Answer:
620
Step-by-step explanation:
selling 400 doughnuts means selling 800 £ worth of doughnuts. 800 x 0.4 ( to find 40 percent) = 320, + 300 because the the fixed cost = 620. :)
The total cost per day of producing 400 doughnuts is £620.
The total cost of producing doughnuts is the sum of fixed cost and variable cost. Fixed cost is the constant that remains constant regardless of the amount of doughnuts made. Variable cost is the cost that varies with the number of doughnuts made.
Total cost = fixed cost + variable cost
Fixed cost = £300
Variable cost = average variable cost x number of output
Average variable cost = 40% x £2
= 0.40 x £2 = 0.80
Variable cost = £0.80 x 400 = £320
Total cost = £320 + £300 = £620
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A type of origami paper comes in 15 cm by 15 cm
square sheets. Hilary used two sheets to make the
origami dog. What is the total area of the origami
paper that Hilary used to make the dog?
Answer:
150 cm squared
Step-by-step explanation:
I guess that's the answer if I'm wrong you can tell me right away so that I can try another method thank you.
rewrite in a slope-intercept form and graph
Answer:
\(y=\frac{3}{2}x+3\)
Step-by-step explanation:
Take the given equation:
\(-3x+2y=6\)
Solve for y so that the equation is written in slope-intercept form:
\(y=mx+b\)
m is the slope and b is the y-intercept. x and y are the coordinate points (x,y).
Solve for y:
Add 3x to both sides of the equation:
\(-3x+3x+2y=6+3x\\\\2y=3x+6\)
Divide both sides of the equation by 2 to isolate y:
\(\frac{2y}{2}=\frac{3x+6}{2} \\\\ y=\frac{3}{2}x+3\)
The slope is \(\frac{3}{2}\) and the y-intercept is 3.
To graph, you need two points. You can use the y-intercept as one.
The y-intercept is the place where the line crosses over the y-axis, where x equals 0, so the point is (0,3).
Next, take any value for x and insert it into the equation. We'll use 2:
\(y=\frac{3}{2}(2)+3\)
Using this, you can solve for the value of y when x is equal to 2.
Simplify:
\(\frac{3}{2} *\frac{2}{1}=\frac{6}{2}=3 \\\\y=3+3\\\\y=6\)
So, when x=2, y is 6 (2,6).
Plot the points (0,3) and (2,6)
Draw a straight line through the two, going past both.
:Done
In the graph, one square is 1 unit
The function g(x) = 3x3 + x is an odd function. Which transformations of g(x) would result in odd functions? Check all that apply. –g(x) g(2x) g(x − 1) g(x) − 3 g(–x)
Answer:
-g(x), g(2x), g(-x)
Step-by-st-ep explanation:
if f (–x) = f (x), so all of the signs are the same
you can also try on desmos, the graph is more helpful than words explain sometimes
The functions that are odd are -g(x), g(2x), and g(-x). The correct option is A, B, and E.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
For an odd function, -f(x) = f(-x).
Given that the function, g(x) = 3x³ + x is an odd function. Therefore, the transformation of the function that will again result in an odd function is,
A.) –g(x)
-g(x) = -(3x³ + x) = -3x³ - x
g(-x) = 3(-x)³ + (-1x = -3x³ - x
Thus, this is an odd function.
B.) g(2x) ⇒ Since this will result in the same function, the only difference will be that the function will be vertically stretched.
E.) g(–x)
-g(x) = -(3x³ + x) = -3x³ - x
g(-x) = 3(-x)³ + (-1x = -3x³ - x
Thus, this is an odd function.
Hence, the functions that are odd are -g(x), g(2x), and g(-x).
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which is a true statement about the slopes of MO and OQ?
Answer: b
Step-by-step explanation: because if u see the numbers and they match
2x^2+8x-1=0
Solve by completing the square
Answer:
x=-4/3
Step-by-step explanation:
The total length of a road trip was 13.2 hours. If highway signs are posted every 0.06 hours, including one at the end of the road trip, how many highway signs will there be on the road trip?
There will be 221 highway signs on the road trip.
What is Total Length?
Whole Length (TL) is the measurement taken in a straight line, with the fish lying on its side, from the tip of the snout to the end of the tail (caudal fin).
The total length of the road trip is 13.2 hours.
Highway signs are posted every 0.06 hours. To find out how many highway signs are on the road trip, we can divide the total length of the road trip by the interval between each sign and then add one more sign for the end of the road trip:
(number of signs) = (total length of road trip) / (interval between signs) + 1
Substituting the values, we get:
(number of signs) = 13.2 / 0.06 + 1
(number of signs) = 220 + 1
(number of signs) = 221
Therefore, there will be 221 highway signs on the road trip.
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Each of three friends flips a coin 86 times. The results for each friend are shown in the tables. Find the relative frequency
the event "heads" for each friend. If the friends combine their results to get 142 heads and 116 tails, what is the relative
frequency for the event "heads"? Use pencil and paper. Suppose each friend flips a coin 860 times. Is there a value you
would expect the relative frequency for the event "heads" to be close to?
The expected frequency of heads should be close to 0.5.
What is Probability?Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible to occur and 1 indicates that the event is certain to occur. Probability is used in many areas of mathematics and science, from predicting weather patterns to predicting stock market performance. Probability is also used to make decisions in everyday life, such as whether to take an umbrella with you when you leave the house.
The relative frequency for the event heads for friends 1 is-
53/86 = 0.615
The relative frequency for the event heads for friends 2 is-
61/86 = 0.710
The relative frequency for the event heads for friends 3 is-
28/86= 0.326
If the friends combine their results to get 142 heads and 116 tails, the relative frequency for the event "heads" is
142/258 = 0.551.
If each friend flips a coin 860 times, the expected relative frequency for the event "heads" is close to 0.5. This is because in a fair coin toss, there is an equal chance of getting heads or tails and the probability of getting either result is 0.5. Therefore, the expected frequency of heads should be close to 0.5.
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find the critical value(s) and rejection region(s) for the type of z-test with level of significance . include a graph with your answer. right-tailed test, a=0.03.
Answer:
c
Step-by-step explanation:
The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.
The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88 OR Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.
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Plz help me pass due :(
Answer:
y=5x-3
Step-by-step explanation:
slope intercept form=y=mx+b
so
2y-10x=-6
2y=10x-6
y=5x-3
The current and voltage of new ultrathin CIGS solar cells vary based on temperature. The graph shows the current, in milliamps per square centimeter (mA/cın”), and voltage, in volts (V), at
various temperatures, in degrees Kelvin (K)
Which of the following best estimates the rate of change of voltage, in volts per degree Kelvin (V/K)?
Given a cone with height 10 feet and diameter of 22 feet, determine the radius of the smaller cone created when a horizontal plane passes through the cone at exactly 4 feet from the base
The radius of the smaller cone created when a horizontal plane passes through the cone at exactly 4 feet from the base is 6.6 feet.
To determine the radius of the smaller cone created when a horizontal plane passes through the cone at exactly 4 feet from the base, we can use similar triangles.
The given cone has a height of 10 feet and a diameter of 22 feet. The radius of the given cone is half of the diameter, so it is 22/2 = 11 feet.
When a horizontal plane passes through the cone at exactly 4 feet from the base, it divides the cone into two parts: the smaller cone and the frustum (the remaining part of the cone).
The height of the smaller cone is the distance from the 4-feet mark to the top of the cone, which is 10 - 4 = 6 feet.
Since the two cones are similar, their corresponding dimensions are proportional. The ratio of the corresponding heights is the same as the ratio of the corresponding radii.
So, we can set up the following proportion:
(r_small / r_given) = (h_small / h_given)
Substituting the values we have:
(r_small / 11) = (6 / 10)
Cross-multiplying:
10 * r_small = 11 * 6
r_small = (11 * 6) / 10
r_small = 66 / 10
r_small = 6.6 feet
Therefore, the radius of the smaller cone created when a horizontal plane passes through the cone at exactly 4 feet from the base is 6.6 feet.
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System Reliability Theory: Models, Statistical Methods, and
Applications by M. Rausand, A. Barros, and A. Hoyland.
QUESTION: Establish a function tree for a (domestic)
refrigerator.
Function Tree for a Domestic Refrigerator: Refrigerator- 1.1 ) Cooling, 1.1.1) Compressor, 1.1.2) Condenser, 1.1.3) Evaporator, 1.1.4) Expansion valve, 1.2) Control, 1.2.1) Thermostat, 1.2.2) Temperature settings, 1.3) Storage, 1.3.1) Shelves, 1.3.2) Door compartments, 1.3.3) Crisper drawers, 1.4) Power supply, 1.4.1) Electrical connection, 1.4.2) Power cord, 1.5) Defrosting, 1.5.1) Defrost timer, 1.5.2) Defrost heater, 1.5.3) Defrost thermostat, 1.6) Insulation, 1.6.1) Inner lining, 1.6.2) Outer casing, 1.7) Display and Controls, 1.7.1 )Temperature display, 1.7.2) Control panel.
The function tree represents the hierarchical breakdown of the different components and subsystems of a domestic refrigerator. Here is an explanation of each component:
Refrigerator: The main unit responsible for cooling and storing food.
1.1 Cooling: The subsystem that performs the cooling process.
1.1.1 Compressor: The component that compresses the refrigerant gas, raising its pressure.
1.1.2 Condenser: The heat exchanger that dissipates heat from the compressed refrigerant, causing it to condense into a liquid state.
1.1.3 Evaporator: The heat exchanger that absorbs heat from the refrigerator's interior, causing the liquid refrigerant to evaporate.
1.1.4 Expansion valve: The component that regulates the flow of refrigerant from the high-pressure side to the low-pressure side, creating a cooling effect.
1.2 Control: The subsystem responsible for regulating temperature and other settings.
1.2.1 Thermostat: The device that senses the temperature and controls the operation of the compressor and other cooling components.
1.2.2 Temperature settings: The user interface for adjusting the desired temperature inside the refrigerator.
1.3 Storage: The subsystem that provides storage compartments for food items.
1.3.1 Shelves: The adjustable platforms that hold food items.
1.3.2 Door compartments: The compartments on the refrigerator door for storing smaller items.
1.3.3 Crisper drawers: The drawers designed for storing fruits and vegetables at specific humidity levels.
1.4 Power supply: The subsystem responsible for providing electrical power to the refrigerator.
1.4.1 Electrical connection: The point of connection between the refrigerator and the electrical supply in the house.
1.4.2 Power cord: The cable that delivers electricity from the electrical connection to the refrigerator.
1.5 Defrosting: The subsystem that removes ice buildup from the evaporator to maintain efficient cooling.
1.5.1 Defrost timer: The timer that initiates defrost cycles at regular intervals.
1.5.2 Defrost heater: The component that melts the ice on the evaporator coils.
1.5.3 Defrost thermostat: The device that monitors the temperature during defrosting and terminates the defrost cycle when the desired temperature is reached.
1.6 Insulation: The subsystem that provides thermal insulation to minimize heat transfer.
1.6.1 Inner lining: The layer of insulation material on the inner walls of the refrigerator.
1.6.2 Outer casing: The outer shell of the refrigerator that provides additional insulation and protection.
1.7 Display and Controls: The subsystem that provides information and control options to the user.
1.7.1 Temperature display: The digital or analog display that shows the current temperature inside the refrigerator.
1.7.2 Control panel: The interface with buttons or dials for adjusting settings and controlling various features.
The function tree for a domestic refrigerator provides a systematic breakdown of its components and subsystems. It helps in understanding the different functions and interactions involved in the operation of a refrigerator. By analyzing this hierarchy, manufacturers and engineers can design and optimize the reliability and performance of each component, leading to improved overall refrigerator reliability and user satisfaction.
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How to do this type of math
Step-by-step explanation:
So what type of maths help do you want
Elizabeth lives in san francisco and works in mountain view. In the morning, she has 3 33 transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same 3 33 choices for her trip home. If elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that she'll use a cab exactly one time?.
The probability that she will choose to use a cab exactly one time is 4/9.
It has been given that In the morning she has 3 transportation choices. And in the evening the same 3 choices.
i) bus
ii) cab
iii) train
Since each choice have an equal chance of being chosen,
The probability of Choosing a bus will be 1/3
The probability of Choosing a cab will be 1/3
The probability of Choosing a train will be 1/3
Now, the Probability of Not Choosing the cab will be the sum of the probabilities of choosing a bus and train i.e, 2/3
Now there will be two possibilities-Either She chooses a cab in the morning and something else in the evening Or She chooses a cab in the evening and something else in the morning.
Therefore, the probability of choosing a cab exactly one time =
( Probability of cab in morning x Probability of no cab in the evening) + (Probability of no cab in morning x Probability of cab in evening)
Probability of choosing a cab exactly once
= 1/3 x 2/3 + 2/3 x 1/3
= 4/9
Therefore, the probability that she will choose to use a cab exactly one time is 4/9.
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The equation of line v is y=9x+1. Line w is perpendicular to line v and passes through (3, – 2). What is the equation of line w?
Answer:
Step-by-step explanation:
Remember the general form of a linear equartion: y=mx + b, where m is the slope and b is the y-intercept (the value of y when x = 0).
The equation of line v (y=9x+1) has a slope of 9. A perpendicular line with have a slope equal to the negative inverse of the reference line. So the line we want will have a slope of -(1/9). That gives us y = -(1/9)x + b. Any vale of b will produce a line that is perpendicular. But we want a line that goes through point (3,-2). All we need to do is find a value for b that will make that wish come true.
Use the point (3,-2) in y = -(1/9)x + b and solve for b:
y = -(1/9)x + b
-2 = -(1/9)*(3) + b
-2 = -(1/3) + b
b = - 1 2/3, or -(5/3)
The equation is y = -(1/9)x + - (5/3)
The equation of line w is \(y+2=\frac{-1}{9} (x-3)\)
Equation of a lineThe equation of a line in point-slope form is expressed as:
\(y-y_1=\frac{-1}{m} (x-x_1)\)The slope of the line y = 9x + 1 is 9.
Substitute the slope m = 9, and the coordinate (3, -2) into the formula to have:
\(y-(-2)=\frac{-1}{9} (x-3)\\y+2=\frac{-1}{9} (x-3)\)
Hence the equation of line w is \(y+2=\frac{-1}{9} (x-3)\)
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"repeated sampling of a certain process shows the average of all
samples ranges to be 1.00 cm. there are random samples and the
ssmple size has been 5. what is the upper control limit for R
chart?
Upper Control Limit for R Chart: UCL = D4 * R-Bar , UCL = 2.114 * 1.000, UCL ≈ 2.115 cm. Therefore, the correct answer is 2.115 cm(d).
To calculate the upper control limit for the R Chart, we need to use the following formula:
Upper Control Limit (UCL) = D4 * R-Bar
Where:
- D4 is a constant value based on the sample size (n=5 in this case).
- R-Bar is the average range of the samples, which is given as 1.000 cm.
The value of D4 for a sample size of 5 is 2.114. (You can find this value in statistical reference tables.)
Now, we can calculate the UCL:
UCL = D4 * R-Bar
= 2.114 * 1.000
= 2.114 cm
Rounding to 3 decimal places, the upper control limit for the R Chart is 2.114 cm.
Therefore, the correct option is: d. 2.115 cm
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The complete question is :
Repeated sampling of a certain process shows the average of all sample ranges to be 1.000 cm. There are 12 random samples and the sample size has been 5. What is the upper control limit for R Chart? Must compute in 3 dec pl. Select one: O a. 2.745 cm O b. 3.005 cm O c. 1.725 cm d. 2.115 cm e. 2.000 cm
Pls help!! I can’t figure out how to do thisss
Answer: 30 and 26
Step-by-step explanation:
Jorge bought a crate of floor tile for $132. The crate had 6 boxes of floor tiles. Each box contained 29 floor tiles. Write and solve an equation to determine the cost per box, b.
The equation to determine the cost per box, b, can be written as 6b = $132, and solving for b yields b = $22.
Let's denote the cost per box as b. Since Jorge bought a crate with 6 boxes of floor tiles, the total cost of the crate is equal to the cost per box multiplied by the number of boxes: 6b.
According to the given information, the crate of floor tiles cost $132. Therefore, we can write the equation as follows: 6b = $132.
To determine the cost per box, we solve the equation for b. Dividing both sides of the equation by 6, we have b = $132 ÷ 6 = $22.
Hence, the cost per box, b, is $22.
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What is the distance between (-5,4) and (-1, 4)
Answer:
5 units
Step-by-step explanation:
Answer:
The distance is 4 units.
Step-by-step explanation:
If you were to count how many squares until you reach (-1,4) from (-5,4)
Then you would get 4 units.
Hope this helps! :)
"Prove that: sin(x-45)=cos(x+45)
Using trigonometric identities sin(x - 45) = -cos(x + 45)
What is a trigonometric identity?A trigonometric identity is an equation that contains a trigonometric ratio.
Since we have the trigonometric identity sin(x - 45) = -cos(x + 45), we need to prove that Left hand sides L.H.S equals Right Hand side R.H.S. We proceed as follows
L.H.S = sin(x - 45)
Using the trigonometric identity sin(A - B) = sinAcosB - cosAsinB where A = x and B = 45, we have that substituting these into the equation
sin(x - 45) = sinxcos45 - cosxsin45
= sinx × 1/√2 - cosx × 1/√2
= sinx/√2 - cosx√2
= (sinx - cosx)/√2
Also, R.H.S = -cos(x + 45)
Using the trigonometric identity cos(A + B) = cosAcosB - sinAsinB where A = x and B = 45, we have that these into the equation
cos(x + 45) = cosxcos45 - sinxsin45
= cosx × 1/√2 - sinx × 1/√2
= cosx/√2 - sinx/√2
= cosx/√2 - sinx/√2
= (cosx - sinx)/√2
= - (sinx - cosx)/√2
Since L.H.S = R.H.S
sin(x - 45) = -cos(x + 45)
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Find the equation of the line that passes through (3,1) and is parallel to y=3−2x. Leave your answer in the form y=mx+c
How do I find the equation of the line y=mx + C, passing through the points M (-2, -3) and T (3, 7)?
How do I find the equation of the line y=mx + C, passing through the points M (-2, -3) and T (3, 7)?
A2A
y = mx + C is often called slope-intercept form.
There are two pieces of information you will need to solve for. #1: The slope, which is m, and #2: the y-intercept, which is C (incidentally I learned this as y = mx + b, instead of y = mx + C, but that is a trivial detail)
Step #1 Find the slope. use the formula slope = (y₂ - y₁)/(x₂ - x₁) => (7 - -3)/3 - -2) = 10/5 = 2. m=2
Step #2 Find the y-intercept. Solve for y = mx + C when x is 2 and x = -2 and y = -3 -3 = 2(-2) + C => -3 = -4 + C add 4 to both sides, 1 = C
Equation: y = 2x + 1.
Check: x = 3 => y = 2(3) + 1 => y = 6 + 1 => y = 7 => (3, 7)
Check: x = -2 => y = 2(-2) + 1 => y = -4 + 1 => y = -3 => (-2, -3)
How many groups of 3/4 are in each of the following quantities? 11/4, 6 1/2
There are complete 3 groups of 3/4 in 11/4.
There are complete 8 groups of 3/4 in 6 1/2.
To find the number of groups of 3/4 in 11/4, we divide it by 3/4.
\(\frac{\left(\frac{11}{4}\right)}{\left(\frac{3}{4}\right)}=3.67\)
So there are complete 3 groups of 3/4 in 11/4.
To find the number of groups of 3/4 in 6 1/2, we divide it by 3/4.
\(\frac{\left(6\frac{1}{2}\right)}{\left(\frac{3}{4}\right)}=\frac{\left(\frac{13}{2}\right)}{\left(\frac{3}{4}\right)}=8.67\)
So there are complete 8 groups of 3/4 in 6 1/2.
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A building in San Francisco has light fixtures consisting of small 2.35-kg bulbs with shades hanging from the ceiling at the end of light thin cords 1.50 m long.If a minor earthquake occurs, how many swings per second will these fixtures make?
The light fixtures will make approximately 0.914 swings per second during a minor earthquake in San Francisco.
To determine the frequency of the swings per second for the light fixtures, we need to use the formula for the period of a pendulum, which is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
In this case, the length of the pendulum is given as 1.50 m, and the mass of the bulb is given as 2.35 kg. We can assume that the shade and cord add negligible mass to the system. The acceleration due to gravity is approximately 9.8 m/s^2.
Plugging in the values, we get:
T = 2π√(1.50/9.8)
T ≈ 1.093 seconds
The frequency of the swings per second is the reciprocal of the period, so:
f = 1/T
f ≈ 0.914 Hz
It's important to note that this is an approximation, and the actual frequency may vary depending on factors such as the amplitude of the oscillations and the specific characteristics of the earthquake.
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A right circular cone is generated by revolving the region bounded by y=3x/4,y=3, and x=0 about the y-axis. Find the lateral surface area of the cone.
The lateral surface area of the cone is 20π square units.
Given that, a right circular cone is generated by revolving the region bounded by y = \(\frac{3}{4}\), y = 3, x = 0 and about the y-axis.
We need to the lateral surface area of the cone.
We know that the surface area of the revolved curve is solved using the formula :
\(S = 2\pi \int\limits^b_a {x\sqrt{(1+f'(x))^2} } \, dx\)
Where,
\(\sqrt{(1+f'(x))^2}\) is an arc length of a curve and x is the radius of revolution.
From the given equation,
f'(x) = 3/4
Substituting in the formula:
\(S = 2\pi \int\limits^b_a {x\sqrt{(1+\frac{3}{4} )^2} } \, dx\)
\(S = 2\pi \int\limits^b_a {\frac{5}{4} x \, dx\)
For the limits, when y = 3,
3 = 3/4 x
x = 4
Therefore,
\(S = 2\pi \int\limits^4_0 {\frac{5}{4} x \, dx\)
Integrating we get,
\(S = 2\pi [\frac{5x^2}{8} ]^4_0\)
On solving we get,
S = 20π
So, the lateral surface area of the cone is 20π square units.
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One in a thousand people have a particular disease, and the test for the disease is 98% correct in testing for the disease. On the other hand, the test has a 1% error rate, if the person being tested, does not have the disease. If someone tests positive, what are the odds they have the disease
The odds a person has the disease they were tested for is 98% or 98:2.
What is the difference between probability and odds?Probability describes how likely is an event to happen by using a percentage from 0 to 100%. On the other hand, the odds focus on the rate between the specific outcome: other outcomes.
What are the odds in this situation:In this case, the specific outcome is to have the disease after being tested, which occurs 98% of the time. This implies only the 2% tested do not have the disease. Now, this relationship can be expressed as:
98: 2
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the dotplot above shows the distribution of calf measurements for 507 adults who attend a local gym. the data is divided into equal-sized subgroups with 25% of the adults in each subgroup. which measure of center can you most accurately estimate from this information?
which measure of center can you most accurately estimate from this information: Median
The median divides the data into equal-sized groups. So approximately 50% of the data is above the median and approximately 50% of the data is below the median.
Calculating the median
The median is the value in a data set, implying that half of data focuses have a value more modest or equivalent to the median and half of data focuses have a value higher or equivalent to the median.
For a little data set, you first count the quantity of data focuses (n) and organize the data focuses in expanding request. Assuming the quantity of data focuses is lopsided, you add 1 to the quantity of places and separation the outcomes by 2 to get the rank of the data point whose value is the median.
The rank is the place of the data point after the data set has been organized in expanding request: the smallest value is rank 1, the second-smallest value is rank 2, and so forth.
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the complete question is:
The dotplot above shows the distribution of calf measurements for 507 adults who attend a local gym. The data is divided into equal-sized subgroups with 25% of the adults in each subgroup.
Which measure of center can you most accurately estimate from this information?
1. mean
2. median
Use Similar triangles to calculate the height, h cm, of triangle ABE
The height of the triangle ABE using similar triangles is 24cm
What is the law of similar triangles?It states that f the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar. Thus, if ∠A = ∠B and AE/DC = AB/BD then ΔABE~ΔBCD
if two triangles are similar, then their corresponding angles are congruent.
if the height of ∆ABE is h , then the height of ∆BCD = 36-h
36-h/h= 10/20
multiply both side by 20h
720-20h= 10h
collect like terms
720= 30h
h= 720/30
therefore h= 24cm
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A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has 4 identical compo- nents, each with a probability of 0.2 of failing in less than 1000 hours.The susys- tem will operate if any 2 of the 4 components are operating. Assume that the components operate independently. Find the probability that a) exactly 2 of the 4 components last longer than 1000 hours. b)the subsystem operates longer than 1000 hours.
