During a hammer thrower’s practice swings, the 7.1-kg head A of the hammer revolves at a constant speed in a horizontal circle as shown. Knowing that the speed of the hammer is 2.5 m/s and θ = 60°, determine (a) the tension in wire BC, (b) the radius of the circle, rho.

The solution represents the number of hours of cleaning and cost of two housekeeping services, Premier and Best House Care.

What is algebraic equation ?

An algebraic equation is a mathematical expression containing one or more variables and an equal sign, where the goal is to find the value(s) of the variable(s) that make the equation true. The equation is formed by combining numbers, variables.

PART A:

Let x be the number of hours of cleaning that Premier Housekeeping provides, and let y be the number of hours of cleaning that Best House Care provides. The system of equations representing the housekeeping services is:

Premier Housekeeping: 25 + 65x = cost in dollars

Best House Care: 75y = cost in dollars

PART B:

The solution of this system of equations represents the point (x,y) in the coordinate plane, where x represents the number of hours of cleaning that Premier Housekeeping provides and y represents the number of hours of cleaning that Best House Care provides. The cost in dollars of each service will be given by the corresponding equation: the cost of Premier Housekeeping will be 25 + 65x, while the cost of Best House Care will be 75y.

The solution represents the number of hours of cleaning and cost of two housekeeping services, Premier and Best House Care.

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Answer: english please so I can answer it

Step-by-step explanation:

Answer:

√80 pulgada

Step-by-step explanation:

Convirtiendo 95 cm a pulgadas,

95/2,54 = 37,40 pulgadas

Ahora, la diagonal dada es de 40 pulgadas

Usando el teorema de Pitágoras, (40)²=(37,4)² + h² (Suponiendo h como altura)

h² = 40² - 37,4²

= 80

o h = √80 pulgada

The absolute value of a negative number will always be a positive number.

As discussed above, regarding the absolute number, therefore, the absolute value of a negative number will always be a positive number.

for example, |-24| = 24

The absolute value of any number will always be a positive number.

As discussed above, regarding the absolute number, therefore, the absolute value of any number will always be a positive number.

for example, |-24| = 24

Positive numbers will always have a higher absolute value than negative numbers.

As discussed above, regarding the absolute number. therefore, the absolute value of any number will always be a positive number, which will be equal in value.

for example, |-24| = 24

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The Z-score is (b) -1.64.

Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.

To find the z-score corresponding to an observation of 4.7, we can use the formula:

z = (x - mu) / sigma

where x is the observation, mu is the mean, and sigma is the standard deviation.

Given that X-N(5.7, 0.61) we can substitute

z = (4.7 - 5.7) / 0.61 = -1.64

So the answer is (b) -1.64.

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Therefore ,on solving the provided question we can say that - Simple Interest after 5 year the car value is £7,689.6

Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it.

here,

rate = 10%

Time = 1 year

Principle = 12000

=>SI = PRT/100

=> SI =  10*1*12000/100

=> SI = 1200

and

=>  After 1 year = 12000 -1200 = 10800

and

for five  years

=> SI = PRT/100

=> SI = 10800 * 7.2 * 4 / 100

=> SI = 3110.4

After 5 year = 10800 - 3110.4  = 7,689.6

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The domain of the given function f(x) = √(x⁴ - 1) include the following: C. {x|x ≤ -1 or x ≥ 1}.

In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined. Additionally, the horizontal extent of a graph represents all domain values (input values) and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Next, we would use an online graphing calculator to plot the graph of the given function f(x) = √(x⁴ - 1). By critically observing the graph of this function shown in the image attached below, we can reasonably and logically deduce the following domain:

Domain = (-∞, 1) U (1, ∞)

By using set builder notation, the domain of this function f(x) = √(x⁴ - 1) can be re-written as follows;

Domain = {x|x ≤ -1 or x ≥ 1}.

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As per the unitary method, the length of his shadow changing is 30 feet.

The term unitary method is known as a process of finding the value of a single unit, and based on this value.

Here we have given that a 6-foot man is running away from the base of a streetlight that is feet high.

Then let us consider that the man be x feet away from the street light and his shadow length be y,

Here we have also consider that let the tip of the shadow be l feet away from the light is written as

=> l = x + y

Here we are given that,

=> dx/dt=2

Then as per the concept of similar triangles, we can write it as,

=> x/5 = 6x+6/31

=> 31x = 30x + 30

=> x = 30

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A detection system has a probability of 0.91 to detect a missile attack. It is recommended to have multiple detection systems as it increases the overall probability of detecting an attack and allows for redundancy in case one system fails.

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Answer:

f(x) = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

given f(- 5) = 2, that is when x = - 5 , y = 2

f(7) = - 4, that is x = 7, y = - 4

the 2points (- 5, 2 ) and (7, - 4 ) lie on the line

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 2 ) and (x₂, y₂ ) = (7, - 4 )

m = [tex]\frac{-4-2}{7-(-5)}[/tex] = [tex]\frac{-6}{7+5}[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex] , then

f(x) = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the line

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

using (- 5, 2 ) , then

2 = - [tex]\frac{1}{2}[/tex] (- 5) + c = [tex]\frac{5}{2}[/tex] + c ( subtract [tex]\frac{5}{2}[/tex] from both sides )

- [tex]\frac{1}{2}[/tex] = c

f(x) = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex] ← equation of line

Answer:

20 blue fish

Step-by-step explanation:

r=red fish, b=blue fish. r = 10+b. 60%r=r+b. (10+b)= 0.6(r+b); 10+b = 0.6(2b+10); 10+b=1.2b+6; 4=0.2b; b=20.

Answer:The temperature dropped 24°F overnight, so the change in temperature would be represented by the expression |-24|, which is the absolute value of -24.

You can also represent it by |38| - |-24| which is equal to 38 - (-24) = 38 + 24 = 62°F.

Step-by-step explanation:

Degree: 2

Leading coefficient: -1 (The leading coefficient is the coefficient of the term with the highest degree in the polynomial, in this case, the coefficient of u², which is -1)

Isabella fills her pool at a rate of 18 liters per minute as per the given condition.

The slope of the volume can be used to determine how quickly it changes when given Time t in minutes and Volume V in liters. That represents a change in volume relative to a change in time.

m = (v2-v1)/(t2-t1).

selecting the first two points (2, 184) and from the provided data (7, 94).

Volume remains in the pool at what rate =

(94-184)/(7-2) = -90/5 = -18.

Therefore the rate at which Isabella fills her pool is 18 liters/minute as per the given question.

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Answer: Yes.

Step-by-step explanation:

0.5 is also the same as 1/2

Answer:

We know that Keilantra has $660 to spend, she has already spent $488.20 on a bicycle, $11.17 on two reflectors and $19.05 on a pair of gloves.

We can represent the amount spent on reflectors as 2 * $11.17 = $22.34

So the total amount spent so far is:

$488.20 + $22.34 + $19.05 = $529.59

We can represent the remaining amount of money she has to spend on outfits as:

$660 - $529.59 = $130.41

We can use this remaining amount to find out the number of outfits she can purchase by dividing the remaining amount by the cost of each outfit:

$130.41 / $37.26 = 3.5

The inequality that represents this situation is:

x <= 3.5

Where x is the number of outfits Keilantra can purchase while staying within her budget.

This inequality tells us that Keilantra can purchase at most 3.5 biking outfits while staying within her budget.

However, since the number of outfits has to be a whole number, the greatest number of outfits that Keilantra can buy is 3.

Answer:

First number 7

Step-by-step explanation:

First, let's make the first number y and the second number x

Next, we write our equations which are y=1/2x+3 and y=1/4x+5

Then, we set those two equations equal to each other and then solve for x

The first step of the equation is to add/subtract like terms, I subtracted 5 on each side of the equation, our new equation is 1/4x=1/2x-2, I then subtracted 1/2x on each side so now our equation is -1/4x=-2. We then multiply 1/4 by its reciprocal on each side. Its reciprocal is -4.

Now that we know x is equal to 8 now we can fill x into the original equations which were y=1/2x+3 and y=1/4x+5 you don't have to solve both, just one of your choosing.

Therefore your answer! .

y = 6(2)^(x-4)-1 is an exponential function with a base of 2 and an exponent of x-4. The coefficient of the base, 6, is called the leading coefficient. The constant term, -1, is the y-intercept, the point where the graph of the function crosses the y-axis. The function is also a shifted version of the basic exponential function y= a*b^x, where a is the leading coefficient and b is the base of the function.

Since the base of the function is 2, the graph of the function will increase or decrease at an increasing rate. The leading coefficient of 6 will affect the steepness of the graph, making it steeper than the basic exponential function y=2^x. The horizontal shift of the graph is 4 units to the left, as the exponent has x-4 instead of x.

In terms of symmetry, the graph of this function has no symmetry.

The function has no rotational symmetry because it is not repeated after any rotation around the origin.

The direction of the ball at this point is <1/8, -4, 96/8>

The position vector of the ball can be found by taking the derivative of the rectangular equation with respect to time:

r(t) = <8t, -16t², 32t³>

To find the speed of the ball at the point where it has traveled 64 feet horizontally, we can use the magnitude of the velocity vector, which is the derivative of the position vector with respect to time:

v(t) = <8, -32t, 96t²>

|v(t)| =√(8² + (-32t)² + 96t⁴) = 8*√(1 + t² + 3t⁴)

We need to find the time t at which the ball has traveled 64 feet horizontally. We know that x = 8t, so we can set x = 64 and solve for t:

8t = 64

t = 8

At t = 8, the speed of the ball is:

|v(8)| = 8√(1 + 8² + 3(8⁴)) = 8√(65) = 8*8 = 64

To find the direction of the ball at this point, we can use the unit vector of the velocity vector:

v(t) = <8, -32t, 96t²> / |v(t)|

v(8) = <8, -256, 6144> / 64 = <1/8, -4, 96/8>

So the direction of the ball at this point is <1/8, -4, 96/8>

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Answer is 60 % is the percentage of boys studying German .

So, for this one, you must first determine the number of French students.

Simple method:

[tex]\frac{1}{9}[/tex]  is 270 divided by 9, which equals 30, hence  [tex]\frac{2}{9}[/tex]of 270 is 60. The result of multiplying [tex]\frac{1}{9}[/tex] by 2 to get [tex]\frac{2}{9}[/tex] is 60.

French is being studied by 60.

When you apply this to the French to Spanish ratio of 3:7, you get 3 and 60 on the same side. In order to get to 60, you must multiply 3 by 20. (or divide 60 by 20 to get 3).

Therefore, 20 is the number you use to apply the same formula to the other side of the ratio.

To reach 140, multiply 7 by 20 (or 7 by 10, then multiply that number by 2).

Spanish is being studied by 140.

After subtracting the French and Spanish from the overall number, you are left with 70 German speakers at 270-140-60.

42 of these 70 are males. 28 females are produced by 70-42. The percentage of males studying German is [tex]\frac{42}{70}[/tex]. This is equivalent to [tex]\frac{6}{10}[/tex], and you multiply a fraction by 10 to convert it to a percentage ([tex]\frac{60}{100}[/tex] in this case).

Additionally, 60% is equal to [tex]\frac{60}{100}[/tex]  .

Your response is thus 60%.

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1.

a+6=6

Solving for a:

a = 0

a-5= -8

Solving for a:

a = -13

a x -10= 100

Solving for a:

a = -10

(5+2a) ÷ 17 = 3

Solving for a:

a = -4

2.

a) The dimensions of the field are 7m by 7m.

b) The perimeter of the field is 28m.

c) To find the area of the field, you could use the equation: length x width = area. In this case, the length and width are both 7m, so the equation would be 7m x 7m = 49m^23

3.

a) T | V

1 | 3

2 | 5

3 | 7

4 | 9

5 | 11

b) The pattern rule is that the value (V) is 2 greater than the previous value.

Answer:

According to phythagorian theorem

Hypotenus (square) = Base(square) + perpendicular (square)

H^2 = B^2 + P^2

now by substitution

H^2 = 9 +16

H^2 = 25

taking roots

Hypotenus= 5

The amount of money that the club expects to warn by the end of the 10 game season would be = $27.06

The profit made at the end of the first game = -12.50

The profit made at the end of the second game= -10.15

The profit made at the end of the third game= 18.65

The profit made at the end of the fourth game= 25.90

The profit made at the end of the fifth game = 45.75

First we find the average profit made in the first five games such as;

= -12.50 + -10.15 + 18.65 + 25.90 + 45.75

= 90.3 −22.65 = 67.65/5 = 13.53

Therefore for the next five games which will make it up to 10 game he is expected to have a profit of 13.53×2 = $27.06.

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Conversion of pressure of 1379 torr to atm= 1.814474

Unit conversion is a multi-step procedure that involves adding, subtracting, multiplying, or dividing by a conversion factor.

Additionally, choosing the right number of significant digits and rounding may be necessary during the process.

The multi-step process of unit conversion involves multiplying or dividing by a numerical factor.

Weight, distance, and temperature can all be measured in a variety of ways.

Temperature is expressed in degrees Celsius, weight is expressed in kilos, and distance is measured in kilometers.

Imagine you are on vacation in India and are informed that the two cities are 100 kilometers apart.

Hence, Conversion of pressure of 1379 torr to atm= 1.814474

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We can use the table to evaluate the compositions of the functions, we will get:

Here we have a table for functions f(x) and g(x), and we want to use that table to evaluate the compositions of the functions.

First, we want to get f(g(6))

Using the table, we can see that g(6) = 0, then:

f(g(6)) = f(0)

And using the table we can see that f(0) = 3, then:

f(g(6)) = 3

The second composition is:

g(f(0))

We know that f(0) = 3

g(f(0)) = g(3)

And using the table g(3)=  8, then:

g(f(0)) = 8

The third one is:

f(f(4))

We can see that f(4) = 7

So: f(f(4)) = f(7)

And again, you can find f(7) on the table to see that f(7) = 4

Then:

f(f(4)) = 4

The last composition is:

g(g(1))

You can see that g(1) = 1

Then:

g(g(1)) = g(1) = 1

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If the artist makes a triangle from three pieces of bamboo that measure 4 inches, 5 inches and 7 inches. The triangle will not be a right triangle because the values are not Pythagorean triple

Pythagorean triples are b² + a² = c² where b, a and c are all positive integers.

These triples are represented as (b, a, c).

Here, b is perpendicular (or right angel) to a, a is the base and the hypotenuse of the right - angled triangle is labeled .

The most known and smallest triplets are (3, 4, 5).

In the problem, the values  4 inches, 5 inches and 7 inches cannot make a Pythagorean triple since

c² = 4² + 5²

c² = 16 + 25

c² = 41

c = √41 ≠ 7

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The equation 7x² - 144 = -x⁴ has the 4 solutions below:

x =  ±3

x =  ±4i

Here we want to solve the equation below:

7x² - 144 = -x⁴

We can redefine the variable:

y = x²

Replacing that we will get:

7y - 144 = -y²

y² + 7y - 144 = 0

So we have a quadratic equation now, the using the quadratic formula we will get:

[tex]y = \frac{-7 \pm \sqrt{7^2 - 4*1*144} }{2} \\\\y = \frac{-7 \pm 25 }{2}[/tex]

Then the two solutions are:

y = (-7 + 25)/2 = 9

y = (-7 - 25)/2 = -16

And we know that:

y = x²

Then:

x = ±√9 = ±3

x = ±√-16 = ±4i

These are the 4 solutions.

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Answer:

Let's call the number of hours it takes to fill the pool "h".

We know that the initial amount of water in the pool is 640 gallons, and water is being added at a rate of 320 gallons per hour. To find out how many hours it will take to fill the pool to 1600 gallons, we can set up the following equation:

640 + (320h) = 1600

To solve for h, we'll subtract 640 from both sides of the equation:

320h = 960

Then divide both sides by 320:

h = 3

So it will take 3 hours to fill the pool with water.

It will take 3 hours to fill the pool.

Amount of water that can fit in the pool= 1600 gallons.

The amount of water already present= 640 gallons.

Therefore, the amount of water required to fill the pool= 1600-640 = 960 gallons

The rate at which the water is being pumped= 320 gallons/ hour

Therefore, the time needed to fill the pool= the quantity to be supplied/ the rate at which the water is being pumped

=> 960/ 320

=> 3 hours.

Therefore, the time required to fill the pool completely is 3 hours.

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A ratio is a comparison of two or more numbers expressed as a fraction, such as 3/4 or 4:5. It is used to compare the size or amount of two or more objects or quantities. Ratios can also be expressed as a percent or as a decimal.

A ratio is a comparison of two or more numbers expressed as a fraction. The ratio is written as two numbers separated by a colon (:), or as a fraction. The numbers in the ratio are compared to each other to indicate the size or amount of the objects or quantities being compared. For example, 3:4 means that for every 3 objects, there are 4 of the other object. This can also be written as a fraction, 3/4, to indicate that for every 3 objects, there are 4 of the other object. Ratios can also be expressed as a percent or as a decimal. For example, 3:4 can be expressed as 75% or 0.75.

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Answer:

x= 108/61; y=-163/61

Step-by-step explanation: