In Jillian's garden, there are 3 rows of carrots, 2 rows of string beans, and 1 row of peas.There are 8 plants in each row. How many plants are in the gradenn?

Answer:

b

Step-by-step explanation:

(a) False. The set {x∈R^n | Ax=b} is not necessarily convex. It depends on the matrix A and the vector b. For example, if A is a non-convex matrix, then the set of solutions {x∈R^n | Ax=b} will also be non-convex.

(b) True. The set {(x₁,x₂) | x₂ ≤ 3x₁²} is convex. The inequality defines a downward parabolic region, and any line segment connecting two points within this region will lie entirely within the region. (c) False. Not all polygons on the R² plane are convex. For example, a polygon with a concave portion, such as a crescent shape, would not be convex.

(d) True. If S⊆R² is convex, then it must enclose a region of finite area. Convex sets do not have "holes" or disjoint parts, so they form a connected and bounded region. (e) False. If S₁⊆R² and S₂⊆R², and S₁∩S₂=ϕ (empty set), then S₁∪S₂ can be convex. If S₁ and S₂ are both convex sets that do not overlap, their union can still be a convex set. (f) True. If S₁⊆R² and S₂⊆R² are both closed sets, then their union S₁∪S₂ must also be closed. However, it may or may not be convex. The convexity of the union depends on the specific sets S₁ and S₂.

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In a certain private school, 46 students study foreign languages. There are 3 students who study exactly one language.

Total = F + G + R - (FG + GR + FR) + X

The first three terms represent the total number of students who study each language. We then subtract the students who study two languages

Plugging in the values we have, we get:

46 = 26 + 18 + 20 - (7 + 9 + 5) + x

46 = 43 + X

X = 3

Thus, there are 3 students who study exactly one language.

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The solution to the simultaneous equation is x = 1 and y = 3

1 / 3 x + y = 10 / 3

2x + 1 / 4 y = 11 / 4

multiply equation one by 3 and multiply equation 2 by 4

Therefore,

x + 3y = 10

8x + y  = 11

hence,

x + 3y = 10

24x + 3y = 33

23x = 23

x = 23 / 23

x = 1

Therefore,

1 + 3y = 10

3y = 10 - 1

3y = 9

y = 9 / 3

y = 3

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Answer: y = -x1 - 1

Step-by-step explanation:

Do both points satisfy this equation?:

(1,-2): -2 = -1 -1 Yes

(-3,2): 2 = -(-3)-1 [or 3-1=2] Yes

The line contains the points (1,-2) and (-3,2) is Y= -x-1. The correct option is B.

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that the points are  (1,-2) and (-3,2). The equation of the line will be the line which satisfies the given points.

Y= -x-1

At points (1,-2),

Y= -x-1

-2=-1-2

-2=-2

At point(-3,2).

Y =-x-1

2=3-1

2 = 2

The line Y= -x-1 is passing through the points  (1,-2) and (-3,2). The correct option is B.

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Answer:

113 moteis

Step-by-step explanation:

A = 7 x 4 = 28 yards^2

1 yard - 0,9 m

1 yard^2 - 0,81 m^2

28 yards^2 - A

A = 28 x 0,81 = 22,68m^2

22,68 x 5 = 113,4

113 moteis

Answer:

140

Step-by-step explanation:

because it is

However, assuming there is a statement that involves the variable x, it would perform some operation or assign a value to x based on the specific syntax of the statement.

Without the statement provided, it is impossible to give a specific answer. Assuming the variable x has been the initialized to an integer value (e.g., x = 3), the following statement will perform an operation or action using the value of x. This could include mathematical operations, comparisons, or use within a loop or conditional statement. Without knowing the specific statement, I cannot provide a more detailed explanation of its function.

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The length of side b is 56m, angle A is 45°, and angle C is 67°.

In the given triangle with side lengths a = 74m, b ≈ 56m, and c = 36m, the length of side b is approximately 56m.

