use matrices to rotate the vector v= <-4,1> by 270°. Write the resulting vector in component form. Equation editor does not include the grouping symbols “<“ and “>” that are necessary for writing a vector in component form. For this question use braces to write a vector in component form for example the vector <2,3> should be written as {2,3}.

The probability that the average of 35 randomly selected numbers will be more than 7.77 is approximately 0.2157.

a. The distribution of X is uniform, meaning each number from 4 to 11 has an equal probability of being selected. The probability of selecting any specific number is 1/8 since there are 8 numbers in the range.

b. If the computer randomly picks 35 numbers, the distribution of the selection can be approximated by a normal distribution. This is known as the Central Limit Theorem. The mean of the distribution will still be the same as in part a, which is (4 + 11) / 2 = 7.5. The standard deviation of the distribution can be calculated using the formula:

Standard deviation = (b - a) / √(12)

where a and b are the lower and upper bounds of the range, respectively. In this case, a = 4 and b = 11.

Standard deviation = (11 - 4) / √(12) ≈ 1.6794

Therefore, the distribution of the selection of 35 numbers can be approximated by a normal distribution with a mean of 7.5 and a standard deviation of 1.6794.

c. To find the probability that the average of 35 numbers will be more than 7.77, we need to calculate the z-score and then use the standard normal distribution table.

z-score = (7.77 - 7.5) / (1.6794 / √35) ≈ 0.7832

Using the standard normal distribution table or a calculator, we can find the probability associated with the z-score of 0.7832. Let's assume it is P(Z > 0.7832).

The probability that the average of 35 numbers will be more than 7.77 can be calculated as:

P(Z > 0.7832) = 1 - P(Z < 0.7832)

Referencing the standard normal distribution table or using a calculator, we find the probability to be approximately 0.2157.

Therefore, the probability that the average of 35 numbers will be more than 7.77 is approximately 0.2157 (rounded to 4 decimal places).

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Angle A is 19 degrees.

Angle C is 90 degrees.

Side a is approximately 7.83.

Side c is approximately 34.50.

To solve the right triangle given that B = 71 degrees and b = 24, we can use the trigonometric ratios sine, cosine, and tangent.

Finding Angle A:

Angle A is the complementary angle to B in a right triangle, so we can calculate it using the equation:

A = 90 - B

Substituting the given value, we have:

A = 90 - 71

A = 19 degrees

Therefore, Angle A is 19 degrees.

Finding Angle C:

Since it is a right triangle, Angle C is always 90 degrees.

Therefore, Angle C is 90 degrees.

Finding Side a:

We can use the sine ratio to find the length of side a:

sin(A) = a / b

Rearranging the equation to solve for a, we have:

a = b * sin(A)

Substituting the given values, we have:

a = 24 * sin(19)

a ≈ 7.83

Therefore, the length of side a is approximately 7.83.

Finding Side c:

Using the Pythagorean theorem, we can find the length of side c:

c^2 = a^2 + b^2

Substituting the given values, we have:

c^2 = 7.83^2 + 24^2

c^2 ≈ 613.68 + 576

c^2 ≈ 1189.68

Taking the square root of both sides to solve for c, we have:

c ≈ √1189.68

c ≈ 34.50

Therefore, the length of side c is approximately 34.50.

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Answer:

1720

Step-by-step explanation:

Move decimal 3 places to the right

Answer: D. DE/DF

Step-by-step explanation: I got it right on edg...

The angle of Sonny's line of sight to both Sam and Sal, we can use the Law of Cosines. The angle of Sonny's line of sight to both Sam and Sal is approximately 77 degrees (rounded to the nearest degree).

Let's consider the triangle formed by Sam, Sonny, and Sal. Let's label the sides of the triangle:

The side opposite Sam as side a (distance between Sonny and Sal)

The side opposite Sonny as side b (distance between Sam and Sal)

The side opposite Sal as side c (distance between Sam and Sonny)

According to the Law of Cosines, we have the formula:

c^2 = a^2 + b^2 - 2ab * cos(C)

Where C is the angle opposite side c.

We want to find angle C, which is the angle of Sonny's line of sight to both Sam and Sal.

Plugging in the given distances:

c = 175 ft

a = 201 ft

b = 153 ft

Using the Law of Cosines:

175^2 = 201^2 + 153^2 - 2 * 201 * 153 * cos(C)

Simplifying and solving for cos(C):

cos(C) = (201^2 + 153^2 - 175^2) / (2 * 201 * 153)

cos(C) = 0.228

To find the angle C, we can take the inverse cosine (cos^-1) of 0.228:

C ≈ cos^-1(0.228) ≈ 77.08 degrees

Therefore, the angle of Sonny's line of sight to both Sam and Sal is approximately 77 degrees (rounded to the nearest degree).

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Answer:

14.5

Step-by-step explanation:

23.78 ÷ 1.64 = 14.5 meaning she bought 14.5 gallons of gas

Answer:

14.5

Step-by-step explanation:

If Elaine spent $1.64 per gallon for 14.5 gallons; she would have paid $23.78 for gas.

$23.78 ÷ $1.64 = 14.5

$1.64 • 14.5 = $23.78

I hope this helps

Answer:

Question 1 : The answer is 143.3 miles

Question 2 : The answer is 120 minutes

Step-by-step explanation:

1.Based on the give conditions:

\(43 \times 90 \div 27 \\ calculate \frac{43 \times 90}{27} = \frac{430}{3} \)\( = 143.3\)

2. 90 miles = 75min

143.3 ÷ 90 = 1.6

75 × 1.6 = 120

so the answer is 120 min

Answer:

7.

Step-by-step explanation:

21 = 3 * 7

28 = 2 * 2 * 7

42 = 2 * 3 * 7

Collecting common factors:

t is common to all 3 sets of factors so

HCF = 7.

The transformations are applied in the following order: horizontal translation, horizontal scaling, vertical reflection, and vertical scaling.

The transformations are applied in the following order:

Horizontal translation: The function is shifted 9 units to the right by subtracting 9 from the input variable x.

f(x) → f(x - 9)

Horizontal scaling: The function is compressed horizontally by a factor of 1/3 by dividing the input variable x by 3.

f(x - 9) → f(1/3(x - 9))

Vertical reflection: The function is reflected about the x-axis by multiplying the output values of f by -1.

f(1/3(x - 9)) → -f(1/3(x - 9))

Vertical scaling: The function is stretched vertically by a factor of 8 by multiplying the output values by 8.

-f(1/3(x - 9)) → -8f(1/3(x - 9))

Therefore, the transformations are applied in the following order: horizontal translation, horizontal scaling, vertical reflection, and vertical scaling.

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The probability of flipping a heads on the coin and rolling a 5 on the die is 1/12 if a coin is flipped and die is rolled once.

The sample space for the coin toss is  {H,T}, so there are two possible outcomes. The favorable one is  H.

The probability of flipping a heads on the coin is equal to 1/2.

Die has six faces, meaning six possible outcomes, but we’re only interested in one of those outcomes: that roll of a 5. That means that only 1 in 6 outcomes is desirable and we can write it as  1/6

The probability of rolling a 5 on the die is equal to 1/6.

Since a coin is flipped and die is rolled independently, the joint probability is a product of above probabilities.

Therefore, the probability of flipping a heads on the coin and rolling a 5 on the die equals

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

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Answer:

Given

Distribution

Addition

Division

The function with the given derivative \(f'(x) = e^{5x}\) and passes through the point P can be found by integrating the derivative. The resulting function will have the form \(f(x) = (1/5)e^{5x} + C\), where C is a constant determined by the point P.  

To find the function f(x) that has a derivative \(f'(x) = e^{5x}\)and passes through the point\(P(x_0, y_0),\) we can integrate the derivative with respect to x.

Integrating \(e^{5x}\) with respect to x gives us \((1/5)e^{5x} + C\), where C is the constant of integration.

Since the function passes through the point \(P(x_0, y_0)\), we can substitute the coordinates of P into the function to find the value of C. This gives us the equation\(y_0 = (1/5)e^{5x_0} + C.\)

Solving for C, we have \(C = y_0 - (1/5)e^{5x_0}\).

Substituting this value of C back into the integrated function, we obtain the final expression for f(x) as \(f(x) = (1/5)e^{5x} + (y_0 - (1/5)e^{5x_0}).\)

Therefore, the function that has the derivative\(f'(x) = e^{5x}\)and passes through the point \(P(x_0, y_0) is f(x) = (1/5)e^{5x} + (y_0 - (1/5)e^{5x_0})\).

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Answer:

(5, 7) or x = 5 and y = 7

Step-by-step explanation:

Since we are given y, we can use the substitution method and substitute x+2 into y since they are equal. With this, you would have 5x - 4(x+2) = -3. You can distribute the -4 into x and 2 to get 5x - 4x - 8 = -3.

We can simplify 5x-4x to get x and get x - 8 = -3. Afterwards we can add 8 to both sides to get x = 5. We can now replug x into the first equation to get y = 5 + 2. Simplified, y = 7.

So the answer would be (5, 7) or x = 5 and y = 7.

Brainliest would be appreciated!

The correct simplified expression is \(\rm 28x^3-33x^2-33x+18\).

Given

Polynomial; \(\rm (7x - 3)(4x^2 -3x - 6)\)

Multiplication is the process of calculating the product of two or more numbers. The multiplication of numbers say, ‘a’ and ‘b’, is stated as ‘a’ multiplied by ‘b’.

Then,

The correct simplification of the expression is;

\(\rm \rm (7x - 3)\times (4x^2 -3x - 6)\\\\7x(4x^2 -3x - 6)-3(4x^2 -3x - 6)\\\\ 28x^3-21x^2-42x-12x^2+9x+18\\\\28x^3-33x^2-33x+18\)

Hence, the correct simplified expression is \(\rm 28x^3-33x^2-33x+18\).

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Answer: 18/1

Step-by-step explanation:

13 + 4 = 17

1/4 + 3/4 = 1

17 + 1 = 18

Answer:

18

Step-by-step explanation:

13 1/4= 13.25 and 4 3/4=4.75. 13.25+4.75=18

Hope this helped!

Answer:

John sold 8 funnel cakes in 1 hour

Step-by-step explanation:

Hope I helped

Answer:

An average of 8 funnel cakes an hour

Step-by-step explanation:

40/5=8 but we don't know if he sold the same amount every hour.

Answer:

(2x-1)

Step-by-step explanation:

\(Volume\ of\ the\ tank\ = 12x^3+20x^2-x-6\\Length\ of\ the\ tank\ = 3x+2\\Breadth\ of\ the\ tank\ = 2x+3\\Height\ of\ the\ tank\ = h\\We\ know\ that\ volume\ of\ a\ cuboid\ = lbh\\Hence, h= Volume / lb\\Here,\\Height\ of\ the\ tank= \frac{(12x^3+20x^2-x-6)}{(3x+2)(2x+3)} \\By\ factorising\ the\ volume\ through\ synthetic\ division\, \\we get,\\(12x^3+20x^2-x-6)= (3x+2)(2x+3)(2x-1)\\Hence, height= (2x-1)\)

Answer:

direct variation

Step-by-step explanation:

The constant of variation k for direct variation is

k = \(\frac{y}{x}\)

Calculate this ratio for each set of points

\(\frac{-10}{2}\) = \(\frac{-20}{4}\) = \(\frac{-35}{7}\) = \(\frac{-40}{8}\) = - 5

Then ordered pairs are in direct variation with k = - 5

The constant of variation for inverse variation is

k = xy

2 × - 10 = - 20

4 × - 20 = - 80

7 × - 35 = - 245

8 × - 40 = - 320

There is no constant thus not inverse variation

Answer:

9.47

Rounded to the nearest 0.01 or

the Hundredths Place.

Explanation

9.4725

You rounded to the nearest hundredths place. The 7 in the hundredths place rounds down to 7, or stays the same, because the digit to the right in the thousandths place is 2.

9.47

When the digit to the right is less than 5 we round toward 0.

9.4725 was rounded down toward zero to 9.47

Hope this helps!

The correct symbol used for a column alias containing spaces is C. " " (quotation marks).

In SQL, when we want to assign a column alias containing spaces, we enclose the alias within double quotation marks. This is done to differentiate the alias from other SQL keywords or to handle cases where the alias includes special characters, spaces, or is case-sensitive.

For example, consider the following SQL query:

SELECT column_name AS "Column Alias"

FROM table_name;

In this query, we are selecting a column named "column_name" from the table "table_name" and assigning it the alias "Column Alias" containing spaces. By enclosing the alias within double quotation marks, we indicate to the database that it should treat the entire string as a single identifier or alias.

Using other symbols such as '', ||, or // will not achieve the desired result of creating an alias with spaces. These symbols have different meanings in SQL.

'' (two single quotation marks) typically represents an empty string or a string literal in SQL.

|| (double vertical bars) is the concatenation operator in some SQL dialects, used to combine strings or values.

// (double forward slashes) is commonly used for comments in various programming languages and does not have any special meaning for column aliases in SQL.

Therefore, the correct symbol to use for a column alias containing spaces is C. " " (quotation marks).

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Answer:

easy bro go and use m-a-t-h w-a-y

Step-by-step explanation:

it's going to help

1) The value of x is 30 degree.

2) The value of x is 32.5 degree.

A triangle's opposite angles are also congruent if its two sides are.

Given:

Using Base Angle Theorem

Two Angles are 35 and 35.

Using Angle Sum Property

3x+ 20 +35+ 35 = 180

3x+ 90 = 180

3x = 90

x= 30

Again Using Base Angle Theorem

let the Angles in left triangle are 50, y and y

Using Angle Sum Property

50+ 2y= 180

2y= 130

y= 65

Again Using Angle Sum Property  in Big Triangle

50+x + 65 + x = 180

2x = 65

x= 32.5  degree

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Answer:

2/12

Step-by-step explanation:

There is a 1/6 chance of rolling a 3 once because there are six sides and only one 3, double that ratio if your want the probability of rolling that same number twice in a row.

Answer:

7542 by the end of the sec week

Answer:

3d-24=3d, no solutions

Step-by-step explanation:

Answer: no solution

Step-by-step explanation:

3(d-8)=3d

3d-24=3d (Distributive property)

-24=0 (subtracted 3d from both sides)

-24 does not = 0, so no solution

Answer:

85.8 in2

32.9 in2

131.6 in2

65.8 in2

By the De Moivre's formula, the complex numbers i⁷¹, i⁴⁷, i¹⁹ are equivalent to - i.

In this question we have eight cases of powers of complex numbers, of which we must determine what cases are equivalent to the complex number - i. This can be checked by means of De Moivre's formula:

zⁿ = rⁿ · (cos nx + i sin nx)

Where:

Please notice that nx must be in radians.

If we know that r = 1, cos nx = 0, sin nx = - 1 and x = π / 2, then we find that:

The complex numbers i⁷¹, i⁴⁷, i¹⁹ are equivalent to - i.

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probability that Regina plays tennis and/or basketball during her 8th grade year at Redland Municipal Middle School, we first need to know the total number of sports offered and the number of students participating in each sport. However, based on the information provided in your question, we do not have sufficient data to determine the probability.

In general, to determine the probability, we would follow these steps:

1. Determine the total number of sports offered at the school (let's call this S).
2. Find out the number of students participating in tennis (T) and basketball (B).
3. Calculate the probability of Regina playing tennis (P_T) by dividing T by S.

4. Calculate the probability of Regina playing basketball (P_B) by dividing B by S.
5. Use the formula P(T or B) = P_T + P_B - P(T and B) to calculate the probability that Regina plays tennis and/or basketball. Here, P(T and B) is the probability of her playing both sports.

Without the specific numbers, we cannot provide a precise probability. Please provide more details about the sports and participation at Redland Municipal Middle School to help us calculate the probability accurately.

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Answer:

k = 42

Step-by-step explanation:

These are complementary angles so they add to 90°

90 = 47 + (k + 1)

90 - 47 = k + 1

43 = k + 1

k = 42

An equation that can be used to determine the number of hours, h, that Moira needs to read to finish the book is h + 178 = 214.

In order to write an equation that model this situation, we would assign a variable to the number of hours that is needed to read to finish the book and the total number of hours respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that she read for 178 hours yesterday as follows;

h + 178 = T

Substituting the given parameters into the algebraic equation, we have the following;

h + 178 = 214

Solving for h, we have the following;

h = 214 - 178

h = 36 hours.

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