Convert the rectangular coordinates to polar coordinates with
r > 0 and 0 ≤ < 2.

a. The value of k from augmented matrix \(\left(\begin{array}{ccc}3&- 5&k\\- 9&15&3\end{array}\right)\) is - 1.

b. The value of k from augmented matrix \(\left(\begin{array}{ccc}k&1&- 6\\5&- 1&6\end{array}\right)\) is - 5.

The complete question is in the attachment. The augmented matrix is a consistent linear system if

a. The augmented matrix \(\left(\begin{array}{ccc}3&- 5&k\\- 9&15&3\end{array}\right)\)

Making the second row become zero R₂ = R₂ + 3R₁

\(\left(\begin{array}{ccc}3&- 5&k\\- 9 \:+\: (3 \times 3)&15 \:+\: (3 \times - 5)&3 \:+\: (3 \times k)\end{array}\right)\)

\(\left(\begin{array}{ccc}3&- 5&k\\- 9 \:+\: 9&15 \:+\: (- 15)&3 \:+\: 3k\end{array}\right)\)

\(\left(\begin{array}{ccc}3&- 5&k\\0&0&3 \:+\: 3k\end{array}\right)\)

From the second row

0x + 0y = 3 + 3k

For the system to be consistent, then

3 + 3k = 0

3k = - 3

k = - 3/3

k = - 1

b. The augmented matrix \(\left(\begin{array}{ccc}k&1&- 6\\5&- 1&6\end{array}\right)\)

Making the second row become zero R₂ = R₂ + R₁

\(\left(\begin{array}{ccc}k&1&- 6\\5 \:+\: k&- 1 \:+\: 1&6 \:+\: (- 6)\end{array}\right)\)

\(\left(\begin{array}{ccc}k&1&- 6\\k \:+\: 5&0&0\end{array}\right)\)

From the second row

(k + 5)x + 0y = 0

For the system to be consistent, then

k + 5 = 0

k = - 5

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Answer:

D. 12

Step-by-step explanation:

93/3 = 31

155/5 = 31

248/8 = 31

In every case, you see that the number of pages is 31 times the number of hours.

For 372 pages, the number of hours is 372/31 = 12

Check: 372/12 = 31

Answer: D. 12

Answer:

hsjsm

Step-by-step explanation:

mmssdn jnhbxjs ẹnienbsd  sywb

Answer:

For the functions to coincide, the value of k in y = (kx)3 must be smaller than in y = kx3. This is because the value of y changes more rapidly when k is cubed inside the parentheses. The behavior of the functions is similar since a vertical stretch is similar to a horizontal compression.

Step-by-step explanation:

PLATO

Answer:

40 degrees

Step-by-step explanation:

It is a vertical angle so because the right side is 40 degrees it is the same on the left side. The measure of Angle 1 is 40 degrees.

Answer:

the correct answer is 4

The equivalent expressions are (b) (7 * 7)^x , (c) 7^x * 7^x and (e) 7^(2x)

The expression is given as:

49^x

Express 49 as 7 * 7

(7 * 7)^x ---- option (b)

Express 7 * 7 as an exponent

7^(2x) ---- option (e)

Express 2x as x + x

7^(x +x)

Expand

7^x * 7^x --- option (c)

Hence, the equivalent expressions are (b), (c) and (e)

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Answer:

Step-by-step explanation:

3/5x+30=150

We move all terms to the left:

3/5x+30-(150)=0

Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R

We add all the numbers together, and all the variables

3/5x-120=0

We multiply all the terms by the denominator

-120*5x+3=0

Wy multiply elements

-600x+3=0

We move all terms containing x to the left, all other terms to the right

-600x=-3

x=-3/-600

x=1/200

The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%

The percentage of a data set is when part of the data is represented per 100 with a symbol of %.

It was stated in the question that 80% of Americans report being afflicted by stress.

Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.

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Answer:

Yes! Extrapolation is fine. Don't worry about it.

Step-by-step explanation:

Because the data we have ranges from 8 to 22 inches, an extrapolation should be made, which is the process of estimating beyond the original observation interval, the value of the variable based on its relationship to another variable. It is similar to interpolation, which produces estimates between known observations, unlike this, extrapolation is subject to greater uncertainty and a higher risk of producing insignificant results, but because the value is 24 inches, it is not too far away. of the upper limit which is 22, the error should not be very big, therefore the answer is: Yes! Extrapolation is fine. Don't worry about it.

Answer:

1529

Step-by-step explanation:

203*12

2436-903

1529

Answer:

1529 stickers left

Step-by-step explanation:

203 × 12 = 2436

2436 - 907 = 1529

By factor decomposition, area of a square and power and root properties, the length of the side is between 72 yards and 76 yards. (Correct choice: B)

The area of a triangle is equal to the square of its side length and the area of land is a composite number, that is, a product of prime numbers. By factor decomposition, the equivalent form of 5,280 square yards is:

5,280 = 2⁵ × 3 × 5 × 11

Then, the equivalent side is equal to the square product of the product:

x = √(2⁵ × 3 × 5 × 11)

x = √(2⁴) × √(2 × 3 × 5 × 11)

x = 2² × √(2 × 3 × 5 × 11)

x = 4√330

As for √330 is between √324 = 18 and √361 = 19, then the length of the side is between 72 yards and 76 yards.

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The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

The sum of the interior angle measures of a regular hexagon is 720°.

Step-by-step explanation:

To find the sum of the interior angle measures of a regular hexagon, we can use the fact that any polygon can be divided into triangles. The formula to find the sum of the interior angles of any polygon with n sides is:

Sum of interior angles = (n - 2) × 180°

In the case of a hexagon, n = 6. So, we can plug this value into the formula:

Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

To explain this using triangles, let's divide the hexagon into triangles. A hexagon can be divided into four triangles by drawing three diagonals from one vertex to the three non-adjacent vertices. Since the sum of the interior angles of each triangle is 180°, and we have four triangles:

Sum of interior angles of hexagon = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

Answer:

Step-by-step explanation:

Answer:

The  probability is  \(P(12.7 < x < 16.8 ) = 0.45\)

Step-by-step explanation:

From the question we are told that

The completion times for a job task range from 10.1 minutes to 19.2 minutes

Generally given that the completion times is uniformly distributed then  the probability that it will require between 12.7 and 16.8 minutes is mathematically represented as

         \(P(12.7 < x < 16.8 ) = \frac{ 16.8 - 12.7}{ 19.2 - 10.1 }\)

          \(P(12.7 < x < 16.8 ) = 0.45\)

Answer:

A

Step-by-step explanation:

Answer:

209952=Area

56=Perimeter

Step-by-step explanation:

3*3*2*2*9*9*6*12=Area

3+3+2+2+9+9+6+12=Perimeter

After solving the quadratic equation, the roots are (x - 2) and (x + 7).

To determine values for various parameters, quadratic functions are employed in a variety of engineering and scientific disciplines. A parabola is used to graphically illustrate them.

The direction of the curve is determined by the highest degree coefficient. Quadratic is a derivative of the term quad, which signifies square.

As per the given equation in the question,

x² + 5x - 14 = 0

b² - 4ac

5² - 4(1)(-14)

25 + 56 = 81

Use the equation,

-b ± \(\sqrt{b^2-4ac}/2a\)

Substitute the values,

(-5 + 9)/2 = 2 and,

(-5 - 9)/2 = -7

Therefore, the root will be (x - 2) and (x + 7).

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Answer:

$8200

Step-by-step explanation:

rounded to the nearest dollar

The required interest earned is $8200.

Given that,
Suppose Shelly invests $2650 semiannually into an annuity for six years. At the end of this time, she has $40,000.
To determine how much of this balance is from interest.

Simple interest is defined as the percentage of earnings on the lending for a period of time.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Total balance earned = $40,000
Total investment in 6 year = 6*2*2650
                                            = 31,800
Interest earned = 40,000 - 31800
                          = $8200

Thus, the required interest earned is $8200.

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The number of shares could he buy is 63.19 and 126.38. Then the profit gained by Bob is $764.68.

Bob Orleans invested $3,000 and borrowed $3,000 to purchase shares in Verizon Communications.

At the time of his investment, Verizon was selling for $47 a share.

If Bob paid a $30 commission, then the number of shares could he buy if he used only his own money and did not use margin.

\(\rightarrow \dfrac{3000- 30}{47}\\\\\rightarrow \dfrac{2970}{47}\\\\\rightarrow 63.19\)

If Bob paid a $60 commission, then the number of shares could he buy if he used his $3,000 and borrowed $3,000 on margin to buy Verizon stock will be

\(\rightarrow \dfrac{6000 - 60 }{47}\\\\\rightarrow \dfrac{5940}{47}\\\\\rightarrow 126.38\)

Assume Bob did use margin and paid a $60 total commission to buy his Verizon stock. Also, assume he paid another $60 to sell his stock and sold the stock for $54 a share. Then the profit will be

\(\rightarrow (126.38 \times 54 - 60) - (6000)\\\\\rightarrow (6824.68 - 60) - 6000\\\\\rightarrow 6764.68 - 6000\\\\\rightarrow \$764.68\)

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Answer:

54 inches

Explanation:

From the question, we have that:

1 yard = 3 inches

We are to find the equivalent value of 18 yards in inches. This can be expressed as:

18 yards = x

where x is the unknown value.

Get the value of x by dividing both equations:

Cross multiply

This shows that there are 54 inches in 18 yards

Answer: one senior ticket is $8 and one student ticket is $14

Hope this helps a little

He will spend 5 minutes bicycling at 11mph and 40 minutes bicycling at 15mph.

From the information, the person is planning to ride his bicycle for 45 minutes every day. He burns 6 calories per minute bicycling at 11 mph and 9.25 calories per minute bicycling at 15 mph

This will be illustrated as:

x + y = 45 ..... i

6x + 9.25y = 400 ..... ii

From equation i, x = 45 - y ..... iii

x = number of minutes cycling at 11mph

y = number of minutes cycling at 15mph

Put equation iii into ii

6x + 9.25y = 400

6(45 - y) + 9.25y = 400

270 - 6y + 9.25y = 400

3.25y = 130

Divide

y = 40

Since x + y = 45.

x = 45 - 50

x = 5

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Answer:

14

Step-by-step explanation:

Knowing the first triangle is isosceles, and given the degree is 69.

We can find the top left angle as 180-69-69=42

42 combine with another angle to make a right angle

90-42=48.

The second triangle is also isosceles, so to find 2

we can use 180-42=138 (supplementary angles rule)

and given 10x-8=138

10x=140

x=14

Complete Question

In a study of the accuracy of fast food? drive-through orders, Restaurant A had  249 accurate orders and 80 that were not accurate.  

a. Construct a 90?% confidence interval estimate of the percentage of orders that are not accurate.  

b.  Compare the results from part? (a) to this 90?% confidence interval for the percentage of orders that are not accurate at Restaurant? B: 0.164< p <0.239. What do you? conclude?

 Choose the correct answer below.  

A. Since the two confidence intervals  overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate.  

B. The lower confidence limit of the interval for Restaurant B is higher than the lower confidence limit of the interval for Restaurant A and the upper confidence limit of the interval for Restaurant B is also higher than the upper confidence limit of the interval for Restaurant A. Therefore, Restaurant B has a significantly higher percentage of orders that are not accurate.  

C. No conclusion can be made because not enough information is given about the confidence interval for Restaurant B.  

D. Since the upper confidence limit of the interval for Restaurant B is higher than both the lower and upper confidence limits of the interval for Restaurant? A, this indicates that Restaurant B has a significantly higher percentage of orders that are not accurate.

Answer:

a

The  90?% confidence interval  is  \(0.2041 < p < 0.282\)

b

Option A is the correct option

Step-by-step explanation:

From the question we are told that  

      The sample size is  n  =  249+80  = 329

        The number that are not accurate is  k  = 80

Generally the sample proportion of orders  that are not accurate is  mathematically evaluated as

                   \(\r p = \frac{ 80 }{329}\)

                    \(\r p = 0.243\)

Given that the confidence level is 90% then the level of significance is mathematically evaluated as

              \(\alpha = 100 -90\)

              \(\alpha = 10\%\)

               \(\alpha = 0.10\)

Next we obtain the critical value of  \(\frac{ \alpha }{2}\) from the normal distribution table, the value is  

               \(Z_{\frac{\alpha }{2} } = 1.645\)

Generally the margin of error is mathematically represented as

              \(E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p )}{n} }\)

=>            \(E = 1.645* \sqrt{ \frac{0.243 (1- 0.243 )}{329} }\)

=>              \(E = 0.0389\)

Generally the 90% confidence interval is  mathematically represented as

         \(\r p -E < p < \r p +E\)

=>       \(0.2041 < p < 0.282\)

Comparing the two 90% confidence of restaurant A and B we see that they overlap and  Since the two confidence intervals overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate.  

Step-by-step explanation:

Use the Ratio Test since Ratio Test guarantee absolutely convergence.

\( \frac{ ( - 1) {}^{k + 1}(k + 1) {}^{a} }{5 {}^{k + 1}(3(k + 1) } \times \frac{5 {}^{k}(3k) }{(k) {}^{a} ( - 1) {}^{k} } \)

This simplifes to

\( \frac{( - 1) {}^{k} ( - 1) ((k + 1)!) {}^{a} }{5 {}^{k}(5)(3k +1) ! } \times \frac{5 {}^{k} (3k)!}{( - 1) {}^{k} (k!) {}^{a} } \)

\( \frac{ - (k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} \)

Take the absolute value

\( \frac{(k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} \)

In order for this series to be convergent,

the limit as k approaches infinity must be less than 1.

In order for this series to have a limit less than 1, our numerator and denominator degree must be equal or the denominator must have the larger degree.

Why

If the numerator has a larger degree, our test would make this divergent, so the limit would be infinity

Since the denominator have 3 binomials, our power for the denominator will be 3, this the numerator having a degree of 3 or less as well.

So one of the answer is 3.

Answer:

60%

Step-by-step explanation:

21/35 = 3/5

= 0.6

=60%

Using the general equation for depreciation which is y = A(1 – r)^t, The value of the car in 4 years is $12528.15

The value of the car is solved by using the formula for depreciation which is  y = A(1 – r)t

definition of variables

where

y = current value, = ?

A = original cost, = $24,000

r = rate of depreciation, = 15% and

t = time, in years. = 4 years

substituting the variables

current value, y = A(1 – r)t

current value, y = 24000 * (1 - 0.15)⁴

current value, y = 12528.15

the depreciation is $12528.15

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