The two additional roots are:-0.17-7i and -2i
Given,
A polynomial function P(x) with rational coefficients has the given roots.
P(x) = 0.17+7i and 2i
we are asked to determine the two additional roots of the given P(x).
we know that a+bi is a root of P(x)=0, then a-bi is also a root of P(x)=0
we have:
0.17+7i and 2i are two roots pf P(x)
so, -0.17-7i and -2i are two additional roots of P(x).
Hence we get the required roots.
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suppose that five microchips in a production run of fifty are defective. a sample of seven is to be selected to be checked for defects. (a) how many different samples of seven can be chosen from the production run of fifty? (b) how many samples will contain at least one defective chip? the set of samples that do not contain any defective chips and the set of samples that contain at least one defective chip are ---select--- sets. so, the number of samples with at least one defective chip is . (c) what is the probability (as a percent) that a randomly chosen sample of seven contains at least one defective chip? (round your answer to one decimal place.) %
The answer to following parts are and this can be solved by using probability.
a) 15,890,700 different samples can be chosen
b) 6,523,881 will contain at least one defective chip
c) 41.1%
What is probability?
A probability is the number of desired outcomes divided by the number of total outcomes.
Main body:
The order in which the microchips are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
Cₙ,ₓ is the number of different combinations of x objects from a set of n elements, given by the following formula.
Cₙ,ₓ =[tex]\frac{ n!}{x!(n-x)!}[/tex]
(a) How many different samples can be chosen?
Samples of 6 from a set of 50.
Then
C₅₀,₆ = [tex]\frac{50!}{6!(50-6)!}[/tex] =15,890,700
15,890,700 different samples can be chosen
(b) How many samples will contain at least one defective chip?
Either a sample contains no defective chip, or it contains at least one. From a), the sum of them is 15890700.
Then
No defective chips:
Four are defective.
So 50-4 = 46 are not.
This is samples of 6 from a set of 46.
C₄₆,₆ = 46!/6!*40!
9,366,819 samples contain no defective chips.
At least one:
9366819 + n = 15890700
n = 6523881
6,523,881 will contain at least one defective chip
(c) What is the probability (as a percent) that a randomly chosen sample of six contains at least one defective chip
6,523,881 out of 15,890,700
6,523,881/15,890,700 = 0.411
As a percent
41.1%
Hence the answer are as follows.
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1. The difference of a number and 46 is at most 153. What is the largest integer that could be used for the number?
2. Vanessa must earn at least 360 points to make an A in her Pre-Algebra class. If she currently scores of 81, 91, and 89 points from her first three test, how many more points does she need to make an A?
3. The band has been selected to march and play in the holiday parade. The 105 members must raise at least $49,500 for the trip. What is the least amount that each one needs to raise (to the next whole dollar)?
4. All the cars a company sells require a down payment of $2,000 and 48 monthly payments. The contract amount for any of the cars is at least $19,940. What is the least amount of the monthly payment (to the next whole dollar)?
5. A particular type of TV is being sold for $1,200 cash for $500 down with 48 monthly payments. Find the amount of the monthly payment if the plan resusts in charges of at least $1,484 over the life of the contract. Find the amount of interest paid if the monthly payment plan is chosen.
please help, its due tomorrow. thank you.
The basic calculation values are;
1. The largest number is 199
2. The score Vanessa needs is 99 points
3. Each person should raise approximately $471
4. The approximate minimum monthly payment is $374
5. The approximate monthly payment is $55.9
The interest is 123.[tex]\overline {6}[/tex]
What are basic mathematical operations?Basic mathematical operations includes addition, subtraction, multiplication, division, and combinations of the above operations.
1. Let x represent the number, we have;
x - 46 ≤ 153
x ≤ 153 + 46 = 199
x ≤ 199
The largest integer that could be used for the number is 199
2. Vannesa's current scores are;
81 points, 91 points, 89 points
The score Vannesa requires so as to get an A is 360 points
The score Vannesa needs = 360 - (81+91+89) = 99
Vannesa needs 99 points to get an A
3. The number of members in the band = 105
The amount the band needs to raise = $49,500
The amount each one should raise therefore is 49500 ÷ 105 ≈ 471
Each one needs to raise $471
4. The down payment is $2,000
Number of monthly payment = 48
Least contract amount = $19,940
The monthly payment = (19,940 - 2,000)/48 ≈374
The least monthly payment ≈ $374
5. The cash price for the TV = $1,200
The down payment = $500
The charges = $1,484
Number of monthly payment = 48
Total payment = $1,200 + $1,484 = $2,684
The monthly payment = 2,684 ÷ 48 ≈ 55.9
The monthly payment is approximately $55.9
The interest is therefore;
[tex] \dfrac{1484}{1200}\times 100 = 123.\overline 6 \%[/tex]
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Jenny wants to record 15 minutes of songs for a film.
