Use a calculator and inverse functions to find the radian measures of the given angle.
Round your answer to the nearest hundredth.
angles whose sine is 0.48 0.50 + 2pn and -3.64 + 2pn
1.07 + 2pn and -1.07 + 2pn
0.50 + 2pn and -0.50 + 2pn
-0.46 + 2pn and 2.68 + 2pn

Answer:

[tex]3(x - 6) - 8x = - 2 + 5(2x + 1) \\ 3x - 18 - 8x + 2 - 10x - 5 = 0 \\ = > - 15x - 21 = 0 = > - 15x = 21 = > x = - \frac{7}{5} [/tex]

Answer:

a) 0.0287 = 2.87% probability that three non-defective components in a batch of seven components.

b) 0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.

Step-by-step explanation:

A sequence of Bernoulli trials composes the binomial distribution.

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 probability that a selected component is non-defective is 0.8

This means that [tex]p = 0.8[/tex]

a) Three non-defective components in a batch of seven components.

This is P(X = 3) when n = 7. So

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

[tex]P(X = 3) = C_{7,3}.(0.8)^{3}.(0.2)^{4} = 0.0287[/tex]

0.0287 = 2.87% probability that three non-defective components in a batch of seven components.

b) 8 non-defective components are drawn before the first defective component is chosen.

Now the order is important, so the we just multiply the probabilities.

8 non-defective, each with probability 0.8, and then a defective, with probability 0.2. So

[tex]p = (0.8)^8*0.2 = 0.0336[/tex]

0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.

Answer:

6) 9 3/5

7) 1/50

8) 28/45

Step-by-step explanation:

6) 8÷5/6=8x6/5=48/5=9 3/5

7) 1/5÷10=1/50

8) 7/5÷9/4=7/5x4/9=28/45

Answer:

0.7880

Step-by-step explanation:

0.7883

Hope it helps!

Answer:

The point estimate for the true difference between the population means is of -2.62 years.

The 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -3.4 years and -1.84 years.

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem, and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction of normal variables:

When we subtract normal variables, the mean is the subtraction of the mean, while the standard deviation is the square root of the sum of variances.

A sample of 138 cars owned by students had an average age of 5.13 years. The population standard deviation for cars owned by students is 3.45 years.

This means that:

[tex]\mu_{s} = 5.13, \sigma_{s} = 3.45, n = 138, s_s = \frac{3.45}{\sqrt{138}} = 0.2937[/tex]

A sample of 111 cars owned by faculty had an average age of 7.75 years.  The population standard deviation for cars owned by faculty is 2.08 years.

This means that [tex]\mu_{f} = 7.75, \sigma_{f} = 2.08, n = 111, s_f = \frac{2.08}{\sqrt{111}} = 0.2658[/tex]

Difference between the true mean ages for cars owned by students and faculty.

s - f

Mean:

[tex]\mu = \mu_s - \mu_f = 5.13 - 7.75 = -2.62[/tex]

This is the point estimate for the true difference between the population means.

Standard deviation:

[tex]s = \sqrt{s_s^2+s_f^2} = \sqrt{0.2937^2+0.2658^2} = 0.3961[/tex]

Confidence interval:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = zs = 1.96*0.3961 = 0.78[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is -2.62 - 0.78 = -3.4

The upper end of the interval is the sample mean added to M. So it is -2.62 + 0.78 = -1.84

The 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -3.4 years and -1.84 years.

Answer:

Fore an=-2(-5)n-1

:substitutute 9 in place of "n" in the equation

= -2(-5)9-1

Multiply -2 and -5 to get positive 10

=(10)(9)-1

Multiply 10 and 9 to get 90

=90-1

Subtract 1 from 90

=89 therefore 9th term is 89

Step-by-step explanation:

For

an= 6(-3)n-1

(Follow the above procedure)

=6(-3)9-1

=-18-1

=-19

For

an= -7n-1

(Follow the same procedure as above)

-7(9)-1

=-63-1

=- 64

The area of a circle is pi times the radius squared (A = π r²).

Answer:

x = 24

Step-by-step explanation:

3X +5 +2x-4 +2x +11 = 180

7x +12 = 180

7x = 180 - 12

7x = 168

7x/7 = 168/7

x =24

Answer:

$9.24

Step-by-step explanation:

1.68÷2=0.84

1.68×5+0.84=9.24

Step-by-step explanation:

Volume of the silo

= 3.14(9.5^2)(48) sq. ft

=13602.48 sq. ft

=13602 sq. ft (cor. to the nearest integer)

Answer:

x + y = 7 an equation to represe.

Bing + us = Bingus. That's all

Answer:

it's very hard lol

Bing+us

=Bingus

Step-by-step explanation:

oh my gawd... hope it's ryt

thanks lol

Answer:

by now you should have the answer right?

Step-by-step explanation:

Answer:

7161 km³

Step-by-step explanation:

28²+b²=32.5²

784+b²=1056.25

b²=1056.25-784

b²=272.25

b=√272.25

b=16.5

1/2x28x16.5x31=7161

Answer:

Box-4 → (+)

Step-by-step explanation:

To find the value in the 4th box, we will expand the given logarithmic expression.

log₄x⁵y³ = log₄x⁵ + log₄y³

             = 5log₄x + 3log₄y

Therefore, each box will have the values as,

Box-1 → 5

Box-2 → log₄

Box-3 → x

Box-4 → (+)

Box-5 → 3

Box-6 → log₄

Box-7 → y

There is the (+) sign in Box-4.

Answer:

length = 8 ft

width = 5 ft

Step-by-step explanation:

width = w

length = w + 3

Area of rectangular garden = 40 square feet

length  *width = 40

(w + 3) *w = 40

w*w + 3*w = 40

w² + 3w = 40

w² + 3w - 40 = 0

w² + 8w - 5w - 8*5 = 0

w(w + 8) - 5 (w +8) =0

(w + 8) (w - 5) = 0

w - 5 = 0       {Ignore w + 8 =0, as measurement will not be in -ve}

w = 5 ft

l = 5 + 3

l = 8 ft

Answer:

The angles are adjacent and x=100

Answer:

1. x = 14

2. c = 12

3. d = 4

4. w = 8

5. z = 54

6. d = 20

7. n = 26.4

8. k = 15

Step-by-step explanation:

Answer:

a= 10.8 c=4.3

Step-by-step explanation:

Use the law of sines.

a/sin 120=8/sin 40

Which simplifies to: 8*sin (120)/sin (40)

When you put the equation into a calculator, it will answer with 10.77

Therefore, it will be 10.8 if round to the nearest tenth

Using the same concept of the answer to a, the equation will be:

10.8*sin 20/sin 120=4.26

Round to the nearest tenth, and c equals to 4.3

Answer:

Well 1 centimeter is 10 millimeters.

260000 mm divided by 10 is 26000

so 26000 centimeters

Answer:

I got you rn

Step-by-step explanation:

its 42 because opposite angles are congruent

Answer:

Step-by-step explanation:

z = 53 + 39     {Exterior angle property of triangle}

z = 92°

Answer:

I don't know thats hard um well yeah

9514 1404 393

Answer:

  4.  b

  5.  a

Step-by-step explanation:

4. The radius is the distance between the center (-6, -8) and the point on the circle (0, 0). The square of that is given by ...

  r^2 = (-6-0)^2 +(-8-0)^2 = 36 +64 = 100

Only one of the offered choices has an r^2 value of 100: Choice B.

__

5. The center and the point are on the same line (y=9), so the radius is the difference of x-coordinates: r = 5-2 = 3. The center is given as (h, k) = (5, 9).

The form of the equation of a circle is ...

  (x -h)^2 +(y -k)^2 = r^2

Filling in the given values, the equation is ...

  (x -5)^2 +(y -9)^2 = 9 . . . . matches choice A

Answer:

I don't know if your ask which nomial it is but its a trinomial if that's what your asking

Answer: I'm assuming that there were multiple choices provided for this question.. but just to help you, when a number is within the absolute value, it changes any number to a positive:

|-2.6| = 2.6

So any number higher than that work for this question :-)

Answer:

80°C

Step-by-step explanation:

you will say :

(176-33) x 5/9 = 70

Answer:A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

8/50 = 4/25

give the sinplest fraction answer