1. How long does pia's journey take?
2. How much longer does Sam spend driving then Pia?

The present value of the trust which grows at the rate of interest 8% for 25 years is equal to $ 36504.477

The future value of the trust is equal to  $250,000

Interest rate is equal to 8% per year

To calculate present value of the trust use the formula,

Present Value = Future Value / (1 + r)^n

r is the annual interest rate

n is the number of years.

Let us consider PV represents the present value of the trust.

Present age = 25 years

Maturity age of the trust = 50 years

Number of years used amount to mature is equal to,

= 50 - 25

= 25 years

Substitute the values into the present value formula we have,

PV = 250,000 / (1 + 0.08)^25

Simplify it we get,

⇒ PV = 250,000 / 6.848475

⇒ PV = 36504.477

Therefore, the present value of the trust mature for 25 years is equal to approximately $36504.477.

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Arabella drive 17. 8 miles a day, Yaya drives 1. 6 times as far for each day. Therefore, 598.08 miles Yaya drive in three weeks.

Miles:

The mile, sometimes the international mile or the regulation mile, to distinguish it from other miles, is an imperial unit of the United Kingdom and a customary unit of distance in the United States; both are based on the old imperial unit of length, 5,280 imperial feet or 1,760 meters. The statute mile was standardized by an international agreement between the Commonwealth of Nations and the United States in 1959, when it was officially redefined as 1,609,344 meters in terms of SI units.

According to the Question:

We know that:

In a week there are 07 days

Therefore,

In 03 weeks there are = 7×3

                                     = 21 days

Given that :

Arabella drive 17.8 miles daily

and Yaya drives 1.6 times far from 17.8 miles daily.

Therefore,

Yaya drives = 17.8 × 1.6 miles

                    = 28.48 miles

Now,

for three weeks = 28.48 × 21

                           = 598.08 miles.

Therefore, 598.08 miles Yaya drive in three weeks.

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Answer:

x=2.4

y=2.5

z=3.3

Step-by-step explanation:

6/5=1.2

1.2 = scale factor

x=2x1.2=2.4

y=3/1.2=2.5

z=4/1.2=3.3

Answer:

Step-by-step explanation:

To make this Cuboid you need to workout how many cubes are missing from this cuboid.

To get the cubes numbers you have to get the volume of this cuboid which is 3x4x3=36

So there is 36 cubes in this cuboid.

And then workout how many cubes are missing from this plan, front and side elevation.

Front Elevation 3x3=9

Side Elevation 4x3=12 then deduct 3 blocks from the left. Then deduct 4 blocks from right top corner which is 4 blocks.

3+4=7 missing blocks, then do this 12-7=5 Side has 5 added blocks fron the front.

Front 9 blocks Side 5 blocks. 9+5=14

So 36-14=22 ANSWER is 22 BLOCKS has been added.

By using the formula for the confidence interval and the standard error, we were able to calculate the lower limit of the interval as 7.59.

To construct a 95% CI for the population mean of a normal distribution, we can use the formula:

CI = sample mean ± z* (standard error)

Where z* is the critical value from the standard normal distribution that corresponds to a 95% confidence level (i.e., 1.96), and the standard error is calculated as:

standard error = population standard deviation / √sample size

In this case, we are given that the population variance is 30, so the population standard deviation is √30 = 5.48 (rounded to two decimal places). The sample size is 20, so the standard error is:

standard error = 5.48 / √20 = 1.226

Now, we can use the formula for the CI:

CI = 10 ± 1.96 x 1.22

Simplifying this expression gives us:

CI = (7.59, 12.41)

This means that we are 95% confident that the true population mean lies within the interval from 7.59 to 12.41. The lower limit of the CI is 7.59, rounded to one decimal place.

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The answer of the given question based on the number line is the difference between 8 and -16 is not 14, it is 24. and 8 and -16 are 24 units apart on the number line.

A number line is a visual representation of the real number system, where numbers are placed in order from left to right, with zero in the center. The number line is an important mathematical tool used in a variety of ways, including:

Understanding and comparing numbers: By plotting numbers on a number line, we can visually see the relative size and position of numbers in relation to each other.

Performing arithmetic operations: The number line can be used to add, subtract, multiply, and divide numbers.

Graphing functions: The number line can be used as the horizontal axis of a graph to plot functions and other mathematical relationships.

Actually, the difference between 8 and -16 is not 14, it is 24.

To find the difference between two numbers on a number line, you need to subtract the smaller number from the larger number. In this case, 8 is larger than -16, so we subtract -16 from 8:

8 - (-16) = 8 + 16 = 24

Therefore, 8 and -16 are 24 units apart on the number line.

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Evaluating the (2.7)³ - (1.6)³ - (1.1)³ using the suitable identity is given by the term 26.19.

The sum of cubes (of two integers) formula is what is known as the a3 + b3 formula. Without computing the two cubes, the total may be calculated using the a cube + b cube formula. The binomials of cubes are factorised using it as well.

Let a = 2.7, b = 1.6, c = 1.1

We see that,

a + b + c = 2.7 + 1.6 + 1.1 = 5.4

Now as we know that,

If a+b+c =  5.4

then using the identity:

a³ - b³ - c³ = ( a+ b+ c ) (a² + b² + c² - ab - bc - ca) + 3 abc

so,

a³ - b³ - c³ = 5.4(2.7² + 1.6² + 1.1² - 4.32 - 1.76 - 2.97) + 14.256

= 5.4(7.29 + 2.56 + 1.41 - 4.32 - 1.76 - 2.97) + 14.256

a³ - b³ - c³ = 26.19

Therefore,  (2.7)³ - (1.6)³ - (1.1)³ is  26.19

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Answer:

z=8

Step-by-step explanation:

Considering the triangle on the RHS,

Let the Unknown side be "x"

from pythagora's theorem,

x ^ 2 = 4 ^ 2 - 2 ^ 2 x = √(4 ^ 2 - 2 ^ 2)

x = √(16 - 4)

x = √12

cos alpha = 2/4 , alpha = arccos(2/4)

alpha = 60°

< ABC + theta + alpha = 180°

theta = 180 - alpha - <ABC

theta = 180 - 60 - 90

theta = 30°

Now Considering the triangle on the LHS,

tan 30 = (√12)/y

y = (√12)/(tan 30°)

y = 6

z = y + 2

z = 8

Therefore , the solution of the given problem of surface area comes out to be  240 tiles will cover the floor.

Calculating how much space would be needed to fully cover the outside will reveal its overall size. The surroundings are considered when determining the same surface with a rectangular form. The surface area of something determines its overall dimensions. The amount of edges present in the space between a cuboid's four trapezoidal corners determines how much water it can hold inside.

Here,

Let's first determine how many 6 inch squares are required to span the floor:

=> 80 square feet is the size of the floor (8 feet by 10 feet).

We require the following because each 6-inch square spans an area of => (1/2) ft x (1/2) ft = 1/4 square feet:

=>  80 square feet 1/4 square foot = 320 tiles in a row of 6 inch tiles.

Since a 12 inch square encompasses a space that is 1 foot by 1 foot, we require:

=>  80 square feet /  12 inch square tile,

which equals 80 tiles.

Using 12 inch squares rather than 6 inch squares allows us to save the following amount of tiles:

=> Number of 6 inch tiles - Number of 12 inch tiles = 320 - 80 = 240 tiles

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The probability density function (PDF) of a chi-squared distribution is used to describe the probability of a certain outcome occurring when a continuous random variable is sampled. The PDF is a mathematical formula that gives the probability of a given value of the random variable, x, occurring. It is typically expressed as f(x).

The chi-squared distribution is a type of continuous probability distribution that is used to describe the sum of the squares of multiple normally distributed random variables. Its PDF is represented as:

f(x) = 1/2k/2π-1/2 * xk/2-1 * e-x/2

Where x is the value of the chi-squared random variable and k is the number of degrees of freedom.

The PDF of the chi-squared distribution is used to calculate the probability of a particular outcome. It is used in hypothesis testing to determine the probability that a given set of data fits a certain distribution. It is also used to estimate the confidence intervals of parameters in various models.

The chi-squared distribution is widely used in statistical applications, such as testing for goodness of fit, tests for independence, tests for homogeneity, and tests for normality. It is also used in the analysis of variance, analysis of covariance, regression analysis, and other advanced statistical techniques.

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Answer:

[tex]X\leq 3[/tex]

Step-by-step explanation:

[tex]X +16\leq 19[/tex]

[tex]X\leq 3[/tex]

Using a simple linear regression analysis, the predicted deposit level for the next quarter is $2998.725 million with a predicted interval of $2997.3531 million to $2999.0969 million within one standard error.

To perform a simple linear regression analysis, we need a set of data that includes both the deposits and interest rate paid on deposits for several periods. Let's assume we have already conducted this analysis and obtained the regression equation:

Deposits = 553.2 + 624.3 * Interest rate

This equation tells us that for each 1% increase in the interest rate paid on deposits, we can expect deposits to increase by $624.3 million.

