3. What is the variance of the following set of data?
4, 44, 404, 244, 4, 74, 84, 64
Use 82 =
Σ(x₁ - x)²
(N-1)
O139
O130
O19,298
16,886

2 Answers:

Choice C and choice E

======================================================

Explanation:

Choice A is ruled out because of the phrasing "rises and falls". A linear function can't do both rising and falling. You must only pick one direction to aim for. Choice B is ruled out for similar reasoning. A parabola is likely a better option for choice B.

Choice C is linear assuming the car stays at 55 mph. Recall that distance = rate*time. In this case, the equation is y = 55x where x is the number of hours and y is the distance traveled in miles. As an example, x = 10 hours leads to y = 550 miles traveled.

Choice D isn't linear. The increase of 2 doesn't match with the increase of 1. Linear functions must have the same amount of increase over the same time gap.

Choice E is linear and the equation is y = 2x, where x is the number of years and y is the number of movies made total. For example, at year x = 10, the director has made y = 2x = 2*10 = 20 movies total.

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

If in doubt, graph the situation. If you get a straight line, then the equation is linear.

Answer: c and e

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

4x+10=6x+2

Subtract 6x from both sides.

4x+10−6x=2

Combine 4x and −6x to get −2x.

−2x+10=2

Subtract 10 from both sides.

−2x=2−10

Subtract 10 from 2 to get −8.

−2x=−8

Divide both sides by −2.

x=

−2

−8

​

Divide −8 by −2 to get 4.

x=4

Answer: x=4

Step-by-step explanation:

1. Group all x terms on the left side of the equation

2. Group all constants on the right side of the equation

3. Isolate the x

If this helped please mark my answer as the brainliest, thank you!

steps below.

Solve  n-3 = 4 x 3 - n/7 : n = 105/8

What is Algebra?

Mathematics has several different subfields, including algebra. Algebra is the study of mathematical symbols and the rules for using them in formulas; it is a common thread that runs through practically all of mathematics.

To solve the equation :

n-3 = 4 x 3 - n/7

Solve for n

n-3 = 4 x 3 - n/7

n - 3 = 12 - n/7

n = 12 + 3 - n/7

n = 15 - n/7

n = (105 - n)/7

7n = 105 - n

7n + n = 105

8n = 105

n = 105/8

Hence, solution for n-3 = 4 x 3 - n/7 is n = 105/8

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The image of the point (8,4) after a rotation of 90° counterclockwise about the origin is (-y,x)=(-4,8).

Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about its origin (-y,x). In other words, reverse x and y and make y negative.

Given the point is (8,4)

After rotating the point to 90° counterclockwise about the origin, we get the point as (-4,8).

Terms like clockwise and anticlockwise are only applicable to rotating motions. A clock's hands move in the same direction as something moving in a clockwise manner. starting at the top and moving to the right, then down, then left, and then back up. The opposing direction of rotation or revolution might be thought of as anticlockwise.

Hence we get the point as (-4,8)

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The number of positive integers smaller than 1000 that are divisible by 7 must be determined using the rule of arithmetic progression.

There are 142 positive integers that are divisible by 7 that are less than 1000.

The positive numbers below 1000 that can be divided by seven include

7, 14, 21, 28,..........994.

The final number under 1000 that is divisible by 7 is 994.

An arithmetic progression's common form is [tex]T_{n} = a + (n-1)d[/tex]

where d is the common difference, n is the number of terms, and a is the first term.

We've :

a is 7 and d is 7.

When we generalize these values, we get at:

[tex]T_{n} = a + (n-1)d\\994 = 7 + (n-1)7\\994 -7 = 7n - 7\\994 = 7n \\n =\frac{994}{7} =142[/tex]

There are hence 142 positive integers below 1000 that are divisible by 7.

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The local bakery baked 120 chocolate cupcakes

The ratio of the strawberry cupcake to chocolate cupcake = 8:4

Number of strawberry cupcakes baked = 240

Ratios: Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other.

Let x represent the total number of cupcakes baked by the bakery

The Sum of the ratio is 8+4 = 12

So, the fraction of strawberry cupcakes baked = 8/12

The total number of cupcakes:

= 8/12 of x =240

8/12x = 240

x = 240*12/8

= 360

So, the number of chocolate cupcakes = 4/12 of 360

= 120

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Answer: 5.009 x 10^-9

Step-by-step explanation:

The independent variable, x in this scenario is; weeks.

The dependent variable, y in this scenario is; height.

It follows from the task content that the two variables which describe the growth model of the plants are; weeks and height.

Since, independent variable as the name implies is one whose values do not arrive from evaluation using other values, the independent variable in this scenario is; weeks.

However, by logic, the height of the plant is determined by the number of weeks and hence is dependent on the variable weeks. Therefore, the dependent variable is; height.

Ultimately, the independent and dependent variables are; weeks and height respectively.

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The strategy we will use is to first draw the diagonal; drop a right triangle to see the vertical distance of 6 units and the horizontal distance of 9 units; use the Pythagorean theorem to solve for the diagonal distance, approximately 10.8 units.

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Answer: The slope would be negative 3/4, so -3/4.

The commission earned by the salesman last month is $160.

For the given question,

The commission earned by the salesman is 20% on his sells.

Last month total sell = $800.

Let x be the total commission earned.

Then,

20% of 800 = x

x = 20× 800 / 100

x = 160

Thus, the commission earned by the salesman last month is $160.

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One way to determine the number is to multiply 2 and 9, this is because the resulting number will be divisible by them perfectly. Let's try:

So our candidate is 18, we need to test if it's divisible by 2 and 9 perfectly:

It is, therefore the number is 18.

Answer:

6.8 hours of pool use for a total monthly charge of $69.80

Step-by-step explanation:

6.8(6)+29=69.80

The 3 numbers are 17/4, and the number is equal to or greater than 8, and 7 respectively. We can solve the equation using a linear equation in one variable.

A linear equation is one in which the variable's maximum power is consistently 1. A one-degree equation is another name for it. A linear equation with one variable has the formula Ax + B = 0, which is its standard form. x is a variable, A is a coefficient, and B is constant in this situation. A linear equation with two variables has the formula Ax + By = C as its standard form. Here, the variables are x and y, the coefficients are A and B, and the constant is C.

1) Given that

five times the difference between a number and two is seven more than that number

Hence, by forming an equation we get

5(n-2) = n+7

5n -10 = n+7

4n = 17

n = 17/4

2)Given that

twice a number decreased by four is greater than ten, what numbers satisfy this condition

Hence, by forming an equation we get

2n -4 > 10

2n -4+4 > 10+4

2n > 14

2n / 2 > 14/2

n > 7

hence, a number greater than 7 will satisfy the equation.

3) Given that

twice a number decreased by two is equivalent to that number increased by five.

2n-2 =n +5

n = 7

Hence the number is 7

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The given algebraic expressions 5xy and -8xy are like terms because of the similarity in their variable and it's power.

As per the question statement, we are given algebraic expressions 5xy and -8xy and we are supposed to tell whether these two terms are like or not.

We know that in Algebra, the phrases or terms that include the same variable and are raised to the same power are referred to as "like terms."

Hence as the variable part in the expressions, 5xy and -8xy, are same hence they can be added and subtracted hence are called like terms.

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Answer: Answer: y=5−2x

Step-by-step explanation:

The equation of the line in the slope-intercept form is y=x2−35.

The slope of the perpendicular line is negative inverse: m=−2.

So, the equation of the perpendicular line is y=−2x+a.

To find a, we use the fact that the line should pass through the given point: 1=(−2)⋅(2)+a.

Thus, a=5.

Therefore, the equation of the line is y=5−2x.

The most appropriate choice for congruency of triangles will be given by -

Congruent Corrosponding parts

PQ = SR

QR = ST

PR = RT

∠QPR = SRT

∠QRP = ∠STR

∠PQR = ∠RST

What is congruency of triangle?

Two triangles are said to be congruent if all the corrosponding sides and corrosponding angles of the triangles are equals.

There are five axioms of congruency of triangles. They are-

SSS axiom, ASA axiom, AAS axiom, RHS axiom, SAS axiom

Here,

[tex]\Delta PQR \cong \Delta TSR\\[/tex]

Congruent Corrosponding parts

PQ = SR

QR = ST

PR = RT

∠QPR = SRT

∠QRP = ∠STR

∠PQR = ∠RST

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a) The angles associated with the cosine function are θ₁ = 45°, θ₂ = 315° and θ₃ = 405°.

b) The secant function of 585° is equal to - √2.

Graphically speaking, trigonometric functions are relations between two sides of a right triangles related to an angle. There are six trigonometric functions: (i) Two fundamentals (sine, cosine), (ii) Four derivates (tangent, cotangent, secant, cosecant). In the first part, we need to find all the possible angles such that the following trigonometric function is met:

cos θ = √2 / 2

The angles are located in the first and fourth quadrants, respectively. The solutions are θ₁ = 45°, θ₂ = 315° and θ₃ = 405°, respectively.

Now, we need to determine the secant function of 585°. Since the secant function has period of 360°, then we must find an angle coterminal to 585° that is between 0° and 360°:

θ' = 585° - 360°

θ' = 225°

And the trigonometric function is rewritten in terms of fundamental trigonometric functions:

x = 1 / cos θ'

x = 1 / cos 225°

x = 1 / (- √2 / 2)

x = - 2 / √2

x = - √2

The secant function of 585° is equal to - √2.

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30 cups of coffee, total 2.1 liters, were distributed equally. 70 milliliters of coffee were in each up.

Given that,

30 cups of coffee, total 2.1 liters, were distributed equally.

We have to find how much milliliters of coffee in each cup.

First we have to convert liters into milliliters.

We know 1 liter=1000 milliliters

So, now we convert 2.1 liters to __ milliliters.

=2.1×1000 milliliters

=21×1/10×1000

=21×100

=2100 milliliters.

So, 2100 milliliters of coffee available for distribution.

We know,

30 cups =2100 milliliters

Then

1 cup = ___ milliliters

1cup=2100/30

1cup=210/3

1 cup= 70

Therefore, 70 milliliters of coffee were in each up.

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Answer: take another pic but put it closer

Step-by-step explanation:

Hey there!

Not very sure if you mean [tex](\frac{5}{6x} )[/tex] or [tex](\frac{5}{6}x)[/tex], but I'll solve both

[tex]\frac{5}{6} x-9+3-\frac{2}{3}[/tex]

First step is to simplify:

[tex]\frac{5}{6} x+-9+3+\frac{-2}{3}[/tex]

Now, we need to combine Like Terms:

[tex](\frac{5}{6}x)+(-9+3+\frac{-2}{3} )[/tex]

[tex]\frac{5}{6} x+\frac{-20}{3}[/tex]

[tex]\frac{5}{6x} -9+3-\frac{2}{3}[/tex]

Simplify:

[tex]\frac{5(1-8x)}{6x} or\frac{-40x+5}{6x}[/tex]

Hope this helps!

1) 9, 7 , 13

Yes because the sum of the two smaller sides is greater than the third side.

2) 26 , 12 , 11

No because the sum of the two smaller sides is not greater than the third side.

3) 11, 2, 9

No because the sum of the two smaller sides is not greater than the third side.

4) 6,11,12

Yes because the sum of the two smaller sides is greater than the third side.

According to the Triangle Inequality Theorem, the total of any two sides in a triangle must be greater than the third side.

Two arcs in a triangle will only come together at their points of intersection if the sum of their radii is larger than the separation between their centers.

In a triangle, the difference between any two sides will be smaller than the third side if any two sides' sums are more than the third.

1) 9, 7 , 13

Yes because the sum of the two smaller sides is greater than the third side.

2) 26 , 12 , 11

No because the sum of the two smaller sides is not greater than the third side.

3) 11, 2, 9

No because the sum of the two smaller sides is not greater than the third side.

4) 6,11,12

Yes because the sum of the two smaller sides is greater than the third side.

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Answer:

274

Step-by-step explanation:

Rent paid by each Ali, Bilal and Karim is Rs.3775,  Rs.925 and  Rs.700 respectively.

A fraction is a valued that is expressed as a part of a whole. Here, the rent paid by each the members is a fraction of the total rent for the 3 years .

Now, according to the question

Karim stayed for 14/3 months in 3 years that is = 14/3*3

= 14 months (1 year and 2 months)

rent paid by each of them for first year = 1800/3

=  Rs.600

As, we know that 1800 is paid for 12 months ( 1 year )

So, rent for 1 month = 1800/12

=  Rs.150

rent paid by each of them for month =  Rs.150/3

=  Rs.50

Karim stayed for 2 more months, so he paid rent for  2 months =  Rs.50*2

=  Rs.100

So. total rent paid by Karin is = 600+100

=  Rs.700

For Bilal, he stayed for 17 months that is 1 year and 5 more months

rent he paid for 1 year =  Rs.600

rent he paid for 2 months when Karim was there too =  Rs.100

rent he paid with Ali when Karim was not there for 3 months = 150/2*3

=  Rs.225

So, total rent paid by Bilal is = 600+100+225

=  Rs.925

Total rent for 3 years is = 1800*3

=  Rs.5400

contribution of Bilal and Karim in the total rent for 3 year = 700+925

=  Rs.1625

So, rent paid by Ali = 5400-1625

=  Rs.3775

Therefore, we can conclude that the Rent paid by each Ali, Bilal and Karim is Rs.3775,  Rs.925 and  Rs.700 respectively.

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Answer:

0.512

Step-by-step explanation:

Answer:

0.512

Step-by-step explanation:

[tex]\frac{512}{1000} =0.512[/tex]

Hope this helps

Answer: B

y=3/5 x +4

Step-by-step explanation:

Insert each equasion into the graph with the points from the table and whichever line , lines up with the points is your answer

Answer:

yes because 5 is bigger than 0.5 and we are using the same type of mesuremenmeasurement