If t varies inversely as the cube of z and directly as the square of r, and t = 4 when z = 3 and r =6, find t when z = 6 and r = 9

The sum of the geometric sequence in this problem is given as follows:

5.77.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number, which is called the common ratio q.

The first term, the common ratio and the number of terms for this problem are given as follows:

\(a_1 = 10, q = -\frac{2}{3}, k = 8\)

The formula for the sum of the first n terms is given as follows:

\(S_n = a_1\frac{1 - r^n}{1 - r}\)

Hence the sum for this problem is given as follows:

\(S_8 = 10 \times \frac{1 - \left(-\frac{2}{3}\right)^8}{1 + \frac{2}{3}}\)

\(S_8 = 5.77\)

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Answer:

41393415 in kg is 1.8776E+07, or about 18775737.2.

Step-by-step explanation:

For this equation, you should divide 41393415 by approximately 2.20462262 to get your answer of 1.8776E+07 or about 18775737.2.

Answer:

Step-by-step explanation:

1)8/12=12/18

2)12/20=18/30

3)4/16=6/24

114 is 95% of 120

100% of 120 is 120, therefore 95 percent of 120 equals 114. To learn how to solve 114 is 95 percent of what number, see the step-by-step instructions below.

114 is 95 Percent of What Number?

Formula = Number x 100

Percent = 114 x 100

95 = 120

The following shows the steps to derive this formula and find out 95% of the number is 114.

Step 1: If 95% of a number is 114, then what is 100% of that number? Set up the equation.

114

95% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

95Y = 114 x 100

95Y = 11400

Y = 11400

100 = 120

Each of the five friends needs to pay £14.40 to cover the cost of the birthday person's meal.

To calculate how much each of the five friends needs to pay, we can use the concept of averages or mean.

The total cost of the meal for 6 people is £12 per person. This means that the total cost of the meal is 6 * £12 = £72.

Since the other five friends have decided to pay for the birthday person's meal, they will evenly divide the total cost of £72 among themselves.

To find the average amount each friend needs to pay, we divide the total cost by the number of friends paying, which is 5:

£72 / 5 = £14.40

Using the concept of averaging or finding the mean allows us to distribute the cost equally among the friends, ensuring fairness in sharing the expenses.

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Answer:

x = 34/13

Step-by-step explanation:

3(5x - 6) + 2(x + 8)

15x - 18 = 2x + 16

15x = 2x + 34

13x = 34

x = 34/13

Best of Luck!

Answer:

17x-2

Step-by-step explanation:

3 (5x - 6) + 2 (x + 8)

Distribute

15x -18 + 2x+16

Combine like terms

17x -2

Answer:

28+12x

Step-by-step explanation:

The perimeter of a square is 4s where s is the side lenght. In your case s is 7+3x so the perimeter will be (28+12x).

The solution to the equation 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the equation 125x³ - 27 = 0 by grouping

Rewriting 125x^ 3 −27 as (5x) ^3 −3³

The difference of cubes can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )

Polynomial 25x^ 2 +15x+9 is not factored since it does not have any rational roots.

Hence, (5x−3)(25x ^2 +15x+9)

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a. The x-coordinate of the vertex (2) represents the time it takes for the ball to reach its maximum height, and the y-coordinate (182) represents the maximum height itself.

b. The tennis ball is initially at a height of 126 feet above the ground.

a. The x-coordinate of the vertex is 2. To find the y-coordinate, we substitute this value back into the equation:

h(2) = -14(2)² + 56(2) + 126

h(2) = -14(4) + 112 + 126

h(2) = -56 + 112 + 126

h(2) = 182

Therefore, the vertex of the equation is (2, 182). In this context, the vertex represents the highest point reached by the tennis ball during its trajectory. The x-coordinate of the vertex (2) represents the time it takes for the ball to reach its maximum height, and the y-coordinate (182) represents the maximum height itself.

b. In order to find the y-intercept, we set t equal to zero and evaluate h(t):

h(0) = -14(0)² + 56(0) + 126

h(0) = 126

The y-intercept is 126. In this context, the y-intercept represents the initial height of the ball when it is thrown. Therefore, the tennis ball is initially at a height of 126 feet above the ground.

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Answer: (-3,0)

Step-by-step explanation:

-1 - 2 = -3

1+2=3

3+2=5

2 is the common thing between 2 and 4, 4 and 6,  6 and 8 so from -2 + 2 = 0

Answer:sorry

Step-by-step explanation:

Sorry I can’t help :(

Answer:

B

Step-by-step explanation:

You divide the 4 to isolate the radical and get √n = -½. Then you can square both sides to get rid of the square root on the n. (-½)² is -½ x -½ = ¼.

Now the n is completely isolated so the answer is n= ¼

Answer:

Step-by-step explanation:

Consider a sample with data values of 10, 20, 12, 17, and 16. (a) Compute the mean and median. Mean = Median = (b) Consider a sample with data values 10, 20, 12, 17, 16, and 12.

Mean = Total of values/ Total number of observations

Total of values = 10+20+12+17+16 = 75

Total number of observations = 5

Mean = 75/5 = 15

Median:

Arrange in ascending order = 10, 12,16,17,20

Median = [n+1] / 2

N = number of observation = 5

Median = [5+1]/2 = 3rd observation

Median = 16

Answer:

In each bag there will be 1.82 ounces of mixture.

Step-by-step explanation:

Since Irene is making bags of trail mix for hiking club, and she will use 22 ounces of walnuts, 11.2 ounces of almonds, and 12.3 ounces of cashews to make 25 bags of trail mix, to determine how many ounces are in each bag you must perform the following calculation:

(22 + 11.2 + 12.3) / 25 = X

45.5 / 25 = X

1.82 = X

Thus, in each bag there will be 1.82 ounces of mixture.

The situation is a function, & the independent and dependent variables are the number of miles and total fee, respectively

The given parameters are

Initial Fee = $2.80

Rate = $3.50 per mile

Let the number of miles be x and the total fee be y

So, we have

Total fee = Initial Fee + Rate * Number of miles

This gives

y = 2.8 + 3.5x

This means that the situation is a function, & the independent and dependent variables are the number of miles and total fee, respectively

Here, we have

Maximum number of miles = 20

This means that the domain is 0 <= x <= 20

Substitute 20 for x in y = 2.8 + 3.5x

y = 2.8 + 3.5 x 20

Evaluate

y = 72.8

This means that the range is 0 <= x <= 72.8

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Applying the formula for each identified shape that are given, the correct areas to each shape are:

a. Square = 134.6 sq. yd

b. Circle = 452.2 sq. cm

c. Parallelogram = 40.6 sq. cm

d. Rectangle = 43.2 sq. ft

e. Trapezium = 25.7 sq. m

f. Triangle = 21.6 sq. ft

a. The shape given is a square.

Area of the square = \(s^2\)

Where,

s = 11.6 yd

Plug in the value of s

Area of the square = \(11.6^2 = 134.6 $ yd^2\)

b. The shape given is a circle.

Area of the circle = \(\pi r^2\)

r = 12 cm

Area of the square = \(\pi \times 12^2 = 452.2 $ cm^2\)

c. The shape given is a parallelogram.

Area of the parallelogram = \(bh\)

b = 7 cm

h = 5.8 cm

Area of the parallelogram = \(7 \times 5.8 = 40.6 $ cm^2\)

d. The shape given is a rectangle.

Area of the rectangle = \(l \times w\)

l = 8.3 ft

w = 5.2 ft

Area of the rectangle = \(8.3 \times 5.2 = 43.2 $ ft^2\)

e. The shape given is a trapezium.

Area of the trapezium = \(\frac{1}{2} (a + b) \times h\)

a = 2.8 m

b = 10.4 m

h = 3.9 m

Area of the trapezium = \(\frac{1}{2}(2.8 + 10.4) \times 3.9 = 25.7 $ m^2\)

f. The shape given is a triangle. (See attachment for the shape).

Area of the triangle = \(\frac{1}{2} \times b \times h\)

b = 9 ft

h = 4.8 ft

Area of the triangle = \(\frac{1}{2} \times 9 \times 4.8 = 21.6 $ ft^2\)

Therefore, applying the formula for each identified shape that are given, the correct areas to each shape are:

a. Square = 134.6 sq. yd

b. Circle = 452.2 sq. cm

c. Parallelogram = 40.6 sq. cm

d. Rectangle = 43.2 sq. ft

e. Trapezium = 25.7 sq. m

f. Triangle = 21.6 sq. ft

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Answer:

2 9/12 and 2 11/12

Step-by-step explanation:

if that is what u are asking. simplist form is 2 3/4 and 2 11/12.

Hope that helps and good luck :)

It looks like you're given a set

{(x, y) : y = 3x + 2}

i.e. the set of points (x, y) = (x, 3x + 2), and you're told that x is taken from the set {-2, -1, 0, 1, 2}.

When x = -2, the corresponding value of y is

y = 3•(-2) + 2 = -6 + 2 = -4

The equation that can be used to solve for the length, y , is y²-5y = 750

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Area is measured in squared unit.

The area of a rectangle is given by the expression:

A = l × w

where l is the length and w is the width of the rectangle.

The width of the rectangle is 5 feet less than that of the length. The length is represented by y. this means that w = y-5

Area = length × width

area = 750

therefore 750 = y ×( y-5)

opening the parentheses,

750 = y² - 5y

therefore the equation that can be used to solve for the length of the rectangle is

y²-5y = 750

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Austin's rate of motion is (1/70)π Radians per second.

To determine Austin's rate of motion in radians per second, we need to use the formula for angular velocity:

ω = Δθ / Δt

Where:

ω = angular velocity (in radians per second)

Δθ = change in angular displacement (in radians)

Δt = change in time (in seconds)

We know that Austin runs three-quarters of a circular track, which means he covers an arc length that is equal to three-quarters of the circumference of the circle. Let's call the radius of the circle "r". Then, the arc length covered by Austin is given by:

s = (3/4) * 2πr

s = (3/2)πr

We also know that it takes Austin 1 minute and 45 seconds to cover this distance. This is the same as 105 seconds (since 1 minute = 60 seconds).

So, Δt = 105 seconds

Now, we can calculate the change in angular displacement (Δθ). The total angle around a circle is 2π radians, so the angle covered by Austin is given by:

Δθ = (3/4) * 2π

Δθ = (3/2)π

Therefore, Austin's rate of motion (ω) in radians per second is:

ω = Δθ / Δt

ω = [(3/2)π] / 105

ω = (3/210)π

ω = (1/70)π radians per second

So, Austin's rate of motion is (1/70)π radians per second.

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The graph of the linear inequality is given by the image presented at the end of the answer.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The function for this problem is given as follows:

y = -3x/4 + 2.

Hence the graph crosses the y-axis at y = 2, and when x increases by 4, y decays by 3.

The inequality is given as follows:

y < -3x/4 + 2.

Meaning that points below the dashed line are the solution to the inequality.

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If Alex spent 6 minutes riding his bike for every one minute he watched TV, then the proportion we write is like the following equation:

TV/Bike = 1 / 6

Now if the bike total was 780, then we solve for the TV in the following equation:

TV/780 = 1/6

multiply both sides by 780:

TV = 780/6

TV = 130 minutes

Alex watched a total of 130 minutes of TV during his vacation

Answer: x=11

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

3.3(x + 1.2) = 40.26

Distribute the 3.3 across the parentheses.

3.3x + 3.96 = 40.26

Combine the constants by subtracting 3.96 from both sides

3.3x = 36.3

Isolate the variable by dividing both sides by 3.3

x = 11

Check your work by plugging x = 11 into the original equation.

3.3(11 + 1.2) = 40.26

3.3(12.2) = 40.26

40.26 = 40.26

Your answer is correct.

Hope this helps!

The ordered pair which is a solution to the system of linear equations (0,2).

In mathematics, a system of linear equations refers to a collection of one or more linear equations which involve the same variables. In order to solve the system of linear equations, multiply each equation by a constant such as the coefficient of one variable becomes the same.

Hence, multiply 2x + 3y= 6 by 3 and –3x + 5y = 10 by 2.

3 (2x + 3y= 6)

6x + 9y = 18

2(–3x + 5y = 10)

-6x + 10 y = 20

Adding the two equations

6x + 9y = 18

-6x + 10 y = 20

19y = 38

y = 2

Substitute y in either of the equations:

2x + 3(2)= 6

2x = 6 – 6 = 0

x = 0

Hence, the solution is (0, 2)

The ordered pair (0,0) is not a solution as it will invalid the given linear equation.

Note: The question is incomplete. The complete question probably is Which ordered pair is a solution to the system of linear equations? 2x + 3y= 6 and –3x + 5y = 10.  (0,2) (2,0) (3,2) (2,3)

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Answer:

a=127

Step-by-step explanation:

Okay so basically thats a straight line that the angles are on right? Yes so that entire angle is equal to 180 so you set up the equation 15+38+a=180 and then you simplify which is 53+a=180, then you subtract 52 from both sides and you get a=127. Hope this helps :)

Any parabola's y-intercept is always at (0,c). In this case its (0, 6)

y = a(0)² + b(0) + c

y = c

The given equation is-

y = −5x² − x + 6

Comparing with intercept equation, the value of c is:

c = 6

Thus any parabola's y-intercept is always at (0,c). In this case its (0, 6)

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The correct question is-

Find the y-intercept for the parabola defined by this equation:

y = −5x² − x +6

Answer:

C) 2.7 x 10-15

Step-by-step explanation:

Sorry if I'm wrong. hope you're having a great day

The computation shows that the value of (9 x 10−13) − (6.3 x 10−15) is C. 2.7 x 10−15

Simplify (9 x 10−13) − (6.3 x 10−15).

This will be solved as follows. It should be noted that one just have to subtract the values.rhat are given based on the information above.

Therefore, (9 x 10−13) − (6.3 x 10−15).

= 2.7 x 10−15

In conclusion, the correct option is C.

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Answer:

Step-by-step explanation:

The equation is poorly written and I cannot unfortunately solve it.

Answer:

Step-by-step explanation: