What is the factor of k2 + k - 42

Answer:

a) [tex] E = \frac{49.2-17.6}{2}= 15.8[/tex]

b) For this case we have 95% of confidence that the true mean would be between [tex]\pm 15.8[/tex] units respect the true mean.

c) [tex]n=(\frac{2.58(45)}{11})^2 =111.39 \approx 112[/tex]

So the answer for this case would be n=112

d) [tex]36.5-2.58\frac{45}{\sqrt{112}}=25.53[/tex]    

[tex]36.5+2.58\frac{45}{\sqrt{112}}=47.47[/tex]

Step-by-step explanation:

Part a

For this case we know that the cinfidence interval for the true mean is given by:

[tex] \bar X \pm E[/tex]

Where E represent the margin of error. For this case we have the confidence interval at 95% of confidence and we can estimate the margin of error like this:

[tex] E = \frac{49.2-17.6}{2}= 15.8[/tex]

Part b

For this case we have 95% of confidence that the true mean would be between [tex]\pm 15.8[/tex] units respect the true mean.

Part c

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =11 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The critical value would be [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:

[tex]n=(\frac{2.58(45)}{11})^2 =111.39 \approx 112[/tex]

So the answer for this case would be n=112

Part d

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

Replcaing the info given we got:

[tex]36.5-2.58\frac{45}{\sqrt{112}}=25.53[/tex]    

[tex]36.5+2.58\frac{45}{\sqrt{112}}=47.47[/tex]

Answer:

2.96

Step-by-step explanation:

The cosine of an angle is the length of the adjacent side divided by the length of the hypotenuse. In this case:

[tex]\cos 65=\dfrac{x}{7}[/tex]

[tex]x=7\cdot \cos 65\approx 2.96[/tex]

Hope this helps!

Answer:

The 95% confidence interval estimate for the population mean life of compact fluorescent light bulbs in this shipment is between 7,255 hours and 7,745 hours.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.95[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96*\frac{1000}{\sqrt{64}} = 245[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 7500 - 245 = 7255 hours.

The upper end of the interval is the sample mean added to M. So it is 7500 + 245 = 7745 hours.

The 95% confidence interval estimate for the population mean life of compact fluorescent light bulbs in this shipment is between 7,255 hours and 7,745 hours.

A means of the estimate numerical, the variation in that estimate is referred to as the confidence interval, therefore its value is "[tex][7255, 7745][/tex]".

[tex]95\%[/tex] C.I. for a mean lifetime is given by

[tex]= [ \overline{X} - \tau_{0.975} \frac{\sigma}{\sqrt{n}} , \overline{X} + \tau_{0.975} \frac{\sigma}{\sqrt{n}} ][/tex], where

[tex]\bar{X}[/tex] (sample mean) [tex]= 7500[/tex]

[tex]\sigma[/tex] (standard deviation)[tex]= 1000[/tex]

[tex]n = 64[/tex]

by putting the value into the above-given formula we get the value that is  [tex]= [7255, 7745].[/tex]

Find out more information about the confidence interval here:

brainly.com/question/2396419

Answer:first one is false, second is true and third is true

Step-by-step explanation:

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Answer: 42.190

Step-by-step explanation:

From the question, the population variances are not equal. The calculation has been attached in the picture below.

The answer is 42.190 to 3 decimal places.

Answer: y= 1/3 x + 5/3

Step-by-step explanation:

1= 1/3(-2) + b where b is the y intercept

  1=   -2/3 + B

+2/3   +2/3

B = 5/3

so we know the slope and the y- intercept

y= 1/3x + 5/3   check:   1=1/3(-2) +5/3

                                    1 =1

Slope intercept form: y = mx + b

m = slope

b = y-intercept

Since we know the slope and one point, we can solve for the y-intercept.

y = 1/3x + b

1 = 1/3(2) + b

1 = 2/3 + b

1 - 2/3 = 2/3 - 2/3 + b

1/3 = b

Now, put the final equation together.

y = 1/3x + 1/3

Best of Luck!

Answer:

B. 10 in.

Step-by-step explanation:

When you do length times width times height 10*10*10 equals 1000

10*10=100 and 100*10=1000

Answer:10 feet

Step-by-step explanation:

edge=[tex]\sqrt[3]{1000}[/tex]= 10 so the answer is B

Answer: an option is 2736

and we only have two possible solutions, the other is 6732

Step-by-step explanation:

we want to write a number:

a73b, where a and b are one digit numbers (0 to 9) in such way that the number is divisible by 36.

Now, we know that 36 is multiple of 6, so 6*6 = 36

The multiples of 36 are always even numbers, so we can discard all the odd options for b.

We also can discard the option a = 0, because we want a 4 digit number.

now, let's do it by brute force.

if a = 1, we have:

173b, now you can give b different values (only even values) and see if some of them is divisible by 36. You will find that none is.

if a = 2

273b

when b = 6, we have:

N = 2736, that is divisible by 36 as:

2736/36 = 79, so this is a multiple of 36.

now, you can keep changing the value of a and find all the different possible solutions.

if a = 3,

373b is not divisible by 36 for any value of b

if a = 4

473b  is not divisible by 36 for any value of b

if a = 5

573b  is not divisible by 36 for any value of b

if a= 6

673b  it is divisible by 36 when b = 2.

6732/36 = 187

if a = 7

773b  is not divisible by 36 for any value of b

if a = 8

873b  is not divisible by 36 for any value of b

if a = 9

973b  is not divisible by 36 for any value of b

So we only have two possible solutions

The different solutions this problem have are 2736 and 6732.

This is a part of a number which consists of numerals from 0 to 9.

a73b is the first number where a and b are one digit numbers (0 to 9) which is divisible by 36.

All multiples of 36 are always even numbers, so odd number options for b isn't considered.

If a = 2 when b = 6, we have:  it is divisible by 36 when b = 2.

N = 2736, which is divisible by 36 to give 76 hence it is a multiple of 36.

673b is divisible by 36 when b = 2.

N = 6732 which is divisible by 36 to give 187 hence it is a multiple of 36.

Hence, the two values are  2736 and 6732.

Read more about Digits here  https://brainly.com/question/13124157

Answer:f(8)=g(8)

Step-by-step explanation:

So in these problems f(8) means that you look at the f(x) function (function 1) and plug in 8 for x.  Then since it says g(8), you look at the g(x) function and substitute x for 8.  If we do that, f(x)=2(8)-3 which is 13.  g(x)=3/2x+1=13.  The two of them are equal when x=8.  So the answer is the third choice

Answer:

f(8)=g(8)

Step-by-step explanation:

Just put the values of given functions in the equation

24 drops of bubble bath

Step-by-step explanation:

this is because the ratio is .5 gallon:1 drop, so 12 gallons would be 24 drops. I hope this helps!

Answer:

In this case, you should check the x-intercept (y = 0).

=> (x-3)(x+4) = 0

=> Two x-intercept at x = 3 and x = -4

C, D are  not right, because there is no two x-intercepts.

A is not correct, because both of x-intercepts are less than 0.

=> Option B is correct.

Hope this helps!

:)

Answer:A

Step-by-step explanation:

-112.84-54.14-(-29.18)

-112.84-54.14+29.18=-137.8

Answer:

Option A is correct.

Answer:

It is the last one

Step-by-step explanation:

Answer:

it is d

Step-by-step explanation:

Answer:

He did not apply the distributive property correctly for 4(1 + 3i).

Step-by-step explanation:

4 (1 + 3 i) minus (8 minus 5 i)

4 + 12i - 8 + 5i

-4 + 17i

Answer:

A. He did not apply the distributive property correctly for 4(1 + 3i).

Step-by-step explanation:

edg 2020

Answer:5^38

Step-by-step explanation:

5^23 x 5^15

5^(23+15)

5^38

Answer:

(B)[tex]-2x^5+\dfrac{x^3}{2}+\dfrac{x}{4}+1[/tex]

–2x5 + StartFraction x cubed Over 2 EndFraction + StartFraction x Over 4 EndFraction + 1

Step-by-step explanation:

Given the polynomial: [tex]\dfrac{x}{4}-2x^5+\dfrac{x^3}{2}+1[/tex]

We are required to pick an equivalent polynomial which is in standard form.

A polynomial is in standard form when it is written in descending powers of x.

Therefore, rearranging the polynomial above, we have:

[tex]-2x^5+\dfrac{x^3}{2}+\dfrac{x}{4}+1[/tex]

The correct option is B.

The correct answer is B. –2x5 + StartFraction x cubed Over 2 EndFraction + StartFraction x Over 4 EndFraction + 1

hope you have a great day :D

Answer:

If a coin is flipped three times, possible outcomes would be:

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

=> possible outcomes that will include exactly 2 tails:

HTT

THT

TTH

TTT

Hope this helps!

:)

Answer:

The answer is 3 or option B.

Step-by-step explanation:

I just answered the question.

Answer:

Step-by-step explanation:

A data arranged in descending order is a data arranged from the biggest to the smallest. The medisn of the data sets is the value at the middle of the dataset after rearrangment.

For the dataset {8, x, 4,1}, the median will be x and 4. Since we have two median values, we will take their average as shown

Median(1) = [tex]\frac{x+4}{2}[/tex]... 1

Simialrly for dataset {9, y, 5,2}, the median will be y and 5.

