Qxd_2[/tex] = 10.20
Now, we can calculate the percentage change in quantity demanded:
% Change in Quantity Demanded = (Qxd2 - Qxd1) / Qxd1 * 100
% Change in Quantity Demanded = (10.20 - 10) / 10 * 100
% Change in Quantity Demanded = 0.20 / 10 * 100
% Change in Quantity Demanded = 2%
Next, we calculate the percentage change in price:
% Change in Price = (New Price - Old Price) / Old Price * 100
% Change in Price = (2.90 - 3) / 3 * 100
% Change in Price = -0.10 / 3 * 100
% Change in Price = -3.33%
The own price elasticity will be:
Elasticity = (% Change in Quantity Demanded) / (% Change in Price)
Elasticity = 2% / -3.33%
Elasticity ≈ -0.60
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Draw a box plot for each set of data. {65,92,74,61,55,35,88,99,97,100,96} Cost of MP3 Players ($)
A construction of the box-and-whisker plot representing the data set is shown below.
What is a box-and-whisker plot?In Mathematics and Statistics, a box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the data (information) provided above, the five-number summary for the given data set include the following:
Minimum (Min) = 35.First quartile (Q₁) = 61.Median (Med) = 88.Third quartile (Q₃) = 97.Maximum (Max) = 100.In conclusion, we can logically deduce that the maximum number is 100 while the minimum number is 35, and the median is equal to 88.
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highest common factor of a² + ab and ab + b²
[tex]a^2+ab=a(a+b)\\ab+b^2=b(a+b)[/tex]
Therefore
[tex]\text{hcf}(a^2+ab,ab+b^2)=a+b[/tex]
A normal distribution has a mean of 137 and a standard deviation of 6. Find the z-score for a data value of 155.
Round to two decimal places
Answer:
3
Step-by-step explanation:
To find the z-score for a data value of 155 in a normal distribution with a mean of 137 and a standard deviation of 6, you can use the formula:
z = (x - μ) / σ
where:
x is the data value,
μ is the mean, and
σ is the standard deviation.
Plugging in the values, we have:
z = (155 - 137) / 6
Calculating this expression:
z = 18 / 6 = 3
The Tenorio Dairy makes cheese to supply to stores in its area. The dairy can make 250 pounds of cheese per day, and the demand at area stores is 180 pounds per day. Each time the dairy makes cheese, it costs $125 to set up the production process. The annual cost of carrying a pound cheese in a refrigerated storage area is $12. Determine the optimal size and the total annual inventory cost.
Answer:
The optimal size of each production run is 180 pounds, and the total annual inventory cost is $832,825.
Step-by-step explanation:
To determine the optimal size and total annual inventory cost, we need to consider the production capacity, demand, setup costs, and carrying costs.
Given:
Production capacity per day = 250 pounds
Demand per day = 180 pounds
Setup cost = $125
Carrying cost per pound per year = $12
First, let's calculate the optimal production size. We want to produce enough cheese to meet the demand without exceeding the production capacity.
Optimal production size per day = Minimum(Production capacity, Demand)
Optimal production size per day = Minimum(250 pounds, 180 pounds) = 180 pounds
Next, let's calculate the total annual inventory cost. This cost includes both the setup cost and the carrying cost.
Total annual inventory cost = (Setup cost * Number of setups per year) + (Carrying cost per pound * Optimal production size * Number of days in a year)
Number of setups per year = Number of production runs per year
Number of production runs per year = Total days in a year / Days per production run
Assuming a year has 365 days and each production run takes one day:
Number of production runs per year = 365 days / 1 day = 365 runs
Total annual inventory cost = ($125 * 365) + ($12 * 180 pounds * 365)
Total annual inventory cost = $45,625 + $787,200
Total annual inventory cost = $832,825
Solve This Mathematical Term
The reason of discontinuity of the given function is described below.
Since we know that,
A continuous function, as the name implies, is one whose graph is continuous with no breaks or jumps. In other words, if we can draw the curve (graph) of a function without ever raising a pencil, we may claim that the function is continuous. The study of a function's continuity is critical in calculus because a function cannot be differentiable unless it is continuous.
A function is considered continuous if its graph is an uninterrupted curve with no holes, gaps, or breaks.