To solve the triangle, we can use the Law of Cosines and the fact that the sum of angles in a triangle is 180 degrees. Given angle B = 67°51', we have:

Using the Law of Cosines, we have:

b² = a² + c² - 2ac * cos(B)

Substituting the known values:

b² = 74² + 36² - 2 * 74 * 36 * cos(67°51')

Calculating the value of b:

b ≈ √(74² + 36² - 2 * 74 * 36 * cos(67°51'))

b ≈ 55.92m (rounded to the nearest whole number, b ≈ 56m)

Using the Law of Cosines again, we have:

cos(A) = (b² + c² - a²) / (2 * b * c)

Substituting the known values:

cos(A) = (56² + 36² - 74²) / (2 * 56 * 36)

Calculating the value of A:

A = cos⁻¹((56² + 36² - 74²) / (2 * 56 * 36))

A ≈ 45° (rounded to the nearest whole number)

Using the fact that the sum of angles in a triangle is 180 degrees:

C = 180° - A - B

Substituting the known values:

C ≈ 180° - 45° - 67°51'

Calculating the value of C:

C ≈ 67°9' (rounded to the nearest whole number, C ≈ 67°)

Therefore, in the given triangle, the length of side b is approximately 56m, angle A is approximately 45°, and angle C is approximately 67°.

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Answer:

D

Step-by-step explanation:

4+4=8 probability of success

4+4+3=11 total senario

therefore 8/11 is your probability of a success

A box of chocolates contains four milk chocolates, four dark chocolates, and three white chocolates. The probability that it is milk or dark chocolate is 8/11.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

The total number of milk chocolate = 4

The total number of dark chocolate = 4

The total number of white chocolate = 3

The total number of milk or dark chocolate = 8

Total number of chocolate a box contains = 11

The probability that it is a milk or dark chocolate = 8/11

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Answer: y=5x+7

Step-by-step explanation:

Since we are given the slope, all we have to do is plug in the given point and solve for the y-intercept.

-3=5(-2)+b             [multiply]

-3=-10+b                [add both sides by 10]

b=7

Now, we know the equation is y=5x+7.

1)

2x - 3y = - 1

For y = x - 1

So,

2x - 3y = - 1, Subsitution

2x - 3(x - 1) = - 1

2x - 3x + 3 = - 1

- x + 3 = - 1

- x = - 1 - 3

- x = - 4

x = 4 ✔

y = x - 1

y = 4 - 1

y = 3 ✔

So => HP = {x, y} = {4, 3}

=== Thanks ===

An airline has a requirement that the total outside dimensions (length, width, and height) of a checked bag not exceed 73 inches. You want to check a bag with a height equal to its width. To find the largest volume bag of this shape that you can check, we will use the constraint provided and optimize the volume.

Let L, W, and H represent the length, width, and height of the bag, respectively. According to the constraint, L + W + H ≤ 73 inches. Since H = W, we can rewrite the constraint as L + 2W ≤ 73.

The volume (V) of the bag can be represented as V = L × W × H. Substituting H = W, we get V = L × W². To maximize the volume, we need to rewrite this equation in terms of one variable. Using the constraint, we can express L as L = 73 - 2W. Now, substitute this into the volume equation: V = (73 - 2W) × W².

To find the maximum volume, we can use calculus or simply observe that the function V(W) is a downward-opening parabolic function. The maximum volume occurs at the vertex, which is found at the W-coordinate W = -b/2a in the general quadratic equation f(x) = ax^2 + bx + c. In our case, a = -2, b = 73, so W = 73/(2×-2) = 18.25 inches.

an airline requires that the total outside dimensions (length width height) of a checked bag not exceed 73 inches. suppose you want to check a bag whose height equals its width, Now that we have W, we can find H (which is equal to W) and L. H = 18.25 inches, and L = 73 - 2(18.25) = 36.5 inches. Thus, the largest volume bag you can check is V = 36.5 × 18.25² ≈ 12,104.16 cubic inches (rounded to two decimal places).

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The scale factor is 2 and center dilation is reduced.

The scale factor is a ratio that describes how much a figure has been enlarged or reduced. It is calculated by dividing the length of the corresponding sides of the original and dilated figures. If the scale factor is greater than 1, then the figure is enlarged, and if it is less than 1, then the figure is reduced.

To find the scale factor in an IXL dilations problem, you need to compare the corresponding sides of the original and dilated figures.

If the original figure has a side length of 4 units, and the dilated figure has a corresponding side length of 8 units, then the scale factor is 8/4=2. This means that the dilated figure is twice as large as the original figure.

The center of dilation is the point about which the figure is enlarged or reduced. It is the fixed point that remains unchanged during the dilation process.

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Answer: A. 0.4899 B. 14

Step-by-step explanation:

If X = random variable

then, the standard deviation of the sampling distribution of X = \(\dfrac{\sigma}{\sqrt{n}}\)

A.

