Directions: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Carla is getting her golf bag prepared for a golf tournament and decides to do a quick experiment with the three brands of golf balls she
has stored in her bag.
She randomly draws 20 golf balls to determine the frequency of occurrence for each brand, returning the drawn ball after each trial.
The data from her experiment is displayed in the table below. Determine the correct values to complete the rest of the table, and
complete the accompanying statement. For this item, any answers that are not whole numbers should be entered as a decimal,
rounded to the hundredths place.
Brand
Best Flight
Distance King
High Loft
Frequency
3
Reset
6
11
Experimental
Probability
0.30
If Carla performed another experiment using the same set of golf balls and drew 12 Best Flight golf balls, she would draw
approximately
Distance King golf balls.

The volume of the solid is a) 1/30 and b) 1/6.

When the solid’s base is located in the xy plane and the cross-section is taken perpendicular to the x-axis with known cross sectional area given by A(x) for all the x in the interval [a,b], then the volume of the solid is given as the definite integral of these cross-sectional areas.

V = ∫_a^b▒A(x)dx

By graphing the given equations, we see that the area is bounded by the line y= x+1 and parabola y=x^2+1 on the interval on x-axis as [0,1].

a) The base of each square has length

f(x) – g(x) = (x + 1) – (x^2 + 1) = x – x^2

and the solid is square.

The area of cross section is

A(x) = (x – x^2)^2 = x^2 – 2x^3 + x^4

Hence, the volume is

∫_0^1▒A(x)dx

∫_0^1▒〖(x^2-2x^3+x^4)dx〗

[1/3 x^3-1/2 x^4+1/5 x^5]1¦0

[1/3 -1/2  +1/5]

1/30

b) The base of each rectangle has length

f(x) – g(x) = x – x^2

and the height of each rectangle is 1.

The area of cross section is

A(x) = (x – x^2)(1) = x - x^2

Hence, the volume is

∫_0^1▒A(x)dx

∫_0^1▒〖(〖x-x〗^2)dx〗

[1/2 x-1/3 x^3]1¦0

[1/2 -1/3]

1/6

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Part A: The vertex, domain, and range of the function are respectively; (5, 0), ( - ∞ , ∞ ),  [0, ∞ ]\

Part B: The function f(x) = |x| is vertically shifted by 3 units to get the function h(x) = |x| + 3. The y-coordinate of the vertex is shifted by 3 units.

Part A: The given function is g(x) = | x - 5 |.

The x-coordinate of the vertex will be: x - 5 = 0

x = 5

Therefore, the y-coordinate of the vertex will be:

y = g(x) = |x - 5|

y = g(5) = |5 - 5|

y = 0

So, the absolute value vertex is (5, 0).

Now, all real numbers fall under the expression's domain, with the exception of cases where it is undefined. In this instance, the phrase is defined even if there is no real number. Thus;

Interval Notation: ( - ∞ , ∞ )

Set builder Notation: { x | x ∈ R }

The set of all legitimate y values is the range.

Interval Notation: [0, ∞ ]

Set builder Notation: { y | y ≥ 0}

Part B: h(x) = |x| + 3 is the transformed version of the parent function f(x) = |x|.

For the parent function f(x) = |x|, the vertex is ( 0, 0).

The range of an absolute function in the form c( | ax + b | ) + k is f(x) ≥ k.

Therefore, the range of the function f(x) = |x| is f(x) ≥ 0 and in interval notation is [ 0, ∞ ).

For the transformed function h(x) = |x| + 3.

The vertex of the function is ( 0, 3 ).

The range of function is h(x) ≥ 3 and in interval notation is [3, ∞ ).

Hence, the y coordinate of the vertex is transformed by 3.

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Answer:

  80 cm

Step-by-step explanation:

You want a function of the length of the perimeter belt around three packed circles of radius 10 cm.

Examination of the attached figure shows the length of the belt is the sum of the lengths of the sides of an equilateral triangle with sides 20 cm, and the circumference of a circle with diameter 20 cm.

  triangle perimeter = 3s = 3(20 cm) = 60 cm

  circle circumference = πd = π(20 cm) = 20π cm

The length of the belt is the sum of these, or

  60 cm +20π cm = (60 +20π) cm

Compared to (a +bπ) cm, we find a=60, and b=20. The desired sum is ...

  a +b = 60 +20 = 80

__

Additional comment

You will notice that equilateral triangle PQR in the attached figure has side lengths that are twice the radius of the circle. The straight segments AB, A'B', A"B" are parallel to the triangle sides, and are the same length. (ABPR is a rectangle.)

Each circular arc, BA', for example, is 1/3 of the circumference of the circle, so the total length of all the arcs is the circumference of one 20 cm circle.

The particle increases its velocity in the following three subintervals:

In this question we find the case of the position of a particle (x) in versus time (t), whose graph is shown below. The velocity associated to a given time t is represented by the slope of the line tangent to that point. The velocity of a particle increases when the signs of function position and function velocity are the same.

By secant line formula, velocity can be approximated by this formula:

v ≈ Δx / Δt

Since time is a non-negative real number, the sign of velocity is derived by the following rules:

Then, the velocity of the particle increases in the following two cases:

The velocity is increasing in the following subinterval 0 < t < 2, 4 < t < 7 and 9 < t < 10.

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For any real number c, it is calculated that √(c²) is; Option D: c

The set of real numbers is defined as the union of the set of Irrational numbers and the set of rational numbers.

Now, we are given the equation as;

√(c²)

Now, from definition of real numbers, it means that they are not imaginary and as such any value of c remains the same. Thus, we have;

√(c²) = c

Now, because c is not classified as an absolute value, and even if since it is square, will be surely positive and as such the final answer for every real number c in the square root will be c.

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The total number of ways in which the selection can be done are 3.

Given is to take out 2 objects without replacement from 3 objects, pencil, eraser, and desk.

The total number of ways in which the selection can be done is -

C(3, 2) = (3!)/(2!)(1!) = 3

C(3, 2) = 3

Therefore, the total number of ways in which the selection can be done are 3.

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The values of l and h, along with w for the rectangular pyramid, that will produce identical volumes, are given by the following relation:

w = 4l.

(the value of the height is free).

The volume of a pyramid is calculated as the multiplication of the base area by the height, which is then divided by three.

Hence, the formula is given as follows:

V = Ab x h/3.

In which:

The base areas are calculated as follows:

Four congruent square pyramids whose combined volume is the same as the volume of a single rectangular pyramid, hence the relation is given as follows:

4l²h/3 = lwh/3.

w = 4l.

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Answer:

The answer is 1.25.

Step-by-step explanation:

You can see what sides match up, and then you divide to find the scale factor.

17.5/14 = 1.25

20/16 = 1.25

Answer: y = -6.

Step-by-step explanation: -6^3 is -216. Sorry if this isn't a clear explanation, but it seems like the correct choice.

Have a great day! :)

The value of p + q is 17.

The probability that one of the three risk factors will be present in exactly the right amount for a randomly chosen individual can be calculated using the inclusion-exclusion principle. The probabilities that a man has risk factors A (but not B or C), B (but not A or C), and C (but not A or B) are, accordingly, denoted by the letters P(A), P(B), and P(C). Next, we have:

P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) + P(A and B and C)

P(A) = P(B) = P(C) = 0.1 and P(A and B) = P(A and C) = P(B and C) = 0.14 are both supplied to us.

 Additionally, it is stated that if a guy possesses both A and B, there is a 1/3 chance that he possesses all three risk factors. Using this knowledge, we can calculate P. (A and B and C).

P(A, B, and C) = P(A, B | C) * P(C) = (1/3) * 0.1 = 1/30 is what we got.

These values are then reinserted into the equation above to produce the following result: P(A or B or C) = 0.1 + 0.1 + 0.1 - 0.14 - 0.14 - 0.14 + 1/30 = 0.44/30 = 11/75

None of the three risk factors are present in a guy in a likelihood of 1 - P(A or B or C) = 1 - 11/75 = 64/75. As a result of the reduction of the proportion 64/75 to 8/9, p = 8 and q = 9, and p + q = 8 + 9 = 17.

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The opposite of the number 19(4/3) is

Additive inverse is the opposite of a number in terms of addition, this is the number that gives zero when added to the original number.

To get a result equal to 0, add the original number and the additive inverse or by simply changing the sign of the integer. On the basis of negation of the original number.

In the problem, the opposite of 19(4/3) is solved as follows

let x be the opposite

19(4/3) + x = 0

x = -19(4/3)

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The pounds of expensive jelly beans that Mike should use, given the amount he wants to sell the mixture, is 30 pounds.

The total weight of the mixture is x + 10 pounds because Mike adding 10 pounds of the cheaper jelly beans while the cost of the expensive jelly beans would be:

= 5 x number of pounds

= 5x

The total cost of the cheaper jelly beans is :

= 10 pounds x 2

= $ 20

The total revenue from the mixture is therefore:

= 4.25x + 42.5

The total cost is :

= 5x + 20

Equating these would find the pounds of expensive jelly beans needed :

5x + 20 = 4.25x + 42.5

0.75x = 22.5

x = 30

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The terms of the expression are 4, 2(5) and -3 and the value of the expression is 11

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

4 + 2(5 + (-3)

Rewrite properly

So, we have

4 + 2(5) + (-3)

For an expression ax + by

The terms are ax and by

This means that the terms of 4 + 2(5) + (-3) are 4, 2(5) and -3

Here, we have

4 + 2(5) + (-3)

Remove the brackets

4 + 2(5) + (-3) = 4 + 10 - 3

Evaluate the like terms

4 + 2(5) + (-3) = 11

Hence, the value is 11

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The domain of the quadratic function is (-∞,∞). The range of the quadratic function is (-∞,3].

What is interval notation?

Interval Notation is a method of representing a subset of real numbers by the numbers that connect them.

The vertex of the quadratic function is (0,3).

The function extended downward direction in a vertical. The function extended on both sides of the x-axis horizontally.

The x-coordinate of the points on the quadratic function is the domain.

The y-coordinate of the points on the quadratic function is the range.

The x-coordinate of the points on the quadratic function is from -∞ to ∞.

The y-coordinate of the points on the quadratic function is from -∞ to 3.

The domain of the function is (-∞,∞).

The range of the function is  (-∞,3].

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The sum of the measures of angles D and E and the measure of angle F will be 3x + 35. Then the correct option is C.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The information is given below.

∠D = 3(x + 10)

∠E = (2x + 15)

∠F = 2(x + 10)

The sum of the measures of angle D and E than the measure of angle F is calculated as,

⇒ ∠D + ∠E - ∠F

⇒ 3(x + 10) + 2(x + 10) - (2x + 15)

Simplify the expression, then we have

⇒ 3(x + 10) + 2(x + 10) - (2x + 15)

⇒ 3x + 30 + 2x + 20 - 2x - 15

⇒ 3x + 30 + 5

⇒ 3x + 35

The sum of the measures of angles D and E and the measure of angle F will be 3x + 35. Then the correct option is C.

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Answer:12

Step-by-step explanation:4/3x-2/3x=2/3x

6+2=8

2/3x=8

x=12

Answer:

X = 12

Step-by-step explanation:

2​x+2=34​x−6

Multiply both sides of the equation by LCM

(32​x+2)×3=(34​x−6)×3

CalculateMore Steps

 2x+6=(34​x−6)×3

CalculateMore Steps

 2x+6=4x−18

Move the variable to the left side

2x+6−4x=−18

Subtract the termsMore Steps 

−2x+6=−18

Move the constant to the right side

−2x=−18−6

Subtract the terms

−2x=−24

Multiply both sides

−2x(−21​)=−24×(−21​)

SimplifyMore Steps

 −2x(−21​)=12

Solution

x=12

The axis of symmetry of the function is x = 0

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

y = -x^2 - 0.1

Differentiate the function

So, we have the following representation

y' = -2x

Set the differentiated function to 0

This gives

-2x =0

Divide both sides by -2

x = 0

Hence, the axis of symmetry is x = 0

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The expression which shows how much additional money generated at an interest rate of 5% than at an interest rate of 3% is: (1,000 (1 + 5 / 1,200) ^12) – (1,000 (1 + 3 / 1,200) ^12). The correct answer is option D.

The amount of money generated at the interest rate of 5% is shown by A₅ :

1,000 (1 + 5 / 1,200) ^12

And similarly, the amount of money generated at the interest rate of 3% is shown by A₃ :

1,000 (1 + 3 / 1,200) ^12

Hence, the additional amount of money will be shown by A₅ – A₃  :

(1,000 (1 + 5 / 1,200) ^12) – (1,000 (1 + 3 / 1,200) ^12)

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Although part of your question is missing, you might be referring to this full question: 1,000 (1 + r/1,200) ^12. The expression above gives the amount of money, in dollars, generated in a year by a $1,000 deposit in a bank account that pays an annual interest rate of r%, compounded monthly. Which of the following expressions shows how much additional money is generated at an interest rate of 5% than at an interest rate of 3%?

A. 1,000 (1 + (5 – 3) / 1,200) ^12

B. 1,000 (1 + (5 / 3) / 1,200) ^12

C. (1,000 (1 + 5 / 1,200) ^12) / (1,000 (1 + 3 / 1,200) ^12)

D. (1,000 (1 + 5 / 1,200) ^12) – (1,000 (1 + 3 / 1,200) ^12)

Answer:

Step-by-step explanation:

25% = 25/100 = 0.25

Then:

Bounce 1:

160 - (160*0.25) = 160 - 40 = 120

Bounce 2:

120 - (120*0.25) = 120 - 30 = 90

Bounce 3:

90 - (90*0.25) = 90 - 22.5 = 67.5

Bounce 4:

67.5 - (67.5*0.25) = 67.5 - 16.875 = 50.625

Answer:

A

Step-by-step explanation:

Answer:

x = 19

z = 19

Step-by-step explanation:

8x - 88 + 5x + 21 = 180

13x - 67 = 180

13x = 247

x = 19

z = 19

The pairs of events that are disjoint and cannot occur at the same time are; Option D: Events A and C

In mathematical set problems, we usually say that two sets are said to be disjointed sets if they have no elements in common.

Since the spinner has 10 sections numbered 1 to 10, then the sample space is;

S = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

We are told that Event A is the event of the Spin of an odd number. Thus;

Event A = { 1, 3, 5, 7, 9 }

Event B: Spin a number greater than 1 Thus;

Event B = { 2, 3, 4, 5, 6, 7, 8, 9, 10}

Event C: Spin a 2. Thus;

Event C = { 2 }

Event D: Spin a multiple of 2. Thus;

Event D = { 2, 4, 6, 8, 10}

Therefore;

A ∩ B = { 3, 5, 7, 9}

B ∩ C = {2}

C ∩ D = { 2 }

A ∩ C = { }

Thus, A ∩ C does not contains any element. So A and C is a disjoint event.

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Based on the information, it can be inferred that the order from lightest to heaviest lure would be: 0.25 (c), 0.372 (d), 0.5625 (b), and 0.625 (a).

To calculate the weights of the lures we must take into account that they are fractional, that is to say that to find an exact number of the weight of each one of the lures we can carry out the division of the fractional to have a decimal number that allows us to organize more easily the pesos.

According to the above information, the weights would be the following:

a. 5/8 = 0.625

b. 9/16 = 0.5625

c. 1/4 = 0.25

d, 3/8 = 0.372

Then, the weights organized from smallest to largest would look like this: 0.25 (c), 0.372 (d), 0.5625 (b), and 0.625 (a).

Note: This question is incomplete because there is some information missing. Here is the complete information:

Options:

a. 5/8OZ

b. 9/16 OZ

c. 1/4OZ

d. 3/8OZ

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7

it could be 7 because if you think about it, 4 can't go into 7 evenly.

so the proper way to solve this would be by finding how many times 4 can go into 7 evenly

4 can go into 7 once evenly

3 times 1 is 3

so you would have 4 left over

1 r4

The expression that is equivalent to 3 squared 256x10y^7 is  [tex]4x^3y^2\sqrt[3]{4xy}[/tex].

