What are the sine, cosine, and tangent of Θ = 3 pi over 4 radians?

Answer:

[tex](a)\ (-7,-3)\ \&\ (7,-3)[/tex]

Step-by-step explanation:

Given

Options a, b and c

Required

Points that are reflections across y-axis

The rule of reflection across the y-axis is:

[tex](x,y) \to (-x,y)[/tex]

Testing the given options:

[tex](a)\ (-7,-3)\ \&\ (7,-3)[/tex]

Rule: [tex](x,y) \to (-x,y)[/tex]

[tex](-7,-3) \to (-(-7),-3)[/tex]

[tex](-7,-3) \to (7,-3)[/tex]

This is true, because the actual reflection equals the given reflection

[tex](b)\ (-5,4)\ \&\ (5,-4)[/tex]

Rule: [tex](x,y) \to (-x,y)[/tex]

[tex](-5,4) \to (-(-5),4)[/tex]

[tex](-5,4) \to (5,4)[/tex]

This is not true, because the actual reflection does not equal to the given reflection

[tex](c)\ (1,-8)\ \&\ (1,8)[/tex]

Rule: [tex](x,y) \to (-x,y)[/tex]

[tex](1,-8) \to (-1,-8)[/tex]

This is not true, because the actual reflection does not equal to the given reflection

Hence

[tex](a)\ (-7,-3)\ \&\ (7,-3)[/tex] is a reflection of each other across y axis

Answer:

The test statistic is [tex]z = -0.28[/tex]

Step-by-step explanation:

First, before finding the test statistic, we need to understand the central limit theorem and difference 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 between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

A random sample of children in two different schools found that 16 of 40 at one school

This means that:

[tex]p_1 = \frac{16}{40} = 0.4, s_1 = \sqrt{\frac{0.4*0.6}{40}} = 0.0775[/tex]

13 of 30 at the other had this infection.

This means that:

[tex]p_2 = \frac{13}{30} = 0.4333, s_2 = \sqrt{\frac{0.4333*0.5667}{30}} = 0.0905[/tex]

Conduct a test to answer if there is sufficient evidence to conclude that a difference exists between the proportion of students who have ear infections at one school and the other.

At the null hypothesis, we test if there is no difference, that is:

[tex]H_0: p_1 - p_2 = 0[/tex]

And at the alternate hypothesis, we test if there is difference, that is:

[tex]H_a: p_1 - p_2 \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the two samples:

[tex]p = p_1 - p_2 = 0.4 - 0.4333 = -0.0333[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0775^2+0.0905^2} = 0.1191[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{-0.0333 - 0}{0.1191}[/tex]

[tex]z = -0.28[/tex]

The test statistic is [tex]z = -0.28[/tex]

Answer: 66.4

Step-by-step explanation:

The trig ratio you would use is inverse cosine or [tex]cos^{-1}[/tex].

Cos is adjacent/hypotenuse

So, the ratio you would use is  [tex]cos^{-1}[/tex] [tex]\frac{2}{5}[/tex].

Insert this in a calculator which come out to be 66.421821522.

But you have to round, so you answer is 66.4.

Step-by-step explanation:

The given figure can be broken into three parts i.e. a triangle, and two rectangles as shown in the figure.

The base and height of triangle is 15 and 7 in. respectively

For II shape, length and width are 8 and 2 in. respectively

For III shape, length and width are 10 and 9 in. respectively.

answer

the answer is is is option a 200

Answer:

Variance of this population = 9,409

Step-by-step explanation:

Given:

Standard deviation of population = 97

Random sample size = 26

Find:

Variance of this population

Computation:

Standard deviation (σ) = 97

Variance = Standard deviation²

Variance = (σ)²

Variance of this population = Standard deviation of population²

Variance of this population = 97²

Variance of this population = 9,409

Answer:

19km

Step-by-step explanation:

190km divided by 10hr = 19km per 1hr

Answer:

The sum of the series is 749

Step-by-step explanation:

Given

[tex]a_1 = 8[/tex]

[tex]a_{14} = 99[/tex]

[tex]n = 14[/tex]

Required

The sum of the series

This is calculated using:

[tex]S_n = \frac{n}{2}[a_1 + a_n][/tex]

Substitute 14 for n

[tex]S_{14} = \frac{14}{2}[a_1 + a_{14}][/tex]

[tex]S_{14} = 7[a_1 + a_{14}][/tex]

Substitute values for a1 and a14

[tex]S_{14} = 7[8 + 99][/tex]

[tex]S_{14} = 7*107[/tex]

[tex]S_{14} = 749[/tex]

Answer:

0.75 = 75% probability that he will have to wait at a red light for more than 15 seconds

Step-by-step explanation:

At each second, the stoplight is equally likely to change, which means that we use the uniform probability distribution to solve this question.

Uniform probability distribution:

Has two bounds, a and b. The probability of finding a value higher than x is given by:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

Red for 60 seconds

So when Jamal arrives it can change in any number of seconds between 0 and 60, that is, [tex]a = 0, b = 60[/tex]

Probability that he will have to wait at a red light for more than 15 seconds?

[tex]P(X > 15) = \frac{60 - 15}{60 - 0} = \frac{45}{60} = \frac{3}{4} = 0.75[/tex]

0.75 = 75% probability that he will have to wait at a red light for more than 15 seconds

Answer:

43

Step-by-step explanation:

1% = 0.01 = 1/100

4300 / 100 = 43

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

43

4300/100=43 .........

9514 1404 393

Answer:

  x-intercept: (-5, 0)

  y-intercept: (0, 5)

Step-by-step explanation:

The x-intercept is where the graph crosses the x-axis. The x-value there is -5. The y-value of any point on the x-axis is 0, so the point coordinates are (-5, 0).

The y-intercept is where the graph crosses the y-axis. The y-value there is 5. The x-value of any point on the y-axis is 0, so the point coordinates are (0, 5).

Answer:

here are the cordinates you need to mark :

Step-by-step explanation:

(1,15) : 1x,15y

(2,20) : 2x,20y

(3,35) : 3x,35y

(4,45) : 4x,45y

(5,70) : 5x,70y

Hope this helps :)

Answer:

answer: 85

Step-by-step explanation:

These add up to 360 and

85 + 85 + 95 + 95 = 360 so 85 is the answer.

Hope that helps!

Answer:

B. f (4) = 4 · [tex]20^{3}[/tex]

Step-by-step explanation:

I did the quiz too

Answer:

y = - 3

Step-by-step explanation:

[tex]y = \frac{1}{4}x[/tex]

y = 0.25 · x

y = 0.25 · - 12

y = - 3

Answer:

75

____ x 294 = 220.5 around 221 students.

100

The keyword of means multiplication.

Consider a percent out of 100.

A way to remember is that: "cent" means 100.

Answer:

cgtcdtxcgv gg ok

Step-by-step explanation:

Answer:

27 cents

Step-by-step explanation:

10% of 90= 9

9x3=27

Answer:

p x t x r / 100

90 x 10 x 3 / 100

=27

Answer:

B. 16.5

Step-by-step explanation:

Here we can use the opposite and the adjacent from the angle with measurement 20, or tan.

tan theta = opposite / adjacent

Substitute values.

tan 20 = 6 / x

Multiply by x.

x * tan 20 = 6

Divide by tan 20.

x = 6 / tan 20

Evaluate tan 20.

x = 6 / 0.36397023

Divide.

x = 16.48486451

Rounded to the nearest tenth, that makes your answer

B, 16.5

Answer:

The only true statement is:

"∠3 + ∠4 = ∠1 + ∠2"

Step-by-step explanation:

When we have two lines intersect each other, there are 4 angles generated in the intersection.

Two vertical angles are angles whose only "contact point" is the intersection itself. The vertical angles are supplementary only if the two lines are perpendicular.

While a linear pair are two angles that are separated by one of the lines, and linear pairs are always supplementary.

Now let's look at the image and see which statements are true and which ones aren't.

"∠2 and ∠3 form a linear pair"

If we look at the image, we can see that ∠2 and ∠3 are not separated by one of the lines, ∠2 and ∠3 are vertical angles, then this statement is false.

"∠1 and ∠4 are supplementary angles"

Two angles are supplementary if the sum of the measures is equal to 180°, such that, as stated before, a linear pair of angles are supplementary angles.

In the case of ∠1 and ∠4, we can see that these angles are vertical angles, and we also can see that the lines are not perpendicular, then angles ∠1 and ∠4 are not supplementary.

"∠2 and ∠3 = 180°"

This is the same as saying that "∠2 and ∠3 are supplementary"

By the exact same reasoning than in the previous statement, we can find that this one is false.

"∠3 + ∠4 = ∠1 + ∠2"

We know that ∠1 and ∠2 are a linear pair, then ∠1 and ∠2 are supplementary angles, then:

∠1 + ∠2 = 180°

And we know that ∠3 and ∠4 also are a linear pair, and then also are supplementary angles, then we also have:

∠3 + ∠4 = 180°

Then is true that:

∠3 + ∠4 = ∠1 + ∠2

This statement is true.

"∠2 and ∠4 are vertical angles"

We can see that ∠2 and ∠4 are separated by one of the lines, then these angles form a linear pair.

The statement is false.

Answer:

I am almost postive it is B, D, E

Answer:

a. dS(t)/dt + [7S(t)/(300 - 5t)] = 1.2 with S(0) = 0.8

b. S(t) =   [tex]\frac{120e^{\frac{7t}{100} } }{7}[/tex]  -  16.34[tex]e^{-\frac{7t}{100}[/tex]

Step-by-step explanation:

a. Write an initial value problem for S(t), the amount of salt in the tank at time t. Do not solve the equation!!

The net mass flow rate of salt dS(t)/dt = mass flow in - mass flow out

mass flow in = concentration of flow in × flow rate in = 0.6 lb/gal × 2 gal/min = 1.2 lb/min

Let S(t) be the mass of salt in the tank at time, t. The concentration of salt in the tank at time, t, C(t) = S(t)/volume of tank at time t ,V

V = V₀ + (r - r')t where V₀ = initial volume of water in tank = 300 gal, r = volume flow rate in = 2 gal/min, r'= volume flow rate out = 7 gal/min and t = time

So, V = V₀ + (r - r')t

V = 300 + (2 - 7)t

V = 300 - 5t

So, C(t) = S(t)/V = S(t)/(300 - 5t) lb/gal

Now, mass flow rate out = concentration in tank × volume flow rate out = S(t)/(300 - 5t) lb/gal × 7 gal/min = 7S(t)/(300 - 5t) lb/min

So, dS(t)/dt = mass flow in - mass flow out

dS(t)/dt = 1.2 lb/min - 7S(t)/(300 - 5t) lb

dS(t)/dt = 1.2 - 7S(t)/(300 - 5t)

So, our differential equation is

dS(t)/dt + [7S(t)/(300 - 5t)] = 1.2 with S(0) = 0.8 since we initially have 0.8 lb of salt

b. Write an expression in terms of S for the amount of salt in the tank when the tank is one-quarter full.

When the tank is one-quarter full, V = volume of tank/4 = 400 gallons/4 = 100 gallons

We now solve our differential equation

dS(t)/dt + 7S(t)/100 = 1.2

Using the integrating factor method, I.F = [tex]e^{\int\limits{\frac{7}{100} \, dt } =[/tex]  [tex]e^{\frac{7t}{100} }[/tex]

[tex]e^{\frac{7t}{100}[/tex]dS(t)/dt +

d[[tex]e^{\frac{7t}{100}[/tex]S(t)]/dt = 1.2

d[[tex]e^{\frac{7t}{100}[/tex]S(t)] = [1.2

integrating both sides, we have

∫d[[tex]e^{\frac{7t}{100}[/tex]S(t)] = ∫[1.2

Let u = 7t/100. So, du/dt = 7/100 and dt = 100du/7

∫[1.2[tex]e^{\frac{7t}{100}[/tex]]dt = ∫[1.2 × 100[tex]e^{u}[/tex]]du/7 = (120/7)∫

[tex]e^{\frac{7t}{100}[/tex]S(t) =  [tex]\frac{120e^{\frac{7t}{100} } }{7}[/tex] + C

S(t) =   [tex]\frac{120e^{\frac{7t}{100} } }{7}[/tex] ÷ [tex]e^{\frac{7t}{100}[/tex]  +  [tex]e^{-\frac{7t}{100}[/tex]

S(t) =   [tex]\frac{120e^{\frac{7t}{100} } }{7}[/tex]  +  C[tex]e^{-\frac{7t}{100}[/tex]

From our initial condition, S(0) = 0.8. So,

S(0) =   [tex]\frac{120e^{\frac{7(0)}{100} } }{7}[/tex]  +  C[tex]e^{-\frac{7(0)}{100}[/tex]

S(0) =   [tex]\frac{120e^{\frac{0}{100} } }{7}[/tex]  +  C[tex]e^{-\frac{0}{100}[/tex]

S(0) =   [tex]\frac{120e^{0}}{7}[/tex]  +  C[tex]e^{0}[/tex]

0.8 =   [tex]\frac{120}{7}[/tex]   +  C

C = 0.8 - 120/7

C = 0.8 - 17.14

C = - 16.34

So,

S(t) =   [tex]\frac{120e^{\frac{7t}{100} } }{7}[/tex]  -  16.34[tex]e^{-\frac{7t}{100}[/tex]

Answer:

area = 5

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The equation is V=4/3 times Pi times radius^3

Answer:

the height is 4.2

Step-by-step explanation:

Answer:

not sure ask teacher for help

Step-by-step explanation:

ok

Answer:

Economics: A social science that studies how people interact with value!

Hope this helps :D