f(x)=x^3- X-1; between 1 and 2
Answer:
Here's one way to do it.
Explanation:
Let
f
(
x
)
=
x
3
−
2
x
2
+
3
x
.
(Needed because the intermediate value theorem is a theorem about functions .)
Observe that the equation
x
3
−
2
x
2
+
3
x
=
5
has a root (a solution) exactly when
f
(
x
)
=
5
So the question now is to show that for at least one number
c
, in
[
1
,
2
]
, we get
f
(
c
)
=
5
.
f
is continuous on
[
1
,
2
]
(Because it is a polynomial and they are continuous everywhere.)
f
(
1
)
=
2
and
f
(
2
)
=
6
5
is between
f
(
1
)
and
f
(
2
)
, so
by the intermediate value theorem, there is at least one number
c
, in
[
1
,
2
]
, for which
f
(
c
)
=
5
.
That is, the original equation has a solution.
Step-by-step explanation:
A spinner with 12 equally sized slices has 12 yellow slices. The dial is spun and stops on a slice at random. What is the
probability that the dial stops on a yellow slice?
Write your answer as a fraction in simplest form.
Answer:
1/1
Step-by-step explanation:
The reason why is because the spinner has 12 slices and on that spinner there is 12 yellow slices meaning all the slices on the spinner are yellow.
This means it is a 100% chance to land on yellow but 100% aas a fraction is 100/100.
You can simplify 100/100 a hundred times to 99/99 to 98/98 you can keep doing it but it's lowest form is the lowest number besides zero and that is 1 so it's lowest form is 1 out of 1 or 1/1 or 100%.
Hope this helps have a great afternoon:)
A baseball measures approximately 74 mm in diameter. What is the volume of a baseball? (Round your answer to the nearest tenth if needed)
Answer:
As Per Given Information
Diameter of of baseball = 74 mm
We've been asked to find the volume of baseball .
As we know
Radius = Diameter/2
Radius = 74/2
Radius = 37 mm ( 1 mm = 0.1 cm)
Radius = 37/10 cm
Radius = 3.7 cm
Now let's calculate the volume of baseball
volume of baseball = 4/3 πr³
Put the given value we obtain
→ volume of baseball = 4/3 × 3.14 × (3.7)³
→ volume of baseball = 4/3 × 3.14 × 50.653
→ volume of baseball = 4/3 × 159.05042
→ volume of baseball = 636.20168/3
→ volume of baseball = 212.06
→ volume of baseball = 212 cm³ ( approx)
So, the volume of baseball is 212 cm³.
Solution:
We know that:
[tex]V_{Baseball} = \frac{4}{3} \pi r^{3} \\ \\ Diameter = 74 \space\ mm\\\\Radius = \frac{Diameter}{2}[/tex]
Finding the area of the baseball:
[tex]V_{Baseball} = (\frac{4}{3})( \pi )(r^{3})[/tex]
[tex]V_{Baseball} = [\frac{4}{3}][ 3.14 ][(\frac{74}{2}) ^{3}][/tex]
[tex]V_{Baseball} = [\frac{4}{3}][ 3.14 ][(37) ^{3}][/tex]
[tex]V_{Baseball} = [\frac{4}{3}][ 3.14 ][50653}][/tex]
[tex]V_{Baseball} = 212067.227 \space\ mm^{3} \space\ (Using\ calculator)[/tex]
Rounding the volume to the nearest tenth:
[tex]V_{Baseball} = 212067.227 \space\ mm^{3} = 212067.2 \space\ mm^{3}[/tex]
Thus, 212067.2 mm³ is the volume of the baseball.
Using the digits 1 to 9, at most one time each, create an equation where x has the smallest possible value. (▢ is empty values)
▢/▢ (▢x+▢) +▢x=▢x+▢
Answer:
1/8(7x +2) +3x = 4x +9
Step-by-step explanation:
The value of x will be smallest when it is most negative. Here, that will occur when the numerator of the rational solution for x is as large a positive number as possible, and the denominator is a small negative number.
If we call the spaces a, b, ..., g, then the value of x is ...
x = (bg -ad)/(ac +b(e-f))
This is smallest (most negative) when bg is as large as possible (8·9), and ad is as small as possible (1·2). Then values for c, e, f can be chosen to make the denominator -1. The solution for x looks like ...
x = (8·9 -1·2)/(1·7 +8(3 -4)) = 70/-1 = -70
The smallest possible value of x is -70. One way to obtain that value is ...
1/8(7x +2) +3x = 4x +9
_____
There are numerous ways to obtain "indeterminate" results where the equation reduces to one with no solution. And there are a number of ways to have the solution be infinity: (ac-b(e-f)) = 0.
∠A and ∠B are supplementary. m∠A = (3x + 6), m∠B = (4x + 20). Find the measure of each angle.
Answer:
Step-by-step explanation:
3x + 6 + 4x + 20 = 180
7x + 26 = 180
7x = 154
x = 22
m<A= 3(22) + 6 = 66 + 6 = 72°
m<B = 4(22) + 20 = 88 + 20 = 108°
PLEASE HELP IM CONFUSED HOW TO FACTORISE THESE
Answer:
c-(y-1)(y+1)
d-(x-8)(x+8)
g-(a-9)(a+9)
h-(x-y)(x+y)
k- -1(x-5)(x+5)
i- -1(b-1)(b+1)
o- (x-20)(x+20)
p- -1(y-30)(y+30)
Step-by-step explanation:
k(special)
-1(x^2-25)
-1(x-5)(x+5)
i
-1(b^2-1)
-1(b-1)(b+1)
(continue with same procedure for such)
c -difference of square
there are all difference of square
The distribution of sample means consists of the____________ of all the possible ___________, __________ of a specific ___________ from a specific population.
Answer:
The distribution of sample means consist of the set of means of all the possible random samples of a specific size(n) from a specific population
Scenario: Stephanie has been driving for four years without any major auto accidents-until today. It was pouring rain when she left class, and within minutes of leaving, she was forced to make an evasive maneuver that caused her to go into a spin on the wet road. After knocking an expensive, high-end luxury car down an embankment, Stephanie came to a stop by smashing into the side of a mid-range sedan.
She was found to be at fault in the accident, so let's look at the extent of the damage she caused:
Luxury car: This car was totaled at a value of $95,000.
Sedan: This car will need $4,000 in repairs.
Hospital bills: The driver of the luxury car had $15,000 in medical bills for a broken arm, while his passenger had $185,000 in medical bills for emergency surgery and recovery.
Like many Americans, Stephanie carries a 100/300/100 liability policy.
What is the total dollar value of the property damage Stephanie caused?
Select one:
$95,000
$110,000
$99,000
$299,000
Answer:
95,000
Step-by-step explanation:
Because I did the math
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 5 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 97? Mark has Number marbles to sell. Don has Number marbles to sell.
Answer:
Mark has 23 marbles, Don has 74 marbles
Step-by-step explanation:
Mark has x marbles, Don has y marbles
y = 5 + 3x
x + y = 97
so
x + (5 + 3x) = 97
4x = 97 - 5 = 92
x = 92/4 = 23
y = 97 - 23 = 74
Kim sold a house for 250,000$,and made a 2% commission.how much money did Kim make from commission for selling the house
Answer:
$5000
Step-by-step explanation:
250000*2%=5000
If
f(x) = ax + b,
where a, and b are constants, what is f(b)?
Select the correct answer below:
O f(b) = 2ab
O f(b) = ab + b
O f(b) = a + b
O f(b) = ab + a
< Previous
Answer:
f(b) = ab+ b
Step-by-step explanation:
Given f(x) = ax + b
To find f(b) plug b in for x.
f(b) = ab + b
help plz and hurry and I’ll mark u Brainlyest
Answer:
O
4
8
12
Step-by-step explanation:
Make a number line and mark the points that represent the following values of x.
x squared=16
Please mark where this is suppose to go on the number line :)
Answer:
Positive 4
Step-by-step explanation:
4 squared is equal to 16 as 4 x 4 = 16. However, if it was -4 squared, it would equal -16.
The first bus stop or a
bus route is 5 1/2 miies
from school. How many
yards is the first bus
stop from school?
Answer:
9680 yards
Step-by-step explanation:
There are 1760 yards in a mile. That times 5 is 8800. To get the full 5.5 just add half of what’s in a mile (880) and you get 9680 yards. :)
Help asap please!!!
The graph represents the relationship between x and y. Four sections of the graph are labeled as A through D
Which section is the graph increasing linearly?
A section A
B section B
C Section C
D section D
Answer:
A
Step-by-step explanation:
look at the lines
A is going up and is linear
5. The ordered pair below represents a point on the line 3y + 4x = 5. What is
the missing y-coordinate of this point? (5, ?). Show work.
Answer:
The value of the missing y coordinate is -5.
Step-by-step explanation:
The given line is :
3y + 4x = 5
We need to find the value of missing y-coordinate of this point? (5, ?). Let it is k. This point will satisfy the given equation. It means, put the value of x 5 in given equation.
[tex]3k+4(5)=5\\\\3k+20=5\\\\3k=-15\\\\k=-5[/tex]
So, the value of the missing y coordinate is -5.
Answer: -5
(Haven't been on in a while lol, hope this helps!)
-Astolfo
SOLVE 5( 2y-1)-2(2-y)+3(2y+9)=0
Answer:
y = -1
Step-by-step explanation:
5(2y−1)−2(2−y)+3(2y+9)=0
Step 1: Simplify both sides of the equation.
5(2y−1)−2(2−y)+3(2y+9)=0
(5)(2y)+(5)(−1)+(−2)(2)+(−2)(−y)+(3)(2y)+(3)(9)=0(Distribute)
10y+−5+−4+2y+6y+27=0
(10y+2y+6y)+(−5+−4+27)=0(Combine Like Terms)
18y+18=0
18y+18=0
Step 2: Subtract 18 from both sides.
18y+18−18=0−18
18y=−18
Step 3: Divide both sides by 18.
18y/18 = -18/18
Answer: y=−1
A person bought some articles at the rate of 5 per rupee (₹) and the same number of articles at the rate of 4 per rupee (₹). He mixed both the types and sold them at the rate of 9 for ₹2. In this business, he suffered a loss of ₹3. The total number of articles bought by him was:
a. 1090
b. 1080
c. 540
d. 545
Answer:
B. 1080Step-by-step explanation:
Lets assume the number of articles was x.
Half of the articles was bought at the price 1/5 rupee each and the other half was bought at the price 1/4 rupee each.
Cost of articles:
1/2x*1/5 + 1/2x*1/4 = 1/2x(1/5 + 1/4) = 1/2x(4/20 + 5/20) = 9/40xMoney made after sale is:
2/9x according to rateThe difference is 3 rupees:
9/40x - 2/9x = 381/360x - 80/360x = 31/360x = 3x = 3*360x = 1080Correct choice is B
Mary and Betty went apple picking. Each time Mary picked 3 apples Betty picked 5 apples. At home the girls found out that Betty collected 16 more apples than Mary. How many apples did each girl pick?
Answer: This is a college question?
Step-by-step explanation:
Mary picked 24 apples and Betty picked 40
Answer:
24 and 40
Step-by-step explanation:
there 16 apart from each other and simplyfy it you get a ratio of 3:5
This double number line diagram shows the amount of flour and eggs needed for 1 batch of cookies.
How much flour is used with 12 eggs?
60,000 + 1,000 + 600 + 10 +1 =
Answer: 61,611
Step-by-step explanation:
Find the value of x, y, and z in the rhombus below.
Answer:
Step-by-step explanation:
Opposite angles of a rhombus are congruent, so [tex]6x+8=86 \longrightarrow x=13[/tex]
Also, adjacent angles of a rhombus are supplementary, so [tex]86+5z+4=86+7y+3=180 \longrightarrow y=13, z=18[/tex]
10! Or 10 factorial please
Answer:
3628800
Step-by-step explanation:
just use a calculator if you need these types of things
if you're using this for a equation then substitute with 10*9*8*...
I need help on what the answer is
Answer:
86 degrees
Step-by-step explanation:
How many weeks in a year (52 total weeks in a
year) should Bobby Jo hit the first target? *
Answer:
Yes
Step-by-step explanation:
Answer:
no answer
Step-by-step explanation:
not enough info
(a+b)=
pls tell the answer
Answer:
I'm Pretty sure a+b is what it says
if 3 = 1/2gt^2, make t the subject of the formula
Answer:
t = √1.5/g
Step-by-step explanation:
1/2gt^2 = 3
Divide both sides by 1/2
gt^2 = 1.5
Divide both sides by g
t^2 = 1.5/g
Square root both sides
t = √1.5/g
A fancy new brand of laundry detergent just launched an aggressive advertisement campaign in the hope that people will use the brand despite its higher price point. An avid consumer is trying to determine whether this fancy new brand of laundry detergent cleans clothes better than his regular brand of laundry detergent. To do this, over the course of a month he randomly uses one of the detergents in each load of laundry and then, when the wash cycle is complete, assigns a value to how clean the clothes are based on the number of garments that are "sufficiently clean," with higher scores being better. If the consumer were to perform a test to tell the difference between the mean scores of each detergent (ignoring the flaws in this test design), what hypothesis would he use?
Step-by-step explanation:
Here is the answer to this question,
His hypothesis would be:
Null hypothesis:
H0: μ(new) - μ(regular) = 0
Alternate hypothesis:
H1: μ(new) - μ(regular) > 0
The consumer is testing to know if his new detergent is better off in cleaning than the regular. The question says that higher scores after cleaning is used to signify which is better based on sufficiently clean garment. Since he is interested in knowing the mean scores of the differences, he should use the hypothesis I stated above.
Find the average speed Distance:1,375km Time: 2 hours 5 minutes
Answer:
550km/h
Step-by-step explanation:
v (speed) = d/t
v = 1375/2.5
v =550
1.
If f(x) =1/2 (2x – 3) + 4, what is the value of f(5)?
Answer:
[tex]f(5) =\frac{15}{2}\\\\f(5) =7\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]f(x) =1/2 (2x - 3) + 4\\\\f(x)=\frac{1}{2} (2x -3)+4\\\\f(5)=?\\\\f(5)=\frac{1}{2} (2(5) -3)+4\\\\f(5) = \frac{1}{2}\times\:7+4\\\\f(5) =\frac{7}{2}+4\\\\f(5) =\frac{15}{2}\\\\f(5) =7\frac{1}{2}[/tex]