A marketing research company desires to know the mean consumption of milk per week among people over age 45. They believe that the milk consumption has a mean of 4.2 liters, and want to construct a 98% confidence interval with a maximum error of 0.08 liters. Assuming a standard deviation of 0.6 liters, what is the minimum number of people over age 45 they must include in their sample

There are 10.5 1/2 cup servings in a package of cheese that contains 5 1/4 cups altogether.

To find the number of 1/2 cup servings in a package of cheese that contains 5 1/4 cups altogether, we first need to convert the total amount of cheese in cups to a number of 1/2 cup servings.

We can do this by dividing the total amount of cheese by the size of a 1/2 cup serving.

First, we need to convert the amount of cheese in cups to a decimal number. Since there are two 1/2 cups in a cup, the decimal equivalent of 1/2 cup is 0.5. Therefore, the decimal equivalent of 5 1/4 cups is 5.25 cups.

Next, we need to divide the total amount of cheese in cups by the size of a 1/2 cup serving. Since the size of a 1/2 cup serving is 0.5 cups,

we can divide 5.25 cups by 0.5 cups to find the number of 1/2 cup servings as follows:

5.25 cups / 0.5 cups = 10.5

Therefore, there are 10.5 1/2 cup servings in a package of cheese that contains 5 1/4 cups altogether.

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Answer:

number of caps is the ratio

blue + white + green = 96

5x + 4x + 7x = 96

16x = 96

x = 6

Blue caps : 5x = 5(6) = 30

white caps : 4x = 4(6) = 24

green caps : 7x = 7(6) = 42

total of : 96 caps

Step-by-step explanation:

The common difference of the sequence is 70, the slope of the 1st and 2nd lines is 70, the slope of the 3rd and 4th points is 70, and the slope is constant.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. Y and x are the net changes in the y and x coordinates, respectively.

Given:

Time in minutes and jumping jack table, coordinates of lines (1, 70) and (2, 140)

(a)

Consider 70, 140, 210, and 280 as an arithmetic sequence then the common difference will be,

Common difference = 140 - 70 = 70

(b)

Calculate the slope of the line as shown below,

[tex]m = (y_2-y_1) / (x_2 - x_1)[/tex]

m = (140 - 70) / (2 - 1)

m = 70 / 1

m = 70

(c)

Calculate the slope for 3rd and 4th points,

m = (280 - 210) / (4 - 3)

m = 70 / 1

m = 70

(d)

As you can, the slope is constant, and the common difference is also constant.

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The equation or tape diagram could be used to represent the context if j represents each bottle of juice costs is; Option D tape diagram

We are told that;

1 bag of popcorn costs $1.59

She bought a 5-pack of juice bottles

Total cost before tax = $13.34

Now, we are told that j represents each bottle of juice costs. Thus;

Cost of the 5 packs of juice = 5j

Thus, the equation of the total cost before tax is;

1.59 + 5j = 13.34

Looking at the options, only the tape diagram in option D correctly represents the required equation.

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Answer:

7.8125%

Step-by-step explanation:

(4200/3200-1)/4 the difference for every month

so this would result to 7.8125% every month

Answer:

Rate = (Percentage/Base)/Time

Rate =(1 000/3 200)/4

Rate = 0.3125/4

Rate = 0.078125       (convert to percent)

Rate = 7.9%        (nearest tenth)

Step-by-step explanation:

The length of each individual piece is x/8

From the question, we have the following parameters that can be used in our computation:

Number of pieces = 8

Length of timber put together = x

The length of each piece of timber is calculated as

The length of each piece = Length of timber put together/Number of pieces

Substitute the known values in the above equation, so, we have the following representation

The length of each piece = x/8

Hence, the length of each piece is x/8

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Answer:

4xy ×3xy -2xy

12xy-2xy

10xy

Answer:

Step-by-step explanation:

Therease should take her 7th dose on Friday at 9:00AM

What is time ?

Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present, and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.

Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.

Time is defined by physicists as the flow of events from the past through the present and into the future. In essence, a system is timeless if it is unchanging. When describing events that take place in three-dimensional space, time can be thought of as the fourth dimension of reality.

The doctor told her to take a dose of 4.8 ml every 12 hours for 7 days.

If Theresa took her first dose at 9:00 AM on Monday,

Simply add 12 hours every time up to the 7th dose,

First dose  ----> 9:00 AM on Monday,

Second dose  ----> 9:00 PM on Monday,

Third dose  ----> 9:00 AM on Tuesday,

Fourth dose  ----> 9:00 PM on Tuesday,

Fifth dose  ----> 9:00 AM on Thursday,

Sixth dose  ----> 9:00 PM on Thursday,

Seventh dose  ----> 9:00 AM on Friday,

Hence, Theresa should take her 7th dose at 9:00 AM on Friday.

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Answer:

To determine how many weeks it will take Clare to save enough money to buy the video game, we need to find the number of weeks it will take for her to save at least $130. Let w be the number of weeks it will take for Clare to save enough money. We can set up the following inequality to represent this situation:

$48 + $5w >= $130

To solve this inequality, we can first add $48 to both sides to get rid of the constant on the left side:

$48 + $48 + $5w >= $130

This simplifies to $96 + $5w >= $130. Subtracting $96 from both sides gives us $5w >= $34. Dividing both sides by $5 gives us w >= 6.8. Since w represents the number of weeks, the solution must be a whole number. Therefore, Clare will need to save for at least 7 weeks in order to have enough money to buy the video game.

In the arrangement of letters and numericals, the total number of different paths can one spell AMC8 are 24 in count.

A basic counting principle is that if there are p ways to do one thing and q ways to do another, then there are p × q ways to do both. Possible results of experiments. The counting principle can be extended to situations where there are two or more alternatives.

We have, the arrangement of letters and numericals in above figure such that

There are three different kinds of paths that are on the above diagram to get the required pattern. The first kind is when you directly count A, M, C in a straight line. The second is when you count A, turn left or right to get M, then go up or down to count 8 and C. The third is the one where you start with A, move up or down to count M, turn left or right to count C, then move straight again to get 8.

There are 8 paths for each kind of path, making for 8×3= 24 paths.

Hence, the required paths are 24 in count.

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Sphere, right cylinder and cube have more than five planes of symmetry.

Symmetry in mathematics means that when one shape is moved, rotated, or flipped, it looks exactly like the other shape. A symmetrical likeness between two halves of an object, when one half is the mirror image of the other, is defined as being proportionate and balanced. As an illustration, many shapes such as square, rectangle, and circle are symmetric along their respective lines of symmetry.

Given,

Sphere and right cylinder have more than five planes of symmetry.

The number of symmetry planes depends on each solid by definition (a figure of three dimensions). The solid is split into two congruent, mirror-imaged parts by the plane of symmetry.

A cube has nine planes of symmetry, a square pyramid has four, hexagonal prims have thirteen, and spheres and cylinders have an infinite number of planes of symmetry, according to the information presented above.

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Answer nah the correct answer is cylinders cubes and cones

Step-by-step explanation:

seen it irl on edgennuitiy

......,,........,.....-.......

The median would best describe the centre of the distribution for a highly skewed right histogram of US household income.  The correct option is A.

The median is the value that separates the distribution into two equal parts and is less influenced by extreme values than the mean.

Since a highly skewed right distribution has a long tail on the right side, the mean is likely to be pulled towards that tail, making it an unreliable measure of the centre.

The mode, or most frequently occurring value, may not be useful for describing the centre of a skewed distribution. The variance is a measure of the spread or dispersion of the data, not its centre.

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The instantaneous rate of change is -6 words per day,

the number of words Alex remembers after 5 days, option (D).

What is the instantaneous rate of change ?

An instantaneous rate is the rate at some instant in time. An instantaneous rate is a differential rate: -d[reactant]/dt or d[product]/dt. We determine an instantaneous rate at time t: by calculating the negative of the slope of the curve of concentration of a reactant versus time at time t.

Have given,

Alex learned 80 new vocabulary words

and after t days he learned,

W(t) = [tex]80 (1-0.1t)^{3}[/tex]

differentiate respect of t

W'(t) = [tex]80 \frac{d}{dt} (1-0.1t)^{3}[/tex]

W'(t) = [tex]80 * 3(1-0.1t)^{2} \frac{d}{dt}(1-0.1t)[/tex]

W'(t) = [tex]240(1-0.1*5)^{2} (0.1)[/tex]

W'(t) = 6

That's mean , the instantaneous rate of change is -6 words per day.

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a) P(X = x₀, Y = 2x₀) = 1/36

P(X = x₀, Y = k) = 1/18 for k between x₀+1 and 2x₀-1 inclusive

Every other event has probability 0. x₀ is any number between 1 and 6 inclusive.

b) P(X = x₀, Y = x₀) = x₀/36

P(X = x₀, Y = k) = 1/36 for k between x₀+1 and 6 inclusive.

x₀ is between 1 and 6 inclusive. Every other event has probability 0.

c) P(X = x₀, Y = x₀) = 1/36

P(X = x₀, Y = k) = 1/18 with k between x₀+1 and 6 inclusive

x₀ between 1 and 6 inclusive. Any other event has probability 0.

Joint probability is the probability of two events happening simultaneously.

Let P(A) = probability that event A takes place and P(B) = probability that event B takes place. Then, probability of event A and B happening together i.e. P(A and B) is called joint probability.

(1) When A and B are independent events: When event A has no impact on event B or vice versa, the two events are said to be independent. For independent events, formula for joint probability is:

P(A and B) = P(A) × P(B)

Example: I am performing two acts at a time (i) tossing a coin and (ii) throwing a dice. What is the probability that the coin shows up “head” and the dice shows up “3”?

There is no doubt that getting “head” on coin and getting “3” on dice are independent events.

Probability of the coin showing up “head” = 1/2

Probability of the dice showing up “3” = 1/6

Therefore, probability of getting “head” on coin and “3” on dice = (1/2)×(1/6) = 1/12

(2) When A and B are dependent events: If event A and event B cannot be considered independent, calculation of joint probability requires knowledge of conditional probability. For dependent events, formula for joint probability is:

P(A and B) = P(A) × P(B, given A) = P(B) × P(A, given B).

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Answer:

12/27 = 4/9

Step-by-step explanation:

Solve for ?:

?/27 = 4/9

Multiply both sides of ?/27 = 4/9 by 27:

(27 ?)/27 = 27×4/9

27×4/9 = (27×4)/9:

(27 ?)/27 = (27×4)/9

(27 ?)/27 = 27/27×? = ?:

? = (27×4)/9

27/9 = (9×3)/9 = 3:

? = 3×4

3×4 = 12:

Answer: ? = 12

Answer:

12/27 = 4/9

Step-by-step explanation:

To get from one fraction to the other, you must find out what the denominator of the fraction we know (4/9) is being multiplied by to get the denominator of ?/27.

We divide 27 by 9 to get 3 then multiply the numerator (4) by 3 as well to get 12, your answer.

The original price is $1049 and the amount saved is $321

From the question, we have the following parameters that can be used in our computation:

Cost after discount = $728

Discount = 30% off

The original price is calculated as

Cost after discount = Original price * (1 - Discount)

So, we have

Original price = Cost after discount/(1 - Discount)

This gives

Original price = 728/(1 - 30%)

Evaluate

Original price = 1049

Here, we have

Amount saved = Original price - Cost after discount

So, we have

Amount saved = 1049 - 728

Evaluate

Amount saved = 321

Hence, the amount saved is $321

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[tex]\frac{1}{(7x)^2}[/tex] is the expression without negative exponents.

What are exponents and indices?

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

An index, or power, is the small floating number that appears after a number or letter. The plural of index is indices.

According to the given question:

(7x)^{-2} is the given indices expression

To expression without negative exponent, the expression

can be written as

[tex](7x)^{-2} = \frac{1}{(7x)^2}[/tex]

Since the exponent -2 is on the whole 7x term. So, the whole term moves to denominator to make the exponent positive.

Therefore [tex]\frac{1}{(7x)^2}[/tex] is the expression without negative exponents

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Solving a system of equations we will see that they need to use:

Let's define the variables:

x = kilograms of the 10% fat-content chocolate.

y = kilograms of the 30% fat-content chocolate.

We know that they want to create 100kg, then:

x + y  =100

And the fat content must be 18%, then we can write the concentration equation:

0.1*x + 0.3*y = 0.18*100 = 18

The coefficients are the percentages in decimal form.

Now we have a little system of equations:

x + y  =100

0.1*x + 0.3*y = 18

Isolating x on the first one we get:

x = 100 - y

Replacing that in the other equation we get:

0.1*(100 - y) + 0.3*y = 18

10 + 0.2*y = 18

0.2*y = 18 - 10 = 8

y = 8/0.2 = 40

They need to use 40kg of the 30% chocolate and 60kg of the 10% chocolate.

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The trigonometric function -cos(-x) will be not equal to cosx thus option (C) will be correct.

The trigonometric functions found in the four quadrants, as well as their graphs, domains, and differentiation and integration, will all be understood.

The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.

It is known that, by cosine function property,

cos(-x) = cosx

So, -cos(-x) = -(cosx)

-(cosx) ≠ cosx

Hence "Cos(-x) will not equal cosx in the trigonometric function".

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Answer:

year 1: 90% × 245000 = 220500

year 2: 90% × 220500 = 198450

year 3: 90% × 198450 = 178605

∴ the car price after 3 years is 178605

explanation:

the value of car decreases 10%. that means the car price is 90%

The price of the car after 3 years will be 178605

We can calculate the value in the following way

Rate of decrease in car's price: 10%

Current price of the car: 245000

Value after 1 year, say value1= current value-10% of current value

[tex]value1=245000-\frac{10*245000}{100}[/tex]

=245000-24500

=220500

After 1 year, the next decrement in the price will be based on the value of the car in that year. In other words, we calculate the value after the second year by decreasing by 10% of value1.

Value of car after 2 years, say value2= value1- 10% of value1

[tex]value2=220500- (\frac{10*220500}{100})[/tex]

=220500-22050

=198450

Similarly,

Value of car after 3 years, say value3= value2- 10% of value2

[tex]value3=198450- (\frac{10*198450}{100})[/tex]

=198450-19845

=178605

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We determined that normal distribution should be used to construct a confidence interval for these two statistical data.

In statistics, the t-distribution is a system of describing a set of data where most of the data fall close to the mean value and the remaining data adjust the tail on both sides.

The normal distribution is one of the systems of describing a set of data that implies data close to the mean value are more probable to occurrence than the other data.

In the statistics, we use t- distribution when the number of samples is less than 30 and the population standard deviation is unknown to us.

we use normal distribution when the sample size is greater than 30 and the population standard deviation is known.

We are given two set of statistical data and for both case population standard deviation is given, and the size of sample is greater than 30.

hence, we will use normal distribution for both cases.

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Answer: the answer to a is 50% chance the answer to b is also 50% chance

Step-by-step explanation:

A sample of 24 pieces of work is considered for the checking the quality of the work,

a) Upper control limit of 99.73% confidence interval is 4

Lower control limit of 99.73% confidence interval is Zero.

The process is in control because all the values of the blemishes per unit are lie within the control limits .

The Control limits consist of two limits lower control limit and upper control limit within which the value of the statistical observations of a product are expected to lie. If the values lie outside these limits, then the process is called out of statistical control. We have,

Kate Drew has been hand-painting wooden Christmas ornaments for several years.

Sample size = 24 pieces

confidence level = 99.73% = 0.9973

The number of blemishes per unit is given as:

1,1,2,3,1,0,2,0,0,1,3,1,0,1,2,0,0,2,1,2,3,2,1,1.

The control limits are to be computed for the number of defects per piece . Let us consider the number of defects per piece be denoted by c. In that case, the control limits for c chart are used. The upper control limit (UCL) and lower control limit (LCL) for c chart is given by,

UCL = c-bar + 3 s.d

LCL = c-bar - 3 s.d

where c-bar = 1/n(€c) average number of defects

So, c-bar is computed as,

c-bar = (1+1+2+3+1+0+2+0+0+1+3+1+0+ 1+2+0 +0+2 + 1+2 +3+ 2+1+1) /24 = 30/24 = 1.25

put the data in Excel sheet and calculate required limits using Excel Commands.

Excel Command for Average, c-bar

=Average( Range of numbers who's average you want to calculate )

In my excel sheet, = Average ( H2 : H25)

= 1.25

Excel Command for Standard deviations,

=STDEV( numbers who's standard deviations you want to calculate)

here, =STD(H2:H25) , output= 0.98907

UCL = 1.25 + 3( 0.98907)

= 4.217

LCL = 1.25 - 3( 0.98907)

= - 1.717

but defective item can never be negative so, Lower control limit is Zero.

Hence, for the given data, the upper control limit for the number of defects is 4 and the lower control limit is 0.

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The graph of g is the graph of f translated up 7 units

From the question, we have the following parameters that can be used in our computation:

g(x) = f(x) + k

Also, we have the value of k to be

k = 7

From the question, we can interpret g(x) = f(x) + k as f(x) is shifted up by k units

This means that

g(x) = f(x) + k

So, we have

g(x) = f(x) + 7

Hence, the transformation is (a) translated up 7 units

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Answer:

[tex]y=2.182[/tex]

Step-by-step explanation:

Solve for y.

[tex]3.082=y+\frac{9}{10}[/tex]

Move all terms not containing [tex]y[/tex] to the right side of the equation.

[tex]y=3.082-\frac{9}{10}[/tex]

Write [tex]\frac{9}{10}[/tex] as a decimal.

[tex]y=3.082-0.9[/tex]

[tex]y=2.182[/tex]

The quadratic equation numerically (using tables of x- and y- values).

Correct option: (a). The value of x are x = -1 and x = 3.

A quadratic equation is a second-order polynomial equation in a single variable x with the formula; ax² + bx + c = 0, where a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem. The answer could be simple or complicated.

The given quadratic equation is:

x² - 3 = 2x

or, x² - 2x - 3 = 0

or, x² - 3x + x - 3 = 0

or, x (x - 3) +1 (x - 3) = 0

or, (x - 3) ( x +1 ) = 0

or, x = +3 , -1

The value of x are x = -1 and x = 3.

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Answer

Step-by-step explanation:

Answer:

A.) The sum will be an even integer.

Step-by-step explanation:

The conjecture that can be made about the sum of two even integers and one odd integer is that the sum will be an even integer. This is because even integers are numbers that are divisible by 2, and odd integers are numbers that are not divisible by 2.

For example, consider the sum of the even integer 6 and the odd integer 7. The sum of these two numbers is [tex]6 + 7 = 13[/tex], which is an odd integer. However, if we add another even integer to the sum, such as 4, the resulting sum is [tex]13 + 4 = 17[/tex], which is an even integer. This shows that the sum of two even integers and one odd integer is always an even integer.

This conjecture can be proven using mathematical induction. We can start by showing that the sum of any two even integers and one odd integer is always an even integer. Then, we can assume that the sum of any n even integers and one odd integer is also an even integer. Finally, we can show that the sum of n+1 even integers and one odd integer is also an even integer, using the assumption that the sum of n even integers and one odd integer is even. This will prove that the conjecture is always true.