Now by mathematical definition of continuity
Left hand limit of a function at any point = right hand limit of function at that point = value of function at that point
Now from the graph we can see that,
At point point 3
The left hand limit and right hand limit are not equal and also the curve is discontinuous.
Hence, the given function is discontinuous function.
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4. A machine depreciates by 40% in the first year, by 25% in the second year and by 10% per annum for the next three years. Each percentage being calculated on the diminishing value, what is the average percentage of depreciation for the entire period?
simplify [tex]2x^{2} +10x\ x^{2}+2x-15[/tex]
Its a fraction
Answer: [tex]=\frac{2x}{x-3}[/tex]
Step-by-step explanation:
[tex]\frac{2x^{2} +10x}{x^{2} + 2x-15}[/tex] >Take out GCF(greatest common factor) on top
>factor the bottom, find 2 numbers that mulitply to
"c" term, -15 and adds to the "b" term, +2
>+5 and -3 mulitpy to -15 and add to +2
> put +5 and -3 into factored form on bottom
[tex]=\frac{2x(x+5)}{(x-3)(x+5)}[/tex] >reduce the x+5 on top and bottom
[tex]=\frac{2x}{x-3}[/tex] >This is simplified
Given the circle below with secants TUV and XWV. If UV = 26, WV = 27 and
TU is 3 more than XW, find the length of TU. Round to the nearest tenth if
necessary.
The length of segment TU for the intersecting chords is determined as 28.
What is the length of TU?The length of segment TU is calculated by applying intersecting chord theorem for two chords in a circle as shown below.
From the given diagram we will have the following equation;
UV (UV + TU) = WV (WV + XW)
We know that TU is 3 more than XW;
TU = XW + 3
So our new equation becomes;
26( ( 26 + XW + 3) = 27( 27 + XW)
26(29 + XW) = 27 (27 + XW)
Simplify further as follows;
754 + 26XW = 729 + 27XW
754 - 729 = XW
25 = XW
The length of segment TU is calculated as;
TU = 3 + 25
TU = 28
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Snacknow, a food service firm, is calculating its monthly productivity report. From the following raw data calculate the labor, Multifactor, and Energy productivity.
Labor rate $10
Units produced 10,000
Labor hours 1,000
Cost of materials $2000
Cost of energy $500
The calculated productivities are:
Labor Productivity: 10 units per labor hour.
Multifactor Productivity: 0.8 units per dollar.
Energy Productivity: 20 units per dollar.
Answers to the aforementioned questionsTo calculate the labor productivity, divide the units produced by the labor hours:
Labor Productivity = Units Produced / Labor Hours
Labor Productivity = 10,000 / 1,000 = 10 units per labor hour.
To calculate the multifactor productivity, divide the units produced by the sum of labor, material, and energy costs:
Multifactor Productivity = Units Produced / (Labor Cost + Material Cost + Energy Cost)
In this case, the labor cost is $10 per labor hour, so the labor cost is 1,000 labor hours * $10 = $10,000.
The material cost is $2,000, and the energy cost is $500.
Multifactor Productivity = 10,000 / ($10,000 + $2,000 + $500)
Multifactor Productivity = 10,000 / $12,500 = 0.8 units per dollar.
Finally, to calculate the energy productivity, divide the units produced by the energy cost:
Energy Productivity = Units Produced / Energy Cost
In this case, the units produced are 10,000, and the energy cost is $500.
Energy Productivity = 10,000 / $500 = 20 units per dollar.
Therefore, the calculated productivities are:
Labor Productivity: 10 units per labor hour.
Multifactor Productivity: 0.8 units per dollar.
Energy Productivity: 20 units per dollar.
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Help please, I need to get through geometry recovery class
To prove ∠AOW = 45°
Given,
∠WOZ = 90°
∠ZOB = 45°
Now,
∠XOA +∠AOW = 90°............(1)
∠XOA = ∠ZOB ( Vertically opposite angle )
∠XOA = 45°
Substitute in (1),
45° + 45° = 90°
Now,
∠WOX = ∠XOA +∠WOA
So,
∠WOA + ∠WOZ + ∠ZOB = 180°( Linear pair )
∠WOA + 90° + 45° = 180°
∠WOA = 45°
Hence proved.
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convert an effective rate of 14,5% per annum, to a nominal rate per annum compounded half yearly
The nominal rate per annum compounded half-yearly, equivalent to an effective rate of 14.5% per annum, is approximately 14.900625%.
To convert an effective rate to a nominal rate compounded half-yearly, we can use the formula:
Nominal rate [tex]= (1 + r/m)^m - 1[/tex]
Where:
r = effective rate
m = number of compounding periods per year
In this case, the effective rate is 14.5% per annum, and we want to convert it to a nominal rate compounded half-yearly.
Since compounding is done semi-annually, m would be 2.
Plugging in the values:
Nominal rate [tex]= (1 + 0.145/2)^2 - 1[/tex]
Simplifying the expression inside the parentheses:
Nominal rate [tex]= (1 + 0.0725)^2 - 1[/tex]
Calculating the exponent:
Nominal rate [tex]= (1.0725)^2-1[/tex]
Performing the calculations:
Nominal rate = 1.14900625 - 1
Nominal rate = 0.14900625
Converting the nominal rate to a percentage:
Nominal rate = 14.900625%
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PLEASE HELP ASAP
ANSWE
Answer:
664 Square yards
Step-by-step explanation:
Surface area= 2lw+2lh+2hw
=2(17×6)+2(17×10)+2(10×6)
=2(102)+2(340)+2(120)
=204+340+120
=664 Square yards
Myron records the number of chirps per minute (x) that crickets make at different temperatures (y) in degrees Fahrenheit.
He determines that the association is linear and that the line of best fit is
y = =+50.
What is the interpretation of the slope and y-intercept of this equation?
A. The slope predicts a temperature increase of about 50° for every
increase of 1 chirp per minute. The y-intercept shows that when
the crickets are not chirping (x=0), the temperature is 0.
B. The slope predicts a temperature increase of about 6° for every
increase of 50 chirps per minute. The y-intercept shows that when
the crickets are not chirping (x=0), the temperature is
OC. The slope predicts a temperature increase of about for every
increase of 1 chirp per minute. The y-intercept shows that when
the crickets are not chirping (x=0), the temperature is 50°.
OD. The chirping increases as the temperature goes down.
The correct interpretation of the slope and y-intercept of the equation y = mx + b in this context is:
A. The slope predicts a temperature increase of about 50° for every increase of 1 chirp per minute. The y-intercept shows that when the crickets are not chirping (x=0), the temperature is 0.
In other words, according to the given equation, for each additional chirp per minute, the temperature is expected to increase by approximately 50 degrees Fahrenheit. Additionally, when there are no chirps (x=0), the equation suggests that the temperature is 0 degrees Fahrenheit.
~~~Harsha~~~
Answer:
C
Step-by-step explanation:
I am pretty certain the math is incorrect on the other posted answer
The slope is rise/run means every degree produces 6 chirps more ....or conversely , 1/6 degree produces one more chirp.
when the temperature is 50 F there are ZERO chirps
Directions: Below are hypotheses stated in different ways. Answer the following questions about each item.
a) In what form is the hypothesis stated?
b) Does it use a directional or non-directional test?
c) What level of measurement is each of the variables?
d) Convert the non-directional into directional.
1. The performance of the Staff Nurses is affected by their level of anxiety.
A. The hypothesis is stated in a correlational form.
B. It does not specify whether it uses a directional or non-directional test.
C. The level of measurement for these variables is not specified.
D. The higher the level of anxiety among Staff Nurses, the lower their performance.
What are the responses to other questions?a. The hypothesis "The performance of the Staff Nurses is affected by their level of anxiety." is stated in a correlational form.
b) The given hypothesis does not specify whether it uses a directional or non-directional test.
c) The variables in this hypothesis are "performance of the Staff Nurses" and "level of anxiety." The level of measurement for these variables is not specified.
d) To convert the non-directional hypothesis into a directional one, we would need to specify the direction of the relationship between the variables. For example: "The higher the level of anxiety among Staff Nurses, the lower their performance."
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A box with square base and a height of 8cm has a volume of 1352cm. Find the length of a side of the base
Answer:
The length of a side of the base of the box is 13 cm.
Step-by-step explanation:
To find the length of a side of the base of the box, we need to use the formula for the volume of a box.
The volume of a box is given by the formula:
V = l^2 * h
Where:
V is the volume,
l is the length of a side of the base, and
h is the height of the box.
Substituting the given values:
V = 1352 cm^3
h = 8 cm
1352 = l^2 * 8
Dividing both sides by 8:
l^2 = 169
Taking the square root of both sides:
l = √169
Calculating the length of a side of the base:
l = 13 cm
Therefore, the length of a side of the base of the box is 13 cm.
find the theoretical probability.
[tex]|\Omega|=8\\|\text{odd}|=4\\\\P(\text{odd})=\dfrac{4}{8}=\dfrac{1}{2}[/tex]
Answer:
4/8
or, 1/2
Step-by-step explanation:
odd numbers (O) = (1,3,5,7) = 4
total numbers (T) = 8
P(odd) = n(O)/n(T)
= 4/8
Original price: $82
Discount: 10%
Sale price: ?
Answer:
$81.18
Step-by-step explanation:
Sale Price = Original Price - (Original Price * Discount Percentage)
Given:
Original Price = $82
Discount Percentage = 10%
Let's calculate the sale price:
Sale Price = $82 - ($82 * 10%)
Sale Price = $82 - ($82 * 0.1)
To simplify the calculation, we can convert 10% to its decimal form by dividing by 100:
Sale Price = $82 - ($82 * 0.1)
Sale Price = $82 - ($82 * 0.01)
Sale Price = $82 - $0.82
Using a calculator, we can find the value:
Sale Price = $81.18
Therefore, the sale price after a 10% discount would be $81.18.
Answer: $73.80 is sale price
Step-by-step explanation:
Original: $82
10% of 82
=.1(82)
=8.2 >this is your discount
Subtract
82-8.2
$73.80 is sale price
challenging was 0.92, with a margin of error of 0.07.
Construct a confidence interval for the proportion of math majors that stated the curriculum was challenging.
The confidence interval using a margin of error of 0.07 is (0.85,0.99)
Confidence IntervalSample proportion = 0.92
Margin of error = 0.07
Lower bound of the confidence interval = Sample proportion - Margin of error
Lower bound = 0.92 - 0.07 = 0.85
Upper bound of the confidence interval = Sample proportion + Margin of error
Upper bound = 0.92 + 0.07 = 0.99
Confidence interval = [Lower bound, Upper bound]
Confidence interval = [0.85, 0.99]
Therefore, the confidence interval for the proportion of math majors who found the curriculum challenging is approximately 0.85 to 0.99.
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Find the area of a circle with radius,
r
= 42cm.
Give your answer rounded to 3 SF.
Answer:
5541.77 cm^2
Step-by-step explanation:
Give a rational Number between 4/7 and 6/11
Hello!
4/7 = 44/77
6/11 = 42/77
42/77 < 43/77 < 44/77
the rationnal number between 4/7 and 6/11 is 43/77
find the general term of the arithmetic sequence if a8=8, a20=44
Answer:
[tex]a_n=3n-16[/tex]
Step-by-step explanation:
[tex]a_n=a_1+(n-1)d\\\\a_8=a_1+(8-1)d\rightarrow 8=a_1+7d\\a_{20}=a_1+(20-1)d\rightarrow 44=a_1+19d[/tex]
[tex]-36=-12d\\3=d[/tex]
[tex]8=a_1+7(3)\\8=a_1+21\\-13=a_1[/tex]
[tex]a_n=-13+(n-1)(3)\\a_n=-13+3n-3\\a_n=3n-16[/tex]
help i have no clue what this is
The value of angle x is determined as 40 degrees.
The value of angle y is determined as 180 degrees.
What is the value of the missing angles?
The value of the missing angles is calculated by applying intersecting chord theorem which states that the angle at tangent is half of the arc angle of the two intersecting chords.
The value of angle x is calculated as follows;
50 = ¹/₂ (140 - x ) (exterior angle of intersecting secants)
2(50) = 140 - x
100 = 140 - x
x = 140 - 100
x = 40
The value of angle y is calculated as follows;
The value of angle y is equal to the value of the remaining arc.
y = 360 - (40 + 140 ) ( sum of angles in a circle)
Simplify further as follows;
y = 360 - 180
y = 180⁰
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Please help urgent thank you so much
Answer: 4, 14
Step-by-step explanation:
Bring everything over to other side that is not in the absolute value:
3 |x - 9| + 5 = 20 >Subtract 5 from both sides
3 |x - 9| = 15 >Divide both sides by 3
|x - 9| = 5 >Create a positive and negative version to
drop the absolute value
x - 9 = 5 x - 9 = -5
x= 14 x = 4
The figure below shows part of a circle, with central angle as marked.
What part of the full circle does the figure represent? Express your
answer as a fraction in simplest terms.
108⁰
+
Answer:
fraction of circle = [tex]\frac{3}{10}[/tex]
Step-by-step explanation:
a complete circle has central angle of 360° , then
fraction of circle = [tex]\frac{108}{360}[/tex] ← divide numerator/ denominator by 36
fraction of circle = [tex]\frac{3}{10}[/tex] ← in simplest form
Music students and art students at a middle school were surveyed to choose a cardiovascular activity: playing sports or dancing.
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Music students 32 15 47
Art students 31 22 53
Column totals 63 37 100
What is the marginal frequency of students who chose dancing?
15
22
37
53
The marginal frequency of students who chose dancing is 37.
The correct answer to the given question is option 3.
The marginal frequency of students who chose dancing can be calculated by adding up the number of students who chose dancing in each row or column. In this case, we need to add up the number of art students who chose dancing (22) and the number of music students who chose dancing (15), which gives us a total of 37. This is the marginal frequency of students who chose dancing.
Based on the survey results, it appears that a slightly higher percentage of art students prefer dancing (41.5%) compared to music students (31.9%). However, both groups of students seem to be fairly evenly split between dancing and playing sports, with a slight preference for playing sports overall.
It's worth noting that cardiovascular activity is important for overall health and well-being, and both dancing and playing sports can provide great opportunities for exercise and physical activity. Additionally, both activities can also be enjoyable and provide a sense of community and social connection, which is important for middle school students who are still developing their social skills and relationships. Ultimately, the choice between dancing and playing sports will depend on individual interests, preferences, and abilities.
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Two of the sides of a right triangle are 4 and 5. What is the length of the third side? Find all possible answers.
To find the length of the third side of a right triangle when two sides are given, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's assume the two given sides are 'a' and 'b', and the unknown third side is 'c' (the hypotenuse).
Using the Pythagorean theorem:
c² = a² + b²
Substituting the given values:
c² = 4² + 5²
c² = 16 + 25
c² = 41
To find the length of 'c', we need to take the square root of both sides:
c = √41
So, the length of the third side is √41 (approximately 6.40) when rounded to two decimal places.
Therefore, the possible length of the third side of the right triangle is √41.
Step-by-step explanation:
We will use a phayragoras theorem
a^2 +b^2= c^2
let side1=4 be a
let side2=5 be b
let the 3rd side be the hypotnuous=c
therfore 4^2+5^2=c^2
=16+25=c^2
=41=c^2.
therfore c=√41
Question 9 of 10
Which is the standard equation for a circle centered at the origin with radius
12
O A. x²2² +²2² = r
OB.x2²=2² +2²
XA
O c. x+y=r
OD. x² +2²=2²
Which is the standard equation for a circle centered at the origin with radius r be,
⇒ x² + y² = r²
Hence option D is correct.
We have to find the standard equation of circle,
Given that,
Center of circle is at (0, 0)
And radius is r
Let a point (x, y) on the circle.
We know that,
The distance between the point (x, y) and origin is also known as radius of the circle,
Since we know that,
The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Therefore distance between (0, 0) and (x, y),
⇒ √[ (x - 0)² + (y - 0)²] = r
Squaring both sides we get,
⇒ (x - 0)² + (y - 0)² = r²
⇒ x² + y² = r²
This is the standard equation of circle.
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The cost of a season train ticket is reduced by $33.10 which corresponds to a 10%
reduction. Find the original cost of the season ticket.
Answer:
Let's denote the original cost of the season train ticket as "x".
According to the given information, a reduction of $33.10 corresponds to a 10% reduction in the original cost. We can set up the following equation to represent this:
10% of x = $33.10
To solve for x, we need to convert 10% to decimal form, which is 0.10. We can rewrite the equation as:
0.10 * x = $33.10
Simplifying the equation, we have:
0.10x = $33.10
To isolate x, we divide both sides of the equation by 0.10:
x = $33.10 / 0.10
x = $331.00
Therefore, the original cost of the season train ticket is $331.00.
Step-by-step explanation: