I’m stuck on this problem

Im Stuck On This Problem

Answers

Answer 1

The value of the f(-8) from the given f(x) is 1/53.

According  to the statement

we have given that the value of f(x) and with the value of this we hav eto find the value of f(-8).

So, For this purpose,

The given value of f(x) :

The function f(x) is

f(x) = 1 / x^2 -11

Now we find the value of the f(-8) then

For this put Put x is -8 in the f(x) then the equation become

f(x) = 1 / x^2 -11

f(-8) = 1 / (-8)^2 -11

f(-8) = 1 / 64 -11

f(-8) = 1 / 53.

here the value becomes 1/53.

So, The value of the f(-8) from the given f(x) is 1/53.

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Related Questions

Helppp!! pleasee i put a ss!

Answers

Answer:

-20

Step-by-step explanation:

He went back 20 and not forward 20.  Everyone would want a penalty if you got to go forward.

The motion of an object was recorded by measuring the velocity of the object in meters per second at various times, as shown in the table.
The scatterplot below was graphed from the data in the table, where t represents the time, and v represents the velocity. Based on the scatterplot, which equation BEST represents the relationship between velocity and time?

Answers

The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.

According to the statement

we have given some data in the form of graph according to the velocity per time and we have to find the relationship between the velocity and time.

So, for this purpose,

we know that the best method show the relationship is a slope intercept form.

So,

The slope intercept form is a the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

And

Using the coordinate points on the plane (0, 6) and (10, 28)

now we Determine the slope

Slope = 28-6/10-0

Slope = 22/10

Slope = 2.2

And then Determine the y-intercept

6 = 2.2(0) + b

b = 6

And now we have to put in the general form of the slope intercept form which is y = mx + b

Then the equation become

y = 2.2x + 6

So, The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.

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The graph shows the amount of money that the journalism club raised for a scholarship fund over a 5-week period. If x represents the number of weeks, which function is the BEST fit for the information in this graph?

Answers

The line of best fit for the information in this graph is:

f(x) = 200x + 100.

How to find the equation of linear regression using a calculator?

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points (t,v) are given as follows:

(2, 500), (3, 700), (4, 900), (5, 110)

Hence, inserting these points into a calculator, the equation is given by:

f(x) = 200x + 100.

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The selling price, s, of an item is s = c mc, where c is the cost of the item and m is the percent markup based on cost. what is the formula solved for m? m = startfraction s minus c over c endfraction m = startfraction s c over c endfraction s minus c = m s c = m

Answers

Answer:

s - c over c = m   or  (s-c)/c = m

Step-by-step explanation:

s = c * mc

s -c = mc

(s - c) / c = m

Answer:

A ) m=s-c/c

Step-by-step explanation:

7
of the trains are arriving late due to a train strike.
Write down the ratio of on-time trains to late trains.
15

Answers

Answer:

15:7

Step-by-step explanation:

you put the numbers in order first the number of on time trains to off time trains

What's the total surface area of a covered box with a length of 4 ft, a width of 3 ft, and a height of 6 ft?

Answers

Answer:  108 square feet

===============================================

Work Shown:

L = 4 = length

W = 3 = width

H = 6 = height

SA = surface area of the box

SA = 2*(LW + LH + WH)

SA = 2*(4*3 + 4*6 + 3*6)

SA = 108

Express each fraction as a decimal:

- 2 4/100

Answers

-0.24

this is because whenever it’s /100, the decimal at the back moves 2 twice

meaning it starts from -24. to -2.4 and lastly -0.24

whenever the dot ends at .24, a zero must be added

PLEASE HELP ITS MATH PLEASE

Answers

Answer:

y=3x-5

Step-by-step explanation:

they are parallel meaning that only the constant is changing

-2 = 3(1) - (something)

-2 = 3 - (something)

something = 5.   - > that was 3+2

so y=3x+(-5)

For a standard normal​ curve, find the​ z-score that separates the bottom​ 70% from the top​ 30%.

Answers

Using the normal distribution, the z-score that separates the bottom​ 70% from the top​ 30% is z = 0.525.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The z-score that separates the bottom​ 70% from the top​ 30% is z with a p-value of 0.7, hence z = 0.525.

