Show your work for multiplying these and put your answer in standard form in the box slow: (no work loses points)

Hello!

The angle of 30º is one of the remarkable angles (the others are 45º and 60º).

These angles are the most used in trigonometry, so it's good to memorize it.

Below, I'll explain to you one way to memorize it as a table:

For the sine and cosine, let's fill these spaces with 1 2 3 on the first line, and 3 2 1 on the second line. Then we're going to divide all of that by 2.

When the numerator is 2 or 3 we will put a square root in it.

For the tangent, it will be a little different:

• Tangent of ,30º ,is √3/3

• Tangent of ,45º ,is 1

• Tangent of ,60º ,is √3

Sin 30º: 1/2 or 0.5

Cos 30º: √3/2

Tan 30º: √3/3

The inequality that can be used with the squeeze theorem to calculate the limit of f(x) is [tex]-x^{2} \leq x^{2} cos\frac{1}{x^{2} } \leq x^{2} or -x^{2} \leq f(x)\leq x^{2}[/tex]

Squeeze Theorem,

If f(x)g(x)h(x) for all numbers and at some point x=k we get f(k)=h(k), then g(k) must also be equal to them, according to the squeeze (or sandwich) theorem. Theorem: By "squeezing" sin(x)/x between two better functions and using them to discover the limit at x=0, we can utilize them to obtain tricky limits like sin(x)/x at x=0.

The given function is [tex]f(x) = x^{2} cos(\frac{1}{x} )[/tex]

The range of the cos function is from -1 and 1.

We have,

[tex]-1\leq cos\frac{1}{x^{2} } \leq 1\\[/tex]

Multiplying the above inequality by x^2, we get :

[tex]-x^{2} \leq x^{2} cos\frac{1}{x^{2} } \leq x^{2}[/tex]

The above equation can be rewritten as,

[tex]-x^{2} \leq f(x)\leq x^{2}[/tex]

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The probability that at least 1 American will say that they have been decapitated is (C) 0.15.

So, the probability that at least 1 person will say yes:

We know that 15% will say yes, then:

Probability formula: P(E) =  favorable events/ Total events

Now, put values and solve as follows:

Therefore, the probability that at least 1 American will say that they have been decapitated is (C) 0.15.

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Based on the ratio of zinc to copper, and the grams of copper in the jar, the grams of zinc will be 156 grams of Zinc

The ratio of zinc to copper is 4 to 19 which means that for every 4 grams of Zinc, the chemical will have 19 grams of copper.

The means that if there is 741 grams of copper, the grams of Zinc will be:

= (Grams of Copper x Ratio of Zinc) / Ratio of copper

Solving gives:

= (741 x 4) / 19

= 2,964 / 19

= 156 grams of Zinc

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The maximum number of people that could go will be 5.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.

It is given that,

An amusement park charges $32 for admission and $6 to park your car.

To ascertain the maximum or lowest values of a scenario with many restrictions, a system of linear inequalities is frequently utilized. Inequalities reflect a limit of what is permitted or achievable rather than a precise quantity.

Suppose that everyone is going in one car and x is the number of persons in the car. The inequality represents the possible number of people that could go for $166 is,

32x+6≤166

32x≤160

x≤160/32

x≤5

Thus, the maximum number of people that could go will be 5.

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Proportionality constant for chicken B is greater. The proportionality constant for chicken A is 1.5 and that of chicken B is 1.67.

Chicken A produces 3 eggs every 2 days.

Chicken B produces 5 eggs every 3 days.

Let k₁ and k₂ be the constant of proportionality for chicken A and chicken B respectively.

According to question,

For chicken A, 3 eggs in 2 days

3 = k₁ 2

k₁ = 1.5

For chicken B, 5 eggs in 3 days

5 = k₂ 3

k₂ = 5/3 = 1.66

Thus, Proportionality constant for chicken B is greater. The proportionality constant for chicken A is 1.5 and that of chicken B is 1.67.

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The parent function is the most basic example of the function type specified.

Solve the equation y=(2)x for y.

Lessen the steps you tap...

Take the parentheses out.

y=2x

Take the parentheses out.

Rmove parenthesis from y=(2)x.

y=2x

Assume that f(x)=2x for y=(2)x and g(x)=2x for y=2x8 respectively.

f(x)=2x\sg(x)=2x−8

Find a, h, and k for each equation to determine the transformation from the first equation to the second.

y=abx−h+k

For f(x)=2x a=1, find a, h, and k.

h=0\sk=0

Find a, h, and k for g(x)=2x8 with a=1, h=8, and k=0.

The value of h determines the horizontal shift.

The graph is moved to the left by h units, which is expressed as g(x)=f(x+h).

The graph is moved to the right by h units when g(x)=f(xh).

Right 8 Units Horizontal Shift

The value of k determines the vertical shift.

The graph is shifted up k units and is denoted by the expression: g(x)=f(x)+k).

g(x)=f(x)k shifts the graph down k units.

No vertical shift

The reflection that spans the x-axis is indicated by the symbol of a.

A signifies that the x-axis of the graph is reflected.

No reflection on the x-axis

The graph's vertical stretch or compression is indicated by the value of a.

A vertical stretch is a>1 (makes it narrower)

A vertical compression (which results in 0a1)

The graph's vertical stretch or compression is indicated by the value of a.

A vertical stretch is a>1 (makes it narrower)

A vertical compression is 0a1 (makes it wider)

Vertical Stretch or Compression: None

Compare the two functions and look for a horizontal or vertical shift, a reflection about the x-axis, and a vertical stretch to identify the transformation.

f(x)=2x is the parent function.

Right 8 Units Horizontal Shift

No vertical shift

No reflection on the x-axis

Vertical Stretch or Compression: None

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Answer: -√3

Step-by-step explanation:

√3 + 1√3 - 1√27

√3 + √3 - √(3^2 x 3)

2√3 - 3√3

(2 - 3)√3

-1√3

-√3

5√2 is the solution of surd .

What does a math surd mean?

= √25+√45-√20

= √70 - √20

= √50

= 5√2

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According to the information, it can be concluded that there is no significant difference in the braking distances of the two models.

To check if there is a wide difference between the braking distances of the two models we can use several alternatives. One of them is to add all the braking distance results of each car and take the average as shown below:

According to the above, it can be concluded that the braking distance of both models only varies by 2 feet, so it is considered that there is not a great difference in braking distances.

Note: This question is incomplete because there is some information missing. Here is the complete information:

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The change in P in percentage terms is 51% decrease.

Since the two variables are connected by the relation, this will be illustrated as:

P=k/Q^2

where k is the proportionality constant.

Now, If Q is increased by 40%, i.e. the update Q' = Q + 0.4Q.

Now, we have

P1 = k/Q^2 and P2 = k/(Q+0.4Q)^2

P2/P1 = {k/(Q+0.4Q)^2}/{k/Q^2}

P2/P1 = 1/(1.4)^2

P2=0.51*P1

P2 = 0.5P1

Hence P reduces by 51%.

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Answer:

Step-by-step explanation:

17+20/4-5

17+5-5

17-10

17

Answer:

[tex](3p, 3p+4)[/tex]

Step-by-step explanation:

[tex]f(3p)=3p+4 \\ \\ \therefore (3p, 3p+4)[/tex]

To proof if a triangle is a right angled triangle, Pythagoras theorems must be obeyed

Pythagoras theorem states that

nows, lets test the triangle with pythagoras theorem

longest side, c = 97, a = 65, b = 72

Answer:

25000000 should be the answer

Step-by-step explanation:

...

Answer:

-1

Step-by-step explanation:

Let's assume 100 as the number. 80% of that number is 80. That's A. And since 80 is two-thirds of that number, the second number has to be 120. Simplifying that would give 5/6. 5-6 = -1

Answer: 1:1.2

       1-1.2= -0.2

Step-by-step explanation:

x = first number

y = second number

80/100*x (80 percent of one number)

2/3*y       (two thirds of the second number)

equating

  80/100*x=2/3*y

=   1.2=y

substituting:

      80/100*x = 2/3 * 1.2

= x=1

substituting the value of x in the original equation

 80/100 * 1 = 2/3 * y

= y=1.2

so, x=1, y=1.2

x:y

=1:1.2

x-y= 1 - 1.2 = -0.2

Kendra travel a total of 204.2 miles

What is addition?

