You have land that you would like to use to create two distinct fenced-in areas in the shape given below. You have 410 meters of fencing materials to use. What values of x and y would result in the maximum area that you can enclose

9514 1404 393

Answer:

  140°

Step-by-step explanation:

Angles 1 and 3 are "corresponding" angles, so are congruent.

  ∠1 = ∠3

  20x +60 = 30x +20

  40 = 10x . . . . . . . . . . . . subtract 20x+20

  4 = x . . . . . . . . . . . . . . divide by 10

  ∠1 = 20x +60 = 20(4) +60 = 80 +60

  ∠1 = 140°

Answer:

140°

Step-by-step explanation:

Angle 1 and angle 3 are corresponding angles ;

Corresponding angles are equal ;

Hence,

Angle 1 = Angle 3

20x + 60 = 30x + 20

Collect like terms

20x - 30x = 20 - 60

-10x = - 40

x = 4

Angle 1 is thus :

20x + 60 ; x = 4

20(4) + 60

80 + 60

= 140°

Answer:

5470

Step-by-step explanation:

[tex]5000(1+\frac{.03}{12})^{12*3}=5470.257[/tex]

The future value of the investment in the savings account with montly compounding is $5470.

When an investment is compouded monthly, it means that it increases in value every month.

The formula for calculating future value:

FV = P (1 + r)^nm

5000 x ( 1.0025)^36 = $5470

To learn more about future value, please check: https://brainly.com/question/18760477

Answer:

90% confidence interval is ( -149.114, -62.666   )

Step-by-step explanation:

Given the data in the question;

Sample 1                                Sample 2

x"₁ = 259.23                            x"₂ = 365.12

s₁  = 34.713                              s₂ = 48.297

n₁ = 5                                       n₂ = 10

With 90% confidence interval for μ₁ - μ₂ { using equal variance assumption }

significance level ∝ = 1 - 90% = 1 - 0.90 = 0.1

Since we are to assume that variance are equal and they are know, we will use pooled variance;

Degree of freedom DF = n₁ + n₂ - 2 = 5 + 10 - 2 = 13

Now, pooled estimate of variance will be;

[tex]S_p^2[/tex] = [ ( n₁ - 1 )s₁² + ( n₂ - 1)s₂² ] / [ ( n₁ - 1 ) + ( n₂ - 1 ) ]

we substitute

[tex]S_p^2[/tex] = [ ( 5 - 1 )(34.713)² + ( 10 - 1)(48.297)² ] / [ ( 5 - 1 ) + ( 10 - 1 ) ]

[tex]S_p^2[/tex] = [ ( 4 × 1204.9923) + ( 9 × 2332.6 ) ] / [  4 + 9 ]

[tex]S_p^2[/tex] = [ 4819.9692 + 20993.4 ] / [  13 ]

[tex]S_p^2[/tex] = 25813.3692 / 13

[tex]S_p^2[/tex] = 1985.64378

Now the Standard Error will be;

[tex]S_{x1-x2[/tex] = √[ ( [tex]S_p^2[/tex] / n₁ ) + ( [tex]S_p^2[/tex] / n₂ ) ]

we substitute

[tex]S_{x1-x2[/tex] = √[ ( 1985.64378 / 5 ) + ( 1985.64378 / 10 ) ]

[tex]S_{x1-x2[/tex] = √[ 397.128756 + 198.564378 ]

[tex]S_{x1-x2[/tex] = √595.693134

[tex]S_{x1-x2[/tex] = 24.4068

Critical Value = [tex]t_{\frac{\alpha }{2}, df[/tex] = [tex]t_{0.05, df=13[/tex] = 1.771  { t-table }

So,

Margin of Error E =  [tex]t_{\frac{\alpha }{2}, df[/tex] × [ ( [tex]S_p^2[/tex] / n₁ ) + ( [tex]S_p^2[/tex] / n₂ ) ]

we substitute

Margin of Error E = 1.771 × 24.4068

Margin of Error E = 43.224

Point Estimate = x₁ - x₂ = 259.23 - 365.12 = -105.89

So, Limits of 90% CI will be; x₁ - x₂ ± E

Lower Limit = x₁ - x₂ - E = -105.89 - 43.224 = -149.114

Upper Limit = x₁ - x₂ - E = -105.89 + 43.224 = -62.666

Therefore, 90% confidence interval is ( -149.114, -62.666   )

Answer:

The 4th graph represents a function

Step-by-step explanation:

trust bro

4th graph is a function

Option D is the correct answer

Answer:

21 cm²

21 square centimeters

Step-by-step explanation:

A = bh

A = 3 × 7

A = 21

Answer:

you swim 20inches and then you walk 50

Step-by-step explanation:

just because

Answer:

profit is 256 dollars

Step-by-step explanation:

20% of 1,280 is 256 dollars

Answer:  T=1700

Step-by-step explanation:

Answer:

4.6

Step-by-step explanation:

yes

Answer:

She must take a sample of 56.

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 Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

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.

Standard deviation estimate of 1.90

This means that [tex]\sigma = 1.9[/tex]

Wow large a sample must she take if she wants the margin of error to be under 0.5 inch?

This is n for which M = 0.5. So

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

[tex]0.5 = 1.96\frac{1.9}{\sqrt{n}}[/tex]

[tex]0.5\sqrt{n} = 1.96*1.9[/tex]

[tex]\sqrt{n} = \frac{1.96*1.9}{0.5}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*1.9}{0.5})^2[/tex]

[tex]n = 55.5[/tex]

Rounding up:

She must take a sample of 56.

Answer:48.013

Step-by-step explanation: just found it

Answer:

C 14n - 8

Step-by-step explanation:

rectangle area = length×width = 12n²-19n-21

width = 3n-7

what do we need to multiply with width to get the full area expression ?

think : what do we need to multiply with 3n to get 12n² (4n)?

and what to multiply with -7 to get -21 (3)?

=> length = 4n+3

perimeter is 2×length + 2×width

p = 2(3n-7) + 2(4n+3) = 6n-14+8n+6 = 14n-8

Answer:

5(x+2)

Step-by-step explanation:

5x + 10=

Factor out 5

5(x+2)

Answer:

[tex]5(x + 2)[/tex]

Step-by-step explanation:

Get 5 out

[tex]5x + 10 \\ 5(x + 2)[/tex]

Answer:

24

Step-by-step explanation:

betty age = 41 - 17

= 24

Answer:

160 units²

Step-by-step explanation:

Surface area of the square pyramid = a² + 2al

Where,

a = side length of the square = 8

l = slant height of the triangular face = 6

Plug in the values

Surface area of the square pyramid = 8² + 2*8*6

= 64 + 96

= 160 units²

Answer:

VU,UV, and probably VU just pick 3 answers cause there is 6 questions in all but i hope these answers help u have a nice day too.

Step-by-step explanation:

Answer:

Factorizing 4x2 - 9y2, we get

(2x)2 - (3y)2, by using the identities of a2 - b2.

= (2x + 3y) (2x - 3y)

Step-by-step explanation:

Answer:

0.48

0.52

No

Yes

Step-by-step explanation:

Result of experiment :

Point up = 48

Point down = 52

Total number of trials = 100

Recall :

Experimental probability = number of outcomes / number of trials

1.)

P(Landing point up) = 48 / 100 = 0.48

2.)

P(Landing point down) = 52 / 100 = 0.52

3.)

The same result will not occur has the outcomes of trials aren't fixed.

4.) Yes, nearly the same result could occur on the second trial, as the number of possible outcubes are just 2 and the number if trials is high.

Answer:

-5/2+-1/2√37≤x≤-5/2+1/2√37

Step-by-step explanation:

Step 1: Find the critical points

-x^2-5x+3=0

For this equation: a=-1, b=-5, c=3

−1x^2+−5x+3=0

x=−b±√b2−4ac/2a

x=−(−5)±√(−5)2−4(−1)(3)/2(-1)

x=5±√37 /−2

x=-5/2+1/2√37

Step 2: Check intervals in between critical points

x≤-5/2+1/2 √37 (Doesn't work in original inequality)

-5/2+-1/2√37≤x≤-5/2+1/2√37 (Works in original inequality)

x≥-5/2+1/2 √37 (Doesn't work in original inequality)

=====================================================

Explanation:

We have n = 5 sides. This means the interior angles sum up to...

S = 180(n-2)

S = 180(5-2)

S = 180(3)

S = 540

All five interior angles of this pentagon add up to 540 degrees.

Answer:

-27

Hope this helped in anyway

Answer:

the answer to this is -27.

Answer:

First one

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

90 because it is the mean

Answer: it’s 83%

Step-by-step explanation: you add them up and divide by 3

Answer:

You saved $30

Step-by-step explanation:

20% + 10% = 30%

30% = 0.30

$100 * 0.30 = $30

$100 - $30 = $70

Hope this is helpful

Evaluting the limand directly at x = 0 yields the indeterminate form 0/0, so we have a candidate for L'Hopital's rule. We get

[tex]\displaystyle\lim_{x\to0}\frac{\sqrt{1+x+x^2}-1}{\tan(5x)} = \lim_{x\to0}\frac{\frac{1+2x}{2\sqrt{1+x+x^2}}}{5\sec^2(5x)} = \frac{1+2\times0}{2\sqrt{1+0+0^2}\times5\sec^2(5\times0)} = \boxed{\dfrac{1}{10}}[/tex]

If you don't know about L'Hopital's rule, or are otherwise not allowed to use it, you can instead rely on algebraic manipulation and a well-known limit,

[tex]\displaystyle\lim_{x\to0}\frac{\sin(ax)}{ax}=\lim_{x\to0}\frac{ax}{\sin(ax)}=1[/tex]

where a ≠ 0. We write

[tex]\displaystyle\frac{\sqrt{1+x+x^2}-1}{\tan(5x)} = \frac{5x}{\sin(5x)}\times\frac{\cos(5x)}5\times\frac{\sqrt{1+x+x^2}-1}x[/tex]

The limit of a product is equal to the product of limits:

[tex]\displaystyle\lim_{x\to0}\frac{\sqrt{1+x+x^2}-1}{\tan(5x)} = \left(\lim_{x\to0}\frac{5x}{\sin(5x)}\right)\times\left(\lim_{x\to0}\frac{\cos(5x)}5\right)\times\left(\lim_{x\to0}\frac{\sqrt{1+x+x^2}-1}x\right)[/tex]

The first limit is 1 and the second limit is 1/5. For the remaining limit, multiply through the fraction by the conjugate of the numerator:

[tex]\dfrac{\sqrt{1+x+x^2}-1}x\times\dfrac{\sqrt{1+x+x^2}+1}{\sqrt{1+x+x^2}+1} = \dfrac{\left(\sqrt{1+x+x^2}\right)^2-1^2}{x\left(\sqrt{1+x+x^2}+1\right)} \\\cdots= \dfrac{x+x^2}{x\left(\sqrt{1+x+x^2}+1\right)} \\\cdots= \dfrac{1+x}{\sqrt{1+x+x^2}+1}[/tex]

The remaining limand is continuous at x = 0, and its limit is

[tex]\displaystyle\lim_{x\to0}\frac{1+x}{\sqrt{1+x+x^2}+1}=\frac{1+0}{\sqrt{1+0+0^2}+1}=\frac12[/tex]

and hence the original limit is again 1 × 1/5 × 1/2 = 1/10.

the answer is [tex]x^{2} \sqrt{x} \leq \geq \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \pi x^{2} \sqrt{x} \frac{x}{y} \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left \{ {{y=2} \atop {x=2}} \right.[/tex]random but marter than einstein

Answer:                                                                    

14 and 1

Explanation:

14 + 14 + 1 + 1 = 30

14 x 1 = 14

The perimeter is the sum of all 4 sides. Divide the perimeter in half fo the some of one length and one width:

Length + width = 15

Area is length x width

Find 2 numbers that when added equal 15 but when multiplied equal 14

15 + 0 = 15, 15 x 0 = 0

14 + 1 = 15, 14 x 1 = 14

The answer is 14 ft long by 1 ft wide