Explain your answer !!

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I see you use the TeX command "\binom" for binomial coefficient, but I think you meant to use "\frac" to write a fraction, namely,

\(\dfrac{\sin(\alpha)+\sin(2\alpha)}{1+\cos(\alpha)+\cos(2\alpha)}=\tan(\alpha)\)

and I assume you're supposed to establish an identity.

Recall the double angle identities for cos and sin :

cos(2α) = cos²(α) - sin²(α) = 2 cos²(α) - 1

sin(2α) = 2 sin(α) cos(α)

Now expand the left side as

(sin(α) + sin(2α)) / (1 + cos(α) + cos(2α)) = (sin(α) + 2 sin(α) cos(α)) / (1 + cos(α) + 2 cos²(α) - 1)

Factor sin(α) from the numerator, and after canceling the 1s in the denominator and factor cos(α) :

… = [sin(α) (1 + 2 cos(α))] / [cos(α) (1 + 2 cos(α))]

Cancel the factors of 1 + 2 cos(α) :

… = sin(α) / cos(α)

which is equivalent to

… = tan(α)

by definition of tan.

Answer:

D) 128

Step-by-step explanation:

Because we will be replacing the variables with numbers we have to that we will have to do the exponent first because of PEMDAS.

\(8-5(3)(-2)^3\)

\(8-5(3)(-8)\)

\(8-15(-8)\)

\(8-(-120)\)

\(8+120=128\)

The surface area of the figure is approximately 997.5π cm².

We have,

The figure has two shapes:

Cone and a semicircle

Now,

The surface area of a cone:

= πr (r + l)

where r is the radius of the base and l is the slant height.

Given that

r = 15 cm and l = 19 cm, we can substitute these values into the formula:

= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)

The surface area of a semicircle:

= (πr²) / 2

Given that r = 15 cm, we can substitute this value into the formula:

= (π(15)²) / 2

= 112.5π cm² (rounded to one decimal place)

The surface area of the figure:

To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:

Now,

Total surface area

= 885π + 112.5π

= 997.5π cm² (rounded to one decimal place)

Therefore,

The surface area of the figure is approximately 997.5π cm².

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Step-by-step explanation:

Answer:

The answer would be A. 3/4

Step-by-step explanation:

To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

Answer: B

Step-by-step explanation:

Answer: $4,998

Step-by-step explanation:

34000*1.147

38998-34000=4998

Answer:

72 quarts

Step-by-step explanation:

1 year = 12 months, and Neil changes the oil each month, and each month he uses 6 quarts of oil.  So, the number of quarts he will need for a year is

6 + 6 + ... + 6, twelve times, which equals 12(6) = 72 quarts.

Answer:

She can buy 7 journals

$30.00-$9.00=$21.00

$3.00x7 journals=$21.00

Answer:

Step-by-step explanation:

Thanks I will go there soon

Answer:

225 red cars & 375 white cars  

Step-by-step explanation:

According to the specified ratio, there are 225 red cars and 375 white cars in the parking lot.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

given, There are 600 cars in the parking lot. The ratio of red cars to white cars is 3:5. let ratio is in the term of variable x

Thus,

3x + 5x = 600

=> 8x = 600

=> x = 75

Total number of red cars = 3x

Total number of red cars = 3 * 75

Total number of red cars = 225

Total number of white cars = 5x

Total number of white cars = 5*75

Total number of white cars = 375

Therefore, there are 225 red cars and 375 white cars in the parking lot as per the given ratio.

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Answer:

m∠1 = 37°

General Formulas and Concepts:

Pre-Algebra

Geometry

Step-by-step explanation:

Step 1: Define

m∠3 = 127°

m∠G = 90°

Step 2: Find m∠2

Step 3: Find m∠1

Answer:

11/6

Step-by-step explanation:

2 7/9 + 8/9

2 7/9 into a mixed fraction which is 25/9

now 25/9 + 8/9 = 33/18 then simplify which is 11/6

The transformation from the graph of f(x) = x to the graph of g(x) = (1/9)·x -2, is a rotation and a translation. The correct option is therefore;

The transformation are a rotation and a translation

A translation transformation is a transformation in which there is a displacement of all points on the preimage figure in a specified direction.

The transformation from f(x) = x to f(x) = (1/9)·x - 2, includes a slope reduction by a factor of (1/9), or rotating the graph of f(x) = x in the clockwise direction, and a translation of 2 units downwards, such that the y-intercept changes from 0 in the parent function, f(x) = x to -2 in the specified function f(x) = (1/9)·x - 2, therefore, the translation includes a rotation clockwise and a translation downwards by two units

The correct option is the second option; The transformation are a rotation and a translation

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Answer:

x=25

All triangles must equal 180

95+35=130

Answer:

Step-by-step explanation:

I and II

Pages in a book and leaves on a tree can be counted precisely. They are discrete.

The height of a person cannot be measured exactly. We can get very good

approximations (to a lot of decimal places) but never exact. This is continuous.

Answer:

-39

Step-by-step explanation:

Substitute x by - 3 and y by 4

(-3)^3 - 3 *4 = - 39

Looking at the diagram, there is a transversal cutting across 2 parallel lines.

Angle 2 and angle 6 lie in similar position on the same side of the transversal. This means that they are corresponding angles. Corresponding angles are equal.

Given that angle 2 = 32 degrees, then angle 6 = angle 2 = 32 degrees

angle 5 and angle 6 are linear pairs. They lie on a straight line. the sum of the angles on a straight line is 180 degrees. It means that

angle 5 + angle 6 = 180

angle 5 + 32 = 180

angle 5 = 180 - 32

angle 5 = 148 degrees

Here, we proceed step by step, to obtain our answer,

\(\frac{1}{2}\)  % of 36 can be written as ,

0.5 % of 36 , which means,

100 % refers to 36, then

0.5 % refers to what,  thus, by cross multiplication we get,

0.5 % of 36 =  \(\frac{0.5 X 36}{100}\) = 0.18 ___(1), which can be expressed in whole numbers as 0.

Now, 30 % of 10 means,

100 % refers to 10, then

30 % refers to what,  thus, by cross multiplication we get,

30 % of 10 = \(\frac{30 X 10}{100}\) = 3 __(2)

From equations (1)  and (2),

the whole numbers that we obtain are 0 and 3, respectively,

Thus the difference between these two whole numbers is,

= 3 - 0 = 3.

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Solution :

The expected matrix is :

\($E_i=\frac{(\text{row total } \times \text{column total})}{\text{grand total}}$\)            Honors        Regular       General

     6 th grade                                       33.0986      46.0070      14.8944

     7 th grade                                       34.8592      48.4542       15.6866

     8 th grade                                       32.0423      44.5387       14.4190

Thus we can say that the level of math is not dependent on the grade level.

Therefore, the provided information is correct. Test Stat = 1.4007, p-value = 0.844070419

\(H_0\) : The level of math is independent of the grade level.

\(H_1\) : The level of math is dependent on the grade level.

The explicit rule is aₙ = 7+5(n-1), where n is the position of the term.

The complete table is given below.

An explicit formula is a formula that allows us to find the nth term of an arithmetic sequence. Based on this formula, the sum of the arithmetic series can be derived.

The first term a₁=7 and the fourth term a₄=22.

The arithmetic explicit formula for the nth term is aₙ=a₁+(n-1)d, where d is a common difference.

So, find the value of d using a₁=7 and a₄=22 in the formula.

22=7+(4-1)d

15=3d

d=5

Therefore, the explicit formula becomes aₙ = 7+5(n-1).

Substitute n=2 and n=3 into the obtained formula.

a₂=7+5(2-1)

=7+5

=12

a₃=7+5(3-1)

=7+10

=17

Therefore, the required answers are a₂=12 and a₃=17.

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Answer:

3 berries

Explanation:

Opportunity costs for the Orange group:

Opportunity cost of pumping 1 gallon of water = 3/1 = 3 berries

Opportunity cost of picking 1 berry = 1/3 = 0.333 gallons of water

Opportunity costs for the Yellow group:

Opportunity cost of pumping 1 gallon of water = 8/2 = 4 berries

Opportunity cost of picking 1 berry = 2/8 = 0.25 gallons of water

Opportunity cost for both groups combined:

Opportunity cost of pumping 1 gallon of water = 3 berries (Orange group should pump water since opportunity cost is lower)

Opportunity cost of picking 1 berry = 0.25 gallons of water (Yellow group should pick berries since opportunity cost is lower)

Opportunity costs are the extra costs or benefits lost resulting from choosing one investment or activity over another alternative. In this case, people can either pump water or pick berries, but they cannot do both at the same time. When they are pumping water, the opportunity cost is the amount of berries that they will not be able to collect, and vice versa.

Step-by-step explanation: The correct graph is #6. Cubic Function

2/3 of 35 is 23. Kofi is 23.

Answer:

\(3\)

Step-by-step explanation:

\(10 \div ( \frac{ {3}^{2} + 1 }{5 - 2} )\)

\( \frac{10(5 - 2)}{ {3}^{2} + 1} \)

\( \frac{10 \times 3}{ {3}^{2} + 1 } \)

\( \frac{30}{ {3}^{2} + 1 } \)

\( \frac{30}{9 + 1} \)

\( \frac{30}{10} \)

\(3\)

The interval notation for the inequality statement "5 less than m is at most 70" is (-∞, 75].

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The statement given is - 5 less than m is at most 70.

The given sentence can be translated into a mathematical inequality as -

m - 5 ≤ 70

To solve for m, we can add 5 to both sides of the inequality -

m - 5 + 5 ≤ 70 + 5

m ≤ 75

Therefore, m is less than or equal to 75.

In interval notation, we can represent this solution as -

(-∞, 75]

Therefore, the interval value is (-∞, 75].

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The graph of f(x) is the second one, so the correct option is B.

Here we have f(x), a piecewise function, and we want to see which one of the four graphs is the correct one.

You can see that the first domain of the function is:

x ≤ -4

So we must have a closed circle at x = -4, when the parabola ends.

The second domain is:

-4 < x < 1

So x here is not equal to -4 nor 1, so this part starts and ends with open circles.

finally, the linear part starts with a closed circle.

Also, notice that the line has a negative slope, so it goes down, then we can discard the first option.

Then we can see that the correct option is the second graph.

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Vector v can be written as the sum of two vector components, \(v_x = -5i\)  and \(v_y = 6j\)

To write vector v as the sum of two vector components, we need to decompose it into two vectors along different directions.

v = -5i + 6j

w = 3i + 4j

We can decompose vector v into two components, one along the x-axis and the other along the y-axis.

Let's denote the component along the x-axis as \(v_x\) and the component along the y-axis as \(v_y.\)

The x-component, \(v_x,\) represents the projection of vector v onto the x-axis and can be found using the dot product of v and the unit vector i:

\(v_x = v . i = (-5i + 6j) . i = -5i . i + 6j . i = -5\)

Similarly, the y-component, \(v_y,\) represents the projection of vector v onto the y-axis and can be found using the dot product of v and the unit vector j:

\(v_y = v . j = (-5i + 6j) . j = -5i . j + 6j . j = 6\)

Now, we can write vector v as the sum of its components:

\(v = v_x + v_y = -5i + 6j\)

So, vector v can be written as the sum of two vector components: -5i along the x-axis and 6j along the y-axis.

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Answer:

[-5, 4) ∪ (4, ∞)

Step-by-step explanation:

Given functions:

\(f(x)=\dfrac{1}{x-3}\)

\(g(x)=\sqrt{x+5}\)

Composite function:

\(\begin{aligned}(f\:o\:g)(x)&=f[g(x)]\\ & =\dfrac{1}{\sqrt{x+5}-3} \end{aligned}\)

Domain: input values (x-values)

For \((f\:o\:g)(x)\) to be defined:

\(x+5\geq 0 \implies x\geq -5\)

\(\sqrt{x+5}\neq 3 \implies x\neq 4\)

Therefore, \(-5\leq x < 4\)  and  \(x > 4\)

⇒  [-5, 4) ∪ (4, ∞)

Answer:

.

Step-by-step explanation:

Answer:

0.24857

Step-by-step explanation:

Less than 1 is 0. and

only even prime is 2