On the coordinate plane, point A is located at ( – 9, – 4) and point B is located at ( – 1,y). The distance between points A and B is 10 units. What are the two possible locations of point B? ,

Step-by-step explanation:

to get a we use cos and for b we use sin

so

cos(45°) =a/5√2....... when u criss cross it

a = cos(45°) × 5√2

a = √2/2 × 5√2

a= 5

sin(45) = b/5√2

b= sin(45) × 5√2

b = 5

In other way if u find the 1st side you r indirectly find the 2nd one which they are equal .

With employees ranging in age from 40 to 30, 36 to 22, there is a 46-year age difference between them. The average difference between each age and the population's mean age is measured.

We employ the following formula to determine the variance of a population:

σ² = Σ(x - μ)² / N

σ² = Σ(x - μ)² / N

where:

σ² =  the population variance

Σ = the sum of

x = the value of each element in the population

μ = the population mean

N = the population size

First, we need to find the population mean:

μ = (40 + 30 + 36 + 22) / 4 = 32

Next, we calculate the sum of the squared deviations from the mean:

(40 - 32)² + (30 - 32)² + (36 - 32)² + (22 - 32)² = 64 + 4 + 16 + 100 = 184

Then, we divide the sum of squared deviations by the population size:

σ² = Σ(x - μ)² / N = 184 / 4 = 46

Therefore, the population variance is 46.

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The actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.

The margin of error in the report stating that a 10-year-old American child spends an average of 20.02 to 25.36 minutes playing outdoors per day can be calculated by subtracting the lower value from the higher value and dividing by 2. In this case, the margin of error is :

To find the margin of error, we need to calculate the halfway point between these two values.
(25.36 - 20.02) / 2 = 2.67

Therefore, the margin of error is approximately 2.67 minutes. This means that the actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.

Thus, the actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.

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Answer:

The equation of the new circle will be x^2 - 10x + y^2 - 12y + 25 = 0.

Step-by-step explanation:

A graph of the image of W(10, 1) after a rotation 90° counterclockwise around the origin is shown in the image attached below.

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise around the origin to vertices W, the coordinates of the vertices of the image ΔA'B'C' are as follows:

(x, y)                               →            (-y, x)

Ordered pair W = (10, 1) → Ordered pair W' = (-1, 10)

In this exercise, we would use an online graphing calculator to plot the image of W after a rotation of 90° counterclockwise around the origin.

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Answer:

To change Tim's running rate from kilometers per hour to minutes per mile, we need to use unit conversion factors.

First, we need to convert the distance from kilometers to miles. One kilometer is equal to 0.621371 miles. Therefore, 50 kilometers is equal to:

50 km * 0.621371 mi/km = 31.06855 miles

Next, we need to convert the time from hours to minutes. One hour is equal to 60 minutes. Therefore, 4.5 hours is equal to:

4.5 hours * 60 min/hour = 270 minutes

Now, we can calculate Tim's running rate in minutes per mile by dividing the time by the distance:

270 min / 31.06855 miles = 8.69805 minutes per mile

So the expression that will allow Tim to change his running rate to minutes per mile is:

(4.5 hours * 60 min/hour) / (50 km * 0.621371 mi/km)

Step-by-step explanation:

duh

If the population standard deviation of a sample increases without other changes, the confidence interval is most likely to widen.

This is because the standard deviation is a measure of the spread of the data, so if it increases, the data points are more spread out from the mean. As a result, the range of values that could reasonably contain the true population parameter (i.e., the confidence interval) needs to be wider to account for the increased variability in the sample.
If the population standard deviation of a sample increases without other changes, the confidence interval is most likely to become wider.
When standard deviation increases, it indicates more variability in the data. As a result, the confidence interval, which is a range of values that estimates the true population parameter with a certain level of confidence, needs to be wider to account for the increased variability. This ensures that the true population parameter is still captured within the interval with the same level of confidence.

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The three intervals do you have the most confidence that the interval captures the population mean (x) is (2.4, 4.5). option (b).

An interval is a range of values that is used to estimate a population parameter, such as the mean.

To answer your question, let's look at the three intervals you provided: (1) (1.3, 4), (2) (2.5, 4.5), and (3) (2, 5). We want to determine which interval has the highest level of confidence in capturing the population mean.

Interval (1) has a range of 2.7 units, which is relatively large. This means that it is possible that the true population mean could fall anywhere within this range.

Interval (2) has a smaller range of 2 units, which means that it is more likely to capture the true population mean. Interval (3) has the largest range of 3 units, which makes it less likely to capture the true population mean compared to interval (2).

Hence the correct option is (b).

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Complete Question:

For which of the three intervals do you have the most confidence that the interval captures the population mean (x)?

a) (13,4)

(b) (2.5, 4.5)

(c) (2,5)

Answer:

Hope this helps :)

Step-by-step explanation:

[tex]10^{27} =-5x[/tex]

The statement provided is actually the opposite of the correct definitions.

In database terminology, a field refers to a single piece of information that is stored in a database table. A field can contain a variety of data types such as text, numbers, dates, and so on. For example, in a database table of customer information, there might be fields for the customer's name, address, phone number, and email.

A record, on the other hand, is a complete set of information about an entity in a database. A record consists of a collection of fields that are all related to each other. For example, in the customer information table mentioned above, a single record might represent a specific customer, and would contain all the fields related to that customer (name, address, phone number, email, etc.).

So to summarize, a field is a single piece of information within a record, while a record is a collection of related fields that together represent a complete set of information about an entity in a database.

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Answer:

min=28

lower=34

median=39

upper=46.5

max=55

inter range=12.5

Step-by-step explanation:

Nice that the numbers are in order for you

The min is your smallest number = 28

To find the next part separate into 4 equal parts so you have 3 lines

The first line is between 34 and 34 the average of the 2 numbers is your lower quartile

lower quartile =34

middle line is your median between 39 and 39

median = 39

upper quartile is that 3rd line between 42 and 51 average is upper

upper quartile = (42+51)/2 = 46.5

max is the highest number = 55

Interquartile range is the difference between upper and lower = 12.5

Answer:

Step-by-step explanation:

By the principle of mathematical induction, the equation 2+7+12+17. +[5n-3]=n/2[5n-1] holds for all positive integers n.

To prove that the equation 2+7+12+17+...+[5n-3] = n/2[5n-1] holds for all positive integers n using mathematical induction, we need to show two things:

Base case: Prove that the equation holds for n=1.

Inductive step: Assume that the equation holds for n=k, and then show that it also holds for n=k+1.

Base case:

When n=1, we have:

2 = 1/2[5(1)-1]

2 = 1/2[4]

2 = 2

Therefore, the equation holds for n=1.

Inductive step:

Assume that the equation holds for n=k, i.e.,

2+7+12+17+...+[5k-3] = k/2[5k-1]

Now, we need to show that the equation also holds for n=k+1, i.e.,

2+7+12+17+...+[5(k+1)-3] = (k+1)/2[5(k+1)-1]

We can simplify the left-hand side of the equation as follows:

2+7+12+17+...+[5(k+1)-3] = [2+7+12+17+...+[5k-3]] + [5(k+1)-3]

Using the assumption from the inductive step, we can substitute k/2[5k-1] for the first part of the equation:

2+7+12+17+...+[5(k+1)-3] = k/2[5k-1] + [5(k+1)-3]

Simplifying the right-hand side of the equation:

2+7+12+17+...+[5(k+1)-3] = (5k² - k + 10k + 5) / 2

2+7+12+17+...+[5(k+1)-3] = (5k² + 9k + 5) / 2

2+7+12+17+...+[5(k+1)-3] = (k+1)/2[5(k+1)-1]

Therefore, the equation holds for n=k+1.

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The triangles given are congruent.

Given are three triangles, we need to state their properties.

So, as we can see that the triangles are following the reflection transformation,

The red triangle is being reflected to form green triangle and green is reflected to form blue triangle.

Since, the reflection transformation forms congruent figures hence the triangles are congruent.

Hence, the triangles given are congruent.

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Step-by-step explanation:

Let's call the length of the base of the triangle "b". We know that the height of the triangle is double the length of the base, so the height can be written as "2b".

We also know that the area of the triangle is approximately 200 square feet. The formula for the area of a triangle is:

A = (1/2)bh

where A is the area, b is the length of the base, and h is the height.

We can substitute in the values we know:

200 = (1/2)bh

Since we know that h = 2b, we can substitute that in:

200 = (1/2)b(2b)

Simplifying:

200 = b^2

This is the equation we can use to find the length of the sign's base, b.

We can set the equation to: 200 = (1/2) × b × (2b)

To find the length of the sign's base, b, we can use the equation for the area of an isosceles triangle: A = (1/2)bh, where b is the length of the base and h is the height. Since we know that the height is double the length of the base, we can substitute 2b for h in the equation: A = (1/2)b(2b). Simplifying, we get A = b^2. Since we know that the area should be approximately 200 square feet, we can set A = 200 and solve for b: b^2 = 200. Taking the square root of both sides, we get b = 14.14 feet. Therefore, the length of the sign's base should be approximately 14.14 feet.

To find the equation for the length of the base of the sign, we'll use the formula for the area of a triangle, which is:

Area = (1/2) × base × height

Since the height of the triangle is double the length of its base (h = 2b), we can rewrite the equation as:

Area = (1/2) × b × (2b)

The owner of Trixie's Sweets and Treats wants the area of the sign to be approximately 200 square feet. So, we can set the equation to:

200 = (1/2) × b × (2b)

Now we have the equation that you can use to find the length of the sign's base, b.

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Here you go I hope this helps you with 2 pictures here.. continuation of the other enjoy I hope I wasn't too late.

The value of limit, [tex]L = \lim_{n→∞} |\frac{ a_{n+1} }{a_n}| \\ [/tex] < 1, for a series [tex] \sum_{n= 1}^{\infty}a_n \\ [/tex], where [tex]a_n = \frac{ ( 6n + 7)8^{n+4} }{11^n}[/tex], then by ratio test says series is absolutely convergent. So, option(a) is true.

Ratio test is one of that is used to determine the convergence or divergence of infinite series. It states that [tex]L = \lim_{n→∞} |\frac{ a_{n+1} }{a_n}| \\ [/tex]

We have a series, [tex] \sum_{n= 1}^{\infty}a_n \\ [/tex], where [tex]a_n = \frac{ ( 6n + 7)8^{n+4} }{11^n}[/tex]. We have to check the convergence of above series with the help of ratio test. Here, [tex]a_n = \frac{ (6n + 7)8^{n+4} }{11^n}[/tex].

[tex]a_{n+1} = \frac{(6(n+1)+ 7)8^{n + 1+4 }}{11^{n+1}}[/tex]

[tex]= \frac{(6n+ 13)8^{n + 5}}{11^{n+1}}[/tex].

Now, [tex]L = \lim_{n→∞} |\frac{ a_{n+1} }{a_n}| \\ [/tex]

[tex] = \lim_{n→∞} |\frac{\frac{(6n+ 13)8^{n + 5}}{11^{n+1}}}{\frac{(6n +7 )8^{n +4 }}{11^{n}}}|\\ [/tex]

[tex] = \lim_{n→∞} |\frac{(6n+ 13)8^{n + 5}}{11^{n+1}}×\frac{11^{n}}{(6n +7 )8^{n +4 }}|\\ [/tex]

[tex] = \frac{8}{11}\lim_{n→∞} |\frac{6n+ 13}{6n+7 }|\\ [/tex]

[tex] = \frac{8}{11}\lim_{n→∞} |\frac{n(6+ \frac{ 13}{n})}{n(6 +\frac{7}{n} )}|\\ [/tex]

[tex] = \frac{8}{11} = 0.72 [/tex] < 1

=> L < 1 , so, from ratio test ∑an converges absolutely. Hence, series is convergent.

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Complete question:

consider the series [tex] \sum_{n= 1}^{\infty}a_n \\ [/tex], where [tex]a_n = \frac{ ( 6n + 7)8^n }{11^n}[/tex]

in this problem you must attempt to use the ratio test to decide whether the series converges

compute

[tex]L = \lim_{n→∞} |\frac{ a_{n+1} }{a_n}| \\ [/tex]

enter the numerical value of the limit if it converges, inf if the limit for diverges to infinity, minf if it diverges to negative infinity, or div if it diverges but not to infinity or negative infinity.

which of the following statements is true?

a) the ratio test says that the series converges absolutely

.b) the ratio test says that the series diverges.

c) the ratio test says that the series converges conditionally.

d). the ratio test is inconclusive, but the series converges absolutely by another test or tests.

e) the ratio test is inconclusive, but the series diverges by another test or tests

.f) the ratio test is inconclusive, but the series converges conditionally by another test or tests.

enter the letter for your choice here: ?

Answer:

0.75

Step-by-step explanation:

Result:

Taxable income of the individual = Rs. 420,000.

To calculate the taxable income, we will subtract the allowance from the individual's yearly income:

Given:

Yearly income = Rs. 4,44,000

Allowance Rs. 24,000

Taxable Income = Yearly Income - Allowance

Taxable Income = Rs. 4,44,000 - Rs. 24,000

Taxable Income = Rs. 420,000.

Therefore, the taxable income of the individual is Rs. 420,000.

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Answer:

300feet²

Step-by-step explanation:

Calculate the area of a parallelogram

A=b×h(b=base,h=height)

b=20feet,h=15feet

A=20feet×15feet=300feet²

So the area is 300 feet²

Answer:

multiply

Step-by-step explanation:

Example:

3(6+7)

18+21

The weight of the remaining paper is 5/12 pounds.

A ream of printer paper is a standard measure of paper quantity that typically consists of 500 sheets. The weight of a ream of paper depends on the type of paper and its thickness. In this problem, we are given that a ream of printer paper weighs 5 1/4 pounds.

Now, Adam used 1/3 of a ream to print flyers. We can find the weight of the paper Adam used by multiplying 1/3 of the weight of a ream of paper by its weight:

Weight of paper used = (1/3) x 5 1/4 pounds

Weight of paper used = (5/3) x (1 1/4) pounds

Weight of paper used = 6 7/12 pounds

To find the weight of the remaining paper, we need to subtract the weight of the paper used from the weight of the full ream:

Weight of remaining paper = Weight of full ream - Weight of paper used

Weight of remaining paper = 5 1/4 pounds - 6 7/12 pounds

Weight of remaining paper = (21/4) pounds - (79/12) pounds

Weight of remaining paper = (21/4) pounds - (6 7/12) pounds

Weight of remaining paper = (21/4) pounds - (6 7/12) pounds

Weight of remaining paper = (84/12) pounds - (79/12) pounds

Weight of remaining paper = (5/12) pounds

Therefore, the weight of the remaining paper is 5/12 pounds.

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ANSWER

[tex] \frac{9}{4} + \frac{2}{8} \\ \\ = \frac{9 + 2}{4} \\ \\ = \frac{11}{4} \\ \\ = 2.75[/tex]

hope it helps

The volume of the pool is 528 cubic feet.

Determine the volumes of each rectangular prism separately and then add them up to determine the volume of Joanie's pool. The rectangular prisms have the following measurements:

4 ft x 8 ft x 6 ft

12 ft x 2 ft x 10 ft

4 ft x 4 ft x 6 ft

Multiply the first rectangular prism's length, width, and height to determine its volume:

4 ft x 8 ft x 6 ft = 192 cubic feet

Multiply the length, width, and height to determine the volume of the second rectangular prism:

12 ft x 2 ft x 10 ft = 240 cubic feet

Multiply the third rectangular prism's length, width, and height to determine its volume:

4 ft x 4 ft x 6 ft = 96 cubic feet

The volumes of the three rectangular prisms are now added up:

192 cubic feet + 240 cubic feet + 96 cubic feet = 528 cubic feet

Therefore, the pool can hold 528 cubic feet of water.

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The length of teh segment LM in the shape is 2 units

From the question, we have the following parameters that can be used in our computation:

The square

Given that

Diagonal = LN

And

LK = 1

Thel length LN ic alculated as

LN  = 2 * LK

substitute the known values in the above equation, so, we have the following representation

LN  = 2 * 1

Evaluate

LN  = 2

Hence, the length is 2

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Mix fraction 3(6/10) written as a decimal is 3.6.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To write 3 6/10 as a decimal, we can first convert the mixed number to an improper fraction.

To do this, we multiply the whole number (3) by the denominator of the fraction (10) and add the numerator (6):

3 6/10 = (3 x 10 + 6)/10 = 36/10

Next, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

36/10 = (18 x 2)/(5 x 2) = 18/5

Now, we have an improper fraction.

To convert it to a decimal, we can divide the numerator by the denominator using long division or a calculator:

18 ÷ 5 = 3.6

Therefore,

3 6/10 written as a decimal is 3.6.

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The vectors is perpendicular to (-4,2) will be (b) (-1,-2)

The dot product of two vectors is found by multiplying the corresponding components of the vectors and adding the results. which is, if the two vectors are (a, b) and (c, d), their dot product is ac + bd.

To calculate the dot product of (-4, 2) with each of the given vectors:

a) (-3.6):

(-4)(-3.6) + (2)(-3.6) = 14.4 - 7.2 = 7.2

b) (-1, -2):

(-4)(-1) + (2)(-2) = 4 - 4 = 0

c) (2, -3):

(-4)(2) + (2)(-3) = -8 - 6 = -14

d) (4, -8):

(-4)(4) + (2)(-8) = -16 - 16 = -32

Therefore, the vector that is perpendicular to (-4, 2) is option (b) (-1,-2).

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Answer:

  (x -4)² +(y +8)² = 873

Step-by-step explanation:

You want the equation of the circle with center (4, -8) through point (16, 19).

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

The value of r² can be found by evaluating the left-side expression at the given point:

  (x -4)² +(y -(-8))² = (16 -4)² +(19 +8)² = 144 +729

  (x -4)² +(y +8)² = 873 . . . . . . . circle equation

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Answer: $1,100 per month for 10 years, if the account earns 2% per year

Step-by-step explanation: $1,100 per month for 10 years, if the account earns 2% per year What the student or parent is asking is: If they deposit $1,100 per month in a savings/investment account every month for 10 years, and they earn 2% per year, how much will the account be worth after 10 years? Deposits are monthly. But interest crediting is annual. What we want is to match the two based on interest crediting time, which is annual or yearly. 1100 per month. * 12 months in a year = 13,200 per year in deposit Since we matched interest crediting period with deposits, we now want to know: If they deposit $13,200 per year in a savings/investment account every year for 10 years, and they earn 2% per year, how much will the account be worth after 10 years? This is an annuity, which is a constant stream of payments with interest crediting at a certain period. [SIZE=5][B]Calculate AV given i = 0.02, n = 10[/B] [B]AV = Payment * ((1 + i)^n - 1)/i[/B][/SIZE] [B]AV =[/B]13200 * ((1 + 0.02)^10 - 1)/0.02 [B]AV =[/B]13200 * (1.02^10 - 1)/0.02 [B]AV =[/B]13200 * (1.2189944199948 - 1)/0.02 [B]AV =[/B]13200 * 0.21899441999476/0.02 [B]AV = [/B]2890.7263439308/0.02 [B]AV = 144,536.32[/B]

Answer: It moves 60 metres in 60/6 mins, or 10 minutes. Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed

Step-by-step explanation: 10 is your answer

Hope this helps

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