A Food Marketing Institute found that 33% of households spend more than $125 a week on groceries. Assume the population proportion is 0.33 and a simple random sample of 349 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.32? There is a probability that the sample proportion of households spending more than $125 a week is less than 0.32. Round the answer to 4 decimal places.

Answer:

[tex]\large\boxed{\tt x^{\frac{5}{6}} + 2x^{\frac{7}{3}}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to simplify the given expression.}[/tex]

[tex]\textsf{We should use the \underline{Distributive Property, and Rule of Multiplying Exponents.}}[/tex]

[tex]\boxed{\begin{minipage}{25 em} \underline{\textsf{\large Distributive Property;}} \\ \\ \textsf{Distributive Property is a property that allows us to multiply the term to the left of the parentheses with the terms inside the parentheses.} \\ \\ \underline{\textsf{\large Example;}} \\ \tt a(b+c) = \boxed{\tt ab+ac} \end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{25 em} \underline{\textsf{\large Rule of Multiplying Exponents;}} \\ \\ \textsf{Whenever we have to multiply 2 terms with exponents, it's important to know the Rule of Multiplying Exponents. This rule states that whenever 2 exponential terms multiply together, their exponents add together. }\\ \\ \underline{\textsf{\large Example;}} \\ \tt x^{3} \times \tt x^{4} = x^{3+4} = \boxed{\tt x^{7}} \end{minipage}}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{We should first use the Distributive Property, then use the Rule of Multiplying}[/tex]

[tex]\textsf{Exponents.}[/tex]

[tex]\tt x^{\frac{1}{3}} (x^{\frac{1}{2}} + 2x^{2})[/tex]

[tex]\underline{\textsf{Use the Distributive Property;}}[/tex]

[tex]\tt x^{\frac{1}{3}} (x^{\frac{1}{2}} + 2x^{2}) = (x^{\frac{1}{3}} \times x^{\frac{1}{2}}) + (x^{\frac{1}{3}} \times 2x^{2})[/tex]

[tex]\underline{\textsf{Use the Rule of Multiplying Exponents;}}[/tex]

[tex]\tt (x^{\frac{1}{3}} \times x^{\frac{1}{2}}) + (x^{\frac{1}{3}} \times 2x^{2}) = x^{\frac{1}{3} + \frac{1}{2}} + 2x^{\frac{1}{3} + \frac{2}{1} }[/tex]

[tex]\underline{\textsf{Find Common Denominators per fractions;}}[/tex]

[tex]\tt x^{\frac{1}{3} + \frac{1}{2}} + 2x^{\frac{1}{3} + \frac{2}{1}} = x^{\frac{2}{6} + \frac{3}{6}} + 2x^{\frac{2}{6} + \frac{12}{6}}[/tex]

[tex]\underline{\textsf{Add;}}[/tex]

[tex]\tt x^{\frac{2}{6} + \frac{3}{6}} + 2x^{\frac{2}{6} + \frac{12}{6}} = x^{\frac{5}{6}} + 2x^{\frac{14}{6}[/tex]

[tex]\underline{\textsf{Simplify Fractions;}}[/tex]

[tex]\large\boxed{\tt x^{\frac{5}{6}} + 2x^{\frac{7}{3}}}[/tex]

Answer:

the answer is 0

Step-by-step explanation:

Yolanda will spend a total of 3 hours / 9 tables,

or **1/3 hour per table**, if she spends an equal amount of time at each table.

Yolana can serve a total of 36 people if she has to serve 9 tables, each of which can hold 4 guests, and she must serve a total of 4 guests per table.

How long does each visitor spend on average?

We need to know the entire length of time Yolana will spend serving all 36 guests in order to calculate the average time spent per guest.

If the entire time is divided by the number of guests,we get:

36 people in 3 hours equals 5 minutes each person.

Thus, each visitor spends 5 minutes on average.

What is the average time?

A measurement of a set of time values' central tendency is the average time. It is determined by multiplying the total number of values in the set by the sum of all the time values.

As an illustration, if you have a series of times of 5, 10, and 15, you would add them all up to reach 30 minutes, divide that number by 3, and get an average time of 10 minutes.

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Answer: We can solve this system of equations by substituting the expression for y in terms of x from the second equation into the first equation, and then solving for x.

First, we substitute y = 2 + x from the second equation into the first equation, giving:

2x - 3(2 + x) = -5

Simplifying this expression by distributing the -3, we get:

2x - 6 - 3x = -5

Combining like terms, we get:

-x - 6 = -5

Adding 6 to both sides, we get:

-x = 1

Multiplying both sides by -1, we get:

x = -1

Therefore, the value of x in the system of equations is -1.

Step-by-step explanation:

The price for product A is Ksh 55,000 and the price for product B is Ksh 32,000.

What is the selling price?

The price you will pay to purchase a share or any other commodity is known as the "buy" or "bid" price. The price you will receive when you sell that share or commodity is the "sell" or "ask" price.

Here, we have

Given: Tom and John are engaged in buying and selling certain products A and B. Tom buys 5 of product A but sells twice as much of product B. John on the other hand sells three times what Tom bought of product A and buys 13 of product B. At the end of the business day, John banks Ksh 110,000/- while Tom banks Ksh 230,000.

Let's assume that the cost price for both products A and B is "x", and the selling price for both products A and B is "y". We can use this information to set up two equations, one for Tom and one for John, that relate the costs and profits for the two products:

Tom: 5x - 2(5y) = P₁

John: 3(5x) - 13x = P₂

where  P₁ and P₂ are the profits made by Tom and John, respectively.

We know that at the end of the business day, John banks Ksh 110,000/- while Tom banks Ksh

230,000. So we can write:

P₁ = 230,000 - 5x

 P₂ = 110,000 - 18x

Substituting these values into the equations for Tom and John, we get:

5x - 2(5y) = 230.000 - 5x

Simplifying these equations, we get:

10x - 10y = 230,000

2x = 110,000

x = 55,000

Substituting this value back into the first equation, we can solve for y:

10(55,000) - 10y = 230,000

Simplifying this equation, we get:

y = 32,000

Hence, the price for product A is Ksh 55,000 and the price for product B is Ksh 32,000.

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Answer:

Step-by-step explanation:

Answer:

[tex]\cos^2x+\cos x-1+\sin^2x[/tex] can be simplified to [tex]\cos x[/tex]

Step-by-step explanation:

Given

[tex]\cos^2x+\cos x-1+\sin^2x[/tex]

We need to use the Pythagorean trig identity in this example.

[tex]\sin^2x+\cos^2x=1[/tex]

Lets simplify.

We can use the Commutative and Associative Properties of Addition to reorder the equation.

[tex]\sin^2x+\cos^2x+\cos x-1[/tex]

Apply the Pythagorean trig identity to [tex]\sin^2x+\cos^2x[/tex].

[tex]1+\cos x-1[/tex]

Group like terms.

[tex]\cos \left(x\right)+\left(1-1\right)[/tex]

1 minus 1 is zero.

That leaves us with

[tex]\cos x[/tex]

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The value of the product  7 × 3 1/4 is 22 3/4

It is important to note that fractions are defined as the part of a whole variable, element or number.

There are different types of fractions, such as;

From the information given, we have;

7 = A whole number

3 1/4 = a mixed fraction

Let's convert it to an improper fraction by multiplying the denominator by the whole number, then adding the numerator

13/4

Multiply the values

7 × 13/4

91/4

Divide the values

22 3/4

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The value of x = 2.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign. When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

According to our question-

y= -5x

6x+y=2

6x-5x=2

x=2

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Answer:

25%

Step-by-step explanation:

The factorised form of the given expression as required to be determined in the task content is; p ( p + 1 ) - q (q - 1).

It follows from the task content that the factored form of the given expression is to be determined.

As evident from the task content; the given expression is; p² - q² + p - q.

On this note, by first collecting like terms; we have;

p² + p - q² - q

By factorisation; we have that;

p ( p + 1 ) - q (q - 1)

Ultimately, the factored form of the given expression is; p ( p + 1 ) - q (q - 1).

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Answer:

Step-by-step explanation:

you need to show us what circle x looks like

Joe will catch Jason in 6 hours running at 7mph while Jason is running at 5.5 mph .

Given,

Jason is 9 miles ahead of Joe running at 5.5 miles per hour and Joe is running at the speed of 7 miles per hour.

Now,

Joe speed is more than Jason.

So,

Differences in speed:

(7 - 5.5) = 1.5 miles per hour.

Now,

Jason is ahead of joe by 9 miles.

To cover 9 miles of distance by joe to catch jason,

Distance = Speed * Time

9 miles = 1.5mph* Time

Time = 6hours.

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Answer: 4

Step-by-step explanation:

If there are two students in the first row and two students sit behind each of those students in the second row, then there are a total of 2 x 2 = 4 students in the second row.

Answer:

In this problem, we have to use the formula

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

A = $600,000.00

n = 1  (annually)

t = 25 years

First, convert R as a percent to r as a decimal

r = R/100

r = 8/100

r = 0.08 per year,

Then, solve the equation for P

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

[tex]P= \frac{6000000}{(1+\frac{0.8}{1})^{1*25} }[/tex]

P = $87,610.74

The principal investment required to get a total amount of $600,000.00 from compound interest at a rate of 8% per year compounded annually over 25 years is $87,610.74.

After answering the presented question, we can conclude that Yet, we equation cannot make final decisions based just on the median.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Whether data is sorted in ascending or descending order, the median is the midway value. In this situation, the median sales amount for Company A is $7,000, which suggests that half of the sales are greater than $7,000 and half are less. The median sales amount for Business B is $6,000, which means that half of the sales are greater than $6,000 and half are less.

The median can be a useful approach to summaries a data set's core tendency. For example, we can see that Company A has a greater median sales amount than Company B, implying that Company A generates more money each sale on average. Yet, we cannot make final decisions based just on the median.

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To rank the libraries from 1 having the greatest total number of comic books to 5 having the least total number of comic books, we need to first calculate the total number of books in each library.

Let's start by using the information given to find the total number of books in each library:

For Library A, we know that 30 comic books are 2% of its total books. So, we can set up the following equation:

 30 = 0.02x

where x is the total number of books in Library A. Solving for x, we get:

 x = 1500

Therefore, Library A has a total of 1500 books.

For Library B, we know that 45 comic books are 5% of its total books. So, we can set up the following equation:

 45 = 0.05x

where x is the total number of books in Library B. Solving for x, we get:

 x = 900

Therefore, Library B has a total of 900 books.

For Library C, we know that 65 comic books are 2% of its total books. So, we can set up the following equation:

 65 = 0.02x

where x is the total number of books in Library C. Solving for x, we get:

 x = 3250

Therefore, Library C has a total of 3250 books.

For Library D, we know that 75 comic books are 10% of its total books. So, we can set up the following equation:

 75 = 0.1x

where x is the total number of books in Library D. Solving for x, we get:

 x = 750

Therefore, Library D has a total of 750 books.

For Library E, we know that 90 comic books are 3% of its total books. So, we can set up the following equation:

 90 = 0.03x

where x is the total number of books in Library E. Solving for x, we get:

 x = 3000

Therefore, Library E has a total of 3000 books.

Now that we have the total number of books in each library, we can rank them based on the number of comic books they have:

Library C: 65 comic books

Library E: 90 comic books

Library B: 45 comic books

Library A: 30 comic books

Library D: 75 comic books

Therefore, the libraries ranked from 1 having the greatest total number of comic books to 5 having the least total number of comic books are: C, E, B, A, D.

A×A is the set {16, 20, 24, 28, 20, 25, 30, 35, 24, 30, 36, 42, 28, 35, 42, 49}

To find A×A, we need to first understand what A represents.

In mathematics, a set is a well-defined collection of distinct objects, called elements or members of the set. These objects can be anything, such as numbers, letters, or even other sets. The elements of a set are typically enclosed in curly braces { } and are separated by commas.

A is a set defined as the set of all whole numbers, x, where 4 ≤ x ≤ 7. In other words, A contains the elements 4, 5, 6, and 7.

To find A×A, we need to take each element in A and multiply it by every other element in A. This means that we need to find the product of (4, 4), (4, 5), (4, 6), (4, 7), (5, 4), (5, 5), (5, 6), (5, 7), (6, 4), (6, 5), (6, 6), (6, 7), (7, 4), (7, 5), (7, 6), and (7, 7).

When we do the multiplication, we get the set {16, 20, 24, 28, 20, 25, 30, 35, 24, 30, 36, 42, 28, 35, 42, 49}.

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According to the given data in question below given are the separate journal entries for each transaction on the books of Metlock, Inc.

"Entries" typically refers to the individual values in a matrix or table. A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns, while a table is an arrangement of data in rows and columns with each intersection representing a single piece of data.

1.On June 10, Metlock, Inc. made an account-based purchase from the Monty Company for $7,400 in goods, FOB shipping point, 3/10, n/30.

Inventory (asset) $7,400

Accounts payable (liability) $7,400

2. On June 11, Metlock, Inc. pays the freight costs of $560:

Freight expense (expense) $560

Cash (asset) $560

3. On June 12, goods totaling $600 are returned to Monty for credit:

Accounts payable (liability) $600

Inventory (asset) $600

4. On June 19, Metlock, Inc pay Monty Company in full, less the purchase discount:

Accounts payable (liability) $7,400

Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]

Cash (asset) $7,178

Note that the purchase discount is calculated as $7,400 x 3%, or $222.

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The information in issue below is taken from Metlock, Inc.'s books, which include separate journal entries for each transaction.

Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]

Cash (asset) $7,178

1.On June 10, Metlock, Inc. made an account-based purchase from the Monty Company for $7,400 in goods, FOB shipping point, 3/10, n/30.

Inventory (asset) $7,400

Accounts payable (liability) $7,400

2. On June 11, Metlock, Inc. pays the freight costs of $560:

Freight expense (expense) $560

Cash (asset) $560

3. On June 12, goods totaling $600 are returned to Monty for credit:

Accounts payable (liability) $600

Inventory (asset) $600

4. On June 19, Metlock, Inc pay Monty Company in full, less the purchase discount:

Accounts payable (liability) $7,400

Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]

Cash (asset) $7,178

Note that the purchase discount is calculated as $7,400 x 3%, or $222.

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Answer:

≈ 11,88

Step-by-step explanation:

Use trigonometry:

cos (62∘) = 8 / x

x = 8 / cos (62∘) ≈ 11,88

The solution of the given problem of percentage comes out to be  $19,000 in 12 years, they should deposit $170.89 at the conclusion of each quarter.

The abbreviation "a%" is used to indicate a value or number in statistics that is expressed as a percentage of 100. Versions with "pct," "pct," or "pc" as the initials are also rare. However, the most popular method to do this is to use the percentage symbol ("%"). Additionally, both hints nor a constant ratio of every element to the overall amount exist. Since numbers commonly add up to 100, they are essentially integers.

Here,

=>  [tex]FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n)[/tex].

By entering these numbers, we obtain:

[tex]= > 19000 = PMT * [(1 + 0.07/4)^(4*12) - 1] / (0.07/4)[/tex]

Upon solving for PMT, we obtain:

[tex]= > PMT = 19000 * (0.07/4) / [(1 + 0.07/4)^(4*12) - 1][/tex]

=> PMT = $174.58 (rounded to the nearest cent)

In order to have $19,000 in 12 years, the investor needs to deposit $174.58 at the conclusion of each quarter at a rate of 7% compounded quarterly.

(b) Using the same procedures as in (a), but with an interest rate of 7.2%, we arrive at:

[tex]= > 19000 = PMT * [(1 + 0.072/4)^(4*12) - 1] / (0.072/4)[/tex]

Upon solving for PMT, we obtain:

[tex]= > PMT = 19000 * (0.072/4) / [(1 + 0.072/4)^(4*12) - 1][/tex]

=>  PMT = $170.89 (rounded to the nearest cent)

In order to have $19,000 in 12 years, they should deposit $170.89 at the conclusion of each quarter.

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Given a solution containing 30 mg of medication per 3 mL, you need to determine how many mL makeup 15 mg of medication. By setting up a proportion, it can be calculated that 1.5 mL should be administered per dose.

To solve this problem, we need to determine how many milliliters correspond to the required dose of medication (15 mg). Given that the pharmacy dispensed a solution containing 30 mg of medication per 3 mL, we can construct a proportion to find the needed milliliter amount.

30 mg/3 ml = 15 mg/x ml

To solve this equation for 'x', multiply both sides by 'x' and then divide by 30 mg to isolate 'x':

x = (15 mg * 3 ml) / 30 mg

Upon completing this calculation, you find that x equals 1.5 ml. Therefore, you would administer 1.5 mL of the medication per dose.

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To administer 15 mg of a liquid oral medication given a concentration of 30 mg/3 mL, you will need to administer 1.5 mL per dose.

To calculate the mL of the liquid oral medication to administer, we need to determine the amount of medication in each mL. In this case, the pharmacy has dispensed a concentration of 30 mg/3 mL, which means there is 10 mg of medication in each mL. Given that the doctor's order is for 15 mg, we can calculate the mL to administer by setting up a proportion:

10 mg/1 mL = 15 mg/x mL

Cross-multiplying, we get:

10x = 15

x = 1.5

Therefore, you will need to administer 1.5 mL per dose.

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The size of the sample required to be representative depends on the variability of the population and the level of precision required in the analysis.

What is Inductive logic ?

Inductive logic, also known as induction, is a type of reasoning that involves drawing general conclusions based on specific observations or examples.

In inductive logic, a sample is considered representative of the population from which it is taken if it possesses the following two characteristics:

Randomness: The sample should be selected randomly from the population. This means that every individual in the population should have an equal chance of being selected for the sample. A random sample helps to reduce the potential for bias in the selection process.

Size: The sample size should be large enough to accurately represent the population. A larger sample size helps to reduce the impact of chance variation and provides a more accurate estimate of the characteristics of the population.

Therefore, The size of the sample required to be representative depends on the variability of the population and the level of precision required in the analysis.

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Answer:

Step-by-step explanation:

ear

The statements that are true with regards to the graph of the functions and the sprinter that wins and lead the race are;

The true statements are; A, B, and C

The graph of a function visually represents the rule of the function showing how the output values of the function changes as the input value varies.

The distance the two sprinter's will run = 80 meters

The speed of sprinter A = 9 meters per second

The speed of sprinter B = 9 meters per second

The head start of sprinter B = 14 meter

The analysis of the statements are as follows

A. The graph of the functions representing the speeds of the sprinters have the same slope of 9 which is the rate of change of distance with time, therefore, the graphs are parallel and will never intersect.

The statement is therefore; True

B. Sprinter B will win the race. - True

Sprinter B has a head start of 14 meters and both sprinters have the same speed, therefore, sprinter B will reach the finish line first and win the race.

C. Sprinter B is leading the race at the 4 seconds mark;- True

Sprinter A will cover a distance of 9 m/s × 4 s = 36 m at the 4 seconds mark, while sprinter B will cover a distance in the 80 m race of 9 m/s × 4 s + 14 m = 50 m at the 4 second mark, therefore, sprinter B will be leading at the 4 second mark

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Answer:

C. 180° (since x and y are supplementary angles).

Using expressions, we can get the following:

a. If W (6.5) =75, H (6.5) = 85

b. If W (2) = 60, H (2) = 70

c. W (x) + 10

Expressions are statements in mathematics that include variables, numbers, or both, as well as at least two terms connected by an operator. Addition, subtraction, multiplication, and division are examples of mathematical operations.

The equation x + y, which combines the terms x and y with an addition operator, serves as an illustration. Expressions can be classified into two categories in mathematics: algebraic expressions, which also contain variables, and numerical expressions, which only contain numbers.

W(x) gives the temperature W in the apartment x hours after midnight.

H(x) gives the temperature H x hours after midnight when it is hot outside.

When it is hot outside, the owner changes the settings to be exactly 10 degrees warmer than W.

So,

H (x) = W(x) + 10

If W (6.5) =75, then

H (6.5) =W (6.5) + 10

= 75+10

= 85

If W (2) = 60, then

H (2) = W (2) + 10

= 60+ 10

= 70

The expression of H in terms of W:

W (x) +10

Hence the equation:

H(x) = w(x) + 10

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Answer: congruent

Step-by-step explanation:

they look like the same shape