Suppose y varies directly with x and inversely with z. If y = 14 when x = 7 and z = 3, what is x when y = 3 and z = 8? Use the step-by-step process you learned to solve this problem.

Step 1: Set up the correct type of variation equation.
y =
✔ kx/z
Step 2: Determine the constant of variation.
k =

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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Answer:

See below

Step-by-step explanation:

The number you described is the same as \(sin(60^{\circ})=\frac{\sqrt{3}}{2}\) where the sine of an angle is the ratio between a right triangle's opposite side to the angle and the hypotenuse. So, in this case, if we had a right triangle with a height of \(\sqrt{3}\) units and a hypotenuse of 2 units, the ratio between the two sides will result in the value you provided. This right triangle in particular would be a 30-60-90 triangle.

In the case of a unit circle, it’s the y-coordinate of the point where a 60° angle in the standard position intersects a unit circle and a right triangle is created from that.

Answer: 8 books

Step-by-step explanation:

y= how much shelf space take up (inches)

x= # of books

y=2x

in this situation 16=y

16=2x

divide both sides by 2

8=x

Answer:

36123.5994797

Answer:

The rates are not equivalent since Maria saves $0.50 more per month than Ralph.

Step-by-step explanation:

We can determine if two rates are equivalent by comparing the rates at which they save per month.

Maria's savings per month:

Both 50 and 4 can be divided by 2, which gives us 25/2.  As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.

Ralph's savings per month:

Both 60 and 5 can be divided by 5, which gives us 12.  Thus, Ralph saves $12 per month.

Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.

Answer:

42 apples

Step-by-step explanation:

42 apples cuz how much Jack used

Answer:

7 units

Step-by-step explanation:

To find the distance between a pair of points, use the distance formula, \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\). Substitute the x and y values of (5,5) and (5, -2) into the formula and simplify:

\(d= \sqrt{(5-5)^2+(5+2)^2} \\d = \sqrt{(0)^2+(7)^2} \\d = \sqrt{0+49} \\d = \sqrt{49}\\d=7\)

So, the answer is 7 units.

Answer:15/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.

L=4W-1

P=2(L+W)=118, using L from above makes this

2(4W-1+W)=118,

2(5W-1)=118

5W-1=59

5W=60

W=12, and since L=4W-1

L=4(12)-1

L=47

So the length is 47ft and the width is 12ft

2.

A=7G+5

7G=A-5

G=(A-5)/7, and we are told A+G=45, using G=(A-5)/7 gives us

A+(A-5)/7=45

(7A+A-5)/7=45

(8A-5)/7=45

8A-5=315

8A=320

A=40

So Ally scored 40 points.

The total number of feathers lost in 14 days if you lose 30 feathers every hour is 10,080 feathers.

Feathers lost every hour = 30 feathers

How many feathers is lost in 14 days?

1 day = 24 hours

14 days = 24 × 14

= 336 hours

Total number of feathers lost in 14 days = Feathers lost every hour × number of hours in 14 days

= 30 × 336

= 10,080 feathers

Therefore, the total number of feathers lost in 14 days is 10,080 feathers

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Answer:

Step-by-step explanation:

Answer: C) Closed circle at -5; shading to the left

The given inequality \(3x \le -15\) solves to \(x \le -5\) when we divide both sides by 3. The inequality sign does not change because we didn't divide both sides by a negative number.

The graph has a closed circle at -5 to include this value as part of the solution set. Shading is to the left to indicate values smaller than -5. Overall, the graph says "x can be -5 or smaller". If you wanted to exclude -5, you would say \(x < -5\) and use an open circle; but that's not the case here.

Answer:

C) Closed circle at -5; shading to the left

Step-by-step explanation:

The required sample sizes for the confidence intervals are given as follows:

a) Estimate of 38%: 566.

b) No estimate: 601.

The margin of error for a confidence interval of proportions, using the z-distribution, is calculated as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The parameters of the equation are listed as follows:

The desired margin of error in this problem is of:

M = 0.04.

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

For item a, the estimate is of \(\pi = 0.38\), hence the sample size is obtained as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 1.96\sqrt{\frac{0.38(0.62)}{n}}\)

\(0.04\sqrt{n} = 1.96\sqrt{0.38(0.62)}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.38(0.62)}}{0.04}\)

\((\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.38(0.62)}}{0.04}\right)^2\)

n = 566.

For item b, when there is no estimate, we use \(\pi = 0.5\), hence:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}\)

\((\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2\)

n = 601.

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P(different color)=7/32

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the two points for each equation are:

For y = 2x + 9:

Point 1: (0, 9)

Point 2: (3, 15)

For -6x = 4 + 2y:

Point 1: (0, -2)

Point 2: (2, -8)

To find two points for each of the given equations, we can arbitrarily choose values for x and then calculate the corresponding y values.

For the equation y = 2x + 9:

Let's choose x = 0:

y = 2(0) + 9

y = 9

So, one point is (0, 9).

Let's choose x = 3:

y = 2(3) + 9

y = 6 + 9

y = 15

Another point is (3, 15).

For the equation -6x = 4 + 2y:

Let's choose x = 0:

-6(0) = 4 + 2y

0 = 4 + 2y

-4 = 2y

y = -2

One point is (0, -2).

Let's choose x = 2:

-6(2) = 4 + 2y

-12 = 4 + 2y

-16 = 2y

y = -8

Another point is (2, -8).

Therefore, the two points for each equation are:

For y = 2x + 9:

Point 1: (0, 9)

Point 2: (3, 15)

For -6x = 4 + 2y:

Point 1: (0, -2)

Point 2: (2, -8)

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Answer:

see explanation

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

a hexagon has 6 sides , then

sum = 180° × (6 - 2) = 180° × 4 = 720°

12

the polygon has 5 sides , so

sum = 180° × (5 - 2) = 180° × 3 = 540°

sum the interior angles and equate to 540

y + 90 + 120 + 90 + 110 = 540

y + 410 = 540 ( subtract 410 from both sides )

y = 130

13

the polygon has 7 sides , so

sum = 180° × (7 - 2) = 180° × 5 = 900°

sum the interior angles and equate to 900

p + 90 + 141 + 130 + 136 + 123 + 140 = 900

p + 760 = 900 ( subtract 760 from both sides )

p = 140

The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).

A function is defined as a relation between the set of inputs having exactly one output each.

On a coordinate plane, a parabola opens down with solid circles along the parabola at (-3, -5), (-2, 0), (-1, 3), (0, 4), (1, 3), (2, 0), (3, -5).

The domain is all real numbers.

The range is all real numbers.

If for an interval I, when x decreases meanwhile staying in interval I, the function's output increases (or can stay same), then we say that the function is increasing in the interval.

The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).

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Answer:

A

Step-by-step explanation:

Step-by-step explanation:

This is a geometric series where our common ratio is -1/2, and a is -4

Since r is less than -1, this series converges so

The sun is

\( \frac{ - 4}{1 + 0.5} \)

\( \frac{ - 4}{1.5} = - \frac{8}{3} \)

The sum is -8)3

Answer:

40%.

Step-by-step explanation:

There are 6 / 15 apples out of the bowl.

6/15 = 2/5 = 0.4

So, 40% of the fruit in the bowl are apples.

Hope this helps!

The possible domain of the convergence are b. (-1,3) and c. (-1,3]

Domain of convergence.

In statistics, domain of the convergence also known as interval of convergence means an interval associated with a given power series such that the series converges for all values of the variable inside the interval and diverges for all values outside it.

Given,

Here we need to identify in which of the options are domain of convergence.

As per the definition of domain of convergence, the interval of the convergence is (-∞ , ∞).

So, the possible convergence in the given options are (b) and (c).

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Answer:

They are intersecting.

Step-by-step explanation:

Since their slopes can't be the same (because their product couldn't be negative in that case), they have to intersect at one point or another.

If tan Ф = 15/8 then we have these trigonometric functions cosec Ф = 17/15, sec Ф = 17/8 and cot Ф = 8/15.

According to the question,

We have the following information:

Tan Ф = 15/8

We know that in this trigonometric function we have perpendicular divided by base.

Now, we can find the hypotenuse using the Pythagoras theorem:

Let's denote hypotenuse with h, perpendicular with p and base with b.

\(h^{2} =p^{2} +b^{2}\)

\(h^{2}\) = \((15)^{2} +(8)^{2}\)

\(h^{2} = 225+64\\h^{2} = 289\\h = \sqrt{289}\)

h = 17 units

Now, we have the following values:

Cosec Ф = 17/15 (Hypotenuse/perpendicular)

Sec Ф = 17/8 (h/b)

Cos Ф = 8/17 (b/h)

Cot Ф = 8/15 (b/p)

Hence, the correct options are A, B and D.

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Answer:

There is only 1 solution

\((x,y) = (1,4)\)

Step-by-step explanation:

Given

Lines A and B

Required

The number of solution for a pair of A and B

From the graph, lines A and B have only one point of intersection.

This point of intersection represents the solution

Since, there is only 1 point, there is only one solution.

And the solution is:

\((x,y) = (1,4)\)

Answer:

(4,0) & (9,5)

Step-by-step explanation:

Where the equations cross are the solutions!

Hope this Helps! :)
Happy Studies

Answer:

Increment in property per year ;

Slope of a linear function

Kindly check explanation for the rest of the answers.

Step-by-step explanation:

The rate of change is the increment in property value per year ; $220

Thsi corresponds to the gradient or slope of a linear function

If 1980 = x and x = 0

Recall :

y = bx + c

Where, b = slope = 220

x = year

y = property threshold

c = intercept value

In 1980, x = 0

y - intercept.

Put x = 0 into the equation :

4190 = 220x + c

4190 = 220(0) + c

4190 = c

3.)

The linear function becomes :

y = 220x + 4190

Property threshold in 2010:

x = 2010 - 1980 = 30

y = 220(30) + 4190

y = 6600 + 4190

y = 10,790

Property threshold in 2010

Year it will exceed 15000

15000 = 220x + 4190

15000 - 4190 = 220x

10810 = 220x

x = 10810 / 220

x = 49.136

That is, property threshold will exceed 15000 after 50 years

1980 + 50 = 2030

Year 2030

The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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The equation y - 5 = (4/3)(x - 6) can be written in point-intercept form as y = (4/3)x - 3, where the slope is 4/3 and the y-intercept is -3.

The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. The point-slope form of a line can be converted to the slope-intercept form of a line, y = mx + b, where b is the y-intercept.

The equation y - 5 = (4/3)(x - 6) can be rearranged into the point-slope form of a line by isolating the y-term and simplifying: y - 5 = (4/3)(x - 6)y - 5 = (4/3)x - 8y = (4/3)x - 3

Now, we have the point-slope form of the line with slope 4/3 and y-intercept -3.

To convert this to the slope-intercept form of a line, we simply rearrange the equation to solve for y:y = (4/3)x - 3 This is the slope-intercept form of the line, where the slope is 4/3 and the y-intercept is -3.

Thus, the equation y - 5 = (4/3)(x - 6) can be written in point-intercept form as y = (4/3)x - 3, where the slope is 4/3 and the y-intercept is -3.

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Answer:

x = 27 , ∠ EAF = 27°

Step-by-step explanation:

∠ GAF = 90° , then

∠ GAC + ∠ CAF = ∠ GAF , that is

x + 63 = 90 ( subtract 63 from both sides )

x = 27

∠ DAE = 90°

since CD is a straight angle of 180° , then

∠ CAE = 90° , so

∠ CAF + ∠ EAF = ∠ CAE , that is

63° + ∠ EAF = 90° ( subtract 63° from both sides )

∠ EAF = 27°