Each term of the expression can be wriiten so as to find their prime factorization which can be done as

256 = 2^3.2^3.2^2

x^10 = x^3.x^3.x

y^7 = y^3.y^3.y

We can perform some simplification by bringing triples out  which will be outside the cube root : which are

2^3.2^3.x^3.x^3.y^3.y^3 = 2.2.3.3.y.y =[tex]4x^3y^2[/tex]

Then remaining terms will now be 2²(x)(y) will be in the cube root which = [tex]2^2xy[/tex]

Then we can write as [tex]4x^3y^2\sqrt[3]{4xy}[/tex]

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Liters of fuel in 1 hr is S/E and Liters of fuel in 60 km is 60/E

Liters of fuel in 1 hr: The Quasi JX travels E kilometers per liter of fuel (EkmL)(EkmL) at S kilometers per hour (Skmhr)(Skmhr). Therefore the Quasi JX requires 1E1E liters of fuel to travel 1 km. Since the Quasi JX travels S kilometers per hour, it requires 1E1E LkmLkm × S km/hr, or SELhrSELhr

Thus, Liters of fuel in 1 hr is S/E.

Liters of fuel in 60 km: The Quasi JX travels E kilometers per liter of fuel (EkmL). Therefore the Quasi JX requires 1E1E liters of fuel to travel 1 km. Given this, the Quasi JX uses 1/E L/km × 60 km, or 60/E L of fuel to travel 60 km.

Thus, Liters of fuel in 60 km is 60/E.

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The expression that represents the number of liters of fuel used in a 60 km drive under ideal driving conditions at a constant speed S is written as 60/E

Here we have given that RO1, Liters of fuel in 1 hour

Here we also know that the Quasi JX travels E kilometers per liter of fuel (E km/L) at S kilometers per hour (S km/hr)

Now, we have to know that the Quasi JX requires 1/E liters of fuel to travel 1 km.

Here the JX travels S kilometers per hour, and here it requires

=> (1/E x L/km) × (S km/hr)

Then it can be written as when we apply the value of Ro1 is 60, then we get

=> 60/E

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Answer:

12.7  ==> distance of RS

24.2 ==> distance of RT

Step-by-step explanation:

Distance is always positive. So if you get a negative value, take the absolute value of the negative number:

For example, between point R and S:

-17.2 - (-4.5) =

-17.2 + 4.5 =  ==> subtracting a negative number is equivalent to adding a

                           positive number

-(17.2 - 4.5) = -12.7

-12.7 ==> |-12.7| = 12.7  ==> distance of RS

For RT:

-17.2 - 7 =

-(17.2 + 7) = -24.2

-24.2 ==> |-24.2| = 24.2 ==> distance of RT

The best price can be obtained by taking the ratio and it is given for the case of two weeks ago.

The ratio of two numbers a and b can be written as a : b = a/b.

The ratio of two quantities is the unit rate of one quantity with respect to the other.

The price of gas per gallon for both the cases are calculated as below,

Two weeks ago it is given as,

Total price ÷ Number of gallons

⇒ 31.14 ÷ 9 = $3.46

And, for last week it is given as,

Total price ÷ Number of gallons

⇒ 52.70 ÷ 15 = 3.51

Thus, the price per gallon is cheaper two weeks ago.

Hence, the best price of gas is obtained for the case of two weeks ago.

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Answer:

a) y = 2,035(1.03)^t

b) 2,359

Step-by-step explanation:

a)

Exponential growth:

y = a(1 + r)^t

where

y = future vale

a = initial value

r = periodic rate of growth

t = number of periods

y = 2,035(1 + 0.03)^t

y = 2,035(1.03)^t

b)

Here we have a = 2,035; r = 3% = 0.03; t = 5

y = 2,035(1 + 0.03)^5

y = 2,359

2,359