Apprοximately 31 mοving bοxes οn the flοοr οf the stοrage unit, given the dimensiοns οf the bοxes and the aisle.
What are dimensiοns?In mathematics and geοmetry, dimensiοns refer tο the number οf cοοrdinates needed tο specify the lοcatiοn οf a pοint οr οbject in space.
Tο calculate the number οf mοving bοxes that can fit οn the flοοr οf the stοrage unit, we need tο first calculate the usable flοοr space by subtracting the width οf the aisle frοm the tοtal width οf the stοrage unit.
The usable floor space can be calculated as follows:
Usable floor space = 10 ft - 3 ft (aisle) = 7 ft
Next, we need to calculate how many boxes can fit in a row along the length and width of the usable floor space.
Along the length of the floor space, we can fit:
Number of boxes along length = 10 ft / 18 in = 20/3 boxes
Similarly, along the width of the floor space, we can fit:
Number of boxes along width = 7 ft / 18 in = 14/3 boxes
Since we can only stack the boxes one layer high, the total number of boxes that can fit on the floor of the storage unit can be calculated by multiplying the number of boxes along the length by the number of boxes along the width:
Total number of boxes = (20/3) x (14/3) = 280/9 ≈ 31
Therefore, we can fit approximately 31 moving boxes on the floor of the storage unit, given the dimensions of the boxes and the aisle.
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Data from an important new study showed that out of 100,000 people a total r? 8,700 reported that they could wiggle their ears and their nose at the same time. What would you say is the probability of a person having this skill?
The probability of a person having this skill is estimated to be 87/1000 or 0.087.
What does a probability means?Probability is a branch of mathematics that deals with determining the likelihood of an event occurring. The probability of an event occurring is equal to the number of favorable events divided by the total number of events. Probability has a value between 0 and 1, with 0 denoting uncertainty and 1 denoting certainty.
Based on the given conditions, we will formulate for 8,700/100,000 to get the probability of a person having this skill to wiggle their ears and their nose at the same time.
Let is cross out the common factor. Now we will have [tex]87/1000[/tex]. Therefore, the probability of a person having this skill is estimated to be [tex]87/1000[/tex] or [tex]0.087[/tex].
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PLEASE HELP ME ASNWER THIS DISCUSSION QUESTIONS!! 50 POINTS!!!!
Step-by-step explanation:
The statement does not make sense. A triangle cannot have two right angles as the sum of the three angles in a triangle is always 180 degrees. Two right angles would add up to 180 degrees, leaving no room for the third angle.
To determine the number of plants needed, first find the perimeter of the square flower bed by multiplying the length of one side by 4 (since there are four sides in a square). 8 x 4 = 32 feet. Then convert the spacing of 8 inches to feet by dividing by 12 (since there are 12 inches in a foot). 8 / 12 = 0.67 feet. Finally, divide the perimeter of the flower bed by the spacing of the plants to get the total number of plants needed. 32 / 0.67 = 47.76. Round up to the nearest whole number to get the final answer of 48 plants.
A square is a type of rectangle because it has four right angles and opposite sides that are parallel and congruent. A square is a type of rhombus because it has four sides of equal length. A square is a type of parallelogram because it has two pairs of opposite parallel sides. A square is a type of quadrilateral because it has four sides. A square is a type of polygon because it is a closed shape with three or more sides.
Find the measure of X
Answer:
≈25,99
Step-by-step explanation:
Use trigonometry:
sin (38∘) = 16 / x
x = 16 / sin (38∘) ≈ 25,99
What are the coordinates of the terminal point determined by t = 10pi/3 ?
The correct option is- A: (-1/2 , -√3/2) are the coordinates found using the terminal points t = 10pi/3.
Explain about the terminal points?On the unit circle, the terminal point. To find any terminal point on the unit circle which start at (1, 0), and determine the angle in degree or radian on the circle that travel counter clockwise whereas if angle is positive as well as clockwise if the angle is negative. The terminal point is the coordinate of the endpoint.
Given values:
t = 10pi/3
convert to degrees
t = 10*pi/3
t = 10*180/3
t = 600 degrees
Find quadrant of 600 degrees.
600 = 360+240
240 comes in III quadrant
Thus, x-coordinate and y-coordinate are negative
Now,
240° = 180°+ 60°
60° is the angle for which terminal point are to be find.
Let ∅=60°
Consider unit circle
radius r = 1 units
Then,
x = -r*cos ∅
x = -cos 60
x = -(1/2)
And,
y = -r*sin ∅
y = -sin 60
y = -(√3)/2
Thus, the coordinates of the terminal point are found as (-1/2 , -√3/2) by
t = 10pi/3.
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Baird Airlines is a small airline that occasionally carries overload shipments for the overnight delivery company Never-Fail, Inc. Never-Fail is a multimillion-dollar company started by Wes Never immediately after he failed to finish his first accounting course. The company’s motto is “We Never-Fail to Deliver Your Package on Time.” When Never-Fail has more freight than it can deliver, it pays Baird to carry the excess. Baird contracts with independent pilots to fly its planes on a per-trip basis. Baird recently purchased an airplane that cost the company $4,940,000. The plane has an estimated useful life of 24,700,000 miles and a zero salvage value. During the first week in January, Baird flew two trips. The first trip was a round trip flight from Chicago to San Francisco, for which Baird paid $300 for the pilot and $250 for fuel. The second flight was a round trip from Chicago to New York. For this trip, it paid $250 for the pilot and $125 for fuel. The round trip between Chicago and San Francisco is approximately 4,900 miles and the round trip between Chicago and New York is 2,000 miles. Required Select if the costs mentioned below are direct or indirect. Determine the total cost of each trip.
Overall price equals direct and indirect costs, or $375 plus $397.96, or $772.96.
What is direct cost?
Direct costs are business expenses you can directly apply to producing a specific cost object, like a good or service. Cost objects are items that expenses are assigned to. Direct costs can be variable or fixed. Variable costs are expenses that change based on how many items you produce or how many services you offer. For example, you would spend more money producing 200 toys as opposed to 100 toys. Fixed costs are expenses that remain the same each month.
What is indirect cost?
Indirect costs are expenses that apply to more than one business activity. Unlike direct costs, you cannot assign indirect expenses to specific cost objects.
Like direct costs, indirect expenses can be either fixed (e.g., rent) or variable (e.g., utilities).
You can allocate indirect costs to determine how much you are spending on expenses compared to your sales. To do this, find the overhead rate, or indirect cost ratio.
Here is the overhead rate formula:
Overhead Rate = Overhead Costs / Sales
given
Costs :Chicago-San Francisco pilot compensation: Direct cost
Straight cost of fuel for a flight from Chicago to San Francisco
Chicago-New York pilot compensation: Direct cost
Gasoline costs for a travel from Chicago to New York: Straight price
aircraft price: indirect expense (as it is a capital expenditure)
Total expense for each journey:
Indirect costs for the Chicago-San Francisco journey are as follows: ($4,940,000 / 24,700,000 miles) x 4,900 miles = $986.99 Direct costs for the trip are as follows: $300 (pilot payment) + $250 (fuel cost) = $550Final price = Direct price + Indirect price, or $550 + $986.99, is $1,536.99.
For the Chicago-New York flight, the direct cost is $250 for the pilot and $125 for fuel, for a total of $375.
The indirect cost is $4,940,000 divided by 24,700,000 miles, or $397.96.
Overall price equals direct and indirect costs, or $375 plus $397.96, or $772.96.
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Somebody can help me with this?
We can conclude after answering the presented question that x = $2.00 equation (price of a queso pizza rebanada) y = $1.25 (price of a pie and championes pizza rebanada)
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or readings of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the calculation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
The two variables are the price of a rebanada de pizza de queso and the price of a rebanada de pizza de pia y championes.
It is x the price of a rebanada de pizza de queso and y the price of a rebanada de pizza de pia y championes.
We have the following equation system:
3x + 4y + 12.50 = 12.50 (costo de las 7 rebanadas de pizza) (costo de las 7 rebanadas de pizza)
3x + 2y = 8.50 (costo de las 5 rebanadas de pizza que no incluyen el tool) (costo de las 5 rebanadas de pizza que no incluyen el tool)
When we solve the equation system, we get:
x = $2.00 (price of a queso pizza rebanada) y = $1.25 (price of a pie and championes pizza rebanada)
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©2023 Edmentum All rights reserved, (-2,2) (3,-1) (4,2) (4, -2) the coordinates of D' if polygon ABCD rotates 90° counterclockwise to create A'B'C'D' the coordinates of C" if polygon ABCD rotates 90° clockwise to create A"B"C"D" the coordinates of A" if X polygon ABCD rotates 180° clockwise to create ABCD the coordinates of B" if X polygon ABCD rotates 270° counterclockwise to create A"B"C"D" last two i got wrong info from here....showing in pictures
The coordinates after each rotation are given as follows:
D' after a 90º counterclockwise rotation: (-2,2).C' after a 90º clockwise rotation: (3,-1).B' after a 270º clockwise rotation: (4,2).A' after a 180º rotation: (4,-2).What are the rotation rules?The function rule for the five more known rotation rules are given as follows:
90° clockwise rotation: (x,y) -> (y,-x)90° counterclockwise rotation: (x,y) -> (-y,x)180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y)270° clockwise rotation: (x,y) -> (-y,x)270° counterclockwise rotation: (x,y) -> (y,-x).More can be learned about rotation rules at brainly.com/question/17042921
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For a negatively skewed distribution, the mean is the smallest of the three measures of central tendency because it is
being pulled down by the small observations or possible outliers.
Answer options
True
False
It is a false statement that for a negatively skewed distribution, the mean is the smallest of the three measures of central tendency because it is being pulled down by the small observations or possible outliers.
Why is the statement about the mean false?For a negatively skewed distribution, the mean is typically pulled towards the tail of the distribution with smaller values, but this does not necessarily mean that it is always the smallest of the three measures of central tendency.
The mode is the measure of central tendency that occurs most frequently in a dataset, and it may be smaller or larger than the mean depending on the shape of the distribution. The median is the middle value in a dataset, and it may also be smaller or larger than the mean depending on the shape of the distribution.
Therefore, the statement "For a negatively skewed distribution, the mean is the smallest of the three measures of central tendency" is not always true.
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Riley is going to invest $74,000 and leave it in an account for 10 years. Assuming the interest is compounded daily, what interest rate, to the nearest tenth of a percent, would be required in order for Riley to end up with $102,000?
For the interest is compounded daily, the interest rate required for for Riley to make the amount $102,000 is 32.85%.
Explain about the daily compounding?Compound interest is computed as interest on the whole of the initial investment or loan amount plus any prior interest. Compound interest grows a sum more quickly than simple interest because it creates "interest on interest".
Compounding builds interest on a loan's outstanding principle as well as any interest that was accrued but not paid during the preceding compounding period. Compound interest can cause loan levels to increase, which can occasionally put debtors in danger.
The formula for the daily compounding:
A = P [tex](1 + r/n)^{nt}[/tex]
A is the amount after compounding = $102,000
P is the principal = $74,000
t is the time = 10 years.
r is the rate of interest
n is the number of time compounded = 365 days.
Put the values:
102,000 = 74,000 [tex](1 + r/365)^{365*10}[/tex]
102,000/74,000 = [tex](1 + r/365)^{3650}[/tex]
1.37 = [tex](1 + r/365)^{3650}[/tex]
[tex]1.37^{1/3650}[/tex] = [tex](1 + r/365)[/tex]
1.00009 = [tex](1 + r/365)[/tex]
1.00009 - 1.0 = r/365
0.0009 = r/365
r = 0.0009*365
r = 0.3285
r = 32.85%
Thus, for the interest is compounded daily, the interest rate required for for Riley to make the amount $102,000 is 32.85%.
