How many different integers are there such that the square of the square of the integer is a two-digit integer

Answers

Answer 1

The number of different integers there are for the condition described in which case, the square of the square of the integer is a two-digit integer as in the task content is 4 possible integers which includes; -2, -3, 2, 3.

How many integers satisfy the given condition?

According to the task content, the square of the square of such integers must be a two-digit number, that is, less than or equal to 99.

The numbers in discuss, x must satisfy;

x⁴ < 99.

The numbers in this regard are therefore, -2, -3, 2, 3.

Ultimately, the integers which satisfy the condition described in which case, the square of the square of the integer is a two-digit integer as in the task content is 4 possible integers which includes; -2, -3, 2, 3.

Related Questions

A trander an article at 10% loss. If he had sold it for Rs.540 more , he would have gain 5% . Find the cost price of the articles.
The answer is :3600

Answers

Answer:

3600

Step-by-step explanation:

Reason is because you put the answer in your question.

Answer:

Rs.10800

Step-by-step explanation:

loss of article(L%)=10%

s.p=?

c.p of an article (c.p)=c.p

Now,

s.p=100-L%×c.p

_____

100

= 100-10 ×c.p

_____

100

=90 ×c.p

___

100

=0.9 × c.p

if article sold with Rs. 540 more

Article profit =5%

s.p =c.p + 540 =100+p%×c.p

______

100

or, c.p +540=105×c.p

______

100

or, c.p +540=1.05×c.p

or,c.p +540=1.05c.p

or, 540=1.05c.p-c.p

or,540=0.05c.p

or, 540=c.p

____

0.05

Therefore, c.p =Rs. 10800

What is the next number in the arithmetic sequence below??
I think it's D but I'm not sure.

Answers

i believe it should be c

PLEASE HELP IM STUCK PLS

Answers

Answer:

y is equal to -16

Answer:

y = 8

Step-by-step explanation:

We can use proportions for this question since y varies directly with x. This means that if x changes, y changes along with the x, and vice versa.

When y = -8, x = 4, so the proportion will be -8 : 4.

We need to find the y when x is 4, so our equation will be:

-8 : 4 = y : -4

Since the proportion will be the same.

Next, we multiply the inner two numbers, and the outer two numbers, saying that the values are the same.

4y = 32

y = 8

So y = 8 will be our answer!

For the first 150 miles of a trip, an car drives at v mph. For the next 200 miles, the car drives at (v
+25) mph. The average speed of the whole trip is 35 mph. Find the value of v.
(A) 20
(B) 25
(C) 30
(D) 35

Answers

If for the first 150 miles of a trip, an car drives at v mph, for the next 200 miles, the car drives at (v+25) mph and the average speed of the whole trip is 35 mph, then the value of v will be 20mph (A).

Given Information:

Average speed = 35 mph

Total distance = 150 + 200 = 350 miles

For the first 150 miles of a trip, an car drives at v mph speed

⇒ Time, t1 = 150/v hrs

For the next 200 miles, the car drives at (v+25) mph speed

⇒ Time, t1 = 200 / (v+25) hrs

Now, the formula for average speed is given as,

Total distance / Total time

= [tex]\frac{350}{\frac{150}{v}+\frac{200}{(v+25)} }[/tex]

⇒ [tex]\frac{350}{\frac{150}{v}+\frac{200}{(v+25)} }[/tex] = 35 mph

[tex]\frac{350 v (v+25)}{150(v+25) + 200v}[/tex] = 35

[tex]\frac{350v^{2} + 8750v}{150v +3750 + 200v}[/tex] = 35

350v² + 8750v = 35 (350v + 3750)

v² + 25v = 35v + 375

v² - 10v = 375

v² - 10v - 375 = 0

Now, the above equation for speed can be written as,

v² - 20v + 15v - 375 = 0

v(v-20) + 15(v-20) = 0

(v-20) (v+15) = 0

v = 20

or v = -15

Since, speed is a scalar quantity, it can't be negative. Thus, v = 20 mph

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50 points!!!
Someone help pls, I can’t understand it and it’s due tomorrow :c

Answers

[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}[/tex]

[tex]\star\:{\underline{\underline{\sf{\purple{Solution:}}}}}[/tex]

❍ Arrange the given data in order either in ascending order or descending order.

2, 3, 4, 7, 9, 11

❍ Number of terms in data [n] = 6 which is even.

As we know,

[tex]\star \: \sf Median_{(when \: n \: is \: even)} = {\underline{\boxed{\sf{\purple{ \dfrac{ { \bigg (\dfrac{n}{2} \bigg)}^{th}term +{ \bigg( \dfrac{n}{2} + 1 \bigg)}^{th} term } {2} }}}}}[/tex]

[tex]\\[/tex]

[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ { \bigg (\dfrac{6}{2} \bigg)}^{th}term +{ \bigg( \dfrac{6}{2} + 1 \bigg)}^{th} term } {2} }[/tex]

[tex]\\[/tex]

[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \dfrac{6 + 2}{2} \bigg)}^{th} term } {2} }[/tex]

[tex]\\[/tex]

[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \cancel{ \dfrac{8}{2}} \bigg)}^{th} term } {2} }[/tex]

[tex]\\[/tex]

[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ 4}^{th} term } {2} }[/tex]

• Putting,

3rd term as 4 and the 4th term as 7.

[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 4 + 7 } {2} }[/tex]

[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 11} {2} }[/tex]

[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} = \purple{5.5}[/tex]

[tex]\\[/tex]

[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}[/tex]

[tex]\star\:{\underline{\underline{\sf{\red{Solution:}}}}}[/tex]

❍ Arrange the given data in order either in ascending order or descending order.

1, 2, 3, 4, 5, 6, 7

❍ Number of terms in data [n] = 7 which is odd.

As we know,

[tex]\star \: \sf Median_{(when \: n \: is \: odd)} = {\underline{\boxed{\sf{\red{ { \bigg( \frac{n + 1}{2} \bigg)}^{th} term}}}}}[/tex]

[tex]\\[/tex]

[tex] \sf Median_{(when \: n \: is \: odd)} = {{ \bigg(\dfrac{ 7 + 1 } {2} \bigg) }}^{th} term[/tex]

[tex]\\[/tex]

[tex] \sf Median_{(when \: n \: is \: odd)} = { \bigg(\cancel{\dfrac{8}{2}} \bigg)}^{th} term[/tex]

[tex]\\[/tex]

[tex] \sf Median_{(when \: n \: is \: odd)} ={ 4}^{th} term[/tex]

• Putting,

4th term as 4.

[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: odd)} = \red{ 4}[/tex]

[tex]\\[/tex]

[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 3 :}}}}}}[/tex]

[tex]\star\:{\underline{\underline{\sf{\green{Solution:}}}}}[/tex]

The frequency distribution table for calculations of mean :

[tex]\begin{gathered}\begin{array}{|c|c|c|c|c|c|c|} \hline \rm x_{i} &\rm 3&\rm 1&\rm 7&\rm 4&\rm 6&\rm 2 \rm \\ \hline\rm f_{i} &\rm 4&\rm 6&\rm 2&\rm 2 & \rm 1&\rm 1 \\ \hline \rm f_{i}x_{i} &\rm 12&\rm 6&\rm 14&\rm 8&\rm 6&\rm \rm 2 \\ \hline \end{array} \\ \end{gathered} [/tex]

☆ Calculating the [tex]\sum f_{i}[/tex]

[tex] \implies 4 + 6 + 2 + 2 + 1 + 1[/tex]

[tex] \implies 16[/tex]

☆ Calculating the [tex]\sum f_{i}x_{i}[/tex]

