people once thought that trying to square a circle was an illness. what was the name of the illness?

Answer:

6700

Step-by-step explanation:

6.7*10³ to ordinary form. You simply move the decimal point three steps back because it's positive and put zeros before the decimal point which you have moved

Answer:

YZ=15

Step-by-step explanation:

All sides of a rhombus are equal so it would be the same length.

Answer:

−16x²

Step-by-step explanation:

Simplifying!

Answer:

-14

Step-by-step explanation:

Remove the parentheses

(11-18)2

multiply

-7x2=

-14

The Theoretical yield of solid precipitate is 1.42g/mol

Now, consider solid precipitate as cacl2

let us take the mass of cacl2 and calculate the moles of cacl2.

Mass of CaCl2 =2.0 g

By, default the molar mass of CaCl2 =110.98 g/mol

To calculate the Moles we have a formula:

Moles=Given mass*1 mol/Molar mass of a precipitate.-----(1)

substitute the values in equation (1)

Moles of CaCl2 =2.0 g * 1 mol/110.98g

                           = 0.018 mol

Take another solid precipitate:

Mass of K2Co3=2.0 g

The molar mass of K2Co3 =138.205 g/mol

Now calculating the moles of K2Co3

substitute the values in equation(1)

Moles of K2Co3 =2.0 g * 1 mol/ 138.205g

                             =0.0145 moles

According to balanced equation 1mole of CaCl2 reacts with 1 mole of K2CO

Thus, 0.018 moles of CaCl2 will react with 0.018 moles of K2CO3

And,0.0145 moles of K2CO3 will produce 0.0145 moles of CaCO3

Molar mass of CaCO3 =100.0869 g/mol

Theoretical yield of CaCO3 =moles of CaCO3 *molar mass of CaCO3

                                                =0.0145 moles * 100.0869 g/mol

                                                 =1.45g/mol

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The expression that equals 3C+3D in standard form is:

x²+7x+1

Given:

C = -x+2

and D = x²+8x-1

we are asked to find out an expression which equals 3C+3D in standard form.

based on the conditions, formulate:

3C+3D

substitute C and D values.

⇒ 3(-x+2) + 3(x²+8x-1)

Apply multiplicative distribution law:

⇒ open the parenthesis.

⇒ -3x+6+3x²+24x-3

calculate the product or quotient

⇒ arrange the like terms.

⇒ 3x²+21x+3

⇒ Reduce the terms.

⇒ x²+7x+1

Hence we get the equation in standard form.

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Answer:

3 km

Step-by-step explanation:

(NOTE: One kilometer is 1000 meters)

Divide 3000 by 1000 to get 3

The values of u, v, u, v, and d(u, v) are given below:(a) u, v = 171(b) ||u|| = 13(c) ||v|| = 17(d) u/||u|| = (-12/13, 5/13), v/||v|| = (-8/17, 15/17)(e) d(u, v) = 2√29

Given inner product defined on Rn, u = (−12, 5), v = (−8, 15) and u, v = u · v. The values of u, v, u, v, and d(u, v) are to be calculated.

Solution: Given inner product defined on Rn, u = (−12, 5), v = (−8, 15) and u, v = u · v.

The dot product of u and v is given by u . v= (-12 * -8) + (5 * 15)u . v= 96 + 75u . v= 171

Now, we have to calculate the norm of u and v, which can be calculated as follows: ||u|| = √u1² + u2²||u|| = √(-12)² + 5²||u|| = √144 + 25||u|| = √169||u|| = 13

Similarly,||v|| = √v1² + v2²||v|| = √(-8)² + 15²||v|| = √64 + 225||v|| = √289||v|| = 17

Now, we have to calculate the unit vector of u and v. T

he unit vector of u and v is given by: u/||u|| = (-12/13, 5/13)v/||v|| = (-8/17, 15/17)Now, we have to calculate d(u, v). The formula to calculate d(u, v) is given by: d(u, v) = ||u - v||d(u, v) = √(u1 - v1)² + (u2 - v2)²d(u, v) = √(-12 - (-8))² + (5 - 15)²d(u, v) = √(-4)² + (-10)²d(u, v) = √16 + 100d(u, v) = √116d(u, v) = 2√29

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I hope this help too.

Answer:-

The linear sequence 27, 25, 23, 21, 19... is an arithmetic progression with (-2) as the common difference.

The nth term of an arithmetic progression is an=a1+(n−1)da_n=a_1+(n-1)dan​=a1​+(n−1)d, where ana_nan​ is the nth term, a1a_1a1​ is the first term, d is the common difference.

In our case, n=50,a1=27,d=−2n=50, a_1=27, d=-2n=50,a1​=27,d=−2 , hence, we get

a50=27+49⋅(−2);a50=27−98=−71.a_{50}=27+49\cdot(-2);\\ a_{50}= 27-98=-71. a50​=27+49⋅(−2);a50​=27−98=−71.

The 50th term of this sequence is (-71).

Answer:

The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.

Answer:

I'm not really sure what you're asking because there's no image.

Step-by-step explanation:

please try to reword it and maybe show a picture .

The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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Answer:

48 days

Step-by-step explanation:

Let us assume the following things

Work done by 1 man in 1 day is \(\frac{1}{x}\)

Work done by 1 woman in 1 day is \(\frac{1}{y}\)

It is mentioned that

six men + ten women finished in 8 days

So,

\(\frac{6}{x} + \frac{10}{y} = \frac{1}{8}\) .............. (1)

And,

four men + six women finished in 12 days

\(\frac{4}{x} + \frac{6}{y} = \frac{1}{12}\) ...............(2)

Now solve these two equations

And we assume \(\frac{1}{x}\) be u and \(\frac{1}{y}\) be v

So

Now the equation is

\(6u\ + 10v\ = \frac{1}{8} \\\\\4u\ + 6v\ = \frac{1}{12}\)

So,

u = 1 ÷ 48 , v = 0

Therefore x = 48

So the time taken for finish the work is 48 days

Answer:

3 pairs of shoes cost 189

Step-by-step explanation:

Oh yes it's quite simple but sort of difficult to explain, I'll try the best I can though!

in "C(x)" what ever is in the ( ) is the x value, so where they give you "C(3)" that means x=3. And since in this x represents number of shoes, that means the cost of three shoes is $189.

Hope this helps! If you have any questions about my answer feel free to ask. Stay safe!

Answer:

Step-by-step explanation:

B

Answer:

the second choice

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Take the 54. The cake reduces her size by 1/3 so you multiply 54*1/3 to get 18 inches or 1.5 feet tall. :)

Answer:

X =30

Step-by-step explanation:

= 60+90

=150

angle sum property

x+150=180

x=180- 150

x= 30

Answer:

Step-by-step explanation:

90 + 60 = 150

(right angles = 90)

There is 180 degrees in a triangle, therefore,

180 - 150 = 30

Therefore, x = 30

p.s. Are you good at history?

p.p.s I dont like summer school either =)

Answer:

\(5:3\)

Step-by-step explanation:

To find the simplest ratio, you need to divide by the greatest common factor. In this case, the GCF is 2. So we need to divide both sides by 2. Doing so will get us 5 and 3

In the first scenario, the mean lifetime of a sample of 200 mobile phones is 1,000 hours with a standard deviation of 130 hours. In the second scenario, a random sample of 20 observations is considered, and the sample variance is found to be 30.5.

In the first scenario, the mean lifetime of a sample of 200 mobile phones is 1,000 hours with a standard deviation of 130 hours. The objective is to test the hypothesis that the sample comes from a population with a mean of 1,200 hours at a 1% significance level. The hypothesis can be tested using a t-test or a z-test, depending on the sample size and the population standard deviation. By calculating the test statistic and comparing it to the critical value at a 1% significance level, the hypothesis can be accepted or rejected.

In the second scenario, a random sample of 20 observations is considered, and the sample variance is found to be 30.5. A 95% confidence interval can be constructed to estimate the population mean. This interval is calculated using the sample mean, the sample variance, and the appropriate critical value from the t-distribution or z-distribution. The confidence interval provides a range within which the true population mean is likely to fall with a 95% confidence level.

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Answer:

i would say 3/8 if thats an option

Step-by-step explanation:

Probability helps us to know the chances of an event occurring. The probability that the two pieces of fruit are oranges is 3/28.

Probability helps us to know the chances of an event occurring.

\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

Given that the two pieces of fruit are randomly picked out of a covered basket with 5 apples and 3 oranges. Therefore, the probability that the two pieces of fruit are oranges is,

Probability = (3/8) × (2/7) = 6/56 = 3/28

Hence, the probability that the two pieces of fruit are oranges is 3/28.

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Answer:

Step-by-step explanation:

10.8

Answer:

Janet's dog weighs 10.8 pounds more

Step-by-step explanation:

The equation that relates the time, t, it takes to travel a given distance, d is d = rt

This is a scalar quantity and can be defined as  the magnitude of the rate of change of its position with time.

d = rt

where d is distance, r is speed or rate, t is time.

We can calculate the time by dividing the distance with the rate (speed).

t =  d/r

This is why it was chosen as the most appropriate choice.

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Answer:

Yearly fee of $48 is better

Step-by-step explanation:

It is obvious. We know that a year have 12 months so if we compare between the $30 per months deal (which is $360 a year when we multiple it with 12) and the $48 a year deal, the difference is $312 which is a lott.

If Maria only want to use it for a month then its fine but if she want to use it more than 1 month, she definitely should choose the no 2 deal because if she even only rent it for 2 months using the no 1 deal ($30+$30=$60), the no 2 deal ($48) is far more better with a $12 difference.

Part A: Just like the top we know that its costs $34 per month and we need to know how much it would costs for 12 months/a year. So we just have to multiple it with 12=$408. Now which is better $495 or $408? Of course its $408 right? Maria could save $87 with renting the trombone than buying the trombone.