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Factorize: p(x)=x^2+9x^2+23x+15

Answers

Answer:

(x+1),(x+3),(x+5)

Step-by-step explanation:

may be this answer helps to solve the problems

If f(5) = 12, f ' is continuous, and 7 f '(x) dx 5 = 16, what is the value of f(7)? f(7) =

Answers

The value of function f(x) at x = 7 is f(7) = 28

For given question,

we have been given the value of function f(x) at x = 5.

f(5) = 12

We have been given that f'(x) is continuous on 5 and 7

Also, [tex]\int\limits^7_5 {f(x)} \, dx =16[/tex]

We need to find the value of f(7)

Since ∀x, f'(x) = f'(x), f is a primitive function of f' .

And f ' is continuous

[tex]\Rightarrow \int\limits^7_5 {f(x)} \, dx =16\\\\\Rightarrow [f(x)]_5^7=16[/tex]

⇒  [f(7) - f(5)] = 16

⇒ f(7) - 12 = 16

⇒ f(7) = 16 + 12

⇒ f(7) = 28

Therefore, the value of function f(x) at x = 7 is f(7) = 28

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Sierra found that 15 meters is equivalent to 49.2 feet. Which of the following is an equivalent ratio?
3 to 8.84
5 to 18.22
7 to 22.96
9 to 25.32

Answers

Answer:

7 to 22.96

Step-by-step explanation:

Hello!

We can represent each ratio as a fraction:

Original: 15 to 49.2 = [tex]\frac{15}{49.2}[/tex]3 to 8.84 = [tex]\frac{3}{8.84}[/tex]5 to 18.22 = [tex]\frac{5}{18.22}[/tex]7 to 22.96 = [tex]\frac{7}{22.96}[/tex]9 to 25.32 = [tex]\frac{9}{25.32}[/tex]

To find equivalent values, we can convert each fraction into a decimal by dividing them.

ConvertOriginal: [tex]\frac{15}{49.2} = 0.304878048780488[/tex][tex]\frac{3}{8.84} = 0.339366515837104[/tex][tex]\frac{5}{18.22} = 0.274423710208562[/tex][tex]\frac{7}{22.96} = 0.304878048780488[/tex][tex]\frac{9}{25.32} = 0.355450236966825[/tex]

The ratio of 7 to 22.96 is equivalent to the ratio of 15 to 49.2.

The answer is 7 to 22.96

An observer (o) spots a plane (p) taking off from a local airport and flying at a 33° angle horizontal to her line of sight and located directly above a tower (t). the observer also notices a bird (b) circling directly above her. if the distance from the plane(p) to the tower (t) is 7,000 feet, how far is the bird (b) from the plane (p)? round to the nearest whole number. two parallel lines bp and ot with a transversal running through p and o. dotted red line from p to t and from b to o. angle pot is 33 degrees. the length of p t is 7000. the length of bp is x. 3,815 feet 5,873 feet 8,343 feet 10,779 feet

Answers

The distance between the bird (B) and plane (P) exists at 10,779 feet.

How to estimate the distance between the bird (B) and plane (P)?

Given the figure attached,

PT = OB = 7000 ft

PB = OT = x feet

and angle of elevation (∠POT) = 30°

By applying the Tan rule in the triangle POT,

tan 33° = Opposite side/Adjacent side = PT/OT

tan 33° = 7000/x

x = 7000/tan33°

x = 10779 feet

The distance between the bird (B) and plane (P) exists at 10,779 feet.

Therefore, the correct answer is option D. 10779 feet.

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Please answer quickly!

Answers

19) The sum of the arithmetic series is - 397. (Correct choice: E)

33) The sum of the geometric series is 1700. (Correct choice: E)

How to determine the sum of a given series

19) Arithmetic series are sets of elements generated by a linear expression of the form:

aₙ = a₁ + (n - 1) · d      (1)

Where:

aₙ - n-th term of the seriesa₁ - First term of the series n - Index of the n-th term of the series.d - Change between two consecutive elements of the series.

