Mrs. Scott decided that she would spend no more than $120 to buy a jacket and a skirt. If the price of the jacket was $20 more than 3 times the price of the skirt, which inequality represents the highest possible price of the skirt

An equation that indicates how fast (velocity) the rock will be falling after 8 seconds is V = (3.7 × 8) m/s.

Given the following data:

In order to determine the velocity at which this rock would fall after 8 seconds, we would apply the first equation of motion.

Mathematically, the first equation of motion is given by this formula:

V = u + at

Where:

Substituting the given parameters into the formula, we have;

V = 0 + 3.7 × 8

V = (3.7 × 8) m/s.

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Complete Question:

The acceleration of gravity on Mars is about 3.7 meters per second squared. Suppose a rock falls from a tall cliff on Mars. Write the equation that indicates how fast the rock will be falling after 8 seconds.

Answer and Explanation:

No, they did not use a ruler to compute the values of trig functions. They used geometry to prove theorems about trigonometry, then used those results and ordinary computations involving addition, subtraction, multiplication, division, and square roots to determine the entries in trigonometric tables.

Claudius Ptolemy (85 C.E.–165) created the first trig tables that we know of, and he included proofs of the theorems he used. One of the main theorems he used is what is now called Ptolemy’s theorem.

In order to prove his sum and difference forumlas, Ptolemy first proved what we now call Ptolemy’s theorem.

Ptolemy’s theorem. The product of the diagonals of a cyclic quadrilateral is equal to the sum of the products of the opposite sides.

A cyclic quadrilateral is a quadrilateral inscribed in a circle as ABCD. Ptolemy’s theorem says:

AC ⋅ BD = AB ⋅ CD + AD ⋅ BC

When one of the diagonals (like ) is a diameter of the circle, that gives you a way to determine the trig functions for sum and differences of angles.

Sometimes, the sum and difference formulas for sine and cosine are still called Ptolemy’s formulas.

sin(α + β) = sin α cos β + cos α sin β

cos(α + β) = cos α cos β − sin α sin β

sin(α − β) = sin α cos β − cos α sin β

cos(α − β) = cos α cos β + sin α sin β

Ptolemy started with angles he knew the trig functions for. These included angles in various isosceles triangles: 45°-45°-90°, 60°-60°-60°, and 36°-72°-72°, the last one described by Euclid in Proposition IV.10. That gave him the trig functions for 36°, 60°, and 90°. Using half-angle formulas (mentioned by Hipparchus (190–120 B.C.E.), he could compute trig functions for half of those angles and a quarter of those angles. Then using the sum and difference formulas he computed the rest of the numbers in his trig table.

Hope this helps! :)

Answer:

[tex]\frac{1}{\sin \left(10^{\circ \:\:}\right)}\:\:\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=4[/tex]

Step-by-step explanation:

Given the expression

[tex]\frac{1}{\sin \left(10^{\circ \:}\right)}-\frac{\sqrt{3}}{\cos \left(10^{\circ \:}\right)}=4[/tex]

Taking the left-hand side and solving it

[tex]\frac{1}{\sin \left(10^{\circ \:}\right)}-\frac{\sqrt{3}}{\cos \left(10^{\circ \:}\right)}[/tex]

as

[tex]\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=5.76[/tex]

and

[tex]\frac{\sqrt{3}}{\cos \left(10^{\circ \:\:}\right)}=1.76[/tex]

so the expression becomes

[tex]\frac{1}{\sin \left(10^{\circ \:\:}\right)}\:\:\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=5.76-1.76[/tex]

                           [tex]=4[/tex]

Thus, we conclude that

[tex]\frac{1}{\sin \left(10^{\circ \:\:}\right)}\:\:\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=4[/tex]

Answer:

45°

Step-by-step explanation:

x° = (180 - 135)°

   = 45°

Hope this helps

With interior alternate angles and adjacent angles concept, the value of x from the given parallel lines is 45°.

Given that, straight line m parallel to straight line n and t is the transversal.

When a transversal connects two coplanar lines, alternate interior angles are created. They are located on the transverse sides of the parallel lines, but on the inner side of the parallel lines. At two different locations, the transversal passes through the two lines that are coplanar.

Here, y=135° (Interior alternate angles are equal)

Now, y°+x°=180° (Adjacent angles on straight line)

135°+x°=180°

x°=45°

Therefore, the value of x from the given parallel lines is 45°.

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Answer:

A = (Ao)(0.5^(t/t1.2))

1 = (Ao)(0.5^(20/4)) = Ao(0.03125)

Ao = 1/0.03125 = 32mg

5 weeks = 5(7) = 35 days

A = 32(0.5^(35/4)) = 32(0.0232) = 0.074mg

Step-by-step explanation:

In a nutshell, the domain and the range of each function are shown below:

In this problem we find a picture containing the graphs of two functions, of which we must find both the domain and the range of each expression. The domain of the function corresponds with all values from the horizontal axis such that the function exists, and range of the function with all the values from the vertical axis.

The domain and range of the first function are x ∈ [- 4, 4] and y ∈ [1, 5], respectively.

The domain and range of the second function are x ∈ [- 3, 1] and y ∈ [-5, - 1].

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Answer:

27

Step-by-step explanation:

13 + 14 = 27

Answer: -13+-14

Step-by-step explanation: the Absolute value is the opposite value of something like 24-57 the absolute value of that would be -24-(-57)

Answer:

the tens place

Step-by-step explanation:

just need to know long division

Answer:

In the tens place :)

Step-by-step explanation:

Hope it helps. I am also doing a semester exam and would greatly appreciate if someone would help me with this:

Answer:

I got 5/12 as my answer.

Answer:

Domain= [0, 13]

Step-by-step explanation:

Domain refers to the possible input values on the x-axis.

Answer:

135

Step-by-step explanation:

2 x 54 = 108 and .50 x 54 = 27 so 108 + 27 = 135

Answer:

20 laps

Step-by-step explanation:

50/2.5=20

you need more information to finish this question. You can't get an answer for a math question like this one with that little information.

Answer:

Step-by-step explanation:

lol it means 4/5,

your in rsm i aleready know

The absolute value of the equation will not work because the value of x would have to be negative for the perimeter to be 6 ft plus or minus 1.5 ft.

The perimeter of the rectangle is given as:

Perimeter = 2(Length + Breadth)

The perimeter of a rectangle is 6 feet plus or minus 1.5 feet.

So, we have:

Perimeter = 2(Length + Breadth) =  6 feet ± 1.5 feet.

Then  Substitute values for length and width

2(Length + Breadth) =  6 feet ± 1.5 feet.

2(4 + x) =  6 feet ± 1.5 feet.

Now,

2(4 + x) =  6 feet + 1.5 feet.

8 + 2x = 6.5 ft

2x = 6.5 - 8

x = -0.25 ft

2(4 + x) =  6 feet - 1.5 feet.

8 + 2x = 4.5 ft

2x = 4.5 - 8

x = -1.75ft

Here Both values of x are negative.

This means that the absolute value model can't work, because a rectangle cannot have a negative dimension.

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Hence , the value of x  (production level) that will create a profit of $200 are 40 and 20.

We have given cost function C = 70x + 200 and revenue function R = 100x − 0.5x² .

It is given that profit is revenue minus cost.

P = R -C

P =  100x − 0.5x² - 70x - 200

P = 30x − 0.5x² -200         ........(1)

It is also given that it will create a profit of $200 .

Putting P = 200 in equation (1) , we get

200 =  30x − 0.5x² -200    

0.5x² - 30x + 400 = 0

Multiplying by 10 we get

5x² - 300x + 4000 = 0

Taking 5 common , we get

x² - 60x + 800 = 0

By splitting in the middle term this equation can be represented by

x² -(40+20)x +800 = 0

(x² - 40x ) - (20x-800) = 0

x(x-40) - 20( x - 40) = 0

(x - 40) (x- 20) = 0

On comparing , we get

x - 40 = 0

x = 40

and x - 20 = 0

       x = 20

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Using the relation between velocity, distance and time, and supposing the group travels for 8 hours a day, it is found that:

1. You were driving 24 hours at 45 mph and 56 hours at 70 mph.

2. You drove 1080 miles at 45 mph and 3920 miles at 70 mph.

Velocity is distance divided by time, that is:

v = d/t.

For the first part, we have that:

Hence:

v = d/t

45 = d/t

d = 45t.

For the second part, we have that:

Hence:

70 = (5000 - d)/(80 - t).

d = 45t, hence:

70 = (5000 - 45t)/(240 - t).

5000 - 45t = 5600 - 70t

25t = 600.

t = 600/25

t = 24. -> (80 - 24) = 56.

d = 45t = 45 x 24 = 1080 -> (5000 - 1080) = 3920.

Hence:

1. You were driving 24 hours at 45 mph and 56 hours at 70 mph.

2. You drove 1080 miles at 45 mph and 3920 miles at 70 mph.

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Answer:

2.3 is the mid point of gh

Answer:

Step-by-step explanation:

y=-3/4 x-3

The value of the resulting expression is 3

Given the following expression as shown below;

3 (22-3-7)

According to the pemdas rule, the multiplication will come first inside the parenthesis

3 (22-3-7) = 3(22 - (21))

3 (22-3-7) = 3(22- 21)

Take the difference of the expression in parenthesis

3 (22-3-7) = 3(1)

Take the product of the result

3 (22-3-7) = 3

Hence the value of the resulting expression is 3

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Answer:

$5.86

Step-by-step explanation:

12% of 50=6 pennies

40% of 50= 20 dimes

6+5= 11 nickels

11+20+6= 37 coins

50 total coins-37= 13 quarters

13 quarters = $3.25

20 dimes = $2.00

11 nickels = $0.55

6 pennies = $0.06

$3.25+$2.00+$0.55+$0.06=$5.86

Answer:

$5.86

Step-by-step explanation:

The sweater that cost more is the sweater bought in Manchester. It is more expensive by C$7.40.

The exchange rate is the price at which one currency is exchanged for another currency. For example, if the exchange rate of the pound and Canadian dollars is 1.60. It means that 1 unit of the pound would buy 1.60 of the Canadian dollars.

The first step is to convert the cost of the sweater that is priced in the British pound to Canadian dollars.

The exchange rate : 1 British pound = 1.6215 CAD

28 X 1.6215 = 45.402

Difference in price = 45.402 - 38 = C$7.402

Based on the above calculation, the sweater when converted from the British pound to the Canadian dollars, it is more expensive to buy the sweater in Manchester than it is to buy it in Canada.

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Answer:

B. 19

12,198÷642 so the final answer will be 19.

Answer:

Step-by-step explanation:

Using a linear function, it is found that he would have to ride his bicycle 7.9 miles a day to meet his goal.

A linear function is modeled by:

y = mx + b

In which:

For this problem, we have that:

When x = 4, y = 39.6, hence:

39.6 = 4m + 8

4m = 31.6

m = 31.6/4

m = 7.9.

He would have to ride his bicycle 7.9 miles a day to meet his goal.

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Answer: y=8 and x=8 radical 3

Answer:

The minimum number of samples required is  [tex]n = 16641 [/tex]  

Step-by-step explanation:

From the question we are told that

    The variance is  [tex]\sigma^2 = 0.25[/tex]

    The margin of error is [tex]E = 0.01[/tex]

From the question we are told the confidence coefficient is  0.99 , hence the level of significance is    

      [tex]\alpha = (1 - 0.99 ) \%[/tex]

=>   [tex]\alpha = 0.01[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  2.58[/tex]

Generally the standard deviation is

      [tex]\sigma =\sqrt{\sigma^2}[/tex]

=>   [tex]\sigma =\sqrt{0.25}[/tex]

=>   [tex]\sigma =0.5[/tex]

Generally the sample size is mathematically represented as  

    [tex]n = [\frac{Z_{\frac{\alpha }{2} } *  \sigma }{E} ] ^2[/tex]

=>      [tex]n = [\frac{2.58 } *  0.5 }{0.01 } ] ^2[/tex]

=>      [tex]n = 16641 [/tex]