Convert the Cartesian coordinates (1,−5) to polar coordinates
with r>0 and 0≤θ<2π. give theta answer in radiants

Isaiah's allοwance fοr the week wοuld be $43.75.

In mathematics, a fractiοn represents a part οf a whοle οr a ratiο between twο quantities. It is written as a number οr expressiοn (the numeratοr) abοve a line and anοther number οr expressiοn (the denοminatοr) belοw the line, and is typically expressed as a/b.

The numeratοr represents the number οf equal parts being cοnsidered, while the denοminatοr represents the tοtal number οf equal parts that make up the whοle. Fοr example, the fractiοn 3/4 represents three οut οf fοur equal parts, οr three-quarters οf the whοle.

Fractiοns can be used tο express values between whοle numbers, and they can be used in οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn. Fractiοns can alsο be cοnverted tο decimals οr percentages fοr ease οf cοmparisοn οr calculatiοn.

Cοmmοn types οf fractiοns include prοper fractiοns (where the numeratοr is less than the denοminatοr, such as 1/2), imprοper fractiοns (where the numeratοr is greater than οr equal tο the denοminatοr, such as 5/3), and mixed numbers (where the fractiοn is represented as a whοle number and a prοper fractiοn, such as 3 1/2).

Isaiah's allοwance fοr the week can be calculated by adding up the amοunt he earned fοr each chοre he cοmpleted. Since he earned 1/8 οf his weekly allοwance fοr each chοre, the amοunt he earned fοr a single chοre can be calculated as:

1/8 * $70.00 = $8.75

Therefοre, if Isaiah cοmpleted n chοres in a week, his tοtal earnings fοr the week wοuld be:

Tοtal earnings = n * $8.75

Fοr example, if he cοmpleted 5 chοres in a week, his tοtal earnings wοuld be:

Tοtal earnings = 5 * $8.75 = $43.75

Sο Isaiah's allοwance fοr the week wοuld be $43.75 if he cοmpleted 5 chοres. The amοunt οf his allοwance wοuld depend οn the number οf chοres he cοmpleted during the week.

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The value of 'x' and 'y' in the given circle and triangle are 30 and 12 respectively.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

From the given information we can form,

x² = 18² + 24². (As tangent is always perpendicular to the radius).

x² = 900.

x = 30.

Now, y = x - radius.

y = 30 - 18.

y = 12.

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The probability that at least 3 of the selected human resource managers say job applicants should follow up within two weeks is 0.55.

From the question, we are to determine the probability that at least 3 of the managers say job applicants should follow up within two weeks

This problem requires the use of the binomial probability distribution. We are given that the probability of success (a human resource manager saying that job applicants should follow up within two weeks) is p = 0.57. The number of trials is n = 6.

To find the probability that at least 3 of the selected human resource managers say job applicants should follow up within two weeks, we need to find the sum of the probabilities of 3, 4, 5, and 6 successes. We can use the binomial probability formula to find these individual probabilities and add them up:

P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

Where X is the number of successes.

Using the binomial probability formula, we get:

P(X = k) = (n Ck) * p^k * (1-p)^(n-k)

Where (n Ck) = n! / (k! * (n-k)!)

So,

P(X = 3) = (6 C3) * 0.57^3 * (1-0.57)^(6-3) = 0.307

P(X = 4) = (6 C4) * 0.57^4 * (1-0.57)^(6-4) = 0.185

P(X = 5) = (6 C 5) * 0.57^5 * (1-0.57)^(6-5) = 0.051

P(X = 6) = (6 C6) * 0.57^6 * (1-0.57)^(6-6) = 0.007

So,

P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.307 + 0.185 + 0.051 + 0.007 = 0.55

Hence, the probability is 0.55.

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Using the unitary method, we found that the equivalent amount of 750 US Dollars in Egyptian pounds is 1100 Egyptian pounds.

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit and then multiplying that value to determine the required value. Therefore, the goal of this method is to establish values in relation to a single unit. Always write the things that need to be calculated on the right side and the things that are known on the left side to simplify things. The unitary approach must be applied whenever we need to determine the ratio of one quantity to another.

