Determine all numbers at which are function Continuous..
f(x)={
x^2 + 5x - 36/
x^2 + 8x - 9
if x≠-9
if x= -9}
a.
continuous at every real number except x = 1 and x = -9
b. continuous at every real number except x = -9
c.continuous at every real number except x = 1
d. continuous at every real number except x = -9 and x = 4

Answer:

A =625 ft^2

Step-by-step explanation:

The perimeter of a square is

P = 4s where s is the side length

100 =4s

Divide each side by 4

100/4 = 4s/4

25 = s

A = s^2 for a square

A = 25^2

A =625

Answer:

9.40%

Step-by-step explanation:

Given:

Annual coupon rate = 11%

Time left to maturity = 11 years

Par value of bond = 1000

Present value of bond = 1153.60

Required: Find Yeild to Maturity (YTM)

To find the yield to maturity, use the formula below:

YTM = [Annual coupon+(Face value-Present value)/time to maturity]/(Face value+Present value)/2

where annual coupon = 1000 * 11% = 110

Thus,

[tex]YTM = \frac{\frac{110+(1000-1139.59}{9}}{\frac{(1000+1139.59)}{2}}[/tex]

YTM = 9.40%

Therefore the approximate YTM is 9.40%

Answer:

Step-by-step explanation:

Using the formula for calculating the energy used up during the process;

Energy used up = Amount of CO₂ created.

Energy used up in the process = Power * Time.

Given Parameters:

Power = 3,030Watts

Converting to Kilowatts, power = 3030/1000 kW

Power (in kW) = 3.03kW

Time taken = 34 minutes

Converting to hour;

Since 60 minutes = 1hr

34minutes = (34/60)hr

34minutes = (17/30)hr

Required:

Energy used up = 3.03 * 17/30

Energy used up = 51.51/30

Energy used up = 1.717 kW/hr

Hence, amount of CO₂ created in kW/hr is 1.7 kW/hr to 1 decimal place.

Answer:

A : A1 = -7, an = an-1 + 3

Step-by-step explanation:

a1=-7, a2=-7+(1)3=-4

a3=-7+(2)3=-1

Answer:

[tex] y'' =12x^2 -72=0[/tex]

And solving we got:

[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]

We can find the sings of the second derivate on the following intervals:

[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up

[tex]x=-\sqrt{6}, y =-180[/tex] inflection point

[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down

[tex]x=\sqrt{6}, y=-180[/tex] inflection point

[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up

Step-by-step explanation:

For this case we have the following function:

[tex] y= x^4 -36x^2[/tex]

We can find the first derivate and we got:

[tex] y' = 4x^3 -72x[/tex]

In order to find the concavity we can find the second derivate and we got:

[tex] y'' = 12x^2 -72[/tex]

We can set up this derivate equal to 0 and we got:

[tex] y'' =12x^2 -72=0[/tex]

And solving we got:

[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]

We can find the sings of the second derivate on the following intervals:

[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up

[tex]x=-\sqrt{6}, y =-180[/tex] inflection point

[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down

[tex]x=\sqrt{6}, y=-180[/tex] inflection point

[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up

Answer:

The last graph (to the far right).

Step-by-step explanation:

As long as each x-value has one y-value, it is a function. However, the last graph has an x-value at -1 where there are two y-values. So, it does not pass the Vertical Line Test, and it is a relation rather than a function.

Hope this helps!

Answer:

the probability that the sample mean will be larger than 1224 is  0.0082

Step-by-step explanation:

Given that:

The SAT scores have an average of 1200

with a  standard deviation of 60

also; a sample of 36 scores is selected

The objective is to determine  the probability that the sample mean will be larger than 1224

Assuming X to be the random variable that represents the SAT score of each student.

This implies that  ;

[tex]S \sim N ( 1200,60)[/tex]

the probability that the sample mean will be larger than 1224 will now be:

[tex]P(\overline X > 1224) = P(\dfrac{\overline X - \mu }{\dfrac{\sigma}{\sqrt{n}} }> \dfrac{}{}\dfrac{1224- \mu }{\dfrac{\sigma}{\sqrt{n}} })[/tex]

[tex]P(\overline X > 1224) = P(Z > \dfrac{1224- 1200 }{\dfrac{60}{\sqrt{36}} })[/tex]

[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{\dfrac{60}{6} })[/tex]

[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{10} })[/tex]

[tex]P(\overline X > 1224) = P(Z > 2.4 })[/tex]

[tex]P(\overline X > 1224) =1 - P(Z \leq 2.4 })[/tex]

From Excel Table ; Using the formula (=NORMDIST(2.4))

P(\overline X > 1224) = 1 -  0.9918

P(\overline X > 1224) = 0.0082

Hence;  the probability that the sample mean will be larger than 1224 is  0.0082

Answer:

Step-by-step explanation:

Margin of error is expressed as M.E = [tex]z * \sqrt{\frac{\sigma}{n} }[/tex] where;

z is the z score at 95% confidence

[tex]\sigma[/tex] is the standard deviation

n is the sample size

Given n = 349, [tex]\sigma = 42[/tex] and z score at 95% confidence = 1.645

Substituting this values into the formula above we will have;

M.E = [tex]1.645*\sqrt{\frac{42}{349} }[/tex]

[tex]M.E = 1.645*\sqrt{0.1203} \\\\M.E = 1.645*0.3468\\\\M.E = 0.5705 (to\ four\ dp)[/tex]

Answer:

Step-by-step explanation:

Question:

4(y - 3) = 48

1. Distribute

4y - 12 = 48

2. Simplify Like terms

4y - 12 = 48

    + 12 + 12

4y = 60

3. Solve

4y = 60

/4       /4

y = 15

4. Check:

4(y - 3) = 48

4((15) - 3) = 48

4(12) = 48

48 = 48     Correct!

Hope this helped,

Kavitha

Answer:

[tex]y=15\\[/tex]

Step 1:

To find y, we first have to multiply [tex]4(y-3)[/tex]. When we do that (4 * y, 4 * - 3), we get [tex]4y-12[/tex].

Step 2:

Our equation looks like this now:

[tex]4y-12=48[/tex]

To solve this equation, we have to add 12 on both sides so we can cancel out the -12 on the left side of the equation.

[tex]4y-12(+12)=48(+12)[/tex]

[tex]4y=60[/tex]

Now, we can divide 4 on both sides to get y  by itself.

[tex]4y/4\\60/4[/tex]

[tex]y=15[/tex]

Answer:

Step-by-step explanation:

From the information given:

mean life span of a brand of automobile = 35,000

standard deviation of a brand of automobile = 2250 miles.

the z-score that corresponds to each life span are as follows.

the standard z- score formula is:

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

For x = 34000

[tex]z = \dfrac{34000 - 35000}{2250}[/tex]

[tex]z = \dfrac{-1000}{2250}[/tex]

z = −0.4444

For x = 37000

[tex]z = \dfrac{37000 - 35000}{2250}[/tex]

[tex]z = \dfrac{2000}{2250}[/tex]

z = 0.8889

For x = 3000

[tex]z = \dfrac{30000 - 35000}{2250}[/tex]

[tex]z = \dfrac{-5000}{2250}[/tex]

z = -2.222

From the above z- score that corresponds to their life span; it is glaring  that the tire with the life span 30,000 miles has an unusually short life span.

For x = 30,500

[tex]z = \dfrac{30500 - 35000}{2250}[/tex]

[tex]z = \dfrac{-4500}{2250}[/tex]

z = -2

P(z) = P(-2)

Using excel function (=NORMDIST -2)

P(z) = 0.022750132

P(z) = 2.28th percentile

For x =  37250

[tex]z = \dfrac{37250 - 35000}{2250}[/tex]

[tex]z = \dfrac{2250}{2250}[/tex]

z = 1

Using excel function (=NORMDIST 1)

P(z) = 0.841344746

P(z) = 84.14th percentile

For x = 35000

[tex]z = \dfrac{35000- 35000}{2250}[/tex]

[tex]z = \dfrac{0}{2250}[/tex]

z = 0

Using excel function (=NORMDIST 0)

P(z) = 0.5

P(z) = 50th percentile

a.  The z score of each life span should be -0.4444, 0.889, and 2.2222.

b.  The percentile of each life span should be 0.0228, 0.8413 and  0.5000.

Given that,

(a)

The z score should be

[tex]Z1 = \frac{34000-35000}{2250} = -0.4444\\\\Z2 = \frac{37000-35000}{2250} = 0.8889\\\\Z3 = \frac{30000-35000}{2250} = -2.2222\\\\[/tex]

The tire with life span of 30000 miles would be considered unusual

(b)

The percentile should be

[tex]Z1 = \frac{30500-35000}{2250} = -2[/tex]

p(Z1 < -2) = NORMSDIST(-2) = 0.0228

[tex]Z2 = \frac{37250-35000}{2250} = 1[/tex]

p(Z2 < 1) = NORMSDIST(1) = 0.8413

[tex]Z3 = \frac{35000-35000}{2250} = 0[/tex]

p(Z3 < 0) = NORMSDIST(0) = 0.5000

Find out more information about standard deviation here:

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Answer:

120

Step-by-step explanation:

Let's say you put them on the shelf one by one, from left to right.

You can pick 1 of the 5 for the first position.

5

Now you have 4 books left. You pick one out of those 4 for the second position.

5 * 4

There are 3 choices left for the 3rd position.

5 * 4 * 3

2 left for the 4th position.

5 * 4 * 3 * 2

Finally, there is one book left for the 5th position.

5 * 4 * 3 * 2 * 1

Now we multiply:

5 * 4 * 3 * 2 * 1 = 120

Answer:

Step-by-step explanation:

Choice d. is correct

Answer:

D

Step-by-step explanation:

Answer:

sorry i am not able to understood

Step-by-step explanation:

Answer:

D. [tex]H_{0}[/tex] : μ = 1.70, [tex]H_{a}[/tex] : μ > 1.70

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

Answer:

you would change it 4 times a year

Step-by-step explanation:

if there is 12 months in a year and 3 mounths equal 6000 then divide 12/3=4

Answer:

The Taylor series is   [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

Step-by-step explanation:

From the question we are told that

      The function is  [tex]f(x) = sin (x)[/tex]

This is centered at  

       [tex]a = 2 \pi[/tex]

Now the next step is to represent the function sin (x) in it Maclaurin series form which is  

          [tex]sin (x) = \frac{x^3}{3! } + \frac{x^5}{5!} - \frac{x^7}{7 !} +***[/tex]

=>       [tex]sin (x) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

   Now since the function is centered at  [tex]a = 2 \pi[/tex]

We have that

           [tex]sin (x - 2 \pi ) = (x-2 \pi ) - \frac{(x - 2 \pi)^3 }{3 \ !} + \frac{(x - 2 \pi)^5 }{5 \ !} - \frac{(x - 2 \pi)^7 }{7 \ !} + ***[/tex]

This above equation is generated because the function is not centered at the origin but at [tex]a = 2 \pi[/tex]

           [tex]sin (x-2 \pi ) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x - 2 \pi)^{2n+1}][/tex]

Now due to the fact that [tex]sin (x- 2 \pi) = sin (x)[/tex]

This because  [tex]2 \pi[/tex] is a constant

   Then it implies that the Taylor series of the function centered at [tex]a = 2 \pi[/tex] is

             [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

Answer:

[tex]\boxed{\sf \ \ \ [-7,0] \ \ \ }[/tex]

Step-by-step explanation:

Hello

[tex]y=x^2+7x=x(x+7) >0\\<=> x>0 \ and \ x+7 >0 \ \ or \ \ x<0 \ and \ x+7<0\\<=> x>0 \ \ or \ \ x<-7\\[/tex]

