If the quadratic functions for the equations are graphed, which is the widest?

A)
y = x^2


B)
y = 2x^2


C)
y = 6x^2


D)
y=1/4 x^2

B can be right but if he dont do the exercises it is wrong

so it is C because d=day so it is 15 day and the results of the function is calories he used to do the exercises so the answer is C

Answer:

  C is the correct answer

Step-by-step explanation:

There is no "work." The question is a reading comprehension question, so the work goes on in your brain, where the words are interpreted. The problem statement tells you ...

  "... the amount of calories he has used, f(d), is a function of the number of days, d, he has exercised with the new routine."

You are comparing this wording to the answer choice wording. The best match is to C (as you know), which says ...

  "f(15) = 5250 means after 15 days of exercising with his new routine, Vincent has used 5250 calories."

Changing the function f(x)=2sin(x/2)-1 to the function g(x)=2sin(x)-5 shifts the graph of f(x) downward by 4 units and changes the period from 4π to 2π.

Changing the function f(x)=2sin(x/2)-1 to the function g(x)=2sin(x)-5 has the effect of shifting the graph of f(x) downward by 4 units and changing the period of the graph from 4π to 2π.

By comparing the two functions, we can see that the constant -1 in f(x) has changed to -5 in g(x), resulting in a downward shift of 4 units. The factor of 1/2 in the argument of the sine function in f(x) has been removed in g(x), which changes the period from 4π to 2π.

Overall, the graph of f(x) has been shifted downward and compressed horizontally to form the graph of g(x).

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In matrix form, we're looking for coefficients [tex]b_3,b_2,b_1,b_0[/tex] such that

[tex]\underbrace{\begin{bmatrix}3^3&3^2&3^1&3^0\\1^3&1^2&1^1&1^0\\(-1)^3&(-1)^2&(-1)^1&(-1)^0\\6^3&6^2&6^1&6^0\\7^3&7^2&7^1&7^0\end{bmatrix}}_{\mathbf A}\underbrace{\begin{bmatrix}b_3\\b_2\\b_1\\b_0\end{bmatrix}}_{\mathbf x}=\underbrace{\begin{bmatrix}4\\2\\1\\5\\9\end{bmatrix}}_{\mathbf b}[/tex]

The best-fit solution is given by [tex]\mathbf x=(\mathbf A^\top\mathbf A)^{-1}\mathbf A^\top\mathbf b[/tex]. You should end up with

[tex]\mathbf x=\begin{bmatrix}b_3\\b_2\\b_1\\b_0\end{bmatrix}\approx\begin{bmatrix}0.0495\\-0.3463\\0.9157\\2.1149\end{bmatrix}[/tex]

Attached is a plot of the given points and the best-fit solution.

To find the polynomial of degree three that best fits the given points, we can use the method of least squares.

To find the polynomial of degree three that best fits the given points, we can use the method of least squares. First, we can rewrite the equation in matrix form as:

[3 4 1] [b3]   [4]

[1 2 1] [b2] =  [2]

[-1 1 1] [b1]   [1]

[6 5 1] [b0]   [5]

[7 9 1]

Using matrix algebra, we can solve for the values of b3, b2, b1, and b0 that give us the best fit polynomial.

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Answer:80

Step-by-step explanation:

Let's pretend we start a stopwatch when the birth and death light flash together.  The birth light will flash at 10 seconds, 20 seconds, 30 seconds, etc.  The death light will flash at 16 seconds, 32 seconds, 48 seconds, etc.

So the trick here is to find the least common multiple (LCM) of 10 and 16.  To do that, we write the prime factorization of each:

10 = 2×5

16 = 2⁴

The LCM must include all these prime factors without any duplicates.  So the LCM = 2⁴×5 = 80.  We can check our answer by dividing:

80 / 10 = 8

80 / 16 = 5

So 80 is indeed a multiple of both 10 and 16.

By using the concept of HCF and LCM, the result obtained is

The birth and death light will flash again after 80 seconds.

What is HCF and LCM of two numbers?

HCF means Highest Common Factors. HCF of two numbers a and b is the highest number which divides both a and b

LCM means Lowest Common multiple. LCM of two numbers a and b is the lowest numbers which is divisible by both a and b

HCF and LCM can be calculated by division method and prime factorization method.

Also there is an important formula relating HCF and LCM

HCF [tex]\times[/tex] LCM = Product of two numbers

Here,

The birth light would flash every 10 seconds,

The death light every 16 seconds,

The immigration light every 81 seconds,

The emigration light every 900 seconds,

They will flash again after LCM (10, 16)

Now,

10 = [tex]2 \times 5[/tex]

16 = [tex]2 \times 2 \times 2 \times 2[/tex]

LCM of 10 and 16 = [tex]2 \times 2 \times 2 \times 2 \times 5[/tex] = 80

The birth and death light will flash again after 80 seconds.

To learn more about HCF and LCM, refer to the link-

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Answer:

240 feets

Step-by-step explanation:

In this question , apply Pythagorean relationship

Lets assume ;the climbing, sliding and walking back to the base forms a right-angle triangle

The tower height = the height of the triangle, h=60f

The sliding lane= the hypotenuse of the triangle=?

\

The distance covered to the base= base of the triangle=80f

Applying the relation ;

a²+b²=c²

80²+60²=c²

6400+3600=c²

10000=c²

√10000=c

100=c

Distance traveled in all=100+60+80=240 feet

Zachary traveled a total of 140 feet including climbing the tower and walking back from the splash pool to the tower.

The question is asking how far Zachary has traveled in total. He first climbs a 60-foot tower and then he lands in the splash pool. After that, he walks 80 feet back to the base of the tower.

To find the total distance he traveled, we need to add the distance he climbed up the tower to the distance he walked back to the tower. This can be done using simple addition.

Therefore, the total distance= distance climbed + distance walked = 60 feet + 80 feet = 140 feet.

So, Zachary traveled a total of 140 feet in all.

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Question 1:

For this case we have that by definition, the GCF of two numbers is the largest number that is a factor of both numbers. For example, the number 10 is the biggest factor that 50 and 30 have in common.

We must find the GCF of the following expression:

[tex]30t ^ 2u + 12tu ^ 2 + 24tu[/tex]

We look for the prime factorization of each number:

[tex]30: 2 * 3 * 5\\12: 2 * 2 * 3\\24: 2 * 2 * 2 * 3[/tex]

The GCF of the three numbers is [tex]2 * 3 = 6[/tex]

So:

[tex]6tu (5t + 2u + 4)[/tex]

Answer:

Option C

Question 2:

For this case we have that by definition of power properties of the same base, that:

[tex]a ^ n * a ^ m = a ^ {n + m}[/tex]

That is, for multiplication of powers of the same base, the same base is placed and the exponents are added.

So:

[tex]b ^ n * b ^ m = b ^ {n + m}[/tex]

ANswer:

[tex]b ^ {n + m}[/tex]

Option A

The greatest common factor of the expression is 6tu, and the factored form is 6tu(5t + 2u + 4), . For the property of exponents, the rule is that when multiplying powers with the same base, you add the exponents, yielding an answer of  b^n+m.

15.The correct option is (C) and 16.The correct option is (A).

To solve the problem factor out the greatest common factor from the expression 30t2u + 12tu2 + 24tu, we have to look for the highest power of each variable and the largest number that can divide each term. The greatest common factor for this expression is 6tu.

Factoring out 6tu gives us:

The correct answer is C. 6tu(5t + 2u + 4).

For the property of exponents problem, when multiplying powers with the same base, you add the exponents. So, bn · bm = bn+m.

The correct answer is A. bn+m.

To find the absolute maximum and minimum values of the function f(x) = x^5 - x^3 + 6, we can use both a graphical approach and a calculus approach. The graphical approach involves plotting the function and identifying the highest and lowest points on the graph. The calculus approach involves taking the derivative of the function, finding critical points, and evaluating the second derivative to determine whether the critical points are maximum or minimum values.

To find the absolute maximum and minimum values of the function, we need to graph it within the given interval and identify the highest and lowest points. By plotting the function and examining the graph, we can see that the absolute maximum value is approximately 6.66 at x ≈ 1, and the absolute minimum value is approximately 5.33 at x ≈ -1.

To find the exact maximum and minimum values, we need to use calculus. We take the derivative of the function f(x) = x^5 - x^3 + 6, which is f'(x) = 5x^4 - 3x^2. Setting f'(x) = 0 and solving for x, we find that x = 0 is a critical point. To determine whether it is a maximum or minimum, we take the second derivative f''(x) = 20x^3 - 6x and evaluate it at x = 0. Since f''(0) > 0, x = 0 is a relative minimum. Plugging x values outside the given interval into the function, we find that f(-1) ≈ 5.33 is the exact minimum value, and f(1) ≈ 6.66 is the exact maximum value.

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Answer: wheres the model?

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

We can use the distance formula with 3 different vertices to figure out the shortest of the three sides.

The distance formula is [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

Where (x_1,y_1) is the first points and (x_2,y_2) is the second set of points, respectively.

Now let's figure out the length of 3 sides.

1. The length between (-6,-5) & (-5,6):

[tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\=\sqrt{(6--5)^2+(-5--6)^2}\\ =\sqrt{(6+5)^2+(-5+6)^2} \\=\sqrt{11^2+1^2} \\=\sqrt{122}[/tex]

2. The length between (-6,-5) & (-2,2):

[tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\=\sqrt{(2--5)^2+(-2--6)^2} \\=\sqrt{(2+5)^2+(-2+6)^2}\\ =\sqrt{7^2+4^2}\\ =\sqrt{65}[/tex]

3. The length between (-5,6) & (-2,2):

[tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\=\sqrt{(2-6)^2+(-2--5})^2}\\ =\sqrt{(-4)^2+(3)^2} \\=\sqrt{25} \\=5[/tex]

Thus, length of the shortest side is 5.

Answer:

5 units

Step-by-step explanation:

Draw the triangle with the vertices given. Identify the smallest side and draw in a right triangle using the smallest side of the original triangle as the hypotenuse of the right triangle, as shown on the grids below.

The horizontal side of the small right triangle measures 3 units and the vertical side of the small right triangle measures 4 units.

Use the Pythagorean theorem to find the length of the hypotenuse.

Therefore, the length of the shortest side of the triangle measures 5 units.

3^2 + 4^2  =  c^2

9 + 16  =  c^2

25  =  c^2

5  =  c

Answer:

55.53 feet.

Step-by-step explanation:

We have been given that a flagpole stands in the middle of a flat, level field. 50 feet away from its base, a surveyor measures the angle to the top of the flagpole as 48 degrees.

We can see from attached photo that flagpole, the surveyor forms a right triangle with respect to ground.    

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

[tex]\text{tan}(48^{\circ})=\frac{h}{50}[/tex]

[tex]\text{tan}(48^{\circ})*50=\frac{h}{50}*50[/tex]

[tex]1.110612514829*50=h[/tex]

[tex]h=1.110612514829*50[/tex]

[tex]h=55.53062574[/tex]

[tex]h\approx 55.53[/tex]

Therefore, the height of the flagpole is approximately 55.53 feet.

Answer:

g(x) = x^2 - 11x + 26

Step-by-step explanation:

In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.

Given the function;

f(x) = x2 - 3x - 2

a shift 4 units to the right implies that we shall be subtracting the constant 4 from the x values of the function;

g(x) = f(x-4)

g(x) = (x - 4)^2 - 3(x - 4) -2

g(x) = x^2 - 8x + 16 - 3x + 12 - 2

g(x) = x^2 - 11x + 26

Answer:

g(x) = (x+4)^2 - 3x - 2

Step-by-step explanation:

A p e x

Answer:

b= -1

Step-by-step explanation:

y=3x+b

8= 3(3)+b

b= -1

The value of b in the equation y = 3x + b that passes through (3, 8) is -1

From the question, we have the following parameters that can be used in our computation:

