Maximize 3x + 4y + 3z on the sphere x² + y2 + z2 = 16. A) There is no maximum. B) The maximum is -434 c) 2034 The maximum is – 17

An account that pays 6% interest and is compounded monthly. At the end of five years, you will have approximately $6,691.13 in the account.

To calculate the amount you will have at the end of five years, we can use the formula for compound interest:

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

Where:

A = the final amount

P = the principal amount (initial investment)

r = annual interest rate (in decimal form)

n = number of times the interest is compounded per year

t = number of years

In this case, the principal amount (P) is $5,000, the annual interest rate (r) is 6% (or 0.06 in decimal form), the interest is compounded monthly, so the number of times compounded per year (n) is 12, and the number of years (t) is 5.

Plugging these values into the formula, we have:

A = $5,000(1 + 0.06/12)^(12*5)

Calculating the expression inside the parentheses first:

(1 + 0.06/12)^(12*5) ≈ 1.33822558

Now, substituting this value back into the formula:

A ≈ $5,000 * 1.33822558

A ≈ $6,691.13

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The numbers of the jerseys of 5 randomly selected Carolina Panthers would fall under the category of quantitative discrete data.

Quantitative data are numerical measurements or counts that can be added, subtracted, averaged, or otherwise subjected to arithmetic operations. Discrete data, on the other hand, can only take on specific, whole number values, as opposed to continuous data which can take on any value within a range.

Qualitative data, on the other hand, are non-numerical data that cannot be measured or counted numerically. Examples include colors, names, opinions, and preferences. Since the numbers of the jerseys are specific numerical values, they are considered quantitative data.

Since they can only take on specific, whole number values (i.e. the jersey numbers are not continuous values like weights or heights), they are considered discrete data. Therefore, the correct option for the given question is option "quantitative discrete".

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Answer:

5 miles=8km

1miles=8/5=1.6km

57.5 miles=(57.5×1.6)km

=92km

To approximate the change in volume of a spherical balloon as the radius increases from 8m to 8.2m, we can use differentials. The volume of a sphere is given by the formula V = (4/3)πr^3.

Taking differentials of both sides, we have dV = 4πr^2 dr.

At r = 8m, we have dV ≈ 4π(8m)^2 (0.2m) ≈ 160π/3 m^3.

Therefore, the change in volume of the spherical balloon as the radius increases from 8m to 8.2m is approximately 160π/3 m^3.
To approximate the change in volume of a spherical balloon using differentials, we'll use the formula for the volume of a sphere (V) and differentiate it with respect to the radius (r):

V = (4/3)πr³

Now, let's differentiate V with respect to r (dV/dr):

dV/dr = d((4/3)πr³)/dr = (4πr²)

Next, we'll find the differential change in radius (dr) which is the difference between the initial radius and the final radius:

dr = 8.2 m - 8 m = 0.2 m

Now, we can approximate the change in volume (dV) using differentials:

dV ≈ (dV/dr) * dr = (4πr²) * dr

Plug in the given values of r = 8 m and dr = 0.2 m:

dV ≈ (4π(8)²) * (0.2) = (4π(64)) * (0.2) = 51.2π m³

So, the approximate change in volume of the spherical balloon as it swells from a radius of 8 m to 8.2 m is 51.2π m³.

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Answer:

x is 90 z is 60 and y is 30

Step-by-step explanation:

The temperature of the soda after 20 minutes is approximately -18 degrees Celsius. To find the initial temperature of the soda, we can evaluate the function T(x) at x = 0.

Substitute x = 0 into the function T(x):

T(0) = -19 + 39e^(-0.45*0).

Simplify the expression:

T(0) = -19 + 39e^0.

Since e^0 equals 1, the expression simplifies to:

T(0) = -19 + 39.

Calculate the sum:

T(0) = 20.

Therefore, the initial temperature of the soda is 20 degrees Celsius.

