The terminal side of Ø is in quadrant II and cos ø = -5/13 What is sin ø?

Hello,

[tex]y = ax + b[/tex]

We know the slope is 2 so :

[tex]y = 2x + b[/tex]

The equation of the line that passes through the point (5,4) so :

[tex]4 = 2 \times 5 + b[/tex]

[tex]4 = 10 + b[/tex]

[tex]b = 4 - 10[/tex]

[tex]b = - 6[/tex]

The equation of the line that passes through the point (5,4) and has a slope of 2 is :

[tex]y = 2x - 6[/tex]

y = 2x - 6

Most lines are written in slope-intercept form, but we can use slope-point form in situations like this.

Slope-Point Form

The formula for slope-point form is [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]. So, we can plug in the information we have, the point and slope.

This is an equation for the line given to us. However, this form can be simplified further.

Slope-Intercept Form

Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept. To find the most simplified form of the equation we need to use the properties of equality.

First, distribute the 2

Next, add 4 to both sides

Now, we have the equation for the line in slope-intercept form. Both of the equations technically meet the requirements for the question, but slope-intercept is more common to use.

Answer:

a)  0.0721

Step-by-step explanation:

Let the random variable X be the score on the ACT exam.

Given:

Therefore, the random variable X is normally distributed:

[tex]X \sim\textsf{N}(21,5^2)[/tex]

Z-score for a sample mean

[tex]\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \overline{X} \sim \left(\mu,\dfrac{\sigma^2}{n}\right) \implies Z=\dfrac{\overline{X}-\mu}{\sigma / \sqrt{n}} \sim \textsf{N}(0,1)[/tex]

[tex]\textsf{then the test statistic is}: \quad z=\dfrac{\overline{x}-\mu}{\sigma / \sqrt{n}}[/tex]

Given:

Therefore, the test statistic is:

[tex]\implies z=\dfrac{19.8-21}{5/ \sqrt{37}}=-\dfrac{6\sqrt{37}}{25}=-1.459863007=-1.46\:\: \sf (3\:s.f.)[/tex]

Using the Z-tables to find the probability:

[tex]\implies \text{P}(Z \leq -1.46)=0.0721[/tex]

Since Angle ABD and Angle DBC are complementary angles, the measure of Angle ABC is 90 degrees.

Hence, option D is the correct answer.

Two angles are called complementary when their measures add to 90 degrees.

From the diagram; Angle ABD and Angle DBC are complementary angles that add up to make 90 degrees.

Since Angle ABD and Angle DBC are complementary angles, the measure of Angle ABC is 90 degrees.

Hence, option D is the correct answer.

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Answer:

rjdjdj shiejd shsuisis shusisos

Answer: Look at step by step

Step-by-step explanation:

(a) There are 119 stocks that increased in price out of 246 stocks so the probability of selecting a stock that is increased in price is 119/246 = 48.37%

(b) There are 112 stocks where it pays dividends so the probability so the probability of selecting a stock that pays dividends is 112/246 = 45.53%

(c) There are 49 stocks which satisfy the question so the probability is 49/246 = 19.92%

(e) There are 34 stocks which increase in price and pay dividends out of the 119 stocks that increase in price so the probability is 34/119 = 28.57%

(f) Using the same logic as (e), the probability is 85/134 = 63.43%

(g) From the requirements, we see that 49 stocks don't satisfy the requirements, so the probability is (246-49)/246 = 80.08%

Answer: m > -16

Step-by-step explanation:

[tex]\frac{3}{4}m > -12\\\\m > -\frac{4}{3}(12)=-16[/tex]

Answer:

BC = 18 cm

Step-by-step explanation:

As we can see from the diagram:

AB + BC + CD = AD

⇒ 10 cm + BC + 11 cm = 39 cm

⇒ BC + 21 cm = 39 cm

⇒ BC = 39 cm - 21 cm

⇒ BC = 18 cm

Answer:

The answer is circle.

Step-by-step explanation:

For all the rest of the shapes, we use certain base x height formulas.  Square uses base x height along with parallelograms and trapezoids. For a triangle, we use [tex]\frac{base x height}{2}[/tex]. Though, for a circle, we use the formula  [tex]\pi r^{2}[/tex] where r= radius.

By applying trigonometric expression and direct comparison, we conclude that a = 2 such cos 255° - cos 195° = √a / 2

In this question we need to simplify a trigonometric expression in order to find the value of a. In this case, we need to use the following formula:

[tex]\cos \theta - \cos \xi = - 2\cdot \sin \left(\frac{\theta + \xi}{2} \right)\cdot \sin \left(\frac{\theta - \xi}{2} \right)[/tex]

Then,

cos 255° - cos 195° = - 2 · sin 225° · sin 30°

cos 255° - cos 195° = - 2 · sin (- 135°) · sin 30°

cos 255° - cos 195° = 2 · sin 135° · sin 30°

cos 255° - cos 195° = 2 · (√2 / 2) · (1/2)

cos 255° - cos 195° = √2 / 2

Then, by direct comparison we find that a = 2.

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The information given about the landscape is illustrated below:

a. You'll need a measuring tape, two range poles, pegs, and three people.

The first person holds the zero mark between their thumbs and fingers, the second person holds the 3m mark on the tape between their thumbs and fingers, and the third person holds the 8m. When all sides of the rope are stretched, a triangle is created, and an angle near one is a right angle.

Wrap one loop of the rope around peg A with a peg through the other loop, draw a circle on the ground, place pegs B and C where the circle crosses the base line, and place peg D half way between pegs B and C, allowing pegs D and A to form lines perpendicular to the base line, forming a right angle.

B. Method 1; Take a measurement of the distance between both trees and divide by 2 to get the midpoint.

Method 2; By use of a compass to bisect the distance between both points.

Method 3; By using a protractor to mark the 90° vertical point when placed between the two endpoints.

C The three different ways he can do this.

1) by using a protractor

2) by finding a point

3) by extending the line of the angle until it reaches the other side of the field.

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The mean and the median based on the information given will be 166.08 and 195.

It should be noted that the mean is also the average. It's gotten by adding all the numbers and dividing by 13. This will be 166.08.

The median is simply the middle number. This will be 195.

The range will be:

= 301 - 7

= 294

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the equation of the new function is:

[tex]g(x) = 2^{x - 5} - 7[/tex]

We have a function:

[tex]f(x) = 2^x[/tex]

And we want to shift it five units to the right, and seven units down, then the new function will be:

[tex]g(x) = f(x - 5) - 7[/tex]

If we now replace f(x), we get:

[tex]g(x) = 2^{x - 5} - 7[/tex]

That is the equation of the new function.

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The formula to find the height of the Cylinder is; h = V/(πr²) and at V = 45π and r = 3, we have; h = 5

We are given the formula for volume of a cylinder as;

V = πr²h

where;

h is height

r is radius

To make h the subject, let us divide both sides by  πr² to get;

V/(πr²) = h

At V = 45π and r = 3, we have;

h = 45π/(πr²)

h = 45/3²

h = 5

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The decimal equivalent of 45⁰ 32’ 55” is 45.55⁰

The given degree is:

45⁰ 32' 55''

This can be converted to decimal as shown below

[tex]45+\frac{32}{60} +\frac{55}{3600}[/tex]

This can be simplified further as:

[tex]45^o32'55'' = 45+0.53+0.0153\\\\45^o32'55'' = 45.55^0[/tex]

Therefore, the decimal equivalent of 45⁰ 32’ 55” is 45.55⁰

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The general solution of the logistic equation is [tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex].

The particular solution of the logistic equation is [tex]y(t) = \frac{14}{1 + 0.4 \cdot e^{-\frac{14\cdot t}{3} }}[/tex].

In this question we are before a type of ordinary differential equation known as equation with separable variables, that is to say, that variables t and y can be separated at each side of the expression in order to find a solution:

dy / dt = 3 · y · (1 - y /14)

dy / [(- 3 / 14 ) · y · (y - 14)] = dt

Then, we simplify the expression by partial fractions and integrate the resulting expression:

- (1 / 14) ∫ dy / y + (1 / 14)∫ dy / (y - 14) = - (14 / 3)∫ dt

- (1 / 14) · ㏑ |y| + (1 / 14) · ㏑ |y - 14| = - (14 / 3) · t + C, where C is the integration constant.

㏑ |(y - 14) / y| = - (14 / 3) · t + C

[tex]1 - \frac{14}{y} = C\cdot e^{-\frac{14\cdot t}{3} }[/tex]

[tex]\frac{14}{y} = 1 - C \cdot e^{-\frac{14\cdot t}{3} }[/tex]

[tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex]

The general solution of the logistic equation is [tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex].

If y(0) = 10, then the particular solution of the differential equation is:

10 = 14 /(1 - C)

1 - C = 1.4

C = - 0.4

The particular solution of the logistic equation is [tex]y(t) = \frac{14}{1 + 0.4 \cdot e^{-\frac{14\cdot t}{3} }}[/tex].

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Answer:

2.603 degrees

Step-by-step explanation:

This word problem is talking about a triangle. 500 meters high would be the height and 11 Kilometers would be the base. We should convert kilometers to meters in order to make this easier. 11 kilometers = 11,000 meters.

Height = 500

Base = 11,000

The hypotenuse ends up being 11,011.35777

in order to find the angle of depression (assuming it is a constant rate) we would measure the angle where the hypotenuse meets the base. (11,000 & 11,011.35777) the angle comes out at 2.603 degrees. Hope this helped!

Answer:

Divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

Step-by-step explanation:

Answer:

The value of the slope b/n these two pts. will be 1.

Step-by-step explanation:

Greetings !

For finding slope from two points of a line (x₁, y₁) and (x₂, y₂), we use the formula (y₂ - y₁) / (x₂ - x₁).

Thus, m=(y₂ - y₁) / (x₂ - x₁)

It's 4 buns & 5 cakes

Hope my explanation to the other one helps, if not, you can draw them; while following the steps & you may get it better.

E.g draw a box for the bun & a circle for the cake, then, adding them up to get the 95p. Also, you keep taking away from 435p

The solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1

The equation is given as:

[tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex]

Split the equation as follows:

[tex]y\ =\ \left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}[/tex]

[tex]y = 1 + x^2[/tex]

Next, we plot the graph of both equations (see attachment)

From the attached graph, the intersection point is (1, 2)

Remove the y value

x = 1

Hence, the solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1

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Answer:

Gievn that l=3m,b=5m,h=4m

L.S.A=2(l+b)h

=2×(3.5)×4

=2×8×4

=64sq.m

Step-by-step explanation:

Answer:

[tex]r=\sqrt{\frac{V}{\pi h}}[/tex]

Step-by-step explanation:

[tex]V = \pi r^{2} h \\ \\ r^{2} =\frac{V}{\pi h} \\ \\ r=\sqrt{\frac{V}{\pi h}}[/tex]

Th measure of arc AB will be 60 degrees

The figure shown shows a circle with lines AC and BD intersecting the circle at the point E

From the figure given the measure of the arc AB is congruent to the arc CD.Given that the measure of arc CD is 60 degrees, hence the measure of arc AB will also be 60 degrees

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Answer:

11664

Step by Step:

Evaluate for x=6,y=1

3(6^2)(6^2)(6−(3)(1))

3(6^2)(6^2)(6−(3)(1))

=11664

well, we know the suits are all reduced by 20%, so the man saved 20% of 231.20

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 231.20}}{\left( \cfrac{20}{100} \right)231.20}\implies 46.24[/tex]

The expected value of the outcome of the bid is $0.18

So let's start by counting how many bids are placed up to a total of 160.

100*160 = 16000.

What will be your arbitrary bid? As each bid has an equal chance of success, the average of all bids is used. (One cent plus 160 dollars) / 2 = 80 dollars (rounded)

Your odds of winning are 1/16000 (1 bid out of 16000).

If you win, your profit is 1920 ($2000 minus $80.00).

1920/16000 is $0.12

Your cost to enter the auction is $1, and your average winning offer is $0.12.

The result is $0.18 (0.12-1=-0.88).

Thus the expected value of the outcome of the bid is $0.18

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Answer:

108°

Step-by-step explanation:

We know for a theorem that A = B, so:

4x + 28 = 2x + 68

Isolating the x:

2x = 40

x = 20

Now let's plug in the equation for A:

4(20) + 28 = 108°

-13, or +11, because they are both 12 places away from -1.