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Based on her recipe, Elena knows that 5 servings of granola have 1,750 calories.

1. If she eats 2 servings of granola, how many calories does she eat?
2. If she wants to eat 175 calories of granola, how many servings should she eat?
3. Write an equation to represent the relationship between the number of calories and the number of servings of granola.

The vectors \(v1\), \(v2, v3, v4,\) and \(v5\) are linearly independent. The basis for the area covered by \(v1, v2, v3, v4,\) and \(v5\).

We can construct a matrix with the vectors as its columns and rows reduce it using Gaussian elimination to find out which of the five vectors is linearly independent. The vectors are linearly independent if the row-reduced matrix has a pivot in each row. If not, some of the vectors rely linearly.

The five-vectors will be indicated as follows:

\(v1 = [1 2 3 4]\)

\(v2 = [0 1 2 3]\)

\(v3 = [1 1 1 1]\)

\(v4 = [1 0 -1 0]\)

\(v5 = [0 1 0 -1]\)

They can be set up as a matrix's columns:

\(A = [1 0 1 1 0; 2 1 1 0 1; 3 2 1 -1 0; 4 3 1 0 -1]\)

To get this matrix's reduced row echelon form, we can row reduce it as follows:

\(R = [1 0 0 -1/2 1/2; 0 1 0 1/2 -1/2; 0 0 1 -1 2; 0 0 0 0 0]\)

The centre point in the row-reduced matrix indicates that the vectors \(v1\), \(v2, v3, v4,\) and \(v5\) are linearly independent.

We can utilize the vectors themselves since they constitute a set that is linearly independent to identify a basis for the space that these vectors cover. The basis for the area covered by \(v1, v2, v3, v4,\) and \(v5\) is therefore only \(v1, v2, v3, v4\), and \(v5.\)

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Answer:

Step-by-step explanation:

Discussion

Think of what it would be like in your own household. If your mom has been away and the food is starting to spoil, you can't be picky. If you are not picky, you will get by until someone goes shopping.

That's the way its going to work in the ecosystem. I would pick B and hope that it the bad times won't last too long.

The anticipated total number of heads produced by this method is 1/2n=N when fair coin is tossed n times, and the results are tallied by counting the heads.

Given that,

A fair coin is tossed n times, and the results are tallied by counting the heads. The coin is then thrown a further n times.

We have to calculate the anticipated total number of heads produced by this method.

We know that,

Either head or tail will appear when a coin is tossed.

The sample space of a random experiment is the collection of all feasible results. Therefore, if your random experiment involves flipping a coin, the sample space is "Head, Tail," or more tersely, "H, T."

So,

1/2n=N

Therefore, the anticipated total number of heads produced by this method is 1/2n=N when fair coin is tossed n times, and the results are tallied by counting the heads.

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Perpendicularity law

A family of many generations but with only a few members of each generation is called a beanpole family pattern

A Beanpole family is a multi-generational family that is long and thin with few aunts, uncles and grandparents. This is a result of extended life expectancy and fewer children being born.

A generation refers to all of the people born and living at about the same time, regarded collectively.

Hence, A family of many generations but with only a few members of each generation is called a beanpole family pattern

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To calculate the probabilities, we need to use the concept of binomial probability.

For a fair coin being tossed 5 times:

(a) Probability of getting five heads:

The probability of getting a head in a single toss is 1/2.

Since each toss is independent, we multiply the probabilities together.

P(Head) = 1/2

P(Tails) = 1/2

P(Five Heads) = P(Head) * P(Head) * P(Head) * P(Head) * P(Head) = \((1/2)^5\) = 1/32 ≈ 0.03125

So, the probability of obtaining five heads is approximately 0.03125 or 3.125%.

(b) Probability of getting four heads:

There are five possible positions for the four heads.

P(Four Heads) = (5C4) * P(Head) * P(Head) * P(Head) * P(Head) * P(Tails) = 5 * \((1/2)^4\) * (1/2) = 5/32 ≈ 0.15625

So, the probability of obtaining four heads is approximately 0.15625 or 15.625%.

(c) Probability of getting one head:

There are five possible positions for the one head.

P(One Head) = (5C1) * P(Head) * P(Tails) * P(Tails) * P(Tails) * P(Tails) = 5 * (1/2) * \((1/2)^4\) = 5/32 ≈ 0.15625

So, the probability of obtaining one head is approximately 0.15625 or 15.625%.

For a fair die being thrown eight times:

(a) Probability of a 6 occurring six times:

The probability of rolling a 6 on a fair die is 1/6.

Since each roll is independent, we multiply the probabilities together.

P(6) = 1/6

P(Not 6) = 1 - P(6) = 5/6

P(Six 6s) = P(6) * P(6) * P(6) * P(6) * P(6) * P(6) * P(Not 6) * P(Not 6) = \((1/6)^6 * (5/6)^2\) ≈ 0.000021433

So, the probability of rolling a 6 six times is approximately 0.000021433 or 0.0021433%.

(b) Probability of a 6 never happening:

P(No 6) = P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) = \((5/6)^8\) ≈ 0.23256

So, the probability of not rolling a 6 at all is approximately 0.23256 or 23.256%.

(c) Probability of an odd number of 6s:

To have an odd number of 6s, we can either have 1, 3, 5, or 7 6s.

P(Odd 6s) = P(One 6) + P(Three 6s) + P(Five 6s) + P(Seven 6s)

\(P(One 6) = (8C1) * P(6) * P(Not 6)^7 = 8 * (1/6) * (5/6)^7P(Three 6s) = (8C3) * P(6)^3 * P(Not 6)^5 = 56 * (1/6)^3 * (5/6)^5P(Five 6s) = (8C5) * P(6)^5 * P(Not 6)^3 = 56 * (1/6)^5 * (5/6)^3P(Seven 6s) = (8C7) * P(6)^7 * P(Not 6) = 8 * (1/6)^7 * (5/6)\)

P(Odd 6s) = P(One 6) + P(Three 6s) + P(Five 6s) + P(Seven 6s)

Calculate each term and sum them up to find the final probability.

After performing the calculations, we find that P(Odd 6s) is approximately 0.28806 or 28.806%.

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The factorization of 2xy + 3y2 - 9yz is y( 2x +3y +9z)

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

For example 5y + 25z can be factored by bringing out the common factors

this means it will be 5( y + 5z).

Similarly l, factoring 2xy + 3y² - 9yz we bring out the common factor which is y.

= y( 2x +3y +9z)

Therefore, the factorization of 2xy + 3y2 - 9yz is y( 2x +3y +9z).

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Let x = the number of 5¢ fare increases

Let y = money the company gets

Equation: y = (360 - 20x) (0.50 + 0.05x)

Solve for x when y = 196

196 = 180 + 18x - 10x - x^2

x^2 - 8x + 16 = 0

Factor to solve for x

(x - 4)^2 = 0

x = 4

Remember what x means

Total fare = 0.50 + 0.05x = 0.50 + 0.20 = 0.70

Total fare = 70¢

Describe four common ways in which individuals respond to perceived inequity are -

Equity, also known as shareholders' equity (or shareholders' equity for private companies), is the sum of money which would be handed back to a company ’s creditors if each of its assets have been liquidated and all of its debt was paid off in the event of liquidation.

Some key features regarding the equity are-

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The smallest integer 160 needs to be multiplied by to give a square number is 15.

A perfect square is a number system that can be expressed as the

square of a given number from the same system.

The smallest integer 160 needs to be multiplied by to give a square number;

60 x 15= 900

Hence,

The square root of 900= 30

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The conclusion about the null hypothesis is that we fail to reject it. We cannot conclude that the proportion is greater than 4/5 based on the available data and the chosen level of significance.

To find the P-value, we need to look up the probability of getting a test statistic as extreme or more extreme than the observed value of 1.52 under the null hypothesis.

Since the alternative hypothesis is one-sided (p > 4/5), we will use the upper tail of the standard normal distribution.

Using a standard normal table or a calculator, we can find that the probability of getting a z-score of 1.52 or higher is approximately 0.0643. This is the P-value.

Now we compare the P-value to the significance level of 0.05. Since the P-value is greater than the significance level, we fail to reject the null hypothesis.

In other words, we do not have enough evidence to conclude that the true population proportion is greater than 4/5 at the 0.05 level of significance.

Therefore, the conclusion about the null hypothesis is that we fail to reject it. We cannot conclude that the proportion is greater than 4/5 based on the available data and the chosen level of significance.

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The unit rate for 2010 dollars in 6 months

Unit rate

2010/ 6 = 335 dollars/ month

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The answer to the expressions are

-5 - 9x - 8x + 2 = -3 -17x

6k - k = 5k

4 - 5(-8 + 2w) = 44 - 10w

8n + 2n - 3 = 10n -3

-5(7p - 3) - 2 = -35p + 13

To solve the question, we will simplify all of the expressions.

First, collect like terms

-5 + 2 - 9x - 8x  = -3 -17x

∴ -5 - 9x - 8x + 2 = -3 -17x

6k - k = 5k

First, clear the brackets

4 - 5(-8 + 2w) = 4 + 40 -10w  

= 44 - 10w

∴ 4 - 5(-8 + 2w) = 44 - 10w

8n + 2n - 3 = 10n -3

∴ 8n + 2n - 3 = 10n -3

First, clear the bracket

-5(7p - 3) - 2 = -35p + 15 -2

= -35p + 13

∴ -5(7p - 3) - 2 = -35p + 13

Hence, the answer to the expressions are

-5 - 9x - 8x + 2 = -3 -17x

6k - k = 5k

4 - 5(-8 + 2w) = 44 - 10w

8n + 2n - 3 = 10n -3

-5(7p - 3) - 2 = -35p + 13

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To start, we need to find g((π/2)). We know that g(x) = cos x, so g((π/2)) = cos(π/2) = 0.

Now we can use this value of g((π/2)) to find f(g((π/2))). We know that f(x) = sin x, so f(g((π/2))) = sin(0) = 0.

Therefore, we have shown that f(g((π/2))) = 0.
To show that f(g(π/2)) = 0, we will first find the value of g(π/2) and then plug it into the function f(x).

1. Find g(π/2):
Since g(x) = cos x, we have g(π/2) = cos(π/2).

The cosine of π/2 (90 degrees) is 0. Therefore, g(π/2) = 0.

2. Find f(g(π/2)):
Now, we need to find the value of f(x) at the point g(π/2), which is f(0).

Since f(x) = sin x, we have f(0) = sin(0).

The sine of 0 is 0. Therefore, f(0) = 0.

Thus, f(g(π/2)) = f(0) = 0.

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Answer:

33.4%= 33.4 ÷100×9000= 3006.0

Given the general n th term of the sequence,

For n = 1,

Therefore, the first statement is true.

Now for n = 2,

Therefore, the first two terms of the sequence is -8 and -5.

So, the common difference is,

Therefore, the common difference is 3.

So, the second statement is true.

Now fifth term is for n = 5.

Therefore,

Therefore the fifth term is 4 but not 7.

Hence, the third statement is false.

(a) The proposition can be expressed as ∀x(Cliff(x) → ∃y(Adjacent(x, y) ∧ NonNull(y, r3))).

(b) The proposition can be expressed as ∀x(NonNull(x, r2) → (∃y(Adjacent(x, y) ∧ Hill(y)) ∧ ¬∃z(Adjacent(x, z) ∧ Hill(z) ∧ ¬(z = y)))).

(c) The proposition can be expressed as ∀x(Resource(x, r1) → (Corner(x) ∧ ¬∃y(Resource(y, r1) ∧ ¬(x = y) ∧ Adjacent(x, y)))).

(a) In propositional logic, we use quantifiers (∀ for "for every" and ∃ for "there exists") to express the properties. The proposition (a) states that for every location that is a cliff (Cliff(x)), there exists an adjacent location (Adjacent(x, y)) to it that contains some non-null quantity of resource r3 (NonNull(y, r3)).

(b) The proposition (b) states that for every location that contains some non-null quantity of resource r2 (NonNull(x, r2)), there is exactly one adjacent location (y) that is a hill (Hill(y)), and there are no other adjacent locations (z) that are hills (¬(z = y)).

(c) The proposition (c) states that resource r1 (Resource(x, r1)) can only appear in the corners of the grid (Corner(x)), and there are no other adjacent locations (y) that contain resource r1 (Resource(y, r1)).

By using logical connectives (∧ for "and," ∨ for "or," ¬ for "not"), quantifiers (∀ for "for every," ∃ for "there exists"), and predicate symbols (Cliff, NonNull, Resource, Hill, Corner), we can express these properties in propositional logic to represent the given statements accurately.

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Answer:

corresponding angles, alternate exterior angles

Step-by-step explanation:

when you have to parallel lines cut be a transversal, you get different pairs of angles that are either equal or supplementary (add to 180).

For example, corresponding angles are congruent, and alternate exterior angles are congruent.

Answer:

-3.375

Step-by-step explanation:

the point of a geometric sequence is that every new term is created by multiplying the previous term by a constant factor that is the same across the whole sequence.

that factor is called the common ratio.

so, 32 was multiplied by the common ratio, and we get -108 as result.

32 × cr = -108

cr = -108/32 = -27/8 = -3.375 = -3 3/8

The

tangent

of the angle in the right triangle is equal to five-fourths, confirming that the angle is approximately 51 degrees. Therefore, the correct answer is option A: 51º.

To find the angle that has a tangent of five-fourths, we can use the inverse tangent function (

arctan

) on a calculator. The inverse tangent function gives us the angle whose tangent is a given value.

Using a calculator, we can input the value 5/4 or 1.25 and find the corresponding angle:

arctan(5/4) ≈ 51.34

degrees

Rounding to the nearest degree, the angle that has a tangent of five-fourths is approximately 51 degrees.

To verify this result using a

right triangle

, we can construct a right triangle where the length of the side opposite the angle is 5 units and the length of the side adjacent to the angle is 4 units. We can then calculate the tangent of the angle and check if it is indeed equal to five-fourths.

Let's label the angle as θ. Using the given side lengths, we have:

Opposite side = 5

Adjacent side = 4

Tangent(θ) = Opposite side / Adjacent side = 5/4 = 1.25

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Answer:

13/12

Step-by-step explanation:

make into inproper fraction then cross multiply then reduce to lowest terms. hope this helps

Answer:

Length of each stump is 2.167 feet

Step-by-step explanation:

8 2/3 divided by 4 is 2.166667

2.166667 simplified is 2.167

The exact value of cos(θ) is: cos(θ) =\frac{4}{5}

To find the exact value of cos(θ) if sin(θ) = \(\frac{3}{5}\) and 0 < θ < 90, we can use the Pythagorean identity: sin²(θ) + cos²(θ) = 1.

Step 1: Plug in the given value of sin(θ).
\((\frac{3}{5}) ^{2}\)+ cos²(θ) = 1

Step 2: Square the value of sin(θ).
\((\frac{9}{25})\)+ cos²(θ) = 1

Step 3: Subtract the squared sin(θ) value from 1.
cos²(θ) = 1 - \((\frac{9}{25})\)

Step 4: Simplify the expression.
cos²(θ) = \((\frac{25}{25})\) - \((\frac{9}{25})\)
cos²(θ) = 16/25

Step 5: Take the square root of both sides to find cos(Θ).
cos(θ) = \(\sqrt{\frac{16}{25} }\)

Since 0 < θ < 90, the cosine value will be positive. So, the exact value of cos(θ) is:

cos(θ) =\(\frac{4}{5}\)

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Answer:

It should be 2:7 because 1/7 + 1/7=2/7

Step-by-step explanation:

The probability that no two teams win the same number of games is 742.

The number of powers of 2 in 40! is

= (40/2) + (40/4) + (40/8) + (40/16) + (40/32)

= 20 + 10 + 5 + 2 + 1

= 38.

780-38 = 742.

Hence, the probability that no two teams win the same number of games is 742.

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Answer:

6.09

Step-by-step explanation:

in ADB

\(a ^{2} + b^{2} = c ^{2} \)

to get hypotenuse=8.96

this is height of ABC so use tan

\( tan(55.8)= 8.96 \x\)

x=6.09

Answer:

D

Step-by-step explanation:

To find x, we first to to find the line between A&B.

Use the pythagoram theorem to do this A^2+B^2=C^2

4.9^2+7.5^2=C^2

80.26=C^2

square root each side

Side AtoB=8.958

We now know the side length of the opposite and adjacent for the angle C. So according to SohCahToa we need to use Tangent.

So Tan(55.8)=(8.958/x)

We you solve for x, the answer is 6.088