To find the temperature of the soda after 20 minutes, we substitute x = 20 into the function T(x):

Substitute x = 20 into the function T(x):

T(20) = -19 + 39e^(-0.45*20).

Simplify the expression:

T(20) = -19 + 39e^(-9).

Use a calculator to evaluate the exponential term:

T(20) = -19 + 39 * 0.00012341.

Calculate the sum:

T(20) ≈ -19 + 0.00480599.

Round the answer to the nearest degree:

T(20) ≈ -19 + 1.

Therefore, the temperature of the soda after 20 minutes is approximately -18 degrees Celsius.

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INCOMPLETE QUESTION

A can of soda is placed inside a cooler. As the soda cools, its temperature Tx in degrees Celsius is given by the following function, where x is the number of minutes since the can was placed in the cooler. T(x)= -19 +39e-0.45x. Find the initial temperature of the soda and its temperature after 20 minutes. Round your answers to the nearest degree as necessary.

Answer:

The answer is $18n/3= p

The option-C is correct, that is 1 to 10 millimeter per year fast is soil creep.

Given that,

In the picture we can see the options.

We have to select the correct option for the given question.

The slow, downward movement of rock and soil down a low grade slope is known as downhill creep, sometimes referred to as soil creep or simply creep. Downhill creep can also refer to the slow deformation of such materials as a result of persistent strain and tension. While creep may appear continuous to the spectator, it actually represents the accumulation of multiple little, discontinuous movements of slope material produced by gravity.

Therefore, The option-C is correct, that is 1 to 10 millimeter per year fast is soil creep.

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The reaction of the graduate student on inflation is that a cost-of-living increase to her stipend.      

Inflation is the pace of expansion in costs over a given time-frame. Inflation is regularly a wide measure, like the general expansion in costs or the expansion in the typical cost for many everyday items in a country.

Inflation is term which states there is an expansion in the cost level for any labor and products.

In the unique situation, a set of experiences graduate living in the US got a payment of 18,000 dollar. However, there is a critical expansion that US economy endures. In this way the expense of products and the administrations accessible to individuals increments quickly. Individuals presently need to spend more on everything. Accordingly the alumni understudy requirements to request the typical cost for most everyday items to be remembered for the payment as need might arise to spend more on living.

Thus, graduate student argue on the a cost-of-living increase to her stipend.      

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This scenario describes a foodborne illness outbreak investigation, where several individuals with similar symptoms of food poisoning have been identified and traced back to a nearby restaurant.

In this situation, the local hospital has encountered multiple cases of individuals exhibiting symptoms consistent with food poisoning. Through interviews, it is discovered that all of them have recently dined at a nearby restaurant, indicating a potential common source of exposure. To further investigate and identify the cause of the illness outbreak, samples from the restaurant's food are collected.

These samples will undergo laboratory testing to check for the presence of pathogens, such as bacteria or viruses, that may be responsible for the foodborne illness. By analyzing the test results, health authorities can pinpoint the specific pathogen and take appropriate measures to prevent further spread and ensure the safety of the community.

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Answer: b) increasing

Step-by-step explanation: It seems evident that the sequence is made up of all the odd numbers.

\(\begin{gathered} \bold{a_1=1}\\ \bold{a_2=3=a_1+2}\\ \bold{a_3=5=a_2+2}\\ \bold{a_4=7=a_3+2} \\ \bold{a_n=a_{n- 1}+2}\end{gathered}\)

As we can see, in the nth position (any position), we take the value of the previous position and add 2 to it. This leads us to conclude that the sequence is monotonic increasing since as we add 2 to the values, these grow up.

Finally, we just need to use the z-coordinate of the point as the third coordinate in our cylindrical coordinates. So our final answer is: (r, θ, z) = (sqrt(x2 + y2), arctan(y/x), z)

To express a point given in Cartesian coordinates (x, y, and z) in cylindrical coordinates (r,, and z), we need to use some trigonometry. Here's how it works:
First, we need to find the distance from the origin to the point in question. This distance is given by the formula:
r = sqrt(x2 + y2)
where sqrt() means "square root" and 2 means "squared". So we take the square of the x-coordinate, add it to the square of the y-coordinate, and then take the square root of the result. This gives us the distance from the origin to the point in the x-y plane.
Next, we need to find the angle that the point makes with the positive x-axis. This angle is given by the formula:
= arctan(y/x)
where arctan() means "inverse tangent." This formula gives us the angle in radians (not degrees) between the positive x-axis and the line from the origin to the point. Note that we need to be careful about the signs of x and y when using this formula since arctan() can only give us angles between -pi/2 and pi/2 (i.e., the first and fourth quadrants).
Finally, we just need to use the z-coordinate of the point as the third coordinate in our cylindrical coordinates. So our final answer is: (r, θ, z) = (sqrt(x2 + y2), arctan(y/x), z)

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Therefore, the point (3,4,5) in Cartesian coordinates can be expressed in cylindrical coordinates as (5,0.93,5), where r = 5, θ ≈ 0.93 radians, and z = 5.

Sure, I can definitely help you with that! To express a point given in Cartesian coordinates (x,y,z) in cylindrical coordinates (r,θ,z), we use the following formulas:

r = √(x^2 + y^2)
θ = arctan(y/x)
z = z

So, if we have a point (x,y,z) in Cartesian coordinates, we can convert it to cylindrical coordinates using these formulas. For example, let's say we have the point (3,4,5) in Cartesian coordinates. To express this point in cylindrical coordinates, we first find r, θ, and z using the formulas above:

r = √(3^2 + 4^2) = √25 = 5
θ = arctan(4/3) ≈ 0.93 radians
z = 5


I hope this helps! Let me know if you have any further questions or if you need me to explain anything in more detail.

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The given polynomial is negative for negative values of x with very large absolute value because the dominant term x⁷ is negative and its absolute value is much larger than the absolute value of the other terms.

When x is negative and has a very large absolute value, the dominant term in the given polynomial is x⁷.

Since x⁷ is being raised to an odd power, it will also be negative.

The other terms in the polynomial are added to this dominant term. Notice that all the other terms have positive coefficients except for -6x³. This term is negative, but its absolute value is much smaller than the absolute value of the dominant term.

Therefore, when negative values of x with very large absolute value are substituted into the polynomial, the dominant term will be a large negative number, which will overpower the other smaller positive terms and the negative term -6x³.

This results in a negative value for the entire polynomial.

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The number of hours Dalvin worked and the number of hours Fatoumata worked is 10 and 5 respectively.

Let us assume the number of hours dalvin worked be x.

the number of hours fatoumata worked be y.

given that Dalvin can iron 10 shirts per hour, and Fatoumata can iron 20 shirts per hour.

from the question

Dalvin worked twice as many hours as Fatoumata means x = 2y ....................(1)

dalvin and fatoumata ironed 200 shirts between them which means

10x + 20y = 200 ...................(2)

now, substitute equation (1) in equation (2)

10(2y) + 20y = 200

20y + 20y = 200

40y = 200

y = 200/40

y = 5

so, the fatoumata worked 5 hours.

take the equation (1)

x = 2y

x = 2(5)

x = 10

so, the dalvin worked 10 hours.

Hence,the number of hours Dalvin worked and the number of hours Fatoumata worked is 10 and 5 respectively.

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Answer:

28cm

Step-by-step explanation:

To calculate the area of this shape, we need to seperate it into two shapes.

We see that the length of the top shape is 2 CM.  Since the top shape is a square, we know it is a 2x2 shape (because two of the other sides are 2cm.)  The area of the top shape, the square, can be found by performing the formula for calculating area (length x width).  2 x 2 = 4 (duh, haha).  Now, we need to find the area of the bottom shape.  Since we're separating them into two shapes, we need to subtract the length of the first shape and this one.  4 x 6 (the area formula) will give us 24.  Now, we need to add our two shapes to get the area of the entire shape.  24 cm + 4 cm = 28 cm.

