Find sin 2x, cos 2x, and tan 2x if sinx =
5
13
and x terminates in quadrant I.
ala
sin 2x
U
х
cos 2x
=
tan 2x
10

Answer:

65.1 and 69.1

Step-by-step explanation:

a^2+b^2=c^2

c=95

b=a+4

Solve for a^2+(a+4)^2=95^2

a=65.1

b=a+4=69.1

Answer:

65.1 and 69.1

Step-by-step explanation:

c² = a² + b²

c= 95

a - one leg

b= (a + 4) - second leg

95² = a² + (a + 4)²

9025 = a² + a² + 2*4a + 16

2a² + 8a - 9009 = 0

[tex]a= \frac{-b +/-\sqrt{b^2 - 4ac} }{2a} \\\\a = \frac{-8 +/-\sqrt{8^2 - 4*2*9009} }{2*2} \\\\a=65.1 \ and \ a=- 69.1[/tex]

A leg length can be only positive. a = 65.1

b = 65.1 + 4 = 69.1

Answer:

Between 303.5 grams and 316.7 grams

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 310.1 grams

Standard deviation = 6.6 grams

Between what two masses do approximately 68% of the data occur?

By the Empirical Rule, within 1 standard deviation of the mean.

310.1 - 6.6 = 303.5 grams

310.1 + 6.6 = 316.7 grams

Between 303.5 grams and 316.7 grams

Answer: 90/pi degrees

Step-by-step explanation:

It forms a 15cm arc from a circle of radius 30 cm.

The diameter is 30*2*pi = 60pi cm. So the arc is 15/60pi = 1/4pi of the way around a 360 degree circle. This is 1/4pi * 360 = 90/pi degrees.

Hope that helped,

-sirswagger21

The pendulum will swing 28.68° if the 30-cm pendulum traverses an arc of 15 cm.

It is defined as the combination of points that, and every point has an equal distance from a fixed point (called the center of a circle).

We know that relationship between arc length s and central angle θ:

s = rθ

Where r is the radius of the circle

We have s = 15 cm

r = 30 cm

15 = (30)(θ)

θ = 0.5 radians

To convert it to a degree, multiply it by 180/π

θ = 0.5(180/π)

θ = 28.647 ≈ 28.68°

Thus, the pendulum will swing 28.68° if the 30-cm pendulum traverses an arc of 15 cm.

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Answer:

  27/8

Step-by-step explanation:

You seem to want to evaluate ...

  [tex]\dfrac{3a^{-3}b^2}{2a^{-1}b^0}[/tex]

I like to simplify the expression first, even though the order of operations would have you evaluate it as is.

  [tex]=\dfrac{3}{2}a^{-3-(-1)}b^{2-0}=\dfrac{3b^2}{2a^2}[/tex]

Substitute the given values for "a" and "b" and do the arithmetic.

  [tex]=\dfrac{3(-3)^2}{2(-2)^2}=\dfrac{3\cdot 9}{2\cdot 4}=\boxed{\dfrac{27}{8}}[/tex]

Answer:

D. 150°

Step-by-step explanation:

x= 150°

Choice D

A = 14 m^2

Step-by-step explanation:

The equation for the area of a triangle is...

[tex]A=\frac{1}{2}bh[/tex]

For this we need the base and the height. Looking at the picture, we can see that the height is 4. The base is split into 2 parts, so we just need to add the 3 and the 4 together, that will make our base 7. Now we can plug these into the equation, but I'm also just going to make the 1/2 a 0.5.

[tex]A=0.5*4*7[/tex]

[tex]A=[/tex]

14 m^2

Answer:

The answer is 8300.

Step-by-step explanation:

1) We round the number up to the nearest hundred, if the last two digits in the number are 50 or above.

2) We round the number down to the nearest 100 if the last two digits in the number are 49 or below.

3) If the last two digits are 00, then we do not have to do any rounding because it is already to the hundred.

Answer:

A

Step-by-step explanation:

Well first find the proportion of the sector of the major Arc(shaded area) and then Multiply by area of the circle πr²

Answer:

CD

Step-by-step explanation:

For all sides except CD, you do not need the distance formula, since they are vertical or horizontal, meaning that you can find their length simply through subtraction. However, with side CD, since it is diagonal, you need to form a right triangle with to solve its length. Hope this helps!

Answer:

They are all multiplied by 6

Answer:

Geometric sequence.

Step-by-step explanation:

Here are the terms :

-2/3, -4, -24, -144

Now the first term T1 = -2/3

The second Term T2 = -4

But T2/T1 = -4÷ -2/3 = -4 x -3/2 = 6

Similarly Term 3, T3 = -24

T3/T2 = -24/-4= 6

Hence the expression is a geometric sequence.

a×r^(n-1); a is the first term

r is the common ratio 6

n is the number of terms.

The linear function that describes the table is f(x) = -2x + 3

The linear function of an equation can be found as follows:

y = mx + b

where

Therefore, using the table

b = 3

using (1, 1)

1 = m + 3

m = -2

Therefore, the function that represent the table is as follows:

f(x) = -2x + 3

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Answer:  f(x) = -2x + 3

Step-by-step explanation:

Answer:

  see the attachment

Step-by-step explanation:

A "line of best fit" generally has about as much data above the line as below it. If the data has any trend, it generally follows the trend.

The best choice here is B.

Answer:Answer:

 see the attachment

Step-by-step explanation:

A "line of best fit" generally has about as much data above the line as below it. If the data has any trend, it generally follows the trend.

The best choice here is B.

Step-by-step explanation:

Answer:

y = -3/5 x +3

Step-by-step explanation:

3x + 5y = 15

Subtract 3x from each side

-3x+3x + 5y = -3x+15

5y = -3x+15

Divide each side by 5

5y/5 = -3x/5 +15/5

y = -3/5 x +3

Answer:

(1)  f(x,y) = 1-|x|-|y|

(a) 3d figure attached

(b) 2d figure attached

(2) f(x,y) = 6-2x-3y

(a) 3d figure attached

(b) 2d figure attached

Step-by-step explanation:

The Function is not given in the question. Lets solve this for 2 common function for the internet. Hopefully it can solves the given problem

(1)  f(x,y) = 1-|x|-|y|

(2) f(x,y) = 6-2x-3y

All the figures are labelled to avoid confusion. (a) part of both functions have 3D sketches. (b) part of both functions have 2d sketches

Answer:

I assume Josh and Peyton are his friends and both gave him advice on what to do with half of the money from the big lottery win.

Let's say Josh said "save it or invest it for your retirement" and Peyton said "use it to keep playing the lottery.

We will now look at the sense in each piece of advice!

Step-by-step explanation:

JOSH

By investing the $250,000 (half of the money won), Patrick will be sure that the money is available for him anytime and would even have gotten interest, by the time he's ready to use it.

PEYTON

By playing the lottery continuously, Patrick could get lucky once in a while and win big again. How big though?

Analyzing with the figures given,

$20 gets Patrick a lottery ticket.

$250,000 will get him 12,500 lottery tickets!

Whether he's buying the tickets at once or he'll play the lottery once in a while, I'll say he has good chances of winning big again.

So if the probability of winning big after purchasing up to 12,500 tickets is close to 1, Patrick should play the lottery with the $250,000

If the probability of winning big after purchasing 12,500 lottery tickets is close to 0 (closer to 0 than it is to 1) then Patrick should invest the $250,000 in retirement.

Answer:

- Not reflexive

- Symmetric

- Transitive

Step-by-step explanation:

- A person is not a sibling of himself so the relation is NOT reflexive

- If a person is a sibling of an other person, the other person is a sibling of the person. Therefore the relation is SYMMETRIC

- If a person A is a sibling of B, and a person B is a sibling of C then, person A is a sibling of person C. Therefore the relation is TRANSITIVE.

Answer:

B:

Step-by-step explanation:

If we rotate the 3-D figure around y-axis we'll obtain a cone with a radius of 3 units

ANSWER:

I believe you wish to calculate the sum of squares total (SST) for this regression analysis. The sum of squares total is 1053.15

Step-by-step explanation:

The sum of squares total is numerically derived by adding the sum of squares regression (regression sum of squares) to the sum of squares error (error sum of squares). The regression sum of squares here is 752.25 and the error sum of squares is 300.9

This gives us a total sum of squares of 1053.15

Sums of squares tell if a linear regression of one variable (or variables) on another is good or not.

The squared differences between the observed dependent variable and its mean is a measure of the total variability of the data set.

So the SST is equal to 752.25 + 300.9 = 1053.15

Answer:person up top is right it’s B

Step-by-step explanation: on edg 2020

Answer:

The answer is B

Step-by-step explanation:

lol yw guys

Answer:

True.

Step-by-step explanation:

A tree diagram is a diagram used in general mathematics, statistics, and probability to show a sequence of events. This tool is used to calculate the number of possibilities of an event to occur. Commonly, the tool of a tree diagram is used to find the possibility of outcome while flipping a coin. It is a diagram in which connections between the events is shown using the strucure of branching connecting lines.

So, the given statement is true, that is a simple way of showing events in a sequence.

Answer:

Option (B)

Step-by-step explanation:

From the figure attached,

AB = 7 units

BC = 17.46 units

AC = 16 units

Now we apply the sine rule in the given triangle ABC,

SinB = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

        = [tex]\frac{AC}{BC}[/tex]

        = [tex]\frac{16}{17.46}[/tex]

        = 0.916

        ≈ 0.92

Therefore, Option (B) will be the answer.

Answer:

DIFFERENT PICS

Step-by-step explanation:

I had one and the awnser was 0.40, and C had a arch whereas B did not.

Answer:

Step-by-step explanation:

let s note a and b

x = ap+b

we can write two equations

(1) 300=3a+b

(2) 450=1.5a+b

multiply by 2 the (2) we got

900 =3a+2b

minus (1) it gives

900 - 300 = 3a+2b-3a-b = b

so b = 600

and from (1) it gives 3a = 300-600 = -300

so a = -100

then

x=-100p+600

thanks

The units of tile will he need to surround his pool is 13.42

The given parameters are:

[tex]AB =2.24[/tex]

[tex]BD =5[/tex]

Start by calculating the distance BC using the following Pythagoras theorem

[tex]BD^2 = AB^2 + BC^2[/tex]

So, we have:

[tex]5^2 = 2.24^2 + BC^2[/tex]

[tex]25 = 5 + BC^2[/tex]

Collect like terms

[tex]BC^2 = 25 - 5[/tex]

[tex]BC^2 = 20[/tex]

Take the square roots of both sides

[tex]BC = 4.47[/tex]

The unit of tiles is then calculated using the following perimeter formula

[tex]Tiles = 2 \times (AB + BC)[/tex]

So, we have:

[tex]Tiles = 2 \times (2.24 + 4.47)[/tex]

[tex]Tiles = 13.42[/tex]

Hence, the units of tile will he need to surround his pool is 13.42

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Answer: THE SECOND ONE

Step-by-step explanation:

Answer: the second one

Step-by-step explanation:

Answer:

[tex]P(X=0)=(9C0)(0.55)^9 (1-0.55)^{9-0}=0.000757[/tex]

[tex]P(X=1)=(9C1)(0.55)^9 (1-0.55)^{9-1}=0.0083[/tex]

[tex]P(X=2)=(9C2)(0.55)^9 (1-0.55)^{9-2}=0.0407[/tex]

[tex]P(X=3)=(9C3)(0.55)^9 (1-0.55)^{9-3}=0.1160[/tex]

And adding we got:

[tex] P(X < 4) = 0.000757 +0.0083+0.0407 +0.1160= 0.2626[/tex]

Step-by-step explanation:

Let X the random variable of interest "number of correct answers", on this case we now that:

[tex]X \sim Binom(n=9, p=0.55)[/tex]

The probability mass function for the Binomial distribution is given as:

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

Where (nCx) means combinatory and it's given by this formula:

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

And we want to find this probability:

[tex] P(X < 4) =P(X=0) +P(X=1) +P(X=2) +P(X=3) [/tex]

And we can find the individual probabilities:

[tex]P(X=0)=(9C0)(0.55)^9 (1-0.55)^{9-0}=0.000757[/tex]

[tex]P(X=1)=(9C1)(0.55)^9 (1-0.55)^{9-1}=0.0083[/tex]

[tex]P(X=2)=(9C2)(0.55)^9 (1-0.55)^{9-2}=0.0407[/tex]

[tex]P(X=3)=(9C3)(0.55)^9 (1-0.55)^{9-3}=0.1160[/tex]

And adding we got:

[tex] P(X < 4) = 0.000757 +0.0083+0.0407 +0.1160= 0.2626[/tex]

Answer:

look to rule number five

Step-by-step explanation:

Rule Number 5 best explains the answer

Answer:

There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours. (P-value = 0).

The null and alternative hypothesis are:

[tex]H_0: \mu=4\\\\H_a:\mu< 4[/tex]

Step-by-step explanation:

The question is incomplete: To test this claim a sample or population standard deviation is needed.

We will estimate that the sample standard deviation is 2 hours, and use a t-test to test that claim.

NOTE (after solving): The difference between the sample mean and the mean of the null hypothesis is big enough to reject the null hypothesis, even when we have a sample standard deviation of 3.5 hours, which can be considered bigger than the maximum standard deviation for the sample.

This is a hypothesis test for the population mean.

The claim is that the batteries power the laptops for significantly less than 4 hours.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=4\\\\H_a:\mu< 4[/tex]

The significance level is 0.05.

The sample has a size n=500.

The sample mean is M=3.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{500}}=0.0894[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{3.5-4}{0.0894}=\dfrac{-0.5}{0.0894}=-5.5902[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=500-1=499[/tex]

This test is a left-tailed test, with 499 degrees of freedom and t=-5.5902, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=P(t<-5.5902)=0[/tex]

As the P-value (0) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours.

Answer:

[tex]x=\frac{5}{7}[/tex]

Step-by-step explanation:

[tex]3x - 2 = 3 - 4x[/tex]

Add [tex]2[/tex] and [tex]4x[/tex] on both sides of the equation.

[tex]3x - 2 +2+4x= 3 - 4x+2+4x[/tex]

[tex]3x+4x=-4x+5+4x[/tex]

[tex]7x=5[/tex]

Divide [tex]7[/tex] on both sides of the equation.

[tex]\frac{7x}{7}=\frac{5}{7}[/tex]

[tex]x=\frac{5}{7}[/tex]

Answer: D

Step-by-step explanation:

In order to increase each ticket by $2, you are ADDING 2 to each value.

So you create a matrix of all 2's and add that to the given matrix.

[tex]\left[\begin{array}{cc}2&2\\2&2\\2&2\end{array}\right] +\left[\begin{array}{cc}8&10\\12&16\\6&8\end{array}\right]\quad =\quad \large \left[\begin{array}{cc}10&12\\14&18\\8&10\end{array}\right][/tex]

Answer:

Unit 8 test answers

Step-by-step explanation:

1: a.)3x4

2:b.)

3:a.)

4:b.)

5:c.) matrix CD would have the dimensions 7x7

6: a.)

7:67

8:c.)

9:b.) Scott sold 1 van

10:d.)