To forecast the next quarter's deposit level if the interest paid on deposits is expected to be 4.75%, we can substitute 4.75 for the interest rate in the regression equation:

Deposits = 553.2 + 624.3 * 4.75

Deposits = 2998.725 million

So, the predicted deposit level for the next quarter is $2998.725 million.

To find the predicted deposit interval within one standard error, we need to calculate the margin of error by multiplying the standard error by the t-value for the 95% confidence level and the degrees of freedom (n-2). For a 95% confidence level with 12 degrees of freedom, the t-value is 2.201. Therefore, the margin of error is:

Margin of error = 2.201 * 0.503701 million * sqrt(1 + 1/12) = 1.3719 million

To find the predicted deposit interval, we add and subtract the margin of error to the predicted deposit level:

Predicted deposit interval = $2998.725 million ± $1.3719 million

So the predicted deposit interval within one standard error is $2997.3531 million to $2999.0969 million.

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P (-1, -2/5) is the point of segment of line .

What is the name of a line segment?

When both end points of a line segment are vertices of a polygon or polyhedron, the line segment is either a diagonal or an edge (of that polygon or polyhedron) if the vertices are close to one another.

                                A line segment is known as a chord when both of its end points are on a curve (such as a circle) (of that curve).

A = (-3,2)

B = (7,-10)

 1: 4

P (x,y) partition A (x₁ , y₁) B (x₂ , y₂) into ratio

 = (4 * -3 + 1 * 7) / (1 + 4)

 = -5/5

 = -1

y = (by₁ + ay₂) / (a+b)

 = (4 * 2 + 1 * -10) / (1 + 4)

 = -2/5

P (-1, -2/5)

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Solving a linear equation we can see that the answer is 40 months.

We know that company A only charges $70 per month, so the cost in dollars after x months is given by the linear equation:

A(x) = 70*x

For company B you need to pay $50 per month plus the $500 phone, so here the cost is:

B(x) =500 + 50*x

We want to find for what value of x we have B(x) = A(x), then we needto solve:

70x = 500 + 50x

70x - 50x = 500

20x = 500

x = 500/20

x = 40

After 40 months the cost will be the same one than in company A.

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Answer:

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

angles 4, 5, and 6 add up to 180

angle 5 is opposite of angle 3 which means they have the same measure, so angle 5 = 90

that means angles 4 and 6 add up to 90 so they are complimentary

Answer:

there

Step-by-step explanation:

Hence, the correct match of probabilities with their corresponding situations is given by option 4.

To match the probabilities with their corresponding situations, we can utilize the formulas given below:

[tex]P(A ∩ B) = P(A) x P(B|A)P[/tex](2 aces) =[tex](4/52) x (3/51) = 1/221[/tex]

P(heart and club) =[tex](13/52) x (13/51) = 169/2652[/tex]P(spade and ace of hearts) = 0P(2 of the same card) = (1/52) + (3/51) + (2/50) + (1/49) + (4/48) + (3/47) + (2/46) + (1/45) = 20/663P(red card and four of spades) = (16/52) x (1/51) = 4/663

Therefore, the probabilities with their corresponding situations are:3: P(spade and ace of hearts) = 0 (Not possible as Ace of hearts is not spade)

4: P(2 aces) = 1/2211: P(heart and club) = 169/26521: P(heart and club) = 169/26522: P(red card and four of spades) = 4/663

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Just ignore this answer, its incorrect

*edited*

Since the value of a is less than 0, the graph of the parabola would be opening downwards. Because of this we can rule out option C. In a quadratic equation, c represents the y-intercept, and, in this case c is negative, meaning the y-intercept is less than 0. Only option B has a downward-opening curve and a y-intercept less than 0, so it is the answer.

Answer: p= 2+c

Step-by-step explanation:

Answer:

Fraction form:

[tex]\text{h} = \dfrac{4}{1.5} \ \text{in}[/tex]

Decimal form:

[tex]2.667 \ \text{in}[/tex]

Step-by-step explanation:

I've attached the work below

The formula use is usually use to find the area of a triangle but allowed us to work backward after inputting given values

Hope it helps, Let me know if you have any more questions/concerns.

The arithmetic mean return is 3.6%, and the standard deviation is 2.14%.

To find the arithmetic mean, we add up the five returns and divide by the number of returns (in this case, 5):

(3% + 6% + 0% + 6% + 3%) / 5 = 3.6%

To find the standard deviation, we first need to find the variance. We can do this by taking each return, subtracting the mean return (3.6%), squaring the result, summing these values, and dividing by the number of returns minus 1 (4 in this case):

((3% - 3.6%)^2 + (6% - 3.6%)^2 + (0% - 3.6%)^2 + (6% - 3.6%)^2 + (3% - 3.6%)^2) / 4 = 0.046

The standard deviation is the square root of the variance:

√0.046 = 0.214 or 2.14%

Therefore, the arithmetic mean return for security y is 3.6%, and the standard deviation (sample) is 2.14%.


