PROBLEM 1: Looking at different combinations of letters we can decide certain facts. Decide how many different "words" can be formed using all the letters from the word PARSLEY they do not have to mean anything) and how many'words" can be formed using all the letters from the word PEPPER (they do not have to mean anything) NOTE: the 2 answers are different because Parsley does not have repeating letters and pepper does. Give the number of words you can form from each and how you got that number HINT: If you have trouble getting started, do the excersize for the words WOW and WET to help see the pattern.

To evaluate the function f(x) = 5x² + 7 at a given value, substitute that value into the function and simplify. The resulting answer is the function's value at that point. For the difference quotient f(x) - f(7)/(x - 7), the value is undefined if x = 7.

To evaluate the function f(x) = 5x² + 7 at a given value of the independent variable and simplify the results, we simply plug in the value of the independent variable into the function. For example, if we want to evaluate f at x = 3, we would calculate f(3) = 5(3)² + 7 = 5(9) + 7 = 45 + 7 = 52. Thus, the evaluated function at x = 3 is 52.

If we were to find the difference quotient f(x) - f(7)/(x - 7), we would need to plug in a value for x that is not 7, as the expression is undefined for x = 7. For any other value of x, we substitute x into the function, subtract f(7), and divide by (x - 7). If x = 7, the result is UNDEFINED.

Answer:

The limit of the function at x approaches to [tex]\frac{\pi}{2}[/tex] is [tex]-\infty[/tex].

Step-by-step explanation:

Consider the information:

[tex]\lim_{x \to \frac{\pi}{2}}\frac{cos(x)}{1-sin(x)}[/tex]

If we try to find the value at [tex]\frac{\pi}{2}[/tex] we will obtained a [tex]\frac{0}{0}[/tex] form. this means that L'Hôpital's rule applies.

To apply the rule, take the derivative of the numerator:

[tex]\frac{d}{dx}cos(x)=-sin(x)[/tex]

Now, take the derivative of the denominator:

[tex]\frac{d}{dx}1-sin(x)=-cos(x)[/tex]

Therefore,

[tex]\lim_{x \to \frac{\pi}{2}}\frac{-sin(x)}{-cos(x)}[/tex]

[tex]\lim_{x \to \frac{\pi}{2}}\frac{sin(x)}{cos(x)}[/tex]

[tex]\lim_{x \to \frac{\pi}{2}}tan(x)}[/tex]

Since, tangent function approaches -∞ as x approaches to [tex]\frac{\pi}{2}[/tex]

, therefore, the original expression does the same thing.

Hence, the limit of the function at x approaches to [tex]\frac{\pi}{2}[/tex] is [tex]-\infty[/tex].

The function cos(x)/(1-sin(x)) approaches an indeterminate form as x approaches π/2 from the right. By applying L'Hopital's Rule, we find that the limit is equivalent to the limit of tan(x) as x approaches π/2 from the right. However, tan(π/2) is undefined, so the limit does not exist.

In this question, we are asked to find the limit of the function cos(x)/(1-sin(x)) as x approaches π/2 from the right. We can't directly substitute x = π/2 because it makes the denominator zero, yielding an indeterminate form of '0/0'.

So, we use L'Hopital's Rule, which states that the limit of a ratio of two functions as x approaches a particular value is equal to the limit of their derivatives.

The derivative of cos(x) is -sin(x) and the derivative of (1-sin(x)) is -cos(x). Using L'Hopital's Rule, we can now re-evaluate our limit substituting these derivatives.
lim [x → (π/2)+] (-sin(x)/-cos(x)) = lim [x → (π/2)+] tan(x)

When substituting x = π/2 into tan(x), we realize that the tan(π/2) is undefined, so the answer is the limit does not exist.

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Answer:

  2.50 per slice would be okay because most people would order 2 slices and that would have them give you an even 5.00. Net profit for this would be 464.00

Step-by-step explanation:

The specials advertised on Domino's website is 5.99 for each pizza, 8 slices.

The break even price is 1.34 per slice. This is important to know because a business never wants to take a loss.

To break even, the club would need to charge $2 per slice. However, for fundraising, they might charge $3 per slice, giving a net profit of $400. Breakeven analysis is crucial in business as it helps in decision making and financial planning.

Based on the information given, we see that the business club wants to purchase 50 pizzas from Domino's and resell them on campus. Assuming each pizza costs $16 (as per the example given for Authentic Chinese Pizza), the initial cost for the club would be $800 (50 pizzas x $16).

To calculate the break-even price per slice, we would need to divide the total cost by the total number of slices: $800 / (8 slices x 50 pizzas) = $2 per slice. However, since this is a fundraiser, the club might want to add in a margin to generate profit, so they might charge for example $3 per slice, resulting in a profit of $1 per slice, or $400 total.

The breakeven analysis is crucial in the development of new products because it helps businesses determine the minimum production and sales levels they must achieve to avoid losing money. This is useful for decision making and financial planning in any business operation.

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Answer:

The correct answer option is C. [tex]\frac{y_4-y_3}{x_4-x_3} \times \frac{y_2-y_1}{x_2-x_1} = -1[/tex].

Step-by-step explanation:

We are given that two line segments AB and CD are formed from the points A ([tex](x_1, y_1)[/tex], B ([tex](x_2, y_2)[/tex], C ([tex](x_3, y_3)[/tex] and D ([tex](x_4, y_4)[/tex].

We are to determine which condition needs to be met in order to prove that AB is perpendicular to CD.

When slopes of two perpendicular lines are multiplied, they give a product of -1.

Hence option C. [tex]\frac{y_4-y_3}{x_4-x_3} \times \frac{y_2-y_1}{x_2-x_1} = -1[/tex] is the correct answer.

a. Parameterize [tex]\Gamma[/tex] by

[tex]\vec r(t)=(t,2t,t)[/tex]

with [tex]0\le t\le1[/tex]. The work done by [tex]\vec F[/tex] along [tex]\Gamma[/tex] is

[tex]\displaystyle\int_\Gamma\vec F\cdot\mathrm d\vec r=\int_0^1(1,-t,t)\cdot(1,2,1)\,\mathrm dt=\int_0^1(1-t)\,\mathrm dt=\boxed{\frac12}[/tex]

b. Break up [tex]\Gamma[/tex] into each component line segment, denoting them by [tex]\Gamma_1[/tex] and [tex]\Gamma_2[/tex], and parameterize each respectively by

both with [tex]0\le t\le1[/tex]. Then the work done by [tex]\vec F[/tex] along each component path is

[tex]\displaystyle\int_{\Gamma_1}\vec F\cdot\mathrm d\vec r_1=\int_0^1(1,t-1,t)\cdot(-1,1,1)\,\mathrm dt=\int_0^1(2t-2)\,\mathrm dt=-1[/tex]

[tex]\displaystyle\int_{\Gamma_2}\vec F\cdot\mathrm d\vec r_2=\int_0^1(1,-2t,1+t)\cdot(2,1,1)\,\mathrm dt=\int_0^1(3-t)\,\mathrm dt=\frac52[/tex]

giving a total work done of [tex]-1+\dfrac52=\boxed{\dfrac32}[/tex].

c. Parameterize [tex]\Gamma[/tex] by

[tex]\vec r(t)=(\cos t,\sin t,1)[/tex]

with [tex]0\le t\le2\pi[/tex]. Then the work done by [tex]\vec F[/tex] is

[tex]\displaystyle\int_\Gamma\vec F\cdot\mathrm d\vec r=\int_0^{2\pi}(1,-\cos t,1)\cdot(-\sin t,\cos t,0)\,\mathrm dr=-\int_0^{2\pi}(\sin t+\cos^2t)\,\mathrm dt=\boxed{-\pi}[/tex]

Answer: 0.0668

Step-by-step explanation:

Given: Mean : [tex]\mu=\text{4 min. 3 sec.=4.05 minutes}[/tex]

Standard deviation : [tex]\sigma = \text{2 seconds=0.033333 minutes }[/tex]

The formula to calculate z-score is given by :_

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 4 minutes  , we have

[tex]z=\dfrac{4-4.05}{0.03333}\approx-1.5[/tex]

The P-value = [tex]P(z\leq-1.5)=0.0668072\approx0.0668[/tex]

Hence, the probability that on a given run, the time will be 4 minutes or less = 0.0668

The probability that on a given run, the time will be 4 minutes or less is approximately 6.68%.

To find the probability that on a given run, the time will be 4 minutes or less, we need to calculate the z-score for 4 minutes and then use the standard normal distribution table to find the probability. The z-score can be calculated using the formula (x - mean) / standard deviation. In this case, the z-score is (4 - 4.05) / 0.0333333⋯ = -1.50. Looking up the z-score in the standard normal distribution table, we find that the probability is approximately 0.0668 or 6.68%.

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Answer:

Graph A

Basically a graph of a function will have no turns if linear, 1 turn if quadratic, 2 turns if cubic, and 3 terms if quartic.

Graph A has a small turn on its right side.

Step-by-step explanation:

I love the way this other guy explained it, basically you count the turns that it says. i.e quartic = 4, so 4 turns, so A in this case

This was so confusing and I've been learning it for over a week and never understood it but literally took me 2 seconds to read his answer and understand it perfectly

Answer:

For any value of x

Step-by-step explanation:

Solve by using system of equations!

3x+12

3(x+4)=3x+12

3x+12=3x+12

x=x

This means that any value of x would create the same answer for both equations.

Answer:

Always.

Step-by-step explanation:

Always.  This is true by distributive property.

Try this suggested solution, note, 'D' means the region bounded by the triangle according to the condition. It consists of 6 steps.

Answers are underlined with red colour.

Answer:

[tex]\sqrt{6}[/tex]

Step-by-step explanation:

Let's define irrational by stating what rational means first, and the use the process of elimination.

A rational number is one that can be expressed as a ratio.  When dividing the numerator of this ratio by the denominator, we will either get a whole number, a decimal that repeats a pattern, or we will get a decimal that terminates.

.14 terminates, so it is rational

1/3 divides to .333333333333333333333333333333333333333 indefinitely, so it is rational

square root of 4 is 2, a whole number, so it is rational

the square root of 6, to 9 decimal places, is 2.449489743... and it goes on without ending and without repeating.  So this is the only irrational number of the bunch.

Answer:

D

Step-by-step explanation:

Answer:

The payment per period is $714.82.

Step-by-step explanation:

Given information: PV=$24,122; n = 70; i = 0.024

The formula for payment per period is

[tex]PMT=\frac{PV\times i}{1-(1+i)^{-n}}[/tex]

Substitute PV=$24,122; n = 70; i = 0.024 in the above formula.

[tex]PMT=\frac{24122\times 0.024}{1-(1+0.024)^{-70}}[/tex]

[tex]PMT=\frac{578.928}{0.80989084337}[/tex]

[tex]PMT=714.822256282[/tex]

[tex]PMT\approx 714.82[/tex]

Therefore the payment per period is $714.82.

Answer:

a.   Single-sample Z-Test

b.   Single-sample t-test

c.   Independent-measures t-test

d.   Repeated-measures t-test (Paired-samples t-test)

e.   Independent-measures ANOVA

Answer: 0.0668

Step-by-step explanation:

Given: Mean : [tex]\mu = 5\text{ minutes}[/tex]

Standard deviation : [tex]\sigma = 2\text{ minutes}[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{X-\mu}{\sigma}[/tex]

To check the probability it takes at least 8 minutes (X≥ 8) to find a parking space.

Put X= 8 minutes

[tex]z=\dfrac{8-5}{2}=1.5[/tex]

The P Value =[tex]P(z\geq1.5)=1-P(z\leq1.5)=1- 0.9331927=0.0668073\approx0.0668[/tex]

Hence, the probability that it takes at least 8 minutes to find a parking space = 0.0668

The probability that it takes atleast 8 minutes to find a parking space is 0.0668

Given the Parameters :

First we find the Zscore :

Zscore = (8 - 5) / 2 = 1.5

The probability of taking atleast 8 minutes can be expressed thus and calculated using the normal distribution table :

P(Z ≥ 1.5) = 1 - P(Z ≤ 1.5)

P(Z ≥ 1.5) = 1 - 0.9332

P(Z ≥ 1.5) = 0.0668

Therefore, the probability, P(Z ≥ 1.5) is 0.0668

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Step-by-step explanation:

The square root of 17 is 4.12. Minus one equals 3.12

The square root of 5 is 2.23.

pi+7 equals 10.142. Divided by five equals around 2.

so you end up with, 3.12, 2.23, and 2.1

Answer:

6π - 9√3 unit^2

Step-by-step explanation:

Area of sector

= 1/6(π (6)^2

= 6π

Area of triangle = √3/4 (6)^2 = 9√3

Area of the shaded segment = Area of sector - Area of triangle

= 6π - 9√3 unit^2

to the risk of sounding redundant.

[tex]\bf \textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left(\cfrac{\pi \theta }{180}-sin(\theta ) \right)~~ \begin{cases} r=&radius\\ \theta =&angle~in\\ &degrees\\ \cline{1-2} r=&6\\ \theta =&60 \end{cases}\implies A=\cfrac{6^2}{2}\left(\cfrac{\pi 60}{180}-sin(60^o ) \right) \\\\\\ A=18\left( \cfrac{\pi }{3}-\cfrac{\sqrt{3}}{2} \right)\implies \boxed{A=6\pi -9\sqrt{3}}\implies \implies A\approx 3.26[/tex]

Answer: $ 18681.45

Step-by-step explanation:

Given: Future value : [tex]FV=\$25,000[/tex]

The rate of interest : [tex]r=0.06[/tex]

The number of time period : [tex]t=5[/tex]

The formula to calculate the future value is given by :-

[tex]\text{Future value}=P(1+i)^n[/tex], where P is the initial amount deposited.

[tex]\Rightarrow\ 25000=P(1+0.06)^5\\\\\Rightarrow\ P=\dfrac{25000}{(1.06)^5}\\\\\Rightarrow\ P=18681.4543217\approx=18681.45[/tex]

Hence, the lump that must be deposit today : $ 18681.45

Answer:

The solution is:

[tex](\frac{137}{13}, -\frac{152}{13})[/tex]

Step-by-step explanation:

We have the following equations

[tex]3x - 2y =55[/tex]

[tex]-2x - 3y = 14[/tex]

To solve the system multiply by [tex]\frac{3}{2}[/tex] the second equation and add it to the first equation

[tex]-2*\frac{3}{2}x - 3\frac{3}{2}y = 14\frac{3}{2}[/tex]

[tex]-3x - \frac{9}{2}y = 21[/tex]

[tex]3x - 2y =55[/tex]

---------------------------------------

[tex]-\frac{13}{2}y=76[/tex]

[tex]y=-76*\frac{2}{13}[/tex]

[tex]y=-\frac{152}{13}[/tex]

Now substitute the value of y in any of the two equations and solve for x

[tex]-2x - 3(-\frac{152}{13}) = 14[/tex]

[tex]-2x +\frac{456}{13} = 14[/tex]

[tex]-2x= 14-\frac{456}{13}[/tex]

[tex]-2x=-\frac{274}{13}[/tex]

[tex]x=\frac{137}{13}[/tex]

The solution is:

[tex](\frac{137}{13}, -\frac{152}{13})[/tex]

Answer:

x = 411/39 and y = -152/13

Step-by-step explanation:

It is given that,

3x - 2y = 55    ----(1)

-2x - 3y = 14  ---(2)

To find the solution of given equations

eq(1)  * 2  ⇒

6x - 4y = 110  ---(3)

eq(2) * 3  ⇒

-6x - 9y = 42  ---(4)

eq(3) + eq(4)  ⇒

6x - 4y = 110  ---(3)

-6x - 9y = 42 ---(4)

  0 - 13y = 152

y = -152/13

Substitute the value of y in eq (1)

3x - 2y = 55    ----(1)

3x - 2*(-152/13) = 55

3x + 304/13 = 55

3x = 411/13

x = 411/39

Therefore x = 411/39 and y = -152/13

You just put the expression in a calculator! We have

[tex]\dfrac{7}{2^6} = \dfrac{7}{64}=0.109375[/tex]

The total tax comes to $5,173.50, with a monthly withholding of approximately $431.13.

To calculate Mr. Profit's federal income tax based on a taxable income of $35,000 in 2007, we need to find the correct tax bracket and perform a series of calculations:

Therefore, Mr. Profit's federal income tax for 2007 would be $5,173.50, and his monthly withholding would be approximately $431.13.

Mr. Profit's earned income level is $35,000. The base tax is $4,386, with an additional tax of $787.50 for amounts over $31,850. Monthly withholding comes to approximately $431.13.

To calculate Mr. Profit's tax liability based on his taxable income, we need to identify which tax bracket his income falls into and then compute the tax accordingly.

Given that Mr. Profit has a taxable income of $35,000, he falls into the 25% tax bracket, where the taxable income is over $31,850 but not over $77,100.

The tax table for this bracket is:

Base tax for incomes from $7,825 to $31,850: $788

The marginal tax rate for income over $31,850: 25%

Let's compute the tax following the provided steps.

Earned Income Level

Mr. Profit's earned income level is his taxable income:

Earned Income Level = $35,000

Base Amount

The base tax amount for his tax bracket:

Base Amount = $4,386

Amount Over

The amount over the lower bound of his tax bracket:

Amount Over = $35,000 - $31,850 = $3,150

Multiply by Percentage

Multiply the amount over by the tax rate for his bracket (25%):

Multiply Line 3 by 25% = $3,150 \times 0.25 = $787.50

Add Base and Multiplication Result

Add the base amount and the calculated tax from step 4:

Add Lines 2 and 4 = $4,386 + $787.50 = $5,173.50

Compute Monthly Withholding

Given that there are 12 months in a year, compute the monthly withholding:

Compute monthly withholding [tex]= $5,173.50 \div 12 \approx $431.13[/tex]

Thus, rounding to two decimal places, we have :

Earned Income Level: $35,000

Base Amount: $4,386

Amount Over: $3,150

Multiply Line 3 by Percentage: $787.50

Add Lines 2 and 4: $5,173.50

Compute monthly withholding: $431.13

The complete question is : 2007 Federal Income Tax Table Single: Over But not over The tax is $0 $7,825 10% of the amount over $0 $7,825 $31,850 $788 + 15% of the amount over $7,825 $31,850 $77,100 $4,386 + 25% of the amount over $31,850 $77,100 $160,850 $15,699 + 28% of the amount over $77,100 $160,850 $349,700 $39,149 + 33% of the amount over $160,850 $349,700 And Over $101,469 + 35% of the amount over $349,700 Mr. Profit had a taxable income of $35,000. He figured his tax from the table above. 1. Find his earned income level. 2. Enter the base amount. = $ 3. Find the amount over $ = $ 4. Multiply line 3 by % = $ 5. Add Lines 2 and 4 = $ 6. Compute his monthly withholding would be = $

Answer:

  sales are increasing at the rate of 6000 units per week

Step-by-step explanation:

Your demand equation appears to be ...

  4p³ +x² =38400

Then differentiation gives ...

  12p²·p' +2x·x' = 0

Solving for x', we get ...

  x' = -6p²·p'/x

Filling in the given values, we find the rate of change of sales to be ...

  x' = -6(20²)(-0.20/wk)/80 = 6/wk . . . . . in thousands of units/wk

Sales are increasing at the rate of 6000 units per week.

Answer:

Only choices B and C are correct.

Step-by-step explanation:

The square root parent function is [tex]f(x)= \sqrt{x}.[/tex]

The function [tex]f(x)[/tex] is not a linear function, therefore it's graph cannot be a straight line. This rules out choice A.

The function [tex]f(x)[/tex] is defined at [tex]x=0[/tex] because [tex]f(0)= \sqrt{0} =0[/tex]. This means that choice B is correct.

The function [tex]f(x)[/tex] is only real for values [tex]x\geq 0[/tex], because negative values of [tex]x[/tex] give complex values for [tex]f(x)[/tex]. This means that choice C is correct.

The function [tex]f(x)[/tex] can take only positive values which means it is confined to only the I quadrant, and is not defined in quadrants II, III, and IV. This rules out Choice D.

Therefore only choices B and C are correct.

Answer:

B & C

Step-by-step explanation:

B and C are the answers

Answer:

Probability that a randomly selected broiler weighs more than 1454 g is 0.3372 or 34% (approx.)

Step-by-step explanation:

Given:

Weights of Broilers are normally distributed.

Mean = 1387 g

Standard Deviation = 161 g

To find: Probability that a randomly selected broiler weighs more than 1454 g.

we have ,

[tex]Mean,\,\mu=1387[/tex]

[tex]Standard\,deviation,\,\sigma=161[/tex]

X = 1454

We use z-score to find this probability.

we know that

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

[tex]z=\frac{1454-1387}{161}=0.416=0.42[/tex]

P( z = 0.42 ) = 0.6628   (from z-score table)

Thus, P( X ≥ 1454 ) = P( z ≥ 0.42 ) = 1 - 0.6628 =  0.3372

Therefore, Probability that a randomly selected broiler weighs more than 1454 g is 0.3372 or 34% (approx.)

Answer: (a)  [tex]\dfrac{1}{7}[/tex]    (b)  [tex]\dfrac{12}{35}[/tex]

Step-by-step explanation:

Given: Number of white balls : 6

Number of red balls = 9

Total balls = 15

(a)  The probability that both balls are white is given by :-

[tex]\dfrac{^6C_2}{^{15}{C_2}}\\\\=\dfrac{\dfrac{6!}{2!(6-2)!}}{\dfrac{15!}{2!(15-2)!}}=\dfrac{1}{7}[/tex]

∴ The probability that both balls are white is  [tex]\dfrac{1}{7}[/tex] .

(b)  The probability that both balls are red is given by :-

[tex]\dfrac{^9C_2}{^{15}C_2}\\\\=\dfrac{\dfrac{9!}{2!(9-2)!}}{\dfrac{15!}{2!(15-2)!}}=\dfrac{12}{35}[/tex]

∴ The probability that both balls are red is [tex]\dfrac{12}{35}[/tex] .

Let's first consider converting to polar coordinates.

[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\begin{cases}x^2+y^2=1\iff r=1\\x^2+(y-1)^2=1\iff r=2\sin\theta\end{cases}[/tex]

We have

[tex]1=2\sin\theta\implies\sin\theta=\dfrac12\implies\theta=\dfrac\pi6\text{ or }\theta=\dfrac{5\pi}6[/tex]

Then [tex]\mathrm dA=r\,\mathrm dr\,\mathrm d\theta[/tex] and the integral is

[tex]\displaystyle\iint_Ry\,\mathrm dA=\int_{\pi/6}^{5\pi/6}\int_{2\sin\theta}^1r^2\sin\theta\,\mathrm dr\,\mathrm d\theta=\boxed{-\frac{\sqrt3}4-\frac{2\pi}3}[/tex]

Answer:

The minimum amount in sales this month to meet her goal is [tex]\$5,714.29[/tex]

Step-by-step explanation:

Let

x----> amount in sales this month

we know that

[tex]7\%=7/100=0.07[/tex]

The inequality that represent this situation is equal to

[tex]2,500+0.07x\geq2,900[/tex]

Solve for x

Subtract 2,500 both sides

[tex]0.07x\geq2,900-2,500[/tex]

[tex]0.07x\geq400[/tex]

Divide by 0.07 both sides

[tex]x\geq400/0.07[/tex]

[tex]x\geq \$5,714.29[/tex]

therefore

The minimum amount in sales this month to meet her goal is [tex]\$5,714.29[/tex]

[tex]\displaystyle\int\frac{4x^2-6}{(x+5)(x-2)(3x-1)}\,\mathrm dx[/tex]

You have a rational expression whose numerator's degree is smaller than the denominator's. This tells you you should consider a partial fraction decomposition. We want to rewrite the integrand in the form

[tex]\dfrac{4x^2-6}{(x+5)(x-2)(3x-1)}=\dfrac a{x+5}+\dfrac b{x-2}+\dfrac c{3x-1}[/tex]

[tex]\implies4x^2-6=a(x-2)(3x-1)+b(x+5)(3x-1)+c(x+5)(x-2)[/tex]

You can use the "cover-up" method here to easily solve for [tex]a,b,c[/tex]. It involves fixing a value of [tex]x[/tex] to make 2 of the 3 terms on the right side disappear and leaving a simple algebraic equation to solve for the remaining one.

So the integral we want to compute is the same as

[tex]\displaystyle\frac{47}{56}\int\frac{\mathrm dx}{x+5}+\frac{10}{35}\int\frac{\mathrm dx}{x-2}+\frac58\int\frac{\mathrm dx}{3x-1}[/tex]

and each integral here is trivial. We end up with

[tex]\displaystyle\int\frac{4x^2-6}{(x+5)(x-2)(3x-1)}\,\mathrm dx=\frac{47}{56}\ln|x+5|+\frac27\ln|x-2|+\frac5{24}\ln|3x-1|+C[/tex]

which can be condensed as

[tex]\ln\left|(x+5)^{47/56}(x-2)^{2/7}(3x-1)^{5/24}\right|+C[/tex]

Answer:

(x+5)^2+(y+7)^2=74

Step-by-step explanation:

So we are given this (x+5)^2+(y+7)^2=r^2

We need to find r so just plug in your point (0,0) for (x,y) and solve for r :)

(0+5)^2+(0+7)^2=r^2

25+49=r^2

74=r^2

So the answer is (x+5)^2+(y+7)^2=74

Answer:

(x+5)^2+(y+7)^2=74

Step-by-step explanation:

Answer with explanation:

It is given that,  for all real numbers x, if 2 x+1 is rational .

      When you will look at the expression ,2 x +1

⇒1 is rational

⇒2 x will be rational, because the expression , 2 x+1, is rational.

⇒2 x is rational, it means , x will be rational,because 2 is rational.

Some important rules considering rational and irrational

1.⇒Product of rational and rational is Rational.

2.⇒Product of Irrational and Rational is Irrational.

3.⇒Product of Irrational and Irrational may be irrational or rational.

≡2 x →is rational, 2 is rational number ,so x will be rational also.

If 2x+1 is rational, hence 2x is rational subtracting 1 which is also rational. Assuming 2x is expressible as a/b, then x is a/2b, again showing x is rational.

To prove that if 2x+1 is rational, then x must also be rational, we must understand the definition of rational numbers and basic properties of arithmetic operations involving rational numbers. A number is considered rational if it can be written as the quotient of two integers (where the denominator is not zero). Given that the sum of two rational numbers is also rational, if 2x+1 is rational, and we know that 1 is rational (since 1 can be written as 1/1), then 2x must be rational because rational minus rational yields a rational result.

Now, assuming 2x is rational, we can express it as a fraction [tex]\frac{a}{b}[/tex], with a and b being integers and b non-zero. Since the multiplication of a rational number by an integer is also rational, and knowing that 2 is an integer, we can then say that x, which is  [tex]\frac{a}{2b}[/tex], is also rational. This is because we can express the result of  [tex]\frac{a}{2b}[/tex] with integers in the numerator and the denominator.

Answer: [tex]P = \$\ 52[/tex]

Step-by-step explanation:

We have the equation [tex]P = 31 + 1.75w[/tex] where P represents the payment and w represents the amount of water used.

To calculate the monthly payment that corresponds to 12 units of water you must do [tex]w = 12[/tex] in the main equation and solve for the variable P.

[tex]P = 31 + 1.75w[/tex]

[tex]P = 31 + 1.75(12)[/tex]

[tex]P = 31 + 21[/tex]

[tex]P = 52[/tex]

Tuyet's payment for a month when 12 units of water are used is $52.

To find Tuyet's payment for a month when 12 units of water are used, we can substitute 12 for 'w' in the equation P = 31 + 1.75w and solve for P.

P = 31 + 1.75(12)

P = 31 + 21

P = 52

Therefore, Tuyet's payment for a month when 12 units of water are used is $52.

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Answer: 0.9032

Step-by-step explanation:

Given: Mean : [tex]\mu = 20,000\text{ hours}[/tex]

Standard deviation : [tex]\sigma = 1800 \text{ hours}[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 17659

[tex]z=\dfrac{17659-20000}{1800}=−1.30055555556\approx-1.3[/tex]

The P Value =[tex]P(z>-1.5)=1-P(z<1.3)=1- 0.0968005\approx0.9031995\approx 0.9032[/tex]

Hence, the probability that the life span of the monitor will be more than 17,659 hours = 0.9032

To find the probability that the life span of the monitor will be more than 17,659 hours, use the z-score formula and the standard normal distribution table. The probability is approximately 0.0968.

To find the probability that the life span of the monitor will be more than 17,659 hours, we need to calculate the z-score and use the standard normal distribution table. The z-score is calculated as:

z = (x - μ) / σ

Where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation. In this case, x = 17,659, μ = 20,000, and σ = 1800. Plugging these values into the formula, we get:

z = (17659 - 20000) / 1800 = -1.3

Now, we can look up the probability corresponding to the z-score -1.3 in the standard normal distribution table. The probability is approximately 0.0968. Therefore, the probability that the life span of the monitor will be more than 17,659 hours is approximately 0.0968.

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