Answer:
[tex]P(x)=-5x^3-40x^2-45x+90[/tex]
Step-by-step explanation:
Equation of a Polynomial
Given the roots x1, x2, and x3 of a cubic polynomial, the equation can be written as:
[tex]P(x)=a(x-x1)(x-x2)(x-x3)[/tex]
Where a is the leading coefficient.
We know the three roots of the polynomial -6, -3, and 1, thus:
[tex]P(x)=a(x+6)(x+3)(x-1)[/tex]
Since the y-intercept of the polynomial is y=90 when x=0:
90=a(0+6)(0+3)(0-1)
90=a(6)(3)(-1)=-18a
Thus
a = 90/(-18) = -5
The polynomial is:
[tex]P(x)=-5(x+6)(x+3)(x-1)[/tex]
We must write it in standard form, so we have to multiply all of the factors as follows:
[tex]P(x)=-5(x^2+6x+3x+18)(x-1)[/tex]
[tex]P(x)=-5(x^2+9x+18)(x-1)[/tex]
[tex]P(x)=-5(x^3-x^2+9x^2-9x+18x-18)[/tex]
[tex]P(x)=-5(x^3+8x^2+9x-18)[/tex]
[tex]\boxed{P(x)=-5x^3-40x^2-45x+90}[/tex]
A sculptor has just finished creating a large wooden sphere for a sculpture he is working on. The sphere has a radius of 4.3 feet and weighs approximately 10,578.59 pounds. What is the approximate density of the wood used to create the sphere? I need help
Garth has a summer job and earns $9.32 per hour. One week, he works 16 34 hours. He deposits $150 in a bank and decides to use the rest of the money to buy raffle tickets. Each raffle ticket costs $0.50. How many raffle tickets can Garth buy?
Answer:
12 ticketsStep-by-step explanation:
Earning = $9.32 per hourWork hours = 16 3/4 = 16.75Earning in week:
$9.32*16.75 = $156.11Remaining money after he deposits $150:
$156.11 - $150 = $6.11How many raffle tickets can be bought:
$6.11/$0.50 = 12 and $0.11 remainsAnswer:
12 tickets
Step-by-step explanation:
Write the fraction as a percent.
1/400
Answer:
0.25%
Step-by-step explanation:
Answer:
0.25%
Step-by-step explanation:
1/4 = 0.25
1/40 = 0.025
1/400 = 0.0025 = 0.25%
Answer: 0.25%
Solve for k, please!
2(k − 5) = 12
Answer:
k = 11
Step-by-step explanation:
Expand brackets
2k - 10 = 12
add 10 on both sides
2k = 22
divide both sides by 2
k = 11
A company wants to test clear deck sealants for weather resistance. Three brands of sealants will be tested using 60 pieces of decking wood. The company wants to create treatment groups of 20 pieces of wood each, and decide to randomize using slips of paper. Select all the approaches that would result in comparable treatment groups. The numbers 1, 2, and 3 are each written on 20 slips of paper, and the slips are placed in a hat and shaken well. The top piece of wood from a stack is selected and a slip of paper is drawn from the hat. That piece of wood is assigned to the group number on the slip. The slip of paper is returned to the hat. This continues until all pieces of wood have been assigned to a group. The numbers 1, 2, and 3 are written on three slips of paper, put into a hat, and shaken well. A slip is drawn and the first 20 pieces of wood on the stack are assigned to the group number on the slip. Another slip is drawn and the next 20 pieces of wood are assigned to that group. The remaining pieces of wood are assigned to the remaining group. Each piece of decking wood is assigned a number from 1 to 60. The numbers 1–60 are written on slips of paper and placed in a hat and shaken well. Twenty slips are drawn, shaking the hat after each slip of paper is drawn, and the pieces of wood corresponding to those numbers are placed in group 1. Twenty more slips are drawn in the same way, and the pieces of wood corresponding to those numbers are placed in group 2. The pieces of wood corresponding to the numbers on the remaining slips are placed in group 3. The numbers 1, 2, and 3 are each written on 20 slips of paper (20 for each number) and the slips are placed in a hat and shaken well. The top piece of wood from a stack is selected, and a slip of paper is drawn from the hat. That piece of wood is assigned to the group number on the slip. The slip of paper is not returned to the hat. This continues until all pieces of wood have been assigned to a group.
Answer:
The Answer is C and D
Step-by-step explanation:
Just did it
What is the value of this expression 3x[(7+8)x2+6]
Answer:
96 or 108
Step-by-step explanatio
students in the third grade class at lowell elementary school Were asked which breakfast they like best from the three choices shown in the bar graph how many more students choose eggs or fruit combined and cereal
Answer:
my guess would be 150 or 20 or 30 plz forgive me if im wrong i tryd
An air conditioning system can circulate 420 cubic feet of air per minute. How many cubic yards of air can it circulate per minute?
Answer:
15.5556 cubic yards
Step-by-step explanation:
A yard is equal to three feet. Divide the volume value by 27 (3 cubed).
H/7 =27 can some one answer this pls
Answer:
h=189
Step-by-step explanation:
solve for H by simplifying both sides of the equation, then isolating the variable.
hope this helped
Please answer this correctly without making mistakes I want ace expert and genius people to answer this correctly without making mistakes
Answer:
6936 pints and 1156 cups
Step-by-step explanation:
Answer:
7514 pints
Step-by-step explanation:
i rechecked and this was correct?
A mother otter spends 1/3 of each day feeding her baby. How many hours does the mother otter spend feeding her baby in 1 week?
Find the value of f(x) = -3x +2
When x=2
Answer:
it is -4
Step-by-step explanation:
-3 * 2 = -6 + 2 = -4
If you take out a loan for $4,000 and you will owe $4,920 after 2 years, what is the rate of simple interest? Express your answer as a percentage rounded to the nearest tenth of a percent if necessary, but do not include the percent sign.
Answer:
11.5
Step-by-step explanation:
Answer:
11.5
Step-by-step explanation:
you have to use this equation to solve it [r = (1/t)(A/P - 1)] and basically just plug the numbers in to get 11.5. (you could also use one of those online calculators)
r = (1/2)((4920/4000) - 1) = 0.115
r = 0.115
A publisher reports that 55% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 280 found that 51% of the readers owned a laptop. Make the decision to reject or fail to reject the null hypothesis at the 0.05 level.
Answer:
We fail to reject the null hypothesis, we accept H₀
Step-by-step explanation:
Population proportion p₀ = 55 % p₀ = 0,55
Sample size n = 280
Sample mean p = 51 % p = 0,51 q = 0,49
n*p and n*q are both bigger than 10 therefore we can approximate the binomial distribution to a normal distribution
Test Hypothesis
Null Hypothesis H₀ p = p₀
Alternative Hypothesis Hₐ p ≠ p₀
Significance level is α = 0,05 but we have a two-tail test then
α/2 = 0,025
z(c) = - 1,96
Computing z(s)
z(s) = ( p - p₀ ) / √(p*q)/n
z(s) = ( 0,51 - 0,55 ) / √(0,51*0,49)/280
z(s) = - 0,04 * 16,73 / 0,5
z(s) = - 1,34
Comparing
z(s) and z(c)
- 1,34 < - 1,96
| z(s) | < | z(c)|
Then z(s) is in the acceptance region, we accept H₀
Help please...................
Answer:
7 1/8
Step-by-step explanation:
4 + 2 = 6
6/8 + 3/8 = 9/8 or 1 1/8
1 1/8 + 6 = 7 1/8
Usually Holly leaves home to school at 9:00, however today she left home 20 minutes later. In order to be at school on time she increased her usual speed by 20% and still was at school 15 minutes later than usual. What is her usual time from home to school
Answer:
Her usual time from home to school is 30 minutes
Step-by-step explanation:
At any point in time;
distance = speed * time
Here, we want to calculate the normal time she spent going from home to school
Let the normal time be x minutes
And the normal speed be t m/min
Today, she increased her speed by 20%
Her speed today will be t + 20/100 * t =
1.2t m/min
Her distance from how to school normally is
xt meters
Now what this means is that, at the increased speed, she was able to get to school 5 minutes earlier
What we are saying is although, she lost 20 minutes initially, she was able to beat down the lateness by 5 minutes
So, the time spent on her increased speed journey is;
(x-5) minutes
At any point in time, the distance will be equal;
Thus, mathematically;
xt = 1.2t(x-5)
xt = 1.2xt - 6t
6t = 1.2xt-xt
6t = 0.2xt
t cancels out
0.2x = 6
x = 6/0.2
x = 30 minutes
Complete the ratio table for Car A.
Answer:
The answer for miles driven is 100 for the first blank, 400 for the second blank, and 600 for the third blank. As you can see, that is how the pattern goes. The blank for Gallons of gas one is 12, and the blank for gallons of gas two is 20.
