The point (-5,-4)
is rotated 90
counterclockwise .

the equation of the plane that passes through the point (2, - 14) and is parallel to the vector (1, 1, 4) is given by:r.(1, 1, 4) = p.(1, 1, 4) => x + y + 4z = 2 + 14 + 4( - 2) => x + y + 4z = 6. Therefore, the equation of the required plane is x + y + 4z = 6.

Given equation of plane are:x - z = 2 ....(1)y + 4z = 2 ....(2)xy - 4z = 4 ....(3)We are supposed to find an equation of the plane that passes through the line of intersection of the planes (1) and (2) and is perpendicular to the plane (3).To find the line of intersection of the planes (1) and (2), we solve the two planes simultaneously. The solution is the line of intersection of the two planes.To find the solution, we first eliminate x by adding equations (1) and (2) to obtain:y + x + 4z = 4 ...(4)Similarly, we eliminate x from equations (1) and (3) to obtain:xy - z - 4z = 4 => y(z + 1) = z + 4 => y = \(\frac{(z + 4)}{(z + 1)}\) ...(5)Now, we eliminate y from equations (4) and (5) to get an expression for z. Substituting that value of z in any of the equations, we can obtain the corresponding values of x and y. Once we have two such points, we can write the equation of the line that passes through them. That will be the line of intersection of the planes (1) and (2).Solving equations (4) and (5), we get z = - 4 or z = 2. Putting z = - 4 in equation (5), we get y = - 2.5 and putting z = - 4 and y = - 2.5 in equation (4), we get x = 0.5. Therefore, the line of intersection of the planes (1) and (2) is (0.5, - 2.5, - 4).Similarly, putting z = 2 in equation (5), we get y = 2 and putting z = 2 and y = 2 in equation (4), we get x = - 2. Therefore, the line of intersection of the planes (1) and (2) is (- 2, 2, 2).We know that the equation of the plane that passes through a point A(x₁, y₁, z₁) and is perpendicular to a vector n = (a, b, c) is given by:a(x - x₁) + b(y - y₁) + c(z - z₁) = 0Therefore, the equation of the plane that passes through the line of intersection of the planes (1) and (2) and is perpendicular to the plane (3) is:x - 0.5y - 2z = 1 ...(6)To obtain the above equation, we first find a vector that is parallel to the line of intersection of the planes (1) and (2). For that, we take the cross-product of the normals to the planes (1) and (2) as follows:n₁ × n₂ = (1, 0, - 1) × (0, 4, 1) = (4, 1, 4)Now, we find a point on the line of intersection of the planes (1) and (2). One such point is (0.5, - 2.5, - 4).Therefore, the required plane is 4x + y + 4z = 14.Therefore, we found the required equation of the plane. The equation of the plane is x + y + 4z = 6.

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Based on the information provided regarding same as cash loans, Chelsea won't be charged interest for the first 6 months of the loan, nor will she have to make payments for the first 6 months. (Option D)

A Same-As-Cash Loan refers to a short-term lending solution in which no interest or monthly payment are required to be paid during a set “Same-As-Cash” period. At the end of a predetermined period, the loan is paid off. Hence, the customer owes no interest or monthly payments during a set promotional period and pays the same amount on the loan as they would have paid up front with cash. These are interest deferred loans in which the loans interest still accrues during that promotional period, however if the customer pays off the entire principal balance before the period ends, they are not required to pay that interest. The advantage of these loans is that customers may spend the same amount they would have if they had paid with cash up front. Hence, if Chelsea opts for loan that offered 6 months, same as cash, there would be no requirement of payment or interest charged for the 6 months.

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The length of side LJ is equal to 11.48 units.

In Mathematics and Geometry, two (2) triangles are only similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Based on the diagram, we can logically deduce the following proportion based on the congruent sides:

XY/JK = YZ/KL = ZX/LJ

8.7/12.18 = 8.2/LJ = 7.8/KL

By cross-multiplying and solving for the length of side LJ, we have the following:

LJ = (12.18 × 8.2)/8.7

LJ = 11.48 units.

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Step-by-step explanation:

bacteria also have small, closed-circle of DNA called plasma and present in their cytoplasm .

Answer:

200g oats

0.96l milk

72g sugar

Step-by-step explanation:

250/5 * 4 = 50 *4 = 200g oats

1.2/5 * 4 = 0.96l milk

90/5 * 4= 18*4 = 72g sugar

Answer:

soy español y no hablo ingles

Answer:

B. Y2-Y1/X2-X1. This would equal -13/-8, which cancels out to positive.

Step-by-step explanation:

The fraction of Carlos sold 1/9 of the advertisements.

Let's start by assigning a variable to represent the number of advertisements Carlos sold. We can call this variable "C".

According to the problem:

Mary sold twice as many advertisements as Carlos, which means Mary sold 2C advertisements.

James sold 3 times as many advertisements as Mary, which means James sold \(3(2C) = 6C\) advertisements.

The total number of advertisements sold is the sum of what each person sold:

Total = Mary + James + Carlos

Total = \(2C + 6C + C\)

Total = 9C

We can see that the total number of advertisements sold is 9 times the number that Carlos sold.

To find the fraction of advertisements that Carlos sold, we can divide the number of advertisements that Carlos sold by the total number of advertisements:

Fraction sold by Carlos = C/Total

Fraction sold by Carlos = \(C/(9C)\)

Fraction sold by Carlos = \(1/9\)

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The solution to the linear system is unique solution which is  x₁ = 1/6, x₂ = 3/2, and x₃ = 17/6.

The correct answer is option  A.

To solve the given system of linear equations using elementary row operations and back substitution, let's start by representing the augmented coefficient matrix:

[1  -4  5  |  23]

[2   1   1  |  10]

[-3  2  -3 |  -23]

We'll apply row operations to transform this matrix into echelon form:

1. Multiply Row 2 by -2 and add it to Row 1:

[1  -4   5   |  23]

[0   9   -9  |  -6]

[-3  2  -3  |  -23]

2. Multiply Row 3 by 3 and add it to Row 1:

[1  -4  5   |  23]

[0   9  -9  |  -6]

[0   -10 6  |  -68]

3. Multiply Row 2 by 10/9:

[1  -4  5    |  23]

[0   1   -1   |  -2/3]

[0   -10 6  |  -68]

4. Multiply Row 2 by 4 and add it to Row 1:

[1  0   1   |  5/3]

[0  1   -1  |  -2/3]

[0  -10 6  |  -68]

5. Multiply Row 2 by 10 and add it to Row 3:

[1  0   1   |  5/3]

[0  1   -1  |  -2/3]

[0  0   -4  |  -34/3]

Now, we have the augmented coefficient matrix in echelon form. Let's solve the system using back substitution:

From Row 3, we can deduce that -4x₃ = -34/3, which simplifies to x₃ = 34/12 = 17/6.

From Row 2, we can substitute the value of x₃ and find that x₂ - x₃ = -2/3, which becomes x₂ - (17/6) = -2/3. Simplifying, we get x₂ = 17/6 - 2/3 = 9/6 = 3/2.

From Row 1, we can substitute the values of x₂ and x₃ and find that x₁ + x₂ = 5/3, which becomes x₁ + 3/2 = 5/3. Simplifying, we get x₁ = 5/3 - 3/2 = 10/6 - 9/6 = 1/6.

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a. The degrees of freedom (df) value for inference about the slope β​ is calculated as the total number of observations minus the number of predictors (excluding the intercept term).

Since the regression analysis has 9 observations, and assuming there is only one predictor (X variable), the df value would be 9 - 1 = 8.

b. To find the t-test statistic values that would give a​ P-value of 0.01 for testing H0​: β=0 against Ha​: β ≠​0, you can use t-distribution tables or statistical software.

Since we are conducting a two-tailed test with a desired significance level of 0.01, we need to find the critical t-values that divide the upper and lower tails, each containing 0.005 (0.01/2) probability.

Using a t-distribution table with 8 degrees of freedom, the critical t-value for a two-tailed test at a significance level of 0.01 is approximately ±3.355.

Therefore, the two t-test statistic values that would give a P-value of 0.01 for testing H0​: β=0 against Ha​: β ≠​0 are -3.355 and 3.355.

c. To find the t-score that should be multiplied by the standard error to calculate the margin of error for a 99% confidence interval for β​, we need to determine the critical value from the t-distribution.

Since we want a 99% confidence interval, we are looking for a critical value that leaves 0.005 probability in the upper tail of the t-distribution (0.01/2).

Using a t-distribution table with 8 degrees of freedom, the critical t-value for a 99% confidence interval is approximately 2.896. Therefore, you would multiply the standard error by 2.896 to find the margin of error for the 99% confidence interval for β​.

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The p-value (0.0251) is greater than the significance level (0.02), we fail to reject the null hypothesis. There is not sufficient evidence at the 0.02 level to dispute the company's claim.

