The radius of a circle is changing at the rate of 1/π inches per second. At what rate, in square inches per second, is the circle’s area changing when the radius is 5 inches?

Answer:

[tex]w \approx 96.6 \, \textrm{m}[/tex]

Step-by-step explanation:

See the attached image for my labeled diagram.

To solve for [tex]w[/tex], we can use the trigonometric ratio tangent.

[tex]\tan(\theta)=\dfrac{\textrm{opposite}}{\textrm{adjacent}}[/tex]

[tex]\tan(44\textdegree)=\dfrac{w}{100 \, \textrm{m}}[/tex]

↓ multiply both sides by 100m

[tex]100 \, \textrm{m} \cdot \tan(44\textdegree)=w[/tex]

↓ plug [tex]100\, \textrm{m} \cdot \tan(44\textdegree)[/tex] into a calculator

[tex]96.56887 \, \textrm{m} \approx w[/tex]

[tex]w \approx 96.56887 \, \textrm{m}[/tex]

↓ round to 3 significant figures

[tex]w \approx 96.6 \, \textrm{m}[/tex]

Answer:

  (c)  see below

Step-by-step explanation:

You want the graph of the compound inequality x > -6 or x > -2.

The graph of the inequality x > -2 is shown as the top selection.

The graph of the inequality x > -6 is shown as the bottom selection.

You will notice that the bottom graph overlaps and includes the top graph. Hence the "OR" of the inequalities will look like the bottom graph, attached.

The distribution of the sample mean for all possible simple random samples of size 15 from the population of net worth in the US will be approximately normal, with a mean of μ and a standard deviation of σ/√15.

Courtney's estimate of the net worth of all people in the US is strongly skewed to the right. This means that the majority of the population has a net worth that is lower than the average net worth. When Courtney selects an SRS of size n = 15 from this population and calculates the sample mean, the shape of the distribution of the sample mean for all possible simple random samples of size 15 from this population will be approximately normal.

The Central Limit Theorem states that if a population has a mean of μ and a standard deviation of σ, then the sampling distribution of the sample mean will be approximately normal, no matter what the shape of the population distribution is, as long as the sample size is large enough. Since Courtney's sample size of 15 is large enough, the sampling distribution of the sample mean will be approximately normal.

The sample mean will have a mean of μ, which is the population mean, and a standard deviation of σ/√n, where n is the sample size. Since Courtney's sample size is 15, the standard deviation of the sample mean will be σ/√15. This means that the sample mean will be normally distributed with a mean of μ and a standard deviation of σ/√15.

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Answer:

  (b)  _Congruent

Step-by-step explanation:

You want to know the relationship between corresponding angles where a transversal crosses parallel lines.

The Corresponding Angles theorem tells you that corresponding angles at a transversal are congruent if and only if the lines are parallel.

Corresponding angles are congruent.

__

Additional comment

This fact is the basis for the simplest method of constructing a line parallel to a given line through an external point. (A transversal is drawn, and the angle is copied, making congruent corresponding angles.)

All of the other angle relationships at a transversal can be derived from this one using the usual relationships of linear pairs and vertical angles.

Answer:

33/100

Step-by-step explanation:

The 100 natural numbers are from 1-100.

In order to find the total numbers divisible by 3, divide 100 by 3:

100/3 = 33.33

Put 33.33 into integer form:

33.33 ==> 33 numbers divisible by 3.

Divide 33 by 100 to get the probability: 33/100

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When 6 times a number is equal to the number increased by 10. The number is 5.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the number be represented as x.

Six times a number is equal to the number increased by 10. This will be:

(6 × x) = x + 10

6x + x = 10

Collect the like terms

6x - x = 10

5x = 10

Divide.

x = 10 / 2

x = 5.

The number is 5

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Answer:30x^2 - 54x - 18

Step-by-step explanation: To find the product of f and g, we can simply multiply the expressions for f and g together. The product of f and g is:

(f * g)(x) = (6x + 2)(-5x - 9)

          = -30x^2 - 54x - 18

So, the product of f and g is -30x^2 - 54x - 18

From 2018 to 2019:

From 2019 to 2020:

Compare the percent increase we obtained:

Period 2018 to 2019 had a higher percent increase.

