Form a fifth-degree polynomial function with real coefficients such that i, 1-2i, and 5 are zeros and f(0) = -75.
f(x)=
(Simplify your answer. Type an expression using x as the variable.)
Answers
well, hmmm keeping in mind that complex roots never come all by their lonesome, their sister always comes along, namely their conjugate, so if we have the complex roots of "i" or namely "0 + i", we also have her sister "0 - i", and if we have "1 - 2i", she also came with "1 + 2i", and we also have the root of 5, and that'd give us the fifth degree polynomial, so
[tex]\begin{cases} x = 0+i &\implies x -i=0\\ x = 0-i &\implies x +i=0\\ x = 1-2i &\implies x -1+2i=0\\ x = 1+2i &\implies x -1-2i=0\\ x = 5 &\implies x -5=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -i )( x +i )( x -1+2i )( x -1-2i )( x -5 ) = \stackrel{0}{y}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{difference of squares} }{( x -i )( x +i )}\implies x^2-i^2\implies x^2-(-1)\implies x^2+1 \\\\[-0.35em] ~\dotfill[/tex]
[tex]( x -1+2i )( x -1-2i )\implies \stackrel{ \textit{difference of squares} }{( [x -1]+2i )( [x -1]-2i )} \\\\\\ (x-1)^2 -(2i)^2\implies (x^2-2x+1)-4i^2\implies (x^2-2x+1)-4(-1) \\\\\\ x^2-2x+1+4\implies x^2-2x+5 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{so we can say}}{a(x^2+1)(x^2-2x+5)(x-5)=y}\hspace{5em}\textit{we also know that } \begin{cases} x=0\\ y=-75 \end{cases} \\\\\\ a(0^2+1)(0^2-2(0)+5)(0-5)=-75\implies -25a=-75 \\\\\\ a=\cfrac{-75}{-25}\implies a=3 \\\\[-0.35em] ~\dotfill[/tex]
[tex]3(x^2+1)(x^2-2x+5)(x-5)=y\implies 3(x^3-5x^2+x-5)(x^2-2x+5)=y \\\\\\ 3(x^5-7x^4+16x^3-32x^2+15x-25)=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} 3x^5-21x^4+48x^3-96x^2+45x-75=y \end{array}}~\hfill[/tex]
Check the picture below.
Related Questions
When you rewrite an addition or subtraction problem using the Distributive Property, you have to ______ both values by a common factor, usually the GCF.
Answers
When you rewrite an addition or subtraction problem using the Distributive Property, you have to factor out both values by a common factor, usually the GCF.
This process involves identifying the common factor (the greatest common factor, or GCF) of the terms and then applying the Distributive Property to rewrite the expression. This common factor can be the greatest common factor (GCF) if it exists, but it does not have to be. The goal is to find a factor that is common to both terms, so that it can be factored out and the expression can be simplified.For example, consider the expression 6 + 8. We can rewrite this using the distributive property by factoring out 2, which is a common factor of both 6 and 8:6 + 8 = 2(3) + 2(4)Then, we can simplify the expression by adding the like terms:2(3) + 2(4) = 6 + 8 = 14Note that in this example, we factored out the common factor 2, which is not the GCF of 6 and 8 (the GCF is 2). However, factoring out 2 allowed us to simplify the expression using the distributive property.
Learn more about GCF here, https://brainly.com/question/219464
#SPJ11
Mayank wants to make 17 payments to his child’s college fund. He assesses his income and comes to the conclusion that he can increase the payment by 4% every year. The value of cost of a college education today is ₹ 9,422. 92. How much should the first payment be to the college fund? Assume discount rate to be 14%
Answers
If the value of cost of a college education today is ₹ 9,422. 92, the first payment to Mayank's child's college fund should be ₹ 2,447.22.
To determine the amount of the first payment to Mayank's child's college fund, we need to calculate the present value of all the payments discounted at a rate of 14%.
We can start by calculating the future value of the 17 payments based on the annual increase of 4%. Using the formula for the future value of an annuity, we get:
FV = Payment * [(1 + r)ⁿ⁻¹] / r
where r is the annual increase rate (4%), n is the number of payments (17), and Payment is the amount of the first payment.
FV = Payment * [(1 + 0.04)¹⁷⁻¹] / 0.04
FV = Payment * 21.6019
Next, we can calculate the present value of the future payments using the formula for the present value of an annuity:
PV = FV / (1 + r)ⁿ
where r is the discount rate (14%) and n is the number of payments (17).
PV = FV / (1 + 0.14)¹⁷
PV = FV / 5.616
Substituting the value of FV, we get:
PV = Payment * 21.6019 / 5.616
PV = 3.8514 * Payment
Finally, we can solve for the value of Payment by dividing the present value of the payments by 3.8514:
Payment = PV / 3.8514
Payment = ₹ 9,422.92 / 3.8514
Payment = ₹ 2,447.22
In summary, Mayank can afford to make 17 payments to his child's college fund, increasing by 4% every year.
By discounting the future payments at a rate of 14%, the present value of all payments can be determined, and the amount of the first payment can be calculated using the formula for the present value of an annuity. The first payment should be ₹ 2,447.22.
To learn more about income click on,
https://brainly.com/question/28595353
#SPJ4
Krissy created the following equation to describe the cost of renting a bicycle. What type of function is this?
Answers
The equation of the cost of renting a bicycle given by Krissy is non-proportional.
Here we see that the function Krissy wrote was
y = 5x + 15.
A function is called a proportional function if y/x is some fixed constant. This means, rearranging the equation should give us
y/x = k, where k is some constant.
Here we have,
y = 5x + 15
Dividing both sides by x will give us
y/x = 5 + 15/x
Now, clearly RHS is not a constant as it has a variable x present. Hence the function is non-proportional.
Another way to check the proportionality of a function is to check whether the function is in the form of
y = cx, where c is a constant. Here, there should not be added or subtracted constant with x. On the concerned equation, RHS had an additional constant of + 15.
Hence, the equation given by Krissy is a non-proportional function.
To learn more about Functions visit
https://brainly.com/question/12431044
#SPJ4
Complete Question
(Image Attached)
PLEASE HELP I NEED THIS ASAP THANK YOU.
Answers
The bases of both the triangles are 15 and 5 units respectively.
Given are right triangles we need to find the bases of the triangles,
Using the trigonometric ratios,
1) Let the base be b,
We know that the tangent of an angle is the ratio of the perpendicular side to the base.
So,
Tan 60° = 15√3/b
b = 15√3/√3
b = 15
Therefore the base of the first triangle is 15 units.
Similarly,
2) The cosine of an angle of rt. triangle is the ratio base to the hypotenuse.
So,
Cos 45° = m/5√2
1/√2 = m/5√2
m/5 = 1
m = 5
Therefore the base of the first triangle is 5 units.
Learn more about trigonometric ratios, click;
https://brainly.com/question/25122825
#SPJ1
Alvin's age is three times Elga's age. The sum of their ages is 88. What is Elga's age?
Answers
The age of Alvin is 66 years. Then the age of Elga will be 22 years.
Given that:
Alvin's age is three times Elga's age. The sum of their ages is 88.
Let 'x' be the age of Alvin and 'y' be the age of Elga. Then the equations are given as,
x = 3y ...(1)
x + y = 88 ...(2)
From equations (1) and (2), then we have
3y + y = 88
4y = 88
y = 22
Then the value of 'x' is calculated as,
x = 3 × 22
x = 66
The age of Alvin is 66 years. Then the age of Elga will be 22 years.
More about the solution of the equation link is given below.
https://brainly.com/question/22613204
#SPJ1
Determine if I triangle can be constructed with the following sides. Explain
2/3 , 4/5 , 1/2
what value of x would allow a triangle to be constructed with the following measures?
a. 21,8,x
b. 13,7,x
Answers
Answer: Yes, a triangle can be constructed with sides of 2/3, 4/5, and 1/2
To determine if a triangle can be constructed, we need to check if the sum of the two smaller sides is greater than the largest side. In this case, 2/3 + 1/2 > 4/5, 2/3 + 4/5 > 1/2, and 1/2 + 4/5 > 2/3, so a triangle can be formed.
Step-by-step explanation: Sincerely, answered by Lizzy ♡ :: as an A+ student, I want to make sure other students can succeed as well, so in my free time: i answer questions like yours on Brainly! if you could click the thanks heart, give me brainliest by clicking the crown, and rate my answer 5 stars, it would be appreciated! have a lovely day! (ᵔᴥᵔ)
SOIVING MUITI-STEP eQuaTiONS digital puzzle DIRECTIONS: Solve each equation and put the puzzle together correctly by matching the equations to their correct answers.
Answers
Answer:
the picture ain't clear.
Solving multi-step equations involves systematically isolating the variable through algebraic operations. In terms of the 'digital puzzle', it would require the matching of solved multi-step equations with their solutions, providing a practical method of practicing algebra skills.
Explanation:Based on your question, it appears you are working on a multi-step equation puzzle. In solving multi-step equations, it is important to systematically isolate the variable. For example, if you have a multi-step equation like 3x + 2 = 14, you would first subtract 2 from both sides and then divide by 3 to get x = 4, which is the solution. Each step involves an algebraic operation, and the aim is to simplify the equation to reach your final answer.
The mentioned 'digital puzzle' is most likely an interactive activity where you have to match these multi-step equations with their corresponding solutions. Simply solve each equation and drag the solution to its corresponding equation. This is a great way to practice algebra skills.
Learn more about Multi-step Equations here:https://brainly.com/question/18686312
#SPJ2
A random sample of 100 customers at a local ice cream shop were asked what their favorite topping was. The following data was collected from the customers.
Topping Sprinkles Nuts Hot Fudge Chocolate Chips
Number of Customers 17 12 27 44
Which of the following graphs correctly displays the data?
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27, and the fourth bar labeled chocolate chips going to a value of 44
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled nuts going to a value of 17, the second bar labeled sprinkles going to a value of 12, the third bar labeled chocolate chips going to a value of 27, and the fourth bar labeled hot fudge going to a value of 44
a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27 ,and the fourth bar labeled chocolate chips going to a value of 44
a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled nuts going to a value of 17, the second bar labeled sprinkles going to a value of 12, the third bar labeled chocolate chips going to a value of 27, and the fourth bar labeled hot fudge going to a value of 44
Answers
Where the above conditions are given, the correct graph is "a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27, and the fourth bar labeled chocolate chips going to a value of 44" (Option A)
How can I choose the best graph for this situation?
We must examine the data to choose the best graph for this case. In this scenario, the toppings have a link with the amount of clients that choose each flavor.
We may conclude that the best choice is A based on the amount of persons who like each topping in the order in which the table organizes them.
Learn more about graphs:
https://brainly.com/question/17267403
#SPJ1
put the word to the meaning 20 points !!!!!!
Answers
Answer:
Alcohol use disorder
Couyog Hi gun gun
Iyogf cool cool chip void viz
56 until igloo Ohio
Ru track trio to
Adverb
6r Yahoo ump
Caracas
Eastwards
In the data set below, what is the interquartile range?
4 5 6 8 8 9
Answers
The answer to this would be 3
G
7
Which is a diagonal through the interior of the cube?
OBE
A
1
C
Mark this and return
1₂
D
I
H
B
LL
Save and Exit
lext
Submit
Answers
The diagonal through the interior of the cube is side CF. Option B
How to determine the diagonalTo determine the diagonal of the cube:
We need to know the properties of a cube. These properties are;
It is a square-shaped, three-dimensional object.It contains 8 vertices, 6 faces, and 12 edges.Every face has a square form to it.The length of each side is equal.Three faces and three edges are met by each vertex.The margins follow the lines that are parallel to it.A cube's angles are all right angles.From the diagram shown, we have that;
Diagonal through interior of the given cube will be the segments joining the vertices A-H, G-B, C-F and D-E.
Learn more about cubes at: https://brainly.com/question/1972490
#SPJ1
The complete question is:
Which is a diagonal through the interior of the cube
A. Line BE
B. Line CF
C. Line DG
D. Line GF
Coin Toss Real life probability
Toss coin 50 times, find probability vs actual results
Answers
The probability of getting heads= 1/2
The probability of getting tails = 1/2
How to determine the probability of heads and tails?To determine the outcome of a possible event (probability) the formula stated below should be used.
Probability = possible outcome/sample space
When a coin is tossed 50 times the sample space ,= 100
The possible outcome for heads = 50
probability = 50/100 = 1/2
The probability for tails = 50/100 = 1/2.
Learn more about probability here:
https://brainly.com/question/30657432
#SPJ1
On a certain hot summer's day, 133 people used the public swimming pool. The daily prices are 1.50 for children and 2.25 for adults. The receipts for admission totaled 270.75 How many children and how many adults swam at the public pool that day?
Answers
That day the number of adults was 95 and the number of children was 38
How many children and how many adults swam at the public pool that day?Let's define the variables:
x = number of adults.
y = number of children.
We know that 133 people used the public swimming pool. then we can write:
x + y = 133
We also know that the receipts for admission totaled 270.75, then we can write other equation as:
2.25x + 1.5y = 270.75
Then the system of equations is:
x + y = 133
2.25x + 1.5y = 270.75
In the first equation we can isolate x to get:
y = 133 - x
Now replace that in the other equation to get:
2.25x + 1.5*(133 - x) = 270.75
0.75x + 199.5 = 270.75
0.75x = 270.75 - 199.5
x = 71.25/0.75 = 95
Then the value of y is:
y = 133 - 95 = 38
Learn more about systems of equations at:
https://brainly.com/question/13729904
#SPJ1
List three values that would make inequality true. 7n is the same or less than 21
Answers
Here are three values that would make the inequality 7n ≤ 21 true are found out to be n = 0, n = 1 and n = 3.
The inequality 7n ≤ 21 means that the product of 7 and n is less than or equal to 21. To make this inequality true, we need to find values of n that satisfy this condition.
If we substitute n = 0, we get 7(0) = 0, which is less than or equal to 21. Therefore, the inequality is true for n = 0.
If we substitute n = 1, we get 7(1) = 7, which is less than or equal to 21. Therefore, the inequality is true for n = 1.
If we substitute n = 3, we get 7(3) = 21, which is equal to 21. Since 21 is also less than or equal to 21, the inequality is true for n = 3.
Note that there are many other values of n that would also make the inequality true, such as any value of n less than or equal to 3.
Learn more about inequality :
https://brainly.com/question/31292339
#SPJ4
a person travels to work at an average speed of 40 mph, and returns home at 60 mph. what, in mph, is the average speed for the entire trip?
Answers
Answer:
50
Step-by-step explanation:
A person travels to work at an average speed of 40 mph, and returns home at 60 mph. the average speed for the entire trip is 48 mph.
To find the average speed for the entire trip, we need to use the formula:
average speed = total distance / total time
Let's assume that the distance to work is d.
The time it takes to travel to work is:
time = distance / speed = d / 40
The time it takes to return home is:
time = distance / speed = d / 60
The total distance for the round trip is:
total distance = d + d = 2d
The total time for the round trip is:
total time = d/40 + d/60
We can simplify the total time by finding a common denominator:
total time = (3d/120) + (2d/120) = 5d/120 = d/24
Now we can plug in the values for total distance and total time:
average speed = (2d) / (d/24) = 48 mph
Therefore, the average speed for the entire trip is 48 mph.
To find the average speed for the entire trip, we can use the harmonic mean formula for two rates: average speed = (2 * speed1 * speed2) / (speed1 + speed2). In this case, speed1 is 40 mph (to work) and speed2 is 60 mph (returning home).
Using the formula: average speed = (2 * 40 * 60) / (40 + 60) = (4800) / (100) = 48 mph.
So, the average speed for the entire trip is 48 mph.
To learn more about average, click here:
brainly.com/question/24057012
#SPJ11
Enter the number that belongs in the green box. 56° 78° 12 [? Round to the nearest hundredth.
Answers
Answer:
Set your calculator to degree mode.
Using the Law of Sines:
sin(56°)/12 = sin(78°)/x
x sin(56°)/12 = sin(78°)
x = 12sin(78°)/sin(56°) = 14.16
A patio is in the shape of a trapezoid. The length of the longer base is 17 feet. The length of the shorter base is two feet less than half the longer base. The height is 2 feet.
What is the area of the patio?
Answers
The area of the trapezoidal shaped patio is 23.5 square feet.
Given that, The length of the longer base of a trapezoid is 17 feet.
The length of the shorter base is two feet less than half the longer base.
The shorter base = 1/2 ×17 -2
= 6.5
The formula for the area of a trapezoid is expressed as, A = ½ (a+b)×h.
where (A) is the area of a trapezoid, 'a' and 'b' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between a and b).
Here, the area = 1/2 (17+6.5)×2
= 23.5 square feet
Therefore, the area of the trapezoidal shaped patio is 23.5 square feet.
#SPJ1
URGENT - Will also give brainliest to simple answer in terms of pi
A circle has radius 1 unit, find the length of the arc defined by each of these central angles
180 degrees
Answers
For a 180-degree central angle on a circle with a radius of 1 unit, the arc length is:
Arc length = (180 degrees) * (pi) * (radius)
= 180 * 3.1415 * 1
= 562.8
So the arc length for a 180-degree central angle on a circle with a radius of 1 unit is 562.8 units.
In general, for any central angle θ on a circle with radius r, the arc length is:
Arc Length = θ * π * r
So for:
θ = 270 degrees, arc length = 851.96
θ = 180 degrees, arc length = 562.8
θ = 90 degrees, arc length = π * r = 3.1415 * 1 = 3.1415
etc.
HELP ASAP I WILL MARK BRAINLIEST IF CORRECT
Answers
Answer:
First problem:
Area of shaded region:
(1/6)π(9^2) - (1/2)(9)(4.5√3) = 7.4 m^2
Second problem:
Area of shaded region:
(1/3)π(6^2) - 2(1/2)(3)(3√3) = 22.1 cm^2
PLEASE HELP ASAP WILL GIVE MORE POINTS AFTER COMPLETION
Answers
Answer:
i think i know 4 and 5
Step-by-step explanation:
for 5 is A,G
and for 4 its D,F
find the exact valuse of the cosine and sine of the angle.Then find the decimal values. θ=210°
Answers
The trigonometric ratio of the angle in radical and decimal form are:
cos 210° = -(√3)/2
sin 210° = -1/2
cos 210° = -0.87
sin 210° = -0.50
How to simplify trigonometric ratios?There are different trigonometric ratios such as:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
We are given the angle as θ = 210°. Thus:
cos 210° = -(√3)/2
Negative because it is in the third quadrant.
sin 210° = -1/2
Negative because it is in the third quadrant.
Similarly, those angles in decimals to the nearest hundredth are:
cos 210° = -0.87
sin 210° = -0.50
Read more about trigonometric ratios at: https://brainly.com/question/13276558
#SPJ1
drew has $ 18. this is $6 more than liam has. how many dollars does liam have
Answers
Answer:
Liam has $12.
Step-by-step explanation:
Since Drew has $18 and that is $6 more than Liam's amount of money, you would subtract 6 from 18.
18-6=12
Hence, Liam has $12.
Please let me know if this helped! If it did, please mark brainliest! If you have any more questions, please let me know! Have a splendid day!!! <3
Un tipo de queso se vende a 8. 99 por libra ¿cual es el costo de un pedazo de queso de 1. 76 libras?
Answers
The cost of a piece of cheese weighing 1.76 pounds at a cost of $8.99 per pound using unitary method is $15.86.
To use unitary method, we can set up a proportion that relates the cost of the cheese to its weight
Cost of cheese / Weight of cheese = Cost per unit of weight
We know that the cost per unit of weight is $8.99 per pound. To find the cost of a piece of cheese weighing 1.76 pounds, we can plug in the values we know and solve for the unknown
Cost of cheese / 1.76 pounds = $8.99 per pound
Multiplying both sides by 1.76 pounds, we get
Cost of cheese = $8.99 per pound × 1.76 pounds
Simplifying the right side, we get:
Cost of cheese = $15.8624
Rounding to two decimal places, the cost of the cheese is $15.86. Therefore, a piece of cheese weighing 1.76 pounds would cost $15.86.
Learn more about unitary method here
brainly.com/question/22056199
#SPJ4
The planet Saturn has several moons, and they can be modeled accurately by spheres. Saturn’s largest moon, Titan, has a radius of about 2575 kilometers. What is the approximate surface area of Titan? Round your answer to the nearest tenth
Answers
Answer:
Step-by-step explanation:
The surface area of a sphere is given by the formula:
Surface Area = 4πr^2
where r is the radius of the sphere.
