A walking path across a park is represented by the equation y= -3x - 6 . A new path will be built perpendicular to this path. The path will intersect at the point (-3 , 3) . Identify the equation that represents the new path . WILL MARK BRAINIEST!

Answer:

26/35

Step-by-step explanation:

If the events are mutually exclusive, all you have to do for P(S or T) is do P(S)+P(T).

So we are doing 1/7 + 0.6.

I prefer the answer as a fraction so I'm going to rewrite 0.6 as 6/10=3/5.

So we are going to add 1/7 and 3/5.

We need a common denominator which is 35.

Multiply first fraction by 5/5 and second fraction by 7/7.

We have 5/35+21/35.

This gives us 26/35.

Answer:4

Step-by-step explanation:16/4 = 4

if 75% of equipment is iron then do the math

So it would be 4(2) + 4 = 75% of 16
So if 75% of 16 is 12 you need that extra 4 to get you to 16

The number of woods in the golf club is equal [tex]4[/tex].

" Number is defined as the count of any given quantity."

According to the question,

[tex]'x'[/tex] represents the number of irons

[tex]'y'[/tex] represents the number of woods

As per given condition we have,

[tex]x= 2y +4[/tex]                                  [tex](1)[/tex]

[tex]x = 75\%(x+ y)\\\\\implies x = \frac{75}{100}(x + y)\\ \\\implies x = \frac{3}{4} (x+y)\\\\\implies 4x= 3x + 3y\\\\\implies x = 3y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)[/tex]

Substitute the value of [tex](2)[/tex] in [tex](1)[/tex] to get the number of woods,

[tex]3y = 2y +4\\\\\implies y =4[/tex]

Therefore,

[tex]x= 3\times 4\\\\\implies x=12[/tex]

Hence, the  number of woods in the golf club is equal [tex]4[/tex].

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Answer:

C: [tex]V=4840 (2 s.f.)[/tex]

Step-by-step explanation:

The formula for the volume of a cone is:

[tex]V= \frac{1}{3} \pi r^2h[/tex]

Therefore,

[tex]V=\frac{1}{3}\times 3.14\times(\frac{34}{2})^2\times 16\\\\V=4840 (2 s.f.)[/tex]

The volume of the cone is 4840 cubic ft if the diameter of the base is 34 feet and the height is 16 feet option (C) is correct.

It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.

[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]

Volume can be defined as a three-dimensional space enclosed by an object or thing.

It is given that:

A pile of tailings from a gold dredge is in the shape of a cone.

The diameter of the base is 34 feet and the height is 16 feet.

As we know,

The volume of the cone is given by:

[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]

r = 34/2 = 17 ft

h = 16 feet

Plug the above values in the formula:

[tex]\rm V=\pi (17)^2\dfrac{16}{3}[/tex]

After solving:

V = 1541.33π cubic feet

Take π = 3.14

V = 1541.33(3.14) cubic feet

V = 4839.78 ≈ 4840 cubic ft

Thus, the volume of the cone is 4840 cubic ft if the diameter of the base is 34 feet and the height is 16 feet option (C) is correct.

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Answer:

9 bottles of water

Step-by-step explanation:

Marginal benefit is a microeconomic concept that explains how much the consumer adds satisfaction to each unit consumed of a given product. Usually, the marginal benefit is decreasing, which makes logical sense, the more a customer consumes a particular good, the smaller the benefit of the next unit.

At first, the first bottle of water has a high benefit as mentioned in the exercise:  9

In the second, you are a little less thirsty, so the benefit will be 10 - 1x2 = $8

In the ninth bottle, you will have very little thirst and the benefit will be 10 - 1x9 = $1

In the tenth bottle there is no benefit, the consumer is indifferent. As a rational consumer, you will buy until the bottle is still usable, even if minimal, for 9 bottles when your benefit is $1.

As an economically rational consumer, you will continue buying bottles of water until the marginal benefit equals or is less than the price of the water. In this case, you will buy a total of 10 bottles of water.

As an economically rational consumer, you will continue buying bottles of water until the marginal benefit equals or is less than the price of the water. In this case, the price of water is $1 per bottle.

The marginal benefit equation is given as MB = $10 - $x, where x represents the number of bottles of water you have had. So, for each bottle of water you consume, the marginal benefit decreases by $1.

To determine the number of bottles of water you will buy, you need to compare the marginal benefit to the price of water:

Therefore, you will buy a total of 10 bottles of water.

Answer:

Product B

Step-by-step explanation:

Divide the number of ounces i the bottle by the price of the bottle. Product A has a unit price of $0.17 and Product B has a unit price of $0.20. Therefore Product B has a lower unit price :))

Answer:

1.5 feet

Step-by-step explanation:

Bob wants to plant a 7 foot by 10 foot garden.

Area = [tex]7\times10=70[/tex] square feet

He wants to make a uniform border of petunias around the outside and still have 28 square feet to plant tomatoes and roses in the middle.

Means we have to factor 28 in a way that the length and width is less than 10 and 7.

28 = 2 x 2 x 7

Means 4 feet can be width and 7 feet the length of the area where tomatoes need to be planted.

So, we have [tex]10-7=3[/tex] feet less than outer garden means at each side [tex]3/2=1.5[/tex] feet decreases.

Similarly, we have [tex]7-4=3[/tex] feet less width and at each side it is 1.5 feet.

Therefore, the border of petunias will be 1.5 feet wide on all sides.

Answer:

Width of the border is 1.5 feet.

Step-by-step explanation:

Let x be the width ( in feet ) of the border,

Given,

The dimension of the garden =  7 foot by 10 foot,

So, the dimension of the middle ( garden area excluded border )= (7 - 2x) foot by (10 - 2x) foot

Hence, the area of the middle = (7 - 2x)(10 - 2x)

According to the question,

[tex](7 - 2x)(10 - 2x)=28[/tex]

[tex]70 -14x-20x + 4x^2=28[/tex]  

[tex]4x^2 -34x+70-28=0[/tex]

[tex]4x^2 -34x+42=0[/tex]        ( Combine like terms )

[tex]4x^2-(28+6)x+42=0[/tex]  ( Middle term splitting )

[tex]4x^2-28x-6x+42=0[/tex]

[tex]4x(x-7)-6(x-7)=0[/tex]

[tex](4x-6)(x-7)=0[/tex]

By zero product property,

4x - 6 or x - 7 = 0

⇒ x = 1.5 or x = 7

Since, width of the border can not be equal to the dimension of the garden,

Therefore, the width would be 1.5 foot.

Answer:

56 degrees

Step-by-step explanation:

So those angles are called alternate exterior angles because they happened at the difference intersections along the transversal on opposite sides of that transveral while on the outside of the lines that the transversal goes through.

If these lines that the transversal goes through are parallel then the alternating angles are congruent.

So they are because of the little >> things on those lines.

So x=56 degrees

Answer:

25 years

Step-by-step explanation:

Solution:-

- Data for the average daily temperature on January 1 from 1900 to 1934 for city A.

- The distribution X has the following parameters:

                    Mean u = 24°C

                    standard deviation σ = 4°C

- We will first construct an interval about mean of 1 standard deviation as follows:

  Interval for 1 standard deviation ( σ ):                                    

                    [ u - σ , u + σ ]

                    [ 24 - 4 , 24 + 4 ]

                    [ 20 , 28 ] °C

- Now we will use the graph given to determine the number of years the temperature T lied in the above calculated range: [ 20 , 28 ].

           T1 = 20 , n1 = 2 years

           T2 = 21 , n2 = 3 years  

           T3 = 22 , n3 = 2 years

           T4 = 23 , n4 = 4 years  

           T5 = 24 , n5 = 3 years

           T6 = 25 , n6 = 3 years  

           T7 = 26 , n7 = 5 years

           T8 = 27 , n8 = 2 years

           T5 = 28 , n9 = 1 years

- The total number of years:

               ∑ni = n1 + n2 + n3 + n4 + n5 + n6 + n7 + n8 + n9

                     =  2 + 3 + 2 + 4 + 3 + 3 + 5 + 2 + 1

                     = 25 years          

Answer:

22,25,27 there are multiple questions that have the same question but different answers on Edge

Step-by-step explanation:

I hope this helped :)

Check the picture below.

Answer:

  x = 5

Step-by-step explanation:

You want to find x such that ...

  x^2 +(x +1)^2 = 61

  2x^2 +2x -60 = 0 . . . . . simplify, subtract 61

  x^2 +x -30 = 0 . . . . . . . divide by 2

  (x +6)(x -5) = 0 . . . . . . . . factor; solutions will make the factors be zero.

The relevant solution is x = 5.

Answer:

  (2.31079, 6.83083)

Step-by-step explanation:

The transformation due to rotation about the origin in the counterclockwise direction by an angle α is ...

  (x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))

Here, that means the new coordinates are ...

  (4·cos(15°) -6·sin(15°), 4·sin(15°) +6·cos(15°)) ≈ (2.31079, 6.83083)

To rotate the point (4,6) counterclockwise about the origin by 15 degrees, we can use the rotation formulas. The new coordinates are approximately (2.833, 6.669).

To rotate a point counterclockwise about the origin, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Using the given point (4,6) and an angle of 15 degrees, we can substitute the values into the formulas to find the new coordinates:

x' = 4 * cos(15) - 6 * sin(15) = 4 * 0.9659258263 - 6 * 0.2588190451 ≈ 2.833166271

y' = 4 * sin(15) + 6 * cos(15) = 4 * 0.2588190451 + 6 * 0.9659258263 ≈ 6.669442572

Therefore, the new coordinates of the point after rotation are approximately (2.833, 6.669).

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Answer:

1/2

Step-by-step explanation:

Given:

sinx=-1/2

cosy=√3/2

finding x

x=sin^-1(-1/2)

x=-π/6

x=-30°

finding y

cosy=√3/2

y=cos^-1(√3/2)

y=π/6

y=30°

Now finding cos(x-y)

cos(-π/6-π/6)

=cos(-π/3)

=1/2!

Answer:

Option B is correct.

Step-by-step explanation:

[tex]10^{(3/4)x}[/tex]

We need to write the above equation in square root form.

We know that 1/4 = [tex]\sqrt[4]{x}[/tex]

So, [tex]10^{(3/4)x}[/tex] can be written as:

[tex](\sqrt[4]{10})^{3x}[/tex]

Option B is correct.

For this case we have that by definition of properties of powers and roots it is fulfilled:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, we have the following expression:

[tex](10) ^ {\frac{3} {4} x}[/tex]

So, in an equivalent way we have:

[tex](\sqrt [4] {10}) ^ {3x}[/tex]

Answer:

Option b

Answer:

V = $3.50t + $90.5....

Step-by-step explanation:

V(t) is a function of t that expresses the value in year 2000+t.  

We know that the increase is $3.50 times t.

So,

V(t) = $3.50t + c  

where c is the constant.

V(15) =  $3.50 (15) + c = $143     [t=15 as mentioned in the question]

and therefore  

c = $143 - $3.50 (15)

c= $143 - $52.50

c= $90.5  

Now we got the value of c. We can write the equation as  

V = $3.50t + $90.5....

The subject of this question is linear equation. The dollar value of a product expected to change over several years can be calculated using the future value formula V = P(1 + r)^(t-15), where P is the present value, r is the rate of change per year, and t represents the year.

To develop a linear equation that represents the dollar value V of a product in a certain year t, you can use the formula for future value received years in the future: V = P(1 + r)^(t-15), where P is the present value in 2015, r is the rate of change per year, and t represents the year.

For example, if a firm's payment was $20 million in 2015 and was expected to increase by 10% per year, then the value in 2020 (t = 20) would be calculated as: V = $20 million * (1 + 0.10)^(20-15).

From this equation, you can predict the future value of the product in terms of the year and rate of inflation.

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Answer:

F and E

Step-by-step explanation:

[tex](3x+4)^2=14[/tex]

We could get rid of the square on the (3x+4) by square rooting both sides:

[tex]3x+4=\pm \sqrt{14}[/tex]

Now you are left with a linear equation to solve.

Subtract 4 on both sides:

[tex]3x=-4 \pm \sqrt{14}[/tex]

Divide both sides by 3:

[tex]x=\frac{-4 \pm \sqrt{14}}{3}[/tex]

You could rearrange the numerator using commutative property:

[tex]x=\frac{\pm \sqrt{14}-4}{3}[/tex]

If you wanted two write the two answers out, you would write:

[tex]x=\frac{\sqrt{14}-4}{3} \text{ or } \frac{-\sqrt{14}-4}{3}[/tex].

So I see this in F and E.

You could separate the fraction:

[tex]x=\frac{\sqrt{14}}{3}-\frac{4}{3} \text{ or } -\frac{\sqrt{14}}{3}-\frac{4}{3}[/tex].

The solutions to the given equation (3x + 4)^2 = 14 are x = (√14 - 4) / 3 and x = (-√14 - 4) / 3.

To find the solutions to the equation (3x + 4)2 = 14, first we need to take the square root of both sides of the equation to remove the square from (3x + 4):

√{(3x + 4)2} = √14, which simplifies to 3x + 4 =  √14 and 3x + 4 = -√14.

Then, we solve for x in each equation by subtracting 4 from both sides, which gives us 3x = √14 - 4 and 3x = -√14 - 4.

Lastly, we divide each side by 3 in both equations to isolate 'x', thus our solutions are: x = (√14 - 4) / 3 and x = (-√14 - 4) / 3.

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Answer:

3.13

Step-by-step explanation:

Given :

y = 2x + 4 -------- eq1

y = 2x - 3 -------- eq2

sanity check : both equations have same slope, so we can conclude that they are both parallel to one another.

Step 1: consider equation 1, pick any random x-value and find they corresponding y-value. we pick x = -2

This gives us y = 2(-2) + 4 = 0

Hence we get a point (x,y) = (-2,0)

Step 2: express equation 2 in general form (i.e Ax + By + C = 0)

y = 2x-3 -------rearrange---> 2x - y -3 = 0

Comparing with the general form, we get A = 2, B = -1, C = -3

Recall that the distance between 2 parallel lines is given by the attached formula (see attached picture).

substituting the values for A, B, C and (x, y) from the previous step:

d = | (2)(-2) + (-1)(0) + (-3) |  / √(2² + (-1)²)

d = | -4 + 0 - 3 |  / √(4 + 1)

d = | -7 |  / √5

d = 7  / √5

d = 3.13

The distance between the pair of given parallel lines is;

A: 3.13

We are given equation of the two lines as;

y = 2x + 4 - - - (eq 1)

y = 2x - 3 - - - (eq 2)

Let us put 1 for x in eq 1 to get;

y = 2(1) + 4

y = 6

Ax + By + C = 0

We have;

2x - y - 3 = 0

Thus;

A = 2

B = -1

C = -3

D = |Ax1 + By1 + c|/√(A² + B²)

Where;

x1 is the value of x imputed into the first equation

y1 is Tha value of y gotten from the input of x1

Thus;

D = |(2 × 1) + (-1 × 6) + (-3)|/(√(2² + (-1²))

D = |-7|/√5

We will take the absolute value of the numerator to get;

D = 7/√5

D = 3.13

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Answer:

A. The CV is a relative measure of risk/return.

Step-by-step explanation:

The coefficient of variation of any investment, is used to measure and calculate the total risk of that investment with respect to its per unit expected return rate.

We can also define the coefficient of variation as a ratio of standard deviation to the expected value of an investment.

The answer is - A. The CV is a relative measure of risk/return.

The coefficient of variation (CV) is a relative measure of risk/return; thus, statement A is correct, and statement D is correct as it relates to the preferences of risk-averse investors. This measure is useful for assessing the consistency of investment returns, especially when comparing different investment options.

The coefficient of variation (CV) is a statistical measure that is used to assess the relative variability of data. It is calculated by dividing the standard deviation by the mean and multiplying by 100. This ratio provides a standardized measure of the dispersion of data points in a data set around the mean, which is particularly useful when comparing the variability between datasets with different units or scales.

Now let's examine the given statements:

A. The CV is a relative measure of risk/return.

B. The CV is an absolute measure of risk/return.

C. The higher the CV value the more acceptable the risk/return profile for a risk-averse investor.

D. The lower the CV value the more acceptable the risk/return profile for a risk-averse investor.

Statement A is correct: the CV is indeed a relative measure because it expresses the standard deviation as a percentage of the mean, making it unitless and thus comparable across different data sets and scales.

Statement D is also correct: a lower CV indicates that the returns are less volatile relative to the mean return, which is generally preferred by risk-averse investors. Risk-averse investors prefer investments with more predictable and stable returns, as such investments are associated with lower levels of relative risk.

[tex]|\Omega|=50\cdot49=2450\\|A|=15\cdot14=210\\\\P(A)=\dfrac{210}{2450}=\dfrac{3}{35}\approx8.6\%[/tex]

The probability of randomly selecting two jelly beans in succession without replacement is;

0.0857

The jar contains 50 jellybeans.

Thus; N = 50

The individual berries include;

5 lemon

10 watermelon

15 blueberry

20 grape

Probability of first being a jelly bean = 15/50

Probability of second being jelly bean = 14/49

Thus,probability of selecting 2 jelly beans in succession without replacement is =

15/50 × 14/49 = 0.0857

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Note that,

[tex]9x^2+24x+20=4\Longrightarrow9x^2+24x+16[/tex]

Which factors to,

[tex](3x+4)^2=0\Longrightarrow3x+4=0[/tex]

And simplifies to solution C,

[tex]\boxed{x=-\dfrac{4}{3}}[/tex]

Hope this helps.

Any additional questions please feel free to ask.

r3t40

Answer:

[tex]\large\boxed{C.\ x=-\dfrac{4}{3}}[/tex]

Step-by-step explanation:

[tex]9x^2+24x+20=4\qquad\text{subtract 4 from both sides}\\\\9x^2+12x+12x+16=0\\\\3x(3x+4)+4(3x+4)=0\\\\(3x+4)(3x+4)=0\\\\(3x+4)^2=0\iff3x+4=0\qquad\text{subtract 4 from both sides}\\\\3x=-4\qquad\text{divide both sides by 3}\\\\x=-\dfrac{4}{3}[/tex]

Answer:

  2/105

Step-by-step explanation:

"r" is the greatest common divisor (GCD) of the two fractions. It can be found using Euclid's algorithm in the usual way.

  (8/15) - (18/35) = 56/105 - 54/105 = 2/105 . . . . . this is (8/15) mod (18/35)

We can see that the next step, division of 54/105 by 2/105, will produce a remainder of 0, so the GCD is 2/105.

The greatest rational number r is 2/105.

_____

Check

The ratios are (8/15)/(2/105) = 28; (18/35)/(2/105) = 27. These whole numbers are relatively prime, so there is no larger r than the one we found.

Rational numbers are numbers that can be represented as a fraction of two integers. The greatest rational number (r) such that [tex]\frac 8{15} \div r : \frac {18}{35} \div r[/tex] is a whole number is [tex]\frac{2}{105}[/tex]

Let the numbers be represented as:

[tex]n_1 = \frac 8{15} \div r[/tex]

[tex]n_2 = \frac {18}{35} \div r[/tex]

To calculate the value of r such that [tex]n_1 : n_2[/tex] is a whole number, we make use of Euclid's algorithm.

Using Euclid's algorithm, the value of r is the common divisor between both fractions

[tex]r = n_1 - n_1[/tex]

[tex]r =\frac 8{15} \div r - \frac {18}{35} \div r[/tex]

Ignore the "r"

[tex]r =\frac 8{15} - \frac {18}{35}[/tex]

Take LCM

[tex]r=\frac {8 \times 7 - 18 \times 3}{105}[/tex]

[tex]r =\frac {2}{105}[/tex]

Hence, the greatest rational number is such that [tex]n_1 : n_2[/tex] is a whole number is [tex]\frac{2}{105}[/tex]

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Step-by-step explanation:

10 is the value of A ......

Answer:

Value of A = 10

Step-by-step explanation:

Here Isoke is solving the quadratic equation by completing the square

        10x² + 40x – 13 = 0

         10x² + 40x – 13 + 13 = 0 + 13

         10x² + 40x + 0 = 13

         10x² + 40x = 13

          10 ( x² + 4x) = 13

   Here it is given as

           A(x² + 4x) = 13  

Comparing both

           We will get A = 10

Value of A = 10

Answer:

The height of the house is between 9 and 10 feet.

Step-by-step explanation:

The shaped formed with the ground, the ladder, and the house is a right triangle.

I'm going to apply Pythagorean Theorem here.

The length of the hypotenuse is given as 24 feet.

The length from the base of the ladder and the house is 22 feet.

So to find the height the ladder reaches on the house, we need to solve

[tex]a^2+22^2=24^2[/tex]

[tex]a^2+484=576[/tex]

Subtract 484 on both sides:

[tex]a^2=576-484[/tex]

Simplify:

[tex]a^2=92[/tex]

Square root both sides:

[tex]a=\sqrt{92}[/tex]

[tex]a \approx 9.59166[/tex] feet

Answer:

Step-by-step explanation:

(a) For a depth of x, the two sides of the rain gutter are length x, and the bottom is length (12-2x). The cross sectional area is the product of these dimensions:

  A = x(12 -2x)

This equation describes a parabola that opens downward. It has zeros at ...

  x = 0

  12 -2x = 0 . . . . x = 6

The maximum area is halfway between these zeros, at x=3.

The maximum area is obtained when the depth is 3 inches.

__

(b) For an area of at least 16 square inches, we want ...

  x(12 -2x) ≥ 16

  x(6 -x) ≥ 8 . . . . . divide by 2

  0 ≥ x² -6x +8 . . . . subtract the left side

  (x -4)(x -2) ≤ 0 . . . factor

The expression on the left will be negative for values of x between 2 and 4 (making only the x-4 factor be negative). Hence the the depths of interest are in that range.

At least 16 square inches of water will flow for depths between 2 and 4 inches, inclusive.

The maximum cross-sectional area of the gutter which allows the most water flow is achieved at a depth of 4 inches. For a flow rate of 16 square inches, we need to solve the equation for the cross-sectional area equal to 16 to find the corresponding depth.

Your question pertains to maximizing the cross-sectional area of a rain gutter made from 12-inch wide aluminum sheets. This involves the use of calculus, specifically optimization, and basic geometry.

Let's denote 'x' as half the width of the base. When the sides are turned up 90 degrees, the sides will be of length 'x'. Since the gutter is 12 inches wide, the equation for the width is 2x+x=12. So, x=4.

To maximize the cross-sectional area, you need to set the derivative of the area function equals to zero.

For your second question, to find the depths that will allow at least 16 square inches of water to flow, equate the cross-sectional area equals to 16, and solve for 'x'.

In conclusion,

The depth that would allow maximum cross-sectional area and the most water flow is when x = 4 inches,. To allow 16 square inches of water to flow, solve for 'x' when the cross-sectional area equals to 16.

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For this case we have that by definition, the arc length of a circle is given by:

[tex]AL = \frac {x * 2 \pi * r} {360}[/tex]

Where:

x: Represents the angle between JM. According to the figure we have that x = 90 degrees.

[tex]r = \frac {16.4} {2} = 8.2[/tex]

So:

[tex]AL = \frac {90 * 2 \pi * 8.2} {360}\\AL = \frac {90 * 2 * 3.14 * 8.2} {360}\\AL = 12.874[/tex]

Rounding:

[tex]AL = 12.9[/tex] miles

Answer:

12.9 miles

Answer: 12.9

Step-by-step explanation:

Answer:

3192 persons! ✔️

Step-by-step explanation:

From the statement, we know that μ = 40 [minutes] and σ = 6 [minutes]

There are 3900 people. And we need to find how many of the lie within one standard deviation below the mean and two standard deviations above the mean.

We need to find the probability between: 34 minutes and 52 minutes. With the help of a calculator we get that the probability is: P(34<z<52) = 0.8186

Therefore, 0.8186×3900 = 3192 persons! ✔️

Answer:

  22 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the necessary relationship. If the sledding slope is modeled as the hypotenuse of a right triangle with 25° as one of the acute angles, the side opposite the angle (the hill height) satisfies ...

  Sin = Opposite/Hypotenuse

  Opposite = Hypotenuse × Sin

  height = (52 ft)sin(25°) ≈ 22.0 ft

The height of the hill is about 22 feet.

The height of the hill can be calculated using the formula Height = sin (angle) x length of ride. By substituting the given values, it comes out to be approximately 22.05 ft.

In this question we are given an angle of elevation and the length of the ride. The problem is essentially about using trigonometry to estimate the height of the hill. The hill forms a right triangle, with the length of the ride as the hypotenuse and the height we want to find as the opposite side. In trigonometry, the sine of an angle is equal to the opposite side divided by the hypotenuse. So to find the height of the hill, we take the sin of the angle, multiplied by the length of the ride.

Therefore, Height = sin (angle) x Length of ride = sin (25°) x 52 ft = approximately 22.05 ft. The estimated height of the hill is around 22.05 ft.

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1. (3 + xz)(–3 + xz)

2. (y² – xy)(y² + xy)

3. (64y2 + x2)(–x2 + 64y2)

Explanation

The difference of 2 squares is in the form (a+b)(a-c).

(3 + xz)(–3 + xz) = (3 + xz)(xz -3)

                           = (xz + 3)(xz - 3)

                          = x²y²-3xy+3xy-9

                          =x²y² - 3²

(y² – xy)(y² + xy) = y⁴+xy³-xy³-x²y²

                          = y⁴ - x²y²

(64y2 + x2)(–x2 + 64y2)= (64y²+x²)(64y²-x²)

                                      = 4096y⁴-64y²x²+64y²x²-x⁴

                                      = 4096y⁴ - x⁴

Answer:

The answer is  

√3/2

Step-by-step explanation:

The value of sin 30°=1/2.

The special right triangle is the triangle used to know the side ratio without using Pythagoras theorem every time.

There are some types of special right triangles present like 30-60-90 triangle, 45-45-90 triangles, and the Pythagorean triple triangles.

Here for deriving the value for sin 30°, we will use the 30-60-90 triangle.

The 30-60-90 triangle is given below.

the value sine is calculated by the ratio of the opposite side and the hypotenuse of the right-angled triangle.

In 30-60-90 triangle the side opposite to 30° angle is x and the hypotenuse is 2x then the side opposite to 60° angle is x√3.

In 30-60-90 triangle,

sin 30°=opposite side/hypotenus

= x/2x

⇒sin 30°=1/2

Therefore, the value of sin 30°=1/2.

Learn more about the special right triangle

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Answer: Price of a discount amision= Full Admission Price - discount Amount

Step-by-step explanation:

We have two variables "X" and "Y", where X= Full Admision Price and  Y= Discount Price of Admision  and we have to get the price of a discount admision or "Z" so the expresion will be Z= X-Y or Price of a discount admision = Full admision Price- discount Amount.

Answer:

73920

Step-by-step explanation:

Number of ways to choose 9 appetizers from 12: ₁₂C₉

Number of ways to choose 3 main courses from 8: ₈C₃

Number of ways to choose 2 desserts from 4: ₄C₂

The total number of ways is:

₁₂C₉ × ₈C₃ × ₄C₂

= 220 × 56 × 6

= 73920