c = √a² + b². This is the formula for the length of the hypotenuse c of a right triangle. Solve this formula for a.

The relationship between ∠E and ∠K is  ∠E = ∠K

Two lines are said to be parallel when they do not meet even at infinity and the distance between them always remains constant.

∠E = ∠G   ( vertical angles) ∠H = ∠F   ( vertical angles) ∠G = ∠K  (corresponding angles) From equations i) and iii)

we get ∠E  = ∠K and they are alternate exterior angles.

The measure of angle K can be found from the equation

 ∠K + ∠J = 180°    (consecutive interior angles)

∠K = 180° - ∠J

∠K + ∠L = 180°

∠K = 180° - ∠L

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Answer:

the tip should be 9 dollars

Step-by-step explanation:

20. A rational function [tex]\frac{p(x)}{q(x)}[/tex] (where [tex]p,q[/tex] are polynomials in [tex]x[/tex]) has a removable discontinuity at [tex]x=a[/tex] if for some positive integer [tex]n[/tex] we can factorize

[tex]p(x) = (x-a)^n p^*(x)[/tex]

[tex]q(x) = (x-a)^n q^*(x)[/tex]

[tex]\implies \dfrac{p(x)}{q(x)} = \dfrac{(x-a)^n p^*(x)}{(x-a)^n q^*(x)} = \dfrac{p^*(x)}{q^*(x)}[/tex]

That is, we "remove" the discontinuity at [tex]x=a[/tex] because while [tex]x\neq a[/tex], we have [tex]\frac{x-a}{x-a}=1[/tex]. The discontinuity is still there, since [tex]\frac{p(a)}{q(a)}[/tex] is undefined, but in the limit sense we can essentially ignore the factors of [tex]x-a[/tex]. The graph of [tex]\frac{p(x)}{q(x)}[/tex] will have all the features of [tex]\frac{p^*(x)}{q^*(x)}[/tex] aside from a hole at [tex]x=a[/tex].

In this case, we have

[tex]f(x) = \dfrac{x+4}{x^2-x-20} = \dfrac{x+4}{(x+4)(x-5)}[/tex]

and when [tex]x\neq-4[/tex], we can cancel the factor of [tex]x+4[/tex] so that

[tex]f(x) = \begin{cases}\dfrac1{x-5} & \text{if }x \neq -4 \\\\ \text{DNE} & \text{if }x = -4\end{cases}[/tex]

("DNE" = "does not exist", i.e. is undefined. For some reason "undefined" wouldn't render...)

This means [tex]x=-4[/tex] is a removable discontinuity.

We cannot do the same with the factor of [tex]x-5[/tex], so in contrast [tex]x=5[/tex] is a non-removable discontinuity.

21. The pieces of [tex]f(x)[/tex] defined on [tex]x<2[/tex] and [tex]x>2[/tex] are themselves continuous since they are polynomials. Then the continuity of [tex]f(x)[/tex] over the entire real line depends on the point where the pieces meet.

Here we have

[tex]f(x) = \begin{cases}x+3 & \text{if }x\le2 \\ cx+6 & \text{if }x>2\end{cases}[/tex]

so the pieces meet at [tex]x=2[/tex]. Continuity at this point requires that the both limits from either side of [tex]x=2[/tex] be the same. This means

[tex]\displaystyle \lim_{x\to2^-} f(x) = \lim_{x\to2} (x+3) = 2+3 = 5[/tex]

[tex]\displaystyle \lim_{x\to2^+} f(x) = \lim_{x\to2} (cx+6) = 2c + 6[/tex]

Solve for [tex]c[/tex].

[tex]2c + 6 = 5 \implies 2c = -1 \implies \boxed{c = -\dfrac12}[/tex]

Answer:

Step-by-step explanation:

The volume of the box is 99 unit cubes.

