Answer:
To find all the real zeros of a polynomial function algebraically, use the Rational Root Theorem to generate a list of possible rational zeros and use synthetic division to test each possible zero. The zeros that remain after testing all the possible zeros are the real zeros of the polynomial function.
To find all the real zeros of a polynomial function algebraically, you can use the Rational Root Theorem and synthetic division. The Rational Root Theorem states that if a polynomial function has integer coefficients, then any rational zero (i.e., a zero that can be expressed as a fraction) must have a numerator that is a factor of the constant term and a denominator that is a factor of the leading coefficient.
Here are the steps you can follow:
1. Write the polynomial function in descending order of degree, with all like terms combined.
2. Use the Rational Root Theorem to generate a list of possible rational zeros. This list will be a set of all the possible fractions that can be formed by dividing a factor of the constant term by a factor of the leading coefficient.
3. Use synthetic division to test each possible zero. Start with the smallest possible denominator and work your way up. If a possible zero is not a zero of the polynomial function, cross it off the list.
4. Repeat step 3 until all the possible zeros have been tested. The zeros that remain are the real zeros of the polynomial function.
For example, let's say we have the polynomial function f(x) = x^3 - 6x^2 + 11x - 6.
Write the polynomial function in descending order of degree: f(x) = x^3 - 6x^2 + 11x - 6.
Use the Rational Root Theorem to generate a list of possible rational zeros: ±1, ±2, ±3, ±6.
Use synthetic division to test each possible zero. We start with x = 1:
1 │ 1 -6 11 -6
│ 1 -5 6
└─────────────
1 -5 6 0
Since the remainder is zero, we have found a zero of the polynomial function at x = 1. We can write the factorization f(x) = (x - 1)(x^2 - 5x + 6).
Now we use synthetic division to test the other possible zeros:
2 │ 1 -6 11 -6
│ 2 12 46
└─────────────
1 -4 23 40
x = 2 is not a zero of the polynomial function.
3 │ 1 -6 11 -6
│ 3 15 78
└─────────────
1 -3 26 72
x = 3 is not a zero of the polynomial function.
-1 │ 1 -6 11 -6
│ -1 7 -4
└────────────
1 -7 18 -10
x = -1 is not a zero of the polynomial function.
-2 │ 1 -6 11 -6
│ -2 16 -50
└────────────
1 -8 27 -56
x = -2 is not a zero of the polynomial function.
-3 │ 1 -6 11 -6
│ -3 27 -102
└────────────
1 -9 38 -108
x = -3 is not a zero of the polynomial function.
6 │ 1 -6 11 -6
Hope this helps, I'm sorry if it doesn't! :]
For the following discrete probability distribution, xi: 3,5,6,7,10 p1: 0,1 0,3 0,3 0,2 0,1What is the mean? What is the standard deviation (to 3 significant digits)?
a) The mean of the given probability distribution is 5.9.
b) The standard deviation of the given probability distribution is 4.64 (to 3 significant digits).
The mean and standard deviation of the discrete probability distribution with xi = 3, 5, 6, 7, 10 and p1 = 0.1, 0.3, 0.3, 0.2, 0.1 are as follows: Calculation of Mean The mean of the discrete probability distribution is calculated by multiplying each xi value by the probability pi, and then adding all the products together.μ = ∑ (xi . pi) = (3 × 0.1) + (5 × 0.3) + (6 × 0.3) + (7 × 0.2) + (10 × 0.1) = 5.9 Therefore, the mean of the given probability distribution is 5.9.Calculation of Standard Deviation The standard deviation of the discrete probability distribution is calculated using the formula below:σ = √[∑(xi - μ)² . pi]The calculations involved in finding the standard deviation are as follows:(3 - 5.9)² × 0.1 = 3.61(5 - 5.9)² × 0.3 = 0.49(6 - 5.9)² × 0.3 = 0.09(7 - 5.9)² × 0.2 = 0.49(10 - 5.9)² × 0.1 = 16.81σ² = 21.49Therefore, the variance is 21.49σ = √21.49 ≈ 4.639 ≈ 4.64 (to 3 significant digits)Hence, the standard deviation of the given probability distribution is 4.64 (to 3 significant digits).
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A group of people were asked if they had run a red light in the last year. 313 responded "yes", and 286 responded "no".
Find the probability that if a person is chosen at random, they have run a red light in the last year.
Give your answer as a fraction or decimal accurate to at least 3 decimal places
Answer:
[tex]0.523[/tex]
Step-by-step explanation:
Total number of respondents = 313 + 286 = 599
Number who responded yes = number running a red light
[tex]\text P(\text {ran a red light)}}\\\\=\dfrac{\text{Number who ran a red light}}{\text{Total number of respondents}}\\\\= \dfrac{313}{599}\\\\= 0.52253[/tex]
Rounded to 3 decimal places the probability is [tex]0.523[/tex]
How is 0.136¯¯¯¯ written as a fraction in simplest form?
Enter your answer in the box.
ANSWER QUICK FOR 50 POINTS
Answer:
17/125
Step-by-step explanation:
0.136×1000÷1×1000=136/1000
136/1000=17/125
Un mueblero compró lo siguiente dos camas a 7565 pesos cada una un juego de sala a 26500 un ropero a 17869 pesos y llevaba 65500 cuánto dinero le sobra
The amount that is left over is: 65,500 - 59,499 = 6,001 pesos. A furniture dealer or business owner is referred to as a "mueblero" in Spanish.
The cost of the furniture was 2 x 7565 = 15,130 pesos in camas.
1 x 26,500 is equal to 26,500 pesos in a game of pool.
One times 17,869 equals 17,869 pesos in a rope.
Total expenditures were 15,130, 26,500, 17,869, and 59,499 pesos.
The amount that is left over is: 65,500 - 59,499 = 6,001 pesos.
A furniture dealer or business owner is referred to as a "mueblero" in Spanish. The question asks how much money the mueblero has left over after making the purchases since he had a specific amount of money to spend and acquired a number of items of furniture for his store.
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four minus three times a number is less than twenty-five
Answer:
the answer could be: 1,2,3,4,5,6,7. If you are not sure about the answer than substitute the number that you pick and solve as if it was a normal equation.
Step-by-step explanation:
4-(3*x)<25
example:
4-(3*1)<25
4-3<25
1<25
Help pls
(2.75 x 10-2) (2.5 × 108) X
Multiplying two numbers written in scientific notation can be done by multiplying their coefficients and adding their exponents, such as [tex](2.75 x 10^-2)[/tex] x [tex]10^(-2+8)[/tex] = [tex]6.875 x 10^6[/tex].
What does an expression mean?
Instead of using estimates produced at random, it is better to use rolling integer variables that can be increasing, decreasing, or blocking. They could only help one another by sharing tools, information, or solutions to issues.
In the given question,
(2.75 x [tex]10^-2[/tex]) (2.5 × [tex]10^8[/tex]) X
To multiply two numbers written in scientific notation, you can simply multiply their coefficients and add their exponents. So:
(2.75 x [tex]10^-2[/tex]) (2.5 × [tex]10^8[/tex]) = (2.75 x 2.5) x [tex]10^(-2+8)[/tex] = 6.875 x [tex]10^6[/tex]
The result is 6.875 x 10⁶, which is the sum of (2.5 x 10⁸) and (2.75 x 10⁻²).
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Find three consecutive even integers if 3 times the first iteger is 2 times the the third
The solution is that the three consecutive even integers are 8, 10, and 12.
Let's assume the first even integer to be x. Since we are looking for three consecutive even integers, the second even integer will be x + 2, and the third even integer will be x + 4.
According to the problem statement, 3 times the first even integer is equal to 2 times the third even integer, which can be written mathematically as:
3x = 2(x + 4)
Solving for x, we get:
3x = 2x + 8
x = 8
Therefore, the first even integer is 8, and the second and third even integers are 10 and 12, respectively.
We can verify that 3 times the first even integer is indeed equal to 2 times the third even integer:
3(8) = 24
2(12) = 24
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Is 0.403 bigger than 0.043
Yes, 0.403 is bigger than 0.043. This is because 0.403 is 10 times bigger than 0.043, since 0.403 is four hundred and three thousandths and 0.043 is forty-three thousandths.
What is bigger?It is impossible to answer this question without more context. Depending on what is being compared, one thing may be bigger than another. For example, if comparing two numbers, the larger number would be considered bigger. If comparing two physical objects, the larger object would be considered bigger.
An easy way to check is to look at the number of digits after the decimal point; 0.403 has three digits, while 0.043 has two. This indicates that 0.403 is bigger.
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Rob's favorite shampoo is available in two sizes: regular and economy. Each size and its price are shown in the table. Size regular economy Quantity (oz) 20 40 Price ($) $8.00 $10.00 6. A coupon offers $1.00 off the regular size. Which size is the better buy then?. pls someone answer its due in 48 minutes
Answer: To determine which size is the better buy, we need to calculate the cost per ounce for each size, taking into account the coupon for the regular size.
For the regular size, the cost per ounce is:
$8.00 / 20 oz = $0.40 per oz
With the $1.00 coupon, the cost for the regular size becomes:
$8.00 - $1.00 = $7.00
So the cost per ounce for the regular size with the coupon is:
$7.00 / 20 oz = $0.35 per oz
For the economy size, the cost per ounce is:
$10.00 / 40 oz = $0.25 per oz
Therefore, the economy size is the better buy as it costs only $0.25 per oz compared to $0.35 per oz for the regular size with the coupon.
Step-by-step explanation:
A life insurance salesman operates on the premise that the probability that a man reaching his sixtieth birthday will not live to his sixty-first birthday is 0.05. On visiting a holiday resort for seniors, he sells 12 policies to men approaching their sixtieth birthdays. Each policy comes into effect on the birthday of the insured, and pays a fixed sum on death. All 12 policies can be assumed to be mutually independent. Provide answers to the following to 3 decimal places. a) What is the expected number of policies that will pay out before the insured parties have reached age 61? b) What is the variance of the number of policies that will pay out before the insured parties have reached age 61? c) What is the probability that at least two policies will pay out before the insured parties have reached age 61?
The probability that at least two policies will pay out before the insured parties have reached age 61 is 0.3400.
The answer is as follows: The expected number of policies that will pay out before the insured parties have reached age 61 isE(x) = np = 12 × 0.05 = 0.6Therefore, the expected number of policies that will pay out before the insured parties have reached age 61 is 0.6.b) The variance of the number of policies that will pay out before the insured parties have reached age 61 isVar(x) = np(1-p) = 12 × 0.05(1-0.05) = 0.570Therefore, the variance of the number of policies that will pay out before the insured parties have reached age 61 is 0.570.c) To find out the probability that at least two policies will pay out before the insured parties have reached age 61, we can use the complement rule that is:P(X ≥ 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)P(X = 0) = (0.95)^12 = 0.2835 (probability that none of the 12 policies will pay out before the insured parties have reached age 61)P(X = 1) = 12C1(0.05)(0.95)^11 = 0.3765 (probability that only one of the 12 policies will pay out before the insured parties have reached age 61)Therefore,P(X ≥ 2) = 1 - P(X = 0) - P(X = 1) = 1 - 0.2835 - 0.3765 = 0.3400Therefore, the probability that at least two policies will pay out before the insured parties have reached age 61 is 0.3400.
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Verifying Inverse Functions In Exercises 17-20, verify thatfandgare inverse functions algebraically. 17.f(x)=4x−9,g(x)=4x+9. 18.f(x)=−3/2x−4,g(x)=−2x+8/3. 19.
f(x)= x^3/4, g(x)=
f and g are inverse functions
17. To verify that f and g are inverse functions, we need to show that f(g(x)) = x and g(f(x)) = x.
So, f(g(x)) = f(4x+9) = 4(4x+9)−9 = 16x+4−9 = 16x−5 = x.
Similarly, g(f(x)) = g(4x−9) = 4(4x−9)+9 = 16x−5+9 = 16x+4 = x.
Therefore, f and g are inverse functions.
18. To verify that f and g are inverse functions, we need to show that f(g(x)) = x and g(f(x)) = x.
So, f(g(x)) = f(−2x+8/3) = −3/2(−2x+8/3)−4 = 6x−4−4 = 6x−8 = x.
Similarly, g(f(x)) = g(−3/2x−4) = −2(−3/2x−4)+8/3 = 3x−2+8/3 = 3x+8/3 = x.
Therefore, f and g are inverse functions.
19. To verify that f and g are inverse functions, we need to show that f(g(x)) = x and g(f(x)) = x.
So, f(g(x)) = f(x3/4) = x3/44 = x3/256 = x.
Similarly, g(f(x)) = g(x4) = x4/4 = x3/4 = x.
Therefore, f and g are inverse functions.
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a tank 12m long, 8m wide and 5m deep is to be made. it is open at the top, determine the iron sheet required for the fabrication. also find volume in litres
Answer:
Surface area of the sheet: 296 square meters
Area of tank: 480 cubic meters
Step-by-step explanation:
Don't forget your units!
"determine the iron sheet required for the fabrication" is asking for the surface area of the rectangular prism.
This is found by adding the five sides of the prism. The top side is excluded because it is open.
Front and back: 2(12m * 5m) = 120m^2
Left and right: 2(8m * 5m) = 80m^2
Floor: (12m * 8m) = 96m^2
120m^2 + 80m^2 + 96m^2 = 296m^2
The volume is found using standard methods. The open top does not have an impact here.
12m * 8m * 5m = 480m^3
This is 5/6 problems finish them all each is 10 points 60 total.
The value of angle X in the given right triangle HXV is 59.5 ⁰.
What is the value of x in the right triangle?The value of angle X in the given right triangle HXV is calculated by applying SOH CAH TOA identity as shown below.
SOH ⇒ sin θ = opposite side / hypothenuse side
CAH ⇒ cos θ = adjacent side / hypothenuse side
TOA ⇒ tan θ = opposite side / adjacent side
For the given triangle HXV, the value of angle X is calculated as follows;
cos X = 33 / 65
cos X = 0.5077
X = arc cos ( 0.5077 )
X = 59.5 ⁰
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A drink recipe book has a table that shows the proportional relationship between cups of water and cups of lemon juice for different amounts of lemonade. In the table, enter the number of cups of water needed for 1 cup of lemon juice
The ratio of water to lemon juice is 7:1. Thus, 7 cups of water are needed for 1 cup of lemon juice.
The table shows the proportional relationship between the amount of water and lemon juice needed to make lemonade in different quantities. The ratio of cups of water to cups of lemon juice remains constant for each quantity of lemonade. For example, to make 2 cups of lemonade, 1.5 cups of water are needed for every 1 cup of lemon juice. This means that if you want to make 4 cups of lemonade, you would need to double the amount of water and lemon juice required for 2 cups. This proportional relationship can be helpful in scaling the recipe up or down to make different quantities of lemonade.
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Complete question:
A drink recipe book has a table that shows the proportional relationship between cups of water and cups of lemon juice for different amounts of lemonade. If you need 6 cups of lemonade, the table shows you need 1 cup of lemon juice. Enter the number of cups of water needed for 1 cup of lemon juice.
Cups of Lemon Juice Cups of Water
1 4
2 8
3 12
4 16
Sue is playing darts. So far, she has hit the bullseye 4 times and missed the bullseye 10 times. What is the experimental probability that Sue will hit the bullseye on her next toss?
The experimental probability that Sue will hit the bullseye on her next toss is 2/7.
What is the experimental probability?
The proportion of outcomes where a specific event occurs in all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.
Here, we have
Given: Sue is playing darts. So far, she has hit the bullseye 4 times and missed the bullseye 10 times.
We have to find the experimental probability that Sue will hit the bullseye on her next toss.
experimental probability = 4/(4+10) = 4/14 = 2/7
The next toss = P = 2/7
Hence, the experimental probability that Sue will hit the bullseye on her next toss is 2/7.
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please i need help ASAP it geometry!!
Answer: 12
The answer to your geometry question is 12, I hope this helps.
look at the attached file
let's recall that Bearing is always a clockwise angle using the North Line, so "of X from Y", means we draw a North line at Y and a line towards X, clockwise is our angle. Check the picture below.
You may use the following formula: Area = length x breadth Mrs Sereme wants to bake 85 scones. Calculate how many baking pns of scones will she make if each scones' dimensions are 4cm x 4 cm.
Answer: Divide the amount that she wants to bake by the dimensions
Step-by-step explanation:
Area of 1 cone =4 times 4= 16cm squared
85/16=5.3125=5 rounded to a whole number
Two times the sum of 5 and some number is 30. What is the number?
Answer:
10
Step-by-step explanation:
5+10=15
15×2=30
so the answer to your question is 10
Answer:
x = 10.
Step-by-step explanation:
Given: Two times the sum of 5 and some number is 30. What is the number?
