Consider the following equation of a parabola.y? + 4y = 8r + 4Step 1 of 3: Find the focus of the parabola.

Answer: 151sq

Step-by-step explanation:

You may use the formula for a cylinder's surface area to determine the candle's surface area:

SA = 2πr^2 + 2πrh

Given: 

Radius (r) = 3 inches

Height (h) = 5 inches

Pi (π) = 3.14 (approximately)

Now, enter the values into the formula to get:

SA = 2 * 3.14 * 3^2 + 2 * 3.14 * 3 * 5

SA = 2 * 3.14 * 9 + 2 * 3.14 * 3 * 5

SA = 56.52 + 94.2

SA ≈ 150.72 square inches

The candle has a surface area of around 151 square inches.

This is False in light of the stated statement. due to the employment of a regression line to calculate the mean of y for x that are outside the x-range of the data.

Y = mX + b, where X is the predictive (independent) factor, m is really the approx slope, and b is the expected intercept, is the methodology for simple linear regression.

Regress, from whence the word "regression" is derived, means "to go back" in Latin (to something). Regression is the method that enables "going back" from muddled, challenging data to a clearer and more significant model in this manner.

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Answer:

Let x be the distance traveled by you to the north and y be the distance traveled by your friend to the west. Let d be the distance between you and your friend at time t. Then, we have:

d^2 = x^2 + y^2

Taking the derivative of both sides with respect to time, we get:

2d (dd/dt) = 2x(dx/dt) + 2y(dy/dt)

Simplifying this expression, we get:

dd/dt = (x(dx/dt) + y(dy/dt)) / d

Since you are driving north at a constant speed v and your friend is driving west at a constant speed w, we have:

dx/dt = v and dy/dt = -w

Substituting these values and simplifying, we get:

dd/dt = (v^2 + w^2)^0.5

Therefore, the speed of separation between you and your friend at time t is the square root of the sum of the squares of your speeds.

To find the second derivative of the distance between you and your friend, we take the derivative of dd/dt with respect to time:

d^2d/dt^2 = (v dv/dt + w dw/dt) / (v^2 + w^2)^0.5

Since v and w are constant, their derivatives with respect to time are zero, so the second derivative of the distance between you and your friend is zero.

Suppose you wait for an hour (i.e., t = 1 hour) before driving off to the north. Then, at time t > 1 hour, the distance between you and your friend is given by:

d = (vt)^2 + ((t-1)w)^2)^0.5

Taking the derivative of both sides with respect to time, we get:

dd/dt = 2v^2t / (2((vt)^2 + ((t-1)w)^2)^0.5)

Simplifying this expression, we get:

dd/dt = v / ((v^2 + ((t-1)w)^2)^0.5)

Therefore, the speed of separation between you and your friend at time t (greater than one hour) is given by v divided by the square root of the sum of the squares of your speed and your friend's speed.

The second derivative of the distance between you and your friend is given by:

d^2d/dt^2 = -vw(t-1) / ((v^2 + ((t-1)w)^2)^1.5)

While an absolute value may be any number, the output from an absolute value expression is always greater than or equal to zero

The absolute value | x | of a real number x is defined as the non-negative value of x without regard to its sign. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero along real number line.

The absolute value of any number is seen to be always greater than or equal to zero. Both a number and its opposite are the same distance from zero on the number line. Since they have the same distance from zero, they have the same absolute value.

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Answer:

a) 20 male fish

b) 9 female fish died

Step-by-step explanation:

total 50 gold fish that means 100%

so 1% means 0.5

then 60% means 0.5 x 60 = 30 female fish

after 30% female fish died from the 60% it becomes

\(30*\frac{30}{100} = 9\)

so it becomes 9 female fish now

a) ealier we had 30 female fish then the male fish are 20
b) ealier we had 30 female fish and from that 9 died

Answer:

give or take 5 miles.

Step-by-step explanation:

im not shor but that is true about the both of them

Answer:

Denasia's mileage has a larger relative error :)

Step-by-step explanation:

I just did the test 3 days ago so yea

Answer:

constant is - 19

Step-by-step explanation:

the constant is the term in an expression with no variable attached to it.

12r + \(\frac{r}{2}\) - 19

the only term without the variable r attached to it is - 19

then the constant term is - 19

The average world population during the time period of 1950 to 2000 is approximately 4.7 billion.

To estimate the average world population, we need to evaluate the population at both endpoints and then take the average.

Substituting t = 0 (which corresponds to the year 1950) into the equation, we get:

P(0) = 2560e^(0.017185*0) = 2560

So the estimated world population in 1950 was 2560 million.

Substituting t = 50 (which corresponds to the year 2000) we get:

P(50) = 2560e^(0.017185*50) = 6789.9...

Rounding to the nearest million, we get P(50) ≈ 6790 million.

The average world population during the time period of 1950 to 2000 is approximately (2560+6790)/2 = 4675 million, or 4.7 billion (rounded to the nearest billion).

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The volume of the triangular prism will be 400 cubic feet.

Given that:

Width, W = 15 feet

Height, h = 8 feet

Base length, b = 6²/₃ feet

Volume is a measurement of three-dimensional space that is utilized. The concept of length is linked to the notion of capacity.

The volume of the triangular prism is calculated as,

V = 1/2 · b · h · W

V = 0.5 · 6²/₃ · 8 · 15

V = 400 cubic feet

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Answer:

( 0 , 1 ) ,  ( 1 , 0 )

( − 5 , 9 ) ,  ( 3 , 0 )

( 0 , 9 ) ,  ( 8 , 6 )

Step-by-step explanation:

Answer:

175

Step-by-step explanation:

Average queue length = (arrival rate * service time) / (1 - arrival rate * service time)

For the given problem, the average queue length is:

Average queue length = (50 * 35) / (1 - 50 * 35)

= 175

Answer:

C

Step-by-step explanation:

To solve this problem, we can use the formula for the volume of a sphere:

V = (4/3)πr³

where V is the volume and r is the radius of the balloon.

Given that the volume is increasing at a rate of 2.1 ft/min, we can express this as:

dV/dt = 2.1 ft/min

We need to find how rapidly the radius (dr/dt) is changing when the radius is 0.65 feet.

To relate the rate of change of volume to the rate of change of radius, we can differentiate the volume formula with respect to time (t):

dV/dt = (dV/dr) * (dr/dt)

We know dV/dt = 2.1 ft/min. Now, let's find (dV/dr):

V = (4/3)πr³

Differentiating both sides with respect to r:

dV/dr = 4πr²

Now, we can substitute the values into the formula:

2.1 ft/min = (4π(0.65)²) * (dr/dt)

Simplifying:

2.1 ft/min = 4π(0.4225) * (dr/dt)

Now, solve for (dr/dt):

(dr/dt) = (2.1 ft/min) / (4π(0.4225))

(dr/dt) ≈ 0.396 ft/min

Therefore, when the radius is 0.65 feet, the radius of the balloon is increasing at a rate of approximately 0.396 ft/min.

Answer:

The mean is 38, the median is 34, the mode is 34

Step-by-step explanation:

mean: add all the numbers then divide by how many numbers there are in the data set, there were 7 test scores so in this case, divide  by 7

median: the number in the middle when you order the numbers from least to greatest

mode: most commonly used number; number that appears most often.

hope this helps!

Answer:

2.29 ft of side length and 1.14 height

Step-by-step explanation:

a) Volume V = x2h, where x is side of square base and h is hite.

Then surface area S = x2 + 4xh because box is open.

b) From V = x2h = 6 we have h = 6/x2.

Substitude in formula for surface area: S = x2 + 4x·6/x2, S = x2 + 24/x.

We get S as function of one variable x. To get minimum we have to find derivative S' = 2x - 24/x2 = 0, from here 2x3 - 24 = 0, x3 = 12, x = (12)1/3 ≅ 2.29 ft.

Then h = 6/(12)2/3 = (12)1/3/2 ≅ 1.14 ft.

To prove that we have minimum let get second derivative: S'' = 2 + 48/x3, S''(121/3) = 2 + 48/12 = 6 > 0.

And because by second derivative test we have minimum: Smin = (12)2/3 + 4(12)1/3(12)1/3/2 = 3(12)2/3 ≅ 15.72 ft2

The box dimensions that minimize the amount of material used are; side length of base = 3.30 ft and height = 1.65 ft

a) We know that a box has length, width and height and so volume of a box is;

V = L × W × H

Now, we are told the base of the box is square and if we label it x, then we have to function that models the volume as;

V = x²h

where x is side of square base and h is height.

Thus surface area function is;

S = x² + 4xh

b) We are told that the volume is 18 ft³ and so;

x²h = 18

Thus;

h = 18/x².

Put 18/x² for h in the surface area function to get: S = x² + 4x(18/x²)

S = x² + 72/x.

To get minimum, we have to find derivative of S. Thus;

S' = 2x - 72/x² = 0,

Thus;

2x³ = 72

x³ = 72/2

x³ = 36

x = 3.3 ft

Thus;

h = 18/3.3²

h = 1.65 ft

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Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July

X pounds - 0.35 * X pounds = 9,500 pounds

Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.

To determine the number of pounds of raw materials that should be purchased in July, we need to calculate the raw materials production needs for August and then consider the inventory policies given in the information provided.

Each unit of finished goods requires 5 pounds of raw materials. The budgeted unit sales for August are 19,000 units. Therefore, the raw materials production needs for August would be 19,000 units multiplied by 5 pounds per unit, which equals 95,000 pounds.

The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Therefore, the desired ending raw materials inventory for July would be 10% of 95,000 pounds, which is 9,500 pounds.

To calculate the raw materials purchases for July, we need to consider the payment terms provided. Thirty-five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.

Let's assume the raw materials purchases for July are X pounds. Then the payment for 35% of X pounds will be made in July, and the payment for 65% of X pounds will be made in August.

The payment for raw materials purchases in July (35% of X pounds) will be:

0.35 * X pounds

The payment for raw materials purchases in August (65% of X pounds) will be:

0.65 * X pounds

Since the raw materials purchases for July should cover the desired ending raw materials inventory for July (9,500 pounds), we can set up the following equation:

Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July

X pounds - 0.35 * X pounds = 9,500 pounds

Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.

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Answer:

Step-by-step explanation:

2/(n+4)

Answer:

Step-by-step explanation:

Given data

distance of the route = 15miles

time taken on Monday= 1.75hours

speed= distance./time

speed= 15/1.75

speed= 8.57 miles per hour

her smart watch is correct

time taken on Thursday= 1.63hours

speed= distance./time

speed= 15/1.63

speed= 9.20 miles per hour

she was jogging at 9.20 miles per hour

Answer:

-24p -8

Step-by-step explanation:

4(–6p − 2)

Distribute

4 * -6p -4*2

-24p -8

We can see that the solid is a cube with sides that measure 8 cm.

We find the volume by multiplying, height, width, and length, so the volume is:

So, the volume is 512 cubic centimeters.

Answer: 0.00923521

Step-by-step explanation:

Given : The probability U.S households play video or computer games=69%=0.69

here, the probability of each U.S household play video or computer games is fixed as 0.69

Then, the probability of each U.S household not play video or computer games= 1-0.69=0.31

For independent events the probability of their intersection is product of probability of each event.

Now, the probability that none play video/computer games will be :-

\((0.31)^4=0.00923521\)

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

Answer: C

Step-by-step explanation:

The rest of the quadrilaterals provided have 2 pairs of parallel lines.

The choice is:

Explanation:

The quadrilateral that has exactly one pair of parallel lines is called a trapezoid.

Here's what a trapezoid looks like :

\(\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\linethickness{0.3mm}\qbezier(0,0)(0,0)(1,3)\qbezier(5,0)(5,0)(4,3)\qbezier(1,3)(1,3)(4,3)\qbezier(3,0)(8.2,0)(0,0)\put(-0.5,-0.3){$\sf A$}\put(5.3,-0.3){$\sf B$}\put(4.2,3.1){$\sf C$}\put(0.6,3.1){$\sf D$}\end{picture}\)

Answer: A

Step-by-step explanation:

Substitute the answers in the choices for x.

Answer:18 students for each teacher and 10 for each tutor, and if the academy had 80 students it would have 8 tutors

The expression is simplified to a²

Index forms are simply defined as models of writing numbers that are too large or small in a more convenient way.

Other names for index forms are;

Some rules of indices are;

We then have;

a(7)/a(5)

subtract the exponents

a²

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Answer:

64,135

Step-by-step explanation:

Because The 64 represents the hundreds place which would be 64,000

and the 13 represents the tens place which would be 13 and the 5

represents the ones place which would just be 5

The function that grows at the fastest rate for increasing values of x is f(x) = 4×2ˣ.

We can see this by comparing the growth rates of the three functions for larger and larger values of x.

As x gets larger, the exponential function f(x) grows much faster than the other two functions, which are both polynomial functions.

if we plug in x = 10, we get:

f(10) = 4×2¹⁰ = 4×1024 = 4096

h(10) = 9×10² + 25 = 925

g(10) = 15×10 + 6 = 156

As we can see, f(10) is much larger than h(10) and g(10), indicating that f(x) grows at a much faster rate than the other two functions.

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Explanation: The distributive property tells us when there's a number outside a set of parenthses, you can multiply it times each of the terms that are inside the set of parenthses and then add those products together.

So in this problem, we can multiply 5(4) + 5(8)

which simplifies to 20 + 40 which equals 60.

Answer:

5(4) + 5(8)

Step-by-step explanation:

Just trust me :D

In order for the account value to reach $91,000 in 12 years, Fwam would therefore need to invest $39,165.95, to the closest hundred dollars, assuming the interest rate is 5.9% compounded daily.

In exchange for using borrowed funds or assets, a borrower must pay the lender interest. It is charged for a certain duration of time, typically until the loan is fully returned, and is typically stated as a percentage of the amount borrowed. This fee is known as the interest rate. For instance, if a bank lends you $1,000 at a 5% annual interest rate, after a year of borrowing the money you would still owe the bank $50 more in interest. The creditworthiness of the borrower, the risk of the loan, and current market conditions are frequently used to establish the interest rate.

given

We know that Fwam expects the account to be worth $91,000 in 12 years and that the interest rate is 5.9% compounded daily in this situation.

We must convert the interest rate and the time period to the proper units before we can use the formula.

We begin by converting the 5.9% yearly interest rate to a daily rate:

daily rate is equal to (1 + 0.059/365)(365/365)-(1-1) = 0.00015999.

4,380 days in 12 years, or 365 days per year.

We can now enter the values into the formula to find P:

$91,000 = P × 2.3226

P = $39,165.95

In order for the account value to reach $91,000 in 12 years, Fwam would therefore need to invest $39,165.95, to the closest hundred dollars, assuming the interest rate is 5.9% compounded daily.

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