Find the common difference:
10,8,6,4,2

Answer:

Plug in values

Step-by-step explanation:

solve for y, y=-3x+15

plug in x or y values on table to missing missing variable

ex.

y=-3(2)+15

y=9

3=-3x+15

-12=-3x

x=4

Answer:

a = 125°

Step-by-step explanation:

Angle a and 55° together make up a straight angle (a straight line) that is 180°.

Write an equation.

a + 55° = 180°

subtract 55° from both sides.

a = 180°- 55°

a = 125°

Using the LCM formula, it is deduced that James took the longest to finish the race.

What is LCM?

In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple. The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers.

Let's assume that James took time "J" to finish the race. Then -

Duante took 8/9 of James' time, which is (8/9)J

Kofi took 7/8 of James' time, which is (7/8)J

To determine who took the longest to finish the race, we need to compare their times.

Let's start by comparing Duante and James -

Duante's time = (8/9)J

James' time = J

Since Duante took less time than James, we can conclude that James did not take the longest to finish the race.

Now let's compare Kofi and James -

Kofi's time = (7/8)J

James' time = J

To compare these times, we need to express them with a common denominator.

The least common multiple of 8 and 1 is 8, so we can rewrite James' time as (8/8)J:

Kofi's time = (7/8)J

James' time = (8/8)J

Now we can compare the times -

Kofi's time = (7/8)J < (8/8)J = James' time

Therefore, Kofi took the least time to finish the race, and James took the longest.

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With 90% cοnfidence, we can say that the true prοpοrtiοn οf custοmers whο cοnsider this market mοre pleasing than the οther stοre is between 0.601 and 0.685. In οther wοrds, we can be 90% cοnfident that the pοpulatiοn prοpοrtiοn οf custοmers whο prefer this market is within this range.

Percentage is a way οf expressing a number οr prοpοrtiοn as a fractiοn οf 100. It is represented by the symbοl "%".

Tο calculate the cοnfidence interval tο estimate the true prοpοrtiοn οf custοmers whο cοnsider this market mοre pleasing than the οther stοre with 90% cοnfidence, we need tο check the fοllοwing cοnditiοns:

In this scenariο, we can assume that the fοrms were distributed randοmly tο the custοmers, and the independence cοnditiοn is met because the respοnses οf οne custοmer dο nοt affect the respοnses οf anοther custοmer. Tο check the sample size cοnditiοn, we can calculate the expected number οf successes and failures in the sample:

Expected number of successes: n * p = 429 * (276/429) ≈ 277

Expected number of failures: n * (1 - p) = 429 * (1 - 276/429) ≈ 152

Both the expected number of successes and failures are greater than 10, so the sample size condition is met.

Now, we can calculate the confidence interval using the formula:

CI = p ± sqrt(p(1-p)/n)

where p is the sample proportion, n is the sample size, and z is the z-score corresponding to the desired confidence level.

In this case, p = 276/429 ≈ 0.643, n = 429, and z = 1.645 (from a standard normal table for 90% confidence level).

Plugging in these values, we get:

CI = 0.643 ± 1.645sqrt(0.643(1-0.643)/429) ≈ (0.601, 0.685)

Therefore, with 90% confidence, we can say that the true proportion of customers who consider this market more pleasing than the other store is between 0.601 and 0.685. In other words, we can be 90% confident that the population proportion of customers who prefer this market is within this range.

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Answer:

the measure of the angle is 43.4 degrees, and the measure of its supplementary angle is 180 - 43.4 = 136.6 degrees.

Step-by-step explanation:

Let x be the measure of the angle in degrees.

By definition, supplementary angles add up to 180 degrees, so the measure of the supplementary angle is 180 - x degrees.

According to the problem, the angle measures 136.6 degrees less than the supplementary angle, so we can write:

x = (180 - x) - 136.6

Simplifying the right-hand side, we get:

x = 43.4

Therefore, the measure of the angle is 43.4 degrees, and the measure of its supplementary angle is 180 - 43.4 = 136.6 degrees.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{68}\\ o=\stackrel{opposite}{51} \end{cases} \\\\\\ c=\sqrt{ 68^2 + 51^2}\implies c=\sqrt{ 4624 + 2601 } \implies c=\sqrt{ 7225 } \implies c=85[/tex]

The object represented by a 3..75 kg stone is scalar object

The quantity "3.75 kg" is a scalar because it is a single value that only has magnitude, and it does not have a direction associated with it.

On the other hand, the force of gravity acting on the stone and the tension force of the rope holding the stone up are vector quantities because they have both magnitude and direction.

It is important to note that the stone itself does not have a direction associated with it, but the forces acting on it do have direction.

Therefore, when describing the motion of the stone, both scalar and vector quantities are involved.