[tex] \implies 12 + 6 + 14 + 8 + 6 + 2[/tex]

[tex]\implies 48[/tex]

As we know,

Mean by direct method :

[tex] \: \: \boxed{\green{{ { \overline{x} \: = \sf \dfrac{ \sum \: f_{i}x_{i}}{ \sum \: f_{i}}}}}}[/tex]

here,

• [tex]\sum f_{i}[/tex] = 16

• [tex]\sum f_{i}x_{i}[/tex] = 48

By putting the values we get,

[tex]\sf \longrightarrow \overline{x} \: = \: \dfrac{48}{16}[/tex]

[tex]\sf \longrightarrow \overline{x} \: = \green{3}[/tex]

[tex]{\large{\textsf{\textbf{\underline{\underline{Note\: :}}}}}}[/tex]

• Swipe to see the full answer.

[tex]\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}[/tex]

a=5
b=12
c=10
d=2

1. 2b-a
2. d(ab-c)
3. 3 + b/d
4. 4a/b+4d
5. b-c+d

Answers

1. 19
2. 14
3. 9
4. 10 rounded didn’t know if you wanted decimals
5. 4

Apyrotechnician plans for two fireworks to explode together at the same
height in the air. They travel at speeds shown below. Firework B is launched
0.25 s before Firework A. How many seconds after Firework B launches will
both fireworks explode?
Firework A Firework B
320 fts
240 fuis
Both fireworks will explode _?seconds after Firework B launches.

Answers

First note down the relevant variables from the question.
Ua (Initial velocity a) = 320ft/s
Ub (initial velocity b) = 240ft/s
Aay (acceleration of a in the vertical axis) = Aby = -32.17ft/s/s

We want to know when they will be at the same height so should use the formula for displacement:
s = ut + 1/2 * at^2

We want to find when both firework a and firework b will be at the same height. Therefore mathematically when: say = sby (the vertical displacements of firework A and B are equal). We also know that firework B was launched 0.25s before firework A so we should either add 0.25s to the time variable for the displacement formula for firework B or subtract 0.25s for firework A.

SO:
Say = Sby
320t + 1/2*-32.17t^2 = 240(t+0.25) + 1/2 * -32.17(t+0.25)^2
320t - 16.085t^2 = 240t + 60 - 16.085(t+0.25)^2
320t - 16.085t^2 = 240t + 60 - 16.085(t^2 + 0.5t + 6.25)
320t - 16.085t^2 = 240t + 60 -16.085t^2 - 8.0425t - 100.53
320t - 240t - 8.0425t - 16.085t^2 + 16.085t^2 = 60 - 100.53
71.958t = -40.53
t = -0.56s (negative because we set t before Firework A was launched)

Now we know both fireworks explode 0.56 seconds AFTER fireworks B launches (because we added 0.25 seconds to the t variable in the equation above for the vertical displacement of Firework B).

You could continue on to find the displacement they both explode at and verify the answer by ensuring that it is equal (because the question stated they should explode at the same height by substituting the value we found for t of 0.56s into the vertical displacement formula for firework A and t+0.25s=0.81s into the same formula for Firework B

Verification:
Say = ut + 1/2at^2
Say = 320*0.56 + 1/2*-32.17*0.56^2
Say = 179.2 + -5.04
Say = 174.16ft

Sby = ut + 1/2at^2
Sby = 240*0.81 + 1/2*-32.17*0.81^2
Sby = 194.4 - 10.5
Sby = 183.9ft

While Say is close to Sby I would have expected them to be almost perfectly equal… can you please check if this matches the answer in your textbook? There could be wires due to rounding. I also usually work in SI units which use the metric system and not the imperial system although that shouldn’t make a difference. The working out and thought process is correct though and this is why trying to verify the answer is an important step to make sure it works out.

Answer: 0.56s (I think)

Find the center of a circle with the equation: x2 y2−32x−60y 1122=0 x 2 y 2 − 32 x − 60 y 1122 = 0

Answers

The equation of a circle exists:

[tex]$(x-h)^2 + (y-k)^2 = r^2[/tex], where (h, k) be the center.

The center of the circle exists at (16, 30).

What is the equation of a circle?

Let, the equation of a circle exists:

[tex]$(x-h)^2 + (y-k)^2 = r^2[/tex], where (h, k) be the center.

We rewrite the equation and set them equal :

[tex]$(x-h)^2 + (y-k)^2 - r^2 = x^2+y^2- 32x - 60y +1122=0[/tex]

[tex]$x^2 - 2hx + h^2 + y^2 - 2ky + k^2 - r^2 = x^2 + y^2 - 32x - 60y +1122 = 0[/tex]

We solve for each coefficient meaning if the term on the LHS contains an x then its coefficient exists exactly as the one on the RHS containing the x or y.

-2hx = -32x

h = -32/-2

⇒ h = 16.

-2ky = -60y

k = -60/-2

⇒ k = 30.

The center of the circle exists at (16, 30).

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Thirty percent of high-school senior boys play in the school band. If a certain high school has 60 senior boys, how many boys play in the school band?
(A) 12
(B) 18
(C) 22
(D) 30

Answers

B) 18 of high school boys play in the school band

PLS HELP IM SO STUCK

Answers

3x-2y= 7

Slope intercept form y= mx+b

3x- 2y= 7

- 3x -3x

-2y/-2= 3x/-2 - 7/2

y= 3x/-2 -7/2

Answer:

3x/2 and the second 7/-2y

Step-by-step explanation:

thats how is what i got

c) Shin thinks of a number. She multiplies it bye 5 then subtract 7. The answer is he

same as 3 times a number plus 11. What number did shin think of?

Answers

Answer:

Step-by-step explanation:

let the number be y

5×y - 7 = 3×y + 11

5y-7 = 3y+11

collect like terms

5y-3y = 11+7

2y = 18

y = 18/2

y = 9

someone help me out please

Answers

Answer:

[tex]\displaystyle x=\frac{5}{4},\;\;1\frac{1}{4}, \;\; or \;\; 1.25[/tex]

Step-by-step explanation:

To solve for x, we need to isolate the x variable.

Given:

[tex]\displaystyle x+\frac{1}{2} =\frac{7}{4}[/tex]

Subtract [tex]\frac{1}{2}[/tex] from both sides of the equation:

[tex]\displaystyle (x+\frac{1}{2})-\frac{1}{2} =(\frac{7}{4})-\frac{1}{2}[/tex]

[tex]\displaystyle x=\frac{7}{4}-\frac{1}{2}[/tex]

Now, we will create common denominators to simplify.

[tex]\displaystyle x=\frac{7}{4}-\frac{2}{4}[/tex]

[tex]\displaystyle x=\frac{5}{4}[/tex]

Find the value of x
a. 13 b. 14/5 c. 5 d. 8

Answers

Using the chord theorem, option C is the best solution since x = 5.

The four line segments that are created by two intersecting chords inside of a circle are explained by the chord theorem, sometimes referred to as the intersecting chords theorem, a statement in fundamental geometry. The products of the line segment lengths on each chord are equal, according to this assertion.

The value of x must be determined in order to answer the question.

We may determine the following using the chord property:

8*x = 4*10,

or, 8x = 40,

or, x = 40/8,

or x = 5.

Given that x = 5, option C is the best option according to the chord theorem.

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A soccer team won only 10 of their first 30 games. How many of their remaining 20 games will they have to win to have a .500 record??

Answers

Answer: 5 games

Step-by-step explanation: A .500 record means that the soccer team won half of their games ( that's how I interpret it). Since they are going to play 30 games, they need to win half of 30 or 15 games to have that record. 15-10 = 5. So, they need to win 5 more games to have a .500 record.

Use the ratio test to determine whether the series is convergent or divergent. 2 4/2^2 8/3^2 16/4^2 ......

Answers

I assume the given series is

[tex]\displaystyle 2 + \frac4{2^2} + \frac8{3^2} + \frac{16}{4^2} + \cdots = \frac{2^1}{1^2} + \frac{2^2}{2^2} + \frac{2^3}{3^2} + \frac{2^4}{4^2} + \cdots = \sum_{n=1}^\infty \frac{2^n}{n^2}[/tex]

By the ratio test, the series diverges, since

[tex]\displaystyle \lim_{n\to\infty} \left|\frac{2^{n+1}}{(n+1)^2} \cdot \frac{n^2}{2^n}\right| = 2 \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = 2 > 1[/tex]

Ann and Tom want to establish a fund for their grandson's college education. What lump sum must they deposit at 12 % annual interest rate, compounded quarterly , in order to have 20,000$ in the fund at the end of 10 years?

Answers

The principal amount that must be deposited as a lump sum amount is = $16,666.7

Calculation of principal amount

The simple interest amount = $20,000

The interest rate = 12%

The time that is given= 10 years

Therefore the principle amount =?

Using the simple interest formula;

SI= P×T×R/100

Make P the subject of formula,

P = SI ×100/T×R

P= 20,000×100/10×12

P= 2,000,000/120

P= $16,666.7

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help me with this, correct answer get brainliest

Answers

Answer:

Step-by-step explanation:

Find the value of the indicated variable.

Answers

102 degrees

Step-by-step explanation:

Angles in a quadrilateral add to 360 degrees.

y = 360 - (120 + 85 + 53)

y = 360 - 258

y = 102 degrees

The answer is 102degrees

greatest common factor of 24,36, and 96

Answers

Answer:

Step-by-step explanation:

[tex]24=2^{3} \times 3 \\ \\ 36=2^{2} \times 3^{2} \\ \\ 96=2^{5} \times 3[/tex]

Hey there!

What is GCF (Greatest Common Factor)?

Basically, the GCF is the biggest number in a data set that all of your numbers share.

What are the factors of the numbers?

24:1, 2, 3, 4, 6, 8, 12, and 24

36: 1, 2, 3, 4, 6, 9, 12, 18, and 36

96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96

What are the like terms that the numbers share?

1, 2, 3, 4, 6, 8, and 12

What is the biggest number out of the like terms?

What is your number?

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Mike wants to find the confidence interval for a set of data. he knows the sample size and the sample proportion. which other piece of information does he need to determine the confidence interval?

Answers

Using the formula for a z-distribution confidence interval of proportions, he also needs to know the confidence level.

What is a confidence interval of proportions?

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.

Of these 3 itens, the problem states that he knows the sample size and the sample proportion, hence he needs to know z to determine the confidence interval. z depends on the confidence level, which is the remaining parameter.

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Measure of angle TRV?

Answers

Answer:

130 degrees

Step-by-step explanation:

We know (x-10)+(2x+10) is 180 degrees.

So first we need to find x. (x-10)+(2x+10)=3x

3x=180

x=60

Angle TRV is 2x+10.

If we input 60 in the place of x, it is 2(60)+10=120+10=130.

The answer is 130 degrees.

how to solve problem in the document

Answers

I’ve attached a photo, with the instructions. Hope it helps. If you have any questions don’t hesitate to ask

Quick algebra 1 question for 25 points!

Only answer if you know the answer, Tysm!

Answers

Using a quadratic regression equation, it is found that the prediction of volunteers in year 10 is of:

A. 47.

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

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

In this problem, we have that the function initially increases, then it decreases, which means that it is a quadratic function. The points (x,y) to be inserted into the calculator are given as follows:

(1, 20), (2,17), (3, 16), (4,16), (5,18), (6,21), (7,25), (8,31)

Inserting these points into the calculator, the prediction of y for a value of x is given as follows:

y = 0.702x^2 - 4.726x + 23.857

Hence, when x = 10, the prediction is:

y = 0.702 x 10² - 4.726 x 10 + 23.857

y = 47.

Hence option A is correct.

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Please help me

Prove the following identity. Include a complete proof in proper form
1/1-sin x-1/1+sin x=2 tan x/COS X

Answers

By using algebra properties and trigonometric formulas we find that the trigonometric expression [tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] is equivalent to the trigonometric expression [tex]\frac{2\cdot \tan x}{\cos x}[/tex].

How to prove a trigonometric equivalence by algebraic and trigonometric procedures

In this question we have trigonometric expression whose equivalence to another expression has to be proved by using algebra properties and trigonometric formulas, including the fundamental trigonometric formula, that is, cos² x + sin² x = 1. Now we present in detail all steps to prove the equivalence:

[tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] Given.

[tex]\frac{1 + \sin x - 1 + \sin x}{1 - \sin^{2}x}[/tex] Subtraction between fractions with different denominator / (- 1) · a = - a.

[tex]\frac{2\cdot \sin x}{\cos^{2}x}[/tex] Definitions of addition and subtraction / Fundamental trigonometric formula (cos² x + sin² x = 1)

[tex]\frac{2\cdot \tan x}{\cos x}[/tex] Definition of tangent / Result

By using algebra properties and trigonometric formulas we conclude that the trigonometric expression [tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] is equal to the trigonometric expression [tex]\frac{2\cdot \tan x}{\cos x}[/tex]. Hence, the former expression is equivalent to the latter one.

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Find the radius of convergence, then determine the interval of convergence

Answers

By the ratio test, the series converges for

[tex]\displaystyle \lim_{k\to\infty} \left|\frac{(x+2)^{k+1}}{\sqrt{k+1}} \cdots \frac{\sqrt k}{(x+2)^k}\right| = |x+2| \lim_{k\to\infty} \sqrt{\frac k{k+1}} = |x+2| < 1[/tex]

so that the radius of convergence is 1, and the interval of convergence is

|x + 2| < 1 ⇒ -1 < x + 2 < 1 ⇒ -3 < x < -1

The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.

Find the radius of convergence R and the interval of convergence:

Ratio test is the test that is used to find the convergence of the given power series.

First aₙ is noted and then aₙ₊₁ is noted.

For ∑ aₙ, aₙ and aₙ₊₁ is noted.

[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|[/tex] = β

If β < 1, then the series convergesIf β > 1, then the series divergesIf β = 1, then the series inconclusive

Here [tex]a_{k}[/tex] = [tex]\frac{(x+2)^{k}}{\sqrt{k} }[/tex] and [tex]a_{k+1}[/tex] = [tex]\frac{(x+2)^{k+1}}{\sqrt{k+1} }[/tex]

Now limit is taken,

[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|[/tex] = [tex]\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }/\frac{(x+2)^{k} }{\sqrt{k} }|[/tex]

= [tex]\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }\frac{\sqrt{k} }{(x+2)^{k}}|[/tex]

= [tex]\lim_{n \to \infty} |{(x+2) } }{\sqrt{\frac{k}{k+1} } }}|[/tex]

= [tex]|{x+2 }|\lim_{n \to \infty}}{\sqrt{\frac{k}{k+1} } }}[/tex]

= [tex]|{x+2 }|[/tex] < 1

- 1 < [tex]{x+2 }[/tex] < 1

- 1 - 2 < x < 1 - 2

- 3 < x < - 1

We get that,

interval of convergence = (-3, -1)

radius of convergence R = 1

Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.

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If 2 = x3, then x equals
A 05
B 01
C | 1
D 5

Answers

Answer:

Step-by-step explanation:

When the dollar price of pounds rises, for example, from $1 = 1 pound to $2 = 1 pound, the dollar has ______ relative to the pound.

Answers

The dollar gains depreciated relative to the pound when the price of pounds in dollars increases, for instance, from $1 = 1 pound to $2 = 1 pound.

What is Depreciated relative?

Devaluation of a currency can take place in both absolute and relative terms. When the value of one currency declines in relation to the values of other currencies, this is referred to as a relative devaluation. For instance, the British pound sterling may be worth more today than it did yesterday in terms of US dollars.

A currency's value declines when compared to other currencies, which is known as currency depreciation. Political unrest, interest rate differences, weak economic fundamentals, and investor risk aversion are a few examples of the causes of currency devaluation.

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In each of the following, the type of variation is given along with 1 data point. Find the variation constant. a. direct variation; y = Kx where x = 3 and y = 6 b. inverse square variation; y = K/x2 where x = –2 and y = 1 c. inverse variation; y = K/x where x = 8 and y = 10 d. inverse variation; y = K/x where x = 3 and y = 3 e. direct square variation; y = Kx 2 where x = 5 and y = 15 f. direct variation; y = Kx where x = –7.5 and y = 6.3

Answers

For direct variation, variation constant = 2.

For inverse square variation, variation constant = 4.

For inverse variation, variation constant =80.

For inverse variation, variation constant = 9.

For direct square variation, variation constant = 0.6

For direct variation, variation constant = -0.84

(a) Direct variation: y = Kx where x = 3 and y = 6

Variation constant(k) = y/x = 6/3 =2

(b) Inverse square variation: y = K/[tex]x^{2}[/tex] where x = -2 and y = 1

Variation constant(k) = y[tex]x^{2}[/tex] = 1(-2)(-2) =4

Variation constant(k) = y*x = 8*10 =80

(d) Inverse variation: y = K/x where x = 3 and y = 3

Variation constant(k) = y*x = 3*3 =9

(e) Direct square variation: y = K[tex]x^{2}[/tex] where x = 5 and y = 15

Variation constant(k) = y/[tex]x^{2}[/tex] = 15/25 =0.6

(f) Direct variation: y = Kx where x = -7.5 and y = 6.3

Variation constant(k) = y/x = -6.3/7.5 = -0.84

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When you send out a resume, the probability of being called for an interview is 0. 40. what is the probability that the first interview occurs on the fifth resume that you send out?

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The probability that the first interview occurs on the fifth resume that you sent is 0.2592.

According to the given question.

The probability of being called for an interview, p = 0.40.

So, the probability of not being called for an interview, q = 1 - 0.40 = 0.60

As we know that binomial distribution summarizes the number of trials, or observations when each trial has the same probability of attaining one particular value. The binomial distribution determines the probability of observing a specified number of successful outcomes in a specified number of trials.

Therefore, the probability that the first interview occurs on the fifth resume that you send out

= [tex]^{5} C_{1} (0.40)^{1} (0.60)^{4}[/tex]

= 5(0.40)(0.1296)

= 0.2592

Hence, the probability that the first interview occurs on the fifth resume that you sent is 0.2592.

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3. Bob has 8 pieces of square index cards that each measures 8 inches per side. Using a pair of scissors, he cuts each piece in half (so the resulting size is 8” x 4”) and then places all the resulting card pieces in a new stack. If he repeats this procedure 4 more times, how many pieces of card stock will he have and what will be the measure of each piece? (Note: All cuts will be made along the longer edge of the piece if the piece of index card is not square.)

Answers

The number of pieces of card stock which would result upon the process repetition is; 256 pieces.

What is the number of card stock pieces resulting from the cutting process?

According to the task content, it follows that since, there are 8 pieces of the 8 inches per side cards initially, the resulting number of cards after carrying out the process of cutting cards into half five, 5 times is;

No of cards = 8 (2)⁵

No. of cards = 256 pieces.

The size of each of the cards in discuss provided that all cuts will be made along and not across the longer edge is; 8 by 1/4 inches.