Symmetry is a way of measuring the shape of a data set. It is defined as the similarity between the upper and lower halves of a distribution.
A symmetric distribution is one where the data is equally distributed around a central point. To calculate this, you need to subtract the mean (the average of the values) from each data point and then divide by the standard deviation (the measure of how much the data is spread out). The formula for symmetry is: (x-mean)/standard deviation. An example of a symmetric distribution would be the scores of a group of students on an easy test. If the mean score was 70 and the standard deviation was 10, then any score between 60 and 80 would be considered symmetric.
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in a room of 60 people. whts the probability that there exist people that share the same birthday? assuming no one was born on feb 29?
The probability that there exists people who share the same birthday is 0.995.
Considering that all the 365 days are equally likely to be the birthday of a person and all the events that a person has birthday on 'y' are independent of others.
Under the said assumptions, let's say that there are n number of people in the room. If we number the people from 1 to n, then the total number of possibilities of birthdays are (365)^n.
Therefore, the possible combinations that all birthdays are different:
365 * 364 * 363 * .... * (365- n+1)
Thus, the probability that all birthdays are different is:
[tex]\frac{365* 364 * 363* .... (365- n+1)}{365^n}[/tex]
To get the probability of at least two people sharing the same birthday is,
[tex]1- \frac{365* 364 * 363* .... (365- n+1)}{365^n}[/tex]
= 1 - 0.0058
= 0.9942
=0.995
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The table shows the change in the annual sales turnover of a company in millions of dollars, S(x), where x represents the years since the company was founded. X 1 3 5 7 9 S(x) $495 $598. 95 $724. 73 $876. 92 $1,061. 08 What is the predicted average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11]? A. $111. 42 per year B. $184. 15 per year C. $92. 08 per year D. $222. 83 per year
The predicted average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11] is $92.08 per year.
To find the predicted average rate of change of the company's sales turnover over the interval [9, 11], we need to find the slope of the line that best fits the data points provided.
The slope of the line can be calculated using the formula:
(change in y) / (change in x) = (S(x2) - S(x1)) / (x2 - x1)
We can use any two of the provided data points to find the slope. Using the data points (9, $1,061.08) and (7, $876.92), we get:
(change in y) / (change in x) = ($1,061.08 - $876.92) / (9 - 7) = $184.15 / 2 = $92.08 per year
This is the average rate of change of the company's sales turnover over the interval [9, 11]. So the answer is C. $92.08 per year.
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Awnse choice cAnswer:
Step-by-step explanation:
Copy the problem, and write a Statement/Reason proof.
The problem is given as follows:
Prove: ΔLUZ ≅ ΔIDA
The triangles above can be said to be congruent because:
[tex]\overline{ZL}[/tex] ≅ [tex]\overline{AI}[/tex] (Corresponding sides)
[tex]\overline{LU}[/tex]≅ [tex]\overline{DI}[/tex] (Corresponding sides)
[tex]\overline{UZ}[/tex] ≅ [tex]\overline{AD}[/tex] (Corresponding sides)
It is also given that:
m ∠ ULZ ≅ m ∠ ADI
since
[tex]\overline{ZL}[/tex] ≅ [tex]\overline{AI}[/tex] (Corresponding sides)
[tex]\overline{LU}[/tex]≅ [tex]\overline{DI}[/tex] (Corresponding sides) and
m ∠ ULZ ≅ m ∠ ADI ;
We can thus conclude that the ΔLUZ ≅ ΔIDA
What is the meaning of congruent triangles?When two triangles are congruent, one can be moved (through one or more stiff movements) to coincide with the other. All congruent sides and angles will be found.
The triangles are congruent if two sides and the included angle of one triangle are congruent to the corresponding sections of another triangle. [Side - Angle - Side]
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What is the answer for 2 x 2 x 11 in exponential?
Answer: Your answer would be 2x ⋅ (2x) ⋅ 11
Step-by-step explanation: I hope this helps!
PLEASE HELP??!!
What is the end behavior of the function f(z)
2c2
1?
O As approaches infinity, f(r) approaches negative infinity. As I approaches
negative infinity, f(x) approaches infinity.
O As I approaches infinity, f(x) approaches infinity. As approaches negative
infinity, f(x) approaches negative infinity.
As I approaches infinity, f(x) approaches negative infinity. As I approaches
negative infinity, f(x) approaches negative infinity.
As I
approaches infinity. f(a) approaches infinity. As 2 approaches negative infinity, f(x) approaches infinity.
