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A random sample of 30 employees of a local company has been taken to measure the systolic blood pressure (mm hg). using only the sample information, a 99% confidence interval estimate for the mean systolic blood pressure (mm hg) for all employees of the company is 113.206 to 126.794. The value of the sample standard deviation (mm Hg) is approximately 2.639.

To find the sample standard deviation (mm Hg), we need to use the given information. Here is the solution:

Given information:

Sample size, n = 30

Confidence interval = 99%

Confidence interval limits = 113.206 to 126.794

Formula to find standard deviation:

σ = (CI width) / (2 × Zα/2)

Whereσ = Sample standard deviation

CI = Confidence interval width

Zα/2 = Z-score for a given confidence interval

Let's calculate the confidence interval width:

CI width = Upper Limit - Lower Limit

CI width = 126.794 - 113.206

CI width = 13.588

To find the z-score for a 99% confidence interval, we can use a z-table or calculator.

The z-score for a 99% confidence interval is 2.576. So,

substituting the values in the formula, we get:

σ = 13.588 / (2 × 2.576)σ = 13.588 / 5.152σ ≈ 2.639 mm Hg

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Answer:

0

Step-by-step explanation:

if f is an even function, it means that:

f(x) = f(-x) for every x of the domain

So, because 7 is in f's domain, f(7) = f(-7),

and so f(7) - f(-7) = 0

As the confidence in the "interval-estimate" increases, the width of the interval (a) decreases.

The width of a confidence interval is a measure of precision of the estimate. A wider interval indicates less precision, while a narrower interval indicates greater precision.

As the confidence level increases, the corresponding critical value z* also increases it means that we are including more of the distribution in the confidence interval, resulting in a wider interval.

Therefore, the width of interval decreases as our confidence in the interval estimate increases, the correct option is (a).

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The given question is incomplete, the complete question is

As our confidence in an interval estimate increases, the width of the interval :

Select One:

(a) decreases

(b) increases

(c) remains the same

(d) increases or decreases depending on the alpha level.

There are approximately 31 quarters in a jar of 250 coins.

The probability of picking a quarter from a jar of coins is 0.125. To calculate the number of quarters in a jar of 250 coins, we need to use the following formula:

Number of Quarters = Total Number of Coins * Probability of Picking a Quarter

Number of Quarters = 250 * 0.125

Number of Quarters = 31.25

So, there are approximately 31 quarters in a jar of 250 coins.

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area of trapezium is 30 in².

A trapezium is a four-sided geometric figure that has only one pair of parallel sides. It is also known as a trapezoid in some countries. The parallel sides of a trapezium are called the bases, and the non-parallel sides are called the legs. The height (or altitude) of a trapezium is the perpendicular distance between the two bases.

The area of a trapezium is given by the formula:

A =½(a×b)h

where "a" and "b" are the lengths of the parallel sides of the trapezium, and "h" is the height (or perpendicular distance) between the parallel sides.

Length of two parallel side

a=7.7in

b=2.3in

Height of trapezium, h=6in

Area of trapezium=½(a×b)h

=½(7.7+2.3)×6

=3×10

=30in²

Hence, area of trapezium is 30 in².

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Answer:

Min = -1

Max = 3

Step-by-step explanation:

Evaluate the values on the ends of the interval

[tex]f(-10) = \sqrt[3]{-10+9}[/tex]

[tex]f(-10)=\sqrt[3]{-1}[/tex]

[tex]f(-10)= -1[/tex]

[tex]f(18)=\sqrt[3]{18+9}[/tex]

[tex]f(18)=\sqrt[3]{27}[/tex]

[tex]f(18)=3[/tex]

Step-by-step explanation:

remember answer 2.

3. I answered already in my other answer.

remember, the diagonals split the angles in half.

so,

d1 = 50°

4. the tangent ratio is sine/cosine (that is the definition of tangent).

c2 = 40°

sin(40) × 5 = OD (half of BD)

cos(40) × 5 = OC

the tangent ratio is

(sin(40) × 5) / (cos(40) × 5) = sin(40)/cos(40) = OD/OC =

≈ 3.2 / 3.8 = 1.6/1.9 =

= 0.842105263...

control : tan(40) = 0.839099631... close enough (we used round numbers with 3 2 and 3.8 - see again 1. and 2.).

The calculated length of r is 27.18 meters

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

The right triangle

Using the tangent of angle 63 degrees, we have

tan(63) = r/13.85

So, we have

r = 13.85 * tan(63)

When evaluated, we have

r = 27.18

Hence, the length of r is 27.18

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Answer: $91.85

Step-by-step explanation:

19.95 + 41.25 + 30.65

= 91.85

And bro, its not that hard to simply calculate it in your head, or even on a paper. Like literally, there's calculators too

By applying the quadratic formula to simplify the following statement, it is possible to find the value of x, which is 3, 5.

The problem is asking us to find all values of $c$ that satisfy the given equation:

[tex]\frac{c}{c-5} =\frac{c}{c-4}[/tex]

To solve for $c$, we can start by cross-multiplying:

[tex]c(c-4)= 4(c-5)[/tex]

Expanding both sides gives:

[tex]c^2-4c=4c-20[/tex]

Simplifying and rearranging terms, we get:

[tex]c^2-8c+20=0[/tex]

We can now calculate $c$ using the quadratic formula:

[tex]c=[/tex] -b ±[tex]\sqrt{b^2-4ac}[/tex]/2a

Plugging in the values $a = 1$, $b = -8$, and $c = 20$, we get:

c= 8 ± [tex]\sqrt{8^2-4(1)(20)}[/tex]/2(1)

Simplifying, we get:

c = 8 ±[tex]\sqrt{64-80}[/tex]/2

c = 8±[tex]\sqrt{-16}[/tex]/ 2

c = 8 ±[tex]\sqrt{4}[/tex]/2

c = 8± 2/2

c = 4±1

So the solutions are:

c= 3,5

Therefore, the values of $c$ that satisfy the equation are $c = 3$ and $c = 5$.

The complete question is:-

Find all values of [tex]'x'[/tex] such that [tex]\frac{c}{c-5} =\frac{c}{c-4}[/tex].

If you find more than one, then list the values separated by commas. If the solutions are not real, then they should be written in [tex]$a + bi$[/tex] form.

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Therefore, the solution to the system of equations is x = 8 and y = 23.

An equation is a statement that shows the equality between two mathematical expressions using symbols, numbers, and/or variables. Equations are used to describe relationships between different quantities, and they are commonly used in many fields, including mathematics, physics, chemistry, engineering, and economics.

by the question.

Let's solve the first equation for y:

y = 3x - 1

Now we substitute this expression for y in the second equation:

2x + 7 = y

We can substitute 3x - 1 for y in this equation:

2x + 7 = 3x - 1

Now we can solve for x:

2x - 3x = -1 - 7

-x = -8

x = 8

Now we can substitute x = 8 into either equation to solve for y. Let's use the first equation:

y = 3x - 1

y = 3(8) - 1

y = 24 - 1

y = 23

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The minimum sample size required for the estimate, considering the z-distribution, is given as follows:

560.

The bounds of the confidence interval are given by the rule presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The margin of error is modeled as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

The parameters for this problem are given as follows:

[tex]M = 0.16, \sigma = \sqrt{5.29} = 2.3, z = 1.645[/tex]

Hence the sample size is obtained as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.16 = 1.645\frac{2.3}{\sqrt{n}}[/tex]

[tex]0.16\sqrt{n} = 1.645 \times 2.3[/tex]

[tex]\sqrt{n} = \frac{1.645 \times 2.3}{0.16}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.645 \times 2.3}{0.16}\right)[/tex]

n = 560. (rounded up).

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Answer:

14x14= 196

Step-by-step explanation:

196cm^2

Answer:

56cm²

Step-by-step explanation:

If its a square, all sides are the same.

A = 14 x 4 = 56cm²

Debt payments relate to gross income in terms of the debt-to-income (DTI) ratio by total debt payments are divided by total. gross income.

How do debt payments relate to gross income?

The debt-to-income (DTI) ratio is a financial measurement used by lenders to assess a borrower's ability to manage debt payments. It is calculated by dividing the borrower's total debt payments by their total gross income. The resulting ratio is expressed as a percentage and indicates the portion of the borrower's income that goes towards paying their debt obligations.

For example, if a borrower has total debt payments of $1,000 per month and a gross income of $4,000 per month, their DTI ratio would be 25% ($1,000 divided by $4,000). A lower DTI ratio indicates that a borrower has more disposable income available after paying their debts and is generally viewed as a positive factor by lenders when considering a borrower for a loan or credit.

So, correct option is total debt payments are divided by total gross income.

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Answer:

D. total debt payments are divided by total gross income

Step-by-step explanation:

D. total debt payments are divided by total gross income

We can start by using the formula for the mean (average):

Mean = (sum of numbers) / (number of numbers)

We are given that the mean of 3, 15, and another number is 40, so we can set up an equation:

40 = (3 + 15 + x) / 3

Multiplying both sides by 3 yields:

120 = 3 + 15 + x

Simplifying this equation gives:

102 = x

Therefore, the missing number is 102.

Therefore , the solution of the given problem of probability comes out to be 0 0.015, 0.018, 0.045 , 0.061 and 0.045.

Every procedure's criteria-based approaches have as their main objective determining the likelihood that a statement is accurate or that an event will take place. Any number from one to one, where 0 typically represents chance and 1 typically reflects degree of certainty, can be used to symbolize chance. A probability illustration shows the likelihood that a particular occurrence will occur.

Here,

The formula below can be used to calculate the likelihood of drawing precisely k red balls in 4 draws:

=> P(b = k) =  (C(6, k) * C(5, 4-k))/C.(11, 4)

By applying this method, the probability distribution for b can be determined as follows:

=> P(b = 0) = (C(6, 0) * C(5, 4-0)) / C(11, 4) = (1 * 5) / 330 = 0.015

=> P(b = 1) = (C(6, 1) * C(5, 4-1)) / C(11, 4) = (6 * 1) / 330 = 0.018

=> P(b = 2) = (C(6, 2) * C(5, 4-2)) / C(11, 4) = (15 * 1) / 330 = 0.045

=> P(b = 3) = (C(6, 3) * C(5, 4-3)) / C(11, 4) = (20 * 1) / 330 = 0.061

=> P(b = 4) = (C(6, 4) * C(5, 4-4)) / C(11, 4) = (15 * 1) / 330 = 0.045

As a result, the following is the probability distribution for the random variable b that represents the number of red balls pulled in 4 subsequent draws from the box:

b P(b)

0 0.015

1 0.018

2 0.045

3 0.061

4 0.045

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The values of g(-4) = 0

                        g(-2) = 2

                        g(0) = 2

                        g(3) = -1

                        g(4) = -2

What is a function?

In mathematics, a function is a rule which assigns a unique output value to each input value in a given set. It shows a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Functions are typically represented by an equation or a graph, and they play an important role in various fields of mathematics, science, engineering, and technology.

Using the given piecewise defined function:

g(x) = x + 4, −5 ≤ x ≤ −1

         2 − x, −1 < x ≤ 5

We can evaluate g at different values in its domain as follows:

g(−4) = (-4) + 4 = 0

g(−2) = (-2) + 4 = 2

g(0) = 2 - 0 = 2

g(3) = 2 - 3 = -1

g(4) = 2 - 4 = -2

Therefore:

g(-4) = 0

g(-2) = 2

g(0) = 2

g(3) = -1

g(4) = -2

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Answer:

10

Step-by-step explanation:

according to the formula of y = P(1-r)^x, P is the initial value, and in this case it looks like it is 10 :)

Answer:

107 degrees

Step-by-step explanation:

since the two angles are on a straight line, and a straight line is 180 degrees,
180-73=x

x=107

If the skills have a choice of making a model plane or a model proposed the materials for plane cost $2 in the materials for the boat cost $4. The relationship between the cost of making planes (y) and the number of planes made (x) is D. y = 2x

Let's assume that x is the number of planes and y is the cost of making the planes.