To determine if there is sufficient evidence to dispute the company's claim, we can set up the following hypotheses:

Null hypothesis (H₀): The proportion of chips that fail in the first 1000 hours is equal to 49%.

Alternative hypothesis (H₁): The proportion of chips that fail in the first 1000 hours is not equal to 49%.

In symbols:

H₀: p = 0.49

H₁: p ≠ 0.49

Where:

p represents the true proportion of chips that fail in the first 1000 hours.

The significance level is given as 0.02, which means we want to test the hypotheses at a 2% level of significance.

Now, let's perform a hypothesis test using the provided sample data.

Given that the sample size is 1300 and the proportion of chips that fail in the first 1000 hours is found to be 46%, we can calculate the test statistic and p-value using the binomial distribution.

The test statistic follows an approximate standard normal distribution when the sample size is large. To calculate the test statistic, we need to compute the standard error (SE) of the sample proportion:

SE = √((p * (1 - p)) / n)

where n is the sample size.

SE = √((0.49 * (1 - 0.49)) / 1300)

≈ 0.0134

We can now calculate the test statistic (Z-score):

Z = (p sample - p) / SE

where p sample is the sample proportion and p is the proportion specified in the null hypothesis.

Z = (0.46 - 0.49) / 0.0134

≈ -2.2388

Using the standard normal distribution table or a statistical calculator, we find that the p-value corresponding to Z = -2.2388 is approximately 0.0251 (two-tailed test).

Since the p-value (0.0251) is greater than the significance level (0.02), we fail to reject the null hypothesis. There is not sufficient evidence at the 0.02 level to dispute the company's claim.

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The complete question is:

A sample of 1300 computer chips revealed that 46% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that 49% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to dispute the company's claim? State the null and alternative hypotheses for the above scenario.

Answer:

the answer is 80

Given:

defective units = 29.1

total production = 9,700

Hence:

substituting values in the formula:

ANSWER

0.3 percent of the production is defective.

The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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B.)

Step-by-step explanation:

area of a 10 inch pizza: A=pi * r^2 = 25 pi

area of a 14 inch pizza : A= 49 pi

the change : 49pi - 25pi = 24 pi or about 75.39822

We are given a right-angled triangle.

Recall that the Pythagorean theorem is given by

Where a and b are the shorter sides and c is the longest side.

For the given case, one shorter side (12) and the longest side (13) is given

Let us find the other shorter side (x)

Therefore, the third side x is 5

Answer:

\(p = (5) \times 4 + 2 \times (5) \times 3 + 8 \times (5) - 3 \\ p = 87\)

The annual interest rate on her purchase will be 3%.

Simple interest is a method of calculating the amount of interest charged on a sum at a given rate and over a specified time period.

In contrast to compound interest, where we add the interest of the previous year's principal to calculate the interest of the next year, the principal amount in simple interest is always the same.

Given that Ella borrows $18,000 to buy a new car. She will pay $3,240 in simple interest at the end of 6 years.

The annual interest rate will be calculated as:-

SI = ( P x R x T ) / 100

3240 = ( 18000 x R x 6 ) / 100

3240000 / 18000 = R x 6

R = 3%

Therefore, the interest rate will be 3%.

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Monday's Z score of 2.5 is greater than 2.00, it indicates that Monday's sales were higher than average.

To find Monday's Z score, we can use the formula:

Z = (X - μ) / σ

Where:

X = Monday's sales ($33250)

μ = Mean daily sales ($29500)

σ = Standard deviation of sales ($1500)

Substituting the values into the formula, we get:

Z = (33250 - 29500) / 1500

Z = 3750 / 1500

Z = 2.5

Monday's Z score is 2.5.

To determine if Monday was an unusually good day, we need to compare the Z score to the threshold of -2.00 and 2.00 for unusual scores.

Since Monday's Z score of 2.5 is greater than 2.00, it indicates that Monday's sales were higher than average, but it does not fall into the range considered unusually good.

Therefore, Monday's sales were above average but not unusually good according to the Z score criterion.

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9514 1404 393

Answer:

  (a)  -2

Step-by-step explanation:

Put -1 where x is and do the arithmetic.

  f(x) = x³ +2x² -3

  f(-1) = (-1)³ +2(-1)² -3

  f(-1) = -1 +2 -3 = 1 -3

  f(-1) = -2

The given series, represented by the expression 6^(-5)/9^x, is convergent for all values of x. The series is convergent from x = -∞ (left end included) to x = +∞ (right end included).

To determine the convergence of the series, we examine the behavior of the terms 6^(-5) and 9^x. The term 6^(-5) is a constant value, and since it is a positive constant, it does not affect the convergence of the series. The term 9^x represents an exponential function with a positive base (9). When x approaches positive or negative infinity, the value of 9^x either increases without bound or decreases without bound, respectively.

In this case, regardless of the value of x, the series 6^(-5)/9^x will always involve dividing a positive constant by a positive term that approaches infinity or zero as x approaches positive or negative infinity, respectively. The division of a positive constant by a term approaching infinity or zero will result in a convergent series.

Therefore, the given series is convergent for all values of x, and it converges from x = -∞ (left end included) to x = +∞ (right end included).

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The solution of the linear equation in one variable 4y - 6 = 2y + 8 is at y = 7.

According to the given question.

We have a linear equation in one variable.

4y - 6 = 2y + 8

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the linear equation in one variable 4y - 6 = 2y + 8 is given by

4y - 6 = 2y + 8

⇒ 4y - 2y - 6 = 8     ( subtracting 2y from both the sides)

⇒ 2y -6 -8 = 0           (subtracting 8 from both the sides)

⇒ 2y - 14 = 0

⇒ 2y = 14

⇒ y = 14/2

⇒ y = 7

Hence, the solution of the linear equation in one variable 4y - 6 = 2y + 8 is at y = 7.

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Converting 7π/21 to degrees will be 60°.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

A plane angle is measured in degrees, with the letter ° typically used to indicate that one full rotation is equal to 360 degrees. Although it is not a SI unit—the radian is the SI unit of angular measure—it is mentioned as an accepted unit in the SI brochure.

Angles are measured in terms of radians. Angles are measured using the degree and radian units. In calculus and the majority of other branches of mathematics, angles are typically or generally measured in radians.

It should be noted that in order to convert radians yo degrees, you've to multiply by 180/π since a full circle is 360°.

This will be illustrated as:

= 7π / 21 × 180 / π

= 7/21 × 180

= 60°

The value is 60°.

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Answer:

11:27 am.

Step-by-step explanation:

The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked

1.25 * 4.8

= 6 km.

So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes

= 0.6 hrs.

So, Tom's speed is 6/0.6 = 10 km/hr.

,

and Tom will take 18/10 = 1.8 hours to finish the route,

= 1 hr 48 minutes

So he finishes the route at

9:39 + 1:48

= 11:27 am.

Answer:

Up left, down right

Step-by-step explanation:

First, polynomials with odd degrees will have end behaviors in two different directions.

Since the leading coefficient is negative, the end behavior will be up left and down right.

So, the end behavior is up left, down right.

The end behavior of a 9th-degree polynomial with negative leading coefficients is up left, downright.

We have to determine

The end behavior of a 9th-degree polynomial with a negative leading coefficient??

If the leading coefficient is negative and the exponent of the leading term is even, the graph falls to the left and right.

The equation of the 9th-degree polynomial is;

\(\rm x^9+3x^8+4x^7+x^6+x^5+9x^3+2x^2+x+1=0\)

The degree of the polynomial is 9 which is odd.

Hence, the end behavior of a 9th-degree polynomial with negative leading coefficients is up left, downright.

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Answer: the answer is 72

Step-by-step explanation:

if 50% of a number is 120 then that means its only half of that number so to find out the whole number multiply 120 by 2 which gives you the answer of 240

Now we need to determine 30% of 240 and the procedure explaining it as such

Step 1: In the given case Output Value is 240.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 240 = 100%.

Step 4: In the Same way, x = 30%.

Step 5: On dividing the pair of simple equations we got the equation as under

240 = 100% (1).

x = 30% (2).

(240%)/(x%) = 100/30

Step 6: Reciprocal of both the sides results in the following equation

x%/240% = 30/100

Step 7: Simplifying the above obtained equation further will tell what is 30% of 240

x = 72%

Therefore, 30% of 240 is 72

I hope this helps

Answer:

  72

Step-by-step explanation:

You want 30% of a number, given that 50% of it is 120, and 80% of it is 192.

The 30% you want will be the difference between 80% and 50%:

  80% -50% = 30%

  192 -120 = 72

30% of the same number is 72.

Answer:

<BYX = 74 degrees

Step-by-step explanation:

The sum of angles of the adjacent sides of the trapezoid is 180 degrees

Given

<A = 106 degrees

<A + <BYX = 180

106 + <BYX = 180

<BYX = 180-106

<BYX = 74 degrees

Answer:

1.55

Step-by-step explanation:

3.19 + 2.39 = 5.58

5.58 / 3.6 = 1.55