Answer:

Banana made=3.22

Pumpkin made=7.86

Rocky road ice cream made=1.89

Step-by-step explanation:

From the question we are told that

1st year sales(banana, pumpkin, and rocky road ice cream) \(S_1= 13\%\)

2nd year sales:\(S_2=18.1\%\)

Rocky road sales doubled

Banana sales increased by 50%

Pumpkin sales increased by 20%

Rocky road ice cream had one less percent then banana

Let

Banana =x

Pumpkin=y

Rocky road ice cream=z

Generally the first year equation is given mathematically as

\(x+y+z=13......(1)\)

Generally the second year equation is given mathematically as

100% increase in Rocky road ice cream sales()z i.e double

\(2*z=2z\)

50% increase in banana ice cream sales()x

\(=>1*0.50=0.5\\=>0.5+1x=1.5x\)

20% increase in pumpkin(y)

\(=>1*0.20=0.2\\=>0.2+1x=1.2y\)

Therefore second year equation is given as

\(1.5x+1.27y+2z=18.1.....(2)\)

Generally where rocky road ice cream had one less percent of sales than the banana ice cream the equation is given as

\(1.5x-2z=1........(3)\)

Therefore combining the three equations

x+y+z=13

1.5x+1.27y+2z=18.1

1.5x-2z=1

matrix form

\(\begin {bmatrix}1 & 1& 1 & 13\\1.5 & 1.2 & 2 & 18.1\\1.5 & 0 & -2 & 1\end{bmatrix}\)

Generally the determinant of the first three columns

\(\triangle=1.8\)

Solving with Crammers Rule by solving Determinant when;

Column 4 replace column 1

\(\triangle_1=5.8\)

Column 4 replace column 2

\(\triangle_2=14.15\)

Column 4 replace column 3

\(\triangle_3=3.4\)

Therefore x is given my

\(x=\frac{\triangle_1}{\triangle}\)

\(x=\frac{5.8}{1.8}\)

\(x=3.22\)

Therefore y is given my

\(y=\frac{\triangle_2}{\triangle}\)

\(y=\frac{14.15}{1.8}\)

\(y=7.86\)

Therefore z is given my

\(z=\frac{\triangle_3}{\triangle}\)

\(z=\frac{3.4}{1.8}\)

\(z=1.89\)

Therefore

Banana made=3.22

Pumpkin made=7.86

Rocky road ice cream made=1.89

Answer:

Turtle = 11 m / min      

Snail = 1 m / min

Total approach speed = 12 m/min

360 m / (12 m/min) = 30 min

Separation is 30  min       at assumed speed of 1 m/min

But we know the separation is 40 min

So turtle moves at 3/4 * 11 m / min = 33 m/ 4 min

Snail moves at 3/4 * 1 m /min = 3/4 m / mi

Total approach speed = (33 + 3) / 4 = 9 m / min

So in 40 min

9 m / min * 40 min = 360 m

(Leaving out those units,  they approach at 12 * unit of speed)

So the unit of speed has to be 360 m / 40 min = 9 m / min

The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.

If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.

A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.

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Given:

To find:

The correct statements

Explanation:

Since the angles PCQ and SCR are vertically opposite angles.

So, we can write it as,

Therefore, the arc PQ is congruent to arc SR.

So, the first statement is correct.

Since the angles PCQ and SCR are vertically opposite angles and the angles QCR and PCS are vertically opposite angles.

So, we can write it as,

Since the central angle of a circle is 360 degrees.

Therefore,

Therefore, the measure of an arc QR is 150 degrees.

So, the second statement is correct.

Let us find the circumference of the circle.

Using the circumference formula,

Therefore, the circumference of the circle is,

So, the third statement is wrong.

Let us find the arc length of PS.

Here,

Using the formula,

Therefore, the arc length of PS is 13.1cm.

So, the fourth statement is correct.

Let us find the arc length of QS.

Here,

Using the formula,

Therefore, the arc length of QS is 15.7cm.

So, the fifth statement is correct.

Final answer: The statements 1, 2, 4, and 5 are correct.

Answer:

23skem

Step-by-step explanation:

07233 that is how on edge 2021

Answer:

C

Step-by-step explanation:

Answer:

d. legs

Step-by-step explanation:

In the Pythagorean Theorem (a^2 + b^2 = c^2)

a = leg

b = leg

c= hypotenuse

Answer:

$1530

Step-by-step explanation:

Hi there!

What we know

If this motorbike was on sale for 15% off, then we know that its discounted price is 85% of the original price (100-15=85)

Then, to find the discounted price, we multiply 1800 by 85%:

1800 × 85%

Change 85% into a decimal

= 1800 × 0.85

= 1530

Therefore the discounted price of the motorbike was $1530.

I hope this helps!

The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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Answer:

Let's make this a ratio:

50:56

Divide by 50 on both sides (since they made it a unit rate).

1:1.12

1.12 is your answer.

The measure of the angles e, d, a, and f will be 26°, 122°, 102°, and 58°, respectively.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

By the supplementary property, the equation is given as,

f + 78° + 44° = 180°

f = 58°

By the complementary property, the equation is given as,

e + 64° = 90°

e = 26°

By the corresponding angles property, the equation is given as,

c = f

c = 58°

By the supplementary property, the equation is given as,

c + d = 180°

58° + d = 180°

d = 122°

By the corresponding angles property, the equation is given as,

b = 78°

By the supplementary property, the equation is given as,

a + b = 180°

a + 78° = 180°

a = 102°

The diagram is given below.

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Upper quartile Q3 formula is expressed as shown;

Q3 = 3/4 (n+1)

Let assume the score is 100% in total;

substitute n = 100 into the formula;

Q3 = 3/4 (100+1)

Q3 = 3/4 (101)

Q3 = 303/4

Q3 = 75.75%

This means that the upper quartile must be greater than 75% since we arrived at a value greater than 75%, hence Javiers score is greater than 75% of all scores.e n =

Answer: (x, y) --> (x, -y)

Step-by-step explanation:

This is a reflection over the x-axis so its only the y-intercept that changes.

Answer:

its a reflection

Step-by-step explanation:

If it were a rotation, it wouldnt have overlapped.

If it were a translation, It would have been the wrong way up and not overlapping.

When reflected over line x, it will overlap because it stays rigid and does not change shape or size.

hope this helps :)

Answer:

B) -4 < y

Step-by-step explanation:

The lowest point on the y axis of the graph is -4 and everything else is higher

Answer:

m = \(\frac{y-q}{x}\)

Step-by-step explanation:

Given

y = mx + q ( subtract q from both sides )

y - q = mx ( divide both sides by x )

\(\frac{y-q}{x}\) = m

The given statement "An algorithm is a calculation that determines how long it will take to solve a problem." is False.

An algorithm is not just a calculation that determines how long it will take to solve a problem. An algorithm is a step-by-step set of instructions or a process used to solve a problem or perform a specific task. It is a systematic approach that allows a computer or human to break down a problem into smaller, manageable parts and reach a solution effectively.

Algorithms are the foundation of computer programming and can be applied in various fields such as mathematics, data processing, and problem-solving. They can be simple, like finding the largest number in a list, or complex, like solving a Rubik's Cube.

Efficiency is a key factor in evaluating algorithms. The time and resources required for an algorithm to solve a problem can vary greatly depending on the method used. However, the primary purpose of an algorithm is to provide a clear and concise procedure to reach a solution, rather than just estimating the time needed to solve a problem.

In summary, an algorithm is a well-defined process designed to perform a specific task or solve a problem, rather than just calculating the time required to do so. Its effectiveness depends on its efficiency, accuracy, and the simplicity of the steps involved.

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