Answer:
absolute maximum = 184absolute minimum = -72Step-by-step explanation:
Given the function f(x) = x⁴-18x²+9 at the interval [-5, 5], the absolute maximum and minimum values at this end points are as calculated;
at end point x = -5
f(-5) = (-5)⁴-18(-5)²+9
f(-5) = 625-450+9
f(-5) = 184
at end point x = 5
f(5) = (5)⁴-18(5)²+9
f(5) = 625-450+9
f(5) = 184
To get the critical point, this points occurs at the turning point i.e at
dy/dx = 0
if y = x⁴-18x²+9
dy/dx = 4x³-36x = 0
4x³-36x = 0
4x (x²-9) = 0
4x = 0
x = 0
x²-9 = 0
x² = 9
x = ±3
Using the critical points [0, ±3]
when x = 0, f(0) = 0⁴-18(0)+9
f(0) = 9
Similarly when x = 3, f(±3)= (±3)⁴-18(±3)²+9
f(±3) = 81-162+9
f(±3) = -72
It can be seen that the absolute minimum occurs at x= ±5 and and absolute minimum occurs at x =±3
absolute maximum = 184
absolute minimum = -72
which of the following descriptions represent the transformation shown in the image? Part 3c
Answer: c) rotation of 180° & shift right 1 unit and down 2 units
Step-by-step explanation:
Rotation of 180° changes the signs of x and y
(x, y) → (-x, -y)
Shift right one unit adds 1 to x, Shift two down subtracts 2 from y
(-x, -y) → (-x + 1, -y - 2)
(x, y) (-x + 1, -y - 2)
(-1, -2) → (2, 0)
(-4, -1) → (5, -1)
(-4, -3) → (5, 1)
Write an equation in point-slope form for each line.
(If possible please show work)
Answer:
y= -2x+3
Step-by-step explanation:
Point slope form= y=mx+b
The m is the slope.
So, we have an incomplete equation right now: y= -2x+b
We want to find b. We can do that by plugging in values for the x and y coordinates. Fortunately, we do have a set of coordinates, (1, 1)!
We plug them in:
1= -2(1)+b
1= -2+b
b=3
So, since we have the slope and the b, also called the y-intercept, we can form an equation!
y= -2x+3
Need Help!!!! What is 1495486+73940426 Thanks!
Answer:
75435912
Step-by-step explanation:
1495486+73940426
= 75435912
Answer:
75,435,912
Step-by-step explanation:
=> 1495486 + 73940426
Using Calculator
=> 75,435,912
Simplify The square root of 5 (6-4 the square root of 3)
Answer:
7.75
Step-by-step explanation:
6-4=2
2 times the square root of 3=3.46410161514
square root of 5 times 3.46410161514=7.74596669242
to 2dp=7.75
How much time will it take Jenny to bike 15 miles if she bikes at a speed of 6 mph?
Answer:
this lesson, we will investigate the relationship between the distance traveled, the rate or speed or travel, and the time that it takes to travel that distance at that rate. We will also look at a few other related products.
Distance = (Rate)(Time)
The equation that relates distance, rate, and time is
d = rt
Where d is the distance traveled, r is the rate, and t is the time. On the CAHSEE exam, you will be given two of these and will be asked to use the above equation to find
took Markus half an hour to drive home from work. He averaged 34 miles per hour. How far does Markus live from his work?SolutionWe are given that it takes 1/2 an hour for the trip. This is a time: t = 1/2We are given that he averages 34 miles per hour. This is a rate: r = 34We are asked how few he has traveled. This is a distance. We use the d=rt equation: d = rt = (34)(1/2) = 17Answer:
2.5 hours
Step-by-step explanation:
First, try rewriting Jenny's speed in it's fraction form: 6 mi/hr
Next, use the units to set up an equation that relates Jenny's speed to the distance they want to travel. Let's call the unknown time t:
6mi/hr=15mi/t
1/t=6/15 (mi/hr•1/mi)
t=15/6 (hrs/mi•mi)= 15/6 (hrs•mi/mi)= 15/6 hrs
t=2.5hrs
So it'd take Jenny 2.5hrs at 6mph to go 15 miles. The key here is to keep track of the units. You can treat them like fractions and reduce them away as if they were numbers or variables.
5x is equal to 8X raise to power - 1/3
Answer:
No solutions.
Step-by-step explanation:
5x = 8x^-1/3
Divide 8 into both sides.
5/8x = x^-1/3
Divide both sides by x.
5/8 = x^-4/3
Multiply both sides by the exponent -3/4.
5/8^-3/4 = x
1.422624 = x
Plug in 1.422624 for x to check.
It does not work. There are no real solutions.
Simplify e^ln4
A. 1/4
B. 4
C. 1n4
D. E^4
Answer:
The answer is option B.
4Step-by-step explanation:
Using the expression
[tex] {e}^{ ln(x) } = x[/tex]
[tex] {e}^{ ln(4) } = 4[/tex]
Hope this helps you
For the data set represented by this box plot, what is the value of the maximum? maximum:
Answer:
140
Step-by-step explanation:
The maximum is the furthest the line that goes out the furthest, the minimum would be about 83-84
Answer:
the other person is correct!
Step-by-step explanation:
A pet store has 32 more dogs than cats. If there are a total of 144 dogs and cats altogether, then how many cats does the pet store have?
PLZ ANSWER ASAP THANKS
Answer:
56 cats
88 dogs
Step-by-step explanation:
x=cats
x+32=dogs
x+x+32=144
2x=144-32
2x=112
x=112/2
x=56 (56 cats)
x+32=88 (88 dogs)
Answer:
56
Step-by-step explanation:
In order to solve this question you need to subtract 32 by 144 then divide that answer by 2.
So we know that they're 32 more dogs then cats and there is 144 dogs and cats all together.
[tex]144 - 32 = 112[/tex]
Divide it in half
[tex]112 \div2=56[/tex]
[tex]56+32 = 88[/tex]
[tex]= 56[/tex]
Therefore they're 56 cats in the pet store.
Hope this helps.
Stuck on this one .......
Answer:
Exponent Product Rule
Step-by-step explanation:
Exponent multiplication: (a^b)(a^c)= a^(b+c)
t^3=(t^2)t
Because t=t^1, we have
t^2+t^1=t^3
This can be shown by the Exponent Product Rule
Answer: t²⁺¹
Step-by-step explanation:
The law of exponents states that when multiplying terms with the same base, you ADD the exponents. Note that "t" has an exponent of 1.
t³ = (t²)t¹ = t²⁺¹
I hope this is what you were looking for.
will give brainliest help plz i can't get back on the password won't go to my email and my little brother changed the password I am scared I lost everything PLZ HELP ME
Reflected across the x-axis ? How is look in the figure
Answer:
Well a shape reflecting across the x axis will look like some thing in the image below.
Look at both images.
A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 30 batteries of each type.
Required:
a. How many ways can a total inventory of 30 batteries be distributed among the eight different types.
b. How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory must include at least four A76 batteries?
c. How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory includes at most three A7b batteries?
Answer:
a. 10295472 ways
b. 4272048 ways
c. 6023424 ways
Step-by-step explanation:
Given that:
Camera shop stocks ----- 8 different types of batteries
one of which is ---- A76
Assume that there are ------ at least 30 batteries of each type.
a.
How many ways can a total inventory of 30 batteries be distributed among the eight different types.
The number of ways a total inventory of 30 batteries be distributed is :
[tex]= \left \{ {{30+8-1} \atop {30}} \right. \}[/tex]
[tex]= \left \{ {{37} \atop {30}} \right. \}[/tex]
[tex]=\dfrac{37!}{30! *7!}[/tex]
[tex]= \dfrac{37*36*35*34*33*32*31*30!}{30!*7*6*5*4*3*2*1}[/tex]
[tex]= \dfrac{37*36*35*34*33*32*31}{7*6*5*4*3*2*1}[/tex]
= 10295472 ways
b.
How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory must include at least four A76 batteries?
If we must include 4 A76 batteries; then the number of ways a total inventory of 30 batteries can be distributed among eight different types of batteries will be:
30 - 4 = 26 batteries
Now;
[tex]= \left \{ {{26+8-1} \atop {26}} \right. \}[/tex]
[tex]= \left \{ {{33} \atop {26}} \right. \}[/tex]
[tex]=\dfrac{33!}{26! \ \ 7!}[/tex]
[tex]=\dfrac{33*32*31*30*29*28*27*26!}{26! \ * \ 7*6*5*4*3*2*1}[/tex]
[tex]=\dfrac{33*32*31*30*29*28*27}{ \ 7*6*5*4*3*2*1}[/tex]
= 4272048 ways
c. If we must include at most three A7b batteries. the number of ways that a total inventory of 30 batteries can be distributed among eight different types of inventory is:
[tex]= \sum \limits ^3 _{x=0} \left \{ {{(30-x)+7-1} \atop {30-x}} \right. \} \\ \\ \\ = \sum \limits ^3 _{x=0} \left \{ {{(30-0)+7-1} \atop {30-0}} \right. \} = (^{36}_{30})+(^{35}_{29})+ (^{34}_{28})+ (^{33}_{27})[/tex]
[tex]= \dfrac{36!}{30! * 6!} + \dfrac{35!}{29! * 6!} + \dfrac{34!}{28! * 6!} + \dfrac{33!}{27! * 6!}[/tex]
= 1947792 + 1623160 + 1344904 + 1107568
= 6023424 ways
Factor by grouping 5x^3+6x^2+25x+30
Answer:
(5x + 6) (x² + 5)
Step-by-step explanation:
5x³ + 6x² + 25x + 30
= x² (5x + 6) + 25x + 30 -- Group 5x³ and 6x²
= x² (5x + 6) + 5 (5x + 6) -- Group 25x and 30
= (5x + 6) (x² + 5) -- Both terms have a common factor of 5x + 6
I have k quarters, five less quarters than nickels and one more than twice as many dimes as quarters. Find the value of the coins in cents in terms of k.
Answer:
(35k + 20) cents
Step-by-step explanation:
First of all, let us have the value of each unit:
1 quarter = 25 cents
1 nickel = 5 cents
1 dime = 10 cents
Given that number of quarter = k
Quarters are 5 lesser than Nickels, so number of nickels = k+5
One more than twice as many dimes as quarters:
k = 2 [tex]\times[/tex] Number of Dimes + 1
So, number of dimes = [tex]\frac{1}{2}(k-1)[/tex]
Value of quarters = [tex]25 \times k[/tex] cents
Value of nickels = [tex]5 \times (k+5) = (5k+25)\ cents[/tex]
Value of dimes = [tex]\frac{1}{2}(k-1) \times 10 = (5k-5)\ cents[/tex]
So, total value of coins =
[tex]25k + 5k +25 +5k-5\\\Rightarrow (35k+20)\ cents[/tex]
Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.78.
Requried:
a. Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85.
b. Compute a 98% CI for true average porosity of another seam based on 16 specimens with a sample average of 4.56.
c. How large a sample size is necessary if the width of the 95% interval is to be 0.40?
d. What sample size is necessary to estimate the true average porosity to within 0.2 with 99% confidence?
Answer:
a) The 95% CI for the true average porosity is (4.51, 5.19).
b) The 98% CI for true average porosity is (4.11, 5.01)
c) A sample size of 15 is needed.
d) A sample size of 101 is needed.
Step-by-step explanation:
a. Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{0.78}{\sqrt{20}} = 0.34[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 4.85 - 0.34 = 4.51
The upper end of the interval is the sample mean added to M. So it is 4.35 + 0.34 = 5.19
The 95% CI for the true average porosity is (4.51, 5.19).
b. Compute a 98% CI for true average porosity of another seam based on 16 specimens with a sample average of 4.56.
Following the same logic as a.
98% C.I., so [tex]z = 2.327[/tex]
[tex]M = 2.327*\frac{0.78}{\sqrt{16}} = 0.45[/tex]
4.56 - 0.45 = 4.11
4.56 + 0.45 = 5.01
The 98% CI for true average porosity is (4.11, 5.01)
c. How large a sample size is necessary if the width of the 95% interval is to be 0.40?
A sample size of n is needed.
n is found when M = 0.4.
95% C.I., so Z = 1.96.
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.4 = 1.96*\frac{0.78}{\sqrt{n}}[/tex]
[tex]0.4\sqrt{n} = 1.96*0.78[/tex]
[tex]\sqrt{n} = \frac{1.96*0.78}{0.4}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96*0.78}{0.4})^{2}[/tex]
[tex]n = 14.6[/tex]
Rounding up
A sample size of 15 is needed.
d. What sample size is necessary to estimate the true average porosity to within 0.2 with 99% confidence?
99% C.I., so z = 2.575
n when M = 0.2.
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.2 = 2.575*\frac{0.78}{\sqrt{n}}[/tex]
[tex]0.2\sqrt{n} = 2.575*0.78[/tex]
[tex]\sqrt{n} = \frac{2.575*0.78}{0.2}[/tex]
[tex](\sqrt{n})^{2} = (\frac{2.575*0.78}{0.2})^{2}[/tex]
[tex]n = 100.85[/tex]
Rounding up
A sample size of 101 is needed.
Find value of z and simplify completely.
Answer:
3√10Given:
A right triangle in which an altitude is drawn from the right angle vertex
To find: value of X
We have leg rule in similarity in right triangle as:
[tex] \frac{leg}{part} = \frac{hypotenuse}{leg} \\ [/tex]
Plugging the given values,
[tex] \frac{z}{3} = \frac{3 + 27}{z} \\ z \times z = 3(3 + 27) \: \: (cross \: multiplication) \\ {z}^{2} = 9 + 81 \\ {z}^{2} = 90 \\ z = \sqrt{90} \\ z = 3 \sqrt{10} [/tex]
Hope this helps...
Good luck on your assignment..
Tom takes a cancer test and the test is advertised as being 99% accurate: if you have cancer you will test positive 99% of the time, and if you don't have cancer, you will test negative 99% of the time. If 1% of all people have cancer and Tom tests positive, what is the prob that Tom has the disease
Answer:
99% chance tommy has it
Step-by-step explanation:
cuz do da math
Which parent function is f(x) = x^2?
O A. An exponential parent function
OB. The linear parent function
C. The absolute value parent function
D. The quadratic parent function
Answer:
D. Quadratic parent function.
Step-by-step explanation:
help!! its algebra..
Answer:
The correct answer to this is "Change in Y over Change in X"
Step-by-step explanation:
Change in Y over Change in X is the basis of the saying "rise over run". When you divide the rise by the run you get the slope.
I hope this helps you out!
Describe fully the single transformation that’s maps triangle A onto triangle B.
Answer:
reflection of the axis y=4
Step-by-step explanation:
becuase it is reflected on itself
Answer:
Reflect Triangle A by the line y = 4
Step-by-step explanation:
The answer is reflect Triangle A by y = 4 because the two triangles are symmetric.
simplify the expression into form a+bi, where rational numbers
(4-i)(-3+7i) - 7i(8+2i)
Answer:
-12+28i+3i-7i-65i+28
14 -41i
PLEASE HELPP! f(x)= -3x + 3
Which of the graphs represent the inverse of the function F??
Answer:
Answer is Y
Step-by-step explanation:
There are members on the board of directors for a certain non-profit institution. a. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? b. If they must form an ethics subcommittee of four members, how many different subcommittees are possible?
Answer: a. 1320
b.495
Step-by-step explanation:
Complete question is provided in the attachment.
Total members on the board = 12
a. Persons to chose : chairperson, first vice chairperson, second vice chairperson, and secretary
i.e. Total 3 posts in an order.
Number of ways to choose 3 persons from 12 in an order = [tex]^{12}P_3[/tex] [By permutation]
[tex]=\dfrac{12!}{(12-3)!}\\\\=\dfrac{12!}{7!}\\\\=12\times11\times10\\\\=1320[/tex]
hence, 1320 different slates of candidates are possible .
b. number of ways to choose 4 members out of 12 ( order not matters)=[tex]^{12}C_{4}[/tex] [By combinations]
[tex]=\dfrac{12!}{4!8!}\\\\=\dfrac{12\times11\times10\times9}{24}\\\\=495[/tex]
Hence, the number of different subcommittees are possible =495
What is the measure of angle ABC? Please answer quickly!
Answer:
ABC = 88
Step-by-step explanation:
Angle Formed by Two Chords = 1/2( sum of Intercepted Arcs)
ABD = 1/2 ( 131+ 53)
ABD = 1/2 (184)
=92
ABC = 180 -ABD
ABC = 88
What are the characteristics of a socialist economy? What are the pros and cons of this type of economy?
Answer:
The pro is Political Control, the cons, however, are many.
Step-by-step explanation:
However, A Socialist Economy cons outweigh its pros. The only thing that is a PRO is you dictating it, preventing people from success. Wanna know the cons? The Cons are more Regulations, to which chokes more businesses of their money, they function, & motive. To which it has a chain reaction of: The Businesses not employing people, more people are out of work, which means more people ain't buying stuff to support the businesses, which means the businesses are out of business, they shut down.
The Economy ain't something that you can stop, or go, & it ain't statistics. An Economy is just.. people, that's it. It's just people, they are the ones that work, run businesses & factories, they are the ones that buy N' sell. They create, craft, invent, innovate, etc.
Here's a quote that I have: "The more you choke it from breathing in, the less it breathes out". That's my stance on regulation & Socialism, to which Socialism is just Voluntary Communism, & A Permanent Ideological belief that Big government Involvement is the way to go.
To which, it's not!
Each of 100 students in the Allen School can only take 1 CSE class each, between the four classes CSE 311, CSE 312, CSE 331, and CSE 332. Each student (independently of others) takes CSE 311 with probability 0.3, CSE 312 with probability 0.4, CSE 331 with probability 0.1, and CSE 332 with probability 0.2. What is the probability that exactly 31 sign up for CSE 311, 39 sign up for CSE 312, 7 sign up for CSE 331, and 23 sign up for CSE 332
Answer:
[tex]P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
Step-by-step explanation:
Sample space, n = 100
Let the number of students signed up for CSE 311 = a
Let the number of students signed up for CSE 312 = b
Let the number of students signed up for CSE 331 = c
Let the number of students signed up for CSE 332 = d
Probability of taking CSE 311, [tex]P_a[/tex] = 0.3
Probability of taking CSE 312, [tex]P_b[/tex] = 0.4
Probability of taking CSE 331, [tex]P_c[/tex] = 0.1
Probability of taking CSE 332, [tex]P_d[/tex] = 0.2
[tex]P(a,b,c,d) = \frac{n!}{a! b! c! d!} p_a^{a} p_b^{b} p_c^{c} p_d^{d} \\P(a=31,b=39,c=7,d=23) = \frac{100!}{31! 39! 7! 23!} * 0.3^{31} * 0.4^{39} * 0.1^{7} 0.2^{23}\\P(a=31,b=39,c=7,d=23) = \frac{4.58*10^{111}}{2.13*10^{56}* 5040 }* (1.57*10^{-55})\\P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
Write the equation of each line in slope-intercept form.
(If possible please show work)
Answer:
[tex]\displaystyle y = -\frac{2}{3}\, x - 9[/tex].
Step-by-step explanation:
The slope-intercept form of a line on a cartesian plane should be in the form:
[tex]y = m\, x + b[/tex],
where:
[tex]m[/tex] is the slope of the line, while [tex]b[/tex] is the [tex]y[/tex]-coordinate of the point where the line intersects the [tex]y[/tex]-axis.The question states that the slope of this line is [tex]\displaystyle -\frac{2}{3}[/tex]. In other words, [tex]\displaystyle m = -\frac{2}{3}[/tex]. The next step is to find the value of [tex]b[/tex]. That could be done using the information that the point [tex](-6,\, -5)[/tex] is on this line.
Note that the slope-intercept form of a line [tex]y = m\, x + b[/tex] is essentially an equation about [tex]x[/tex] and [tex]y[/tex]. For a point [tex](x_0,\, y_0)[/tex] to be on that line, [tex]x = x_0[/tex] and [tex]y = y_0[/tex] should satisfy its equation. In other words, it must be true that [tex]y_0 = m\, x_0 + b[/tex].
For the point [tex](-6,\, -5)[/tex], [tex]x_0 = -6[/tex] and [tex]y_0 = -5[/tex]. The equation would be:
[tex]\underbrace{-5}_{y_0} = m \times \underbrace{(-6)}_{x_0}+ b[/tex].
Besides, the slope of this line is already known to be [tex]\displaystyle m = -\frac{2}{3}[/tex]. Therefore, this equation would become:
[tex]\displaystyle \underbrace{-5}_{y_0} = \underbrace{\left(-\frac{2}{3}\right)}_{m} \times \underbrace{(-6)}_{x_0}+ b[/tex].
Solve this equation for [tex]b[/tex]:
[tex]b = -9[/tex].
Hence, the slope-intercept form ([tex]y = m\, x + b[/tex]) of this line would be:
[tex]\displaystyle y = -\frac{2}{3}\, x - 9[/tex].
-5 x = 4 what property of equality was use to solve this equation
Answer:
Division property of equality.
Find sin θ if cos θ = 4/7 and θ in quadrant IV.
Answer:
sinΘ = - [tex]\frac{\sqrt{33} }{7}[/tex]
Step-by-step explanation:
Using the trigonometric identity
sin²Θ + cos²Θ = 1, thus
sinΘ = ± [tex]\sqrt{1-cos^20}[/tex]
Since Θ is in the fourth quadrant then sinΘ < 0
Given
cosΘ = [tex]\frac{4}{7}[/tex] , then
sinΘ = - [tex]\sqrt{1-(\frac{4}{7})^2 }[/tex] = - [tex]\sqrt{1-\frac{16}{49} }[/tex] = - [tex]\sqrt{\frac{33}{49} }[/tex] = - [tex]\frac{\sqrt{33} }{7}[/tex]