The point guard of a basketball team has to make a decision about whether or not to shoot a three-point attempt or pass the ball to another player who will shoot a two-point shot. The point guard makes three-point shots 30 percent of the time, while his teammate makes the two-point shot 48 percent of the time.

The present value of the loan is approximately 4. $42,817,078.

The present value of a loan is the current worth of all future cash flows associated with the loan. To calculate the present value of the loan, we need to discount each cash flow to its present value using the market rate of 7% per annum, compounded semi-annually.

Let's break down the cash flows:

1. $11 million is received now and has no discounting since it's already in present value.
2. $22 million is received at the end of month 6. We need to discount it to its present value. Since it's six months in the future, we need to calculate the present value of $22 million in six months at a rate of 7% per annum, compounded semi-annually.
3. $11 million is received at the end of 12 months. We need to discount it to its present value. Since it's one year in the future, we need to calculate the present value of $11 million in one year at a rate of 7% per annum, compounded semi-annually.

To calculate the present value, we can use the formula:

PV = FV / (1 + r/n)^(n*t)

Where:
PV is the present value,
FV is the future value,
r is the interest rate,
n is the number of compounding periods per year, and
t is the number of years.

Let's calculate the present value of each cash flow:

1. PV of $11 million received now = $11 million

2. PV of $22 million received in six months:
PV = $22 million / (1 + 0.07/2)^(2*0.5)
PV = $22 million / (1.035)^(1)
PV ≈ $21,233,298

3. PV of $11 million received in one year:
PV = $11 million / (1 + 0.07/2)^(2*1)
PV = $11 million / (1.035)^(2)
PV ≈ $10,583,780

Now, let's add up the present values of each cash flow to find the total present value of the loan:

Total PV = $11 million + $21,233,298 + $10,583,780
Total PV ≈ $42,817,078

Rounded to the nearest dollar, the present value of the loan is approximately $42,817,078.

Based on the provided answer choices, the closest option to the calculated present value is (4) $42,524,656.

To learn more about loan, refer below:

https://brainly.com/question/11794123

#SPJ11

The \(|f(an) - f(am)| < ε\). This is a contradiction, which implies that

OO = U dan. Q-continuity is also known as uniform continuity.

We know that if f is a continuous function on the interval [a, b], it must also be uniformly continuous on the same interval. Let's take ε > 0. Since f is continuous at 3, there is a δ > 0 such that

\(x - 3| < δ = > |f(x) - f(3)| < ε / 2\)

Let's pick an arbitrary x' in the interval (3 - δ, 3 + δ). This means that f is uniformly continuous on the interval [3, b], which implies that DaCD. This implies that

\(|x' - x| < a = δ / 2\). Therefore, x' is not in the interval (x - a, x + a). Hence, f is not a-continuous for a = δ / 2 > 0. Now, let's consider an = 1 / n. Suppose that OO ≠ U dan. Therefore, there exists a natural number N such that |an - am| < δ / 2 for all m, n ≥ N

Using the triangle inequality, we can write:

\(|f(an) - f(am)| < = |f(an) - f(x')| + |f(x') - f(x)| + |f(x) - f(am)|\)

Since |an - am| < δ / 2, we know that an and am are both in the interval

\((x - δ / 2, x + δ / 2)\).

To learn more about continuity, visit:

https://brainly.com/question/21447009

#SPJ11

Answer:

21m²

Step-by-step explanation:

area = length X width

= 7 X 3

= 21m²

Answer:

X=18, Y=6

Step by Step Explanation:

This is a little long winded.. Let's solve for Y first.

First looking at the problem, you can note a few things. First of all, there is an Isosceles triangle, and there is an equilateral triangle. Where they connect, there is a 90° angle.

Now, all equilateral triangles have the same angle measurement. 60°. Now, if you look where the right angle is, it is showing a 60° angle, a total of 90°, and an unknown area. So simply subtract. 90-60=30. Divide that by 5, and you have your answer of 6.

Now let's solve X. X is very simple. On an isosceles triangle, the two top sides are the same length. And one of the top sides is the same size as the equilateral triangle. And on equilateral triangles, all sides are the same.

So the 11 transfers over to the X side. So let's make a small equation. 11=X-7. To make it even, let's add 7 to both sides. 11+7=X+7-7. Simplify to get 18=X, which is your answer.

Answer:

X=18 y=6

Step-by-step explanation:

explain and solve

Answer:

1) P(none are red) = 51.2%

2) P(third one is the first one that is yellow) = 12.8%

Step-by-step explanation:

We are given;

P(Yellow) = 20% = 0.2

P(red) = 20% = 0.2

P(Orange) = 10% = 0.1

P(Blue) = 10% = 0.1

P(green) = 10% = 0.1

P(brown) = 30% = 0.3

1) Probability that one is not red is;

P(one not red) = 1 - P(red)

P(one not red) = 1 - 0.2

P(one not red) = 0.8

Since 3 are selected, we will apply multiplication rule for independent events to get;

P(none are red) = 0.8 × 0.8 × 0.8

P(none are red) = 0.512

P(none are red) = 51.2%

2) To find the probability, that the third one is the first one that is yellow, we will use multiplication rule for independent events to get;

P(third one is the first one that is yellow)

= (1 - P(Yellow)) × (1 - P(Yellow)) × P(Yellow)

P(third one is the first one that is yellow) = (1 - 0.2) × (1 - 0.2) × 0.2

P(third one is the first one that is yellow) = 0.128

P(third one is the first one that is yellow) = 12.8%

The length of one leg of the right triangle is 5√10

The leg of a right triangle can be found as follows;

Therefore, using trigonometric ratios,

sin 45 = opposite / hypotenuse

sin 45 = x / 10√5

1 / √2 = x / 10√5

cross multiply

10√5 = x√2

divide both sides by √2

x = 10√5 / √2

x = 10√5 / √2 × √2 / √2

x = 10√10 / 2 = 5√10

learn more on right triangle here: https://brainly.com/question/3398476

#SPJ1

The surface area of the box, in square feet, that Zoe decorates is 430.35 square feet

To determine the surface area from the net of the box, we simply calculate the area of each shape.

From the given figure, we have the following shapes and dimensions:

The area is then calculated using:

Area = Areas of the rectangle + Area of the triangle

So, we have:

Area = 15 * 12 + 13.89 * 15 + 0.5 * 12 * 7

Evaluate the sum of products

Area = 430.35

Hence, the surface area of the box, in square feet, that Zoe decorates is 430.35 square feet

Read more about surface areas at:

https://brainly.com/question/6613758

#SPJ1

Answer:577.35 square feet

Step-by-step explanation:

‍♀️

The reqired equation will be  :|C-78|=2.5 which we use to find the minimum or maximum amount

we have to determine the equation which can be used to find the minimum or maximum amount, c, of chocolate chips that he can weigh out.

From the question statement, we can easily the information that

Sam tends to use an industrial kitchen to bake several batches of his famous chocolate chip bars.

Also, it is mentioned that he needs to weigh out 78 ounces of chocolate chips, plus or minus 2.5 ounces.

The equation is |C-78|=2.5

Hene, the required equation will be  :|C-78|=2.5

To know more about end semester test follow

brainly.com/question/20349931

#SPJ1

Answer:

18 is the answer

Step-by-step explanation:

because you times 2 my 9

Answer:

18

Step-by-step explanation:

9 x 2 9 + 9 ? u good people ?

Answer:

1:24

Step-by-step explanation:

add all the dogs then divide it by 2

and get 1:24

The hiker's distance and bearing from their starting point are approximately 7.155 miles and 28.07°, respectively.

Given that two hikers travel 8 mi southeast and then 6 mi east, we are to find the hikers distance and bearing from their starting point at this time.Long ExplanationThe bearing of the hiker refers to the angle between the hiker's direction and North. So, let us assume that the hiker has initially moved at a direction East, as shown below:We are given that the hiker has traveled 8 miles to the southeast.

Therefore, from the diagram, the distance traveled in the East direction is 8 sin(45) miles, and the distance traveled in the South direction is 8 cos(45) miles. East = 8 sin(45) = 8/√2 = 4√2 miles South = 8 cos(45) = 8/√2 = 4√2 miles We are then told that the hiker travels 6 miles east, from the last position.

To know more about distance  visit:-

https://brainly.com/question/13034462

#SPJ11

We need to decide whether the given equations are always or never true for values of x .The given equations are ,

solve out for x,

\(\longrightarrow x -x =12+1\\ \)

\(\longrightarrow 0 =13\\ \)

This can never be true. Hence the equation is never true for any values of x.

solve out for x,

\(\longrightarrow x -x =\dfrac{3}{4}+\dfrac{3}{4}\\ \)

\(\longrightarrow 0=\dfrac{3}{2}\)

This can never be true. hence the equation is never true for any values of x.

solve out for x,

\(\longrightarrow 4x +12=8x+12-4x\\\)

\(\longrightarrow 4x -8x +4x =12-12\\\)

\(\longrightarrow 0=0\)

hence this equation is true for all values of x.

solve out for x,

\(\longrightarrow 2x -x -x =8+8\\ \)

\(\longrightarrow 0=0 \)

hence the equation is true for all values of x.

solve out for x,

\(\longrightarrow 2x +10+3x =5x-25\\ \)

\(\longrightarrow 5x -5x =-25-10\\\)

\(\longrightarrow 0 =-35\)

This can never be true. hence the equation is never true for any values of x.

and we are done!

Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer: \(\frac{4s^2 -56s+196}{\pi}\)

Step-by-step explanation:

\(P=4s \implies C+4s=28\\\\\implies C=28-4s\\\\\implies r=\frac{28-4s}{2\pi}=\frac{14-2s}{\pi}\\\\\therefore f(s)=\pi \left(\frac{14-2s}{\pi} \right)^2\\\\=\pi \cdot \frac{196+4s^2 -56s}{\pi^2}\\\\=\frac{4s^2 -56s+196}{\pi}\)

Answer:

On average, you can expect to win $21.00 in this scenario.

Step-by-step explanation:

The expected value of this scenario can be calculated as follows:

Expected value = (Probability of Heads x Payoff of Heads) + (Probability of Tails x Payoff of Tails)

The probability of getting Heads or Tails is both 0.5 (assuming a fair coin). Therefore:

Expected value = (0.5 x $179) + (0.5 x -$137)

Expected value = $89.50 - $68.50

Expected value = $21.00

Therefore, on average, you can expect to win $21.00 in this scenario. However, it's important to note that this is just an average and that in any given flip, you could win or lose the full amount.

Know more about, https://brainly.in/question/53682118

#SPJ11

The compass needle always points north because it is magnetic north pole.

Earth has magnetic field due to magnetic elements present in Earth's core in molten form. They are assumed to be in the form of giant bar to ease the calculations concerning magnetic field and polarity. The assumptions are geographic south pole harbours magnetic north pole and vice versa for the opposite pole.

So, we know that like poles attract each other and unlike poles repel each other. The north end of magnetic needle will point towards the magnetic south pole which is geographic north pole. Thus, we see compass needle directed to North pole.

Learn more about magnets -

https://brainly.com/question/2320811

#SPJ4

Answer:

Im not too sure because I haven't done this in a while but, I think the answer is 60cm, don't come at me if its wrong plssss

Step-by-step explanation:

if u divide it along the far left, closer to 12cm, u would have 2 rectangles. they would Both be close and If u added up 12cm and 12cm that would give you 24cm, and if you go to the other rectangle it would be 18 cm plus 18cm that would be 36cm. u do not multiply since it is perimeter and not area. Hope it helped!

Answer:

60 cm

Step-by-step explanation:

18+18+12+12

30+30

60

the 4 unknown sides we know that the 2 lengths equal 18 cm because both of them together are the same length as the base and the 2 widths add up to be 12 cm since it is the same size as the 12 cm width when added together if that makes sense

Hopes this helps

Answer: 89.5

Step-by-step explanation:

Answer:

89.5

Step-by-step explanation:

Since this is an average question, you have to add all four grades. You should get 358. Then you have to divide by four. You should get 89.5, and that would be your answer.

Answer:

I think it's c all real number

Answer:

B. Positive real numbers (y > 0)

Step-by-step explanation:

Just took the quiz

The volume of the right prism include the following: 8,640 in³.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Next, we would determine the area of the triangle at the base of the right prism as follows:

Base area = 1/2 × ( 36 × 12)

Base area = 1/2 × 432

Base area = 216 in².

Now, we can calculate the the volume of this right prism:

Volume = base area × height

Volume = 216 × 40

Volume = 8,640 in³.

Read more on right prism here: https://brainly.com/question/31245490

#SPJ1

Answer:

x= 12

Step-by-step explanation:

Simplifying

7x + 21 = 105

Reorder the terms:

21 + 7x = 105

Solving

21 + 7x = 105

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-21' to each side of the equation.

21 + -21 + 7x = 105 + -21

Combine like terms: 21 + -21 = 0

0 + 7x = 105 + -21

7x = 105 + -21

Combine like terms: 105 + -21 = 84

7x = 84

Divide each side by '7'.

x = 12

Simplifying

x = 12

Answer:

12

Step-by-step explanatio

The value of logm 4/m is 1.139 - 2 logm m. This means that we can express logm 4/m in terms of other logarithmic values without finding the exact value of m.

Given that logm 3 = 0.903, logm 4 = 1.139, and logm 7 = 1.599. We are to find logm 4/m.

Using the properties of logarithm, we have,

logm 4/m = logm 4 - logm m

               =1.139 - logm m               .....................................(1)

Again, using the properties of logarithm, we know that:

logm 4 = logm (2 × 2)  

        = logm 2 + logm 2

         = 1.139 = 2logm 2                    ..................................(2)

Substituting equation (2) into (1) gives:

logm 4/m = 2logm 2 - logm

           m = 2logm (2/m)          ..................................................(3)

Using the property of logarithm once again, we know that:

loga b = logc b / logc a                     ............................................(4)

Substituting equation (4) into equation (3), we have:

logm 4/m = 2 logm 2 - logm

m= logm [(2/m)² / m]                       .............................................(5)

Now, we are to find logm 4/m by substituting the given values.

Using equation (2), we have:

logm 2 = (1.139)/2

     = 0.5695

Using equation (5), we get:

logm 4/m = logm [(2/m)² / m]

logm 4/m = logm [4/m²m]

 logm 4/m = logm 4 - logm

logm 4/m = 1.139 - 2 logm m

Therefore, by using the properties of logarithm, we have found that logm 4/m = 1.139 - 2 logm m. This means that we can express logm 4/m in terms of other logarithmic values without finding the exact value of m.

To know more about the logarithmic values, visit:

brainly.com/question/29131050

#SPJ11

The probability that three students, with different names, line up in alphabetical order from front-to-back can be expressed as a common fraction.

Explanation:

There are 3! = 6 ways in which the three students can line up in a single file. However, only one of these arrangements is in alphabetical order from front-to-back. Therefore, the probability of the three students lining up in alphabetical order is:

1/6

This can be expressed as a common fraction, indicating that there is only one favorable outcome out of six possible outcomes. Therefore, the probability of the three students lining up in alphabetical order is 1/6, or approximately 0.1667.

To learn more about common fraction click here, brainly.com/question/30603575

#SPJ11

Answer: 6x

Step-by-step explanation:

so consider x as the number,

twice of x= 2x

2x tripled= 2x*3

               = (2*3)x

               = 6x

Answer:

122°

Step-by-step explanation:

All triangles have a total of 180°.

Angle 1 will be X

Angle 2 will be Y

Angle 3 will be z

180 - (x + y) = z

Answer:

3.6 V and 34 mA

Step-by-step explanation:

The equation of the straight line, in point-slope form, is  

          \(y +3 = \frac{1}{4} ( x + 4)\)

we have , the required line is perpendicular to the given line.

Also let us take any two coordinates of the given line , like  (-1 , 1 ) and  

( 0 , -3) . So the slope (m₁) of given line = \(\frac{y2 -y1}{x2 - x1 }\)

                                      m₁ = -4

as the required line is perpendicular to the given line so , we know

for two perpendicular lines

                                   m₁  m₂ =  -1

therefore ,                 m₂ = 1/4

Now the required line passes through (-4,-3)

and the equation of straight line in point slope form is given by

                                               \((y_{} - y_{1}) = m (x - x_{1} )\)

here m = 1/4

y₁ = -3

x₁  = -4

therefore the required equation  in point-slope form is

         y + 3 = 1/4 ( x +4 )

learn more about straight line here :

https://brainly.com/question/28951560

#SPJ4