GIven: \(\sigma= 1.2, \n= 6\)

The standard deviation of the sampling distribution of X = \(\dfrac{1.2}{\sqrt{6}}=0.4899\)

B. Let n be the sample size,

\(0.325=\dfrac{1.2}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=\dfrac{1.2}{0.325}\\\\\Rightarrow\ \sqrt{n}=3.69230769231\\\\\Rightarrow\ n= (3.69230769231)^2=13.6331360947\approx 14\)

Hence, the required sample size = 14

\( f(n) = O(g(n)) \) means that there exist positive constants \( c \) and \( n_0 \) such that for all \( n \geq n_0 \), the value of \( f(n) \) is bounded above by \( c \cdot g(n) \). In other words, the growth rate of \( f(n) \) is no greater than the growth rate of \( g(n) \) up to a constant factor.

On the other hand, \( f(n) = \Theta(g(n)) \) implies that there exist positive constants \( c_1 \), \( c_2 \), and \( n_0 \) such that for all \( n \geq n_0 \), the value of \( f(n) \) lies between \( c_1 \cdot g(n) \) and \( c_2 \cdot g(n) \). In simpler terms, \( f(n) \) and \( g(n) \) have the same growth rate within constant bounds.

In summary, \( f(n) = O(g(n)) \) states that \( f(n) \) has an upper bound in terms of the growth of \( g(n) \), while \( f(n) = \Theta(g(n)) \) asserts that \( f(n) \) and \( g(n) \) have equivalent growth rates within constant bounds.

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The expected number of defective items and the probability of at least 4 are defective is equal to 3.6 and 0.370 or 37.0%.

Total number of items 'n' = 18

Probability of an item being defective 'p' =20%

                                                                    = 0.2  

Expected number of defective items,

Use the formula for the expected value of a binomial distribution,

E(X) = np

where X is the number of defective items.

Plug in the values we have,

E(X) = 18 x 0.2

      = 3.6

Expect average items out of 18 to be defective = 3.6  .

Probability that at least 4 items are defective,

Calculate the probability of 4, 5, 6, ..., 18 defective items

Use the complement rule to simplify it,

P(at least 4 defective)

= 1 - P(less than 4 defective)

Using the CDF function,

'binomcdf' is the binomial cumulative distribution function.

18 is the number of trials,

0.2 is the probability of success,

And 3 is the maximum number of successes

P(less than 4 defective)

= binomcdf (18, 0.2, 3)

= P(X <= 3)

=\(\sum_{x=0}^{3}\) ¹⁸Cₓ × (0.2)^x × (0.8)^(18-x)

= ¹⁸C₀× (0.2)^0 × (0.8)^(18-0) + ¹⁸C₁× (0.2)^1 × (0.8)^(18-1) + ¹⁸C₂× (0.2)^2 × (0.8)^(18-2) + ¹⁸C₃× (0.2)^3 × (0.8)^(18-3)

= (0.8)^(18) + 18× (0.2) × (0.8)^(17) + 153 × (0.04) × (0.8)^(16) + 1632× (0.008) × (0.8)^(15)

= 0.630

Plug in the values,

P(at least 4 defective)

= 1 - 0.630

= 0.370

Therefore, the expected items to be defective and probability that at least 4 items out of 18 are defective is equal to 3.6 and 0.370 or 37.0%.

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Answer:

16

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Remember: Mode=most

There are 2 threes, 1 six, 1 seven, and 1 sixteen, meaning that there are more threes.

Answer:

3

Step-by-step explanation:

Mode is the most frequent number that occurs in a set of numbers.

The most frequent number that occurs in set [3,3,6,7,16] is 3

The mode is 3

Hope this helps :)

B! That should be your answer!!!! Good luck and I hope u ace what you are doing.

If a bacterial growth rate is 3 cells every 2 minutes and there were initially 260, there will be 290 cells after 21 minutes which is found by using multiplication and addition.

what is Multiplication?

Multiplication is an arithmetic operation that combines two or more numbers to find their product. It is one of the fundamental operations in mathematics and is denoted by the "×" or "*" symbol.

The growth rate of the bacteria is 3 cells every 2 minutes. This means that in a span of 2 minutes, the number of cells increases by 3.

To find the total number of cells after 21 minutes, we need to calculate the number of 2-minute intervals in 21 minutes. Since there are 10 intervals of 2 minutes in 20 minutes (10 intervals * 2 minutes = 20 minutes), we know that the number of cells at the end of 20 minutes is 260 + (10 intervals * 3 cells) = 290 cells.

Now, for the remaining 1 minute, we can calculate the additional cells. In this case, the growth rate is still 3 cells every 2 minutes. Therefore, in 1 minute, the number of cells increases by (1/2) * 3 = 1.5 cells. Thus, the total number of cells after 21 minutes is 290 + 1.5 = 291.5 cells.

Since we cannot have a fraction of a cell, we round the result to the nearest whole number. Therefore, after 21 minutes, there will be 290 cells.

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Answer:

A unit is a measure of ratio between two quantities. In this instance, the unit is a pound. The ratio you need to take is the price of each fruit and divide it by the number of pounds each fruit has to get a price per pound. See below for solution.

Step-by-step explanation:

A. 4.19 dollars / 2.5 pounds = 1.676 dollars / pound

B. 5.49 dollars / 4 pounds = 1.3725 dollars / pound

C. 6.99 dollars / 5 pounds = 1.398 dollars / pound

D. 9.59 dollars / 6.5 pounds = 1.475 dollars / pound

The lowest is B, the apples.

Answer:

C) 17.1 square units

Step-by-step explanation:

Use Heron's formula to calculate the area of the triangle:

\(Area = \sqrt{s(s-a)(s-b)(s-c)}\)  where  \(s=\frac{a+b+c}{2}\) which represents the semi-perimeter of the triangle:

\(s=\frac{9.9+6.1+6}{2}=11\)

Therefore:

\(Area = \sqrt{11(11-9.9)(11-6.1)(11-6)}\\\)

\(Area = \sqrt{11(1.1)(4.9)(5)}\\\)

\(Area = \sqrt{296.45}\\\)

\(Area = 17.2\)

Therefore, the closest answer choice is C) 17.1 square units

Answer:

2224.32 cm³

Step-by-step explanation:

La fórmula para el volumen de una pirámide hexagonal = 1/3 (1/2 × P × a) × h

Donde a = Apotema = 9,93 cm

P = Perímetro =

Pirámide hexagonal = 6 × Bordes de la base = 6 × 8 cm = 48 cm

h = Altura = 28 cm

Por eso,

Volumen de la pirámide hexagonal = 1/3 (1/2 (48 × 9.93) × 28 cm

= 1/3 × 238.32 × 28 cm

= 2224.32 cm³

Volumen de la pirámide hexagonal = 2224.32 cm³

The probability that the mean depth in 15 randomly selected Medium Ground Finches is at least 10 millimeters is approximately 0.0429 or 4.29%.    

Since we are dealing with a sample mean, we need to use the central limit theorem. Under certain conditions, the sample mean of a large enough sample (in this case 15) will be normally distributed with mean equal to the population mean (y) and standard deviation equal to the population standard deviation (o) divided by the square root of the sample size (n). That is:

mean of sample means = y = 9.6 mm

standard deviation of sample means = o / sqrt(n) = 1.1 / sqrt(15) = 0.2845 mm

Now we want to find the probability that the sample mean is at least 10 mm. We can standardize the sample mean using the formula:

z = (x - y) / (o / sqrt(n))

where x is the sample mean we are interested in. Substituting the given values, we get:

z = (10 - 9.6) / (1.1 / sqrt(15)) = 1.725

Using a standard normal distribution table or calculator, we can find the probability of a z-score being greater than 1.725 to be approximately 0.0429. Therefore, the probability that the mean depth in 15 randomly selected Medium Ground Finches is at least 10 millimeters is approximately 0.0429 or 4.29%.

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Answer:

\(\frac{1}{2}\) or 0.5

Step by Step Explanation:

1. Multiply the Numerators and Denominators

\(\frac{2}{3}\) \(\frac{x}{x}\) \(\frac{3}{4}\) = \(\frac{6}{12}\)

2. Simplify

\(\frac{6}{12}\) = \(\frac{1}{2}\)

3. Solution

\(\frac{1}{2}\) or 0.5

The correlation coefficient between X and Y will be positive.

The correlation coefficient is a measure of the strength of the linear relationship between two variables. When two variables have a positive linear relationship, as the value of one variable increases, the value of the other variable also increases.

When two variables have a negative linear relationship, as the value of one variable increases, the value of the other variable decreases. In this case, since high scores on X are associated with high scores on Y and low scores on X are associated with low scores on Y, the relationship between X and Y is positive.

The correlation coefficient measures the strength of the linear relationship between two variables. A positive correlation coefficient indicates that there is a positive linear relationship between the two variables, so the correlation coefficient between X and Y will be positive.

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