Find a polynomial of lowest degree that has the indicated zeroes: 1+i, 1-i, 3

It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.

The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.

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One bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

William uses 40 milliliters of liquid plant food per week, so to find out how much plant food he needs for 12 weeks, we can simply multiply the weekly usage by the number of weeks:

Amount of plant food needed for 12 weeks = 40 milliliters/week x 12 weeks = 480 milliliters

So, William needs 480 milliliters of liquid plant food for 12 weeks.

Since the bottle of liquid plant food, William purchased contains 0.5 liters or 500 milliliters of liquid plant food, we can see that one bottle is enough for 12 weeks since 480 milliliters is less than the total amount of liquid plant food in the bottle.

In fact, we can calculate how many weeks one bottle of liquid plant food will last William by dividing the total amount of liquid plant food in the bottle by the amount used per week:

Time to use up the liquid plant food = (Total amount of liquid plant food) / (Amount used per week) = 500 ml / 40 ml/week ≈ 12.5 weeks

So, we can say that one bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

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The correct question should be:

William bought a 0.5 -liter bottle of liquid plant food. He uses 40 milliliters each week? How much plant food does William need for 12 weeks? Is one bottle enough for 12 weeks?

The volume of the solid obtained by rotating the region bounded by y = x^2 and y = 6 about the line x = -3 is approximately 481.39 cubic units.


To find the volume of the solid, we can use the method of cylindrical shells. The region bounded by y = x^2 and y = 6 in the first quadrant is a parabolic shape above the x-axis.
To set up the integral for the volume, we consider an infinitesimally small vertical strip of thickness Δx at a distance x from the line x = -3. The height of the strip is given by the difference between the two curves: h = 6 – x^2. The circumference of the cylindrical shell is given by the formula 2πr, where r is the distance between x and the line x = -3, which is r = x + 3.

The volume of the infinitesimal shell is then given by dV = 2π(x + 3)(6 – x^2)Δx. Integrating this expression from x = 0 to x = 3, we obtain the volume V = ∫[0,3] 2π(x + 3)(6 – x^2)dx. Evaluating this integral, we find V ≈ 481.39 cubic units.
In summary, the volume of the solid obtained by rotating the region bounded by y = x^2 and y = 6 about the line x = -3 is approximately 481.39 cubic units.

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To evaluate the definite integral ∫[0,6] (49 - x^2) dx, we can apply the rules of integration. The antiderivative of 49 - x^2 with respect to x is (49x - (x^3)/3).

Using the Fundamental Theorem of Calculus, we can evaluate the definite integral by substituting the upper and lower limits of integration into the antiderivative:

∫[0,6] (49 - x^2) dx = [49x - (x^3)/3] evaluated from x = 0 to x = 6

Substituting the limits of integration:

[49(6) - (6^3)/3] - [49(0) - (0^3)/3]

= [294 - 72] - [0 - 0]

= 222

Therefore, the value of the definite integral ∫[0,6] (49 - x^2) dx is 222.

To verify this result using a graphing utility, one can graph the function f(x) = 49 - x^2 and use the integral feature to calculate the definite integral from 0 to 6. The result should match the evaluated value of 222.

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The general solution of the differential equation y''(x) + y(x) = sec(x) tan(x) is y(x) = c₁cos(x) + c₂sin(x) + (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x); here c₁ and c₂ are constants.

To solve the differential equation y''(x) + y(x) = sec(x) tan(x) using variation of parameters, we first need to find the solutions to the homogeneous equation y''(x) + y(x) = 0.

The auxiliary equation for the homogeneous equation is r² + 1 = 0, which has complex roots r = ±i.

The corresponding solutions to the homogeneous equation are y₁(x) = cos(x) and y₂(x) = sin(x).

Next, we need to find the particular solution using the method of variation of parameters. Let's assume the particular solution has the form y_p(x) = u(x)cos(x) + v(x)sin(x).

Now, we need to find u(x) and v(x) by substituting this form into the original differential equation and solving for u'(x) and v'(x).

Differentiating y_p(x), we get y_p'(x) = u'(x)cos(x) - u(x)sin(x) + v'(x)sin(x) + v(x)cos(x).

Taking the second derivative, y_p''(x) = -u(x)cos(x) - u'(x)sin(x) + v(x)sin(x) + v'(x)cos(x).

Substituting these derivatives into the original differential equation, we have:

(-u(x)cos(x) - u'(x)sin(x) + v(x)sin(x) + v'(x)cos(x)) + (u(x)cos(x) + v(x)sin(x)) = sec(x)tan(x).

Simplifying, we get:

u'(x)sin(x) + v'(x)cos(x) = sec(x)tan(x).

To find u'(x) and v'(x), we solve the following system of equations:

u'(x)sin(x) + v'(x)cos(x) = sec(x)tan(x),

u(x)cos(x) + v(x)sin(x) = 0.

We can solve this system using various methods such as substitution or elimination.

Solving the system, we find:

u'(x) = sin(x)sec(x),

v'(x) = -cos(x)sec(x).

Integrating these expressions, we obtain:

u(x) = -ln|sec(x) + tan(x)| + C₁,

v(x) = -ln|sec(x) + tan(x)| + C₂.

