What i the lope of the line that pae through the point (1, -9)(1,−9) and (4, -7)(4,−7)?

The given problem is asking for a test to see if the sample mean is significantly different from 85 at the 0.05 level. To solve the problem, we can use the following formula:$$t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$$where$\bar{x}$ = sample mean$\mu$ = population mean$s$ = sample standard deviation$n

$ = sample sizeTo calculate the t-value, we need to calculate the sample mean and the sample standard deviation. The sample mean is calculated as follows:$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$where $x_i$ is the score of the $i$th student and $n$ is the sample size.

Using the given data, we get:$$\bar

{x} = \frac{78+89+67+85+90+83+81+79}{8}

= 81.125$$The sample standard deviation is calculated as follows:$$

s = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}}$$Using the given data, we get:$$

s = \sqrt{\frac{(78-81.125)^2+(89-81.125)^2+(67-81.125)^2+(85-81.125)^2+(90-81.125)^2+(83-81.125)^2+(81-81.125)^2+(79-81.125)^2}{8-1}}

= 7.791$$Now we can calculate the t-value as follows:$$

t = \frac{\bar{x} - \mu}{\frac{s}

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Step-by-step explanation:

IF  x-4   is a factor, then putting in x = + 4    will make the polynomial = 0

5 ( 4^3) - 20 (4^2) - 5(4)  + 20   =   0    Yes...it is a factor

\(x - 4 = 0 \\ x = 4 \\ \)

substitute value of x in the function to see if it equals to zero , if not it won't be a factor of the function

\(5 {x}^{3} - 20 {x}^{2} - 5x + 20 = 0 \\ 5(4) ^{3} - 20( {4})^{2} - 5(4) + 20 = 0 \\ 5(64) - 20(16) - 20 + 20 = 0 \\ 320 - 320 - 20 + 20 = 0 \\ 0 = 0\)

so (x-4) is a factor for the function

Answer:

D

Step-by-step explanation:ik

The work done in each of the cases is:

B) W =  8,400 N*m

C) W = 17,500 N*m

The work can be defined by the product between the force and the distance translated.

W = Force*Distance

So, if there is a force of 120N and the vehicle moves 70 meters, the work done is:

W = 120N*70m = 8,400 N*m

C) Similar case to the above one, here the force is F = 3.5 KN = 3,500N

And the distance is d = 15m

Then in this case the work done is:

W = 3,500N*15m = 17,500 N*m

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Answer:

x= 42

Step-by-step explanation:

x/2+9=30

x+18=60

x=60-18

x= 42

The maximum amount of mushrooms Alberto can eat in a day is 4 kg.

Alberto can eat at most 4 kg of mushrooms in a day. If he picks 4 kg of mushrooms himself, he will not gain any monetary profit, and if he picks oranges, the monetary gain will be less than picking mushrooms.

He can sell mushrooms in the market for 514.79 per kg, whereas he can sell oranges for 38.7 per kg. It is evident that he will gain a lot of monetary profit by selling mushrooms rather than oranges.

Alberto can buy mushrooms from the market and sell them for a higher price. But it does not mean that he can eat more mushrooms. Alberto can consume a maximum of 4 kg of mushrooms whether he picks them himself or buys them from the market.

Therefore, the maximum amount of mushrooms Alberto can eat in a day is 4 kg.
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The correct option is A.

The linear equation y = 2x + 1 is shown in Graph A.

The equation of a straight line's shape with slope and y-intercept is as follows:

y = mx + b

where

y is equal to a point's y-coordinate on a line.

m is the line's slope.

The point on the line whose y-coordinate is y has the x-coordinate of x.

B is the line's y-intercept, or b.

As opposed to y = mx + b, y = 2x + 1

As we can see, the

m = 2 slope

b = 1 as the y-intercept

The graph that crosses the y-axis at the point where y = 1 is only option A, as shown by the intercept value.

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Note the correct question would be as bellow,

Which graph shows the linear equation y = 2x + 1

The smaller number is 1 and the larger number is 15.

Let me explain the solution in more detail.

We are given two pieces of information:

1) One number is 15 times greater than another number: This can be represented as y = 15x, where y represents the larger number and x represents the smaller number.

2) 5 times the larger number minus twice the smaller number is 73: This can be represented as 5y - 2x = 73.

To solve the system of equations, we use the substitution method. We solve one equation for one variable and substitute it into the other equation.

In this case, we solve equation (1) for y by expressing y in terms of x: y = 15x.

Then we substitute this expression for y in equation (2):

5(15x) - 2x = 73

Multiplying 5 by 15x gives us 75x:

75x - 2x = 73

Simplifying the equation, we combine like terms:

73x = 73

Dividing both sides of the equation by 73, we get:

x = 1

Now that we have the value of x, we substitute it back into equation (1) to find the value of y:

y = 15(1)

y = 15

Therefore, the smaller number is 1 and the larger number is 15, satisfying both conditions given in the problem.

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Answer:

75/100

=15/20

3/4

The probability is3/4

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Hope this helped have an amazing day!

The maximum area of the rectangle inside the ellipse is 2ab.

Given that,

Ellipse = x2 / a2 + y2 / b2 = 1

we know the general coordinates of any point in an ellipse of the equation

x2 / a2 + y2 / b2 = 1 is (acosθ,bsinθ)

So, we take general vertices of rectangles as

(acosθ,bsinθ), (acosθ,-bsinθ), (-acosθ,bsinθ), and (-acosθ,-bsinθ)

So, we can see that length and breadth of the rectangle is 2acosθ and 2bsinθ

So, its area will be ab4sinθcosθ (Length x Breadth)

Applying trigonometric formula 2sinθcosθ=sin2θ, let area equals to A

Now A=2absin2θ

Now as the area is the maximum given in the question, we have to differentiate it with respect to θ

dA/dθ=2abcos2θ×2 (using dsin2θ / dθ=2cos2θ)

Equating dA / dθ=2abcos2θ×2=0, it means cos2θ=0 , which means 2θ =  π / 2 and θ=π / 4

So now we to put θ=π / 4 in the equation of area which is A=2absin2θ

We get as A=2absin2π / 4=2absinπ / 2=2ab

Hence the max area of the rectangle inside the ellipse is 2ab.

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The sum of the algebraic expressions (–2.1x + 3.7) and (5 + 4.9x) as required in the task content is; Choice C; 2.8x + 8.7.

It follows from the task content that the sum of the algebraic expression given is to be determined.

Therefore, we have;

(–2.1x + 3.7) + (5 + 4.9x)

= -2.1x + 4.9x + 3.7 + 5

= 2.8x + 8.7.

Ultimately, the sum of the given algebraic expressions is; 2.8x + 8.7.

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Answer:

ITS C

Step-by-step explanation:I JUST TOOK THE TEST AND GOT A 100

sorry caps

Answer:

"16c"

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Answer:

16cm²

Step-by-step explanation:

Area of trapezium = ½(sum of parallel sides) x height

height= 4cm

parallel sides= 3cm and 5cm

½(3+5)cm x 4cm

½(8)cm x 4cm

32cm²÷ 2

16cm²

Answer:

x = -4

Step-by-step explanation:

\(x + 5 = 3x + 13\)

Subtract \(3x\) from both sides of the equation. You get:

\(-2x + 5 = 13\)

Subtract 5 from both sides:

\(-2x = 8\)

\(x = -4\)

Answer:

The slope of the line is 1/1, or 1.

Step-by-step explanation:

Walk/run, or x/y. X axis is over 1 and y axis is up 1.

Answer: y=3x-18

Step-by-step explanation:

So the first line that goes through (0,2) and (6,0) is y=(-1/3)x+2

You can calc the slope between (0,2) and (6,0) and the (0,2) gives you the intercept of 2.

Now for line B - - -  The slope of the perpendicular line is negative inverse: =3. (-1/3) ----> take the negative of negative 1/3 and it's positive 1/3, and now the inverse is 3.

The general equation for any perpendicular line through the equation we figured out in part A is y=3x+c, where c is your constant (y intercept) which is labeled R.

We can plug in the known point (6,0) in that equation y=3x+c and solve for C to figure out R.
0=3*6+c
0=18+c , so c must equal -18.

Now try out -18 in the equation to see if it works:::
y=3x-18

0=3*6-18

0=18-18

0=0

385 sets of three teams { a , b , c } were there in which a beat b , b beat c , and c beat a.

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Given.

Assume that each team played 40 times, winning 20 games and losing 20 games. We can see that each side must have beaten each other once and won against each other once.

Combinations are:

As a result, if we choose any three teams, there will be just one set of games in which A defeats B, B defeats C, and C defeats A. As a result, we simply need to choose three teams from the available 21 options. (Remember that order is irrelevant to set notation.)

Thus

²¹C₃

= 21*20*19/3!

= 7*10*19

= 1330.

However, this is based on 40 games for each side. They actually only participated in 20 games, thus we divided this total by two (665) to arrive at the actual answer.

20 games were played by each side. There must be 21 teams because they cannot compete against one another.

Three-team groups can be chosen.

21!/3!18! = 1330 ways

During the round robin, each will have played the other.

For instance, AB, BC, and CA.

There are two typical results.

The other two players can be defeated by one person. Another winner and loser will result from those two players competing. A team will so win two games, lose two games, and win one game.

Alternatively, each side could have a win and a loss. The question is how many of those three-person groupings are there.

One team wins twice in the first scenario mentioned above. That means two of that team's victories. The games in the group have been chosen. This is achievable.

45 ways divided by 21 players from 10!/2!8! =

945 ways

Therefore, there must be 385 methods left over to represent the scenario in the question after deducting 945 from 1330.

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Answer:

the x-intercepts are -5 and 2

Step-by-step explanation:

\(y=2x^2+6x-20\)

x-intercept is when y is set equal to zero

So, y = 0

\(0 = 2x^2+6x-20\)

\(2x^3+6x-20 = 0\\Taking \ 2 \ common\\2(x^2+3x-10) = 0\\Dividing \ both \ sides \ by \ 2\\x^2+3x-10 = 0\\Using \ mid\ term \ break \ formula\\x^2+5x-2x-10 = 0\\x(x+5)-2(x+5)=0\\Taking \ (x+5) \ common\\(x+5)(x-2) = 0\)

Either,

x+5 = 0     OR    x-2 = 0

x = -5       OR       x = 2

So, the x-intercepts are -5 and 2

Answer:

The x-intercepts would be (2, 0) and (-5, 0).

Step-by-step explanation:

To find the x-intercepts, substitute in 0 for y and solve for x.

0 = 2x^2 + 6x - 20.

Solve the equation.

x = 2, -5.

Answer:

scale

Step-by-step explanation:

The answer should be scale

Answer:

x = 180 -117

x = 63°

y = 90 - 63

y = 27°

Step-by-step explanation:

Answer:

and 4 easy

2

Step-by-step explanation:

The given equation is

x^2 + 7x = 8

By subtracting 8 from both sides, it becomes

x^2 + 7x - 8 = 0

We would find two terms such that their sum or difference is 7x and the product is - 8x^2. The terms are - x and 8x. Replacing 7x with - x and 8x, we have

x^2 - x + 8x - 8 = 0

By factorising, we have

x(x - 1) + 8(x - 1) = 0

Since x - 1 is common, it becomes

(x + 8)(x - 1) = 0

x + 8 = 0 or x - 1 = 0

x = - 8 or x = 1

Option C is correct

Answer:

the answer is 1.0 if u use sin to solve it, thus, u would get 0.9 of which if u round it u will get the answer above

Answer: and Step-by-step explanation:

sin(61) = x/55

55(sin(61)) = x

48.1 = x

Hope this helps!

Answer:

its 216 cubic feet.

Step-by-step explanation:

6x6x6 is 216

Answer:

75 cm

Step-by-step explanation:

It is given that the triangles are similar. It means that the ratio of their areas are equal to the ratio of their bases and ratio of their altitudes.

Let \(A_1\) be the area of 1st triangle.

Let \(A_2\) be the area of 2nd triangle.

Let \(h_1\) be the altitude of 1st triangle.

Let \(h_2\) be the altitude of 2nd triangle.

Let \(b_1\) be the base of 1st triangle.

Let \(b_2\) be the base of 2nd triangle.

Then \(A_1: A_2 = h_1 : h_2 = b_1 : b_2 ...... (1)\)

\(A_1 = 42 cm^{2} \\A_2 = 262.5 cm^{2}\\h_1 = 7 cm\\b_2 = ?\)

We know that area of a triangle is:

\(A = \dfrac{1}{2} \times b \times h\)

Area of smaller triangle:

\(\frac{1}{2} \times b_1 \times 7 = 42\\\Rightarrow b_1 = 12 cm\)

Now, using part of equation (1):

\(A_1: A_2 = b_1 : b_2 \\\Rightarrow \dfrac{42}{262.5} = \dfrac{12}{b_2}\\\Rightarrow b_2 = 75 cm\)

Hence, base of larger triangle = 75 cm

Answer:

Large number=12

Smaller number=6

Step-by-step explanation:

Let the two numbers be x and y

x+y=18

x-y=6

The actual factor of safety is 0.0874. a) One roof support load data: P = (600 × 100) / 4 = 150000 N

b) The value of z that corresponds to a reliability of 0.995 against compressive failure is 2.81.

c) The design factor associated with a reliability of 0.995 against compressive failure is 3.15.

d) The required diameter dowel for a reliability of 0.995 is calculated by:

\[d = \sqrt{\frac{4P}{\pi Su N_{d}}}\]

Where, \[Su\]-N[10.18, 0.4) ksi\[N_{d}\]= 0.2\[d

= \sqrt{\frac{4(150000)}{\pi (10.18) (0.2)}}

= 1.63 \,inches\]

The diameter of the dowel needed for a reliability of 0.995 is 1.63 inches.

e) A standard dowel with a diameter of at least 1.63 inches is required for a minimum reliability of 0.995 against failure. From the standard diameters given in the question, a 6-inch diameter dowel is the most suitable.

f) The actual factor of safety is the load that will cause the dowel to fail divided by the actual load. The load that will cause the dowel to fail is

\[P_{f} = \pi d^{2} Su N_{d}/4\].

Using the value of d = 1.63 inches,

\[P_{f} = \frac{\pi (1.63)^{2} (10.18) (0.2)}{4}

= 13110.35 \, N\]

The actual factor of safety is: \[\frac{P_{f}}{P} = \frac{13110.35}{150000} = 0.0874\]

Therefore, the actual factor of safety is 0.0874.

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The solutions are:

sin(a)  = 24/25

tan(a) = 24/7

For a given point (x, y) and an angle "a" measured counterclockwise from the positive x-axis to a ray that connects the origin with our point, we can think on the situation as a triangle rectangle.

Where the ray is the hypotenuse, the x-component is the adjacent cathetus, and the y-component is the opposite cathetus.

So we have:

x = adjacent cathetus

y = opposite cathetus

h = hypotenuse = √(x^2 + y^2)

Then the trigonometric relations become:

cos(a) = x/√(x^2 + y^2)

sin(a) = y/√(x^2 + y^2)

tan(a) = y/x

Now, we know that we have:

cos(a) = 7/25

then we can see that:

x = 7

and

h = 25 = √(7^2 + y^2)

We can solve the above equation for y:

25 = √(7^2 + y^2)

25 = √(49 + y^2)

25^2 = 49 + y^2

625 - 49 = y^2

√576 = y = 24

Then we have:

x = 7

y = 24

h = 25

Now we can return to our known trigonometric relations and get:

sin(a) = y/√(x^2 + y^2) = 24/25

tan(a) = y/x = 24/7

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The area of the gable if it is a triangle with two sides of 81 feet that meet at a 112 degrees angle is 3041.22 square feet

The two sides of the triangle=81

AB=AC=81 feet

∠A=112 degrees

∠BAD=∠DA =56 degrees

Here we have to use trigonometric functions

To find the height of the triangle we have to use the cos function

cos θ=Adjacent side/Hypotenuse

cos 56=Height/81

Height=81×cos 56

=45.29 feet

To find the length of the DC, we have to use the sine function

sin θ=Opposite side / Hypotenuse

sin 56=Base / 81

Base DC=81×sin 56

=67.15 feet

The base of the triangle BC=BD+DC

=67.15+67.15

=134.3 feets

The area of the triangle=(1/2)×b×h

Where b is the base and h is the height

=(1/2)×134.3×45.29

=3041.22 square feet

Hence, the area of the gable if it is a triangle with two sides of 81 feet that meet at a 112 degrees angle is 3041.22 square feet

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Answer:

yes

Step-by-step explanation:

if you imagine folding it up it will be 3D

It depends on what method you're using to approximate. Newton's method is a popular choice. Let \(h(x) = g(x) - f(x) = 3\log_{10}(x-2) - \log_{10}(x)\), with derivative

\(h'(x) = \dfrac1{\ln(10)} \left(\dfrac{3}{x-2} - \dfrac1x\right)\)

which follows from

\(\dfrac{d}{dx} \log_{10}(x) = \dfrac{d}{dx} \dfrac{\ln(x)}{\ln(10)} = \dfrac1{\ln(10)\,x}\)

Judging by the plots, we have \(f(x)=g(x)\) for some \(x\) between 3 and 4. So let's take an initial approximation of \(x_0 = 3\). Newton's method involves taking the tangent line approximation to \(f(x)\) at \(x=x_0\), then using the \(x\)-intercept of this tangent line as the next approximation, \(x_1\).

The linear approximation at \(x_0=3\) is

\(h(x) \approx h(x_0) + h'(x_0) (x - x_0) \approx 1.15812x - 3.95148\)

with intercept at \(x_1 \approx 3.41198\).

Repeat until you reach the desired threshold of accuracy. The next linear approximation at \(x_1\) is

\(h(x) \approx h(x_1) + h'(x_1) (x - x_1) \approx 0.79545 x-2.79758\)

with intercept \(x_2 \approx 3.51698\).

The next approximation at \(x_2\) is

\(h(x) \approx h(x_2) + h'(x_2) (x - x_2) \approx 0.735382 x-2.58956\)

with intercept \(x_3 \approx 3.52137\).

And so on. The actual solution has an approximate value of about

3.521379706804567569604081

so after just 3 approximations we're already less than \(10^{-5}\) away.