The graphs of six linear equations are shown below. Which of these graphs have a greater rate of change than the equation y=1/2 x+3?

Answer:

We can rewrite the given expressions as:

(3x² - y² - 2yz - z²) and (y² - z² - 2zx - x²)

To find the H.C.F., we can use the Euclidean algorithm. We start by dividing the first expression by the second expression:

(3x² - y² - 2yz - z²) ÷ (y² - z² - 2zx - x²)

Using long division or synthetic division, we get:

(3x² - y² - 2yz - z²) = (3x + y + z)(x - y + z) + 2y(x - z)

Therefore, the remainder is 2y(x - z). We can now divide the second expression by this remainder:

(y² - z² - 2zx - x²) ÷ 2y(x - z)

Using long division or synthetic division, we get:

(y² - z² - 2zx - x²) = -x(x - y + z) + z(x - y + z)

Therefore, the remainder is z(x - y + z).

Since the second remainder is not zero, we need to continue with the algorithm. Now we divide the remainder 2y(x - z) by the remainder z(x - y + z):

2y(x - z) ÷ z(x - y + z)

Using long division or synthetic division, we get:

2y(x - z) = 2y(x - y + z) - 2y²

Therefore, the remainder is -2y². Now we divide the previous remainder z(x - y + z) by this new remainder:

z(x - y + z) ÷ (-2y²)

Using long division or synthetic division, we get:

z(x - y + z) = -1(-2y²) + z²

Therefore, the H.C.F. of the original expressions is the absolute value of the last remainder, which is |-2y²| = 2y².

Therefore, the H.C.F. of (3x² - y² - 2yz - z²) and (y² - z² - 2zx - x²) is 2y².

The null hypothesis (H0) is that the average delivery time for U.S. packages during December is 2 days, while the alternative hypothesis (Ha) is that the average delivery time is longer than 2 days.

Based on your question, you want to test if the average delivery time for U.S. packages in December is longer than 2 days. In this hypothesis test, you would have the following hypotheses:

Null Hypothesis (H0): The average delivery time for U.S. packages in December is 2 days.
Alternative Hypothesis (H1): The average delivery time for U.S. packages in December is greater than 2 days.

Thus, H0: μ ≤ 2 (where μ is the population mean delivery time)
Ha: μ > 2

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A graph of the given quadratic equation is shown below.

The axis of symmetry is equal to 3.

The vertex is equal to (3, -1).

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

Since the leading coefficient (value of a) in the given quadratic function y = x² - 6x + 8 is positive 1, we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts. Also, the value of the quadratic function f(x) would be minimum at -1.

In conclusion, the axis of symmetry is 3 while the vertex is given by the ordered pair (3, -1).

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Answer:

The total area of the shaded region is 16 square units

Step-by-step explanation:

Main Steps:

Step 1. Find length of Square edge & Equilateral triangle leg

Step 2. Find the length from top to bottom of the full diamond

Step 3. Find the Area of the full diamond

Step 4. Find the Area that isn't shaded

Step 5. Find the Area that is shaded

Step 1. Find length of Square edge & Equilateral triangle edge

Since the Square has an area of 16 square units, using the formula for area of a square, the edge length must be 4 units

[tex]A_{square}=edge^2[/tex]

[tex](16~\text{units}^2)=edge^2[/tex]

[tex]4~\text{units}=edge[/tex] of square

Since one edge of the equilateral triangle shares one edge of the square, they are the same length.  Thus, the equilateral triangle also has edge length of 4 units.

Step 2. Find the length from top to bottom of the full diamond

Equilateral triangles have a height that is exactly [tex]\dfrac{\sqrt{3}}{2}[/tex] the length of their base.  So the height of the equilateral triangle is [tex]\dfrac{4\sqrt{3}}{2}[/tex], or more simply [tex]2\sqrt{3}~\text{units}[/tex].

The full diamond, from top to bottom, is the height of two of those equilateral triangles, plus the height of the central square:

[tex]2\sqrt{3}~\text{units} + 4~\text{units} + 2\sqrt{3}~\text{units}[/tex]

Combining like terms, the length of the Diamond diagonal from top to bottom is [tex](4 + 4\sqrt{3})~\text{units}[/tex].

Note, that due to symmetry of construction, this is also the length of the diamond's diagonal from left to right.

Step 3. Find the Area of the full diamond

One fact from geometry is that the area of a rhombus (all side lengths congruent), is given by the following formula:

[tex]A_{\text{rhombus}}=\frac{1}{2}d_{1}d_{2}[/tex], where d1 and d2 are the lengths of the two diagonals.

The "diamond" that was constructed, has all sides congruent (all sides the same length), so it is a rhombus (with matching diagonal lengths that we just calculated in Step 2)

Thus, the Area of the rhombus is:

[tex]A_{\text{rhombus}}=\frac{1}{2}((4 + 4\sqrt{3})~\text{units})((4 + 4\sqrt{3})~\text{units})[/tex]

Using FOIL,

[tex]A_{\text{rhombus}}=\frac{1}{2}(4^2 + 4*4\sqrt{3}+4*4\sqrt{3}+ (4\sqrt{3})^2)~\text{units}^2[/tex]

[tex]A_{\text{rhombus}}=\frac{1}{2}(16 + 32\sqrt{3}+ (16*3))~\text{units}^2[/tex]

[tex]A_{\text{rhombus}}=\frac{1}{2}(64 + 32\sqrt{3})~\text{units}^2[/tex]

Distributing...

[tex]A_{\text{rhombus}}=(32 + 16\sqrt{3})~\text{units}^2[/tex]

Step 4. Find the Area that isn't shaded

The area that isn't shaded is the area of the square, plus 4 equilateral triangles.

[tex]A_{\text{not shaded}}=4~A_{\text{equilateral triangle}}+A_{\text{square}}[/tex]

Recall that the area of a triangle is 1/2 * b * h

[tex]A_{\text{equilateral triangle}}=\frac{1}{2}(4)(2\sqrt{3})~\text{units}^2[/tex]

[tex]A_{\text{equilateral triangle}}=4\sqrt{3}~\text{units}^2[/tex]

[tex]A_{\text{not shaded}}=4~A_{\text{equilateral triangle}}+A_{\text{square}}[/tex]

[tex]A_{\text{not shaded}}=4~(4\sqrt{3}~\text{units}^2)+(16~\text{units}^2)[/tex]

[tex]A_{\text{not shaded}}=(16\sqrt{3}~\text{units}^2)+(16~\text{units}^2)[/tex]

[tex]A_{\text{not shaded}}=(16+16\sqrt{3})~\text{units}^2[/tex]

Step 5. Find the Area that is shaded

Lastly, the area that is shaded is the area of the full diamond/rhombus, minus the area that is not shaded:

[tex]A_{\text{shaded}}=A_{\text{Rhombus}}-A_{\text{not shaded}}[/tex]

[tex]A_{\text{shaded}}=((32+16\sqrt{3})~\text{units}^2)-((16+16\sqrt{3})~\text{units}^2)[/tex]

Combining like terms and simplifying...

[tex]A_{\text{shaded}}=16~\text{units}^2[/tex]

Answer:

Above picture is,

the explanation.

95% of samples will produce a confidence interval that captures the true proportion. The correct answer is A.

When we say we are 95% confident in a particular interval estimate, it means that if we were to take many different samples from the same population and compute a confidence interval for each sample using the same method, about 95% of those intervals would contain the true population parameter.

So, Option A correctly states that 95% of samples will produce a confidence interval that captures the true proportion. Option B is incorrect because it refers to the sample proportion, rather than the true population proportion. Option C is also incorrect because it refers to the sample, rather than the confidence interval.

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If students earned an average of 13.8 credits per hour, then best point estimate for average number of credit hours per semester is 13.8.

The "best-point" estimate is defined as a single value that is used to approximate an unknown population parameter, based on a sample of data. It is called the "best" point estimate because it is the one that is closest to the true value of the population parameter.

The "best-point" estimate for average number of "credit-hours" per semester for all students at "local -college" is "sample-mean", which is written as :

⇒ sample mean = (sum of credit hours in sample)/(sample size),

Since study found that students earned an average of 13.8 credit hours per semester, we use this value as an estimate for population mean.

⇒ sample mean = (118 ) × (13.8)/(118),

Simplifying,

We get,

⇒ sample mean = 13.8 credit hours per semester,

Therefore, the best point estimate is 13.8 credit hours per semester.

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The expected value 'w' for the total raffle tickets sold for $1.00 with other conditions is equal to $0.784.

Number of raffle tickets sold for $1.00 = 2000

Expected value of w is ,

= Expected value of the prize won - cost of a single ticket $1.00

The probability of winning a $25 prize is

=  20/2000

= 0.01.

The expected value of winning this prize is equal to

= (25 - 1) × 0.01

= 0.24

The probability of winning a $50 prize is

= 10/2000

= 0.005.

The expected value of winning this prize is equal to

=  (50 - 1) × 0.005

= 0.245

The probability of winning a $300 prize is

= 2/2000

= 0.001.

The expected value of winning this prize is,

= (300 - 1) × 0.001

= 0.299

This implies,

The expected value of w is equal to

= 0.24 + 0.245 + 0.299

= 0.784

Therefore, the expected value of winning a prize minus the cost of the ticket is $0.784.

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Answer:

x=18.75

Step-by-step explanation.

We have to realize that this is a line. A line has 180 degrees.

Therefore we can make the equation;

(6x+30)+2x=180

8x+30=180

8x=150

x=18.75

please mark as branliest

Answer:

x=18.75

Step-by-step explanation:

We can see that these 2 angles are on a straight line, meaning that these 2 angles must add up to 180°.

We can set up an equation:

180=(6x+30)+2x

combine like terms

180=8x+30

subtract 30 from both sides

150=8x

divide both sides by 8

x=18.75

Hope this helps! :)

The graph of the data set is in the image at the end, and it can be modeled by the quadratic:

y = 2*(x + 1)² - 3

Here we have the table:

x            y

-2,         -1

-1,          -3

0,           -1

1,             2

2,            7

The graph of it can be seen in the image at the end, there we can see that this seems to be a quadratic function

At the graph we also can see that (-1, -3) is te vertex, then if the leading coefficient is a, we can write the quadratic equation as:

y = a*(x + 1)² - 3

And we know that the equation passes throug (0, -1), replacing that we will get.

-1 = a*(0 + 1)² - 3

-1 = a - 3

-1 + 3 = a

2 = a

The function is:

y = 2*(x + 1)² - 3

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The probability of iii-2 and iii-3 having 2 colorblind children and 5 normal children is approximately 0.16, or 16%.

To calculate the probability of having 2 colorblind children and 5 normal children, we need to use the binomial probability formula, which is:

P(X=x) = (n choose x) x pˣ x (1-p)ⁿ⁻ˣ

where:

P(X=x) is the probability of getting k successes in n trials

(n choose k) is the binomial coefficient, which is the number of ways to choose k items from a set of n items

p is the probability of success in each trial

(1-p) is the probability of failure in each trial

x is the number of successes we want to have

In this case, we want to find the probability of having 2 colorblind children and 5 normal children, so we can plug in the values:

P(X=2) = (7 choose 2) * 0.25² * 0.75⁵

Using a calculator or computing by hand, we get:

P(X=2) = 0.16 or 16%.

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The volume of the Pentagonal pyramid is 8.25 units² and surface area is 12.2 units²

A Pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces.

The volume of of a pyramid is expressed as;

V = 1/3 b × h

where b is the area of the base

Area of the base = 1/2 nsa

where s is the side length and n is the number of sides and a is the apothem.

side length = apothem × 2tan(180/n)

= √3/2 × 2tan36

= √3 × tan36

= 1.26m

Therefore,

A = 1/2( 5 × 1.26 × √3/2)

A = 1/2 ( 5.5)

A = 2.75 units²

Volume of the pyramid = 2.75 × 3

= 8.25 units²

Area of a face = 1/2bh

= 1/2 × 1.26 × 3

= 3.78/2

= 1.88 units²

Total surface area = 1.88 × 5

= 9.45 units² + 2.75units²

= 12.2 units²

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Triangle QRT with coordinates Q(-2,-1), R(1,5), and T(-8,-4) is a scalene triangle.

