Answer:
P(3) = 0
Step-by-step explanation:
Factor Theorem is a consequence of Remainder Theorem.
Remainder Theorem states that if polynomial f(x) is divided by a binomial (x - a) then the remainder is f(a).
Factor Theorem states that if f(a) = 0, then the binomial (x - a) is a factor of f(x).
We have the polynomial
[tex]P(x) = x^5-3x^4+5x^3-15x^2-6x+18[/tex]
To prove that x-3 is a factor of P, we calculate P(3):
[tex]P(3) = 3^5-3*3^4+5*3^3-15*3^2-6*3+18[/tex]
[tex]P(3) = 243-243+135-135-18+18[/tex]
[tex]P(3) = 0[/tex]
Thus, x-3 is a factor of P(x)
8 Hassan has a jug with a capacity of 800 ml.
He estimates that his bucket holds 20 times that of his jug.
Work out an estimate of the capacity of his bucket.
Give your answer in litres.
Answer:
The capacity of bucket is 16 liters
Step-by-step explanation:
Let j be the quantity of water in the jug
Then
[tex]j = 800ml[/tex]
Let B be the quantity of water held by the bucket
Then t is given that the bucket holds 20 times of water than the jug
[tex]B = 20j[/tex]
Putting the value of j
[tex]B = 800(20) = 16000[/tex]
We also know that
1 liter = 1000 ml
In order to convert ml into liters, we have to divide the quantity by 1000
[tex]B = \frac{16000}{1000} = 16\ liters[/tex]
Hence,
The capacity of bucket is 16 liters
The diameter of a car's tire is 5oem. While the car is being driven, the tire picks up a nail. It takes 1
second for the nail to rotate to the top of the tire.
a) Graphically model the height of the nail above the ground over time, from the point it punctures the
tire. Include 3 rotations of the tire in your model.
b) Algebraically model the path of the nail in terms of sine and cosine.
c) How high above the ground is the nail after 6.35 second?
d) At what time(s) in the first 3 rotations of the tire is the nail 13cm above the ground?
e) If the car drives for 6 minutes, how many times will the nail have rotated around the tire?
f) State the domain and range of the path of the nail.
g) What assumptions must you make about the drive in order for the function to accurately model the
nails path?
Answer:
2
3
4
5
6
7
RESULT
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00:04
01:32
Step-by-step explanation:
4x – 20 = -18
Can someone help with this
Answer:x = 1/2
Step-by-step explanation:
4x-20=-18
(Add 20 on both sides)
4x=2
(Divide by 4 on both sides)
X = 2/4
(Simplify)
X=1/2
Write the following equation symbolically.
The sum of h and 5 is equal to 8 less than 6 times y.
Answer:
I believe the answer is
h + 5 = 8 < 6y
Help me out with question 10 (geometry)
Step-by-step explanation:
make it braintliest please
Answer:
x=29
Step-by-step explanation:
180=2x -13 +7x-68
combine like terms
180 = 9x-81
add 81 on both sides
261 =9x
divide 9 on both sides
29 =z
Suppose a normally distributed set of stock prices with 3500 observations has a mean of 101 and a standard deviation of 10. Use the 68-95-99.7 Rule to determine the number of observations in the data set expected to be between the values 91 and 121.
Answer:
The number of observations in the data set expected to be between the values 91 and 121 is of 2853.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 101, Standard deviation = 10
Percentage of of observations in the data set expected to be between the values 91 and 121.
91 = 101 - 10
So 91 is one standard deviation below the mean.
121 = 101 + 2*10
So 121 is two standard deviations above the mean
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
Of those 50% below the mean, 68% are between one standard deviation below the mean(91) and the mean(101).
Of those 50% above the mean, 95% are between the mean(101) and two standard deviations above the mean(121).
So the percentage of observations in this interval is of:
[tex]P = 0.5*0.68 + 0.5*0.95 = 0.815[/tex]
Number of observations in the interval
81.5% of 3500. So
0.815*3500 = 2853
The number of observations in the data set expected to be between the values 91 and 121 is of 2853.
in may a coat costs £64
-4x -3 = -19
I'm having trouble with algebra please help.
Answer:
Step-by-step explanation:
-4x - 3 = - 19
Bringing like terms on one side
-4x = - 19 + 3
-4x = - 16
x = - 16/-4
x = 4
Answer:
x=4
Step-by-step explanation:
-4x-3=-19
add -3 to the right side of the equation so -19+3
which will give you -16
then divide by -4
so x=4
The system when solved is.
Answer:
(-19, -7)
Step-by-step explanation:
y=x+12
x+12+x=-26
2x=-14
x=-7
y + x = -26
y -7 = -26
y = -19
When solving any expression, what operation do we do first multiplication or division?
Answer:
Division
Step-by-step explanation:
BIDMAS
Brackets, indices, division, multiplication, addition, subtraction
or
BODMAS
Brackets, operations, division, multiplication, addition, subtraction
Write an equation in slope-intercept form for the line with slope-3and y-intercept 3
Answer:
pls explain better so make a mew question and take a picture
subtract 8 - 6 2/3 in the simplest form
Answer:
The answer is [tex]\frac{4}{3}[/tex] or 1 [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
What do you define the circumference of a circle asap!!!
Answer:
to find the circumfrence of a circle you need to do 2 times pi times the radus. the circumfrence of a circle is the outside rim of the circle.
Step-by-step explanation:
Who walks at a faster rate: Nicole, who walks 60 feet in 10 seconds, or Carey, who walks 42 feet in 6 seconds?
Answer:
Carey
Step-by-step explanation:
Nicole's speed is 6 feet per second.
Carey's speed is 7 feet per second.
19 e) Find the value of x. ASAP. Will give brainliest!
Answer:
X= 40
Step-by-step explanation:
A triangle always equals 180°. In order to find x, add 75 and 65,
75 + 65 =140
then divide 140 and 180,
180 / 140 = 40
then in order to make sure it's the right answer add 75,65, and 40 together. If it equals to 180, then it's the right answer.
Follow the pattern and find the missing number 0.85 0.86 0.88
Answer:
0.91
Step-by-step explanation:
Its 0.91 because 0.85 + 1 = 0.86 + 2 = 0.88 + 3 = 0.91
I will give brainlist need answer thx
Answer:
1288
Step-by-step explanation:
S = n/2(2a+(n-1)d)
S = 23/2(2(23)+(23-1)3)
S = 1288
4. Mary bought 12 pounds of blueberries to make 5 pies. She divided the blueberries
many pounds of blueberries were in each pie?
2.4 pounds
5. Write each quotient as a fraction or mixed number.
Quot
Problem
4:5
5:4
12:20
Answer:
Step-by-step explanation:
12/5=2.4 lb of blueberry in each pie
4/5=4/5 not a mixed number
5/4=1 1/4
12/20=3/5
A car travelled 217 miles in three and a half hours. How much longer will it take for the car to travel another 334.8 miles?
A box of cereal contains 4 3/4 cups of cereal. Each serving is 1/4 cup. How many servings of cereal are in the box?
Answer:
19
Step-by-step explanation:
Tell whether each pair of angles are elther supplementary or congruent.
Please help I have no idea what I'm doing with any of this!!
Answer: you are doing hell jesus
Step-by-step explanation:
When making bread from scratch, the receptor calls for 4/5 cup of water. If you need to make a smaller portion of the recipe, how much water would you need in order to make only 1/12 th of the recipe?
Give answer as a fraction, reduced to lowest temrs
Answer:
When making bread from scratch, the recipe calls for 2/3 cup of water
Step-by-step explanation:
The area of a rectangular rug is 24 1/12 square yards. The lenghth of the rug is 5 2/3 yards. What is the width?
Answer: 136 17/36
Step-by-step explanation:
Trevor's bank pays 1.94% simple interest. Of his principal is $241, and he left all of it in his account for 54 days. How much interest will Trevor earn?
9514 1404 393
Answer:
$0.70
Step-by-step explanation:
The interest is computed using the formula ...
I = Prt
where r is the annual rate, and t is the time in years. Banks compute interest using "ordinary interest", which assumes a 360-day year. Trevor's interest is ...
I = $241(0.0194)(54/360) = $0.70
Could someone please tell me how to graph y=−4x+3
Answer:
Ok, so when you graph, you want to make sure your point are right. 4, would be im guessing +4, so you would find +4, on your graph across the X axis. Keep that in mind. Then find +3, across the Y axis on your graph. Join the points, and you have your answer.
Step-by-step explanation:
I hope this helps you
Nine times the difference of 5 and y
Simplify the following equation: 5a + 3b = 5 +10a +-6b
Answer:
a=-1+[(9b)/5]
b=(5/9)+[(5a)/9]
Step-by-step explanation:
Find the value of x please also this is geometry
Given:
A figure of a triangle.
To find:
The value of x.
Solution:
In a triangle, angle bisectors intersect each other at a point which is know as incenter. This point is equidistance form the each side.
Using the above property, we get
[tex]4x-2=6x-8[/tex]
[tex]4x-6x=2-8[/tex]
[tex]-2x=-6[/tex]
Divide both sides by -2.
[tex]x=\dfrac{-6}{-2}[/tex]
[tex]x=3[/tex]
Therefore, the value of x is 3.
Help pleaseee like ASAP
Answer: B,C,E,F
Step-by-step explanation:1/6 times 5 on top and bottom to get choice B. 1/6 times 3 on top and bottom to get choice C . 1/6 times 4 on top and bottom to get choice E .1/6 times 2 on top and bottom to get choice F.