What is 7x-1+6x-1=180? SHOW WORK!!!!!!

In the given question both the options D and E are necessary for the Central Limit Theorem to hold.

The Central Limit Theorem (CLT) is a fundamental concept in statistics that describes the behavior of sample means when the sample size is large. According to the CLT, the distribution of sample means approaches a normal distribution regardless of the shape of the original population distribution, given certain conditions.

Option A states that each individual measurement must be normally distributed. This is not a necessary condition for the CLT to hold. The original population distribution does not have to be normal; it can be any distribution shape.

Option B states that each individual measurement must be identically distributed. This is not a necessary condition for the CLT to hold. The measurements can have different distributions, as long as they satisfy the other conditions.

Option C states that each individual measurement must be independent of every other measurement. This is a necessary condition for the CLT to hold. The independence of measurements ensures that each observation contributes to the overall sample mean independently, without being influenced by other observations.

Therefore, options D and E are the correct choices. Both the independence of measurements (option C) and a sufficient sample size (option B) are necessary conditions for the Central Limit Theorem to hold.

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If there are 30 students in the class, then the number of students who play soccer but do not play basket-ball are 13 students.

The total-students in the class is = 30 students,

The Number of students who play basketball is = (2/5) × 30 = 12,

The Number of students who play soccer is = (7/10) × 30 = 21,

⇒ Number of basketball players who also play soccer = (2/3) × 12 = 8,

So, out of the 21 students who play soccer, 8 also play basketball.

To find the number of students who play soccer but not basketball, we can subtract the number of students who play both from the total number of soccer players:

⇒ 21 - 8 = 13 students play soccer but not basketball.

Therefore, the required number of students are 13 students.

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The three of them working together can complete a quilt in 8 days.

The three of them working together can complete the task in 8 days. This can be calculated using the following formula:

Time Taken = (1/Time Taken by Yu Jie) + (1/Time Taken by Mufeed) + (1/Time Taken by Mya)

Time Taken = (1/16) + (1/12) + (1/14)

Time Taken = 3/28

Time Taken = 8/4

Time Taken = 8 days

Therefore, the three of them working together can complete the task in 8 days. This is because each person is completing a fraction of the total task each day. The more people working together, the faster the task will be completed.

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Answer:

300 ≥ 5.5 + 37.95x

Step-by-step explanation:

when she plans to drive 50 miles that means she has to pay
50 * 0.11 = 5.5
$5.5 to drive the 50 miles.
Additional to the $5.5 she has to pay the daily cost of $37.93 per day.

The total cost of renting the car therefore is
5.5 + 37.95x
with x being the amount of days.
To stay within her budget this cost can't be higher than 300
Therefore
300 greater or equal to 5.5 + 37.95x

according to this inequality, x can be no higher than 7. when x = 7 the total cost is $ 271.15
Taylor can't rent the car up to 7 days while staying within her budget.

We conclude that the measure of angle ∠b is 43°.

So, a measure of angle b:

Let us name the other angle as c:

As we can clearly observe that ∠c and ∠b are vertically opposite angles.

Hence, ∠b = 43°.

Therefore, the measure of angle ∠b is 43°.

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The slope of the line is given by m = 5/2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 3 , -1 )

Let the second point be Q ( 5 , 4 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 4 - ( - 1 ) ) / ( 5 - 3 )

Slope m = ( 4 + 1 ) / 2

Slope m = 5/2

Hence , the slope of the line is m = 5/2

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Answer:

La fracción de bombones que se comieron entre los dos es \(\frac{7}{10}\)

La caja tenía 40 bombones.

Step-by-step explanation:

Sabes que Andrés se comió 1/5 de los bombones de una caja y Ana 1/2 de la misma. Para conocer la fracción de bombones que se comieron entre ambos, debes sumar las fracciones que comieron cada uno:

\(\frac{1}{5} +\frac{1}{2}\)

Para hacer suma de fracciones con distinto denominador, lo primero que hay que hacer es determinar un denominador común. Para eso debes calcular el mínimo común múltiplo (mcm) entre los denominadores.

En este caso, el mcm entre 5 y 2 es 10.

Ahora tienes que multiplicar cada numerador por el número que hayas multiplicado el denominador. Para ello, dividís el m.c.m entre el denominador inicial y el resultado se multiplica por el numerador de esa fracción:

Entonces:

\(\frac{1}{5} +\frac{1}{2}=\frac{2}{10} +\frac{5}{10}\)

Ahora  simplemente sumas los denominadores:

\(\frac{1}{5} +\frac{1}{2}=\frac{2}{10} +\frac{5}{10}=\frac{7}{10}\)

La fracción de bombones que se comieron entre los dos es \(\frac{7}{10}\)

Sabes que quedaron 12 bombones en la caja. Representando 1 la cantidad total de bombones, y si se comieron 7/10 de la caja, entonces quedaron:

\(1-\frac{7}{10}\)

Restando de manera similar al procedimiento usado para la suma se obtiene:

\(1-\frac{7}{10}=\frac{3}{10}\)

Finalmente podes aplicar la siguiente regla de tres: si 3/10 representa los 12  bombones que quedaron en la caja, entonces en 1 (que representa la cantidad total de bombones) cuantos bombones hay?

\(cantidad total de bombones=\frac{1*12}{\frac{3}{10} }\)

cantidad total de bombones=40

La caja tenía 40 bombones.

Answer:

Spends $20 and she has $5 leftover.

Step-by-step explanation:

The two consecutive odd integers are 9 and 11 (from x=9) or 3 and 5 (from x=3).

Let's assume the two consecutive odd integers as x and x+2 (where x is the lowest integer).

According to the given information, the product of the two consecutive odd integers is 41 less than 7 times their sum. Mathematically, we can represent this as:

(x)(x+2) = 7[(x) + (x+2)] - 41

Expanding the equation:

x^2 + 2x = 7(2x + 2) - 41

x^2 + 2x = 14x + 14 - 41

x^2 + 2x = 14x - 27

Moving all terms to one side of the equation:

x^2 + 2x - 14x + 27 = 0

x^2 - 12x + 27 = 0

Now, we can solve this quadratic equation to find the values of x. We can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this equation, a = 1, b = -12, and c = 27. Plugging these values into the quadratic formula:

x = (-(-12) ± √((-12)^2 - 4(1)(27))) / (2(1))

x = (12 ± √(144 - 108)) / 2

x = (12 ± √36) / 2

x = (12 ± 6) / 2

This gives us two possible values for x:

When x = (12 + 6) / 2 = 18 / 2 = 9

When x = (12 - 6) / 2 = 6 / 2 = 3

Therefore, the two consecutive odd integers are 9 and 11 (from x=9) or 3 and 5 (from x=3).

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|CD| is parallel to |AB|

Also;

ANSWERS:

(a) The measured angle ACD is 65degrees

(b) The measured angle DCB is 35degrees

(c) The measured angle ACB is 30 degrees

The number of columns in the first matrix must equal the number of rows in the second matrix in order to multiply matrices with different dimensions.

    3. Determine the dot product of the corresponding row in matrix A          and the corresponding column in matrix B for each element in matrix C.

    4: The final response is matrix C, which is the union of the 2x3 matrix A and the 3x4 matrix B.

     Therefore, the result is a 2x4 matrix, which is produced by taking the dot product of the rows and columns of matrix A and matrix B.

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Answer:

28 blocks are filled in so I don't know how this a decimal... maybe it's .28

Step-by-step explanation:

The combinations of side lengths that will form a triangle with vertices X, Y, and Z are C and D.

For a set of three side lengths to form a triangle, the sum of any two sides must be greater than the third side. Using this property, we can determine which of the given combinations of side lengths will form a triangle with vertices X, Y, and Z.

A. XY = 8 mm, YZ = 12 mm, XZ = 23 mm

Here, XY + YZ = 8 mm + 12 mm = 20 mm, which is less than XZ = 23 mm. Therefore, this combination of side lengths will not form a triangle.

B. XY = 11 mm, YZ = 9 mm, XZ = 23 mm

Here, XY + YZ = 11 mm + 9 mm = 20 mm, which is less than XZ = 23 mm. Therefore, this combination of side lengths will not form a triangle.

C. XY = 11 mm, YZ = 12 mm, XZ = 20 mm

Here, XY + YZ = 11 mm + 12 mm = 23 mm, which is greater than XZ = 20 mm. Therefore, this combination of side lengths will form a triangle.

D. XY = 14 mm, YZ = 12 mm, XZ = 29 mm

Here, XY + YZ = 14 mm + 12 mm = 26 mm, which is greater than XZ = 29 mm. Therefore, this combination of side lengths will form a triangle.

Therefore, the combinations of side lengths that will form a triangle with vertices X, Y, and Z are C and D.

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Which of the following combinations of side lengths will form a triangle with vertices X, Y, and Z?

A.XY = 8 mm , YZ = 12 mm , XZ = 23 mm

B.XY = 11 mm , YZ = 9 mm , XZ = 23 mm

C.XY = 11 mm , YZ = 12 mm , XZ = 20 mm

D.XY = 14 mm , YZ = 12 mm , XZ = 29 mm

Answer:

$72.80

Step-by-step explanation:

You would multiply 52 with .40 to get 20.8. This is how much the price increased by. Then you would add the 20.8 to your original price of 52 to get 72.80.

(Also you use .40 initially because percent means out of 100. So 40% is the same as .4)

The new price after the sale of a new computer is, $72.8

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The price of the computer was $52 on the day he bought it.

And, The next day it had been marked up by 40%.

Let the new price after the sale of a new computer = x

So, We can formulate;

⇒ x = $52 + 40% of $52

⇒ x = $52 + 40 × 52/100

⇒ x = $52 + $20.8

⇒ x = $72.8

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Answer:

negative

slope= -1/4

Step-by-step explanation:

For men- P(450 < X < 650) = Φ((650 - 550) / 100) - Φ((450 - 550) / 100) = Φ(1) - Φ(-1) ≈ 0.6826. Women- P(325 < X < 475) = Φ((475 - 400) / 75) - Φ((325 - 400) / 75) = Φ(1) - Φ(-1.067) ≈ 0.7422

To answer this question, we can use the normal distribution formula and technology such as Excel or statistical software. For men, the distribution of bladder volumes is approximately normal with a mean of 550 ml and a standard deviation of 100 ml. We can calculate the probability of a man having a bladder volume between two values using the formula:

P(a < X < b) = Φ((b - μ) / σ) - Φ((a - μ) / σ)

where Φ is the standard normal cumulative distribution function, μ is the mean, and σ is the standard deviation.

For example, the probability of a man having a bladder volume between 450 and 650 ml is:

P(450 < X < 650) = Φ((650 - 550) / 100) - Φ((450 - 550) / 100) = Φ(1) - Φ(-1) ≈ 0.6826

For women, the distribution of bladder volumes is approximately normal with a mean of 400 ml and a standard deviation of 75 ml. We can use the same formula to calculate the probability of a woman having a bladder volume between two values.

For example, the probability of a woman having a bladder volume between 325 and 475 ml is:

P(325 < X < 475) = Φ((475 - 400) / 75) - Φ((325 - 400) / 75) = Φ(1) - Φ(-1.067) ≈ 0.7422

In conclusion, using the normal distribution formula and technology, we can calculate the probability of a person having a bladder volume within a certain range given the mean and standard deviation of bladder volumes in men and women.

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It is given that the point G lies on the line segment FH and divides it in the ration 5:2.

So we will use the section formula to obtain the coordinates of the point G.

Now the x-coordinate of the point G will be:-

Now the y-ccordinate of the point G will be:-

So the coordinates of the point G are (-6, 14).

Hence the correct option is (D).

The given vectors are: u = (20 + i, i, 2)v = (1 + i, 2, 41)The dot product of u and v is:u.v = (20 + i)(1 + i) + (i)(2) + (2)(41 - 1)= 20 + 20i + i + i² + 2i + 80= 101 + 22i

To find the imaginary part of u.v, we can simply extract the coefficient of i, which is 22. Hence, the imaginary part of u.v is 22. Therefore, the answer is rounded off to 22.00.

A quantity or phenomenon with two distinct properties is known as a vector. magnitude and course. The mathematical or geometrical representation of such a quantity is also referred to by this term. In nature, velocity, momentum, force, electromagnetic fields, and weight are all examples of vectors.

A movement from one point to another is described by a vector. Direction and magnitude (size) are both properties of a vector quantity. A scalar amount has just greatness. An arrow-labeled line segment can be used to represent a vector. The following describes a vector between two points A and B: A B → , or .

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Answer:

5

Step-by-step explanation:

First multiply inside of the parenthesis with 3 then add the like terms

3x + 6 - 6 = 15 ➡ 3x = 15 divide both sides with 3 and x = 5

Answer:

jonwjwjejejeken 20 ow91

Answer:
The length of the rectangle is 80 cm.

What is circumference ?
Circumference is the distance around the edge of a circle. It is the total length of the boundary of a circle. In other words, it is the perimeter of the circle.

\(C=2\pi r\)
where r is the radius of the circle

Step-by-step explanation:
Let's start by using the given information about the wire and the circle. The circumference of a circle is given by the formula:

C=2πr
where C is the circumference and r is the radius of the circle.
We are given that the circumference of the circle made by the wire is 176 cm, so we can write:

176 = 2πr

Simplifying this equation, we get:

r = 88/π

Now, when the wire is cut and made into a rectangle, the length of the wire is equal to the perimeter of the rectangle. The perimeter of a rectangle is given by the formula:

P = 2(l + b)

where P is the perimeter, l is the length, and b is the breadth of the rectangle.

We are given that the breadth of the rectangle is 8 cm, so we can write:

P = 2(l + 8)

But we also know that the length of the wire is equal to the circumference of the circle, which we found to be 176 cm. So we can write:

P = 176

Substituting this into the previous equation, we get:

176 = 2(l + 8)

Simplifying this equation, we get:

l + 8 = 88

l = 80

Therefore, the length of the rectangle is 80 cm.

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Step-by-step explanation:

Point D is the center of dilation.

If you draw lines connecting the pre image and new image corresponding vertices, they will all pass through Point D.

Answer:

A = 2 1/2 ft^2

Step-by-step explanation:

The area of a rectangle is given by

A = l*w

A = 3 * 5/6

A = 5/2 ft^2

A = 2 1/2 ft^2

Answer:

A=2.5 ft^2

Step-by-step explanation:

A=3

A=3(5/6)

A=2.5 ft^2

Agent 014 conducted a test on 103 rockets to assess the destructiveness of the government's new xy0450 missile. By assuming normality, she calculated a 94% confidence interval for the destructive force of the rockets, which was determined to be (306.71, 521.29). We are now tasked with determining the average of these 103 rockets.

In a normal distribution, the mean (average) is a central measure of the data. It represents the sum of all values divided by the total number of observations. In this case, we need to find the average of the 103 rockets tested by Agent 014.

To find the average, we sum up all the individual destructive force measurements of the rockets and divide it by the total number of rockets (103):

The average of Agent 014's 103 rockets cannot be determined precisely. It falls within the range of the confidence interval (306.71, 521.29).

Average = (Sum of Destructive Forces) / (Total Number of Rockets)

However, in this given scenario, we don't have the individual destructive force measurements of each rocket. We only have the confidence interval (306.71, 521.29). The confidence interval provides a range of values within which we can be 94% confident that the true average lies.

In this case, since the confidence interval is given, we can make a reasonable assumption that the average lies somewhere within this range. Therefore, the average of the 103 rockets tested by Agent 014 falls between 306.71 and 521.29.

However, without further information or the actual individual measurements, we cannot determine the exact average of the 103 rockets. We can only state that the average lies within the confidence interval provided.

In conclusion, based on the information given, the average of Agent 014's 103 rockets cannot be determined precisely. It falls within the range of the confidence interval (306.71, 521.29).

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Answer:

14

Step-by-step explanation:

Convert \(\frac{7}{2}\) to a fraction with a common denominator

\(\frac{7}{2} (\frac{2}{2} )=\frac{14}{4}\)

You now divide the fractions to find the amount of correct measurements needed.

\(\frac{\frac{14}{4} }{\frac{1}{4} }\) For dividing by a fraction it is the same a multiplying by its reciprocal.

This becomes \(\frac{14}{4} (\frac{4}{1} )=\frac{14}{4} (4)=14\)

You will need 14 correct measurements.

The value of the "7" in 432.0769 is 7/1000 or option A.

In the number 432.0769, the digit "7" is in the thousandths place, which means that it represents seven parts of one thousandth. The digit to the left of the thousandths place is the hundredths place, which represents one hundredth of a number. Therefore, the difference between the thousandths and hundredths place is a factor of ten, which means that the value of the digit "7" is ten times greater than the value of the digit to its right.

To put it in another way, the number 432.0769 can be broken down into its decimal representation:

4 hundreds + 3 tens + 2 ones + 0 tenths + 7 hundredths + 6 thousandths + 9 ten-thousandths

Hence the correct option is (a).

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The probability that the article will have no errors when typed by either typist is 0.03235, or about 3.24%.

To approximate the probability that an article typed by either typist will have no errors, we can use the concept of a mixed Poisson distribution.

Since the article is equally likely to be typed by either typist, we can consider the combined distribution of the two typists.

Let's denote X as the random variable representing the number of errors per article. The average number of errors per article when typed by the first typist (λ₁) is 3, and when typed by the second typist (λ₂) is 4.2.

For a Poisson distribution, the probability mass function (PMF) is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

To calculate the probability of no errors (k = 0) in the mixed Poisson distribution, we can calculate the weighted average of the two Poisson distributions:

P(X = 0) = (1/2) * P₁(X = 0) + (1/2) * P₂(X = 0)

Where P₁(X = 0) is the probability of no errors when typed by the first typist (λ₁ = 3), and P₂(X = 0) is the probability of no errors when typed by the second typist (λ₂ = 4.2).

Using the PMF formula, we can calculate the probabilities:

P₁(X = 0) = (e^(-3) * 3^0) / 0! = e^(-3) ≈ 0.0498

P₂(X = 0) = (e^(-4.2) * 4.2^0) / 0! = e^(-4.2) ≈ 0.0149

Substituting these values into the weighted average formula:

P(X = 0) = (1/2) * 0.0498 + (1/2) * 0.0149

        = 0.03235

Approximately, the probability that the article will have no errors when typed by either typist is 0.03235, or about 3.24%.

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Expression: 2500 + m

Just substitute m with 300 and solve like that.

2500 + 300 = 2800