The equation of the graph

Where, we have

y = 3x + b

Also, we have the point

(3, 8)

This means that

x = 3 and y = 8

When these values are substituted into the equation, we have

8 = 3 * 3 + b

This gives

8 = 9 + b

Evaluate the like terms

b = -1

Hence, the value of b is -1

Answer:

24cm and 225cm

Step-by-step explanation:

Answer:

1) [tex]24cm^2[/tex]

2) [tex]30cm[/tex]

Step-by-step explanation:

1) Remember that: The area of a quadrilateral circumscribed about a circle equals  semi-perimeter (half the product of the perimeter of the quadrilateral) and the radius of the circle.  

By the other hand in a quadrilateral circumscribed the sum of the measures of any pair of two opposite sides is equal to the sum of the measures of the other pair of the opposite sides.

Then you know that the sum of all sides should be 12cm+12cm=24cm

Area= Semi-perimeter*r

where

Semi-perimeter= perimeter/2= sum of all sides/2

r= radius of the circle

Then:

[tex]Area=(24cm/2)*(2cm)= 24cm^2[/tex]

2) Perimeter= sum of all sides

And as the sum of the measures of any pair of two opposite sides is equal to the sum of the measures of the other pair of the opposite sides.

Perimeter=15cm+15cm=30cm

Answer:

1

Step-by-step explanation:

Factor and cancel common factors from numerator and denominator.

[tex]\displaystyle\frac{2y^3-y^2+2y-1}{y^3-y^2+y-1}\times\frac{2y^2-3y+1}{4y^2-4y+1}\\\\=\frac{(y^2+1)(2y-1)\times (2y-1)(y-1))}{(y^2+1)(y-1)\times (2y-1)^2}=\frac{(y^2+1)(2y-1)^2(y-1)}{(y^2+1)(2y-1)^2(y-1)}\\\\=1[/tex]

Answer:

π/49·(44 -π)

Step-by-step explanation:

Using the "shell" method, a differential of volume is the product of the area of a cylindrical shell and its circumference around the axis of rotation. Here, that area is ...

dA = y·dx = cos(7x)dx

The radius will be the difference between x and the axis of rotation, x=3, so is ...

r = 3 -x

Then the differential of volume is ...

dV = 2πr·dA = 2π(3-x)cos(7x)dx

The volume will be the integral of this over the limits x ∈ [0, π/14].

∫dV = 6π·∫cos(7x)dx -2π·∫x·cos(7x)dx . . . from 0 to π/14

= (6/7)π·sin(7x) -(2/49)π·(cos(7x) +7x·sin(7x)) . . . from 0 to π/14

= (6/7)π(1 -0) -(2/49)π((0 -1) +(π/2-0))

= π(42/49 +2/49 -π/49)

= (π/49)(44 -π) . . . . cubic units . . . . . approx 2.61960 cubic units

Final answer:

The volume of the solid created by rotating the bounded region about the axis x=3 is found using cylindrical shells and evaluating the integral from x=0 to x=π/14 of the expression 2π(3-x)cos(7x)dx.

Explanation:

To find the volume of the solid obtained by rotating the region bounded by the curves y=0, y=cos(7x), x=π/14, and x=0 about the axis x=3, we need to use the method of cylindrical shells.

For a small strip at position x with height y and thickness dx, rotating around x=3 creates a cylindrical shell with circumference 2π(3-x), height cos(7x), and thickness dx.

The volume of each shell is V = 2π(3-x)cos(7x)dx, and summing these from x=0 to x=π/14 gives us the total volume.

So, the volume V is the integral:

∫0π/14 2π(3-x)cos(7x)dx.

This volume is found by evaluating the definite integral.

The correct statement is: Angle G is congruent to angle P.

Congruency in geometry refers to the similarity between two shapes or figures. When two shapes are congruent, their corresponding angles and sides are equal in measure, preserving the same shape and size but allowing for possible reflection or rotation.

