if x : y = 0.75 : 0.90 and y : z = 1/3 : 1/4
(A) simplify the ratio x : y and y : z

(B) find x : y : z

[tex]y = - 5x + n \\ [/tex]

[tex] - 2 = - 5( - 1) + n \\ - 2 = 5 + n \\ n = - 7[/tex]

[tex]y = - 5x - 7 \\ 5x + y = - 7[/tex]

Answer:

○ [tex]5x + y = -7[/tex]

Step-by-step explanation:

The formula for forming the equation of a line given a point and a slope is:

[tex]\boxed{y- y_1 = m(x - x_1)}[/tex],

where:

m = slope (-5)

[tex]y_1[/tex] = y-coordinate of point (-2)

[tex]x_1[/tex] = x-coordinate of point (-1).

Substituting these values into the formula:

[tex]y - (-2) = -5(x - (-1))[/tex]

⇒ [tex]y + 2 = -5(x + 1)[/tex]

⇒ [tex]y + 2 = -5x -5[/tex]      [expanding the brackets]

⇒ [tex]y = -5x -5 - 2[/tex]      [subtracting 2 from both sides]

⇒ [tex]y = -5x - 7[/tex]

⇒ [tex]5x + y = -7[/tex]            [adding [tex]5x[/tex] to both sides]

This means that the second option is correct.

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[tex]\Large\texttt{Answer}[/tex]

[tex]\bold{n-13}[/tex]

[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]

[tex]\Large\texttt{Process}[/tex]

⇨ Again letting n be the number

[tex]\bold{n}[/tex]

⇨ Subtract 13 from n

[tex]\bold{n-13}[/tex]

*unlike addition, the order DOES matter, because

[tex]\bold{n-13\ne 13-n}[/tex]

Hope that helped

1. The variance of the distribution of means option A) 15/20 = 0.75

2.  The decision that counselor  should make regarding the null hypothesis is that: option "Fail to reject it"

3. The effect of the  size is: option c:  (5 − 4.4)/.85 = .71

Note that:

Sample size =  20.

Note that for us to be able to get the answer in question one, we have to divide the unbiased estimate for the population variance by the use of  20 so that we can be able to get our unbiased estimate for the variance: And as such;

15/20 = 0.75.

The term fail to reject implies that  the null hypothesis is one that has not been disproven or wrong and therefore the use of the term "failure to reject." It is one that should not be taken with acceptance.

Therefore, 1. The variance of the distribution of means option A) 15/20 = 0.75

2.  The decision that counselor  should make regarding the null hypothesis is that: option "Fail to reject it"

3. The effect of the  size is: option c:  (5 − 4.4)/.85 = .71

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The given transformation is a reflection across the y-axis that changes the coordinates EFGH into E'F'G'H' as follows:

E(-4, -1) → E'(4, -1)

F(-2, -1) → F'(2, -1)

G(-1, -2) → G'(1, -2)

H(-1, -4) → H'(1, -4)

The transformation rules for reflection are:

Reflection at y-axis: y = f(-x);

Reflection at x-axis: y = -f(x);

The given polygon has four vertices EFGH.

Their coordinates are:

E(-4, -1), F(-2, -1), G(-1, -2), and H(-1, -4)

When the transformation rule: reflection across the y-axis is applied, the coordinates become:

y = f(-x); rule

For E(-4, -1), x-coordinate is -4. So, -(-4) = 4

⇒ E'(4, -1)

For F(-2, -1), x-coordinate is -2. So, -(-2) = 2

⇒ F'(2, -1)

For G(-1, -2), x-coordinate is -1. So, -(-1) = 1

⇒ G'(1, -2)

For H(-1, -4), x-coordinate is -1. So, -(-1) = 1

⇒ H'(1, -4)

Thus, the transformed coordinates are:

E(-4, -1) → E'(4, -1)

F(-2, -1) → F'(2, -1)

G(-1, -2) → G'(1, -2)

H(-1, -4) → H'(1, -4)

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Answer:

-5/3

Step-by-step explanation:

Do PEMDAS

8 - 11 = -3

-3 ^ 3 = -27

-(-27) = 27

I-14I = 14

3 x 14 = 42

27 - 42 = -15

2^4 = 16

16 - 7 = 9

-15/9 = -5/3

The radii and the heights of the two cylinders are

The volume of a cylinder is

V = πr²h

When the volumes of two cylinders are almost equal, then it means that:

V1 ≈ V2

This gives

πr²h ≈ πR²H

Divide both sides by π

r²h ≈ R²H

Assume that r = 5 and h = 6

So, we have:

5² * 6 ≈ R²H

Evaluate the product

150 ≈ R²H

Assume H = 10

So, we have:

150 ≈ R² * 10

Divide by 10

R² ≈ 15

Take the square root of both sides

R ≈ 3.87

Hence, the radii and the heights of the two cylinders are

Cylinder 1

Height = 6 and Radius = 5

Cylinder 2

Height = 10 and Radius = 3.87

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Answer:

These radius and height values will produce the same volume:

radius = 6 units and height = 18 units

radius = 9 units and height = 8 units

Answer: The gas would not have remained liquid

Step-by-step explanation:

Since the freezing point of gasoline starts at -40°F, and the temperature that day was -49°F, we can conclude that the gasoline would not have remained liquid

Formula for the Slope: (y2 - y1) / (x2 - x1)

You can use any two points to find the slope, as long as those two points are on the line.

Point 1 = (-2, 8)

Point 2 = (0, 0)

Slope = (0 - 8) / (0 - - 2)

Slope = -8 / 2

Slope = -4

Hope this helps!

Answer:

-4

Step-by-step explanation:

The formula to find the slope is (change in y)/(change in x). In other words, rise over run.

If we look at the data, we can see that the x and y value changes.

x value: -3 --> -2 --> -1 --> 0 --> 1

y value: 12 --> 8 --> 4 --> 0 --> -4

When y changed from 12 to 8, the x changed from -3 to -2.

y: 12 --> 8

x: -3 --> -2

There was a difference of -4 in the y and a difference of 1 in the x.

At the top, I wrote that the slope was (change in y)/(change in x)

With -4 and 1 we found, we can say that the slope is -4/1.

If we simplify this answer, we end up with -4.

So -4 is the slope of the data.

Answer:

A     [tex] \dfrac{2x^3}{3yw} [/tex]

Step-by-step explanation:

[tex] \dfrac{xy(24x^2y^3w)}{36y^5w^2} = [/tex]

[tex] = \dfrac{2 \times 12 x^3y^4w}{3 \times 12y^5w^2} [/tex]

[tex] = \dfrac{2x^3}{3yw} [/tex]

The height from the ground to the base of the window is 16 inches.

The ladder and the wall of the window form a right angled triangle. A right angled triangle is a three-sided polygon. The square of the longest side of a right angled triangle is equal to the sum of the squares of the other two sides.

In order to determine the length from the ground to the window, the law of similar triangles would be used. The similar triangles are triangle WXY and triangle VXZ. It is expected that the length of the sides are proportional to each other.

XY / XZ = WY / VZ

(8 / 24) = WY / 48

WY = (8 X 48) / 24 = 16 inches

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the ratio of the area of square KLMN to the area of LOK is 2a^2/b h

From the image given, we can deduce the following;

The formula for area of a square is

Area = a^2

Where, 'a' is the side

The formula for area of a triangle

Area = 1/ 2 base × height

Now, let's find the ratio

Ratio = area of KLMN/ area of LOK

Ratio = [tex]\frac{a^2}{\frac{1}{2} bh}[/tex]

Ratio = [tex]\frac{a^2}{\frac{bh}{2} }[/tex]

make the expression linear

Ratio = 2a^2/bh

The ratio of  the area of square KLMN to the area of LOK is 2a^2/bh

Thus, the ratio of the area of square KLMN to the area of LOK is 2a^2/b h

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If an arc has measure 7π/4 radians then it will be having 315 degrees and 60° in radian is π/3.

Given that arc has measure of 7π/4.

We are required to convert the measure from radian to degree measure.

Converting means chaning of units from one to another.

To convert 7π/4 into degrees we have to just put π=180 then we will get the value in degrees.

7π/4=7*180/4

=7*45

=315 degrees

Now we have to convert 60 degrees into radians.

60 degrees=60*π/180

=π/3

Hence if an arc has measure 7π/4 radians then it will be having 315 degrees and 60° in radian is π/3.

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Answer:

12

Step-by-step explanation:

Factoring out a 1/4 from 1/4a - 3, you get 1/4 (a - 12) as 12 * 1/4 = 3. Thus, ? = 12.

The value of P such that P*3=1 is 4

The set of Real numbers, R is given as

m*n=(√m +√n) (√m-√n).

The values of P, if P*3=1 is represented as:

P * 3=(√P +√3) (√P-√3).

The result of this operation is 1.

So, we have:

(√P +√3) (√P-√3) = 1

Apply the difference of two squares

P - 3 = 1

Add 3 to both sides

P = 4

Hence, the value of P such that P*3=1 is 4

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Answer:

a. 3x^3 + 2x^2 - 3x +10

Step-by-step explanation:

(x+2)(3x^2-4x+5)

x(3x^2-4x+5) +2(3x^2-4x+5)

3x^3-4x^2+5x+6x^2-8x+10

3x^3-4^2+6x^2+5x-8x+10

3x^3+2x^2-3x+10

0.8926 percent of the time, the shipment will be rejected.

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A delivery of 50 cheap digital watches, 10 of which are flawed.

A digital watch's likelihood of malfunctioning

P = 10/50

= 0.2

Size of sample: n = 10

Additionally, if they find one or more samples to be defective, they reject the entire cargo.

Making use of the binomial probability formula:

[tex]P(x)={ }^{n} C_{x} p^{x}(1-p)^{n-x}[/tex]

The random variable x should stand in for the quantity of defective watches.

The chance that the delivery will be refused is:

[tex]P(x \geq 1)=1-P(0)[/tex]

= [tex]1-{ }^{10} C_{0}(0.2)^{0}(0.8)^{10}[/tex]

= 1 - (0.8)[tex]^{10}[/tex]

= 0.8926

As a result, 0.8926 percent of the time, the shipment will be rejected.

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I understand that the question you are looking for is:

A shipment of 50 inexpensive digital​ watches, including 10 that are​ defective, is sent to a department store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective. What is the probability that the shipment will be​ rejected

The equation of the halfpipe is  Option A , (0, 20); Y equals one over eighty times x squared plus 20.

The equation of the halfpipe is  Y = X²/80 +20.

What is parabola ?

The equation of parabola is given by  

(X-h)² = 4p(Y-k)²

In this case h = 0

So we get  

Y = X²/4P +k

Focus point is (h, p+k) , (p+k) = 40

Hence h, k = (0,20)

P = 40-k = 20

Equation Y = X²/80 +20

Therefore, the equation of the halfpipe is  Y = X²/80 +20

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The complete question is -

A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 20 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?

(0, 20); y equals one over eighty times x squared plus 20

(0, 20); y equals one over eighty times x squared minus 20

(0, 10); y equals one over forty times x squared plus 10

(0, 10); y equals one over forty times x squared minus 10

Answer:

Points ABC and points OBC form two separate triangles. Triangle ABC is made up of angles BAC, ABC, ACB, while triangle OBC is made up of angles BOC, OBC, OCB. Since interior angles of triangles add up to 180 degrees, m<BAC + m<ABC + m<ACB = 180 and m<BOC + m<OBC + m<OCB = 180. 180 is equal to 180, so m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB.

Since OB bisects <ABC and OC bisects <ACB, m<ABO = m<OBC and m<ACO = m<OCB. We can also say that m<ABC = 2m<ABO and m<ACB = 2m<ACO. Substitute and simplify the equation.

m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB

m<BAC + 2m<ABO + 2m<ACO = m<BOC + m<ABO + m<ACO

m<ABO + m<ACO = m<BOC - m<BAC

The indicated maximum or minimum value of f is subject to the given constraint maximum is 125/27.

An instance of a constraint is the fact that there are only such a lot of hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. One that restricts, limits, or regulates; a take a look at.

A constraint is something that limits or controls what you can do. Their decision to abandon the trip was made due to monetary constraints. Water shortages in the location can be the primary constraint on development.  Synonyms: restriction, issue, lessen, rein greater Synonyms of constraint.

Constraints are used to limit the kind of records which can move right into a desk. This guarantees the accuracy and reliability of the facts inside the table. If there's any violation between the constraint and the facts motion, the motion is aborted. Constraints can be column stage or desk level.

From &22 = x²y 2

2

Given 2²+7+2=5

= <**,4),2=>

By Logange's multijet

(2643805 = 12'aresta

Mithaling by by and

and y

x²²* = P ←

: +(1,2,2) = $

= 125

279

The maximum value is 12r

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Answer:

15. 155°

16. 115°

Step-by-step explanation:

15.

Use the big triangle.

At the top, the supplement of 60° is 120°.

The angle measuring 120° and the angle measuring 35° are the remote interior angles to exterior angle x.

120° + 35° = x

x = 155°

16.

See picture below.

x = 115°

Answer:

  15)  x = 155°

  16)  x = 115°

Step-by-step explanation:

The theorem that relates an exterior angle of a triangle to the opposite (remote) interior angles is helpful for these problems. It says the exterior angle is equal to the sum of the remote interior angles.

Remove the altitude line and consider the interior angle of the triangle next to the exterior angle marked 60°. That interior angle will be ...

  180° -60° = 120°

Then the angle we just found and the one marked 35° are "remote" to the exterior angle marked x. The theorem cited at the beginning tells us ...

  x = 35° +120°

  x = 155°

Extend the left side of the "parallelogram" (the side with the arrow) upward until it meets the top horizontal line. This cuts off a triangle with an exterior angle marked x, an interior angle marked 50°, and another remote interior angle at the top edge of that triangle.

The opposite angles of a parallelogram are congruent, so the external angle to the triangle at the top edge will be x, and the adjacent interior angle in the triangle will be (180° -x).

The exterior angle (x) is equal to the sum of the remote interior angles (50° and (180° -x)), so we have ...

  x = 50 +(180 -x)

  2x = 230 . . . . . . add x, simplify

  x = 115 . . . . . . . divide by 2

The measure of the angles marked x is 115°.

Answer:

Number of the squares on chessboard = 64

Exponent form = [tex]8^{2}[/tex]

Step-by-step explanation:

8 x 8 = 64

exponent form of  of the chessboard

= [tex]8^{2}[/tex]

The distance between the bird and the aircraft is 10824 feet.

Any triangle with one angle at a right angle or two perpendicular sides is referred to as a right triangle, right-angled triangle, orthogonal triangle, or more formally, a rectangle triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.

The straight line that "just touches" the curve at a certain point is known as the tangent line to a plane curve. It was described by Leibniz as the line connecting two points on the curve that are endlessly near to one another.

Angle of elevation = 29°

Length of plane to the tower = 6000 feet

So, it forms a right angled triangle.

So, we will use "Tangent":

tan29° = AB/CB

.55 = 6000/CB

CB = 6000/0.55

CB = 10824ft

Consider, ΔABC,

Hence, The distance between the bird and the aircraft is 10824 feet.

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The general soultion of the given differential equation  12y'' − 5y' − 3y = 0 is

y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].

According to the given question.

We have a differential equation

[tex]12y^{"} -5y^{'} -3y = 0[/tex]

The above equation can be written as

[tex](12D^{2} -5D -3)y = 0[/tex]

The auxillary equation for the above differential equation is

[tex]12m^{2} -5m-3 = 0[/tex]

[tex]\implies 12m^{2} -9m+4m -3 = 0[/tex]

⇒ 3m(4m - 3) +1(4m - 3) = 0

⇒ (3m + 1)(4m -3) = 0

⇒ m = -1/3 or 3/4

Therefore,

[tex]C.f = c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex]

Here, P.I = 0

As we know that the general solution of the differential equation is given by

y = PI + CF

Thereofre, the general soultion of the given differential equation  12y'' − 5y' − 3y = 0 is

y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].

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[tex]2 \sqrt{4} + 3 \sqrt{9} \\ 2(2) + 3(3) \\ 4 + 9 = 13[/tex]

Answer:

13

Step-by-step explanation:

2×√4+3×√(9

2x2+3x3

The congruence postulate or theorem that is stated is the: C. AAS congruence theorem.

Triangles that are referred to as congruent triangles are triangles that have corresponding congruent sides and corresponding congruent angles.

According to the angle-angle-side congruence theorem (AAS) two triangles are congruent if two angles and a non-included side of one triangle are congruent to two corresponding angles and a non-included side of the other are congruent to each other.

For example, in triangles GUM and RED given in the image attached below, we have the following:

∠G ≅ ∠R [a pair of congruent angles]

∠M ≅ ∠D [a pair of congruent angles]

GU ≅ RD [a pair of non-included congruent side]

Thus, both triangles are congruent by the AAS, which is the congruence theorem that is stated above.

The answer is: C. AAS.

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Answer:

aas

Step-by-step explanation:

The value of the f(-8) from the given f(x) is 1/53.

According  to the statement

we have given that the value of f(x) and with the value of this we hav eto find the value of f(-8).

So, For this purpose,

The given value of f(x) :

The function f(x) is

f(x) = 1 / x^2 -11

Now we find the value of the f(-8) then

For this put Put x is -8 in the f(x) then the equation become

f(x) = 1 / x^2 -11

f(-8) = 1 / (-8)^2 -11

f(-8) = 1 / 64 -11

f(-8) = 1 / 53.

here the value becomes 1/53.

So, The value of the f(-8) from the given f(x) is 1/53.

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