The rational root of the function f(x) = x³ - 3x² + 2 is - 1.
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
Given, A polynomial function of degree three f(x) = x³ - 3x² + 2.
Now, The roots of the function is when f(a) = 0.
The last term is, 2, Hence the roots must be,
± 1, ± 2, The factors of 2.
f(-1) = - 2.
f(1) = 0.
f(-2) = - 18.
f(2) = - 2.
So, The only rational root is x = - 1 and the other roots are irrational and can be obtained by the obtained quadratic equation after factoring or by long division.
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Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. They randomly survey 387 drivers and find that 298 claim to always buckle up. Construct a 84% confidence interval for the population proportion that claim to always buckle up.
Answer:
The 84% confidence interval for the population proportion that claim to always buckle up is (0.74, 0.80).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
They randomly survey 387 drivers and find that 298 claim to always buckle up.
This means that [tex]n = 387, \pi = \frac{298}{387} = 0.77[/tex]
84% confidence level
So [tex]\alpha = 0.16[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.16}{2} = 0.92[/tex], so [tex]Z = 1.405[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 - 1.405\sqrt{\frac{0.77*0.23}{387}} = 0.74[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 + 1.405\sqrt{\frac{0.77*0.23}{387}} = 0.8[/tex]
The 84% confidence interval for the population proportion that claim to always buckle up is (0.74, 0.80).
What is the greatest common factor of the two terms
24x^6 and 18x^4
30x^3y^5 and 25x^2y
24x⁶ and 18x⁴ —> 6x⁴
30x³y⁵ and 25 x²y —> 5x²y
The question is in the picture (:
Answer:
[tex] \frac{(x - 2)(x + 2)}{x - 8} [/tex]
Please show steps on how to solve
log7 -2b-9=-6
Answer: b= - -log10(7)+3/2
Step-by-step explanation: log 10 (7) -2b-9=-6 : b= - -log10(7)+3/2 (Decimal : b = -1.07745...)
so these are the steps how I got it I did log 10 (7)-2b-9=-6 subtract log 10 (7) -9 from both sides log 10 (7)-2b-9-(log10(7)-9)=-6-(log 10 (7) -9)
Simplify -2b= -log10(7)+3
Divide both sides by -2 -2b/2= - log 10(7)/-2+ 3/-2 if you simplify it should give you b= - -log10(7)+3/2 that should be your answer but i'm not sure those I think that's how you do it let me know if you got it right bye!
Find the circumference of a circle with a radius of 6 cm.
Hi besties i need. help ASAP please and. ty
Answer:
37.7
Step-by-step explanation:
Circumference = [tex]2\pi r[/tex]
Circumference = [tex](2)(\pi )(6)[/tex]
Circumference = 37.69911184 / 37.7
Therefore, circumference of the circle with the radius 6 cm is 37.7.
Answer:
37.7
Step-by-step explanation:
formula for circumference of a circle=2πr
2×π×6=37.7cm
1/4 x 1/6 x 1/12= What fraction did Phil eat of the pizza
Answer:
[tex] \frac{1}{288} [/tex]
Step-by-step explanation:
the 1 will always stay the same because all of them are 1's
4×6=24
24×12=288
Answer:
garage bozo
Step-by-step explanation:
Which does NOT have a value of 4 when
simplified?
1. 5.6x0.15 + (-3.16)
1. (-7x23) + (-43)
III. -5.6+4(3)
Answer:
3 beause when you dividend it -5.6+4(3) .
A spinner with 12 equally sized slices is shown below. (The 12 slices are red.) The dial is spun and stops on a slice at random. What is the
probability that the dial stops on a red slice?
Write your answer as a fraction or a whole number.
Answer:
100/100
Step-by-step explanation:
XD
Write the number 9.9 x 10-5 in standard form.
Which of the following plots has exactly 2 clusters and
1 outlier
What are the coordinates of the solution of these two linear equations
Answer:
(-2 -3)
Step-by-step explanation:
_____________________
A rectangular prism has a length of 4 feet, a width of 8 feet and a height of 5 feet. What is the volume of the prism
Determine the equation of the circle graphed below.
9514 1404 393
Answer:
(x -6)^2 +(y -6)^2 = 10
Step-by-step explanation:
To use the standard form equation for a circle, we need to know the center and the square of the radius. The center can be read from the graph as (6, 6). The square of the radius can be found using the distance formula.
d^2 = (x2-x1)^2 +(y2-y1)^2
The radius is the distance between the two points shown, so we have ...
d^2 = (7-6)^2 +(9-6)^2 = 1^2 +3^2 = 10
__
The equation of a circle centered at (h, k) with radius r is ...
(x -h)^2 +(y -k)^2 = r^2
For (h, k) = (6, 6) and r^2 = 10, the equation is ...
(x -6)^2 +(y -6)^2 = 10
Find the mean of the following data set 5,9,3,12,14,67,22,45,1,12,14
Answer:
18.5 i believe
Step-by-step explanation:
sorry if im wrong, have a great day!!
C. 20 people show up to the party, and Robert decides to give them each the
same amount of pizza. How much pizza does each person get?
Answer:
Step-by-step explanation:3/5 of the pizza
What are the solutions to the quadratic equation x2-16=0
Answer:
x = -4, 4
Step-by-step explanation:
Hi there!
[tex]x^2-16=0[/tex]
Rewrite 16:
[tex]x^2-4^2=0[/tex]
The difference of squares rule states that [tex]a^2-b^2=(a+b)(a-b)[/tex]. With this, apply the difference of squares to the equation:
[tex](x+4)(x-4)=0[/tex]
The zero-product property states that if the product of two numbers is 0, then one of the numbers must be equal to zero. Set each term equal to 0 and find the solutions:
[tex]x+4=0\\x=-4[/tex]
[tex]x-4=0\\x=4[/tex]
Therefore, the solutions are -4 and 4.
I hope this helps!
i need this done fast
Answer: 1) V≈1244.07 in 2) V≈54286.72 ft 3) V≈23816.41 yd
Step-by-step explanation:
Express 5 cm in metre and kilometre.in decimals........................
Answer:
0.05 metre
5×10^5 kilometer
1.9685
Find the value of x for the right triangle. Round your answer to the nearest hundredth.
450
19
Answer:
450 foe
Step-by-step explanation:
Which angles are supplementary to
∠4? Select all that apply.
∠2 ∠7
∠5 ∠6
∠1
Answer:
The supplementary angle are:
∠2
∠3
∠6
∠7
The ratio of softballs to teams is 26:2. How many softballs would 8 teams have?
Answer:
104 softballs
Step-by-step explanation:
26 x 4 = 104
Which coordinate point represents the y -intercept of the equation 3x + 2y = 18
Answer:
(-6,18)
Step-by-step explanation:
3x + 2y = 18
2y= -3x + 18
y=-3/2 x + 18
give x=0
y=-3/2 *0+18
y=18#
y=18
3x+2(18)=18
3x+36=18
3x=18-36
3x=-18
x=-18/3
x=-6
Todd Lyle worked Monday through Friday from 8:00 A.M. to 5:00 P,M. with an hour off for lunch. He is paid $10,50 an hour. Find his earnings for the week.
Answer:
$315
Step-by-step explanation:
He earns $63 everyday, and then you just have to multiply that by 5 since he works 5 days in a week.
Consider a random variable Z which has a standard normal distribution (mu = 0, sigma = 1). Choose which of the following values would be equivalent to the following probability:
P (Z > 0.54)
A. P(Z > 0.54.
B. P(Z < 0.54).
C. 1 - P(Z < - 0.54).
D. 1 - P(Z < 0.54).
Answer:
A. P ( Z > 0.54) = 0,7054
B. P ( Z < 0.54) = 0.2946
C.1) 1 - 0.2946 = 0.7054
D.1) 1 - 0.2946 = 0.7054
Step-by-step explanation:
A) P ( Z > 0.54) = 1 - P ( Z ≤ 0.54)
P ( Z ≤ 0.54) = 0,2946 from z-table
P ( Z > 0.54) = 1 - 0,2946
P ( Z > 0.54) = 0,7054
B) P ( Z < 0.54) = 0.2946
C) 1 - P ( Z < - 0,54)
1 - 0.2946 = 0.7054
D) 1 - P ( Z < 0,54)
1 - 0.2946 = 0.7054
a serving of crackers has 1.5 grams of fat. How many grams of fat are in 3.75 servings
Answer:
5.625
Step-by-step explanation:
You just have to multiply 1.5 by 3.75 which is 5.625.
So there are 5.625 grams of fat in 3.75 servings.
5.625 grams of fat are in 3.75 servings.
You just have to multiply 1.5 by 3.75 which is 5.625.
So there are 5.625 grams of fat in 3.75 servings.
What is a Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
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What type of symmetry’s are shown?
Answer:
18o rotational symetry
Step-by-step explanation:
Is it possible to design a table
where no two legs have the same length? Assume
that the endpoints of the legs must all lie in the same
plane. Include a diagram as part of your answer.
Find the exact value of tan A in simplest radical form.
PLEASE HELP
Answer:
[tex] \tan(A) = \frac{opp}{adj} \\ \tan(A) = \frac{ \sqrt{72} }{3} \\ \tan(A) = \frac{ \sqrt{36 \times 2} }{3} \\ \tan(A) = \frac{6 \sqrt{2} }{3} \\ \tan(A) = 2 \sqrt{2} [/tex]
A triangle on the coordinate plane has vertices (-8,3), (3,9), and (9,3). What is the area, in square units, of the
triangle?
Please help
Answer:
51 sq units
Step-by-step explanation:
after plotting the vertices, the height of the triangle is 6 and the base is 17
A = 1/2(6)(17)
A = 51 sq units
Find the slope of the line tangent to the function y=6-3x at the point (5,0)
Answer:
-3
Step-by-step explanation:
To get the slope of the line tangent to the function y = 6 - 3x
First, we need to differentiate;
dy/dx = 0 -3x^{1-1}
dy/dx = 0 - 3x^0
dy/dx = 0 - 3
dy/dx = -3
Hence the slope of the line tangent to the function at the point is -3