The table shows the playing time of 3 songs she has recorded.
Song
A
B
C
Playing time
4 minutes and 33 seconds
3 minutes and 42 seconds
3 minutes and 06 seconds
How much more time, in minutes and seconds, does she need to record?
The number of home runs by player A and player B for a season are consecutive odd integers whose sum is 108.
Determine the number of home runs hit by player A and player B.
The number of home runs hit by player A is (?) The number of home runs hit by player B is (?)
The number of home runs hit by player A nd player B are respectively 53 and 55which are consecutive odd integers.
Let the number of home runs hit by A is x.
Therefore the number of home runs hit by B is x+2 as they are consecutive odd numbers.
If x is odd then x + 1 is even and x+2 is odd.
The sum of their home runs is 108.
We will form a linear equation in x to represent this situation.
x + (x+2) = 108
now we will solve this equation to find the value of x.
or, 2x + 2 = 108
or, x + 1 = 54
or, x = 53
Hence the number of home runs hit by A is 53 .
Number of home runs hit by B = 53+2 = 55
Therefore the number of homeruns hit by players A and B are 53 and
55.
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This morning, Ravi's car had 15.04 gallons of fuel. Now, 4.9 gallons are left. How much fuel did Ravi use
gallons
Through subtraction method, we find out that the gallons of fuel used by Ravi is equal to 10.14 gallons.
It is given that -
The original gallons of fuel that Ravi had in the morning = 15.04 gallons
Now, the gallons of fuel left = 4.9 gallons
We have to find out the gallons of fuel used by Ravi.
The amount of fuel Ravi used =
Original gallons of fuel - Gallons of fuel left
= (15.04-4.9) gallons
= 10.14 gallons.
Thus, through subtraction method, we find out that the gallons of fuel used by Ravi is equal to 10.14 gallons.
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HELP ASPPP PLEASE THANK SHOW UR WORK PLEASE
Step-by-step explanation:
y + 4 = 8 ( x - 6 )
Multiple 8 by -6 and x
y+4 = 8x -48
Subtract 4 from both sides
y = 8x -52
Take two points from this equation, I took (7,4) and (8,12)
Find the slope with these points, which should give you 8
Step-by-step explanation:
when we have the equation in the form of
y = ax + b
then "a" is the slope.
in our equation
y + 4 = 8(x - 6)
the only thing that contributed to the factor of x is
8(x ...)
so, in the end the equation is (we sit need to bother about the rest)
y = 8x ...
so, the slope is 8.
question 9
this is trickier.
again, we want the form
y = ax + b
we have
6y - 3x = 12
6y = 3x + 12
y = 3/6 x + 2 = 1/2 x + 2
so, the slope is 1/2.
A discount of 25 % is allowed on an article marked at rs 17 500. calculate the discount.
Answer:
$4375
Step-by-step explanation:
25 percent *17500 =
(25:100)*17500 =
(25*17500):100 =
437500:100 = 4375
2(x-3)^2-12=116 help
Step-by-step explanation:
[tex]2(x - 3) {}^{2} - 12 = 116 \\ [/tex]
[tex]2 \times ( {x}^{2} - 6x + 9) - 12 = 116[/tex]
[tex] {2x}^{2} - 12x + 18 - 12 = 116[/tex]
[tex] {2x}^{2} - 12x - 110 = 0[/tex]
[tex] {x}^{2} - 6x - 55 = 0[/tex]
[tex] {x}^{2} - 11x + 5x - 55 = 0[/tex]
[tex]x(x - 11) + 5(x - 11) = 0[/tex]
[tex](x +5 )(x - 11) = 0[/tex]
Find the missing angle
Answer:
60
Step-by-step explanation:
All of the angles of a trapezoid add up to 360 degrees so,
2h+2h+h+h=360 degrees
6h=360 degrees
h = 60 degrees
2h=120degrees
Two Triangles are similar. The
scale factor of the smaller
triangle to the larger triangle is 1/3.
If the perimeter of the larger
triangle is 27 m, what is the
perimeter (in m) of the smaller
triangle?
The perimeter of the smaller triangle is 3m.
What is a perimeter of a triangle?
The total of a triangle's three sides is the perimeter. The Greek words "peri" (which means around) and "metron," which means measure, are combined to get the English word perimeter. The perimeter of any 2D shape is the total distance encircling it. Since a shape's perimeter indicates how long its boundary is, it is stated in linear units.
Here,
The ratio of given perimeters is 1:3 so the ratio of their sides and their altitudes will also be in the ratio of 1:3.
The ratio of the areas is 1^2/3^2=1/9. (ratio of their sides: a/b, ratio of their areas: a^2/b^2)
Now, we have 1/9=A/27
where A = area of the smaller triangle
Now, cross-multiply the given quantity
1*27=9*A
27=9A
A=27/9
A=3 m is the area of the smaller triangle.
Hence, the perimeter of the smaller triangle is 3m.
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Select the correct answer.
Which function is the inverse of f(x) = (x − 3)³ + 2?
O A.
f¹(x)=√x-2 +3
O B.
f¹(x)=√x +3 - 2
O c.
f¹(x)=√x+2 - 3
O D.
f¹(x)=√x-3 +7
The inverse of the function is 3+[tex]\sqrt[3]{x\x-2}[/tex].
What is inverse of the function?
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1. One should not confuse (-1) with exponent or reciprocal here.
Given, f(x) = (x − 3)³ + 2
replace f(x) with y
y = (x − 3)³ + 2
y-2 = (x − 3)³
∛y-2 = x-3
∛y-2 +3 = x
Put y =x
we get
∛x-2 +3 =y
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Zayne wants to join a gym.
Get Fit Gym charges a $140 enrollment fee and $50 per month.
Fit R Us charges a $245 enrollment fee and $35 a month.
He thinks Get Fit Gym is the better deal. Do you agree or disagree? Explain you're answer
Zayne is right as Get Fit Gym is the better deal.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have Zayne who wants to join a gym. Get Fit Gym charges a $140 enrollment fee and $50 per month. Fit R Us charges a $245 enrollment fee and $35 a month. He thinks Get Fit Gym is the better deal.
The price for one month at Get Fit Gym will be -
C[G] = 140 + 50 x 1 = 140 + 50 = $190
The price for one month at Fit R Us will be -
C[F] = 245 + 35 x 1 = 245 + 35 = $280
Therefore, Zayne is right, Get Fit Gym is the better deal.
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How many edges does the following shape have?
Answer:
6
Step-by-step explanation:
Two beetles sit at the top edge of the house roof. The roof has two faces. The first face is such that the horizontal shift by 3 cm along this face means 2 cm shift vertically. Simultaneously the beetles start moving downwards, the first beetle by the first face, the second -- the second face of the roof. The first beetle moves twice as fast as the second beetle. Find the altitude of the second beetle above the first beetle when they will be 72 cm apart horizontally, if the second face of the roof is perpendicular to the first face?
Answer:
9 cm
Step-by-step explanation:
Given two beetles on a roof with a first face having a slope of -2/3 and the second face perpendicular to it. The first beetle travels down the first face twice as fast as the second beetle travels down the second face. You want to know their vertical separation when their horizontal separation is 72 cm.
SeparationIn a given unit of time, the first beetle will travel 2×3 = 6 cm horizontally, and 2×(-2) = -4 cm vertically. The second beetle will travel 2 cm horizontally and -3 cm vertically in the same time, a perpendicular distance half as far.
After that one unit of time, the separation between the beetles is ...
horizontally: 6 +2 = 8 cm
vertically: -3 -(-4) = 1 cm
ScaleWe notice the vertical separation is (1 cm)/(8 cm) = 1/8 of the horizontal separation. When the horizontal separation is 72 cm, the vertical separation will be ...
