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Answer:

The correct option is;

r = √(x² + y²)

θ = tan⁻¹(y/x)

Step-by-step explanation:

The rectangular coordinate of a complex number on the complex plane is given as (x, y)

Given that the complex number is represented by a point on the plane, we have;

The distance, r, of the point from the origin, (0, 0) is r = √(x² + y²)

The direction, θ, by which we rotate to be in line with the point on the complex number is given by tan⁻¹(y/x)

The factorization of x2 - 6x + 5 is (x - 1)(x -5)

From the graph, the zeros of the function are:

x = 1 and x = 5

Set the zeros to 0

x - 1 = 0 and x - 5 = 0

Multiply the zeros

(x - 1)(x -5) = 0

Hence, the factorization of x2 - 6x + 5 is (x - 1)(x -5)

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We can construct the 95% confidence interval for the true proportion. To do this, we need to calculate the margin of error, which is equal to the critical value (1.96) multiplied by the standard error (0.014). This equals 0.028.

The 95% confidence interval is then the sample proportion (0.38) plus or minus the margin of error (0.028). This is \((0.38 - 0.028, 0.38 + 0.028) = (0.352, 0.408).\)

The test statistic in this case is the Z-statistic, as we are assuming that the underlying population is normally distributed. To conduct the hypothesis test, we must first state the null and alternative hypotheses.

Null Hypothesis (H0): The proportion of students at the school who fear public speaking is equal to or greater than 40%.
Alternative Hypothesis (H1): The proportion of students at the school who fear public speaking is less than 40%.

We must then calculate the test statistic, which is the Z-statistic in this case. To do this, we need to first calculate the sample proportion, which is the number of students who fear public speaking (137) divided by the total number of students surveyed (361). This equals 0.38. We then need to calculate the standard error of the sample proportion (SE), which is the square root of \((pq/n)\), where p is the sample proportion (0.38) and q is the complement of the sample proportion (1-0.38 = 0.62). SE = \((0.38 x 0.62)/361 = 0.014.\) The Z-statistic is then calculated as the difference between the sample proportion (0.38) and the population proportion (0.40) divided by the standard error \((0.014). Z = (0.38 – 0.40)/0.014 = -0.14.\)

To conclude, we can use the Z-statistic and 95% confidence interval to test the hypothesis that the proportion of students at the school who fear public speaking is less than 40%. The Z-statistic of -0.14 falls within the critical region and the 95% confidence interval does not include 0.40, suggesting that the proportion of students at the school who fear public speaking is indeed less than 40%.

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Answer:

y = - 9x + 14

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 4, 50 ) and (x₂, y₂ ) = (5, - 31 )

m = \(\frac{-31-50}{5-(-4)}\) = \(\frac{-81}{5+4}\) = \(\frac{-81}{9}\) = - 9 , then

y = - 9x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, - 31 )

- 31 = - 9(5) + c = - 45 + c ( add 45 to both sides )

14 = c

y = - 9x + 14 ← equation of line

Answer:

I uploaded the answer to^{}

a file hosting. Here's link:" i don't believe them but try to see it

Answer:

SS

Step-by-step explanation:

Ju

The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

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The equation that represent the relationship of the coffees is 3x + 5y = 68.

At a coffee shop, two sizes of coffee are sold. A medium coffee costs $3, and a large coffee costs $5.

The equation that represent the relationship between the number of medium coffees sold, x, and the number of large coffees sold, y, in an hour where sales totalled $68 is as follows:

where

Therefore, the equation is as follows:

3x + 5y = 68

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Answer:

I drew it out and attached it as an image

Step-by-step explanation:

Add the 3 ratios together: 1 + 3 + 2 = 6

Divide perimeter by total:

30/6 = 5

Multiply each ratio by 5:

1 x 5 = 5

3 x 5 = 15

2 x 5 = 10

The greatest side is 15 cm

The function that takes three decimal numbers as inputs and finds the sum of those inputs and returns the sum has been given below

What is programming?

Program is the set of instructions given to the computer so that the computer can execute those instructions. The act of writing program is called programming.

The program has been shown below

#include<stdio.h>

using namespace std;

int main()

{

double n1, n2, n3;

double s;

printf("Enter first numbers");

scanf(%lf, &n1);

printf("Enter second numbers");

scanf(%lf, &n2);

printf("Enter third numbers");

scanf(%lf, &n3);

s = n1 + n2 + n3;

printf("Sum = %f", s);

return 0;

}

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Answer:

tour change would me $1.75

Answer:

\(6 {a}^{4} + 5b\)

Step-by-step explanation:

\(2a \times a\times a \times 3 a+ b + 4b \\ 2a \times a = 2 {a}^{2} \\ 2 {a}^{2} \times a = 2 {a}^{3} \\ 2 {a}^{3} \times 3a = 6 {a}^{4} \\b + 4b = 5b\)

Therefore the answer is

\(6 {a}^{4} + 5b\)

\(2a \cdot a \cdot a \cdot 3a +b+4b\\\\=6a^{1+1+1+1} +5b\\\\=6a^4 +5b\)

Answer:

x x 8= y

Step-by-step explanation:

The fractional part of the integer is represented by the place value after the decimal. The number 0.56, for example, is made up of 5 tenths and 6 hundredths.

This can also be written as 0.56 = 0.5 + 0.06. In other words, it means, 0.56 = 5/10 + 6/100.

To add decimals, align the decimal points such that all the digits are aligned according to their place values. Add like you would full numbers, starting on the right and working your way to the left. In the sum, align the decimal point with the decimal points in the values being added.

Decimals are one of the forms of numbers in Algebra that have a whole integer and a fractional part separated by a decimal point. The decimal point is the dot that appears between the full number and the fractions section. 34.5, for example, is a decimal number.

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x=16

Step-by-step explanation:

A straight angle is 180°

you get 180°- 62°=a

then You add up a and 46=b

lastly we know that a triangle's angle is 180° so we get 180°- b

tYou should try it yourself

Answer:

1000 cm

Step-by-step explanation:

Recall that 100 cm = 1 m.

This results in the conversion factor    100cm

                                                              -------------

                                                                   1 m

Then 10 m times the conversion factor shown above yields 1000 cm

A system of equations that can be used to find the number of packages of Brand X hot dog buns and Brand Y hot dog buns that Christopher buys is:

12x + 8y = 120  

4.5x + 3.5y = 49.50.

The number of packages of Brand X bought is 4 and the number of packages of Brand Y bought is 9

The following equations can be derived from the question

12x + 8y = 120  equation 1

4.5x + 3.5y = 49.50 equation 2

x represents the number of packages of Brand X

y represents the number of packages of Brand Y

The elimination method would be used to determine the values of x and y

Multiply equation 1 by 4.5 and equation 2 by 12

54x + 36y = 540 equation 3

54x + 42y = 594 equation 4

 Subtract equation 3 from 4

6y = 54  

Divide both sides of the equation by 6

y = 9

Substitute for y in equation 1

12x + 8(9) = 120

12x + 72 = 120

12x = 48

x = 4

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Answer:

9/12 = 4/x

Step-by-step explanation:

The height of the larger triangle is 9. The base of the larger triangle is 12. So let's make the ratio 9/12.

The height of the smaller triangle is 4. The base of the smaller triangle is x. So let's make the ratio 4/x.

Since both triangles are congruent, let's make these both equal each other to solve for x (if you need to).

Thus, it's 9/12 = 4/x.

Answer:

y

2

​

=−

2

z

​

+7

Steps for Solving Linear Equation

z=18−2×2−2y2

Multiply 2 and 2 to get 4.

z=18−4−2y

2

​

Subtract 4 from 18 to get 14.

z=14−2y

2

​

Swap sides so that all variable terms are on the left hand side.

14−2y

2

​

=z

Subtract 14 from both sides.

−2y

2

​

=z−14

Divide both sides by −2.

−2

−2y

2

​

​

=

−2

z−14

​

Dividing by −2 undoes the multiplication by −2.

y

2

​

=

−2

z−14

​

Divide z−14 by −2.

y

2

​

=−

2

z

​

+7

Step-by-step explanation:

the given equation defines a paraboloid that lies below the plane z=0. Specifically, it is situated above the xy-plane, which means that the z-values of all points on the surface are greater than or equal to zero.

we can break down the equation z=18-2x^2-2y^2. This equation represents a paraboloid with its vertex at (0,0,18) and axis of symmetry along the z-axis. The first term 18 is the z-coordinate of the vertex and the last two terms -2x^2 and -2y^2 determine the shape of the paraboloid.

Since the coefficient of x^2 and y^2 terms are negative, the paraboloid is downward facing and opens along the negative z-axis. Therefore, all points on the paraboloid have z-values less than 18. Additionally, since the paraboloid is situated above the xy-plane, its z-values are greater than or equal to zero.

the paraboloid defined by the equation z=18-2x^2-2y^2 is situated below the plane z=0 and above the xy-plane. Its vertex is at (0,0,18) and it opens along the negative z-axis.

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Answer:

5

Step-by-step explanation:

Answer:

In the Alan account is 77$

Step-by-step explanation:

The answer is 77$ because the sum of their savings is $89 and the difference is $12 you have to substract 89-12 and the result is 77$.

The money saved in Alan's savings account is $38.5.

Given that, Kira has more in her savings account than Alan has in his.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let the money in Kira's savings account be x and the money in Alan's savings account be y.

The sum of their savings is $89.

So, x+y=89 --------(I)

The difference is $12

So, x-y=12 --------(II)

Add equation (I) and (II), we get

x+y+x-y=89+12

⇒ 2x=101

⇒ x=$50.5

Substitute x=50.5 in equation (I) and simplify, we get

50.5+y=89

⇒ y=89-50.5

⇒ y=$38.5

Therefore, the money saved in Alan's savings account is $38.5.

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The significance of an association and some problems encountered when tests of significance are applied to coefficients of association are discussed below.

Any of the several coefficients or factors used in statistics to quantify a relationship between two or more variables. The chi-square test, Spearman rank-order correlation coefficient, and Pearson's correlation coefficient are a few examples of association metrics. Measures of association are frequently used in a wide range of research areas, but they are especially common in the disciplines of epidemiology and psychology because they enable the measurement of relationships between exposures and conditions or behaviors.

Any of a number of studies, such as correlation and regression analysis, can be used to find a measure of association. (Although the terms correlation and association are sometimes used synonymously, correlation strictly speaking refers to linear correlation, whereas association refers to any link between variables.) The procedure used to gauge an object's strength The properties of the data for each variable affect association. Data can be measured on an ordinal/rank scale, a nominal/categorical scale, or an interval/ratio scale.

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Answer:

A

Step-by-step explanation:

given the standard form of the sine function

y = a sin(bx + c) + d

amplitude = | a | , period = \(\frac{2\pi }{b}\)

shift = - \(\frac{c}{b}\) , d = vertical shift

given

y = 5sin(2x - \(\frac{\pi }{3}\) ) + 1 ← in standard form

with b = 2

then

period = \(\frac{2\pi }{2}\) = π

Answer:

1/3

Step-by-step explanation:

There are 12 different sums.

4 of the sums are 9, 9, 10, 11.

All other sums are 8 or less.

p(9 or more) = 4/12 = 1/3

the equation of the line tangent to the function at (3, 6) is y = 11x - 21.

1. f(x) = x^2 + 5x - 6, at (3, 6)

Answer: y = 8x - 21

f'(x) = 2x + 5

f'(3) = 2(3) + 5 = 11

The equation of the line tangent to the function at (3, 6) is y = 11x - b.

Substitute 6 for y and 3 for x to get 6 = 11(3) - b

Solve for b to get b = 21

Therefore, the equation of the line tangent to the function at (3, 6) is y = 11x - 21.

The equation of the line tangent to the function at (3, 6) is y = 8x - 21. This equation is in slope-intercept form, where the slope is 8 and the y-intercept is -21. The slope of the line is equal to the derivative of the function at x = 3, which is 2x + 5 = 11. Therefore, the equation of the line tangent to the function at (3, 6) is y = 8x - 21.

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It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y

Given data ,

A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6

Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.

As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required

Hence , the equation of line is solved

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Answer:

8cm

Step-by-step explanation:

multiply

Answer:

5m 25 cm

Step-by-step explanation:

1 m= 100 cm

3m + 20 cm = 320 cm

2m + 5 cm= 205 cm

2. Add the numbers

320 cm + 205 cm = 525 cm

3. Convert into m again

525/100

5.25 m Or 5 m 25 cm

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Answer:

If the remainder we get is zero then it is terminating otherwise the number will be repeating.

Step-by-step explanation:

In order to find whether a number is terminating or repeating, divide the numerator with the denominator. If the remainder we get is zero, then it is a terminating number and if we do not get zero as remainder, it is a repeating number.

In division algorithm, when the remainder is zero, we get a terminating algorithm as the algorithm stops or terminates.

Answer:

y = 3x - 8

Step-by-step explanation:

passes through (5, 7) and (4, 4)

Find slope:

(7 - 4) / (5 - 4)

= 3/1

= 3

This is your slope.

Now plug in a set of coordinates.

y = 3x + b

7 = 3(5) + b

7 = 15 + b

b = -8

Your equation is: y = 3x - 8

Check your work by plugging in the second coordinate pair.

y = 3x - 8

4 = 3(4) - 8

4 = 12 - 8

4 = 4

Your solution is correct.

Step-by-step explanation:

B the median is less than the mean