Find the slope that contains the points (-1, 4) and (2,6).

the approximate volume of the sphere is 523.33 mm³. The formula for the volume of a sphere is:

V = (4/3)πr³

where V is the volume and r is the radius of the sphere.

If we approximate π as 3.14, and assume a radius of 5 mm, we can calculate the volume as follows:

V = (4/3) x 3.14 x 5³

V ≈ 523.33 mm³

Therefore, the approximate volume of the sphere is 523.33 mm³.

The volume of sphere is the capacity it has. It is the space occupied by the sphere. The volume of sphere is measured in cubic units, such as m3, cm3, in3, etc. The shape of the sphere is round and three-dimensional. It has three axes as x-axis, y-axis and z-axis which defines its shape. All the things like football and basketball are examples of the sphere which have volume.

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Answer:

(0,0) is a solution.

Step-by-step explanation:

To see if this is true you can put (0,0) into the \(y\) and \(x\) variables like so: \(0>-3(0)+4\). When you solve this you get \(0>4\) so this statement is true

Answer:

Yes

Step-by-step explanation:

The bottom left corner is a right angle

a. To determine the probabilities associated with different service lives, we can use the properties of the normal distribution. Given that the mean service life is six years with a standard deviation of one-half year, we can calculate the probabilities as follows:

(1) Probability of service lives of at least five years:

We need to calculate the area under the normal curve to the right of five years. Using the Z-score formula, we find the Z-score corresponding to five years: Z = (5 - 6) / 0.5 = -2. We can then look up the corresponding probability in a standard normal distribution table or use statistical software to find the probability associated with a Z-score of -2. This gives us the probability of service lives of at least five years.

(2) Probability of service lives of exactly six years: Since the service life follows a normal distribution, the probability of exactly six years is zero since it is a continuous distribution. We can assign a very small positive probability to approximate "exactly" six years. (3) Probability of service lives of seven and one-half years: Similarly, we calculate the Z-score corresponding to seven and one-half years: Z = (7.5 - 6) / 0.5 = 3. We find the probability associated with a Z-score of 3 to determine the probability of service lives of seven and one-half years or longer. b. If the manufacturer offers service contracts of four years, we want to find the percentage of televisions that fail from wear-out during this period. We can calculate this by finding the area under the normal curve to the left of four years. Using the Z-score formula, we find the Z-score corresponding to four years: Z = (4 - 6) / 0.5 = -4. The corresponding probability gives us the percentage of televisions expected to fail during the four-year service period.

c. To achieve an expected wear-out rate of 2 percent or 5 percent, we need to determine the service period corresponding to these rates. We can use the Z-score formula in reverse to find the Z-score that corresponds to the desired wear-out rate. From there, we can calculate the corresponding service period by rearranging the Z-score formula and substituting the desired wear-out rate and the given mean and standard deviation values.

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The expression of the league fee is an algebraic expression

The expression that represents the league fee is 14x

The expression is given as:

14x + 20(2y + ) 5z + 10

The expression is not properly stated;

Only the league fee can be deducted from the given expression.

From the question, we understand that there are 14 players in total

i.e you (1) and (13) others

This means that the total league fee for the 14 players is:

Total = 14 * League fee for each player.

One of the terms of the expression is 14x.

So, we have:

14 * League fee for each player. = 14x

Hence, the expression that represents the league fee is 14x

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Perceived lack of anonymity is the source of bias that is most relevant to the given situation.

The data collected in the study, which is Mood on a Happy/OK/Sad scale, is qualitative or categorical data.

This describes an observational study.

What is Statistics?

Statistics is a field of study that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and statistical methods to extract meaningful insights from data and to draw conclusions or make decisions based on the findings.

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the volume and the total surface area of the cone are 628 cm³ and 502  cm²

The formula for calculating the volume of a cone is expressed as;

V = πr² h/3

such that the parameters are expressed as;

Substitute the values, we have;

Volume = 3.14 × 10² × 6/3

Find the square and substitute the values

Volume = 3. 14 × 100 × 6/3

Volume = 1884/3

Volume = 628 cm³

The total surface area = πrl+πr²

Substitute the value

= 3.14 × 10 × 6 + 3.14 × 10²

= 502  cm²

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Answer:

The error made by the student was that they didn't distribute the 7 first, they just added -2 and 7. The correct way would be to distribute first:

-2+7(x+8)

-2+7x+56

54+7x

*Hey! Hope this helped : )*

Answer:

7x + 54

Step-by-step explanation:

Given

- 2 + 7(x + 8)

The student made the error of adding before multiplying, that is

- 2 + 7 = 5 , then multiplying (x + 8) by 5

However, multiplication is performed before addition/ subtraction, thus

- 2 + 7(x + 8) ← distribute by 7

= - 2 + 7x + 56 ← collect like terms

= 7x + 54

Answer:

350

Step-by-step explanation:

Answer:35

Step-by-step explanation:

Answer:

4%

Step-by-step explanation:

to find percentage do 37 divided by 925 helps it helps :)

Answer:

33.5

Step-by-step explanation:

40 % of 33.5 is 13.4

33.5/x  = 40/100

13.4

Answer:

33.5

Step-by-step explanation:

Answer: 1 tablespoon

Step-by-step explanation:

In mathematics, an inverse function is one that "reverses" another function. The inverse of each function y = 3x + 1 is y = x−13.

The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f is bijective.

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.

Let the function be y = 3x+1

Replacing f(x) with y, we get

y = 3x+1

simplifying the above equation, we get

x = 3y + 1

Subtracting 1 from both sides to get

3y = x − 1

Dividing both sides by 3, we get

y = x−13

Replace y with f⁻¹(x), we get

f⁻¹(x) = x−13

The inverse of each function y = 3x+1 is f⁻¹(x) = x−13.

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Answer:

Step-by-step explanation:

Answer:

The war provided Great Britain enormous territorial gains in North America, but disputes over subsequent frontier policy and paying the war's expenses led to colonial discontent, and ultimately to the American Revolution.

Step-by-step explanation:

Answer:

First u get the Y by itself then you read the less than or equal to or greater than or equal to.

Step-by-step explanation:

hope it helps

We can use Coulomb's law to calculate the magnitude of the electric field at a distance r away from a point charge Q:

E = k * Q / r^2

where k is Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge.

In this problem, we have a point charge Q of -10 nC located at (1.2 cm, 0 cm), and we want to find the x-component of the electric field at a distance r = 5.3 cm away at position (-4.1 cm, 0 cm).

To find the x-component of the electric field, we need to use the cosine of the angle between the electric field vector and the x-axis, which is cos(180°) = -1.

So, the x-component of the electric field at position (-4.1 cm, 0 cm) is:

E_x = - E * cos(180°) = - (k * Q / r^2) * (-1)

where k = 9 x 10^9 N*m^2/C^2 is Coulomb's constant.

Substituting the given values, we get:

E_x = - (9 x 10^9 N*m^2/C^2) * (-10 x 10^-9 C) / (0.053 m)^2

E_x ≈ -30,566.04 N/C

Rounding this to two significant figures and including the appropriate units, we get:

The x-component of the electric field is about -3.1 x 10^4 N/C (to the left).

The required sum of the measures of angles D and F is 260 degrees.

Let's represent the measures of angles D, E, and F as D, E, and F, respectively.

From the given information, we have the following equations:

D + E = 110 (The sum of the measures of angles D and E is 110)

E + F = 150 (The sum of the measures of angles E and F is 150)

Now, we want to find the sum of the measures of angles D and F, which is D + F.

To find D + F, we need to eliminate E from the equations. We can do this by adding equations (1) and (2):

(D + E) + (E + F) = 110 + 150

Now, the E terms cancel out:

D + F = 260

So, the sum of the measures of angles D and F is 260 degrees.

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The area of parallelogram with "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches" is 60√3 inch².

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus. A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a type of polygon with four sides (also known as a quadrilateral) in which each parallel pair of sides is the same length.

Here,

A parallelogram has adjacent angles that add up to 180 degrees.

Since one angle of parallelogram is 120°.

240+2x=360

2x=120

x=60

The other will be 60°

The area of parallelogram= lh

l=15 inch

h=b(sin 60°)

=8*√3/2

h=4√3 inch

area of parallelogram= 15*4√3

= 60√3 inch²

The parallelogram's area is 60√3 inch² when "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches."

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Sam lives 162 miles away from the mountains.

Let's assume that the distance between Sam’s home and the mountains be x miles. Then, let us use the formula for distance which is:Distance = Speed × TimeFor Sam’s journey to the mountain, we know that he took 7 hours, therefore his speed was:S = D / T = x / 7For his return journey, Sam took 5 hours and he traveled 18 mph faster than he did on the way there; therefore, his speed is:S = (x / 5) + 18

Now we know that the distance he traveled to the mountains and back was the same. Therefore:Distance to the mountains = Distance from the mountainsx = (x / 7) × 2 + [(x / 5) + 18] × 2Then we simplify to get rid of the denominators:10x = 2x + 28x + 180Now we solve for x:8x = 180x = 22.5Therefore the distance between Sam's home and the mountains is 22.5 × 7 = 157.5 miles. However, that is only the distance to the mountain. We need to find the total distance of the round trip which is:Total distance = Distance to the mountains + Distance from the mountainsTotal distance = 157.5 + 157.5Total distance = 315 milesTherefore Sam lives 315 / 2 = 157.5 miles away from the mountains.

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Answer:

22 + x ≤ 40

x ≤ 18 pounds

Step-by-step explanation:

Maximum weight = 40 pounds

Initial weight = 22 pounds

Let Maximum weight that can be added = x

Mathematically, this means :

Initial weight + additional weight ≤ 40

That is ;

22 + x ≤ 40

Additional weight, x :

x ≤ 40 - 22

x ≤ 18 pounds

The coordinates of G which divides EF in the ratio 1:2 is (-6,1)

Coordinates: In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

given that EF with E(-7, 4) and F(-4,-5),

and if G lies on EF such that the ratio of EG to GF is 1:2

Now here we need to find the coordinates of G which divides EF in the ratio 1:2

to find the value of G once refer the graph from the diagram

here lets take the ratio in the form of fraction

which mean EG:GF

                   =1/1+2:2/1+2

                   =1/3:2/3

there, firstly find the difference between the coordinates of E and F

⇒ (-7-(-4),4-(-5)) = (-3,9)

secondly find 2/3rd of the distance using the above points

(here we can take 1/3rd too if we use 1/3rd then we have to use E coordinates)

2/3(-3)=-2

2/3(9)=6

Add these to the coordinates of F

which is equal to= (-4+(-2),-5+6)

                           = (-6,1)

the coordinates of G which divides EF in the ratio 1:2 is (-6,1)

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Answer:

{-1, 0, 1, 3}

Step-by-step explanation:

A relation is a set of ordered pairs of numbers. The domain of a relation is the set of all the first elements (or x-values) in the ordered pairs. In this case, the relation is (-1,5) , (0,4), ( 1,2) , (3,-2), so the domain is the set of all the x-values in these ordered pairs, which is the set {-1, 0, 1, 3}. Therefore, the domain of the relation is {-1, 0, 1, 3}.

Answer:22

Step-by-step explanation: 1/2 = .5

.5x.5x.5

0.125 x 176= 22

Answer:

k=-148.08

Step-by-step explanation:

1. Subtract 73.1: k/2.4=-61.7

2. Multiply both sides by 2.4: k=-148.08

Answer:

k=-148.08

Step-by-step explanation:

1. Subtract 73.1: k/2.4=-61.7

2. Multiply both sides by 2.4: k=-148.08

Answer:  the degree will go down 90 degrees

Step-by-step explanation: An obtuse triangle is one that has an angle greater than 90°. An acute triangle is defined as a triangle in which all of the angles are less than 90°.

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. It can tell us a lot about the graph of the polynomial, it can mainly tell us whether the graph is in a downward direction or upward direction.

If the leading coefficient is positive, then the graph will start at the origin and will extend upwards, with the degree of the polynomial determining how steep the graph is. If the leading coefficient is negative, then the graph will start at the origin and extend downwards.

If the leading coefficient is 0, then the graph will be a horizontal line. The leading coefficient can also tell us about the end behavior of the graph. If the degree of the polynomial is even, then the end behavior will be a horizontal line. If the degree of the polynomial is odd, then the end behavior will be a vertical line. Knowing the leading coefficient of a polynomial gives us a basic idea of what the graph of the polynomial will look like.

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