First, write the equation:
2(5 + x) = 30
Simplify the brackets with distribution property:
10 + 2x = 30
Then collect like terms:
2x = 30 - 10
Finally, calculate:
2x = 20 (Divide both sides by 2)
x = 10
Compute the expected age of a super shopper. (Round your answer to two decimal places. )
(A) The expected age μ of a super shopper 41.81
and, (B) the standard deviation σ for ages of super shoppers is 12.67
Given the data:
Age range, years 18-28 29-39 40-50 51-61 62 and over
Midpoint (x) 23 34 45 56 67
Percent of super shoppers 9% 46% 22% 11% 12%
Midpoint, x : 23 34 45 56 67
Frequency, f : 0.09_ 0.46 _ 0.22 __0.11 __ 0.12
The mean (m)= Σfx / Σf
= [(23 × 0.09) + (34 × 0.46) + (45 × 0.22) + (56 × 0.11) + (67 × 0.12)] ÷
(0.09 + 0.46 + 0.22 + 0.11 + 0.12)
= 41.81 / 1
Therefore, Mean = 41.81
Standard Deviation:
The standard deviation (or σ) is a measure of the distribution of data from the mean. A low standard deviation means the data is clustered around the mean, and a high standard deviation means the data is more scattered.
Standard deviation = Sqrt[(Σ(X² * f) / Σf) - m²)]
= ((23²× 0.09) + (34²× 0.46) + (45²× 0.22) + (56²× 0.11) + (67²× 0.12)) / 1
1908.51 - 41.81^2
= √(160.4339)
= 12.666250
= 12.67
Complete Question:
Age range, years 18-28 29-39 40-50 51-61 62 and
over Midpoint x 23 34 45 56 67
Percent of super shoppers 9% 46% 22% 11% 12%
For the 62-and-over group, use the midpoint 67 years.
(a) Compute the expected age μ of a super shopper. (Round your answer to two decimal places.)
μ = yr
(b) Compute the standard deviation σ for ages of super shoppers. (Round your answer to two decimal places.)
σ = yr
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I need help with please as fast as possible
RT is equal to 46 and angle ∠VUT is 26°.
What is a quadrilateral?A quadrilateral is a fοur-sided pοlygοn with fοur edges and fοur cοrners in geοmetry. The name cοmes frοm the Latin wοrds quadri, a variatiοn οf fοur, and latus, which means "side."
Tο find x nοte that the diagοnals οf a rectangle are cοngruent. This means that RT = SU.
So, 3x + 8 = 6x - 7
8 + 7 = 6x - 3x
3x = 15
x = 15/3
x = 5
RT = 2RV
= 2(3x + 8)
= 2(3(5) + 8)
= 2(15+ 8)
= 2(23)
= 46
Thus, RT is equal to 46
For m∠VUT,
Given ∠VRU = 64°
Using complementary angles
64° + ∠VRS = 90°
∠VRS = 90° - 64°
∠VRS = 26°
Now, using alternate angle theory as RT is a transverse
∠VRS = ∠VTU = 26°
Now, as the diagonals are congruent ∠VTU = ∠VUT
∠VUT = 26°
Thus, RT is equal to 46 and angle ∠VUT is 26°.
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Li-ming received a statement on her Certificate of Deposit showing that her investment had returned $2,240
$
2
,
240
over its life. If the Certificate of Deposit pays a simple interest rate of 3.2%
3.2
%
and her initial investment was $20,000
$
20
,
000
, how long had the money
Li-ming's initial investment was $20,000, the interest rate was [tex]3.2[/tex] % (or 0.032 as a decimal), and the total interest earned was $ [tex]2,240[/tex] .
What is the deposit pays a simple interest rate?We can use the formula for simple interest to solve for the time:
Simple Interest [tex]= Principal \times Rate \times Time[/tex]
where Principal is the initial investment, Rate is the interest rate, and Time is the time period.
In this case, we know:
Principal = $[tex]20,000[/tex]
Rate = [tex]3.2[/tex] %
Simple Interest = $ [tex]2,240[/tex]
Substituting these values into the formula, we get:
$ [tex]2,240 = $20,000 \times 0.032 \times Time[/tex]
Simplifying the equation, we get:
Time = $ [tex]2,240 / ($20,000 \times 0.032)[/tex]
Time [tex]= 3.5[/tex] years (rounded to one decimal place)
Therefore, Li-ming's money was invested for 3.5 years to earn a simple interest of $ [tex]2,240[/tex] at a rate of [tex]3.2[/tex] %.
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Suppose a point has polar coordinates (4, - (3pi)/4) with the angle measured in radians. Find two additional polar representations of the point. Write each coordinate in simplest form with the angle in [- 2pi, 2pi]
If a point has polar coordinates (4, - (3pi)/4) with the angle measured in radians, two additional polar representations of the points are (4, 5pi/4) and (4, -11pi/4)
To find two additional polar representations of the point (4, - (3pi)/4), we need to add and subtract integer multiples of 2pi from the angle measure while keeping the same radius.
First, let's add 2pi to the angle measure:
(4, - (3pi)/4 + 2pi) = (4, 5pi/4)
This gives us a new polar representation of the same point with a positive angle measure within the interval [-2pi, 2pi].
Next, let's subtract 2pi from the angle measure:
(4, - (3pi)/4 - 2pi) = (4, -11pi/4)
This gives us another polar representation of the same point with a negative angle measure within the interval [-2pi, 2pi].
Therefore, the three polar representations of the point (4, - (3pi)/4) are:
(4, - (3pi)/4)
(4, 5pi/4)
(4, -11pi/4)
Each of these polar representations describes the same point in the polar coordinate system, but with a different angle measure.
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Sol has to paint 365. 7 square feet of wall space. He wants to paint 0. 4 of the area light green. How many square feet does he want to paint light green?
Sol wants to paint 146.28 square feet of the wall light green.
The problem states that Sol has to paint 365.7 square feet of wall space, but he wants to paint only a fraction of the total area light green. The fraction he wants to paint light green is given as 0.4.
To find out how many square feet of the wall he wants to paint light green, we need to multiply the total area of the wall by the fraction of the area he wants to paint light green.
So, we can calculate the area of the wall that Sol wants to paint light green as:
Area of wall to be painted light green = 0.4 x 365.7
= 146.28 square feet
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Same facts as in #3, except now Elaine can set aside $50 per month. What rate of return does she need on her account? _____
The rate of return that Elaine needs on her account is of 22.16% to reach her goal of $4,000 in 4 years.
To calculate the rate of return for a savings account, you can use the formula:
Rate of return = [tex](Ending balance / Beginning balance)^{(1/n) - 1}[/tex]
where n is the number of years.
In Elaine’s case, she needs to save up $4,000 in 4 years. If she can set aside $50 per month, she will have saved $2,400 in 4 years. To calculate the rate of return she needs on her account, we can use the formula above.
To calculate the rate of return she needs on her account, we can use the formula above.
Let’s assume that she has $0 in her account at the beginning of the 4 years and $2,400 at the end of the 4 years.
Rate of return = [tex](2400 / 0)^{(1/4) - 1}[/tex]
= [tex](2400)^{(1/4) - 1}[/tex]
= 0.2216 or 22.16%
Therefore, Elaine needs a rate of return of 22.16% on her account to reach her goal of $4,000 in 4 years.
Keep in mind that this is a very high rate of return and may not be achievable with a savings account.
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Complete question is:
Elaine needs to save up $4,000 in 4 years. If she can set aside $50 per month, what rate of return does she need on her account?
There are 32 stamps.on each roll. Mark has 288 stamps. How many rolls does he have?
Answer:
9
Step-by-step explanation:
No. of rolls Mark have =
[tex] \frac{288}{32} = 9[/tex]
pls mrk me brainliest
Given: PP(xx) = x^3−2x^2 + 9x−18
a) How many roots does P(x) have?
b) What are the possible rational roots?
c) Find all the roots.
a) Number of roots in the given polynomial is three.
b) Possible rational roots of the given polynomial are {±1, ±2, ±3, ±6, ±9, ±18}
c) The roots of the given polynomial are {2, 3i, -3i}.
Given polynomial is `P(x) = x³ - 2x² + 9x - 18`.a) Number of roots in the given polynomial is three. b) Possible rational roots of the given polynomial are expressed in the form of `p/q`, where p is a factor of the constant term `-18` and q is a factor of the leading coefficient `1`.Constant term of the given polynomial is `-18`. The factors of `-18` are 1, 2, 3, 6, 9, and 18. Leading coefficient of the given polynomial is `1`. The factors of `1` are ±1.∴ Possible rational roots of the given polynomial are {±1, ±2, ±3, ±6, ±9, ±18}.c) Let us check whether the possible rational roots satisfy the given polynomial. To check the roots, we can use synthetic division, which is an efficient method to check the roots of a polynomial. When `x = -1` is substituted in the given polynomial, we get P(-1) = (-1)³ - 2(-1)² + 9(-1) - 18= -1 + 2 - 9 - 18= -26, which is not equal to `0`.When `x = 1` is substituted in the given polynomial, we get P (1) = 1³ - 2(1)² + 9(1) - 18= 1 - 2 + 9 - 18=-10, which is not equal to `0`.
When `x = -2` is substituted in the given polynomial, we get P(-2) = (-2)³ - 2(-2)² + 9(-2) - 18= -8 + 8 - 18 - 18= -36, which is not equal to `0`.When `x = 2` is substituted in the given polynomial, we get P(2) = 2³ - 2(2)² + 9(2) - 18= 8 - 8 + 18 - 18= 0, which is equal to `0`.∴ `x = 2` is a root of the given polynomial. By using synthetic division method, we can find the remaining two roots. x - 2 | 1 - 2 9 - 18| | 2 0 18| | 1 0 9 0|Therefore, the factors of the given polynomial are `(x - 2)(x² + 9)`.The quadratic factor, `x² + 9`, does not have any real roots, as the discriminant is negative.∴ The roots of the given polynomial are {2, 3i, -3i}.
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A table costs five times as much as a chair. A trader bought six more chairs than tables and spent $18 594. If a chair costs $1033,how many chairs and tables did he buy
The trader bought 3 512 tables and 6(3 512) = 21 072 chairs.A table costs five times as much as a chair.
The cost of a chair is given as $1033. So, c = 1033Substituting c = 1033 in 5t + 1033 = 18 594,5t = 18 594 - 1033 5t = 17 561 t = 17 561/5 t = 3512.2Let c be the number of chairs and t be the number of tables.As the table costs 5 times as much as the chair, the total cost of the tables is 5t. The total cost of the chairs is c. The total cost of the tables and chairs is 5t + c = $18 594.Therefore, 5t + c = 18 594.The cost of a chair is given as $1033. So, c = 1033Substituting c = 1033 in 5t + 1033 = 18 594,
5t = 18 594 - 1033 5
t = 17 561
t = 17 561/5
t = 3512.2Therefore, the trader bought 3 512 tables and 6(3 512) = 21 072 chairs.
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(09.02 MC)
Which equation could be used to solve for the measure of angle P?(1 point)
Circle N is shown with a quadrilateral OPQR inscribed inside it. Angle O is labeled x degrees. Angle P is labeled y degrees. Angle Q is labeled z degrees. Angle R is labeled w degrees.
In order to solve for the measure of angle P, the equation x + y + z + w = 360° can be used.
What is an angle?An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles are measured in degrees or radians and are used to describe the direction of two intersecting lines in a plane. Angles are also used to measure the central angle of a circle and the angle between two curves.
This equation is known as the Angle Sum Theorem, which states that the sum of the measures of the angles of a triangle or a quadrilateral equals 360°. The measure of each angle of the quadrilateral can be used in the equation to solve for the measure of angle P, which is labeled as y. This equation can be written as x + y + z + w = 360° and then solved for the measure of angle P by subtracting x + z + w from both sides of the equation. This would result in y = 360° - (x + z + w). By substituting the measure of each angle into the equation, the measure of angle P can be found.
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01.(+3) + (+8)
02.(-20) + (-13)
The answer to this question is:
01. (+11)
02. (-33)
The positive integers are added directly to the positive integers as in 01 solutions 3+8 gives 11
where else in the 02 solutions both the integers are negative and when negative integers are added to each other it is added but the sign remains negative (-20)+(-13) gives (-33).
The other formulas are:
(+) × (+) = +; (+) ÷ (+) = +
(-) × (-) = +; (-) ÷ (-) = +
(+) × (-) = -; (+) ÷ (-) = -
(-) × (+) = -; (-) ÷ (+) = -
Answer:
[tex]01.(+3) + (+8) = +11)[/tex]
[tex]02.(-20) + (-13) = (-33)[/tex]