Veronica takes of an hour to write of a page of calligraphy.
How long will it take Veronica to write one page of calligraphy?

Answer: look at the picture

Step-by-step explanation: Hope this help

Answer:

Step-by-step explanation:

-427 - 34 i

Therefore, S is linearly dependent.

The given set S = {(3,5), (1,0), (0,1)} is not a basis for R² because S is linearly dependent. A set of vectors in a vector space is considered linearly dependent if at least one vector in the set can be expressed as a linear combination of the other vectors in the set. If a set of vectors in a vector space is linearly dependent, then it cannot be a basis for the vector space. Therefore, option (a) is the correct answer.

Specifically, in the given set S = {(3,5), (1,0), (0,1)},

we have:(1) (3,5) = 3(1,0) + 5(0,1)(2) 1(1,0) = (1,0)(3) 0(0,1) = (0,0)

From equation (1), we see that (3,5) is a linear combination of the other two vectors in the set.

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The answer is , that S is not a basis for R2 because a basis must be a linearly independent set that spans R2.

The set S={(3,5), (1,0), (0,1)} is not a basis for R2 because it is linearly dependent.

To determine if a set is linearly dependent or not, you can check if one of its vectors is a linear combination of the others.

This means that one of the vectors can be expressed as a combination of scalars multiplied by the remaining vectors.

In the case of S, we can see that:

(3,5) = 3(1,0) + 5(0,1)

Therefore, the vector (3,5) can be expressed as a linear combination of the other two vectors in S.

This means that S is linearly dependent.

Therefore, we can conclude that S is not a basis for R2 because a basis must be a linearly independent set that spans R2.

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Answer:

x = 5

y = 5

Step-by-step explanation:

In this question you need to solve one equation in order to plug the value into the second one and solve it as well. Lets start with the top one...

2x - x = 5

1x = 5

x = 5

Now we plug that value of x into the second equation

4x - 2y = 10

4(5) - 2y = 10

20 - 2y = 10

-2y = -10

y = 5

Finally, we can see that both x and y have a value of 5.

Answer:

?=45 degrees

Step-by-step explanation:

All of the angles are congruent.

So the equation is:45+90+?=180

?=45 degrees

Answer: 45 degrees

Step-by-step explanation:

Answer:

The solution to the system of equations is

x = -2

y = 5

Explanation:

Given the pair of equations:

3x + y = -1 ............................................................................(1)

2x - 2y = -14 .......................................................................(2)

To solve the system by elimination, first of all

Divide equation (2) by 2, to simply have:

x - y = -7 ...............................................................................(3)

To eliminate y

Add equation (1) and (3) together

3x + x + y - y = -1 - 7

4x = -8

Divide both sides by 4

x = -8/4 = -2

To eliminate x

Multiply equation (3) by 3

3x - 3y = -21 .........................................................................(4)

Subtract equation (4) from equation (1)

3x - 3x + y - (-3y) = -1 - (-21)

y + 3y = -1 + 21

4y = 20

Divide both sides by 4

y = 20/4 = 5

Therefore, x = -2, and y = 5

Answer:

5 ham sandwiches

Step-by-step explanation:

To find the number of ham sandwiches sold, we should find the pair of numbers that have a difference of 6 and add to 16.

While this method isn't always very efficient, it worked pretty well for this case!

Therefore, the answer is 5 ham sandwiches.

Answer:

5

Step-by-step explanation:

11 and 5 have a 6 number gap between them 5 plus 11 gets you 16

Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours

Answer:

x^2+8x +16 >> (x+4)^2

x^3-64 >> (x-4)(x^2+4x+16)

x^2-16 >> (x-4)(x+4)

Step-by-step explanation:

Each polynomial is matched to its factored form. These are the correct answers. I did this on EDGE!

Polynomial is an expression that consists of indeterminates(variable) and coefficients.

Polynomial is an expression that consists of indeterminates(variable) and coefficients, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

To know which polynomial to match, solve the factors.

