6(k+8)=96
k=12 k=-4
k=9
k=8

The dimensions of the closed cylinder that maximize its volume are radius=25 cm and height=40 cm. The maximum volume is 62,500 cubic cm.

Given that the total surface area of the closed cylinder is 5000 cm^2, we can write the equation for the total surface area as:

2πrh + 2πr^2 = 5000

We want to find the dimensions that maximize the volume of the cylinder. The volume of a cylinder is given by:

V = πr^2h

We can use the equation for the total surface area to solve for h in terms of r:

h = (5000 - 2πr^2) / (2πr)

Substituting this expression for h into the equation for the volume, we get:

V = πr^2[(5000 - 2πr^2) / (2πr)]

Simplifying this expression, we get:

V = (2500πr - πr^3)

To find the maximum volume, we take the derivative of V with respect to r and set it equal to zero:

dV/dr = 2500π - 3πr^2 = 0

Solving for r, we get r=25 cm.

We can then substitute this value of r into the expression for h to get h=40 cm.

Therefore, the dimensions of the cylinder that maximize its volume are radius=25 cm and height=40 cm.

Substituting these values into the equation for the volume, we get:

V = π(25)^2(40) = 62,500 cubic cm.

To verify that this is a maximum point, we can take the second derivative of V with respect to r:

d^2V/dr^2 = -6πr

At r=25 cm, this is negative, which indicates that we have a maximum point. Therefore, the dimensions calculated above do indeed maximize the volume of the cylinder.

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Answer:

Yes

Step-by-step explanation:

Answer: B

16/100 = 0.16

0.16 is 16/100 exactly.

1/16 = 0.000625

1/6 = 16.666...

1/3 = 33.33...

So, the answer is 16/100.

Hope this helps!

The fraction is equivalent to the decimal number 0.16 will be 16/100. Then the correct option is B.

The equivalent is the expression that is in different forms but is equal to the same value.

The decimal number is the sum of a whole number and part of the fraction number. The fraction number is greater than zero but less than one.

The decimal number is given below.

⇒ 0.16

The fraction is equivalent to the decimal number 0.16 will be

Multiply and divide the number by 100. Then the fraction number will be

⇒ 0.16 x 100 / 100

⇒ 16 / 100

The fraction is equivalent to the decimal number 0.16 will be 16/100. Then the correct option is B.

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We must study 270 cars to achieve a 90% confidence interval.

To construct a 90% confidence interval for the proportion of cars that are recalled at least once with a margin of error of no more than ±5 percentage points, you must determine the required sample size.

Here's a step-by-step explanation:

1. Identify the desired confidence level (Z-value):

For a 90% confidence interval, the Z-value is 1.645.

2. Determine the margin of error (E):

In this case, it is ±5 percentage points, or 0.05.

3. Estimate the population proportion (p):

Since we do not have an estimate for the proportion of cars recalled at least once, we will use p = 0.5 as a conservative estimate.

4. Use the formula for sample size (n) in proportion problems:

n = (Z² × p × (1 - p)) / E²

n = (1.645² × 0.5 × (1 - 0.5)) / 0.05²

n ≈ 270.6025

Since you cannot have a fraction of a car, you should round up to the nearest whole number.

Therefore, you must study approximately 270 cars to achieve a 90% confidence interval with a margin of error of no more than ±5 percentage points for the proportion of cars that are recalled at least once.

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The charge on the 150 nF capacitor is 3200 nF, the charge on the 120 nF capacitor is 3200 nF, the total energy stored in the network is \(76.8 \times 10^{-6} \mathrm{~J}\), the energy stored in the 150 nF capacitor is \(34.1 \times 10^{-6} \mathrm{~J}\), the energy stored in the 120 nF capacitor is \(42.67 \times 10^{-6} \mathrm{~J}\), the potential difference across the 120 nF and 150 nF capacitor is 21.33V, 26.67 V.

The equivalent capacitance when the capacitors are connected in series is,

\($$C_{\text {eq }}=\left(\frac{1}{C_1}+\frac{1}{C_2}\right)^{-1}=\left(\frac{1}{150 \mathrm{nF}}+\frac{1}{120 \mathrm{nF}}\right)^{-1}=66.67 \mathrm{nF}$$\)

the charge on each capacitor remains the same because they connected in series. Hence, the charge on each capacitor is,

