What is called angle?.
When two rays intersect an angle is created, As different classification of angles are there on the basis of measurement of angles and on the basis of properties of angles.
What is definition of term "Angle" ?When two rays or straight lines intersect at one of their ends, an angle is created. Vertex of an angle refers to the point at which two points meet. The Latin word "angulus," which means "corner," is the origin of the English term "angle."
Symbol of Angle
The symbol ∠ represents an angle. Angles are measured in the form of degrees (°) using a protractor.
For example, 45 degrees is represented as 45°
Sections of Angles
A vertex is also the corner of an angle or at the place where two lines or sides come together to intersect at the point. In the above figure, O is the vertex.Arms: The angle's two sides which are connected at a single terminal. An angle's OA and OB are its arms.Initial Side: Also known to as the reference line, this is the first side of the angle that is to be drawn. The reference line is called OB.Terminal Side: The side that the angle measured is performed up to. OA is the terminal side.Types of Angles
Based on their measurements, here are the many types of angles:
An acute angle that measures less than 90° at the vertex of the lines.An obtuse angle measured between 90° to 180°.A right angle is exactly measures 90° at the vertex.An angle measuring precisely 180° is called a straight angle.A reflex angle is measured between 180°- 360°.A complete angle is measured is equal 360°.Interior and Exterior Angles:
Interior angles: Interior Angles are angle formed inside the shape.
Exterior angles: Exterior angles are to be angles that is formed outside a shape, between any side of shape and to an extended adjacent side.
Complementary and Supplementary Angles:
Complementary angles: Angles that add up to 90° (a right angle) are called complementary angles.
Supplementary angles: Angles that add up to 180° (a straight angle) are called supplementary angles.
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How do you tell if the leading coefficient of a graph is positive or negative?.
it is negative or positive depending upon the sign of the coefficients associated with the variable x
How do you define leading coefficient?
In a polynomial function, the leading term is the term containing the highest power of x. The coefficient of the leading term is called the leading coefficient.
it is negative or positive depending upon the sign of the coefficients associated with the variable x
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Given the equation of a circle, identify the center and the radius by completing the square.
x² + y² - 32x+24y +396 = 0
Center:
Radius:
The center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.
The equation of the circle is given as x² + y² - 32x+24y +396 = 0.
Comparing the given equation with general equation of circle, x² + y² + 2gx + 2fy + c = 0.
The center of circle is C = (-g, -f)
The radius of circle is r = √g² + f² - c
Therefore, from the given equation,
2g = -32
g = -16
2f = 24
f = 12
C( -16, 12)
And the radius is
r = √(-16)² + (12)² - 396
= √256 + 144 -396
=√4
= 2
Hence, the center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.
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The function f(x) is a cubie function and a limited table of values is provided below. Write the equation of the cubic polynomial in standard form.
The required cubic polynomial is
f(x) = [tex]-2x^3-2x^2-28x+48[/tex]
What is a polynomial?
An algebraic expression of the form [tex]a_0 + a_1x+ .... + a_nx^n[/tex] ([tex]a_0 \neq 0[/tex]) is called a polynomial of degree n.
The zeroes of the cubic polynomial are -4, 2, 3
Let the cubic polynomial is
f(x) = a(x - (-4))(x - 2)(x - 3)
f(x) = a(x + 4)(x - 2)(x - 3)
If x = -5, f(x) = 112
112 = a(-5 + 4) (-5 - 2)(-5 - 3)
112 = -56a
a = [tex]-\frac{112}{56}[/tex]
a = -2
f(x) = -2(x+ 4)(x - 2)(x - 3)
[tex]f(x) = -2(x+ 4)(x^2 -3x -2x +6)\\f(x) = -2(x + 4)(x^2 - 5x + 6)\\f(x) = -2(x^3 - 5x^2+4x^2+6x - 20x+24)\\f(x) = -2(x^3 - x^2 - 14x +24)\\f(x) = -2x^3 -2x^2 - 28x + 48[/tex]
(x +4)(x - 2)(x - 3)
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A student-faculty government committee of 4 people is to be formed from 16 student volunteers and 5 faculty volunteers. Find the probability that the committee will consist of the following, assuming the selection is made at random: (a) All faculty members. Round your answer to five decimal places. The probability that the committee will consist of all faculty members is (b) Two students and two faculty members.Round your answer to five decimal places. The probability that the committee will consist of two students and two faculty members is (c) All students. Round your answer to five decimal places. The probability that the committee will consist of all students is (d) One faculty member and three students. Round your answer to five decimal places. The probability that the committee will consist of one faculty member and three students is
16 student volunteers and 5 faculty volunteers will make up the four-person student-faculty government committee. the probability of the likelihood that the following members will be on the committee:
A) All academic staff
Probability is equal to 5C4 / 21C4 or 5/5985.
The likelihood that the committee will be made up of only academics is 0.000835.
b) Two pupils and two professors equal (16C2 x 5C2) / 21C4.
There is a 0.40100 chance that the committee will be made up of two students and two faculty members.
b) All pupils = 16C4 / 21C4 = 1820 / 5985
The likelihood that every student will be represented on the committee is 0.30409
d) Three students and one professor equal 5c1 * 16c3 / 21c4 or 5 * 560 / 5985.
There is a 0.46783 percent chance that the committee will be made up of one professor member and three students.
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What would probably happen if you try to make bread without using year?
Answer:
Your dough may not rise as tall as you're used to, and you may also notice differences in flavor and texture.
Step-by-step explanation:
If your question was without using yeast.
Answer:
The bread won't rise if you don't add yeast to the dough, which helps makes it thick. Starting with a tiny amount, the bread expands as it is kneaded and allowed to rise. Therefore, the only difference you would see if you used less than the advised quantity, let's say half as much, is that the bread rises considerably more slowly and not as much.
Triangle abc is an isosceles triangle in which side ab = ac. What is the perimeter of triangle abc? 5 + units 10 + units units 50 units.
The perimeter of triangle abc = 10+√10 unit where the triangle is an isosceles triangle.
What is meant by perimeter?A perimeter is a closed path that surrounds or covers a two-dimensional shape or length.The perimeter of a circle or an ellipse is its circumference. Calculating the perimeter has a variety of practical applications.
A shape's perimeter is the length of its outline. To get the perimeter of a rectangle or square, sum the lengths of all four sides. In this situation, x is the rectangle's length, and y is its width.
Length of ac = 3-(-2) = 5 unit
ab=ac
ab = 5 unit
By Pythagorean theorem
bc²=3²+1² =10
bc=√10 unit =3.16 unit
Perimeter of triangle abc=ab + ac +bc = 5 + 5 + √10
= 10+√10 unit
Therefore, Perimeter of triangle abc = 10+√10 unit
Hence, The perimeter of triangle abc = 10+√10 unit where the triangle is an isosceles triangle.
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How do you tell if a polynomial graph is positive or negative?.
If the leading coefficient is positive, bigger inputs only make the leading term more and more positive
How do you tell if a graph has a positive or negative coefficient?
If the leading coefficient is positive, bigger inputs only make the leading term more and more positive. The graph will rise to the right. If the leading coefficient is negative, bigger inputs only make the leading term more and more negative. The graph will descend to the right.
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Create a list of 6 one digit whole numbers with an average of 5, a median of 6, a range of 9, and no mode.
A list of 6 one digit whole numbers with an average of 5, a median of 6, a range of 9, and no mode is
0, 1, 5, 7, 8, and 9How to create the listsince the numbers will have no mode so they are all different
Assuming the numbers are: a, b. c. d. e. and f
The average is 5
(a + b + c + d + e + f ) / 6 = 5
a + b + c + d + e + f = 30
The median is 6
(c + d)/2 = 6
c + d = 12 (assume c = 5 and d = 7)
range is 9
f - a = 9, since it is a one digit number a range of 9 is possible for 9 - 0
hence a = 0 and f = 9
substituting assumed values to the average
0 + b + 5 + 7 + e + 9 = 30
b + e + 21 = 30
b + e = 9 (let b = 8and e = 1)
hence the numbers are
0, 1, 5, 7, 8, and 9
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The distribution of ages of licensed drivers shopping at the Kalish County Mall is normally distributed with mean 41 and standard deviation 7. A person will be selected at random. Round your answers to the nearest hundredth. What is the probability that the person is age 48 or older?
The probability that the person is age 48 or older is; 0.16
How to calculate probability from z-score?
The formula for z-score of a normal distribution is;
z = (x' - μ)/σ
where;
x' is sample mean
μ is population mean
σ is standard deviation
We are given;
σ; standard deviation = 7
μ; population mean = 41
The probability that the person is age 48 or older is expressed as;
P(X ≥ 48); z = (48 - 41)/7
z = 1
From online p-value from z-score calculator, we have;
p-value = 0.158655
Approximating to the nearest hundredth = 0.16
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the regression sum of squares (ssr) can be greater than the total sum of squares (sst). group of answer choices true false
The given statement is False . That is regression sum of squares (ssr) can be greater than the total sum of squares (sst).
Regression sum of squares (ssr)
The sum of squares regression is the sum of the differences between the predicted value and the mean of the dependent variable.
SSR = ∑( yᵢ-cap - y-bar)² and i = 1 to N
Total Sum of Squares (SST) :
Total Sum of Squares is the deviation of the value of the dependent variable from the sample mean of the dependent variable. Essentially, the total sum of squares quantifies the total sample variation. It can be found using the formula:
SST = ∑(yᵢ - y-bar )²
The first is that the regression sum of squares cannot be computed as a total sum of squares. Let's find an explanation for this. We know that the sum of squares can be divided. There's the dualism of squares, some of the squares and regressions, sums of squares, dead food. A regression sum of squares is not formed, it is a total sum of squares. This means the statement is false. The next processing is the value, which is always positive, but we know that the value the confession of the adjustment, in the range -1 to 1.
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bryon collects data on the depth of a river at various points and the velocity of the river at these points. his data have a correlation coefficient of -0.9382.
The scatterplot that represents Bryson's data is the scatterplot that is downward sloping.(Check the graph attached)
What is negative correlation?
Correlation is a statistical measure used to measure the relationship that exists between two variables.Negative correlation means that the two variables move in opposite directions. If one variable increases, the other variable decreases. When there is a negative correlation, the graph of the variables is downward sloping.A link between two variables known as "negative correlation" occurs when one variable rises measure as the other falls, and vice versa. In statistics, -1.0 denotes a perfect negative correlation, 0 denotes no connection, and +1.0 denotes a perfect positive correlation. The relationship between two variables is always absolutely opposite when there is a perfect negative correlation.To know more about negative correlation check the below link:
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If an average of 39 customers are served per hour, what is the probability that the next customer will arrive in 3 minutes or less?
The probability that the next customer will arrive in 3 minutes or less is 6.0286.
What is the Poisson distribution?
The Poisson distribution is a discrete probability distribution in probability theory and statistics that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and regardless of the time since the last event.
This is a Poisson distribution formula:
P(X > t) = e^(-λt)
Where,
λ is the arrival rate
t is the arrival time
λ = 39/60
t = 3 minutes
We want to find the probability that the next customer will arrive in 3 minutes or less. This is expressed as;
P (X ≤ 3) = 1 - (P(X > 3))
so,
P (X ≤ 3) = 1 - e^((39/60) × 3)
P (X ≤ 3) = 1 - 7.0286
P (X ≤ 3) = 6.0286
hence, the probability that the next customer will arrive in 3 minutes or less is 6.0286.
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An ANOVA procedure is applied to data obtained from 6 sample where each sample contains 20 observations. The degrees of freedom for the critical value of F are 6 numerator and 20 denominator degree of freedom. 5 numerator and 20 denominator degree of freedom. 5 numerator and 114 denominator degree of freedom. 6 numerator and 20 denominator degree of freedom
The degree of freedom for the numerator is 5 and the degree of freedom for the denominator is 114.
What is Analysis of variance (ANOVA)?Analysis of variance (ANOVA) is a type of statistical test used to determine if there is a statistically significant difference among two or more categorical groups by testing for differences of means using variance. An ANOVA test is used to analyze the differences between group means in a sample.
In this case, the number of groups, k is the number of distinct groups = 6
The total number of samples, N = number of groups x number of samples per each group
Thus, N = 6 x 20 = 120
Degree of freedom (df):
df within = df of numerator = k – 1 = 6 – 1 = 5
df between = df of denominator = N – k = 120 – 6 = 114
Hence, the required degrees of freedom are 5 numerator and 114 denominator.
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In a survey of randomly selected students, 8 out of every 10 students said they use their phones to play games. If there are 820 students at
Jamison Middle School, how many students can be expected to play games on their phones?
Answer:
656
Step-by-step explanation:
820/10 to get 1/10 of 820 (82)
Multiply by 8 to get 656
A confidence interval is made from a __________ to estimate the truth for a ______________.
To determine the accuracy of a "population parameter," a "sample statistic" is used to create a confidence interval.
Define the word confidence interval?Although they are connected, confidence level and confidence interval are not the same thing.
A wide range of values that are bound by the statistic's mean and that are likely to include an unidentified population parameter. The proportion of probability, or surety, that perhaps the confidence interval might include the real population parameter when a random sample is drawn numerous times is referred to as the confidence level. We are 99% confident (confidence level) that the majority of all these observations (confidence intervals) include the genuine population parameter, to use colloquial language. The researchers come at an upper and lower limit that 95% of the time contain the true mean by creating a 95% confidence interval that use the sample's median and standard deviation and adopting a normal distribution represented by the bell curve.Thus, to evaluate the accuracy of a "population parameter," a "sample statistic" is used to create a confidence interval.
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Can someone translate this photo it’s Russian
Giving 30 points
If not an appropriate answer
Report
Thankyou :D
The words in the image is translated from Russian language to English language as "Don't you really think you can learn something for yourself? - Ilya. She spoke with that goal that she hated in herself, i don't believe it. For example, here Vekshina! Exactly, I don't know"
Translating Russian to EnglishTo translate this paragraph to English, if you're not a native Russian speaker or fully understand the language to read and write, we can easily apply an online free tool for this type of text. This tool can translate texts as well as words in an image.
Using that here, the paragraph can roughly be translated as
"Don't you really think you can learn something for yourself? - Ilya. She spoke with that goal that she hated in herself, i don't believe it. For example, here Vekshina! Exactly, I don't know"
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6. MODELING REAL LIFE The Navajo rug is made of
isosceles triangles. You know ZB = ZD. Use.
the SAS Congruence Theorem to prove that
AABC=ACDE.
A
B
D
E
By using SAS congruence theorem we have proved that ΔABC≅ΔCDE.
What is meant by SAS(Side-Angle-Side)?Two triangles are congruent if any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle included between the sides of the second triangle.
Triangle SAS-Congruence
Example: AB= PQ, AC=PR, and the angle between AC and AB equals the angle between PR and PQ, i.e. A = P.
That is specifically stated in the SAS rule. When two sides and the included angle of one triangle equal two sides and the included angle of another, the triangles are congruent. An included angle is one that is formed by the intersection of two given sides.
In the illustration,
∠B≅∠D
By using SAS congruence,
If the two triangles are congruent then their sides are equal.
Therefore,
[tex]\bar{AB}[/tex]=[tex]\bar{CD}[/tex]
And [tex]\bar{AC}[/tex]=[tex]\bar{CE}[/tex]
[tex]\bar{BC}[/tex]=[tex]\bar{DE}[/tex]
ΔABC≅ΔCDE
Hence, Δ ABC ≅ Δ PQR.
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suppose that ab is the diameter of a circle with center o and that c is a point on one of the two arcs joining a and b. show that and are orthogonal.
For the circle , AC and CB are orthogonal
According to the question ,
AB is the diameter of a circle with center O and the C is a point on one
of the two arcs joining A and B
Let AO = -u and OB = u and CO = v
To prove that AC and AB is orthogonal .
We have to show their dot product is zero i.e. CA . CB = 0
=> CO + CA = -u
=> CA = -v -u
=> CO + CB = -v
=> CB = -v + u
So, the dot product,
CA . CB = (-v -u ) . ( -v +u)
=> v .v + u . v - v . u - u .u
=> |v|² +u . v - u . v - |u|²
=> |v|² - |u|² = 0
Hence , the length of v is same as the length of u
Therefore , AC and AB are orthogonal
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1. Select all the correlation coefficients that indicate that an increase in one variable
results in a decrease in the other.
A. r=-0.9894
B. r=-0.5776
C.r=0.2361
D. T= 0.4429
E. r= 0.9919
The correlation coefficients that indicate that an increase in one variable results in a decrease in the other;
B. r=-0.5776
C.r=0.2361
What is correlation coefficient and how to interpret it?Correlation coefficient is a measure of how similar two datasets are acting.
When the correlation coefficient comes out as -1, it means that both the datasets are negatively oppositely correlated. One data increases, other data starts decreases in the opposite direction.
When the correlation coefficient comes out below 0, then values are negatively correlated. SO,
All of the given option are negatively correlated.
If the correlation coefficient comes out as 0, that means both the data sets are uncorrelated.
Therefore, the correlation coefficients that indicate that an increase in one variable results in a decrease in the other;
B. r=-0.5776
C.r=0.2361
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Select the graph that correctly displays the solution of the system of inequalities.
y> 2x²+x-3
y<-x² + 5x
A graph that correctly displays the solution of the system of inequalities is graph D.
What are the rules for writing an inequality?In Mathematics, there are two (2) main rules that are generally used for writing and interpreting an inequality plotted on a graph and these include the following:
The line on a graph should be a dashed (dotted) line when the inequality symbol is (> or <).The line on a graph should be a solid line when the inequality symbol is (≥ or ≤).Additionally, the y-value for these system of inequalities intersects the x-axis at 5 and the boundary line is dashed (dotted) and shaded above to indicate that the boundary is not part of the solution, and this must be represented with the greater than (>) inequality symbol.
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Answer:
should be that graph, picture below!
Step-by-step explanation:
taking test!
What is the double plus 1 number sentence?.
The doubles Plus 1 is a strategy to learn addition and subtraction faster and make it easy to do.
we know that adding the same number twice is easier than adding two different numbers
like: 8+8 = 16 this is easier to remember and do
8+9 = 17 here we might make mistakes
so if we use the double plus one strategy to solve 8+9
we write it as 8+9 = (8+8)+1 = 16+1 = 17
hence this makes is easier for us to understand and do it faster.
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A 16,000-gallon pool is being filled at a rate of 50 gallons per minute. At this rate, how many minutes will it take to fill this pool 3\4 full?
The amount of time it will take 16000 gallons to fill the pool 3/4 full is 320 minutes.
What is time?Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.
To calculate the amount of time it takes to fill 3/4 of the pool , we use the formula below.
Formula:
R = g/t............. Equation 1Where:
R = Rate at which the pool is being fiiledg = Gallons required to fill 3/4 of the poolt = TimeFrom the question,
Given:
g = (16000)×3/4 = 12000 gallonsR = 50 gallons per minuteSubstitute these values into equation 1 and solve for t
50 = 16000/tt = 16000/50t = 320 minutesHence, the time it will take is to fill the pool 3/4 full 320 minutes.
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g a fair coin is flipped n times and the results recorded. how many different sequences of heads and tails are possible?
The probability of heads and tail on coin flipped can be determined using Pascal's Triangle
Probability for flipping coin can be determined using Pascal's Triangle, here's how it's works:
1st level of Pascal's Triangle is 1, it means only 1 possibility when the coin not flipped
2nd level of Pascal's Triangle is 1 1, it means there's 2 possibility when the coin flipped 1 times, 1 heads and 1 tail
3rd level of Pascal's Triangle is 1 2 1, it means there's 3 possibility when the coin flipped 2 times, 2 heads (1 probability), 1 head 1 tail (2 probability), and 2 tails (1 probability)
4th level of Pascal's Triangle is 1 3 3 1, it means there's 4 possibility when the coin flipped 3 times, 3 heads (1 probability), 2 heads 1 tail (3 probability), 1 head 2 tails (3 probability) and 3 tails (1 probability)
And the list will go on depends how many the coins flipped
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Peter estimates that it takes him 1/4 hours to prepare dough, 1/10 hours to grate cheese, 1/3 of an hour to prepare toppings, and 2/5 an hour to bake the pizza.
What fraction of time did it take peter in total to prepare the pizza?
What was the actual time it took in minutes and hours?
Answer:
13/12 hours or 1 hour and 5 minutes--------------------------------
Add up all fractions to get total time to prepare the pizza1/4 + 1/10 + 1/3 + 2/5 = Common denominator is LCM(3,4,5,10) = 6015/60 + 6/60 + 20/60 + 24/60 = 65/60 hours = (13/12 hours simplified fraction)65 minutes =1 hour and 5 minutesAnswer:
13/12 hours
1 hour 5 minutes
Step-by-step explanation:
Given timings:
1/4 hours to prepare dough.1/10 hours to grate cheese.1/3 of an hour to prepare toppings.2/5 if an hour to bake the pizza.To find the total time it took Peter to prepare the pizza, sum the fractions.
[tex]\implies \dfrac{1}{4}+\dfrac{1}{10}+\dfrac{1}{3}+\dfrac{2}{5}[/tex]
[tex]\implies \dfrac{1 \cdot 15}{4\cdot 15}+\dfrac{1\cdot 6}{10\cdot 6}+\dfrac{1 \cdot 20}{3\cdot 20}+\dfrac{2 \cdot 12}{5\cdot 12}[/tex]
[tex]\implies \dfrac{15}{60}+\dfrac{6}{60}+\dfrac{20}{60}+\dfrac{24}{60}[/tex]
[tex]\implies \dfrac{15+6+20+24}{60}[/tex]
[tex]\implies \dfrac{65}{60}[/tex]
[tex]\implies \dfrac{13 \cdot 5}{12 \cdot 5}[/tex]
[tex]\implies \dfrac{13}{12}[/tex]
Therefore, it took Peter 13/12 hours to prepare the pizza.
Convert hours into minutes by multiplying the hours by 60:
[tex]\implies \dfrac{13}{12} \cdot 60=\dfrac{780}{12}=65\; \sf minutes[/tex]
As 60 minutes = 1 hour, then:
⇒ 65 minutes = 1 hour and 5 minutes.
Therefore, the actual time it took for Peter to prepare the pizza is 1 hour and 5 minutes.
Find the number of elements inA_1 ∪ A_2 ∪ A_3if there are 100 elements in each set and if a) the sets are pairwise disjoint. b) there are 50 common elements in each pair of sets and no elements in all three sets. c) there are 50 common elements in each pair of sets and 25 elements in all three sets. d) the sets are equal.
a) Number of elements in the union of all three sets when the sets are pairwise disjoint is 300
b) Number of elements in the union of all three sets when there are 50 common elements in each pair of sets and no elements in all three sets is 150
c) Number of elements in the union of all three sets when there are 50 common elements in each pair of sets and 25 elements in all three sets is 175
d) Number of elements in the union of all three sets when the sets are equal is 100
What do you mean by relation and function?
(INPUT, OUTPUT) is a representation of an ordered pair.
The relationship between INPUT and OUTPUT is demonstrated by the relation. A function, on the other hand, is a relation that yields one OUTPUT for each given INPUT. Although all relations are functions, not all functions are relations. A function is a relationship that states that there should only be one output for each input, or we could refer to it as a particular category of relationship (a collection of ordered pairs) that adheres to a rule.
Given are three distinct sets, A1, A2, and A3, each with 100 members. The number of elements in the uninon set, A1 U A2 U A3, are as follows, according to the circumstances.
First off, if we remember the formula, it will be really simple to determine how many components make up the union set;
n(A1 U A2 U A3) = n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 ),
a) This states that we dont have any common elemets in any pair of these sets,
n( A1 ∩ A2 ) = 0, n( A2 ∩ A3 ) = 0 , n( A1 ∩ A3 ) = 0 and also n( A1 ∩ A2 ∩ A3 ) = 0 and as given n( A1 ) = n( A2 ) = n( A3 ) = 100 .
Hence the no of elements in the union set A1 U A2 U A3 will be
n(A1 U A2 U A3)
= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )
= 100 + 100 + 100 - 0 - 0 - 0 + 0
= 300
b) We have
n( A1 ) = n( A2 ) = n( A3 ) = 100
n( A1 ∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = 50 and n( A1 ∩ A2 ∩ A3 ) = 0 .
Hence the no of elements in the union set A1 U A2 U A3 will be
n(A1 U A2 U A3)
= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )
= 100 + 100 + 100 - 50 - 50 - 50 + 0
= 150
c) We have
n( A1 ) = n( A2 ) = n( A3 ) = 100
n( A1 ∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = 50 and
n( A1 ∩ A2 ∩ A3 ) = 25 .
Hence the no of elements in the union set A1 U A2 U A3 will be
n(A1 U A2 U A3)
= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )
= 100 + 100 + 100 - 50 - 50 - 50 + 25
= 175
d) This states that all the common elemets are present in the three sets, so
n( A1 ) = n( A2 ) = n( A3 ) = 100 as well as n( A1∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = n( A1 ∩ A2 ∩ A3 ) = 100
Hence the no of elements in the unino set A1 U A2 U A3 will be
n(A1 U A2 U A3)
= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )
= 100 + 100 + 100 - 100 - 100 - 100 + 100
= 100
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Using the following set of data (the same as in the previous problem), find the sample standard deviation: 12,7,6,4, 11 Select the correct answer below. O 3.4 O 6.4 O 9.4 O 8.4 O 5.4
The sample standard deviation of 12,7,6,4 and 11 will be 3.4.
According to the question,
We have the following set of data:
12,7,6,4 and 11
Now, we know that the following formula is used to find the sample standard deviation for a set of data:
Sample standard deviation = [tex]\sqrt[]{\frac{sum of (xi - mean)^{2} }{n-1} }[/tex]
whereas n is the number of data set and xi is the different numbers of the data set
Number of scores in data set = 5
So, we have the mean:
(12+7+6+4+11)/5
40/5
8
Now, subtracting each number from the mean:
12-8 = 4
7-8 = -1
6-8 = -2
4-8 = -4
11-8 = 3
Now, we will square these numbers:
4*4 = 16
-1*-1 = 1
-2*-2 = 4
-4*-4 = 16
3*3 = 9
Now, we have the following step for sample standard deviation:
(16+1+4+16+9)/(5-1)
46/4
11.5
Now, the square root of this number will be final answer:
[tex]\sqrt{11.5}[/tex]
3.4
Hence, the correct option is A.
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Eighty percent of seniors at the local high school graduate each year. If there are 750 seniors this year, how many will graduate?.
By calculating the percentage of seniors that graduate each year, it can be concluded that this year 600 seniors will graduate.
It is given to us that -
Eighty percent of seniors at the local high school graduate each year
There are in total 750 seniors this year
We have to find out the number of seniors who will graduate.
Since it is mentioned that Eighty percent of seniors at the local high school graduate each year and there are in total 750 seniors this year, then the number of seniors who will graduate this year will be equal to -
80% of 750
= (80/100) * 750
= 600
Therefore by calculating the percentage of seniors that graduate each year, it can be concluded that this year 600 seniors will graduate.
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what is 3 3/4 - 2 1/5 as a mixed number
Answer:
1 11/20
Step-by-step explanation:
3 3/4 - 2 1/5 = 3 15/20 - 2 4/20 = 1 11/20
a pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length h ft is to be built. if fencing costs $5/ft for the legs and $10>ft for the hypotenuse, write the total cost c of construction as a function of h.
The total cost "C" for the construction as a function of h is C = 5h/√2 + 10h .
In the question ,
it is given that ,
the shape of the triangle is = isosceles triangle
length of the legs of the triangle = x ft ,
length of the hypotnuse of the triangle = f ft ,
the cost of fencing for legs = $5 per feet ,
the cost of fencing for hypotnuse = $0 per feet .
The pen is in shape of an isosceles right angle. This means one of angle is 90 degrees and 2 sides of triangle are equal and base angles are equal too.
So , By Pythagoras Theorem ,
x² [tex]+[/tex] x² [tex]=[/tex] h²
2x² = h²
x² = h² / 2
x = √h²/ √2 = h/√2
the cost will be written as ,
Cost = 5×(x) + 10×(h)
Cost = 5×(h/√2) + 10h
C = 5h/√2 + 10h
Therefore , The cost function is C = 5h/√2 + 10h .
The given question is incomplete , the complete question is
A pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length h ft is to be built. if fencing costs $5/ft for the legs and $10/ft for the hypotenuse, write the total cost c of construction as a function of h.
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