Segment addition, step by step on how u figure it out.

To determine the sum of money Jeff should invest on January 21, 2020, in order to reach $80000 on August 8, 2020, at an annual interest rate of 5%, we need to calculate the present value of the future amount using the time value of money concepts.

We can use the formula for the present value of a future amount to calculate the initial investment required. The formula is:

Present Value = Future Value / (1 + interest rate)^time

In this case, the future value is $80000, the interest rate is 5% per year, and the time period is from January 21, 2020, to August 8, 2020. The time period is approximately 6.5 months or 0.542 years.

Plugging these values into the formula, we have:

Present Value = $80000 / (1 + 0.05)^0.542

Evaluating the expression, we find that the present value is approximately $75609. Therefore, Jeff should invest approximately $75609 on January 21, 2020, to amount to $80000 on August 8, 2020, at a 5% annual interest rate.

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The given circle has its center at (−3,3) and has a radius of 5 units. Then, the shortest distance D between the point and the circle is given by.

Answer: 20 cards.

Step-by-step explanation: If Sarah can make 4 cards in 60 minutes, then she can make 1 card in 60/4 = 15 minutes.

Therefore, in 300 minutes, she can make 300/15 = <<300/15=20>>20 cards.

Answer:

55%

Step-by-step explanation:

The angle between the string and the horizontal is decreasing at a rate of 1/1200 radians per second.

The given situation can be modeled using the right triangle formed by the kite, the ground, and the kite string.

Let x be the horizontal distance, y be the vertical distance (100 ft), and r be the length of the string (200 ft).

We have: x^2 + y^2 = r^2 x^2 + 100^2 = 200^2

Now, differentiate both sides with respect to time t:

2x(dx/dt) = 2r(dr/dt) 2x(dx/dt) = 0 (since the length of the string is constant)

Given that the kite moves horizontally at 7 ft/s, dx/dt = 7.

We can now find x:

x^2 + 100^2 = 200^2 x^2 = 200^2 - 100^2 x = √(30000) = 100√3

Now we can plug in the value of dx/dt and find dy/dt:

2(100√3)(7) = 0 dy/dt = 0 (since the kite's vertical position is constant)

Let θ be the angle between the string and the horizontal.

We have:

tan(θ) = y/x = 100 / (100√3) θ = arctan(1/√3)

Differentiate both sides with respect to time t:

sec^2(θ)(dθ/dt) = (1/√3)(dx/dt - dy/dt)/x^2

We know that sec^2(θ) = 1 + tan^2(θ), so:

(1 + (1/3))(dθ/dt) = (1/√3)(7 - 0)/(100√3)^2

dθ/dt = (1/4)(1/300)

dθ/dt = 1/1200

Thus, the angle between the string and the horizontal is decreasing at a rate of 1/1200 radians per second.

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Answer:

X^2 -4

Step-by-step explanation:

Not entirely sure but would u just expand the brackets. As this is a difference between 2 squares the answer should be correct but it not sure.

Answer:y=3x+6

Step-by-step explanation:

Because the slope intercept equation is y=mx+b

Answer:

\(\textsf{y=\frac{1}{3}x+3}\)\(y = \frac{1}{3} x+3\)

Step-by-step explanation

\(\textsf{*slope intercept form: y = mx +b}\)

---------------------------------------------

\(\textsf{x - 3y = -9}\)

Subtract x from both sides:

\(\textsf{-3y = -x - 9}\)

Divide both sides by -3:

-3y/-3 = -x/-3 - 9/-3

\(\textsf{y = 1/3x +3}\)

\(-jurii\)

Answer:

64 frogs

Step-by-step explanation:

After 7 months: 2 x 2 = 4

After 14 months: 4 x 2 = 8

After 21 months: 8 x 2 = 16

After 28 months: 16 x 2 = 32

After 35 months: 32 x 2 = 64

Carla's net worth, which is positive, is $17.50.

The net worth is the difference between total assets (income) and total liabilities (expenses).

For example, Carla's earnings totaled $83 while her expenses were $65.50, leaving her a net worth (income) of $17.50.

Earnings:

Babysitting = $57

Feeding = $26

Total earnings = $83

Expenses:

Gloves = $18

Circus tickets = $35

Music = $12.50

Total expenses = $65.50

Net worth = $17.50 ($83 - $65.50)

Thus, Carla's net worth, which is the difference between her total income and total expenses, is $17.50.

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Answer:

it will be 44 degree because all angles in rhombus are equal

Answer:

m> 55 (you only flip the direction of the sign when you divide by a negative number)

Step-by-step explanation:

Answer:

m > 55

Step-by-step explanation:

simplify both sides of the inequality

m - 19 > 36

Add 19 to both sides

36+19

m>55

Hope this helps :D

Answer:

41

Step-by-step explanation:

Its correct ^^

Answer:

When x = -3  y = -1

When x = -3/4  y = 7/2

Step-by-step explanation:

y = 4x^2 + 17x + 14

y = 2x + 5​

Set each equation equal to each other

4x^2 + 17x + 14  = 2x + 5​

Subtract 2x from each side

4x^2 + 17x-2x + 14  = 2x-2x + 5​

4x^2 + 15x + 14  =  5​

Subtract 5 from each side

4x^2 + 15x + 14-5  =  5​-5

4x^2 + 15x +9  = 0

Factor

(4x+3) ( x+3) =0

Using the zero product property

4x+3 =0    x+3 =0

4x = -3      x=-3

x = -3/4     x=-3

Now we need to find y for each x

x =-3   y = 2x+5  =2(-3)+5 = -6+5 = -1  

When x = -3  y = -1

x = -3/4   y = 2(-3/4) +5 = -3/2 +5 = 7/2

When x = -3/4  y = 7/2

The centroid of the region bounded by \(\(y=x^2\) and \(y=2x\)\)in the first quadrant is\(\((1, \frac{8}{5})\).Hence, the answer is \((1, \frac{8}{5})\).\\\)
To find the centroid of the region bounded by\(\(y=x^2\) and \(y=2x\)\)in the first quadrant, we need to calculate the coordinates of the centroid, denoted by\(\((\bar{x}, \bar{y})\),\) using the following formulas:

\(\[\bar{x} = \frac{1}{A} \int_{x_1}^{x_2} x \cdot (f(x) - g(x)) \, dx\]\[\bar{y} = \frac{1}{2A} \int_{x_1}^{x_2} (f(x))^2 - (g(x))^2 \, dx\]\\\)
where \(A\) represents the area of the region, \\((f(x)\) is the upper curve (\(y=2x\)), and \(g(x)\) is the lower curve (\(y=x^2\)).\\\)
First, we need to find the intersection points of the two curves. Setting \(f(x) = g(x)\), we have:

\(\(2x = x^2\)Rearranging, we get:\(x^2 - 2x = 0\)Factoring out \(x\), we have:\(x(x - 2) = 0\)So, the intersection points are \(x = 0\) and \(x = 2\).Next, we calculate the area \(A\) by integrating \(f(x) - g(x)\) from \(x = 0\) to \(x = 2\):\(A = \int_0^2 (2x - x^2) \, dx\)\\\)
Simplifying the integral:

\\((A = \left[x^2 - \frac{1}{3}x^3\right]_0^2\)\(A = (2^2 - \frac{1}{3} \cdot 2^3) - (0^2 - \frac{1}{3} \cdot 0^3)\)\(A = (4 - \frac{8}{3}) - (0 - 0)\)\(A = \frac{4}{3}\)Now, we can calculate \(\bar{x}\):\(\bar{x} = \frac{1}{A} \int_0^2 x \cdot (2x - x^2) \, dx\)Simplifying the integral:\)