Finally, the particular solution is given by:

y_p(x) = (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x).

The general solution to the differential equation is the sum of the homogeneous and particular solutions:

y(x) = c₁cos(x) + c₂sin(x) + (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x).

Here, c₁ and c₂ are constants.

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Given the volume of the cone to be 60π, the radius, height, and diameter of the cone would be:

Volume of a Cone = 1/3 × πr²h

Given that the volume of the cone is: 60π

Thus:

Thus:

Volume = 1/3 × π × 6² × 5

Volume = 1/3 × π × 6² × 5 = 60π

Therefore, given the volume of the cone to be 60π, the radius, height, and diameter of the cone would be:

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Answer:

Here is the answer as a picture.

Answer:

-4t-11

Step-by-step explanation:

rearrange the numbers

2t-6t-9+2

Add negative 2

2t-6t-11

2-6

-4t-11

Answer: Answer:

B. 7 feet

Step-by-step explanation:

Given:

NS = (x + 10) ft

SR = (x + 3) ft

Required:

RS

SOLUTION:

Based in the centroid theorem, the centroid, S will divide the median, line segment NR, into NS and SR, such that NS : SR = 2 : 1.

Therefore:

NS = 2(SR)

x + 10 = 2(x + 3) (substitution)

Solve for x

x + 10 = 2x + 6

Collect like terms

x - 2x = -10 + 6

-x = -4

divide both sides by -1

x = 4

SR = (x + 3) ft (SR is same as RS)

Plug in the value of x

SR = (4 + 3) ft

SR = RS = 7 ft

Answer:

100π

Step-by-step explanation:

V = (4/3)πr^3

(500/3)π = (4/3)πr^3

r^3 = 125

r = 5

Surface area of sphere = 4πr^2

= 4π(5^2) = 100π

Answer:

1/24

Step-by-step explanation:

We want to find the probability of picking a watermelon AND picking a green apple right after. These events are completely independent of each other as the watermelon is put back, and picking a watermelon/green apple does not affect the chances of getting the other the next/previous time. The formula for this is P(A) * P(B), with P(A) being the probability of event A happening and P(B) being the probability of event B happening. It does not matter which event is which.

Let's say picking a watermelon is event A and picking a green apple is event B.  There are 6 watermelons and 6+5+1 = 12 jolly ranchers, so there is a 6/12 = 1/2 chance of picking a watermelon. There is 1 green apple and still 12 jolly ranchers, so there is a 1/12 chance of picking a green apple jolly rancher.

Multiplying these two, we get (1/2) * (1/12) = 1/24

Answer: 24a+9b

Step-by-step explanation: I distributed(multiplied) the 6 and -3 to the terms in the parenthesis which added up to 36a+30b-12a-21b. Then I added the terms together which equals 24a+9b. Hope this helps!

Answer

\( \frac{ 6 {y}^{4} {w}^{2} }{{x}} \)

Step-by-step Explanation

\( \huge \frac{12 {x}^{3} {y}^{6} {w}^{5} }{ 2{x}^{4} {y}^{2} {w}^{3} } \\ \\ \huge= \frac{6 {x}^{3} {y}^{6} {w}^{5} }{{x}^{4} {y}^{2} {w}^{3} } \\ \\ \huge = 6 {x}^{3 - 4} {y}^{6 - 2} {w}^{5 - 3} \\ \\ \huge= 6 {x}^{ - 1} {y}^{4} {w}^{2} \\ \\ \huge = \frac{ 6 {y}^{4} {w}^{2} }{{x}^{1}} \\ \\ \huge = \frac{ 6 {y}^{4} {w}^{2} }{{x}} \)

Answer:

\(\frac{6w^2 y^4}{x}\)

Step-by-step explanation:

\(\frac{12x^3 y^6 w^5}{2x^4 y^2 w^3}\)

\(= \frac{12w^5 x^3 y^6}{2w^3 x^4 y^2}\)

\(= \frac{12w^2 y^4}{2x}\)

\(= \frac{6w^2 y^4}{x}\)

Hope this helped you!

The expression \((3xy^{-3})^{-2}\) without negative exponents is  \(\frac{y^6}{9x^2}\).

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents are 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.

Given, An expression in exponents \((3xy^{-3})^{-2}\).

Now, Changing the place of exponents from the numerator to the denominator or vice versa changes its sign.

Therefore, \((3xy^{-3})^{-2} = 3^{-2}x^{-2}y^{6}\).

\(3^{-2}x^{-2}y^{6} = \frac{y^6}{3^2x^2}\).

\(\frac{y^6}{3^2x^2} = \frac{y^6}{9x^2}\).

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Answer:

-10

Step-by-step explanation:

We can figure out that the number line is by four.

How?

There is one line between 10 and 2. Sooo:

10 - 2 = 8

8 / 2 = 4

If we check it (10 - 4 - 4 = 2) it checks out!

Using this information we can figure out what the blue dot is.

2 (given) - 4 (incriments of number line) - 4 - 4 = - 10

There is our answer, -10!

Answer:

R=6\8-y

Step-by-step explanation:

6+8=orange

to get red you will have to subtract

so = R = 6\8-y

Answer:

6

Step-by-step explanation:

4 marbles we have to take out (without looking) to be sure that we have at least two marbles of the same color.

There are 4 black, 4 red, and 4 white marbles in a box.

So, in order to have atleast two marbles of the same color we must take out atleast four marbles.

That is 1 black, 1 red, and 1 white of each color and the fourth one may be of any color. So we have atleast two marbles of the same color.

Therefore we have to rake out atleast 4 marbles in order to have at least  two marbles of the same color.

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Answer:

4 4/7

Step-by-step explanation:

32/7 already reduced (simplified) Improper fraction, rewrite it as a mixed number: 32 ÷ 7 = 4 and remainder = 4 => 32/7 = (4 × 7 + 4)/7 = 4 + 4/7 = 4 4/7

The best interpretation of the statement "the chances of winning a prize are 1 out of 10" is that if many people buy a ticket, about 1 in 10 will win.

This statement means that for every 10 tickets sold, on average, only one ticket will win a prize. It does not guarantee that you will win a prize if you buy a single ticket or even several tickets. The probability of winning a prize remains the same for every ticket purchased. It is important to note that winning a prize in a lottery is largely a matter of luck, and the odds are always against the player. While buying more tickets may increase your chances of winning, it does not guarantee a win.

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Answer:

the greatest common factor of 10 and 70 is 10

Answer:

5

Step-by-step explanation:

have a good day

Answer:10pi cm^2

Step-by-step explanation:

The first step in solving an equation with variables on both sides is to simplify each side by combining like terms and applying any necessary operations (e.g., addition, subtraction).

In order to solve an equation with variables on both sides, it is important to follow a systematic approach. The first step involves simplifying each side of the equation by combining like terms and applying any necessary operations such as addition or subtraction.

The second step is to eliminate the variable term on one side of the equation. This is done by performing inverse operations to isolate the variable term. For example, if there is a variable term added to or subtracted from a constant term on one side, we can perform the inverse operation (subtraction or addition) to remove the variable term.

After eliminating the variable term, the third step is to simplify the resulting equation further if needed. This may involve combining like terms or performing additional operations.

The fourth step is to isolate the variable by performing inverse operations on the remaining terms to move them to the opposite side of the equation. This helps in isolating the variable term on one side and the constant term on the other side.

Lastly, when solving any equation, it is crucial to maintain equality. This is achieved by performing the same operations on both sides of the equation. Whatever operation is performed on one side must also be performed on the other side to preserve equality and find the correct solution.

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Answer:

I haven't learn this yet but maybe try asking desmos that app helps me a lot!

Answer:

The greatest common factor of 64 and 72 is 8.

Answer:

Step-by-step explanation:

Only the first table represents a linear function. In order to be in linear function, the graph of the function must be a straight line.

At year 2, you will have approximately $25,915.13 in your bank account, assuming an initial investment with a 5% interest rate compounded annually. The correct answer is (a).


To find out how much money you will have in your bank account at year 2, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (in this case, $30,000)
P = Principal amount (initial investment)
R = Annual interest rate (5% or 0.05)
N = Number of times interest is compounded per year (assumed to be once per year)
T = Number of years (in this case, 3)
Let’s solve for P, the principal amount at year 0:
30,000 = P(1 + 0.05/1)^(1*3)
30,000 = P(1.05)^3
Dividing both sides of the equation by (1.05)^3:
P = 30,000 / (1.05)^3
P ≈ 25,915.13
Therefore, at year 2, you will have approximately $25,915.13 in your bank account.
The correct answer is (a) $25,915.13.

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To find the area of a quadrilateral with given coordinates, you can use the Shoelace Formula.

The Shoelace Formula, also known as Gauss's area formula, provides a method to calculate the area of any polygon given its coordinates. Here's how it works for a quadrilateral:

Let's say you have the coordinates of the four vertices of the quadrilateral: (x1, y1), (x2, y2), (x3, y3), and (x4, y4).

1. Write down the coordinates in a clockwise order:

  (x1, y1), (x2, y2), (x3, y3), (x4, y4), (x1, y1).

2. Multiply each x-coordinate by the y-coordinate of the next vertex.

  For example, for the first vertex (x1, y1), multiply x1 by y2, and for the second vertex (x2, y2), multiply x2 by y3, and so on.

3. Multiply each y-coordinate by the x-coordinate of the next vertex.

  For example, for the first vertex (x1, y1), multiply y1 by x2, and for the second vertex (x2, y2), multiply y2 by x3, and so on.

4. Add up all the results from Steps 2 and 3.

5. Take the absolute value of the sum calculated in Step 4 and divide it by 2.

By following the steps of the Shoelace Formula, you can calculate the area of a quadrilateral given its coordinates. Remember to ensure that the coordinates are listed in a clockwise or counterclockwise order to obtain the correct result. This method can be applied to any quadrilateral shape and provides an efficient way to find its area without requiring complex calculations or trigonometric functions.

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Answer:

b gang

Step-by-step explanation: