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Answer:

30.5°

Step-by-step explanation:

Supplementary angles add up to 180°. You know one angle is 149.5°, so you can find the other angle.

Measure of its supplementary angle = 180° - 149.5°

                                                             = 30.5°

Answer:

5⁰ × 7⁰ × 3⁰ = 1

Step-by-step explanation:

5⁰ × 7⁰ × 3⁰ = ?

5⁰ = 1

7⁰ = 1

3⁰ = 1

1 × 1 × 1 = 1

Answer:

x² - x - 2 = 0

Step-by-step explanation:

Given:

- 4(x - x²) = 8

Find:

Standards form

Computation:

- 4(x - x²) = 8

(x - x²) = -2

x - x² = -2

x² - x - 2 = 0

Answer:

√x4

Step-by-step explanation:

(x^2+x−3)⋅(x^2−4)

(y^2+6y+8)−(y^2+y−12)

Answer:

a) 0.0618 = 6.18% probability that the sample will contain at least three defectives.

b) 0.076 = 7.6% probability that the sample will contain at least three defectives

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Sample of 20 items is selected from the machine.

This means that [tex]n = 20[/tex]

5% defectives

This means that [tex]p = 0.05[/tex]

(a) the normal approximation to the binomial

The mean is:

[tex]\mu = E(X) = np = 20*0.05 = 1[/tex]

The standard deviation is:

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20*0.05*0.95} = 0.9747[/tex]

The probability is, using continuity correction, [tex]P(X \geq 3 - 2.5) = P(X \geq 2.5)[/tex] , which is 1 subtracted by the pvalue of Z when X = 2.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.5 - 1}{0.9747}[/tex]

[tex]Z = 1.54[/tex]

[tex]Z = 1.54[/tex] has a pvalue of 0.9382

1 - 0.9382 = 0.0618

0.0618 = 6.18% probability that the sample will contain at least three defectives.

(b) the exact binomial tables

This is:

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.358[/tex]

[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.377[/tex]

[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.189[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.358 + 0.377 + 0.189 = 0.924[/tex]

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.924 = 0.076[/tex]

0.076 = 7.6% probability that the sample will contain at least three defectives

Answer:

{(3,1),(2,4),(6,8)}

Step-by-step explanation:

Since for inverse of (x,y), it's(y,x)

i.e. the forst term and second term of order pair switch their places

Answer:

a. $4

b. Noah has 5/5. Elena has 4/5.

Step-by-step explanation:

Noah has $5.

a.

Elena has 80% of Noah's money.

80% of $5 = 0.80 * $5 = $4

b.

Noah has $5. We can consider $5 to be the full amount.

A full amount is 100% or 1 or 5/5.

Elena has 80% of Noah's money, so she has 80/100 of Noah's money.

80/100 reduces to 4/5.

Noah has 5/5, and Elena has 4/5.

The money that Elena has is $2.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

The given problem can be solved as follows,

(a) The amount of money Elena has is 40% of that of Noah.

It can be written as follows,

40% × 5

= 40/100 × 5

= 2

(b) Since the Elena has 40% of the Noah's money,

In the form of fraction it can be written as follows,

40% = 40/100

        = 2/5

This can be represented in a diagram as follows,

In the diagram shown the circle has in total 5 sectors of which 2 yellow sectors represent Elena's money.

Hence, the amount of money Elena has is $2 which is shown in the diagram.

To know more about percentage click on,

brainly.com/question/29306119

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Answer:

the total surface area of the prism is 245.67

Step-by-step explanation:

Given;

height of the triangular prism, h = 8

length of the triangular bases, = 7, 8, and 9

The total surface area of the prism is calculated as;

T.S.A = ph + 2B

Where;

p is the perimeter of the base

B is area of the base

P = 7 + 8 + 9 = 24

Area of the base can be calculated using Hero's formula;

[tex]S = \frac{7+8+9}{2} = 12\\\\Base \ area (B) = \sqrt{12(12-7)(12-8)(12-9)} = 26.833[/tex]

T.S.A = (24 x 8)   +  2 x 26.833

T.S.A = 192 +  53.666

T.S.A = 245.67

Therefore, the total surface area of the prism is 245.67

Answer:

About 4.5 hours, you can say 5 hours

Step-by-step explanation

You can solve this by constructing a linear equation, which would turn out like this, 25x+60=172.50. How I got this is that it says his charge is 25 per hour, that is basically multiplication by an unknown number, so put that as a variable. Next it says he has a service fee of 60 dollars, this is what's called an initial fee. Now all we need to do is solve for x, which turns into 4.5. I don't know if they ask to round your answer or something, I hope this is right.

Answer:

x = 9

Step-by-step explanation:

[tex]a^{2} = c^{2} - b^{2}[/tex]

[tex]a^{2} = 15^{2} - 12^{2}[/tex]

[tex]a^{2} = 225 - 144[/tex]

[tex]a^{2} = 81[/tex]

[tex]\sqrt{a^2} = \sqrt{81}[/tex]

[tex]a = 9[/tex]

Answer:

8.3

Step-by-step explanation:

Given,

Circumference of the circle = 52 cm

Therefore ,

By the problem,

[tex] = > 2\pi r = 52[/tex]

[tex] = > 2 \times 3.14 \times r = 52[/tex]

[tex] = > r = \frac{52}{3.14 \times 2} [/tex]

=> r = 8.2802547771

Rounded to nearest tenth,

=> r = 8.3 (Ans)

Answer:

-60

Step-by-step explanation:

-45+s=-105

s=-105+45

s=-60

Answer:

Ryan practiced 33.66 minutes on Wednesday

Step-by-step explanation:

You do 43.2+37.48 and it equals 80.68

Then you do 114.34-80.68 which equals 33.66

the answer is B) both expressions are equivalent to 76 when t=3

Hope this helps :)

Answer:

D

Step-by-step explanation:

Hope i helped :)

Answer:

Step-by-step explanation:

θ = 2π/9 radians

arc length = rθ = 8π/9 units

area of sector = πr²/9 = 16π/9 square units

Answer:

hkhqews

Step-by-step explanation:

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Answer: 7

Step-by-step explanation:

2x - 3 = x + 4

2x - x - 3 = 4           Mius x from the both side

       x - 3 = 4          

             x = 7          Add the 3 from both side

Answer:

c. No, there are more than two possible outcomes for each trial.

Step-by-step explanation:

Binomial probability distribution:

Only two possible outcomes, success or failure.

In each trial, the probability of a success must be the same.

The number of trials must be fixed.

You ask ten randomly chosen college students to rate their experience at the dining hall on a scale of 1-5.

There are 10 trials, which is a fixed number and respects the binomial distribution. However, there are five possible outcomes(numbered 1 to 5). Since there is more than two possible outcomes, the scenario cannot be modeled using a binomial distribution, and the correct answer is given by option c.

9514 1404 393

Answer:

  b.  60

Step-by-step explanation:

We assume the percentage for the sample holds for the whole class, so the estimated number preferring November is ...

  0.248 × 230 = 57.04 ≈ 60

About 60 students prefer November.

Answer:

18/21

Step-by-step explanation:

7x3 = 21

6x3=18

Answer:

18

Step-by-step explanation:

[tex]\frac{6}{7} =\frac{x}{21} \\\\\frac{6}{7} =\frac{18}{21}[/tex]

Multiply 3 to 6 since 7 x 3 is 21,

so 6 x 3 = 18

Answer:

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

If the figure is a parallelogram, the opposite sides are the same length

3x+20 = 5x-12

Subtract 3x from each side

3x+20 -3x = 5x-12-3x

20 = 2x-12

Add 12 to each side

20+12 = 2x-12+12

32 = 2x

Divide each side by 2

32/2 = 2x/2

16 =x

Answer:

0.03

Step-by-step explanation:

.25% for the tails times .5 for the odd number on the dice times 0.25 for the clubs because it is a 13/52 chance you will pull a clubs and put that all together and you get 0.03125 simplified and you get 0.03

Answer:

0.03

Step-by-step explanation:

The probability of landing on 1 tail is 1/2, since it is 1 out of 2 options, a tail or a head. If you want the probability of two tails, it would be 1/2 * 1/2 = 1/4.

Next we can take the probability of rolling an odd number on a fair die. A fair die has 3 even numbers: 2,4,6; and 3 odd numbers: 1,3,5. Since 3/6 or 1/2 of the numbers are odd, there is a 50% chance that it would roll an odd number.

Finally, drawing a club out of standard deck of cards is 1/4, since there are 4 choices: hearts, spades, clubs, or diamonds. You now get the idea, and you can figure out that the probability would be 1/4.

Our last step is to multiply all the answers we get, since to get all of them at once would lower your chances. 1/4 * 1/2 * 1/4 = 1/32 = 0.03125; rounded to 0.03.

Answer:

33.97 m

Step-by-step explanation:

Given that,

The height of a man = 2 m

He stands on a horizontal ground 30m from a tree.

The angle of elevation of the top of the tree from his eyes is 28°.

We need to find the distance between the man eyes to the top of the tree. Let the height of the tree be h

Using trigonometry to find such that,

 [tex]\tan28=\dfrac{h}{30}\\\\h=\tan28\times 30\\\\h=15.95[/tex]

Now let us consider that the distance between the man eyes to the top of the tree is x. Using Pythagoras theorem,

[tex]x^2=30^2+15.95^2\\\\x=33.97\ m[/tex]

So, the distance between the man eyes to the top of the tree is 33.97 m.

Answer:

its b, and why does everyone want brainllest

Step-by-step explanation:

Answer:

Answer option 2

Step-by-step explanation: