A greenhouse in a tri-county area has kept track of its customers for the last several years and has determined that it has about 10,000 regular customers. Of those customers, 28% of them plant a vegetable garden in the spring. The greenhouse obtains a random sample of 800 of its customers. Is it safe to assume that the sampling distribution of , the sample proportion of customers that plant a vegetable garden, is approximately normal? Answer Yes or No.

Answer:

5000(1+0.0245) raise to 5

$5643.26

Step-by-step explanation:

The amount of money that will received after 5 years is $5643.256

Compound Interest

The compound interest of a primary money P with rate of interest r for time t is the total money that include interest and primary as well and can be calculated with the formula

[tex]A=P(1+\frac{r}{100})^t[/tex]

Here we have given

Primary money = P = $5000

Rate of interest = r = 2.45 %

Time = 5 year

Substitute these values into above formula and we get

[tex]A=5000(1+\frac{2.45}{100})^5[/tex]

[tex]A=5000(1.0245)^5[/tex]

A = $5643.256

Therefore the total amount that will received after 5 year is $5643.256

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The answer is 240 chairs.

Answer: Triangle, Square, Rectangle, Trapezium

Step-by-step explanation:

Cutting the cube from above, in a way that the slice is diagonal, making the slice touches two points that's almost at the edges diagonally facing each other of the cube will give a Trapezium (A)

Cutting the cube from above, in a way that the slice cuts exactly through the edges diagonally facing each other will give a Triangle (B)

Cutting the cube from above perpendicularly to the length, the two new faces made from the cube are squares (C)

Cutting the cube from above perpendicularly too will give two rectangles from the above face (D)

Step-by-step explanation:

The domain of f(x) is all values of x for which f(x) is defined.

For f(x) to be defined, the expression under the radical must be non-negative.

Therefore, the domain is x ≥ 0, or in interval notation, [0, ∞).

Answer: There are 50 ways to select in this way and there is only 1 combination is possible i.e. 3 students and 4 professors.

Step-by-step explanation:

Since we have given that

Number of professors = 5

Number of students = 5

We need to find the number of ways of 7 members in such that number of professors must be one more than students.

So, if we select 3 students, then there will be 4 professors.

So, Number of ways would be

[tex]^5C_3\times ^5C_4\\\\=10\times 5\\\\=50[/tex]

Hence, there are 50 ways to select in this way and there is only 1 combination is possible i.e. 3 students and 4 professors.

Answer:

The volume of the solid is [tex]\frac{48\pi}{5}[/tex]

Step-by-step explanation:

Consider the provided information.

The​ cross-sections perpendicular to the​ y-axis are circular disks with diameters running from the​ y-axis to the parabola [tex]x=\sqrt6y^2[/tex]

Therefore, diameter is [tex]d=\sqrt6y^2[/tex]

Radius will be [tex]r=\frac{\sqrt6y^2}{2}[/tex]

We can calculate the area of circular disk as: πr²

Substitute the respective values we get:

[tex]A=\pi(\frac{\sqrt6y^2}{2})^2[/tex]

[tex]A=\pi(\frac{6y^4}{4})=\frac{3\pi y^4}{2}[/tex]

Thus the volume of the solid is:

[tex]V=\int\limits^2_0 {\frac{3\pi y^4}{2}} \, dy[/tex]

[tex]V=[{\frac{3\pi y^5}{2\times 5}}]^2_0[/tex]

[tex]V=\frac{48\pi}{5}[/tex]

Hence, the volume of the solid is [tex]\frac{48\pi}{5}[/tex]

The volume of solid represent the how much space an object occupied. In the given problem volume can be determine by taking the integration of Area of solid.

The volume of solid is [tex]\frac{48\pi }{5}[/tex].

Given:

The​ cross-sections perpendicular to the​ y-axis are circular disks with diameters running from the​ y-axis to the parabola is [tex]x=\sqrt{6}y^2[/tex].

The diameter of the solid is [tex]d=\sqrt{6}y^2[/tex].

Calculate the radius of the solid.

[tex]r=\frac{d}{2}\\r=\frac{\sqrt{6}y^2}{2}[/tex]

Write the expression for area of circular disk.

[tex]A=\pi r^2\\A=\pi (\frac{\sqrt{6}y^2}{2})^2\\A=\frac{3\pi y^4}{2}[/tex]

Calculate the volume of solid.

[tex]V=\int\limits^2_0 {\frac{3\pi y^4 }{2} } \, dy\\V=[\frac{3\pi y^5}{2\times 5}]_{0}^{2}\\V=\frac{48\pi }{5}[/tex]

Thus, the volume of solid is [tex]\frac{48\pi }{5}[/tex] .

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Answer:

[tex]\left\{\begin{array}{l}y\ge 2x+4\\ \\y<-x+2\end{array}\right.[/tex]

Step-by-step explanation:

1. The solid line passes trough the points (0,4) and (-2,0). The equation of this line is:

[tex]\dfrac{x-0}{-2-0}=\dfrac{y-4}{0-4}\\ \\y-4=2x\\ \\y=2x+4[/tex]

The origin doesn't belong to the shaded region, so its coordinates do not satisfy the inequality. Thus,

[tex]y\ge 2x+4[/tex]

2. The dotted line passes trough the points (0,2) and (2,0). The equation of this line is:

[tex]\dfrac{x-0}{2-0}=\dfrac{y-2}{0-2}\\ \\y-2=-x\\ \\y=-x+2[/tex]

The origin belongs to the shaded region, so its coordinates  satisfy the inequality. Thus,

[tex]y< -x+2[/tex]

Hence, the system of two inequalities is

Answer:

  783.9

Step-by-step explanation:

The same tool that gave you the answer to the second part will give you the answer to the first part.

_____

You will note the box is checked saying "Log Mode". This mode uses linear regression on the logarithms of the y-values. When the box is unchecked, regression is used on the actual y-values.

The latter method tends to favor matching the larger y-values at the expense of matching smaller ones. It gives a different equation.

Answer:

E(X) = 6.0706

Step-by-step explanation:

1) Define notation

X = random variable who represents the number of heads in the 10 first tosses

Y = random variable who represents the number of heads in range within toss number 4 to toss number 10

And we can define the following events

a= The first coin has been selected

b= The second coin has been selected

c= represent that we have 2 Heads within the first two tosses

2) Formulas to apply

We need to find E(X|c) = ?

If we use the total law of probability we can find E(Y)

E(Y) = E(Y|a) P(a|c) + E(Y|b)P(b|c) ....(1)

Finding P(a|c) and using the Bayes rule we have:

P(a|c) = P(c|a) P(a) / P(c) ...(2)

Replacing P(c) using the total law of probability:

P(a|c) = [P(c|a) P(a)] /[P(c|a) P(a) + P(c|b) P(b)] ... (3)

We can find the probabilities required

P(a) = P(b) = 0.5

P(c|a) = (3C2) (0.4^2) (0.6) = 0.288

P(c|b) = (3C2)(0.7^2) (0.3) = 0.441

Replacing the values into P(a|c) we got

P(a|c) = (0.288 x 0.5) /(0.288x 0.5 + 0.441x0.5) = 0.144/ 0.3645 = 0.39506

Since P(a|c) + P(b|c) = 1. With this we can find P(b|c) = 1 - P(a|c) = 1-0.39506 = 0.60494

After this we can find the expected values

E(Y|a) = 7x 0.4 = 2.8

E(Y|b) = 7x 0.7 = 4.9

Finally replacing the values into equation (1) we got

E(Y|c) = 2.8x 0.39506 + 4.9x0.60494 = 4.0706

And finally :

E(X|c) = 2+ E(Y|c) = 2+ 4.0706 = 6.0706

In this problem, we have to consider a conditional expected value for the flips of a randomly chosen misshapen coin. We start with a known result (2 heads in 3 flips) and then compute the expected outcome for the next 7 flips for both coins. The final answer is the average of these expectations.

This question involves the realm of probability theory and specific concept of expected value. Given two distinct coins with varying chances of landing on heads, we need to calculate the expected number of heads when one of these coins is randomly chosen and flipped 10 times.

The usual expected number of heads will be the sum of the individual expected values for each, which in turn is the product of the number of trials (10 flips) and the probability of success (landing on a head). However, the condition that two of the first three flips landed on heads slightly modifies this calculation process.

The main challenge here is that we start with a known result (2 heads in 3 flips), and we then have 7 additional flips with unknown results. Since we don't know which coin we have, we must consider the expected outcomes for both coins and then divide by 2. The theoretical probability does not predict short-term results, but gives information about what can be expected in the long term.

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Answer:

55 trees per hectare.

Step-by-step explanation:

An apple orchard contains 50 trees per hector. The average yield per tree is 600 apples.

If the trees are spaced more closely, when being planted, the yield per tree drops by 10 apples for each extra tree.

Let x extra tree is planted and then the average yield per tree reduces by 10x.

Therefore, yield as a function of x can be written as  

Y(x) = (50 + x)(600 - 10x) = 30000 + 100x - 10x²

Therefore, condition for maximum yield is [tex]\frac{dY(x)}{dx} = 0[/tex]

So, 100 - 20x = 0

⇒ x = 5

So, when the number of trees that should be planted per hectare is (50 + 5) = 55, then only the yield will be maximum. (Answer)

4 inches of rain would fall in 6 hours

Given that, A rain storm came through Clifton park  

And it was accumulating [tex]\frac{2}{3}[/tex] inches of rain/hour

So amount of rain accumulated in 1 hour = [tex]\frac{2}{3}[/tex]

Thus amount of rain accumulated in six hours is calculated by multiplying the amount of water accumulating per hour and 6

Amount of water accumulated in 6 hours = Amount of water accumulated in 1 hour [tex]\times[/tex] 6

[tex]\text { Amount of water accumaulated in 6 hours }=\frac{2}{3} \times 6=4[/tex]

Another way:

Let "n" be the amount of rain accumulated in 6 hours

1 hour ⇒ [tex]\frac{2}{3}[/tex] rain accumulated

6 hours ⇒ "n"

By cross multiplication, we get

[tex]6 \times \frac{2}{3} = 1 \times n\\\\n = \frac{2}{3} \times 6 = 4[/tex]

Hence, 4 inches of rain would fall in 6 hours.

If the rain fell at a constant rate of 2/3 inch per hour, then 4 inches of rain would fall in a total of 6 hours. This calculation is made by multiplying the rate of rainfall by the total time.

The question asks how many inches of rain would fall in Clifton park in 6 hours if the rate was consistently 2/3 inch per hour. Given the constant rate of rainfall, we can calculate the total inches of rain that fell in 6 hours by multiplying the rate (2/3 inches/hour) by the total time in hours (6 hours).

So, doing the multiplication:

(2/3 inch/hour) * (6 hours) = 4 inches of rain.

This means that if the rain continued to fall at the same rate, we would expect 4 inches of rain to accumulate in Clifton park over 6 hours.

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Answer:

Step-by-step explanation:

volume of water

[tex]=\frac{1}{2}*50*40*60=60000 ~cm^3[/tex]

when the base is 100×60

let h be depth of water.

100×60×h=60000

h=60000/6000=10 cm.

Answer:the car was traveling at a speed of 80 ft/s when the brakes were first applied.

Step-by-step explanation:

The car braked with a constant deceleration of 16ft/s^2. This is a negative acceleration. Therefore,

a = - 16ft/s^2

While decelerating, the car produced skid marks measuring 200 feet before coming to a stop.

This means that it travelled a distance,

s = 200 feet

We want to determine how fast the car was traveling (in ft/s) when the brakes were first applied. This is the car's initial velocity, u.

Since the car came to a stop, its final velocity, v = 0

Applying Newton's equation of motion,

v^2 = u^2 + 2as

0 = u^2 - 2 × 16 × 200

u^2 = 6400

u = √6400

u = 80 ft/s

To find out how fast the car was traveling when the brakes were first applied, we need to solve a quadratic equation. After simplifying and rearranging the terms, we find that the car's initial velocity is not equal to 0, indicating that the car was already moving before the brakes were applied.

To determine how fast the car was traveling when the brakes were first applied, we can use the equation of motion relating distance, initial velocity, deceleration, and time. In this case, the given distance is 200 feet and the deceleration is 16 ft/s². Initially, the car was traveling at a certain velocity, which we need to find.

Using the equation x = xo + vot + 1/2at², where x is the final distance, xo is the initial position, vo is the initial velocity, a is the deceleration, and t is the time, we can plug in the known values and solve for vo:

200 ft = 0 + vo * t + 1/2 * (-16 ft/s²) * (t)²

Simplifying the equation and rearranging terms gives us a quadratic equation:

-8t² + vot - 200 = 0

Using the quadratic formula, we can solve for t:

t = (-vo ± √(vo² - 4 * (-8) * (-200))) / (2 * (-8))

Since the car is initially traveling, the positive root is used:

t = (-vo + √(vo² + 6400)) / (-16)

Simplifying the equation further:

t = (-vo + √(vo² + 6400)) / (-16)

Now we can solve for vo by substituting t = 0 into the equation:

0 = (-vo + √(vo² + 6400)) / (-16)

vo - √(vo² + 6400) = 0

Squaring both sides of the equation:

vo² - (vo² + 6400) = 0

Subtracting vo² from both sides of the equation:

-6400 = 0

This is a contradiction, which means that the car's initial velocity vo is not equal to 0. Therefore, the car was already moving when the brakes were first applied.

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Answer:

V'(t) = [tex]-250(1 - \frac{1}{40}t)[/tex]

If we know the time, we can plug in the value for "t" in the above derivative and find how much water drained for the given point of t.

Step-by-step explanation:

Given:

V = [tex]5000(1 - \frac{1}{40}t )^2[/tex]  , where 0≤t≤40.

Here we have to find the derivative with respect to "t"

We have to use the chain rule to find the derivative.

V'(t) = [tex]2(5000)(1 - \frac{1}{40} t)d/dt (1 - \frac{1}{40}t )[/tex]

V'(t) = [tex]2(5000)(1 - \frac{1}{40} t)(-\frac{1}{40} )[/tex]

When we simplify the above, we get

V'(t) = [tex]-250(1 - \frac{1}{40}t)[/tex]

If we know the time, we can plug in the value for "t" and find how much water drained for the given point of t.

Sum of Option 2 does not equal to others

Step-by-step explanation:

We have to find each sum to check which is a outlier.

so,

Option 1:

∑i^2 where i = 1 to  3

[tex]Sum = 1^2+2^2+3^2\\=1+4+9\\=14[/tex]

Option 2:

∑i^3 where i = 1 to 2

So,

[tex]Sum = 1^3+2^3\\= 1 +8\\=9[/tex]

Option 3:

∑(i+1) where i = 1 to 4

[tex]Sum = (1+1) + (2+1) +(3+1) +(4+1)\\=2+3+4+5\\=14[/tex]

Option 4:

∑(2i-2) where i = 4 to 5

[tex]Sum = [2(4)-2]+[2(5)-2]\\=(8-2)+(10-2)\\=6+8\\=14[/tex]

Hence,

Sum of Option 2 does not equal to others

Keywords: Sum, Formulas

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The sum from i equals 1 to 2 of i cubed does not equal the others.

To determine which sum does not equal the others, we need to evaluate each sum.

From the evaluations, we can see that the sum from i equals 1 to 2 of i cubed does not equal the others.

Answer:

A) First number: 13

B) Second number: 21

C) Third number: 63

Step-by-step explanation:

Let x, y and z be 1st, 2nd and 3rd numbers respectively.

We have been given that sum of three numbers is 97. We can represent this information in an equation as:

[tex]x+y+z=97...(1)[/tex]

The 3rd number is 3 times the second. We can represent this information in an equation as:

[tex]z=3y...(2)[/tex]

The second number is 8 more than the first. We can represent this information in an equation as:

[tex]y=x+8...(3)[/tex]

Substituting equation (3) in equation (2), we will get:

[tex]z=3(x+8)[/tex]

Substituting [tex]z=3(x+8)[/tex] and [tex]y=x+8[/tex] in equation (1), we will get:

[tex]x+x+8+3(x+8)=97[/tex]

[tex]x+x+8+3x+24=97[/tex]

[tex]5x+32=97[/tex]

[tex]5x+32-32=97-32[/tex]

[tex]5x=65[/tex]

[tex]\frac{5x}{5}=\frac{65}{5}[/tex]

[tex]x=13[/tex]

Therefore, the first number is 13.

Now, we will substitute [tex]x=13[/tex] in equation (3) as:

[tex]y=21[/tex]

Therefore, the second number is 21.

Now, we will substitute [tex]y=21[/tex] in equation (2) as:

[tex]z=3(21)[/tex]

[tex]z=63[/tex]

Therefore, the third number is 63.

Answer:

4y/(y+4)

Step-by-step explanation:

2y/(y-3) x [(4y -12) /(2y+8)]

To determine this, at first we have to break the parentheses. Since there is no matching values, we have to multiply the numerators and denominators.

[2y x (4y - 12)] / (y-3) x (2y + 8)

or, [(2y*4y) - (2y*12)]/[(y*2y) + (y*8) - (3*2y) - (3*8)]

(using algebraic equation)

or, (8y^2 - 24y)/(2y^2 + 8y - 6y - 24)

or, (8y^2 - 24y)/(2y^2 + 2y - 24)

or, 8y(y - 3)/2(y^2 + y - 12) (taking common)

or, 4y(y - 3)/(y^2 + 4y - 3y - 12)

or, 4y(y - 3)/[y(y + 4) - 3 (y + 4)] (Using factorization or Middle-Term factor)

or, 4y (y - 3)/(y + 4)(y - 3)

or, 4y/(y + 4) [as (y-3)/(y-3) = 1, we have dropped the part]

The answer is = 4y/(y+4)

Answer:

y = 6

Step-by-step explanation:

Its going by 6's

The value of Bill Casler's CD (certificate of deposit) when it matures is $1060 and Bill receives $1036.36 from his friend.

First, we'll calculate the value of the CD (certificate of deposit) when it matures. To do this, we can use the formula for simple interest, which is PRT (Principal, Rate, Time). Here, P = $1000, R = 8% (or 0.08) and T = 9/12 years (converted to years).

So, the interest earned = 1000 * 0.08 * (9/12) = $60. The value of the CD when it matures would thus be the principal plus the interest earned, which is $1000 + $60 = $1060.

Now, for the second part of the question, we need to find out how much Bill received from his friend. The friend wants to earn a 10% annual simple interest return on his loan to Bill, so we'll equate the maturity value to the formula for simple interest. Here, P represents the amount loaned and we need to solve for P. Thus 1060 = P + P*0.10*(3/12).

Solving for P, we get P = $1036.36. So, Bill received $1036.36 from his friend.

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To find the value of the CD when it matures, use the simple interest formula. Add the interest earned to the principal to find the value. To find how much Bill received from his friend, set up an equation with the interest earned by the friend as 10% of the loan amount.

To find the value of the CD when it matures, we can use the formula for simple interest which is I = PRT, where I is the interest, P is the principal, R is the interest rate, and T is the time in years. In this case, P = $1000, R = 8%, and T = 9/12 years. Plugging the values into the formula, we get:
I = $1000  imes 0.08  imes (9/12)

I = $60

So, the interest earned is $60. To find the value of the CD when it matures, we simply add the interest to the principal:

Value = $1000 + $60

Value = $1060

For the second question, we need to find how much Bill received from his friend. Since the friend will earn a 10% annual simple interest return on his loan to Bill, we know that the interest earned by the friend is 10% of the amount he lent. Let's call this amount X. So, the interest earned by the friend is 10% of X. To find X, we can set up an equation:

10% of X = $1060

0.10X = $1060

X = $1060 / 0.10

X = $10,600

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Answer:

Solutions of the equation are 22.5°, 30°.

Step-by-step explanation:

The given equation is sin(5θ) - sin(3θ) = cos(4θ)

We take left side of the equation

sin(5θ) - sin(3θ) = [tex]2cos(\frac{5\theta+3\theta}{2})sin(\frac{5\theta-3\theta}{2})[/tex]

= [tex]2cos(4\theta)sin(\theta)[/tex] [From sum-product identity]

Now we can write the equation as

2cos(4θ)sin(θ) = cos(4θ)

2cos(4θ)sinθ - cos(4θ) = 0

cos(4θ)[2sinθ - 1] = 0

cos(4θ) = 0

4θ = 90°

θ = [tex]\frac{90}{4}[/tex]

θ = 22.5°

and (2sinθ - 1) = 0

sinθ = [tex]\frac{1}{2}[/tex]

θ = 30°

Therefore, solutions of the equation are 22.5°, 30°

Answer:

  k = 4

Step-by-step explanation:

The remainder theorem tells you that the remainder from division of f(x) by (x-1) is f(1). Evaluating the expression for x=1 gives ...

  2(1³) -3(1²) +k(1) -1 = 2 -3 +k -1 = k -2

We want this to be equal to 2, so ...

  k -2 = 2

  k = 4

Applying the Remainder Theorem to the given polynomial, we can substitute x = 1 into the polynomial equation and solve for k, which gives us k = 4.

The question asks to find the value of k when given polynomial 2x^3 - 3x^2 + kx - 1 is divided by x - 1 and the remainder is 2. We utilize the Remainder Theorem for this, which states that when a polynomial f(x) is divided by x-c, the remainder is equal to f(c).

So, by substituting x = 1 in the given polynomial as per the Remainder Theorem, we have: 2(1)^3 - 3(1)^2 + k(1) - 1 = 2. Simplifying this equation leads us to: 2 - 3 + k -1 = 2, which can further be simplified to k - 2 = 2. Thereby, solving for k gives us k = 4.

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Answer: B

Step-by-step explanation:

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. Since the machines are identical and running at the same constant rate, it means each of them as the same rate. The rate of each machine can produce would be determined by dividing the combined unit rate by 6. It becomes

270/6 = 45 bottles per minutes

The rate for 10 machines running at the same constant rate would be

10 × 45 = 450 bottles per minutes.

If the 10 machines produce 450 bottles per minutes, then,

In 4 minutes, the 10 machines will produce 4 × 450 = 1800 bottles

Answer:

  7h +11r = 350

Step-by-step explanation:

Let h and r represent minutes of hiking and running, respectively. Then calories burned by a 150-lb person doing these activities will total 350 when ...

  7h +11r = 350

_____

7 calories per minute are burned by hiking, so 7h will be the calories burned by hiking h minutes.

11 calories per minute are burned by running, so 11r will be the calories burned by running r minutes.

The total of calories burned in these activities will be 7h+11r, and we want that total to be 350.

Answer: The correct option is C

Step-by-step explanation:

Looking at the right angle triangle ABC, three sides are known and the angles are unknown. To find sin A, we will take A to be our reference angle, we will have the following

Hypotenuse = AB = 26

Opposite side = BC = 24

Adjacent side = AC = 10

Applying trigonometric ratio

SinA = opposite/hypotenuse

SineA = 24/26

To find cos A, A remains our reference angle, we will have the following

Hypotenuse = AB = 26

Opposite side = BC = 24

Adjacent side = AC = 10

Applying trigonometric ratio

CosA = adjacent/hypotenuse

CosA = 10/26

The correct option is C

Answer: 2w

Step-by-step explanation: if the garden is shaped like a square, then all the sides are equal,

length = breadth, and the Area of a square or rectangle is the length multiplied by the breadth

and to find the length and breadth, we find the square root of the area

The area is 4w2

We know that 4 is the perfect square of 2, making 2 the square root of 4

And w2 is the square of w

This is elementary algebra, a x a = a2

b x b = b2, w x w = w2

So adding both together, the square root of 4w2 = 2w

The length of each side of the square-shaped garden with area 4w2 is 2w.

The student has given the area of a square-shaped garden as 4w2. Since the area of a square is calculated by squaring the length of one of its sides (side2), to find the length of each side, we need to find the square root of the area. The square root of 4w2 is 2w, because (2w)2 equals 4w2. Therefore, the length of each side of the garden is 2w.

Staement 1 and statement 4 are true

Staement 1: It is incorrect because thirds and eighths cannot be divided to make ninths

Statement 4: It is incorrect because a quotient cannot be greater than the number that is divided.

Given that, Eli evaluated 23 ÷ 38 and got an answer of 179.

Now, let us check the given statements

1) It is incorrect because thirds and eighths cannot be divided to make ninths

It seems right because when 3 is divided by 8, it will give an fractional value. So this statement is correct

2) It is correct because 38 of 23 is 179

It is wrong as 38 x 23 ≠ 179 and not even related to the question.

3) It is correct because 179 • 38 equals 23

It is wrong because 179 x 38 ≠ 23

4) It is incorrect because a quotient cannot be greater than the number that is divided.

It is right as the dividend can not be smaller than the quotient.

Hence, the 1st and 4th statements are right.

Answer:

[tex]z=-2.32[/tex]  

[tex]p_v =P(Z<-2.32)= 0.010[/tex]  

If we compare the p value and using any significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significant lower than the proportion 2 at 5% of significance.  

Step-by-step explanation:

1) Data given and notation  

[tex]X_{1}=37[/tex] represent the number of people with characteristic 1

[tex]X_{2}=58[/tex] represent the number of people with characteristic 2

[tex]n_{1}=139[/tex] sample 1 selected

[tex]n_{2}=147[/tex] sample 2 selected

[tex]p_{1}=\frac{37}{139}=0.266[/tex] represent the proportion of people with characteristic 1

[tex]p_{2}=\frac{58}{147}=0.395[/tex] represent the proportion of people with characteristic 2

z would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the value for the test (variable of interest)

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the proportion 1 is less than the proportion 2, the system of hypothesis would be:  

Null hypothesis:[tex]p_{1} \geq p_{2}[/tex]  

Alternative hypothesis:[tex]p_{1} < p_{2}[/tex]  

We need to apply a z test to compare proportions, and the statistic is given by:  

[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex]   (1)

Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{37+58}{139+147}=0.332[/tex]

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:  

[tex]z=\frac{0.266-0.395}{\sqrt{0.332(1-0.332)(\frac{1}{139}+\frac{1}{147})}}=-2.32[/tex]  

4) Statistical decision

For this case we don't have a significance level provided [tex]\alpha[/tex] we can assuem it 0.05, and we can calculate the p value for this test.  

Since is a one left tailed test the p value would be:  

[tex]p_v =P(Z<-2.32)= 0.010[/tex]  

So if we compare the p value and using any significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significant lower than the proportion 2 at 5% of significance.  

Final answer:

To find the sample mean difference, multiply the t statistic by the standard error. With a t statistic of 2.00 and a standard error of 4 points for samples with n = 16 scores, the sample mean difference is 8 points.

Explanation:

The student asks how to calculate the sample mean difference given the standard error and the t statistic for two samples each with n = 16 scores. This information is used to conduct a hypothesis test to compare two population means, using the t distribution when the population standard deviations are unknown and the sample sizes are small.

The formula to find the sample mean difference when given the t statistic and the standard error is:

sample mean difference = t statistic × standard error

Plugging the given values:

sample mean difference = 2.00 × 4 = 8

Therefore, the estimated sample mean difference is 8 points.

Erica will take 4.5 minutes to run from home to school

Given that , Arica can run [tex]\frac{1}{6}[/tex] of a kilometer in a minute  

Her school is [tex]\frac{3}{4}[/tex] th of a kilometer away from her home  

We have to find at this speed how long will it take Erica to run from home to school

The relation between speed distance and time is given as:

[tex]\text { Distance }=\text { speed } \times \text { time }[/tex]

Plugging in values, we get

[tex]\frac{3}{4}=\frac{1}{6} \times \text { time taken }[/tex]

[tex]\begin{array}{l}{\text { Time taken to reach school }=\frac{3}{4} \times 6} \\\\ {\text { Time taken to reach home }=\frac{3}{2} \times 3} \\\\ {\text { Time taken to reach home }=\frac{9}{2}=4.5}\end{array}[/tex]

Hence, she takes 4.5 minutes to reach school from her home