A florist wants to determine if a new additive would help extend the life of cut flowers longer than the original additive. The florist randomly selects 20 carnations and randomly assigns 10 to the new additive and 10 to the original additive. After three weeks, 6 carnations placed in the new additive still looked healthy and 2 carnations placed in the original additive still looked healthy. The difference in proportions (new – original) for the carnations that still looked healthy after three weeks was 0. 4. Assuming there is no difference in the additives, 200 simulated differences in sample proportions are displayed in the dotplot. Using this dotplot and the difference in proportions from the samples, is there convincing evidence that the new additive was more effective?

A Yes, because a difference in proportions of 0. 4 or more occurred 7 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.

B Yes, because a difference in proportions of 0. 4 or less occurred 193 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.

C No, because a difference in proportions of 0. 4 or more occurred 7 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.

D No, because a difference in proportions of 0. 4 or less occurred 193 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective

You can find the angle θ in degrees between the calculated vector and the x-axis, measured counterclockwise from the x-axis.

To determine the angle θ in degrees between a calculated vector and the x-axis, measured counterclockwise from the x-axis, you can use trigonometry. The x-component and y-component of the vector are needed for this calculation.

Calculate the ratio of the y-component to the x-component of the vector:

y/x = tan(θ)

Use the inverse tangent function (arctan or atan) to find the angle θ:

θ = atan(y/x)

Convert the angle from radians to degrees by multiplying by 180/π:

θ_degrees = θ * (180/π)

By following these steps, you can find the angle θ in degrees between the calculated vector and the x-axis, measured counterclockwise from the x-axis.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Answer:

The second one

Step-by-step explanation:

Let k: y = a₁x + b₁ and l: y = a₂x + b₂. Then

We have the line y = -x + 5 ⇒ a₁ = -1.

Therefore

a₂ · (-1) = -1

-a₂ = -1     Ichange the signs

Answer:

Y= -3X+5

Y=-3(-4)+5

Y=12+5

Y=17

(-4,17)

Step-by-step explanation:

Replace x with -4

multiply -3 and -4

add 12 and 5 and thats the answer for y

If the mean number of people who attended three basketball games was 8,242, that means the sum of the number of people who attended all three games is equal to 8,242 multiplied by the number of games, which is 3.

What does math mean?

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Total attendance = mean attendance * number of games

Total attendance = 8,242 * 3

Total attendance = 24,726

So the total attendance at the three games is 24,726 people.

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When it's a quarter full, the shipping container holds a volume of 350 cubic feet.

Bassically, we want to find one quarter (1/4) of the volume of the rectangular prims.

The dimensions are 20ft by 8ft by (8ft + 9in)

Let's rewrite that last part only using feet.

Remember that 12 in = 1ft

Then:

9 in = (9/12)ft = 0.75 ft

Then we can rewrite the dimensions as:

20ft by 8ft by 8.75 ft

The volume is the product between these numbers, and we want one fourt of the volume, so we need to find:

V = (1/4)*(20ft)*(8 ft)*(8 .75 ft) = 350ft³

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The number of arithmetic operations executed by Horner's method can be characterized as O(n) since each coefficient ai is multiplied by x and added to the intermediate result only once. There are a total of n coefficients in the polynomial, so the number of arithmetic operations is proportional to n, resulting in O(n) complexity.

To compute the polynomial p(x) = Σ(ai * xi), a simple O(n^2) time algorithm can be used. The algorithm can be outlined as follows:

sql

Copy code

Input: Polynomial coefficients a0, a1, ..., an and value of x

Output: Value of p(x)

1. Initialize result = 0

2. For i from n to 0:

    3. result = result * x + ai

4. Return result

This algorithm iterates through the coefficients of the polynomial in decreasing order, multiplying the current result by x and adding the next coefficient ai. The time complexity of this algorithm is O(n^2) because there are n iterations, and each iteration involves a multiplication and addition operation.

To compute the polynomial p(x) in O(n log n) time, a more efficient calculation of xi can be used. The algorithm can be outlined as follows:

markdown

Copy code

Input: Polynomial coefficients a0, a1, ..., an and value of x

Output: Value of p(x)

1. Initialize result = 0

2. Initialize power = 1

3. For i from 0 to n:

    4. result = result + ai * power

    5. power = power * x

6. Return result

This algorithm calculates xi efficiently by repeatedly squaring the current power of x. It iterates through the coefficients of the polynomial in increasing order, multiplying each coefficient ai by the corresponding power of x and adding it to the result. The time complexity of this algorithm is O(n log n) because there are n iterations, and in each iteration, the power of x is updated by squaring, which can be done in logarithmic time.

Horner's method is a more efficient way to compute the polynomial p(x) by rewriting it in a nested form. In Horner's method, the polynomial is expressed as p(x) = a0 + x(a1 + x(a2 + x(...(an-1 + x.an)...))). The number of arithmetic operations executed by Horner's method can be characterized as O(n) since each coefficient ai is multiplied by x and added to the intermediate result only once. There are a total of n coefficients in the polynomial, so the number of arithmetic operations is proportional to n, resulting in O(n) complexity.

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Answer:

3x - 15 + 5x + 9 = 180

8x - 6 = 180

8x = 186

x = 23.25

So angle ABC measures 3(23.25) - 15 = 54.75°, and angle LMN measures

5(23.25) + 9 = 125.25°.

B is correct.

Answer:

d

Step-by-step explanation:

\(20 + .05x = 10 + .25x\)

\(.20x = 10 \)

\(x = 50\)

Answer:

x = 4

Step-by-step explanation:

Step 1: Write equation

-72 = 3(-4x - 8)

Step 2: Solve for x

Distribute 3: -72 = -12x - 24

Add 24 to both sides: -48 = -12x

Divide both sides by -12: x = 4

Step 3: Check

Plug in x to verify if it's a solution.

-72 = 3(-4(4) - 8)

-72 = 3(-16 - 8)

-72 = 3(-24)

-72 = -72

Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

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

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

The floor area of the engineer's model of the sugar factory is 10.825 square feet.

To determine the floor area of the engineer's model of a sugar factory in square feet, we need to convert the given measurements from inches to feet. Since there are 12 inches in a foot, we can divide both dimensions by 12 to convert them.

The length of the model in feet is 30 inches / 12 = 2.5 feet, and the width is 52 inches / 12 = 4.33 feet.

To find the floor area, we multiply the length by the width:

Area = Length × Width

= 2.5 feet × 4.33 feet

= 10.825 square feet

It's important to note that the given measurements are not a standard aspect ratio or scale for a sugar factory. The given dimensions may be scaled down for the model's convenience, so the calculated floor area is only applicable to the scale of the model.

In actuality, a sugar factory would have much larger dimensions.

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Answer:

x < 7

Step-by-step explanation:

-6x > -42

Divide each side by -6, remembering to flip the inequality

-6x/-6 < -42/-6

x < 7

Answer:

\(\boxed{x<7}\)

Step-by-step explanation:

\(-6x > -42\)

Divide both sides by -6 (flip sign).

\(\displaystyle \frac{-6x}{-6} < \frac{-42}{-6}\)

\(x<7\)

Answer:

Fantasia's family's car is more fuel-efficient.

Step-by-step explanation:

Given that, Tiyleah's family's car is getting 40 miles per gallon, and Fantasia's family's car uses 7 liters per 150 km.

The comparison can be done by observing the distance traveled by the cars in an equal amount of fuel. The car which covers more distance in an equal amount of fuel is more fuel-efficient.

First, convert the given units to have the same unit of measurement,

As 1 gallon =3.7854 liters and 1 mile = 1.609344 km

So, 40 miles =40 x 1.61=64.40 km

Now, The distance covered by Tiyleah's family's car is 64.40 km in 3.7854 liters.

So, the distance covered by Tiyleah's family's car in 1 liter of fuel is \(\frac{64.40}{3.7854}=17.01\) km

In a similar way,

As Fantasia's family's car uses 7 liters per 150 km.

So, the distance traveled by Fantasia's family's car in 1 liter of fuel =150/7=21.43 km

Observe that, in 1 liter of fuel, Tyleah's family's car covered 17.01 km while Fantasia's family's car covered 21.43 km which is more.

Hence, Fantasia's family's car is more fuel-efficient.

segment EH and segment E'H' both pass through the center of dilation.

A fixed point in the plane around which all points are enlarged or contracted is the center of a dilation.

The center, which may be found within, outside, or on a figure, is the only invariant (not changing) point under a dilation (k 1).

In the figure attached, triangle EFG is shown.

H is located at (0, 1)

The center of dilation is located at (0, 2)

Then, H' is located at (0, 0), so that the distance between the center of dilation and H' is twice the distance between the center of dilation and H.

E is located at (0, 5)

Then, E' is located at (0, 8), so that the distance between the center of dilation and E' is twice the distance between the center of dilation and E.

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Answer:

3x^3 -16x^2 +27x -10

Step-by-step explanation:

(x^2+6x-5) (-3x+2) = -3x(x^2+6x-5)+2(x^2+6x-5) = -3x^3 -18x^2 +15x + 2x^2+12x-10 = -3x^3 -18x^2 +2x^2+15x+12x-10 = -3x^3 -16x^2 + 27x -10

When both groups are shifted to a situation in which they earn an alternative reward after being trained to navigate a runway for food, the group that received three food pellets will continue to perform the task at a high level while the group that received one food pellet will experience difficulty.

It is known that rats have a natural preference for higher rewards. As a result, the group that received three pellets will be more motivated to complete the task since they have already tasted a higher reward. Therefore, they will continue to perform at a high level in the new environment.

On the other hand, the group that received only one pellet may find it challenging to adapt to the new situation since they are now receiving a lower reward. As a result, they may struggle to complete the task, and their performance may decrease.

In conclusion, the group that received three pellets will perform better than the group that received one pellet when both groups are shifted to a situation in which they earn an alternative reward. This is because the rats have a natural preference for higher rewards.

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Answer:

7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".

3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".

To solve the equation, we can start by distributing the 3 on the left side:

3(m + 2) = 15

3m + 6 = 15

Then, we can subtract 6 from both sides:

3m + 6 - 6 = 15 - 6

3m = 9

Finally, we can divide both sides by 3:

3m/3 = 9/3

m = 3

Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.

5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".

To simplify the expression, we can use the distributive property to expand the second term:

5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m

Therefore, the simplified expression is m^2 + 3m.

Answer: C

Step-by-step explanation:

The solution is Option A.

The value of the equation is 6x³ - 12x² - 48x is A = 6x ( x + 2 ) ( x - 4 )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 6x³ - 12x² - 48x   be equation (1)

On simplifying the equation , we get

Taking 6x as the common factor , we get

A = 6x ( x² - 2x - 8 )

On simplifying the equation , we get

A = 6x ( x + 2 ) ( x - 4 )

Therefore , the value of A is 6x ( x + 2 ) ( x - 4 )

Hence , the equation is 6x ( x + 2 ) ( x - 4 )

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L = 1.3245 is  the legnths of the pen's sides .

What is area and perimeter?

Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.

The equation for perimeter is 2L + W = 30 ( I'm assuming that the shed takes up one of the Widths, but you can use the Length if you want, it doesn't matter.)

So W = 30 - 2L.

Area = L x W = L (30 - 2L) = 30L - 2L^2.

This is a quadratic equation, easily graphed as a parabola, with a maximum point at L = 1.3245 .

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The expected value of the cardinality of a randomly chosen subset is n^2 / 2^n. To find the expected value of the cardinality of a randomly chosen subset, we need to consider the probabilities of selecting subsets with different cardinalities.

Let's consider a set with n elements. The total number of subsets of this set is 2^n, including the empty set and the set itself. Among these subsets, the number of subsets with cardinality n is C(n, n) = 1, and the number of subsets with cardinality n - 1 is C(n, n-1) = n.

The probability of selecting a subset with cardinality n is P(n) = 1/2^n, since there is only one subset with n elements out of the total 2^n subsets. The probability of selecting a subset with cardinality n - 1 is P(n - 1) = n/2^n, as there are n subsets with n - 1 elements out of the total 2^n subsets.

Now, let's calculate the expected value of the cardinality of the chosen subset:

E(X) = n * P(n) + (n - 1) * P(n - 1)

Substituting the probabilities we found:

E(X) = n * (1/2^n) + (n - 1) * (n/2^n)

Simplifying further:

E(X) = n/2^n + (n^2 - n)/2^n

Combining like terms:

E(X) = (n + n^2 - n)/2^n

Simplifying the numerator:

E(X) = n^2 / 2^n

Therefore, the expected value of the cardinality of a randomly chosen subset is n^2 / 2^n.

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6.6,your answer is correct.

As the theorem is a^2+b^2=c^2 you first must assign the proper components to each variable. Since 12 is the longest since it is the hypotenuse that means it is c so in this case 144. And since 10 is the leg it is a.

To solve you must take

10^2+b^2=12^2

100+b=144

144-100=44

Since b^2 is 44 you must find the square root \(\sqrt{44}\)=6.6

The difference in the account balances at the end of the loan terms is $313.98.

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

The formula for calculating compound interest is:

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

where:

A is the final amount after t years,

P is the principal amount,

r is the interest rate,

n is the number of times the interest is compounded per year, and

t is the number of years.

P = $12,000, r = 3.75% = 0.0375, n = 12, t = 66 months = 5.5 years

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

A = 12,000 * (1 + 0.0375/12)^(12*5.5)

A = 12,000 * (1 + 0.0375/12)^66

A =  12,000 * (1.003125)^66

A = $14,743.98

difference =$14,743.98 - $14,430 = $313.98

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Answer:B

Step-by-step explanation:

The new coordinates after dilation and the reflection across the y - axis will be (6, 3), (18, 3) and (6, 18).

A dilation is a transformation that enlarges or reduces a figure in size.

Given is figure [A] as shown in the figure which is dilated three times the size and is reflected across the y-axis.

Given are the coordinates of the triangle as -

(-2, 1), (-6, 1) and (-2, 6)

When the image is dilated by K, then each coordinate will become -

(x, y) = (Kx, Ky)

Therefore, the new coordinates will be -

(-6, 3), (-18, 3) and (-6, 18)

Now, in reflection across the y - axis, the coordinates will become (-x, y) from the coordinates (x, y).

Therefore, the final coordinates will be -

(6, 3), (18, 3) and (6, 18)

Therefore, the new coordinates after dilation and the reflection across the y - axis will be (6, 3), (18, 3) and (6, 18).

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The expected count that can be deduced from the arrivals to the second compartment will be 200.

It should be noted that in order to perform a goodness of fit test, the expected number of rats that are in each compartment will be gotten.

Therefore, the expected number of rats that will be in the second compartment will be:

= 1/5 × 1000

= 200

In conclusion, the correct option is 200.

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Answer:

V = \(\frac{Bh}{3}\)

Step-by-step explanation:

B = 3 × \(\frac{V}{h}\) ( multiply both sides by h to clear the fraction )

Bh = 3V ( divide both sides by 3 )

\(\frac{Bh}{3}\) = V

Polynomial factoring is the opposite of polynomial multiplication. A polynomial's leftover will be 0 if it is divided by its factors after factoring.

A multiple is a number that is the result of multiplying the provided number by other numbers, as opposed to a factor, which divides the given number perfectly without leaving a remainder.

When a polynomial f(x) is divided by (x - c), and (x - c) is a factor of the polynomial f(x), the remainder of the division is simply equal to 0. Therefore, if the remainder of a division like the ones mentioned above equals zero.

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Answer:

0.5

Step-by-step explanation:

Rise over run. 6/12 or divide. 6 divided by 12 equals 0.5.

Answer: 1/2

Step-by-step explanation:

6/12 simplified is 1/2