(will give 50 points) Which graph shows the solution to the system of linear equations?

y equals one half times x

x + 2y = −8

coordinate plane with one line that passes through the points 0 comma negative 4 and 2 comma negative 5 and another line that passes through the points 0 comma 0 and 2 comma 1
coordinate plane with one line that passes through the points 0 comma 2 and negative 3 comma 3 and another line that passes through the points 0 comma 0 and negative 3 comma negative 1
coordinate plane with one line that passes through the points 3 comma negative 3 and 0 comma negative 2 and another line that passes through the points 0 comma 0 and 3 comma 1
coordinate plane with one line that passes through the points 0 comma 4 and negative 1 comma 1 and another line that passes through the points 0 comma 0 and 1 comma 3

Answer:

Step-by-step explanation:

21:

3,7

Answer:

100/60 = 42 / x

Step-by-step explanation:

Given that :

Number of dogs at shelter = 42

Capacity of shelter = 60%

Number of dogs shelter can cater for :

Let number of dogs shelter can cater for = x

60% of 42 = x

(60/100) * 42 = x

60/100 = x / 42

Reciprocal of both sides

100/60 = 42 / x

Answer:

60/100=42/x

Step-by-step explanation:

If the scale of drawing is 1 inches : 250 inche and the real horse height is 15 inche, then the height of the horse in drawing is 0.06 inches.

The ratio that describes the relationship between the true figure itself and model is called the scale. It serves as a representation of the real statistics in smaller units on maps. A scale of 1:5, for instance, indicates that 1 on the map is approximately the size of 5 in the actual world.

The scale of drawing the horse = 1 inch :

Therefore in scale

Horse height in drawing equals one inch

The  height of the horse = 250 inche

The original height of the horse = 15 inche

The height in the picture = x inches

To find the height the horse in the picture, we have to use proportion

1 inch : 250 inche = x inches : 15 inche

1 / 250 = x / 15

1 × 15= 250x

250x = 15

x = 15/250

x = 0.06 inches

Therefore, the height of the horse in drawing is 0.06 inches

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Answer:

9 divided by thirteen.

Step-by-step explanation:

we know that the fraction symbol that appears between the numerator and the denominator (the ___ line) represents division. So, we could say that 9 over 13 is 9 divided by thirteen.

Answer:

9) 25

10) 100

Step-by-step explanation:

9)

if the total class is 5x, and the people who wear glasses is 2x,

that means that the people who do not wear glasses would be 3x

(because 5x - 2x = 3x)

the problem tells us that there are 15 people who do not wear glasses.

15 = 3x

15/3 = 3x/3

15/3 = x

5 = x

since x is 5, the total number of students is 25

because 5 * 5 = 25

10)

to start, divide 250 by 50.

250/50 = 5

250 is 5 times greater than 50.

since the ratio of dollar to game point is proportional,

you just need to multiply 5 by 20$ to get the answer

5 * 20 = 100$

P(80 < X < 125) = 0.9525 - 0.0918

P(80 < X < 125) = 0.8607

This means that approximately 86.07% of people have IQ scores between 80 and 125.

To answer this question, we need to calculate the standardized score (also known as z-score) for both 80 and 125:

z-score for 80: (80-100)/15 = -1.33

z-score for 125: (125-100)/15 = 1.67

Once we have the z-scores, we can use a standard normal distribution table or calculator to find the proportion of scores between them. Alternatively, we can use the following formula:

P(80 < X < 125) = P(Z < 1.67) - P(Z < -1.33)

Using a standard normal distribution table or calculator, we can find that P(Z < 1.67) is approximately 0.9525 and P(Z < -1.33) is approximately 0.0918.

Therefore:

P(80 < X < 125) = 0.9525 - 0.0918

P(80 < X < 125) = 0.8607

This means that approximately 86.07% of people have IQ scores between 80 and 125.

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The radius of the given region is calculated as; 19.329 km

We are told that the region is circular and as such the formula for the area of a circle is;

A = πr²

We are told that the population is 44600

Population density is defined as the average number of individuals in a population per unit are.

In this question, the population density is given as 388 people per sq. km

Thus;

Area = Population/population density

πr² = 44600/388

r² = 44600/388π

r² = 373.595

r = 19.329 km

We conclude that is the radius

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Answer:

n = 24

Step-by-step explanation:

Given the fraction:

\($\frac{n}{n+101}$\)

To find:

Smallest positive integer \($n$\) such that the fraction is equal to a terminating decimal.

Solution:

The rule that a fraction is equal to a terminating decimal states that, the denominator must contain factors of only 2 and 5.

i.e. Denominator must look like \(2^m\times 5^n\), only then the fraction will be equal to a terminating decimal.

Now, let us have a look at the denominator, \(n+101\)

Let us use hit and trial method to find the value of \(n\) as positive integer.

n = 1, denominator becomes 102 = \(2 \times 3 \times 17\) not of the form \(2^m\times 5^n\).

n = 4, denominator becomes 105 = \(5 \times 3 \times 7\) not of the form \(2^m\times 5^n\).

n = 9, denominator becomes 110 = \(2 \times 5 \times 11\) not of the form \(2^m\times 5^n\).

n = 14, denominator becomes 115 = \(5 \times 23\) not of the form \(2^m\times 5^n\).

n = 19, denominator becomes 120 = \(5 \times 3 \times 2^3\) not of the form \(2^m\times 5^n\).

n = 24, denominator becomes 125 = \(2^0 \times 5 ^3\) It is of the form \(2^m\times 5^n\).

So, the answer is n = 24

A. 24.12 days

B. 18.1%

C. 29868 years

Using the formula for exponential decay:

N(t) = N0 * (1/2)^(t/T)

We can rearrange this equation to solve for t:

t = T * log(0.125) / log(0.5)

simplifying, we get:

t = 8.04 * log(0.125) / log(0.5) ≈ 24.12 days

Therefore, it takes about 24.12 days for only 12.5% of the sample to remain.

Using the same formula for exponential decay

N(11) = N0 * (1/2)^(11/12.3)

Dividing N(11) by N0 and multiplying by 100 gives us the percentage remaining:

N(11)/N0 * 100 = (1/2)^(11/12.3) * 100 ≈ 18.1%

Therefore, about 18.1% of the tritium sample will remain after 11 years.

The rate of decay of C-14 is given by:

A(t) = A0 * (1/2)^(t/T)

t = T * log(A(t)/A0) / log(0.5)

Plugging in the values for A(t), A0, and T, we get:

t = 5730 * log(15.1/15.3) / log(0.5) ≈ 29868 years

Therefore, the age of the paper that the map is written on is about 29868 years.

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the value of tan(3π/4 + 7π) is 1. we can get this answer by using  the trigonometric identity tan(x + π) = -tan(x) . to rewrite expression

what is trigonometric identity?

A trigonometric identity is an equation that is true for all values of the variables in the equation, where the variables are angles or trigonometric functions of angles. Trigonometric identities are important in mathematics, physics, and engineering,

what is expression?

itis a mathematical phrase  containing numbers, variables, and mathematical operations some of them are addition, subtraction, multiplication, and division. It represents a mathematical relationship between one or more quantities or variables.

In the given question,

We know that the value of tan(3π/4) is -1.Now, let's consider the expression tan(3π/4 + 7π).We can use the following trigonometric identity to rewrite this expression:

tan(x + π) = -tan(x)

tan(3π/4 + 7π) = tan(3π/4 + π + 6π) = -tan(3π/4 + π)

Now, we know that tan(3π/4) is -1, and we can use the following trigonometric identity to find the value of tan(3π/4 + π):

tan(x + π) = -tan(x)

Using this identity, we can rewrite the expression as:

tan(3π/4 + π) = -tan(3π/4) = -(-1) = 1

Therefore, the value of tan(3π/4 + 7π) is 1.

In summary, we used the trigonometric identity tan(x + π) = -tan(x) to rewrite the expression tan(3π/4 + 7π) as -tan(3π/4 + π), and then we used the same identity again to find the value of tan(3π/4 + π), which is 1.

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Answer:

(3,5)count manually to get(3,5)

The distance between the two points is √34

The formula for calculating the distance between two points is expressed as:

Given the coordinate points (1, 4) and (-2, -1). Substitute into the formula to have:

D = √(-1-4)² + (-2-1)²

D = √(-5)² + (-3)²

D = √25 + 9

D = √34

Hence the distance between the two points is √34

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Answer:

170.8

Step-by-step explanation:

Answer:

5 trips

Step-by-step explanation:

330 people / 68 spots = 4.853

Because passengers cannot take 0.853 of a bus, it rounds up to 5.

In order to solve this exercise we must apply:

1) The Law of Sines

2) Heron's formula:

Now, we take the triangle of our problem and we put names to the sides and angles:

Sides of the triangle:

a = XY = ?

b = WY = 15 mi

c = XW = ?

Angles of the triangle:

α = ∠XWY = 180° - 112° - 27° = 41°

β = ∠WXY = 112°

γ = ∠XYW = 27°

Where in order to find α we took in account that the inner angles of a triangle sums 180°.

------------------------

With Heron's formula we see that we can obtain the area of the triangle but we need the lenghts a, b and c of the sides. So we will use the Law of Sines to determine each side and then with that data we will calculate the area using Heron's formula.

1) We calculate the lenghts of a and c, we apply the Law of Sines with the data that we know.

Now we know the length of the three sides:

a ≅ 10.61374

b = 15

c ≅ 7.34467

2) We calculate the semi-perimeter of the triangle:

Now, using the semi-perimeter, the length of the sides and Heron's formula we calculate the area of the triangle:

Answer

The area of the triangle △WXY to the nearest tenth is 36.1 mi².

Answer:

21/16

Step-by-step explanation:

Divide the number of peach pies by the number of strawberry pies.

Answer:

8x+161

Step-by-step explanation:

Answer:

7 pounds.

Step-by-step explanation:

3.60 for 3 pounds

1.20 per pound.

8.40/1.20 = 7 pounds

Answer:

Around 8 or 9

Step-by-step explanation:

210/ 24= 8.75

if ur rounding then the answer is 9

Answer:

8

Step-by-step explanation:

It is shown that: (a) The function f+g is convex.

(b) If c ≥ 0, then cf is convex. (c) If c ≤ 0, then cf is concave. The proposition is proven.

To prove the proposition, we'll need to show that each part (a), (b), and (c) holds true. Let's start with part (a).

(a) The function f+g is convex:

To prove that the sum of two convex functions is convex, we'll use the definition of convexity. Let's consider two points, x and y, in the interval I, and a scalar λ ∈ [0, 1]. We need to show that:

\((f+g)(λx + (1-λ)y) ≤ λ(f+g)(x) + (1-λ)(f+g)(y)\)

Now, since f and g are both convex, we have:

\(f(λx + (1-λ)y) ≤ λf(x) + (1-λ)f(y) \: (1) \\

g(λx + (1-λ)y) ≤ λg(x) + (1-λ)g(y) \: (2)\)

Adding equations (1) and (2), we get:

\(f(λx + (1-λ)y) + g(λx + (1-λ)y) ≤ λf(x) + (1-λ)f(y) + λg(x) + (1-λ)g(y) \\

(f+g)(λx + (1-λ)y) ≤ λ(f+g)(x) + (1-λ)(f+g)(y)\)

This shows that

\((f+g)(λx + (1-λ)y) ≤ λ(f+g)(x) + (1-λ)(f+g)(y),\)

which means that f+g is convex.

(b) If c ≥ 0, then cf is convex:

To prove this, let's consider a scalar λ ∈ [0, 1] and two points x, y ∈ I. We need to show that:

\((cf)(λx + (1-λ)y) ≤ λ(cf)(x) + (1-λ)(cf)(y)\)

Since f is convex, we know that:

\(f(λx + (1-λ)y) ≤ λf(x) + (1-λ)f(y)\)

Now, since c ≥ 0, multiplying both sides of the above inequality by c gives us:

\(cf(λx + (1-λ)y) ≤ c(λf(x) + (1-λ)f(y))

\\ (cf)(λx + (1-λ)y) ≤ λ(cf)(x) + (1-λ)(cf)(y)

\)

This shows that cf is convex when c ≥ 0.

(c) If c ≤ 0, then cf is concave:

To prove this, we'll consider the negative of the function cf, which is (-cf). From part (b), we know that (-cf) is convex when c ≥ 0. However, if c ≤ 0, then (-c) ≥ 0, so (-cf) is convex. Since the negative of a convex function is concave, we conclude that cf is concave when c ≤ 0.

In summary, we have shown that:

(a) The function f+g is convex.

(b) If c ≥ 0, then cf is convex.

(c) If c ≤ 0, then cf is concave.

Therefore, the proposition is proven.

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a) This implies that (f + g)(λx + (1 - λ)y) ≤ λ(f(x) + g(x)) + (1 - λ)(f(y) + g(y)), which proves that f + g is convex, b) This implies that (cf)(λx + (1 - λ)y) ≤ λ(cf(x)) + (1 - λ)(cf(y)), proving that cf is conve, c) Therefore, Proposition 1 is proven, demonstrating that the function f + g is convex, cf is convex when c ≥ 0, and cf is concave when c ≤ 0.

To prove Proposition 1, we will demonstrate each part individually:

(a) To prove that the function f + g is convex, we need to show that for any x, y in the interval I and any λ ∈ [0, 1], the following inequality holds:

(f + g)(λx + (1 - λ)y) ≤ λ(f(x) + g(x)) + (1 - λ)(f(y) + g(y))

Since f and g are convex functions, we know that for any x, y in I and λ ∈ [0, 1], we have:

f(λx + (1 - λ)y) ≤ λf(x) + (1 - λ)f(y)

g(λx + (1 - λ)y) ≤ λg(x) + (1 - λ)g(y)

By adding these two inequalities together, we obtain:

f(λx + (1 - λ)y) + g(λx + (1 - λ)y) ≤ λf(x) + (1 - λ)f(y) + λg(x) + (1 - λ)g(y)

This implies that (f + g)(λx + (1 - λ)y) ≤ λ(f(x) + g(x)) + (1 - λ)(f(y) + g(y)), which proves that f + g is convex.

(b) To prove that cf is convex when c ≥ 0, we need to show that for any x, y in I and any λ ∈ [0, 1], the following inequality holds:

(cf)(λx + (1 - λ)y) ≤ λ(cf(x)) + (1 - λ)(cf(y))

Since f is a convex function, we have:

f(λx + (1 - λ)y) ≤ λf(x) + (1 - λ)f(y)

By multiplying both sides of this inequality by c (which is non-negative), we obtain:

cf(λx + (1 - λ)y) ≤ c(λf(x)) + c((1 - λ)f(y))

This implies that (cf)(λx + (1 - λ)y) ≤ λ(cf(x)) + (1 - λ)(cf(y)), proving that cf is convex when c ≥ 0.

(c) To prove that cf is concave when c ≤ 0, we can use a similar approach as in part (b). By multiplying both sides of the inequality f(λx + (1 - λ)y) ≤ λf(x) + (1 - λ)f(y) by c (which is non-positive), we obtain the inequality (cf)(λx + (1 - λ)y) ≥ λ(cf(x)) + (1 - λ)(cf(y)), showing that cf is concave when c ≤ 0.

Therefore, Proposition 1 is proven, demonstrating that the function f + g is convex, cf is convex when c ≥ 0, and cf is concave when c ≤ 0.

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When p = 0, the consumer would optimally choose a quantity of q∗ = 40 units (40,000 gallons).

(a) q∗ = 40 units (40,000 gallons)

(b) marginal value at q∗ = $40.00 per 1000 gallons

(c) total benefit = $1,600.00

to illustrate the figure, we can plot the demand curve using the given price equation p = 80 - 2q. the x-axis represents the quantity of water (q) in units of 1000 gallons, and the y-axis represents the price per 1000 gallons ($/1000 g). the demand curve will be a downward-sloping line starting at p = 80 when q = 0, and intersecting the price axis at p = 0 when q = 40.

(a) to determine the optimal quantity (q∗) that the consumer would choose, we set the marginal benefit (mb) equal to the price (p). the marginal benefit is the derivative of the total benefit with respect to quantity. in this case, the marginal benefit is constant and equal to the price, so mb = p. (b) at the optimal quantity q∗, the marginal value received for the last unit of quantity is equal to the price. since the price is given as $80.00 per 1000 gallons, the marginal value at q∗ is $80.00 per 1000 gallons.

(c) the total benefit is calculated by multiplying the price per unit (p) by the quantity (q∗). in this case, when the price offered is $0.00 per 1000 gallons, the total benefit is $80.00 per 1000 gallons multiplied by 40 units (40,000 gallons), resulting in a total benefit of $1,600.00.

note: in this specific case, where the price offered is $0.00 per 1000 gallons, the total benefit, consumer surplus, and total net benefit would all be equal, as there is no payment required.

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Answer:

Mr. Hernadez got paid $4,224 for his work

In total he got paid $176 dollars.Correct me if ik wrong but I hope I helped

Hope this helps you. Thank you....

Using the reflection concept, it is found that the function g is given by:

\(g(x) = |6x| - 2\)

-------------------

-------------------

Reflecting over the x-axis:

\(g(x) = f(-x)\)

\(g(x) = |6(-x)| - 2\)

\(g(x) = |-6x| - 2\)

Modulus is an even function, thus \(|-6x| = |6x|\), and:

\(g(x) = |6x| - 2\)

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The points on the graph at which the tangent line is horizontal are:

(-1.414, 4.886) and (1.414, 1.114).

Since the horizontal tangent is parallel to the x-axis, its slope, or derivative, should also have a value of 0 at the tangent point. This is the key concept for finding the point on the graph where the tangent line is horizontal.  

The function is given as:

y = ¹/₃x³ - 2x + 3

The tangents are horizontal where the derivative is zero. The derivative of the given function is:

y' = x² -2

This is zero when:

0 = x² -2

2 = x²

x  = ±√2 . . . x-values where the derivative is zero

The corresponding y-values are:

y = (¹/₃x² - 2x + 3)

 y = (¹/₃(2) - (2(±√2)) + 3

The turning points are (-1.414, 4.886) and (1.414, 1.114).

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Complete question is:

For the function, find the points on the graph at which the tangent line is horizontal. If none exist, state that fact.

y = ¹/₃x³ - 2x + 3

To find the points on the graph at which the tangent line is horizontal, we need to find the x-values where the derivative of the function is equal to zero.

To find the points on the graph at which the tangent line is horizontal, we need to find the x-values where the derivative of the function is equal to zero. The derivative represents the rate of change or slope of the function at any given point.

Let's say we have a function f(x). To find the derivative of f(x), we differentiate the function with respect to x. The resulting derivative function is denoted as f'(x) or dy/dx.

Next, we set the derivative function f'(x) equal to zero and solve for x. The x-values obtained from this equation represent the points on the graph where the tangent line is horizontal.

If there are no solutions to the equation f'(x) = 0, it means there are no points on the graph where the tangent line is horizontal.

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If Station 1 (at 74, 41) is 44 km away and Station 2( at 0,43 ) is 38 km away. The required approximate location of the GPS receiver is (42, 10).

The location of the GPS receiver can be determined with the help of trilateration. Trilateration is a process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres, or triangles. If three stations (or more) are in known locations, with a known distance from the point of interest, we can determine the position of the GPS receiver with the help of trilateration.

It can be determined by the following method:

1: Plot the given stations on a coordinate plane. Stations are:

Station 1: (74, 41)

Station 2: (0, 43)

2: Calculate the distance of the GPS receiver from each station using the distance formula.

Distance Formula: The distance formula is used to find the distance between two points in the coordinate plane. The distance between points (x1,y1) and (x2,y2) is given by

d = √[(x2 - x1)² + (y2 - y1)²]

Station 1: Distance from station 1 = 44 kmSo, d1 = 44 km

Station 2: Distance from station 2 = 38 kmSo, d2 = 38 km

3: Plot the given distances as the circle on the coordinate plane.

Circle 1: Centred at (74, 41) with a radius of 44 km.

Circle 2: Centred at (0, 43) with a radius of 38 km.

4: The intersection of two circles. Circle 1 and Circle 2 intersect at point P (approx) (42, 10). So, the approximate location of the GPS receiver is (42, 10).

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The exact forecasted number of customers to be served on each of the next five business days, rounded to one decimal place, are as follows:

Tuesday: 389.1

Wednesday: 368.7

Thursday: 326.5

Friday: 510.9

To forecast the number of customers served on each of the next five business days using Winters' method, we need to follow these steps:

Calculate the seasonal factor for each day by multiplying the seasonal index by the level.

Monday: 1.10 × 20 = 22

Tuesday: 0.95 × 20 = 19

Wednesday: 0.90 × 20 = 18

Thursday: 0.80 × 20 = 16

Friday: 1.25 × 20 = 25

Update the level and trend using the following formulas:

New Level = α × (Actual Value / Seasonal Factor) + (1 - α) × (Previous Level + Previous Trend)

New Trend = β × (New Level - Previous Level) + (1 - β) * Previous Trend

For Tuesday:

New Level = 0.2 × (30 / 22) + 0.8 × (20 + 1) = 20.3636

New Trend = 0.1 × (20.3636 - 20) + 0.9 × 1 = 0.0364

Forecast the number of customers served on each subsequent day using the formula:

Forecast = (New Level + Forecasted Trend) × Seasonal Factor

Tuesday Forecast = (20.3636 + 0.0364) × 19 = 389.0909

Wednesday Forecast = (20.3636 + 0.0364) × 18 = 368.7273

Thursday Forecast = (20.3636 + 0.0364) × 16 = 326.5455

Friday Forecast = (20.3636 + 0.0364) × 25 = 510.9091

Therefore, the forecasted number of customers to be served on each of the next five business days, rounded to one decimal place, are as follows:

Tuesday: 389.1

Wednesday: 368.7

Thursday: 326.5

Friday: 510.9

The question should be: A local bank is using Winters' method with α = 0.2, β= 0.1, and γ = 0.5 to forecast the number of customers served each day. The bank is open Monday through Friday. At the end of the previous week, the following seasonal indexes have been estimated: Monday, 1.10; Tuesday, 0.95; Wednesday, 0.90; Thursday, 0.80; Friday, 1.25. Also, the current estimates of level and trend are 20 and 1. After observing that 30 customers are served by the bank on this Monday, forecast the number of customers who will be served on each of the next five business days. Round your answers to one decimal place, if necessary.

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The least scores Juan could have had in the two tests are 85 and 100

Let the test scores be x and y

Where x is the current test and y is the previous test

Using the interpretation of the parameters in the question, we have the following:

x = y + 15 --- the relationship between the test scores

The average test scores can be represented as

1/2(x + y) ≥ 92

Substitute x = y + 15 in 1/2(x + y) ≥ 92

1/2(y + 15 + y) ≥ 92

Evaluate the like terms

1/2(2y + 15) ≥ 92

So, we have

2y + 15 ≥ 184

This gives

2y ≥ 169

Divide by 2

y ≥ 84.5

From the question both numbers are integers

So, we can assume that y = 85

Substitute y = 85 in x = y + 15

x = 85 + 15

Evaluate

x = 100

Hence, the possible test scores are 85 and 100

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There is insufficient evidence to conclude that the population mean is not 44 at the 0.10 level of significance.

The null hypothesis (H0)  (μ = 44)

the alternative hypothesis (Ha)  (μ ≠ 44).

This is a two-tailed test because we are considering the possibility that the sample mean differs from the population mean in either direction.

Given:

- Sample size (n) = 100

- Sample mean (x) = 47

- Population mean under null hypothesis (μ) = 44

- Population standard deviation (σ) = 20

We can use the z-test formula:

z = (x - μ) / (σ/√n)

Substituting the given values:

z = (47 - 44) / (20/√100)

z = 3 / 2

z = 1.5

This z-value indicates how many standard deviations the sample mean is from the population mean.

At the 0.10 level of significance, the critical z-value for a two-tailed test can be found from the standard normal distribution table, or more easily remembered, it's approximately ±1.645.

The computed z-value of 1.5 is less than the critical z-value of 1.645, so we fail to reject the null hypothesis.

Therefore, there is insufficient evidence to conclude that the population mean is not 44 at the 0.10 level of significance.

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There is not enough evidence to support the claim that the population mean is not equal to 44

We have to test the following hypothesis against the alternative hypothesis. The population mean is assumed to be normally distributed in the hypothesis test.

$H_0: μ = 44$ (null hypothesis)

$H_1: μ ≠ 44$ (alternative hypothesis)

The level of significance is 0.10.

The significance level (α) is equal to 1 - confidence level, where a confidence level of 90 percent will correspond to a significance level of 0.10.

In order to test the hypothesis using a z-value, we can use the formula:

$$z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$$

where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size.

The sample mean is given as $\bar{x} = 47$, the population standard deviation is given as $\sigma = 20$, the population mean is $\mu = 44$, and the sample size is $n = 100$.

Now, we can substitute these values in the formula and get the z-score.

$$z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}

     = \frac{47 - 44}{\frac{20}{\sqrt{100}}}

     = 1.5$$

The absolute value of the z-value is 1.5. For a two-tailed test, the critical value of z for a significance level of 0.10 is 1.645.

Since our z-value is less than 1.645, we cannot reject the null hypothesis.

Therefore, we can conclude that there is not enough evidence to support the claim that the population mean is not equal to 44.

Thus, is correct "There is not enough evidence to support the claim that the population mean is not equal to 44".

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The appropriate alternative hypothesis is the opposite of null hypothesis that there is a difference in mean SSHA scores between men and women.

The alternative hypothesis is the opposite of the null hypothesis, which is typically stated as there being no difference between the two groups. In this example, the null hypothesis is that there is no difference in mean SSHA scores between men and women. The alternative hypothesis is then that there is a difference in mean SSHA scores between men and women. This can be stated as "There is a difference in mean SSHA scores between men and women". This is the appropriate alternative hypothesis for this test of significance.

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