Find the sine and cosine for each angle shown (30°, 45°, 60°, and 90%). Round off to 5 decimal places, if necessary.
sin(30) =
sin(45) =
sin(60°) =
sin(90°) =
cos(30°) =
cos(45°) =
cos(60°) =
cos(90°) =

Answer:

88

Step-by-step explanation:

126=w+38

w=126-38

=88

Answer:

110- 37.25=72.25

72.25 divided by .20 =361.25

but since you can not drive part of a mile it would be 361 miles in one day.

Step-by-step explanation:

Final answer:

After subtracting the fixed daily rental rate from the daily budget and dividing the remainder by the cost per mile, it is calculated that the business person can travel 363.75 miles with the $110 budget.

Explanation:

To calculate how many miles the business person can travel on the $110 budget using the daily car rental rate provided, we can set up an equation based on the cost structure of Value Rent-A-Car. The rental cost consists of a fixed daily rate plus a variable cost per mile.

The fixed daily rate is $37.25, and the cost per mile is $0.20 (20 cents). With a daily budget of $110, we first subtract the fixed rate from the daily budget to find out how much money is left for the variable cost per mile:

Daily budget for miles = Total daily budget - Fixed daily rate
Daily budget for miles = $110 - $37.25
Daily budget for miles = $72.75

Now, we divide the money left for miles by the cost per mile to find the number of miles the business person can travel:

Number of miles = Daily budget for miles / Cost per mile
Number of miles = $72.75 / $0.20
Number of miles = 363.75 miles

The business person can travel 363.75 miles on the daily budget of $110, given the cost structure of the car rental.

Answer:

A triangles angles equal 180 so add 90 and 60 then subtract that from 180. 2) yes. they have same angles so they must be congruent

A triangle with two angles that measure 34°.

Then the correct option is A.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

here, we have,

In triangle ΔABC, the measure of the third angle is calculated as,

∠C + ∠B + ∠A = 180°

∠C + 112° + 34° = 180°

∠C = 34°

The measure of the two angles of the triangle is identical.

Then the triangle will be an isosceles triangle.

A triangle with two angles that measure 34°.

Then the correct option is A.

More about the triangle link is given below.

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Complete Question:

Triangle ABC is shown.

Which triangle listed below must be similar to triangle ABC?

(1 point)

(A) A triangle with two angles that measure 34°

(B) A triangle with angles that measure 34° and 66°

(C) A scalene triangle with only one angle that measures 112°

(D) An isosceles triangle with two angles that measure 56°

Include with your answer choice below, reasoning why your choice is correct.

(2 points)

Use formulas, definitions, or theorems in your reasoning.

- What is it about the angles?

- Anything with the angle sums?

- What about the type of triangles?

Answer:

Step-by-step explanation:

Find a common denominator or greatest common factor. 63 and 27 are both multiples of 9. When you divide each by 9 you get 7:3. 14 and 6 are both multiples of 2. When you divide each by 2 you get 7:3 again. So these ratios are equivalent.

Start with any set of numbers. Multiply them each by the same factor and the new set will be an equivalent ratio.

Answer:

240 square units

Step-by-step explanation:

Area of shape =area of rectangle + area of triangle

[tex] = 20 \times 10 + \frac{1}{2} \times 20 \times 4 \\ = 200 + 40 \\ = 240 \: {units}^{2} [/tex]

Answer:

D.

Step-by-step explanation:

Its given that the rectangle has a perimeter of 60 units. A rectangle has four sides, and to get the perimeter, you add up all four sides. You are given one side is 20 units, and the other as 'x.'

So,

x + x + 20 + 20 = 60

2x + 40 = 60

Example for *wrong* answer:

Letter C, x + 20 = 60, that would'nt equal 60 because youre only adding two sides instead of all four.

Hopefully this helps :)

Answer:

[tex]22\ m < x < 74\ m[/tex]

Step-by-step explanation:

Let

x ----> the length for the third side

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Applying the triangle inequality theorem

1) [tex]26+48> x[/tex]

solve for x

[tex]74> x[/tex]

Rewrite

[tex]x < 74\ m[/tex]

2) [tex]26+x>48[/tex]

solve for x

subtract 26 both sides

[tex]x> 22\ m[/tex]

therefore

The range of  possible lengths, in meters, for the third side is equal to

[tex]22\ m < x < 74\ m[/tex]

The range of the possible length of the third side of the triangle is 22 to 74 (exclusive)

Assume the lengths of a triangle are x, y and z.

The following are the possible inequalities that relate the side lengths

[tex]x + y > z[/tex]

[tex]y + z > x[/tex]

[tex]x + z > y[/tex]

The unknown side length is x.

So, we have:

[tex]x + 26 > 48[/tex]

[tex]48 + 26 > x[/tex]

[tex]x + 48 > 26[/tex]

Solve for x in the three inequalities

[tex]x + 26 > 48[/tex]

[tex]x > 22[/tex]

[tex]48 + 26 > x[/tex]

[tex]74 > x[/tex]

[tex]x + 48 > 26[/tex]

[tex]x > -22[/tex]

The values of x cannot be negative.

So, we ignore the inequality [tex]x > -22[/tex]

We are left with

[tex]74 > x[/tex] and [tex]x > 22[/tex]

Combine the inequalities

[tex]74 > x > 22[/tex]

Rewrite as:

[tex]22 < x < 74[/tex]

Hence, the range of the possible length is 22 to 74 (exclusive)

Read more about triangle inequalities at:

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Rani and her friends can purchase their supplies for $48 after a 20% discount on the original price of $60.

Rani and her friends need to calculate the sale price of the supplies after a 20% discount. The original price is $60, and the discounts amount in money can be determined by multiplying this original cost by 20% or 0.20. This gives you a discount amount of $12. To determine the final price after the discount, you subtract the discount amount from the original price. Therefore: $60 - $12 = $48. Hence, the sale price of the supplies that Rani and her friends need is $48.

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Answer:

Step-by-step explanation:

You know the relation between X and Z is ...

  Z = (X -μ)/σ

Solving for X, we find ...

  Zσ +μ = X

You're trying to find the exam scores that correspond to the Z-values you found in question 3.

  A = 90th percentile and above = 1.28(8) +78 = 88.24 ≈ 88

  B = 80th percentile and above = 0.84(8) +78 = 84.72 ≈ 85

  C = 70th percentile and above = 0.52(8) +78 = 82.16 ≈ 82

  D = 60th percentile and above = 0.25(8) +78 = 80

So, your blanks are filled like this ...

  A: 88 — 100

  B: 85 — 87

  C: 82 — 84

  D: 80 — 81

  F: 0 — 79

_____

Comment on this curve

The setup guarantees that 60% of the class will fail. It is more common to have those below Z = -2 get an F, and those above Z = 2 get an A.

Answer:

Positive correlation              

Step-by-step explanation:

Correlation:

Thus, the correct answer is

Positive correlation  

Answer:

Negative Correlation

Step-by-step explanation:

The false statement is "the median of the data is 37" because the IQR of the data is 20 option (a) is correct.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

It is given that:

A box plot is shown in the picture;

As we know,

The interquartile range(IQR):

IQR = Q3 - Q1

IQR = 50 - 30

IQR = 20

From the box plot:

The median of the upper half of the data is 49.

The median of the data is 37.

Three-fourths of the data is less than 49.

Thus, the false statement is "the median of the data is 37" because the IQR of the data is 20 option (a) is correct.

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Susan have 9 books.

Explanation:

Given that Marge has 4 more than 2 times as many books as Susan.

Let x represents the number of books that Susan has.

The relationship is written as

[tex]4+2x=22[/tex]

To find: Number of books that Susan have.

The number of books that Susan have can be determined by solving the expression for x.

Thus, we have,

[tex]4+2x=22[/tex]

Subtracting 4 from both sides of the equation, we get,

[tex]2x=18[/tex]

Dividing both sides by 2, we get,

[tex]x=9[/tex]

Therefore, Susan has 9 books.

Answer:

n=14

Step-by-step explanation:

do 28/2=14

The value of n is 14 when area is 28 square feet.

The area of Rectangle is length times of width.

The formula for the area of a rectangle is

Area = length × width

The width = 2ft and

the area = 28 sq ft.

So, we can write the above equation as

28 = n×2

2n = 28

Divide both sides by 2.

n=14

Hence, the value of n is 14 when area is 28 square feet.

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Answer:

y + 12 = 3(x-2)

Step-by-step explanation:

To start, you want the slope of the other line. Well, the slope of a parallel line is the same, so since the first line's slope is 3, so will the other one. then, because there is no other answer with a slope of 3, you automatically know it is the third answer. you don't need to work this problem further, but if you need to in the future, just comment and I will help you.

Answer:

j

Step-by-step explanation:

j

Answer:

K=6

Step-by-step explanation:

Subtract 5 from 11

Answer:

3/(30×30×30) = 3/27000 = 0.0001 or 0.01%

Step-by-step explanation:

Answer:

here we have 3 dials in the slot machines and each dial has 30 position

so probability of getting a number of the each dial   =  

30

1

​

since all dials are independent so probability of getting same number would be

P ( getting jack pot) =  

30

1

​

30

1

​

30

1

​

   =    

27000

1

​

   = 0.003% option D is correct.

Step-by-step explanation:

Answer:

Top Left.) None of these, these are vertical angles.

Top Right.) Alternate Exterior

Middle Left.) None of these

Middle Right.) Corresponding

Bottom.) Alternate interior angles

Answer:

If necessary, first "unwind" the angle:   Keep subtracting 360 from it until it is lies between 0 and 360°. (For negative angles add 360 instead).

Sketch the angle to see which quadrant it is in.

Depending on the quadrant, find the reference angle:

Answer:

the (2x) obviously because it is close to an acute angle and the (13x) is closer to a right angle

Step-by-step explanation:

Answer:

4t^2-32t+64=4(t^2-8x+16)

Step-by-step explanation:

f(x)=4x^2-8x+4

f(t-3)=4(t-3)^2 - 8(t-3)+4=

4(t^2-2*t*3+9)-8t+24+4=

4(t^2-6t+9)-8t+28=

4t^2-24t+36-8t+28=

4t^2-32t+64=4(t^2-8x+16)

Answer:11

Step-by-step explanation:

5x-6-x+9

When x=2 we have

5(2)-6-2+9

10-6-2+9

10+9-6-2

19-6-2=11

Answer:

11

Step-by-step explanation:

5x - 6 - x + 9

4x + 3

x = 2

4(2) + 3 = 11

Answer:

True

Step-by-step explanation:

We want to determine whether the given statement is true or false.

The difference of -10 and 4 is

[tex] - 10 - 4 = - 14[/tex]

We multiply the result by 2 to obtain;

[tex]2( - 14) = - 28[/tex]

Therefore two times the difference of -10 and 4 amounts to -28 is a true statement.

R=7

I hope that help you! :)

Answer:

Step-by-step explanation:

Rate of interest is 5%.

Time =3years

Amount =$852

Then, we need to find P

Generally compound interest is given as

A=P(1+r/n)^nt

A=final amount

P=initial principal balance

r=interest rate

n=number of times interest applied per time period=12

t=number of time periods elapsed

A=P(1+r/n)^nt

852=P(1+0.05/12)^(12×5)

852=P(1+0.004167)^60

852=P(1.004167)^60

852=1.2834P

Then, P=852/1.2834

P=$663.88

Then the principal amount invested is $663.88

Approximately $664

Answer:

y = 2x + 8

6x + 3y = 19

6x + 3(2x + 8) = 19

6x + 6x + 24 = 19

12x = -5

x = -5/12

y = 2(-5/12) + 8

y = -5/6 + 48/6

y = 43/6

Final answer:

Using the base angle and the height of the cone, we can use trigonometry to find that the width of the base of the cone needs to be approximately 41.57 inches, making option C the correct answer.

Explanation:

The question asks for the width of the base of a cone given that its base angle is 60° and its height is 24 inches. To solve this, we need to understand that the base angle of 60° creates a right-angled triangle when a line is drawn from the apex of the cone to any point on the base's circumference, with the height of the cone being one side of this triangle and half of the cone's base width being the other side.

Using trigonometry, specifically the tangent function, which is the opposite side (half the base width) over the adjacent side (height), we can solve for the base width. Given that tan(60°) = √3 and the height is 24 inches, the formula becomes √3 = (base width/2) / 24, solving for the base width gives us roughly 41.57 inches, which makes option C correct.

Answer: a. 4/9

b. 270 students

Step-by-step explanation:

Answer:

270

Step-by-step explanation:

120÷4= 30

30×5=150

150+120=270

Answer: We find out what these numbers have in common for example:

11yd+5yd=16yd so what is 13yd+6yd it is 19yd. This is your answer.

Step-by-step explanation: I hope this helps!

Answer:

The answer is A

Step-by-step explanation:

There is no way to prove any of the others to be true

Final answer:

The median EF in an isosceles trapezoid is parallel to its bases, making option A the correct answer.

Explanation:

The student asked a question related to properties of an isosceles trapezoid and its median. In an isosceles trapezoid, the median is a line segment that connects the midpoints of the non-parallel sides. The properties of a trapezoid's median include that it is parallel to the two bases and that its length is equal to the average of the lengths of the two bases. Therefore, the correct statement from the list provided is that the median EF is parallel to the bases.

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