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-2.5(-3+4.2n+8)​

The months of the birthdays in set notation are { January, April, May }

In mathematics, sets are collections of discrete objects or elements.

Set notation describes the many symbols used while navigating between and within sets. The curly brackets symbol is the most basic way to express a set's elements. A = a, b, c, and d is an illustration of a set.

The birthdays of the five friends are January 18, April 19, April 29, May 11, and May 21.

There are two types of ways in which we can write in set notation.

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The number of oranges that are expected to weigh more than 4 oz is:

1400 - (1400 × 0.0228)≈ 1368.

The mean weight of the oranges growing in an orchard is 8 oz and standard deviation is 2 oz, the distribution of the weight of oranges can be represented as normal distribution.

From the batch of 1400 oranges, the number of oranges is expected to weigh more than 4 oz can be found using the formula for the Z-score of a given data point.

\(z = (x - μ) / σ\)

Wherez is the Z-score of the given data point x is the data point

μ is the mean weight of the oranges

σ is the standard deviation

Now, let's plug in the given values.

\(z = (4 - 8) / 2= -2\)

The area under the standard normal distribution curve to the left of a Z-score of -2 can be found using the standard normal distribution table. It is 0.0228. This means that 0.0228 of the oranges in the batch are expected to weigh less than 4 oz.

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The equation which can be used to represent the relationship is c = k × v

The constant of proportionality of this relationship is 3.5

v = represent videos streamed

c = represent cost

constant of proportionality = k

c = $24.50

v = 7

c = k × v

24.50 = k × 7

24.50 = 7k

divide both sides by 7

k = 3.5

In conclusion, the equation which represents the situation is c = k × v where k = 3.5.

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The height of the prism is 5x + 3 units.

What is volume?

A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

Given:

The volume of a rectangular prism is given by the expression

10x^3 + 46x^2 – 21x – 27. The area of the base of the prism is given by the expression 2x^2 + 8x – 9.

We have to find the height of prism.

Volume of the rectangular prism = Base × Height

The expression is in the Question be

10x ³ + 46 x² - 21x -27

And the  area of the base of the prism is given by the expression

2x² + 8x - 9 .

Put in the formula

10x ³ + 46 x² - 21x -27  = 2x² + 8x - 9  × Height

The factor of 10x ³ + 46 x² - 21x -27 are (5x +3 )(2x² + 8x - 9) .

put in the formula

(5x +3 )(2x² + 8x - 9) = (2x² + 8x - 9) × Height

Cancelled 2x² + 8x - 9 on both side.

(5x+3)unit = Height

Hence, the height of the prism is 5x + 3 units.

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Therefore, the correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

Based on the given information, D represents the null hypothesis (H₀) and E represents the alternative hypothesis (Hₐ).

The null hypothesis (H₀) is a statement that there is no significant difference between the observed data and the expected results. In this case, the null hypothesis is that the population mean (μ) is greater than or equal to 1000.

The alternative hypothesis (Hₐ) is a statement that there is a significant difference between the observed data and the expected results. In this case, the alternative hypothesis is that the population mean (μ) is less than 1000.

Correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

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If length of a rectangle is 4 inches shorter than its width and perimeter of  rectangle is 80 inches , then the length of rectangle is 18 in and width of rectangle is 22 in .

The Perimeter of rectangle can be calculated by using formula : \(2(l+w)\) ;

let the width of rectangle be = w ,

it is given that the length is 4 inches shorter than width , that means ;

the width of rectangle is ⇒ \(w-4\) ;

So , the perimeter becomes ⇒ \(80=2(l+w)\)

⇒ \(80=2(w-4+w)\)

⇒ \(40=2w-4\) ;

⇒ \(2w=44\) ;

⇒ \(w=22\) ;

and substituting \(w=22\) , we get \(l=22-4 = 18\) in

Therefore , the length of rectangle is 18 in and width is 22 in .

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Answer:Mean = 40, Standard deviation = 0.39

Step-by-step explanation: The mean of the sampling distribution is equal to the population mean, which is 40.

The standard deviation of the sampling distribution is equal to the population standard deviation (3) divided by the square root of the sample size (60).

Answer: 10

Step-by-step explanation:

Because Lauren gave 1/6 of the stamps to Brianna, we divide 12 by 6 to get 1/6 of 12.

12/6=2

The question asks how many stamps Lauren kept for herself, so subtract 2 from 12.

12-2=10

Lauren kept 10 stamps for herself.

Answer:

$44,000 is the total budget

1.1.5550

2.1.5500

3.1.6000

The centroidal moments of inertia can be calculated by determining the moments of inertia for each component and applying the parallel axis theorem.



To determine the centroidal moments of inertia for the given built-up steel beam, we need to calculate the individual moments of inertia for each component and then use the parallel axis theorem to find the total centroidal moments of inertia.

First, we calculate the moment of inertia for the W18x97 wide flange beam using its properties. The moment of inertia for a wide flange beam can be found in engineering handbooks or online databases.Next, we calculate the moment of inertia for the vertical plate. Since it is centered on the web of the wide flange, its centroid coincides with the centroid of the wide flange.Similarly, we calculate the moment of inertia for the horizontal plate. Since it is also centered on the web, its centroid coincides with the centroid of the wide flange.

Finally, we use the parallel axis theorem to find the total centroidal moments of inertia. The parallel axis theorem states that the moment of inertia about any axis parallel to an axis through the centroid is equal to the sum of the moment of inertia about the centroidal axis and the product of the area and the square of the distance between the two axes.In this case, the total centroidal moments of inertia will be the sum of the moment of inertiainertia of the wide flange beam, the vertical plate, and the horizontal plate.

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We need to use the relationship between the measure of an angle and the measure of its corresponding arc in a circle. The value of x is 9.

To find the value of x in the given scenario, we need to use the relationship between the measure of an angle and the measure of its corresponding arc in a circle.

The measure of an inscribed angle (m∠TUV) is equal to half the measure of its intercepted arc (m⌒TV). In this case, m∠TUV is given as 67∘, and m⌒TV is represented by (16x−10)∘.

Setting up the equation: 67 = (16x−10)/2

Simplifying the equation: 67 = 8x − 5

Adding 5 to both sides: 72 = 8x

Dividing by 8: x = 9

Therefore, the value of x is 9.

Hence, the correct answer is option C: 9.

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Answer:

I don't know the exact answer

Step-by-step explanation:

But it is non-Linear. Because it isn't a straight line.

Hope this helps some

Compute the Gaussian density for the following cases. (a) x=0, m=0, s-1. Give the name of question5a (b) x-2, m=0, s-1. The value of the account on January 1, 2021, would be $2,331.57.

To calculate the value of the account on January 1, 2021, we need to consider the compounding interest for each year.

First, we calculate the value of the initial deposit after three years (12 quarters) using the formula for compound interest:

Principal = $1,000

Rate of interest per period = 8% / 4 = 2% per quarter

Number of periods = 12 quarters

Value after three years = Principal * (1 + Rate of interest per period)^(Number of periods)

                           = $1,000 * (1 + 0.02)^12

                           ≈ $1,166.41

Next, we calculate the value of the additional $1,000 deposit made on January 1, 2019, after two years (8 quarters):

Principal = $1,000

Rate of interest per period = 2% per quarter

Number of periods = 8 quarters

Value after two years = Principal * (1 + Rate of interest per period)^(Number of periods)

                         = $1,000 * (1 + 0.02)^8

                         ≈ $1,165.16

Finally, we add the two values to find the total value of the account on January 1, 2021:

Total value = Value after three years + Value after two years

                ≈ $1,166.41 + $1,165.16

                ≈ $2,331.57

Therefore, the value of the account on January 1, 2021, is approximately $2,331.57.

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Answer: D(2750) = 637.5

if total sales = $2750 then total donation = $637.5

Step-by-step explanation:

GIven: A local coffee shop has made a flat donation of $500 and also give a percent of their total sales over a specified weekend.

The total donation can be modeled by the function rule D(s)=500+0.05s,

where s = total sales at the coffee shop during the fundraising weekend in dollars.

Now, D(2750) = 500+0.05(2750)

= 500+ 137.5

= 637.5

i.e. if total sales = $2750 then total donation = $637.5

If there are 450 grams of element and half life is 8 minutes, then it will take 28.83 minutes the element to decay to 37 grams

Half life of radio active element = 8 minutes

Initial quantity of radio active element = 450 gram

Final quantity of radio active element = 37 grams

y = a(0.5)^(t/h)

Substitute the values in the equation

37 = 450 (0.5)^(t/8)

Move 37 to left hand side of the equation

37 / 450 = 0.5^(t/8)

Convert the terms to logarithm

t/8 = \(log_{0.5}\frac{37}{450}\)

t/8 = 3.60

t = 8 × 3.60

Multiply the numbers

t = 28.83 minutes
Therefore, the it will take 28.83 minutes to decay to 37 grams

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The minimum sterilization time required to achieve a 99.9% confidence level in successfully sterilizing 50 L of medium containing 10^6 contaminating organisms is approximately 1.95 minutes.

To calculate the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms, we need to use the concept of decimal reduction time (D-value) and the number of organisms.

The D-value represents the time required to reduce the population of microorganisms by one log or 90%. In this case, the given D-value is 0.65 minutes.

To achieve a 99.9% confidence level, we need to reduce the population of microorganisms by three logs or 99.9%, which corresponds to a 10^-3 reduction.

To calculate the minimum sterilization time, we can use the following formula:

Minimum Sterilization Time = D-value × log10(N0/Nf)

Where:

D-value is the decimal reduction time (0.65 minutes).

N0 is the initial number of organisms (10^6).

Nf is the final number of organisms (10^6 × 10^-3).

Let's calculate it step by step:

Nf = N0 × 10^-3

= 10^6 × 10^-3

= 10^3

Minimum Sterilization Time = D-value × log10(N0/Nf)

= 0.65 minutes × log10(10^6/10^3)

= 0.65 minutes × log10(10^3)

= 0.65 minutes × 3

= 1.95 minutes

Therefore, the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms using this procedure is approximately 1.95 minutes

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Answer:

3no reason is given

4no both are 90 degree

6no by SAS axiom

Answer:

k = - 8

Step-by-step explanation:

given that (x - a) is a factor of f(x) , then f(a) = 0

given

(x - 1) is a factor of f(x) then f(1) = 0 , that is

3(1)³ + 5(1) + k = 0

3(1) + 5 + k = 0

3 + 5 + k = 0

8 + k = 0 ( subtract 8 from both sides )

k = - 8

Where a and b are determined by the value of D.

A parabola is a type of graph, or curve, that is represented by an equation of the form y = ax² + bx + c. The vertex of a parabola is the point where the curve reaches its maximum or minimum point, depending on the direction of the opening of the parabola. In this case, the vertex of the parabola is at (-4,-1).
To find the equation of the parabola, we need to know two more points on the graph. We are given that when the y-value is 0, the x-value is 10-D. We can use this information to find another point on the graph.
When the y-value is 0, we have:
0 = a(10-D)² + b(10-D) + c
Simplifying this equation gives:
0 = 100a - 20aD + aD² + 10b - bD + c
Since the vertex is at (-4,-1), we know that:
-1 = a(-4)² + b(-4) + c
Simplifying this equation gives:
-1 = 16a - 4b + c
We now have two equations with three unknowns (a,b,c). To solve for these variables, we need one more point on the graph. Let's use the point (0,-5) as our third point.
When x = 0, y = -5:
-5 = a(0)² + b(0) + c
Simplifying this equation gives:
-5 = c
We can now substitute this value for c into the other two equations to get:
0 = 100a - 20aD + aD² + 10b - bD - 5
-1 = 16a - 4b - 5
Simplifying these equations gives:
100a - 20aD + aD² + 10b - bD = 5
16a - 4b = 4
We now have two equations with two unknowns (a,b). We can solve for these variables by using substitution or elimination. For example, we can solve for b in the second equation and substitute it into the first equation:
16a - 4b = 4
b = 4a - 1
100a - 20aD + aD² + 10(4a-1) - D(4a-1) = 5
Simplifying this equation gives:
aD² - 20aD - 391a + 391 = 0
We can now use the quadratic formula to solve for D:

D = [20 ± sqrt(20² - 4(a)(391a-391))]/2a
D = [20 ± sqrt(400 - 1564a² + 1564a)]/2a
D = 10 ± sqrt(100 - 391a² + 391a)/a
There are two possible values for D, depending on the value of a. However, since we don't have any information about the sign of a, we cannot determine which value of D is correct. Therefore, the final equation of the parabola is:
y = ax² + bx - 5

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Hello !

\(a - (a - b) - b - (b - a)\\\\= a - a + b - b - b+a\\\\\boxed{= a - b}\)

Answer:

Step-by-step explanation:

a - ( a - b ) - b - ( b - a )

= a - a + b - b - b + a

= a - b

To find the minimum score required for an A grade, we need to determine the cutoff point that corresponds to the top 13% of scores.

Given that the scores on the test are normally distributed with a mean of 69.5 and a standard deviation of 9.5, we can use the standard normal distribution to calculate the cutoff point. Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the top 13% is approximately 1.04. To find the corresponding raw score, we can use the formula:

x = μ + (z * σ)

where x is the raw score, μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values, we have:

x = 69.5 + (1.04 * 9.5) ≈ 79.58

Rounding this to the nearest whole number, the minimum score required for an A grade would be 80. Therefore, a student would need to score at least 80 on the test to achieve an A grade according to the professor's grading scheme.

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The Interquartile range i.e 1.5 (IQR) is used to identify outliers in a set of data which is the correct answer would be option (A).

We may build up a "fence" outside of Q1 and Q3 by using the Interquartile range (IQR) method of spotting outliers. Outliers are values that fall outside of this range.

To construct this barrier, we take 1.5 times the IQR, deduct it from Q1, and add it to Q3. This provides us with the lowest and maximum fence posts against which we will compare each observation.

Outliers are observations that are greater than 1.5 IQR below or above Q1. Minitab's default strategy for identifying outliers is this.

Therefore, the Interquartile range (IQR) is used to identify outliers in a set of data.

Hence, the correct answer would be option (A).

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Answer:

-143/12  or -11 11/12

Step-by-step explanation:

Convert each to improper fraction and multiply straight across (numerator times numerator, denominator times denominator)

-1 5/6 x 6 1/2

= -11/6  x  13/2

= -143/12

Answer:

-143/12 as a fraction and 11.916666666... (six repeating) as a decimal

Step-by-step explanation:

Turn into improper fractions.

(-6/6 + -5/6) = -11/6

2/2 + 2/2 +2/2 + 2/2 +2/2 + 2/2 + 1/2 = 13/2

-11/6 times 13/2

-11 times 13 = -143

6 times 2 = 12

-143/12 = 11.916666666... (six repeating)

Answer:

c(2) = -10

Step-by-step explanation:

The first equation says that the first term of the sequence is -20.

The second equation is saying that to find any term of the sequence, add 10 to the previous term.

c(2) = c(2-1) + 10

c(2) = c(1) + 10

c(2) = -20  + 10 = -10

Answer:

4

Step-by-step explanation:

y=mx+b

b=y-intercept.

In this case...

mx=-5<-- this is the slope of the line.

b=4<-- y intercept.

Hope this helps, any further questions, please feel free to ask.

Answer:

78.5

Step-by-step explanation:

The radius of the circle is 25 so youu multiply that by 3.14

25*3.14=78.5

Answer:

Endpoint A (10,2)

Step-by-step explanation:

                A(x,y)

Endpoint (-2,-2)

Midpoint (4,0)

(-2+x)/2=4,  -2+x=8,  x=8+2,x=10

(-2+y)/2=0, -2+y=0,y=2

so A (10,2)