Q=C V=(66.67 nF) (48 V)=3200 nC

the charge on the 150 nF capacitor is  \(Q_{150}\)=3200 nC

the charge on the 120 nF capacitor is \(Q_{120}\)=3200 nC

the total energy stored in the network is,

\($$$U=\frac{Q^2}{2 C}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(66.67 \times 10^{-9} \mathrm{~F}\right)}=76.8 \times 10^{-6} \mathrm{~J}$$\)

the energy stored in the 150 nF capacitor is,

\($U=\frac{Q_{150}{ }^2}{2 C}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(150 \times 10^{-9} \mathrm{~F}\right)}=34.1 \times 10^{-6} \mathrm{~J}$$\)

the energy stored in the 120 nF capacitor is,

\($U=\frac{Q_{150}{ }^2}{2 \mathrm{C}}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(120 \times 10^{-9} \mathrm{~F}\right)}=42.67 \times 10^{-6} \mathrm{~J}$$\)

the potential difference across the 150 nF capacitor is,

\($$V_{150}=\frac{Q_{150}}{C_{150}}=\frac{3200 \times 10^{-9} \mathrm{C}}{150 \times 10^{-9} \mathrm{~F}}=21.33 \mathrm{~V}$$\)

the potential difference across the 120 nF capacitor is,

\($$V_{120}=\frac{Q_{100}}{C_{120}}=\frac{3200 \times 10^{-9} \mathrm{C}}{120 \times 10^{-9} \mathrm{~F}}=26.67 \mathrm{~V}$$\)

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QN:-- For the capacitor network shown in (Figure 1) , the potential difference across ab is 48 V .

Find the charge on the 150 nF capacitor.

Find the charge on the 120 nF capacitor.

Find the total energy stored in the network.

Find the energy stored in the 150nF capacitor.

Find the energy stored in the 120nF capacitor.

Find the potential difference across the 150 nF capacitor.

Find the potential difference across the 120 nF capacitor.

In algebra, fractions can be added, subtracted, multiplied, and divided just like in basic arithmetic.

The components of a whole or group of objects are represented by fractions. A fraction consists of two parts. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the whole or collection. The denominator is the figure that appears below the line.

Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the fundamentals of algebra. Additionally, the algebraic expressions contain the fundamental arithmetic operations of addition, subtraction, multiplication, and division.

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a) 500 -25x ≥ 200 b) 12 weeks

1) Gathering the data

$500

At least : ≥ 200

Withdrawal = -25

A) Since she wants at least 200 in the account, and the summer has 12 weeks, We can write this inequality:

500 - 25x ≥ 200

B) To find how many weeks we need to solve an equation

500-25x= 200

-25x = 200 -500

-25x = -300

25x = 300

x=12

Under these conditions, 12 weeks in the 13th week she won't be able to keep at least $200 in her account with these weekly withdrawals

Answer:

letter D.

Step-by-step explanation:

im not sure but I try it

a.(answer):

Y represents table spoons in oil and the X represents the table spoons in vinegar.

b.(answer):

oil needed is one(1) tablespoon the amount of vinegar used is 1.5 tablespoons to make the salad dressing the correct and for it to be proportional.

linear equation

y = 3/2x

c.(answer)

For every 1 tablespoon of vinegar there is 1.5 table spoons of oil X=1,Y=1.5.

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In an ideal and unlimited environment, a population's growth follows an exponential model.

Exponential growth is when a population's growth rate keeps increasing over time because the population has access to an unlimited supply of resources, and its rate of reproduction is not limited by a lack of food, water, or space. In a population, exponential growth would result in an increase in the number of individuals in the population over time. Thus, in an ideal, unlimited environment, a population's growth follows an exponential model.Exponential growth can be mathematically represented by the following formula:Nt = Noertwhere:Nt = the population size at time tNo = the initial population sizee = Euler's numberr = the per capita growth rate of the populationt = the amount of time that has elapsed.

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Calculating this expression will give us the amount the farmer needs to save annually over the 8-year period.

Given:

Payment required at the end of each year: P50,000

Number of years until the daughter starts college: 8

Interest rate: 7% (compounded annually)

We can calculate the annual savings using the formula for the present value of an ordinary annuity:

P = \dfrac{PMT \times (1 - (1 + r)^{-n}{r}

Where:

P = Present value (amount to be saved annually)

PMT = Payment amount (P50,000)

r = Interest rate per period (7% or 0.07)

n = Number of periods (8)

Let's substitute the given values into the formula:

\[ P = \dfrac{50,000 \times (1 - (1 + 0.07)^{-8}{0.07} \]

Calculating this expression will give us the amount the farmer needs to save annually over the 8-year period.

