lify 8
7x2-x+8 – 5x2 + 3x – 10

The evaluation is 10.67 of given geometric progression.

A geometric progression is a set of elements where each succeeding element is created by multiplying the one before it by a number called the common ratio. The standard representation for a geometric progression series is a, ar, ar²,..., where an is the first term and r is the common ratio of the sequence.

The ratio between two consecutive numbers, or a number divided by the number before it in the sequence, is known as the common ratio since it is the same for all numbers or common.

The sum of a finite geometric series can be found using the formula:

\(a (1-r^{n}) / (1-r)}\).

Where a is the first term and r is the common ratio between successive terms.

To find the ratio of successive terms by plugging into the formula

r = aₙ +1 / (aₙ)

Simplifying,

r =1/4

And the first term is;

when n=1, a = 8

Substituting all the values to the formula,

The summation of GP

= 8 x { 1 - (1/4)¹⁰ } / {1- (1/4)}

= 8 { 1 - (1/1048576) / (3/4)

= 8 x {(1048576 - 1) / 1048576} x (4/3)

= 8 x (1048575 / 1048576) x (4/3)

= 8 x 349525 / 262144

= 2796200 / 262144

= 10.6666

The decimal form is 10.67.

Therefore, the evaluation is 10.67.

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Answer:

36.25%

Step-by-step explanation:

400 - 255 = 145

145/400 = 0.3625

0.3625 = 36.25%

Answer:

36.25%

Step-by-step explanation:

(400-255)/400=145/400=0.3625=36.25%

Answer:

  -0.1, 1.3

Step-by-step explanation:

You want the solutions to the quadratic equation 5x² -2x -1 = 4x.

The equation can be put in standard form by subtracting 4x:

  5x² -6x -1 = 0

  5(x² -6/5x +(6/10)²) -1 -5(6/10)² = 0 . . . . . complete the square

  5(x -0.6)² = -2.8 . . . . . . . . . . . . . subtract 2.8

  x = 0.6 ± √0.56 = -0.1 or 1.3 . . . . . . . divide by 5 and take square root

Solutions to the equation are x = -0.1 and x = 1.3.

__

Additional comment

The square is completed by making the trinomial in parentheses have the form x² -2ax +a², where 'a' is half the coefficient of the x-term. When we add a² inside parentheses, we need to subtract an equivalent quantity outside parentheses.

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Step-by-step explanation:

Given

\( {a}^{5} . {a}^{ - 3} \\ = {a}^{5 - 3} \\ = {a}^{2} \)

Hope it will help :)❤

Answer:

=a^5 - a^-3

=a^ 5 -3

= a^2.

The monthly payment and total cost for the bank loan are $180.55 and $2,166.60, respectively.

To calculate the monthly payments and total cost, we'll assume that the interest is calculated using the simple interest method for the bank loan and the add-on method for the store loan. For the bank loan: Principal amount (cost of sofa, table, and chairs) = $1,980; Interest rate = 13% per year; Repayment period = 1 year (12 months). Monthly interest rate = 13% / 12 = 1.0833%; Number of months = 12. Using the formula for calculating monthly payments on a simple interest loan: Monthly payment = (Principal amount + (Principal amount * Monthly interest rate * Number of months)) / Number of months. Substituting the values into the formula: Monthly payment = (1980 + (1980 * 0.010833 * 12)) / 12; Monthly payment ≈ $180.55; Total cost = Monthly payment * Number of months = $180.55 * 12 = $2,166.60. For the store loan:Principal amount (cost of sofa, table, and chairs) = $1,980; Interest rate = 11% per year; Repayment period = 1 year (12 months). Using the add-on method, the interest is simply added to the principal amount. Interest = Principal amount * Interest rate  = $1,980 * 0.11 = $217.80. Total amount to be repaid = Principal amount + Interest = $1,980 + $217.80 = $2,197.80. Monthly payment = Total amount / Number of months = $2,197.80 / 12 ≈ $183.15.

Therefore, the monthly payment and total cost for the bank loan are $180.55 and $2,166.60, respectively. On the other hand, the monthly payment and total cost for the store loan (using the add-on method) are $183.15 and $2,197.80, respectively. The bank payment and total cost are lower even though the stated interest rate is higher because the bank loan uses the simple interest method, which calculates interest based on the remaining balance after each payment. This results in lower interest charges over time. On the other hand, the add-on method used by the store loan calculates the interest based on the original principal amount, resulting in higher interest charges. Despite the higher stated interest rate, the bank loan's lower interest charges lead to lower monthly payments and a lower total cost compared to the store loan.

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The value of x and y in the right triangle are as follows:

x = 15√3 units

y = 30 units

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles of a right angle triangle is 180 degrees.

The side x and y can be found using trigonometric ratios,

tan 60° = opposite / adjacent

tan 60° = x / 15

cross multiply

x = 15 tan 60°

x = 15 × √3

x = 15√3 units

Let's find y as follows:

cos 60° = adjacent / hypotenuse

cos 60° = 15 / y

cross multiply

y = 15 / cos 60

y = 15 ÷ 1 / 2

y = 15(2)

y = 30 units

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Answer:

$0.84

Step-by-step explanation:

To find the cost of 4 flowers, we need to divide both sides of the equation: 20 = 4.2 by 5.

20 / 5 = 4

4.2 / 5 = 4.2/5 -> 0.84

Next, change both values in the equation with the quotients (4 and 0.84):

4 = 0.84

Our new equation explains that 4 flowers equals the price of $0.84.

The equivalent of the radical expression (√2 + √5) / (√2 - √5) is -(7 + 2√10)/3 in its simplest form

An equation shows the relationship between two or more numbers and variables.

Given the surd:

(√2 + √5) / (√2 - √5)

Multiplying through by the conjugate surd, that is √2 + √5

= [(√2 + √5) / (√2 - √5)] * [(√2 + √5) / (√2 +√5)]

= (2 + 2√10 + 5)/(2 - 5)

Further simplifying:

= -(7 + 2√10)/3

The equivalent of (√2 + √5) / (√2 - √5) is -(7 + 2√10)/3

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For breakfast, you have had 1/2 a serving of cereal and 1/4 cup of raisins, which count as one serving of fruit.

For breakfast, you have had one serving of cereal and one serving of fruit. In general, one serving of cereal is considered to be one cup, while one serving of fruit is considered to be one half cup. Therefore, in your bowl of oatmeal, you would have had two servings of cereal, and in your quarter cup of raisins, you would have had one serving of fruit. For lunch, you have had one serving of fruit in your glass of orange juice.

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8/36 and 21/36 are not in the least term fractions to the original fractions.

Fractions as used in mathematics refers to group of numbers that has some unique properties which include:

The numerator refers to the number on the upper part of the separator

The separator is the divide between the numerator and the denominator

The denominator is the number below the numerator

The fractions in the least form include

Hence it is shown that the fractions are proper fractions not in the least form of the original fractions

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Answer:

x = 3a- 7/2

Step-by-step explanation:

Multiply 3 by both sides

2x+7=6a

Divide both sides by 2

x = 3a- 7/2

Step-by-step explanation

The area of a triangle is found by multiplying the height and base of a triangle then dividing it by two since you can use that same formula to find a rectangle but not dividing. A rectangle you multiply the base and height while a triangle will equal half the area of that rectangle

Strategies such as fast-tracking, crashing, prioritization, and resource optimization can be employed to reduce the project completion time by 5 weeks.


To reduce the completion time of the project by 5 weeks, we need to analyze the provided information and make appropriate adjustments. The initial completion time of the project is 25 weeks.

To achieve a reduction of 5 weeks, we can consider several strategies:

1. Fast-tracking: This involves overlapping or parallelizing certain project activities that were initially planned to be executed sequentially. By identifying tasks that can be performed concurrently, we can potentially save time. However, it's important to evaluate the impact on resource allocation and potential risks associated with fast-tracking.

2. Crashing: This strategy focuses on expediting critical activities by adding more resources or adopting alternative approaches to complete them faster. By compressing the schedule of critical tasks, we can reduce the overall project duration. However, this may come at an additional cost.

3. Prioritization: By reevaluating the project tasks and their priorities, we can allocate resources more efficiently. This ensures that critical activities receive higher attention and are completed earlier, resulting in an accelerated project timeline.

4. Resource optimization: Analyzing the resource allocation and identifying potential areas for optimization can lead to time savings. By ensuring that resources are utilized effectively and efficiently, we can streamline the project execution process.

It's important to note that implementing any of these strategies requires careful evaluation, considering factors such as project constraints, risks, cost implications, and stakeholder agreements. A comprehensive analysis of the project plan, resource availability, and critical path can guide the decision-making process for reducing the project completion time.

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Answer:

Both angles have a measure of 134degrees, y = 27degrees.

Step-by-step explanation:

As per what is given in the problem:

There are 2 parallel lines, both are intersected by a transversal.

Remember the theorem, when two parallel lines are intersected by a transversal, then the alternate exterior angles are congruent.

The is meanse that:

3y + 53 = 7y - 55

Solve using inverse operations:

3y + 53 = 7y - 55

     +55         +55

3y + 108 = 7y

-3y            -3y

108 = 4y

/4      /4

27 = y

Now, substitute back in to find the value of the angle:

3y + 53

y = 27

3 ( 27 ) + 53

81 + 53

= 134

Since the angles are alternate exterior, they are congruent, hence both angles have a measure of 134degrees.

Answer:

hjgfghjk

Step-by-step explanation:

:)

The difference quotient evaluated in x = 2 gives:

[ f(2 + h) - f(2)]/h = h + 9

So the last option is the correct one.

Here we know the function:

f(x) = x^2 + 5x + 6

And we want to find the difference quotient:

[ f(2 + h) - f(2)]/h

Let's evaluate the function:

f(2 + h) = (2 + h)^2 + 5*(2 + h) + 6

            = 2^2 + h^2 + 4h + 10 + 5h + 6

            = h^2 + 9h + 20

f(2) = 2^2 + 5*2 + 6

f(2) = 4 + 10 +  6 = 20

Then we have:

[ f(2 + h) - f(2)]/h

[h^2 + 9h + 20 - 20]/h

[h^2 + 9h ]/h

Taking the quotient we get:

[h^2 + 9h ]/h = h + 9

So the correct option is the last one.

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Answer:

an=87+(n-1)(-3.6)

Step-by-step explanation:

hope this helps

Answer:

an=87+(n-1)(-3.6)

We determined the value of z =24 unit

A closed geometrical shape that has four straight side having two parallel side length and two unparallel sides are called trapezoid. The unparallel sides are equal in length.

Given, a trapezoid RTUW whose base are RW and TU, legs are UW and RT

as per question V and S are the midpoints of the legs UW and RT.

hence, VS is parallel to the base and called median.

As per the properties of trapezoid, length of the median is equal to the average length of the bases.

length of median = sum of length of the bases/2

SV = (TU+RW)/2

we are given that, SV= -z+42, TU = z-12 and RW =z

now, -z+42 = (z-12+z)/2

-2z+84 = 2z-12

4z = 96

z = 24

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Answer:

given;

inscribed angle =35°

central angle=35×2=70°

radius [r]=10in

area of shaded region=70°/360×πr²

=70°/360×π×10²=159π/9 in²

A discrete probability distribution is a statistical distribution that relates to a set of outcomes that can take on a countable number of values, whereas a continuous probability distribution is one that can take on any value within a given range.Therefore, the main difference between the two types of distributions is the type of outcomes that they apply to.

An example of a discrete probability distribution is the probability of getting a particular number when a dice is rolled. The possible outcomes are only the numbers one through six, and each outcome has an equal probability of 1/6. Another example is the probability of getting a certain number of heads when a coin is flipped several times.

On the other hand, an example of a continuous probability distribution is the distribution of heights of students in a school. Here, the range of heights is continuous, and it can take on any value within a given range.

The expected value of a probability distribution measures the central tendency or average of the distribution. In other words, it is the long-term average of the outcome that would be observed if the experiment was repeated many times.

For a discrete probability distribution, the expected value is computed by multiplying each outcome by its probability and then adding the results. In mathematical terms, this can be written as E(x) = Σ(xP(x)), where E(x) is the expected value, x is the possible outcome, and P(x) is the probability of that outcome.

For example, consider the probability distribution of the number of heads when a coin is flipped three times. The possible outcomes are 0, 1, 2, and 3 heads, with probabilities of 1/8, 3/8, 3/8, and 1/8, respectively. The expected value can be computed as E(x) = (0*1/8) + (1*3/8) + (2*3/8) + (3*1/8) = 1.5.

Therefore, the expected value of the distribution is 1.5, which means that if the experiment of flipping a coin three times is repeated many times, the long-term average number of heads observed will be 1.5.

Answer:

#1: s'(t)= -32t+20

#2: -32t+20=0

t=2/3

#3: s(2/3)=-16(2/3)^2+20(2/3)+3=83/9

Step-by-step explanation:

first find the derivative of the original funtion #1

set the equation equal to 0 because when s't=0 is the maximum height

put the t at highest point into the funtion to solve for distance

Answer

well first u put it as 2/2 which is 2 then you have to times it by 69 which is 138 then divide that by 6.5 which is 21

Step-by-step explanation:

actual answer is 4 if you were serious about this

Answer: 4

Step-by-step explanation:

Use your hands:

2 on one hand

2 on the other hand

Put them together which is 4

(1) The right solution of given equation is  8.(2)The equation 8x = 64 has only one solution

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Part A: Masha's solution is incorrect.

In Step 2, Instead of dividing 64/8 she did mistake she subtract 64 by 8

So, the correct step to solving this equation is

8x = 64

x = 64/8

x=8

Hence the right solution of given equation is  8

Part B: The equation 8x = 64 has only one solution, which is x = 8. This is because there is only one value of x that satisfies the equation.

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(1) The right solution of given equation is 8.

(2)The equation 8x = 64 has only one solution

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Part A: Masha's solution is incorrect.

In Step 2, Instead of dividing 64/8 she did mistake she subtract 64 by 8

So, the correct step to solving this equation is

8x = 64

x = 64/8

x=8

Hence the right solution of given equation is 8

Part B: The equation 8x = 64 has only one solution, which is x = 8. This is because there is only one value of x that satisfies the equation.

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The probability of finishing the project in 62 weeks or less is 0.8413. The probability of finishing the project in 66 weeks or less is 0.9772, and the probability of the project taking longer than 65 weeks is 0.3085.

The probability that the construction project will be finished in 62 weeks or less is approximately 0.8413. The probability that the project will be finished in 66 weeks or less is approximately 0.9772. The probability that the project will take longer than 65 weeks is approximately 0.3085.

In the first part, to calculate the probability that the project will be finished in 62 weeks or less, we use the cumulative distribution function (CDF) of the normal distribution with a mean of 60 weeks and a standard deviation of 4 weeks. By finding the area under the curve up to 62 weeks, we get a probability of approximately 0.8413.

In the second part, to calculate the probability that the project will be finished in 66 weeks or less, we again use the CDF of the normal distribution. By finding the area under the curve up to 66 weeks, we get a probability of approximately 0.9772.

In the third part, to calculate the probability that the project will take longer than 65 weeks, we subtract the probability of finishing in 65 weeks or less from 1. This gives us a probability of approximately 0.3085.

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To determine the necessary sample size to obtain an interval width of 50 ppm for a confidence level of 95%, we need to use the formula for sample size calculation for estimating a population mean.

The formula for sample size calculation is:

n = (Z * σ / E)^2

In this case, the desired margin of error is 50 ppm, which means the interval width is 2 * E = 50 ppm. Therefore, E = 25 ppm.

The Z-score corresponding to a 95% confidence level is approximately 1.96.

Given that the investigators made a rough guess of 175 for the value of σ (standard deviation) before collecting data.

We can substitute these values into the sample size formula:

n = (1.96 * 175 / 25)^2

Simplifying the calculation:

n = (7 * 175)^2

n = 1225^2

n ≈ 1,500,625

Therefore, a sample size of approximately 1,500,625 would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%.

To obtain an interval width of 50 ppm with a confidence level of 95%, a sample size of approximately 1,500,625 is required. This is calculated using the formula for sample size estimation, considering a desired margin of error of 25 ppm and a standard deviation estimate of 175. The Z-score corresponding to a 95% confidence level is used to determine the sample size.

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The equation of each line in slope intercept form y = 2x + 3,x = 4

The equation of a line in slope-intercept form (y = mx + b), the slope (m) and the y-intercept (b). The slope-intercept form is a convenient way to express a linear equation.

Equation of a line with slope m and y-intercept b:

y = mx + b

Equation of a vertical line:

For a vertical line with x = c, where c is a constant, the slope is undefined (since the line is vertical) and the equation becomes:

x = c

An example for each case:

Example with given slope and y-intercept:

Slope (m) = 2

y-intercept (b) = 3

Equation: y = 2x + 3

Example with a vertical line:

For a vertical line passing through x = 4:

Equation: x = 4

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Answer:

y=mx+b

Step-by-step explanation:

Answer: x=9

Step-by-step explanation:

:)

Answer:

6/7

Step-by-step explanation:

Total number of jerseys = 4 + 3 = 7

Now, the probability of picking a purple Jersey = number of purple jerseys/total number of jerseys = 3/7

Now let’s look at picking a jersey with even number

Even number jerseys are yellow two and yellow four and also purple two

So we have 3 even numbered jersey. The probability of picking an even numbered jersey is 3/7

In probability, once we have or, we add

The probability of picking an even numbered jersey or a purple jersey = 3/7 + 3/7 = 6/7