312/132 (fraction simplified as a mixed number)

a) By Pythagoras theorem , h^2 is = a^2 + b^2 where a is the hypotenuse and a and b are the legs.

=) 15^2 = x^2 + y^2

That is the relation

b) area of triangle = 1/2 x height x base

=) 1/2 * x * y = 30

=) xy = 15cm

Step-by-step explanation:

Here is the answer for your question

i think hhjs is how it goes

Answer:

16

Step-by-step explanation:

a = 5

b = 3

a - b = 2

▪︎5 - 3 = 2

ab = 15

▪︎5(3) = 15

a^2 - b^2 = ?

5^2 = 25

3^2 = 9

25 - 9 = 16.

a^2 - b^2 = 16.

Answer: SInce this is multiple choice I won't provide an explanation. The answers are B) (-1, -4) and E) (4, 6)

Answer:

DM=38\ cmDM=38 cm

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

Triangles DEF and OEN are similar by AA Similarity Postulate

Remember that if two triangles are similar, then the ratio of its corresponding sides is proportional

In this problem

\frac{DE}{OE}=\frac{DF}{ON}

OE

DE

=

ON

DF

substitute the given values

\frac{44}{22}=\frac{DF}{38}

22

44

=

38

DF

2=\frac{DF}{38}2=

38

DF

DF=2(38)=76\ cmDF=2(38)=76 cm

\begin{gathered}DF=2DM\\76=2DM\\DM=38\ cm\end{gathered}

DF=2DM

76=2DM

DM=38 cm

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Answer:

C

Step-by-step explanation:

Answer:B

Step-by-step explanation: There is a mathematical way to do this , but the simplest way is just to imagine all of the transformations and choose the most reasonable one. All of the other answers are ridiculous.

Step-by-step explanation:

Starting out with the Taylor series,

[tex]\displaystyle f(x) = \sum_{n=0}^{\infty} \dfrac{f^{(n)}(a)}{n!}(x-a)^n[/tex]

where [tex]f^{(n)}[/tex] is the nth derivative of f(x) and if we set a = 0, we get the special case of the Taylor series called the Maclaurin series:

[tex]\displaystyle f(x) = \sum_{n=0}^{\infty} \dfrac{f^{(n)}(0)}{n!}x^n[/tex]

Expanding this series up to the 1st 3 terms at a = 0,

[tex]f(x) = f(0) + \dfrac{f'(0)}{1!}x + \dfrac{f''(0)}{2!}x^2[/tex]

Let's find the derivatives of [tex]e^{\frac{x}{2}}[/tex]:

[tex]f'(x) = \frac{d}{dx} (e^{\frac{x}{2}}) = \frac{1}{2}e^{\frac{x}{2}} \Rightarrow f'(0) = \frac{1}{2}[/tex]

[tex]f''(x) = \frac{1}{4}e^{\frac{x}{2}} \Rightarrow f''(0) = \frac{1}{4}[/tex]

We can now write the Maclaurin series for [tex]e^{\frac{x}{2}}[/tex]as

[tex]e^{\frac{x}{2}} = 1 + \frac{1}{2} x + \frac{1}{8} x^2[/tex]

Answer:

36 meters

Step-by-step explanation:

A=1/2b×h

108sq. m=1/2.6m×h

both side canceling meter

h=2×108m/6

h=36m. answer

The height of the triangle is 12 meters, and the base of the triangle is 18 meters.

Let's denote the height of the triangle as "h" meters. According to the given information, the base of the triangle is 6 meters longer than the height, so the base can be represented as "(h + 6)" meters.

The area of a triangle is given by the formula: Area = (1/2) * base * height

We are given that the area of the triangle is 108 square meters, so we can write the equation as:

108 = (1/2) * (h + 6) * h

Now, let's solve for "h":

108 = (1/2) * (h² + 6h)

Multiply both sides by 2 to eliminate the fraction:

216 = h² + 6h

Rearrange the equation in standard quadratic form:

h² + 6h - 216 = 0

Now, let's solve this quadratic equation for "h." We can factor it or use the quadratic formula. Factoring, we get:

(h + 18)(h - 12) = 0

Setting each factor to zero:

h + 18 = 0     or     h - 12 = 0

Solving for "h" in each case:

h = -18 (discard this negative value as height cannot be negative)     or     h = 12

Since height cannot be negative, we take the positive value of "h," which is 12 meters.

Now, we can find the base by using the given relationship: base = height + 6

base = 12 + 6 = 18 meters

So, the height of the triangle is 12 meters, and the base of the triangle is 18 meters.

Learn more about triangles here:

https://brainly.com/question/29083884?

#SPJ2

Answer:

sssssssss

Step-by-step explanation:

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Answer:

Sorry dont understand

Answer:

Patrice does not have sufficient evidence to reject the fast-food chain's claim.

Step-by-step explanation:

unless she already ate some fries, not enough evidence

Given:

The piecewise function is:

[tex]f(x)=\begin{cases}9x & \text{ if } x<-1 \\ x-4 & \text{ if } x\geq -1 \end{cases}[/tex]

To find:

The values of [tex]f(-3),f(0), f(-1)[/tex].

Solution:

In the given piecewise function,

[tex]f(x)=9x[/tex] for [tex]x<-1[/tex] and [tex]f(x)=x-4[/tex] for [tex]x\geq -1[/tex].

Putting [tex]x=-3[/tex] in [tex]f(x)=9x[/tex], we get

[tex]f(-3)=9(-3)[/tex]

[tex]f(-3)=27[/tex]

Putting [tex]x=0[/tex] in [tex]f(x)=x-4[/tex], we get

[tex]f(0)=0-4[/tex]

[tex]f(0)=-4[/tex]

Putting [tex]x=-1[/tex] in [tex]f(x)=x-4[/tex], we get

[tex]f(-1)=-1-4[/tex]

[tex]f(-1)=-5[/tex]

The required values are [tex]f(-3)=27,f(0)=-4,f(-1)=-5[/tex].

Therefore, the correct option is D.

Answer:

[tex]d = 2\sqrt{30}[/tex]

Step-by-step explanation:

Given

[tex]Volume = 300\pi ft^3[/tex]

[tex]Height =10ft[/tex]

Required

The diameter

The volume of a cylinder is:

[tex]V = \pi r^2h[/tex]

So, we have:

[tex]300\pi = \pi * r^2*10[/tex]

Divide both sides by the common factors

[tex]30 = r^2[/tex]

Take square roots of both sides

[tex]r = \sqrt{30}[/tex]

The diameter is:

[tex]d=2r[/tex]

So:

[tex]d = 2* \sqrt{30}[/tex]

[tex]d = 2\sqrt{30}[/tex]

or

[tex]d = 10.95[/tex]

Answer: $15219.20

Step-by-step explanation:

Based on the information given, firstly we need to calculate the discount which will be:

= 18% × $18560

= 0.18 × $18560

= $3340.80

Then, the amount that Dao will pay will be:

= Sticker price - Discount

= $18560 - $3340.80

= $15219.20

Therefore, Dao will pay $15219.20

Answer:

4%

Step-by-step explanation:

264 interest/3 years=88 interest/year

principal x interest rate =interest/year

2200 x interest rate =88

interest rate =88/2200

interest rate =.04 or 4%

Answer:

d = [tex]\frac{2x + 3}{p}[/tex]  - x

Step-by-step explanation:

First divide both sides by p.

then subtract x from both sides

Answer:

[tex]\displaystyle d = \frac{2x + 3}{d} - x[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle p(d + x) = 2x + 3[/tex]

Step 2: Solve for d

Answer:

Y = 0.0315x + 9.4764

Residual = 2.35

Correlation Coefficient = 0.847

Step-by-step explanation:

From the R output given :

Intercept = 9.4764

Slope = 0.0315

x = number of manufacturing enterprise employing 20 or more workers

y = annual mean concentration of Sulphur dioxide

The regression equation :

y = bx + c

b = slope ; c = intercept

y = 0.0315x + 9.4764

Prediction using the regression equation :

The predicted y value, when x = 250

y = 0.0315(250) + 9.4764

y = 17.3514

The residual, if actual annual concentration = 15

Y residual = 17.35 - 15 = 2.35

The correlation Coefficient value, R

R = √R²

R = √0.717

R = 0.847

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

Explanation:

The observations are in ascending order, which means the set is sorted from smallest to largest.

The X is at the right-most endpoint, so X is the largest value (aka the max).

The min is 33, so,

max - min = range

X - 33 = 58

X = 58+33

X = 91 is the max

Answer:

Step-by-step explanation:

The range of the data is the highest value - the lowest value.

The lowest in the list is 33 so the highest must be 33 + 58

= 91.

An ordered pair is written as (x, y)

P(-3) = 18

The -3 is the x value and the 18 is the y value

Answer: (-3,18)

Answer:

30 plus 70 equals 100

Step-by-step explanation:

it tells the gum explicit equation

Answer:

the first one is 4 and the second one is 0

Answer:

We want to find:

[tex]\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n}[/tex]

Here we can use Stirling's approximation, which says that for large values of n, we get:

[tex]n! = \sqrt{2*\pi*n} *(\frac{n}{e} )^n[/tex]

Because here we are taking the limit when n tends to infinity, we can use this approximation.

Then we get.

[tex]\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n} = \lim_{n \to \infty} \frac{\sqrt[n]{\sqrt{2*\pi*n} *(\frac{n}{e} )^n} }{n} = \lim_{n \to \infty} \frac{n}{e*n} *\sqrt[2*n]{2*\pi*n}[/tex]

Now we can just simplify this, so we get:

[tex]\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\[/tex]

And we can rewrite it as:

[tex]\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n}[/tex]

The important part here is the exponent, as n tends to infinite, the exponent tends to zero.

Thus:

[tex]\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n} = \frac{1}{e}*1 = \frac{1}{e}[/tex]

Answer:

1) the planning value for the population standard deviation is 10,000

2)

a) Margin of error E = 500, n = 1536.64 ≈ 1537

b) Margin of error E = 200, n = 9604

c) Margin of error E = 100, n = 38416

3)

As we can see, sample size corresponding to margin of error of $100 is too large and may not be feasible.

Hence, I will not recommend trying to obtain the $100 margin of error in the present case.

Step-by-step explanation:

Given the data in the question;

1) Planning Value for the population standard deviation will be;

⇒ ( 50,000 - 10,000 ) / 4

= 40,000 / 4

σ = 10,000

Hence, the planning value for the population standard deviation is 10,000

2) how large a sample should be taken if the desired margin of error is;

we know that, n = [ ([tex]z_{\alpha /2[/tex] × σ ) / E ]²

given that confidence level = 95%, so [tex]z_{\alpha /2[/tex]  = 1.96

Now,

a) Margin of error E = 500

n = [ ([tex]z_{\alpha /2[/tex] × σ ) / E ]²

n = [ ( 1.96 × 10000 ) / 500 ]²

n = [ 19600 / 500 ]²

n = 1536.64 ≈ 1537

b) Margin of error E = 200

n = [ ([tex]z_{\alpha /2[/tex] × σ ) / E ]²

n = [ ( 1.96 × 10000 ) / 200 ]²

n = [ 19600 / 200 ]²

n = 9604

c)  Margin of error E = 100

n = [ ([tex]z_{\alpha /2[/tex] × σ ) / E ]²

n = [ ( 1.96 × 10000 ) / 100 ]²

n = [ 19600 / 100 ]²

n = 38416

3) Would you recommend trying to obtain the $100 margin of error?

As we can see, sample size corresponding to margin of error of $100 is too large and may not be feasible.

Hence, I will not recommend trying to obtain the $100 margin of error in the present case.

Answer:

116 degrees

Explanation:

If we divide the triangle from the vertex of the triangle, the vertex angle of each triangle would lie on a straight line in the triangle. Angle on a straight line is 180 degrees.

If the vertex angle of one triangle is 64 degrees then the vertex angle x of the other triangle is 180 degrees - 64 degrees = 116 degrees.