So values of x which is not in this domain is

[tex]-7\leq x\leq 0[/tex]

which is [-7,0]

hope this helps

Answer:

x < 4 or x = ( -∞, 4)

Step-by-step explanation:

or

[tex]\text{Solve the inequality for x:}\\\\6x-5<2x+11\\\\\text{Subtract 2x from both sides}\\\\4x-5<11\\\\\text{Add 5 to both sides}\\\\4x<16\\\\\text{Divide both sides by 4}\\\\\boxed{x<4}[/tex]

Ans   k = 4

Step-by-step explanation:

Here g(x) =[tex]\frac{-1}{3}x + 1[/tex] and

        f(x) = [tex]\frac{-1}{3} x -3[/tex]

Now,  g(x) = f(x) + k

    or,      [tex]\frac{-1}{3}x + 1[/tex]  =  [tex]\frac{-1}{3} x -3 + k[/tex]

    or,      1 + 3 = k

    So,  k = 4   Answer.

Answer:

see graph

Step-by-step explanation:

A reflection across the y-axis means the point is equal but opposite distance from the y-axis. This has no change on the y-value of the point, because no matter the y-value, the point will still be the same distance from the y-axis. Long story short, if you're reflecting across the y-axis, change the sign of the x-coordinate. If you're reflecting across the x- axis, change the sign of the y-coordinate.

Answer:

The 95% confidence interval for the mean score, , of all students taking the test is

        [tex]28.37< L\ 30.63[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is [tex]n = 59[/tex]

    The mean score is  [tex]\= x = 29.5[/tex]

     The standard deviation [tex]\sigma = 5.2[/tex]

Generally the standard deviation of mean is mathematically represented as

                [tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

               [tex]\sigma _{\= x} = \frac{5.2 }{\sqrt{59} }[/tex]

             [tex]\sigma _{\= x} = 0.677[/tex]

The degree of freedom is mathematically represented as

          [tex]df = n - 1[/tex]

substituting values

        [tex]df = 59 -1[/tex]

        [tex]df = 58[/tex]

Given that the confidence interval is 95%  then the level of significance is mathematically represented as

         [tex]\alpha = 100 -95[/tex]

        [tex]\alpha =[/tex]5%

        [tex]\alpha = 0.05[/tex]

Now the critical value at  this significance level and degree of freedom is

       [tex]t_{df , \alpha } = t_{58, 0.05 } = 1.672[/tex]

Obtained from the critical value table  

    So the the 95% confidence interval for the mean score, , of all students taking the test is mathematically represented as

      [tex]\= x - t*(\sigma_{\= x}) < L\ \= x + t*(\sigma_{\= x})[/tex]

substituting value

      [tex](29.5 - 1.672* 0.677) < L\ (29.5 + 1.672* 0.677)[/tex]

       [tex]28.37< L\ 30.63[/tex]

Answer:

301.44

Step-by-step explanation:

V=π r² h

V=π (4)² (12)

V= 603.19

divide by 2 to find half full: ≈ 301

301.44

Answer:

a) the angle of ascent is 8.2°

b) the horizontal distance traveled is 4375 m

Step-by-step explanation:

depth of ocean = 626 m

distance traveled in the ascent = 4420 m

This is an angle of elevation problem with

opposite side to the angle = 626 m

hypotenuse side = 4420 m

a) angle of ascent ∅ is gotten from

sin ∅ = opp/hyp = 626/4420

sin ∅ = 0.142

∅ = [tex]sin^{-1}[/tex] 0.142

∅ = 8.2°  this is the angle of ascent of the submarine.

b) The horizontal distance traveled will be gotten from Pythagoras theorem

[tex]hyp^{2}[/tex] = [tex]opp^{2}[/tex] + [tex]adj^{2}[/tex]

The horizontal distance traveled will be the adjacent side of the right angle triangle formed by these distances

[tex]4420^{2}[/tex] = [tex]626^{2}[/tex] + [tex]adj^{2}[/tex]

adj = [tex]\sqrt{4420^{2}-626^{2} }[/tex]

adj = 4375 m  this is the horizontal distance traveled.

Answer:

x = 1

Step-by-step explanation:

Set up the rational expression with the same denominator over the entire equation.

Since the expression on each side of the equation has the same denominator, the numerators must be equal

5x =4x+1

Move all terms containing x to the left side of the equation.

Hope this can help you

Answer:

The standard deviation of the sample mean is  [tex]\sigma _ {\= x } = 2.711[/tex]

Step-by-step explanation:

From the question we are told that

   The mean is  [tex]\= x = 60[/tex]

    The standard deviation is  [tex]\sigma = 21[/tex]

     The sample size is [tex]n = 60[/tex]

Generally the standard deviation of the sample mean is mathematically represented as  

               [tex]\sigma _ {\= x } = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

               [tex]\sigma _ {\= x } = \frac{ 21 }{\sqrt{60} }[/tex]

               [tex]\sigma _ {\= x } = 2.711[/tex]

Answer:

[tex]\boxed{\sf \ \ \ 10^2+11^2+12^2=13^2+14^2 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

let's note a a positive integer

5 consecutive integers are

a

a+1

a+2

a+3

a+4

so we need to find a so that

[tex]a^2+(a+1)^2+(a+2)^2=(a+3)^2+(a+4)^2\\<=>\\a^2+a^2+2a+1+a^2+4a+4=a^2+6a+9+a^2+8a+16\\<=>\\3a^2+6a+5=2a^2+14a+25\\<=>\\a^2-8a-20=0\\<=>\\(a+2)(a-10)=0\\<=>\\a = -2 \ or \ a = 10\\[/tex]

as we are looking for positive integer the solution is a = 10

do not hesitate if you have any question

Answer:

[tex]\huge \boxed{{x\geq -3, \ x \neq 2}}[/tex]

Step-by-step explanation:

The function is given,

[tex]\displaystyle f(x)=\frac{\sqrt{x+3 }}{(x+8)(x-2)}[/tex]

The domain of a function are all possible values of x.

There are restrictions for the value of x.

The denominator of the function cannot equal 0, if 0 is the divisor then the fraction would be undefined.

[tex]x+8\neq 0[/tex]

Subtract 8 from both parts.

[tex]x\neq -8[/tex]

[tex]x-2\neq 0[/tex]

Add 2 on both parts.

[tex]x\neq 2[/tex]

The square root of x + 3 cannot be a negative number, because the square root of a negative number is undefined. x + 3 has to equal to 0 or be greater than 0.

[tex]x+3\geq 0[/tex]

Subtract 3 from both parts.

[tex]x\geq -3[/tex]

The domain of the function is [tex]x\geq -3[/tex], [tex]x\neq 2[/tex].

The domain of the given function will be x ≥ -3 and x ≠ 2.

The entire range of independent input variables that can exist is referred to as a function's domain or,

The set of all x-values that can be used to make the function "work" and produce actual y-values is referred to as the domain.

As per the data given in the question,

The given expression of function is,

f(x) = [tex]\sqrt{\frac{x+3}{(x-8)(x-2)} }[/tex]

The fraction would indeed be undefined if the base of the function were equal to zero, which is not allowed.

x + 8 ≠ 0

x ≠ -8

And, x - 2 ≠ 0

x ≠ 2

Since the square root of a negative number is undefined, x+3 cannot have a negative square root. x+3 must be bigger than zero or identical to zero.

So,

x + 3 ≥ 0

x ≥ -3

So, the domain of the function will be x ≥ -3 and x ≠ 2.

To know more about Domain:

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Answer:

I think it is

Step-by-step explanation:

Answer:

5n√2m^ - 3mn

Step-by-step explanation:

Answer:

Option D

Step-by-step explanation:

A type I error occurs when you reject the null hypothesis when it is actually true.

The null hypothesis in this case is minimum breaking strength is less than or equal to 0.5.

A type one error would be allowing the production process to continue when the true breaking strength is below specifications.