Graph the equation y = 3x - 6
Select two points to graph the line.

Answer:

13.1

Step-by-step explanation:

Answer:

Around 13 ounces

Step-by-step explanation:

Answer:

\(4y^{2}\)

Step-by-step explanation:

A = Area

w = width

l = length

\(A=lw\)

in this equation the area is \(32xy^{3}\) and the length is \(8xy\).

To find the equation we simply have to divide the area (\(32xy^{3}\)) by the length (\(8xy\)).

\(32xy^{3} =(8xy)w\)

When dividing, it's important to remember two things:

Using these two rules, we divide the common bases (number by number, x by x, y by y):

\(\frac{32}{8}=4\)

\(\frac{x}{x}=1\)

\(\frac{y^{3} }{y}=y^{2}\)

Multiplying all of them together, we find that the width is:

\(4y^{2}\)

The linear equation that passes through the two given points is:

y = (-1/4)*x - 2/4

A general linear equation is written as:

y = m*x + b

Where m is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of the line is:

m = (y₂ - y₁)/(x₂ - x₁)

Here we know that the line passes through (-1, -1/4) and (1, -3/4)

Then the slope is:

m = (-3/4 + 1/4)/(1 + 1)

m = (-2/4)/2 = -2/8 = -1/4

the line is:

y = (-1/4)*x + b

To find the value of v we can replace the point  (1, -3/4) so we get:

-3/4 = (-1/4)*1 + b

-3/4 + 1/4 = b

-2/4 = b

The linear equation is:

y = (-1/4)*x - 2/4

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This question is incomplete, the complete question is;

Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places.

x² + 9y² = 9

(a) About

y = 3

(b) About  

x = 3

Answer:

a) the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288

b) the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288

Step-by-step explanation:

a) the volume of solid of revolution

about y=3

Using SHELL METHOD;

Volume V = 2π . \(\int\limits^1_{y=-1} \,\) (3-y) (2.3√(1-y²)) dy

= 12π . \(\int\limits^1_{y=-1} \,\)  (3-y) √(1-y²) dy

= 12π . \(\int\limits^1_{y=-1} \,\)  (( 3√(1-y²) - y(√(1-y²)) dy

= 12π[ \(\frac{3}{2}\)π - 0 ]

= 18π² = 177.652879 ≈ 177.65288

Therefore, the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288

b)

the volume of solid of revolution

about x=3

Using SHELL METHOD;

Volume V = \(\frac{4}{3}\)π . \(\int\limits^3_{y=-3} \,\) (3-x) (\(2.\frac{1}{3}\)√(9-x²)) dx

= \(\frac{4}{3}\)π . \(\int\limits^3_{y=-3} \,\) (3-x) √(9-x²) dx

= \(\frac{4}{3}\)π . \(\int\limits^3_{y=-3} \,\) (3√9-x² -x√(9-x²) dx

=  \(\frac{4}{3}\)π [ \(\frac{27}{2} \pi\) - 0 ]

= 18π² = 177.652879 ≈ 177.65288

Therefore, the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288

Step-by-step explanation:

Based on the information given, we have a diagram with two sides labeled as 13.3 mm and 5.5 mm, and another side labeled as X mm.

To find the length of X, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.

Perimeter = 13.3 mm + 5.5 mm + X mm

The perimeter is the total distance around the triangle. Since we have three sides, the perimeter is the sum of the lengths of those sides.

To find X, we can subtract the sum of the known sides from the perimeter:

X mm = Perimeter - (13.3 mm + 5.5 mm)

Since the value of X is not given, we cannot calculate it without the perimeter value. If you provide the perimeter value, I can help you find the length of X.

Answer:

B. (-1,7)

Step-by-step explanation:

If the train travels at an average speed of 50 Km/h, it would be late by 10 minutes.

Speed is simply referred to as distance traveled per unit time.

It is expressed as:

Speed = distance / time

Given that the train running between two stations 50 Km apart arrives on time if it travels at an average speed of 60 km/h.

The time taken by the train to travel 50 km at an average speed of 60 km/h can be calculated using the formula:

Speed = distance / time

time = distance / speed

time = 50 km / 60 km/h

time = 5/6 hour

Next, if the train travels at an average speed of 50 km/h, the time taken to cover the same distance of 50 km would be:

Speed = distance / time

time = distance / speed

time = 50 km / 50 km/h

time = 1 hour

Now, the difference in time between the two scenarios would be:

time difference = 1 hour - 5/6 hour

time = 1/6 hour

Convert to minutes

time = 1/6 × 60

time = 10 minutes

Therefore, the train would be late by 10 minutes.

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Steve is correct. Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0.

By using a number line, Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0. One temperature is negative and the other is positive, but by adding their distances, he can find the difference. Kelly's method of subtracting -5.1 from the temperature at 12 PM on Wednesday is not necessarily incorrect, but it does not give the exact difference in temperature between the two times. Therefore, using Steve's method, the change in temperature would be the sum of the distance from 0 to the temperature at 7 AM (which is 2.5) and the distance from 0 to the temperature at 12 PM (which is also 2.5), resulting in a difference of 5 degrees.

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*this answer i made was incorrect please avoid it*

Answer:

15

Step-by-step explanation:

Pythagoras theorem

a^2+b^2=c^2

12*12=144

9*9=81

144+81=225

sq root of 225 = 15

(i) Probability is a notion in Mathematics which describes the likelihood of an event or a set of events occurring. It is a measure of uncertainty when estimating the outcome of an experiment or an observation.

(ii) The axioms of probability are:

the non-negativity (that the probability of an event is greater than or equal to zero), and

the additivity (that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities).

(iii) When two fair dice are thrown the probability of getting:

a) The sum of 9 = 1/9

b) Two odd numbers = 1/4

c) two prime numbers = 1/9

d)  two factors of 12 = 1/9

(iv) Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, presentation, etc.

To find probability when two dice are thrown, we have:

(a) The sum of 9:

We will estimate the number of ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3) = 4 ways

A die has 6 possible outcomes, the total number of possible outcomes is 6x6=36 = 4/36 = 1/9.

(b) Two odd numbers:

We count the number of ways to get two odd numbers: (1,3), (1,5), (1,7), (3,1), (3,5), (3,7), (5,1), (5,3), and (5,7).

possible outcomes = 9,

So, the total possible outcomes = 6x6=36 = 9/36 = 1/4.

(c) Two prime numbers

We estimate the number of ways we can get two prime numbers: (2,3), (3,2), (5,2), and (2,5)

possible outcomes = 4,

So, the total possible outcomes = 6x6 =36 = 4/36, = 1/9.

(d) Two factors of 12:

We count the number of ways and divide by the total possible outcomes.

The factors of 12 are 1, 2, 3, 4, 6, and 12: (2,6), (3,4), and (4,3) = 3 ways

possible outcomes = 6

Therefore, the total number of possible outcomes = 6x6=36 = 3/36, = 1/12

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Answer:

Step-by-step explanation:

Triangle ABC is a right angled triangle. A right angle triangle has three sides (The hypotenuse which is the longest side and the other two sides which are the adjacent and the opposite).

The side facing the angle of a right angled triangle is the opposite side depending on the angle in consideration.

According to the triangle, AB = hyp = 5, BC = 3 and AC = 4

Side AB is facing the right angle, side BC is opposite to the angle A while side AC is opposite to the angle B.

Based on the conclusion in the last paragraph, it can be concluded that the  length of the side opposite Angle B is AC and since the measurement of AC is 4 units, then the length we are looking for is 4 units.

Answer:

B. 4 units

Step-by-step explanation:

SOLUTION:

We use the intersecting tangents theorem;

Thus;

Thus,

Answer:

0.4114 = 41.14% probability that he answers at most three of them are correct

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is answered correctly, or it is not. The probability of a question being answered correctly is independent of any other question. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

20 questions:

This means that \(n = 20\)

Assume that each question has five possible choices, and only one of them is correct.

This means that \(p = \frac{1}{5} = 0.2\)

What is the probability that he answers at most three of them are correct?

This is:

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)\)

So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{20,0}.(0.2)^{0}.(0.8)^{20} = 0.0115\)

\(P(X = 1) = C_{20,1}.(0.2)^{1}.(0.8)^{19} = 0.0576\)

\(P(X = 2) = C_{20,2}.(0.2)^{2}.(0.8)^{18} = 0.1369\)

\(P(X = 3) = C_{20,3}.(0.2)^{3}.(0.8)^{17} = 0.2054\)

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0115 + 0.0576 + 0.1369 + 0.2054 = 0.4114\)

0.4114 = 41.14% probability that he answers at most three of them are correct

The amount of water tank  with water after 10 minutes will be 4950 liters.

To solve this problem, we need to keep track of the net flow of water into the tank over the course of 10 minutes. The tap filling water adds water to the tank, while the tap emptying water removes water from the tank.

Let's calculate the net flow rate of water per minute:

Flow rate = (filling tap flow rate) - (emptying tap flow rate)

Flow rate = 40 L/min - 25 L/min

Flow rate = 15 L/min

Now, we can calculate the net flow of water over 10 minutes:

Net flow of water = (flow rate) * (time)

Net flow of water = 15 L/min * 10 min

Net flow of water = 150 L

Therefore, over the course of 10 minutes, the net flow of water into the tank is 150 liters.

Initially, the tank had 4800 liters of water. Adding the net flow of water, we can determine the final amount of water in the tank:

Final amount of water = (initial amount of water) + (net flow of water)

Final amount of water = 4800 L + 150 L

Final amount of water = 4950 L

After 10 minutes, there will be 4950 liters of water in the tank.

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Answer:

B. f and g are reflections of each other about the y-axis.

Step-by-step explanation:

I calculated it logically

The value x in the secant line using the Intersecting theorem is 4.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the figure:

First sectant line segment = ( x - 1 ) + 5

External line segment of the first secant line = 5

Second sectant line segment = ( x + 2 ) + 4

External line segment of the second secant line = 4

Using the Intersecting secants theorem:

5( ( x - 1 ) + 5 ) = 4( ( x + 2 ) + 4 )

Solve for x:

5( x - 1 + 5 ) = 4( x + 2 + 4 )

5( x + 4 ) = 4( x + 6 )

5x + 20 = 4x + 24

5x - 4x = 24 - 20

x = 4

Therefore, the value of x is 4.

Option C) 4 is the correct answer.

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Answer:

corresponding

Step-by-step explanation:

<1 and <5 are corresponding angles because they are on the same side of the transversal and on the same side of l and m

Answer:

S₁₆ = 344

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = - 1 and d = a₂ - a₁ = 2 - (- 1) = 2 + 1 = 3 , then

S₁₆ = \(\frac{16}{2}\) [ (2 × - 1) + (15 × 3) ]

     = 8 (- 2 + 45)

     = 8 × 43

     = 344

The correct statements are:

a) The independent variable is the number of people.

b) The initial value (initial fee) for the picnic is $40.

d) As the number of people increases, the total cost of the picnic increases.

A general linear equation is given by:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is given by the formula:

m = (y - y')/x - x'

Now let's analyze the table:

The x-values are the ones in the left and the y-values are the ones on the right, now from the table we can use two points, let's use the first two:

(6, 52) and (9, 58).

Then the slope is:

a = (58 - 52)/9 -6 = 2

Then the line is something like:

y = 2*x + b

To find the value of b, we use the point (6, 52). This means that when x = 6, y must be equal to 52.

We will get:

52 = 2*6 + b

52 = 12 + b

52 - 12 = b = 40

Then the linear equation is:

y = 2*x + 40

Now let's see which statements are correct.

a) The independent variable is the number of people.

True, the "x" represents the number of people.

b) The initial value (initial fee) for the picnic is $40.

True, the y-intercept does not depend on the value of x, so we can say that you need to pay that indifferent of the number of people that goes.

c)The rate of change is $8.67 per person.

False, the rate of change is equal to the slope, in this case is $2 per person.

d) As the number of people increases, the total cost of the picnic increases.

True.

e)  If 4 people attended the picnic, the total cost would be $46.

To see if this is true or not, we just need to evaluate the function that we got in x = 4.

y = 2*4 + 40 = 48

So we can see that this is false.

Therefore, the correct statements are A, B, D

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Answer:

$250

Step-by-step explanation:

because we have to do 5,000 of 5% = 250 in sale's tax or interest.

The solution is, $250 is the amount of interest.

Interest is the outlay you pay to borrow money. Interest is often deliberated as an annual percentage of a loan amount.

here, we have,

Explanation:

given that,

A $5000 loan at 5% dated July 5 is due to be paid on November 10.

Since the borrower is to pay 5% of the money by  November 10(Due time)

so, we get,

5% of the principal is simply

(5/100)* 5000

= $250

Hence, The solution is, $250 is the amount of interest.

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Answer:

1)  H0 :  σ₁ ²≥ σ₂²;   Ha:  σ₁² < σ₂²

2)  χ²= 43.52

3) The critical region is χ²≤ 5.23

4) Reject the alternate hypothesis.

5) We conclude that the alternate hypothesis is false and accept the null hypothesis.

Step-by-step explanation:

The claim is that it fills bottle with a lower variation which is the alternate hypothesis

1)  Ha:  σ₁² < σ₂² where  σ₁² is the variation of the new machine and σ₂² is the variation of the old machine.

The null hypothesis is opposite of alternate hypothesis H0 :  σ₁ ²≥ σ₂²

2) The test statistic is χ²= ns²/σ ² which under H0 has  χ² distribution with n-1 degrees of freedom assuming the population is normal.

The calculated χ²= ns²/σ ² = 68( 0.12)²/ (0.15)²=0.9792/0.0225= 43.52

3) The critical region is entirely in the left tail. χ²≤χ²( 0.99)(15)= 5.23

4) The alternate hypothesis is false hence reject it.

5) The calculated χ²=  43.52 does not lie in the critical region χ²≤ 5.23 therefore H0 is accepted and concluded that new machine does not fill bottles with a lower variation.

Answer:

1.58 ish

Step-by-step explanation:

For a logx y = z, x^z = y
So here, log4 9= 1.58 or so
1.5849625007

Answer:

a_n = 47 - 8n

Step-by-step explanation:

a_1 = 39

a_2 = 31

a_3 = 23

31 - 39 = -8

23 - 31 = -8

This is an arithmetic sequence with constant difference -8.

a_1 = 39

a_2 = 39 - 8

a_3 = 39 - 8 - 8 = 39 - 2(8)

a_4 = 39 - 8 - 8 - 8 = 39 - 3(8)

...

a_n = 39 - (n - 1)(8)

a_n = 39 - 8(n - 1)

a_n = 39 - 8n + 8

a_n = 47 - 8n

Answer:

\(a_n=47-8n\)

Step-by-step explanation:

Given sequence:

Calculate the differences between the terms:

\(39 \underset{-8}{\longrightarrow} 31 \underset{-8}{\longrightarrow} 23\)

As the differences are constant (the same), this is an arithmetic sequence with:

\(\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\end{minipage}}\)

Substitute the found values of a and d into the formula to create an equation for the nth term of the sequence:

\(\implies a_n=39+(n-1)(-8)\)

\(\implies a_n=39-8n+8\)

\(\implies a_n=47-8n\)

The solution of the simultaneous equation is given by x = (15 + z - 4y )/2

A system of linear algebra (or linear system) is a collection of one or more numerical solutions using the same variables. is a set of three equations with the variables x, y, and z.

The answer to a linear system is to give each variable a value that simultaneously satisfies all of its equations. The solution to the above system is given by the ordered triple that comes after.

Even though the coefficients of equations are typically real or complex figures and the solutions are sought in the same set of numbers, the theory and methods are applicable to coefficients and solutions in any field.

the given equation is 2x + 4y − z = 15

we add z to both sides

2x+4y = 15 +z

we subtract 4y from both sides

2x = 15 +z - 4y

now we divide throughout by 2

x = (15 + z - 4y )/2.

hence the value of x is (15 + z - 4y )/2

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Answer:

Open circle at -1 and shading to the left

Step-by-step explanation:

Given the question :

Which number line shows the solution to the inequality −2(3x − 1) < 8? Group of answer choices Open circle at 2 and shading to the right Open circle at 2 and shading to the left Open circle at -1 and shading to the right Open circle at -1 and shading to the left.

−2(3x − 1) < 8

Open the bracket and simplify :

-2(3x - 1) < 8

-6x + 2 < 8

-6x < 8 - 2

-6x < 6

Divide both sides by - 6

-6x/-6 < 6/-6

x > - 1

Or - 1 < x

Since - 1 is less than x, from - 1 we draw to the left

Jordan spend 25 minutes writing each dayNoHow much time does Jordan spend writing each dayFrom the question, we have the following parameters that can be used in our computation:D + W = 75W + 25 = DSo, we haveW + W + 25 = 75EvaluateW = 25This means that Jordan spends 25 minutes on writing is it possible?Based on the answer in (a), the truth statement is No

Answer:

2107 marbles can be stored in the container.

Step-by-step explanation:

Since a merchant keeps marble in a cylindrical plastic container that has a diameter of 28cm and height of 35cm, and a marble has a diameter of 25mm, to determine the number of marbles that can be stored in such a container if air space accounts for 20 % between marbles, the following calculation must be performed, knowing that the volume of a cylinder is equal to height x π x radius²:

35 x 3.14 x (28/2) ² = X

109.9 x (14 x 14) = X

109.9 x 196 = X

21,540.4 = X

In turn, the volume of each 25mm diameter marble is equal to:

25mm = 2.5cm

4/3 x 3.14 x 1.25³ = X

4.18666 x 1.953125 = X

8.1770 = X

21,540.4 x 0.8 = 17,232.32

17,232.32 / 8,177 = 2,107.41

Therefore, 2107 marbles can be stored in the container.

Answer: Could you take a pic of the sheet because there is no sign ( x, +, etc.)

Step-by-step explanation:

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.