We can expect to ask about 2-3 students before finding someone who prefers a salad for lunch, on average.
What is probability?Calculating the possibility or probability that a specific event will occur uses the concept of probability.
It is a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of the event.
Fractions, decimals, and percentages can all be used to express probabilities.
Assuming that each student's preference for lunch is independent of the others, the probability of any given student preferring a salad is 20% or 0.2.
The probability of the first student you ask preferring a salad is 0.2. If they don't prefer a salad, you move on to the next student.
The probability of the second student preferring a salad, given that the first student didn't, is also 0.2. The probability of neither of the first two students preferring a salad is (1-0.2) × (1-0.2) = 0.64.
In general, the probability of the nth student preferring a salad, given that none of the previous n-1 students did, is also 0.2. The probability of none of the first n-1 students preferring a salad is (1-0.2)ⁿ-¹.
So the expected number of students you must ask before finding someone who prefers a salad is:
E(x) = 1×(0.2) + 2×(1-0.2)(0.2) + 3(1-0.2)²×(0.2) + ...
This is an infinite series, but we can approximate it by truncating it after a certain number of terms. Let's say we stop after 10 terms:
E(x) ≈ 1×(0.2) + 2×(1-0.2)(0.2) + 3(1-0.2)²×(0.2) + ... + 10×(1-0.2)⁹ × (0.2)
E(x) ≈ 2.48
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the sum of two consecutive odd numbers is 124 what equation would you use to solve this problem
Answer:
x + (x+2) = 124
Step-by-step explanation:
Let x be the first odd number, then the next consecutive odd number would be x+2.
According to the problem, the sum of these two numbers is 124.
So, we can set up the following equation:
x + (x+2) = 124
Simplifying this equation:
2x + 2 = 124
Subtracting 2 from both sides:
2x = 122
Dividing both sides by 2:
x = 61
Therefore, the first odd number is 61, and the next consecutive odd number is 63.
To check, we can add them together:
61 + 63 = 124
So the solution is x = 61.
Answer:
x + x + 2 = 124
(and then you could solve that x=61 and the two numbers are 61 and 63)
Step-by-step explanation:
"sum" means adding. "consecutive" means the two numbers are in a row, or one right after the other. Like 3 and 4 are consecutive numbers and 3 and 5 are consecutive odd numbers. 3 and 11 are not consecutive.
So let one number be x.
Then next odd number after that is +2...so the 2nd number is x+2.
And they add up to 124. Write the equation like this:
x + x + 2 = 124
If you want or need to solve then:
combine like terms.
2x +2 = 124
subtract 2.
2x = 122
divide by 2.
x = 61
then x+2 is 63.
Explain why the initial value of any function of the form f(x) =a(b^x) is equal to a
The function f(x) = a(b^x) is an exponential function, where "a" is the initial value or y-intercept of the function, and "b" is the base of the exponent, which determines the rate of growth or decay.
When x = 0, we have:
f(0) = a(b^0)
Since any number raised to the power of 0 is 1, we can simplify the expression to:
f(0) = a(1) = a
Therefore, when x is equal to 0, the value of the function is just the initial value "a". This is true for any exponential function of the form f(x) = a(b^x).
In other words, the initial value of an exponential function is the value of the function when x = 0, and in this case, that value is just "a".
Find XZ and the area of △WXY.
Answer:
XY = 7.5 cm
Area = 105 cm²
Step-by-step explanation:
First, let us use the sin Θ to find the value of XY.
Sin Θ = Opposite ÷ Hypotenuse
Sin 43 = XY ÷ 11
0.6819 = XY ÷ 11
0.6819 × 11 = XY
7.5 cm = XY
The formula to find the area of the triangle is:
[tex]\sf Area=\frac{1}{2}*base*height\\\\\sf Area=\frac{1}{2}*28\:cm\:*7.5\\\\Area=105\:cm^2[/tex]
The radius of a circle is 19 cm. Find the area
Answer: 1134.11
A=3.14*r^2
Step-by-step explanation:
Answer:
a ≈ 1134.11 cm2
Step-by-step explanation:
The formula:
[tex]a=\pi r^{2}[/tex]
[tex]a=\pi (19)^{2} =361\pi[/tex]
[tex]a=1134.11cm^{2}[/tex]
Hope this helps
which polynomial function could be represented by the graph below?
Answer: B: [tex]f(x) = x^2 - 4x-5[/tex]
Step-by-step explanation:
Lets write this first in vertex form:
We know the vertex of this function is at (2, -9)
this gives us h,k values. Since there is no stretch or compression, and no negative coefficient we can simply plug in:
f(x) = [tex](x-2)^2 - 9[/tex]
Expanding this, we get answer B.
Determine the equation of the hyperbola with center (-10, 5), a focus at (-10, 15),
and a co-vertex at (-18,5).
The equation of the hyperbola with center (-10, 5), a focus at (-10, 15),
and a co-vertex at (-18,5) is:
[(y - 5)² / 36] - [(x + 10)² / 64] = 1
Determining the equation of the hyperbolaFrom the question, we are to determine the equation of the hyperbola with the given center, focus and co-vertex.
The equation of a hyperbola with center (h, k), a focus at (h, k + c), and a co-vertex at (h + b, k) is given by
[(y - k)² / a²] - [(x - h)² / b²] = 1
Where a² = c² - b²
From the given information,
The center of the hyperbola is (-10, 5)
Thus,
h = -10, k = 5
The focus is at (-10, 15)
By comparison with (h, k + c)
k + c = 15
5 + c = 15
c = 15 - 5
c = 10
The co-vertex is at (-18, 5)
By comparing with (h + b, k)
h + b = -18
-10 + b = -18
b = -18 + 10
b = -8
From the formula a² = c² - b²
Then,
a² = c² - b²
a² = 10² - 8²
a² = 100 - 64
a² = 36
Now,
We can write the equation of the hyperbola
[(y - k)² / a²] - [(x - h)² / b²] = 1
Substitute the values
[(y - (5))² / (36)] - [(x - (-10))² / (-8)²] = 1
[(y - 5)² / 36] - [(x + 10)² / 64] = 1
Hence,
The equation of the hyperbola is:
[(y - 5)² / 36] - [(x + 10)² / 64] = 1
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ASAAAPPP NEEDDD HELLLPPPP
Answer:
40°
Step-by-step explanation:
360-240=120
120÷3=40°
Answer
40°
Add of all angles would be 360° .
so equation would be
360° - 240° = 3x
360 - 240 is 120
so
120 = 3x
Dive the both sides of equation by 3 (*just to make it simple and clear. you cam just move 3 to other side of equation . since its multiplied in its side, it would change to division*)
120/3 = 3x/3
40° = x
all the X angle would be 40°
240 + 40 + 40 + 40 = 360°
can you
please answer this
Answer:
3 and 4
Step-by-step explanation:
- 2 < x < 5
has solutions x = - 1, 0, 1, 2, 3, 4
x > 2
has solutions
x = 3, 4, 5, 6, ...........
the integer values that satisfy both are x = 3, 4
Find the value of k.
140°
k
Not drawn accurately
Answer:
140° + 90° + 90° + k = 360°
320° + k = 360°
k = 40°
Therefore , the solution of the given problem of angles comes out to be k has a value of 40 degrees.
What does an angle mean?The largest and smallest walls of a skew are found at the intersection of the pathways connecting its ends. Two pathways could meet at a crossroads. Another result of two entities interacting is an angle. More than anything else, they resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their endpoints to produce a two-dimensional curve.
Here,
According to the information provided, it seems that there is a 140° angle followed by an angle designated as "k". These two angles appear to be adjacent, and since the sum of all angles on a straight line is 180 degrees, we may construct the following equation:
=> 140° + k = 180°
We can now calculate the value of k as follows:
=> k = 180° - 140°
=> k = 40°
So, "k" has a value of 40 degrees.
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4-1
Find the critical value(s) and rejection region(s) for the type of z-test with level of
significance x. Include a graph with your answer.
Right-tailed test, a = 0.01
The critical value is Z = 2.331. The rejection region is Z > 2.33
What is meant by critical value?
A critical value is a value used in hypothesis testing to determine whether to reject or fail to reject the null hypothesis.
What is meant by rejection region?
The rejection region is the set of values that lead to the rejection of the null hypothesis in favor of the alternative hypothesis.
According to the given information
To find the critical value(s) and rejection region(s) for a right-tailed z-test with level of significance x = 0.01, we can use the following formula1:
Critical value: Z = Zα where α = x and Zα is the Z-score that corresponds to an area of α in the standard normal distribution table
Rejection region: Z > Zα
For a right-tailed test with α = 0.01, we can find the critical value using a standard normal distribution table1. The critical value is Z = 2.331. The rejection region is Z > 2.33
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Real-life Problems Question 6
The amount of money that Theresa has left is equal to £2,740.
How to write a linear equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to the cost of flights for each of them and the cost of accommodation for each of them respectively, and then translate the word problem into a linear equation as follows:
Let the variable a represent cost of flights for each of them.
Let the variable f represent cost of accommodation for each of them.
Since Theresa paid for herself and 11 friends to go on holiday with a flight cost of £339 and accommodation cost of £266, a linear equation to describe this situation is given by;
y = 12(a + b)
y = 12(266 + 339)
y = £7,260
For the amount of money left, we have:
Amount of money left = £10,000 - £7,260
Amount of money left = £2,740.
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where does 3 1/2 go on the number line
Answer:
3 1/2 is located between 3 and 4 on the number line.
Helppppppopppopppoo please
This tetrahedron is known as a triangular pyramid and it has four triangular faces, four vertices, and six edges.
How are the sides of the triangular pyramid classified ?We can name the faces of the triangular prism as:
V1 for vertex A.V2 for vertex B.V3 for vertex C.V4 for vertex DThe edges would be:
E1 for connecting V1 and V2.E2 for V1 and V3.E3 for V1 and V4.E4 for V2 and V3.E5 for V2 and V4.E6 for V3 and V4.The faces would be:
F1 triangle formed by vertices V1, V2, and V3F2 triangle by V1, V2, and V4F3 triangle by V1, V3, and V4F4 triangle by V2, V3, and V4Find out more on triangular pyramids at https://brainly.com/question/30615121
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What is the total measurements of this roof in square feet?
The total measurements of the roof in square feet as required to be determined in the task content is; 2649 ft².
What is the total area of the roof in square feet?It follows from the task content that the total area of the roof as given in the task content is to be determined.
On this note, the area of the roof is the total area of the 71ft by 39 ft rectangle minus the area of the shaded region with dimensions 15 ft by 8 ft.
Therefore;
Area = (71 × 39) - (15 × 8)
= 2649 ft².
Ultimately, the total area measure of the roof in square feet is; 2649 square feet.
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Nina wants to buy a ticket at the movies. She needs at least $15. How did you decide which inequality symbol to use?
Answer: >$15
Step-by-step explanation: She needs at least $15, so, we use the greater then symbol, because she’ll be fine if she has more than $15(>15) but she won’t be able to buy the ticket if she has under $15(<15)
4. The total annual cost to attend a community college is $5,000. The college offered a high
school senior a scholarship for $1,800. The student can get a loan for $1,200 but will
need to earn enough to pay the remaining cost. It is 4 months until the remaining cost
must be paid.
What is the minimum amount the student needs to earn per month to save enough money
to pay the remaining cost?
$300
$600
$500
$800
The minimum amount the student needs to earn per month to save enough money to pay the remaining cost is $500.
The total annual cost to attend community college is $5,000. The college offered a high school senior a scholarship for $1,800 and the student can get a loan for $1,200. To find the minimum amount the student needs to earn per month to save enough money to pay the remaining cost, follow these steps:
1. Subtract the scholarship and loan amounts from the total cost: $5,000 - $1,800 - $1,200 = $2,000.
2. Divide the remaining cost by the number of months (4) until the cost must be paid: $2,000 / 4 = $500.
Therefore, the minimum amount the student needs to earn per month to save enough money to pay the remaining cost is $500.
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Below are the number of siblings that each of Sarah's six friends has.
4,1,0,3,2, 2
Using this data, create a dot plot where each dot represents a friend.
Number of siblings 4,1,0,3,2,2
PLEASE HELP ME IM SO CONFUSED!!! Please help right away!
The dot plot where each dot represents a friend is given below
We are given that;
Number of siblings= 4,1,0,3,2, 2
Now,
To create a dot plot using this data, we need to follow these steps:
Draw a horizontal number line with the values from 0 to 4, which are the possible numbers of siblings that Sarah’s friends have. Label the number line as “Number of siblings”.
For each value in the data set, place a dot above the corresponding number on the number line. If there are more than one friend with the same number of siblings, stack the dots vertically.
Give the dot plot a title, such as “Number of Siblings of Sarah’s Friends”.
The dot plot should look something like this:
Therefore, by the dot plot is shown above.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer: D (t−3)(t−5)(t+4)
Step-by-step explanation:
Hope this helps! :)
The number of people in a town of 10,000 who have heard a rumor started by a small group of 10,000 people is given by the following function: N(t)= 10000/5 + 1245e^-0.97(t)
Part I: On Day #0 (t = 0), how many people knew the rumor?
Answer:
N(0)=10000/(5+1245)
Step-by-step explanation:
substitute zero in for t. Anything to the zero power equals 1.
Answer:
8 people
Step-by-step explanation:
N(0)=10000/(5+1245e^-0.97(0))
N(0) = 10000/(5+1245e^0)
e^0 = 1
= 10000/5+1245(1)
= 10000/5+1245
= 10000/1250
= 8
substitute zero in for t. Anything to the zero power equals 1.
Make up two data sets. List all the values in each dat set and write a story to describe where they may have come from. The data sets should meet the following conditions:
- The data should come from random samples taken from a population
- The centers of the distributions should be similar
- The variables of the distributions should be different
Pls show work
Answer:
- The centers of the distributions should be similar
Step-by-step explanation: - The centers of the distributions should be similar
HOCKEY Andrew went to the hockey game. He paid $13.50 for admission. He bought a program for $4.75, a bag of a popcorn for $3.50, and a large drink for $3.35. How much did he spend in all ?
Answer:
$25.10
Step-by-step explanation:
We can find the total amount Andrew spent at the hockey game by finding the sum of each individual cost, including the costs for admission, the program, the popcorn, and the large drink
Total amount spent = 13.50 + 4.75 + 3.50 + 3.35
Total amount spend = $25.10
Silver Stirrup Horse Rescue is going to paint the front of the big red barn. The triangular top portion of the barn is 20 feet across and 8 feet tall. The rectangular bottom portion is also 20 feet across, buts it’s 13 1/2 feet tall. The rescue will use extra-double gallons of paint that cover over 100 sq ft each.
How many gallons of paint does the rescue need to cover the entire front of the barn?
Write your answer as A Whole Number, Proper fraction or Mixed Number
HELP MEE PLEASEEE
I NEEED HELPPPO
The two lengths of the chords of circle are solved and x = 5 units
Given data ,
Let the length of the two chords be represented as AB and CD
Now , AB = 21 and CD = 3x
where E is the extended point of the two chords which intersect at point E
Now , from the intersection of chords outside the circle ,
BE ( AE ) = DE ( CE )
On simplifying , we get
4 ( 25 ) = x ( 4x )
100 = 4x²
Divide by 4 on both sides , we get
x² = 25
Taking square roots on both sides , we get
x = 5 units
Hence , the chords are solved and x = 5 units
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Qui peut résoudre ce calcul svp
(2+1x)(3-2x)-(2x+1)(-1x+2)
Answer:
6-x-2x^2 - (-2x^2 +3x+2)=6-x-3x-2=-4x+4
GASES The volume V of a gas varies inversely as its pressure P. If V=80 cubic centimeters when P = 2000 millimeters of mercury, find V when P=320 millimeters of mercury.
A. 500cm3
B. 12.8cm3
C. 8000cm3
D. 80cm3
Answer:
A. 500 cm3
Step-by-step explanation:
The general inverse variation equation is
y = k/x, where y varies inverse as x and k is the constant of proportionality.
Thus, if we substitute V for y and P for x in the equation, we have
V = k / x
To find k, we can plug in 80 for V and 2000 for P and solve for k:
80 = k / 2000
160000 = k
Finally, to find V when P = 320 millimeters, we can plug in 160000 for k and 320 for P and solve for V:
V = 160000 / 320
V = 500 cm3
Larry put $1,287 into a savings account 8 years ago. The account earned 4% simple annual interest. He made no additional deposits or withdrawals. Based on this information, what is the balance in dollars and cents in Larry's savings account at the end of these 8 years? Record your answer and fill in the box on your answer document. Be sure to use the correct place value. Answer:
Therefore, the balance in Larry's savings account at the end of 8 years is $1,699.84.
What kind of mathematics is employed in finance?
Algebra. A financial management expert is often required to solve for variables in banking and investing financial models. Even if most of the work is now done for us by programmes like Excel, having a solid grasp of the fundamentals of algebra is still commonly seen as being very beneficial.
After eight years, the balance in Larry's savings account can be determined using the straightforward interest formula:
A = P(1 + rt)
where A represents the final balance, P the initial principal, r the yearly interest rate expressed as a decimal, and t the period of time in years.
In this case, we have P = $1,287, r = 0.04, and t = 8.
A = $1,287(1 + 0.04*8)
= $1,287(1.32)
= $1,699.84
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When the inequality x > 5 is graphed, the dot will be is it open or closed
The dot in the graph of the inequality, x > 5, will be opened
Graph of inequality: Determining if the dot will be opened or closedFrom the question, we are to determine if the dot in the graph of the given inequality will be opened or closed
The given inequality is x > 5
If the sign of an inequality has the equals sign included, that is greater than or equal to (≥) OR less than or equal to (≤), the dot in the graph will be closed.
But if the inequality is less than or greater than (< or >), the dot in the graph will be opened.
Hence,
The dot in the graph of x > 5 will be opened since the inequality sign is not greater than or equal to (≥) OR less than or equal to (≤).
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need help fast don’t need explanation just answer my last question
The equation of the asymptotes for the given function y = 8/x are x = 0 and y = 0.
What is an asymptote?
an asymptote is a straight line or a curve that a function approaches but never touches as the independent variable (usually denoted by "x") approaches a certain value or becomes very large or small.
In the case of a straight line asymptote, the function approaches the line as x approaches positive or negative infinity. If the line is horizontal, then the function approaches a horizontal asymptote, and if the line is vertical, then the function approaches a vertical asymptote. For example, the function y = 1/x has a vertical asymptote at x = 0, because as x approaches 0, the function approaches infinity (or negative infinity) and never touches the vertical line x = 0.
The given equation y = 8/x represents a hyperbolic function. The graph of this function has two asymptotes, one in the x-axis (y = 0) and the other in the y-axis (x = 0).
To find the equation of the asymptotes, we can use the fact that as x becomes very large or very small, the function approaches the asymptotes. The equation of the vertical asymptote, which is x = 0, can be obtained by taking the limit of the function as x approaches 0 from both the positive and negative sides. We get:
lim x→0+ 8/x = +∞
lim x→0- 8/x = -∞
So the vertical asymptote is x = 0.
The equation of the horizontal asymptote, which is y = 0, can be obtained by taking the limit of the function as x becomes very large. We get:
lim x→±∞ 8/x = 0
So the horizontal asymptote is y = 0.
Therefore, the equation of the asymptotes for the given function y = 8/x are x = 0 and y = 0.
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can dog food is on sale for 20% off the original price what is the discount of the kid is the original price is $1.35
the discount on the dog food is $0.27, and the discounted price is $1.08.
What is the percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
If the original price of the dog food is $1.35 and it is on sale for 20% off, the discount would be:
Discount = 20% of $1.35
Discount = 0.20 x $1.35
Discount = $0.27
Therefore, the discounted price of the dog food would be:
Discounted price = Original price - Discount
Discounted price = $1.35 - $0.27
Discounted price = $1.08
So the discount on the dog food is $0.27, and the discounted price is $1.08.
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Solve for x to the nearest 10th.
57 = 2070(0.93)^x - 11
The solution to the equation 57 = 2070(0.93)^x - 11 to the nearest tenth is x ≈ 86.5.
What is an equation?A mathematical assertion that two expressions are equal is known as an equation.
A typical equation contains one or more variables, which are elements with several possible values.
Finding the values of the variables that make an equation true is the aim of equation solving.
A linear equation, which has the form:, is the most widespread sort of equation.
ax + b = 0
where the objective is to find the value of the variable x and a and b are constants.
What are variables ?A variable in mathematics is a symbol or letter that designates a value that is subject to variation or change. In algebraic expressions and equations, variables are used to denote unknown or fluctuating quantities, such as a building's height or the number of apples in a basket.
Typically, letters from the alphabet, such as x, y, and z, are used to represent variables. Mathematical expressions can be created using variables, constants (numbers), and operators (+, -, x, /, etc.) in an algebraic expression. As an illustration, the phrase 2x + 3y - 5z combines the three variables x, y, and z in a linear fashion.
According to the question ,
By adding 11 to both sides, we may isolate the exponential term first:
57 + 11 = 2070(0.93)^x
Streamlining the left side: 68 = 2070(0.93)^x
By 2070, divide both sides: 0.03285024 = (0.93)^x
Using both sides' natural logarithms: ln(0.03285024) = ln[(0.93)^x]
By applying the logarithm property, which states that ln(ab) = b ln(a):
ln(0.03285024) = x ln(0.93)
By dividing both sides by ln(0.93), one can find x:
x = ln(0.03285024) / ln(0.93)
When we evaluate this expression with a calculator, we obtain:
x ≈ 86.5
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