Addition is a basic arithmetic process in which we bring 2 or more number to get a new total. it is denoted by '+'

We are given that Kendra is going from Cincinnati to Toledo and she takes a halt at Dayton

Now the distance between Cincinnati and Dayton is 54 miles.

and the she has to travel 150.2 miles more

Hence the distance between Dayton and Toledo is 150.2 miles

To find out total distance travel add the two distances

We get 54+150.2 = 154.2 miles

Hence the total distance traveled by Kendra is 204.2 miles

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Answer:

a=4, b=5, c=3

=4+5+3/2

=12/2

=s=6

Now,

we have,

√s(s-a)(s-b)(s-c)

√6(6-4)(6-5)(6-3)

√6×2×1×3

√36

=6

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

volume of a rectangular prism

Step 02:

geometry:

1. volume of a rectangular prism

- One formula for the volume of a right rectangular prism is V = l w h , where l represents length , w represents width , and h represents height.

- Another formula for the volume of a right rectangular prism is V = Bh , where B is the base area and h is the height.

That is the solution.

Answer:y=1/2x+8

Step-by-step explanation: You find the slope using the equation

m= y2-y1/x2-x1= 1/2

and then you use point-slope form y-y1=m(x-x1)

There are 36 grams of carbohydrates in each serving. The total number of grams of carbohydrates that should be consumed daily is 300.

Given that,

There are 36 grams of carbohydrates in each serving, according to the nutrition label is 12% of the daily value.

We have to find how many grams are advised each day.

We can write 12% as 0.12.

Let x be the total number of grams of carbohydrates that should be consumed daily.

We can write the equation as

0.12x=36

x=36/0.12

x=3600/12

x=300

Therefore, the total number of grams of carbohydrates that should be consumed daily is 300.

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assuming is simple interest

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to 3.75\%\to \frac{3.75}{100}\dotfill &0.0375\\ t=years\dotfill &5 \end{cases} \\\\\\ A=4000[1+(0.0375)(5)] \implies A=4000(1.1875)\implies A = 4750[/tex]

Answer:

b

Step-by-step explanation:

Total area

A = semi circle + triangle.

1. Area of the semi circle:

2. Area of the triangle:

h = 6; to find base we use the Pythagoras theorem, as follows:

Then,

Total area = 14 + 24 = 38 m²

Perimeter =

6 (π + 2) + 10 + 8 = 49 m

The figure consist of triangle, rectangle and semi circle.

Determine the area of figure.

Thus area of figure is 30.3 meter square.

The radius of the tire given the inches travelled in 100 revolution is 12 inches.

A tire has the shape of a circle. A circle is a bounded object which points from its center is equidistant to its circumference. One revolution is equal to the circumference of the tire. The circumference of a circle is the distance round the circle.

Circumference of a circle = 2πr

Where:

Circumference = total distance / number of revolutions

7540 / 100 = 75.40 inches

75.40 inches = 22/7 x r x 2

75.40 = 44/7 x r

r = 75.40 x 7/44 = 12 inches

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The function g(x) of graph has the following equation: g(x) = (10)ˣ⁻³

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

Two functions' graphs, f(x) and g, are provided to us (x).

The exponential function f(x) is defined as follows: f(x) = (10)ˣ

Finding the equation for the converted function g is now required of us (x).

The graph of the function g(x) may be shown to travel through the points (3,1), (4,10), (5,100), and so forth.

This indicates that the following is the equation or expression for the function g(x):

g(x) = (10)ˣ⁻³

Given that we have g(x) for x=3 , (10) ³⁻³

When x=4, we obtain g(x) = (10) ⁴⁻³

g(x) = (10)¹

g(x) = 10

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Chuck needs to sell more than 1000000 dollars of Jewelry.

In this question, a jewelry store offers Chuck a job paying 40 thousand dollars per year plus 2% of every sale that he makes.

We have been given the equation models the money Chuck makes if he sells x dollars of jewelry y= 40000 +0.02x

Also, he has second option that he can take the job and make 60000 dollars per year.

We need to find the amount of  jewelry Chuck needs to sell so that the first option is more profitable.

We need to find the value of x for which y > 60000

so we get an inequality.

i.e., 40000 +0.02x > 60000

0.02 x > 60000 - 40000

0.02x > 20000

x > 1000000

Therefore, Chuck needs to sell more than 1000000 dollars of Jewelry.

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Given:

The volume of storage boxes at 4,800 cubic feet

And the cost of storage = 4.5 cents per cubic feet

so, to find the monthly cost of the storge, we will multiply the cost by the volume as follows:

convert to dollars by divide by 100

So, the answer will be the monthly cost = $216

Answer:

8 3/8 gallons

Step-by-step explanation: