HELP

Which of the following equations represents a line that passes through the points (-5,4) and (10,14)

|. y = 6/5x -2
||. 6x+5y=-10

I'll give you brain crown thingy if you get it right

If nth partial sum of series S is given by Sₙ = n+1/n²+1, the value of S is equal to 0.7834.

To find the sum S of the series, we need to take the limit of the nth partial sum as n approaches infinity. This is because the series contains an infinite number of terms, and the sum is the value that the series approaches as we add more and more terms.

We can write the formula for the nth partial sum as:

Sₙ = 1/2 + 2/5 + 3/10 + ... + n/(n²+1)

To find the sum S, we take the limit of Sₙ as n approaches infinity:

S = [tex]\lim_{n \to \infty}[/tex] Sₙ

We can use the formula for the nth partial sum to simplify Sₙ:

Sₙ = 1/2 + 2/5 + 3/10 + ... + n/(n²+1)

= [1/(1²+1)] + [1/(2²+1)] + [1/(3²+1)] + ... + [1/(n²+1)]

= Σ[1/(k²+1)], k=1 to n

Using calculus or other advanced techniques, we can find that the limit of Σ[1/(k²+1)] as n approaches infinity is approximately 0.7834. Therefore, the sum of the series S is approximately:

S ≈ 0.7834

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Therefore, the probability of selecting two Democrats and two Republicans from a committee of four people is approximately 0.476 or 47.6%.

To find the probability of selecting two Democrats and two Republicans from a committee of four people out of a city council consisting of five Democrats and five Republicans, we can use the formula for probability:

Probability = (number of ways to select two Democrats and two Republicans) / (total number of ways to select any four people)

The number of ways to select two Democrats and two Republicans can be found by multiplying the number of ways to select two Democrats from the five available Democrats and the number of ways to select two Republicans from the five available Republicans. This can be expressed as:

(Number of ways to select 2 Democrats from 5 Democrats) * (number of ways to select 2 Republicans from 5 Republicans)

= (5 choose 2) * (5 choose 2)

= 10 * 10

= 100

The total number of ways to select any four people from the city council is:

(Number of ways to select 4 people from 10 people)

= (10 choose 4)

= 210

Therefore, the probability of selecting two Democrats and two Republicans is:

Probability = (number of ways to select two Democrats and two Republicans) / (total number of ways to select any four people)

= 100 / 210

= 10 / 21

≈ 0.476 or 47.6% (rounded to the nearest tenth)

Therefore, the probability of selecting two Democrats and two Republicans from a committee of four people is approximately 0.476 or 47.6%.

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Applying the central angle theorem, we have:

a. m<CBD = 70°   b. m<A = 50°      c. m<CBD = 2x

The central angle theorem states that the measure of the central angle is equal to the measure of its intercepted arc, similarly, the inscribed angle has half of the measure of the intercepted arc and also half of the central angle.

a. m<A = 35°

m<CBD = m(CD)

Find arc CD:

m(CD) = 2(35)

m(CD) = 70 degrees.

m<CBD = 70°

b. m<CBD = m(CD) = 100°

m<A = 1/2(CD)

m<A = 1/2(100)

m<A = 50°

c. If m<A = x, therefore:

m<CBD = 2x

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Answer:

A = 383 [tex]\frac{1}{4}[/tex] m²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

   = [tex]\frac{1}{2}[/tex] × 42 × 18 [tex]\frac{1}{4}[/tex] ( change mixed number to improper fraction )

  = 21 × [tex]\frac{73}{4}[/tex]

  = [tex]\frac{21(73)}{4}[/tex]

   = [tex]\frac{1533}{4}[/tex]

  = 383.25

 = 383 [tex]\frac{1}{4}[/tex] m²

All the rays in tiffany's designs that she is going to use on a stained glass window above her front door are EA , ED , EB , GC GH

Rays are a part of a line that has a fixed starting point but no endpoint.

Rays are written in a specific form

first letter should be the fixed point and the second letter should be point with no endpoint

E is fixed point A is no end point = EA

E is fixed point D is no end point = ED

E is fixed point B is no end point = EB

G is fixed point C is no end point = GC

G is fixed point H is no end point = GH

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The maximum annual variable cost Amber Hawke can have is $2,120.

Number of miles driven by Amber Hawke in a year = 12,000 miles

The annual vehicle fixed cost Amber have is = $2,200

Cost per mile for her compact car = $0.36

To find the maximum annual variable cost we have to solve it as shown below,

(x+$2,200)/12,000 = $0.36      [x is annual variable]

By solving the above equation, we can obtain the annual variable.

(x+$2,200) = $0.36 x 12,000

(x+$2,200)  = $4,320

x = $4,320 - $2,200

x = $2,120

From the above anaylis, we can conclude that Amber Hawke can have maximum of $2,120 annual variable cost.

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Answer:

termined your answer.

One value besides 90% that is included in the interval in which the overall percentage of favorable responses is likely to lie is 88.7%.

To determine this value, we need to subtract the margin of error from the percentage of favorable responses and also add the margin of error to the percentage of favorable responses.

Subtracting 1.3% from 90%, we get:

90% - 1.3% = 88.7%

Adding 1.3% to 90%, we get:

90% + 1.3% = 91.3%

Therefore, the interval in which the overall percentage of favorable responses is likely to lie is 88.7% to 91.3%.

The requried ball reached a maximum height of approximately 62 feet

Let the ball is thrown vertically upward, we can use the following formula to find the maximum height it reaches:

[tex]h(t) = -16t^2 + vt + h_0[/tex]

here, h(t) is the height of the ball at time t, v is the initial velocity of the ball (in feet per second), and h0 is the initial height of the ball (in feet). We can also use the fact that the ball remains in the air for 3.8 seconds, which means that the time it takes to reach the maximum height is half of that or 1.9 seconds.

At the highest point, the ball's velocity is zero, so we can find the initial velocity by setting v = 0 in the above formula and solving for h₀:

h₀ = h(t) + 16t²

   = 4 + 16(1.9)²

   ≈ 4 + 57.76

   ≈ 61.76

Therefore, the ball reached a maximum height of approximately 62 feet

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Step-by-step explanation:

The answer is C because 60 ÷ 20 is 3 that means he take 3 mins to red every page and 25 × 3 = 75 so yeah.

Answer:

A

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{2}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

2x = 2[tex]\sqrt{2}[/tex] ( divide both sides by 2 )

x = [tex]\sqrt{2}[/tex]

the triangle is a 45- 45- 90 and is isosceles with congruent legs, then

x = y = [tex]\sqrt{2}[/tex]

The required width of the aquarium is 1.5033 feet.

To find the width of the aquarium, we can use the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

We are given the length and height of the aquarium, as well as its volume (33.75 gallons). However, the volume is in gallons, while the dimensions are in feet. We need to convert the volume to cubic feet so that we can use the formula.

1 gallon is equivalent to 0.13368 cubic feet (approximately). Therefore, we have:

Volume = 33.75 gallons x 0.13368 cubic feet/gallon

Volume = 4.51 cubic feet

Now we can substitute the given values into the formula and solve for the width:

4.51 cubic feet = 2 feet x Width x 1.5 feet

Simplifying the equation, we have:

Width = 4.51 cubic feet / (2 feet x 1.5 feet)

Width = 1.5033 feet (rounded to four decimal places)

Therefore, the width of the aquarium is approximately 1.5033 feet.

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[tex]\tan(A )=\cfrac{\stackrel{opposite}{15}}{\underset{adjacent}{36}} \implies \tan(A)=\cfrac{5}{12}[/tex]

The next term of the geometric sequence is A₆ = -273

Given data ,

Let the geometric progression be represented as A

Now , the value of A is

A = -1, -3, -9, -27, -81,...

The common ratio in this sequence is -3/-1 = 3.

To find the next term, we multiply the last term (-81) by the common ratio (3):

-1, -3, -9, -27, -81, -243

Hence , the 6th term of the GP is -243

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Step-by-step explanation:

Area of a triangle=½ × b × h

²/15 = ½ × b × ²/5

²/15 = ½b × ²/5

²/15 = ¹/5b

²/15 ÷ ¹/5 = ¹/5b ÷ ¹/5

²/15 ÷ ¹/5 = b

²/15 × 5/1 = b

⅔ = b

Therefore the length of the base is ⅔ft.

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The value of ∠A for given problem will be 38.68°.

If 2 sides of right angled triangle are given, trignometric ratios can be used to find the value of missing angles as:

[tex]sin\theta= opposite\;side\;/\;hypotenuse[/tex]

[tex]cos\theta= adjacent\;side\;/\;hypotenuse[/tex]

[tex]tan\theta= opposite\;side\;/\;adjacent\;side[/tex]

where, perpendicular of triangle( side opposite to the angle θ) is called opposite side. and base( side adjacent to angle θ) is called adjacent side.

For given problem, given, (for ∠A)

opposite side(BC): 5

hypotenuse(AB): 8

[tex]sin\theta= 5\;/\;8[/tex]

[tex]\theta=sin^{-1} \;(5\;/\;8)[/tex]

[tex]\theta=38.68\textdegree[/tex]

Therefore, angle A= 38.68°

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Answer:

Graph B

Step-by-step explanation:

Graph B is not a function, because it fails the "vertical line test". Which means the plots that would be placed on the line intersecting the X axis would have the same X value, and X values CANNOT repeat when it comes to functions. So the Answer is B because the X Values would repeat if you were to write the coordinates of the points down.

The domain of the function in the graph is the set of all real numbers.

For an equation of the form:

y = f(x)

We define the domain as the set of possible inputs for the equation, that is, the possible values of x.

Remember that the values of x appear on the horizontal axis. Now, if you look at the given graph, you can see that the function keeps going in both directions (left and right). Then it covers the whole horizontal axis, which means that the domain is the set of all real numbers.

So the correct option is the last one.

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The statements regarding the scatter plot are given as follows:

The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:

(Years of experience,  yearly income).

As the line of best fit is an increasing line, there is a positive linear association between years of experience and yearly income.

For a person with 14 years of experience, we have point (14,50) on the line of best fit, meaning that a good estimate is of $50,000.

Outliers are in fact points away from the line of best fit, which is the case for item b.

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We can be 90% confident that the true population proportion lies between 0.433 and 0.567.

In statistics, proportion refers to the percentage or fraction of a population or sample that possesses an important trait.

If we wanted to know, for instance, what percentage of individuals in a particular city possessed cars, we would pick a sample of people from that city, count how many of them did, and express that number as a percentage of the whole sample size.

When drawing conclusions about a wider population from a sample, proportions are frequently used. Based on the sample proportion, one can estimate or evaluate the population proportion using confidence intervals and hypothesis tests.

A range of values used to estimate or define a population parameter, such as a mean, percentage, or variance, is referred to in statistics as an interval. The lower and upper bounds of an interval estimate are determined using the sample data and a degree of confidence or probability.

For instance, a range of values near the sample mean that we may reasonably be convinced contains the true population mean would make up a confidence interval for the population mean. The margin of error reveals the accuracy of the estimate, while the confidence level shows the likelihood that the interval contains the actual population mean.

According to question,

We can apply the following formula to create a confidence interval for a population proportion:

Confidence Interval is calculated as Sample Proportion +/- Error Margin.

where the margin of error takes into account the uncertainty in calculating the population proportion from the sample proportion and the sample proportion is the portion of the sample that possesses the feature of interest.

The sample proportion in this instance is:

x/n = 75/150 = 0.5

The following formula can be used to determine the margin of error:

Error margin is equal to z*√(p(1-p)/n)).

where z is the desired level of confidence's associated z-score. Using a typical normal distribution table, the z-score is 1.645 with a 90% degree of confidence.

When we enter the values, we obtain:

1.645√(0.5(1-0.5)/150) = 0.067 is the margin of error.

the 90% confidence interval for the population proportion is:

0.5 +/- 0.067, or (0.433, 0.567)

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The actual length of roof of house is 25 feet.

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

From the given figure, model has 24 inches and roof has 15 inches and the base angle of roof is 37°.

The actual house dimension is 40 feet.

40 feet = 480 inches

a) Scale factor = 24/480

= 1/20

So, measure of actual roof is 1/20 = 15/x

x=300 inches

300 inches = 300/12 = 25 feet

b) Using cosine rule formula

25=√(40²+25²-2×40×25 cosC)

625=2225-2000cosC

-1600=-2000cosC

cosC=4/5

cosC=0.8

∠C=37°

Therefore, the actual length of roof of house is 25 feet.

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In the Venn diagram , the given statement is valid.

What is Venn diagram?

Venn diagrams are frequently used in mathematics, statistics, logic, teaching, linguistics, computer science, and business. They are also known as Set diagrams or Logic diagrams.

Here the given Venn diagram , the Jimmy is one of the kids. because from all kids  some are rude and some are not rude .Then the given statement is Valid.

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The table that represents the relationship between the number of cheesecakes the bakery makes & the number of blocks of cream cheese the bakery uses is option- D, found using unitary-method.

What is unitary-method?

The unitary method is used to evaluate the value of a single unit or object, and then we can evaluate the necessary value by multiplying the single unit value. The unitary method involves determining the value of a single unit before determining the value of the necessary quantity of units. In the unitary method, the value of one unit quantity is determined before the values of the other units are determined. Direct variation and inverse variation are the two forms of variations.

Given that number of cheesecakes that can be made using 6 blocks of cream cheese is 72 cheesecakes

6 blocks of cheese= 72 cheesecakes

1 block of cheese = 72 ÷ 6 cheesecakes

                             = 12 cheesecakes.

2 blocks of cheese= 12 x 2 cheesecakes

                               =24 cheesecakes

3 blocks of cheese = 12 x 3 cheesecakes

                                = 36 cheesecakes

6 blocks of cheese = 12 x 6 cheesecakes

                                =72 cheesecakes

7 blocks of cheese = 12 x 7 cheesecakes

                                =84 cheesecakes

8 blocks of cheese = 12 x 8 cheesecakes

                                =96 cheesecakes

12 blocks of cheese = 12 x 12 cheesecakes

                                =144 cheesecakes

13 blocks of cheese = 12 x 13 cheesecakes

                                =156 cheesecakes

18 blocks of cheese = 12 x 18 cheesecakes

                                =216 cheesecakes

25 blocks of cheese = 12 x 25 cheesecakes

                                =300 cheesecakes

The option in which the cheesecakes directly variate with cheese blocks is option -D

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Refer to the attachment for the options.

Answer:

Step-by-step explanation:

Area is equal to 1/2 times base times height

1/2 × 4 × 8= 16 m²

Answer:

16m

Step-by-step explanation:

area = base x height x 1/2

4 x 8 x 1/2

4 x 8 = 32

32 x 1/2= 16

Bulk Pete's has the smaller unit price, so that coffe has the better price.

First, we know that five pounds of Kroger Dark Ground at $17.81, then the cost of a single pound of this cofee is given by the quotient:

$17.81/5 lb = $3.56 per lb.

That is the unit price of this coffe

While we know that Bulk Pete's Italian Roast at $3.11 per pound.

So we already can see that Bulk Pete's coffec has a smaller cost per pound, so that one has the better price.

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The length AC of the triangle ABC to the nearest whole number would be = 28

To calculate the missing length of the triangle, the sine rule can be used. That is , a/sinA = b/sinB.

Where;

a= 20

A= 30°

b= ?

B= 45°

That is;

20/sin30° = b/sin45°

b= 20× 0.707106781/0.5

b= 14.14213562/0.5

b= 28.28

b= 28

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1. Exponential function would best fit the data because as x increases the y values change 2. Multiplicatively. The 3. common ratio of this function is approximately 4. 0.993.

An exponential function is a mathematical function of the form f(x) = a raised x, where x is the variable (often a real integer) and an is a constant (referred to as the exponential function's base). The variable x occurs in the exponent of this function, which results in a quickly growing (or decreasing) curve as x rises or falls.

Numerous crucial applications of exponential functions can be found in disciplines like engineering, biology, physics, and finance. They are used to simulate phenomena like exponential population expansion, radioactive decay, and compound interest that expand or degrade over time. The base a number, which might be larger or less than 1, defines the pace of growth or decay of the function.

From the given table we see that the relation between the values of x and f(x) is exponential.

This is because as the value of x increases the value of f(x) changes multiplicatively.

Since, the function is exponential there is a slope or common ratio between f(1) and f(2) would be 39496/39775 = 0.993.

Hence, 1. Exponential function would best fit the data because as x increases the y values change 2. Multiplicatively. The 3. common ratio of this function is approximately 4. 0.993.

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Answer:

C. 25; 56

Step-by-step explanation:

In a stem and leaf plot the number on the left (the stem) is the first digit, and the numbers on the right are the second digits so the first number has a 2 in the first place and a 5 in the second place and the last number has a 5 in the first place and a 6 in the last place

The relationship between pints and cups where p represents pints and n represents cups is n = 2p.

We have,

3 cups converts to 1.5 pints

and 5 cups converts to 2.5 pints.

We know from constant of proportionality

y = kx

k = y/x

Put y= 2.5 and x= 5

Then, k = 5/2.5

k = 2

So, the relationship between pints and cups where p represents pints and n represents cups is

n = 2p

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