Quadratic Expression: is an expression with the variable with the highest exponent being 2
General form: ax^2 + bx + c
Greatest common factor (GCF): the largest whole number that divides evenly into a set of numbers
When factoring out the GCF of this expression we must look at the "a" term and "c" term
the greatest common factor of the terms a and c is 8we can that factor out the 8 from the original expression, putting it outside the brackets and dividing the original terms by the GCF8/8 =1 and -24/8= -3[tex]8(x^2-3)[/tex] which is the expression factored.
Luka and Janie are playing a coin toss game. If the coin lands heads up, Luka earns a point; otherwise, Janie earns a point. The first player to reach 18 points wins the game. If 17 of the first 33 tosses have been heads, what is the probability that Janie wins the game?
The probability that Janie wins the game is approximately 0.0955.
What is binomial distribution?The probability distribution of a binomial random variable is known as the binomial distribution. The sample space of a random experiment serves as the domain of a random variable, which is a real-valued function. To further comprehend this, let's look at an illustration.
We can approach this problem using the binomial distribution. Let X be the number of heads in the remaining tosses until one player wins the game, and let p be the probability that the coin lands tails (since if it lands tails, Janie earns a point). Since the first 33 tosses have already been made, there are 50 - 33 = 17 tosses remaining until one player wins.
Since 17 of the first 33 tosses were heads, there were 33 - 17 = 16 tails. Therefore, the probability of getting a tail is p = 1/2.
Let Y be the total number of tosses until one player wins. Since each toss is independent and has a probability of 1/2 of resulting in a head, Y follows a geometric distribution with parameter p = 1/2.
The game ends when one player reaches 18 points, which means there must be at least 35 tosses. Therefore, the probability that Janie wins the game is:
P(Janie wins) = P(Y = 35) + P(Y = 37) + P(Y = 39) + ... + P(Y = 67)
We can use the formula for the geometric distribution to calculate each of these probabilities:
[tex]P(Y = k) = (1 - p)^{(k-1)} * p[/tex]
where k is the number of tosses until one player wins. Plugging in p = 1/2, we get:
[tex]P(Y = k) = (1/2)^{(k-1)} * (1/2)[/tex]
Now we can substitute this into the expression for P(Janie wins):
P(Janie wins) = (1/2)³⁴ + (1/2)³⁶ + (1/2)³⁸ + ... + (1/2)⁶⁶
This is a finite geometric series with first term (1/2)³⁴ and common ratio 1/4 (since each successive term is multiplied by (1/2)²). Therefore, we can use the formula for the sum of a finite geometric series to simplify the expression:
P(Janie wins) = [(1/2)³⁴ * (1 - (1/4)¹⁷)] / (1 - 1/4)
= [(1/2)³⁴ * (1 - (1/2)³⁴)] / (3/4)
= 0.0955
Therefore, the probability that Janie wins the game is approximately 0.0955.
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1 How many US dollars do you get for £100? 2 How many Sri Lankan rupees do you get for £50? 3 How many euros do you get for £30? 4 How many pounds do you get for 380 Sri Lankan rupees?
Answer:1: $124.25 2: 20,222.50Rs, 3: 33.90 euro, 4:0.94 pounds
Step-by-step explanation:
Two people rented a car from the same agency. The first person drove 1010 miles and paid $232.30 for mileage. The second person drove 765 miles and paid $175.95 for mileage. What is the agency's fee per mile?
Please answer the question
two students evaluate the expression 17(4+15)
17(4+15)
= 17*19
=323
Answer:- 323
Pls help
The scores on a standardized test are normally distributed with a mean of 110 and standard
deviation of 15. What test score is 0.3 standard deviations above the mean?
O
Houghton Mifflin Harcourt Publishing Company
5.
S
WRITE Math Draw two different figures that
each have a perimeter of 20 units.
S
+htt
E
S
Answer:
To draw a figure with a perimeter of 20 units, you can start by drawing a shape with sides that add up to 20 units. For example, you could draw a rectangle with sides of 5 units and 5 units and two sides of 2.5 units each. This would give you a perimeter of 20 units.
Another example could be drawing a square with sides of 5 units each. This would also give you a perimeter of 20 units.
For the second figure, you could draw a triangle with sides of 8 units, 6 units, and 6 units. This would give you a perimeter of 20 units.
Alternatively, you could draw a pentagon with sides of 4 units each. This would also give you a perimeter of 20 units.
Step-by-step explanation:
find the number of ways that the digit 0,1,2and3 can be permuted to give rise to a number greater than 2000
12 or 128
by the way question is not complete
the answer is 128 , if repetition is allowed
and answer is 12 , if repetition is not allowed
When tracey and Chris’s daughter Emily was born, they set up a trust fund to mature on her 18th birthday. They invested $25,000. When Emily turned 18, the trust fund was worth $100,000. At what continuous rate of interest r was the money invested? (Use A=Pe^rt) enter your answer as a percentage rounded to one decimal point.
Answer: The continuous interest rate at which the money was invested is approximately 15.4%.
Step-by-step explanation: We can use the formula for continuous compounding to find the value of r:
A = Pe^(rt)
Where A is the final value, P is the initial investment, e is the base of the natural logarithm, r is the continuous interest rate, and t is the time.
Plugging in the given values, we get:
$100,000 = $25,000e^(r*18)
Dividing both sides by $25,000 and taking the natural logarithm of both sides, we get:
ln(4) = 18r
Solving for r, we get:
r = ln(4)/18 ≈ 0.154
Multiplying by 100 to convert to a percentage and rounding to one decimal point, we get:
r ≈ 15.4%
Therefore, the continuous interest rate at which the money was invested is approximately 15.4%.
Tiffany drew the design below that she is going to use on a stained glass window above her front door identify all the days in Tiffany’s design. See image below.
Answer:
Step-by-step explanation:
did you figure it out? i need help too
just part f pls the answer is 0.9449 but don't know how to get to it
The probability of disposing more than seven pineapple pies cumulatively throughout four hours due to greater than one hour exhibiting a dispersion of over two pies is 0.1618.
How to calculate the probabilityThe likelihood of selling more than 2 pineapple pies in at least one hour can be computed through the application of the complement rule:
P(at least two hours with a minimum of two pies dispersed) = 1 - P(less than two hours meeting the criterion of having more than two pies sold)
P(X < 2) = P(X = 0) + P(X = 1) = (e^(-4)*4^0)/0! + (e^(-4)*4^1)/1!
= 0.0183 + 0.0732 = 0.0915
Consequently, the probability of vending more than two pineapple pies during a given hour is 1 - 0.0915 = 0.9085.
Finally, we can calculate the probability of trading beyond seven pineapple pies total with Poisson distribution parameters λ = 4:
P(X > 7) = 1 - P(X <= 7) = 1 -[P(X=0) + P(X=1) + ... + P(X=7)]
= 1 - [e^(-4)(4^0)/0! + e^(-4)(4^1)/1! + ... + e^(-4)*(4^7)/7!]
= 1 - (0.0183 + 0.0732 + 0.1465 + 0.1954 + 0.1954 + 0.1563 + 0.1042 + 0.0595)
= 0.1472
Therefore, the likelihood of disposing more than seven pineapple pies cumulatively throughout four hours due to greater than one hour exhibiting a dispersion of over two pies is 0.1472/0.9085 = 0.1618.
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Find the indefinite integral
The indefinite integral will be ∫x⁵e^(x⁶ - 4) dx = (1/6)e^(x⁶ - 4) + C
How do we find the indefinite integral?Lets say u = x⁶ - 4 and du/dx = 6x⁵
it then becomes ∫x⁵e^(x⁶ - 4) dx = ∫e^(x⁶ - 4 * 1/6)du
e^(x⁶ - 4) = ∫(1/6)e^(x⁶ - 4)du = (1/6) ∫e^(x⁶ - 4) du = (1/6)e^(x⁶ - 4) + C
= ∫x⁵e^(x⁶ - 4) dx = (1/6)e^(x⁶ - 4) + C
An indefinite integral that when you differentiate it will give you the main or first function.
The above answer is based on the question below as seen in the photo;
Find the indefinite integral (Use C for the constant of integration)
∫x⁵e^(x⁶ - 4) dx
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Shannon’s Brewery in Keller, Texas is expanding distribution to a number of cities along the I-35 corridor south from Dallas to the Gulf Coast. Shannon’s typically distributes through large distributors such as Ben E. Keith located in Denton, Texas. However, Shannon Carter, CEO of Shannon’s Brewery, wants to employ a series of missionary sales persons to service restaurants, bars, supermarkets, and liquor stores. Their job will be to promote Shannon’s craft beers to these retailers and encourage them to place orders with Shannon’s normal distributor in that area. Based on research, Shannon Carter has identified an initial 688 retailers that are potential adopters of his beers. He estimates that it will take ten visits per year to acquire and then service each account. Each sales call is expected to take 32 minutes. Assume a 40-hour work week for sales reps and that 50% of each rep's time will be consumed by non-selling tasks and travel time. How many missionary sales reps will Shannon need to hire? (Note: you must convert the time allotted for each sales call from minutes to hours.) Round your answer up to the nearest 1/10 of a rep (in reality, as noted above, you would round to the next whole rep).
Answer:
mark me brilliant
Step-by-step explanation:
First, we need to determine the amount of time each sales representative can spend on selling each week.
A 40-hour work week is equivalent to 2,400 minutes (40 hours x 60 minutes/hour).
If 50% of each rep's time is consumed by non-selling tasks and travel time, then they have 1,200 minutes (2,400 minutes x 50%) available for selling each week.
Each sales call takes 32 minutes, so a rep can make 75 sales calls per week (1,200 minutes available for selling ÷ 32 minutes per sales call).
It takes 10 visits per year to acquire and service each account, which means a sales rep needs to visit each of the 688 potential adopters 10 times per year, or 6,880 visits in total per year.
Each sales rep can make 75 visits per week, which means they can make 3,900 visits per year (75 visits per week x 52 weeks in a year).
Therefore, Shannon will need to hire 1.76 sales reps (6,880 total visits needed ÷ 3,900 visits per year per sales rep).
Rounding up to the nearest 1/10 of a rep, Shannon should hire 1.8 sales reps.
What is the range of the equation shown in the graph?
The range of equation represented by the graph is [1, ∞}.
What is range?The set of all potential values that a function could output or produce is known as its range. To put it another way, it is the collection of all values that the function "hits" or "reaches" when given various input values.
It's crucial to remember that not every function has a range that encompasses all potential values. For instance, the set [-1, 1] is the range of the function g(x) = sin(x), which only returns values between -1 and 1.
The range of the function are all the output values of the of the function or the y-coordinates of the graph.
For the given graph we see that the y-coordinates corresponding to the graph are from: 1 to ∞.
Hence, the range of equation represented by the graph is [1, ∞}.
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Find the future value of an investment of $12500 if it is invested for four years and compounded semiannually at an annual rate of 4%. Use the $1.00 future value table or the future value and compound interest formula.
Answer:
$14,636.97
Step-by-step explanation:
FV = PV x (1 + r/n)^(nt)
where r is the annual interest rate (as a decimal), n is the number of compounding periods per year, t is the number of years the money is invested, and PV is the present value.
In this case, r = 0.04 (4% as a decimal), n = 2 (since it is compounded semiannually), t = 4, and PV = $12500. Substituting these values into the formula, we get:
FV = $12500 x (1 + 0.04/2)^(2x4)
FV = $12500 x (1.02)^8
FV = $14,636.97
Therefore, the future value of the investment after four years is $14,636.97.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$12500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 12500\left(1+\frac{0.04}{2}\right)^{2\cdot 4} \implies A \approx 14645.74[/tex]
SOMEONE HELPP ME PLEASEE. can you also show work if that’s possible. Make it simple
The solution is: the value of x is : x = 98.5.
Formula
<x = 1/2 (arc 1 + arc2)
This is the basic angle formula for the way two chords intersect.
Givens
arc1 = 96
arc2 = 101
Solution
<x = 1/2 (arc1 + arc2) Substitute values
<x = 1/2(96 + 101)
<x = 1/2(197)
<x = 98.5
Answer
x = 98.5
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radius of a circle with a circumference of 28 pie
Answer:
Radius: 14
Step-by-step explanation:
We know
Circumference of circle = 2 · r · π
Circumference = 28π
Find radius!
Let's solve
28π = 2 · r · π
14π = r · π
r = 14
So, the radius is 14
Answer:
The radius is 14.
Step-by-step explanation:
Since the circumference is 28pi, we can find the diameter.
C = pi•d
C = 28pi
28pi = pi•d
divide both sides by pi.
d = 28
The diameter is 28.
So, cut it in half to find the radius. 28/2 is 14. The radius is 14.
Luann has a piece of ribbon that is 1 yard long she cuts off 33 inches to tie a gift box how many inches of ribbon are not used?
The unused length of the ribbon is 3 inches.
Given that, Luann has a piece of ribbon that is 1 yard long she cuts off 33 inches to tie a gift box,
We need to find the unused length of the ribbon,
Since, 1 yard = 36 inches
Therefore, Luann has 36 inches long ribbon, in which she used 33 inches,
So, the left length = 36 - 33 = 3 inches.
Hence, the unused length of the ribbon is 3 inches.
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does each of the following nets form a rectangular prism a triangular prism or cube if yes name the polyhedron
Rectangular prism and triangular prism is discussed below.
Rectangular prism
In geometry, a rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges.Rectangular prism
In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise it is obliqueTo solve more questions on Prisms, visit the link-
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I dont nkow wht to do here
pls answer
woth 20 point!!
Answer: 25.461 cm
Step-by-step explanation:
The circumference of a circle can be found using the formula C = πd, where d is the diameter and π (pi) is a constant value of approximately 3.14159.
Substituting d = 8.1 cm into the formula, we get:
C = πd
C = 3.14159 x 8.1 cm
C = 25.461 cm (rounded to 3 significant figures)
Therefore, the circumference of the circle with diameter 8.1 cm is approximately 25.461 cm.
i need help in these 2 questions please help me as fast as you can.
Answer:
Step-by-step explanation:
How many times can 1/5 go into nine
Answer:
1.8
Step-by-step explanation:
In 2000, the population of a town was 50,000. In 2010, the population of the town was 48,000. What is the percent change in the town’s population? Your answer should be written as a percent, i.e., 55%.
To calculate the percent change in population, we first need to find the difference between the two population numbers, then divide that difference by the original population, and finally, multiply by 100 to get the percentage change.
The difference in population is:
50,000 - 48,000 = 2,000
To find the percent change, we divide the difference by the original population:
2,000 / 50,000 = 0.04
Finally, we multiply by 100 to get the percentage change:
0.04 x 100 = 4%
Therefore, the percent change in the town's population from 2000 to 2010 is a decrease of 4%.
Step-by-step explanation:
To find the percent change, we need to calculate the difference between the initial population and final population, and then divide it by the initial population.
Change in population = Final population - Initial population
= 48,000 - 50,000
= -2,000
Since the change is negative, it means that there was a decrease in the population.
Percent change = (Change in population / Initial population) x 100%
= (-2,000 / 50,000) x 100%
= -0.04 x 100%
= -4%
Therefore, the percent change in the town's population is -4%.
Daniel randomly surveyed 120 students at his school and found that 96 of them have at least one sibling. Based on these data, how many of the 425 students at his school would be expected to have at least one sibling?
There is an estimate that 340 of the school's 425 students have at least one sibling.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
To estimate the number of students in the school who have at least one sibling, we can use the proportion from the sample.
The proportion of students with at least one sibling can be calculated as:
= 96/120
= 0.8
Expected number of students with at least one sibling in the school:
= Proportion x Total number of students
= 0.8 x 425
= 340
Therefore, it would expect 340 of the 425 students at the school to have at least one sibling.
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The entire graph of the function h is shown below write the domain and range of h using interval notation.
The domain and the range of the graphed function are given as follows:
Domain: (-3, 5].Range: [-5, 4).What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function, that is, all the values assumed by the independent variable x in the function.The range of a function is the set that contains all possible output values of the function, that is, all the values assumed by the dependent variable y in the function.From the graph of the function, the domain and range are obtained as follows:
Domain: (-3, 5], as x ranges from an open circle at x = -3 to a closed circle at x = 5.Range: [-5, 4), as y ranges from a closed circle at y = -5 to a closed circle at y = 4.Missing InformationThe graph is given by the image presented at the end of the answer.
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Find the cosecant of ∠C.
27
36
C
D
E
The calculated value of the cosecant of ∠C is 1.33
Finding the cosecant of ∠C.From the question, we have the following parameters that can be used in our computation:
CD = 27
CE = 36
The cosecant of ∠C. is then calculated as
Cosecant ∠C. = CE/CD
substitute the known values in the above equation, so, we have the following representation
Cosecant ∠C. = 36/27
Evakuate
Cosecant ∠C. = 1.33
Hence, teh solution is 1.33
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Mark the following numbers on the number line below.
8 1/2. 9 3/4. 40/5. 44/5
Answer:
If this helpful
MARK ME AS BRAINLIEST PLEASE
Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed.
C=0.90, x=13.7, s =3.0, n= 10
The population is normally distributed is 90 %.
Given that
C = 0.90,
x = 13.7,
s = 3.0,
n = 10
Use the following formula is necessary:
CI = x t*(s /[tex]\sqrt{n}[/tex])
Where CI stands for confidence interval, x represents sample mean, s represents sample standard deviation, n represents sample size, and t represents the desired level of confidence and the t-value from the t-distribution with n-1 degrees of freedom.
According to the information given, we have:
Since alpha + C equals 1, C = 0.90,
which means that alpha is 0.10. x = 13.7 s = 3.0 n = 10
The t-distribution must be used in place of the z-distribution because n is small (n 30).
Which has a degree of freedom of n-1 = 9 and a confidence level of 90%. About 1.833 is the t-value.
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Find the surface area of a square pyramid with side length 3 m and slant height 6 m.
HELP MEH ASAP
Nine people sit in chairs in a room.
In how many ways can four of these people be chosen to stand up?
Enter your answer in the box.
ways
There total of 126 ways in which nine people can sit on chairs in the room when four of these people be chosen to stand up.
The problem is asking how many ways we can choose 4 people out of 9 to stand up. This is a combination problem since the order in which the people are chosen is irrelevant. We can utilize the combination formula, which is,
n choose k = n!/(k!(n-k)!), where n is the total number of items to choose from, and k is the number of items to choose. In this case, we have n=9 people and k=4 people to choose. Putting all the values in formula,
9 choose 4 = 9!/(4!(9-4)!)
9 choose 4 = 362880/(24 x 120)
9 choose 4 = 126.
Therefore, there are 126 ways to choose 4 people out of 9 to stand up.
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