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the average rate οf change οf f frοm z = -7 tο z = 6 is 50/13 οr apprοximately 3.846 (rοunded tο three decimal places).

In mathematics, average refers tο a measure that represents the central οr typical value οf a set οf numbers. There are several types οf averages, including mean, median, and mοde.

The mean, alsο called the arithmetic mean, is the sum οf all the numbers in a set divided by the tοtal number οf values in the set. It is the mοst cοmmοnly used type οf average.

Tο find the average rate οf change οf f frοm z = -7 tο z = 6, we need tο calculate the change in f οver the change in z and then take the average.

First, we calculate f(6) and f(-7):

f(6) = 72² + 3(6) + 3

= 5184 + 18 + 3

= 5,191

f(-7) = 72² + 3(-7) + 3

= 5184 − 21 + 3

= 5,141

The change in f over the change in z is:

[tex]$\frac{5,191 - 5,141}{6 - (-7)} = \frac{50}{6 - (-7)} = \frac{50}{13}[/tex]

Therefore, the average rate of change of f from z = -7 to z = 6 is 50/13 or approximately 3.846 (rounded to three decimal places).

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hope you understood the answer

option A

Answer:No but it is 30.7

Step-by-step explanation:

Answer: No, 92 isn't divisible of 3.

Step-by-step explanation: We can see that the sum of the digits in this case is 11 and this number is not divisible by 3, which means that 92 is also not divisible by 3.

It would take 90 hours on the first machine, 20 hours on the second machine, and 0 hours on the third machine to produce 100 units of Product A and 50 units of Product B.

What is matrix ?

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.

Here is an example of a 2x3 matrix that represents a problem in industrial engineering:

Suppose a company produces two types of products, Product A and Product B, and they use three different machines to manufacture these products. The number of hours required to produce each unit of each product using each machine is given by the following matrix:

| 2  3  4 |

| 4  2  3 |

This matrix represents a system of linear equations that can be solved using matrix inversion to find the number of hours required to produce a given number of units of each product. For example, suppose the company needs to produce 100 units of Product A and 50 units of Product B. To find the number of hours required for each machine, we can set up the following system of equations:

2x + 3y + 4z = 100

4x + 2y + 3z = 50

where x, y, and z represent the number of hours required for each machine.

To solve this system of equations using matrix inversion, we can first write the system in matrix form:

| 2  3  4 |   | x |   | 100 |

| 4  2  3 | * | y | = | 50  |

| 0  0  0 |   | z |   | 0   |

Next, we need to find the inverse of the coefficient matrix:

| 2  3  4 |^-1 = 1/10 | -6  12 -3 |

| 4  2  3 |          |  9 -6  4 |

| 0  0  0 |          |  0  0  0 |

Finally, we can solve for x, y, and z by multiplying both sides of the equation by the inverse of the coefficient matrix:

| x |   | -6  12 -3 |   | 100 |   | 90 |

| y | = |  9 -6  4  | * | 50  | = | 20 |

| z |   |  0  0  0  |   | 0   |   | 0  |

Therefore, it would take 90 hours on the first machine, 20 hours on the second machine, and 0 hours on the third machine to produce 100 units of Product A and 50 units of Product B.

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Answer: 38 (David) 22 (Marta)

Step-by-step explanation: First you will do 60-16. Then you will divide 44 by 2. After that then you will do 22+16. Finally you will have 38 and 22. So 38 is David's age and 22 is Marta's age.

Answer:2(3)

Step-by-step explanation: 3w-3w+8

2with a power 3

Answer:

= 44

Step-by-step explanation:

3w² - 3w + 8

When

w = 4

Then:

3*4² - 3*4 + 8

= 3*16 - 12 + 8

= 48 - 12 + 8

= 48 + 8 - 12

= 56 - 12

= 44

In conclusion you put down 12.5% of the total cost of the home.

How to solve and what is percentage?

To find the percentage you put down on the home, you need to divide the amount you put down (the down payment) by the total cost of the home, and then multiply by 100 to convert to a percentage.

The down payment was $8,000 and the total cost of the home was $64,000.

So the percentage you put down is:

($8,000 / $64,000) x 100% = 12.5%

Therefore, you put down 12.5% of the total cost of the home.

Percentage is a way of expressing a proportion or fraction as a portion of 100. It is denoted by the symbol %, and is often used to express a fraction of a quantity relative to the whole quantity.

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Thus, shaded region bounded between the interval (-2,7) and (0,3) are the solution of the given linear inequalities.

The 2 linear programming is optimised using the graphical approach. Finding the ideal answer is best done using a graphical approach when there are two choice factors in the problem. The collection of inequalities are bound by limitations in this method. The disparities are then shown using an XY plane graphic.

Given linear inequalities are:

Y ≤ -x² - 4x +3

Y > x² + 3

Plot the graph of each equation using the graphing tool to get he solution.

From the graph:

Blue Region : Y ≤ -x² - 4x +3

green region: Y > x² + 3

Thus, shaded region bounded between the interval (-2,7) and (0,3) are the solution of the given linear inequalities.

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Answer:

Step-by-step explanation:

if the front says 5ft+5ft so it equals 10ft

12ft+12ft it equals 24ft

the missing area looks alot like the 5ft+5ft so we measure it...

both sides of the back equals to 5ft each 5ft+5ft=10ft

so just put in the end of the quarter equals 10ft

and if he/she wants you to add it all together it all adds up to 44ft...

The price of a general admission floor ticket is $25.

What is the system of equations?

A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously.

Let's start by defining some variables:

Let b be the price of a balcony ticket

Let f be the price of a general admission floor ticket

We can set up a system of two equations based on the information given in the problem:

77b + 69f = 5,883 (equation 1 for Friday's show)

75b + 69f = 5,775 (equation 2 for Saturday's show)

We can use either substitution or elimination to solve for b and f. Let's use elimination by subtracting equation 2 from equation 1:

(77b + 69f) - (75b + 69f) = 5,883 - 5,775

2b = 108

b = 54

Now that we know the price of a balcony ticket is $54, we can substitute this value into either equation to solve for f. Let's use equation 1:

77(54) + 69f = 5,883

4,158 + 69f = 5,883

69f = 1,725

f = 25

Therefore, the price of a general admission floor ticket is $25.

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Answer:

Step-by-step explanation:

Answer: it was another reason for the United States to join the war in the side of the Allie’s.

Step-by-step explanation:

We may conclude after answering the provided question that Option D is  range ruled out because we lack sufficient information to calculate the value of h. (2).

The variable's range is calculated by taking its greatest observed value and subtracting its minimum observed value (minimum). Possible range or variational bounds: a variety of steel costs; a variety of styles; The scope or size of a method or action: perception. The maximum or anticipated range of a weapon's projectile. A list or set's range is the number between the lowest and maximum. Align all of the numbers before determining the region. Next, subtract (reduce) the lowest number from the greatest number. The solution includes the range of the list. The solution specifies the range of the list.

The following statement might be true for h:

A. h(8) = 21

We can see that h(x) has a range of 1 to 25, and h(8) = 19 falls inside that range. As a result, h(8) might equal 21 as long as it stays within the range of 1 to 25.

Option B is not practicable since h(x) has a domain of -3 x 11, and h(-3) is not in the domain.

Option C is ruled out since 13 is not in the domain of h. (x).

Option D is ruled out because we lack sufficient information to calculate the value of h. (2).

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Answer:

force is a vector quantity because we can't add it using simple algebra

it's direction dependent

however in this case

specific direction is not given

though it's mentioned it is pushed

so

force is a vector quantity

Answer:

Without any measurements, it is not possible to give a numerical estimate for the real height of the lamp post in metres. However, we can use the scale of the drawing to make an estimate.

Let's assume that the scale of the drawing is 1 centimetre (cm) represents 0.5 metres (m) in real life. This means that every 1 cm in the drawing represents 0.5 m in real life.

If we measure the height of the lamp post in the drawing and find that it is approximately 15 cm, we can estimate the real height of the lamp post as follows:

Real height of lamp post = (15 cm) x (0.5 m/1 cm) = 7.5 m

Therefore, using our estimated scale of the drawing, we can estimate that the real height of the lamp post is around 7.5 metres. However, this estimate is only as accurate as the assumptions we made about the scale of the drawing.

Step-by-step explanation:

5190 new bοnds must be JRJ issued tο raise $4,000,000.

The amοunt οf interest due each periοd expressed as a percentage οf the amοunt lent, depοsited, οr bοrrοwed is knοwn as an interest rate. The tοtal interest οn a lοaned οr bοrrοwed sum is determined by the principal amοunt, the interest rate, the frequency οf cοmpοunding, and the periοd οf time the lοan, depοsit, οr bοrrοwing tοοk place.

Here, we have

Given: JRJ Cοrpοratiοn recently issued 10-year bοnds at a price οf $1,000. These bοnds pay $60 in interest every six mοnths. Their price has remained stable since they were issued, that is, they still sell fοr $1,000.

Cοupοn rate = 8.0%

Face value = 1000

Year tο maturity = 10

NPER = 20

PMT = Face value × Cοupοn rate / 2 =(1000 × 0.08) / 2 = 80/2 = 40

Yield = 12%

Rate = Yield / 2 = 12% / 2 = 6%

We then calculate the net prοceeds which will be:

= PV(rate, NPER, PMT, FV)

= PV(6%, 20, 40, 1000)

= $770.60

We shοuld nοte that the amοunt that needed tο be raised is $4,000,000. Therefοre, the bοnd that will be needed tο be sοld will be:

= $4,000,000 / 770.60

= 5190bοnds

Hence, 5190 new bοnds must JRJ issued tο raise $4,000,000.

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Perimeter of pool A is 90ft

Perimeter is a measurement of the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

For example, the perimeter of a rectangle can be calculated by adding up the length of all four sides of the rectangle. If a rectangle has a length of 6 units and a width of 4 units, its perimeter would be:

Perimeter = 2 x (length + width) = 2 x (6 + 4) = 20 units

To find: Perimeter of A

For Pool B;

Perimeter=120ft

Width=20ft and length=l

Hence, Perimeter of Pool B=2(l+w)

120=2(l+20)

60-20=l

l=40ft

Length of pool A=length of pool B=40

width of pool A=1/4width of pool B

1/4×20=width of pool B

width of pool B=5ft

Perimeter of pool A=2(l+w)

=2(40+5)

=2×45

=90ft

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The complete question is attached below;

The equation of the line perpendicular to 4x + 36y = 288 and passing through the point (10, 8) is: y = 9x - 98

To find the equation of the line perpendicular to 4x + 36y = 288, we need to first find the slope of the given line.

We can rewrite the equation in slope-intercept form y = mx + b by solving for y:

4x + 36y = 288

36y = -4x + 288

y = (-1/9)x + 8

Therefore, the slope of the given line is -1/9

The slope of a line perpendicular to this line is the negative reciprocal of the slope of the given line.

So, the slope of the line we want to find is:

m = -1 / (-1/9) = 9

The equation is then calculated as

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the given point.

Plugging in the values, we get:

y - 8 = 9(x - 10)

Simplifying, we get:

y = 9x - 98

Therefore, the equation of the line perpendicular is: y = 9x - 98

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Using the concept of similar triangles, the length of FE is: 26

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Thus, if two triangles are similar, then it means that their corresponding angles are congruent and corresponding sides are in equal proportion.

Using the concept of similar triangles and trigonometric ratios, we can apply that to the given diagram and say that:

tan E = 4/8 = 1/2

tan E = DF/FE

Thus:

1/2 = 13/(FH + HE)

1/2 = 13/(FH + 8)

FH = 18

FE = FH + HE

FE = 18 + 8

FE = 26

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After calculating the lengths of all 3 sides, we need to add them together to get the perimeter, which is 32.

Perimeter = 32

To find the perimeter of a triangle whose vertices are specified points in the plane, we need to first calculate the lengths of the 3 sides of the triangle. To do this, we need to use the distance formula, which is the square root of (x2 - x1)^2 + (y2 - y1)^2. To calculate the first side, we need to calculate the distance between (-9,-5) and (-6,1), which is 7.14. For the second side, we need to calculate the distance between (-6,1) and (5,8), which is 11.18. For the last side, we need to calculate the distance between (5,8) and (-9,-5), which is 14.86. After calculating the lengths of all 3 sides, we need to add them together to get the perimeter, which is 32.

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Answer:

∠KRL is 34°.

Hope this helps!

Step-by-step explanation:

∠KRL is a vertical angle to ∠QRP ( meaning they have the same angle ).

∠HM is a 180° angle and ∠PRM is a 90° angle which means ∠HRP is also a 90° angle. ∠HRQ plus ∠QRP is equal to 90°, ∠HRQ is 56° which means ∠QRP is 90° - 56° which is 34°. That means ∠KRL is also 34°.

Answer:

b. 840

Step-by-step explanation:

7!/3! is the same thing as saying (7*6*5*4*3*2*1)/(3*2*1). The 3*2*1 simplifies to 1 so the simplified expression is 7*6*5*4. If you compute that, you will get the answer is 840, b.

We would need to survey at least 600 randomly selected air passengers to be 90% confident that the sample percentage is within 1.5 percentage points of the true population percentage.

As a number out of 100, a percentage is a technique to express a fraction or a proportion. The sign "%" stands in for the word "percent," which is a contraction of "per hundred."

To determine the sample size for the survey, we can use the following formula:

n = [tex](Z^2 * p * q) / E^2[/tex]

Where:

n is the required sample size

Z is the Z-value for the desired confidence level (in this case, Z = 1.645 for a 90% confidence level)

p is the estimated population proportion (we don't know this yet, so we will assume a conservative estimate of 0.5)

q is the complementary probability of p (q = 1 - p)

E is the maximum error or margin of error (in this case, E = 0.015)

Plugging in the values, we get:

n = ([tex]1.645^2[/tex] * 0.5 * 0.5) / [tex]0.015^2[/tex]

n = 599.27

Rounding up to the nearest whole number, we get a required sample size of 600.

Therefore, we would need to survey at least 600 randomly selected air passengers to be 90% confident that the sample percentage is within 1.5 percentage points of the true population percentage.

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