If we know that a₁ = 27, n = 20 and d = - 5, then sum of the first 20 terms of the series is:

x = 27 + 22 + 17 + 12 + 7 + 2 + (- 3) + (- 8) + (- 13) + (- 18) + (- 23) + (- 28) + (- 33) + (- 38) + (- 43) + (- 48) + (- 53) + (- 58) + (- 63) + (- 68)

x = - 397

The sum of the arithmetic series is - 397. (Correct choice: E)

33) Geometric series are sets of elements generated by a exponential expression of the form:

aₙ = a₁ · rⁿ     (2)

Where:

aₙ - n-th term of the seriesa₁ - First term of the seriesr - Ratio between two consecutive elements of the series.

If we know that a₁ = 1458 and r = 1 / 3, then the sum of the first 6 terms of the geometric series is:

x = 1458 + 162 + 54 + 18 + 6 + 2

x = 1700

The sum of the geometric series is 1700. (Correct choice: E)

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Rose and Tyler divided their 1.5kg of pizza
dough in the ratio 2:3.
How much did Rose receive?

Answers

Answer:

0.6kg

Step-by-step explanation:

first roses share becomes 2:5

then you change the kilograms into grams for an easier working

then you multiply 2:5 by 1500g to get roses share

Build Your Math Skills 2C, Round decimals to the nearest hundredth (0.01): 2.364

Answers

Answer:2.36

Step-by-step explanation:

Solve the system of equations.

y equals x plus 8
y equals 3 x plus 2

Answers

Answer:

The answer is (3,11) or x = 3, y = 11

Step-by-step explanation:

:)

Answer:

(3, 11 )

Step-by-step explanation:

y = x + 8 → (1)

y = 3x + 2 → (2)

substitute y = 3x + 2 into (1)

3x + 2 = x + 8 ( subtract x from both sides )

2x + 2 = 8 ( subtract 2 from both sides )

2x = 6 ( divide both sides by 2 )

x = 3

substitute x = 3 into either of the 2 equations and solve for y

substituting into (1)

y = 3 + 8 = 11

solution is (3, 11 )

subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5

Answers

- 1.3 is the number we get when we subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5. This can be obtained by finding sum separately and then subtracting them.

What is the required number:

Here in the question it is given that,

subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5

By separating them as two parts

sum of -5/6 and -1 3/5  sum of 2 2/3 and -6 2/5

⇒ sum of -5/6 and -1 3/5  

- 5/6 + - 1 3/5 = - 5/6 + - 8/5  (∵ a b/c = (ac+b)/c(5+3)/5 = 8/5)

                      = (- 25 - 48)/30  (LCM = 30)

                      = - 73/30

⇒ sum of 2 2/3 and -6 2/5

2 2/3 + -6 2/5 = 8/3 + -32/5

                       = (40 - 96)/15  (LCM = 15)

                       = - 56/15

subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5

= (sum of 2 2/3 and -6 2/5) - (sum of -5/6 and -1 3/5)

= (- 56/15) - (- 73/30 )  

= - 56/15 + 73/30

= - 112/30 + 73/30   (LCM = 30)

= - 39/30

= - 13/10

= - 1.3

Hence - 1.3 is the number we get when we subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5.

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Choose the most appropriate translation of the english sentence. the amount of time spent spent driving is 5 hours

Answers

The most appropriate translation of the English sentence. the amount of time spent driving (which depends on the speed of the car) is 5 hours. is time(speed) = 5, making option C the right choice.

The time spent by a body covering a certain distance at a certain speed is given as time = distance/speed.

In the question, we are asked to translate the English sentence, :"the amount of time spent driving (which depends on the speed of the car) is 5 hours".

In the given sentence, the time spent driving is given to be 5 hours, depending on the speed of the car.

Thus, the time can be shown as a function of speed with a value of 5.

Thus, the translation can be, time(speed) = 5.

Thus, the most appropriate translation of the English sentence. the amount of time spent driving (which depends on the speed of the car) is 5 hours. is time(speed) = 5, making option C the right choice.

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The provided question is incomplete. The complete question is:

"Choose the most appropriate translation of the English sentence. the amount of time spent driving (which depends on the speed of the car) is 5 hours.

a. speed(time) = 5

b. time(5) = 50 mph

c. time(speed) = 5

d. time(speed) > 0"

What are the domain and range of g of x equals negative 3 times the square root of the quantity x minus 1? d: (1, [infinity]) and r: (0, [infinity]) d: [–3, [infinity]) and r: [0, [infinity]) d: (–3, [infinity]) and r: (–[infinity], 0) d: [1, [infinity]) and r: (–[infinity], 0]

Answers

The domain of it is d: [1,+infinity) and the range is r: (-infinity,0].

Answer:

d: d [1, infinity) and r (-infinity, 0)

Step-by-step explanation:

right on the test :3 good luck dear!!

1. If R = 32 - 11 (OC+2y). then find R when: x=2 and y=4

Answers

The correct equation says to find R = 32 - 11 (X+2y). This gives us the value of -78.

How to solve for the equation below

We have this

R = 32 - 11 (X+2y)

we have the following values for x and y as 2 and 4 respectively.

What we have to do would be to find the value of R after we have put in these values in the equation.

To do this, we would then have:

R = 32 - 11(2 + 2*4)

R = 32 -11(2+8)

R = 32 - 11 * 10

R = 32 - 110

This would give us the value that says

R = -78

Hence the value of R is given as -78

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find the slope given the following information
(3,7) and (-4,10)

Answers

Answer:

m=-3/7

Step-by-step explanation:

m=rise/run=Δy/Δx

m=y2−y1/x2−x1

m=10−7/−4−3

m=3/−7

m=−3/7

Help please!

A collection of numbers M consists of all positive integers less than 20. If a collection of numbers N is a collection created by randomly choosing five numbers from M. Which of the following must be true about M?
i. The range must be at least 4
ii. The median must be at least 3
iii. The mean can be above 17

a. i only
b. ii only
c. i and ii only
d. i and iii only

Answers

The answer choice which represents statements which are correct regarding the datasets described in the task content is; Choice C; i and ii only.

Which of the answer choices represents statements which are true about the dataset described?

It follows from the task content that the universal set M is described to contain all positive integers less than 20 while the collection of numbers N is created randomly by choosing five numbers from it.

Consequently, it follows that since 5 number are to be chosen, the range must be at least 4 as this follows from the extreme case scenario of selecting consecutive numbers. Hence, statement i is correct.

Also, the median must be at least three as the extreme case scenario in which numbers 1,2,3,4 and 5 are chosen still renders the median to be 3.

The mean of the five numbers cannot be above 17 because, when when numbers, 15,16,17,18 and 19 are chosen, the mean is 17 and does not exceed 17. Hence, statement iii is incorrect.

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What number is represented by the question mark?
111= 0, 3213=0, 7756= 1,7662= 2, 6855= 3, 8096= 5,6666=4 . 8193= 3,9313= 1,8639= 4,1234=0, 2581 = 2,7186= 3, 2679=?

Answers

Based on the sequence of numbers given, the number that is represented by the question mark is 2679 = 2.

What is the sequence given?

The sequence requires that you count the number of circles that a group of number has. For instance 9 has one circle and 8 has two circles because of the way they are drawn.

The numbers 111, 3213, and 1234 will therefore be equal to 0 because there is no number that has a circle in it.

The number 8096 however, will be equal to 5 because there are 5 circles. Two in 8. 1 in 0. 1 in 9. 1 in 6.

This means that the last number of 2679 will therefore be equal to 2 because there are two circles. One circle is in 6, and the other circle is in  9.

In conclusion, the number represented by the question mark is 2.

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Find the product of (x − 8)2 and explain how it demonstrates the closure property of multiplication.

Answers

The product of [tex](x - 8)^2[/tex] is not a polynomial equation because a polynomial equation means a coefficient of x that has a power of two or more powers.

What is a Polynomial Equation?

The equations developed with variables, exponents, and coefficients exists named polynomial equations. It can include various exponents, where the higher one stands named the degree of the equation.

