The susceptibility of the root stocks of a variety of orange tree to a specific larva is investigated by a group of researchers. Forty orange trees are exposed to the larva and then examined by the researchers 6 months after exposure. The number of larvae per gram is recorded on each root stock. The mean and standard deviation of the logarithm of the counts are recorded to be 9.02 and 1.12, respectively.


Required:

Use the sample information to construct a 90% confidence interval on the mean of the logarithm of the larvae counts.

Answer:

a(10) = 3^9 = 19683

Step-by-step explanation:

In this sequence each new term is equal to 3 times the previous term.  Thus, 3 is the common ratio.  The first term is 1.

The general formula for the nth term of a geometric sequence i

a(n) = a(1)*r^(n -1), where r is the common ratio.

Here, a(n) = 1*3^(n - 1), and so

the 10th term is

           a(10) = 1*3^(10 - 1), or

            a(10) = 3^9 = 19683

The directional derivative of f(x, y, z) = yx + 24 at a point is not provided in the given submission. Therefore, the main answer is missing.

In the 80-word explanation, it is stated that the directional derivative of f(x, y, z) = yx + 24 at a specific point is not given. Consequently, a complete solution cannot be provided based on the information provided in the submission.

Certainly! In the given submission, there is an incomplete question or statement, as the actual point at which the directional derivative is to be evaluated is missing. The function f(x, y, z) = yx + 24 is provided, but without the specific point, it is not possible to calculate the directional derivative. The directional derivative represents the rate of change of a function in a specific direction from a given point. Without the point of evaluation, we cannot provide a complete solution or calculate the directional derivative.

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The equation y = 3/8x can be used to compare the number of marbles Molly uses, x, to the number of blue marbles, y, in each bag.

To calculate the number of blue marbles Molly uses, we can use the equation y = 3/8x.

To start, we need to identify the variables in the equation. In this case, x represents the number of marbles Molly uses and y represents the number of blue marbles.

Next, we can substitute in the given information. In this case, we know that 3 out of every 8 marbles are blue, so we can set y equal to 3 and x equal to 8.

This gives us the equation 3 = 3/8x. We can then solve for x by dividing both sides by 3/8 to get x = 8.

This tells us that for every 8 marbles Molly uses, 3 of them are blue.

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The expression that represents the area of the base of the pyramid(right pyramid) is given by: Option A: 3v/h unit²

A right rectangular pyramid is a pyramid, with four slant sides, and a rectagular base, such that all the sides are congruent and the vertex is atop of the midpoint of the base rectangle.

Suppose the base of the pyramid has length = l units, and width = w units.

Suppose that the height of the pyramid is of h units, then:

\(v = \dfrac{l \times w \times h}{3} \: \rm unit^3\) is the volume of that pyramid.

The base is a rectangle with length = L units, and width = W units, so its area is:

\(b = l \times w\: \rm unit^2\)

Thus, we can express the area of its base in terms of its volume as:

\(v = \dfrac{l \times w \times h}{3} \: \rm unit^3 = \dfrac{b\times h}{3}\\\\3v = b\times h\\\\\\b = \dfrac{3v}{h} \: \rm unit^2\)

Thus, the expression that represents the area of the base of the pyramid (right pyramid) is given by: Option A: 3v/h unit²

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Answer:

3V/h units^2

Step-by-step explanation:

The absolute minimum value of the function

\(f(x)=2x3 21x2−48x 6\)

,\(−8≤x≤2\) is -414 at

x = 6.

To find the absolute minimum value of the function

\(f(x) = 2x^3 - 21x^2 - 48x + 6\) in the interval

-8 ≤ x ≤ 2, follow these steps:

1. Determine the derivative of f(x) with respect to x to find critical points:

 \(f'(x) = 6x^2 - 42x - 48\)

2. Set f'(x) to 0 and solve for x to find critical points:

 x = 6, -2

3. Check the function's value at the critical points and the endpoints of the interval:

\(f(-8) = 2560,  f(-2) = 72,  f(6) = -414,  f(2) = -52\)

4. Compare the values and determine the absolute minimum value, Therefore,The absolute minimum value of the function is -414 at x = 6.

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Answer:

the answer should be $211.2 or $211 when rounded

Step-by-step explanation:

1. The original price is $440

2. There is a 20% discount

3. The discount is increased by 10%, making it a 30% discount

first you need to do $400 * (100% - 30% - 10%) = $280

$400 * 60% = $280

This is assuming that in this case "further marked down" means the 10% discount is added to the original 20% discount to make a 30% discount. However this could mean the price after the first markdown gets the 10% discount which would get different result:

$440 * 60% = $264

$264 * 80% = $211.2 or $211 when rounded

Answer:

um, I don't know.

Step-by-step explanation:

The nth term of a sequence is given as

f(n) = 2 + (-3)(n-1)

To find the 10th term, Let n = 10

Substitute the value of n= 10 into the expression

f(10) = 2 + (-3) (10 - 1)

f(10) = 2 + (-3) (9)

f(10) = 2 + (-27)

F(10) = 2 - 27

f(10) = -25

The answer is -25

The quotient of the given expression (x³+6x²+3x-10)÷(x+2) is x²+4x-5.

Given that, (x³+6x²+3x-10)÷(x+2).

Here,

x+2|x³+6x²+3x-10|x²+4x-5

 (-)x³(-)+2x²

_____________

         4x²+3x-10

   (-)4x²(-)+8x

_______________

               -5x-10

          (-)-5x(-1)-10

_______________.

                   0

Remainder = 0

Quotient = x²+4x-5

Therefore, the quotient of the given expression (x³+6x²+3x-10)÷(x+2) is x²+4x-5.

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If the polynomial p(x) is divided by (x-1) three times and has a remainder of 1 at the end, then -1 is a double root of p(x). This means that (x+1) is a factor of p(x) raised to the power of 2.

When a polynomial is divided by (x-1), the remainder represents the value of the polynomial at x=1. Since the remainder is 1, it implies that p(1) = 1. Dividing p(x) by (x-1) three times indicates that the polynomial has been factored by (x-1) three times. Consequently, the polynomial can be written as p(x) = (x-1)^3 * q(x) + 1, where q(x) is the quotient obtained after dividing p(x) by (x-1) three times. Since the remainder is 1, it means that when x=1, p(x) leaves a remainder of 1.

Thus, (1-1)^3 * q(1) + 1 = 1, which simplifies to q(1) = 0. This implies that (x-1) is a factor of q(x), meaning that q(x) can be written as q(x) = (x-1) * r(x), where r(x) is another polynomial.

Substituting this into the earlier expression for p(x), we get p(x) = (x-1)^3 * (x-1) * r(x) + 1. Simplifying further, p(x) = (x-1)^4 * r(x) + 1. Now, we can see that p(x) is divisible by (x+1) since (x+1) is a factor of (x-1)^4, and the remainder is 1. Therefore, -1 is a double root of p(x) because (x+1) appears twice in the factored form of p(x).

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Answer:

Angelica’s house is 7.81 miles from the gas station

Step-by-step explanation:

By pythogorean theorem, AG² = AP² + GP²

A (4,3), G(10,8), P(10,3)

Since AP lies along the x axis, the distance is calculated using the x coordinates of A and P

AP = 10 - 4 = 6

GP lies along the y axis, so the distance is calculated using the y coordinates of G and P

GP = 8 - 3 = 5

AG² = 6² + 5²

= 36 + 25

AG² = 61

AG = √61

AG = 7.81

Answer:

x = 5°

Step-by-step explanation:

Because of the given congruency,

Angle A = Angle D = 50° = 10x

10x = 50

x = 5°

HOPE IT HELPS!!!

1/2 of 32 is equal to 16.

Answer:

16

Step-by-step explanation:

Step 1:

0.5 × 32

Answer:

16

Hope This Helps :)

Answer:

55

Step-by-step explanation:

along line s, r intersects it, and you can see a right angle

90+35+angle 2 =180

you end up with 55, which is the measure

Answer:

12

Step-by-step explanation:

let x = number of 3 wheel stollers

let y = number of 4 wheel strollers

x + y = 28

y = 28 - x

3x + 4y = 100

3x + 4(28 - x) = 100

3x + 112 - 4x = 100

-x = -12

x = 12

And there you go, your answer is 12.

Answer:

B

Step-by-step explanation:

12

Answer:

This question is only if 25 points. And you have typed 50 points.

Answer is 16-4-2-1

16-4-2-1

Step-by-step explanation:

The \(x^{th}\) number in the sequence will be   \(F[x]=\dfrac{5}{2} F[x]\)

The given function is

\(F[x]=\dfrac{3}{2} \times \dfrac{5}{2}^{x-1}\)

Now at  \(x=x+1\) for the function

\(F[x+1]=\dfrac{3}{2} \times \dfrac{5}{2}^{x+1-1}\)

\(F[x+1]=\dfrac{3}{2} \times \dfrac{5}{2}^{x }\)

Now we can write

\(F[x+1]=\dfrac{3}{2} \times \dfrac{5}{2}^{x-1} \dfrac{5}{2}^1\)

Since     \(F[x]=\dfrac{3}{2} \times \dfrac{5}{2}^{x-1}\)

so

\(F[x]=\dfrac{5}{2} F[x]\)

Thus the \(x^{th}\) number in the sequence will be   \(F[x]=\dfrac{5}{2} F[x]\)

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Answer:

A

Step-by-step explanation:

Took exam and got 100

Answer:

-A+B+C-D or B+C-D-A

Step-by-step explanation:

Simplify the expression

Answer:

The answer is A) The car travels 53 mph(Miles Per Hours).

212/4 = 53

318/6 = 53

424/8 = 53

530/10 = 53

Step-by-step explanation:

Answer:

B)  rate of change is 53, your car travels 53 miles every 1 hour .

Step-by-step explanation:

Given : Table for time and distance.

To Find : The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.

Solution : We have given that Table for time and distance.

rate  of  change= .

rate  of  change= .

rate of change =  53.

rate  of  change= .

rate of change =  53

rate of change =  .

rate of change =  53.

rate of change =    .

rate of change =  53.

Therefore, B)  rate of change is 53, your car travels 53 miles every 1 hour .

Answer: A

Step-by-step explanation:

9514 1404 393

Answer:

  H  y +268 = 12(x +20)

Step-by-step explanation:

The point-slope form of the equation for a line is ...

   y -k = m(x -h) . . . . . . line with slope m through point (h, k)

The first point in the table is (x, y) = (-20, -268), so the equation with these filled in is ...

  y -(-268) = m(x -(-20))

  y +268 = m(x +20) . . . . . . matches F or H

We can see that the values of y change by a lot more than the values of x. That means the slope is a lot more than 1. This observation eliminates choice F, so we are left with ...

  H.  y +268 = 12(x +20)

Answer:

ok ummm

Step-by-step explanation:

For a given pottery of tetrahedron shape , Total possible inequivalent ways to decorate the corners with the gems are twenty-four.

A pottery is a shape of tetrahedron. Tetrahedron has four corners. We have gems of three colours.

We have to place one gem at each corner to decorate the pottery.

To find the inequivalent ways or possible combinations to decorate the pot with the gems, we will use formula of permutation, P(n,r)

P(n,r) = n!/(n-r)!

here, n = 4, r = 3

P( 4, 3) = 4!/(4-3)!

= 4!/3! = 4×3 ×2×1!/1!

= 4×3×2 = 24

So, the required possible ways are 24.

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The argument that generalizes from a sample to a whole class is stronger (other things being equal) when its premises are false, the sample is smaller, or the sample is unbiased.  When the premises of an argument are false, it weakens the argument's validity because it indicates a lack of accuracy or reliability in the information used to draw the conclusion.

Therefore, an argument that generalizes from a sample to a whole class becomes weaker if its premises are false. Additionally, the size of the sample plays a crucial role in the strength of the argument. Generally, a larger sample size provides more representative data, increasing the argument's strength. Conversely, a smaller sample size reduces the generalizability of the findings, making the argument weaker. Furthermore, an unbiased sample is essential for a stronger argument. Bias in the sample selection can lead to skewed or distorted results, undermining the validity of the generalization. An unbiased sample ensures that each member of the population has an equal chance of being included, increasing the argument's strength. Therefore, when considering all these factors, the statement "all of the above" is the correct answer as it encompasses the premises being false, a smaller sample size, and an unbiased sample, all of which contribute to a stronger argument when generalizing from a sample to a whole class.

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Answer:

27

Step-by-step explanation:

factors are numbers that divide exactly into a number , leaving no remainder.

then the only factor of 27 from the list is 27

Answer: we would need 7 bags of fertilizer to cover the area of the triangle.

Step-by-step explanation:

To find the area of a triangle, we can use Heron's formula. Heron's formula states that the area of a triangle can be found by taking the square root of the semi-perimeter multiplied by the difference of the semi-perimeter and each side length.

The semi-perimeter of the triangle is (2.1+1.8+2.7)/2 = 2.7

The area of the triangle is sqrt(2.7*(2.7-2.1)(2.7-1.8)(2.7-2.7)) = sqrt(2.70.60.9*0) = 1.35

Each bag of fertilizer covers 0.2 square miles, so we need to divide the area of the triangle by the area covered by each bag to find how many bags are needed: 1.35 / 0.2 = 6.75

Rounding up to the nearest whole number, we would need 7 bags of fertilizer to cover the area of the triangle.

The problem demonstrates inverse variation, where the cost per person (c) is inversely proportional to the number of people (p). As evidenced by the given information, when 44 people go, the cost is $30 per person, and when 20 people go, the cost increases to $66 per person.

If the cost per person, c, varies inversely with the number of people, p, on the trip, we can set up the following equation:

c = k/p

where k is the constant of variation.

We are given that when 44 people go on the trip, the cost per person is $30. We can use this information to solve for the constant of variation, k:

30 = k/44

To find k, we multiply both sides of the equation by 44:

k = 30 * 44

k = 1320

Now we can use the value of k to determine the cost per person when 20 people go on the trip:

c = k/p

c = 1320/20

c = 66

Therefore, if 20 people go on the trip, it will cost $66 per person.

The correct term for the relationship described in the problem is "indirect variation," also known as "inverse variation." In an inverse variation, as one quantity increases, the other quantity decreases, and vice versa. The equation representing this relationship is of the form y = k/x, where y and x are the two variables, and k is the constant of variation. In this case, the cost per person (c) and the number of people (p) exhibit an inverse variation relationship.

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Answer:

7.85

Step-by-step explanation:

W - 2.3 = 5.55

5.55 + 2.3 = 7.85

W = 7.85

Just do the inverse to subtraction.

Answer:

1/2

Step-by-step explanation:

When you find the sine of an angle, it is the opposite side / hypotenuse. This means that the hypotenuse of this triangle is 2 and the side opposite to 60° is √3. This means that the side adjacent to 60° is 1 (Pythagorean Theorem). When you find the cosine of an angle, it is the adjacent side / hypotenuse, which in this case will be 1 / 2. Hope this helps!

Answer:

1/2.

Step-by-step explanation:

Sine = opposite side / hypotenuse.

The side opposite 60 degrees has length√3 and the hypotenuse = 2.

By Pythagoras the side adjacent to the angle 60 = √( 2^2 - 3)

= 1 unit.

So cos 60 = adjacent / hypotenuse = 1/2.

The factor of the polynomial is (√5x - i√2)(√5x + i√2)(x + 4).

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

Given

5x³ + 20x³ + 2x +8 is a polynomial.

The factor of the polynomial.

5x³ + 20x³ + 2x +8 is a polynomial.

Take common, we get

5x²(x + 4) + 2(x + 4)

(5x² + 2) (x + 4)

[(x√5)² - (i√2)](x + 4)

(√5x - i√2)(√5x + i√2)(x + 4)

Thus, the factor of the polynomial is (√5x - i√2)(√5x + i√2)(x + 4).

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Answer:

> Option D, or (5x2 + 2) (x + 4), is the correct choice.

Step-by-step explanation:

> This is the only correct answer choice for this equation.

Answer:

343

Step-by-step explanation:

There are quarters(25¢), loonies ($1), and toonies ($2)

And total number of coins is 9

If loonies ($1), and toonies ($2) are one, then quarters(25¢) is 7

If quarters(25¢), and toonies ($2) are one, then loonies ($1)is 7

If loonies ($1), and quarters(25¢) are one, then toonies ($2) is 7

So possible number number of combination for an item that cost between $10 and $12 is

= 1^3 * 1^3 * 7^3

= 343

hope this helps, stay safe :)

The number of different combinations of coins could Teo use to pay for an item that costs between $10 and $12 is 17.

Combinations are defined as the arrangement of objects or numbers in a way such that the order of the arrangement does not matter.

Given that,

Teo has a combination of quarters, loonies, and toonies in his pocket.

Total number of coins = 9

1 quarter = $0.75

1 loonie = $1

1 toonie = $2

If he uses fewer toonies than loonies,

Total number of combinations of 9 coins = 1³ × 1³ × 7³ = 343

We need the number of combinations in between $10 and $12.

We can form the following combinations.

(2 × $1) + $2 gives $4. Remaining can be 8, 9 and 10 quarter coins.

(3 × $1) + (2 × $2) gives $7. Remaining can be 4, 5 and 6 quarter coins.

(3 × $1) + (1 × $2) gives $5. Remaining can be 7, 8 and 9 quarter coins.

(4 × $1) + (3 × $2) gives $10. Remaining can be 1 or 2 quarter coins.

(4 × $1) + (2 × $2) gives $8. Remaining can be 3, 4 and 5 quarter coins.

(4 × $1) + (1 × $2) gives $6. Remaining can be 6, 7 and 8 quarter coins.

Total number of combinations = 3 + 3 + 3 + 2 + 3 + 3 = 17

Hence the total number of combinations are 17.

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