A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of 36
stores this year shows mean sales of 78
units of a small appliance with a standard deviation of 13
units. During the same point in time last year, a random sample of 49
stores had mean sales of 90
units with standard deviation 16
units.

It is of interest to construct a 95 percent confidence interval for the difference in population means 1−2
, where 1
is the mean of this year's sales and 2
is the mean of last year's sales.

40% of Canadians read at least 10 books a year.

A percentage is a way of expressing a portion or a part of a whole as a fraction of 100. It is represented by the symbol "%". Percentages are often used to compare different quantities or to describe how much of a total is made up by a specific amount or group. For example, if you score 80 out of 100 on a test, your score can be expressed as 80%, meaning you got 80 out of 100 possible points.

If two out of every five Canadians read at least 10 books a year, then we can write this as a fraction:

2/5

We can multiply this fraction by 100 to turn it to a percentage:

(2/5) x 100 = 40%

Therefore, 40% of Canadians read at least 10 books a year.

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Answer:

To calculate the fixed expenses each month, we need to add up all the monthly expenses:

Mortgage: $985.64

Cell phone: $58.30

Groceries: $154.00 x 2 = $308.00

Clothing (with 25% job-related): $180.00

Water & electric: $128.40

Weekly dinner & movie: $55.00 x 4 = $220.00

Total monthly fixed expenses: $1,880.34

To calculate how much could be saved per month, we need to first calculate the discretionary income:

Realized income: $2,943.20

Fixed expenses: $1,880.34

Discretionary income: $2,943.20 - $1,880.34 = $1,062.86

25% of discretionary income: 0.25 x $1,062.86 = $265.72

Therefore, the amount that could be saved per month by putting 25% of the discretionary income in a savings account is $265.72.

The answer is X + 5 = 10

X = 5

Note that the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

To calculate the %DV for saturated fat, we need to first calculate how many grams of saturated fat are in the 2 tablespoon (tbsp) serving size.

From the label, we see that the serving size contains 3.5g of saturated fat.

To calculate the %DV for saturated fat, we use the equation:

%DV = (amount of nutrient per serving / DV) x 100%

Plugging in the values for saturated fat, we get:

%DV = (3.5g / 19g) x 100%

%DV = 0.1842 x 100%

%DV ≈ 18%

Therefore, the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

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After 6 fluid ounces , Naya uses 4 glasses as a result.

A unit of weight is an ounce. There are various kinds of ounces, including avoirdupois, troy, and fluid ounces. One sixteenth of a pound is equivalent to one avoirdupois ounce .  A troy ounce, often known as an apothecaries' measure, is equivalent to 480 grains or one-twelfth of a pound. A volume unit is a fluid ounce. 1/8 of a cup, 2 tablespoons, or 6 teaspoons make to one fluid ounce

In Naya's pitcher, there are three glasses of salted lassi.

She fills each glass with six fluid ounces of lassi.

By translating cups to fluid ounces and dividing the entire amount of lassi by the amount put into each glass, we can determine how many glasses Naya uses if she consumes all of the lassi.

8 fluid ounces make constitute a cup.

Consequently, 3 cups equal 24 fluid ounces (3 x 8).

24 divided by 6 results in:

4 glasses are equal to 24/6.

Naya uses four glasses as a result.

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Answer:

a) To find the exponential growth function, we can use the formula:

P(t) = P0 * e^(rt)

Where:

P(t) = the population at time t

P0 = the initial population (in this case, 5.51 million)

e = the mathematical constant e (approximately 2.71828)

r = the annual growth rate (in decimal form)

t = the number of years

Substituting the given values, we have:

P(t) = 5.51 * e^(0.0382t)

b) To estimate the population of the city in 2018, we can substitute t = 6 (since 2018 is 6 years after 2012) into the exponential growth function:

P(6) = 5.51 * e^(0.0382*6) ≈ 6.93 million

Therefore, the estimated population of the city in 2018 is approximately 6.93 million.

c) To find when the population of the city will be 10 million, we can set P(t) = 10 and solve for t:

10 = 5.51 * e^(0.0382t)

e^(0.0382t) = 10/5.51

0.0382t = ln(10/5.51)

t ≈ 11.7 years

Therefore, the population of the city will be 10 million in approximately 11.7 years from 2012, or around the year 2023.

d) To find the doubling time, we can use the formula:

T = ln(2) / r

Where:

T = the doubling time

ln = the natural logarithm

2 = the factor by which the population grows (i.e., doubling)

r = the annual growth rate (in decimal form)

Substituting the given value of r, we have:

T = ln(2) / 0.0382 ≈ 18.1 years

Therefore, the doubling time for the population of the city is approximately 18.1 years.

Answer: 5 * 5 = 20

20 divided by 1 = 20

If there are 5 apples with an apple:orange ratio of 1:4, there are 20 oranges.

The next entry on the long division would be 0.054, and 0.0054

Long division is a method of dividing two numbers using a step-by-step process. Here's how to perform long division:

Step 1: Write the dividend (the number being divided) and the divisor (the number you're dividing by) in the long division format, with the dividend inside the division symbol and the divisor outside.

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Answer:

1. Using the kinematic equation h(t) = -16t^2 + v0t + h0, where h0 is the initial height, v0 is the initial velocity, and t is time, we have:

h(t) = -16t^2 + 72t + 4

To find the maximum height, we need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 72:

t = -b/2a = -72/(2(-16)) = 2.25 seconds

To find the maximum height, we substitute t = 2.25 seconds into the equation for h(t):

h(2.25) = -16(2.25)^2 + 72(2.25) + 4 = 82 feet

The range of the function h(t) is [4, 82], since the T-shirt starts at a height of 4 feet and reaches a maximum height of 82 feet before falling back to the ground.

2. Using the same kinematic equation as before, we have:

h(t) = -16t^2 + 80t + 3

To find the maximum height, we again need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 80:

t = -b/2a = -80/(2(-16)) = 2.5 seconds

To find the maximum height, we substitute t = 2.5 seconds into the equation for h(t):

h(2.5) = -16(2.5)^2 + 80(2.5) + 3 = 80 feet

The range of the function h(t) is [3, 80], since the T-shirt starts at a height of 3 feet and reaches a maximum height of 80 feet before falling back to the ground.

Step-by-step explanation:

The degree measure of the angles are;

1. 5π/3 = 300°

2 3π/4 = 135°

3. 5π/6 = 150°

4. -3π/2 = 90°

A degree is a unit of measurement which is used to measure circles, spheres, and angles while a radian is also a unit of measurement which is used to measure angles.

A circle has 360 degrees which are its full area while its radian is only half of it which is 180 degrees or one pi radian.

therefore π = 180°

1. 5π/ 3 = 5×180/3 = 300°

2. 3π/4 = 3× 180/4 = 540/4 = 135°

3. 5π/6 = 5×180/6 = 150°

4. - 3π/2 = -3 × 180/2 = -270° = 90°

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Answer: a.     c(n) = 15 + 0.75(n - 10)

b.   15 + 0.75(n - 10) = 2.50(n - 10)=

Simplifying and solving for n, we get:

n = 50

c.  n > 50

Step-by-step explanation:

a. The cost c of the credit union account in terms of the number of checks written n can be expressed as:

c(n) = 15 + 0.75(n - 10)

The first term, 15, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.

The cost c of the bank account in terms of the number of checks written n can be expressed as:

c(n) = 2.50(n - 10)

The first term, 0, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.

b. We want to find the number of checks for which the bank account is more expensive than the credit union account. Let x be the number of checks that makes the cost of the two accounts equal. Then we have:

15 + 0.75(n - 10) = 2.50(n - 10)

Simplifying and solving for n, we get:

n = 50

So if the number of checks written in a month is greater than 50, the bank account will be more expensive than the credit union account.

c. The solution to the inequality is:

n > 50

This means that the number of checks written in a month must be greater than 50 for the bank account to be more expensive than the credit union account.

Answer:

a) To find out how big of a loan you can afford, we can use the formula for the monthly payment of a mortgage:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]

where M is the monthly payment, P is the principal (the amount borrowed), i is the monthly interest rate (which is the annual interest rate divided by 12), and n is the number of monthly payments (which is the number of years times 12).

In this case, we know that M = $1,000, i = 0.053/12, and n = 30 x 12 = 360. We want to solve for P, the principal we can afford.

Substituting these values into the formula, we get:

$1,000 = P [ 0.004416(1 + 0.004416)^360 ] / [ (1 + 0.004416)^360 - 1 ]

Simplifying and solving for P, we get:

P = $183,928.72

Therefore, you can afford a loan of approximately $183,928.72.

b) The total money paid to the loan company will be the monthly payment multiplied by the number of payments over the life of the loan. In this case, we have:

Total money paid = $1,000 x 360 = $360,000

Therefore, the total amount of money paid to the loan company will be $360,000.

c) To find out how much of that money is interest, we can subtract the principal from the total amount paid. In this case, we have:

Interest paid = Total money paid - Principal = $360,000 - $183,928.72 = $176,071.28

Therefore, the amount of money paid in interest will be $176,071.28.

Answer: Amaterasu

Step-by-step explanation: The sun goddess Amaterasu is considered the most important of the Shinto gods because she is believed to be the ancestor of the Japanese imperial family, and therefore the protector of the Japanese people. She is also associated with agriculture, which was a vital part of Japanese society.

The effective tax rate for a taxable income of $115,500 is A) 18.71%

The introductory $10,275 is subjected to a 10% tax burden, with the converted dollar amount representing $1,027.50 in taxes. The additional taxable sum of $30,900 ($41,175 - $10,275) is accessed at a 12% charge and aggregates to $3,708 worth of duties. An extra levy of 22% is imposed on the total $47,900 that lies between the two stipulated ranges ($89,075 - $41,175). The final evaluation stands at 24%, which provides an identical tax rate for the remaining $25,350 ($115,500 - $89,075). ).

Effective Tax Rate = (Total Tax Paid / Taxable Income) x 100%; which further articulates to ($21,357.50 / $115,500) x 100%,

= 18%

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The similes in the story are:

A simile is a figure of speech that compares two things using the words "like" or "as." It is a type of metaphor that helps to create a vivid and engaging image in the reader or listener's mind.

Similes are often used in literature, poetry, and everyday language to make a comparison more relatable and understandable. For example, "He is as brave as a lion" or "She sings like an angel." These similes help to convey a certain quality or trait by comparing it to something else that is well-known or familiar.

Note: It seems there may be a typo in the last sentence of the story, where the word "e" appears instead of "elephant" or another word that would make sense in context.

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Answer:

To find the slope of the line tangent to the graph of the function at x = -3, we need to find the derivative of the function and evaluate it at x = -3.

First, let's find the derivative of the function y = x^4 + 2x^3 + 2x + 2:

y' = 4x^3 + 6x^2 + 2

Now, let's evaluate y' at x = -3:

y'(-3) = 4(-3)^3 + 6(-3)^2 + 2

= -108 + 54 + 2

= -52

Therefore, the slope of the line tangent to the graph of the function y = x^4 + 2x^3 + 2x + 2 at x = -3 is -52.

The ratio of US to British coins is 25 to 4.

The second term, £50, is a fixed sum she receives regardless of the number of hours worked.

The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.

1. The ratio of US to Euro coins is 5 to 2, and the ratio of Euro to British coins is 5 to 1. To find the ratio of US to British coins, we can combine these ratios.

First, we need to make sure that the ratios have a common term. We can do this by multiplying the first ratio (US to Euro) by 5, which gives us a ratio of 25 to 10.

Next, we can use the second ratio (Euro to British) to convert Euro coins to British coins. Since the ratio is 5 to 1, for every 5 Euro coins, there is 1 British coin. So for every 10 Euro coins, there are 2 British coins.

Finally, we can combine the US to Euro ratio (25 to 10) with the Euro to British ratio (10 to 2) to get the ratio of US to British coins.

25 : 10 :: 10 : 2

Multiplying both sides by 2, we get:

50 : 20 :: 10 : 2

Simplifying, we get:

The ratio of US to British coins is 25 to 4.

2. To calculate Amanda's monthly pay, we can use the formula:

m = 10h + 50

where m is the total money Amanda receives in a month, and h is the number of hours she works.

The first term, 10h, represents her pay for the number of hours she works, which is £10 per hour. The second term, £50, is a fixed sum she receives regardless of the number of hours worked.

3. To calculate the cost of the holiday package for d days, we can use the formula:

C = 190 + 50d

where C is the cost of the holiday package, and d is the number of days.

The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.

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Answer:

thats 4th grade math... 0_0               but the answer is 414 ft².

Step-by-step explanation:

So you need to do 23x18 which equals 414. Listen to your teacher in class please kid. But you do you boo

The coordinates of the vertices of the image is A'(0, -3), B'(3, -2), C'(1, -1). The correct option is B.

Triangle ABC is rotated 180 degrees clockwise about the origin and then reflected across the line y=-x.

We are to find the coordinates of the vertices of the image.

We know that

if a point (x, y) is rotated 180 degrees clockwise, then its co-ordinate changes as follows :

(a, b)   ⇒    (-a, -b).

So, after getting rotated 180 degrees clockwise, the coordinates of the vertices of triangle ABC becomes

A(-3, 0)   ⇒  (3, 0)

B(-2, 3)   ⇒   (2, -3)

C(-1, 1)    ⇒   (1, -1).

Therefore, the correct option is B. A'(0, -3), B'(3, -2), C'(1, -1).

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The diagram of the Gateway Arch on the coordinate plane, analyzed using quadratic equations indicates;

1. The vertex point is (50, 630)

2. The solution point are; (20, 0), and (80, 0)

3. Vertex form; f(x) = -0.7·(x - 50)² + 630

4. Factored form; f(x) = -0.7·(x - 20)·(x - 80)

A quadratic equation is an equation of the form f(x) = a·x² + b·x + c

1. The vertex obtained from the graphical diagram of the Gateway Arch indicates that the point corresponding to the vertex point is; (50, 9 × 70 = 630)

The vertex point is; (50, 630)

2. The solution are the points the curve of the Gateway intersects the x-axis, which are points where the y-axis values are zero, therefore;

The solutions are; (20, 0), and (80, 0)

3. The vertex form of a quadratic equation is; f(x) = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex

Therefore;

(h, k) = (50, 630)

f(20) = 0 = a·(20 - 50)² + 630

a·(20 - 50)² = -630

a = -630/((20 - 50)²) = -630/900 = -7/10

a = -7/10 = -0.7

The vertex form quadratic equation is therefore; f(x) = -0.7·(x - 50)² + 630

4. The factored form of a quadratic equation is; f(x) = a·(x - r₁)·(x - r₂)

r₁ = 20, and r₂ = 80, a obtained from the vertex is; a = -0.7

The factored form is therefore; f(x) = -0.7·(x - 20)·(x - 80)

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Answer:

40 m²

Step-by-step explanation:

Area of triangle:

To find the area of triangle, multiply the base and area and then divide it by 2.

      base = b = 8 m

height      = h = 10m

      [tex]\boxed{\bf Area \ of \ triangle = \dfrac{1}{2}*b*h}[/tex]

                                     [tex]= \dfrac{1}{2}*8 * 10\\\\= 4 * 10\\\\= 40 \ m^2[/tex]

The range is expressed in interval notation as (-1, ∞)

To find the linear function f(x), let us use the table given.

A linear function with the following equation that passes through the points (a, g(a)) and (b, g(b)):

[tex]g(x) - g(a) = \frac{g(b)-g(a)}{b-a} (x-a)[/tex]

Because the g(x) line crosses through points (-6, 14) and (-3, 8), we have:

a = -6, g(a) = 16, b = -3 and, g(b) = 10

Therefore g(x)

[tex]g(x) - (16) = \frac{10-16}{-3-(-6)} (x--(6))\\g(x) - 16 = \frac{10-16}{-3+6} (x+6)\\g(x) - 16 = \frac{-6}{3} (x+6)\\g(x) - 16 = -2(x +6)\\g(x) = -2x -12+16\\g(x) = -2x+4[/tex]

now find the (f+g)(x).

[tex](f+g)(x) = f(x) + g(x) = x^{2} + 2x -5 -2x + 4\\(f+g)(x) = f(x) + g(x) = x^{2} - 1\\[/tex]

(f+g)(x) = (x-1)(x+1), therefore we get the values x = 1 and x = -1

The parabola's vertice has x-coordinate 0 (the midway between the roots). At x = 0, we get:

[tex](f +g)(x) = 0^{2} - 1 = -1[/tex]

Furthermore, because the coefficient of [tex]x^{2}[/tex] is 1, which is positive, this function indicates a parabola that has been opened upwards.

As a result, the function's minimal value is y = -1. As a result, the function's range includes all real numbers equal to or greater than -1.

The range is expressed in interval notation as (-1, ∞)

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Answer:

Step-by-step explanation:

A=1/2(b1+b2)h

=1/2 (11yd+11yd)(7yd)

=1/2(22yd)(7yd)

=(11yd)(7yd)

=77yd

1.  The new volume will be 60 cubic feet. 2. Molly will earn $31.25 if she sells all of the dog beds after subtracting the cost of the fabric.

In general, volume refers to the amount of space occupied by an object or substance, measured in three dimensions: length, width, and height. It is a physical quantity that is typically expressed in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).

1. The volume of the cuboid is calculated as follows:

Volume = length x width x height

Volume = 5 ft x 3 ft x 2 ft

Volume = 30 cubic feet

If we double the height, the new height will be 2 x 2 ft = 4 ft. The new volume can be calculated as:

New Volume = length x width x new height

New Volume = 5 ft x 3 ft x 4 ft

New Volume = 60 cubic feet

Therefore, the new volume will be 60 cubic feet.

2. Step 1: Determine how many dog beds Molly can make with the fabric she bought.

Molly bought 12.5 yards of fabric, and she uses 2.5 yards of fabric for each dog bed. We can use division to find how many dog beds she can make:

12.5 yards / 2.5 yards per dog bed = 5 dog beds

Therefore, Molly can make 5 dog beds with the fabric she bought.

Step 2: Calculate the cost of the fabric for each dog bed.

Molly bought the fabric for $4.50 per yard, and she uses 2.5 yards of fabric for each dog bed. Therefore, the cost of the fabric for each dog bed is:

$4.50 per yard x 2.5 yards per dog bed = $11.25 per dog bed

Step 3: Calculate the revenue from selling one dog bed.

Molly sells each dog bed for $17.50.

Step 4: Calculate the profit from selling one dog bed.

Profit = revenue - cost

Profit = $17.50 - $11.25

Profit = $6.25

Step 5: Calculate the total revenue from selling all of the dog beds.

Molly can make 5 dog beds, and each dog bed sells for $17.50. Therefore, the total revenue is:

5 dog beds x $17.50 per dog bed = $87.50

Step 6: Calculate the total cost of the fabric for all of the dog beds.

Molly uses 2.5 yards of fabric for each dog bed, and she can make 5 dog beds. Therefore, the total cost of the fabric is:

2.5 yards per dog bed x 5 dog beds = 12.5 yards

$4.50 per yard x 12.5 yards = $56.25

Step 7: Calculate the total profit from selling all of the dog beds.

Profit = revenue - cost

Profit = $87.50 - $56.25

Profit = $31.25

Therefore, Molly will earn $31.25 if she sells all of the dog beds after subtracting the cost of the fabric.

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For the given equation we have horizontal length of 5 and vertical width of 4 units. The graph that depicts this hyperbola is: Option B.

A hyperbola is a particular kind of conic section in mathematics, which is a curve created by the intersection of a cone and a plane. The collection of all points in a plane that have a constant difference between them and two fixed points, known as the foci, is referred to as a hyperbola. The distance between the foci is referred to as this consistent difference and is represented by the symbol 2a.

Two separate branches that are mirror reflections of one another make up a hyperbola. The vertices are the two locations where the two branches of a hyperbola are joined.

For the given equation of the parabola, the value of a and b = 5 and 4.

Thus, we have horizontal length of 5 and vertical width of 4 units

The graph that depicts this hyperbola is: Option B.

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The complete question is:

a. TRUE, b. TRUE, c. TRUE, d. TRUE, e. TRUE, f. FALSE, g. TRUE

a. TRUE: The probability of an event can never be negative, and can at most be equal to 1, which represents certainty.

b. TRUE: The sample space is the set of all possible outcomes of an experiment, and the probability of the sample space is always equal to 1, since one of the outcomes must occur.

c. TRUE: If the events in a sequence are disjoint, then they have no outcomes in common, so the probability of the union of the events is the sum of the probabilities of the individual events.

d. TRUE: If one event is a subset of another event, then the probability of the subset is less than or equal to the probability of the superset. This follows from the fact that the subset contains fewer outcomes than the superset.

e. TRUE: The probability of the union of two events is the probability of the first event plus the probability of the second event, minus the probability of the intersection of the events, which is the probability of both events occurring together. This is known as the inclusion-exclusion principle.

f. FALSE: The formula (P(A ∩ B) = P(A)P(B)) only applies to independent events, but not all independent events are mutually exclusive. For example, if A is the event of rolling a 4 on a die, and B is the event of rolling an even number, then A and B are independent, but not mutually exclusive.

g. TRUE: If two events are mutually exclusive, then they have no outcomes in common, so the occurrence of one event tells us that the other event cannot occur. This dependence means that the events are not independent.

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