\(\(\bar{x} = \frac{1}{\frac{4}{3}} \left[\frac{1}{2}x^2 - \frac{1}{3}x^3\right]_0^2\)\(\bar{x} = \frac{3}{4} \left[\frac{1}{2}(2^2) - \frac{1}{3}(2^3)\right] - (0 - 0)\)\(\bar{x} = \frac{3}{4} \left[\frac{1}{2}(4) - \frac{1}{3}(8)\right)\)\(\bar{x} = \frac{3}{4} \left[2 - \frac{8}{3}\right)\)\(\bar{x} = \frac{3}{4} \left[\frac{6}{3} - \frac{8}{3}\right)\)\(\bar{x} = \frac{3}{4} \left[-\frac{2}{3}\right)\)\(\bar{x} = -\frac{1}{2}\)\\\)
Since we are only interested in the first quadrant, the negative value for \(\bar{x}\)

is not applicable. Therefore, the centroid of the region bounded by \\((y=x^2\) and \(y=2x\)\)in the first quadrant does not have the x-coordinate of 1.

As for the y-coordinate, we can calculate \(\bar{y}\):

\(\(\bar{y} = \frac{1}{2A} \int_0^2 (2x)^2 - (x^2)^2 \, dx\)\)

Simplifying the integral:

\(\(\bar{y} = \frac{1}{2 \cdot \frac{4}{3}} \left[\frac{4}{3}x^3 - \frac{1}{5}x^5\right]_0^2\)\(\bar{y} = \frac{3}{8} \left[\frac{4}{3}(2^3) - \frac{1}{5}(2^5)\right] - (0 - 0)\)\(\bar{y} = \frac{3}{8} \left[\frac{4}{3}(8) - \frac{1}{5}(32)\right]\)\(\bar{y} = \frac{3}{8} \left[\frac{32}{3} - \frac{32}{5}\right]\)\\\)
\(\(\bar{y} = \frac{3}{8} \left[\frac{160 - 96}{15}\right]\)\(\bar{y} = \frac{3}{8} \left[\frac{64}{15}\right]\)\(\bar{y} = \frac{8}{5}\)\\\)
Therefore, the centroid of the region bounded by \(\(y=x^2\) and \(y=2x\) in the first quadrant is \((1, \frac{8}{5})\).\)

Hence, the answer is \(\((1, \frac{8}{5})\).\)

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The coordinates of the centroid of the region bounded by y = x² and y = 2x in the first quadrant are

\($\left(\frac{4}{3}, \frac{16}{15}\right)$\), which is closest to \($(1,4/5)$\)

hence the answer is \($\boxed{(1,4/5)}$\).

The given curves are y = x² and y = 2x. These two curves intersect at x = 0 and x = 2.

Thus, the region is bounded by the curves y = x², y = 2x and x = 0, x = 2.

This region can be seen in the figure below:

The centroid of the region bounded by y = x² and y = 2x in the first quadrant is given by the formula below:

\($$\bar{x}=\frac{1}{A}\int_{a}^{b} x f(x) d x$$\)

\($$\bar{y}=\frac{1}{A} \int_{a}^{b} \frac{f(x)^{2}}{2} d x$$\)

We have \($f(x) = 2x-x^2$\) and the limits of integration are\($a=0$\) and \($b=2$\).

The area of the region is given by

\($$A=\int_{a}^{b} f(x) d x$$\)

\($$A=\int_{0}^{2} (2x-x^2) d x$$\)

\($$A=2$$\)

Therefore, we can find the coordinates of the centroid using the following integrals:

\(\[\bar{x} = \frac{1}{2} \int_{0}^{2} x(2x-x^2) dx\]\[\bar{y} = \frac{1}{2} \int_{0}^{2} \frac{(2x-x^2)^2}{2} dx\]\)

Evaluating the integrals we have

\($$\bar{x}=\frac{4}{3}$$\)

\($$\bar{y}=\frac{16}{15}$$\)

Thus, the coordinates of the centroid of the region bounded by y = x² and y = 2x in the first quadrant are

\($\left(\frac{4}{3}, \frac{16}{15}\right)$\),

which is closest to\($(1,4/5)$\) hence the answer is \($\boxed{(1,4/5)}$\).

