The probability that more than 2 students will attend is 0.9179.
Part (a) List the values that X may take on.
X may take on the values 0, 1, 2, 3, ..., 13.
Part (b) Give the distribution of X.
The distribution of X can be represented as follows: X-0:0, 1:0.23, 2:0.23, 3:0.23, 4:0.23, 5:0.23, 6:0.23, 7:0.23, 8:0.23, 9:0.23, 10:0.23, 11:0.23, 12:0.23, 13:0.23
Part (c) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)
We can expect 3 students to attend the festivities.
Part (d) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.)
The probability that at most 3 students will attend is 0.6923.
Part (e) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)
The probability that more than 2 students will attend is 0.9179.
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Solve for x and simplify answer
4
\x=-18
3
The value of the variable is x = -6/9
What is a fraction?A fraction is defined as the part of a whole number.
The different types of fractions are;
Mixed fractionsSimple fractionsComplex fractionsImproper fractionsProper fractionsWe are given the equation:
4/x = -18/3
To make 'x' the subject, cross multiply
-18x = 12
Now, divide both sides by the coefficient of x, we get;
x = 12/-18
x = -6/9
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How do you solve the problem: 5/8 * a/b = - 1/4?
Answer:a=-2
b=5
Step-by-step explanation:
[tex]\frac{a}{b} =\frac{\frac{-1}{4} }{\frac{5}{8} } \\\frac{a}{b} =\frac{-1}{4}*\frac{8}{5}\\\frac{a}{b}=-2/5[/tex]
10x³•2 √5x4 I need help
Answer:
20√5x7
Step-by-step explanation:
if (x) - **4, g(x) = x= 2, and h(x) = 4x+1, what is (f• Hºg)(x)?
2x+16
o (fe hºg)(x) =
2x+4
o (fonog)(x)=
4x-3
o (f• hºg)(x)- Ax=1
4x-5
o (f• nºg)(x) = AX-
The solution is, the value of (f• Hºg)(x) = 4x+2.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
given that,
f(x) = x-4
g(x) = x+ 2,
and h(x) = 4x+1
now, (f• Hºg)(x)
= (f•(4(x+2)+1)(x)
=((4x+6)-4)
=4x+2
Hence, The solution is, the value of (f• Hºg)(x) = 4x+2.
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Complete the Recursive formula.
Answer:
[tex]-13[/tex]
Step-by-step explanation:
The common difference of the arithmetic sequence is [tex]-13[/tex].
You paid $29.75 in tax when you bought a $350 bike. What is the percent tax?
The percent tax you paid when you bought the bike is approximately 8.493%.
What is percentage ?
Percentage can be defined as the product of ratio of given value, total value and hundred.
given ,
You paid $29.75 in tax when you bought a $350 bike
To find the percent tax, we can divide the amount of tax by the total cost (including tax) and multiply by 100 to express the result as a percentage.
tax = 29.75
total = 350
percent tax = (tax / total) * 100
So the percent tax would be
percent tax = (29.75 / 350) * 100
= 8.493%
Therefore, The percent tax you paid when you bought the bike is approximately 8.493%.
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Find the area of the figure. Round to the nearest tenth, if necessary.
1: Amelia is organising a game for a charity fête.
She has put 1 orange, 1 pink, 1 green and 2 yellow counters into a bag.
To play, each person will pay £1 and take out a counter at random.
They will then replace the counter and then take a second counter at random.
The person will win £2.50 if both counters are the same colour.
autet
Amelia expects 200 people to play the game.
How much money would Amelia expect to raise for charity?
The amount of money that Amelia is expected to raise is given as follows:
£78.13.
How to obtain the expected amount?The outcomes of a person winning, and their probabilities, as given as follows:
Two orange: 1/4 x 1/4 = 1/16.Two pink: 1/4 x 1/4 = 1/16.Two yellow: 2/4 x 2/4 = 4/16.Hence the probabilities of winning and losing are given as follows:
Winning: 6/16.Losing: 10/16.Then the distribution of earnings for each person is given as follows:
P(X = -1) = 10/16. -> Lose.P(X = 2.5) = 6/16 -> wins.Hence, considering 250 people, the expected amount raised is given as follows:
E(X) = 250/16 x (2.5 x 6 - 1 x 10)
E(X) = £78.13.
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A fruit juice recipe calls for 5 parts orange juice and 6 parts pineapple juice. Which proportion can be used to find the amount of orange juice, j, that is needed to add to 21 L of pineapple juice?
30 over 21 equals j over 100
6 over 5 equals j over 21
6 over j equals 5 over 21
5 over 6 equals j over 21
For given ratio of orange juice and pineapple juice i.e. 5/6, proportion used to find the amount of orange juice, j, that is needed to add to 21 L of pineapple juice will be 5 over 6 equals j over 21 i.e. 5/6=j/21.
What exactly is a ratio?
Fractions are commonly used to describe ratios and proportions. A ratio is demonstrated when a fraction is expressed as a:b, whereas a percentage indicates that two ratios are equal. a and b can be any two numbers in this situation. The ratio and proportion are two fundamental ideas that lay the groundwork for comprehending other concepts in mathematics and science.
We use the concept of ratio and proportion in our daily lives, such as in business when dealing with money or in cooking.
As a result, when b is larger than zero, the ratio, such as a:b, defines the relationship between two variables. For example, the 2:4 ratio is expressed as 2:4 = 1:2.
Now,
Given that In recipe ratio of orange juice / pineapple juice =5/6
then to make a recipe with 21 L of pineapple juice, the orange juice (j)
needed will be
5/6=j/21
j=17.5 L
hence,
proportion used to find the amount of orange juice, j will be 5 over 6 equals j over 21 i.e. 5/6=j/21.
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Answer: its D
Step-by-step explanation:
pls i belieive most of yall are npcs
Need help solving three questions on algebra homework
The values of the composite functions are (f + h)(5) = 7, (h - f)(2) = 0, (fh)(3) = 0 and (h/f)(0) = 3/5
How to evaluate the composite functionsFrom the question, we have the following parameters that can be used in our computation:
The graphs
Using the graphs as a guide, we have the following:
(f + h)(5) = f(5) + h(5)
(f + h)(5) = 3 + 4
(f + h)(5) = 7
(h - f)(2) = h(2) - f(2)
(h - f)(2) = 1 - 1
(h - f)(2) = 0
(fh)(3) = f(3) * h(3)
(fh)(3) = 4 * 0
(fh)(3) = 0
(h/f)(0) = h(0)/f(0)
(h/f)(0) = 3/5
Hence, the value of the function (h/f)(0) is 3/5
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The fish in a hatchery tank have mean length = 9.7 inches, with standard deviation = 1.2 inches. If a random sample of 40 fish is taken from the tank, what is the probability that their average length is less than 10 inches?
The probability that the average length of a random sample of 40 fish is less than 10 inches is 0.8869 or 88.69%.
What is probability ?
Probability is a metric used to determine how likely an event or result is to occur. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event.
A group of potential possibilities is referred to as an event in probability theory. By dividing the number of positive possibilities by the total number of possible outcomes, the probability of an event happening is determined.
The fish in the hatchery tank are distributed in length according to a normal distribution, with a mean length of 9.7 inches and a standard deviation of 1.2 inches.
With a mean that is equal to the population mean and a standard deviation that is equal to the population standard deviation divided by the square root of the sample size, the distribution of the sample means will also follow a normal distribution.
The formula to calculate the z-score for the sample mean is:
z = (x - μ) / (σ /[tex]\sqrt{n}[/tex] )
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, we want to find the probability that the sample mean is less than 10 inches. So we need to calculate the z-score for a sample mean of 10 inches:
z = (10 - 9.7) / (1.2 /[tex]\sqrt{40}[/tex]) = 1.21
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 1.21 is approximately 0.8869. This means that there is an 88.69% chance of getting a sample mean less than 10 inches.
Therefore, the probability that the average length of a random sample of 40 fish is less than 10 inches is 0.8869 or 88.69%.
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In which quadrant does the point (-21 , 13) lie?
Hannah has to make 168 gallons of punch for a big party. The punch is made of soda and fruit drink. The cost of the soda is $1.57 per gallon and the cost of the fruit drink is $2.41 per gallon. Hannah's budget requires that the punch cost $1.66 per gallon. How many gallons of soda and how many gallons of fruit drink does she need?
Gallons of soda =
Gallons of fruit punch =
The number of gallons of fruit drink is 118 gallons and the number of gallons of soda is 150 gallons.
How much fruit drink and soda does he need?The system of equations that represents the question is:
f + s = 168 equation 1
2.41f + 1.57s = (1.66 x 168)
2.41f + 1.57s = 278.88 equation 2
Where:
f = number of gallons of fruit drink s = number of gallons of sodaThe elimination method would be used to determine the required values
Multiply equation 1 by 2.41
2.41f + 2.41s = 404.88 equation 3
Subtract equation 2 from equation 3
126 = 0.84s
s = 126 / 0.84
s = 150
Substitute for s in equation 1
f + 150 = 168
f = 168 - 150
f - 118 gallons
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Write a recursive formula for an, the nth term of the sequence 50, -10, 2, ....
a1
an
11
Answer:do homework
Step-by-step explanation:
1. Find the semester GPA for the following. Show or explain your work.
Class Credit Hours Grade
MAT 171 4 C
HEA 112 2 A
ENG 111 3 B
ACA 111 1 D
BIO 112 4 A
2. Annie is a junior at a local university. She has 80 credit hours and a GPA of 2.1.
She wants to raise her GPA for a scholarship this semester.
She takes 16 credit hours and makes all A's, earning a 4.0 for this semester.
Annie averages the previous GPA of 2.1 and the current semester GPA of 4.0. She adds 2.1 + 4.0, then divides by 2, obtaining 3.05.
She believes she should now have a GPA of 3.05.
Is her reasoning correct? Justify your answer with 2 - 3 sentences.
Answer:
aiaiiwakkaoajdjsjzjhsjaj
What are the answers to these?
The values of the vacant spaces are $3.75, 4 oranges, 10 oranges, $15 and 20 percent of 160 is 32
What are the values?The table can be completed using the following values
If 8 oranges cost $10,
Then 1 orange will cost 10/8 = $1.25
This means that 3 oranges will cost 1.25*3 = $3.75
$5 can buy 8/10*5 = 40/10 = 4 oranges
In the same way, $12.50 will buy 8/10 * 12.50 = 10 Oranges
In the same manner, 12 oranges will cost 1.25*12 = $15
20% of 160 can be calculated as follows
Recall that percentage is a proportion of 100
This implies that 20/100 * 160 = 3200/100 = 32
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The perimeter is 30cm.
Work out the lengths of all the sides.
3x + 2
X
4x - 6
Answer: To solve for the length of all sides, we need to set the perimeter equal to the sum of the lengths of the three sides:
30 cm = 3x + 2 + x + 4x - 6
30 cm = 8x + 2
Now we can solve for x:
30 cm = 8x + 2
28 cm = 8x
x = 28/8
x = 3.5
So each of the sides is 3.5 cm long, and the lengths of the three sides are:
3x + 2 = 3 * 3.5 + 2 = 11.5 cm
x = 3.5 cm
4x - 6 = 4 * 3.5 - 6 = 11.5 cm
Therefore, the lengths of the sides are 11.5 cm, 3.5 cm, and 11.5 cm.
Step-by-step explanation:
Answer:
(3x+2+4x-6)2=30
7x-4=30
7x=34
x=34/7
To find the side lengths of the rectangle;
3x+2=116/7. and. 4x-6=94/7
SAQ-18. The firm provides the following information: Annual requirement Cost per unit ........ Rent, tax, and insurance Insurance per order...... Required: a. EOQ ..... Rs. 20 Rs. 2 per unit ..Rs. 200 ...............100,000 units Carrying cost per unit per year ...........10% of unit price Cost per order...... ...........Rs. 300 b. Total Cost of EOQ c. Number of order
Note that the Economic Order Quantity is given as approximately 4,472.13 Units.
Economic Order Quantity, also known as Economic Purchasing Quantity, is the order quantity in inventory management that minimizes overall holding costs and ordering expenses. It is one of the most ancient traditional production scheduling models.
EOQ = √[(2 * AR* OC)/CC]
Were AR = Annual Requirement = 100,000 units
OC = Ordering Cost = Rs 20 per unit
CC = Carrying Cost = 10% of Per Unit Cost
Per Unit Cost = Rs. 2
Thus,
EOQ = √[(2 * 100,000* 20)/10% * 2]
EOQ = √[(4000000)/0.2]
EOQ = √20000000
EOQ = 4472.135955
EOQ [tex]\approx[/tex] 4,472.13 Units.
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what is the length of (3,5),(7,3)
Answer:
Step-by-step explanation:
The length of the line segment between two points in a plane can be calculated using the distance formula. Given two points (x1, y1) and (x2, y2), the distance between them is given by the following formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the two points are (3, 5) and (7, 3). Plugging these values into the formula, we get:
d = √((7 - 3)^2 + (3 - 5)^2)
d = √((4^2) + (2^2))
d = √(16 + 4)
d = √20
So, the length of the line segment between the two points (3, 5) and (7, 3) is √20.
A bag contains 2 gold marbles, 7 silver marbles, and 29 black marbles. The rules of the game are as follows: you randomly select one marble from the bag. If it is gold, you win $4, if it is silver, you win $2. If it costs $1 to play, what is your expected profit or loss of you play this game?
Total number of marbles is 5 + 7 + 29 = 41.
Your expected profit or loss of you play this game $0.17 loss?
The given parameters are
2 gold marbles,
7 silver marbles,
and 29 black marbles
Also you win $4, if it is silver, you win $2. If it costs $1 to play
Event P(Event) Net Winnings P(Event) * Net Winnings
Gold 5/41 4 - 1 = 3 15/41
Silver 7/41 2 - 1 = 1 7/41
Black 29/41 -1 -29/41
sum -7/41 = $0.17 loss
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Use this table to answer the question. Round to the nearest percent.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of Planes are Green?
There are 29% of the Planes are Green.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Total number of green planes = 250
The total number of green vehicles = 870
The percent of green planes = (number of green planes/number of total green vehicles) x 100
The percent of green planes = (250/870) x 100
The percent of green planes = 0.2873 x 100
The percent of green planes = 28.73
Round to the nearest percent, and we get
The percent of green planes = 29%
Thus, 29% of Planes are Green.
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A boat has a top speed of 26 knots and a displacement of approximately 81000 tons. (1 knot= 1 nautical mile per hour; 1 metric ton =1000 kilograms)
Express the top speed in miles per hour and the displacement in metric tonnes.
(1 knot=1 nautical mile per hour; 1 metric tonne=1000 kilograms)
On solving the provided question we can say that 2 decimal places =29.92 miles per hour
what is decimal?Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. A decimal point separates the complete number and the fractional portion of a decimal number. The dot between the whole number and the fractions is known as the decimal point. A decimal number is, for instance, 25.5. In this instance, 25 is the entire number, while 5 is the
top speed is 26 knots,
1 knot = 1.15078 miles per hour
26 knots = 26 * 1.15078
= 29.92028 miles per hour
2 decimal places
=29.92 miles per hour
boat has a displacement of 96000 tons
1 ton = 0.907185 metric tonnes
96000 tons = 0.907185 * 96000
= 87,089.76 metric tonnes
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A magician has a magic trick that uses an 18" length of string that is cut into two pieces. One piece is two inches longer that the other. Find the length of each piece. Use algebraic equations.
The length of each piece is 10 in and 8 in.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The total length of the string = 18 in
One piece = x + 2
Another piece = x
Now,
Solve for x.
x + 2 + x = 18
2x + 2 = 18
2x = 18 - 2
2x = 16
x = 8
Now,
One piece = 8 + 2 = 10 in
Another piece = 8 in
Thus,
The length of each piece is 10 in and 8 in.
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(SAT Prep) Find the value of x.
Answer: 36˚
Step-by-step explanation:
180 - 3x = 2x
180 = 5x
.: x = 36˚
< Question 4, 1.2.23 >
points
O Points: 0 of 1
Use the method of successive differences to determine the next number in the given sequence.
7; 35; 173; 771; 2529; 6667; 15,095
Assuming that the pattern continues, the eighth term would be
The pattern does not have a consistency to get the differences
How to find the patternThe method of successive differences involves finding the difference between each consecutive term in a sequence, and then using those differences to find the next term.
Here's how the method would work for the sequence given:
7; 35; 173; 771; 2529; 6667; 15,095
Difference between terms:
28; 138; 598; 1758; 4138; 8428
Second difference between terms:
110; 460; 1160; 2380; 4290
Third difference between terms:
350; 700; 1220; 1910
Fourth difference between terms:
350; 520; 690
There is no consistency between the patterns.
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ax+bx=c make x subject
Answer:
x=c/(a+b)
Step-by-step explanation:
ax+bx=c
x(a+b)=c
x(a+b)/(a+b)=c/(a+b)
x=c/(a+b)
Answer:
[tex]x=\dfrac{c}{a+b}[/tex]
Step-by-step explanation:
To make x the subject of the equation ax + bx = c, rearrange the equation using algebraic operations to isolate a single x-variable.
Given equation:
[tex]ax + bx = c[/tex]
Factor out x from the left side of the equation:
[tex]x(a+b)=c[/tex]
Divide both sides of the equation by (a + b):
[tex]\dfrac{x(a+b)}{(a+b)}=\dfrac{c}{(a+b)}[/tex]
Simplify:
[tex]x=\dfrac{c}{a+b}[/tex]
Solve for x
2,4, and 6 i need help with
Answer:
2. 56°
4. 56°
For number 6, it is not shown on the photo, sorry!
Step-by-step explanation:
2. The square at the corner means that it is 90°, so 90 - 34 = 56
4. The line is straight, so it means that it is 180°, so 180 - 124 = 56
Solve -27 19 - 2x.
Enter your responses in the boxes.
-27 19 - 2x
H
-27-
23
-
-www
= -2x
1 = x
19-
-2x
Answer:
Simplifying
-27 = 19 + -2x
Solving
-27 = 19 + -2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2x' to each side of the equation.
-27 + 2x = 19 + -2x + 2x
Combine like terms: -2x + 2x = 0
-27 + 2x = 19 + 0
-27 + 2x = 19
Add '27' to each side of the equation.
-27 + 27 + 2x = 19 + 27
Combine like terms: -27 + 27 = 0
0 + 2x = 19 + 27
2x = 19 + 27
Combine like terms: 19 + 27 = 46
2x = 46
Divide each side by '2'.
x = 23
Simplifying
x = 23
Please help me I need help with algebra 2
Answer:If (x + 1) is a factor of the polynomial p(x), then p(x) can be written as:
p(x) = (x + 1) q(x)
for some polynomial q(x). By substituting x = -1 into this expression, we can find the value of c:
p(-1) = (-1 + 1) q(-1) = 0 q(-1) = 0
So,
0 = 5(-1)^4 + 7(-1)^3 - 2(-1)^2 - 3(-1) + c
= -5 + 7 - 2 + 3 + c
= c = 3
So, the value of c that makes (x + 1) a factor of the polynomial p(x) = 5x^4 + 7x^3 - 2x^2 - 3x + c is c = 3.
A water reservoir is shaped like a rectangular solid with a base that is 40 yards by 40 yards, and a vertical height of 30 yards. At the start of a three-month period of no rain, the reservoir was completely full. At the end of this period, the height of the water was down to 5 yards. How much water was used in the three-month period?
In response to the above question, we may state that in the rectangle [tex]4,241,455[/tex] gallons [tex]= 4,570,000[/tex] Cubic feet[tex]x 7.48052[/tex] Gallons/cubic foot.
What is rectangle?In the geometry of the Euclidean plane, a rectangle is a quadrilateral having four right angles. You may also refer to it as an equiangular quadrilateral, meaning that all of its angles are equal. A straight angle could also be present in the parallelogram.
Rectangles with four evenly sized sides are called squares. Four 90-degree vertices and equal parallel sides make up a quadrilateral with the shape of a rectangle.
As a result, it's also known as an equirectangular rectangle. A rectangle is also referred to as a parallelogram, since its opposite sides are parallel and equal.
Volume of rectangular solid is L × W × H
[tex]50 × 30 × 20 = 30000[/tex] cubic yards
[tex]50 × 30 × 6 = 9000[/tex]cubic yards
[tex]30000–9000 = 21000[/tex]cubic yards
This needs to be converted to gallons of water. We are given the conversion factor between a gallon of water and cubic feet, therefore even though we have cubic yards rather than cubic feet, we must first convert the [tex]21,000[/tex] Cubic yards to cubic feet.
A cubic yard has a volume of 27 cubic feet.27 cubic feet per cubic yard times [tex]21,000[/tex]cubic yards equals 567,000 cubic feet.
7.48052 gallons make up 1 cubic foot.
Therefore, 4,241,455 gallons are equal to 567000 cubic feet times 7.48052 gallons/cubic foot.
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