Closure property under multiplication notes that any two rational numbers' outcome will be a rational number, i.e. if a and b exist in any two rational numbers, ab will also be a rational number.

Example: (3/2) × (2/9) = 1/3.

The product of [tex]$(x - 8)^2[/tex]

Simplifying the equation as (x − 8)(x − 8)

Apply Perfect Square Formula, and we get

[tex]$(a-b)^{2}=a^{2}-2 a b+b^{2}$[/tex]

[tex]$&(x-8)^{2}=x^{2}-2 x \cdot 8+8^{2} \\[/tex]

[tex]$&=x^{2}-2 x \cdot 8+8^{2}[/tex]

Simplifying the above equation, we get

[tex]$x^{2}-2 x \cdot 8+8^{2}=x^{2}-16 x+64 \\[/tex]

[tex]$&=x^{2}-16 x+64[/tex]

This is not a polynomial equation because a polynomial equation means a coefficient of x that has a power of two or more powers.

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While playing baseball, sofia takes note of the extreme vectors for which she bats. what is the angle between her two extreme bats? extreme 1: <-8, 12> extreme: 2: <13, 15>

Answers

The angle between the two extreme vectors of Sofia bats is 74.60 degrees.

In this question,

The angle between two vectors will be deferred by a single point, which is called as the shortest angle at which we have to turn around one of the vectors to the position of co-directional with another vector.

The extreme vectors of Sofia bats are  [tex]\vec u = < -8, 12 >[/tex] and [tex]\vec v = < -8, 12 >[/tex]

The angle between the vectors is

[tex]\theta = cos^{-1} \frac{\vec u.\vec v}{||\vec u|| ||\vec v||}[/tex]

The dot product is calculated as

[tex]\vec u. \vec v = (-8)(13)+(12)(15)[/tex]

⇒ [tex]-104+180[/tex]

⇒ 76

The magnitude can be calculated as

[tex]||\vec u|| = \sqrt{(-8 )^{2} +(12)^{2} }[/tex]

⇒ [tex]\sqrt{64+144}[/tex]

⇒ [tex]\sqrt{208}[/tex]

[tex]||\vec v|| = \sqrt{(13 )^{2} +(15)^{2} }[/tex]

⇒ [tex]\sqrt{169+225}[/tex]

⇒ [tex]\sqrt{394}[/tex]

Thus the angle between the vectors is

[tex]\theta = cos^{-1} \frac{76}{(\sqrt{208} )(\sqrt{394} )}[/tex]

⇒ [tex]\theta = cos^{-1} \frac{76}{\sqrt{81952} }[/tex]

⇒ [tex]\theta = cos^{-1} \frac{76}{286.27 }[/tex]

⇒ [tex]\theta = cos^{-1} (0.2654)[/tex]

⇒ [tex]\theta=74.60[/tex]

Hence we can conclude that the angle between the two extreme vectors of Sofia bats is 74.60 degrees.

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40 points answer ASAP PLEASE!
For what values of x does f(x) = 0?
A.−4, 0, 2
B.−2, 0, 4
C.−5, 0, 17
D.−17, 0, 5

Answers

I think it is 2, 0, 4 but it would be very helpful if you put in an image of the graph.

Have a great day :D

2. G.GPE.7 Consider ∆ABC below. What is the perimeter of ∆ABC? * A. 16.9 B. 12.9 C. 18.6 D. 17.4

Answers

Answer:B

Step-by-step explanation:

A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the
translation?
(x + 5, y-3)
(x + 5, y + 3)
(x, y)(x-3, y + 5)
(x, y) (x + 3, y + 5)
(x, y)
O(x, y)
Mark this and return
Save and Exit
lext
Submit

Answers

Answer:

(x+5, y-3)

Step-by-step explanation:

I would say this because when a plane is translated up it would be positive and when it's translated to the left it would be negative,

Sketch a graph of the following rational function: h(x)= x²-1/ x³-2x²-x+2​

Answers

Note that

[tex]\frac{x^2-1}{x^3 - 2x^2 -x+2}=\frac{x^2 -1}{x^2 (x-2)-(x-2)}=\frac{x^2 -1}{(x^2 -1)(x-2)}[/tex]

So, for all [tex]x \neq \pm 1[/tex], [tex]f(x)=\frac{1}{x-2}[/tex].

So, the graph looks like something like as following in the image.

Other Questions
The guidelines for __________ in group practice have been drawn from a variety of professional associations, including the aca, the asgw, and the amcd. Which compliance-gaining strategy is considered to be the most assertive?O challengingO suggesting alternativesO promisingO acknowledging differences Given the function f(x) = -5x-x+ 20, find f(3).O-28O-13O62O64 What is the average dose of radiation that most people are exposed to every year not including dental or medical personnel dealingwith X-rays?OA. 40 uSvOB. 1000 u SvOC. 2400 u SvOD. 100,000 u Sv What sentence best expresses the main idea of the passage? Many people agree that the growth of aquaculture is important, but others are not sure it is worth it. Many places in the world are already fished to their limits, and native fish populations are decreasing. The practice of aquaculture is growing in every part of the world. Aquaculture is not experimental, and it is not new. Which line most accurately represents the line of best fit for the scatter plot?A graph shows numbers from 0 to 14 on the x axis at increments of 2 and the numbers 0 to 28 on the y axis at increments of 4. Scatter plot shows ordered pairs 2, 5 and 5, 6 and 6, 8 and 8, 10 and 9, 12 and 10, 12 and 11, 14 and 12, 16 and 13, 20. A line labeled A joins ordered pair 0, 0 and 4, 28. A line labeled B joins the ordered pairs 0, 0 and 8, 28. A line labeled C joins the ordered pairs 0, 0 and 13, 28. A line labeled D joins the ordered pairs 0, 0 and 14, 18 Line A Line B Line C Line D The catholic church used a variety of methods to regain power and influence after the black death. which statements about these methods are true? Increasing the amount of debt makes debt blank______ risky and equity blank______ risky. Drag the factors to the correct locations on the image. Each factor can be used more than once, but not all factors will be used. What is the factored form of this expression? x3 - 6x2 - 9x + 54Tiles go here( )( )( )Tile options:x - 6x - 9x + 9x - 3x + 3x + 6 What type of gestures would a third-base coach use to communicate with a runner on second base? If country a has a comparative advantage in the production of automobiles and country b has a comparative advantage in the production of boats, which country will gain from trade? The probability of event a is x, and the probability of event b is y. if the two events are independent, which condition must be true? 12. Rotate Rectangle ABCD 90 counterclockwise.Then, translate it along the vector (3,4).ADBC-4 -242O-2.-424XA'(B'(C'(D'(A"(B"(C"(D"())))HELP ME PLS How did the philosophy of nationalism contribute to hostilities betweenSerbia and Austria-Hungary leading up to World War I?A. Nationalism allowed Serbia to justify its invasion of Austria-Hungary's Balkan territories.B. Nationalism motivated Austria-Hungary to attempt to unite allSerb people in one country.C. Nationalism caused many Serbs living in Austria-Hungary todemand their independence.D. Nationalism led to Serb outrage after Austria-Hungary refused toally with Serbia. Where is Catalhoyuk? Determine the acid dissociation constant (Ka) for a 0.200 M solution of hydrogen sulfate ion withthe pH of 1.35 if the reaction for the dissociation of this acid isHSO 4 H+ + SO 4-(Hint: [H+] = 10-PH; Ka = [product]/[reactant]) Which linear inequality will not have a shared solution set with the graphed linear inequality? y < five-thirdsx 2 y < negative five-thirdsx 1 y > five-thirdsx 2 y > negative five-thirdsx 2 How a clients academic/education, career, personal, and social development impacts assessment choice? If species a provides a habitat to species b as part of a mutualistic relationship, what is the probable effect on the abundance and distribution of species b? Finding mole ratios from chemical formulaeThis is the chemical formula for nickel tetracarbonyl (a powerfully poisonous liquid used in nickel refining):Ni(CO)4A chemical engineer has determined by measurements that there are 93. moles of carbon in a sample of nickel tetracarbonyl. How many moles of oxygen are inthe sample?Round your answer to 2 significant digits.