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Answer: Linear, Nonlinear, Linear, Nonlinear

Step-by-step explanation:

First 1: as x increased y also increased which means the thing is a line hint linear

Second 1: According to the points (u can graph them out if u want to) it goes down then up which isn't a straight line hence quadratic or nonlinear

Third 1: first degree hint linear

Fourth 1: Absolute value thing looks like a V when u plot it so its not linear

Answer:

HA , LJ , and IK contain the center of dilation. Line segments that contain the center of dilation in the preimage also contain the center of dilation in the image. GF , HI , and KL do not contain the center of dilation. Line segments that do not contain the center of dilation in the pre image are mapped onto distinct lines parallel to the original, corresponding line segment. HL does not contain the center of dilation either but it does lie on a line that passes through the center of dilation. Line segments that lie on lines passing through the center of dilation in the preimage lie on the same lines in the image.

Step-by-step explanation:

Plato’s Answer

Answer:

Step-by-step explanation:

HA , LJ , and IK contain the center of dilation. Line segments that contain the center of dilation in the preimage also contain the center of dilation in the image. GF , HI , and KL do not contain the center of dilation. Line segments that do not contain the center of dilation in the pre image are mapped onto distinct lines parallel to the original, corresponding line segment. HL does not contain the center of dilation either but it does lie on a line that passes through the center of dilation. Line segments that lie on lines passing through the center of dilation in the preimage lie on the same lines in the image.

Answer:

60 cents

Step-by-step explanation:

.6 x 5= 3

Answer:

12 2/5   or   12.4

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Square root of 92 is 9.591663047

so round that to 9.59

Answer:

m∠DFA = 115°

Step-by-step explanation:

Given:

Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

⇒ m∠CEB = m∠CAB = m∠CDB = m∡BC ÷ 2

                                                    = 164° ÷ 2

                                                    = 82°

The interior angles of a triangle sum to 180°

⇒ m∠DCF + m∠CDF + m∠DFC = 180°

⇒ 33° + 82° + m∠DFC = 180°

⇒ m∠DFC = 65°

Angles on a straight line sum to 180°

⇒ m∠DFC + m∠DFA = 180°

⇒ 65° + m∠DFA = 180°

⇒ m∠DFA = 115°

Answer:

  115°

Step-by-step explanation:

The measure of angle DFA where chords DB and CA cross is half the sum of arcs DA and CB. Arc CB is given as 164°, but arc DA must be figured from the inscribed angle that subtends it, angle DCA. That angle is given as 33°.

An arc is twice the measure of the inscribed angle it subtends, so arc DA is ...

  arc DA = angle DCA × 2 = 33° × 2 = 66°

  angle DFA = (66° +164°)/2 = 230°/2

  angle DFA = 115°

Answer:

2/7

Step-by-step explanation:

gradient y²-y¹/x²-x¹=4-2/4-(-3)

=2/7

{Taking (x¹,y,¹)=(-3,2)

and(x²-y²)=(4,4)

Attached is a two-way frequency table, to help Hugo organize the results.

A two-way frequency table is a table used to organize and display the relationship between two categorical variables. It is constructed by counting the number of occurrences of each combination of categories and presenting the results in a table format.

1. Identify the categorical variables and list their possible categories.

cat, no cat, dog, no dog

2. Count the number of observations for each combination of categories.

cat = 17

no dog = 20

no cat no dog = 7

3. Organize the counts in a table with the categories of one variable as rows and the categories of the other variable as columns.

          | dog | no dog | total

cat      |        |              |   17  |

no cat |        |     7       |        |

total    |        |     20    |   41  |

4. Fill in the table with the counts of the observed combinations of categories.

cat but no dog = 20 - 7 = 13

both cat and dog = 17 -13 = 4

total no cat = 41 - 17 = 24

total dog = 41 - 20 = 21

dog but no cat = 24 - 7 = 17

          | dog | no dog | total

cat      |   4   |      13     |   17  |

no cat |   17  |     7       |   24  |

total    |   21  |     20    |   41  |

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Given table shows the counts of respondents of a survey that asked 1000 adults about their employment status and whether they owned stocks:

Employment Status Owning Stocks Not Owning Stocks Employed 400 300

Unemployed 50 250 Retired 150 100We have to complete the following parts:

a) How many of the respondents are unemployed or do not own any stocks?

b) If a respondent is chosen at random, what is the probability that the respondent owns stocks?

c) If a respondent is chosen at random, what is the probability that the respondent is retired and does not own stocks?d) If a respondent is chosen at random, what is the probability that the respondent is employed or retired?

e) If a respondent is chosen at random, what is the probability that the respondent is employed, given that the respondent does not own stocks?

Solution:

a) The total number of respondents who are unemployed or do not own any stocks is 50 + 250 + 100 = 400.

b) Probability that a respondent owns stocks = Number of respondents owning stocks / Total number of respondents= (400 + 50 + 150) / 1000= 0.6

c) Probability that a respondent is retired and does not own stocks= Number of retired respondents not owning stocks / Total number of respondents= 100 / 1000= 0.1

d) Probability that a respondent is employed or retired= (Number of employed respondents / Total number of respondents) + (Number of retired respondents / Total number of respondents)= (400 / 1000) + (150 / 1000)= 0.55

e) Probability that a respondent is employed, given that the respondent does not own stocks= (Number of employed respondents not owning stocks / Total number of respondents not owning stocks)= 300 / 350= 0.86

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Answer:

C and D

Step-by-step explanation:

Hope this Helped! Please tell me if I'm wrong!

The situations that describe a quantity that changes in an exponential manner relative to the other quantity are,

A. The value of a printer decreases in value by 15% each year.

E. The amount of money in Devonte's savings account in it he earns 3.5% interest each year.

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents is only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

The situations that describe a quantity that changes in an exponential manner relative to the other quantity are,

The value of a printer decreases in value by 15% each year,

It is an exponentially decaying function.

Suppose the first year it decayed to 85% of it's original value, next year it will decay 15% of 85% of its value.

The amount of money in Devonte's savings account it he earns 3.5% interest each year.

Suppose he earned 3.5% for $100, which is 103.5, next year he will earn

3.5% on $103.5, an exponentially growing function.

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Answer:

Angle 1 = 88 degrees

Angle 2 = 42 degrees

Angle 3 = 113 degrees

Step-by-step explanation:

Angle 2 is a vertical angle to the angle whose measure is 42 degrees. Therefore, they are congruent. (Angle 2 = 42 degrees)

The Interior Angle Sum states that the sum of all the angles inside of a triangle always add up to 180 degrees.

180- (50+42)

180-92

Angle 1 = 88 degrees

180- (42+25)

180-67

Angle 3 = 113 degrees

Hope this helps. Have a nice day you amazing bean child.

Answer:

All my answers and work is in the screenshot! :)

Step-by-step explanation:

Answer:

26.75 unit^2 to the nearest hundredth.

Step-by-step explanation:

Integrating between the 2 limits:

            2                            2

Area =   ∫    e^2x dx     =   [   1/2 e^2x ]

            0                            0

= 1/2( e^4 - e^0]

= 1/2(54.598 - 1)

= 26.749

Answer:

21

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

AD        AH

-----  =  ---------

AB         AH +y

3        9

---- = ------

10         9+y

Using cross products:

3(9+y) = 9*10

27+3y = 90

3y = 90-27

3y =63

y = 63/3

y = 21

Answer:

y = 21

Step-by-step explanation:

According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, according to the Side Splitter Theorem:

\(\boxed{\sf AD : DB = AH : HC}\)

From inspection of the given triangle, the lengths of the line segments are:

To find the value of y, substitute the given line segment lengths into the proportion and solve for y:

\(\begin{aligned}\sf AD : DB &=\sf AH : HC\\\\3:7&=9:y\\\\\dfrac{3}{7}&=\dfrac{9}{y}\\\\3 \cdot y&=9 \cdot 7\\\\3y&=63\\\\\dfrac{3y}{3}&=\dfrac{63}{3}\\\\y&=21\end{aligned}\)

Therefore, the value of y is 21.

Answer: 1,809.56 ft.²

Step-by-step explanation:

       This formula relates the diameter of a sphere to its surface area:

A = πd²

       We will input the value given and solve:

A = πd²

A = π(24)²

A ≈ 1,809.56 ft.²

Step-by-step explanation:

Use the diameter to find the radius, which is diameter times 0.5. The radius is 12.

Now, the SA equation for a sphere is 4 times pi times radius squared.

12 squared is 144, so 4 * 144 * pi

Here are either answer:

- Without finding the decimal form of pi, 576pi feet squared

- Using the decimal form of pi, it's approximately 1809.56 feet squared

Answer:

Are you in Mr. Burg...'s class?  I have no clue what the answer is though.

Step-by-step explanation:

The measure of side BC is 2.3 inches.

What is congruency?

Two triangles are same to be congruent if all 3 corresponding sides ar equal and every one the 3 corresponding angles ar equal in measure. These triangles will be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The symbol of congruence is’ ≅’.

Main body:

We need to suppose that these 2 triangles are congruent.

ΔABC ≅ ΔDEF

so using it,

BC/AC = DF/EF

BC/4 = 20/28

BC = 2.3 inches

Hence the value of BC is 2.3 inches APPROX.

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