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Answer:

Step-by-step explanation:

144/25=x/5

times both sides by 5

144/5=x

simplify

x=144/5 or 28.8

Answer: x= 144/5

Step-by-step explanation:

Cross-Multiply

144/25 = 25x

Swap the sides so you can solve

720 =25x

Divide both sides

25x=720

x=144/5

Since the sequence is always decreasing and cannot go below the lower bound, it becomes increasingly closer to the lower bound, and thus converges to a limit.

A sequence is said to be decreasing if each term is smaller than the previous one, and bounded below if there exists a lower bound such that no term in the sequence is smaller than this bound. In this case, the sequence is decreasing and bounded below by 0.

When a sequence is both decreasing and bounded below, it must have a limit because the terms cannot continue to decrease indefinitely, as they cannot go below the lower bound (in this case, 0). This means that as we progress through the terms of the sequence, the difference between consecutive terms will decrease and eventually approach a constant value.

The limit of a sequence is a value that the terms of the sequence approach as they get closer and closer to the end. In this situation, the limit is the smallest possible value that the sequence can approach, without going below the lower bound.

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Your longitude in DMS is 135 degree. So the option D is correct.

This is because there are 12 hours left in the local time ( i.e. 12 hours noontime or mid-day).

As UT (or GMT) time is 9 p.m., there are 9 hours between GMT time and local time.

9 hours = 9 × 60 minutes = 540 minutes

Now, we know that:

Every four minutes, the Earth turns one degree.

Thus, 1-degree longitude difference = 4 minutes

Or, 4 minutes of time difference = 1 degree of longitude

Or, 1 minute of time difference = 1/4 degree of longitude

Or, 540 minutes of time difference = (1/4) × 540 degrees of longitude

540 minutes of time difference = 135 degrees of longitude

Also, we can infer that the current location is in the Western hemisphere because we know that it is 9 hours behind GMT (or UT) time.

Hence, the longitude of the current location = 135⁰

So the option 4 is correct.

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The complete question is:

Your chronometer is set for Greenwich Mean Time (GMT or Universal Tim, UT). High noon at your present location is 9 pm UT. What is your longitude in DMS (not decimal degrees)?

1. 30° 18'W

2. 30° 16'W

3. 30° 17'W

4. none of the above

The 0.05(x+4)+0.10(x) = $1.25 equation could be used to determine the number of dimes, x, in his pocket.

An equation is a mathematical expression containing an equal sign that states the equality of two expressions. It is essentially a statement of balance, showing that two expressions are equal in value. Equations are used to solve a wide variety of problems in mathematics, science, and engineering. For example, the equation x+2=4 expresses the fact that when 2 is added to any number x, the result is 4.

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8 persons can be arranged in a row in 384 different ways, with each wife positioned to the left of her husband.

8! = 40,320 ways to arrange the 8 people in a row, without any restrictions. To take into account the restriction that each wife must be somewhere to the left of her husband, we can first arrange the 4 couples in a row. There are 4! = 24 ways to do this. For each of these arrangements, we can then arrange the couples in the row. There are 2 ways to arrange each couple, so the total number of arrangements is 24 x 2⁴ = 384. Therefore, there are 384 ways to arrange the 8 people in a row, with each wife somewhere to the left of her husband.

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The domain of a function f(x) = 2√(-x² + 10x) in interval notation is given by (-∞, 0] ∪ [10, ∞).

Function f(x) = 2√(-x² + 10x).

Domain of a function is the set of all possible input values of x for which the function is defined.

Values of x for which the expression inside the square root is non-negative.

As the square root of a negative number is not a real number.

Take out the common factor -x we have,

-x² + 10x ≥ 0

⇒ -x(x - 10) ≥ 0

⇒ -x ≥ 0 or ( x - 10 ) ≥ 0

The inequality is satisfied when x ≤ 0 or x ≥ 10.

This implies,

The domain of the function f(x) = 2√(-x² + 10x) is the set of all real numbers such that x ≤ 0 or x ≥ 10.

In interval notation form,

The domain is represented as,

(-∞, 0] ∪ [10, ∞).

Therefore, the domain of the given function is equal to (-∞, 0] ∪ [10, ∞).

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The above question is incomplete , the complete question is:

What is the domain of a function f(x) = 2√-x²+ 10x