The triangles SAT and SAO are congruent by the Side-Angle-Side (SAS) congruence theorem.

The Side-Angle-Side congruence theorem states that if any of the two sides on a triangle are the same, along with the angle between them, then the two triangles are congruent.

For the triangles SAT and SAO in this problem, we have that:

The common angle are between the common sides, hence the SAS congruence theorem was used to determine the congruence of the two triangles.

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Answer: 160

Step-by-step explanation:

12+37+78

A radical equation is an equation that contains a variable within a radical expression.

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The first question is about the relationship between opinion on gun ownership and race-ethnicity. 67% of White respondents, 28% of Black respondents, and 64% of Hispanic respondents shared the view that widespread gun ownership protects law abiding citizens from crime.

The opinion on gun ownership is dependent on race-ethnicity. Roughly 20% of undergraduates at a university are vegetarian or vegan. We need to find the probability that, among a random sample of 3 undergraduates, at least one is vegetarian or vegan.

P(at least one is vegetarian or vegan) = 1 - P(none of them is vegetarian or vegan) P(none of them is vegetarian or vegan)

= (0.8)^3

= 0.512

P(at least one is vegetarian or vegan) = 1 - 0.512

= 0.488

The probability that, among a random sample of 3 undergraduates, at least one is vegetarian or vegan is 0.488.

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Answer:

Mila bought stock in company two years ago that was worth x dollars. During first year that she owned the stock, it decreased by 35%. During second year the value of the stock decreased by 32%, an expression in terms of a that represents the value of the stock after the two years have passed is 2x+0.67.

Step-by-step explanation:

What do you mean by percentage?

It is not always obvious from the context what a % is in relation to because of inconsistent usage. The typical meaning of a "10% rise" or "10% decline" in a quantity is that this refers to the quantity's starting value. As an illustration, the new price of a $200 item would be $220 if the price increased by 10%, or $20. The final price is equal to 100% of the starting price (100% + 10% = 110%).

Other instances of % changes include:

If a quantity is increased by 100%, the final amount will be 100% more than the original amount (100% of initial + 100% of increase = 100% of initial). The quantity has therefore doubled.

If an amount is increased by 800%, the final sum will be nine times as large as the original (100% + 800% = 900% = 9 times as large).

When something is reduced by 60%, the final sum equals 40% of the original (100% - 60% = 40%).

A reduction of 100% results in a final value of 0% (100% - 100% = 0%).

In general, if a quantity is changed by x percent, the final amount will be 100 + x percentage of the original amount, or (1 + 0.01x) times the original amount.

x-35%+x-32%

⇒

⇒

⇒2x+0.67

Barbara wrote an equation, 1.25x + 1.49, to find the number of bottles (x) she needs to sell in order to earn $100.

The equation 1.25x + 1.49 represents the total earnings Barbara would make by selling x bottles of water at $1.25 per bottle and x bottles of iced tea at $1.49 per bottle. The term 1.25x represents the earnings from selling water, and 1.49 represents the earnings from selling iced tea.

To find the number of bottles (x) Barbara needs to sell to earn $100, we set the equation equal to $100 and solve for x:

1.25x + 1.49 = 100

By rearranging the equation and isolating the variable x, we can solve for x. This equation can be solved using algebraic techniques such as combining like terms, subtracting 1.49 from both sides, and dividing by 1.25.

Once we determine the value of x, we will know the number of bottles Barbara needs to sell in order to earn $100.

Please note that without the complete equation or additional information, we cannot provide the specific solution for x or the exact number of bottles Barbara needs to sell to earn $100.

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a) Poles: 0, -2i, +2i; Zeros: +I, -i. b) Number of asymptotic branches: 2. c) Asymptotes: Re(s) = -1, Re(s) = -∞. d) Center point(s): No center point(s). e) Branch departure/arrival angles: 180°, 0°, 180°.


a) The poles of the transfer function L(s) = (s² + 1) / (s(s² + 4)) are obtained by setting the denominator equal to zero, resulting in poles at s = 0, s = -2i, and s = +2i. The zeros are obtained by setting the numerator equal to zero, resulting in zeros at s = +I and s = -i.
b) The number of asymptotic branches is determined by the difference between the number of poles and zeros, which is 2 in this case.
c) The asymptotes can be found using the formula Re(s) = (2k + 1)π / n, where k ranges from 0 to (n-1), and n is the number of asymptotes. In this case, there are two asymptotes with Re(s) = -1 and Re(s) = -∞.
d) There are no center point(s) since the transfer function has no finite zeros or poles.
e) The branch departure/arrival angles can be calculated using the formula ∠G(s) = (2k + 1)180° / n, where k ranges from 0 to (n-1), and n is the number of asymptotes. In this case, the branch departure/arrival angles are 180°, 0°, and 180°, corresponding to the two poles and one zero.

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