(b) If the radius of wheel is 7cm, how far it travels in three rotation​

The sine of an acute angle is less than one because it is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Since the side opposite the angle is shorter than the hypotenuse, the ratio is always less than one.

To what does sin equate?

In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.

It's also the same reason why the cosine of an acute angle is always less than one because it is the ratio of the adjacent side of the angle to the hypotenuse.

It's important to note that this is only true for acute angles, angles smaller than 90 degrees.

For obtuse angles, greater than 90 degrees, the sine and cosine values are greater than one.

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Draw a line and locate the origin '0', mark the positive numbers on the right and the negative number on the left of '0' at an equal distance.

A number line is a horizontal straight line in which the integers are placed in equal intervals. All the numbers can be represented in a number line. This line can be extended indefinitely at both ends. 

A number line is a graphical representation of numbers on a straight line. It is used for comparing and ordering numbers. It can be used for representing any real number that includes every whole number and natural number.

Draw a line and locate the point ‘0’. This point is known as the origin. If the given number is positive, draw it on the right side of the origin. If it is a negative number, draw it on the left side of zero. Divide each unit into the values equal to the denominator of the given fraction.

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The requried derivative of the given function is [tex]F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex].

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol

here,
Given expression,
[tex]F(x) = \int\limits^{x^2}_x {e^{t^7}} \, dx[/tex]

Following the Leibniz rule
[tex]F'(x) = \frac{d}{dx}[ \int\limits^{x^2}_x {e^{t^7}} \, dx]\\F'(x) = \int\limits^{x^2}_x \delta/\delta x (e^{t^7}) + (e^{(x^2)^7}) d/dx (x^2) - e^{x^7}d/dx [x] \\F'(x) = 0 + 2xe^{x^{14}} - e^{x^7}\\F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex]

Thus, the requried derivative of the given function is [tex]F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex].

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The correct order of match is 1-a, 2-b, 3-d and 4-c.

The term "conic" refers to a curve formed by the intersection of a right circular cone with a plane. In Euclidean geometry, it has distinctive features. The cone is split into two nappes, the upper nappe and the lower nappe, at its vertex.

A plane crosses the cone, and the resulting section is referred to as a conic section.

Given the equations,

the equation for parabola is given by

(y - b)² = 4p(x - a)

Vertex is (a,b)

equation 2 follows the same

x = -2(y - 4)² + 3

this is the equation for parabola.

Equation for ellipse is

(x − a)²/h² + (y − b)²/k² = 1

the equation x²/4 + (y - 8)²/144 = 1

(x/2)² + ((y - 8)/12)² = 1

the equation is same is equation for ellipse,

Equation for circle

(x - h)² + (y - k)² = r²

fourth equation

(x - 9)² + (y + 2)² = 7²

is same as equation of circle

Equation for hyperbola

(x − a)²/h² − (y − b)²/k²  = 1

equation (x - 3)²/5 - (y + 4)²/25 = 1

is same as equation of hyperbola.

Hence the correct order is a, b, d, and c.

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Volume of prism is given by V= base area × height cubic unit. The expression 48 × 3  unit³ can be used to represent the volume of the prism.

Prism is a three-dimensional geometrical figure having identical two ends. A prism has flat faces, similar bases and equal cross sections. A prism is normally bounded by plane faces.

Volume of prism is calculated by the product of base area and height of the prism. At first, we need to calculate the base area and then height is multiplied with it.

Prisms are different types such as triangular prism, rectangular prism, pentagonal prism and hexagonal prism so depending on the figure area for the base is different. As a result, different shaped prism has different formula for volume calculation.

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Answer:

[tex]h=\pm6[/tex]

Step-by-step explanation:

[tex]3h^4=3888\\h^4=1296\\h=\pm6[/tex]

Respuesta:  Racional

Explicación:

El número es racional ya que podemos representarlo como una fracción de enteros.

Más específicamente, -97.54 = -9754/100

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

Translation to English:

Answer: Rational

Explanation:

The number is rational since we can represent it as a fraction of integers.

More specifically,  -97.54 = -9754/100

Therefore, the solution of the given problem of function comes out to be [tex]f^{-1}[/tex] =  x+ 6 /7.

Mathematics includes the study of numbers, equations and associated structures, forms and the environments in which they occur, quantities and their changes, and spatial relationships. A function is an association between such a set of inputs, each of which has an output. Simply described, a function is an association between the inputs and outputs in which each input results in a single, distinct result. Each operation has a domain and a scope, which are also referred to as codomains.

Here ,

In our case, f(x) = y = 7x-6.

The following procedures must be taken in order to determine the inverse function of the given function:

First, x and y must be switched, thus

x= 7y-6

We must add 6 to both sides in order to solve for y in the following step.

x+6=7y

7 divided by both sides, that is

y = x+ 6 /7

Therefore, the solution of the given problem of function comes out to be

[tex]f^{-1}[/tex] =  x+ 6 /7.

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If each score is doubled, and then 5 is subtracted from that result, then the mean and standard deviation will be 115 and 36 respectively.

A huge group of test results has a mean of 60 and a standard deviation of 18. If each score is doubled and then 5 is deducted from the result, the mean and standard deviation are “ mean = 115; standard deviation = 36”. Mean = 2 x 60 -5 = 120 -5 = 115

2 x 18 = 36 standard deviation

The mean is the average and is calculated as the sum of all the results from the example divided by the total number of events.

The standard deviation (SD) is a statistic used to assess the degree of variation or dispersion in a set of data values.

A low standard deviation indicates that the information points slant toward being near the mean of the set, whereas an exclusive expectation deviation or a high standard deviation indicates that the information points tilt toward being near the mean of the set.

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Area of the pond is 86.625 m²

Given data :

Diameter of the pond = 14m

Radius of the inner circle (pond), r = 7 m

Width of the concrete path = 1.75m

Radius of outer circle (Including pond + Path), R = 7 + 1.75 = 8.75 m

Area of the path = Area of the outer circle − Area of the inner circle.

= πR² - πr²

= 22 / 7 x ( 8.75 + 7) ( 8.75 − 7 )

= 86.625 m²

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It will cost $10.00 to waterproof a canvas truck cover that is 15' x 24'.

To find this, we need to first convert the dimensions of the canvas truck cover from feet to yards, since the cost is given per square yard. 15' x 24' = 180 sq ft. 1 sq yard is equal to 9 sq ft, so 180 sq ft/9 sq ft/yard = 20 sq yard. Then we multiply the square yards by the cost per square yard to find the total cost:

It's important to note that the measurements of the canvas truck cover are given in feet and the cost is given per square yard. It's important to convert it to square yards to match the unit of measurement and calculate the cost.

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62.5 of the yellow balloons lack strings. The ratio of positive outcomes to all outcomes in that sample space is generally referred to as the probability.

The ratio of positive outcomes to all outcomes in that sample space is generally referred to as the likelihood. The formula is: Probability of an Event P(E) = (Number of Favorable Outcomes) (Sample space).

The ratio of positive outcomes to all outcomes in that sample space is generally referred to as the likelihood.

A sample is created in this way, and using the data collected, the calculation can be done. The formula for calculating probabilities is probability = Favorable instances / Possible cases x 100, given as a percent.

25/40 * 100 = 0.625*100 = 62.5.

62.5 of the yellow balloons lack strings.

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A solid right prism ABCDEF  has a height of 16.  A part of the prism is sliced off with a straight cut through points  X, Y, and Z. CXYZ is a  triangular pyramid and its surface area is 48 + 9√3 + 3√91  or 92.2

The situation can be depicted in the attached picture. CXYZ is a triangular pyramid.

The surface area of CXYZ is equal to:

area CXYZ = area ΔCXY +  area ΔCYZ +  area ΔCXZ + area ΔXYZ

ΔABC and ΔCXY are congruent, hence ΔCXY is a equilateral triangles with its sides are 1/2 those of ΔABC.

CX = CY = XY = 1/2 x 12 = 6

To find the area of ΔCXY, find its height first.

√3/2 = h/6

h = 3√3

Area ΔCXY = 1/2 x 3√3 x 6 = 9√3

ΔCXZ is a right triangle at C. Hence,

Area ΔCXZ =  1/2 x CX x CZ

                   = 1/2 x 6 x 8 = 24

ΔCYZ = ΔCXZ

Hence,

Area ΔCYZ =  24

To find the area of ΔXYZ, find XZ first using the Pythagorean Theorem.

XZ² = CX² + XZ²   (XZ = 8, since Z is midpoint of CD)

XZ² =  6² + 8²

XZ² = 10²

XZ = 10

Find the height of ΔXYZ

h = √(10² - 3² )

h = √91

Therefore,

Area ΔXYZ = 1/2 x XY x h

                   = 1/2 x 6 x √91 =3√91

Finally,

area CXYZ = area ΔCXY +  area ΔCYZ +  area ΔCXZ + area ΔXYZ

                  = 9√3 + 24 + 24 + 3√91

                  = 48 + 9√3 + 3√91

                  = 92.2

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Answer:

v = 4

Step-by-step explanation:

⭐What is the midsegment of  a triangle?

⭐What are some properties of the midsegment?

Thus, we have to make an equation using the properties of the midsegment to solve for v.

Working:

[tex]SU = \frac{1}{2}(QR)[/tex]

[tex]19v - 38 = \frac{1}{2}(-5v + 96)[/tex]

[tex]38v - 76 = -5v + 96[/tex] . . . . .  multiply both sides by 2 to get rid of the fraction

[tex]43v = 172[/tex] . . . . . add 5v and 76 to both sides

∴ [tex]v = 4[/tex] . . . . . . . . . divide both sides by 43 to isolate v

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The average speed of the plane from Winnipeg to Red Deer is 400 km/h

Average speed is total distance travelled over total time taken.

Since a plane flew from Red Deer to Winnipeg, a flying distance of 1260 km. On the return journey, due to a strong head wind, the plane travelled 1200 km in the same time it took to complete the outward journey. On the outward journey, the plane was able to maintain an average speed 20 km/hr greater than on the return journey.

Let

Since the plane travels 1260 km on the outward journey, we have that

1260 = vt  (1)

Also,  the plane travels 1200 km on the inward journey, we have that

1200 = v't  (2)

Since the plane was able to maintain an average speed 20 km/hr greater than on the return journey, we have that

v = v' + 20 (3)

Substituting equation (3) into (1), we have that

1260 = (v' + 20)t  (4)

The required equations are

1260 = v't + 20t  (4)

1200 = v't  (2)

Subtracting equations, (2) from (4), we have that

1260 = v't + 20t  (4)

-

1200 = v't  (2)

60 = 20t

t = 60/20

t = 3 h

From equation (2), we have that the average speed

v' = 1200/t

Substituting t = 3 into the equation, we have that

v' = 1200/3

v' = 400 km/h

So, the average speed is 400 km/h

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The equation of a parabola that intersects the x-axis at points (-1, 0) and

(3, 0) is y = x² - 2x - 3.

What is a parabola?

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola.

Since the parabola intersects x-axis at points (-1,0) and (3,0), the parabola has its axis parallel to y-axis.

The general equation for such parabola is,

y = ax² + bx + c

The roots of the quadratic equation is found when y = 0

We know that when y = 0, x = -1 , 3

So (x+1) (x - 3) = 0

Solving the above equation we can find the equation of parabola

x² - 3x + x -3 = y

Therefore y = x² - 2x- 3 is the equation of a parabola that intersects the x-axis at points (-1, 0) and (3, 0).

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Total 56 bags of hardwood and 140 bags of pine bark bags are sold.

In the given question, a local boys club sold 196 bags of mulch and made a total of $357.

It sold two types of mulch: hardwood for $2.00 a bag and pine bark for $1.75 a bag.

We have to find how many bags of each kind of mulch did it sell.

Let total number of x bags of hardwood sell.

Let total number of y bags of pine bark sell.

Now the equation should be

2x + 1.75y = 357............................(1)

Total number of bags sold 196.

So x + y = 196............................(2)

From the equation 2 the value of x = 196-y. Now putting the value of x in equation 1.

2(196 - y) + 1.75y = 357

392 - 2y + 1.75y = 357

392 - 0.25y = 357

Subtract 392 on both side, we get

-0.25y = -35

Divide by -0.25 on both side, we get

y = 140

Now putting the value of y in x = 196-y

x = 196 - 140

x = 56

Hence, 56 bags of hardwood and 140 bags of pine bark bags are sold.

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Answer:

Step-by-step explanation:

The four options just swap the order, and you should choose them all

a. The current sale price for the computer system is given as follows: $618.4.

b. The amount paid by the club members, with the discount, is given as follows: $587.48.

The prices are found applying the proportions, which are the decimal equivalent of the percentages relative to each discount.

The selling price is of:

$773.

The markdown is of 20%, hence the current sale price is 100 - 20 = 80% of the selling price, hence:

0.8 x 773 = $618.4.

Club members get an additional discount, of 5%, meaning that they pay 95% of $618.4, and the amount is obtained as follows:

0.95 x 618.4 = $587.48.

The problem is given by the image presented at the end of the answer.

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The measure of length of FG is 105 units.

What is bisection?

To determine the roots of a polynomial problem, utilise the bisection method. It splits and separates the interval in which the equation's root is located. The continuous functions intermediate theorem serves as the method's guiding premise.

From the given diagram, since Line DF bisects angle EDG, then -

EF = FG

Given the following parameters -

EF = 9n - 3

FG = 8n + 9

Equating both expressions -

9n - 3 = 8n + 9

9n - 8n = 9 + 3

n = 12

Get the measure of FG -

FG = 8n + 9

FG = 8(12) + 9

FG = 96 + 9

FG = 105

Hence, the line FG measures as 105 units.

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[tex]4(x+7) \leqslant 4(2x+8)\implies 4x+28\leqslant 8x+32\implies 28\leqslant 4x+32 \\\\\\ -4\leqslant 4x\implies \cfrac{-4}{4}\leqslant x\implies \boxed{-1\leqslant x}[/tex]

notice, in the division by "4" we didn't flip the inequality sign, because the division was by a positive value, we only flip it when the division involves a negative value.

Dimensions of the parallelogram are:

Its perimeter is:

Its area is:

Perimeter is 2 times greater:

Area is 2*2 = 4 times greater:

Perimeter is 3 times greater:

Area is 3*3 = 9 times greater:

Perimeter is 2 times smaller:

Area is 2*2 = 4 times smaller:

The time taken for his return flight, in hours could be  4 hours.

What is time ?

Time is defined as the sequence of events that occurs which can be from past through present or to future.

Given,

Benji's flight from Chicago to San Jose took 0.5 hour longer than his return flight from San Jose to Chicago.

If Benji's flight from Chicago to San Jose was 4.5 hours long

let,

chicago to san jose = san jose  to chicago+0.5

4.5 - 0.5  = san jose to chicago

san jose to chicago  = 4 hours

Hence,  How  long was his return flight, in hours is 4 hours.

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Answer:

SAA

Step-by-step explanation:

The probability of Johnny not getting a job offer from either company is 0.8

Suppose Johnny applied for a job at companies A and B.

Through extensive research, Johnny determined he has a 60% chance of getting a job offer from company A,

A = 0.6

a 50% chance of getting a job offer from company B,

B = 0.5

and a 30% chance of getting a job offer from both companies A and B.

What is the probability of Johnny not getting a job offer from either company?

Suppose, probability of an event  A occurring is P(A)

and that of is B IS P(B)

P(A) = 0.6

and

P(B)= 0.5

probability of either  or P(AUB)=0.3

Now we need to find the probability of neither  nor, which is

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∩B)  = P(A) + P(B) -P(A∪B)

             = 0.6 + 0.5 - 0.3

            = 0.8

Now the events are mutually exclusive, so

Therefore, the probability of neither  nor  is 0.8

The probability of Johnny not getting a job offer from either company is 0.8

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The volume of the fish tank in the shape of a right circular cylinder with a radius of 3 in and a height of 10 in is 90π cubic inches.

Therefore the answer is 90π in³.

Recognize that the fish tank is in the shape of a right circular cylinder.

Remember that the formula for the volume of a cylinder is

V = πr^2h

where r is the radius and h is the height.

Plug in the given values for the radius (r = 3 inches) and the height (h = 10 inches) into the formula.

Perform the calculation:

πr^2h

= π(3^2)(10)

= π×9×10

= 90π cubic inches

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