To expand the expression (x + 10)(3x² + 5x - 2), we can use the distributive property, which states that for any numbers a, b, and c, the product (a + b)(c) can be written as a * c + b * c. Applying this property to the given expression, we get (x + 10)(3x² + 5x - 2) = (x * 3x² + 10 * 3x²) + (x * 5x + 10 * 5x) + (x * -2 + 10 * -2) = 3x³ + 30x² + 5x² + 50x - 2x - 20. Combining like terms, we get 3x³ + 35x² + 51x - 20. Thus, the expanded form of the expression (x + 10)(3x² + 5x - 2) is 3x³ + 35x² + 51x - 20.

Answer: the answer is A

Step-by-step explanation:

A right Riemann sum has the formula  A=∑ni=1Δxf(xi) A = ∑ i = 1 n Δ x f ( x i ) where x is the width of each of the n rectangles and f(xi) is the height.

A specific method of approximating an integral with a finite sum in mathematics is known as a Riemann sum. Riemann is the name of a German mathematician who lived in the 19th century. Approximating the area of functions or lines in graphs, as well as the length of curves and other approximations, is a highly typical application. The picked points in each subinterval of the partition are all in the upper Riemann sum, given an interval partition. The interval is often separated into subintervals of equal size.

Riemann  sum formula is A=∑f(xi)Δx A = ∑ f ( x i ) Δ x ,

where A is the curve's area under the evaluable interval,

f(xi) f ( x i ) is each rectangle's height (or the average of the two heights in the case of a trapezoid)

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183  tickets must be sold to break even. The price at which a good or service must be provided in order to recoup its expenses of production.

The band costs $650,

decorations cost $45

refreshments cost $2.20 per person

let x be the  no of ticket

Total cost = 650+ 45+ 2.20x

break even

tickets cost = $6

6x =   650+ 45+ 2.20x

6 x - 2.20x = 695

3.8 x  = 695

x = 182.89

183  tickets must be sold to break even.

tickets must be sold to clear $700

700/6 =116.6

700/ 7.5 = 93.33

117 tickets must be sold to clear $700

94 tickets must be sold to clear $700,  If admission tickets are $7.50 each.

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The length of one side of the pentagon after translation is 9 units

Step-by-step explanation:

To be clear, "A translation is an isometry that translates all points of a figure the same distance in the same direction." The dimensions of any geometric figure will never change as a result of translation. The figure's measurements won't change; it will simply be moved from one location to another.

This means that even after being translated 2 units to the left, a regular pentagon with sides of 9 units will still have a side length of 9 units.

The length of one side of the pentagon after translation is 9 units(option B)

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Answer:

Step-by-step explanation:

we are told that JK and KL sides are the same (b/c of the marks) so set them equal and solve for x

8x =  13x-15

8x - 8x  + 15   =  13x - 8x  -15 + 15

15 = 5x

divide by 5

3 = x

Use the fact that it's 180°  around the interior angles of the triangle to solve for y

180  = 5y -3  + 52 + 76

52 = 5y - 3

55 = 5y

11 = y

The set {(1, 2), (1, 4), (1, 6)} represents a function because each value of x corresponds to only one value of y.

In contrast, the sets {(3, 5), (-1, 7), (3, 9)} and {(1, 2), (3, 2), (5, 7)} do not represent functions because they contain multiple values of x that correspond to the same value of y. Specifically, the set {(3, 5), (-1, 7), (3, 9)} contains two values of x (3 and -1) that correspond to the same value of y (7), while the set {(1, 2), (3, 2), (5, 7)} contains two values of x (3 and 1) that correspond to the same value of y (2).

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Answer:

2

Step-by-step explanation:

Applying the net operating income ratio, the rent per unit needs to be $8,354.22 to generate an NOI of $100,000.

The net operating income (NOI) is the result of the subtraction of the operating expenses from the gross operating income.

The net operating income ratio can be computed by subtracting the given operating expenses ratio from the operating gross income, which represents 100%.

                                                                                            Total

Rent per unit (per month) = $696.19 ($8,354.22/12)   $150,376

Vacancy Rate (5% of Potential Gross Income)                   7,519

Effective Gross Income                                                $142,857

Operating Expenses (30% of Effective Gross Income) 42,857

Net Operating Income (NOI)                                      $100,000

Number of Units 18

Gross operating income = net operating income + operating expenses

Operating expenses = 30% of effective gross income

Net operating income = 70% of effective gross income (100 - 30%)

= $100,000

Effective Gross Income (100%) = $142,857 ($100,000 ÷ 70%)

Vacancy rate = 5% of potential gross income

Effective Gross Income = 95% (100 - 5)

Potential gross income = $150,376 ($142,857 ÷ 95%)

Number of units = 18

Rent per unit = $8,354.22 ($150,376/18)

Rent per month = $696.19 ($8,354.22 ÷ 12)

Thus, a rent of $8,354.22 per unit can generate a Net operating income of $100,000.

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Answer:

Step-by-step explanation: So First you  would need to multiply 2x3 because if you need to triple two cups you have to multiply so the answer is 6 cups

a) The table with the output values is completed on the first image at the end of the answer.

b) The graph of the proportional relationship is given by the second image at the end of the answer.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

He covers a 150-square-foot floor in 3 hours, hence the constant of proportionality is obtained as follows:

k = 150/3 = 50 sq feet per hour.

Then the equation is given as follows:

y = 50x.

Then the numeric values for the table are given as follows:

The problem is given by the image shown at the end of the answer.

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Answer:

128

Step-by-step explanation:

DO the "E"

  125 + 28/7   -1    do the  division next

  125  +   4     - 1     now do the + or -  or both

     128

Answer:

5x + 100 = 7x + 30

100 - 30 = 7x - 5x

70 = 2x

x = 35

3y + 16 = 5y

16 = 5y - 3y

16 = 2y

y = 8

Step-by-step explanation:

________________________________

=> 5x + 100 = 7x + 30

=> 100 – 30 = 7x – 5x

=> 70 = 2x

=> x = 70/2

=> x = 35

The value of x is 35.

________________________________

=> 16 = 5y – 3y

=> 16 = 2y

=> y = 16/2

=> y = 8

The value of y is 8.

_______________________________

Step-by-step explanation:

since it is geometric sequence we will use the formula

[tex]tn = {ar}^{n - 1} [/tex]

a = 6

r = 4

The first term

T1(a) = 6

The second term

[tex]t2 = {a \times r}^{2 - 1} [/tex]

[tex]t2 = {6 \times 4}^{1 } = 24[/tex]

The Third Term

[tex]t3 = {a \times r}^{3 - 1} = {a \times r}^{2} [/tex]

[tex]t3 = {6 \times 4}^{2} = 6 \times 16 = 96[/tex]

The fourth term

[tex]t4 = {a \times r}^{4 - 1} = {a \times r}^{3} [/tex]

[tex]t4 = {6 \times 4}^{3} = 6 \times 64 = 384[/tex]

The fifth term

[tex]t5 = {a \times r}^{5 - 1} = {a \times r}^{4} [/tex]

[tex]t5 = {6 \times 4}^{4} = 6 \times 256 = 1,536[/tex]

i hope these helped

Answer:

6, 24, 96, 384, 1536, ...

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given:

Substitute the given values of a and r into the formula to create an equation for the nth term:

[tex]a_n=6(4)^{n-1}[/tex]

To find the first 5 terms of the geometric sequence, substitute n = 1 through 5 into the equation.

[tex]\begin{aligned}\implies a_1&=6(4)^{1-1}\\&=6(4)^{0}\\&=6(1)\\&=6\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_2&=6(4)^{2-1}\\&=6(4)^{1}\\&=6(4)\\&=24\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_3&=6(4)^{3-1}\\&=6(4)^{2}\\&=6(16)\\&=96\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_4&=6(4)^{4-1}\\&=6(4)^{3}\\&=6(64)\\&=384\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_5&=6(4)^{5-1}\\&=6(4)^{4}\\&=6(256)\\&=1536\end{aligned}[/tex]

Therefore, the first 5 terms of the given geometric sequence are:

Answer:

umm i would say 40$

Step-by-step explanation:

sorry if i have misunderstood the question

Answer:

72kg

Step-by-step explanation:

Stephen = 72

Saravanan = x

Shamsul = (x • 1.5) since Shamsul's mass is 1.5 times Saravanan's mass

1. make an equation:

( 72 + x + (x • 1.5) ) ÷ 3 = 64

2. solve it:

( 72 + x + (x • 1.5) ) ÷ 3 = 64

( 72 + x + (x • 1.5) ) = 64 • 3

( 72 + x + (x • 1.5) ) = 192

x + 1.5x = 192 - 72

2.5x = 120

x = 120 ÷ 2.5

x = 48

Thus shamsul's mass is:

48 • 1.5 = 72kg

The missing parts of the table for the compound interest problem are;

2)  $487.91

3) 435(1.039)^(t) and  $487.91

4) 435(e)^(0.039t) and $499

1) In this account, we are given the formula for the compound interest as;

P(1 + rt)

The balance after t years is expressed as;

435(1 + 0.039t)

Balance after 3 years is;

435(1 + 0.039(3)) = $485.90

2) In this account, we are given the formula for the compound interest as;

P(1 + (r/n))^(nt)

The balance after t years is expressed as;

435(1.039)^(t)

Balance after 3 years is;

435(1.039)^(3) = $487.91

3) Same as 2 above

4) In this account, we are given the formula for the compound interest as;

P₀e^(rt)

The balance after t years is expressed as;

435(e)^(0.039t)

Balance after 3 years is;

435(e)^(0.039 * 3) = $499

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Answer:

[tex]\frac{10}{30}[/tex]

Step-by-step explanation:

Answer:

10/30

Step-by-step explanation:

Gonzalez Family Sprinklers used 15 liters and Walkers Family Sprinklers used 40 liters.