For Titan, with a radius of 2575 kilometers, the surface area would be:
Surface Area = 4π(2575)^2
Surface Area ≈ 8.34 x 10^7 square kilometers
Rounding to the nearest tenth, the surface area of Titan is approximately 8.3 x 10^7 square kilometers.
for each meal purchased at a restaurant, all customers are allowed to randomly select one of three discount tickets. the tickets are all equally likely to be selected and consist of discounts for $1, $3, or $5 on the next purchase of a meal. a customer purchased two meals. the customer will select one discount ticket, replace it, and then select a second discount ticket. what is the probability that the customer will select two tickets with discounts of $3 and $5 ?
Answers
The probability that the customer will select two tickets with discounts of $3 and $5 is $1/9 or approximately $0.111.
The study of random occurrences or phenomena falls under the category of probability, which is a branch of mathematics. It represents the probability of an event happening. A number between 0 and 1, where 0 denotes impossibility and 1 denotes certainty, is used to symbolize it. By dividing the number of favorable outcomes by the total number of potential outcomes, the probability of an occurrence is determined. Numerous disciplines, including science, engineering, finance, economics, and social sciences, to mention a few, make extensive use of probability theory.
Since the customer selects a ticket, replaces it, and selects another ticket, the two selections are independent events. The probability of selecting a $3 discount ticket on the first meal is $1/3, and the probability of selecting a $5 discount ticket on the second meal is also $1/3.Therefore, the probability of selecting both a $3 and a $5 discount ticket is:
[tex]\frac{1}{3} . \frac{1}{3} = \frac{1}{9}[/tex]
So the probability that the customer will select two tickets with discounts of $3 and $5 is $1/9 or approximately $0.111.
To learn more about probability, refer to:
https://brainly.com/question/13604758
#SPJ4
Use the test for primality to determine whether the following numbers are prime or not. Test for Primality Given an integer n > 1, to test whether n is prime check to see if it is divisible by a prime number less than or equal to its square root. If it is not divisible by any of these numbers, then it is prime. (a) Let n = 323. How many prime numbers are less than or equal to the square root of n? Let n = 421. How many prime numbers are less than or equal to the square root of n?
Answers
For n = 421, find its square root: √421 ≈ 20.52. There are 8 prime numbers less than or equal to 20.52: 2, 3, 5, 7, 11, 13, 17, and 19. Testing for divisibility, 421 is not divisible by any of these prime numbers, so n = 421 is prime.
To test whether 323 is prime, we need to find the prime numbers less than or equal to its square root. The square root of 323 is approximately 17.97, so we need to find the prime numbers less than or equal to 17. The prime numbers less than or equal to 17 are 2, 3, 5, 7, 11, 13, and 17. We can check whether 323 is divisible by any of these numbers. If it is not divisible by any of them, then it is prime.
323 is divisible by 17, so it is not prime.
To test whether 421 is prime, we need to find the prime numbers less than or equal to its square root. The square root of 421 is approximately 20.52, so we need to find the prime numbers less than or equal to 20. The prime numbers less than or equal to 20 are 2, 3, 5, 7, 11, 13, 17, and 19. We can check whether 421 is divisible by any of these numbers. If it is not divisible by any of them, then it is prime.
421 is not divisible by any of these numbers, so it is prime.
For n = 323, first find its square root: √323 ≈ 17.97. There are 7 prime numbers less than or equal to 17.97: 2, 3, 5, 7, 11, 13, and 17. Testing for divisibility, 323 is divisible by 17 (323 = 17 * 19), so n = 323 is not prime.
For n = 421, find its square root: √421 ≈ 20.52. There are 8 prime numbers less than or equal to 20.52: 2, 3, 5, 7, 11, 13, 17, and 19. Testing for divisibility, 421 is not divisible by any of these prime numbers, so n = 421 is prime.
Learn more about prime numbers at: brainly.com/question/30358834
#SPJ11
Using the Normal Model with Binomial Problems np >= 10
nq >= 10
Normal model
Binomial Problem
1. A basketball player makes
72.5% of her free throws.
What is the probability that
she makes at least 15 of her
next 60 shots?
2. 14% of smart phones require
servicing in their first year.
What is the probability that
no more than 10 smart
phones in a shipment of 100
will need such repair?
3. 6% of scratch-off lottery
tickets have a prize of a free
ticket. What is the
probability that this prize is
on 15 or more of the 200
tickets at the local
convenience store?
Answers
Answer:
Step-by-step explanation:
This is a binomial problem where the basketball player has a probability of success of 0.725 (making a free throw) and is attempting 60 shots. The number of successful shots is a binomial random variable X ~ Bin(60, 0.725). We need to find the probability that she makes at least 15 of her next 60 shots, which is P(X ≥ 15). This can be computed using the binomial cumulative distribution function (CDF) as follows:
P(X ≥ 15) = 1 - P(X < 15) = 1 - binom.cdf(14, 60, 0.725) ≈ 0.998
Therefore, the probability that she makes at least 15 of her next 60 shots is approximately 0.998.
This is also a binomial problem where the probability of success is 0.14 (a smartphone requiring servicing) and the number of trials is 100 (smartphones in a shipment). We need to find the probability that no more than 10 smartphones in the shipment will require servicing, which is P(X ≤ 10). This can be computed using the binomial CDF as follows:
P(X ≤ 10) = binom.cdf(10, 100, 0.14) ≈ 0.289
Therefore, the probability that no more than 10 smartphones in the shipment will require servicing is approximately 0.289.
This is also a binomial problem where the probability of success is 0.06 (a scratch-off lottery ticket having a prize of a free ticket) and the number of trials is 200 (tickets at the local convenience store). We need to find the probability that this prize is on 15 or more of the tickets, which is P(X ≥ 15). This can be computed using the binomial CDF as follows:
P(X ≥ 15) = 1 - P(X < 15) = 1 - binom.cdf(14, 200, 0.06) ≈ 0.021
Therefore, the probability that the prize is on 15 or more of the 200 tickets at the local convenience store is approximately 0.021.
!ASAP PLEASE! Which function is shown in the graph?
Answers
The piecewise function can be defined as, f(x) = x+3, if x<0 and f(x) =3, if x≥0, Option B is correct.
We have,
A relation is a function if it has only One y-value for each x-value.
From the given figure it is easily noticed that the function is increasing in nature for x<0 and the function is constant in nature for x>0 because the value of y remains unchanged for any value of x, where x≥0
The value of function is 3 at x=0.
The value of the function is always 3 for all x≥0 .
f(x)=3 for x≥0
The function is a straight line with intercepts (-3,0) and (0,3).
slope = 3-0/0+3
=1
Let us find the y intercept
0=1(-3)+b
b=3
Now equation is y=x+3
For x<0, the function is,
f(x)=x+3
Therefore the piecewise function can be defined as, f(x) = x+3, if x<0 and f(x) =3, if x≥0.
To learn more on Functions click:
brainly.com/question/30721594
#SPJ1
100 POINTS! I need help on a math assignment for naming the first 100 decimal places of PI, can anyone help me?
Answers
Answer:
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
Step-by-step explanation:
because its fun
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 10 to 14.5 on the number line. A line in the box is at 12.5. The lines outside the box end at 5 and 20. The graph is titled Fast Chicken.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
Which drive-thru typically has less wait time, and why?
Fast Chicken, because it has a smaller median
Fast Chicken, because it has a smaller mean
Super Fast Food, because it has a smaller median
Super Fast Food, because it has a smaller mean
Answers
The drive-thru is able to estimate their wait time more consistently will be;
⇒ Super Fast Food , because it has a smaller IQR.
Since, The range of values in the middle of the scores is known as the interquartile range, or IQR.
The appropriate measure of variability is the interquartile range when a distribution is skewed and the median is used instead of the mean to show a central tendency.
Since, IQR is the difference between the third quartile and the first quartile, which is represented by the box in the box plot.
Now, In this case, the IQR for Burger Quick is,
15.5 - 8.5 = 7.0,
while the IQR for Fast Chicken is,
14.5 - 10 = 4.5.
Hence, A smaller IQR indicates that the data is more consistent and less spread out.
Thus, The correct option here is Super Fast Food, because it has a smaller IQR (Interquartile Range).
Learn more about IQR on:
brainly.com/question/4102829
#SPJ1