A cube is a three-dimensional object that has six faces, twelve edges and eight vertices. The length, width and height of a cube usually has equal dimensions. The volume of the box is a function of the dimension of the cubes in it and the number of layers.

Volume of a box = number of layers x amount of units

9 x 11 - 99 unit cubes

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Answer:

jdiddbhhuduh9ruruuehgruhrhudhheherj

The line which is described as in the task content has equation; (y - 6) = 12 (x-2).

From the task content, it follows that two points which can be used to evaluate the slope of the graph is positive.

Hence, the equation of the line in discuss is which passes through the points given is; (y - 6) = 12 (x-2) in which case, the positive slope number is 12.

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Answer:

1160cm squared

Step-by-step explanation:

as for me I've calculated the surface area of a closed cuboid.

this is because we are not informed whether it is open or closed.

and so my teacher told me that if you're not informed, if a cuboid is open or closed, just assume that the cuboid is closed.

and that is what I have done.

hope it helps.

in case of any questions feel free to ask.

Answer:

(A, B, C, D)

What is the sample space of the probability?

Sample space is the set of all possible outcomes of a random experiment.

Here given possible outcomes are A, B, C, D

Hence, Sample space of probability = (A, B, C, D), total 4 different choices

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Answer :

The set of all possible out in a random experiment is refer to as sample space.

The reading above is an example of discrete(finite) sample space.

Following the Discrete Probability Law if a sample space consist of a finite number ex:{1 ,2 ,3} . The probability is the sum of the probabilities of the elements.

Therefore answering a multiple choice questions with A,B,C and D are four choices with possible answer of A,B,C and D.

Supposing that 20 out of 100 people choose black or gray, the percentage is of 20%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

Hence, if 20 out of 100 people choose black or gray, the percentage is given by:

[tex]P = \frac{20}{100} \times 100\% = 20\%[/tex]

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By graphing the function, we can see that we have 3 real solutions and 2 non-real solutions.

To check this, we need to graph the equation and see how many times it intersects the x-axis.

Because the degree is 5, we know that there are 5 solutions in total.

Now if we look at the graph, we can see that it intersects the x-axis on 3 points, so there are 3 real solutions. And because there are 5 solutions in total, we conclude that the other 2 solutions are non-real.

So we have 3 real solutions and 2 non-real solutions.

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The population standard deviation is the standard deviation of the whole population denoted by sigma.

The sample mean is denoted by x bar and standard deviation by sx and it is the mean and standard deviation of the sample not the population from which the sample is chosen.

The data given in problem answers the first part.

The mean weight  of the sample denoted by  x bar x ¯ was two ounces with a standard deviation denoted by sx of 0.12 ounces.

The population standard deviation is denoted by σ known to be 0.1 ounce.

a. i. x ¯ =___2_____ ii. σ =___0.1_____ iii. sx =___0.12_____

e. Sub part i) 1.959 ; 2.041

Sub part iii) The error bound is 0.041

f. Sub Part i) 1.935 ; 2.065

Sub Part iii) The error bound is 0.0645

Part b)

The random variable X  is any number defining the weights of the  sample chosen from the population.

Part c)

The random variable X bar is the average weight of the sample obtained by adding the total weights of the sample divided by the number of the sample size.

Part d)

The normal distribution is used to solve the problem because the sample size is less than 30.

Part e

The 90 % confidence interval is calculated as ∝ = 1- 90%

∝ = 0.1

∝/2= 0.1/2= 0.05

xbar± z(∝/2) σ /√n

Putting the values

2± 1.645 (0.1)/√16

2± 0.041

or

Sub part i) 1.959 ; 2.041

Sub part iii) The error bound is 0.041

Part f

The 98 % confidence interval is calculated as ∝ = 1- 98%

∝ = 0.02

∝/2= 0.1/2= 0.01

xbar± z(∝/2) σ /√n

Putting the values

2± 2.58 (0.1)/√16

2± 0.0645

or

Sub Part i) 1.935 ; 2.065

Sub Part iii) The error bound is 0.0645

Part g

The confidence interval in part f is larger than the confidence interval in part e because we are 98 percent confident about the accuracy of the result. The interval is 0.01 for two tailed test which is very less as compared to 0.05 for 90% confidence interval.

The larger the area of the confidence interval less sure we are about the accuracy of the result hence getting a smaller value .

Part h

On the average 90 % of the 16 sample will have the true value of the mean.

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Answer:

1.1%

Step-by-step explanation:

To convert from percentage to decimal you simply divide by 100 so to convert from decimal to percentage you do the opposite, by multiplying by 11. In doing so, you get 1.1%. Think about it this way, if you wanted 100% of an item, you would basically just be multiplying by 1... which is 100% divided by 100. But if you wanted 50%, you would want half, or other in other words divide it in half, which is the same as multiplying by 0.50 which is 50% divided by 100

Answer:

  8,000,000 m²

Step-by-step explanation:

The largest rectangular area is enclosed when half the fence is used for sides in one direction, and the other half of the fence is used for sides perpendicular.

Here, no fence is needed on the river side, so 8000/2 = 4000 meters of fence will be used parallel to the river. The other 4000 m of fence will be split between the two ends of the enclosure, so its area will be ...

  4000 m × 2000 m = 8,000,000 m² . . . largest enclosed area

We can let x represent the length of fence perpendicular to the river. The amount of fence available for the side parallel to the river is ...

  L = 8000 -2x . . . . . the rest of the 8000 m of fence after 2 sides are used

The area is ...

  A = x(8000 -2x) = 2x(4000 -x) . . . . area is product of length and width

This equation for the area describes a parabola that opens downward and has zeros at x=0 and x=4000. Its maximum will be on the line of symmetry, halfway between these zeros. The value of x that gives maximum area is ...

  (0 +4000)/2 = 2000

The plot will extend 2000 meters out from the river and will have a length of ...

  8000 -2(2000) = 4000 . . . meters

The maximum area is (2000 m)(4000 m) = 8,000,000 m².

The attached graph shows area as a function of the dimension perpendicular to the river.

Stokes' theorem relates the surface integral of the curl of [tex]\vec F[/tex] across [tex]S[/tex] to the line integral of [tex]\vec F[/tex] along the boundary of [tex]S[/tex].

The boundary of [tex]S[/tex] is a circle with radius 7 centered at the origin in the [tex]x,y[/tex]-plane. Parameterize this path by

[tex]\vec r(t) = 7\cos(t)\,\vec\imath + 7\sin(t)\,\vec\jmath[/tex]

with [tex]0\le t\le2\pi[/tex]. Observe that [tex]z=0[/tex], so [tex]\cos(z) = 1[/tex] and the [tex]\vec\jmath[/tex]-component of [tex]\vec F[/tex] contributes nothing. The double integral then reduces to

[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec S = \int_0^{2\pi} \vec F(\vec r(t)) \cdot \frac{d\vec r}{dt} \, dt \\\\ ~~~~~~~~ = \int_0^{2\pi} \left(e^{49\cos(t)\sin(t)}\,\vec\imath + 49\cos(t)\sin(t)\,\vec\jmath\right) \cdot \left(-7\sin(t)\,\vec\imath + 7\cos(t)\,\vec\jmath\right) \, dt \\\\ ~~~~~~~~ = -7 \int_0^{2\pi} e^{49\cos(t)\sin(t)} \sin(t) \, dt[/tex]

Observe that by substituting [tex]t=u+\pi[/tex], we have

[tex]\sin(t) = \sin(u+\pi) = \sin(u)\cos(\pi) + \cos(u)\sin(\pi) = -\sin(u)[/tex]

so that the integral over [tex][\pi,2\pi][/tex] can be expressed in terms of the integral over [tex][0,\pi][/tex] as

[tex]\displaystyle \int_\pi^{2\pi} e^{49\cos(t)\sin(t)} \sin(t) \, dt = \int_0^\pi -e^{49\cos(t)\sin(t)} \sin(t) \, dt[/tex]

Then the integrals over [tex][0,\pi][/tex] and [tex][\pi,2\pi][/tex] cancel each other and integral of the curl of [tex]\vec F[/tex] is

[tex]\displaystyle -7 \int_0^{2\pi} e^{49\cos(t)\sin(t)} \sin(t) \, dt = -7 \int_0^\pi 0 \, dt = \boxed{0}[/tex]

Answer:

56.57 rounded to the nearest hundredths

Step-by-step explanation:

a^2 + b^2  =  c^2

20^2 + x^2 = 60^2

400 to x^2 = 3600

x^2 = 3200 take the square root of each side.

x = 56.57 rounded to the nearest hundredths

The correct difference between the expressions is 4z⁵. The correct option is the first option 4z⁵

From the question, we are to simplify the given expression by subtracting the expressions

The given expression is

-3z⁵ - (-7z⁵)

Clear the parenthesis by multiplying

-3z⁵ +7z⁵

Simplifying

4z⁵

The simplified form of the expression is 4z⁵

Hence, the correct difference between the expressions is 4z⁵. The correct option is the first option 4z⁵

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Given: the number is less than 20; three-factor pairs; each factor pair individually adds up to 19, 11, and 9

Solve for her number.

Step-by-step explanation:

If you think about it for a little bit, you will eventually find that 18 + 1 = 19 and 18 × 1 = 18 which is less than 20.

Then we know 18 has 2 more factor pairs : 9 × 2 and 6 × 3 which add up to 11 and 9.

Therefore our answer is: 18

18 × 1

9 × 2

6 × 3

The trick is to pick the largest sum of one-factor pair (19 in this question) and then choose the number below it.

Answer:

  C, E, D

Step-by-step explanation:

A "unit rate" is a rate that has 1 unit in the denominator. Here, the rates are all given in terms of the number of apples in 1 basket. (The 1 basket is the 1 unit.)

When rates are given with some number of units other than 1 in the denominator, divide the numerator by the denominator to find the unit rate.

Here, the unit rates are all more than one apple in each basket, so the number of apples must be a multiple of the number of baskets. Phrases "A" and "B" both have more baskets than apples, so will not be used.

  C: (304 apples)/(8 baskets) = (304/8) apples/basket = 38 apples/basket

  D: (294 apples)/(7 baskets) = (294/7) apples/basket = 42 apples/basket

  E: (405 apples)/(9 baskets) = (405/9) apples/basket = 45 apples/basket

  (38 apples)/(1 basket) = C: 38 apples/basket

  (45 apples)/(1 basket) = E: 45 apples/basket

  (42 apples)/(1 basket) = D: 42 apples/basket

The solution to the equation 3 and 4 by elimination is x = -2 and y = -2

2x = 3y + 2. (1)

3x = 5y + 4. (2)

2x - 3y = 2. (3)

3x - 5y = 4 (4)

6x - 9y = 6. (5)

6x - 10y = 8. (6)

-10y - (-9y) = 8 - 6

-10y + 9y = 2

-y = 2

y = -2

2x - 3y = 2. (3)

2x - 3(-2) = 2

2x + 6 = 2

2x = 2 - 6

2x = - 4

x = -4/2

x = -2

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Options A and D are having a slope equal to -3/5.

Given that the slope of the line is -3/5.

That is, m = -3/5

We need to find which ordered pairs could be points on a parallel line.

The formula for slope between two coordinates is m = (y₂ - y₁)/(x₂ - x₁).

Now,

Using (–8, 8) and (2, 2);

m = (2 - 8)/(2 - (-8))

⇒m = -6/10

⇒m = -3/5

Using (–5, –1) and (0, 2);

m = (2 - (-1))/(0 - (-5))

⇒m = 3/5

Using (–3, 6) and (6, –9);

m = (-9 - 6)/(6 - (-3))

⇒m = -15/9

⇒m = -5/3

Using (–2, 1) and (3, –2);

⇒m = (-2 - 1)/(3 - (-2))

⇒m = -3/5

Using (0, 2) and (5, 5);

m = (5 - 2)/(5 - 0)

⇒m = 3/5

We know that the condition for parallel lines slope is [tex]m_{1} =m_{2}[/tex].

Therefore, options A and D are having a slope equal to -3/5.

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The number is 6400.

We have given that,

divided 80 by my number, and then added 13.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Suppose the number is x

[tex]\frac{x}{80}+13=93[/tex]

Subtract  13  from both sides

[tex]\frac{x}{80}+13-13=93-13[/tex]

[tex]\frac{x}{80}=80[/tex]

Multiply both sides by 80

[tex]\\\frac{80x}{80}=80\cdot \:80[/tex]

x=6400

Therefore the number is 6400.

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The surface area of the solid formed is approximately, 598.3 in².

Surface area of the solid is the area covered by the solid all round.

The given parameters are:

Surface area of the solid formed = 5(10×10) + (0.5×10×8.67) + 3(10×1.83) = 598.3 in²

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Answer:

Step-by-step explanation:

Answer:

16 I can't find the lengths but Angle A = Angle B = Angle C = 60 degrees.

17 X = 55 degrees, Y = 60 degrees, Z = 65 degrees.

18 Angle B and Angle C

19 BC and AC

20 They are all 60 degrees and are all equal to each other.

Hope I helped!

Answer:

The last investment (C) has the least interest of $600

The other two investments (A and B) have the same amount of interest of $1800.

Step-by-step explanation:

Simple Interest Formula

I = Prt

where:

Investment A

Substitute the given values into the formula and solve for I:

⇒ I = 2000(0.1)(9)

⇒ I = $1800

Investment B

Substitute the given values into the formula and solve for I:

⇒ I = 3000(0.03)(20)

⇒ I = $1800

Investment C

Substitute the given values into the formula and solve for I:

⇒ I = 2000(0.1)(3)

⇒ I = $600

The last investment (C) has the least interest of $600.

The other two investments (A and B) have the same amount of interest of $1800.

Step-by-step explanation:

I guess that means

1.05 / 2.1

or

1.05 ÷ 2.1

both mean the same thing.

so, let's look at

1.05 / 2.1

this is the same as

105/100 / 210/100 = (105×100) / (210×100) =

= (105×100) / (210×100) × (1/100 / 1/100)

as long as we multiply numerator (top) and denominator (bottom) always with the same thing, the general fraction or division is unchanged.

(105×100) / (210×100) × (1/100 / 1/100) =

= (105 × 100/100) / (210 × 100/100) = 105 / 210

so, yes, the division of 105 / 210 is the same as 1.05 / 2.1

Answer:

0.87

Step-by-step explanation:

After decreasing new value would be : 100%  - 13% = 87%

87 % = 87/100 = 0.87

Renting a car on a monthly basis after 19 days makes it cheaper than renting on a daily basis.

How to solve such questions?

The key concept for solving such questions is by calculating the number of days on which both renting a car on a monthly basis equals renting a car on daily basis. So on the very next day as renting a car on daily basis still adds up the expense it will become costlier and renting a car on monthly basis makes it cheaper.

Given:-

Cost of renting car on a daily basis = $40

Cost of renting car on a monthly basis = $750

Let number of days on which both renting a car on a monthly basis equals renting a car on daily basis be x.

Therefore

40 × x = 750

x =  [tex]\frac{750}{40}[/tex]

x = 18.75 days

From 19th day onwards cost of renting on a daily basis will exceed cost of renting car on a monthly basis.

Thus , Renting a car on a monthly basis after 19 days makes it cheaper than renting on a daily basis.

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