(1/8)(72 cm) = 9 cm
The second beetle is 9 cm above the first when their horizontal separation is 72 cm.
__
Additional comment
The rise/run for the first face is given as (-2 cm)/(3 cm) = -2/3. The second face is perpendicular, so will have a rise/run = -1/(-2/3) = 3/2. That is, for a run of -2 cm, the rise will be -3 cm.
We note that the right triangles with legs "rise" and "run" are congruent for the two beetles. Traveling at the same speed, each beetle will cover a hypotenuse length in a given unit of time, hence the lengths "rise" and "run" on their respective roof faces. Since beetle 1 travels twice as fast, its distance will be 2·rise and 2·run in each time unit.
The attached diagram shows the geometry of the problem. The measures show beetle 1 has traveled twice as far as beetle 2 when they are separated horizontally by 72 cm. The grid is set so you can see the slopes are -2/3 and 3/2.
<95141404393>
Use the elimination method to solve the system of equation.
7x+4y=39
2x+4y=14
Answer:
x=5, y=1
Step-by-step explanation:
you subtract to get rid of 'y' in the equation like you are subtracting two numbers
7x+4y=39
2x +4y =14
5x=25
simplify to get 'x'
x=5
to get 'y' substitute the value of 'x' in one of the equations
2x+4y=14
(2x5)+4y=14
10+4y=14
subtract 10 to get 'y' on its own
4y= 4
simplify to get 'y'
y= 1
Find the least common denominator for this pair of algebraic fractions:
p/4 and p/16
The least common denominator for this pair of algebraic fractions: p/4 and p/16 is 16.
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In the case, the fraction is illustrated as p/4 and p/16.
It should be noted that the lowest common multiple for 4 and 16 is 16. This is the denominator.
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What is an equation of the line that passes through the point (-4,7) and is parallel to the line 3x-y=4
Answer:
y=3x+19
Step-by-step explanation:
pls mark
Hi can someone check my work and make sure I got it all right? I got a decimal on number 5 which is why I’m unsure If I got it right or wrong
All the answers are correct, but the 5th one is wrong, the correct answer for the 5th question is y = 6.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.
A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
The answer of 5th question,
The given expression is,
(5y - 3)/63 = 9/21
105y -63 = 567
105y = 630
y = 630/105
y = 6.
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Leticia is selling raffle tickets for her class fundraiser. Her class receives four-fifths of the money raised from selling the raffle tickets. Prior to the selling of raffle tickets, her class fund had a balance of $200.00.
Which function can be used to find m, the amount of money in Leticia's class fund, based on t, the amount of money Leticia has made from selling raffle tickets?
The function for the given situation is m=200+0.8t.
Given that, Leticia is selling raffle tickets for her class fundraiser. Her class receives four-fifths of the money raised from selling the raffle tickets.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, the amount of money in Leticia's class fund=m and the amount of money Leticia has made from selling raffle tickets is t
Now, the function is
m=200+4/5 t
⇒m=200+0.8t
Therefore, the function for the given situation is m=200+0.8t.
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please i need it quick
The solutions of the trigonometric equation are π / 3, π / 2, 3π / 2 and 5π / 3.
How to solve a trigonometric equation
In this problem we need to find the solutions of a trigonometric equation, which can be done by means of algebra properties and trigonometric formulas. Now we proceed to present the entire procedure:
Step 1 - Introduce the trigonometric equation:
cos 2x - cos x = - 1
Step 2 - Use the trigonometric formula cos 2x = cos² x - sin ² x:
cos² x - sin ² x - cos x = - 1
Step 3 - Use fundamental trigonometric formula:
cos² x - 1 + cos² x - cos x = - 1
2 · cos² x - cos x = 0
Step 4 - Use algebra properties to factor the expression:
cos x · (2 · cos x - 1) = 0
Step 5 - Find the solutions of the expression:
cos x = 0 → x = {π / 2, 3π / 2}
2 · cos x - 1 = 0
2 · cos x = 1
cos x = 1 / 2 → x = {π / 3, 5π / 3}
The solutions of the trigonometric equation are π / 3, π / 2, 3π / 2 and 5π / 3.
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Given: If a triangle is equilateral, then the triangle is isosceles.
Identify the following statements as the inverse, the converse and the contrapositive.
To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.
So, inverse of the given statement is "If △ABC is not equilateral , then it is not isosceles"
We have to find the inverse of the given statement:
" If ∆ABC is equilateral, then it is isosceles."
A triangle is said to be equilateral if all of the three sides are equal in measure and a triangle is said to be isosceles if two sides of a triangle are equal in measure.
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Given the figure below find if fgh is an equalateral triangle then choose from the answer choices
Answer: Triangle FGH is an equilateral with values of x as 9.
Step-by-step explanation: The triangle given is an equilateral because all the given side are equal. The value of x is 9.
I don’t know if the question is messed up but adding up all three side after plugging in 9 for x does not give you 180 even though a triangle must be 180 degrees. However, I did try all choices and that was the best one.Answer:
x = 9
Step-by-step explanation:
if x = 2 then
4x + 1 = 93x + 10 = 165x - 8 = 2 (not equal)If x = 22.25 then
4x + 1 = 913x + 10 = 77.5 5 x - 8 = 102(not equal)if x = 180 then
4x+1= 7213x + 10 = 5505x - 8 = 892(not equal)If x = 9 then
4x + 1 = 373x + 10 = 375x - 8 = 37(equal!)Josh has to walk 9/10 of a kilometre to school.He is 1/3 of the way there. How much further will he have to walk?
In traveling across flat land you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5. After you drive 13 miles closer to the mountain, the angle of elevation is 9.
The height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.
It is given that:
In traveling across flat land you notice a mountain directly in front of you.
Applying tan ratio:
tan3.5 = h/(15+x)
Here h is the height of the mountain and x is the distance between the base of the mountain and to the second position of the car.
h = (15 + x) tan3.5
h = x tan9
(15 + x) tan3.5 = x tan9
x = 9.44
h = 9.44 tan9
h = 1.49 miles
Thus, the height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.
The complete question is:
In traveling across flat land you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5. After you drive 13 miles closer to the mountain, the angle of elevation is 9.
Approximate the height of the mountain. (Round your answer to one decimal place.)
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8-3-3-4-5-6-7-8= the answer is -28
Answer: Correct, the answer is -28
Step-by-step explanation:
8-3=5
5-3=2
2-4=-2
-2-5=-7
-7-6=-13
-13-7=-20
-20-8=-28
If p is a number between -1 and 0, which of the following operations would result in the SMALLEST number?
a 14-ounce can of green beans contains two teaspoons of salt. how much sodium is present in 2 teaspoons (11.5 grams) of salt?
The percentage of salt in green beans can is 2.89%.
It is important to know about the percentage first, the percentage is a part of the sample in the population. It can be determined by this formula
A% = x / N . 100%
where A% is the percentage, x is the sample and N is the total population
From the question above, we know that :
x = 11.5 grams
N = 14 ounce = 396.89 grams
By substituting the parameter to the equation, we get
A% = x / N . 100%
A% = 11.5 / 396.89 . 100%
A% = 2.89%
Hence, the total salt in the can is 2.89%
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(Algebra 1) please help
The domain for plotting the growth function will be [0, 5].
A function's domain is the set of its possible inputs or the set of input values for which the function is defined. The domain is the set of objects that the machine will accept as inputs in the function machine metaphor.
If the f(n) = 11.04 cm
By substituting the value in the equation,
11.04 = 10(1.02)n
(1.02)n = 11.04/10
(1.02)n = 1.104
Take log on both the sides,
log(1.02)n = log(1.104)
n[log(1.02)] = log(1.104)
n = 4.996 ≈ 5 years
Therefore, the span of the study was 0–5 years.
As a result, the domain for plotting the growth function will be [0, 5].
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The equation y=4–x is graphed on the coordinate plane. Which point(s) will NOT be on the line? Select all that apply.
Answer: (6,1), (2,-1) etc
Step-by-step explanation:
Just pick any points on the graph and see if they aren't on the line and if they aren't, then you can pick that one.
Of the 50 students in ski club, 14 are freshmen. What percent of the
members are not freshmen?
Answer:
72% are not freshmen.
Step-by-step explanation:
The not freshmen students are,
→ 50 - 14
→ 36 students
Then percent of not freshmen,
→ (36/50) × 100
→ 0.72 × 100
→ 72%
Hence, the answer is 72%.