The probability that exactly 2 of the 4 components in the subsystem last longer than 1000 hours is 0.1536.
The probability that the subsystem operates for more than 1000 hours, requiring at least 2 components to be functioning, is 0.768.
a) To find the probability that exactly two components last longer than 1000 hours, we can use the binomial probability formula. Let's denote the probability of a component lasting longer than 1000 hours as p and the probability of failure as q (1 - p).
The probability of exactly two components lasting longer than 1000 hours is given by:
P(X = 2) = C(4, 2) * p^2 * q^(4 - 2)
where C(4, 2) represents the number of ways to choose 2 components out of 4, which is calculated as 4! / (2! * (4 - 2)!), equal to 6.
Given that p = 0.8 (1 - 0.2) and q = 0.2, we can substitute these values into the formula:
P(X = 2) = 6 * (0.8)^2 * (0.2)^(4 - 2)
= 6 * 0.64 * 0.04
= 0.1536
Therefore, the probability that exactly two components last longer than 1000 hours is 0.1536.
b) To find the probability that the subsystem operates for more than 1000 hours, we need to consider the different combinations of components that can last longer than 1000 hours. In this case, any combination of two or more components operating will result in the subsystem operating.
We can calculate the probability of the subsystem operating for more than 1000 hours by summing the probabilities of each combination:
P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4)
Using the binomial probability formula, we can calculate each individual probability and then add them together to obtain the final probability.
P(X = 2) = 0.1536 (calculated in part a)
P(X = 3) = C(4, 3) * p^3 * q^(4 - 3)
= 4 * (0.8)^3 * (0.2)^(4 - 3)
= 0.2048
P(X = 4) = p^4 * q^(4 - 4)
= (0.8)^4 * (0.2)^(4 - 4)
= 0.4096
Therefore, the probability that the subsystem operates for more than 1000 hours is:
P(X ≥ 2) = 0.1536 + 0.2048 + 0.4096
= 0.768
Therefore, the probability that the subsystem operates for more than 1000 hours is 0.768.
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Jarry has a jar with 273 marbles in it. The jar can hold 1,000 marbles in all. Which equation can be use to find m, the number of marbles still needed to fill the jar?
Answer:
1000-273=M
Step-by-step explanation:
Jarry has 273 and needs 1000 so take the number he needs by the marbles he has to find the marbles he needs to fill the jar. Hope this helped
The required equation that models the number of marbles still needed to fill the jar is M = 1000 - 273.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
Jarry has a jar with 273 marbles in it. The jar can hold 1,000 marbles in all.
Let the number of marbles that are still to be filled by M
And the equation is given as,
M = 1000 - 273
Thus, the required equation that models the number of marbles still needed to fill the jar is M = 1000 - 273.
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Given triangle ABC with points:
A - (1, -3)
B - (3, 0)
C - (4, -2)
Rotate ABC 90 degrees counterclockwise about the origin then reflect it over the x-axis. Determine the ordered pairs for A', B', and C'.
The points A', B', and C' are (3, 1), (0, 3) and (-2, 4) respectively. The solution has been obtained by using the concept of transformation.
What is transformation?
Transformations allow for the translation, rotation, and reflection of shapes on a coordinate plane. Any line, point, or vector can be rotated, translated, or reflected.
We are given coordinates of triangle ABC as A (1, -3), B (3, 0) and C (4, -2).
Now, we need to rotate the triangle ABC 90 degrees about the origin.
We know that the rotation rule for rotating 90 degrees about the origin is that (x, y) becomes (y, -x).
So, from this we get the coordinates as
A' (3, -1)
B' (0, -3)
C' (-2, -4)
Now, on reflecting it over the x - axis, we get
A' (3, 1)
B' (0, 3)
C' (-2, 4)
Hence, the points A', B', and C' are (3, 1), (0, 3) and (-2, 4) respectively.
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