Montana decided to start his ball from the second diamond from the left along the bottom rail. He is planning to aim at the third diamond from the top right. If he hits the ball sufficiently hard, will the ball eventually reach a pocket? If so, show the path of the ball. Explain the steps used to solve the problem and write a concluding statement

The sample space for this situation consists of all possible outcomes of the four calls. It can be represented by a set, a tree diagram, or a table.

The sample space for this situation can be represented by the set of all possible outcomes of the 4 calls: S = { nnnn, nnn s, nnsn, nnss, nsnn, nsns, nssn, nsss, snnn, snns, snsn, snss, ssnn, ssns, sssn, ssss }.

The sample space can also be represented by a tree diagram. The top of the tree diagram represents the start of the calls, and each branch splits into two possible outcomes: sale or no sale. The sample space consists of all possible paths through the tree, including the path that contains two successive sales and the path that contains two successive no sales.

For example, the path { nnnn } represents the outcome of four consecutive no sales. The path { ssss } represents four consecutive sales. The path { nnss } represents two successive no sales followed by two successive sales.

The sample space can also be represented by a table. The table consists of four columns, each representing a call. The rows represent the possible outcomes of the four calls. For example, the row { nnnn } represents four consecutive no sales. The row { ssss } represents four consecutive sales. The row { nnss } represents two successive no sales followed by two successive sales.

Overall, the sample space for this situation consists of all possible outcomes of the four calls. It can be represented by a set, a tree diagram, or a table.

Learn more about sample space here:

https://brainly.com/question/28043513

#SPJ4

The measure of the two angles will be x > 25° and y = 180° - x°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

The two lines are parallel and the third line is a transversal line.

If one angle is greater than 25°. Then the other angle is given as,

Let the angles be 'x' and 'y'. Then angles are supplementary angles. Then the inequality is given as,

x > 25°               ...1

x + y = 180°

y = 180° - x       ...2

From equations 1 and 2, then we have

y = 180° - x

The measure of the two angles will be x > 25° and y = 180° - x°.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ1

Answer:

Below

Step-by-step explanation:

Just count the number of results on the Right

        that have at least two heads = 11

  out of 16 combos      =   11/16 = .6875

If  the length of AB is the same as the length of DC, AC = 9, and

DE = 4, the length of DC is 6 units.

Since DE is parallel to AB and AC = 9, then we can use alternate interior angles to find the length of DC.

Using alternate interior angles, we have:

∠DAC = ∠EAB (Since they are alternate interior angles of two parallel lines)

And from the diagram, we have:

∠DAC = 90° (Since AC is perpendicular to DC)

∠EAB = 90° (Since AB and DE are parallel)

So, we have two right angles, ∠DAC = ∠EAB.

Let find the length of DC:

DC^2 = AC × DE

DC^2 = 9× 4

DC^2 = 36

DC = √36

DC = 6

Therefore, the length of DC is 6 units.

Learn more about length here:https://brainly.com/question/2217700

#SPJ1

Answer:
The mole ratio that will produce the most product is a/4b. This is because mole a is in excess and will have the most product possible, 4 moles of b for every 1 mole of a. This results in 4 moles of the product being produced. Hope this helped

For a standard normal distribution (mean = 0, standard deviation = 1), 80% of the data falls below a z-score of approximately 0.84.

A z-score represents the number of standard deviations a data point is from the mean of the standard normal distribution. For example, if a data point has a z-score of 1.96, it is 1.96 standard deviations above the mean of the standard normal distribution.

Standard normal distribution tables give the area under the standard normal curve to the left of a given z-score. The area to the right of a z-score is simply 1 minus the area to the left of the z-score. So if we want to find the z-score that corresponds to 80% of the data above it, we would look for the z-score that has an area of 0.2 to its right. The closest value listed on a standard normal distribution table to 0.84 is typically 0.841, which corresponds to an area of 0.2 under the standard normal curve to the right of that z-score.

To learn more about standard deviation please click on below link.

https://brainly.com/question/16555520

#SPJ4

Answer: $925.93

Step-by-step explanation:

See image:

The function has a minimum value of f ( 2 ) = -15

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

y = a ( x - h )² + k

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the function be represented as f ( x )

Now , the equation will be

f ( x ) = 2x² - 8x - 7   be equation (1)

Now , from the equation of parabola ,

if ( a > 0 ) , the function has a minimum value

So , f ( x ) = 2x² - 8x - 7 has a minimum

The minimum will occur when the tangent slope is 0 or expressed in another way, when the derivative of f ( x ) is equal to 0

The derivative of the function is

f' ( x ) = 4x - 8

when f' ( x ) = 0

Substituting the values in the equation , we get

4x - 8 = 0

Adding 8 on both sides of the equation , we get

4x = 8

Divide by 4 on both sides of the equation , we get

x = 2

So , f ( 2 ) = 2 ( 2 )² - 8 ( 2 ) - 7

f ( 2 ) = 2 ( 4 ) - 16 - 7

f ( 2 ) = -8 - 7

f ( 2 ) = -15

Hence , the minimum value of function is -15

To learn more about parabola click :

https://brainly.com/question/24042022

#SPJ1

Answer:

1st box = 2/3

2nd box = 16/3

==============================================

Work Shown for the 1st box

2/3 = x/1

x = 2/3

There's not much in terms of steps

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

Another approach for the 1st box

2/x = 3/1

2*1 = x*3

2 = 3x

x = 2/3

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

Work Shown for the 2nd box

2/3 = x/8

2*8 = 3*x ... cross multiplying

16 = 3x

x = 16/3

Optionally this can be converted into a mixed number

16/3 = (15+1)/3

16/3 = 15/3 + 1/3

16/3 = 5 + 1/3

16/3 = 5 & 1/3

Answer: We can use the formula for compound interest to solve this problem:

A = P * (1 + r/n)^(nt)

where:

A = final amount

P = initial amount (what we want to find)

r = annual interest rate as a decimal (2.5% as 0.025)

n = number of times the interest is compounded per year

t = number of years

Plugging in the known values:

640 = P * (1 + 0.025)^(4)

Solving for P:

P = 640 / (1 + 0.025)^(4)

P = $600.28

So Margot invested $600.28 initially.

Step-by-step explanation:

Answer:

Ordered Pair Verification Solution

getachew tafere

Which ordered pair makes both inequalities true? y≤ -x + 1 y > x

(-3,5)

(-2, 2)

(-1, -3)

(0, -1)

The ordered pair (-1, -3) makes both inequalities true.

getachew tafere

A person deposited $5,000 into a bank account and made no other withdrawals or deposits. Each year, 2.7% interest was added to the account.

Write an exponential function for the situation.

Let y be the amount of money in the bank account after t years, where t >= 0.

The exponential function for this situation is:

y = 5000 * (1 + 0.027)^t

This function models the amount of money in the bank account after t years, given the initial deposit of $5,000 and an annual interest rate of 2.7%.

getachew tafere

Margot invests her money in a certificate of deposit that earns 2.5% compounded annually. After 4 years, Margot's investment is worth $640. How much money did Margot invest initially? Round your answer to the nearest cent.

Let's call the initial amount of money Margot invested as x. We can use the formula for compound interest to find x:

x * (1 + 0.025)^4 = 640

Dividing both sides by (1 + 0.025)^4, we get:

x = 640 / (1 + 0.025)^4

Approximating the expression (1 + 0.025)^4, we get:

x = 640 / 1.103822

x = approximately $580.64

So Margot initially invested approximately $580.64.

Step-by-step explanation:

Answer: 25

It could also be 31 though.

The material needed to fix the Rectangular side of tent was 150 sq. ft.

What are Solids?

Solids are 3-D shapes which are extension of 2-D figures. Solids are nothing just some 2-D figures which have some height of their own.

There are various solids like- cube, cuboid, cylinder, prism, sphere, cone , etc.

3-D solids have height so they don't have perimeter but they have total surface area and volume.

We can obtain a solid by the rotation of an appropriate 2-D figures.

Now for the given question:

The ripped side of the tent is a rectangular figure with length 15 ft and breadth 10 ft.

Material required to repair the ripped part of tent = Area of the rectangle of the ripped side of the tent.

Area of rectangle = length × breadth

                             = 15 × 10

                             = 150 sq. ft.

Hence, Material required to fix the ripped tent is 150 sq. ft.

To know about Rectangle visit:

https://brainly.com/question/2607596

#SPJ1

Answer:

Yes, these system of inequalities do have solutions. The solutions for y> 3x+ 14  would be contained in region B and C and the solutions for y<3x+2 would be in regions B and A. Therefore, the answer is region B.

Step-by-step explanation:

If you graphed y> 3x+ 14, you would see that the right side of the coordinate grid would be left blank and empty while the left side would be colored within a dotted line which would be y=3x+ 14. We will call those regions B and C. When you graph y<3x+2 you would see that this time the left side of the coordinate grid would be left blank and the right would be colored in. If you then graph both y> 3x+ 14 and y<3x+2 you would see that only region B is left blank. Therefore, region B would be the solutions for the system of the two inequalities.

Based on the given parallelogram, we find that:

Remember that:

11. It was given that:

∠B = 4x - 5

∠D = 3x + 10

∠B?

∠C?

Since ∠B and ∠D are opposite angles, then ∠B and ∠D are congruent.

∠B = ∠D

4x - 5 = 3x + 10

x = 15

∠B = 4x - 5

∠B = 4(15) - 5

∠B = 60 - 5

∠B = 55°

∠B and ∠C are adjacent angles, then ∠B and ∠C are supplementary.

∠B + ∠C = 180°

55° + ∠C = 180°

∠C = 125°

12. ∠B = 53°

∠B and ∠D are opposite angles and congruent; then:

∠B = ∠D = 53°

∠A and ∠C are opposite angles and congruent; then:

∠A = ∠C

∠B and ∠A are adjacent angles and supplementary; then:

∠A + ∠B = 180°

∠A + 53° = 180°

∠A = 127°

∠C = 127°

13. ∠A = 3∠B

∠A and ∠B are adjacent angles and supplementary; then:

∠A + ∠B = 180°

3∠B + ∠B = 180°

4∠B = 180°

∠B = 45°

∠A = 3∠B

∠A = 3(45°)

∠A = 135°

Learn more about Parallelogram here: brainly.com/question/29147156

#SPJ1

For the function g(x) the changes are mentioned as -

"Slope becomes (-a) from (a) and the y - intercept becomes {-(b + 1)} from b".

In mathematics, the inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective.

Given is the function -

g(x) = - f(x) - 1

Since the function g(x) is not given, we can assume -

f(x) = ax + b                           .... Eq { 1 }

Now -

g(x) = - f(x) - 1

So, we can write -

g(x) = - (ax + b) - 1

g(x) = - ax - b - 1

g(x) = - ax + {-(b + 1)}                                        ... Eq { 2 }

So, we can see that -

Slope becomes (-a) from (a) and the y - intercept becomes {-(b + 1)} from b.

Hence, for the function g(x) the changes are mentioned as -

"Slope becomes (-a) from (a) and the y - intercept becomes {-(b + 1)} from b".

To solve more questions on function, visit the link below-

brainly.com/question/28229665

#SPJ1

The range and interquartile range of the data set 2, 4, 7, 8, 16, 19, 21 are 19 and 8 respectively.

The range of a data set is the difference between the maximum and the minimum values. In other words, the range is the difference of the highest value and the lowest value of a data set.

Therefore, let's find the range of the data sets. Firstly, let's arrange the data sets in ascending order as follows:

2, 4, 7, 8, 16, 19, 21

range = 21 - 2

range = 19

Let's find the interquartile range of the data set.

The interquartile range is the range of values that resides in the middle of the scores.

Hence,

interquartile range = 8

learn more on range and interquartile range here: https://brainly.com/question/3612669

#SPJ1

Russia has 33 nuclear reactors, which puts it in the top 10 countries in the world with the most nuclear reactors. This puts Russia in the 99th percentile, meaning that 99% of countries have fewer nuclear reactors than Russia.

The 99th percentile is a very high ranking, and it indicates that Russia has a large number of nuclear reactors compared to other countries. This is a testament to the country's commitment to nuclear energy, and it is a sign of the country's technological and economic power.

Overall, Russia has 33 nuclear reactors, which puts it in the 99th percentile. This is a very high ranking, and it shows that Russia is one of the most powerful countries in the world when it comes to nuclear energy. This is a testament to the country's commitment to nuclear energy, and it is a sign of its commitment to sustainability.

To know more about nuclear reactors:

https://brainly.com/question/24432180

#SPJ4

5/45 = 1/9 represents the probability of the best-case scenario. 40/45 = 8/9 represents the probability of the worst-case scenario.

When two socks from the same pair are missing, the likelihood of the best-case scenario increases. As a result, all four pairs of socks are present. Now, 10C2 = 45 gives the total number of possible methods to choose 2 socks from a total of 5 x 2 = 10 socks. The probability of choosing one pair of socks from five pairs is equal to the number of ways to choose two socks from a pool of ten socks, and this is provided by the formula 5C1 = 5.  given by 5 / 45 = 1 / 9. The worst case situation is when they are not from the same pair of socks. As a result, all three pairs of socks are present. Now, 10C2 = 45 gives the total number of possible methods to choose 2 socks from a total of 5 x 2 = 10 socks. 10C2 - 5C1 = 45 - 5 = 40 is the number of ways to choose two socks from a group of ten so that they are not from the same pair.  given that by 40 / 45 = 8 / 9

To learn more about probability click here

brainly.com/question/9793303

#SPJ4

The length of QS is obtained as follows:

QS = 28.

The length of QS is obtained applying the proportions in the context of the problem.

The ratio of the side lengths is given as follows:

PQ : QR : RS = 3 : 3 : 1.

The ratio of the side lengths can be simplified as follows:

PQ : QS = 3:4.

Which means that QS is equals to 4/(4 + 3) = 4/7 of the length of segment PS.

The segment PS has a length of 49 units, hence the length of segment PS is given as follows:

PS = 4/7 x 49

PS = 28 units.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

The solution is (6, 32) and it means that the total cost of 6 kites from 2 different businesses is $32.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

From the graph of two lines,

The intersection point is the solution to the two lines system of equations.

Now,

The intersection point = (6, 32)

This means,

x = 6 and y = 32

x = number of kites

y = total cost of the kites

Thus,

The solution is (6, 32).

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ1

In a case whereby Tara is a sales representative for a cosmetic company. She is paid R5.15 per hour each week plus a commission of 10% on the amount of sales over R5 000, the job that would pay more is the second job because  R490.4 > R432. Yes she should change job.

The concept that will be used here is simplification.

We will need to know the amount that she gets from each job so as to know the job would pay more, this can be done as :

The first job:

R5.15*40hours * (7260-5000)*10%

=R5.15*40hours * (2260)*10%

=R432

Hence the salary here  is R432

The second job:

=40 hour* R5 + 7260 *4%

=40 hour* R5 + (7260 *4%)

= R490.4

Hence R490.4 > R432, therefore she should change job.

Learn more about commission at:

https://brainly.com/question/957886

#SPJ1

The correct answer is option (A). The answer is metes and bounds.

Given that,

Despite being antiquated, the most adaptable method of defining land, capable of characterizing even the most atypical of parcels, may be summed up as a very exact, compass-directed stroll around a parcel's boundaries.

To find : This approach is frequently known as ?

Metes and bounds are limits of  piece of a land that may be located on its natural features. Metes and bounds markers are frequently employed in a land's "legal description." Legal description, which is recorded with the land's deed, is the geographical description of a piece of land that pinpoints its exact location.

To learn more about metes and bounds click here :

brainly.com/question/14327693

#SPJ4

Step-by-step explanation:

3.

[tex]( \frac{25 + 3}{0.5} ) - 16.4 \div 4[/tex]

6.

[tex]56 - 4.1[/tex]

The rate of change between Thursday and Friday is 6 minutes per day.

How to convert Hours to Minutes?

As we know 1 hour = 60 minutes. Here we can see that 60 minutes come together to form an hour hence we can conclude that hour is a bigger unit . Whenever we convert a bigger unit to a smaller unit we always multiply the bigger unit with the smaller unit from relation.

1 hr.= 60 min.

Minute is smaller so we will multiply by 60.

5 hr.= 5×60= 300 min.

10 hr.= 10×60= 600 min.

As we know 1 hour = 60 minutes. Here we can see hour is a bigger unit than minutes ones. Whenever we convert a smaller unit to the bigger unit we always divide the bigger unit number with the smaller unit number of the relation.

1 hr.= 60 min

here minute is smaller so we will divide out question by 60.

240 min = [tex]\frac{240}{60}[/tex] = 4 hr.

360 min = [tex]\frac{360}{60}[/tex] = 6 hr.

Now for the given question:

Time taken by Jackson to complete homework on Thursday= 35 min.

Time taken by Jackson to complete homework on Friday= 41 min.

Rate of change = (Time taken by Jackson to complete homework on Friday)-(Time taken by Jackson to complete homework on Thursday)

        = 41 - 35

        = 6

Note: for rate of change we always subtract smaller number from the bigger one.

Hence rate of change of time taken by Jackson to complete its homework between Thursday and Friday is 6 minutes per day.

To know about Unit Conversion visit:

https://brainly.com/question/13016491

#SPJ1

Equation: y= x × 2 + 20

4 = $28

7 = $34

10 = $40

x is the number of kites purchased, and its $2 dollars for one kite. There is a $20 shipping fee added on.

Multicollinearity occurs when independent variables in a regression model are correlated.

Multicollinearity is a statistical concept that describes the correlation of several independent variables in a model. If the correlation coefficient between two variables is +/- 1.0, they are considered perfectly collinear. When independent variables are multicollinear, statistical inferences are less reliable.
Multicollinearity is a problem because it undermines an independent variable's statistical significance. Other things being equal, the larger a regression coefficient's standard error, the less likely it is that this coefficient will be statistically significant.
When two or more predictors in a regression model are moderately or highly correlated with one another, multicollinearity exists. Unfortunately, it can wreak havoc on our analysis, limiting the research conclusions we can draw.

Go through the given link below to know more aboutGo multicollinearity:-

https://brainly.com/question/15856348

#SPJ4

The expected loss due to default on the portfolio of 5 loans is 6,250, and the standard deviation of the expected loss is 556.25.

The expected loss due to default on the portfolio of 5 loans is given by the formula:

Expected Loss = Probability of Default x Expected Loss per Loan

Expected Loss = 0.25 x (25,000) = 6,250

The variance of the expected loss due to default on the portfolio of 5 loans is given by the formula:

Variance of Loss = Probability of Default x Variance of Loss per Loan

Variance of Loss = 0.25 x (5000)2 = 312,500

Therefore, the standard deviation of the expected loss due to default on the portfolio of 5 loans is given by the formula:

Standard  Deviation of Loss = √Variance of Loss

Standard Deviation of Loss = √312,500 = 556.25

The expected loss due to default on the portfolio of 5 loans is 6,250, and the standard deviation of the expected loss is 556.25.

Learn more about standard deviation here:

https://brainly.com/question/23907081

#SPJ4

The number of sides is 72 sides

A polygon can be defined as a plane figure that is known by a finite number of straight line segments that are joined to form a closed polygonal chain.

To determine the number of sides in a polygon given the exterior angle value, we have make use of the formula;

360 degrees/ divide the exterior angle given

Now, substitute we have to substitute the value, we get;

360/5

Divide the values, we get;

72  sides

Hence, the number is 72

Learn about polygons at:

https://brainly.com/question/1592456

#SPJ1