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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.

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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Answer:

Total deposit: $501.6

Total Balance: $985.05

Step-by-step explanation:

Aisha's original total is 523.45. Since she is depositing a check for $435.62 and a check for 65.98, you add both check totals to the original balance, by lining up the numbers and adding down the line. This will be the total deposit:

435.62

+ 65.98

    =

$501.6

$501.6 is the total deposit. To find the total checking balance, add the total deposit to $523.45.

523.45

+501.6

    =

1025.05

This is her total balance before Aisha receives $40.

Next, you subtract what she wants to deposit, $40, since she is taking $40 out of her checking account.

1025.05

- 40.00

   =

985.05

The total checking balance is $985.05

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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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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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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There are 342,700,125,300 ( or 60C11  ) ways of selecting 11 members for a committee from organization of 60 member by applying Combinations.

There are 60 people in total in my organisation where there are 35 women and 25 men.

A committee is to be formed where we need to select 11 people from 60 people of the organization.

The total number of ways the commicommittee can be formed is calculated with the help of combinations and permutations.

Since we are not specified that there will be some order in selection of committee members so we can assume that there is no such order.

Therefore, we apply the formula of combinations as the order of items does not matter in case of combinations.

Number of ways the committee can be formed is = nCr = [tex]\frac{n!}{(n-r)!(r!)}[/tex]

where, n is the total number of people in the organization  and r is the number of people we require in the committee.

Thus, Number of ways the committee can be formed is = 60C11

= [tex]\frac{60!}{(60- 11)!(11!)}[/tex]

= 342,700,125,300

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Answer: 6 units

Step-by-step explanation:

let w=width, a=area, and l=length

given:

w=l-5

a=6

solve with the formula a=l*w

a=l*w

6=l*(l-5)

6=l^2-5l

0=l^2-5l-6

0=(l-6)(l+1)

l=6 or l=-1

the length can't be negative, so l=6

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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The addition of the given expression will gives 6a - 5b

Since we know that numerical expression is an algebraic information stated in the form of numbers and variables that are unknown.

WE are given the expression as;

2a + 3b; 4a - 8b​

We need to add the expression so,

2a + 3b + 4a - 8b​

Combine the like terms then we get;

2a + 4a + 3b - 8b

6a - 5b

The simplification of the given expression will be 6a - 5b.

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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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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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Answer:

0.75

Step-by-step explanation:

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

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 .

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: ?

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: $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:

multiply

Step-by-step explanation:

Example:

3(6+7)

18+21

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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The equation of the circle is given by

Information given in the question

coordinates of the diameter (17, -3) and (-13, 3)

The equation of circle. is given according t the formula

(x - h)²+ (y - k)² = r²

where  

h and k refers to points at the center,

Points at the center is solved by

x-coordinate (h)

= (17 + (-13)) / 2

= 4 / 2

= 2

y-coordinate (k)

= (-3 + 3) / 2

= 0 / 2

= 0

So, the center of the circle is (2, 0).

comparing with the given options only A has centers as (2, 0) hence option A is the best choice

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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:

Having simplified the above equation, the solution to the expression x = 10³⁰

We can simplify the equation using logarithmic rules

1/5 log x - log 1000 = 3

log[tex]x^{1/5}[/tex] - log 1000 = 3

log ([tex]x^{1/5}[/tex] /1000) = 3

[tex]x^{1/5}[/tex] /1000 = 10³

[tex]x^{1/5}[/tex]= 1000  * 10³

[tex]x^{1/5}[/tex] = 10⁶

x = (10⁶)⁵

x =  10³⁰

Therefore, the solution to the equation is x = 10³⁰

Note that the logarithm is the inverse function of exponentiation in mathematics. That is, the exponent to which b must be increased to obtain x is the logarithm of a number x to the base b. For example, since 1000 = 10³, 1000's logarithm base 10 is 3, or log₁₀ = 3.

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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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The equation for the scaled version of the function f(x) = x² is g(x) = a × x²

The function g(x) can be considered a scaled version of the function f(x) = x². To create a scaled version of a function, we can multiply the original function by a scaling factor. Let's call this scaling factor "a." Now, the equation for g(x) can be written as:

g(x) = a ₓ f(x)

Since f(x) = x², we can substitute it into the equation for g(x):

g(x) = a ₓ x^2

In this equation, "a" represents the scaling factor. If "a" is greater than 1, the function g(x) will stretch vertically, meaning its parabola will be more narrow compared to f(x). If "a" is between 0 and 1, the function g(x) will be compressed vertically, resulting in a wider parabola. If "a" is negative, the parabola will be reflected over the x-axis.

In summary, the equation for the scaled version of the function f(x) = x² is g(x) = a × x², where "a" is the scaling factor. Depending on the value of "a," the resulting parabola will be either stretched or compressed vertically, and may be reflected over the x-axis if "a" is negative.

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The integers that are pairwise relative are;

(a) 11, 15, 19

(c) 12, 17, 31, 37

(d) 7, 8, 9, 1

To determine if the integers are pairwise relative, their greatest common divisor (GCD) must be 1.

(a) for first question;

11, 15, 19 have no common factor, so they meet the condition.

(b) for second question; 14, 15, 21

14, 15, 21, 14 and 21 have a common factor of 7, so these integers are not pairwise relative.

(c) for 12, 17, 31, 37, no common factor

(d)  for 7, 8, 9, 1, no common factor other than 1.

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