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Answer:

False

Step-by-step explanation:

The intercept is the point where the graph crosses over the y-axis

Answer:

no because on is equal to 3 when plugged in and the other is equal to 4 when plugged in.

Step-by-step explanation:

\(3(3)-5=4\\4(3)-9=3\)

Answer:

What is the volume of the new prism? 1,485 cm^3

The new volume is 27 times the original volume

Step-by-step explanation:

I got it right on ed 2020

Answer:

A rectangular prism with length 5.5 centimeters, width 2.5 centimeters, and height 4 centimeters.

A rectangular prism has sides of 4 cm, 2.5 cm, and 5.5 cm. The figure is dilated by a scale factor of 3.

What is the volume of the new prism?

✔ 1,485

cm3.

What can be concluded about the effect of the change on the new volume?

The new volume is

✔ 27

times the original volume.

Step-by-step explanation:

Answer:

  35/132

Step-by-step explanation:

The probability of selecting a boy for president is 7/12, the ratio of the number of boys to the number of candidates. Then the probability of selecting a girl for vice president is 5/11, the ratio of the number of girls to the remaining number of candidates. The joint probability is ...

  (7/12)(5/11) = 35/132 . . . P(b=P&g=VP)

__

We can also look at this another way.

The number of ways two candidates can be selected from 12 is 12P2 = 132. The number of ways that the first can be a boy and the second can be a girl is (7)(5) = 35. Then the probability of a (BG) pair from the 12 candidates is 35/132.

_____

Additional comment

These numbers assume that selection is random and all possibilities are equally-likely. That is unlikely to be the case in an election.

The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45

We have to given that;

One bag contains 3 red lollipops and 2 green lollipops.

And, The other bag contains four purple lollipops and five blue lollipops.

Hence, The probability of choosing a green lollipop is,

P₁ = 2 / 5

And, The probability of choosing a purple lollipop is,

P₂ = 4 / 9

Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,

P = P₁ ×  P₂

P = 2/5 × 4/9

P = 8/45

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Given:-

To find the volume of the cone.

From the given image it is clear,

So now we substitute the known values. so we get,

So the required volume is 125ft^3.

Answer:

30 is your answer.

I HOPE IT WILL HELP YOU.

Thank you.

^ - ^

Do you have a picture of your question?

To solve this problem, I'll use proportions.

Result z = 45.56

It's correct

The cross-sectional area of the water in the pipe is approximately 442.73 square centimeters.

To find the cross-sectional area of the water in the pipe, we can start by visualizing the given information.

Let's denote the center of the circle as O. We are given that PQ = 9.6 cm, and the surface of the water is 3 cm below the center O.

First, let's find the radius of the circle. Since PQ is a chord of the circle, it passes through the center O. Thus, the radius of the circle is half of PQ, which is 9.6 cm / 2 = 4.8 cm.

Now, we need to find the height of the water in the pipe, which is the distance from the center O to the water surface. This height is given as 3 cm.

To calculate the cross-sectional area of the water in the pipe, we need to determine the area of the shaded region, which is a circular segment.

The formula for the area of a circular segment can be given as:

A = r^2 * (θ - sinθ) / 2

where A is the area, r is the radius, and θ is the central angle of the segment.

In this case, we need to find the central angle θ. We can determine θ by finding the inverse sine of the ratio of the height of the segment to the radius of the circle.

sinθ = height / radius = 3 cm / 4.8 cm ≈ 0.625

Taking the inverse sine of 0.625, we find θ ≈ 39.23 degrees.

Now we can calculate the area A using the formula:

A = (4.8 cm)^2 * (39.23° - sin(39.23°)) / 2

Evaluating this expression, we find:

A ≈ (23.04 cm^2) * (39.23° - 0.625) / 2

A ≈ (23.04 cm^2) * 38.605 / 2

A ≈ 885.46 cm^2 / 2

A ≈ 442.73 cm^2

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Step-by-step explanation:

I suspect you mean

11³ × 11 = ?

11³ ÷ 11 = ?

11³ × 11 = 11⁴

11³ ÷ 11 = 11²

why ?

11³ = 11×11×11

11³ × 11 = 11×11×11 × 11 = 11×11×11×11 = 11⁴

11³ ÷ 11 = 11×11×11 / 11 = 11×11 × 1 = 11×11 = 11²

Answer:

The probability is 0.22

Step-by-step explanation:

We know that:

40% of the students play tennis

24% of the students play baseball

58% of the students play neither.

If we add these numbers, we get:

40% + 24% + 58% = 122%

Here we should get exactly 100%, but we get more because we are counting some of the students twice, and that happens because some of the students play both sports, so these students are counted in both percentages.

And we can conclude that exactly 122% - 100% =  22% of the students play both sports:

Now, the probability that a randomly picked student plays both sports, is equal to the quotient between the percentage of students that play both sports and the 100%, this is:

p = 22%/100% = 0.22

The probability is 0.22

The high temperature for today using a 3-day moving average is 92 degrees.

To calculate the high temperature for today using a 3-day moving average, we take the average of the temperatures from the past three days, including today.

Given the daily high temperatures in St. Louis for the last week:

92, 92, 93, 95, 95, 86, 95 (yesterday)

To find the 3-day moving average for today's high temperature, we consider the temperatures from yesterday, the day before yesterday, and three days ago.

(95 + 86 + 95) / 3 = 92

Therefore, the high temperature for today, calculated using a 3-day moving average, is approximately 92 degrees Fahrenheit, rounded to one decimal place.

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The area covered by the Jim's 24 step is 12 meter.

According to the statement

we have given that the Carly takes three steps to walk the same distance as Jim walks in four steps. Each of Carly's steps covers 0.5 meters.

And we have to find that the how many meters does Jim travel in 24 steps.

So, For this purpose, we know that the

From the given information:

Let Carly's steps is C and Jim's step is J.

So,

3C = 4J

And

C = 0.5 meters

so, The area covered by the Carly's three steps is:

Area covered by the Carly's three steps = 3*0.5

Area covered by the Carly's three steps = 1.5 meters.

And

The area covered by the Jim's 24 step is:

area covered by the Jim's 24 step = 24*0.5

area covered by the Jim's 24 step = 12 meter.

So, The area covered by the Jim's 24 step is 12 meter.

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Option (c) is true only when b < h.

We have to find which of the following must be true about the area a of the triangle if the base b of a triangle is increasing at a rate of 3 inches per minute while its height h is decreasing at a rate of 3 inches per minute.Area of a triangle is given by: A = (1/2)bhDifferentiating both sides with respect to time, we get:dA/dt = (1/2)(b dh/dt + h db/dt)Given, db/dt = 3 (in/min), dh/dt = -3 (in/min)dA/dt = (1/2)(b(-3) + h(3))= (3/2)(h - b)

Since h and b are both decreasing at the same rate, their difference (h-b) will remain constant. Therefore, dA/dt will be zero, which means the area a of the triangle remains constant.Answer: e. a remains constant.Explanation:When the height h and the base b of a triangle are changing with time, its area A is given by A = (1/2)bh.

To differentiate the given formula with respect to time, we will apply the product rule as follows:dA/dt = (1/2)d/dt (bh) = (1/2)(db/dt)h + (1/2)b(dh/dt)Differentiating this with respect to time again, we get:d^2A/dt^2 = (1/2)(d^2b/dt^2)h + (1/2)(db/dt)(dh/dt) + (1/2)b(d^2h/dt^2) = (1/2)(d^2b/dt^2)h - (1/2)3b^2where we have used the fact that db/dt = 3 in/min and dh/dt = -3 in/min.

Since the second derivative of the area with respect to time is negative, it means the area of the triangle is decreasing. Therefore, option (c) is true only when b < h.

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