ab= 6 / a+b = 5

find a² + b²

If the first and last terms of an arithmetic series are 5 and 27, respectively, and the sum of the series is 192, then the number of terms in the series can be calculated as 12.

To find the number of terms in the arithmetic series, we can use the formula for the sum of an arithmetic series:

Sum = (n/2)(first term + last term)

We are given the first term (5), the last term (27), and the sum (192). Plugging these values into the formula, we have:

192 = (n/2)(5 + 27)

Simplifying the equation:

192 = (n/2)(32)

192 = 16n

Dividing both sides of the equation by 16:

n = 192/16

n = 12

Therefore, the number of terms in the arithmetic series is 12.

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Just take it in co-ordinate pairs

Take two points

Slope:-

\(\\ \sf\longmapsto m=\dfrac{40-60}{41-58}\)

\(\\ \sf\longmapsto m=\dfrac{-20}{-17}\)

\(\\ \sf\longmapsto m=\dfrac{20}{17}\)

\(\\ \sf\longmapsto m\approx 1.2\)

Equation of line in point slope form

\(\\ \sf\longmapsto y-y_1=m(x-x_1)\)

\(\\ \sf\longmapsto y-60=1.2(x-58)\)

\(\\ \sf\longmapsto y-60=1.2x-69.6\)

\(\\ \sf\longmapsto 1.2x-y-9.6=0\)

\(\\ \sf\longmapsto y=1.2x-9.6\)

Graph attached

Answer:

Here's what I get.

Step-by-step explanation:

1. Representation of data

I used Excel to create a scatterplot of the data, draw the line of best fit, and print the regression equation.

2. Line of best fit

(a) Variables

I chose arm span as the dependent variable (y-axis) and height as the independent variable (x-axis).

It seems to me that arm span depends on your height rather than the other way around.

(b) Regression equation

The calculation is easy but tedious, so I asked Excel to do it.

For the equation y = ax + b, the formulas are

(DOWN BELOW)

This gave the regression equation:

y = 1.0595x - 4.1524

(c) Interpretation

The line shows how arm span depends on height.

The slope of the line says that arm span increases about 6 % faster than height.

The y-intercept is -4. If your height is zero, your arm length is -4 in (both are impossible).

(d) Residuals

The residuals appear to be evenly distributed above and below the predicted values.

A graph of all the residuals confirms this observation.  

The equation usually predicts arm span to within 4 in.

(e) Predictions

(i) Height of person with 66 in arm span

(ii) Arm span of 74 in tall person

The correct answer is option A which is y = 25x + 100.

Given the following:

To join a local square dancing group, Jan has to pay a $100 sign-up fee plus $25 per month

We need to write an equation for the cost (y) based on the number of months.

To solve the above problem, the answer is;a. y = 25x + 100

Explanation; Let's break down the problem

The $100 sign-up fee is a fixed cost that is added only once to the monthly fee which is $25. Thus the equation for the cost (y) based on the number of months can be expressed as; y = 25x + 100 where:y is the cost for the number of monthsx is the number of months

Therefore the correct answer is option A which is;y = 25x + 100.

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To join a local square dancing group,

Jan has to pay a $100 sign-up fee plus $25 per month.

The equation for the cost (y) based on the number of months is

y = 25x + 100,

where x is the number of months.

Option A is the correct equation for the cost based on the number of months.

Writing the equation:

y = 25x + 100

Where:

y = Cost based on the number of months

x = Number of months

Therefore, when Jan has been part of the local square dancing group for 1 month, the total cost will be:

$25 * 1 + $100 = $125

And if Jan has been a part of the group for 4 months, then the total cost would be:

$25 * 4 + $100 = $200

Therefore, option A is the correct answer.

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Let x = the number of games. The problem can be rewritten as a system of equations:

Person 1 = 72.48 + 6x

Person 2 = 18.08x

We are looking for when the number of games for both are the same; so:

72.48 + 6x = 18.08x

Then:

72.48 = 18.08x - 6x

72.48 = 12.08x

x = 72.48/12.08

x = 6

For diameter 12 inches the would take approximately 904.78 cubic inches of air to inflate the soccer ball.

Diameter is a straight line segment that passes thrοugh the center οf a circle οr sphere, cοnnecting twο pοints οn the circumference. It is the lοngest chοrd οf the circle οr sphere and its length is twice the radius.

Tο find οut hοw much air is needed tο inflate the sοccer ball, we need tο first calculate the vοlume οf the ball. The fοrmula fοr the vοlume οf a sphere is:

V = (4/3)π\(r^3\)

where r is the radius of the sphere.

Since the diameter of the soccer ball is 12 inches, the radius is half of that, or 6 inches. We can substitute this value into the formula and simplify:

V = (4/3)π(\(6^3\)) = 904.78 cubic inches

This is the volume of the fully inflated soccer ball. If the ball is currently deflated, we need to add enough air to bring its volume up to 904.78 cubic inches.

The amount of air needed will depend on the pressure of the air being used to inflate the ball. If we assume that the pressure is constant, we can use the ideal gas law to calculate the volume of air needed:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.

Since we are assuming that the pressure and temperature are constant, we can simplify the formula to:

V = (n/R)P

where n/R is a constant for a given amount of gas, and P is the pressure.

Without knowing the pressure of the air being used, we cannot calculate the exact amount of air needed. However, we can assume a standard pressure of 14.7 pounds per square inch (psi) and use this to calculate the volume of air needed.

Assuming a pressure of 14.7 psi, we can calculate the volume of air needed as follows:

V = (n/R)P = (1/14.7)(14.7) = 1 cubic inch

Therefore, it would take approximately 904.78 cubic inches of air to inflate the soccer ball. However, the exact amount of air needed will depend on the pressure of the air being used.

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Overall, a bar graph would effectively convey the color information of fish found in Lake Powell by visually representing the different color categories and their corresponding frequencies or proportions.

The best option would depend on the specific data and purpose of the visualization. However, if the goal is to represent the color categories of fish in Lake Powell, a bar graph could be a suitable choice. Each bar would represent a color category, and the height of the bar could represent the frequency or proportion of fish in that color category.

By assigning each color category to a bar and varying the height of each bar based on the frequency or proportion of fish in that category, the bar graph provides a clear and visual representation of the distribution of fish colors in Lake Powell.

This allows viewers to easily compare the prevalence of different color categories, identify any dominant or rare colors, and gain insights into the overall color composition of the fish population in the lake.

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Answer:

400 centimeters

Step-by-step explanation:

hope this helps. have a nice day

Answer:

70

Step-by-step explanation:

If y=30 when x=6, 5x=y (because they are in direct proportion).

So, when x=14 replace x.

5*14=y

y=70

you can prove this because 70/14=30/6=5

so, the proportions are equal

Answer:

Susan has:

40 nickels & 10 dimes

Step-by-step explanation:

Since she has a total of 50 nickles and dimes I knew that it could be separated into 5 sets of 10. Knowing that 4(10) is equal to 40+10 is equal to 50, I used the 10 for the amount of dimes and used 40 for the amount of nickles. So the nickles (40) are 4 times the dimes (10). We can prove this by multiplying the dimes by 4 (4(10)) and you get 40 and add on the 10 you get the total amount of 50.

I hope this helps:)

There are 40 nickels and 10 Dimes.

Two or more expressions with an Equal sign is called as Equation.

Let N be the number of nickels

Let D be the number of dimes

Susan has a collection of 50 nickels and dimes.

N + D =50...(1)

Number of nickels is four times the number of dimes

N = 4D    

Substitute N in equation 1

4D+D=50

5D=50

Divide both sides by 5

D=10

Now put D value in equation 1

N+10=50

Subtract 10 from both sides

N=40  

Hence, there are 40 nickels and 10 Dimes.

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Answer:

17 months for the mini ipad and 120 after 3 months

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

.25x + .125x + 24 = 60

.25x + .125x = .375x

.375x + 24 = 60

60 - 24 = 36

.375x = 36

36/ .375

x = 96

Answer:

96

Step-by-step explanation:

I TOOK IT ON EDGGGGGGG

Answer:

15

Step-by-step explanation:

Replace each instance of 'x' with '(-6):'

f(-6) = 3 - 2(-6)

       = 3 + 12 = 15

Answer:11486.34

Step-by-step explanation:

p is semiperimeter

p=(a+b+c)/2

p=(174+138+188)/2

For Heron equation,

S=\(\sqrt{p*(p-a)*(p-b)*p-c}\)

so, it is 11487.34

Answer:

  11,486.3 square units

Step-by-step explanation:

You want the area of the triangle with side lengths a=174, b=138, c=188.

The area of a triangle can be found from the lengths of the three sides using Heron's formula:

  A = √(s(s -a)(s -b)(s -c)) . . . . . . . where s = (a+b+c)/2, the "semiperimeter"

The calculation is shown in the second attachment.

  s = (174 +138 +188)/2 = 500/2 = 250

  A = √(250(250 -174)(250 -138)(250 -188)) = √(250(76)(112)(62))

  A = √131936000 ≈ 11486.3

The area of the triangle is about 11486.3 square units.

__

Additional comment

An effectively equivalent way to find the area is to use the Law of Cosines to find an angle, then use the trig formula for the area.

  C = arccos((a²+b²-c²)/(2ab)) = arccos(13976/48024) ≈ 73.080899°

  Area = 1/2(ab·sin(C)) = 1/2(24012·0.9567166) ≈ 11486.3

We say this is "effectively equivalent" not only because it gives the same area, but because using the relation between cos(C) and sin(C), you can demonstrate that this formula gives Heron's formula for the area.

The probability that it takes from 2 to 3 minutes to fill an order is approximately 0.2562 or 25.62%.

Given that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes.

We know that the probability density function (PDF) of exponential distribution is given by:

f(x) = (1/β) * e^(-x/β)

where β is the mean of the distribution.

Therefore, in this case, the PDF is:

f(x) = (1/1.5) * e^(-x/1.5)

To find the probability that it takes from 2 to 3 minutes to fill an order, we need to calculate the area under the PDF curve between 2 and 3 minutes.

P(2 < x < 3) = ∫2^3 f(x) dx

= ∫2^3 (1/1.5) * e^(-x/1.5) dx

= [-e^(-x/1.5)]2^3

= e^(-2/1.5) - e^(-3/1.5)

= 0.2562

Therefore, the probability that it takes from 2 to 3 minutes to fill an order is approximately 0.2562 or 25.62%.

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The Solution to the given questions are:

A central angle is an angle whose vertex is at the centre of a circle and whose sides intersect the circle at two distinct points. The measure of a central angle is equal to the measure of the arc intercepted by the angle, where the arc is the portion of the circle between the two points of intersection.

An intercepted arc is a segment of a circle's circumference that is bounded by two points on the circle and contains all the points of the circle's circumference that lie between those two points. In other words, it is the portion of the circle that is "cut out" or intercepted by two points on the circle.

In this given question,

The circumscribed angle can be measured by dividing the central angle by 2.

Hence,

112°/2= 56°.

Therefore, the measurement of circumscribed angle is 56°.

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the fox population in a certain region has an annual growth rate of 8 percent per year. it is estimated that the population in the year 2000 was 7600.

(a) function model for the t year after 2000 (exponential model):

\(p(t) = 7600 (1.08)^t\)

The function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the another variable).

A function is described as a relationship between a group of inputs and one output each. A function is, to put it simply, a connection between inputs in which each input is connected to exactly one output.

Population in 2000,

P(0) = 7600

Growth rate = 8% each year

(a) function model for the t year after 2000 (exponential model):

\(p(t) = 7600 (1.08)^t\)

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Answer:

y=1/3x+4

Step-by-step explanation:

Answer:

2826 ft

Step-by-step explanation:

area of a circle equals \(\pi r^{2}\) so first we square the radius.

\(30^{2}\) =900

Now use 3.14 as pi

\(900*3.14= 2826\)

The given equation is

Subtracting 7x from 10x, we get

Subtracting 1 from both sides, we get

Dividing both sides by -3, we get

Hence the answer is x=-12.

Answer:

B. x= -12

Step-by-step explanation:

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

Check the picture below.

so we only want the area in pink.

\(\stackrel{\textit{left and right}}{2(4)(11)}~~ + ~~\stackrel{\textit{front and back}}{2(4)(11)}\implies \text{\LARGE 176}~cm^2\)

Answer:

not 100% sure what the question is

but he has 85 movies

that are about 9350 minutes runtime which is about 155.8 hours of film

Step-by-step explanation:

The number that, when raised to the power of three, equals 500000 is approximately 100.

To find this number, we can use the cube root function:

x^3 = 500000

x = cube root of (500000)

x = approximately 100

So, the number that, when raised to the power of three, equals 500000 is approximately 100.

Answer:

1 pounds of grapes it is 7.98$

Step-by-step explanation:

HOPE THIS HELPS

PLZZ MARK BRAINLIEST

The U.S. government used coercive treaties, broken promises, military force, and economic pressures to persuade Native Americans to settle on reservations, often resulting in displacement and loss of land.

The history of Native American reservations in the United States is complex and multifaceted. While it is important to note that not all Native Americans were tricked into settling on reservations, there were various factors and events that led to the establishment of reservations and the displacement of Native peoples. Here are some key points:

Treaties and Agreements: In the 19th century, the U.S. government negotiated numerous treaties and agreements with Native American tribes. These agreements were often presented as a means to protect tribal lands, resources, and cultural autonomy. However, some of these treaties were negotiated under coercive circumstances, with unequal bargaining power and the threat of military force.

Broken Promises: Many of the treaties and agreements made between the U.S. government and Native American tribes were not honored. The government frequently violated its promises and encroached upon tribal lands, often due to the discovery of valuable resources like gold, timber, or fertile land. This led to the forced removal of Native peoples from their ancestral territories.

Indian Removal Act: In 1830, the Indian Removal Act was passed by the U.S. Congress. This legislation authorized the relocation of Native American tribes from their homelands to designated reservations in the West. The act was justified under the premise of opening up land for white settlement and facilitating the assimilation of Native Americans into Euro-American society.

Military Force: In some cases, the U.S. government used military force to remove Native American tribes from their lands and confine them to reservations. The most well-known example is the forced relocation of thousands of Cherokee people along the Trail of Tears in the 1830s.

Economic and Social Pressures: Native American communities faced increasing economic and social pressures as European settlers expanded westward. Encroachment on tribal lands, depletion of natural resources, introduction of diseases, and the decline of traditional livelihoods further marginalized Native peoples and made the reservations appear as a solution to their dire circumstances.

It is essential to approach this topic with sensitivity and recognize the diverse experiences and perspectives of Native American tribes throughout history. The process of reservation establishment involved a complex interplay of political, economic, and social factors, and it is not accurate to portray it solely as a deliberate trickery by the government.

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Answer:

option c is incorrect

because the value of tan B will be perpendicular/base

so tan B=5/12.

mark me brainlist

The mean number of claims per policy is 1.4 and the sample variance and standard deviation are 0.956 and 0.977 respectively is the answer.

a) To find the mean number of claims per policy, we need to calculate the weighted average of the number of claims.

Number of claims: 0, 1, 2, 3, 4, 5, 6

Number of policies: 21, 13, 5, 4, 2, 3, 2

First, we calculate the product of the number of claims and the corresponding number of policies for each category:

0 claims: 0 * 21 = 0

1 claim: 1 * 13 = 13

2 claims: 2 * 5 = 10

3 claims: 3 * 4 = 12

4 claims: 4 * 2 = 8

5 claims: 5 * 3 = 15

6 claims: 6 * 2 = 12

Next, we sum up these products: 0 + 13 + 10 + 12 + 8 + 15 + 12 = 70

Finally, we divide the sum by the total number of policies (50) to find the mean:

Mean number of claims per policy = 70 / 50 = 1.4

Therefore, the mean number of claims per policy is 1.4.

b. To find the sample variance and standard deviation, we need to calculate the deviations from the mean for each category, square the deviations, and then calculate the average.

Deviation from the mean:

0 - 1.4 = -1.4

1 - 1.4 = -0.4

2 - 1.4 = 0.6

3 - 1.4 = 1.6

4 - 1.4 = 2.6

5 - 1.4 = 3.6

6 - 1.4 = 4.6

Square the deviations:

(-1.4)^2 = 1.96

(-0.4)^2 = 0.16

(0.6)^2 = 0.36

(1.6)^2 = 2.56

(2.6)^2 = 6.76

(3.6)^2 = 12.96

(4.6)^2 = 21.16

Now, we sum up these squared deviations:

1.96 + 0.16 + 0.36 + 2.56 + 6.76 + 12.96 + 21.16 = 46.92

To find the sample variance, divide the sum of squared deviations by the number of data points minus 1 (n-1):

Sample variance = 46.92 / (50 - 1) = 46.92 / 49 ≈ 0.956

To find the sample standard deviation, take the square root of the sample variance:

Sample standard deviation = √(0.956) ≈ 0.977

Therefore, the sample variance is approximately 0.956 and the sample standard deviation is approximately 0.977.

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Answer:

6060 feet

Step-by-step explanation:

6371-311=6060