8/3+7/5a

Simplify your answer as much as possible.

Answer:

-12, -7, -4, 0, 3, 10

Step-by-step explanation:

just ask !

Ken will receive a total dividend payment of $75 for that quarter.

We have to given that,

Ken owns 500 shares of LaceNBrace, which makes hockey equipment.

And, He receives a notice stating the company will be paying $0.15 dividend per share.

Now, For the total dividend payment Ken receives for that quarter, we can multiply the dividend per share by the total number of shares he owns:

= $0.15 per share x 500 shares

= $75

Therefore, Ken will receive a total dividend payment of $75 for that quarter.

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Answer:

(assuming all members of the gang get equal percentages)

For a gang of 8: 12.5% (100/8)

If 2 are killed: 16.67% (100/6), so percentage increases by roughly 4.2% (16.67-12.5)

Percent that belongs to 3: 12.5%*3=37.5%

Percent that belongs to 3 if 2 are killed: 16.67%*3=50.0%

Each robber's share still increases by 4.2% (50%-37.5%=12.5%, 12.5%/3=4.2%)

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Step-by-step explanation:

Answer:

When \(x=0\), the value of f(x) is 1.

Each time x increases by 1, f(x) is multiplied by 4.

Equation of function: \(f(x)=1\cdot 4^x\)

Step-by-step explanation:

The detailed explanation is attached below.

Answer:

1000 g

Step-by-step explanation:

That is the answer

Answer:

Step-by-step explanation:

1 gram.

30% of the students scored between 70 and 79 on the math quiz.

To calculate the percentage of students who scored between 70 and 79, we need to determine the total number of students and the number of students within the given range. Let's calculate it.

The total number of students can be found by summing up the frequencies for all score ranges:

Total number of students = 3 + 2 + 6 + 4 + 5 = 20 students

The number of students who scored between 70 and 79 is given as 6 students.

Now, we can calculate the percentage:

Percentage of students who scored between 70 and 79 = (Number of students in the range / Total number of students) x 100

= (6 / 20) x 100

= 30%

Therefore, 30% of the students scored between 70 and 79 on the math quiz.

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Note the full question is ;

The histogram shows scores on a math quiz for a group of students. How many students scored between 70 and 79?

2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).

To express 2 cos 35 sin 67 as a sum, we can use the trigonometric identity for the product of two sine or cosine functions.

Specifically, the identity states that 2 cos A sin B can be written as

sin(A + B) + sin(A - B).

Applying this identity, we have:

2 cos 35 sin 67 = sin(35 + 67) + sin(35 - 67)

Simplifying the expressions inside the sine functions:

sin(102) + sin(-32)

Since the sine function is an odd function,

sin(-x) = -sin(x),

so we can rewrite the equation as:

sin(102) - sin(32)

Therefore, 2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).

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Answer:

(1, 5)

Step-by-step explanation:

The solution to the system of equations is the point of intersection of the two lines.  From inspection of the graph, the point of intersection is at (1, 5).

Proof

The solution to a system of equations is the point at which the two lines meet.  

⇒ g(x) = f(x)

⇒ 3x + 2 = |x - 4| + 2

⇒ 3x = |x - 4|

⇒ 3x = x - 4   and   3x = -(x - 4)

⇒ 3x = x - 4

⇒ 2x = -4

⇒ x = -2

Inputting x = -2 into the 2 equations:

⇒ g(-2) = 3 · -2 + 2 = -4

⇒ f(-2) = |-2 - 4| + 2 = 8

Therefore, as the y-values are different, x = -2 is NOT a solution

⇒ 3x = -(x - 4)

⇒ 3x = 4 - x

⇒ 4x = 4

⇒ x = 1

Inputting x = 1 into the 2 equations:

⇒ g(1) = 3 · 1 + 2 = 5

⇒ f(1) = |1 - 4| + 2 = 5

Therefore, as the y-values are the same, x = 1  IS a solution

and the solution is (1, 5)

Answer:

Step-by-step explanation:

8.008.009

Answer:

a,c

Step-by-step explanation:

the area of the rectangle will be 1.5w².

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Area of rectangle is A = a*b

The given length of the rectangle is w

The width will be 1.5w

So the rectangle of the white figure is Area = w*1.5w = 1.5 w²

hence the area of the rectangle will be 1.5w².

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a) A formula that describes aₙ is; aₙ = 30(⁶/₇)^(n - 1)

b) The arc length of the tire on the 11th swing is; 6.422 feet

c) The number of swings it takes for the arc length to be less than one is; 21

The general formula for the nth term of a geometric progression is;

aₙ = ar^(n - 1)

where;

a is first term

r is common ratio

a) We are given the initial arc length is 30 ft. Thus

a = 30

It swings with 6/7th of the previous length and so; r = 6/7. Thus;

A formula that describes aₙ is;

aₙ = 30(⁶/₇)^(n - 1)

b) The arc length of the tire on the 11th swing is;

a₁₁ = 30(⁶/₇)^(11 - 1)

a₁₁ = 6.422 feet

c) The number of swings it takes for the arc length to be less than one foot is expressed as;

30(⁶/₇)^(n - 1) = 1

(⁶/₇)^(n - 1) = 1/30

(n - 1) In (6/7) = In 30

Solving gives gives n = 21

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\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)

Make sure your calculator is in Degree mode.

Answer:

The scientific notation is a method of writing very large or very small numbers in a more compact and easy to read format. It is expressed in the form of a x 10^n, where "a" is a number between 1 and 10, and "n" is an integer.

To write 464000 in correct scientific notation, we need to move the decimal point to the left until we get a number between 1 and 10. We count the number of places we moved the decimal point, and that will be the exponent of 10.

So, we can write 464000 as:

4.64 x 10^5

Therefore, the correct scientific notation of 464000 is 4.64 x 10^5.

Step-by-step explanation:

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

it is the mode.

Step-by-step explanation:

i. e 5 is the most occuring number in the set of data listed above

In a graph, we can define a domain and a range.

The domain is all the x values used in the graph.

The range is all the y values used in the graph.

These concepts can also be applied for functions:

The domain is all possible x values that can be used in the function

The range is all possible y values (the value of the function) that can be outputted in the function.

So the correct answer is the second one: the range states the values of y.

Answer:

126 minutes

Step-by-step explanation:

17.12 - 2 = 15.12

15.12 divided by 0.12 = 126 min

Answer:

x = 29

Step-by-step explanation:

Given:

m<PQS = 107°

m<RQS = 49°

m<PQR = (2x)°

Required:

Value of x

Solution:

m<RQS + m<PQR = m<PQS (angle addition postulate)

Plug in the values

49 + 2x = 107

Subtract 49 from each side

2x = 107 - 49

2x = 58

Divide both sides by 2

x = 58/2

x = 29

Answer:

  about 5368.6 miles per day

Step-by-step explanation:

The units "km/hour" has hours in the denominator. To get days in the denominator, you need a fraction with hours in the numerator and days in the denominator: hours/day. To keep the same value, that fraction must have the same time period in the numerator as the denominator: (24 h)/(1 da).

  {360 km/h)×(24 h)/(1 da) = (360×24) km/da = 8640 km/da

Similarly to replace km in the numerator with miles, you need to multiply by a fraction that has miles in the numerator and km in the denominator.

  (8640 km/da)×(1 mi)/(1.609344 km) = 8640/1.609344 mi/da

  ≈ 5368.6 mi/da

Step-by-step explanation:

The way you can think about volume is that we have some cross sectional area times the height of the solid.

27.

The volume of a square based pyramid is

\(v = {s}^{2} ( \frac{h}{3} )\)

where h is the height of the pyramid

s is the side length of the square base.

S=7

h=12

\(v = {7}^{2} ( \frac{12}{3} ) = 49 \times 4 = 196\)

28. The volume of a rectangular prism

\(v = l \times w \times h\)

where l is length

w is width

h is height

\(v = 11 \times 11 \times 8 = 968\)

29.

Use the same formula in 27

\(v = 100(3) = 300\)

30.

Volume of a Cylinder is

\(v = \pi {r}^{2} h\)

where r is the radius of the circle

where h is the height

r is half of the diameter

The diameter is 22, thus the radius is 11.

\(v = {11}^{2} (8)(\pi)\)

\(v = 968\pi\)

pi is approximately 3.14

\(v = 3041.06\)

31. Volume of A Sphere

\( \frac{4}{3} \pi {r}^{3} = v\)

The radius is half of diamter, thus r=7

\( \frac{4}{3} \pi( {7}^{3} ) = 1436.76\)

We have proven trigonometric  equation a² + b² = p² + q², using the given equations a sin θ + b cos θ = p --- (1) and a cos θ - b sin θ = q --- (2).

To prove that a² + b² = p² + q², we need to manipulate the given equations and show their equivalence.

Given equations:

a sin θ + b cos θ = p --- (1)

a cos θ - b sin θ = q --- (2)

Square equation (1):

(a sin θ + b cos θ)² = p²

Expanding and simplifying:

a² sin² θ + 2ab sin θ cos θ + b² cos² θ = p² --- (3)

Square equation (2):

(a cos θ - b sin θ)² = q²

Expanding and simplifying:

a² cos² θ - 2ab sin θ cos θ + b² sin² θ = q² --- (4)

Now, adding equations (3) and (4):

a² sin² θ + a² cos² θ + b² sin² θ + b² cos² θ + 2ab sin θ cos θ - 2ab sin θ cos θ = p² + q²

Using the trigonometric identity: sin² θ + cos² θ = 1, we simplify:

a² + b² = p² + q²

We have proven that a² + b² = p² + q², using the given equations (1) and (2).

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Answer:

1.833, 3.3052, 3.35, 3.5

Step-by-step explanation:

Hope this helps! :)

Answer:

$ 850.25

Step-by-step explanation:

I will assume anything over 40 hours is 'overtime'

total pay will be

   regular pay    +   overtime pay

 17.90 * 40 hr    +   (17.90 * 1.5)(5hr) = $ 850.25