Simplify the expression:
89 - 9

HELP PLZ

Answer:

80

Step-by-step explanation:

180-(60+40)=180-60-40=180-100=80

Answer:

Angle CAB= 80 Degrees

Step-by-step explanation:

The angle A can be found by taking the sum of angles in the 2 separate triangles and adding them together.

We know that a straight line is 180 degrees. The angle ADC is given to be 90 degrees, therefore angle BDA is also 90 degrees because 180-90=90 degree (congruent angle). (both the small triangles are right angle triangles) This gives us 2 angle measurements in each triangle. This means for both triangkes we can add the 2 angle measurements to find the sum of both andlges and subtract that number from 180 because 180 is the sum of all angles in a triangle.

For Triangle BDA we add angle B (40 degrees) and angle D (90 degrees)

Angle= 180- (40+90)

Angle= 180-130

Angle= 50 degrees

For triangle DAC we add angle D(90 degrees) and angle C(60 degrees)

Angle= 180- (90+60)

Angle = 180-150

Angle= 30 degrees

To find the angle measurement for angle CAB we add the answer from both the calculations as shown above (add 50 and 30)

Angle CAB= 50+30

Angle CAB= 80 degrees

Therefore angle CAB= 80 degrees

Answer:

Step-by-step explanation:

A

The difference in the areas of the signals based on the information given is 549.5km².

The formula to calculate the area of a circle will be:

= πr²

where r = radius

Mast 1 broadcast radio signals that can be heard within a radius of 15km. The area will be:

= πr²

= 3.14 × 15²

= 706.5km²

Mast 2 broadcast radio signals that can be hear within a radius of 20km. The area will be:

= πr²

= 3.14 × 20²

= 1256km²

The difference in the areas will be:

= 1256km² - 706.5km²

= 549.5km²

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Complete question

Mast 1 broadcast radio signals that can be heard within a radius of 15km.

Mast 2 broadcast radio signals that can be hear within a radius of 20km.

Calculate the difference in the areas of the signals.

Answer: B.

Step-by-step explanation:

Answer:

93/100

Step-by-step explanation:

In a group of 100 students, 60 are freshman, 55 are female, and 22 are female freshman. Find the probability that a student picked from this group at random is either a freshman or female

Number of Freshman = 60

Number of female = 55

Number of Freshman female 22

Total number of students = 100

The probability that a student picked from this group at random is either a freshman or female

Thus P(freshman or female) = 60/100 + 55/100 - 22/100 = 93/100

Answer:

Step-by-step explanation:

I'm assuming you're trying to solve this for x. We use the difference identity for cosine and rewrite:

\(cos(x-30)=cosxcos30+sinxsin30\) and simplify using the unit circle to help.

\(cosx(\frac{\sqrt{3} }{2})+sinx(\frac{1}{2})=0\\cosx(\frac{\sqrt{3} }{2})=-\frac{1}{2} sinx\\cosx=-\frac{1}{2}(\frac{2}{\sqrt{3} })sinx\\cosx=-\frac{1}{\sqrt{3} }sinx\\1=-\frac{1}{\sqrt{3} }\frac{sinx}{cosx}\\1=-\frac{1}{\sqrt{3} }tanx\\-\sqrt{3} =tanx\)

and on the unit circle, the angle where the tangent is negative square root of 3 is -60° which is also a positive 300°

Answer:

x = n*360° + 120°      or     x = n*360° + 300°

Step-by-step explanation:

cos(x-30°)=0

x-30° = 90° or x-30° = 270°

it means can be : x-30° = n*360° + 90°    or    x-30° =n*360° + 270°

x = n*360° + 120°      or     x = n*360° + 300°   n is integers

Check the picture below.

so, since we know the height of the triangle and its base is simply a + b, then

\(\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=\stackrel{a}{9}+\stackrel{b}{3}\\ \qquad 12\\ h=3\sqrt{3} \end{cases}\implies A=\cfrac{1}{2}(12)(3\sqrt{3})\implies A=18\sqrt{3}\)

Answer:

m∠QRS = 30°

m∠SRT = 75°

Step-by-step explanation:

Now,

The sum of m∠QRS and m∠SRT is equal to m∠QRT which is 105°

So,

m∠QRS + m∠SRT = m∠QRT

(6x)° + (14x + 5)° = (105)°

6x + 14x + 5 = 105

20x + 105 - 5

20x = 100

x = 100/20

x = 5

Thus, The value of x is 5°

Now,

m∠QRS = (6x)° = 6 × 5 = 30°

m∠SRT = (14x + 5)° = 14(5) + 5 = 70 + 5 = 75°

39° is the angle of elevation from a point on the level ground 200 feet away from the building.

A frequently used concept in relation to height and distance is the angle of elevation, particularly in trigonometry. It is described as an angle between the horizontal plane and an oblique line connecting the observer's eye to an object above his eye.

This angle eventually forms above the surface. As the name suggests, the angle of elevation is shaped in such a way that it is above the observer's eye.

The triangular scenario is ΔABC

The height of building, AB = 250 ft

Distance of building from elevation point, BC = 200 ft

We have to find angle of elevation, ∠c = θ

\($ \text {Tan}\ \theta = \frac{BC}{AB} = \frac{200}{250}\)

\($ \text {Tan}\ \theta = \frac{4}{5}\)

Tan θ = 0.8

θ = 39°

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To evaluate the limit as h approaches 0 for the vector-valued function F(h) = ⟨-7, sin(h), 6⟩ - ⟨0, 0, h⟩, we can subtract the two vectors component-wise and take the limit. The resulting vector will be ⟨0, 0, 0⟩.

The vector-valued function F(h) is defined as F(h) = ⟨-7, sin(h), 6⟩ - ⟨0, 0, h⟩. To evaluate the limit as h approaches 0, we subtract the two vectors component-wise:

F(h) - ⟨0, 0, h⟩ = ⟨-7, sin(h), 6⟩ - ⟨0, 0, h⟩ = ⟨-7, sin(h) - 0, 6 - h⟩ = ⟨-7, sin(h), 6  h⟩.

Now, we take the limit as h approaches 0:

lim(h→0) F(h) - ⟨0, 0, h⟩ = lim(h→0) ⟨-7, sin(h), 6 - h⟩.

Taking the limit component-wise, we get:

lim(h→0) -7 = -7,

lim(h→0) sin(h) = sin(0) = 0,

lim(h→0) 6 - h = 6 - 0 = 6.

Thus, the limit of F(h) as h approaches 0 is ⟨-7, 0, 6⟩. In other words, as h approaches 0, the function F(h) approaches the vector ⟨-7, 0, 6⟩ in three-dimensional space.

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We are given the following parent function f(x)

The transformed function g(x) is

Notice that the change is done in the horizontal direction.

Recall that the transformation rule for the horizontal translation to the left is given by

Where c is the number of units by which the graph is shifted to the left.

So, we should expect that the graph is horizontally shifted to the left by 1 unit.

Therefore, the above is graph represents the transformed function g(x) which is horizontally shifted to the left by 1 unit.

Answer:

497,511

Step-by-step explanation:

To find (f o g)(-4), we substitute -4 into g(x) to get -4, and then substitute -4 into f(x) to get -11.

The question asks us to find (f o g)(-4), where f(x) = 3x + 1 and g(x) = x. To find (f o g)(-4), we need to substitute -4 into g(x) and then take that result and substitute it into f(x).

First, let's find g(-4) by substituting -4 into g(x):
g(-4) = -4

Now, let's substitute g(-4) into f(x):
f(g(-4)) = f(-4)

Substituting -4 into f(x):
f(-4) = 3(-4) + 1
       = -12 + 1
       = -11

Therefore, (f o g)(-4) = -11.

In mathematics, a function is an expression, rule, or law that specifies a connection between two variables (the independent variable and the dependent variable). Functions are common in mathematics and are required for the formulation of physical connections in the sciences.

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Answer:

374 feet^2

Step-by-step explanation:

Surface area:

area of cross section x 2 = 110feet^2

area of tope x 2 = 264 feet^2

sum / Surface area: 374 feet^2

The required interior angle of 20-gon measures 162 degrees.

The interior angle measure for the n-sided polygon is given by
Interior angle measure = (n-2) x 180° / n, where n is the number of sides (or vertices) of the polygon.

Here,

To find the measure of each interior angle of a 20-gon (icosagon), we can use the formula:

For a 20-gon, n = 20. Substituting this into the formula, we get:

Interior angle measure = (20-2) x 180° / 20

= 18 x 180° / 20

= 162°

Therefore, each interior angle of 20-gon measures 162 degrees.

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To determine the value of C1, we need to solve the equation that ensures the probability of finding the electron somewhere in space is equal to one.

In quantum mechanics, the probability of finding the electron at a given point in space is determined by the wave function squared, denoted as |ϕn,l,m(x,y,z)|^2. The equation given is ∭R3fn,l,m(x,y,z)dV=1, which represents the integral of the squared wave function over the entire space.

To determine C1, we need to evaluate the integral using the wave function ϕ1,0,0(x,y,z). By substituting the specific wave function into the integral equation, we can solve for C1 such that the integral evaluates to 1. This calculation involves integrating the squared wave function over the volume element dV in three-dimensional space.

By solving the integral equation, we can determine the appropriate value of C1 that ensures the probability of finding the electron somewhere in space is equal to one.

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The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:

f(x) = A * sin(Bx + C) + D

where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.

Amplitude: The given amplitude is 10. So, A = 10.

Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.

Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.

f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:

41 = 10 * sin(2π/5 * 3 + C) + 31

10 * sin(2π/5 * 3 + C) = 41 - 31

10 * sin(2π/5 * 3 + C) = 10

sin(2π/5 * 3 + C) = 1

To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.

2π/5 * 3 = π/2 - C

6π/5 = π/2 - C

C = π/2 - 6π/5

Now we have all the values to construct the sinusoidal function:

f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31

Simplifying further:

f(x) = 10 * sin(2π/5 * x - 2π/10) + 31

f(x) = 10 * sin(2π/5 * x - π/5) + 31

Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

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1. A person should choose one family pizza.

2. The area of two medium pizza < area of 1 large pizza.

3. The area of two medium pizza is 1413.8 square cm and the area of one large pizza is 1661.9 square cm.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

I would one family pizza.

I would choose one family because the total area of two medium pizzas is less than the area of a family pizza.

This means that the two medium pizzas will have less pizza to share between the same number of people, so everyone will get a smaller slice of pizza.

To calculate the areas of the pizzas, we need to use the formula for the area of a circle -

Area of a circle = π × (radius)²

For the family pizza with a diameter of 46 cm, the radius is 23 cm. Therefore, the area of the family pizza is -

Area of family pizza = π × (23 cm)² ≈ 1661.9 square cm

For two medium pizzas with a diameter of 30 cm, the radius is 15 cm. Therefore, the area of each medium pizza is -

Area of each medium pizza = π × (15 cm)² ≈ 706.9 square cm

The total area of two medium pizzas is -

Total area of two medium pizzas = 2 × (Area of each medium pizza) ≈ 1413.8 square cm

Since the total area of two medium pizzas is less than the area of the family pizza, it means that two medium pizzas have less pizza to share between the same number of people.

Therefore, choosing one family pizza would be a better option.

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A family pizza or two medium?

* Each medium pizza is 30 cm in diameter

* The family pizza has only a diameter of 46 cm

1. What do you choose?

2. Why?

3. Please conclude your facts

Answer:

C.  37.5

Step-by-step explanation:

From inspection of the given triangle, we can see that the straight line that divides the triangle into two smaller triangles is an angle bisector since it divides the angle into two congruent angles.

Angle Bisector Theorem

An angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

\(\implies x:15=40:16\)

Solve for x:

\(\implies \dfrac{x}{15}=\dfrac{40}{16}\)

\(\implies \dfrac{x}{15}=2.5\)

\(\implies x=2.5\times 15\)

\(\implies x=37.5\)

My age is 2 years from the given condition.

Given that, if you square my age and subtract 28 times my age, the result is 60.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let x be my age.

Now, square my age is x²

28 times my age =28x

The square of my age and subtract 28 times my age, the result is 60.

x²-28x=60

⇒ x²-28x-60=0

⇒ x²+30-2x-60=0

⇒ x(x+30)-2(x+30)=0

⇒ (x+30)(x-2)=0

⇒ x=2

Hence, my age is 2 years from the given condition.

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Answer:

3 ;p

Step-by-step explanation:

Answer:

x=8 and y=2

Step-by-step explanation:

x+y=10

x=4y

x+y=10

4y+y=10

5y=10(divide both sides by 5)

y=2

x=4y=4*2=8

Answer:

2 and 8.

Step-by-step explanation:

y = -x + 10

y = 4x

If we subtract we eliminate y:

0 = -x + 10 - 4x

0 = -5x + 10

5x = 10

x = 2.

and y = 4 * 2 = 8.

Answer:

If real GDP in a particular year is $80 billion and nominal GDP is $240 billion, the GDP price index for that year is: 300.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

25 + 2(m-5)

25 + 2m - 10

25 + 50 - 10

75 - 10 = 65

Answer:

(6,2)

Step-by-step explanation:

y=-1/2x+5

y=2x-10​

-1/2 x+5 =2x-10  to find the solution y=y ( point of intersection of two lines)

-1/2 x-2x = -10-5 solve for x

-5/2 x=-15

x=-30/-5=6

y=2x- 10 substitute  x in the equation to get y

y=2(6)-10

y=2

(2,3)

Dont put the other answer, it’s wrong I

did the math.

Using the .01 level of significance means that, in the long run, a Type I error occurs 1 time in 100. This means that if we perform a statistical test 100 times, and we set the level of significance at .01, then we can expect to observe one false positive result due to chance alone. So, the correct option is 1).

A Type I error occurs when we reject a true null hypothesis, or when we conclude that there is a significant difference or relationship between two variables when in fact there is not.

By setting the level of significance at .01, we are minimizing the risk of making a Type I error while increasing the risk of making a Type II error, which occurs when we fail to reject a false null hypothesis. So, the correct answer is 1).

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Answer:

The larger number is 105

Step-by-step explanation:

When proportionally increased the numbers 2:5 can be multiplied by 21.

This gives you a ratio of 42:105

The difference of those numbers are 63

Hope that helps, let me know if this answer does or don't!