Find the p-value for this test based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table)
a. xยฏxยฏ = 380; s = 39; n = 18

The probability is given by -0.004 , that the mean of the sample would differ from the population mean by less than 0.9 watts.

Normal distribution also known as the Gaussian probability, is a probability distribution that is symmetric about the mean, showing that data bear the mean are more frequent in occurrence than data far from the mean.

In a set with mean μ and standard deviation (which is the square root of the variance) σ , the z score of a measure X is given by:

Z =X-μ/σ

we have given μ = 495

σ =root(100),   n = 85

This is the p-value of Z when X = 495 +1.7 =496.7 subtracted by the p-value of Z when X = 495 - 1.7 = 493.3

When X = 496.7

Z =X-μ/10

Z = 496.7 -495/10

Z = 0.447 p-value = 0.447

When X = 493.3

Z =X-μ/σ

Z = 493.3- 495/10

=- 0.443 p-value

0.443 - 0.447= -0.004

Hence the probability is -0.004.

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At the start of 2014 lucys house was worth $250,000.

The table that shows ta proportional relationship is the C. Minutes read.

The constant of proportionality is D. 20.

Given are three tables.

Proportional relationships are relationships for which the equations are of the form y = kx, where k is a constant.

Here k is also called constant of proportionality.

In a proportional relationships, the y values will be moving in a constant manner with that of x.

For the Minutes Read table,

Minutes read can be related to the number of days as,

Minutes read = 20 (Number of days).

So this is a proportional relationship.

Constant of proportionality = 20

Hence the table which shows a proportional is the c. Minutes Read table and the constant of proportionality is D. 20.

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For two vectors u and v, the magnitude and direction of the sum of vectors, u +v, are equal to the 1.75 and 35.14°.

The formula to determine the magnitude of a vector (in two dimensional space) v = (x, y) is [tex]|v| =\sqrt {(x² + y²)}[/tex]. We have two vectors say v and u.

Magnitude of vector u = 5

direction of vector u = 265°

Magnitude of vector v = 8

direction of vector v = 105°

[tex]\vec u = ( 5cos(265°), 5sin(265°)) [/tex]

[tex]= (−0.436 , −4.981) [/tex]

[tex]\vec v = ( 8cos(105°), 8sin(105°)) [/tex]

[tex]= (−1.294 ,4.829 ) [/tex]

We have to determine the magnitude and direction of the sum, [tex] \vec u + \vec v[/tex]. Vector addition means putting two or more vectors together. Two vectors, a and b, can be added together using vector addition, and the resultant vector can be written as : a + b.

[tex] \vec u + \vec v = (-0.436 + (-1.294), -4.981 +4.829) [/tex]

[tex]= (- 1.730, -0.251) [/tex]

Now, the magnitude of the sum of two vectors is [tex]| \vec u + \vec v | = \sqrt{ {(u + v)_x}^{2} + {(u+v)_y}^{2} } [/tex]

[tex]= \sqrt{ 1.730² + 0.251²} [/tex]

[tex]= 1.74811355466 [/tex] ~ 1.75

Now, direction of vector which is sum of vectors : Let x be angle between componets of vector ( u + v) then direction is [tex]tan ( \theta) = \frac{-0.251}{-1.730} [/tex]

[tex]\theta = tan^{-1}(0.1451)[/tex]

= 35.14°

Hence, required value is 35.14°.

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Answer:

9.7 in²

Step-by-step explanation:

We Know

A baseball has a radius of 1.75 inches.

How much material is needed to cover the baseball?

They basically ask us to find the area of the circle.

Area of circle =  r² · π

r = 1.75 inches

π = 3.14

We Take

1.75² · 3.14 = 9.61625 in²

So, you need about 9.7 in² material to cover the baseball.

The board is 3 1/6 feet left. The correct option is C.

To find out how much of the board is left, we need to subtract the length of the section that was cut off from the original length of the board:

6 2/3 - 3 1/2

To subtract these two mixed numbers, we need to find a common denominator. The smallest common denominator of 3 and 2 is 6:

Next, we can simplify the fractions,

62/3 - 3 1/2

= 20/3 - 7/2

= (40 - 21)/6

= 19/6

= 3 1/6 feet.

Therefore, the answer is C. 3 1/6 feet.

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The area of the door is 8 feet x 4 feet = 32 square feet.

So a new door would cost 32 square feet x $5.00 per square foot = 160.00

Rewriting multiplication of a sum or difference as an addition or subtraction problem is known as the distributive property.

The distributive property allows you to break down a multiplication problem involving a sum or difference into separate addition or subtraction problems. Here's a step-by-step explanation:
Step:1. Identify the sum or difference within the multiplication problem. For example, in the problem (a + b) * c, the sum is (a + b).
Step:2. Apply the distributive property by multiplying each term inside the parentheses by the outside term. In our example, this would be: a * c + b * c.
Step:3. The result is the rewritten problem as an addition or subtraction problem. In this case, it is a * c + b * c.

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The molarity of acetic acid in the vinegar is 0.561 M and the mass percent of acetic acid in the vinegar is 33.6%.

In this problem, we are given the volume and concentration of the base (NaOH) used to titrate a sample of vinegar, and we need to find the molarity of acetic acid in the vinegar and the mass percent of acetic acid.

To start, we can use the balanced chemical equation for the reaction between acetic acid and NaOH to find the moles of NaOH used in the titration:

CH₃COOH + NaOH → CH₃COONa + H₂O

From the equation, we can see that the ratio of moles of acetic acid to moles of NaOH is 1:1. Therefore, the number of moles of NaOH used is the same as the number of moles of acetic acid in the original vinegar sample.

Molarity of acetic acid in the vinegar:

moles of NaOH = concentration of NaOH × volume of NaOH used

moles of acetic acid = moles of NaOH

molarity of acetic acid = moles of acetic acid / volume of vinegar sample

Substituting the given values, we get:

moles of NaOH = 0.231 M × 0.02430 L = 0.00561 moles

moles of acetic acid = 0.00561 moles

molarity of acetic acid = 0.00561 moles / 0.0100 L = 0.561 M

Mass percent of acetic acid in the vinegar:

mass of acetic acid = density × volume × molarity × molecular weight

mass percent = (mass of acetic acid / mass of vinegar sample) × 100%

Substituting the given values and the molecular weight of acetic acid (60.05 g/mol), we get:

mass of acetic acid = 1.01 g/mL × 0.0100 L × 0.561 mol/L × 60.05 g/mol = 3.39 g

mass percent = (3.39 g / (1.01 g/mL × 0.0100 L)) × 100% = 33.6%

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The delivery radius which will allow the pizza restaurant to deliver to approximately 20,000 people is: B: 2. 5 miles

Population density can be defined as the number of individuals within a species in a specific geographic area.

The formula for population density is expressed as;

Population density = Number of people/Land area

We are given the parameters as:

Number of people = 20000

Population density = 1000

Land area = 20000/ 1000

Land area = 20 square miles

Area of a circle is: πr²

Substitute the value of area in the formula to get:

20 = 3. 142 × r²

r² = 20/ 3. 142

r² = 6. 37

r  = √6. 37

r = 2. 5 miles

Thus, the delivery radius which will allow the pizza restaurant to deliver to approximately 20,000 people is 2. 5 miles

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a) The probability of picking a red marble first and a yellow marble second is 6/25. So, correct option is A.

b) The probability of spinning a 5 two times in a row is 1/64. So, correct option is c.

a) To calculate the probability of picking a red marble first, replacing it, and then picking a yellow marble, we need to multiply the probabilities of each event.

The probability of picking a red marble first is 2/5, since there are 2 red marbles out of a total of 5 marbles. Since we replace the red marble, the probability of picking a yellow marble on the second draw is also 3/5, since there are still 3 blue marbles and 2 red marbles in the jar.

Therefore, the probability of picking a red marble first and a yellow marble second is:

(2/5) x (3/5) = 6/25

So the correct answer is option a) 6/25.

b) The probability of spinning a 5 on a single spin of the spinner is 1/8, since there is only one 5 out of 8 possible outcomes.

To find the probability of spinning a 5 two times in a row, we need to multiply the probability of spinning a 5 on the first spin by the probability of spinning a 5 on the second spin. Since the spins are independent events, we can use the multiplication rule of probability.

Therefore, the probability of spinning a 5 two times in a row is:

(1/8) x (1/8) = 1/64

So the correct answer is option (c) 1/64.

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E = 2400/d is the equation for the illumination, E, in lux as a function of the source's distance, d, in meters.

From the given problem, we can let the illumination of light be 'E' and the distance from the source be 'd' such that if the illumination of a light source varies inversely with the square of the distance from that source, we will have:

E α 1/d

E = k/d

Given the following

d = 120 m

E = 20 lux

Substitute

20 = k/120
k = 2400

Determine the equivalent formula

E = 2400/d

Therefore  the formula for the illumination, E, in lux, as a function of the distance, d, from the source in meters is E = 2400/d

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The wellbeing of a community can be significantly harmed by poor service delivery. It may result in dangers to one's health and safety, a decline in quality of life, negative economic effects, and social unrest.

The quality of service that is rendered to the members of a community contributes to the level of development and self actualization of the members of the community.

As such, the community may suffer economically as a result of poor service delivery. Poor transportation infrastructure, for instance, can drive up the cost of goods and services, and bad water supply can have an impact on the local economy's agricultural and industry.

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Answer:

The answer is

1)0.96 to 2d.p

2)0.28 to 2d.p

3)3.49 to 2d.p

Step-by-step explanation:

tan0=3/4

0=tan‐¹[3/4]

0=36.9°

0≈37°

1) sin2(0)

sin (2×37)=sin 74=0.96 to 2.dp

2)cos 2(37)

sin(2×37)=cos 74=0.28 to 2d.p

3) tan20

=tan(2×37)=tan74=3.49 to 2d.p

When moving from a 95% confidence interval to a 90% confidence interval, the width of the interval will decrease. (option b).

To understand this, let's consider a simple example. Suppose we want to estimate the mean height of all high school students in a particular region. We take a sample of 100 students and calculate the mean height to be 65 inches, with a 95% confidence interval of (63, 67) inches. This means that if we were to repeat this process many times, we would expect the true population mean height to be within this interval 95% of the time.

Now, if we were to calculate a 90% confidence interval instead, we would obtain a narrower interval because we are now willing to accept a greater risk of being wrong.

It is important to note that the width of the confidence interval depends on the sample size and the variability of the data.

As the sample size increases or the variability decreases, the confidence interval will become narrower. Conversely, as the sample size decreases or the variability increases, the confidence interval will become wider.

Hence the correct option is (b)

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Answer: x=25/3 or 8[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Since they are similar triangles the sides inc/dec by proportion

the longest sides of the triangle went from 48 to 16  which is 48/16=3

The larger triangle is 3 times bigger so each of the sides are 3 times bigger or you can look at it like the smaller triangle is 1/3 smaller than bigger.

so short side is 25 on bigger triangle and went down to x or 25/3=x

The ratios are all equal to 0.22, we can conclude that the number of games and price do form a proportional relationship.

What is a proportional relationship?

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.

To determine if the number of games and price form a proportional relationship, we need to check if the ratio between the number of games and price is the same for all the data points given in the table.

Let's calculate the ratios for each data point:

For 2 games at $9.00: 2/9 = 0.22

For 5 games at $22.50: 5/22.50 = 0.22

For 7 games at $31.50: 7/31.50 = 0.22

Since the ratios are all equal to 0.22, we can conclude that the number of games and price do form a proportional relationship.

Specifically, the ratio between the number of games and price is a constant value of 0.22, which means that if we double the number of games, the price will also double, and if we triple the number of games, the price will triple, and so on. Therefore, we can say that the relationship between the number of games and price is proportional.

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Answer:

  (a)  x² +y² -14x +16y +49 = 0

Step-by-step explanation:

You want the equation (x -7)² +(y +8)² = 64 written in general form.

In general form, the terms are written in lexicographical order of decreasing degree, and the right side of the equation is 0.

We know the square of a binomial is ...

  (a +b)² = a² +2ab +b²

so we can write down the squares of the binomials:

  x² -14x +49 +y² +16x +64 = 64

Rearranging and subtracting 64 from both sides, we have ...

  x² +y² -14x +16y +49 = 0

The area of the circle is 452.38 square inches.

An area in geometry is a measurement of how much space a two-dimensional form or surface takes up. Usually, it is expressed in square units like square meters or square feet.

The volume of space encircled by a circle's perimeter, or circumference, is its area.

The area of the circle is calculated by the formula,

Area = πr²

Here, r is the radius of the circle.

The given radius of the circle is 12 inches. The area of the circle is calculated as,

Area = πr²

Area = π x ( 12 )²

Area = 452.38 square inches

Therefore, the circle will have an area of 452.38 square inches.

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Answer:

225°/360° = 5/8

Length of arc = (5/8)(2π)(1) = 5π/4 units, or about 3.927 units

Answer: 16π square yards.

Step-by-step explanation:

The area of a circle is given by the formula:

A = πr^2

where r is the radius of the circle.

In this case, we are given the diameter of the circle, which is 8 yards. The radius is half the diameter, so:

r = d/2 = 8/2 = 4 yards

Substituting this value of r into the formula, we get:

A = π(4)^2 = 16π square yards

Therefore, the area of the circle is 16π square yards.

Answer: 50.24cm

Step-by-step explanation: Assuming π = 3.14, substitute the values into the equation πr^2

To get r we do 8/2 = 4

So 3.14 * 4^2 = 50.24

The correct equation which represents the number of meters, M, swam to the number of laps, L is,

⇒ M = 25L

We have to given that;

The table shows the number of meters swam by a swimmer after a given number of laps.

Now, Take two points from table as;

⇒ (L, M) = (1, 25) and (2, 50)

Hence, We can find the rate of change as;

⇒ m = (50 - 25) / (2 - 1)

⇒ m = 25

Thus, The correct equation which represents the number of meters, M, swam to the number of laps, L is,

⇒ M - 25 = 25 (L - 1)

⇒ M - 25 = 25L - 25

⇒ M = 25L

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The baby's weight at birth is

The linear model's y-intercept (b) is required to ascertain the infant's birth weight.

We can determine the slope (m) of the line from given coordinates (1, 8) and (11, 12):

slope(m) = (y2 - y1)/(x2 - x1) = (12 - 8)/(11 - 1) = 0.4

To find the y-intercept, we then apply the previously computed slope with one point (1, 8):

y = mx + b

8 = 0.4(1) + b

b = 7.6

Therefore, it can be deduced that the baby weighed 7.6 pounds at its time of birth when x=0.

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the greatest number of pigs Kevin can keep in the field is 4.

How to solve the question?

To determine the maximum number of pigs that Kevin can keep in his field, we need to divide the total area of the field by the area required by each pig.

If we let x represent the maximum number of pigs that can be kept in the field, then we can write the equation:

36x ≤ A

where A is the total area of the field in square meters.

To solve for x, we can divide both sides of the inequality by 36:

x ≤ A/36

This means that the maximum number of pigs that can be kept in the field is equal to the total area of the field divided by 36.

For example, if the field has an area of 144 square meters, then the maximum number of pigs that can be kept in the field is:

x ≤ 144/36 = 4

Therefore, the greatest number of pigs Kevin can keep in the field is 4.

It is important to note that the above calculation assumes that each pig will have exactly 36 square meters of space. In reality, the actual amount of space required per pig may vary depending on factors such as breed, age, and weight. Additionally, it is important to consider other factors such as food, water, and shelter when determining the number of pigs that can be kept in a field.

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Concept testing is the test done before product launch, clients try a sample product and are then surveyed about whether they would buy the product again. So, option D is correct.

In concept testing, the companies will give newly launched products or new ideas or prototype products to the potential customers, to take reactions from them. This feedback is collected and assisted and analyze the feedbacks in order to improve their products sale.

The main aim of this concept testing is to collect information, patron needs, and assertions and can take powerful good decisions. This can gauge the market price and sale of the products through advertising.

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The complete question is:

type of test before product launch, customers try a sample product and are then surveyed about whether they would buy/use the product again. this process is known as:

a. premarket testing

b. alpha testing

c. prelaunch testing

d. concept testing

e. market testing.

It will take approximately 2.55 years for the investment to grow to $4288, assuming no withdrawals are made.

What is an investment?

An investment is the purchase of an asset or item with the goal of generating income or appreciation in value over time. Investments can include a wide range of assets such as stocks, bonds, real estate, commodities, and more. The aim of investing is typically to grow wealth over the long term, although some investments may be made with a shorter-term goal in mind, such as generating income or protecting against inflation.

To solve this problem, we can use the formula for compound interest:

A = P[tex](1 + r/n)^{(nt)}[/tex]

where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, t is the time in years.

We can rearrange this formula to solve for t:

t = (1/n) × log(A/P) / log(1 + r/n)

where log denotes the natural logarithm.

In this problem, P = $4000, r = 0.04 (4% as a decimal), n = 4 (compounded quarterly), and A = $4288. Plugging in these values, we get:

t = (1/4) × log(4288/4000) / log(1 + 0.04/4)

t = (1/4) × log(1.072) / log(1.01)

t ≈ 10.18 quarters

Therefore, it will take approximately 10.18 quarters for the investment to grow to $4288. To convert this to years, we divide by 4 (since there are 4 quarters in a year):

t ≈ 2.55 years

So, it will take approximately 2.55 years for the investment to grow to $4288, assuming no withdrawals are made.

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Complete question is: Nicole deposited $4000 into an account with a 4% annual interest rate compounded quarterly assuming that no withdrawals are made  2.55 years will it take for the investment to grow to $4288.