PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.

The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.

According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.

The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:

Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25

Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.

So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.

Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

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Answer:

c:x=6√3,y=12

Step-by-step explanation:

the shape

Answer:

C

Step-by-step explanation:

The base angles are congruent, both 60°, thus the triangle is isosceles and x is a perpendicular bisector ( divides the base into 6 and 6 )

Using the tangent ratio in the right triangle on the left and exact value

tan60° = \(\sqrt{3}\) , then

tan60° = \(\frac{opposite}{adjacent}\) = \(\frac{x}{6}\) ( multiply both sides by 6 )

6 × tan60° = x , that is

x = 6\(\sqrt{3}\)

Using the cosine ratio in the same right triangle and exact value

cos60 = \(\frac{1}{2}\) , then

cos60° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{6}{y}\) ( multiply both sides by y )

y × cos60° = 6 , that is

y × \(\frac{1}{2}\) = 6 ( multiply both sides by 2 )

y = 12

Answer:

x

−

3

x

−

2

Step-by-step explanation:

Answer:

\(x = 2\)

\(y = 5\)

Step-by-step explanation:

The graph is in the attached image above

Answer:

=======================

Given equations:

Solve by graphing, graph each line and find the point the lines intersect, this point is the solution.

See the attached, the solution is (2, 5)

Answer:

There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.

The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.

hope it helps you...

Answer:

their sizes vary

Step-by-step explanation:

their sizes vary

Answer: 0.1008188

Step-by-step explanation:

The question will usng the poisson distribution formula:

Given :

Mean(λ) number of occurrence in a given interval = 3

P(X=x) = Probability of exactly x occurrence in a given interval

Number of desired occurence(x) = 5

P(X=x) = [(λ^x) * (e^-λ)] / x!

Where ; e = base of natural logarithm = 2.7182818

P(X=5) = [(3^5) * (e^-3)] / 5!

P(X=5) = [(243) * (0.0497870)] / 120

P(X=5) = [12.098257] / 120

P(X=5) = 0.1008188

Answer:0.10

Step-by-step explanation:

Answer:

about -1

Step-by-step explanation:

0.9999999999 minus 2

Answer:

Area of annulus is 40.85cm² to 2d.p

Step-by-step explanation:

Area of shaded part=Area of bigger circle -Area of smaler circle

Area of annulus= πR²- πr²= π(R²-r²)

A=3.142(7²-6²)

A=3.142(49-36)

A=3.142×13

A=40.846cm²

A=40.85cm² to 2d.p

Work Shown:

LCM = (product of two numbers)/(HCF of the two numbers)

LCM = 1536/16

LCM = 96

x+7>=12

Hope this helps?

Can you mark my answer as brainliest please?

Answer:

see the attachment photo!

Answer:

4(2x + 1)

Step-by-step explanation:

14x + 4 - 6x

Rearrange the expression with like terms together

14x - 6x + 4

8x + 4

Factorize the expression

4(2x + 1)

Take LCM

Now

Answer:

23/20

Step-by-step explanation:

2/5 + 3/4

LCM = 5 * 4 = 20

=》2/5 * 4/4 = 8/20

=》3/4 * 5/5 = 15/20

So,

2/5 + 3/4

= 8/20 + 15/20

= 23/20

_________

Hope it helps ⚜

The requried center and radius of the given circle are (2, -4) and 5.

The standard equation of a circle is given as,
(x - h)² + (y - k)² = r²

Where, (h, k) is the center of the circles and r is the radius of the circle,

The equation of the given circle is,
(x - 2)² + (y + 4)² = 25

Comparing the above equation with the standard equation we have,
(h, k) = (2, -4)

r² = 5²; r =5

Thus, the requried center and radius of the given circle is (2, -4) and 5.

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Recall the half-angle identity for cosine:

cos²(x) = 1/2 (1 + cos(2x))

Then we can rewrite the integrand as

cos³(4x) = cos(4x) cos²(4x) = 1/2 cos(4x) (1 + cos(8x))

So we have

\(\displaystyle \int \cos^3(4x) \, dx = \frac12 \int (\cos(4x) + \cos(4x)\cos(8x)) \, dx\)

Next, recall the cosine product identity,

cos(a) cos(b) = 1/2 (cos(a - b) + cos(a + b))

so that the integral is equivalent to

\(\displaystyle \int \cos^3(4x) \, dx = \frac12 \int \cos(4x) \, dx + \frac14 \int (\cos(4x - 8x) + \cos(4x + 8x)) \, dx\)

\(\displaystyle \int \cos^3(4x) \, dx = \frac34 \int \cos(4x) \, dx + \frac14 \int \cos(12x) \, dx\)

Computing the rest is trivial:

\(\displaystyle \int \cos^3(4x) \, dx = \boxed{\frac3{16} \sin(4x) + \frac1{48} \sin(4x) + C}\)

If we write a quadratic in vertex form:

\(y=a(x-h)^2+k\)

Then:

\(\bold{a}\)   \(\longrightarrow\)    is the coefficient of \(x^2\)

\(\bold{h}\)   \(\longrightarrow\)    is the axis of symmetry.

\(\bold{k}\)   \(\longrightarrow\)    is the max/min value of the function.

Also:

If \(a > 0\) then the parabola will be of the form \(\cup\) and will have a minimum value.

\(a < 0\) then the parabola will be of the form \(\cap\) and will have a minimum value.

For the given functions:

\(a < 0\)

\(f(x)=-(x-1)^2+5\)        this has a maximum value of \(\bold{5}\)

\(a > 0\)

\(f(x)=(x+2)^2-3\)           this has a minimum value of \(\bold{-3}\)

Total amount of money in the account will be $456.

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest.

The formula for simple interest is: Simple Interest = Principal × Rate × Time

Principal (P) is $300

Rate (R) is 6.5%

Time (T) is 8 years.

Simple Interest = $300 × 0.065 × 8

Simple Interest = $156

Total Amount = Principal + Simple Interest

Total Amount = $300 + $156

Total Amount = $456.

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Therefore, there are approximately 889 faculty members at the college.

Ratio is a mathematical concept that expresses the relationship between two or more quantities or values. It is a way to compare the size of two numbers, by dividing one number by the other. The result of this division is a numerical expression of the relative size of the two numbers.

Ratios are often expressed as a fraction or a colon (:) between the two numbers. For example, if there are 4 red balls and 6 blue balls in a bag, the ratio of red balls to blue balls can be expressed as 4/6 or 4:6. This means that for every 4 red balls in the bag, there are 6 blue balls.

Ratios are commonly used in various fields, such as finance, statistics, and science, to compare different values and make meaningful interpretations.

To solve this problem, we need to use the ratio between faculty members and students, which is given as 1:18. This means that for every one faculty member, there are 18 students.

If there are 16000 students in the college, we can find the number of faculty members by dividing the number of students by the ratio of students to faculty members:

Number of faculty members = 16000 / 18

This gives us 888.888, but since we are asked to round to the nearest whole number, we should round up to 889. Therefore, there are approximately 889 faculty members at the college.

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The statement is asserting that the universal class (V) is defined as the collection of all sets, where every set is included. It signifies that V encompasses all possible sets within the given set theory framework.

The statement "The universal class set, or universe, is the class of all sets: V = {x: x = x}" is referring to the concept of the universal class or the universe in set theory.

In set theory, the universal class set, denoted as V, represents the collection or class that contains all sets. It includes every possible set that can be defined or exists within the context of the set theory being considered.

The notation "{x: x = x}" is used to define the elements of the universal class. Here, "x = x" represents a condition that is always true for any object or element, regardless of its nature. In other words, this condition holds for everything in the universe, as anything is equal to itself.

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The Surface Area of cylinders are: 100 yd² , 264 m², 226  mm²

The Surface Area of Can is 219 cm².

We know the formula for Surface Area of Cylinder

= 2πrh

1. Radius = 2 yd

Height = 8 yd

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 2 x 8

= 100 yd²

2. Radius = 7 m

Height = 6 m

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 6 x 7

= 264 m²

3. Radius = 3 mm

Height = 12 mm

So,  Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 3 x 12

= 226  mm²

4. Radius = 3.5 cm

Height = 10 cm

So, Surface Area of Can

= 2πrh

= 2 x 3.14 x 3.5 x 10

= 219 cm²

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Volume of given two cylinders are 115.52π m³ and 350π in³

What is the formula for the volume of a cylinder?

\(V = π {r}^{2} h\)

where r is the radius of the cylinder, h is the height of the cylinder, and π is a constant approximately equal to 3.14.

4) Given, radius =3.8 m and height = 8 m

Substituting the given values into the formula, we get:

\(V = π × (3.8)^2 × 8 \\ V = 115.52\pi \: cubic \: meters\)

Therefore, the volume of the cylinder is approximately 361.984 cubic meters.

5) Given, radius = 5 in and height = 14 in

Substituting the given values:

\(V = π(5²)(14) \\ V = π(25)(14) \\ V = 350π\)

Therefore, the volume of the cylinder is 350π cubic in (or approximately 1099.56 cubic meters if you want to use a numerical approximation for π).

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To determine if each expression is decreased or increased by 8% you can substitute the n in the expressions by 100 and then evaluate the expression, if the result is 92 it decrease, if it is 108 it increase:

First expression: decrease n by 8%

Second expression: increase n by 8%

Third expression: increase n by 8%

Fourth expression: decreased n by 8%

Answer:

48/13

Step-by-step explanation:

To make this into an improper fraction, convert the integer into a fraction using the denominator of the fraction

3 * 13/13 = 39/13

Then add it to the rest of the fraction

39/13 + 9/13

= 48/13

Answer: 48/13

Step-by-step explanation: first multiply 3 x 13 to get 39. do this because you get the fraction for the whole number, 3. then, add 39 to the numerator (9). you will get 48/13. you do this because you are adding the whole number (3) to the fraction so that way it is an improper fraction.

9514 1404 393

Answer:

  y = 4x +3

Step-by-step explanation:

The slope formula can be used to find the slope:

  m = (y2 -y1)/(x2 -x1)

Using the first two lines of the table, we find the slope to be ...

  m = (11 -7)/(2 -1) = 4/1 = 4

__

The y-intercept can be found from the relation ...

  b = y -mx

Using the slope we found, and the first line of the table, we find the intercept to be ...

  b = 7 -4(1) = 3

__

Then the equation is ...

  y = mx +b . . . . . . slope-intercept form of the equation for a line

  y = 4x +3

The output value of (f∘g)(x) is:  \((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)

The domain of (f∘g)(x) is (-∞, -3) U (-3, ∞).

In this scenario, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations (multiplication) in simplified form as follows;

\(f(x) = \frac{x-6}{x +3}\)

g(x) = 4x - 15

Next, we would write the numerators and denominators in factored form as follows;

(x - 6)(4x - 15)

4x² - 15x - 24x + 60

4x² - 29x + 60

Now, we can derive the corresponding composite function of f(x) and g(x);

\((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)

For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;

x + 3 ≠ 0

x ≠ -3

Domain = (-∞, -3) U (-3, ∞).

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The value of a year of college is more than $70000

The person decided to turn down this offer and instead attend a year of college

The total monetary cost of the year of college, including tuition, fees, and room and board expenses, is $43,000.

This means that the person has forgone the salary from working as a floor trainer. This is the opportunity cost of attending the college

Opportunity cost = $27000

Cost of attending college = $43000

Total cost = $27000+ $43000= $70000

Despite a cost of $70000 the person decides to attend the college showing that he values the college More than the salary that he would have earned from working

So he values the college more than $70000

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Answer:

3/2 or 1.5

Step-by-step explanation:

(3/4) / (1/2) = (3/4) * (2/1)

                 = 6/4

                 = 3/2

It is given that,

→ 3/4 ÷ 1/2

We can divide the given values,

→ 3/4 ÷ 1/2

→ 3/4 × 2/1

→ 6/4

→ 3/2 (or) 1.5

Thus, 3/2 (or) 1.5 is the answer.

Answer:

143 in.²

Step-by-step explanation:

area = l × b = 7 × 10 = 70 in.²

12 × 4 = 48 in.²

5 × 5 or 5² = 25 in.²

now,

add them

70 + 48 + 25 = 143 in.²

therefore, area of the given figure is 143 in.².

hope this helps you !