Find the area of the parallelogram with vertices:________.
P(0,0,0), Q(4,-5,3), R(4,-7,1), S(8,-12,4).

Hi there! Hopefully this helps!

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[tex]p - 18 = 3[/tex]

Add 18 to both sides.

[tex]p = 3 + 18[/tex]

Answer:

hope this attachment will help you

Answer:

Step-by-step explanation:

Deposit made                                =   + $ 100 . 00

withdrawal made                           =   - $ 60 .00

check of last month encashed      =   - $ 87 . 90

interest paid by bank                       = + $ 00 . 23

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

Net effect                                           = - $ 47.67

the account balance reduces by amount = $ 47.67

Answer:

5...is the width of the rectangle .

Answer:

$37500

Step-by-step explanation:

For this we can simply create a proportion of the percentages.

.4 / 1 == 15000 / x

Now we solve for x:

x = 15000/.4

x = 37500

Thus, the cost of the car was $37,500.

Cheers.

Answer:

Following are the answer to this question:

Step-by-step explanation:

For Option a:

Its optimal mixed approach for Player A's to Player A  

A1 with a chance of .05 utilizing technique  

Using the .60 chance strategy for A2  

Use the .35 possibility strategy for A3  

For Option b:

Optimal level mixed approach for team B:  

Use the strategy for B1 with a probability of 50  

Using the chance strategy for B2 at .50  

no  use strategy for B3  

For Option c:

The estimated gain of Player A will be= 3.500

For Option d:

The estimated loss of Player B will be 3.500

.066

1 Centimeter = 0.03280839895 Feet

The conversion of 2 centimeters into feet would be 0.066 feet.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.

We have to determine the conversion of 2 centimeters into feet.

Since one centimeter = 0.03280839895 feet

Therefore two centimeters = 2×0.03280839895 feet

⇒ two centimeters = 0.0656167

Round the answer to the nearest hundredth.

⇒ two centimeters = 0.066

Therefore, the conversion of 2 centimeters into feet would be 0.066 feet.

Learn more about the number system here:

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Answer:

The answer is in the image.

Step-by-step explanation:

Answer:

Cone- 1 isosceles triangle revolved 180° about its height

2 isosceles triangle revolved 180° about its height

cylinder 1 rectangle revolved 180° about either axis of symmetry

2 revolved 360° about any side

Step-by-step explanation: plato edmentum

Answer:

uoooooohuuuuuuuuuuuihouu

Answer:

the Answer what have to be the fist bc c is the only on that is not with a ,g or b

Step-by-step explanation:

Answer:

The series converges to   [tex]$ \frac{1}{1-9x} $[/tex]     for   [tex]$ \frac{-1}{9} < x < \frac{1}{9} $[/tex]                

Step-by-step explanation:

Given the series is     [tex]$ \sum_{n=0}^{\infty} 9^n x^n $[/tex]

We have to find the values of x for which the series converges.

We know,

[tex]$ \sum_{n=0}^{\infty} ar^{n-1} $[/tex] converges to  (a) / (1-r) if r < 1

Otherwise the series will diverge.

Here, [tex]$ \sum_{n=0}^{\infty} 9^n x^n = \sum_{n=0}^{\infty} (9x)^{n} $[/tex] is a geometric series with |r| = | 9x |

And it converges for |9x| < 1

Hence, the given series gets converge for [tex]$ \frac{-1}{9} < x < \frac{1}{9} $[/tex]

And geometric series converges to [tex]$ \frac{a}{1-r} $[/tex]

Here, a = 1 and r = 9x

Therefore, [tex]$ \frac{a}{1-r} = \frac{1}{1-9x} $[/tex]

Hence, the given series converges to   [tex]$ \frac{1}{1-9x} $[/tex]     for   [tex]$ \frac{-1}{9} < x < \frac{1}{9} $[/tex]

Answer:

Axioms are generally statements made about real numbers. ... Sometimes they are called algebraic postulates. Often what they say about real numbers holds true for geometric figures, and since real numbers are an important part of geometry when it comes to measuring figures, axioms are very useful

Answer:

Length = 20 metres

Width = 10 mteres

Step-by-step explanation:

Let the width be x metres

Let the length be 2x metres

Perimeter = 60 metres

therefore, by the problem ,

2(length+breadth)= perimeter

=>2(2x+x)=60

=>2 *3x=60

=>6x=60

=>x=10

length = 20 metres

width = 10 mteres

Answer:

Step-by-step explanation:

70 ÷ 15 = 4.66

4.66 × 39 = 181.974

Answer:

15.38%

Step-by-step explanation:

there are four 10 cards and four jack cards.

4+4=8

you want to get one from 52 cards, so it's 8 out of 52. 8/52

to calculate the percentage, you multiply 8 by 100, then divide by 52.

8*100/52=15.38 (rounded answer)

Answer:

The weight of luggage for a flight with 142 passengers is 2,106

Step-by-step explanation:

The total weight of luggage stored in the baggage compartment can be estimated by the least squares regression equation:

y=118+14*x

where y is the total weight of luggage stored in the luggage compartment and x is the number of passengers on a bus.

If you want to predict the weight of luggage for a flight with 142 passengers, this means that x must have a value of 142. So, replacing in the expression:

y=118+14*142

you get:

y=118+1,988

y=2,106

The weight of luggage for a flight with 142 passengers is 2,106

Step-by-step explanation:

one-tenth of 19,548 is 1954.8

Answer:

Step-by-step explanation:

[tex]3x+ 2y=18\\\\Let \:x\:equal\:to\:0\\\\3(0)+2y=18\\\\0+2y=18\\\\2y=18\\\\Divide \:both\:sides\:of\:the\:equation\:by \:2\\\frac{2y}{2} =\frac{18}{2} \\\\y =9\\(0,9)[/tex]

Answer:

y = 9

Step-by-step explanation:

3x + 2y = 18

required:

find the y-intercept

we have to eliminate x to get the y intercept value

3(0) + 2y = 18

2y = 18

y = 18/2

y = 9

so the x & y intercept would be (0, 9)

Step-by-step explanation:

Using Point - Slope formula :

[tex](y - y_1) = \frac{(y_2 - y_1)}{(x_2 - x_1)} (x - x_1)[/tex]

[tex](y - 5) = \frac{2}{4} (x - 3)[/tex]

2y - 10 = x - 3

[tex]y = \frac{1}{2} x + \frac{7}{2} [/tex]

m = 1 / 2

b = 7 / 2

Answer:

10 hours

Step-by-step explanation:

speed = distance/time

s = d/t

d = st

d = 75 km/h * 8 h = 600 km

t = d/s

t = 600 km/(60 km/h) = 10 h

Answer: 10 hours

Answer:

The question is incomplete. The complete table is:      

Score in percent (X): 80, 75, 70, 90, 95, 100, 75, 60, 75, 95

Time in minute (Y) : 45, 48, 40, 50, 40, 30, 30, 39, 38, 55

The answer is 0.55 %

Step-by-step explanation:

ΣX = 815

ΣY = 425

ΣX x Y = 34565

Σ = 67925

Σ[tex]$Y^2$[/tex] = 18699          

So, correlation coefficient, b

[tex]$b= \frac{n \Sigma XY- \Sigma X \Sigma Y}{\sqrt{n \Sigma X^2-( \Sigma X)^2} \times \sqrt{(n \Sigma Y^2 -(\Sigma Y)^2}}$[/tex]

[tex]$b = \frac{(10 \times 34565)-(815 \times 425)}{\sqrt{(10 \times 67925)-(815)^2} \times \sqrt{(10 \times 10699)-(425)^2}}$[/tex]

[tex]$b= -\frac{725}{9779 \times 2702}$[/tex]

b = -0.0741

Correlation Determination:

[tex]$B^2 = (-0.0741)^2$[/tex]

    = = 0.0055 = 0.55%

Therefore,  0.55 percentage of the variation in y can be explained by x variable.

Answer:

5/13 (irreducible)

Step-by-step explanation:

1/3=2/6=3/9=4/12 are all thirds of the total.

Answer: [tex]\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV[/tex] = 1087.5

Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = [tex]\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right][/tex][tex]\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right][/tex]

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

[tex]a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0[/tex]

Then, replacing with point P and normal vector n:

[tex]36(x-5) + 20(y-0) + 45(z-0) = 0[/tex]

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

[tex]z = \frac{180-36x-20y}{45}[/tex]

When z = 0:

[tex]y = 9 + \frac{-9x}{5}[/tex]

When z=0 and y=0:

x = 5

Then, triple integral is:

[tex]\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx[/tex]

Calculating:

[tex]\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx[/tex]

[tex]\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx[/tex]

[tex]\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}} \, dy } \, dx[/tex]

[tex]\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx[/tex]

[tex]\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx[/tex]

[tex]\frac{1}{45} [30375-60750+118462.5-39150][/tex]

[tex]\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx[/tex] = 1087.5

The volume of the tetrahedon is 1087.5 cubic units.

The tripple integration will be   [tex]\int\limits^a_E \int\limits^a_E \int\limits^a_E {xy} \, dV[/tex] = 1087.5

The triple integration is used to identify the volumes of the objects or for analyzing three dimension of the object.

To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedron is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = [tex]\left[\begin{array}{ccc}i&j&k\\5&-9&-0\\0&9&-4\end{array}\right] \left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right][/tex]

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

[tex]a(x-x_o)+b(y-y_o)+c(z-z_o)=0[/tex]

Then, replacing with point P and normal vector n:

[tex]36(x-5)+20(y-0)+45(z-0)=0[/tex]

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

[tex]z=\dfrac{180-36x-20y}{45}[/tex]

When z = 0:

[tex]y=9+\dfrac{-9x}{5}[/tex]

When z=0 and y=0:

x = 5

Then, triple integral is:

[tex]\int\limits^5_0 \int\int xy\ dzdydx[/tex]

Calculating:

[tex]\int\limits^5_0 \int\int xy\ dzdydx[/tex]

[tex]\int\limits^5_0 \int\int xy\ (\dfrac{180-36x-20y}{45}-0)dydx[/tex]

[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 180xy-36x^2y-20xy^2dydx[/tex]

[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 90xy^2-18x^2y^2-\dfrac{20}{3}xy^3dydx[/tex]

[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 2430x-1458x^2+\dfrac{94770}{125}x^3-\dfrac{23490}{375}x^4dx[/tex]

[tex]\dfrac{1}{45} [30375-60750+118462.5-39150][/tex]

[tex]\int\limits^5_0 \int\int xy\ dzdydx=1087.5[/tex]  

The volume of the tetrahedron is 1087.5 cubic units.

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Answer: Population

Step-by-step explanation: Population is refers to the whole or entire members or of a given set. This is different from a sample which is used to refer to members of a subset (a subset is a certain portion or fraction of an entire set). In the scenario above, since the evaluation was based on the entire number of registered voters in the country, this means we are referring to a population. The inference about the percentage of democratic voters was drawn from a pool of all the entire number of registered voters available in the country and not from a certain subset or portion of registered voters. Hence, the evaluated group is a population.

Answer:

600 Ω see attachement

Step-by-step explanation:

Answer:

1. 770

2. 13.31

Step-by-step explanation:

n = 1000

P (probability of those with account) = 23% = 0.23

q(probability of those without account) = 1-p = 0.77

a. We are expected to find the expected number of those without checking account

= n * q

= 1000 * 0.77

= 770

b. Standard deviation

= √n*p*t

= √1000x0.77x0.23

= √177.1

= 13.31

Answer:

  3×5×53

Step-by-step explanation:

You can use divisibility rules to find the small prime factors.

The number ends in 5, so is divisible by 5.

  795/5 = 159

The sum of digits is 1+5+9 = 15; 1+5 = 6, a number divisible by 3, so 3 is a factor.

  159/3 = 53 . . . . . a prime number,* so we're done.

795 = 3×5×53

_____

* If this were not prime, it would be divisible by a prime less than its square root. √53 ≈ 7.3. We know it is not divisible by 2, 3, or 5. We also know the closest multiples of 7 are 49 and 56, so it is not divisible by 7. Hence 53 is prime.

Answer:

The  correct option is C

Step-by-step explanation:

From the question we are told that

   The sample size is  [tex]n = 2500[/tex]

    The sample  proportion is  [tex]\r p = 0.21[/tex]

    The margin of error is  [tex]E = 0.054[/tex]

The  90% confidence interval is  mathematically represented

         [tex]\r p - E < p < \r p + E[/tex]

=>      [tex]0.21 - 0.054 < p < 0.21 + 0.054[/tex]

=>      [tex]0.156< p < 0.264[/tex]