Is (1, 2) a solution of 6x-y > 3?

\(81x^4-16y^4\implies 3^4x^4-2^4y^4\implies (3x)^4-(2y)^4\implies \underset{\textit{difference of squares}}{[(3x)^2]^2-[(2y)^2]^2} \\\\\\ \underset{\textit{difference of squares}}{[(3x)^2-(2y)^2]}[(3x)^2+(2y)^2]\implies (3x-2y)(3x+2y)[(3x)^2+(2y)^2] \\\\\\ (3x-2y)(3x+2y)[(3^2x^2)+(2^2y^2)]\implies (3x-2y)(3x+2y)(9x^2+4y^2)\)

The principal amount of the loan is  $5200 with a simple interest charged on it at an annual rate of 10.2%. The amount of interest she paid on the loan is $662.  The number of months she took to pay the total loan would be 15 months.

Formula used,

Interest = Principal amount × Rate of interest × Time ---- (1)

S.I.=P×R×T

Given that:

P = $5200, R= 10.2% , S.I.= $663

On putting the values in equation (1) we get,

663 = 5200 ×0.102×T

Simplifying the above equation, we obtain,

663= 530.4× T

T = 663÷530.4

T= 1.25 years

For time taken in months, we have to multiply the time by 12 months :

T = 1.25×12

T= 15 months

Time= 15 months

Hence, the loan was taken for a period of 15 months.

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The probability that the mean shipping time for the 70 shipments is less than 2.43 days is approximately 0.0764.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

We can use the Central Limit Theorem (CLT) to approximate the distribution of the sample mean. According to the CLT, if the sample size is large enough, the distribution of the sample mean is approximately normal, regardless of the distribution of the original variable.

The mean of the sample mean distribution is equal to the population mean, which is 2.93 days, and the standard deviation of the sample mean distribution is equal to the population standard deviation divided by the square root of the sample size, which is:

σ/√n = 2.93/√70 = 0.35

Therefore, we can standardize the sample mean by subtracting the population mean and dividing by the standard deviation:

Z = (x - μ) / (σ/√n) = (2.43 - 2.93) / 0.35 = -1.43

We want to find the probability that the sample mean is less than 2.43 days, which is equivalent to finding the probability that the standardized sample mean is less than -1.43. Using a standard normal table or calculator, we find that the probability is approximately 0.0764.

Therefore, the probability that the mean shipping time for the 70 shipments is less than 2.43 days is approximately 0.0764.

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Answer:

64

Step by step solution:

Not exactly sure what it means to expand the product. But to solve, you always do what's in the paranthesis first. So 2 x 4 = 8. The little number 2 means squared or to the power of, which bascially means you multiply the number by how ever many it tells you. So since it says 8 to the power of 2, you just multiply 8 x 8 which equals 64.

Answer:

k k hhi i i kjh hi hi pi i i hi hi kp i pi hj

Answer:

A. -7 A2. -7

B.-14 B2. 2

C.-14 C2.14

D. 1 D2. -7

9514 1404 393

Answer:

  a. -7, -7

  b. -14, 2

  c. -14, -14

  d. 1, -1

  e. misuse of the associative property leads to different results

Step-by-step explanation:

Your calculator (or a spreadsheet) can figure these easily.

a. -12 +(-4 +9) = 12 +5 = -7

  (-12 +(-4)) +9 = -16 +9 = -7

__

b. (14 -20) -8 = -6 -8 = -14

  14 -(20 -8) = 14 -12 = 2

__

c. (14 +(-20)) +(-8) = -6 -8 = -14

  14 +(-20 +(-8)) = 14 +(-28) = -14

__

d. -1 -(-1 +(-1)) = -1 -(-2) = -1 +2 = 1

  (-1 -(-1)) +(-1) = (-1+1) -1 = 0 -1 = -1

__

e. The associative property works for addition. When the associative property is used to rearrange subtraction problems, the minus signs need to be kept with the numbers, as in (c). That is, the problem needs to be expressed as a sum of signed numbers.

In (d), the term -(-1 +(-1)) was broken in the middle when the sum was rearranged for the second expression. Only terms in the same level of parentheses can be rearranged by the associative property.

The total length of the nylon rope that Jamie will use would be 15.3 feet of nylon rope.

Within this scenario specifically, one side of the right-angled triangle comprises the height of the tent (standing at 6.5-feet), and the other forms as the measure from the center of the tent to where Jaime stakes the ropes stretching outwards in another direction (with a calculated measure of 4-feet). Subsequently, we will refer to the extent of the nylon rope as R.

The Pythagorean theorem formula is:

R ² = 6.5 ² + 4 ²

R ² = 42. ²25 + 16

R ² = 58.25

R = 7. 63 ft

There are two ropes so the length would be :

= 7. 63 + 7. 63

= 15. 3 ft

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Answer:

It would be C.

Step-by-step explanation:

This is because they allow it to be 50 dollars and less, making it C.

Answer:

2·2·2·2 = 16

Step-by-step explanation:

everytime a number is raised by another, that means you are going to multiply the base number  times itself as many times as the exponents tells you. this is a little but tricky to explain, so let me give you some examples:

2² → in this case the base number is 2 and the exponent is 2 as well, so you will multiply 2 times itself, 2 times:

2² = 2 · 2 = 4

2³ → in this case the base number is 2 and the exponent is 3, so you will multiply 2 times itself, 3 times:

2³ = 2 · 2 · 2 = 8

In the question asked, 2 is being raised by 4, so you will multiply 2 times itself, 4 times:

2^4 = 2·2·2·2 = 16

the same format will be used regardless of the base number and the exponent

i hope this helps! :)

Answer:

6

Step-by-step explanation:

100/18=5 1/2

18*6=108

Answer : 18x5=90 18x6=108

Step-by-step explanation:

The equation of A which is a function of just q is;

A = [(4q² - 1100)/2q]

The value of dR/dt when q = 15 and dp/dt = 5 is; dR/dt = -33.33

We are given;

Relationship between price(p) and quantity(q) expressed as;

p² + 2q² = 1100

We now differentiate the above with respect to t to get;

2p(dp/dt) + 4q(dq/dt) = 0

Now, when the revenue is R, then;

dR/dt = A(dp/dt)

Let us make dp/dt the subject of the formula in the differentiated form above to get;

2p(dp/dt) = -4q(dq/dt)

dp/dt = -2(q/p)(dq/dt)

Making p the subject of the formula;

p² + 2q² = 1100.

p² = 1100 - 2q²

p = √(1100 - 2q²)

Therefore;

dp/dt = -2[q/(√(1100 - 2q²))](dq/dt)

The formula for revenue is usually expressed as; R = pq

Thus;

We now differentiate both sides with respect to t to get;

dR/dt = p(dq/dt) + q(dp/dt)

From dp/dt = -2(q/p)(dq/dt), we see that;

dq/dt = -(p/2q)(dp/dt)

Therefore;

dR/dt = -(p²/2q)(dp/dt) + q(dp/dt)

p = √(1100 - 2q²)

Therefore;

dR/dt = [(2q² - 1100)/2q + q](dp/dt)

This is broken down to get;

dR/dt = [(4q² - 1100)/2q](dp/dt)

We are told that;

dR/dt = A*dp/dt

Therefore;

A = [(4q² - 1100)/2q]

We want to find dR/dt when q = 15 and dp/dt = 5.

Thus;

dR/dt = [(4(15)² - 1100)/(2 × 15)] × 5

dR/dt = -(200/30) × 5

dR/dt = -33.33

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Complete Question is;

The price (in dollars) p and the quantity demanded q are related by the equation: p^2+2q^2=1100.If R is revenue, dR/dt can be expressed by the following equation: dR/dt=A*dp/dt,

where A is a function of just q.

A = ?

Find dR/dt when q=15 and dp/dt=5.

dR/dt = The price (in dollars) p and the quantity demanded q are related by the equation: p^2+2q^2=1100.If R is revenue, dR/dt can be expressed by the following equation: dR/dt=A*dp/dt,

where A is a function of just q.

Answer:

243212

Step-by-step explanation:

Substitute the given value of t into the given formula. To find t, subtract 1997 from 2020.

2020−1997=23

Now substitute 23 into the equation for t and calculate.

N(t)N(23)==≈410(1.32)t410(1.32)23243,212

The number of unique visitors to the college website in the year 2020 was approximately 243,212.

Answer:

56 minutes

Step-by-step explanation:

https://quizlet.com/530747948/statistics-unit-2-the-normal-distribution-test-review-flash-cards/

Answer:

Greg's savings: 19 x 1

Step-by-step explanation:

57 / 3 = 19

19 is prime, so Greg's savings has to be 19 x 1.

Answer:

37.5 is the answer

Step-by-step explanation:

all you do is just multiply the 2 numbers

The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.

We are given that;

The concrete portion of the patio cost=$3 per square

To construct and the brick portion of the patio cost= $6 per square

Now,

The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:

6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft

Therefore, the area of the concrete portion is:

24 ft x 12 ft = 288 ft^2

The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:

3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft

Therefore, the area of one brick rectangle is:

12 ft x 24 ft = 288 ft^2

Since there are two brick rectangles, the total area of the brick portion is:

2 x 288 ft^2 = 576 ft^2

Now we can multiply the areas by their costs per square foot to get the costs of each portion:

Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456

The total cost of constructing the patio is the sum of the costs of each portion:

Total cost = $864 + $3456 = $4320

Therefore, by area the answer will be $4320.

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Answer:

2/15

Step-by-step explanation:

The probability of the event for the given odds in favor (4 to 7) is found as 4/11.

To continue solving, we must represent the ratio as a fraction.

Thus, we have the depiction shown below.

Odds ratio equals 4/7

We use the following equation to translate the aforementioned odd's expression into a probability expression.

This is displayed as

P = (Odds + 1)/(Odds).

Replace the unknown values in the equation above.

The following equation is what we have.

P = (4/7)/(4/7 + 1)

Analyze the amount

This results

P = (4/7)/(11/7)

Put the quotient in product form.

P = (4/7) * (7/11)

Evaluate

P = 4/11

Thus, the probability of event for the given odds in favor (4 to 7) is found as 4/11.

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The probability is 0.8427.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

Here we are total number of insurance agents = 89

And  number of insurance agents do own a handgun = 75

So we asked probability that a insurance agent will own a handgun  

Probability = no.of insurance agents/no.of insurance agents who owns a handgun

Probability = 75/89 = 0.8427

The probability that the agent will own a handgun is .84

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Answer:

It Shall be any marvel movie

Step-by-step explanation:

I don't have a favorite

:( From: iOE ):

Probability of Wes and Maureen being sent to Washington DC from a class of 38

p = 5.26%

:

Answer:

second option

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - \(\frac{2}{3}\) and (a, b ) = (1, - 7 ) , then

y - (- 7) = - \(\frac{2}{3}\) (x - 1) , that is

y + 7 = - \(\frac{2}{3}\) (x - 1)

Answer:

b. Linear Programming model

Step-by-step explanation:

Correct option is b. Linear Programming model.

As we know that, Linear programming model is a technique that used to find the optimal solution of a given problem with the available resources.

Answer:

2.5

Step-by-step explanation:

the length has increased by 7.5/3 = 2.5.

so the scale factor is 2.5

Answer:

(2,6)

Step-by-step explanation:

Google

Answer:

subtraction of 6 3/4 from 24 3/4

Step-by-step explanation:

24 3/4 - 6 3/4 = 18