The number of cubes form a pattern.
a) Draw an expression for the number of cubes in figure n.
b) How many cubes are there in the 50th figure?
c) What number has the figure consisting of 156 cubes​

The present value of 30 annual payments of $4,500 per annum where the first payment is made 5 years from now with a discount rate of 9% per annum is $49,999.998. Therefore, the correct option is a. $49,999.998.

Present Value (PV) is the value at which the money that is expected to be received at some future time is worth in today's dollars. It is also called the "discounted value." It is used to measure the value of a future amount in today's dollars. Therefore, it is an essential component of discounted cash flow analysis, used to calculate the value of an investment or debt instrument over time.

The formula to calculate the present value of annuity formula is as follows: PV = [PMT * (1 - (1 / (1 + r)n))]/r

Where,PV = present value of annuity

PMT = payment made every year

r = rate of interest per year

n = number of years

An annuity is a fixed sum of money paid each year.

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B) The length of GB is 3 in the given triangle.

The centroid of a triangle is the point at which the three medians of the triangle intersect. A median of a triangle is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. The three medians divide the triangle into six smaller triangles, each with a vertex at the centroid.

The ratio in which the centroid divides a median of a triangle is 2:1. That is, the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side.

So, if G is the centroid and B is the midpoint of the side opposite to point A, the ratio of EG: GB is 2:1.

so the length of GB = EG/2

so the length of GB = 3

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Complete question:

In ΔAEC, G is the centroid , as shown in the figure .

if EG = 6 ,find GB

A) 2

B) 3

C) 6

D) 9

The correct function that describes the line segment from P(2,7,3) to Q(3,1,1) is r(t) = ⟨2 + t, 7 - 6t, 3 - 2t⟩; 0 ≤ t ≤ 1.

The function that describes the line segment from point P(2,7,3) to Q(3,1,1), we can use the parametric form of a line. The general form of a line equation is r(t) = ⟨x₀ + at, y₀ + bt, z₀ + ct⟩, where (x₀, y₀, z₀) is a point on the line and (a, b, c) are direction ratios.

1. First, we find the direction ratios by subtracting the coordinates of P from Q:

  a = 3 - 2 = 1

  b = 1 - 7 = -6

  c = 1 - 3 = -2

2. Next, we substitute the point P(2,7,3) into the line equation and simplify:

  r(t) = ⟨2 + t, 7 - 6t, 3 - 2t⟩

3. The parameter t represents the distance along the line segment. Since we want to describe the segment from P to Q, we need t to vary from 0 to 1, ensuring that we cover the entire segment.

4. Comparing the obtained equation with the given options, we find that the correct function is r(t) = ⟨2 + t, 7 - 6t, 3 - 2t⟩; 0 ≤ t ≤ 1.

Therefore, option A, r(t) = ⟨2 - t, 7 + 6t, 3 + 2t⟩; 0 ≤ t ≤ 1, is the correct answer.

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The number of possible king-queen pairs can be determined by multiplying the number of candidates for king by the number of candidates for queen.

To calculate the number of king-queen pairs, we multiply the number of candidates for king by the number of candidates for queen. In this case, there are four candidates for homecoming queen and three candidates for king. Therefore, the total number of king-queen pairs would be 4 multiplied by 3, which equals 12.

Each candidate for king can be paired with each candidate for queen, resulting in multiple possible combinations. By multiplying the number of candidates for each position, we account for all possible pairings. In this scenario, there are three potential kings and four potential queens. For each king, there are four possible queens he can be paired with. Since there are three kings, we multiply 3 by 4 to get the total number of 12 king-queen pairs.

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The volume of the composite solid is 310.86 cubic centimeter where it has a cylinder and cone.

The composite figure has a cylinder and cone

The volume of cylinder =πr²h

The radius of cylinder is 3 cm and height is 10 cm

Volume of cylinder = 3.14×3²×10

=3.14×9×10

=282.6 cubic centimeter

Now let us find volume of cone

Volume of cone = πr²h/3

Radius of cone is 3 cm and height is 3 cm

Volume of cone = 3.14×9×3/3

=28.26cubic centimeter

Total volume = 282.6 + 28.26

=310.86 cubic centimeter

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Answer:

y= 9 ( 5 dollars bill)

x=10 ( one dollar bill)

Step-by-step explanation:

let x be the one dollar bill and y the 5 dollar bill

x+y=19 ⇒ x=19-y

x+5y=55 ( solve by substitute x=19-y)

19-y+5y=55

4y=55-19

4y=36 ⇒ y=36/4

y= 9 ( 5 dollars bill)

x+y=19

x+9=19

x=19-9

x=10 ( one dollar bill)

check :

x+5y=55

10+5(9)=

10+45 = 55 dollars

Answer:

BC = 60

Step-by-step explanation:

We can model the line with the expression

AB + BC = AC Sub each equation

8x + 9 + 6x + 6 = 141 Combine like terms

14x + 15 = 141 Subtract 15

14x = 126 Divide by 14

x = 9

Now we can use x to find BC

BC = 6x + 6

BC = 6(9) + 6

BC = 54 + 6

BC = 60

Based on the given insurance plan, if you have a $12,500 hospitalization, you would pay $2,500.

You would pay $2,500.

The $2,500 is equal to the deductible amount specified in the insurance plan. A deductible is the initial amount you need to pay out of pocket before your insurance coverage kicks in. In this case, the deductible is $2,500, so you are responsible for paying that amount.

The $2,500 is the total amount you would pay for the hospitalization. It represents the deductible portion, which you need to cover before the insurance starts sharing the costs with you. After you meet the deductible, the coinsurance comes into effect. The 20% coinsurance means that you would be responsible for paying 20% of the remaining expenses, while the insurance would cover the remaining 80%. However, since the out-of-pocket maximum is $5,200, and your hospitalization cost is $12,500, you would not reach the out-of-pocket maximum in this case. Therefore, you would pay the deductible amount of $2,500.

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a) The probability of exactly 2 flaws in 1 millimeter of wire is approximately 0.2645.

b)  There is no positive constant c that satisfies all the properties of a cumulative distribution function.

(a) The probability of exactly 2 flaws in 1 millimeter of wire is given by the Poisson probability mass function:

P(X = 2) = (e^(-λ) * λ^x) / x!

where λ = 2.3 and x = 2.

Substituting these values, we get:

P(X = 2) = (e^(-2.3) * 2.3^2) / 2! = 0.2645 (rounded to four decimal places)

Therefore, the probability of exactly 2 flaws in 1 millimeter of wire is approximately 0.2645.

(b) The probability of at most 2 flaws in 5 millimeters of wire is given by the cumulative distribution function of a Poisson distribution with mean λ = 5*2.3 = 11.5:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= (e^(-11.5) * 11.5^0) / 0! + (e^(-11.5) * 11.5^1) / 1! + (e^(-11.5) * 11.5^2) / 2!

= 0.0086 + 0.0495 + 0.1420

= 0.2001 (rounded to four decimal places)

Therefore, the probability of at most 2 flaws in 5 millimeters of wire is approximately 0.2001.

(c) The cumulative distribution function F(x) is given by:

F(x) = c(8x^2 – 3x), 0 <= x <= 2

Since F(x) is a cumulative distribution function, it satisfies the following properties:

F(x) is non-negative for all x

F(x) is non-decreasing as x increases

Lim x->-∞ F(x) = 0 and Lim x->+∞ F(x) = 1

Using these properties, we can solve for the constant c:

Lim x->-∞ F(x) = 0 => c(8*(-∞)^2 – 3*(-∞)) = 0 => c = 0

Lim x->+∞ F(x) = 1 => c(8*(+∞)^2 – 3*(+∞)) = 1 => c = 0 (since 8*(+∞)^2 is much larger than 3*(+∞))

Therefore, there is no positive constant c that satisfies all the properties of a cumulative distribution function.

Hence, the given function cannot be a cumulative distribution function.

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Analyzing the function f(x) = -2•x³ + 5•x² - 3•x + 1, using the criteria f(x) = f(-x) for even functions and f(x) = -f(-x) for odd functions, gives the correct option as the option

A. Neither even or odd

An even function satisfy the equation f(x) = f(-x)

An even function is one that is symmetrical about the y-axis

An odd function satisfy the equation f(x) = -f(-x)

The shape graph of an odd function is inverted as it crosses the y-axis.

Analyzing the function f(x) = -2•x³ + 5•x² - 3•x + 1 gives;

f(1) = -2•1³ + 5•1² - 3•1 + 1 = -1

f(-1) = -2•(-1)³ + 5•(-1)² - 3•(-1) + 1 = 11

f(1) ≠ f(-1)

-f(-1) = -2•(-1)³ + 5•(-1)² - 3•(-1) + 1 = 11

f(1) ≠ -f(-1)

The function is therefore;

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Answer:

ok you deleted my other answer

Step-by-step explanation:

im just finishing this challenge and you are the last question i need to answer

We evaluated the function and we got

                                 \(h(-2)=-14\\h(0)=0\\h(2)=6\)

Let us evaluate that function for \(x = -2\)

 We can substitute the value of \(x\) in the given expression      

                                      \(h(-2)=5(-2)-(-2)^{2}\)

                                                 \(=-10-4\\=-14\)

                                      \(h(-2)=-14\)

Now, we can evaluate the function for \(x=0\)

Let's substitute the value of \(x\) in the given expression

                              \(h(0)=5(0)-0^{2} \\h(0)=0\)

Now, we can evaluate the function for \(x=2\)

Let's substitute the value of \(x\) in the given expression

                              \(h(2)=5(2)-2^{2} \\h(2)=10-4\\h(2)=6\)

Hence, we evaluate the function

            \(h(-2)=-14\\h(0)=0\\h(2)=6\)

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Effective situational leaders demonstrate a high degree of flexibility.

Flexibility is a key quality for situational leaders since they must modify their style of leadership according to the circumstances, the demands of their team, and the objectives to be met. They are able to modify their strategy, communication style, and decision-making process to suit the demands of various situations.

Flexibility stands out as a crucial feature that enables leaders to negotiate a variety of situations and guide their teams to success, even though honesty, extraversion, empathy, and other qualities are also important in leadership.

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Answer:

\(5^{12}\)

Step-by-step explanation:

Lets say there's a number 'x' and there's an expression \((x^a)^b\) where 'a' & 'b' are also numbers , the simplified form of the expression is \(x^{a \times b}\).

So ,

\((5^4)^3 = 5^{4 \times 3} = 5^{12}\)

Answer:

the inequality would look like this
|x-102.6| _>_2.4

An alien is unhealthy if its body temperature is less than 100.2ºF or more than 105ºF.

Answer:

yes

Step-by-step explanation:

brainiest plz

Answer: Biden 2020

Step-by-step explanation:

Answer:

Identity property of addition: The sum of 0 and any number is that number. For example, 0 + 4 = 4 0 + 4 = 4 0+4=40, plus, 4, equals, 4.

Step-by-step explanation:

Answer:

csc θ * sin θ

Simplified using trig identities:  

csc (x) = 1/sin(x)  

so, csc (0) = 1/sin(0)  

1/sin(0) * sin (0), the result will be sin(0) / sin (0) which is equal to 1.  

Therefore, the answer is 1.

Step-by-step explanation:

Expression in sin θ and cos θ below

4cos ec^2  2θ as 2 /    2 (4 sin θ cos θ )^2

or

cos ec^2 θ as 1 / sin ^2  θ

. Accept terms like

cos ec^2 θ = 1  +cot^2 θ =1 +  cot^2 θ /sin^2 θ

The number of oranges that are expected to weigh more than 4 oz is:

1400 - (1400 × 0.0228)≈ 1368.

The mean weight of the oranges growing in an orchard is 8 oz and standard deviation is 2 oz, the distribution of the weight of oranges can be represented as normal distribution.

From the batch of 1400 oranges, the number of oranges is expected to weigh more than 4 oz can be found using the formula for the Z-score of a given data point.

\(z = (x - μ) / σ\)

Wherez is the Z-score of the given data point x is the data point

μ is the mean weight of the oranges

σ is the standard deviation

Now, let's plug in the given values.

\(z = (4 - 8) / 2= -2\)

The area under the standard normal distribution curve to the left of a Z-score of -2 can be found using the standard normal distribution table. It is 0.0228. This means that 0.0228 of the oranges in the batch are expected to weigh less than 4 oz.

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Answer:

45262

Step-by-step explanation:

Answer: 45,262

Step-by-step explanation:

Answer:

(24x^2 + 14x – 20) /(3x+5) =  h

Step-by-step explanation:

The area of a trapezoid is given by

A =1/2 (b1+b2) h

12x^2 + 7x – 10 = 1/2 ( x+3+ 3x+2)h

Multiply each side by 2

24x^2 + 14x – 20 =  ( x+3+ 3x+2)h

Combine like terms

24x^2 + 14x – 20 =  ( 4x+5)h

Divide each side by (4x+5)

(24x^2 + 14x – 20) /(4x+5) =  ( 4x+5)h/(4x+5)

(24x^2 + 14x – 20) /(4x+5) =  h

5.30 % rate of return would you expect on a 5-year treasury security, assuming the pure expectations theory is valid.

To reflect the true cost and purchasing power of money that is borrowed or invested, an interest rate is called a real interest rate that has been adjusted for inflation. The nominal interest rate depicts the cost of money and reflects the state of the market. A good's nominal value is its price in terms of money. Its value in relation to another good, service, or collection of goods is what determines its true worth. Given that it is the current interest rate in the economy, it is frequently referred to as the market interest rate (usually charged by banks and other institutions). Depending on the bank or the type of loans or deposits, this nominal interest rate may be 8%, 10%, or 12%.

Nominal interest rate = Real interest rate + Inflation rate

= 2.5% + 2.8%

= 5.30%

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To prove that the argument is valid using propositional logic, we can apply logical rules and deductions. Let's break down the argument step by step:

(A + B) ^ (C V -B) ^ (-D --> C) ^ A ^ D

We will represent the proposition as follows:

P: (A + B)

Q: (C V -B)

R: (-D --> C)

S: A

T: D

From the given premises, we can deduce the following:

P ^ Q (Conjunction Elimination)

P (Simplification)

Now, let's apply the rules of disjunction elimination:

P (S)

A + B (Simplification)

Next, let's apply the rule of disjunction introduction:

C V -B (S ^ Q)

Using disjunction elimination again, we have:

C (S ^ Q ^ R)

Finally, let's apply the rule of modus ponens:

-D (S ^ Q ^ R)

C (S ^ Q ^ R)

Since we have derived the conclusion C using valid logical rules and deductions, we can conclude that the argument is valid.

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Answer:

After the first year, the value of the house would increase by 6% and become:

$198,000 + (6%/100) x $198,000 = $210,000

Similarly, after the second year, the value of the house would increase by 6% and become:

$210,000 + (6%/100) x $210,000 = $222,600

We can repeat this process for all five years to determine the final value of the house after 5 years:

$198,000 x (1 + 6%/100)^5 = $267,015.23

To find the value of the house as a percentage of the value exactly one year earlier, we can compare the value after 5 years with the value after 4 years:

$222,600/$210,000 = 1.0571

This means that the value of the house after 5 years is approximately 105.71% of the value exactly one year earlier, which is an increase of 5.71%.

Answer:

D

Step-by-step explanation:

Every input can only have one output for it to be considered a function. There are repeats of x values with different y values in all of these except for D so D is the correct answer.

The equation for the materials quantity variance is (AQ × AP) – (SQ × SP).

The materials quantity variance is a measure of the difference between the actual quantity (AQ) of materials used and the standard quantity (SQ) of materials that should have been used, multiplied by the standard price (SP) per unit. The variance indicates whether more or fewer materials were used compared to the standard, and it quantifies the cost impact of the difference.

The formula (AQ × AP) – (SQ × SP) calculates the materials quantity variance by multiplying the actual quantity (AQ) by the actual price (AP) per unit and subtracting the product of the standard quantity (SQ) and the standard price (SP) per unit. This formula directly compares the actual and standard quantities and calculates the cost impact of any deviations.

Therefore, the correct equation for the materials quantity variance is (AQ × AP) – (SQ × SP).

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The distribution that the residuals in our model to follow is equals to the normal probability distribution. So, option(a).

Because residuals are defined as the difference between any data point and the regression line, they are sometimes called "errors". An error in this context does not mean that there is anything wrong with the analysis. In other words, the residual is the error that is not described by the regression line. The residue(s) can also be expressed by "e". The formula is written as, Residual = Observed value – predicted value or

\(e = y – \hat y \).

In order to draw valid conclusions from your regression, the regression residuals should follow a normal distribution. The residuals are simply the error terms or differences between the observed value of the dependent variable and the predicted value. Therefore, the residuals should have a normal distribution.

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Complete question:

we desire the residuals in our model to have which probability distribution? select answer from the options below

a) normal

b) binomial

c) poisson

Answer:

70°

Step-by-step explanation:

This triangle is an isosceles triangle because two sides are marked that they are the same. So the "base angles" are also the same. Angle D and Angle F are equal to each other (the angles are congruent and the measures are equal).

All the angles in a triangle add up to 180° We know the one marked angle is 40°. Let Angle D be x and so Angle F is also x.

x + x + 40 = 180

combine like terms

2x + 40 = 180

subtract 40

2x = 140

divide by 2

x = 70

Angle D is 70°