Part 1: Joe and Hope were both asked to factor the following polynomial completely. Is one of them correct? Both of them? Neither of them? Explain what each of them did was correct and/or incorrect.

Part 2:

Find all the values of k so the the quadratic expression factors into two binomials. Explain the process used to find the values.

3x^2 + kx - 8​

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Explanation:

area of rectangle = L*W = 129

L*W = 129

x*(2x-9) = 129

2x^2-9x = 129

2x^2-9x-129 = 0

Apply the quadratic formula. We'll use a = 2, b = -9, c = -129.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-9)\pm\sqrt{(-9)^2-4(2)(-129)}}{2(2)}\\\\x = \frac{9\pm\sqrt{1113}}{4}\\\\x \approx \frac{9\pm33.36165464}{4}\\\\x \approx \frac{9+33.36165464}{4}\ \text{ or } \ x \approx \frac{9-33.36165464}{4}\\\\x \approx \frac{42.36165464}{4}\ \text{ or } \ x \approx \frac{-24.36165462}{4}\\\\x \approx 10.59041366\ \text{ or } \ x \approx -6.09041364\\\\[/tex]

We ignore the negative solution because a negative length makes no sense.

The length is approximately L = 10.5904 cm.

The width is 2L-9 = 2*10.5904-9 = 12.1808 cm approximately.

As a quick check,

L*W = 10.5904*12.1808 = 128.99954432

which isn't too far off from 129. We have rounding error which is why we don't perfectly land on the target area value. If you wanted to get closer to the value 129, then use more decimal digits in the approximations of L and W.

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

If you draw a diagonal in the rectangle, then you form two identical or congruent right triangles.

Focusing on one of those triangles, we have

Apply the pythagorean theorem

a^2+b^2 = c^2

c = sqrt( a^2 + b^2 )

c = sqrt( (10.5904)^2 + (12.1808)^2 )

c = 16.1408940520653

c = 16.14

The diagonal is roughly 16.14 cm long.

Answer:

[tex]\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{1}{2}[/tex]

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                                     [tex]\displaystyle \lim_{x \to c} x = c[/tex]

L'Hopital's Rule

Differentiation

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                    [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

We are given the limit:

[tex]\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)}[/tex]

When we directly plug in x = 0, we see that we would have an indeterminate form:

[tex]\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{0}{0}[/tex]

This tells us we need to use L'Hoptial's Rule. Let's differentiate the limit:

[tex]\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)}[/tex]

Plugging in x = 0 again, we would get:

[tex]\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \frac{0}{0}[/tex]

Since we reached another indeterminate form, let's apply L'Hoptial's Rule again:

[tex]\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)}[/tex]

Substitute in x = 0 once more:

[tex]\displaystyle \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)} = \frac{1}{2}[/tex]

And we have our final answer.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

In this question, the variance of the population is tested. From the data given in the exercise, we build the hypothesis, then we find the value of  test statistic and it's respective p-value, to conclude the test. From this, it is found that the conclusion is:

The p-value of the test is 0.0038 < 0.05, which means that the investor can conclude that the variance of the share price of the bond fund is different than claimed at α = 0.05.

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

Claimed variance of 0.19:

This means that at the null hypothesis, it is tested if the variance is of 0.19, that is:

[tex]H_0: \sigma^2 = 0.19[/tex]

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

Test if the variance of the share price of the bond fund is different than claimed at α = 0.05.

At the alternative hypothesis, it is tested if the variance is different of the claimed value of 0.19, that is:

[tex]H_1: \sigma^2 \neq 0.19[/tex]

The test statistic for the population standard deviation/variance is:[tex]\chi^2 = \frac{n-1}{\sigma_0^2}s^2[/tex]

In which n is the sample size,  is the value tested for the variance and s is the sample standard deviation.

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

0.19 is tested at the null hypothesis, as the variance:

This means that [tex]\sigma_0^2 = 0.19[/tex]

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He takes a random sample of the share prices for 22 days throughout the last year and finds that the standard deviation of the share price is 0.2517.

This means that [tex]n = 22, s^2 = (0.2517)^2 = 0.0634[/tex]

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Value of the test statistic:

[tex]\chi^2 = \frac{n-1}{\sigma_0^2}s^2[/tex]

[tex]\chi^2 = \frac{21*0.0634}{0.19}[/tex]

[tex]\chi^2 = 7[/tex]

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P-value of the test and decision:

The p-value of the test is found using a chi-square for the variance calculator, considering a test statistic of [tex]\chi^2 = 7[/tex] and 22 - 1 = 21 degrees of freedom, and a two-tailed test(test if the mean is different of a value).

