which of the following demonstrates how the first 21 on the left side of the triangle is calculated using the combination pattern?

Answer:

lmkjhvjgcfnhjkhbmgnc gfghh

Step-by-step explanation:

Explanation:

For any quadrilateral that is inscribed in a circle, ie has all four points on the circle like this, the opposite angles are always supplementary. They add to 180 degrees.

x+125 = 180

x+125-125 = 180-125 ... subtract 125 from both sides

x = 55

Answer:

A. 0.89.

Step-by-step explanation:

The value of correlation coefficient ranges from -1 to 1. Any value outside this range cannot possibly be correlation coefficient of a scatter plot representing relationship between two variables.

The scatter plot given shows a positive correlation between average daily temperatures and number of visitors, as the trend shows the two variables are moving in the same direction. As daily temperature increases, visitors also increases.

From the options given, the only plausible correlation that can represent this positive relationship is A. 0.89.

Answer:

D.

m = 2 = figures/month

b = 20 = # of action figures

Answer:

The  probability is  [tex]P(X < 900 ) = 0.0918[/tex]

Step-by-step explanation:

From the question we are told that

   The sample mean is  [tex]\= x = 1100[/tex]

    The  standard deviation is  [tex]\sigma = 150[/tex]

     The random number value is  x =900

The probability that a trainee earn less than 900 a month is mathematically represented as

       [tex]P(X < x) = P(\frac{X -\= x}{\sigma} < \frac{x -\= x}{\sigma} )[/tex]

Generally the z-value for the normal distribution is mathematically represented as

       [tex]z = \frac{x -\mu }{\sigma }[/tex]

So From above we have

      [tex]P(X < 900 ) = P(Z < \frac{900 -1100}{150} )[/tex]

      [tex]P(X < 900 ) = P( Z <-1.33)[/tex]

Now from the z-table

    [tex]P(X < 900 ) = 0.0918[/tex]

Answer:

I think that is the C

Step-by-step explanation:

Answer:

Option B is the correct answer.

Step-by-step explanation:

here, arc RT =162°

as in question given that the value of arc RT is 162° the value of angle RST is 1/2 of 162°.

so, its value must be 81°only.

hope it helps..

Answer:

[tex] \boxed{\sf Area \ of \ the \ rectangle = 91 \ yd^{2}} [/tex]

Given:

Length of the rectangle = 4 yd longer than its width

Perimeter of the rectangle = 36 yd

To Find:

Area of the rectangle

Step-by-step explanation:

Let the width of the rectangle be 'w' yd

So,

Length of the rectangle = (w + 4) yd

[tex] \therefore \\ \sf \implies Perimeter \: of \: the \: rectangle = 2(Length + Width) \\ \\ \sf \implies 36 = 2((4 + w) + w) \\ \\ \sf \implies 36 = 2(4 + w + w) \\ \\ \sf \implies 36 = 2(4 + 2w) \\ \\ \sf 36 =2(2w+4) \: is \: equivalent \: to \: 2(2w + 4) = 36: \\ \sf \implies 2(2w + 4) = 36 \\ \\ \sf Divide \: both \: sides \: of \: 2 (2w + 4) = 36 \: by \: 2: \\ \sf \implies 2w + 4 = 18 \\ \\ \sf Subtract \: 4 \: from \: both \: sides: \\ \sf \implies 2w = 14 \\ \\ \sf Divide \: both \: sides \: of \: 2w = 14 \: by \: 2: \\ \sf \implies w = 7[/tex]

So,

Width of the rectangle = 7 yd

Length of the rectangle = (7 + 4) yd

= 13 yd

[tex] \therefore \\ \sf Area \ of \ the \ rectangle = Length \times Width \\ \\ \sf = 7 \times 13 \\ \\ \sf = 91 \: {yd}^{2} [/tex]

Answer:

n = 17

Step-by-step explanation:

Assuming

- probability of success (making free throw) does not vary

We have

n = 17 (trials)

p = 0.479

x > 9

The answer is "[tex]\bold{p(x>9)=0.2550319}[/tex]"

[tex]\to X:[/tex] Number of creating free throws in a set [tex]\bold{17\ \ x \sim bin(17,0.479)}[/tex]

Know we calculating the P(makes more than 9 of them)

[tex]=\bold{9(X>9)=1-P(Z<=9)}[/tex]

Using the R-code:

[tex]\to \bold{1-p\ binom(9,17,0.479)}\\\\\to \bold{[1]0.2550319}\\\\\bold{\therefore}\\\\ \to \bold{p(x>9)=0.2550319}[/tex]

Learn more:

binomial distribution: brainly.com/question/9065292

Answer:

see explanation

Step-by-step explanation:

Pythagorean Theorem

7² + 8² = x²

49 + 64 = x²

113 = x²

x = √113 or 10.63

Distance Formula

√(-4 - 4)² + (4 - -3)²

= √8² + 7²

= √113 or 10.63

the bag is 200g

total weight with oranges is 1400g

deduct the bags weight from total weight

1400 - 200

1200g

this is the weight of the three oranges

so each orange would be

1200 ÷ 3

400g

Answer:

A

Step-by-step explanation:

[tex]g(x) = \frac{3}{{x}^{2} + 2x} \\ {x}^{2} + 2x - \frac{3}{g(x)} = 0 \\ x = \frac{1}{2} \Big( - 2 + \sqrt{12 + \frac{12}{g(x)} }\Big) \\ x = - 1 + \sqrt{1 \pm \frac{3}{g(x)} } [/tex]

Now replace $x$ by $g^{-1}(x)$ and $g(x)$ by $x$ and you have your answer.

Answer:

Step-by-step explanation:

(4x³ - 5x² + 3x ) - 4(5x² - 7x³ - 8x)

Remove the brackets and simplify.

We have

4x³ - 5x² + 3x - 20x² + 28x³ + 32x

Group like terms and simplify

That's

4x³ + 28x³ - 5x² - 20x² + 3x + 32x

We have the final answer as

- 3 - ( 4x + 3y - 2z ) - 4 + 2( 5x - 4y + 6z)

Remove the brackets and simplify

That's

- 3 - 4x - 3y + 2z - 4 + 10x - 8y + 12z

Group like terms and simplify

- 4x + 10x - 3y - 8y + 2z + 12z - 3 - 4

We have the final answer as

Hope this helps you

Answer:

x= -5, -1

Step-by-step explanation:

To find the zeroes of a function,

First expand the terms to get the form  [tex]ax^{2} + bx +c[/tex] where 'a, b, and c' are constants

     [tex]f(x)= (x+3)^{2} -4[/tex]

    [tex]f(x)= x^{2}+6x+9-4[/tex]

    [tex]f(x)= x^{2} +6x +5[/tex]

Now, factor the equation

This can be done using the quadratic formula or other methods

  One simple method is to find the two values that would get:

A good way to verify is to expand the terms and make sure the function looks the same

In this case, the equation can broken into

    f(x)= (x+1)*(x+5)

Now, look at each term individually and set each of them to equal 0

   x+1 =0

   x+5=0

Solve for x in each case

  x= -1

  x= -5

Now, ordering them from least to greatest would be: x= -5, -1

Answer:

woman is 37, girl is 7

Step-by-step explanation:

7(x-2) = y-2

4(x+3) = y+3

7x - 14 = y - 2

7x - 12 = y

4x + 9 = y

3x - 21 = 0

x = 7

y = 37

Answer:

Option b.

Step-by-step explanation:

Note: The given expression is not in correct form. Consider the given expression is [tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex].

Let as consider the given expression is  

[tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex]

We know that,

[tex]i^0=1,i^2=-1,i^3=-i,i^4=1[/tex]

Using these values, we get

[tex]i^0\times i^1\times i^2\times i^3\times i^4=1\times i\times (-1)\times (-i)\times 1[/tex]

[tex]=i^2[/tex]

[tex]=-1[/tex]

The value of given expression is -1.

Therefore, the correct option is b.

Answer: 3

Step-by-step explanation:

7x=21 21/7=3

Answer:

The dentist should fail to reject the Null hypothesis

Step-by-step explanation:

From the question we are told that

       The sample size is  n =  400

       The  sample  mean is  [tex]\= x = 149[/tex]

       The  level of significance is  5%  = 0.05  

       The  Null hypothesis is  [tex]H_o : p = 0.40[/tex]

        The Alternative  hypothesis is  [tex]H_a : p < 0.40[/tex]

         The  p-value is  [tex]p-value = 0.131[/tex]

Looking at the given data we can see that the p-value is greater than the level of significance hence the dentist should fail to reject the Null hypothesis  

Answer:

[tex]\Large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]

Step-by-step explanation:

Hello,

Based on the indication, we can write this polynomial as below, k being a real number that we will have to identify (degree = 3 and we have three zeroes -3, -1, and 2).

   [tex]\Large \boxed{k(x+3)(x+1)(x-2)}[/tex]

We know that the point (1,10) is on the graph of this function, so we can say.

[tex]k(1+3)(1+1)(1-2)=10}\\\\4*2*(-1)*k=10\\\\-8k=10\\\\k=\dfrac{10}{-8}=-\dfrac{5}{4}[/tex]

Then the solution is:

[tex]\large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

The perimeter of a rectangle is expressed as 2(L+B) where;

L is the length and B is the breadth of the triangle.

P = 2(L+B)

68 = 2(L+B)

L+B = 68/2

L+B = 34

L = 34 - B ... 1

Area of the rectangle A = LB... 2

Substituting equation 1 into 2 will give;

A = (34-B)B

A = 34B-B²

To maximize the area of the triangle, dA/dB must be equal to zero i.e

dA/dB = 0

dA/dB = 34 - 2B = 0

34-2B = 0

2B = 34

Dividing both sides of the equation by 2 we will have;

B = 34/2

B = 17

Substituting B = 17 into equation 1 to get the length L

L = 34-17

L = 17m

This shows that the rectangle with maximum area is a square since L = B = 17m

The dimension of the rectangle is Length = 17m and Breadth = 17m

The dimensions are 17m and 17m.

The perimeter of a rectangle is given as:

= 2(length + width)

Since in their case, the lengths have same values, this will be:

Perimeter = 2(l + l)

Perimeter = 4l

4l = 68

L = 68/4

L = 17m

Therefore, the dimensions are 17m and 17m.

Read related link on:

https://brainly.com/question/15366172

Answer:

x = 3 ± sqrt(11)

Step-by-step explanation:

x^2 - 6x + 9 = 11

Recognizing  that this is a perfect square trinomial

(x-3) ^2 =11

Taking the square root of each side

sqrt((x-3) ^2) = ± sqrt(11)

x-3 =± sqrt(11)

Add 3 to each side

x = 3 ± sqrt(11)

Answer:

[tex]\large\boxed{\sf \ \ x = 3+\sqrt{11} \ \ or \ \ x = 3-\sqrt{11} \ \ }[/tex]

Step-by-step explanation:

Hello,

   [tex]x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=\sqrt{11} \ or \ x-3=-\sqrt{11}\\<=> x = 3+\sqrt{11} \ or \ x = 3-\sqrt{11}[/tex]

Do not hesitate if you have any question

Hope this helps

Add the top and bottom numbers together, divide that by 2 then multiply by the height.

15.3 + 19.5 = 34.8

34.8/2 = 17.4

17.4 x 11.1 = 193.14

Answer is 193.1 m^2

Answer:

84%

Step-by-step explanation:

We find the z-score here

z= x-mean/SD = 32-40/8 = -1

So the probability we want to find is;

P(z>-1)

This can be obtained using the standard score table

P(z>-1) = 0.84 = 84%

Answer:

Dian has $250 originally.

Step-by-step explanation:

Let the total money Dian has originally = $S

Dian gave [tex]\frac{2}{5}[/tex] of her total money to Justin,

Money given to Justin = [tex]\frac{2}{5}(\text{S})[/tex]

Money left with Dian = S - [tex]\frac{2}{5}(\text{S})[/tex]

                                   = [tex]\frac{\text{5S-2S}}{5}[/tex]

                                   = [tex]\frac{3S}{5}[/tex]

Since Dian has $150 left then the equation will be,

[tex]\frac{3S}{5}=150[/tex]

S = [tex]\frac{150\times 5}{3}[/tex]

S = $250

Therefore, Dian has $250 originally.

Answer: [tex]\dfrac{1}{12}[/tex]

Step-by-step explanation:

Given: Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow.

We assume that repetition is not allowed

Total number of ways to draw two tiles = [tex]^4P_2=\dfrac{4!}{(4-2)!}[/tex]  [By permuattaions]

[tex]=\dfrac{4\times3\times2}{2}=12[/tex]

Favourable outcome = First green then red  (only one way)

So, the probability of drawing the green before the red [tex]=\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{1}{12}[/tex]

hence, the required probability =[tex]\dfrac{1}{12}[/tex]

Answer:

(H1, T1)

Step-by-step explanation:

Since we know that the only number option is 1, we can cancel out the first 3 options. and obviously, there are only heads, and tails. So, using only the # 1 and heads and tails, we can conclude that the answer is (H1, T1).

Answer:

D. (H1, T1)

Step-by-step explanation:

Since all outcomes require card #1 is chosen, so any answer with 2 or 3 can be rejected, therefore the answer is

D. (H1, T1)

Answer:

The correct option is (D).

Step-by-step explanation:

In this case, we need to test whether the  mean pulse rate (in beats per minute) of students in a large math class is greater than 71.

The hypothesis can be defined as follows:

H₀: The mean pulse rate of students in a large math class is not greater than 71, i.e. μ ≤ 71.

Hₐ: The mean pulse rate of students in a large math class is greater than 71, i.e. μ > 71.

It is provided that the sample mean pulse rate, of a simple random sample of the students is 71.7.

The sample mean is not very different from the population mean.

So, it cannot be said in confidence that the sample is unusual.

Thus, the correct option is (D).

"The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim."

Answer:

the probability that the company's total hospital costs in a year are less than 50,000  = 0.7828

Step-by-step explanation:

From the given information:

the probability that the company's total hospital costs in a year are less than 50,000 will be the sum of the probability of the employees admitted.

If anyone is admitted to the hospital, they have [tex]\dfrac{1}{3}[/tex] probability of making at least one more visit, and a [tex]\dfrac{2}{3}[/tex]  probability  that this is their last visit.

If zero employee was admitted ;

Then:

Probability = (0.80)⁵

Probability = 0.3277

If one employee is admitted once;

Probability = [tex](0.80)^4 \times (0.20)^1 \times (^5_1) \times (\dfrac{2}{3})[/tex]

Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{2}{3})[/tex]

Probability = 0.2731

If one employee is admitted twice

Probability = [tex](0.80)^3 \times (0.20)^2 \times (^5_2) \times (\dfrac{2}{3})^2[/tex]

Probability = [tex](0.80)^3 \times (0.20)^2 \times (\dfrac{5!}{(5-2)!}) \times (\dfrac{2}{3})^2[/tex]

Probability = 0.1820

If two employees are admitted once

Probability = [tex](0.80)^4\times (0.20)^1 \times (^5_1) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]

Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]

Probability = 0.0910

∴

the probability that the company's total hospital costs in a year are less than 50,000  = 0.3277 + 0.2731 + 0.1820

the probability that the company's total hospital costs in a year are less than 50,000  = 0.7828

Answer:

[tex] S.A = 246.6 in^2 [/tex]

Step-by-step explanation:

The figure given above is a square pyramid, having a square base and 4 triangular faces on the sides that are of the same dimensions.

Surface area of the square pyramid is given as: [tex] B.A + \frac{1}{2}*P*L [/tex]

Where,

B.A = Base Area of the pyramid = 9*9 = 81 in²

P = perimeter of the base = 4(9) = 36 in

L = slant height of pyramid = 9.2 in

Plug in the values into the given formula to find the surface area

[tex] S.A = 81 + \frac{1}{2}*36*9.2 [/tex]

[tex] = 81 + 18*9.2 [/tex]

[tex] = 81 + 165.6 [/tex]

[tex] S.A = 246.6 in^2 [/tex]

Answer:

Hope this is correct

HAVE A GOOD DAY!

Answer:C

Step-by-step explanation:

Pemdas

3+5(10)

5*10=50

3+50=53