Answer:
d
Step-by-step explanation:
It would help me soooo much if you could solve these two
Answer:
8) 27.75
10) See down below. May be 1.83 OR 123.75, depending on what your problem says
Step-by-step explanation:
Problem 8)
Let's first take apart [tex]2^{3}[/tex], which will be 8. Now, let's plug that back into the equation real quick:
12 + (8 ÷ [tex]\frac{2}{3}[/tex]) + 3.75
Since dividing a fraction can also be equal to multiplying the reciprocal of that same fraction, ÷ [tex]\frac{2}{3}[/tex] can be re-written as: * [tex]\frac{3}{2}[/tex]
Let's put that into the equation now and solve:
12 + (8 * [tex]\frac{3}{2}[/tex]) + 3.75
= 12 + 12 + 3.75
= 27.75
Problem 10) (I'm unsure if the sign after 80 is ÷ or +, but I'll do equations for both)
(If the sign after 80 is ÷, check these steps on how to solve):
Same methods as problem 8. Let's first break down [tex]4^{2}[/tex], which will be 16. Then, let's set the ÷ [tex]\frac{2}{5}[/tex] to * [tex]\frac{5}{2}[/tex] and solve:
80 ÷ (16 * [tex]\frac{5}{2}[/tex]) + 3.75
= 80 ÷ (40) + 3.75
= [tex]\frac{80}{40+3.75}[/tex]
= 1.82857
(If the sign after 80 is +, check these steps):
80 + (16 * [tex]\frac{5}{2}[/tex]) + 3.75
= 123.75
what is 5/8Y + 7 = 3/4Y - 3
Answer:
y = 1/80
Step-by-step explanation:
[tex] \sf\frac {5}{8y} + 7 = \frac{3}{4y}- 3[/tex]
Substract 7 from both sides
[tex] \sf\frac {5}{8y} + 7 - 7 = \frac{3}{4y}- 3 - 7[/tex]
Calculate
[tex] \sf\frac {5}{8y} = \frac{3}{4y}-10[/tex]
Substract 3/4y from both sides
[tex] \sf\frac {5}{8y} - \frac{3}{4y} = \frac{3}{4y} - \frac{3}{4y} -10[/tex]
Calculate
[tex] \sf\frac {5}{8y} -\frac{3}{4y}= -10[/tex]
L.C.M = 32y²
[tex] \sf \frac{−4y}{ {32y}^{2} } = -10[/tex]
-4y/32y² Divide further
[tex] \sf \frac{ - 4}{ 32y } = -10[/tex]
Divide further
[tex] \sf \frac{ - 1}{ 8y } = -10[/tex]
Cross - multiply
[tex] \sf \: 8y \times - 10 = - 1[/tex]
Multiply
[tex] \sf \: - 80y = - 1[/tex]
Divide both sides by -80y
[tex] \sf \: \frac{ - 80y}{ - 80} = - \frac{ - 1}{ - 80} [/tex]
Calculate
[tex] \sf \: y = \frac{1}{80} [/tex]
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what is an appropriate way to visualize a list of the eye colors of 120 people? select all that apply.
The appropriate way to visualize a list of the eye colors of 120 people is pie chart and dot plot.
A pie chart is a circular statistical graphic in which the slices represent numerical proportions. In a pie chart, the arc length of each slice reflects the amount it stands for.
Pie charts can be used to show percentages of a whole group and show percentages at a particular moment. In contrast to bar graphs and line graphs, pie charts do not show changes over time.
A dot plot, also known as a strip plot or dot chart, is a simple style of data visualization in which data points are shown as dots on a graph with an x- and y-axis.
The things you and your partner choose to eat are a wonderful example.
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The following question may be like this:
What is an appropriate way to visualize a list of the eye colors of 120 people? select all that apply.
pie chart box plotscatter plotdot plot.emmanuel weighs 150 pounds. about how many hours will it take him to metabolize one standard drink?
Emmanuel weighs 150 pounds. about 2 hours will it take him to metabolize one standard drink
Every hour, the body processes one normal drink. If you have 5 standard drinks, your body will take 5 hours to absorb the alcohol.
In general, the liver can digest one ounce of liquor (or one standard drink) in one hour. If you consume more than this amount of alcohol, your system will get saturated, and the excess alcohol will accumulate in your blood and physiological tissues until it can be metabolized.
It takes your liver around an hour to break down the amount of alcohol in a standard alcoholic drink (one beer, one glass of wine, or one shot).
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Evaluate the expression.
4×(7×5)
=
Answer:
4x(7x5) = 4x(35)
To evaluate the expression, we must first perform the operations inside the parentheses. In this case, 7x5 = 35. Then we can multiply 4 with that result, which gives us 4x35 = 140. So the final value of the expression is 140.
Answer: 140
Step-by-step explanation:
4 x (7 x 5)
7 x 5 = 35
4 x 35
= 140
need the answer asap ! thank you to anyone who helps <3 !
Answer:
B
Step-by-step explanation:
What you're seeing is a (x,y,z) plane.
At this point, it's just plug and play.
Looking at choice B....
(1) + (2) + (2)(3) = 1 + 2 + 6 which is indeed 9
(2)(1) + (2)(2) + 3(3) = 2 + 4 + 9 which is indeed 15
(1) + (-3) = 1 - 3 which is indeed -2
Help!!
I’m really bad at this
For Figure 2, Triangles are congruent by SSS (side side side).
What is a triangle?
In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.
Based on the sides of a triangle, a triangle is classified into 3 types, namely:
Scalene Triangle – All the sides are of different measures.
Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
Equilateral Triangle – All the 3 sides of a triangle are of the same measure.
Based on the angles of a triangle, a triangle is classified into 3 types, namely:
Acute Angle Triangle – All the angles of a triangle is less than 90°.
Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.
Right Angle Triangle – One of the angles of a triangle is equal to 90°.
Now ,
As in given figure for triangles
2 sides of both are parallel and one is common for both
Hence,
These are congruent by SSS theorem.
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Please help I dont know where to start
the standard deviation of a simple random sample of 40 calling times on a payphone is found to be 2. 6 minutes. Find the test statistic to test a claim that the standard deviation of all phone calls on a payphone is less than 2. 9 minutes. Use a 0. 05 significance level
32. 152
31. 348
48. 519
34. 966
Here we have to compare a standard deviation of test statistic with the expected standard deviation of the population. So a chi square test is used. The chi square value got after the calculations is 31.348.
It is a hypothesis testing method. Significance level is 0.05.
The equation for chi square is
Χ² = (n-1)s²/ σ₀²
Lets look into what each term means
n is the sample size which is 40
s² is the sample variance = 2.6²
σ² is the population variance =2.9²
X² = (40-1)×2.6²/ 2.9²
= 39× 6.76/ 8.41
= 31.3483947681
= 31.348
So the X² value is 31.348
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How to find proportional parts in triangles and parallel lines?
If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally splits these two sides. If DE = BC, then ADDB=AEEC.
If a line parallel to one side of a triangle contacts the other two sides, the two sides are proportionately divided.
The formula for a proportional equation is y = kx. The letters y and x denote the variables in the equation. The letter k represents the proportionality constant, which is fixed.
Because matching angles produce the AA similarity shortcut, when a line is drawn parallel to one side of a triangle, two similar triangles are generated. Because the triangles are comparable, the parallel line segments are proportionate segments.
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A radar gun meaured the peed of a baeball at 5 mile per hour. If the baeball wa going 4.2 mile per hour, what wa the percent error in thi meaurement?
The percent error in this measurement would be 16%.
1. Calculate the difference between the measured speed and the actual speed: 5 mph - 4.2 mph = 0.8 mph
2. Calculate the percent error: (0.8 mph / 4.2 mph) x 100 = 19.05%
3. Round to the nearest whole number: 19.05% = 19%
The percent error in this measurement is 19%, which means that the measured speed was 19% higher than the actual speed.
This can be caused by a variety of factors, including the radar gun being set to an incorrect sensitivity, the speed of the ball being too high for the radar gun to accurately measure, or the radar gun not being able to accurately detect the speed of the ball due to environmental factors such as wind or lighting.
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If Ronald and his family drive 72 miles per hour (mph), how far do they travel in 1 hour
Answer:
72 miles
Step-by-step explanation:
its obvious
5,000 books in the town's library of this 4,600are fiction. To find the percent of the books that are fiction, first set up the percent equation. Then find the percent.
please answer this it is done in a few minutes
The set up percent equation is:
4600 = m . 5000
The percent of books that are fiction will be:
m = 92%.
Now, According to the question:
A relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
Number of books in the town's library = 5,000
Number of books that are fiction= 4,600
The set up percent equation is:
4600 = m . 5000
where, m is the books' fiction
The percent of books that are fiction will be:
m = 4600/5000 × 100
m = 92%.
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Solve m=n^2 for n
Pls I need it asap
Answer:
n = √m
Step-by-step explanation:
Now we have to,
→ find the required value of n.
The equation is,
→ m = n²
Then the value of n will be,
→ m = n²
→ n² = m
→ [ n = √m ]
Hence, the value of n is √m.
Help me pls it’s due tomorrow and pls have a explanation!!
Answer: 16/24
Step-by-step explanation: You should convert 7/8 and 2/3 to get a common denominator, in this situation the common denominator is 24. You multiply 2/3 by 8 on both sides of the fraction and the same with 7/8 except with 3. When you convert it 7/8 becomes 21/24 which is the total amount of grapes she bought, the amount she used comes out to be 16/24.
(01.03 MC)
What is the domain of the rational function f(x)=
x²+x-20 -?
X-4x²-9x+36
The domain of the rational function in this problem is given as follows:
All real values except x = -3, x = 3, x = 4.
How to obtain the domain of the function?The domain of a function is the set composed by all the input values that the function accepts.
The function in this problem is a fraction, meaning that the denominator cannot be zero.
The denominator is given as follows:
x³ - 4x² - 9x + 36.
The roots of the denominator are given as follows:
x = -3, x = 3, x = 4.
Hence the domain is all real values except those, meaning that the second option is the correct option.
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How do you solve this type of problem?
Answer:
(3x+4)+55°+85°=180°
(3x+4)+140°=180°
(3x+4)=180°-140°
(3x+4)=40°
3x+4=40
3x=40-4
3x=36
x=12
(3x+4)
(3×12)+4
=40°
The Nelson family drank 1/4 of a gallon of orange juice on Saturday morning and 2/5 of a gallon of orange juice on Sunday morning. How much orange juice did they drink in all?
Answer: 13/20
Step-by-step explanation: First to find the first part, we need to find a common denominator. So we must ask ourselves, which number is a multiple that both 5 and 4 have in common? The answer then would be 20. So, it would look like this:
[tex]\frac{1}{4} = \frac{?}{20}[/tex]
[tex]\frac{2}{5} = \frac{?}{20}[/tex]
So to find what "?" equals for both fractions, we must use this formula:
Amount = Right denominator / Left denominator (1st part)
So, now we do 20 / 5 and 20 / 4
20 / 5 = 4
20 / 4 = 5
So, the 2nd part is taking the quotient from that and multiplying it by the left numerators. This would look like this:
5 * 1 = 5
4 * 2 = 8
So your "?" should look like this:
[tex]\frac{1}{4} = \frac{5}{20}[/tex]
[tex]\frac{2}{5} = \frac{8}{20}[/tex]
Then, you'd just add! So, 8 + 5 = 13 and 20 + 20 would stay that same ; 20. So your result is [tex]\frac{13}{20}[/tex]
I hope this helped!
Both lines on the graph represent proportional relationships. What is the constant of proportionality for each line? Choose one option from each drop-down menu to answer the question. Line passes through the point Choose.. . The constant of proportionality between and for line is Chooss.. Choose.. The constant Line passes through the point of proportionality between and for line is Chooss.. pls help soon
Line a which passes (1, 4) has a constant of proportionality of 4.
Line b runs through (5, 2), with a constant of proportionality of 2/5.
What is the Constant of Proportionality?The constant of proportionality is often represented by the letter "k" and it is used in a mathematical relationship known as a proportionality relationship. The proportionality relationship can be written as y = kx, where y and x are the two variables and k is the constant of proportionality.
This means that the value of y is directly proportional to the value of x and is equal to k times the value of x. The value of k can be found by dividing the value of y by the value of x, when the two variables are in proportion.
Line a passes through the (1, 4), therefore:
constant of proportionality = y/x = 4/1 = 4.
Line b passes through the (5, 2), therefore:
constant of proportionality = y/x = 2/5.
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at the time of this writing 1 u.s. dollar is worth 1.28 canadian dollars. an automobile in toronto sells for 25,500 canadian dollars. the same car sells in detroit for 21,000 u.s. dollars. what is 25,500 canadian dollars equivalent to in u.s. dollars?
1.21 Canadian dollars is equivalent to 1 US dollar
What is 25,500 Canadian dollars equivalent to in US dollars?A monetary exchange rate, also known as a foreign exchange rate, is the rate at which one currency can be exchanged for another. Exchange rates are determined by the foreign exchange market and can fluctuate based on supply and demand.
Since an automobile in Toronto sells for 25,500 Canadian dollars and the same car sells in Detroit for 21,000 US dollars.
Thus, 25,500 Canadian dollars equivalent in US dollars will be:
25,500 Canadian dollar /21,000 US dollars = 1.21
Thus, 1.21 Canadian dollar is equivalent to 1 US dollar dollars
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If the price of gas increases by 5% again next week, will the price be 10% higher than it was
originally? Explain your reasoning.
If the price of gas increases by 5% again next week, then the price be approx 10% higher than it was originally because again shows that their is two times increment of 5%.
Let the price of gas is x.
The price of gas is increased by 5% in a week. So after increment the price of gas = x + x × 5%
After increment the price of gas = x + 5x/100
After increment the price of gas = (100x + 5x)/100
After increment the price of gas = 105x/100
After increment the price of gas = 1.05x
The gas price again increase by 5%.
Now the price of gas after again increment = 105x/100 × 105%
The price of gas after again increment = 105x/100 × 105/100
The price of gas after again increment = 11025x/10000
The price of gas after again increment = 1.1025x
Now we find the total increment in two weeks
Percent Increment = (1.1025x - x)/x × 100
Percent Increment = 0.1025x/x × 100
Percent Increment = 0.1025 × 100
Percent Increment = 10.25%
Then we can say that approx 10% the cost of oil increased then originally.
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Yusuf drove 156 miles in 3 hours. If he continued at the same rate, how far would he travel in 2 hours?
The distance travelled by Yusuf in 2 hours is 104 miles.
What is the distance travelled by Yusuf?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given that, Yusuf drove 156 miles in 3 hours.
We determine the speed of Yusuf.
Speed = Distance / time
Speed = 156 miles / 3 hours
Speed = 52 miles per hour
Now, the distance travelled in 2 hours will be;
Speed = Distance / time
Distance = Speed × time
Distance = 52 miles per hour × 2 hours
Distance = 104 miles.
Therefore, the distance covered is 104 miles.
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if JKLM is a parallelogram, what is m
m is the angle formed by the two parallelogram sides that are next to each other. Because all angles in a parallelogram are equal, m is equal to all other angles in the parallelogram.
What is a parallelogram?A parallelogram is a four-sided form having two parallel sides and four right angles on each side. Both sides are straight and opposite sides are equal in length. A parallelogram's opposing angles are also equal.
M is the angle subtended by the parallelogram JKLM. A parallelogram is a four-sided form with parallel and equal-length opposing sides. A parallelogram's angles are also equal in size. As a result, m is an angle of the parallelogram JKLM and is proportional to the other angles of the parallelogram JKLM.
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Your cousin is building a new house. The layout of the first floor is shown in the diagram above. Using the
diagram and knowledge of polynomials find the following:
1. Write a polynomial that represents the length of the north side of the house. Then simplify the
expression.
2. Write a polynomial expression that represents the area of the kitchen. Then multiply to put the
polynomial in standard form.
3. Write a polynomial expression that represents the area of the bedroom. Then multiply to put the
polynomial in standard form.
4. Find the dimensions of the bathroom in terms of x. (Hint the west and east side of the house
should be equal.)
The length of the north side of the house is 2x^2 + 9x - 32
The length of the north side of the house.From the question, we have the following parameters that can be used in our computation:
The figure
On the figure, we have
North side = 5x - 4 + x^2 - 23 + x^2 + 4x - 5
Evaluate
North side = 2x^2 + 9x - 32
The area of the kitchenHere, we have
Length = 2x + 1
Width = x^2 + 4x - 5
So, we have
Area = (2x + 1) * (x^2 + 4x - 5)
Area = 2x^3 + 8x^2 -10x + x^2 + 4x - 5
Area = 2x^3 + 9x^2 - 6x - 5
The area of the bedroomHere, we have
Length = 5x - 4
Width = 5x + 4
So, we have
Area = (5x - 4) * (5x + 4)
Area = 25x^2 - 16
Dimension of the bathroomFrom the figure, we have
Dimensjon = 5x - 4 by (2x + 1 + x + 6 - 5x - 4)
Dimensjon = 5x - 4 by - 2x + 3
Hence, the dimension of the bathroom is 5x - 4 by - 2x + 3
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A 4-kilogram bag of apples costs $8.80. What is the unit price?
Answer: 0.455
Step-by-step explanation:
I figured how to get $1? (The unit price?) so I did 4 divided by 8.8
Answer: The unit price is $2.20 per kilogram of apples
Step-by-step explanation:
Divide $8.80 with 4
8.80/4 = 2.20 per kilogram
If f(x) =-2x^2 +5 then find ( - 5)
Answer:
-45
Step-by-step explanation:
f(x) = -2x² + 5
f(-5) = -2(-5)² + 5
= -2(25) + 5
= -2 × 25 + 5
= -50 + 5
= -45