Given,

 The amount of money  in US dollars = 750 US Dollars

The conversion to Egyptian pounds can be done using the unitary method.

1 usd = 18.48 Egyptian pounds

The unitary method can be used to convert single units to multiple units.

So,

750 usd = 750 * 18.48 = 1110 Egyptian pounds.

Therefore using the unitary method, we found that the equivalent amount of 750 US Dollars in Egyptian pounds is 1100 Egyptian pounds.

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The remainder when -233 is divided by 11 is 9. To find the remainder when a is divided by b, we can use the formula:

r = a % b

Where % is the modulo operator, which gives the remainder when one number is divided by another.

In this case, we have a = -233 and b = 11. Plugging these values into the formula, we get:

r = -233 % 11

Using a calculator or doing the division by hand, we find that the remainder is -2. However, since we are looking for the positive remainder, we can add b to this value to get the correct answer:

r = -2 + 11 = 9

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Given:

What is the interest earned when $46,230 is invested for 9 years at 7.8% p.a?

To find:

The interest

Solution:

The mode of the set of variables "17,7,6,3,17,17,4,3,9,5,17,17" is 17 .

The Mode of a data set is defined as the value that appears most frequently in the dataset. The mode is one of the measures of central tendency, along with the mean and median.

The mode is useful in describing the most common value in a dataset, and can be specially helpful when dealing with categorical or discrete data.

The mode can be more than one value or may not exist at all in some datasets.

From the given set of variables "17,7,6,3,17,17,4,3,9,5,17,17",

The number 17 appears 6times, which is more than any other number in the dataset.

Therefore, the mode is 17.

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Answer:

You must get a 89%

Step-by-step explanation:

81+89=170

170/2= 85%

(1)

21m^2 ÷ 7m = 3m

The quotient is 3m and there is no remainder.

(3)

(-48p^4) ÷ (-9p^2) = 5p^2 + (3p^2/(-9p^2)) = 5p^2 - (1/3)

The quotient is 5p^2 - (1/3) and the remainder is -(1/3).

(5)

(5x^3 - 3x^2) ÷ x^2 = 5x - 3

The quotient is 5x - 3 and there is no remainder.

(7)

(2y^3 + 4y^2 + 3) ÷ 2y^2 = y + (y+3)/(2y^2) = y + (3)

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Answer:

x = -2

x = 3

Step-by-step explanation:

[tex]\sqrt{26^{2} - 24^{2}} = \sqrt{(26-24)(26+24)} = \sqrt{2(50)} = \sqrt{100} = 10 \\[/tex]

[tex]x = \sqrt{10^{2} - 6^{2}} = \sqrt{100 -36} = \sqrt{64} = 8 \\[/tex]

[tex]\implies \bf x = 8[/tex]

Answer:

8

Step-by-step explanation:

Begin with the bigger right angle triangle

Hypotenuse is 26, second side is 24, third side is unknown (a)

26² - 24² = a²

676 - 576 =a²

100 = a²

Therefore a is 10

Now use the value of a which is 10 to solve the smaller triangle

Hypotenuse is 10, one side is 6, third side x is unknown

10²- 6²= x²

100 - 36 =x²

64 =x²

X is 8

The area of a cross section that passes through the center of a sphere with a diameter of 7 centimeters will be 12.25π cm².

Three-dimensional objects with a sphere-like shape exist in all three dimensions. Three axes, the x-axis, y-axis, and z-axis, are used to define the sphere. The key distinction between a circle and a sphere is this. In contrast to other 3D shapes, a sphere lacks any vertices or edges.

The sphere's points are evenly spaced apart from one another on its surface. In light of this, the sphere's surface and core are always equally separated from one another. The sphere's radius is the measurement between these points. Ball, globe, planets, and other objects are all examples of spheres.

Given : Diameter of Sphere = 7 cm

∴ Radius = 7/2 = 3.5 cm.

Since It is a cross section in a sphere, so, it would be circle.

So, Area of the cross section = Area of circle

Hence, Area of Cross section = πr²

                                                 = π (3.5)²

                                                 =  12.25π cm²

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$600

B. $600 per week

For Activity 2, the Normal Cost is $1,000 and the Crash Cost is $4,600, so the Crash cost per week is $60.

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The area of the resulting shape is 90 sq meters

The cylinder represents the given parameter

Such that we have the following dimensions

Radius = 6 cm

Height = 15 cm

When the solid cylinder is cut vertically through its center, we have a rectangle with the following dimensions

Length = 6 cm

Width = 15 cm

The area is then calculated as

Area = Length * Width

So, we have

Area = 6 * 15

Evaluate

Area = 90

Hence, the area is 90 square meters

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For the airplane, we have v = -453.01, 79.88. Similarly, for the wind, we have w = -75.18, -27.36.

The actual speed would be 530.79 mph.

The actual ground speed and direction of the airplane are 530.79 mph and 174.32 deg, respectively.

The component form of the velocity of the airplane can be found by using the formula:

v = r < cos theta, sin theta >, where r is the speed and theta is the bearing. For the airplane, we have v = 460 < cos 170, sin 170 > = <-453.01, 79.88>. Similarly, for the wind, we have w = 80 < cos 200, sin 200 > = <-75.18, -27.36>.

To find the actual ground speed and direction of the airplane, we need to add the velocity vector of the airplane and the wind vector. This gives us the velocity vector = v + w = <-453.01, 79.88> + <-75.18, -27.36> = <-528.19, 52.52>.

The actual speed can be found by taking the magnitude of the velocity vector, which is given by |v+w| = sqrt((-528.19)^2 + (52.52)^2) = 530.79 mph.

The actual direction can be found by using the formula theta = arctan(y/x), where x and y are the x and y components of the velocity vector. In this case, we have theta = arctan(52.52/-528.19) = -5.68 deg. However, since the velocity vector is in the third quadrant, we need to add 180 deg to get the actual direction, which is 180 + (-5.68) = 174.32 deg.

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The line of intersection of the 3x+2y+z=−1  and 2x−y+4z planes is the set of all points (4t-7s-11, t, s), where t and s are parameters. And The line of intersection of the 4x+y+z=0 and 2x−y+3z=2 planes is the set of all points ((-3/6)t+(1/6)s-(1/3), t, s), where t and s are parameters.

The line of intersection of the given planes can be found by solving the system of equations formed by the equations of the planes.

For Exercise 45, we have the system of equations:
3x+2y+z=−1
2x−y+4z=5

To solve this system, we can use the elimination method. We can multiply the second equation by 2 and subtract it from the first equation to eliminate the x variable:

3x+2y+z=−1
-(4x-2y+8z=10)
______________
-x+4y-7z=-11

Now we can express one variable in terms of the other two variables. For example, we can solve for x in terms of y and z:

-x+4y-7z=-11
x=4y-7z-11

The line of intersection of the given planes is the set of all points (x, y, z) that satisfy this equation. We can write the equation of the line in parametric form by letting y=t and z=s:

x=4t-7s-11
y=t
z=s

The line of intersection of the given planes is the set of all points (4t-7s-11, t, s), where t and s are parameters.

For Exercise 46, we have the system of equations:
4x+y+z=0
2x−y+3z=2

We can use the elimination method again to solve this system. We can multiply the first equation by 2 and subtract the second equation from it to eliminate the x variable:

8x+2y+2z=0
-(2x−y+3z=2)
______________
6x+3y-z=-2

Now we can express one variable in terms of the other two variables. For example, we can solve for x in terms of y and z:

6x+3y-z=-2
6x=-3y+z-2
x=(-3/6)y+(1/6)z-(1/3)

The line of intersection of the given planes is the set of all points (x, y, z) that satisfy this equation. We can write the equation of the line in parametric form by letting y=t and z=s:

x=(-3/6)t+(1/6)s-(1/3)
y=t
z=s

The line of intersection of the given planes is the set of all points ((-3/6)t+(1/6)s-(1/3), t, s), where t and s are parameters.

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The point (7,8) is located at the intersection of the vertical line x=7 and the horizontal line y=8.

The equation x-7=0 can be solved to find the value of x. To do this, we can add 7 to both sides of the equation to isolate the variable on one side of the equation. This gives us: x-7+7=0+7 or x=7. Now that we know the value of x, we can plot the point on the line with the y-coordinate y=8. To do this, we can start at the origin (0,0) and move 7 units to the right along the x-axis to the point (7,0). Then, we can move 8 units up along the y-axis to the point (7,8). This is the point that corresponds to the equation x-7=0 with the y-coordinate y=8. The plot of this point is shown below:



As shown in the plot above, the point (7,8) is located at the intersection of the vertical line x=7 and the horizontal line y=8.

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The integer values of k such that [18]25 is equal to [7]k are 4, 11, 18, 25

To find all integer values of k such that [18]25 is equal to [7]k, we need to use the following steps:

Start with the given equation: [18]25 = [7]k

Use the definition of modular arithmetic to write the equation in a different form: 25 ≡ k (mod 7)

Simplify the equation: 4 ≡ k (mod 7)

Find all integer values of k that satisfy the equation. The smallest positive integer value of k that satisfies the equation is 4. We can add multiples of 7 to find other integer values of k: 4 + 7 = 11, 4 + 14 = 18, 4 + 21 = 25, etc.

The integer values of k that satisfy the equation are 4, 11, 18, 25, etc.

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The equation 4(5r-15)=13+11+8r has a unique i.e., one solution.

The given equation is: 4(5r-15) = 13+11+8r.

Simplifying the left-hand side, we get 20r-60 = 32+8r.

Bringing all the r terms to the left-hand side and the constants to the right-hand side, we get:

20r - 8r = 32 + 60

12r = 92

r = 7.67

Therefore, we get a unique solution for the given equation, which is r = 7.67.

There are a few possible reasons why an equation may not have any solution or may have infinitely many solutions. In this case, since we obtained a unique solution, neither of these situations applies.

One common reason why an equation may not have any solution is that the equation may be inconsistent, meaning that the left-hand side and right-hand side of the equation cannot be made equal for any value of the variable. For example, the equation 2x + 3 = 2x + 4 has no solution since the two sides of the equation can never be equal for any value of x.

On the other hand, an equation may have infinitely many solutions if it is an identity, meaning that the left-hand side and right-hand side of the equation are always equal, regardless of the value of the variable. For example, the equation x + 1 = x + 1 is an identity since the left-hand side and right-hand side are always equal for any value of x.

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Step-by-step explanation:

the ratio is 30/21600 = 3/2160 = 1/720

that means for every degree the hour hand moves, the second hand does 2 full rotations (2×360°).

h = s×30/21600 = s/720

FYI :

as there are 12 hours on a clock, every hour means 360/12 = 30° rotation for the hour hand.

so, for each hour the second hand moves 21600°.

that means 21600/360 = 60 full rotations.

that means one rotation of the second hand is 1 minute.

so, the second hand is truly a second hand (counting the seconds).

60 seconds in a minute (a full rotation by the second hand), that means each second corresponds to 360/60 = 6° rotation of the second hand.

The expanded form of the expression as a sum constant multiple of logarithms is:

log₄(xy⁵z⁴) = log₄(x) + 5log₄(y) + 4log₄(z)

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

According to the problem, we will use some of the basic logarithmic properties,

Given expression,

log₄(xy⁵z⁴)

We can use the properties of logarithms to expand the expression:

log₄(xy⁵z⁴) = log₄(x) + log₄(y⁵) + log₄(z⁴)

Using the properties of logarithms, we can separate the terms inside the logarithm as separate logarithms, where the multiplication of variables is represented as a sum of logarithms.

So, we have:

log₄(xy⁵z⁴) = log₄(x) + 5log₄(y) + 4log₄(z)

Therefore, the expanded form of the expression as a sum constant multiple of logarithms is:

log₄(xy⁵z⁴) = log₄(x) + 5log₄(y) + 4log₄(z)

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{z}{20}=\cfrac{4}{z}\implies z^2=4(20)\implies z^2=4(4\cdot 5)\implies z^2=4^2\cdot 5 \\\\\\ z=\sqrt{4^2\cdot 5}\implies z=4\sqrt{5}[/tex]

Hannah will have $681.98 in her savings account after 3 years at 2.75% simple annual interest.

To calculate the amount of money Hannah will have in the account after 3 years, we can use the formula for simple interest:

Simple interest = principal x rate x time

where:

principal is the amount of money initially deposited

rate is the annual interest rate (expressed as a decimal)

time is the number of years

In this case, the principal is $630, the rate is 2.75% (or 0.0275 as a decimal), and the time is 3 years. Plugging these values into the formula, we get:

Simple interest = $630 x 0.0275 x 3 = $51.98

This means that after 3 years, Hannah will have earned $51.98 in simple interest. To find the total amount of money in her account, we need to add this interest to the original principal:

Total amount = principal + simple interest

Total amount = $630 + $51.98 = $681.98

Therefore, after 3 years Hannah will be having $681.98 in her account after 3 years at 2.75% simple annual interest.

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The complete question is :

Hannah deposits $630 in a savings account at 2. 75% simple annual interest. How much money will she have in the account after 3 years?

The ramp rises about 10.4 inches off the ground to the nearest inch.

A ramp is an inclined plane that connects two different levels, allowing people or objects to move between them with less force than if they had to be lifted vertically.

We can use trigonometry to solve this problem. Let's call the height of the ramp "h". Then we have:

tan(3.2°) = h/15

To solve for h, we can multiply both sides by 15:

h = 15 tan(3.2°)

Using a calculator, we get:

h ≈ 0.87 feet

To convert this to inches, we can multiply by 12:

h ≈ 10.4 inches

So, the ramp rises about 10.4 inches off the ground to the nearest inch.

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If the two rates remain the same, the number of hours needed for the values of the two stocks to be equal is 2.17 hours.

The slope, rate of change, or change in throughout the change in of a line determines its rate of change. A graph's slope triangle or 2 points in a column can be used to compute the slope.

Let 'x' be the time taken by each stock to reach at same value.

Then,

13.45 + 0.07x = 13.95 - 0.16x

13.45 - 13.95 = -0.16x - 0.07x

x = 0.5/0.23

x = 2.17 hours

If the two rates remain the same, the number of hours needed for the values of the two stocks to be equal is 2.17 hours.

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Given vectors ū = (u1, u2) and ✓ = (v1, v2), we can find vector w = 4ữ - 5✓ by using the formula:
w = (4u1 - 5v1, 4u2 - 5v2)
To find the magnitude of vector w, we can use the formula:
|w| = √((4u1 - 5v1)² + (4u2 - 5v2)²)

Since we do not have the exact values of u1, u2, v1, and v2, we cannot compute the exact values of w and |w|.
w = (4u1 - 5v1, 4u2 - 5v2), |w| = √((4u1 - 5v1)² + (4u2 - 5v2)²)

Problem 4:
Given the point P(-15, 8) on the terminal side of angle O in standard position, we can find the values of the six trigonometric functions of O using the following formulas:
sin O = y/r
cos O = x/r
tan O = y/x
csc O = r/y
sec O = r/x
cot O = x/y
Where x = -15, y = 8, and r = √(x² + y²) = √((-15)² + 8²) = √(225 + 64) = √289 = 17

Therefore, the exact values of the six trigonometric functions of O are:
sin O = 8/17
cos O = -15/17
tan O = -8/15
csc O = 17/8
sec O = -17/15
cot O = -15/8

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Answer:

I think question #1 is C

Question #2 is C

and Question #3 is A

The original list price for the product was $487.09.

To find the original list price for the product, we need to reverse the discounts and markup that were applied to it. Here is a step-by-step explanation:

Therefore, the original list price for the product was $487.09.

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