From the information, the Gonzalez family's sprinkler was used for 35 hours. The Walker family's sprinkler was used for 40 hours. There was a combined total output of 2125L of water.

Let Gonzalez = g

Let Walker = w

The equation will be:

g + w = 55 .... i

35g + 40w = 2125 ....

From equation i g = 55 - w

Put the above into equation ii

35g + 40w = 2125

35(55 - w) + 40w = 2125

1925 - 35w + 40w = 2125

Collect like terms

5w = 2125 - 1925

5w = 200

Divide

w = 200 / 5

w = 40

Walkers Family Sprinklers used 40 liters.

Since g + w = 55

g + 40 = 55

g = 55 - 40

g = 15

Gonzalez Family Sprinklers used 15 liters.

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The irrational solution of an exponential function, 3⁽¹⁻⁴ˣ⁾ = 4ˣ in exact form, is equals to the 0.190 in a decimal rounded to three decimal places.

The exponential function is a mathematical function of the form f(x) = aˣ , where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0. The most commonly used exponential base is the transcendental number e, which is approximately equal to 2.71828.

We have given an exponential equation is

3⁽¹⁻⁴ˣ⁾ = 4ˣ

Require to solve this Exponential equation.

Now, 3⁽¹⁻⁴ˣ⁾= 4ˣ

taking logarithm both sides we get,

ln ( 3⁽¹⁻⁴ˣ⁾ ) = ln(4ˣ)

=> (1-4x) ln(3) = xln(4) [using ln( aˣ)= x ln(a) ]

=> ln (3) - 4x ln (3) = x ln (4)

=> ln (3) = x ln(4) + 4x ln(3)

=> ln (3) = x[ ln (4) + 4 ln (3) ]

=> x = ln (3) / [ ln (4) + 4 ln (3) ]

=> x ~ 0.190

Therefore, solution set is ln (3) / [ ln (4) + 4 ln (3) ].

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(b) is the correct response. the students spend on textbooks in a semester between $250 and $2,000

The Gaussian distribution is another name for the normal distribution. It is a typical continuous probability distribution with a standard deviation of one and a mean of zero.

The tails of the curve are asymptotic, extending to infinity without touching the horizontal axis, and the curve is unimodal and symmetric about the mean. Since the majority of observations are centered on the mean, mean=mode=median.

99.7% of the area under the curve is approximately -3, or 3 standard deviations from the mean, according to the 68-95-99.7 rule. The z score is determined utilizing the accompanying recipe:

For z=3, solve for both x by equating the z score formula with -3 and 3.

3 = x 235 5 x = (3 5) + 235 x = 250 for z=-3:

3 = x 235 5 x = (3 5) + 235 x = 220 A student spends between $220 and $250 on textbooks each semester.

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Full Question = The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of $235 and a standard deviation of $5. According to the standard deviation rule, how much did almost all (99.7%) of the students spend on textbooks in a semester?

a. Between 230 and 240 dollars.

b. Between 220 and 250 dollars.

c. Between 175 and 295 dollars.

d. Less than 220 dollars or more than 250 dollars.

e. Less than 230 dollars or more than 240 dollars.

Answer:

There were 56 signers.

Step-by-step explanation:

First, set up the two equations for the two situations we are given.

7 is 10% of y . . . . .(1):

[tex]7 = \frac{10}{100}(y)[/tex]

n is 80% of y . . . . .(2):

[tex]n = \frac{80}{100}(y)[/tex]

Now, solve for y in the 1st equation, and substitute y in the second equation to solve for n.

[tex]7 = \frac{10y}{100}[/tex]

[tex]700 = 10y\\[/tex]

[tex]70 = y[/tex]

[tex]n = \frac{80*70}{100}[/tex]

[tex]n = \frac{5600}{100}[/tex]

[tex]n = 56[/tex]

Answer:

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

7 is 10% of y, find y:

n is 80% of y, find n: