One angle of a right triangle measures 24°. What is the measure of the other acute angle?

We have

arctan(-1) = -π/4

cos(-π/4) = 1/√2

and

arccos(√3/2) = π//6

sin(π/6) = 1/2

Then

cos(arctan(-1)) / sin(arccos(√3/2)) = (1/√2) / (1/2) = √2

Answer: 2.8%

Step-by-step explanation: 1/6 * 1.6 = 1/36   1/36 = 0.0277 = 2.8%

The questions are all illustrations of conditional probabilities, and they can be solved using the general conditional probability formula; P(A|B) = P(A and B)/P(B)

The conditional probability P(A|B) is calculated using:

P(A|B) = P(A and B)/P(B)

Using the above formula, we have:

P(has at least 4 sides| not a hexagon) = 38/50

P(has at least 4 sides| not a hexagon) = 0.76

P(not a square | has less than 7 sides) = 30/45

P(not a square | has less than 7 sides) = 0.67

P(not an octagon | not a triangle) = 39/51

P(not an octagon | not a triangle) = 0.76

P(octagon | sum of interior angle measures is at least 600) = 9/25

P(octagon | sum of interior angle measures is at least 600) = 0.36

The conditional probability is calculated using:

P = P(perfect attendance and honor roll)/P(Honor roll)

So, we have:

P = 25%/38%

Evaluate

P = 0.66

Hence, the probability that a student has a perfect attendance, given that he made the honor roll is 0.66

The conditional probability is calculated using:

P = P(Home has a pool and at least 3 bedrooms)/P(at least 3 bedrooms)

So, we have:

P = 25%/70%

Evaluate

P = 0.36

Hence, the probability that a home has a pool, given that it has at least 3 bedrooms is 0.36

Using the conditional probability formula in (a), we have:

P(uses Ins tag ram| does not use Sna pch at) = 45/(20 + 45)

P(uses Ins tag ram| does not use Sna pch at) = 0.69

P(does not use Ins tag ram| uses Sna pch at) = 25/(30 + 25)

P(uses Instag ram| does not use Sna pch at) = 0.45

Using the conditional probability formula in (a), we have:

P(plays sport| has a part-time job) = 22/68

P(plays sport| has a part-time job) = 0.32

P(has a part-time job| plays sport) = 22/40

P(has a part-time job| plays sport) = 0.55

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Step-by-step explanation:

speed = distance/time

time = t = distance/speed

t = 180/b + (400-180)/c = 180/b + 220/c = 20(9/b + 11/c)

Answer:

ans willbe -8

Step-by-step explanation:

-1/2 × 2 =-1

-1×2=-2

-2×2=-4

-4×2=-8

The properties that equilateral triangles and isosceles triangles have in common is that they have two equal sides.

A triangle is a polygon that has three sides and three angles. Types of triangles are isosceles, equilateral and scalene triangle.

An equilateral triangle is a triangle that have three equal sides while isosceles triangle have two equal sides.

The properties that equilateral triangles and isosceles triangles have in common is that they have two equal sides.

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The total number of student tickets were sold is 183 if the theater production cost $18 for students and $25 for non-students.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the x number of students tickets were sold and

y number of tickets were sold for non students.

Then we can frame two linear equations:

x + y = 320 ...(1)

18x + 25y = 6719 ...(2)

From equation (1) take the value of y and plug into the equation (2)

18x + 25(320 - x) = 6719

18x + 8000 - 25x = 6719

7x = 1281

x = 183 tickets

Thus, the total number of student tickets were sold is 183 if the theater production cost $18 for students and $25 for non-students.

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Answer:

36 [tex]cm^{2}[/tex]

Step-by-step explanation:

Answer:

36cm² is the answer.....

Answer:

10 + 7 + 4 + . . .; n = 5​

The series is arithmetic

Common difference between terms = (-3)

10 - 3 = 7

7 - 3 = 4

Or:

10 + (-3) = 7

7 + (-3) = 4

--------------------------------------------------------------------------

Another example:

Arithmetic:

5, 9, 13, 17

common difference = 4

5 + 4 = 9

9 + 4 = 13

Geometric:

4, 8, 16, 32

4 × 2 = 8

8 × 2 = 16

16 × 2 = 32

common ratio = 2

--------------------------------------------------------------------------

10 + 7 + 4 + . . .; n = 5​

a₁ = 10

a₂ = 7

a₄ = a₃ + d = 4 + (-3) = 4 - 3 = 1     (d = common difference)

a₅ = a₄ - 3 = 1 - 3 = -2

Or with formula:

[tex]d=a_{n} -a_{n-1}[/tex]

d = a₂ - a₁ = 7 - 10 = -3

aₙ = a₁ + (n - 1)d

fourth term = a₄ = 10 + (4 - 1)(-3) = 10 + 3(-3) = 10 + (-9) = 10 - 9 = 1

fifth term = a₅ = 10 + (5 - 1)(-3) = 10 + 4(-3) = 10 + (-12) = 10 - 12 = -2

Sum of the finite series (if n = 5):

[tex]S_{n} =\frac{n(a_{1} +a_{n} )}{2} \\S_{5} =\frac{5(a_{1} +a_{5} )}{2} \\S_{5} =\frac{5(10 +(-2) )}{2} \\S_{5} =\frac{5(8 )}{2} =\frac{40}{2} =20[/tex]

Manual count: S₅ = 10 + 7 + 4 + 1 + (-2) = 20

The equivalent expression of the given expression 50 - 10 - 15 will be 50 + (- 10) + (- 15). Then the correct option is C.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

→ 50 - 10 - 15

Then the expression can be written as

→ 50 + (- 10) + (- 15)

Thus, the correct option is C.

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1) All angles of a rectangle are right angles, so the measure of angle CBA is 90 degrees.

2) Since all angles of a rectangle are right angles, angle BAD measures 90 degrees. Subtracting the 25 degrees of angle BAW from this, we get that angle CAD has a measure of 65 degrees.

3) Opposite sides of a rectangle are parallel, so by the alternate interior angles theorem, the measure of angle ACD is 25 degrees.

4) Because diagonals of a rectangle are congruent and bisect each other, this means BW=WA. So, since angles opposite equal sides in a triangle (in this case triangle ABW) are equal, the measure of angle ABW is 25 degrees. This means that the measure of angle CBD is 90-25=65 degrees.

5) In triangle AWB, since angles in a triangle add to 180 degrees, angle BWA measures 130 degrees.

6) Once again, since diagonals of a rectangle are congruent and bisect each other, AW=WD. So, the measures of angles WAD and ADW are each 65 degrees. Thus, because angles in a triangle (in this case triangle AWD) add to 180 degrees, the measure of angle AWD is 50 degrees.

Answer:

357.46 meters squared

Step-by-step explanation:

16 x 12.2 x 1/2 = 97.6

12.2 x 10.6 = 64.66

97.6 x 3 = 292.8

292.8 + 64.66 = 357.46

Answer:

34000

Step-by-step explanation:

Answer:

90 degrees.

Step-by-step explanation:

Assuming x is the bottom right of the blue triangle, x would be 90 degrees, since the triangle has a right angle.

Right angles are always 90 degrees.

I think is may be what you're looking for, hope this helps! If not, please do let me know.

Answer:

17.5%

Step-by-step explanation:

I took the test and got it right

Answer:

THE ANSWER IS C) "17.5%"

Para estudiantes de Español:

LA RESPUESTA ES C) "17.5%"

Step-by-step explanation:

PICK C)!

ELIJA C)!

Answer:

C. 6 units

Step-by-step explanation:

(-3, 2) and (-3, -4)

2-(-4)=6

-3-(-3)=0

Answer:

He can save 20 dollars

Step-by-step explanation:

He can buy one 100 token amount and one 25 token amount. This will cost 20 + 10 dollars, or 30 dollars. If each friend buys 25 tokens, it will cost

10 * 5 dollars, or 50 dollars. 50 - 30 = 20. So he can save 20 dollars.

Answer:

6.75 square feet

Step-by-step explanation:

[tex]4.5 \times 1.5 = 6.75[/tex]

So the volume is 6.75 square feet.

Answer: the product of this question is 858

Step-by-step explanation:

Answer:

ok so first you add all the prices together.

$9:00+$7:00+$8:00+$6:00+$4:00=34

then divide 34 by the number of prices.

34/5

then you get the mean

$6.8 is the mean

Step-by-step explanation:

Answer:

Maya is correct. She wrote equivalent fractions with the same denominator and then correctly compared the fractions. Aimee wrote equivalent fractions with the same numerator but did not correctly compare the fractions. Only Maya is correct.

When you're comparing fractions, you have to set them equal to the same denominator, not the same numerator.

Hope this helps

Answer:

x = 20

Step-by-step explanation:

You know that these 2 triangles are similar, so you can set a proportion! That is a quality that all similar triangles have.

I've redrawn the triangles to make it easier to view, as well as setting up the proportion. Please do know you can use 6 to 12 = 25 to x, there are multiple ways of solving this.

There are 3 shapes present.

Triangle - 2

Circle - 4

Square - 2

The ratio of triangles to circles: 2 triangles to 4 circles ⇒ 2/4

2/4 simplified to 1/2.

Answer:

890.625

Step-by-step explanation:

2.5x2.5x2.5 (Volume of Cube)=15.625

Density is 57

57=x/15.625

890.625=x

Answer:

12^2x = 7^4 = 2401

7^2=12^x

We know that a^x * a^x = a^(x+x) or a^2x

Multiply each side by 12^x

7^2 * 12^x=12^x * 12^x

7^2 * 12^x = 12^(x+x)

Replace 12^x with 7^2 on the left hand side since they are equal

7^2 * 7^2 = 12^ (2x)

7^(2+2) = 12^(2x)

7^4 = 12^2x

2401 = 12^2x

Step-by-step explanation: