find the unknown angles

Answer:

97.98

Step-by-step explanation:

The area of the parallelogram PQR is the magnitude of the cross product of any two adjacent sides. Using PQ and PS as the adjacent sides;

Area of the parallelogram = |PQ×PS|

PQ = Q-P and PS = S-P

Given P(0,0,0), Q(4,-5,3), R(4,-7,1), S(8,-12,4)

PQ = (4,-5,3) - (0,0,0)

PQ = (4,-5,3)

Also, PS = S-P

PS = (8,-12,4)-(0,0,0)

PS = (8,-12,4)

Taking the cross product of both vectors i.e PQ×PS

(4,5,-3)×(8,-12,4)

PQ×PS = (20-36)i - (16-(-24))j + (-48-40)k

PQ×PS = -16i - 40j -88k

|PQ×PS| = √(-16)²+(-40)²+(-88)²

|PQ×PS| = √256+1600+7744

|PQ×PS| = √9600

|PQ×PS| ≈ 97.98

Hence the area of the parallelogram is 97.98

Answer:

It is over then 749mm. so 800mm.

If it is less or same as 749mm, It is 700mm.

Answer:

[tex]\huge \boxed{\mathrm{800 \ mm}}[/tex]

Step-by-step explanation:

765 mm to nearest 100 mm would be to round up 765 to nearest hundred.

765 rounded up to nearest hundred’s place would be 800.

The place after 7 is 6, which is higher or equal to 5, so we add 1 to the hundred’s place followed by zeros.

Answer:

0.6048

Step-by-step explanation:

Given the following :

Assume a normal distribution :

Mean (m) = 105

Standard deviation (sd) = 20

Find the probability that a randomly selected adult has an IQ between 88 and 122 .

Z = (x - m) / sd

For IQ score of 88:

Z = (88 - 105) / 20

Z = (-17) / 20

Z = - 0.85

For IQ score of 122:

Z = (122 - 105) / 20

Z = (17) / 20

Z = 0.85

P(-0.85<Z<0.85) = P(Z < 0.85) - P(Z < - 0.85)

P(-0.85<Z<0.85) = (0.8023 - 0.1977)

P(-0.85<Z<0.85) = 0.6048

Answer:

24

Step-by-step explanation:

first 2×2=4

then 16÷4

4×6

24

Answer:

10

Step-by-step explanation:

Cube root of 1000

That's 10

Answer:

Calculator to find all the properties of a cube given any one property. ... Definition: The number of cubic units that will exactly fill a cube. Try this ... The volume of a cube is found by multiplying the length of any edge by itself twice.

Rodell needs a larger sample size than two sports teams to represent a whole school.

Important Information : Study is conducted about favourite gaming app among students at school, 30 & 15 students of football & basketball team are polled.

Finding : Issue in Rodell's method of collecting data

The issue in this sampling : Rodell needs a larger sample size than two sports teams to represent a whole school.

Sample selected from universe should be very carefully chosen, to be a good representative of universe.

Here, Rodell has chosen only two sports' team members as sample for the study of favourite gaming app. Such kind of sample having more uneven concentration of any type of population members doesn't denote sample being a good representative of population.

To learn more Sampling, refer https://brainly.com/question/24842573?referrer=searchResults

Answer:

93 miles

Step-by-step explanation:

Use the distance formula:

d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]

Plug in the values:

d = [tex]\sqrt{(121 - 57)^2 + (79 - 11)^2}[/tex]

d = [tex]\sqrt{4096 + 4624}[/tex]

d = [tex]\sqrt{8720}[/tex]

d = 93.4

= 93 miles

Answer:

93 miles.

Step-by-step explanation:

To find this answer, we can use the distance formula: D= SQ root of (X2 - X1)^2 + (Y2-Y1)^2

Then, we have to plug in the corrdinates accordingly:

D = SQ root of (121 - 57)^2 + (79 - 11)^2

D = SQ root of (64^2) + (68^2)

D = SQ root of 4096 + 4624

D = SQ root of 8720

D = 93.3809402394

D rounded to the nearest mle is 93 miles

Hope this helps :)

Answer:

44 in

Step-by-step explanation:

The circumference of the tire will be the same as the distance the unicycle moves in one complete revolution.

Find the circumference with the formula C = [tex]\pi[/tex]d, where d is the diameter

Plug in the values:

C = [tex]\pi[/tex](14)

C = approx. 44 in

Answer:

Below

Step-by-step explanation:

● 2w^2 (w+6) + 7(w+6)

● (w+6) (2w^2 + 7)

Answer/Step-by-step explanation:

To complete the table, given the function,   [tex] f(x) = \frac{1}{3}x^2 [/tex], plug in each value of x to find f(x).

Thus:

x = -6

[tex] f(-6) = \frac{1}{3}(-6)^2 = \frac{1}{3}(36) [/tex]

[tex] f(-6) = 12 [/tex]

[tex] f(-3) = \frac{1}{3}(-3)^2 = \frac{1}{3}(9) [/tex]

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

[tex] f(0) = \frac{1}{3}(0)^2 = \frac{1}{3}(0)  [/tex]

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

[tex] f(3) = \frac{1}{3}(3)^2 = \frac{1}{3}(9) [/tex]

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

[tex] f(6) = \frac{1}{3}(6)^2 = \frac{1}{3}(36) [/tex]

[tex] f(6) = 12 [/tex]

Answer: 0.0682

Definition

Numerical: It's involving only numbers.

This means we will convert this number from word into numbers.

Answer:

Step-by-step explanation:

682.010

Answer:

Step-by-step explanation:

Computation:

Length of arc = Θ/360[2πr]

20 = Θ/360(2)(22/7)(24)

Θ = 47.72°

Angel = 47.72° (Approx)

Length of arc = Θ/360[2πR]

10 = [47.72 / 360][2][22/7][R]

R = 12 cm

Radius of the smaller sector = 12 cm

Perimeter of the shape = 20 + 24 + 24

Perimeter of the shape = 68 cm

Answer:

d ≈ 8.5

Step-by-step explanation:

Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Simply plug in our 2 coordinates into the formula:

d = √[(5 + 3)² + (-2 - 1)²]

d = √[(8)² + (-3)²]

d = √(64 + 9)

d = √73

d = 8.544

d ≈ 8.5

Answer:

D. 13*3^x

Step-by-step explanation:

[tex]3^x +4*3^x^+^1= \\3^x+4*3(3^x)=\\3^x(1+[4*3])=\\3^x(1+12)=\\3^x(13)=\\13*3^x[/tex]

The solution of 3ˣ + 4·3ˣ⁺¹ is 13·3ˣ which is the correct answer would be an option (D)

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

⇒ 3ˣ + 4·3ˣ⁺¹

⇒ 3ˣ + 4·3ˣ3¹

⇒ 3ˣ( 1 + 4·3)

⇒ 3ˣ( 1 + 12)

⇒ 3ˣ(13)

⇒ 13·3ˣ

Hence, the solution of 3ˣ + 4·3ˣ⁺¹ is 13·3ˣ which is correct answer would be option (D)

Learn more about exponential function here:

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Answer:

12950

Step-by-step explanation:

comedy : 20% => 20 × 18500 ÷ 100 = 3700

drama : 23% => 23 × 18500 ÷ 100 = 4255

other : 27% => 27 × 18500 ÷ 100 = 4995

all together: (20 + 23 + 27) × 18500 ÷ 100 = 3700+4255+4995 = 12950

The solution is 12950.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

from the given graph, we get,

comedy : 20%

=> 20 × 18500 ÷ 100

= 3700

drama : 23%

=> 23 × 18500 ÷ 100

= 4255

other : 27%

=> 27 × 18500 ÷ 100

= 4995

so, we get,

all together: (20 + 23 + 27) × 18500 ÷ 100

                   = 3700+4255+4995

                   = 12950.

To learn more on percentage click:

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Answer:

The number is 12

Step-by-step explanation:

Let x = number

2x+16 = 40

Subtract 16 from each side

2x+16-16 =40-16

2x = 24

Divide by 2

2x/2 =24/2

x = 12

Answer:

A 99% confidence for the true population mean watermelon weight is [56.77 ounces, 63.23 ounces] .

Step-by-step explanation:

We are given that you measure 46 watermelons' weights, and find they have a mean weight of 60 ounces.

Assume the population standard deviation is 8.5 ounces.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{} n} }[/tex]  ~  N(0,1)    

where, [tex]\bar X[/tex] = sample mean weight = 60 ounces

             [tex]\sigma[/tex] = population standard deviation = 8.5 ounces

             n = sample of watermelons = 46

             [tex]\mu[/tex] = population mean watermelon weight

Here for constructing a 99% confidence interval we have used a One-sample z-test statistics because we know about the population standard deviation.