To classify the triangle QRT by its sides, we need to find the lengths of its three sides and compare them. We can use the distance formula to calculate the length of each side

The length of RT = √[(1 - (-8))² + (5 - (-4))²] = √[9² + 9²]

= √[162]

= 9√(2) units

The length of QT = √[(-8 - (-2))² + (-4 - (-1))²]

= √[(-6)² + (-3)²]

= √[45]

= 3√(5) units

The length of QR = √[(1 - (-2))² + (5 - (-1))²]

= √[3² + 6²]

= √[45]

= 3√(5)

Since all three sides have different lengths, triangle QRT is scalene

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The given question is incomplete, the complete question is:

Given the coordinates, classify triangle QRT by its sides. Q(-2, -1), R(1,5), T(-8,-4)

Answer:

x= (2010/(c+12)) +25

Step-by-step explanation:

2010= (x-25) (c+12)

x-25 = 2010/(c+12)

x= (2010/(c+12)) +25

The measure of the sides of the triangle is x = 15√3

Given data ,

We know that in the right triangle supplied, the bottom leg (adjacent side to the 30-degree angle) is "15" and the left leg (adjacent side to the 60-degree angle) is "x"

The ratio of the lengths of the side across from the angle and the side next to it is known as the tangent of an angle in a right triangle

From the trigonometric relations , we get

tan 60 = opposite side / adjacent side

tan(60°) = √3 = x/15

Multiply by 15 on both sides , we get

x = 15√3

Hence , the measure of side is x = 15√3

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The distance AB is 10 units and other coordinates are calculated below

Given that

C = (3, 3) and D = (3, y)

The length is 7 units

So, we have

y - 3 = 7

Evaluate

y = 4

So, one possible value of y is 4

Given that

B = (r, 2) and C = (5, 2)

The length is 10 units

So, we have

r - 5 = 10

Evaluate

r = 15

So, one possible value of r is 15

Finding the coordinates of A

We have

AB = 4 units and B = (15, 2)

So, we have

A = (15, 2 + 4)

Evaluate

A = (15, 6)

Here, we have

A = (a - 7, b) and D = (a + 3, b)

The distance because they have the same y-coordinates is

Distance = |a - 7 - a - 3|

Evaluate

Distance = 10

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Answer: $13

Step-by-step explanation:

Let x be the price of each ticket (to the aquatic show and fireworks display).

Then, we know that:

$48 = $22 + 2x

Simplifying this equation, we get:

$48 - $22 = 2x

$26 = 2x

x = $13

Therefore, the price of each ticket is $13.

There is a 0.5477 probability that a randomly selected customer will arrive less than 5 minutes after the previous customer during the 3 pm to 5 pm time period. (option a)

Given that the arrival rate of cars at the bank's drive-through window during the 3 pm to 5 pm time period is 15 customers per hour, we can calculate the average time between arrivals as follows:

Average time between arrivals = 1 / arrival rate

= 1 / 15

= 0.0667 hours (since there are 60 minutes in an hour, this is equivalent to 4 minutes)

Now, we need to find the probability of a customer arriving less than 5 minutes after the previous customer. Since the time between arrivals follows the exponential distribution, we can use the cumulative distribution function (CDF) of the exponential distribution to calculate this probability. The CDF gives us the probability of an event occurring within a certain time frame.

To find the probability of a customer arriving less than 5 minutes after the previous customer, we need to calculate the probability of an arrival occurring within a 5-minute time frame, which is equivalent to 0.0833 hours. So, we can substitute λ = 15 and x = 0.0833 in the formula for the CDF and get:

F(0.0833) = 1 - e¹⁵ˣ⁽⁻⁰°⁰⁸³³⁾

= 0.5477 (rounded to four decimal places)

Therefore, the answer is option (a) 0.5477.

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Answer:

  [tex]\sqrt[6]{2}[/tex]

Step-by-step explanation:

You want the expression 2^(2/3)/2^(1/2) in simplest radical form.

The quotient property tells you ...

  (a^b)/(a^c) = a^(b-c)

The relation between fractional exponents and roots is ...

  [tex]a^\frac{b}{c}=\sqrt[c]{a^b}[/tex]

  [tex]\dfrac{2^\frac{2}{3}}{2^\frac{1}{2}}=2^{\frac{2}{3}-\frac{1}{2}}=2^\frac{1}{6}=\boxed{\sqrt[6]{2}}[/tex]

Answer & Step-by-step explanation:

Part A: The explicit equation for f(n) that represents the number of lionfish in the bay after n years can be written as:

f(n) = 9000 * (1 + 0.69)^n

where 9000 is the initial number of lionfish, 0.69 is the growth rate, and n is the number of years.

Part B: To find the number of lionfish in the bay after 6 years, we substitute n = 6 into the explicit formula from Part A and simplify:

f(6) = 9000 * (1 + 0.69)^6 = 9000 * (1.69)^6 = 9000 * 11.34 = 102,060.5

Rounding to the nearest whole number, there will be approximately 102,061 lionfish in the bay after 6 years.

Part C: The recursive equation for f(n) can be found by subtracting 1,400 from the previous year's population and then applying the annual growth rate. Thus, we have:

f(1) = 9000 f(n) = f(n-1) - 1400 + 0.69f(n-1) = 0.69f(n-1) - 1400

where f(1) is the initial number of lionfish and n represents the number of years after the first year.

The diameter of the circle is d = 124.73 cm

The diameter of a circle is the line that passes through the center of the circle and touches the circumference at two points.

To find the diameter of the circle, we use the formula for the area of the circle given by A = πd²/4 where d = diameter of circle

Making d subject of the formula, we have that

d = √(4A/π)

Given that the area is

substituting the values of the variables into the equation, we have that

d = √(4A/π)

d = √(4 × 98 cm²/22/7)

d = √(4 × 98 cm² × 7/22)

d = √(4 × 98 cm² × 7/22)

d = √(2744 cm²/22)

d = 124.73 cm

So, the diameter d = 124.73 cm

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The equation of the parabola is:y = -13/36(x + 2)² + 5.

Equation is a mathematical statement that two expressions are equal. It is written as an expression that shows the equality of two values using mathematical symbols. Equations are used to solve problems by finding the unknown value. They are used in almost all branches of mathematics, and help to explain the behavior of physical and chemical systems.

The equation of a parabola with vertex (x_0,y_0) and that passes through (x_1,y_1) can be expressed as
y = a(x - x_0)² + y_0
where a is a constant.

In this case, the vertex of the parabola is (-2, 5) and it passes through (4, -8). We can substitute these values for x_0, y_0 and x_1, y_1 into the equation to get:

y = a(x - (-2))² + 5

We can solve for a by substituting the coordinates of the given point (4, -8) into the equation:

-8 = a(4 - (-2))² + 5

-8 = a(6)^2 + 5

-8 = 36a + 5

-13 = 36a

a = -13/36

Therefore, the equation of the parabola is:

y = -13/36(x + 2)²+ 5

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The required equation of the parabola is y = -13/36(x + 2)² + 5.

A parabola is a type of curve that is defined by a quadratic equation of the form y = ax² + bx + c.

In geometric terms, a parabola is the set of all points in a plane that are equidistant from a fixed point (called the focus) and a fixed line (called the directrix).

The equation of a parabola with vertex (x₁, y₁) that passes through
(x₂, y₂) can be expressed as

                        => y = a(x - x₁)² + y₁

Where a is a constant.

Here we have

The vertex of the parabola is (-2, 5) and it passes through (4, -8).

Substitute (-2, 5) in the formula y = a(x - x₁)² + y₁

=>  y = a(x - (-2))² + 5

Solve for a by substituting the coordinates of the given point (4, -8) into the equation:

=> -8 = a(4 - (-2))² + 5

=> -8 = a(6)² + 5

=> -8 = 36a + 5

=> -13 = 36a

=> a = -13/36

Therefore,

The required equation of the parabola is y = -13/36(x + 2)² + 5.

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Answer:

Subtract 142 from 180 since angle of a straight line adds upto 180 degrees..

Ans will be =38

To decrease the type II error in a hypothesis test while maintaining the type I error at its current level, we need to increase the sample size.

Type I error shows when we reject a null hypothesis which is actually true. Type II error shows when we fail to reject a null hypothesis which is actually false.

Increasing the sample size can decrease the probability of making a Type II error, as it increases the power of the hypothesis test. Probability of correctly rejecting a false null hypothesis is called power.

By increasing the sample size, we can increase the power of the test while maintaining the significance level (and thus the type I error) at its current level.

This means that we will be less likely to miss a true effect (i.e., lower the probability of making a Type II error) while still controlling the probability of false positives (i.e., Type I error) at the desired level.

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Answer:

The answer is 29/35

Step-by-step explanation:

2/5+3/7

find the LCM of 5 and 7

[7(2)+5(3)]/35

14+15/35=29/35

Answer:      B

Step-by-step explanation:

It is speeding up

Answer:

R93,750. (I have changed R to $ in explanation)

Step-by-step explanation:

To determine the cost of the car inclusive of VAT, trade-in, and other fees, we first need to calculate the VAT amount. Assuming the VAT rate is 15%:

VAT = 0.15 x $75,000 = $11,250

Next, we can calculate the total cost of the car, inclusive of VAT:

Total cost of car = Cost of car + VAT

Total cost of car = $75,000 + $11,250

Total cost of car = $86,250

We also need to take into account the trade-in and the other fees. The trade-in value of $9,500 and the other fees of $2,000 are subtracted from the total cost of the car:

Total cost of car inclusive of VAT and other fees = Total cost of car + Trade-in value - Other fees

Total cost of car inclusive of VAT and other fees = $86,250 + $9,500 - $2,000

Total cost of car inclusive of VAT and other fees = $93,750

Therefore, the cost of the car, inclusive of VAT, trade-in, and other fees, is $93,750.

The proper way to determine the seat width of a wheelchair for an individual is to measure the widest aspect of their hips or thighs, and then add approximately 2 inches to that measurement to determine the minimum seat width.

The extra 2 inches are required to allow for comfortable placement, movement, and sitting in the wheelchair. It's crucial to remember that this serves only as a basic guideline and that the actual seat width needed may change based on the demands and preferences of the individual.

For instance, people with particular medical issues or disabilities could need seats that are larger or narrower than average. Therefore, it is advised that a healthcare professional be consulted to help identify the best seat width for a particular person, such as an occupational therapist or physical therapist.

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The sample size required if we wish to develop a 90% confidence interval for the average diameter is more than 0.1 units. 

To decide the test estimate required for a 90% certainty interim for the normal distance across, we have to know the taking after :

1. The level of certainty (which is 90% in this case).

2. The standard deviation of the populace (which we'll expect is known).

3. The margin of error (which is the greatest separation between the test cruel and the genuine populace cruel that we're willing to endure).

Assuming we know the standard deviation of the populace, ready to utilize the equation:

n = (z²* σ²) / E²

where:

n is the test measure

z is the z-score compared to the level of certainty (which is 1.645 for 90% certainty)

σ is the standard deviation of the populace

E is the edge of mistake

We ought to select esteem for E, which speaks to the most extreme separation between the test cruel and the genuine populace cruel(mean) that we're willing to endure.

For case, in the event that we need the interim to have a width of no more than 0.1 units, at that point we would select E = 0.1/2 = 0.05.

So, stopping within the values we know, we get:

n = (1.645² * σ²) / E²

In case we accept that the standard deviation of the populace is 0.5 units (fair as a case), at that point we get:

n = (1.645² * 0.5²) / 0.05²

n = 67.65

Adjusting up to the closest numbers, we would require a test estimate of 68 to create a 90% confidence interim for the normal breadth with an edge of blunder of no more than 0.1 units. 

To know more about sample size refer to this :

https://brainly.com/question/30224379

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