Margie has a $50 budget to purchase a $45 pair of boots. If there is an 8% sales tax rate, then how much under budget will Margie be.

The trigonometric function gives the ratio of different sides of a right-angle triangle.The correct option is C.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

Let the length of the line segement CD be represented by x.

In ΔABC, Using the pythgorus theorem, we can write,

AB² = BC² + AC²

AB² = 30² + 16²

AB = 34 units

In ΔABC, the measure of ∠A be written as,

tan(∠A) = BC/AC

tan(∠A) = 30/16

∠A = tan⁻¹ (30/16)

∠A = 61.9275°

Now, in ΔABD, the measure of ∠A can be written as,

Cos(∠A) = AB/AD

Cos(61.9275°) = 34/(AC+CD)

0.47 = 34/(16+CD)

16 + CD = 72.25

CD = 56.25 ≈ 56

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The table of contents for the equations is solved

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The total number of people = 76

The number of people who opted for lunch = 28

The number of people who opted for dinner = 33

The number of males who opted for dinner = 19

The number of females who opted for lunch = 18

The total number of females = 36

Now , the table is created from the following equations

+-----------+-------+---------+-------+

|           | Males | Females | Total |

+-----------+-------+---------+-------+

| Breakfast | 11    | 4       | 15    |

+-----------+-------+---------+-------+

| Lunch     | 10    | 18      | 28    |

+-----------+-------+---------+-------+

| Dinner    | 19    | 14      | 33    |

+-----------+-------+---------+-------+

| Total     | 40    | 36      | 76    |

+-----------+-------+---------+-------+

Hence , the equations is solved

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Answer:

Surface area of a square pyramid is:

112 cm²

Step-by-step explanation:

The surface area of square pyramid is given by:

S=2bs+b²

Where b is the length of base and s is the slant height.

and Area of base=b²

Here, s=12 cm

and Area of base=b²=16 cm²

⇒ b=4 cm

Hence, Surface Area=2×12×4+4×4

                                 = 112 cm²

Hence, surface area of a square pyramid is:

112 cm²

The speed of the traveler off the walkway is 4ft/s, while the speed of the moving walkway is 2ft/s. This is found by simultaneously solving the equations formed by the given speeds of the traveler with and against the walkway.

The speed of the traveler, independent of the moving walkway, as well as the speed of the moving walkway itself can be determined using the given speeds of the traveler with the walkway and against it. When the traveler walks in the same direction as the moving walkway, their speeds add together, which is given as 6ft/s. Conversely, when the traveler walks against the movement of the walkway, their velocities subtract which is given as 2ft/s.

That is to say, if we denote the traveler's speed as *T* and the walkway's as *W*, then we have these two equations: *T* + *W* = 6, and *T* - *W* = 2. Solving these equations simultaneously, we find that *T* = 4ft/s, which is the traveler's speed off the walkway, and *W* = 2ft/s, which is the speed of the moving walkway

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We can solve the system of equations x + y = 44 and y = 10x by substitution. When we substitute y = 10x into the first equation, we find that x = 4. Substituting x = 4 into the equation y = 10x gives y = 40.

To solve the system of equations by substitution, we first identify the two equations given: x + y = 44 and y = 10x. We can use the second equation as our substitution into the first equation. This gives us x + 10x = 44, which simplifies to 11x = 44. Solving for x, we divide both sides by 11 to get x = 4.

Next, we substitute x = 4 into the second initial equation, y = 10x, which gives us y = 10*4 = 40.

So, the solution to this system of equations is x = 4 and y = 40.

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[tex] |\Omega|=5\cdot4=20\\
|A|=1\\\\
P(A)=\dfrac{1}{20} [/tex]

The probability that the spinner stops at purple and a pink card is selected is 1/20

The given parameters are:

There is 1 purple color on the spinner and 1 pink card in the card.

So, the probability that the spinner stops at purple and a pink card is selected is:

P(Purple and Pink) = 1/5 * 1/4

Evaluate the product

P(Purple and Pink) = 1/20

Hence, the probability that the spinner stops at purple and a pink card is selected is 1/20

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Using proportions, it is found that the scale of the drawing is of 1 ft:0.4 cm.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, we have that 35 cm represent 87.5 ft. How many cm represent a ft?

The rule of three is given by:

35 cm - 87 ft

x cm - 1 ft

Applying cross multiplication:

[tex]87x = 35[/tex]

[tex]x = \frac{35}{87}[/tex]

[tex]x = 0.4[/tex]

Hence, the scale of the drawing is of 1 ft:0.4 cm.

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Answer:

The greatest possible number of red sweets is 28.

Explanation:

Let g represent the number of green sweets.  We know that the ratio of blue to green is 2:7; this means the number of blue sweets is 2/7 the number of green sweets, or 2/7g.

We also know that the number of green sweets to the number of red sweets is 3:1; this means the number of red sweets to the number of green sweets is 1:3, or that the number of red sweets is 1/3 the number of green sweets:

1/3g

We know that there are fewer than 140 total sweets; this gives us the inequality

g + 2/7g + 1/3g < 140

We must find a common denominator; 21 will work:

21/21g + 6/21g + 7/21g < 140

34/21g < 140

Divide both sides by 34/21:

(34/21g)÷(34/21) < 140÷(34/21)

g < 140÷(34/21)

To divide fractions, flip the second one and multiply:

g < 140×(21/34)

g < 2940/34

This means the number of red sweets will be 1/3 of this:

r < 2940/34 × 1/3

r < 2940/102

102 will go into 2940 28 times, so 28 is the largest number of red sweets.

     Greatest possible number of red sweets in the box will be 28.

 It's given in the question,

        [tex]\frac{b}{g}=\frac{2}{7}[/tex] ⇒ [tex]b=\frac{2}{7}g[/tex] ------(1)

        [tex]\frac{g}{r}=\frac{3}{1}[/tex] ⇒ [tex]r=\frac{1}{3}g[/tex] -------(2)

Since, total number of blue, green and red sweets in the box are less than 140,

[tex]b+g+r< 140[/tex]

Substitute the values of 'b' and 'r' from equations (1) and (2),

[tex]\frac{2}{7}g+g+\frac{1}{3}g< 140[/tex]

[tex]\frac{6g+21g+7g}{21}< 140[/tex]

[tex]\frac{34}{21}g< 140[/tex]

[tex]g< \frac{140\times 21}{34}[/tex]

Since, [tex]g=3r[/tex],

[tex]3r< \frac{140\times 21}{34}[/tex]

[tex]r< \frac{140\times 21}{34\times 3}[/tex]

[tex]r<28.82[/tex]

   Therefore, greatest possible number of red sweets will be 28.

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Answer:

The answer is D, and with the others you aren't experimenting with anything

Step-by-step explanation:

It is given Sally is making sun tea. Every hour the concentration of the tea doubles.Let the concentration of tea  at start is  nil.Then after  first hour concentration will be 2.After third hour concentration will be double of 2 that is 4.After fourth concentration will be 4(2)=8.After fifth hour concentration will be 8(2)=16.After sixth hour concentration will be 16(2)=32.

It is given:it takes 6 hours for the tea to be ready.WE need to find  how long would it take the tea to reach half of the final concentration.Half of final concentration is 32÷2=16.

Concentration of 16 is after fifth hour.

Since angle LMN = angle PQR, angle M = angle Q

Since angle Q = 55 degrees, Angle M also = 55 degrees

We know that the three angles of a trainangle should be equal to 180 degrees

So, L + M + N = 180

Angle L is the unkown x

x + 55 + 39 = 180

x +94 =180

x = 180-94

x = 86 degrees