Using the calculator, the p-value of the test is 0.0038.

The p-value of the test is 0.0038 < 0.05, which means that the investor can conclude that the variance of the share price of the bond fund is different than claimed at α = 0.05.

For more on hypothesis tests using variances/standard deviation, you can check https://brainly.com/question/13993951

Answer:

I hope this is correct but 8.5 or 8 1/2 Units

Answer:

i think it is 8 1/2.

Step-by-step explanation:

my reasoning is that because v=lwh. the length is 4 and hw is 2 1/8. so i multiplied those together.

The centroid and center of mass need not be the same point. They are the same only when a body's mass is uniformly distributed.

Answer:

3rd option

Step-by-step explanation:

(1/2)^-2t

= (2^-1)^-2t

= 2^2t

= (2^2)^t

Answered by GAUTHMATH

Answer:

7

Step-by-step explanation:

Answer:

x=4

y=7

Step-by-step explanation:

12=3x

x=4

6=y-1

y=6+1

y=7

Answer:

x=4

Step-by-step explanation:

Answer:

x > 8

Step-by-step explanation:

You can start y multiplying both sides by 4 to cancel out the division by 4:

x/4 > 2

*4      *4

x > 8

Answer:

x > 8

Step-by-step explanation:

x/4 > 2

=> x > 2 × 4

=> x > 8

..... Here

This is the answer

Answer:

Step-by-step explanation:

A right triangle has one right angle and two acute angles.

A and B are the acute angles.

A+B =  90°

One acute angle is 45 less than twice the other acute angle.

A = 2B-45°

(2B-45°) + B = 90°

3B = 135°

B = 45°

A = 45°

Answer:

Step-by-step explanation:

The question has an error. Volume is expressed in cubic units. You probably mean cm³ .

Volume = 8 cm³

Length of each edge = ∛8 = 2 cm

Answer:

2cm

Step-by-step explanation:

Volume of cube=a^3 cubic units

8=a^3

a=cuberoot of 8

which is 2

Answer:

i can't rn but i could explain to you how... so first put a point on 0,5 then move down one and right one... then keep moving down one and right one

and there you go thats your graph

Step-by-step explanation:

Answer:

H0 : The variables are independent

H1 : The variables are not independent

Step-by-step explanation:

In a Chisquare test ; The null hypothesis is used to lay claim that the variables are independent, that is no relationship exists between the categorical variables in the population while the alternative hypothesis negates the null thus claiming that the variables aren't independent.

The null hypothesis, H0 : The variables are independent, A = B = C

The alternative hypothesis ; H1 : The variables are not independent, A ≠ B ≠ C

Answer:

Step-by-step explanation:

Garden is two times as long as it is wide.

L = 2W

Perimeter is 120 feet

2L + 2W = 120

L +W = 60

(2W) + W = 60

3W = 60

W = 20 feet

L = 2W = 40 feet

Answer:

535525-62635-$6#62626636$66$6$63663636$6$62

brainly is dustbin

Answer:

Step-by-step explanation:

400*e^(.09*3)

$523.97

answer is b

Answer: Option B

$523.97

Explanation:

= 400×e^(0.09×3)

= $523.97

Must click thanks and mark brainliest

Answer:

3rd option (top right)

Step-by-step explanation:

3rd option represents a linear equation

y = -2x-1

Answered by GAUTHMATH

The identity as been verified/proved as:

[tex]1 - \tan\ a\ tan\ b = 1 - \tan\ a\ tan\ b[/tex]

Given that:

[tex]\frac{\cos(a + b)}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

Apply cosine identity to the numerator

[tex]\frac{\cos\ a\ cos\ b - \sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

Split the fraction:

[tex]\frac{\cos\ a\ cos\ b}{\cos\ a\cos b} - \frac{\sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

Cancel out common terms

[tex]1 - \frac{\sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

In trigonometry, we have:

[tex]\frac{\sin \theta}{\cos \theta} = \tan \theta[/tex]

So, the equation becomes:

[tex]1 - \tan\ a\ tan\ b = 1 - \tan\ a\ tan\ b[/tex]

Hence, the identity has been verified

Read more about trigonometry identities at:

https://brainly.com/question/21055284

Answer:

4000 because a cow is 4000 and he gave 40000

cause he used it for sinething

Answer:

C. 44.98

Step-by-step explanation:

Hi there!

We are given the right triangle ABC, m<B=12°, and CB =44

We want to find the length of AB

We can use trigonometry to do it

Let's find the ratio in reference to angle B, as that angle is given.

In reference to angle B the opposite angle is AC, the adjacent side is CB, and the hypotenuse is AB

Now let's recall the 3 most commonly used functions:

[tex]sine=\frac{opposite}{hypoptenuse}[/tex]

[tex]cosine=\frac{adjacent}{hypotenuse}[/tex]

[tex]tangent=\frac{opposite}{adjacent}[/tex]

Let's find the cosine of angle B, as it uses CB and AB, which are the given side and the side we need to find

In that case,

cos(12)=[tex]\frac{CB}{AB}[/tex]

cos(12)=[tex]\frac{44}{AB}[/tex]

Multiply both sides by AB

[tex]AB[/tex]*cos(12)=44

Divide both sides by cos(12)

AB=[tex]\frac{44}{cos(12)}[/tex]

Now plug [tex]\frac{44}{cos(12)}[/tex] into your calculator. Make sure your calculator is on degree mode

AB≈44.98

So the answer is C

Hope this helps!

Answer:

3(x + 8)

Step-by-step explanation:

"The product of three and the sum of a number and eight".

First, note that:

1) Product means multiply.

2) Sum means addition.

With that in mind, also note the order of operations. The order of operations is defined as PEMDAS, or:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

Also, let "a number" be denoted as the variable, x.

~

Firstly, "the sum of a number and eight": x + 8

Next, "The product of...": 3 *

Putting the two parts together will generate: 3(x + 8)

3(x + 8) is your answer.

~

Answer: 15 cups

Step-by-step explanation:

Answer:

5 %

Step-by-step explanation:

1000 g = 1 kg

50 kg = 0.05 kg

0.05 = 5%

Therefore, 50 g as a percentage of 1kg is 5%.

9514 1404 393

Answer:

  a) $164,413.47

  b) $96,000

  c) $68,413.47

Step-by-step explanation:

a) The account value is given by the annuity formula:

  A = P(12/r)((1 +r/12)^(12·t) -1)

where monthly payment P earns interest at annual rate r compounded monthly for t years.

  A = $400(12/0.05)((1 +0.05/12)^(12·20) -1) = $400(240)(1.712640285)

  A ≈ $164,412.47

You will have $164,413.47 in the account after 20 years.

__

b) You put $400 in the account each month for 240 months, for a total of ...

  $400 × 240 = $96,000 . . . . total of your deposits

__

c) The account balance in excess of your deposits is the amount of interest you earned:

  $164,413.47 -96,000 = $68,413.47 . . . . interest earned

Answer:

15

Step-by-step explanation:

The figure has total 15 faces, the correct option is A.

A hexagon is a polygon with six sides.

A hexagonal pyramid has 8 faces

From (2 hexagonal base + 6 lateral surfaces)

A hexagonal prism has 7 faces

From ( A hexagonal base + 6 lateral faces)

Total faces the figure has is 8 +7 = 15

To know more about Hexagon

https://brainly.com/question/3295271

#SPJ5

Answer:

Determination of type of error arising from the situations

Situation       Type of Error

1.                    Nonresponse

2.                   Bad sampling method

3.                   Question wording

4.                   Undercoverage

Step-by-step explanation:

Types of errors:

a. question wording means that the manner a question is worded elicits some particular responses, which may not accurately reflect reality.

b. undercoverage occurs when some elements of the target population is not represented on the survey frame.

c. processing error arises from data processing

d. bad sampling method is caused by the voluntariness of those who choose to respond.

e. response error is caused by a questionnaire that requires framing improvements, misinterpretation of questions by interviewers or respondents, and errors in respondents' statements.

f. nonresponse error arises as a result of incomplete information or partial response.

g. random sampling error arises from the limited sample size when compared with the population size.

Answer:

33%

Step-by-step explanation:

$16,500-$11,055= $5,445

$5,445÷$16,500= 0.33 which in percentage format is 33%

HOPE THIS HELPS! MARK BRAINLIEST PLEASE!!!!!