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What is the equation in point-slope form of a line that passes through the points (7, 8) and (-4, 6)?
y-6=-14(x+4)
y-6= (x+4)
y+6=(x-4)
y+6=-11(x− 4)
Therefore , the solution of the given problem of equation comes out to be (7, 8) and (-4, 6).(x - 7).
Explain equation.Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this case, leveling generates b + 7 rather than another algorithm that could analyze data provided by y + 7, split 12 into two parts, and create y + 7.
Here,
We must first determine the line's inclination. The slope calculation, which is as follows:
=> m = (y2 - y1) / (x2 - x1)
where the coordinates for the two locations are (x1, y1) and (x2, y2).
We have the following using the locations (7, 8) and (-4, 6):
=> m = (6 - 8) / (-4 - 7) = -2 / (-11) = 2/11
=> y - y1 = m(x - x1)
Let's pick point (7, 8) on the line as our starting place. Next, by replacing m with 2/11 and (x1, y1) with (7, 8), we obtain:
=> y - 8 = (2/11)(x - 7)
=> y - 8 = (2/11)x - (14/11)
=> y = (2/11)x + (74/11)
Thus, y - 8 = (2/11) is the equation of the point-slope line passing through the locations (7, 8) and (-4, 6).(x - 7).
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Triangle is reflected across the y-axis and then dilated by a factor of 1/2 centered at the origin. Which statement correctly describes the resulting image, triangle ? Image of right triangle ABC in a graph with vertices A (minus 4, minus 2), B (4, minus 2), and C (4, 4) A. Both the reflection and dilation preserve the side lengths and angles of triangle . B. Neither the reflection nor the dilation preserves the side lengths and angles of triangle . C. The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths. D. The dilation preserves the side lengths and angles of triangle . The reflection does not preserve side lengths and angles.
The dilatiοn preserves the side lengths and angles οf triangle. The reflectiοn dοes nοt preserve side lengths and angles.
What Is dilatiοn?A geοmetrical adjustment that changes an οbject's size is dilatiοn. In mοre detail, dilatiοn entails extending οr cοntracting an item by increasing each pοint's distance frοm a fixed center pοint by a predetermined amοunt, knοwn as the scale factοr.
Let's start by applying the reflectiοn alοng the y-axis. All οf the vertices will have their x-cοοrdinates negated as a result, but their y-cοοrdinates will remain unchanged.
After reflectiοn, pοint A (-4, -2) will appear as A'. (4, -2). In the same way, B (-4, -2) will becοme B' (-4, -2), and C (4, -4) will change intο C'. (-4, 4).
Applying a dilatatiοn by a factοr οf 1/2 with the οrigin as the center will cοme next. This will result in a halving οf all distances frοm the οrigin.
After dilatiοn, pοint A' (4, -2)'s image will be A'' (2, -1), B' (-4, -2) will change tο B'' (-2, -1), and C' (-4, -4) will becοme C''. (-2, 2).
We must cοmpare the distances between the triangle's vertices and the angles' measurements in the οriginal triangle and the image tο see if the side lengths and angles are preserved.
The distance between pοints A and B is 8, but the distance between A'' and B'' is 4, as we can see. Similarly, the separatiοn between B and C is 6, whereas between B'' and C'' is 3. The dilatiοn dοes nοt preserve the triangle's side lengths as a result.
Nevertheless, it is clear that the angles between the sides were kept because the transfοrmatiοn invοlved bοth a reflectiοn and a dilatatiοn, bοth οf which prοtect angles.
Therefοre the cοrrect οptiοn is D. The dilatiοn preserves the side lengths and angles οf the triangle, while the reflectiοn dοes nοt preserve side lengths and angles.
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Find the distance between the two equations (see photo)
Answer:
z^138 and z^×2183 is the answer
Find
Midpoint
Slop
Distance
Line equation
Answer:
Step-by-step explanation:
midpoint [tex]=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2})[/tex]
[tex]=(\frac{3+7}{2} ,\frac{1+5}{2})[/tex]
[tex]=(5,3)[/tex]
slope [tex]=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]=\frac{5-1}{7-3}[/tex]
[tex]=\frac{4}{4}[/tex]
[tex]=1[/tex]
distance [tex]=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]=\sqrt{(7-3)^2+(5-1)^2}[/tex]
[tex]=\sqrt{4^2+4^2}[/tex]
[tex]=\sqrt{16+16}[/tex]
[tex]=\sqrt{32}[/tex]
[tex]=\sqrt{16\times2}[/tex]
[tex]=4\sqrt{2}[/tex]
Line equation:
[tex]y-y_1=m(x-x_1)[/tex] (this is the point- gradient form)
[tex]y-1=1(x-3)[/tex] (m=1 is slope, and I used point (3,1) for [tex](x_1,y_1)[/tex] )
[tex]y-1=x-3[/tex]
[tex]y=x-2[/tex]
OV is a radius of circle O. VW is tangent to circle O at point V, VW = 8, and OW = 10.
What is the length of OV?
A 2
B 6
C 16
D 36
classify each polygon by its number of sides then label it as convex or concave.
Hexagon - concave, Quadrilateral - Convex, Decagon - concave, Dodecagon - concave.
What is polygon?
A polygon is a 2-dimensional closed shape made up of straight line segments. It is a flat shape with three or more straight sides and angles.
A polygon is a closed plane figure with straight sides, defined by three or more line segments that meet at points called vertices. The sides of a polygon do not cross each other, and the angles between adjacent sides are called interior angles.
The classification of polygons is based on the number of sides they have. For example, a polygon with three sides is called a triangle, a polygon with four sides is called a quadrilateral, and so on.
Polygons can also be classified as either convex or concave. A convex polygon has all its interior angles less than 180 degrees, meaning that all its corners point outwards. In contrast, a concave polygon has one or more interior angles greater than 180 degrees, which means that at least one of its corners points inwards.
The classification of a polygon by its number of sides and whether it is convex or concave can help us to identify and describe its properties and characteristics.
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Bikini hot is putting all of its swimsuits on sale during the month of January a suit that regularly sells for $42 cost $33.60 in January what is the discount rate for the suit
Answer:
Step-by-step explanation: You start by subtracting the original price from the new price.
Which is $42 from $33.60
$42-$33.60=$8.40
So $8.40 is your discount rate.
What is the surface area of the cylinder with height 6 m and radius 4 m? Round your answer to the nearest thousandth.
Step-by-step explanation:
Right cylinder
Solve for surface area
A≈251.33m²
r Radius
4
m
h Height
6
m
Solution
A=2πrh+2πr2=2·π·4·6+2·π·42≈251.32741m²
Answer:
I think 251.33m² is your answer
Step-by-step explanation:
Life is full of equation solving. You probably don't even realize when you are solving equations.
Take, for instance, your cell phone plan. Your cell phone carrier charges you a flat rate of $60 a month for unlimited talk/text and 4 GB of data. You are charged $5 for every GB you go over. If one month you use 7 GB, how much did you spend? Thought question: If this pattern continues, should you think about switching to the 10 GB plan for $80?
You spent $75 for the month when you used 7 GB of data. It would be worthwhile to upgrade to the 10 GB plan for $80 if you frequently exceed the 4 GB cap.
What is flat rate?No matter how much of a good or service is used or consumed, a flat rate is a set amount that is charged. There are no extra fees or variable expenses; there is just one price that includes all related costs and fees. Utility bills, subscription services, and other recurring costs are frequently priced using flat rates. While they offer a predictable cost and can make budgeting and financial planning easier, they might be beneficial for clients who utilise a high volume of the product or service.
Given that, you are charged $5 for every GB you go over.
Here,
Extra data used = 7 GB - 4 GB = 3 GB
Cost of extra data = 3 GB x $5/GB = $15
Thus,
Total cost = $60 + $15 = $75
Hence, you spent $75 for the month when you used 7 GB of data.
It would be worthwhile to upgrade to the 10 GB plan for $80 if you frequently exceed the 4 GB cap. To decide which plan would be more affordable in the long run, you would need to evaluate the expenses of the two options and take into account your average monthly data use.
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If t=22, what is √t+14
The expression √t+14 will be equal to 6.
What exactly are expressions?
In computer programming, an expression is a combination of one or more constants, variables, operators, and functions that are interpreted and evaluated by the computer to produce a value.
Expressions can be simple, such as a single variable or constant, or they can be more complex, involving multiple operators and functions.
For example, in the expression "2 + 3 * 4", the operators "+" and "*" are used to perform arithmetic operations, and the constants "2", "3", and "4" are operands that are used in those operations.
Now,
If t=22, then
√t+14 = √(22+14) = √36 = 6
Therefore,
the value of expression √t+14 is 6.
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50 Points, need help ASAP, Mathematics
1) The statement is true
2) The statement is true
3) No because names have equal probability of being picked
4) This is an unbiased sample
What is sampling bias?Sampling bias is a type of bias that occurs when a sample selected for a study or survey is not representative of the population being studied. This can lead to results that are not accurate or generalizable to the population as a whole.
Sampling bias can arise from various factors, such as the method used to select the sample, the size of the sample, and the characteristics of the individuals who participate in the study or survey.
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100 POINTS PLEASEE HELP BRAINLIEST
The characteristic that is representative of a FUSION reaction is: B. The reaction happens predominantly in stars, like our sun.
What is reaction?A reaction is a process that involves the transformation of one or more substances into new substances with different physical and/or chemical properties. Reactions can be classified as either physical or chemical depending on the nature of the change that occurs. In a physical reaction, the identity of the substances remains the same, but their physical properties, such as size, shape, or phase, may change. Examples of physical reactions include melting, freezing, boiling, and condensation.
Here,
Fusion reactions involve the joining together of two atomic nuclei to form a heavier nucleus, releasing a large amount of energy in the process. These reactions occur naturally in stars, including our sun, where the high temperatures and pressures allow the atomic nuclei to overcome their mutual repulsion and come close enough to fuse. While scientists are working on developing fusion reactors for use on Earth, the technology is still in the experimental stage and is not yet cost-effective for widespread use. However, fusion reactions do not produce long-lasting radioactive waste as in the case of nuclear fission reactions.
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Find the equation of the line that has a slope of -8 and a y-intercept of 2.
Answer: y= -8x +2
Step-by-step explanation:
y = mx + b
M is the slope
B is the y intercept
Consider the line y = 5x - 3 Find the equation of the line that is parallel to this line and passes through the point (- 8, 2) Find the equation of the line that is perpendicular to this line and passes through the point (- 8, 2) Note that the ALEKS graphing calculator may be helpful in checking your answer
Answer:
First, we know the slopes of perpendicular lines are negative reciprocals of each other. So, the negative reciprocal of -1 is 1. This is the slope of our new line. From here, we can use this new slope along with our given point to find the y-intercept (b) of our new equation:
y = mx + b
-4 = 1(-2) + b
-4 = -2 + b
-2 = b
The y-intercept of our new line is (0,-2). Now, we can write our equation of the new line:
y = x - 2
Solve using the table shown
Using the values in the table, we can see that the summation is equal ot -0.65
How to find the summation?Here we want to find the summation:
[tex]\Sigma [x*P(x)][/tex]
This is equivalent to a expected value, where we take the summations of the outcomes times the probability of each one.
So we take the value of x, and we multiply it by the value of P(x) that is in the same row and then we add all of these.
To do so, we just need to replace the values of the table, we will get:
[tex]\Sigma [x*P(x)] = -1*0.999 + 349*0.001\\ = -0.65[/tex]
That is the expected value.
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2. Kaden has 105 tickets to give away. He
gives 5 tickets to each person who asks
for tickets. He records the number of
tickets he has left by subtracting 5 from
the previous total. How many times can
Kaden give away 5 tickets?
A. 110
B. 100
C. 21
D. 15
Answer: C. 21
Step-by-step explanation:
= 105/5
= 21
Answer:
c
Step-by-step explanation:
105/5
=21
so the answer is 21
Please help i’m not smart
five positive consecutive integers starting with a have an arithmetic mean of b. what is the arithmetic mean of 5 consecutive integers that start with b? (a) a 3 (b) a 4 (c) a 5 (d) a 6 (e) a 7
the arithmetic mean of the five consecutive integers starting with "b" is (a+4), which is option (c).
Let's call the five consecutive integers starting with "a" as a, a+1, a+2, a+3, and a+4.
The arithmetic mean of these five integers can be calculated as (a + (a+1) + (a+2) + (a+3) + (a+4))/5 = b. Simplifying this expression, we get:
5a + 10 = 5b +
a + 2 = b
So, the arithmetic mean of the five consecutive integers starting with "b" would be:
(b + (b+1) + (b+2) + (b+3) + (b+4))/5
= (5b + 10)/5 (since the integers are consecutive, we can express them in terms of b)
= b + 2
Substituting b = a + 2 (from the above equation), we get:
b + 2 = a + 4
Therefore, the arithmetic mean of the five consecutive integers starting with "b" is (a+4), which is option (c).
In other words, if the arithmetic mean of five consecutive integers starting with "a" is "b", then the arithmetic mean of five consecutive integers starting with "b" is two more than the last integer of the five consecutive integers starting with "a".
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This figure is made up of a rectangle and parallelogram. What is the area of this figure? Enter your answer in the box. Do not round any side lengths. units² Coordinate plane with axes labeled x and y. A closed figure is formed by a parallelogram and rectangle. The vertices are negative 10 comma 2, negative 7 comma 3, negative 1 comma 3, 1 comma negative 3, negative 2 comma negative 4, and negative 4 comma 2.
Answer:
To find the area of the figure, we need to find the area of the rectangle and the area of the parallelogram, and then add them together.
First, we need to identify which sides of the figure belong to the rectangle and which sides belong to the parallelogram. Looking at the coordinates of the vertices, we can see that the vertices (-10,2), (-7,3), (-1,3), and (1,-3) form a parallelogram, while the vertices (-7,3), (-2,-4), and (-4,2) form a rectangle.
To find the area of the parallelogram, we can use the formula:
Area = base × height
where the base is the length of one of the sides of the parallelogram, and the height is the perpendicular distance between the base and the opposite side. We can choose any side of the parallelogram as the base, but it is usually easiest to choose the side that is perpendicular to the x-axis, since its length is simply the difference between the x-coordinates of the two endpoints.
Using the coordinates (-10,2) and (-7,3) as the endpoints of the base, we find that the length of the base is:
|-7 - (-10)| = 3
To find the height, we need to find the perpendicular distance between the base and the opposite side of the parallelogram. We can do this by drawing a vertical line from one endpoint of the base to the opposite side, and then measuring the length of this line. We can see that the line from (-10,2) to (-1,3) is perpendicular to the base, so its length is the height of the parallelogram:
|-1 - (-10)| = 9
Therefore, the area of the parallelogram is:
Area = base × height = 3 × 9 = 27
To find the area of the rectangle, we simply need to multiply the length and width of the rectangle. We can see that the length is the distance between (-7,3) and (-4,2):
|-4 - (-7)| = 3
and the width is the distance between (-7,3) and (-2,-4):
|(-2) - (-7)| = 5
Therefore, the area of the rectangle is:
Area = length × width = 3 × 5 = 15
Finally, we can find the area of the whole figure by adding the area of the rectangle and the area of the parallelogram:
Area of figure = Area of rectangle + Area of parallelogram
= 15 + 27
= 42
Therefore, the area of the figure is 42 square units.
Need to know what it is
Answer: There is no solution to the equation.
The probability of a number cube landing on 5 is 1/6. If a number cube is tossed 72 times, how many times can it be expected to land on 5?
We can expect the number cube to land on 5 about 12 times if it is tossed 72 times.