I'm supposed to write the following intervals as sets indescriptive form:

a. (t, infinity), t a fixed real number

b. (0, 1/n), n a fixed natural number

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I think it is:
a. (t, infinity) = {x: t < x < infinity}
b. (0,1/n) = {x: 0 < x < 1/n}

Is this correct?
Also, how do you indicate that t is a fixed realnumber and n a fixed natural number?

Answer:

The slope is -6 and the y intercept is -1

Step-by-step explanation:

Lets put the  equation in slope intercept form (y=mx+b) where m is the slope and b is the y intercept

-6x-y =1

Add y to each side

-6x-y+y = 1+y

-6x = 1+y

Subtract 1 from each side

-6x-1 = y+1-1

-6x-1 =y

y = -6x-1

The slope is -6 and the y intercept is -1

Answer:

y=2/5x+3/5

Step-by-step explanation:

Use the slope formula to get the slope:

m=4/10

m=2/5

The y intercept is 3/5

The equation is y=2/5x+3/5

Answer:

y = (2/5)x + 3/5

Step-by-step explanation:

Points to remember

Equation of the line passing through the poits (x1, y1) and (x2, y2)  and slope m is given by

(y - y1)/(x - x1) = m    where slope m = (y2 - y1)/(x2 - x1)

To find the slope of line

Here (x1, y1) =  (-4, -1) and  (x2, y2) = (6, 3)

Slope = (y2 - y1)/(x2 - x1)

 = (3 - -1)/(6 - -4)

 = 4/10 = 2/5

To find the equation

(y - y1)/(x - x1) = m  

(y - -1)/(x - -4) = 2/5

(y + 1)/(x + 4) = 2/5

5(y + 1) = 2(x + 4)

5y + 5 = 2x + 8

5y = 2x + 3

y = (2/5)x + 3/5

Not sure why, but I wasn't able to post my solution as text, so I've written it elsewhere and am posting screenshots of it here.

In the fifth attachment, the first solution is shown above the second one.

Answer: Option (4) is correct.

Step-by-step explanation:

Given that,

B = {John, Paul, George, Ringo, Pete, Stuart}

Now, we have select the Set that is equal to the Set B.

From all the options given in the question, option (4) is correct.

It contains all the elements of Set B but only the arrangement or sequence of the Set is different.

Correct Set 4 = {Paul, Ringo, Pete, John, George, Stuart} = Set B

The set matching B = {John, Paul, George, Ringo, Pete, Stuart} from the options provided is {Paul, Ringo, Pete, John, George, Stuart}, as it contains all the same members regardless of order and no other elements.

The question asks to select all answers that are equal to the set B = {John, Paul, George, Ringo, Pete, Stuart}. A set, in this context, is defined as a collection of distinct objects, considered as an object in its own right. In a set, the order of elements does not matter, but duplication of elements is not allowed. From the provided options, the only answer that matches set B exactly is {Paul, Ringo, Pete, John, George, Stuart}, since it contains all the same elements as set B, regardless of order, and does not include any additional elements.

Answer:

$15400

Step-by-step explanation:

Principle amount, P = $14000

Time, T = 1 year

Rate of interest, R = 10%

We know that maturity amount,

[tex]A = P\left (1+\frac{R}{100} \right )^{n}[/tex]

where n is number of years

[tex]A = P\left (1+\frac{R}{100} \right )^{n}[/tex]

[tex]A = 14000\left (1+\frac{10}{100}\right )^{1}[/tex]

[tex]A = 14000\left (1+\frac{1}{10}\right )[/tex]

[tex]A = 14000\left (\frac{11}{10}\right )[/tex]

[tex]A = 15400[/tex]

The maturity amount is $15400

Kayla should take out a loan of $12,727.27 to have $14,000 after accounting for a 10% discount rate over one year.

Kayla needs to determine the amount she must borrow so that after accounting for the interest rate of 10%, she will have proceeds of $14,000 to invest in new equipment for her shop. The equation to calculate this is the present value (amount borrowed) equals the future value (amount after interest) divided by one plus the interest rate to the power of the period, which in this case is one year.

Using this formula:

Amount Borrowed = $14,000 / (1 + 0.10)1

Amount Borrowed = $14,000 / 1.10

Amount Borrowed = $12,727.27

Therefore, Kayla should ask for a loan of $12,727.27 to receive $14,000 after one year.

Answer:

The correct answer is last option

Step-by-step explanation:

From the figure we can see two right angled triangle.

Points to remember

If two right angled triangles are congruent then their hypotenuse and one leg are congruent

To find the correct options

From the figure we get all the angles of 2 triangles are congruent.

one angle is right angle. But there is no information about the hypotenuse and legs.

So the correct answer is last option

There is not enough information to determine congruency.

Answer:

$500 000

Step-by-step explanation:

 Let r = revenue

and c = costs

and n = number of units. Then

r = 50n and

c = 40n + 100 000

At the break-even point,

r = c

50n = 40n + 100 000

10n = 100 000

    n = 10 000

The break-even point is reached at 10 000 units. At that point,

r = 50n =50 × 10 000 = 500 000

A sales revenue of $500 000 is needed to break even.

Belle Corp. needs to achieve a sales revenue of $500,000 to cover both its variable and fixed costs and thus reach the break-even point.

To calculate the breakeven point of Belle Corp., we need to understand that breakeven is the point where total costs (fixed and variable) equal total sales revenue. The formula for calculating the breakeven point in units is Total Fixed Costs / Contribution Margin per Unit. The contribution margin per unit is the Selling Price per Unit minus the Variable Cost per Unit.

For Belle Corp.,

To calculate sales revenue necessary to breakeven, we multiply the breakeven point in units by the selling price per unit. Therefore, Sales revenue needed to break-even = Breakeven units * Selling Price per unit = 10,000 units × $50 = $500,000.

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Answer: [tex]R^{2}[/tex] = 0.89

Step-by-step explanation:

Coefficient of determination is represented by [tex]R^{2}[/tex]. This tells us that how much of the variation in the dependent variable is explained by the independent variable.

It is the ratio of explained variation by the independent variables to the total variation in the dependent variable.

Hence,

Coefficient of determination = [tex]\frac{Explained\ Variation}{Total\ Variation}[/tex]

= [tex]\frac{18.592}{20.711}[/tex]

[tex]R^{2}[/tex]= 0.89

∴ 89% of the variation in the dependent variable is explained by the independent variables.

The coefficient of determination is calculated by dividing the explained variation by the total variation. For the student's data, the coefficient of determination is approximately 0.8978, which translates to about 89.78% of the variation in the dependent variable being explained by the regression line.

The student is asking about the coefficient of determination, which is a statistical measure in a regression analysis. To find the coefficient of determination, we use the explained variation and the total variation from the regression equation. It is calculated by dividing the explained variation by the total variation and then squaring the result if needed to find r squared.

In this case, the explained variation is 18.592 and the total variation is 20.711. The formula to find the coefficient of determination (r²) is:

r² = Explained Variation / Total Variation

Plugging in the values we have:

r² = 18.592 / 20.711

r² ≈ 0.8978

Expressed as a percentage, the coefficient of determination is approximately 89.78%, which means that about 89.78% of the variation in the dependent variable can be explained by the independent variable using the regression line.

The numbers on a six sided die are: 1, 2, 3, 4 ,5 ,6

There are 4 numbers that are either equal to 3 or greater than 3: 3, 4, 5 ,6

The probability of getting one is 4 chances out of 6 numbers, which is written as 4/6.

4/6 can be reduced to 2/3 ( simplified fraction)

Final answer:

The probability of rolling a number greater than or equal to 3 on a six-sided die is 2/3 or 0.6667 when rounded to four decimal places.

Explanation:

To find the probability of rolling a number greater than or equal to 3 on a standard six-sided die, we count the favorable outcomes and then divide this number by the total number of possible outcomes. The sample space, S, of a six-sided die is {1, 2, 3, 4, 5, 6}.

Numbers greater than or equal to 3 are 3, 4, 5, and 6. So, there are 4 favorable outcomes. The total number of possible outcomes is 6 (since there are 6 sides on the die).

The probability is thus the number of favorable outcomes (4) divided by the total number of possible outcomes (6), which simplifies to 2/3 or approximately 0.6667 when rounded to four decimal places.

Answer:

Step-by-step explanation:

Given that [tex]r = 0.952[/tex]

We have coefficient of determination

[tex]r^2 =0.952^2\\=0.906304[/tex]

=90.63%

This implies that nearly 91% of variation in change in dependent variable is due to the change in x.

The coefficient of determination is the square of the correlation (r) between predicted y scores and actual y scores; thus, it ranges from 0 to 1.

An R2 of 0 means that the dependent variable cannot be predicted from the independent variable.

An R2 of 1 means the dependent variable can be predicted without error from the independent variable.

Answer:

Area of the rectangle is increasing with the rate of 84 cm/s.

Step-by-step explanation:

Let l represents the length, w represents width, t represents time ( in seconds ) and A represents the area of the triangle,

Given,

[tex]\frac{dl}{dt}=6\text{ cm per second}[/tex]

[tex]\frac{dw}{dt}=5\text{ cm per second}[/tex]

Also, l = 12 cm and w = 4 cm,

We know that,

A = l × w,

Differentiating with respect to t,

[tex]\frac{dA}{dt}=\frac{d}{dt}(l\times w)[/tex]

[tex]=l\times \frac{dw}{dt}+w\times \frac{dl}{dt}[/tex]

By substituting the values,

[tex]\frac{dA}{dt}=12\times 5+4\times 6[/tex]

[tex]=60+24[/tex]

[tex]=84[/tex]

Hence, the area of the rectangle is increasing with the rate of 84 cm/s.

Answer:

  a) 297°

  b) 4.52 minutes

Step-by-step explanation:

a) Consider the attached figure. The boat's actual path will be the sum of its heading vector BA and that of the current, vector AC. The angle of BA north of west has a sine equal to 5/11. That is, the heading direction measured clockwise from north is ...

  270° + arcsin(5/11) = 297°

__

b) The "speed made good" is the boat's speed multiplied by the cosine of the angle between the boat's heading and the boat's actual path. That same value can be computed as the remaining leg of the right triangle with hypotenuse 11 and leg 5.

  boat speed = √(11² -5²) = √96 ≈ 9.7980 . . . . miles per hour

Then the travel time will be ...

  time = distance/speed

  (3900 ft)×(1 mi)/(5280 ft)×(60 min)/(1 h)/(9.7980 mi/h) ≈ 4.523 min

Answer:

y=4 sin(4x)

Step-by-step explanation:

So you are given y(0)=0.  This means when x=0, y=0.

So plug this in:

0=c1 cos(4*0)+c2 sin(4*0)

0=c1 cos(0)   +c2 sin(0)

0=c1 (1)          +c2 (0)

0=c1               +0

0=c1

So our solution looks like this after applying the first boundary condition:

y=c2 sin(4x).

Now we also have y(pi/8)=4.  This means when x=pi/8, y=4.

So plug this in:

4=c2 sin(4*pi/8)

4=c2 sin(pi/2)

4=c2 (1)

4=c2

So the solution with the given conditions applies is y=4 sin(4x) .

Testing:

y'=16 cos(4x)

y''=-64 sin(4x).

y''+16y=0

-64 sin(4x)+16(4 sin(4x))

-64 sin(4x)+64 sin(4x)

0

So the solution still works.

The solution of the differential equation y'' + 16 y = 0 is,

y = 4 sin4x

Here,

The second-order differential equation is,  y'' + 16y = 0.

And, y = c₁ cos 4x + c₂ sin 4x  is a two-parameter family of solutions of the second-order DE y'' + 16y = 0.

We have to find the solution of the differential equation that satisfies the given side conditions,   y(0) = 0, y(π/8) = 4.

What is Differential equation?

A differential equation is a mathematical equation that relates some function with its derivatives.

Now,

y = c₁ cos 4x + c₂ sin 4x is a two-parameter family of solutions of the second-order DE y'' + 16y = 0.

Apply given conditions y(0) = 0,   y(π/8) = 4 on y = c₁ cos 4x + c₂ sin 4x.

We have given y(0) = 0,

This means x = 0, y = 0

So put this in  y = c₁ cos 4x + c₂ sin 4x.

We get,

0 = c₁ cos 4*0 + c₂ sin 4*0

0 = c₁

c₁ = 0

Hence equation become,

y = c₂ sin4x

And, y(π/8) = 4 , this means that x = π/8 , y = 4

So put in equation y = c₂ sin4x we get,

4 = c₂ sinπ/2

c₂ = 4

Hence, the solution become after putting the value of c₁ = 0 and c₂ = 4,

y = c₁ cos 4x + c₂ sin 4x

y= 4 sin4x

So, The solution of the differential equation y'' + 16 y = 0 is,

y = 4 sin4x

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Answer:

1/16

Step-by-step explanation:

Lets say you are trying to get the cherry when you are spinning. That means that in each slot there is a 1/4 chance of getting the cherry because out of 4 choices only one is the cherry. That is only for one slot and there are 3 slots. That means you take the probability for each slot which is 1/4 and multiply them together. Then you get 1/4*1/4*1/4 since there are 3 slots which is 1/64. However that is only for the cherry and there are 4 different items that you could get. This means there is 1/64 chance for each of the 4 items which is 1/64+1/64+1/64+1/64 which is 4*1/64 which is 1/16.

The probability of winning the slot game is calculated by multiplying the probabilities of each independent event. In this case, the probability of the same item appearing in all three slots is 1 * 1/4 * 1/4, which results in a winning probability of 1/16 or 0.0625.

The subject of this question is the probability of winning in the context of a slot machine game. In this scenario, the slot machine has four different items (cherry, lemon, star, bar) and each item is equally likely to appear on a spin. The player wins if all three slots display the same item.

Firstly, for the first slot, any one of the four items could appear, so the odds are simply 1 (it is certain an item will appear). For the first item to then appear in the second and third slots (i.e., for all three slots to show the same item), with each slot being an independent event, the probability is 1/4 for each subsequent slot.

Therefore, the probability of winning is given by the product of probabilities for each independent event, i.e., 1 * 1/4 * 1/4 = 1/16. Hence, the player's probable chance of winning in a single spin is 1 in 16 or 0.0625 in decimal form.

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Answer:

Resistance

Conductance

Step-by-step explanation:

In any graph the slope represents the ratio of y axis to x axis.

So, in the first case the voltage (V) is on the y axis and current (I) on the x axis. Here the slope is V/I = R. Therefore, slope represents resistance.

In the second case current (I) is on the y axis and voltage (V) is on the x axis. Here the slope formed will be I/V = 1/R = G. Therefore, slope represents conductance.

Final answer:

In physics, particularly when discussing Ohm's Law, the slope of a V versus I plot represents the resistance of the resistor, and conversely, the slope of an I versus V plot signifies the conductance. These relationships illustrate the fundamental interplay between current, voltage, and resistance in electrical circuits.

Explanation:

If a resistor follows Ohm’s Law, when plotting V (voltage) as a function of I (current), with V on the y-axis, the slope of the graph represents the resistance (R) of the resistor. This is directly derived from Ohm's Law, V = IR, which shows that voltage (V) is equal to the current (I) multiplied by the resistance (R). The slope in this context is R, because the graph shows how much voltage is needed to achieve a certain current flow, exhibiting a linear relationship. This slope is a constant value for ohmic devices, showcasing that the resistance does not change with varying voltage or current in these cases.

Conversely, when plotting I as a function of V, with I on the y-axis, the slope represents the conductance (the reciprocal of resistance). From the equation I = V/R, we could also interpret that the slope in a graph of I versus V would represent 1/R, indicating how current changes in response to changes in voltage. This also demonstrates a linear relationship for ohmic devices, where the conductance remains constant.

In essence, these plots offer a visual representation of Ohm's Law in action, and the slope on these graphs provides valuable information about the resistor’s resistance or conductance, highlighting the fundamental relationship between voltage, current, and resistance in an electrical circuit.

Answer:

B) x = 3

Step-by-step explanation:

The given triangle has three angles:

∠R, ∠S and ∠T

The exterior angle theorem says that

∠S+∠T = ∠R

Putting the values of angles

(57+x) + 25x = 45x

57 + x + 25x = 45x

57+26x = 45x

57 = 45x - 26x

57 = 19x

x = 57/19

x = 3

Hence, the correct answer is:

B) x = 3 ..

Answer:

B

Step-by-step explanation:

X = 3

Answer:  The lines L1 and L2 are parallel.

Step-by-step explanation:  We are given to determine whether the following lines L1 and L2 passing through the pair of points are parallel, perpendicular or neither :

L1 : (–5, –5), (4, 6),

L2 : (–9, 8), (–18, –3).

We know that a pair of lines are

(i) PARALLEL if the slopes of both the lines are equal.

(II) PERPENDICULAR if the product of the slopes of the lines is -1.

The SLOPE of a straight line passing through the points (a, b) and (c, d) is given by

[tex]m=\dfrac{d-b}{c-a}.[/tex]

So, the slope of line L1 is

[tex]m_1=\dfrac{6-(-5)}{4-(-5)}=\dfrac{6+5}{4+5}=\dfrac{11}{9}[/tex]

and

the slope of line L2 is

[tex]m_2=\dfrac{-3-8}{-18-(-9)}=\dfrac{-11}{-9}=\dfrac{11}{9}.[/tex]

Therefore, we get

[tex]m_1=m_2\\\\\Rightarrow \textup{Slope of line L1}=\textup{Slope of line L2}.[/tex]

Hence, the lines L1 and L2 are parallel.

Answer:

Parallel

Step-by-step explanation:

Answer:

99.85%

Step-by-step explanation:

Most of today's student calculators have probability distribution functions built in.  Here we are to find the area under the standard normal curve between 58 mph and 76 mph, if the mean speed is 67 mph and the std. dev. is 3 mph.

Here's what I'd type into my calculator:

normalcdf(58, 76, 67, 3)

The result obtained in this manner was 0.9985.  

This states that 99.85% of the vehicles clocked were traveling at speeds between 58 mph and 76 mph.

Answer: 99.9%

Step-by-step explanation:In a normal distribution (bell-shaped distribution), the percent that is between the mean and the standard deviations are:

between the mean and mean + standard deviation the percentage is = 34.1%

between the mean + standard deviation and mean + 2 times the standard deviation is = 13.6%

between the mean + 2 times the standard deviation and the mean + 3 times the standard deviation is: 2.14%

And is the same if we subtract the standard deviation.

So in the range from 58 to 67, we can find 3 standard deviations, and in the range from 67 to 76, we also can find 3 standard deviations:

58 + 3 + 3 + 3 = 67

67 + 3 + 3 + 3 = 76

So the total probability is equal to the addition of all those ranges:

2.14% + 13.6% + 34.1% + 34.1% + 13.6% + 2.14% = 99.9%

So 99.9% of the cars have velocities in the range between 58 miles per hour and 76 miles per hour

The probability that Little Joe, who has no brothers, is an only child is calculated using conditional probability and results in a 1/4 chance.

The question asks us to find the probability that Little Joe, who has no brothers, is an only child. The sample space for the number of children in a family can be defined as {1, 2, 3, 4}, since each of these outcomes has an equal probability of 1/4. We will define event A as Little Joe being an only child, and event B as the family having no additional male children. Since Little Joe is a boy and has no brothers, cases with more than one male child should not be a part of our conditional sample space.

To solve this, we are looking at the conditional probability P(A|B). The probability that Little Joe is an only child given he has no brothers is P(A|B) = P(A and B) / P(B). We can determine that P(A and B) is simply the probability that there is one child and that child is a boy (Little Joe), which is 1/4. Event B can happen in three scenarios: Little Joe is an only child, Little Joe has one sister, or Little Joe has two or three sisters, and each scenario has an equal probability. Therefore, P(B) = 1/4 (only child) + 1/4 (one sister) + 1/4 (two sisters) + 1/4 (three sisters), which adds to 1/4 * 4 = 1.

The answer therefore is P(A|B) = (1/4) / 1 = 1/4. There is a 1/4 chance that Little Joe, who has no brothers, is an only child.

Answer: 0.9762

Step-by-step explanation:

Let A be the event that days are cloudy and B be the event that days are rainy for January month .

Given : The probability that the days are cloudy = [tex]P(A)=0.42[/tex]

The probability that the days are cloudy and rainy = [tex]P(A\cap B)=0.41[/tex]

Now, the conditional probability that a randomly selected day in January will be rainy if it is cloudy is given by :-

[tex]P(B|A)=\dfrac{P(B\cap A)}{P(A)}\\\\\Rightarrow\ P(B|A)=\dfrac{0.41}{0.42}=0.97619047619\approx0.9762[/tex]

Hence, the probability that a randomly selected day in January will be rainy if it is cloudy  = 0.9762

the probability that a randomly selected day in January will be rainy if it is cloudy is approximately 97.62%.

The question asks us to find the probability that a day will be rainy given that it is cloudy. From the information provided, we know that in this city, 42% of the days in January are cloudy, and 41% are both cloudy and rainy. To find the probability that it is rainy given that it is cloudy, we use the concept of conditional probability.

The formula for conditional probability is P(A|B) = P(A u2229 B) / P(B), where P(A|B) is the probability of A given B, P(A \\u2229 B) is the probability of both A and B occurring, and P(B) is the probability of B occurring.

Let A be the event that it is rainy and B be the event that it is cloudy. Therefore, P(A|B) = P(A u2229 B) / P(B) = 0.41 / 0.42 = 0.9762 or 97.62%.

Hence, the probability that a randomly selected day in January will be rainy if it is cloudy is approximately 97.62%.

Answer: 0.0192

Step-by-step explanation:

Given : The mean per capita consumption of milk per year : [tex]\mu=140\text{ liters}[/tex]

Standard deviation : [tex]\sigma=22\text{ liters}[/tex]

Sample size : [tex]n=233[/tex]

Let [tex]\overline{x}[/tex] be the sample mean.

The formula for z-score in a normal distribution :

[tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For  [tex]\overline{x}=137.01[/tex]

[tex]z=\dfrac{137.01-140}{\dfrac{22}{\sqrt{233}}}\approx-2.07[/tex]

The P-value = [tex]P(\overline{x}<137.01)=P(z<-2.07)= 0.0192262\approx 0.0192[/tex]

Hence, the probability that the sample mean would be less than 137.01 liters is 0.0192 .

Answer:  The probability that both televisions work : 0.5329

The  probability at least one of the two televisions does not​ work : 0.4671

Step-by-step explanation:

Given : The total number of television : 11

The number of defective television : 3

The probability that the television is defective : [tex]p=\dfrac{3}{11}\approx0.27[/tex]

Binomial distribution formula :-

[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where P(X) is the probability of getting success in x trials, p is the probability of success and n is the total trials.

If two televisions are randomly​ selected, then the probability that both televisions work:

[tex]P(0)=^2C_0(0.27)^0(1-0.27)^{2-0}=(1)(0.73)^2=0.5329[/tex]

The probability at least one of the two televisions does not​ work :

[tex]P(X\geq1)=1-P(0)=1-0.5329=0.4671[/tex]

Answer:

A∩(A∪B)=A

Step-by-step explanation:

Let's find the answer as follows:

Let's consider that 'A' includes all numbers between X1 and X2 (X1≤A≥X2), and let's consider that 'B' includes all numbers between Y1 and Y2 (Y1≤B≥Y2). Now:

A∪B includes all numbers between X1 and X2, as well as the numbers between Y1 and Y2, so:

A∪B= (X1≤A≥X2)∪(Y1≤B≥Y2)

Now, A∩C involves only the numbers that are included in both, A and C. This means that 'x' belongs to A∩C only if 'x' is included in 'A' and also in 'C'.

With this in mind, A∩(A∪B) includes all numbers that belong to 'A' and 'A∪B', which in other words means, all numbers that belong to (X1≤A≥X2) and also (X1≤A≥X2)∪(Y1≤B≥Y2), which are:

A∩(A∪B)=(X1≤A≥X2) which gives:

A∩(A∪B)=A

Answer:

D.  (3, -1).

Step-by-step explanation:

The vertex for ( x - a)^2 + b  is (a, b).

Comparing (x - 3)^2 - 1 with this we get:

a = 3 and b = -1.

Answer: Last Option

(3, -1)

Step-by-step explanation:

We have the following quadratic function:

[tex]f(x) =(x-3)^2 - 1[/tex]

By definition for a quadratic function in the form:

[tex]f (x) = a (x-h) ^ 2 + k[/tex]

the vertex of the function is always the point (h, k)

Note that for this case the values of h, a, and k are:

[tex]a = 1\\h = 3\\k = -1[/tex]

Therefore the vertex of the function [tex]f(x) =(x-3)^2 - 1[/tex] is the point

(3, -1)

Answer:

Accumulated amount will be $2504.90.

Step-by-step explanation:

Formula that represents the accumulated amount after t years is

A = [tex]A_{0}(1+\frac{r}{n})^{nt}[/tex]

Where A = Accumulated amount

[tex]A_{0}[/tex] = Initial amount

r = rate of interest

n = number of times initial amount compounded in a year

t = duration of investment in years

Now the values given in this question are

[tex]A_{0}[/tex] = $1000

n = 12

r = 4.6% = 0.046

t = 20 years

By putting values in the formula

A = [tex]1000(1+\frac{0.046}{12})^{240}[/tex]

  = [tex]1000(1+0.003833)^{240}[/tex]

  = [tex]1000(1.003833)^{240}[/tex]

  = 1000×2.50488

  = 2504.88 ≈ $2504.90

Therefore, accumulated amount will be $2504.90.

Answer: 50% is the probability

Step-by-step explanation:

There are to people showing up at to different times now the probability is out of a 100%.

So 100 divided by 2 will equal to a 50

Answer:

The Range Rule of Thumb says that the range is about four times the standard deviation. So, if you need to calculate it, you need to divide range (Maximum - Minimum) with 4, S=[tex]\frac{R}{4}[/tex].

Step-by-step explanation:

R=1490 - 904

S = 586 / 4 = 149.5

If you compare the exact standard desviation (149.5 cm) with the estimated (146.5 cm), it is a difference of 3 cm, is not neccesary round the result.

Hope my answer has been useful.

Answer:

x_bar = 1197 cm^3 , s.d_e = 146.5 cm^3

Outside the 15 cm^3 tolerance. Not a good estimation.

Step-by-step explanation:

Given:

- Lowest value of brain volume L = 904 cm^3

- Highest value of brain volume H = 1490 cm^3

- Exact standard deviation s.d_a = 174.7 cm^3

Find:

Use the range rule of thumb to estimate the standard deviation s and compare the result to the exact standard deviation of 174.7 cm^3 assuming the estimate is accurate if it is within 15 cm^3.

Solution:

- The rule of thumb states that the max and min limits are +/- 2 standard deviations about the mean x_bar. Hence, we will set up two equations.

                           L = x_bar - 2*s.d_e

                           H = x_bar + 2*s.d_e

Where, s.d_e is the estimated standard deviation.

- Solve the two equations simultaneously and you get the following:

                          x_bar = 1197 cm^3 , s.d_e = 146.5 cm^3

- The exact standard deviation is s.d_a = 174.7 cm^3

So, the estimates differs by:

                           s.d_a - s.d_e = 174.7 - 146.5 = 28.2 cm^3

Hence, its outside the tolerance of 15 cm^3. Not a good approximation.

Answer:

[tex]H_0:\mu =873\\\\H_a: \mu<873[/tex]

Step-by-step explanation:

Given : In a study investigating a link between walking and improved​ health, researchers reported that adults walked an average of 873 minutes in the past month for the purpose of health or recreation.

Claim : The true average number of minutes in the past month that adults walked for the purpose of health or recreation is lower than 873 minutes.

i.e. [tex]\mu<873[/tex]

We know that the null hypothesis contains equal sign , then the set of hypothesis for the given situation will be :-

[tex]H_0:\mu =873\\\\H_a: \mu<873[/tex]

The null hypothesis assumes no difference, so it reflects an average walking time of 873 minutes (H0: μ = 873). The alternative hypothesis reflects the research query, suggesting the true average is less than 873 minutes (Ha: μ < 873).

In statistics, the null hypothesis and the alternative hypothesis are often used to test claims or assumptions about a population. In this case, the research is about whether the true average number of minutes in the past month that adults walked for the purpose of health or recreation is lower than 873 minutes.

The null hypothesis (H0) is often a statement of 'no effect' or 'no difference'. Here, it would be: H0: μ = 873. This means that the population mean (μ) of walking time is equal to 873 minutes.

The alternative hypothesis (Ha) is what you might believe to be true or hope to prove true. In this study, it would be: Ha: μ < 873. This means that the population mean of walking time is less than 873 minutes.

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Answer: Dividend paid = $750,000

Explanation:

In order to compute the dividends paid by the firm in 2014 , we'll use the following formula :

Retained earning at end = Retained earning at beginning +Net income -Dividend paid

$5,200,000 = $4,900,000 +  $1,050,000 - Dividend paid

Dividend paid = $4,900,000 +  $1,050,000 - $5,200,000

Dividend paid = $750,000