Step-by-step explanation:
The waiting time for a bus has a uniform distribution between 2 and 13 minutes. What is the probability that the waiting time for this bus is less than 4.5 minutes on a given day
Answer: 0.2273
Step-by-step explanation:
Probability density function for uniform distribution is given by :-
[tex]f(x)=\dfrac{1}{b-a}[/tex], where x is uniformly distributed in [a,b].
Let x denotes the waiting time for this bus.
Given : The waiting time for a bus has a uniform distribution between 2 and 13 minutes.
Probability distribution function of x for interval [2,13] will be :-
[tex]f(x)=\dfrac1{13-2}=\dfrac{1}{11}[/tex]
Required probability : P(x<4.5) = [tex]\int^{4.5}_{2}f(x)\ dx[/tex]
[tex]=\int^{4.5}_{2}\dfrac1{11}\ dx\\\\=\dfrac1{11}[x]^{4.5}_{2}\\\\ = \dfrac1{11}(4.5-2)\\\\=\dfrac1{11}(2.5)\approx0.2273[/tex]
Hence, the probability that the waiting time for this bus is less than 4.5 minutes on a given day = 0.2273
PLZZ HELPP ILL GIVE BRAINLIST
Which ratios form a proportion?
A) 4/10 and 10/25
B) 4/9 and 9/4
C) 3/5 and 9/25
D) 4/11 and 6/13
PQR is a translation of PQR. What are the rules?
Answer:
Step-by-step explanation:
Find the missing exponent in each expression
Answer:
See below.
Step-by-step explanation:
Multiplying terms with exponents make the exponents add together.
13.) x² · x⁵ = x⁷
14.) b⁵ · b³ = b⁸
15.) y⁴ · y⁷ = y¹¹
16.) m⁴ · m¹ = m⁵
Which of the following rational numbers is equal to that? please help quickly
Answer:
31/9. you have to count by nines, get three whole numbers which are not fractions, and you are left with 4. and a whole 3 plus 0.4 = 3.4 hope that helps homie
The distance between -18 and 15 is equal to ______.
A. 18 - 15
B. 15 - 18
C. -18 - 15
D. 15 - (-18)
Answer:
It would be equal to 15 - (18)
Answer:
it would actually be (B)
The areas of two similar triangles are 18cm^2 and 8cm^2. One of the sides of the first triangle is 4.5cm. What is the length of the corresponding side of the other triangle? Please answer ASAP!!! Thank you!!!
Answer:
3 cmStep-by-step explanation:
The area is the product of two dimensions, therefore the scale factor is:
A/A' = (b*r*h*r)/(b*h) = r²r² = 18/8r = √9/4 = 3/2 = 1.5The length of the corresponding side will be:
a/a' = ra' = a/ra' = 4.5 / 1.5 a' = 3 cmSelect all of the solutions to the equation below.
12x2=24
−23–√
23–√
−2–√
2–√
−2
2
Answer:
12 x 2+23 x −24=0. Enter an equation ... The first term is, 12x2 its coefficient is 12 . ... B ± √ B2-4AC x = ———————— 2A In our case, A = 12. B = 23. C = -24
Step-by-step explanation:
12 x 2+23 x −24=0. Enter an equation ... The first term is, 12x2 its coefficient is 12 . ... B ± √ B2-4AC x = ———————— 2A In our case, A = 12. B = 23. C = -24
What are the angles of 1 and 2
Angle BAC and angle FAC are examples of what type of angle pair?
Angle BCE and Angle DCA are examples of what type of angle pair?
geometry texts refer to an angle with a measure of 180° as a straight angle. In Figure 12 , ∠ BAC is a straight angle.
Step-by-step explanation:
fill in the boxes to show two ways you can find 8+6
Answer:
(4+3) + (4+3) and (7-1) + (9-1)
Step-by-step explanation:
You can always break it down in half to make it easier.
Oliver surveyed 880 of the students in his school about their favorite color. Students
could choose between red and blue. 35% said their favorite color was blue. How many
students' favorite color was red?
Answer:
572
Step-by-step explanation:
10%=88
5%=44
30%=264
35%=308= favourite colour blue
880-308=572= favourite colour red
The volume of a right rectangle prism is found by multiplying the length of the base by the width of the base by the height of the prism. A right rectangular prism has a volume of 50 cubic inches. If the height of the prism is 4 inches, what is the area of the base of the prism?
9514 1404 393
Answer:
12.5 square inches
Step-by-step explanation:
The area of the base can be written as ...
B = LW
Then the volume formula ...
V = LWH
can be written in terms of the base area as ...
V = BH
The base area can be found by dividing by the height:
B = V/H = (50 in³)/(4 in) = 12.5 in²
The area of the base is 12.5 square inches.