Median(2) = [tex]\frac{y+5}{2}[/tex] ...2

Since the medians of  the two given datasets are equal, we will equate equation 1 and 2 and calculate for y-x as shown;

[tex]\frac{x+4}{2} = \frac{y+5}{2}[/tex]

[tex]x+4 = y+5\\x-y = 5-4\\x-y = 1\\y-x = -1[/tex]

Therefore y-x = -1

(y-x)² = (-1)²

= 1

Answer:

Step-by-step explanation:

The numbers in the first column are an arithmetic sequence with a common difference of 2. The next few numbers will be 6, 8, 10, ...

The numbers in the second column are an arithmetic sequence with a common difference of 3. The next few numbers will be 9, 12, 15, ...

The numbers in the third column are an arithmetic sequence with a common difference of 5. The next few numbers will be 15, 20, 25, ...

To use the table, Mark can extend each sequence until he has a row with 45 in the third column, or he can multiply or add rows to give a result of 45 in the third column. For example, multiplying the first row by 9 gives 18:27:45 meaning that Mark needs 18 liters of blue and 27 liters of yellow to make 45 liters of green paint.

Answer:

-4.8

Step-by-step explanation:

Answer:

−24/5

Step-by-step explanation:

3x3/5x(-8x1/3)

Use the order of operations method, PEMDAS, in order to solve this expression.

Answer:

 y = -√(x -5) +2

Step-by-step explanation:

This looks like a square root function reflected vertically, and translated up 2 and right 5.

 y = -√(x -5) +2

_____

g(x) = a·f(x -h) +k   represents a translation of f(x) by (h, k) and a vertical scaling by a factor of "a". If "a" is negative, the function is reflected across the x-axis.

Answer:

x = 25

Step-by-step explanation:

Log10 ( x - 21 ) + Log10 ( x ) = 2,

Log10 ( ( x - 21 )x ) = 2,

( x - 21 )x = 100,

Simplify:

x^2 - 21x = 100,

x^2 - 21x - 100 = 0,

x = - ( -21 ) + √ ( -21 )^2 - 4 * 1 ( -100 )/2 * 1 : 25

                             and

x = - ( -21 ) + √ ( -21 )^2 - 4 * 1 ( -100 )/2 * 1 : -4

( x = 25 ) ⇒ true

( x = - 4 ) ⇒ false

Answer: x = 25

Answer:

The height of the building: g

Distance from the building to the base of the ladder: 57

The length of the ladder: m

Angle the ladder makes with the building: k

Angle the ladder makes with the ground: 55

Step-by-step explanation:

Based off the location of the variables and numbers, the descriptions match where they are.

Hope that helps!

Answer:

No. See below.

Step-by-step explanation:

No, Seth lost the plot at the end.

At x = 3,

y = 4x + 1 = 12 + 1 = 13

At x = -2,

y = 4x + 1 = -8 + 1 = -7

Therefore, the curves intersect at (3,13) and (-2,-7)

Answer:

a:b

3:7

Step-by-step explanation:

a:b  also means a/b

Taking the equation

7a = 3b

Dividing each side by b

7a/b = 3b/b

7 a/b = 3

Divide each side by 7

a/b = 3/7

The ratio is 3/7

a:b

3:7

Answer:

a:b = 3/7

Step-by-step explanation:

we need to find the ratio a:b which is the same as a/b.

7a=3b

Devide left and right of the = sign by b gives

7a/b = 3 * b/b

7a/b = 3 * 1

7a/b = 3

Multiply left and right of the = sign by 1/7 gives

1/7 * 7a/b = 1/7 * 3

7/7 * a/b = 3/7

1 * a/b = 3/7

a/b = 3/7

Since a/b is the same as a:b, we now have the answer.

a:b = 3/7

Answer:

400

Step-by-step explanation:

20 x 20= 400

Answer:

I'd say that if it is the total area square and half of the circle. the answer could be 557.08

Step-by-step explanation:

area of the square 20*20= 400

area of the circle= Pi*radio to the square divided by two cause its only the half of a circle so it is like 3.1416*10^2=100*3.1416=714.16/2=157.08

now we can sum up the square area and the circle

400+157.08= 557.08

I'm not actually sure itll depend if the wide and height of the square is the same. here im guessing that its 20 both. and another thing I didnt round the answer it was just that

Answer:

36960 people

Step-by-step explanation:

Answer:

36,960 people

Step-by-step explanation:

[tex]\frac{is}{of}=\frac{percent}{100}[/tex] is the formula to solve for this equation, here plugging in all our numbers gives us [tex]\frac{x}{480,000} = \frac{77}{100}[/tex].

We do not know our "is" so we replace it for x and solve → [tex]x=(480,000)(\frac{77}{100} )[/tex] = 36,960 people