The correct statement that compares the angles is: Angle G is congruent to angle P. Congruent angles are angles that have the same measure. So, if angle G is congruent to angle P, it means that they have the same measure. For example, if angle G measures 30 degrees, then angle P would also measure 30 degrees.

Answer:

Step-by-step explanation:

There are several different ways you can work problems like this. The method you may prefer may be different from the one I prefer. At least, they include ...

___

1. There are 12 inches in a foot.

  23 ft 7 in - (13 ft 11 in) = (23 -13) ft (7 -11) in = 10 ft (-4) in = 9 ft 8 in

__

2. There are 4 quarts in a gallon.

  18 gal 2 qt - (5 gal 3 qt) = (18 -5) gal (2 -3) qt = 13 gal (-1) qt = 12 gal 3 qt

__

3. There are 3 feet in a yard and 12 inches in a foot.

  21 yd 1 ft 7 in -(12 yd 2 ft 9 in) = (21 -12) yd (1 -2) ft (7 -9) in

  = 9 yd (-1) ft (-2 in)

  = 8 yd 2 ft (-2) in

  = 8 yd 1 ft 10 in

Answer:

2.74 seconds

Step-by-step explanation:

The apple will hit the ground when its height above the ground is zero:

0 = -16t^2 +120

t^2 = 120/16 . . . . . . divide by 16 and add t^2, then simplify and take the square root:

t = √7.5 ≈ 2.73861 ≈ 2.74 . . . . seconds

Answer:

(1) 40 is a common multiple of 6 and 10

False:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42...

Multiples of 10: 10, 20, 30, 40...

(2) The fraction 5/6 is greater than 7/10

True:

Find common denominators. Note that what you multiply to the denominator, you multiply to the numerator.

(5/6) x (5/5) = 25/30

(7/10) x (3/3) = 21/30

25/30 > 21/30 ∴ 5/6 is greater than 7/10

(3) The fraction 42/60 is an equivalent form of 7/10

True:

Find a common denominator. Note that what you multiply to the denominator, you multiply to the numerator.

(7/10) x (6/6) = 42/10

42/10 = 42/10 ∴ 7/10 = 42/10

(4) The only value that can be used as a common denominator is 60.

False:

While 60 is a plausible denominator, there are other denominators that can be used. Remember that what you do to the denominator, you do to the numerator.

(5) Ten is a multiple of 6.

False:

Multiples of 6: 6, 12, 18, 24, 30...

~

The validity of the true or false statements about the fractions 5/6 and 7/10 cannot be determined without the specific statements. In mathematics, comparing fractions requires finding a common denominator or converting them to decimals.

The question pertaining to whether the following statements about the fractions 5/6 and 7/10 are true involves understanding these numerical values and their relationships.

Please note that information from different sections that seem to provide contradictory answers cannot be used verbatim to answer your question directly, as the true or false nature of statements about these fractions was not specified in the excerpts provided. In mathematics, it is crucial to consider each expression individually and to apply mathematical principles to determine the validity of each statement.

Given that the statements to be verified are not presented, as a tutor on the Brainly platform, it is important to guide you on how to assess the veracity of statements about these fractions or any other numerical expressions. For instance, you would have to compare the two fractions by finding a common denominator or by converting both of them to decimal forms, to determine which one is greater, if that was part of the statements.

Answer:

  d)  9 inches

Step-by-step explanation:

By the Pythagorean theorem:

  WZ² = 15² -12.5² = 68.75

  WX² = 13² -12.5² = 12.75

Then the length of XZ can be found from ...

  XZ = √(WZ² +WX²) = √81.5 ≈ 9.028 . . . . closest to 9 inches (choice D)

Answer:

Number of adult tickets = 3 tickets

Number of children tickets = 5 tickets

Step-by-step explanation:

A- The system of equations:

Assume that the number of adult tickets is x and that the number of children tickets is y

We are given that:

i. The total number of people in the group is 8, which means that the total number of tickets bought is 8. This means that:

x + y = 8 ..................> equation I

ii. The price of an adult ticket is $12 and that of a child ticket is $10. We know that the group spent a total of $86. This means that:

12x + 10y = 86 ...............> equation II

From the above, the systems of equation is:

x + y = 8

12x + 10y = 86

B- Solving the system using elimination method:

Start by multiplying equation I by -10

This gives us:

-10x - 10y = -80 .................> equation III

Now, taking a look at equations II and III, we can note that coefficients of the y have equal values and different signs.

Therefore, we will add equations II and III to eliminate the y

    12x + 10y = 86

+( -10x - 10y = -80)

Adding the two equations, we get:

2x = 6

x = 3

Finally, substitute with x in equation I to get the value of y:

x + y = 8

3 + y = 8

y = 8 - 3 = 5

Based on the above:

Number of adult tickets = x = 3 tickets

Number of children tickets = y = 5 tickets

C- Explanation of the meaning of the solution:

The above solution means that for a group of 8 people to be able to spend $86 in a theater having the price of $12 for an adult ticket and $10 for a child' one, this group must be composed of 3 adults and 5 children

Hope this helps :)

Answer:

14 years old

Explanation:

Use this system of equations if G=George and J=Jeannie:

G-12=J

50=(G+5)+(J+5)

So, change second equation becomes

40-G=J

Then use substitution:

G-12=40-G

2G=52

G=26

Then, to find Jeannie’s age, go back to one of the equations and substitute G.

26-12=J

So, J=14

Jeannie is currently 14 years old.

To solve any questions relating to ages, I find it easier to make a table, like in the picture below.

See picture for answer and clear diagram.

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

Notes/Explanations + answer in written form

Jennies age now = x

So Georges age now would be: x + 12   (since he is 12 years older)

Jennies age in 5 years would be: x + 5   (since it is 5 years later)

Georges age in 5 years would be: x + 12 + 5 = x + 17

We are told that their ages in 5 years would add up to 50. So we can write an equation like so:

x + 17   +   x + 5 = 50                 (All you have to do now is solve it)

2x + 22 = 50                             (combine like terms)

2x = 28                                      (subtract 22 from both sides)

x = 14                                         (divide both sides by two)

That means that Jennies age is 14 years

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

Note:

Please comment below if you have any questions - I would be more that happy to help / explain anything!

Answer:

To find the median, set the numbers in order and the median is the number in the middle. If there was an even number of number then you would the two middle numbers and average it.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

So the median in this case would be 5

Answer: 6

Step-by-step explanation:

Median means the middle. You cross out a number from each side until you get one number and it’s 6. If there was uneven amount of numbers, and you were left with two numbers you add them and divide of how many numbers there are

Answer: 827 pounds.

Step-by-step explanation:

The formula for calculate density is:

[tex]d=\frac{m}{V}[/tex]

Where "m" is the mass and "V" is the volume.

The formula for calculate the volume of a cylinder is:

[tex]V=\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

Calculate the volume of the cylindrical maple tree stump, which is 3 feet high and has a radius of 1.5 feet:

[tex]V=(3.14)(1.5ft)^2(3ft)=21.195ft^3[/tex]

Substitute the volume into and the density 39 pounds per cubic foot, into the formula [tex]d=\frac{m}{V}[/tex] and solve for "m". Then, the weight of the stump to the nearest pound is:

[tex]39\frac{lb}{ft^3}=\frac{m}{21.195ft^3}\\\\m=(39\frac{lb}{ft^3})(21.195ft^3)\\\\m=827lb[/tex]

Answer:

Step-by-step explanation:

4. The graph is showing you x < -7 ∪ 5 < x. The difference between the end points is 12, suggesting that the inequality will be of the form | f(x) | > 6. We want the expression for f(x) to be zero at the midpoint of the excluded interval, which is (-7+5)/2 = -1. The inequality that matches this requirement is ...

  | x+1 | > 6 . . . . . . . matches choice A

__

7. The graph shows a domain of x-values less than 3, so the domain in interval notation is (-∞, 3).

The graph shows the range of y-values from -∞ to -1, including -1. In interval notation, the range is (-∞, -1].

None of the answer choices match ...

  Domain (-∞, 3), range (-∞, -1].

(Your computer might say C is correct, but it is not. Talk to your teacher about this question.)

Answer:

  If no one came to the dinner, the charity would still raise about $1250

Step-by-step explanation:

The variable x represents the number of people who attend the charity dinner. When x=0, no people came to the dinner.

The variable y represents the amount of money raised (in dollars). When x=0, the value of y is about 1250. That is, the charity raises about $1250 when no people came to the dinner.

Answer:

D.  If no one came to the dinner, the charity would still raise about $1250

Step-by-step explanation:

I just took the test, and I got 100%!!!

Replace cos^2(θ) with 1-sin^2(θ), and cot(θ) with cos(θ)/sin(θ).

  cos^2(θ)cot^2(θ) = cot^2(θ) - cos^2(θ)

  (1 -sin^2(θ))cot^2(θ) =  . . . . . replace cos^2 with 1-sin^2

  cot^2(θ) -sin^2(θ)·cos^2(θ)/sin^2(θ) = . . . . . replace cot with cos/sin

  cot^2(θ) -cos^2(θ) = cot^2(θ) -cos^2(θ) . . . as desired

Answer:

1. a. 25(1) + 10(2) + 3(3) + 10(4) = 94/140 = .671

2. b. Mark’s average < Jay’s average

Step-by-step explanation:

1. What is Mark’s slugging average?

The slugging average gives more weight to the multi-base hits (compared to single-base hits) in opposition with the batting average.

So, a single hit is worth 1 point, a double is worth 2 points, a triple 3 points and a homerun is worth 4 points.  It's a weighted average calculation.

Mark had 25 singles, 10 doubles, 3 triples and 10 homeruns during 140 presences 140 at bat.

25(1) + 10(2) + 3(3) + 10(4) = 94/140 = .671

2. How does Mark's average compares to Jay's?

Let's first calculate Jay's slugging average then we'll be able to decide.

Jay had 10 singles, 6 doubles, 5 triples and 14 homeruns in 90 presences.

10 (1) + 6 (2) + 5 (3) + 14 (4) = 10+12+15+56 = 93 / 90 = 1.033

We can definitely say that Mark's slugging average (0.671) calculated above is lower than Jay's average (1.033).  So,

b. Mark’s average < Jay’s average

Answer:

1/2

Step-by-step explanation:

sin(K)=5/10=1/2

The sine function in mathematics relates angles of a right triangle to the ratios of its side lengths. The value of sin(K) depends on the value of angle K, measured in radians.

In mathematics, the sine function is a trigonometric function that relates the angles of a right triangle to the ratios of the side lengths. The value of sin(K) depends on the value of angle K, which is measured in radians.

For example, if K = π/2, then sin(K) = 1. If K = 0, then sin(K) = 0.

To find the value of sin(K), you can use a calculator or reference table that provides the values of sine for different angles.

Answer:

Step-by-step explanation:

The ratio of interest rates is 8% : 4% = 2 : 1. Since the amount of interest earned in each account is the same, the ratio of amounts invested will be the inverse of that, 1/2 : 1/1 = 1 : 2.

Then 1/(1+2) = 1/3 of the money is invested in the 8% account. That amount is ...

  $9102/3 = $3034 . . . . invested at 8%

The remaining amount is invested at 4%:

  $9102 - 3034 = $6068 . . . . invested at 4%

_____

The interest earned in 1 year in each account is

  0.08·$3034 = 0.04·$6068 = $242.72

_____

If you really need an equation, you can let x represent the amount invested at the higher rate. (Using this variable assignment avoids negative numbers later.) Then 9102-x is the amount invested at the lower rate.

  0.08x = 0.04(9102-x)

  0.12x = 0.04·9102 . . . . . eliminate parentheses, add 0.04x

  x = (0.04/0.12)·9102 = 9102/3 . . . . . divide by the coefficient of x. Same answer as above.