A.) (x-4)(x²+4x+16)

\((x-4)(x^2+4x+16)\\\\=x(x^2+4x+16)-4(x^2+4x+16)\\\\= x^3 + 4x^2 + 16x - 4x^2-16x-64\\\\=x^3 -64\)

Hence, (x-4)(x²+4x+16) will match x³-64.

B.) (x+4)²

\((x+4)^2\\\\= x^2+8x+16\\\)

Hence, (x+4)² will match x²+8x+16.

C.) (x-4)(x+4)

\((x-4)(x+4)\\\\ = x^2-16\)

Hence, (x-4)(x+4) will match x²-16.

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\( \sqrt{625} \)

\( \sqrt{25 \times 25} \\ \\ = 25\)

Hope This Helps You

Answer:

\((2, 4)\rightarrow\text{First system}\)

\((4, -2)\rightarrow\text{Second system}\)

Step-by-step explanation:

First system:

We can substitute 2x for y:

\(6x-y=8\\6x-2x=8\\4x=8\)

Divide both sides by 4

\(x=2\)

Substitute 2 for x to solve for y:

\(y=2x=2(2)=4\)

\((x, y)=(2, 4)\)

Second system:

We can isolate x in the second equation by subtracting 4y from both sides:

\(x=-4-4y\)

Now, substitute this value for x in the first equation:

\(3(-4-4y)+5y=2\\\)

Distribute the 3 to each term in the parentheses:

\(3(-4)+3(-4y)+5y=2\\-12-12y+5y=2\\-12-7y=2\)

Add 12 to both sides:

\(-7y=14\)

Divide both sides by -7

\(y=-2\)

Now, substitute -2 for y to solve for x:

\(x=-4-4y=-4-4(-2)=-4+8=4\)

\((x, y)=(4, -2)\)

By a continuous random variable with PDF fx(x). Define Y = X2 – 2X.a) E(Y) = 1/3 – 2/3 = -1/3

b) The PDF of Y is fy(y) = fx(1 + √(1 + y)) + fx(1 – √(1 + y)) for y >= -1.

c) When X is uniform over [0, 1], fx(x) = 1 for 0 <= x <= 1, and fx(x) = 0 otherwise. Therefore, the PDF of Y is fy(y) = 1/2(√(4 + y) – |y|)/2 for -4 <= y <= 0, and fy(y) = 0 otherwise.

a) The expected value of Y is the integral of y times the PDF of Y over all possible values of Y. Substituting Y = X2 – 2X, we get Y = (X – 1)2 – 1, so the integral becomes the integral of [(x-1)² - 1]fx(x)dx over all possible values of X.

Using integration by parts, we get E(Y) = integral from -infinity to infinity of [(x-1)² - 1]fx(x)dx = integral from -infinity to infinity of (x² - 4x + 2)fx(x)dx = integral from -infinity to infinity of x²fx(x)dx - 4 integral from -infinity to infinity of xfx(x)dx + 2 integral from -infinity to infinity of fx(x)dx.

By definition, the first integral is E(X²), the second is E(X), which is 1 by the Law of the Unconscious Statistician, and the third is 1, since fx(x) is a valid PDF. Therefore, E(Y) = E(X²) - 4E(X) + 2 = (1/3) - 4(1) + 2 = -1/3.

b) To find the PDF of Y, we use the change of variables formula, which says that if Y = g(X), then the PDF of Y is fy(y) = fx(x)/|g'(x)|, where x is any value such that g(x) = y. In this case, g(x) = x² - 2x, so g'(x) = 2x - 2.

Solving for x in terms of y, we get x = 1 ± sqrt(1 + y). Therefore, for y >= -1, we have fy(y) = fx(1 + √(1 + y))/|2√(1 + y)| + fx(1 – sqrt(1 + y))/|-2√(1 + y)| = fx(1 + √(1 + y)) + fx(1 – √(1 + y)).

c) When X is uniform over [0, 1], fx(x) = 1 for 0 <= x <= 1, and fx(x) = 0 otherwise. Therefore, for -4 <= y <= 0, we have fy(y) = fx(1 + √(1 + y)) + fx(1 – √(1 + y)) = 1/2 + 1/2 = 1. For y < -4 or y > 0, we have fy(y) = 0, since there are no values of X such that Y = y. Therefore, fy(y) = 1/2(√(4 + y) – |y|)/2 for -4 <= y <= 0, and fy(y) = 0 otherwise.

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Answer:

The slope is 3/2 and the y intercept is 4

Step-by-step explanation:

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

2y -3x=8

Add 3x to each side

2y-3x+3x= 8+3x

2y = 3x+8

Divide by 2

2y/2 = 3/2x +8/2

y = 3/2x +4

The slope is 3/2 and the y intercept is 4

Answer:

x=w/m

Step-by-step explanation:

x = w/m, this is the answer its really no explanation brainly police dont take this down you can check for yourselves.

Answer:

I think it's A( i edited)

Step-by-step explanation:

Bc at the end of the arrow on A it ends at 2.5 which fits the equation y=2.5x

Answer:

The answer is A.

Step-by-step explanation:

Betrys needs another 400 grams of diced potatoes to make her vegetable stew for 8 people.

We know that Betrys is cooking for 8 people, and we know that a recipe for 2 people needs 10 ounces.

8 people is 4 times 2 people, then for 8 people you need 4 times 10 ounces, this is 4*10 oz = 40 ounces.

Now we can apply a change of units, remember that:

1 oz = 28 grams

Then the total amount she needs is:

40 oz = 40*28 g = 1,120 g

So she needs in total 1,120 grams, and in the balance, she already has 720 grams, so the amount that she needs is given by the subtraction:

1,120 g - 720g = 400

Betrys needs another 400 grams of diced potatoes to make her vegetable stew for 8 people.

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Answer:

y 0, because the function comes close to zero but never touches it and goes infinitely in the positive direction.

Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

9514 1404 393

Answer:

  log₁₂(4)

Step-by-step explanation:

The applicable rule of logarithms (to the same base) is ...

  log(a^b) = b·log(a)

__

Then the expression simplifies as follows:

  \(3\log_{12}(2)+\dfrac{1}{3}\log_{12}(2^3)-\log_{12}(2^2)\\\\=3\log_{12}(2)+\dfrac{3}{3}\log_{12}(2)-2\log_{12}(2)=(3+1-2)\log_{12}(2)\\\\=2\log_{12}(2)=\log_{12}(2^2)=\boxed{\log_{12}(4)}\)

After you collect your data, you have several options in regards to the null hypothesis. First, you could fail to reject the null hypothesis.

The data did not provide enough evidence to support the alternative hypothesis, and you accept the null hypothesis as the most likely explanation. Second, you could reject the null hypothesis. This means that your data provided enough evidence to support the alternative hypothesis, and you reject the null hypothesis as the most likely explanation. To neither accept nor reject the null hypothesis. The less common option and occurs when your data does not provide enough evidence to reject the null hypothesis, but also does not provide enough evidence to accept it as the most likely explanation.

The null hypothesis after you collect your data include failing to reject it, rejecting it, or neither accepting nor rejecting it.

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These are the polynomial equations:

A = x^ (1/4) - ∛x + 4√x - 8x + 16

B = 3x² - 5x⁴ + 2x - 12

C = x³ - 7x² + 9x - 5x⁴ - 20

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

These are the non-polynomial equations:

E = 4/x⁴ + 3/x³ - 2/x² - 1

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

Polynomials are mathematical expressions that only use addition, subtraction, multiplication, and non-negative exponentiation of the variables, along with coefficients (constants that multiply with the variables), coefficients, and constants.

Some of the elements of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. An equation must always begin with the "=" sign and have terms on both sides.

Let the polynomial equations be represented by the following letters: A, B, C, D, E, and F.

In the equation, we can solve for other values to obtain:

Moreover, a polynomial equation is not an algebraic equation that has a negative exponent or an exponent that is fractional. Thus, negative exponent expressions are not polynomials.

A = x^ (1/4) - ∛x + 4√x - 8x + 16

This polynomial exists.

B = 3x² - 5x⁴ + 2x - 12

This polynomial exists.

C = x³ - 7x² + 9x - 5x⁴ - 20

This polynomial exists.

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

It is a polynomial.

E = 4/x⁴ + 3/x³ - 2/x² - 1

It is not a polynomial.

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

A polynomial is not what it is.

The polynomials are thus resolved.

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Answer:

D.

Step-by-step explanation:

The length of the unmarked side of the triangle is found by using Pythagoras:

x sqrt (10^2 - 6^2)

= sqrt 64

= 8.

The length of the curved part = 1/2 * pi * 10 = 5pi

Perimeter = 8 + 6 + 5pi

= 14 + 5pi

Answer:

D.  14 + 5π  inches

Step-by-step explanation:

1.  solve for the side of  a triangle using Pythagorean = \(\sqrt{(10^2 - 6^2)}\) = 8 in.

2. circumference of a half circle = πd /2  = π*10 / 2 = 5π in.

3. total perimeter = (8 + 6) + 5π = 14 + 5π

therefore, the answer is D.  14 + 5π  inches

The probability of running out of water decreases.

The given problem can be solved by using the concept of the normal distribution. Normal distribution, also called Gaussian distribution, is a probability distribution that occurs naturally in many situations. In this distribution, data values cluster around a central point, and the further away a value is from the center, the less likely it is to occur. The normal distribution has two parameters: the mean (μ) and the standard deviation (σ). The mean is the center of the distribution, and the standard deviation is a measure of how spread out the distribution is. The normal distribution is symmetric about the mean. It is a continuous distribution, meaning that it can take any value between negative infinity and positive infinity. The area under the normal curve represents the probability of a random variable taking a certain value or falling within a certain range of values. The total area under the normal curve is equal to 1.
Given:
The average person drinks 3 Liters of water when hiking the Mission Peak (with a standard deviation of 1 Liter).
You are planning a hiking trip to the Mission Peak for 10 people and will bring 35 Liters of water.
What is the probability that you will run out?
We need to find the probability that the amount of water consumed by 10 people will be greater than 35 Liters. Let X be the random variable representing the amount of water consumed by each person. X is normally distributed with mean μ = 3 Liters and standard deviation σ = 1 Liter.
Then, the total amount of water consumed by 10 people is given by the sum of 10 independent identically distributed (i.i.d.) random variables:
Y = X1 + X2 + ... + X10
where X1, X2, ..., X10 are i.i.d. random variables with the same distribution as X.
The total amount of water you bring is 35 Liters. Therefore, you will run out of water if:
Y > 35
or equivalently:
(Y - μ10) / σ10 > (35 - μ10) / σ10
where μ10 = 10μ = 30 Liters and σ10 = √(10)σ = √(10) Liters.
Thus, the probability that you will run out of water is:
P(Y > 35) = P[(Y - μ10) / σ10 > (35 - μ10) / σ10]
= P(Z > (35 - μ10) / σ10)
where Z is the standard normal variable.
Using the standard normal table, we find that:
P(Z > (35 - μ10) / σ10) = P(Z > (35 - 30) / √10)
= P(Z > 1.5811)
= 0.0564 (rounded to four decimal places)
Therefore, the probability that you will run out of water when hiking the Mission Peak with 10 people is 0.0564.
What if the hiking trip will have 20 people and the amount of water you bring also doubles to 70 Liters. What is the probability you will run out?
In this case, the number of people has doubled, so the total amount of water consumed will also double. Thus, the total amount of water consumed by 20 people is given by:
Y = X1 + X2 + ... + X20
where X1, X2, ..., X20 are i.i.d. random variables with the same distribution as X.
The total amount of water you bring is 70 Liters. Therefore, you will run out of water if:
Y > 70
or equivalently:
(Y - μ20) / σ20 > (70 - μ20) / σ20
where μ20 = 20μ = 60 Liters and σ20 = √(20)σ = 2.2361 Liters.
Thus, the probability that you will run out of water is:
P(Y > 70) = P[(Y - μ20) / σ20 > (70 - μ20) / σ20]
= P(Z > (70 - μ20) / σ20)
where Z is the standard normal variable.
Using the standard normal table, we find that:
P(Z > (70 - μ20) / σ20) = P(Z > (70 - 60) / 2.2361)
= P(Z > 4.4721)
= 0 (rounded to four decimal places)
Therefore, the probability that you will run out of water when hiking the Mission Peak with 20 people is zero.

Will the probability of running out of water increase or decrease? Why?

The probability of running out of water decreases when the number of people increases and the amount of water brought doubles. This is because the total amount of water consumed increases proportionally to the number of people, but the standard deviation of the distribution of the amount of water consumed decreases proportionally to the square root of the number of people. This means that the distribution of the total amount of water consumed becomes narrower and more concentrated around the mean as the number of people increases.

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Answer:

d ≈ 5.4

Step-by-step explanation:

calculate the distance d using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (2, 2 ) and (x₂, y₂ ) = (4, 7 )

d = \(\sqrt{(4-2)^2+(7-2)^2}\)

   = \(\sqrt{2^2+5^2}\)

  = \(\sqrt{4+25}\)

  = \(\sqrt{29}\)

 ≈ 5.4 ( to the nearest tenth )

The dimensions that maximize the enclosed area are L = 41.665 feet and W = 41.665 feet for each corral and the maximum area is 10868.09 square feet.

To find the dimensions that maximize the enclosed area, we need to use optimization techniques. Let's denote the length of each rectangular corral by L and the width by W. We can write the total enclosed area as A = 6LW.

The perimeter of each corral is given by P = 2L + 2W, and we have a total of 6 corrals, so the total length of fencing required is 6P = 12L + 12W.

We are given that we have 1,000 feet of fencing, so we can write 12L + 12W = 1000, or equivalently, L + W = 83.33 (rounded to two decimal places).

We can now use this equation to express one of the variables (say, W) in terms of the other: W = 83.33 - L.

Substituting this expression for W into the formula for the enclosed area, we get A = 6L(83.33 - L) = 499.98L - 6L^2.

To find the value of L that maximizes the area, we need to take the derivative of A with respect to L and set it equal to zero: dA/dL = 499.98 - 12L = 0. Solving for L, we get L = 41.665 (rounded to three decimal places).

Substituting this value back into the expression for W, we get W = 83.33 - L = 41.665.

The maximum area is A = 6LW = 10868.09 square feet (rounded to two decimal places).

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The best statement that describes the angle JKL is inscribed angle.

An inscribed angle in a circle is formed by two chords that have a common end point on the circle. The chord JK and LK intersect in the circle.

The angle ∠JKL is not an obtuse angle because it's less than 90 degrees.

The angle ∠JKL is not a vertical angle because it's not vertically opposite  any angle.

The angle ∠JKL is not a central angle because it was not from from the centre of the circle.

The angle is an inscribed angle because it was formed by the intersection of two chords in the circle.

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Answer:

14 is the value

Step-by-step explanation:

Answer:

a. \(8x^{2} -14x-15\)

b. \((x+3)(x+2)\)

Step-by-step explanation:

A. There are 3 methods (that I know of). The easiest method is the lattice multiplication, while the most commonly used is the FOIL method (First+Outer+Middle+Last)

For F, take the first terms of the 2 and multiply

\(4x*2x=8x^{2}\)

For O, take the outer terms and multiply

\(4x*-5=-20x\)

For I, take the inner terms and multiply

\(3*2x=6x\)

For L, take the last terms and multiply

\(3*-5=-15\)

After that, add all of them up

\(8x^{2} +(-20x)+6x+(-15)=8x^{2}-14x-15\)

B. Since the equation is in the form x^2+bx+c,

\((x+?)(x+?)\)

Now we need to find 2 numbers that will add up to 5 and multiply to 6.

Here are some of the combinations of numbers that multiply to 6

3*2

1*6

-3*-2

-1*-6

3 and 2 add up to 5 so:

\((x+3)(x+2)\)