56 women make up an all female choir in a church. Two women are chosen to sing together for a duet. How many possible pairs could be chosen for the duet?

The equation of a straight line can be written if its slope and any one point lying on it is given. The  equation of the line for given slope and point is  (y - 3) = -1 / 7 × (x - 3). The correct answer is option B.

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

Given that,

The slope of the line = -1 / 7

The coordinate of the point on the line = (3,3)

The equation of a line having slope m and passing through a point (x₁, y₁) is given as,

(y - y₁) / (x - x₁) = m

Thus, the equation of the line for given slope and point is given as,

(y - 3) / (x - 3) = -1 / 7

=> (y - 3) = -1 / 7 × (x - 3)

Hence, the equation of the line for given slope and point is  (y - 3) = -1 / 7 × (x - 3).

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The formula that is used to calculate the midpoint for the given two point is written as ( (x₁ + x₂)/2 , (y₁ + y₂)/2).

Mid point:

Midpoint refers the point on a line that is at an equal distance from either end.

Given,

Here we have to explain the concept of midpoint in a simple manner.

According to the definition, midpoint refers the central point between the two points.

So, in a simple manner we have said that the mid point is calculated by finding the average of the two given point.

For example, (x₁, y₁) and (x₂, y₂) are the points, then the midpoint (xₙ, yₙ) is calculated by using the formula,

(xₙ, yₙ) = ( (x₁ + x₂)/2 , (y₁ + y₂)/2)

Similarly, if one point and the midpoint is given, then the another point is calculated by apply the remaining point as (x, y) and solve it accordingly, then we can get the value of it.

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we know that [tex]r[/tex]

area of the circle is equal to

A=  [tex]\pi[/tex] × [tex]r^{2}[/tex]

solve for [tex]r[/tex]

[tex]r[/tex] = [tex]\sqrt{\frac{A}{\pi } }[/tex]

for A=60cm2

[tex]r[/tex] = [tex]\sqrt{\frac{60}{\pi } cm}[/tex]

we know that

[tex]\sqrt{60\\}[/tex] = [tex]\sqrt{2^{4} }[/tex] × 3 × 5

=2[tex]\sqrt{15}[/tex]

so,

[tex]\sqrt{\frac{60}{\pi } }[/tex] = 2 [tex]\sqrt{\frac{15}{\pi } }[/tex]

2[tex]\sqrt{\frac{15}{\pi } } = 2\frac{\sqrt{15} }{\pi }[/tex]  × [tex]\frac{\sqrt{\pi } }{\sqrt{\pi } }[/tex]

= 2 [tex]\frac{\sqrt{15\pi } }{\pi }[/tex]cm

this means the answer is-

2 [tex]\frac{\sqrt{15\pi } }{\pi } cm[/tex]

The simplified expression using the commutative property is in the first option :  1/3 + 2/3 + 3/5   = 1 + 3/5 = 1 3/5 .

now the given expression is 1/3 + 2/3 + 3/5 .

Therefore this expression can be simplified using the commutative property where we put the like terms together.

1/3 + 3/5  + 2/3

= 1/3 + 2/3 + 3/5 (here we use commutative property on the second and third terms of the expression)

= 1 + 3/5 (we know that 1/3 +2/3 = 1)

=1 3/5

Hence by using the commutative property we calculate the sum easily.

The commutative property applies to the arithmetic operations of addition and multiplication. This suggests that no matter how the numbers are arranged or placed, the result of adding or multiplying them remains the same.

As an illustration, 1 + 5 = 6 and 5 + 1 = 6. No matter how two numbers are added, the sum is unaffected. Multiplication uses the same principle. The commutative property does not hold for division and subtraction because the results are completely different when the numbers are rearranged.

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The Linear function representing the total cost , where x is the number of tickets is  c(x) = 5. 50 + 20. 50x  , the correct option is (a) .

In the question ,

it is given that ,

the total cost for 5 tickets = $108

the service fees for the tickets to a basketball game = $5.50

we need to find the cost function for 5 tickets .

we substitute , the value of x = 5 in each option and check which option gives the cost as $108 .

Option (a)

c(x) = 5.50 + 20.50x

= 5.50 + 20.50(5)

= 108

Option(b)

c(x) = 5. 50x + 20. 50

= 5.50(5) + 20.50

= 48

Option(c)

c(x) = 5. 50 + 21. 60x

= 5.50 + 21.60(5)

= 113.5

Option(d)

c(x) = 5. 50x + 21. 60

= 5.50(5) + 21.60

= 49.1

So, from the answers above we can conclude that the cost function representing the cost for 5 tickets is c(x) = 5. 50 + 20. 50x   .

Therefore , The Linear function representing the total cost , where x is the number of tickets is  c(x) = 5.50 + 20.50x  .

The given question is incomplete , the complete question is

Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108 . Which linear function represents c, the total cost, when x tickets are ordered ?

(a) c(x) = 5.50 + 20.50x

(b) c(x) = 5.50x + 20.50

(c) c(x) = 5.50 + 21.60x

(d) c(x) = 5.50x + 21.60.

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Answer:bgvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvddddddddddddddddddddddddddd

Step-by-step explanation:

Answer:

Step-by-step explanation:

well it will be 16 because a square has 4 sides so you multiply by the grams that would be 4. 4*4= 16

As per the concept of inequality, the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal is 15 + 4m ≥ 35

Inequality

Inequality shows a non equal relationship between two numbers or two expressions.

Given,

Jason is training to run in a marathon. His goal for this week is to run a minimum of 35 miles. So far this week, he has already run 15 miles.

Here we need to determine the inequality could be used to determine the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal.

Here we know that, his goal for this week is to run a minimum of 35 miles.

For this week, he has already run 15 miles.

In the given inequality that could be used to determine the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal.

=> 15 + 4m ≥ 35

Here we know that, 4m = number of m miles run in 4 days.

Therefore, inequality that could be used to determine the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal is written as,

=> 15 + 4m ≥ 35

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Answer:

60

Step-by-step explanation:

I believe two angles should add up to 180 in a parallelogram

Answer:

a) 190 - 70(2/3) = 430/3 = 143 1/3 degrees

b) 190 - (2/3)x = 120

70 = 2x/3

210 = 2x

Step-by-step explanation:

x = 105 minutes

Answer:

X is horizontal axis, Y is vertical axis

Step-by-step explanation:

(x,y) in the notation

Answer:

x=59

Step-by-step explanation:

this is a full circle which is 360 degrees

We subtract 296 from 360 first

360-296=64

Then subtract 29 from 64

64-29=35

now we can set x-24 equal to 35

X-24=35

  +24 +24

x=59

Hopes this helps please mark brainliest

Answer:

Slope is -48, y-intercept is 432

[tex]y = - 48x + 432[/tex]

Step-by-step explanation:

[tex]m = \frac{432 - 288}{0 - 3} = \frac{144}{ - 3} = - 48[/tex]

[tex]432 = - 48(0) + b[/tex]

[tex]432 = 0 + b[/tex]

[tex]b = 432[/tex]

[tex]y = - 48x + 432[/tex]

The answer should be C.

The range of definition of the cosine function is all real numbers. [tex]R[/tex]

It is also periodic in [tex]2\pi[/tex].

It is an even function. [tex]f(x)=f(-x)[/tex]

It can also be written in this form.

Answer:

34562

Step-by-step explanation:

you add them together

I Think thatthe answer is 2

The distance between the cars increasing 2 hours later is 65mph

Let’s say, the velocity in the west is x, the velocity in the south is y, and the distance between them is s at any time t. Since the west and south directions are perpendicular to each other, this will be for a right-angled triangle.

So, we have [tex]x^2 + y^2 = s^2[/tex] --------------(1)  

(please note all of them are changing as t increases.)

So, x=u×t and y=v×t,

so using (1), we can write

[tex][(u\times t)^2 + (v\times t)^2] = s^2[/tex]

[tex]s= \sqrt{(u^2 + v^2)}* t[/tex]

Using the value of u and v,

get [tex]\sqrt{(u^2 + v^2)}[/tex]= 65

So, s= 65 t

ds/dt = 65 mph

There fore the distance between the cars increasing 2 hours later is 65mph

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The apple mean weight's 95% confidence interval is;

CI = (119.14, 125.86) (119.14, 125.86)

The confidence interval above should be understood as;

We have a 95% confidence that each apple's average weight, across all of the apples they send, falls between 119.14 and 125.86 grams.

Ours is given;

12 for the standard deviation.

Sample size: 49; n

x = 122.5 is the indicated mean weight.

The current confidence interval formula is;

CI = x⁻ ± z(σ/√n)

Tables indicate that z = 1.96 at a 95% confidence level.

Thus;

CI = 122.5 ± 1.96(12/√49)

CI = 122.5 ± 3.36

CI = (122.5 - 3.36), (122.5 + 3.36)

CI = (119.14, 125.86)

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The equation that models the amount of time that is left on the cd is 80 - m.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, the blank CD can hold 80 minutes of music you have burned m minutes of music onto the cd. The time left will be:

= Total minutes - Time used

= 80 - m

This illustrates the equation.

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The polynomial equation  0 = 3x⁵ − x⁴ − 5x² + 1 contains 2 complex roots as a result.

Describe a polynomial.

A mathematical expression that contains at least two terms with variables or integers is referred to as a polynomial. A polynomial may include several terms.

Below is a polynomial equation that is given:

0 = 3x⁵ − x⁴ − 5x² + 1

Which can also be written as

3x⁵ − x⁴ − 5x² + 1 = 0

A polynomial of degree 5 is used in the accompanying polynomial equation.

Using a graphing application to solve it graphically is the simplest approach.

The polynomial equation obviously has a maximum of 5 roots because it is an equation of degree 5.

Now that we have the graph, we can use it to find the equation's roots.

There are 2 complex roots because there are only 3 real roots and 2 remaining are complex roots.

The polynomial equation  0 = 3x⁵ − x⁴ − 5x² + 1 contains 2 complex roots as a result.

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Answer: t = 5d t = 1/5d

Step-by-step explanation:

Answer:

f ≤ 4

Step-by-step explanation:

f/4 + 6 ≤ 7

f/4 ≤ 7 - 6

f/4 ≤ 1

f ≤ 4

Answer:

 F<4

________

________

Answer:6.5

Step-by-step explanation:

Here j = 0.5 and k = 0.25

7j+5-8k

= 7(0.5)+5-8(0.25)

= 3.5+5-2

= 6.5

The smallest possible value of the sum of the eight integers is given by:

116.

The eight integers in the problem are given as follows:

n, ..., n + 7.

Hence:

The smallest integer is more than 3/5 of the largest integer, hence the following inequality is built to relate them:

n > 3/5(n + 7)

Applying the distributive property on the right side, we have that:

n > 0.6n + 4.2.

0.4n > 4.2

n > 4.2/0.4

n > 10.5.

Hence the integers are:

11, 12, 13, 14, 15, 16, 17, 18.

(as 11 is the smallest integer possible).

Then the value of the sum is obtained as follows:

11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 = 116.

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Zeros of f(x) = [tex]x^{2} +6x[/tex] is (0,0) and (-6,0).

Given, f(x) = [tex]x^{2} +6x[/tex]

                = x(x+6)

For zeros, function f(x) = 0

x(x+6) = 0

x = 0    x+6 = 0

                x = -6

Putting values of x in equation,

For x = 0

f(x) = [tex]0^{2}+6(0)[/tex]

     = 0

Therefore, (0,0)

For x = -6

f(x) = [tex](-6)^{2}+6(-6)[/tex]

     = 36 - 36

     = 0

Therefore, (-6,0)

Hence, zeroes for f(x) is (0,0) and (-6,0).

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Answer: 11 Cents per ounce of Juice

Step-by-step explanation:

The first step here is going to be to find how many ounces are in a gallon. This can be determined as shown using the given information you stated above:

1 gallon * 4 quarts * 2 pints * 2 cups * 8 ounces = 128 ounces in 1 gallon

Step 2 is multiplying 128 ounces by 2 because we have two gallons of juice in the bottle:

128 ounces per gallon* 2 gallons = 256 ounces

Step 3 is dividing the total cost of the juice, which is $28.16, by the number of total number ounces (256)

$28.16 / 256 ounces = .11 dollars per ounce (aka 11 cents per ounce)

The tons of waste recycled in 2021 was 619.4286 tons.

According to the question,

We have the following information:

In 2021: There were 2341 people living in the town. Each person in the town recycled an average of 264.6kg of waste. Aleks knows that 1 ton = 1000kg.

Now, the total waste recycled in 2021 can be found using multiplication:

Number of people*waste recycled by each person

2341*264.6

619428.6 kg

Now, we will convert this from kilogram to tons.

1 ton = 1000 kg

1 kg = 1/1000 ton

So, we will divide the waste in kilogram by 1000:

Total waste recycled = 619428.6/1000

Total waste recycled = 619.4286 tons

Hence, the tons of waste recycled in 2021 was 619.4286 tons.

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