According to the problem, the cost of making one plane is $2, so the cost of making x planes would be:

Cost of making planes = 2x

Therefore, the relationship between the cost of making planes (y) and the number of planes made (x) can be represented as:

y = 2x

Therefore  the correct answer is D) y=2x.

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Answer: The last one

Step-by-step explanation: there is two zeros and every input (x) can only have one output.

Answer:

The last one

Step-by-step explanation:

zero and every input (x) can only have one out put

The integer that describes 50 feet below sea level is -50.

The integer that describes 50 feet below sea level is -50. Negative integers are used to represent values below zero.

In this case, the value of 50 feet below sea level is represented by a negative integer because it is below the reference point of sea level, which is typically defined as zero.

Sea level is the average height of the surface of the sea, and is often used as a reference point for measuring elevations and depths.

When a location is above sea level, positive integers are used to represent the height or elevation, while negative integers are used to represent depths or elevations below sea level.

In summary, the integer -50 represents 50 feet below sea level because it is a negative integer that describes a depth below the reference point of sea level.

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Complete question

What integer describes 50 feet below sea level

The value of v/2 +(3/4 +w) when v = 1 and w = 5/8 is 1 7/8

substitution of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables.

Since V = 1 and W = 5/8, by substituting 1 for V and 5/8 for w in the expression

v/2 +(3/4 +w) = 1/2+ ( 3/4 + 5/8)

= 1/2 + (6+5)/8

= 1/2 + 11/8

= (4+11)/8

= 15/8

= 1 7/8

Therefore the value of v/2 +(3/4 +w) when v is 1 , and w is 5/8 is 1 7/8

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 The value of the investment after 3.5 years is $ 2000.

What is the interest rate?

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate. The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

Here, we have

Given: if $2000 is invested at 4% interest compounded monthly, the value of the investment after t years is given by 2000(12.04/12)¹²ⁿ.

We have to find the value of the investment after 3.5 years.

= 2000(12.04/12)¹²ⁿ

n = 3.5

= 2000(12.04/12)¹²⁽³°⁵⁾

= = 2000(12.04/12)⁴²

= 2000(1)

= $ 2000

Hence,  the value of the investment after 3.5 years is $ 2000.

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Answer:

  (x, y) = (-2, -1) or (1, 2)

Step-by-step explanation:

You want to find the algebraic solutions to the system of equations ...

The x-value of the solutions will be the solutions to ...

  f(x) = g(x)

  f(x) -g(x) = 0

  (x² +2x -1) -(x +1) = 0 . . . . substitute for f(x) and g(x)

  x² +x -2 = 0 . . . . . . . . . simplify

  (x +2)(x -1) = 0 . . . . . factor

The zero product rule says the solutions will be values of x that make one or the other of the factors zero.

  x = -2 or +1 . . . . . . . values that make the factors zero

  y = x +1 = -1 or +2 . . . . from the equation for g(x)

Solutions are (x, y) = (-2, -1) or (1, 2).

We already know that g(x) is satisfied by these x- and y-values.

  f(x) = x² +2x -1 = (x +2)x -1

  f(-2) = (-2 +2)(-2) -1 = 0 -1 = -1 . . . . . (-2, -1) is a solution

  f(1) = (1 +2)(1) -1 = 3 -1 = 2 . . . . . . . . . (1, 2) is a solution

These values agree with the above, so we have shown the solutions satisfy both equations in the system of equations.

Answer:

9.2(x- 7) = 9

Step-by-step explanation:

I tried my best to solve this sorry if it is wrong.

Have a good day  :)

The location of Connor's work place with respect to his home is √10 units.

The location of Vikram's martial art school with respect to his home is √34 units.

In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

Next, we would determine Connor's location with respect to his home as follows;

Distance = √[(-2 - 1)² + (2 - 3)²]

Distance = √[(-3)² + (-1)²]

Distance = √[9 + 1]

Distance = √10 units.

For Vikram, we have:

Distance = √[(-2 - 3)² + (4 - 1)²]

Distance = √[(-5)² + (3)²]

Distance = √[25 + 9]

Distance = √34 units.

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