A particular fruit's weights are normally distributed, with a mean of 525 grams and a standard deviation of 31 grams.
If you pick 6 fruit at random, what is the probability that their mean weight will be between 526 grams and 540 grams (Give answer to 4 decimal places.)

Therefore, the formula for T1 is T1(x1,x2) =\((24x1/5 - 18x2/5, -36x1/5 + 6x2/5).\)

Given T is a linear transformation from R2 into R2, we need to show that T is invertible and find a formula for T1.T(x1,x2) = (3x1-9x2, -3x1+5x2)Let A be the standard matrix for T, then we have to find the determinant of A as it will help us determine whether T is invertible or not.The standard matrix for T is given as :A = [3 -9-3 5]Now, to calculate the determinant of A, we have to use the formula as:det(A) = ad - bcwhere a = 3, b = -9, c = -3, d = 5Now, substituting the values of a, b, c, d, we get,det(A) = (3 × 5) - (-9 × -3) = 15 - 27= -12Since the determinant of A is not equal to zero, therefore, T is invertible.

For finding the formula for T1, we need to calculate the inverse of T. We can find the inverse of T as:\([A|I] → [I|A-1]\)Now, appending the identity matrix to A, we get the following matrix.[A|I] = \([3 -9|1 0-3 5|0 1]→ [I|A-1] = [1 3/5|-9/5-3/5]\)

Therefore, the inverse of T is T-1(x1,x2) = (3x1/5 + 9x2/5, -9x1/5 - 3x2/5)Now, we can find T1 by substituting T-1 in T, we get,T1(x1,x2) = T(T-1(x1,x2)) =\(T(3x1/5 + 9x2/5, -9x1/5 - 3x2/5) = (3((3x1/5 + 9x2/5)) - 9(-9x1/5 - 3x2/5), -3((3x1/5 + 9x2/5)) + 5(-9x1/5 - 3x2/5)) = (24x1/5 - 18x2/5, -36x1/5 + 6x2/5)\)

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Answer:

1/81

Step-by-step explanation:

(1/3)⁴ = (1⁴/3⁴) = (1/81)

Answer:

C) 153.9 in²

Step-by-step explanation:

14 ÷ 2 = 7

π = 3.14

3.14×7×7 = 153.9 in²

hope this helps!

Answer:

answer should be 154 but 153.9 in sq is the closest.

we have to find the area right?

The estimate for the sum of the numbers is 230, and the actual sum of the numbers is 209.

To estimate the sum of the numbers, we can round each number to the nearest ten and then add them together. When rounding off to the nearest tens, we look at the number at the tenth position. If it is five and above, we round it off to the next nearest tens number and if it is below five, we round it off to the previous nearest tens number.

76 rounds to 80   since 6 is above 5
6 rounds to 10 since 6 is above 5
25 rounds to 30 since 5 is located at 5 and above interval
5 rounds to 10 since 5 is located at 5 and above interval
10 rounds to 10 since 0 is below 5
87 rounds to 90 since 7 is above 5

So, the estimate for the sum of the numbers is: 80 + 10 + 30 + 10 + 10 + 90 = 230

To find the actual sum of the numbers, we simply add them together without rounding:

76 + 6 + 25 + 5 + 10 + 87 = 209

The complete question is: 76. 6 25. 5 10. 87 =

What was Sela's estimate and what is the actual sum of the number?

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Step-by-step explanation:

1/2 as an exponential expression with a base of 2 can be written as:

\( \huge \purple{ {2}}^{ \red{\frac{1}{2} }} \)

Answer:

7.3 feet

Step-by-step explanation:

osK=

hypotenuse

adjacent

​

=

35

x

​

\cos 78=\frac{x}{35}

cos78=

35

x

​

35\cos 78=x

35cos78=x

Cross multiply.

x=7.2769\approx \mathbf{7.3}\text{ feet}

x=7.2769≈7.3 feet

Type into calculator and round to the nearest tenth of a foot.

Answer:7.3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

1 ÷ 1/5= 1 x 5/1 =5

I hope im right!!

A dilation is the only transformation that does not preserve congruence. All other types of transformations, including translations, rotations, and reflections, do preserve congruence.

A transformation that does not preserve congruence is a dilation. A dilation is a transformation that changes the size of a figure, but not its shape. This means that the new figure will not be congruent to the original figure.

In contrast, other types of transformations, such as translations, rotations, and reflections, do preserve congruence. These transformations move the figure to a new location on the coordinate grid, but do not change its size or shape. As a result, the new figure is congruent to the original figure.

In summary, a dilation is the only transformation that does not preserve congruence. All other types of transformations, including translations, rotations, and reflections, do preserve congruence.

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According to its meaning, it can be inferred that the words that match are: oreja - ear, mano - hand, boca - mouth, codo - elbow.

To make the correct match with the words of the options we can use a dictionary to identify the meaning and thus find which word matches the same meaning in Spanish.

In this case, it is much easier to find the match of each word because they refer to basic body parts that we can identify with a basic dictionary. Additionally, we can use tools such as the internet to search for unknown words and associate them with the concept that we previously know. According to the above, the matches are:

Ear - Oreja.

Hand - Mano.

Mouth - Boca.

Elbow - Codo.

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The solution for the equation is,

1. x = 2 and y = 1

2. no solution

3. y = 0 and x = 11

4. x = 4/3 and y = 10/3

How do linear equations work?

Since each term in a linear equation has an exponent of 1, graphing an algebraic equation always yields a straight line. It is called a "linear equation" because of this.

There are linear equations with one variable and those with two variables.

Given sets of equations,

1. x - y = 1

x + y = 3

add both the equations we get,

x - y + x + y = 1 + 3

2x = 4 (+y and -y eliminated)

x = 4/2 = 2

substitute value of  x

x + y = 3

2 + y = 3

y = 3 - 2 = 1

x = 2 and y = 1

2.  x + y = 1

x + y = 11

The two lines that are used to symbolize the equations in this instance are parallel, hence the problem has no solution.

3. x + 4y = 11

x - 6y = 11

We may remove the equations since x is a common constant in both equations.

x + 4y -(x - 6y) = 11 - 11

4y + 6y = 0

y = 0 and x = 11

4. -3x + 3y = 6

6x + 3y = 18

subtract equation 1 from 2

6x + 3y -(-3x + 3y) = 18 - 6

6x - 3y + 3x - 3y = 12

9x = 12

x = 12/9 = 4/3

substitute value of x

-3x + 3y = 6

-3(4/3) + 3y = 6

-4 + 3y = 6

y = 10/3

Hence the solution is 1. x = 2 and y = 1

2. no solution,

3. y = 0 and x = 11

4. x = 4/3 and y = 10/3.

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Answer:

Angle x would be 87 degrees.

Step-by-step explanation:

Angles inside of a triangle add up to 180 degrees. So 51+42=93 and if you subtract 93 from 180, you get 87.

Answer:

G.

Step-by-step explanation:

Answer:

same thing for the rest, you just change the value of the radius according to the question

Step-by-step explanation:

area = pi * radius²

1)

a = pi * 10²

a = ~3.14 * 100

a = 314 mi²

Answer:

We are given

\(( \sqrt{3} + \sqrt{7} )( \sqrt{7} - \sqrt{3} )\)

Answer:

4

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\) and \(\sqrt{a}\) × \(\sqrt{a}\) = a

Given

(\(\sqrt{3}\) + \(\sqrt{7}\) )(\(\sqrt{7}\) - \(\sqrt{3}\) )

Each term in the second factor is multiplied by each term in the first factor, that is

\(\sqrt{3}\) (\(\sqrt{7}\) - \(\sqrt{3}\) ) + \(\sqrt{7}\) (\(\sqrt{7}\) - \(\sqrt{3}\) ) ← distribute both parenthesis

= \(\sqrt{21}\) - 3 + 7 - \(\sqrt{21}\) ← collect like terms

= 4

The earthquake in China was 2511.89 times more intense than the one in northern Algeria. Logarithms are used to calculate the difference in intensity between earthquakes on the Richter scale.

To calculate the difference in intensity, use the formula:

Intensity Ratio = 10^((Magnitude2 - Magnitude1)/b)

where Magnitude1 and Magnitude2 are the magnitudes of the earthquakes, and b is a constant value of 1.5 for the Richter scale.

Step 1: Subtract the magnitudes:
7.9 - 4.81 = 3.09

Step 2: Divide by b:
3.09 / 1.5 = 2.06

Step 3: Raise 10 to the power of the result:
10^2.06 ≈ 2511.89

The earthquake in China was 2511.89 times more intense than the one in northern Algeria.

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Answer:

0.0233 or about 2.33%

Step-by-step explanation:

On a TI-84, you can use the cumulative distribution function (2nd->DISTR->normalcdf) to determine the probability that in a normal distribution, a randomly selected variable will fall into a certain interval that you supply.

normalcdf(132.7, 1e99, 95.1, 18.9) = 0.0233274727 ≈ 2.33%

Therefore, the probability that a randomly selected adult has an IQ greater than 132.7 is 0.0233 or about 2.33%

Answer:

Step-by-step explanation:

55*9%= 4.95 or 5.00

If you start at 10% you get 5.50. Go down a % to get the 4.95.

There are 686,000 different license plates.

To solve this problem, we can fix one person's position and arrange the remaining (n-1) people around the table.

Since the seats are indistinguishable, we divide the total number of arrangements by n to avoid counting duplicate arrangements.

The number of different ways to sit n people around a round table is (n-1)!.

A license plate can have four one-digit numbers or two one-digit numbers and two letters.

For the first case, where the license plate has four one-digit numbers, there are 10 choices for each digit (0-9).

Therefore, there are 10 choices for the first digit, 10 choices for the second digit, 10 choices for the third digit, and 10 choices for the fourth digit. In total, there are 10^4 = 10,000 different license plates.

For the second case, where the license plate has two one-digit numbers and two letters, there are 10 choices for each digit and 26 choices for each letter (assuming only uppercase letters).

Therefore, there are 10 choices for the first digit, 10 choices for the second digit, 26 choices for the first letter, and 26 choices for the second letter. In total, there are 10^2 * 26^2 = 676,000 different license plates.

Different license plate = 10,000 + 676,000

                                     = 686,000

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The product in simplest form is \(-250\sqrt[3]{50}\) .

In the question,

It is given that,

\(5*\sqrt[3]{5} * (-10\sqrt[3]{50})\)

By radical laws, \(\sqrt{a} * \sqrt{b} = \sqrt{ab}\)

So,

The given question becomes:

\(-50*\sqrt[3]{50*5} = -50*\sqrt[3]{250} = -250\sqrt[3]{5} }\)

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when two ads two the result will be 4 like this

2+2=4

Answer: The first one is 9/49 and in decimal form it's 0.18367... the second one in fraction form is 16807/161051 and in decimal form is 0.10435824...

Step-by-step explanation: hope this helped

Answer:

I believe the answer is 36

Step-by-step explanation:

36 is a whole number the others aren't

The probability that a defective component can be detected by only one inspector is 0.2112. the probability that all three defective components in a batch escape detection by both inspectors is 0.00178.

(a) To calculate the probability that a defective component will be detected by only one inspector, we can use the formula for conditional probability: P(detected by first inspector | not detected by second inspector) = P(detected by first inspector and not detected by second inspector) / P(not detected by second inspector).

The probability that a defective component will be detected by the first inspector and not detected by the second inspector can be calculated as follows: P(detected by first inspector and not detected by second inspector) = P(detected by first inspector) * P(not detected by second inspector | detected by first inspector) = 0.88 * (1 - 0.88) = 0.1056.

The probability that a defective component will not be detected by the second inspector is: P(not detected by second inspector) = 1 - P(detected by second inspector) = 1 - 0.88 = 0.12.

The probability that a defective component will be detected by exactly one of the two inspectors can be calculated as follows: P(detected by exactly one inspector) = P(detected by first inspector and not detected by second inspector) + P(detected by second inspector and not detected by first inspector) = 0.1056 + 0.1056 = 0.2112.

(b) To calculate the probability that all three defective components in a batch escape detection by both inspectors, we can use the formula for independent events: P(all three defective components escape detection) = P(first defective component escapes detection) * P(second defective component escapes detection) * P(third defective component escapes detection) = (1 - 0.88)^3 = 0.00178.

So the probability that all three defective components in a batch escape detection by both inspectors is 0.00178.

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Complete question : components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). the first inspector detects 88% of all defectives that are present, and the second inspector does likewise. at least one inspector does not detect a defect on 24% of all defective components. what is the probability that the following occur? (a) A defective component will be detected only by the first inspector? A defective component will be detected by exactly one of the two inspectors? (b) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?

Answer: I’m pretty sure it’s 15 cm

Step-by-step explanation:

There are approximately 11.25 cups of granulated sugar in a 5 pound bag.

To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.

First, we multiply the number of pounds (5) by the conversion factor:

5 pounds * 2.25 cups/pound = 11.25 cups

Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.

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Answer: 134.4933

Step-by-step explanation: 58.1987 minus 192.692 is 134.4933

Answer:

1

Step-by-step explanation:

so u group like term

5x=27-22 ( because u are moving a positive number to the other side of the = sign

5x=5 ( u divide the numbers with the number with the varible or alphabet)

so x = 1

Answer:

A = 95 ( being vertically opposite angle)

The dot product of u and v is -64. The distance between u and v is 16.

The dot product of two vectors u and v is calculated by multiplying the corresponding components of each vector and then summing the results. Therefore, the dot product of u and v is:

u•v = (−3)(9) + (10)(−5) + (9)(7) = −27 − 50 + 63 = −64

The distance between two vectors u and v is calculated by taking the square root of the dot product of the two vectors. Therefore, the distance between u and v is:

Distance(u,v) = √(u•v) = √(−64) = 16

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Answer:

1. 10 root 3

2.

A=30

B = 60

Step-by-step explanation:

In picture