The Probability of receiving 7 three times is 0.0025566, but the likelihood of getting 7 just once is 3.7528.
What is Probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or probability of several outcomes. Statistics is the study of events that follow a probability distribution.
The given question is related to the binomial distribution.
Given n = 10 trials. The probability of one successful trial is p = 1/8. You want k=3 successes and n − k = 7 failures. The probability is:
[tex](\frac{n}{k}) p^k (1-p)^{n-k}[/tex]
One way to understand this formula: You want k successes (probability: pk) and n−k failures (probability: (1−p)n−k). The successes can occur anywhere in the trials, and there are (n/k) to arrange k successes in n trials.
substituting the values in the given formula.
[tex](\frac{10}{3}) 1/8^3 (1-1/8)^{10-3}[/tex]
Probability of getting 7, 3 times = [tex](\frac{10}{3}) 1/8^3 (7/8)^7[/tex]
Probability of getting 7, 3 times = [tex](\frac{10}{3}) 1/216 (7/8)^7[/tex]
Probability of getting 7, 3 times = 0.0025566
The Same goes for the probability of getting 7 only one times
the probability of getting 7 only one time = [tex](\frac{10}{1}) 1/8^1 (1-1/8)^{10-1}[/tex]
the probability of getting 7 only one time = 3.7528
Therefore, The Probability of getting 7, 3 times is 0.0025566 and the probability of getting 7 only one time is 3.7528.
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The school marching band has a budget of up to $650.00 to cover 11 new uniforms
and competition fees that total $300.00.
Write an inequality to represent this situation.
The inequality to represent this situation is (11x+300)≤650
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
Here, given that,
The school marching band has a budget of up to $650.00 to cover 11 new uniforms.
and competition fees that total $300.00.
Let, the cost of each new uniform = $x
Then cost for 11 uniforms = $11x
i.e. total cost = $ (11x + 300)
hence, we get,
$(11x+300)≤$650
(11x+300)≤650
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Given: rstu is rsqp is prove: pq = ut the reason in line 2 of the proof would be "opposite sides of a parallelogram are equal. " true false.
The given statement opposite sides of a parallelogram are equal is true.
Proof,
We can see that RUTS is a parallelogram
here it is given that ,RU=TS and PQ = UT.
bringing the diagonal RT into scene we can see that,
∠URT = ∠STR
∠UTR=∠SRT
as these are the pairs of alternate angles.
RU || ST and PQ || UT
RT=TR , being the common side.
Therefore,
ΔRUT ≅ ΔTSR
by AAS theorem
Hence , we can say that PQ=UT matches the sides of congruent triangles.
Therefore proved that the opposite sides of a parallelogram are equal.
A triangle can be proved congruent by using SAS , ASA, RHS or SSS, AAA etc congruency rules.
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False. The reason in line 2 of the proof would be "opposite angles of a parallelogram are equal. "
Given: rstu is rsqp
To prove: pq = ut
1. Draw a parallelogram with vertices r,s,q,p
2. Since rstu is rsqp, opposite angles of the parallelogram are equal
3. Therefore, by the property of a parallelogram, opposite sides of the parallelogram are equal
4. Thus, pq = ut
The reason in line 2 of the proof is that opposite angles of a parallelogram are equal, not opposite sides, which is the reason given in line 3.
False. The reason in line 2 of the proof would be "opposite angles of a parallelogram are equal. "
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A nutritional company analyzed the amount of sugar in a chocolate cake in nine different bakeries in Toledo. The values in the list below represent the number of grams of sugar in a chocolate cake at each of these bakeries. 134, 108, 106, 119, 134, 107, 135, 87, 98 Based on the data above, what is the median number of grams of sugar in a chocolate cake at these bakeries?
Based on the data above, what is the median number of grams of sugar in a chocolate cake at these bakeries is equal to: A. 108.
What is a median?In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.
How to calculate the median number of grams?First of all, we would sort the number of grams from the least to greatest as follows:
87, 98, 106, 107, 108, 119, 134, 134, 135
Therefore, the median number of grams of sugar is equal to the middle number:
Median = 108.
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Complete Question:
A nutritional company analyzed the amount of sugar in a chocolate cake in nine different bakeries in Toledo. The values in the list below represent the number of grams of sugar in a chocolate cake at each of these bakeries. 134, 108, 106, 119, 134, 107, 135, 87, 98.
Based on the data above, what is the median number of grams of sugar in a chocolate cake at these bakeries?
108
110
111
114
134
Z
5.
x
с
Pentagon ABCDE is plotted on the grid below.
A
Part B
B
E
-10 -9 -8 7 6-54 -3
2
D
10
9
8
-7
6
-5
4
10
1
2
3
-4
S
-6
-7
-8
-9
-10
1
2 3 4 5
alt
ctri
6 7 8 9 10
Part A
On the grid, draw the translation of pentagon ABCDE five units to the right and
three units down. Label the translated figure A'B'C'D'E'.
On the lines below, explain how you determined the location of A'.
Therefore , as a result, A = 84.3 sq unit is the answer to the pentagon presented challenge.
The Pentagon contains what?In geometry, a penta is a polygon having five sides. A simple pentagon's interior angles add up around 540°. It is possible to create simple or self-intersecting pentagons. A regular pentagon that intersects itself is a pentagram. A 2D polygon with five sides and 5 corners is called a pentagon. The English word "five" is derived from the Greek terms "gon" and "penta." The outcome of mixing the two syllables "Penta + Gon" is Pentagon.
Here,
The equation that is widely used to determine the area of the any regular hexagon that use the apothem or side is
Area for normal polygons = 1/2 perimeter the polygon apothem.
Thus ,area of pentagon
=> A = 1/4 * √5(5+2√5)
=>A = 84.3 sq unit
Therefore , the solution of the given problem of pentagon comes out to be A = 84.3 sq unit
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Can you pls helps me with this question of percentage?
Answer:
16 percent increase in the number of train passengers from 2010 to 2012.
HELP I NEED HELP WITH GEOMETRY
The third side is the hypotenuse of a right angle triangle and the length is equal to 4.
What is the Pythagoras ruleThe Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We shall represent the length of the third side with the letter x, such that by Pythagoras rule we evaluate for the hypotenuse as follows:
x² = 3² + (√7)²
x² = 9 + 7
x² = 16 {take square root of both sides}
x = √16
x = 4.
Therefore, the length of the third side which is also the hypotenuse is equal to 4 using the Pythagoras rule.
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Simplify the given expression using the order of operations and exponent rules. Write the answer without negative exponents(assume no division by zero)
The simplification of the Indices ((7c⁶d³)/(8c⁴d³))^-2 is 64c²/49
What is Indices?An index is a small number that tells us how many times a term has been multiplied by itself. The plural of index is indices. Below is an example of a term written in index form: 43. 4 is the base and 3 is the index.
Simplifying (7c⁶d³)/(8c⁴d³))^-2
Firstly we open the parentheses
(7^-2c^6-2d^3-2 ) ÷ 8^-2c^4-2d^3-2
= 7^-2c⁴d ÷ 8^-2c²d
= 7^-2/8^-2(c^4-2d^1-1)
= 7^-2/8^-2(c²)
= 1/49÷ 1/64(c²)
= 1/49× 64(c²)
= 64c²/49
Therefore the simplification of (7c⁶d³)/(8c⁴d³))^-2 is 64c²/49
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G(x)=-2x squared + 7x-3 what is the value of g(-2)
g(-2)= -25
[tex]g(x)=-2x^2+7x-3\\\\g(-2)= -2(-2)^2+7(-2)-3\\g(-2)=-2(4)-14-3\\g(-2)=-8-17\\g(-2)=-25[/tex]
Plug in -2 into x and solve as shown above.
Mrs. Bowlin had 4 colors of construction paper. If she had the same
number of pieces of each color, how many pieces of each color did
Mrs. Bowlin have? PLEASE ANSWER QUICKKK!
Answer: any number that can divide by 4 so 4, 8, 12, 16 would all work
Step-by-step explanation: there are 4 groups each has somthing in it if you take everything out of all of the groups it will be divisible by 4 because they all have the same amount of things so any number divisible by 4 will work
A slice of chocolate fudge cake contains 7.25 grams of sugar. How many grams of sugar are in of a 2/3 slice of chocolate? Write your answer as a mixed fraction in simplest form.
Answer:
4 2/3
Step-by-step explanation:
7.25 ÷ 3 = 2 5/12 × 2 = 4 2/3
Help! I don't understand this AT ALL. A system consists of two different proportional relationships. What is the solution of the system?
Answer:
(0,0)
Step-by-step explanation:
Proportional Relationships ALWAYS goes through the origin so the answer is (0,0)
What is the y intercept for the 3rd graph.
Right triangle MHB is shown on the coordinate grid where m/MHB=45°.
B
-11-10-9-8-7-6
What is the exact length of MB?
-4-3-2
7y
5
4
3
2
10 1
-1
M-2
2
H
3
X
4
Therefore , the solution of the given problem of triangle comes out to be and MB or x = √106.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
Here,
Given : A right triangle ,
=> 2√53 = BH
=> MH = √106
∠m / ∠MHB = 45°
Using Pythagoras theorem :
=> ( 2√53)² = (√106)² + x²
=> 4 * 53 - 106 = x²
=> x² = 212 -106
=> x = √106
Therefore , the solution of the given problem of triangle comes out to be
and MB or x = √106.
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The following two-way table shows the distribution of high school students categorized by their grade level and music-listening preference.
A 4-column table with 3 rows. Column 1 has entries junior, sophomore, total. Column 2 is labeled Earbuds with entries 4, 4, 8. Column 3 is labeled Speakers with entries 12, 12, 24. Column 4 is labeled total with entries 16, 16, 32. The columns are titled music-listening preferences and the rows are titled grade level.
Suppose a high school student is selected at random. Let event A = junior and event B = earbuds. Are events A and B independent?
Yes, P(A) = P(A|B).
Yes, P(A) = P(B|A).
No, P(A) ≠ P(A|B).
No, P(A) ≠ P(B|A).
The correct statement regarding whether juniors and earbuds are independent events are given as follows:
Yes, because P(A|B) = P(A).
What are independent events?If two events are independent, the multiplication of the probabilities of each event is equals to the probability of both events, that is:
P(A and B) = P(A) x P(B).
The conditional probability formula is given as follows:
P(B|A) = P(A and B)/P(A).
Hence, for independent events, we have that:
P(B|A) = P(B).
And also:
P(A|B) = P(A).
A probability of an event is calculated as the division of the number of total outcomes by the number of desired outcomes.
Out of 32 students, 16 are juniors, hence the probability of a junior student is given as follows:
P(A) = 16/32 = 0.5.
Out of 8 students with earbuds, 4 are juniors, meaning that the conditional probability is given as follows:
P(A|B) = 4/8 = 0.5.
As the probability is equal, these two events are independent, and the first statement is correct.
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5 out of every 8 students surveyed owns a bicycle. There are 65 bicycles. How many students were surveyed?
Answer:
104 students
Step-by-step explanation:
This is an example of a proportion problem. However, its only 5 out of 8, we need it to say 65 out of x. We can solve this by multiplying both the top and bottom by 13. (Because to get 65 from 5, we need to multiply by 13)
5 bikes x 13 = 65 bikes
____
8 students x 13 = 104 students
Set up and solve an equation to find the value of x
Answer:
x = 2
Step-by-step explanation:
If ΔCAB≅ΔIPS, the PS=AB
11x + 6 = 4(2x + 3)
11x + 6 = 8x + 12
3x = 6
x = 6/3 = 2
Find the radius of convergence R of the series.
[infinity] n
bn (x − a)n, b > 0
n = 1
R =
Find the interval of convergence of the series. (Enter your answer using interval notation.)
The interval of convergence is from (a - b) to (a + b), where b is a positive number.
1. The radius of convergence R is given by the formula R = 1/|b|.
2. The interval of convergence is given by the formula (a - b, a + b).
The radius of convergence R of a series is a measure of how quickly the series converges. It is calculated by taking the inverse of the coefficient of the term with the highest power of the variable in the series. In this case, the coefficient of the highest power of the variable is b, so the radius of convergence is 1/|b|.
The interval of convergence is the region in which the series converges. It is determined by the coefficient of the term with the highest power of the variable in the series. In this case, the coefficient of the highest power of the variable is b, so the interval of convergence is (a - b, a + b). This means that the series converges for values of x in the range from (a - b) to (a + b).
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Two-thirds of the members of Highland Church attended the International Dinner during their annual missions conference. When seven of the members were not able to attend, the total number of attendees was Seventy-one. How many members does Highland Church have?
The total number of members Highland Church have, 113
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Given that,
Two-thirds of the members of Highland Church attended the International Dinner
The members were not able to attend = 7
The total number of attendees = 71
Suppose the total members of Highland Church = x
So, 2/3x = 71
⇒ x = 106.5 ≈ 106
The total number in church = attendees + non attendees
= 106 + 7
= 113
So, 113 members lives in Highland Church
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how to find perimeter of cylinder?
Answer:
calculate the perimeter of the circle base using C = 2πR. multiply this value by the cylinders height to get its lateral surface area A= 2πRH
Step-by-step explanation:
Using the standard 28/36 guidelines, what is the maximum mortgage payment allowed for someone with an annual salary of $73,025?.
The maximum mortgage payment allowed for someone with an annual salary of $73.025 would be $2,190.75 per month.
The correct answer is an option A.
In this question we need to find the maximum mortgage payment allowed for someone with an annual salary of $73,025 using the standard 28/36 guidelines.
We know that the standard 28/36 rule used to calculate the amount of debt an individual or household should assume.
This rule says that a household should spend a maximum of 28% of its gross monthly income on total housing expenses and no more than 36% on total debt service.
Let the maximum mortgage payment allowed be x dollars
So, x = ((73025 x 36) / 100) / 12
x = (2,628,900 / 100) / 12
x = $2,190.75
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A complete question is:
Using the standard 28/36 guidelines, what is the maximum mortgage payment allowed for someone with an annual salary of $73,025?
a. $2,190. 75
b. $2,044. 70
c. $1,703. 92
d. $1,217. 8.
Answer:
a
Step-by-step explanation:
What are the 3 fraction models?
The 3 fraction models are the area model, which uses a shaded area to represent the fraction; the number line model, which uses a line to represent the fraction; and the set model, which uses a set of objects to represent the fraction.
1. Area Model: A visual representation of a fraction that shows a shaded area representing a whole, and the fraction is represented by the shaded area in relation to the whole.
2. Number Line Model: A visual representation of a fraction that uses a line to represent the whole, and the fraction is represented by a point on the line in relation to the whole.
3. Set Model: A visual representation of a fraction that uses a set of objects to represent the whole, and the fraction is represented by the number of objects in relation to the whole.
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The 3 fraction models are as follows;-
1- the area model- A visual representation of a fraction that shows a shaded area representing a whole, and the fraction is represented by the shaded area in relation to the whole.
2-the linear model-A visual representation of a fraction that uses a line to represent the whole, and the fraction is represented by a point on the line in relation to the whole.
3- the set model- A visual representation of a fraction that uses a set of objects to represent the whole, and the fraction is represented by the number of objects in relation to the whole.
fraction model
A fraction bar model is where you draw a long rectangle and divide it into equal parts to show a fraction.
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1) a child puts $1 into a piggy bank. one week later he puts $1.25. two weeks later he puts $1.50 in the bank and so on. how much money does he put in the bank on the 25th week?
omg save me and explain
Answer:kkkkkkk
Step-by-step explanation:
Find the average rate of change on the interval - 1≤ * ≤ 4
for the equation y=*? + 4x+1.
The average rate of change on the interval -1 ≤ x ≤ 4 for the equation y = x^2 + 4x + 1 is 13/5.
What is the rate of change?
The rate of change refers to how much a function's output (y) changes with respect to a change in its input (x).
To find the average rate of change on the interval -1 ≤ x ≤ 4 for the equation y = x^2 + 4x + 1, we can use the formula:
average rate of change = (y2 - y1) / (x2 - x1)
Where y2 and y1 are the function values at x2 and x1 respectively.
So, we have:
average rate of change = (f(4) - f(-1)) / (4 - (-1))
where f(4) = 4² + 44 + 1 = 17 and f(-1) = (-1)² + 4(-1) + 1 = 4
Therefore,
average rate of change = (17 - 4) / (4 - (-1)) = 13 / 5
Hence, The average rate of change on the interval -1 ≤ x ≤ 4 for the equation y = x^2 + 4x + 1 is 13/5.
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The table below shows Zoey's earnings on the job
How much does she make in 18.2518.25 hours?
Answer:
she is going to make $408.90 in 18.2518.25 hours
The diagram represents two statements: p and q.
Which represents regions A, B, and C?
Opvq
Op-q
q^p
O q-p
A represents the p region, B represents the (q∩p) region and C represents the q region.
What is a Venn diagram?A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.
Given is a Venn diagram,
Studying the Venn diagram, we get that,
A represents the region occupied by p, that means A is representing the region that belongs to p.
B is the region B includes the area which commonly lies both in p AND q at the same time that means B displays the region in which both p AND q.
C represents the region occupied by q, that means C is representing the region that belongs to q.
Hence, A's region is p, B's region is (q∩p) and C's region is q.
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What is the slope of the line that contains the points (9, -4) and (1, -5)?
Answer:
m = 1/8
Step-by-step explanation:
m = y2-y1/x2-x1
m = -5+4/1-9
m = -1/-8
m = 1/8
Answer:
slope of line =y2-y1/x2-x1
lets consider (x1,y1)=(9,-4) so value of x1=9 and y1=-4
(x2,y2)=(1,-5) so value of x2=1 y=-5
answer =y2-y1/x2-x1=-5-(-4)/1-9=-1/-8
slope=1/8
i hope it helps
btw i am from india
8(6x-4) Write the expanded from of the expression
Answer:
48x - 32
Step-by-step explanation:
8(6x-4)
We want to distribute the 8 to each term inside the parentheses
8 *6x - 8* 4
48x - 32
[tex] \longmapsto \: 8(6x - 4 )[/tex]
[tex] \longmapsto \: 48x - 32[/tex]
Please answer MCQ 10
VII) (-i)^19 = -i. Option C
VIII) The imaginary part of i/1 + i = 1/2. Option C
IX) The modulus of 3 - 4i is 5. Option C
X) For Z = a + ib, sin θ = a/b. Option A
XI) There are 3 elements in the set. Option A
What are the imaginary numbers?We know that the imaginary numbers has to do with the numbers that we can be not be able to find on the number line. These are not real numbers but they are very important in the process of computation. There are two parts of a complex number. We have the imaginary part and we have the real part.
It is sometimes possible that we can be able to represent the complex number by the use of an Argand diagram which shows the complex number in the polar form.
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How do I do this.............................. Help
Every day, the Mercer Pet Store uses 5 bags of dog food to feed the dogs. How many
days will 5 5/8 bags of dog food last?