So, 99% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.58 < N(0,1) < 2.58) = 0.99  {As the critical value of z at 0.5% level  

                                                     of significance are -2.58 & 2.58}  

P(-2.58 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{} n} }[/tex] < 2.58) = 0.99

P( [tex]-2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] ) = 0.99

P( [tex]\bar X-2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] ) = 0.99

99% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] , [tex]\bar X+2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] ]

                                            = [ [tex]60-2.58 \times {\frac{8.5}{\sqrt{46} } }[/tex] , [tex]60+2.58 \times {\frac{8.5}{\sqrt{46} } }[/tex] ]

                                            = [56.77 ounces, 63.23 ounces]

Therefore, a 99% confidence for the true population mean watermelon weight is [56.77 ounces, 63.23 ounces] .

Answer:

-727.5034 and 2464.2534

Step-by-step explanation:

Find explanation in the attachment

Answer:

Standard deviation of the binomial distribution

                               = [tex]\sqrt{n p q} = \sqrt{192} = 13.856[/tex]

Step-by-step explanation:

Explanation:-

Given size 'n' = 800

The population proportion 'p'=0.6

Let 'X' be the random variable of the binomial distribution

a)  mean of the binomial distribution  = n p = 800 ×0.6

                                                             μ  = 480

b)  variance of the binomial distribution

                                                                      = n p q

                                                                      =  800 X 0.6 ×0.4

                                                                 σ²  = 192

Standard deviation of the binomial distribution

                                                             σ    = [tex]\sqrt{n p q} = \sqrt{192} = 13.856[/tex]

Answer:

1.0000

Step-by-step explanation:

It is know that 20% of air bags produced by the manufacturing plant are defective.

20% of x

Therefore, the probability that two are defective will be

20/100 × 5

0.2×5=1.0000

answer

20

Step-by-step explanation:

I think you mean for times the difference of seven and 12 or (12-7)×4 if not sorry

Answer: 10

Step-by-step explanation:

4(x - 7) = 12

x - 7 = 3

x = 10

Answer:

108 skittles

Step-by-step explanation:

If she divides a bag of 324 skittles between 3 people, then we want to find a third of 324 - aka [tex]324\div3[/tex].

324 divided by 3 is 108, so each person will get 108 skittles.

Hope this helped!

Answer:

lim x->0 (-8+x)/x^2

just plug in x = 0

(-8+0)/0

now this fraction is a negative number divided by 0.

So, it equals -infinity.

The limit value is infact -infinity,

so the given option, "Does Not Exit" is the best choice.

Answer:

17523° Celsius

Step-by-step explanation:

using the formula c=59(F-32), you have to plug the 329 into F like so-

C=59(329-32)

and then you're free to calculate! first you distribute the 59 like so...

C= (59 times 329)(59 times -32) getting C=19411-1888 which u then solve again to get 17523° Celsius

Answer:

17.

Step-by-step explanation:

Divide 2225 by 24 and round down. (92) Multiply 92 by 24 and subtract that (2208) from the total number (2225). you get 17

Answer:

The answer is 90 degrees

Step-by-step explanation:

Both A and B make a right angle, which is 90 degrees.

Hope it helped :)

The value of m∠A + m∠B is 90°

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

Three lines intersect to form 5 angles such that:

From the top left ∠B made and after this 90° made.

∠D = 124°

From the figure, we can clearly see ∠A = ∠C (vertically opposite angles)

We can calculate ∠C = 360°-90°-90°-124° ⇒ 56°

Also ∠A = 56°

and ∠B = 90° - 56° ⇒ 34°

Now we can calculate the sum of the angle ∠A+∠B = 56+34 ⇒ 90°

Thus, the value of m∠A + m∠B is 90°

Learn more about the vertically opposite angles here:

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Answer:

Step-by-step explanation:

2/(5d-77)=55

2=55(5d-77)

2/55=5d-77

5d=2/55 + 77

d = (2/55 + 77)/5

Hope you can calc that yourself

Answer:

  x = 25

Step-by-step explanation:

Make use of the fact that the sum of angle measures in a triangle is 180°.

  (2x+15)° +(3x+5)° +(x+10)° = 180°

  6x +30 = 180 . . . collect terms, divide by °

  x +5 = 30 . . . . . . divide by 6

  x = 25 . . . . . . . . . subtract 5

_____

Check

This value of x makes the angle measures be ...

  A = (x+10)° = 35°

  B = (3x+5)° = 80°

  C = (2x+15)° = 65°

These angles total 180°.

Answer:

$465.50

Step-by-step explanation:

Let the price be x, then: