Answer:
k = 5
Step-by-step explanation:
Given that (x - h) is a factor of f(x) then f(h) = 0
Given (x - 1) is a factor of f(x), then f(1) = 0, that is
3(1)³ - 8(1) + k = 0
3 - 8 + k = 0
- 5 + k = 0 ( add 5 to both sides )
k = 5
The value of k in the polynomial f(x) = 3x³ - 8x + k is 5.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, f(x) = 3x³ - 8x + k, and (x - 1) ⇒ x = 1 is a factor of f(x),
∴ If we replace 1 in place x and make f(x) = 0 and equate we will have the value of k.
So, 0 = 3(1) - 8(1) + k.
0 = 3 - 8 + k.
k = 5.
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A grocery store purchases cantaloupes from two warehouses, A and B. The
distribution of the diameters from Warehouse A is approximately normal with a
mean of 120 mm and standard deviation of 6 mm.
(a) For a cantaloupe selected at random from Warehouse A, what is the
probability that the cantaloupe will have a diameter greater than 127 mm?
A randomly selected cantaloupe from Warehouse B has the probability of 0.763
that it will have a diameter greater than 127 mm. The grocery store purchases
40% of their cantaloupes from Warehouse B.
(b) For a cantaloupe selected at random from the grocery store, what is the
probability that the cantaloupe will have a diameter greater than 127 mm?
(c) If the randomly selected cantaloupe's diameter is greater than 127 mm, what
is the probability the cantaloupe came from Warehouse B?
A: The probability of cantaloupe having dia. more than 127 is 0.12167.
B: Cantaloupe selected at random from the warehouse, then the probability that has a diameter of more than 127 mm is 0.3782.
C: The probability that the cantaloupe will be from warehouse B given randomly selected cantaloupe's diameter is greater than 127 mm, is 0.8069.
What is probability?The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability is a measure of the likelihood of an event occurring. Also, the favorable number of outcomes cannot be negative.
Given two warehouses, A and B
mean for warehouse A = μ = 120 mm
The standard deviation for warehouse A = σ = 6mm
A: a cantaloupe selected at random from Warehouse A
to find the probability of cantaloupe having a diameter greater than 127 mm = P(x > 127)
P(x > 127) = 1 - P(x ≤ 127)
P(x ≤ 127) = P((x - μ)/σ)
P(x ≤ 127) = P((127 - 120)/6)
P(x ≤ 127) = P(z ≤ 1.66)
P(x ≤ 127) = 0.87833
P(x > 127) = 1 - P(x ≤ 127)
P(x > 127) = 1 - P(x < 127) = 0.12167
probability of cantaloupe having dia. more than 127 is 0.12167.
B: Let event A for distributor A and let event B for distributor B
and event C for a diameter greater than 127 mm.
and given A randomly selected cantaloupe from Warehouse B has a probability of 0.763 that it will have a diameter greater than 127 mm,
and the percentage of cantaloupe provided by B is 40%
rest 60% for A,
therefore, for cantaloupe selected at random, the probability of having a diameter greater than 127 mm is
P(C) = P(C|A)P(A) + P(C|B)P(B)
= 0.12167(0.6) + 0.763(0.4)
= 0.073 + 0.3052
P(C) = 0.3782
cantaloupe selected at random from the warehouse, then the probability that has a diameter of more than 127 mm is 0.3782.
C: the probability the cantaloupe came from Warehouse B, given that the randomly selected cantaloupe's diameter is greater than 127 mm,
P(B|C) = P(B ∩ C)/P(C)
P(B|C) = (P(C|B)P(B))/P(C)
substitute values
P(B|C) = ((0.763)(0.4))/0.3782
P(B|C) = 0.3052/0.3782
P(B|C) = 0.8069
The probability that the cantaloupe will be from warehouse B given randomly selected cantaloupe's diameter is greater than 127 mm, is 0.8069.
Hence the probabilities are,
A; 0.12167
B; 0.3782
C; 0.8069.
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Determine the value of x in the figure.
A)
x = 141
B)
x = 94
C)
x = 137
D)
x = 43
Answer:
what figure?!
Step-by-step explanation:
im not sure scence i dont know what figure but if u were u i would do l × w
Answer:
137
Step-by-step explanation:
An object travels along a horizontal straight path at a constant rate. The object travels 1 20 20 1 of the length of the path in 3 4 4 3 second. At that rate, how many seconds does it take the object to travel the entire length of the path?
Answer:
the number of seconds that needed for the overall path length is 15 seconds
Step-by-step explanation:
The computation of the number of seconds that needed for the overall path length is shown below:
The tiny portion is 1 ÷ 20
And, the entire length is 20 ÷ 20
Now if 1 ÷ 20 is travelled in 3 ÷ 4 path so the time needed is
= 20 × 3 ÷ 4
= 15 seconds
Hence, the number of seconds that needed for the overall path length is 15 seconds
Simplify the expression:
2/3y+5-3-11/12y
Thanks!
Answer:
-1/4y+2
Step-by-step explanation:
5-3=2
2/3-11/12=-1/4
help me please!! i’ll make you a brainliest:))
Answer:
y= -5
Step-by-step explanation:
3. The point D(3, -2) is
rotated 90° cw about
the origin. What is the
coordinate point
for D'?
Answer:
D' = ( -3, -2)
Step-by-step explanation:
Rate me branliest please :)
What is the area of the triangle to the nearest hundredth?
Answer: 111.85 cm^2
Good Luck!
Round to the nearest thousandth:9.4048
Answer:
9.405
Step-by-step explanation:
makayla is reading a 400 page book for her book club.she reads 32 pages each hour
Answer:
12.5 hours
Step-by-step explanation:
[tex]\frac{400}{32}[/tex] = 12.5
Answer:
12 hours and 30 minutes
Step-by-step explanation:
400/32 = 12.5
Find the slope of the graph. Write it as a fraction or whole number (not a mixed number) 
Answer:
slope =-4 or -4/1
Step-by-step explanation:
the graph shows 4 down and 1 over
Please help! Only if you know!
Answer:
Acute Scalene
Step-by-step explanation:
What’s the anwser to this problem
Answer:
B
Step-by-step explanation:
Take his original balance (-142) and add the deposit (500) to get $358.
Hope this helps!
Answer:
B. $358
Step-by-step explanation:
the way you would get this would be to add -142+500
The tree in Maya's backyard is 6 meters high. How high is it in centimeters?
Be sure to include the correct unit in your answer.
Answer:
Step-by-step explanation:
600cm
What is the exterior angle sum of a 500-gon
Answer:
360° 32 I belive?
( Brainlyst will help me rank up! Thanks! )
Geometry B Final Exam
Consider the circle centered at point D. Angle ADC measures 108 degrees.
What is the measure of angel ABC?
Enter a number in the box.
Correct answer pls and 122 degrees
The answer is 54 degrees I took the exam I got it right
The measure of angle ABC is half the angle ADC and measures 54°
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
∠ABC = (1/2)∠ADC (angle at center is twice the angle at circumference)
∠ABC = (1/2) * 108 = 54°
The measure of angle ABC is half the angle ADC and measures 54°
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Write the exponent for the expression. 1.6 exponet 2
Answer:
The exponent is 2. As a expression it is 1.6^2
Step-by-step explanation:
I don't really have an explanation its just common sense.
An electric technician is paid $9.60 per hour. Based on 40 hours per week, what is this technicians annual salary?
Answer: $19968
Step-by-step explanation: Assuming the electric technician works 52 weeks a year with an average of of $40 of paid work, the electrician would make about $19,968 or close to $20,000 a year.
Jenny is a member of a summer swim team.
a. Using the graph, determine how many calories she burns in one minute.
Answer:
4 calories
Step-by-step explanation:
5 minutes equals 20 calories. 20 divide by 5 is 4. 1 minute equals 4 calories.
Answer:
6 2/3
Step-by-step explanation:
Tommy had 13 hits in 40 at bats for his baseball team. What is his batting average? (Batting average is the number of hits divided by the number of at bats, expressed as a decimal.)
Answer:
0.325 hits per bat
Step-by-step explanation:
13/40=0.325
1/40=1/4•1/10=0.25•0.1=0.02513/40=1/40•13=0.025•13=0.325Which expression is equivalent to 32 + 16? (1 point) a 8(4 + 2) b 8(24 + 8) c 7(4 + 2) d 7(24 + 8)
pls help
Answer:
Option a 8(4+2)
Step-by-step explanation:
32+16
=8*4+8*2
=8(4+2)
Answer:
8(4+2) ur welcome
Please help me Find X:
Answer:
x=50
Step-by-step explanation:
since all the angles of a triangle when added equal 180 we are going to have an equation like this:
180=102+28+x
180=130+x
so to find the value of x we have to subtract the final number by the value already given to us so something like:
180-130
which equals 50
-7x – 3x + 2 = –10x + 9
Answer:
No solution
Step-by-step explanation:
Combine terms
Add x
Add 2
Divide
HELP ME, PLZ. 100 POINTS !!!
using cauchy theorem, find x:
[tex]13\sqrt{x^{2}-x^{4} }+9\sqrt{x^{2} +x^{4} }=16[/tex]
Answer:
x=2√5/5
x=-2√5/5
Step-by-step explanation:
13√(2√5/5)^2-(2√5/5)^4+9√(2√5/5)^2+(2√5/5)^4=16
13√(4×5/25)-(16×25/625)+9√(4×5/25)+(16×25/625)
13√(4/5)-(16/25)+9√(4/5)+(16/25)
13√(4/25)+9√(36/25)
13×2/5+9×6/5
26/5+54/5
16=16 (proven)
Please help me! please!
Answer:
(c)
Step-by-step explanation:
(c). Stopping for traffic
The original price of a car was reduced by $3000. Its
discounted price is now $16,000.
Answer:
if $3000 was reduced from X which is now $16,000 x or the original price is $19,000
Step-by-step explanation:
$19,000- $3,000=$16,000
Whixh term describes the set of all possible output values for a function?
A. Output
B. Domain
C. Range
D. Input
Will give Brainlist .Question is in the picture.Only answer if you know the correct answer.
HELPPP PLSSSS
What is the measure of angle U ??????
Answer:
m<U = 120 degrees
Step-by-step explanation:
9x - 6 = 7x + 22
2x = 28
x = 14
m<U = 9(14) -6
m<U = 126 - 6
m<U = 120 degrees
Hope this helps!!!
Answer:
120
Step-by-step explanation:
U = W
(9x-6) = (7x+22)
SOLVE
subtract 7x from each side.
2x-6 = 22
add 6
2x = 28
divide by 2
x = 14
plug 14 into x and solve.
9(14)-6 = 120
7(14)+22 = 120
both angles are the same
hope that helped
Find the midpoint of A and B where A has coordinates (2, 3)
and B has coordinates (8,9).
Answer:
(5,6)
Step-by-step explanation:
Midpoint formula: (x1+x2/2 , y1+y2/2)
So you plug it in
your x's: 2 and 8
your y's: 3 and 12
(2+8/2 , 3+9/2)
(10/2 , 12/2)
(5,6)
could i be marked brainliest?
A circular garden has a radius of 8 feet. What is the arc length intercepted by a central angle of 150°?
Plz Help
Answer:
The arc length is 20.95 feet
Step-by-step explanation:
We calculate this using;
length of arc = theta/360 * 2 * pi * r
where theta is the central angle
So we have
length = 150/360 * 2 * 22/7 * 8
length = 20.95 feet