8. Angles x and y are located in the first quadrant
such that sin x=5/3 and cos y=5/13
a) Determine an exact value for cosx.
b) Determine an exact value for siny.

The amounts, using proportions, are given as follows:

A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem from which the fraction was built.

The tip is of 20% of the total bill of $54.65, hence it's value is given as follows:

Tip = 0.2 x 54.65 = $10.93.

(because 0.2 is the decimal equivalent to the percentage of 20%, then it is multiplied by the total amount to find the desired amount).

The total cost of the meal is given by the sum of the bill of the meal plus the tip, hence:

Total Cost = 54.65 + 10.93 = $65.58.

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Answer:127 degrees

Step-by-step explanation: 180-74 = 106 106+21 = 127 180-127 = 53 180-53 =127

Joseph removes 5/8 gallon of white paint from a can.The amount of paint in the can  = - 2.8 gallons

Step-by-step explanation:

Let X be the starting amount of paint in the can, in gallons.

"Removes 5/8 gallon" can be written -(5/8)gal

"Adds 3/8 gallon" becomes +(3/8)gal

The result is :  X - (5/8)gal + (3/8)gal = Remaining Paint (gallons)

Consolidating:  Remaining (gallons) = X - (2/8)gal

If we want the overall increase/decrease, subtract the initial volume:

Initial - Remaining = Change in amount of paint in can

Change =  (X-(2/8)gal) - X = - (2/8) gallons

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Value of angle T is 60°, angle U is 60°, TS is 13 cm and SU is 22.49 cm.

Given in question,

Triangle STU,

TU = 13 cm

∠S = 60°

ST = TU

    = 13 cm

∠U = ∠S    (Their sides are equal)

     = 60°

∠S + ∠T + ∠U = 180°

60 + ∠T + 60 = 180

      ∠T + 120 = 180

                ∠T = 180 - 120

                      = 60

Hence, ∠T is 60°.

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Answer: The answer to that would be 3.

Step-by-step explanation: So 5 / 1  2/3 = 3

Sorry my handwriting is so sloppy! Hope it helps!

Answer:

(2.3*10^2)(3*10^5)

in scientific notation 

Step-by-step explanation:

6.9 × 10^7

If h(x)=(fog)(x) then h'(3) = 12.

Given:

Let f and g be differentiable functions such that f(3)=5,g(3)=7,f'(3) = 13, g'(3) = 6,f'(7) = 2 and g'(7) = 0

h(x)=(fog)(x)

h(x) = f(g(x))

h'(x) = f'(g(x)) * g'(x)

h'(3) = f'(g(3) * g'(3)

= f'(7) * 6

= 2*6

= 12

Therefore If h(x)=(fog)(x) then h'(3) = 12.

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Answer:

f ≤ - [tex]\frac{19}{3}[/tex]

Step-by-step explanation:

8 - (- 4f - 3 ) ≤ - f - 8 + 2f ← distribute parenthesis on left side by - 1

8 + 4f + 3 ≤ f - 8

4f + 11 ≤ f - 8 ( subtract f from both sides )

3f + 11 = - 8 ( subtract 11 from both sides )

3f ≤ - 19 ( divide both sides by 3 )

f ≤ - [tex]\frac{19}{3}[/tex]

Answer:

Step-by-step explanation:

Answer:

x = - 2 ± [tex]\sqrt{\frac{19}{3} }[/tex]

Step-by-step explanation:

3x² + 12x = 7 ← factor out 3 from each term on the left side

3(x² + 4x) = 7

to complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 4x

3(x² + 2(2)x + 4 - 4) = 7

3(x + 2)² - 12 = 7 ( add 12 to both sides )

3(x + 2)² = 19 ( divide both sides by 3 )

(x + 2)² = [tex]\frac{19}{3}[/tex] ( take square root of both sides )

x + 2 = ± [tex]\sqrt{\frac{19}{3} }[/tex] ( subtract 2 from  both sides )

x = - 2 ± [tex]\sqrt{\frac{19}{3} }[/tex]

Answer:

4

Step-by-step explanation:

The answer really just popped into my head.

4^2 + 4^2 = 32

4x4=16

Step-by-step explanation:

a) 100

b)45

trust me it will helps you

The region which have strongest negative correlation is Midwest.

Given that,

From your data folder, import the states.csv dataset into rstudio. create a scatter plot with high (x-axis) and pctdemocrat (y-axis) data points that are colored according to region. Stat smooth is used

To find : Which region has the strongest negative correlation

What Is Negative Correlation?

A link between two variables known as "negative correlation" occurs when one variable rises as the other falls, and vice versa. In statistics, -1.0 denotes a perfect negative correlation, 0 denotes no connection, and +1.0 denotes a perfect positive correlation. The relationship between two variables is always absolutely opposite when there is a perfect negative correlation.

Therefore, the region which have strongest negative correlation is Midwest.

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The average rate of change between year 1 and year 10 is given as follows:

4.3 thousand cars a year.

The average rate of change of a function is obtained by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In this problem, the function is presented as follows:

C(x) = 0.15x³ - 3.28x² + 23.75x - 2.1.

The interval is:

[1,10], hence a = 1, b = 10.

At x = 1, the numeric value is found replacing each instance of x by 1, hence:

C(1) = 0.15(1)³ - 3.28(1)² + 23.75(1) - 2.1 = 18.52 thousand cars.

At x = 10, the numeric value is found replacing each instance of x by 10, hence:

C(10) = 0.15(10)³ - 3.28(10)² + 23.75(10) - 2.1 = 57.4 thousand cars.

Then the average rate of change is obtained as follows:

r = (57.4 - 18.52)/(10 - 1) = 4.3 thousand cars a year.

The problem is given by the image shown at the end of the answer.

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The values of m<1, m<2, m<3, m<4, m<5, m<7, m<8 are given by 49, 131, 49, 131, 49, 49, 131 respectively.

Given the measure of angle 6 is 131.

We can see that from the figure, angle 6 and angle 2 are corresponding angles and angle 6 and angle 4 are alternative angles.

So, angle 2 = angle 6 = 131

angle 4 = angle 6 = 131

Since angle 1 and angle 4; angle 2 and angle 3 are Linear pairs. So.

angle 3 = 180 - angle 2  = 180-131 = 49

angle 1 = 180 - angle 4 = 180-131 = 49

Since, angle 1 and angle 5; angle 4 and angle 8; angle 3 and angle 7 are corresponding angles to each other.

angle 5 = angle 1 = 49

angle 7 = angle 3 = 49

angle 8 = angle 4 = 131

Hence the values of m<1, m<2, m<3, m<4, m<5, m<7, m<8 are given by 49, 131, 49, 131, 49, 49, 131 respectively.

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Answer:

Step-by-step explanation:

Emma's age= x

Kate's age= x-12

sum of their ages=24

so Emma's age= 24-12

x=24-12

x=12

Emma's age=12

506.433 minutes elapse before the minute hand next points in the same direction as the hour hand.

Conversion of hours to minute:

As we all know, an hour is made up of sixty minutes, therefore

1 hour=60minutes

Thus, all you need to do to convert time from hours to minutes is to multiply the time in hours by 60 to get the time in minutes.

If you want to convert minute to hours divide the given time in minutes by 60.

The hands line up 11 times every 12 hours, or roughly every 1:05.5 hours; the precise number is 1:05.4545 repeating.

The repetition time is 8:43.6363. When expressed in seconds, the result is 8:43:38.1818 repeating, or 8:43:38 and 2/11.

This is 261 and [tex]\frac{9}{11}[/tex] degrees, or 261.818 repeated.

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Answer:

Of the homeowners, half have either a dog or a cat.

Step-by-step explanation:

Since 2/3 of all homeowners have a pet, and 3/4 of those have dogs or cats, we simply need to multiply 2/3 and 3/4 to see what fraction of all homeowners have a dog or a cat.

2/3 x 3/4 = 6/12

6/12 = 1/2

We can double check this. If there are 60 homeowners, and 2/3 have a pet, that would mean that 40 of those homeowners have a pet.

If 3/4 of the 40 homeowners have either a dog or a cat, that would equate to 30 homeowners having either a dog or a cat.

Since 30 is half of 60, this would mean that 1/2 of the 60 homeowners have a dog or cat!

Hope this answer helped you!

Answer:

D

Step-by-step explanation:

First, we should find the equations of the two lines. The red line is just horizontal, and represents y = 4 while the blue line intersects the y-axis at -4 and every time it goes right one, it goes up 4, so it has a slope of four(also it looks kinda steep, so it cannot have a slope of 1/4). This means the equation is y = 4x - 4.

Notice the red line is dashed, that means the inequality is either less than or greater than. Also, the shaded part is below the vertical line, enclosing all the values of y less than 4, so the first inequality would be y < 4.

The blue line is solid, so it is either greater than or equal to or less than or equal to. To find out which one, we check to se where the point (0, 0) fits in:

y ? 4x - 4

0 ? 0 - 4

0 ? -4

Only a greater than or equal to sign would fit in: 0 ≥ -4

This means the answer is:

y < 4

y ≥ 4x - 4

which is option D

Answer:

Step-by-step explanation:

1)

The equation of a straight line:

y = k·x + b

x = 0

b = y = - 4

k = (y - y₀) / (x - x₀) = ( 4 - (-4)) / (2 - 0) =  8 / 2 = 4

y = 4·x - 4

2)

The equation of a straight line:

y = 4

3)

Shaded area:

y ≤ 4

y ≥ 4x - 4

Right answer:

D.

y ≤ 4

y ≥ 4x - 4

Step-by-step explanation:

look at where the dotted line is : it is vertical at x = -3.

that is automatically is equation : x = -3.

now, look at where the shaded side of that line is - to the left or to the right of the line ?

it is to the left of the line. and that message all values smaller than x = -3. but not equal indicated by the dotted line (that means the line itself is not included).

so, this is described by x < -3.

therefore, the first answer option is out.

now, look at the solid line.

what is the y-intercept (the y- value when x = 0) ?

when x = 0, the y-value is -1.

and everything to the left and below of the line is included (incl. the line itself, hence the solid line), so, the line inequality is then (just given by the available choices)

y <= -x - 1

and the 3rd answer option is therefore correct.

Answer:

[tex]\begin{cases}x < -3\\y \leq -x-1\end{cases}[/tex]

Step-by-step explanation:

When graphing inequalities:

From inspection of the given graph, there is a dashed line at x = -3 with shading under the line (to the left).

Therefore, the inequality that represents this is:  

The solid line has a negative slope.  For each decrease of 1 unit in the y-direction, the x-values increase by 1 unit.  Therefore, the slope of this line is -1.  

From inspection of the given graph, the y-intercept of the solid line is -1.

Therefore, the equation of this line is  y = -x - 1.  

As the shading is under the line, the inequality that represents this is:

Therefore, the system of linear inequalities that represents the graph is:

[tex]\begin{cases}x < -3\\y \leq -x-1\end{cases}[/tex]

The rate of change of the volume of the sphere is 100,530.96 mm^3/s

How to calculate rate of change of the volume of the sphere?

Given,

radius = r = 80 / 2 = 40 mm

rate of change radius = [tex]\frac{dr}{dt}[/tex] = 5 mm/s

Formula to calculate volume of the sphere is

[tex]V = \frac{4}{3}\pi r^{3}[/tex]

Differentiating the volume formula and we get new formula to calculate rate of change of the volume.

[tex]\frac{dV}{dt} = \frac{4}{3}\pi 3r^{2}\frac{dr}{dt}[/tex]

Simplify to

[tex]\frac{dV}{dt} = 4\pi r^{2}\frac{dr}{dt}[/tex]

Now, we put the given value to formula and calculate it

[tex]\frac{dV}{dt} = 4\pi (40)^{2}(5)[/tex]

[tex]\frac{dV}{dt} = 100,530.96[/tex] mm^3/s

Thus, the rate of change of the volume of the sphere is 100,530.96 mm^3/s

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The interest on the loan is $1200.

Given,

In the question:

You get a loan from the loan star bank to help pay for your home.

and, if you borrowed $12,000 at 10% for one year.

To find the interest on the loan.

Now, According to the question;

Based on the given conditions:
Formulate:

Borrowed= $12,000

At 10% for one year

12000 x 10%

Convert percentage into decimal

12000 x 0.1

calculate the product or quotient:

= 1200

Hence, The interest on the loan is $1200.

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Answer:

alternate interior angles theorem

Step-by-step explanation:

alternate interior angles theorem states that, if 2 parallel lines and a transversal form alternate interior angles, then, said angles are congruent.

Answer:

40;100

step by step explanation:

The required equation model is y =  -(4.4/1009)x + 16, its slope is -(4.4/1009), and the y-intercept of the line of fit is 16.

The given table shows the amounts of storage left y 7 (in gigabytes) on a music-playing device when there are x songs on MTR the device.

As per the given table, take two points (0, 16) and (1009, 11.6)

The required equation will be as:

y - 16 = [(11.6 - 16)/(1009-0)](x-0)

y - 16 = -(4.4/1009)x

y =  -(4.4/1009)x + 16

The above equation models the amount of storage left as a function of the number of songs.

Here slope is -(4.4/1009), and y-intercept is 16

Therefore, the required equation model is y =  -(4.4/1009)x + 16, its slope is -(4.4/1009), and the y-intercept of the line of fit is 16.

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Answer:

[tex]y=-7x+6[/tex]

Step-by-step explanation:

1 ) Our given equation is [tex]Y\left(x\right)+8=-7\left(x-2\right)[/tex]

2 ) We can now graph this equation ( desmos is a good online graphing calculator ). The graph is shown in the attachment...

3 ) Now that the equation has been graphed we can see that the slope intercept form is [tex]y=-7x+6[/tex]

Hope this helps! :)

Answer:

Step-by-step explanation:

so use the properties of powers, recall that powers like [tex]x^{2^{2} }[/tex] is the same as [tex]x^{2} *x^{2}[/tex] which can also be written as  [tex]x^{2*2}[/tex] = [tex]x^{4}[/tex].

I want to make this clearer.

[tex]x^{3^{3} }[/tex] = [tex]x^{3}[/tex]  * [tex]x^{3}[/tex] * [tex]x^{3}[/tex]  = [tex]x^{3*3*3}[/tex] =[tex]x^{27}[/tex]

I'm not sure if that's making it clearer or not.

so for your question  of  [tex](8x^{6}) ^{2/3}[/tex]  we can rewrite it to look like the above multiplication of powers

[tex]8x^{6*(2/3)}[/tex]

[tex]\frac{6}{1}[/tex] * [tex]\frac{2}{3}[/tex] = [tex]\frac{12}{3}[/tex]  = 4

[tex]8x^{4}[/tex]

The first step in simplifying is to apply that outer exponent of [tex]\frac{2}{3}[/tex] to each factor inside the parentheses.

      [tex]\left(8\cdot x^6\right)^{2/3} = \left(8\right)^{2/3} \cdot \left(x^6\right)^{2/3}[/tex]

Now using the concept that [tex](a)^{m/n} = \sqrt[m]{a^n}[/tex] for positive real numbers a and integers m and n, we can evaluate the first part:

       [tex](8)^{2/3} = \sqrt[3]{8^2} = \sqrt[3]{64} =4[/tex]

For the second part, we use the power-to-a-power rule, that says [tex](a^m)^n = a^{m\cdot n}[/tex]:

    [tex]\left(x^6\right)^{2/3} = x^{6\cdot \frac{2}{3}} = x^4[/tex]

Putting that all together, we have

    [tex]\left(8 x^6\right)^{2/3} = \left(8\right)^{2/3} \cdot \left(x^6\right)^{2/3} = 4x^4[/tex]

The solution to the inequality expression is f >-3

From the question, we have the following parameter that can be used in our computation:

-2f - 3.7 < 2.3

Add 3.7 to both sides of the expression

This gives

-2f < 6

Divide both sides of the expression by -2

So, we have the following representation

f >-3

Hence, the solution is f >-3

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By using some exponent properties we will get:

2*(1/b)^15

Remember that the product of exponents can be written as:

(a^x)*(a^y) = a^(x*y)

In this case, we have the expression:

2*b^(-1.5)*b^10

Using the above property we can rewrite:

2*b^(-1.5)*b^10 = 2*b^(-1.5*10) = 2*b^(-15)

And a negative exponent means that we need to take the inverse of the base, then:

2*b^(-15) = 2*(1/b)^15

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