We can conclude that the number of defective products
To test the hypothesis that the number of defective products follows the binomial distribution, we need to calculate the expected frequency for each category and compare it with the observed frequency using the chi-square test.
First, let's calculate the expected frequency for each category:
E(0) = 200 * (0.95)^20 = 7.64
E(1) = 200 * 20 * (0.95)^19 * (0.05)^1 = 32.15
E(2) = 200 * 190 * (0.95)^18 * (0.05)^2 = 67.53
E(3) = 200 * 1140 * (0.95)^17 * (0.05)^3 = 90.71
E(4) = 200 * 4845 * (0.95)^16 * (0.05)^4 = 85.64
E(5) = 200 * 15504 * (0.95)^15 * (0.05)^5 = 61.29
E(6) = 200 * 38760 * (0.95)^14 * (0.05)^6 = 34.71
Next, we calculate the chi-square test statistic:
X^2 = (28-7.64)^2/7.64 + (44-32.15)^2/32.15 + (37-67.53)^2/67.53 + (48-90.71)^2/90.71 + (30-85.64)^2/85.64 + (9-61.29)^2/61.29 + (4-34.71)^2/34.71 = 84.31
Since we have 7 categories, the degrees of freedom for the chi-square distribution is 7-1=6. The critical value for alpha=1% and df=6 is 16.81. Since the test statistic is greater than the critical value, we reject the null hypothesis that the number of defective products follows the binomial distribution.
Therefore, we can conclude that the number of defective products does not follow the hypothesized distribution at alpha=1%.
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Select each expression that is equivalent to 3/16 if x = 3/4
I need an answer ASAP.
A. 2x+1/16
B.3/4 to the power of 2 - 6/16
D. x-1/4
E 2x-x2-3/4
Option (b) "3/4 to the power of 2 - 6/16" is the expression that is equivalent to 3/16.
What are expressions?A formula is a set of two or more numbers or variables and one or more mathematical operations. This mathematical operation is addition, subtraction, multiplication, or division. The formula has the following structure:
The expression is (number/variable, arithmetic operator, number/variable).
Solution according to the given information:
Given, x = 3/4
Option(a): 2x+1/16 = (2×3/4) +1/16
= 3/2 + 1/16
=25/16
Which is not equal to 3/16
Option(b): (3/4)² - 6/16 = 9/16 - 6/16 = 3/16
Which is equivalent to 3/16
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What is the standard equation of this ellipse: Vertices: (0,12)
(0,-12) Foci: (0,8) (0,-8). Why do I keep getting
(x^2)/80+(y^2)/144?
The standard equation of this ellipse is x²/144 + y²/80 = 1.
The standard equation of an ellipse is (x-h)²/a² + (y-k)²/b² = 1, where (h,k) is the center of the ellipse, a is the semi-major axis, and b is the semi-minor axis.
In this case, the center of the ellipse is (0,0) since the vertices and foci are both on the y-axis. The distance between the vertices is 24 (12 - (-12)), so the semi-major axis is 12. The distance between the foci is 16 (8 - (-8)), so the distance between the center and each focus is 8. Using the formula c² = a² - b², where c is the distance between the center and each focus, we can solve for b:
c² = a² - b²
8² = 12² - b²
64 = 144 - b²
b² = 80
So the equation of the ellipse is (x-0)²/12² + (y-0)²/80 = 1, or x²/144 + y²/80 = 1.
You keep getting (x²)/80 + (y²)/144 because you are switching the values of a and b. The semi-major axis should be in the denominator of the x term, and the semi-minor axis should be in the denominator of the y term.
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Two fire towers are located 5 miles apart on a straight road. They both spot the same fire on the north side of the road and report its location in terms of angles from the road. From the tower A, the fire is 22 degrees. From the tower B (5 miles east of tower A), the fire is 37 degree. How far from tower B is the point on the road closest to the fire? Please sketch and show the fire location. The point on the road closest to the fire will be on a line to the fire directly perpendicular to the road. Round to two decimal places
Tower B is 2.34 miles far from the point on the road closest to the fire.
The point on the road closest to the fire can be found by drawing a line perpendicular to the road that passes through the fire location. Let x be the distance from tower B to this point. Then, using trigonometry, we can find that the distance from tower A to the fire location is x/tan(22) and the distance from tower B to the fire location is (5 - x)/tan(37). Since the fire location is the same from both towers, these distances must be equal, so we can set up the equation x/tan(22) = (5 - x)/tan(37) and solve for x, which is approximately 2.34 miles.
To sketch the fire location, draw a straight road with two fire towers located 5 miles apart. From tower A, draw a line at an angle of 22 degrees towards the north side of the road to represent the direction of the fire location. From tower B, draw a line at an angle of 37 degrees towards the same side of the road. The point where these two lines intersect represents the location of the fire. Draw a line perpendicular to the road passing through this point to find the closest point on the road to the fire.
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#3 Write each in terms of sin x
a) cos²x
b) 3 sin²x - 4 cos²x
[tex]\boxed{sin^{2}x + cos^{2}x = 1}[/tex]
a) [tex]cos^{2}x = 1 - sin^{2}x[/tex]
b) [tex]3sin^{2}x - 4cos^{2}x = 3sin^{2}x - 4(1 - sin^{2}x) = \\[/tex]
[tex]= 3sin^{2}x - 4 + 4sin^{2}x = 7sin^{2}x - 4[/tex]
Which angle is formed by EA−→
and EG−→−?
Select all that apply.
Answer:
Step-by-step explanation:
[tex]\angle 2,\angle AEG, \angle GEB[/tex]
Sansa and Arya visited the Snack Shack during a baseball game. Sansa bought 2 candles and 1 licorice stick for $3.25. Arya bought 1 candy and 4 licorice sticks for $2.50.
What Is the cost for 1 of each of these Items?
The cοst fοr οne οf each item is:
Candle: $1.625
Licοrice stick: $0.975
Candy: $2.50
What is an equatiοn?In mathematics, an equatiοn is a statement that asserts the equality οf twο expressiοns, typically separated by an equals sign (=). The expressiοns οn either side οf the equals sign are called the left-hand side (LHS) and the right-hand side (RHS) οf the equatiοn.
Let's use variables tο represent the cοst οf each item. Let c be the cοst οf a candle and l be the cοst οf a licοrice stick, and let y be the cοst οf a candy.
Frοm the given infοrmatiοn, we can set up twο equatiοns tο represent the tοtal cοst fοr each persοn:
2c + l = 3.25 (Equatiοn 1)
y + 4l = 2.50 (Equatiοn 2)
We can then sοlve fοr each variable by using algebraic manipulatiοn.
Frοm Equatiοn 1, we can isοlate l by subtracting 2c frοm bοth sides:
l = 3.25 - 2c
We can substitute this expressiοn fοr l intο Equatiοn 2, and sοlve fοr y:
y + 4(3.25 - 2c) = 2.50
y + 13 - 8c = 2.50
y = 2.50 - 13 + 8c
y = 8c - 10.5
Nοw we can substitute the expressiοn fοr y and the expressiοn fοr l intο a single equatiοn tο sοlve fοr c:
2c + (8c - 10.5) = 3.25 + 2.5
10c - 10.5 = 5.75
10c = 16.25
c = 1.625
Sο a candle cοsts $1.625. We can use this value tο find the cοst οf a licοrice stick:
l = 3.25 - 2c
l = 3.25 - 2(1.625)
l = 0.975
Sο a licοrice stick cοsts $0.975. Finally, we can find the cοst οf a candy using the expressiοn we fοund earlier:
y = 8c - 10.5
y = 8(1.625) - 10.5
y = 2.5
Sο a candy cοsts $2.50.
Therefοre, the cοst fοr οne οf each item is:
Candle: $1.625
Licοrice stick: $0.975
Candy: $2.50
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What is the quotient of (−168) ÷ (−14) ÷ (−3)?
please help
Answer:
= -4
Step-by-step explanation:
To solve this expression, we need to perform the division in the correct order, following the rules of mathematical operations. We can simplify the expression as follows:
(-168) ÷ (-14) ÷ (-3) = (-168) ÷ [(-14) x (-3)] [dividing by a negative number is the same as multiplying by its reciprocal]
= (-168) ÷ 42
= -4
Therefore, the quotient of (-168) ÷ (-14) ÷ (-3) is -4.
Consider the system of linear equations
3x + y + z = 1
2x + y - 4z = 2
Which one of the following is not a solution to this system? A.(-1,4,0)
B. (-6, 18, 1)
C. (9,-24,-2)
D. (4,-10, -1)
E. (3/2, - 1/2, - 3)
The option E. (3/2, - 1/2, - 3) is not a solution to the system of linear equations.
The system of linear equations given is:
3x + y + z = 1
2x + y - 4z = 2
The answer that is not a solution to this system is option. To check this, we can substitute (3/2, - 1/2, - 3) into the system and solve:
3*(3/2) + (-1/2) + (-3) = 1
2*(3/2) + (-1/2) - 4*(-3) = 2
After simplifying, we get 9/2 - 1/2 + 9/2 ≠ 1 and 9 - 1 - 12 ≠ 2, so option E. (3/2, - 1/2, - 3) is not a solution to the system of linear equations.
A system of equations is a set of two or more equations in which we will find unknowns.
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What is the slope of the line that contains the points (2, -8) and (-4, 4)? PLAAA HEELLO MEEEEE
Answer:
-2
Step-by-step explanation:
[tex]m=\frac{4-(-8)}{-4-2} \\m=\frac{4+(+8)}{-4-2} \\m=\frac{12}{-6} \\m=\frac{2}{-1} \\m=-2[/tex]
An amusement park charges an admission fee of $40 dollars per person. The cost, C (in dollars), of admission for a group of p people is given by the following function.
What is the cost of admission for a group of 5 people?
The cost of admission for a group of 5 people is $200 dollars.
The cost of admission for a group of 5 people is given by the function C(p) = 40p, where p is the number of people in the group. To find the cost for a group of 5 people, we simply plug in 5 for p and solve for C:
C(5) = 40(5)
C(5) = 200
Therefore, the cost of admission for a group of 5 people is $200 dollars.
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Jill's gym class lasted 50 minutes. She walked around the school track for the first 15 minutes. Then, she played kickball for 25 minutes. She got to play on the playground for the rest of class. After kickball, how long did Jill get to play on the playground?
Jill played for 10 mins. 25+15=40 50-40=10
To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
The algebraic equation "4x = 22.2 - 1.9" could be used to find the price of one tire patch.
What is the algebraic equation?Mathematical equations with one or more variables and algebraic operations like addition, subtraction, multiplication, division, exponentiation, and roots are known as algebraic equations. By identifying the values of the unknown variables that fulfill the equation, these equations can be used to illustrate mathematical connections between variables and to solve issues.
Although algebraic equations can take many different forms, they often require utilizing the equal sign (=) to make one expression equal to another. For instance, the algebraic equation x + 2 = 7 shows the connection between the constants 2 and 7 and the unknown variable x.
The equation that could be used to find the price of one tire patch is:
4x = 22.2 - 1.9
This equation represents the total cost of the four tire patches (4x) subtracted from the initial balance on Rhyan's gift card ($22.20) and the remaining balance after the sale ($1.90).
Simplifying the equation, we get:
4x = 20.3
Dividing both sides by 4, we get:
x = 5.075
So the price of one tire patch is $5.075.
Therefore, the equation "4x = 22.2 - 1.9" could be used to find the price of one tire patch. None of the other equations listed would lead to the correct answer.
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Answer:
yo
Step-by-step explanation:
C and E
Madeline drew a triangle on her paper. Angle A of the triangle was 1/3 as big as angle B. Angle C was smaller than angle A. Which list can represent the angle measures in this triangle? A: 20,40,120 B: 30,60,90 C: 15,45,120 D: 25,40,120
Answer: A: 20,40,120
Step-by-step explanation:
Angle A is smaller than Angle B as it is less than 1 time as big as it.
The list of angles from smallest to largest is C, A, and B.
120 x (1/3) = 40
20 < 40
Hope this helps!
what is the frequency of each interval
81-100. ------2
1-20----------2
21-40---------4
41-60----------1
61-80----------1
Hamid wants to find out what people in Melworth think about the sports facilities in the town. Hamid plans to stand outside the Melworth sports centre one Monday morning. He plans to ask people going into the sports centre to complete a questionnaire. Carol tells Hamid that his survey will be biased. Give one reason why the survey will be biased.
Because it only covers those who are entering the sports centre, the survey will be prejudiced.
Why are surveys biased?This means that the survey will only reflect the opinions of those who are likely to have positive perceptions of the sports facilities and who are interested in using them. It does not include the viewpoints of those who do not use or hold a poor opinion of the sporting facilities.
Those who don't use the facilities, for instance, could have bad perceptions of the sports centre if it is renowned for being pricey or challenging to get to. The survey will miss important information if it simply polls visitors to the sports centre.
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A bag with 10 marbles has 3 blue marbles and 7 yellow marbles. A marble is chosen from the bag at random. What is the probability that it is red? Write your answer as a fraction in simplest form
The probability that the selected marble is red is 0
How to determine the probability that the marble is red?From the question, we have the following parameters that can be used in our computation:
Number of marbles = 10
Blue = 3
Yellow = 7
Using the above as a guide, we have the following:
P(Red) = Number of red/Number of marbles
Substitute the known values in the above equation, so, we have the following representation
P(Red) = 0/10
Evaluate
P(Red) = 0
Hence, the probability is 0
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Select the correct answer. A firework cracker weighing 1.5 kilograms, is launched at 15(m)/(s) by propelling chemicals from combustion at a speed of 55(m)/(s). What is the mass of the chemicals being propelled?
The mass of the chemicals being propelled is 0.41 kilograms.
The correct answer is: 0.41 kilograms.
To find the mass of the chemicals being propelled, we can use the formula for momentum:
momentum = mass x velocity
Since the momentum of the cracker before it is launched is zero, and the momentum after it is launched is the sum of the momentum of the cracker and the momentum of the chemicals, we can set up an equation:
0 = (1.5 kg)(15 m/s) + (mass of chemicals)(55 m/s)
Next, we can rearrange the equation to solve for the mass of the chemicals:
(mass of chemicals)(55 m/s) = -(1.5 kg)(15 m/s)
mass of chemicals = -(1.5 kg)(15 m/s) / (55 m/s)
mass of chemicals = -22.5 kg / 55 m/s
mass of chemicals = -0.41 kg
So the mass of the chemicals being propelled is 0.41 kilograms.
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The function f(x) contains the point (4, −10). Show all calculations steps and state the image
(the new location) of point under each of the following general transformations:
a. = ( + 2) − 3
b. − 1 = 2( − 4)
c. − 1/3 = (−2)
d. 2 = ((+2)/3)
(the new location) of point under each of the following general transformations are as follows:
a. Image: (3, -10)
b. Image: (-1, -10)
c. Image: (-4/3, -10)
d. Image: (14/3, -10)
What is general transformations?
A transformation is a procedure that involves either changing an object's orientation to create an image or expanding or reducing its size to create a new one.
We'll use the given point (4, -10) as the input for each transformation, and apply the transformation to find the new location of the point.
a. f(x) = (x + 2) - 3
f(4) = (4 + 2) - 3 = 3
Therefore, the new location of the point under the transformation f(x) = (x + 2) - 3 is (3, -10).
b. f(x) = 2(x - 4) - 1
f(4) = 2(4 - 4) - 1 = -1
Therefore, the new location of the point under the transformation f(x) = 2(x - 4) - 1 is (-1, -10).
c. f(x) = -1/3x
f(4) = -1/3(4) = -4/3
Therefore, the new location of the point under the transformation f(x) = -1/3x is (-4/3, -10).
d. f(x) = (2/3)x + 2
f(4) = (2/3)(4) + 2 = 8/3 + 2 = 14/3
Therefore, the new location of the point under the transformation f(x) = (2/3)x + 2 is (14/3, -10).
In each case, the image of the point is the new location after applying the transformation.
a. Image: (3, -10)
b. Image: (-1, -10)
c. Image: (-4/3, -10)
d. Image: (14/3, -10)
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7.1 Bellwork
1 of 31 of 3 Items
Question
Classify each polygon by the number of sides. Then say whether it is convex or concave, regular or not regular.
shape:
, convex or concave:
, regular or not regular:
.
The polygons are classified as :-
1.CONVEX
2.CONCAVE
3.CONCAVE
4.REGULAR
5.CONCAVE
6.IRREGULAR
What are polygons?A polygon is a geometrical figure, with finite sides and angles, they can be regular and irregular.
Regular Polygon
A regular polygon is that which has all its sides and angles equal, for example an equilateral triangle and a square.
Irregular Polygon
A irregular polygon is that which has all its sides and angles unequal,
For example, a scalene triangle, a rectangle, a kite, etc.
Convex Polygon
A Convex polygon is that which has all its angles less than 180 degrees,
Concave Polygon
A Concave polygon is that which has its angles greater than 180 degrees,
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The complete question attached
The game of Yahtzee is played with five fair dice. The goal is to roll certain hands', such as Yahtzee (all five dice showing the same number) or a full house (three of a kind and two of a kind). In the first round of a player's turn, the player rolls all five dice. Based on the outcome of that roll, the player has a second and third round, where he/she can then choose to re-roll any subset of the dice to get a desired hand. (a) What is the probability of rolling a Yahtzee on the first round? (b) Suppose that, on the second round, the dice are (2,3, 4,6,6). You decide to re-roll both sixes in the third round. What is the probability that you roll either a small straight or a large straight (a large straight is where all five dice are in a row)?
a) The probability of rolling a Yahtzee is 0.00077
b) The probability of rolling either a small straight or a large straight is 0.1389
Given data:
(a)
To calculate the probability of rolling a Yahtzee on the first round, we need to determine how many outcomes correspond to a Yahtzee and divide it by the total number of possible outcomes when rolling five dice.
A Yahtzee occurs when all five dice show the same number. There are 6 possible outcomes (each number from 1 to 6), and each outcome has only 1 way of occurring. So, there are 6 ways to roll a Yahtzee.
The total number of possible outcomes when rolling five dice is 6^5 (since each die has 6 sides).
Probability of rolling a Yahtzee = (Number of Yahtzee outcomes) / (Total number of outcomes)
[tex]= \frac{6} {6^5}[/tex]
≈ 0.00077 (rounded to 5 decimal places)
(b)
In the second round, you have (2, 3, 4, 6, 6). In the third round, you choose to re-roll both sixes.
A small straight is when you have four consecutive numbers among the dice (e.g., 1, 2, 3, 4, or 2, 3, 4, 5, or 3, 4, 5, 6).
There are three possible small straights: (2, 3, 4, 5), (3, 4, 5, 6), and (1, 2, 3, 4). Each of these outcomes has only one way of occurring.
A large straight is when all five dice are in a row (e.g., 1, 2, 3, 4, 5 or 2, 3, 4, 5, 6).
There are two possible large straights: (1, 2, 3, 4, 5) and (2, 3, 4, 5, 6). Each of these outcomes has only one way of occurring.
Total favorable outcomes (small straights + large straights) = 3 + 2 = 5
Total number of possible outcomes when re-rolling two dice = 6^2 = 36
Probability of rolling either a small straight or a large straight = (Number of favorable outcomes) / (Total number of outcomes)
[tex]=\frac{5}{36}[/tex]
≈ 0.1389 (rounded to 4 decimal places)
Hence, the probability that you roll either a small straight or a large straight after re-rolling the dice is approximately 0.1389.
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Solve the simultaneous equations by substitution
3x+5y=11
6x+5y=17
Answer:
hi
Step-by-step explanation:
this is the answer
hope this helps
good luck;)
James created a scale drawing of the school library in his art class. In the scale drawing, the length of the library is 13 inches. The length of the actual library is 78 feet. Which scale did James use to create the scale drawing of the school library?
The scale unit that James used to create scale drawing of school library is 1 inch = 6 feet.
What is scale unit?A measurement scale used to represent actual dimensions in a model or drawing. Scales include units of measurement such as inches, feet, and meters, scale unit. A scale used to represent actual dimensions on a drawing or map.
What is scale drawing?A scale map is a two-dimensional representation of a real-world object or place. Maps and floor plans are examples of scale drawings. The scale shows what the length on the scale drawing represents in actual length .
According to the question:
Given, 78 feet length of library is represented by 13 inch
Let, "x" be the number of feet that 1 inch represents.
∴ 13x = 78 feet
⇒x = 78/13
⇒x = 6
So, 1 inch equals 6 feet.
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Answer:
the answer would be 1 inch = 6 feet
Step-by-step explanation:
What is scale unit?
A measurement scale used to represent actual dimensions in a model or drawing. Scales include units of measurement such as inches, feet, and meters, scale unit. A scale used to represent actual dimensions on a drawing or map.
What is scale drawing?
A scale map is a two-dimensional representation of a real-world object or place. Maps and floor plans are examples of scale drawings. The scale shows what the length on the scale drawing represents in actual length .
Solution:
Given, 78 feet length of library is represented by 13 inch
Let, "x" be the number of feet that 1 inch represents.
∴ 13x = 78 feet
⇒x = 78/13
⇒x = 6
So, 1 inch equals 6 feet.
A cell phone plan charges $45.75 per month, plus $9.55 in taxes, plus $0.35 per
minute for calls beyond the 500-min monthly limit. Write a piecewise defined
function to model the monthly cost C(x) as a function of the number of minutes used
x for the month.
Answer: We can write the piecewise defined function for the monthly cost C(x) as follows:
C(x) =
45.75 - 9.55, if x ≤ 500
45.75 - 9.55 + 0.35(x - 500), if x > 500
Explanation:
For the first 500 minutes, the monthly cost is a flat rate of $45.75 for the plan fee and $9.55 for taxes, so the total cost is simply the sum of these two amounts: C(x) = 45.75 + 9.55 = 55.30, for x ≤ 500.
For any additional minutes beyond the 500-min limit, there is an additional charge of $0.35 per minute, so the cost increases linearly with the number of extra minutes used. The expression (x - 500) represents the number of minutes beyond the limit, so we multiply this by the rate of $0.35 per minute and add this amount to the base cost of $55.30, giving the piecewise expression:
C(x) =
55.30, if x ≤ 500
55.30 + 0.35(x - 500), if x > 500
Therefore, the piecewise defined function for the monthly cost C(x) is:
C(x) =
45.75 - 9.55, if x ≤ 500
45.75 - 9.55 + 0.35(x - 500), if x > 500
Note: The two expressions are equivalent, but the second expression is simplified by combining the constants.
Step-by-step explanation:
Simplify: 27 − 3 exponent 3 + 4 x 2 exponent 2 − 6.
Answer:
10
Step-by-step explanation:
27-[tex]3x^{3}[/tex]+(4 x [tex]2x^{2}[/tex]) - 6
= 27 - 27 + (4 x 4) - 6
= 0 + 16 - 6
= 10
Answer: 10
Step-by-step explanation:
27 - 3^3 + 4 × 2^2 - 6
= 27 - 27 + 4 × 4 - 6 (since 3^3 = 27 and 2^2 = 4)
= 0 + 16 - 6= 10
Therefore, the simplified value of the expression is 10.
Can someone help me write a proof for this
∆ABC = ∆BCD because they are congruent
What are congruent triangles?If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
AB is parallel to CD and AB is equal to CD,
Therefore AC = BD( opposite sides of a parallelogram are equal
therefore CB is common to both triangle
We can therefore say that all the corresponding three sides of the two triangles are equal
i.e AC = BD
AB = CD
CB = CB
therefore triangle ABC and BCD are congruent
This means ;
∆ABC = ∆BCD
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Apply Cramer's Rule to solve the system of equations, -- 3.79 +33 = 1 2-12 4.- 3.3 = 0 If it is not possible to use Cramer's rule, indicate that using the checkbox -1 IL 12 It is not possible to use C
It is not possible to use Cramer's Rule to solve the system of equations you provided. This is because Cramer's Rule can only be applied to systems of linear equations that have the same number of equations as there are unknowns.
In the system you provided, there are four equations but only two unknowns. This means that Cramer's Rule cannot be applied.
Instead, you can use other methods such as substitution or elimination to solve the system. However, it is important to note that with more equations than unknowns, it is possible that there may be no solution or an infinite number of solutions.
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Help me, please. Please provide a clear answer
Answer:
see explanation
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
4x + 21 + x - 10 + 2x + 8 = 180
7x + 19 = 180 ( subtract 19 from both sides )
7x = 161 ( divide both sides by 7 )
x = 23
Then angles in triangle are
4x + 21 = 4(23) + 21 = 92 + 21 = 113°
x - 10 = 23 - 10 = 13°
7x + 8 = 7(23) + 8 = 161 + 8 = 169°
the only 2 possible angle measures are A and E
Pls give simple working
Answer:
Step-by-step explanation:
f(x)=x^4−x^2+9
The diameter of a circle is 4 m. Find its area to the nearest whole number.
The table below gives approximate probabilities for scoring 0, 1, 2, 3, or 4 runs in one inning of Major League Baseball. (Although it is possible to score more than 4 runs in one inning, the probability is very small, so it is ignored in this question.) 3 P(x) | 0 0.74 10.12 20.07 30.04 4 0.03 Round solutions to three decimal places, if necessary. Compute the sum of these probabilities: EP(z) = Compute the mean number of runs per inning, using this probability distribution: Compute the standard deviation of this probability distribution:
The sum of these probabilities is 1, the mean number of runs per inning is 0.46, and the standard deviation of this probability distribution is 0.839.
The sum of these probabilities is simply the sum of the values in the table:
EP(x) = 0.74 + 0.12 + 0.07 + 0.04 + 0.03 = 1
The mean number of runs per inning can be calculated using the formula for the expected value of a discrete random variable:
E(x) = ∑xP(x) = (0)(0.74) + (1)(0.12) + (2)(0.07) + (3)(0.04) + (4)(0.03) = 0.46
The standard deviation of this probability distribution can be calculated using the formula for the standard deviation of a discrete random variable:
σ = √[∑(x - E(x))^2P(x)]
=> √[(0 - 0.46)^2(0.74) + (1 - 0.46)^2(0.12) + (2 - 0.46)^2(0.07) + (3 - 0.46)^2(0.04) + (4 - 0.46)^2(0.03)]
=> 0.839
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