Which is larger: 90%of 20 OR 20% of 95

Recall that

\((a+b)^2=a^2+2ab+b^2\)

So we have

\(\left(x+\dfrac1x\right)^2=x^2+2+\dfrac1{x^2}\)

Given that \(x+\frac1x=5\), we get

\(x^2+\dfrac1{x^2}=5^2-2=\boxed{23}\)

Answer: 78 paperback books.

Step-by-step explanation:

1. Since 2/3 of the books are hardcover books, then 1/3 of the books are paperback books.

2. 234/3 = 78 books.

Answer:

78 paperback books

Step-by-step explanation:

234 x (2/3) = 156

234 - 156 = 78

Answer:

55.25

Step-by-step explanation:

So, all you gotta do is get rid of the decimal, times them both, then add the decimal back into it, and how you do that is you see how many numbers are behind a decimal point in the first place, in this case, it's two (8.5, 6.5) and you got your answer!

Hope this helps! <D

Answer:

They'll each want a quarter of a cupcake.

Step-by-step explanation:

The number of people in the family is 14.

The number of cupcakes ordered is 4.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Number of cakes for the family = 3 (1/2)

Number of friends = 2

Now,

Each person's amount of cake = 1/4

The number of people in the family.

= 3(1/2) ÷ 1/4

= 7/2 x 4

= 14

The total number of cupcakes ordered.

= 2 x 1/4 +3(1/2)

= 1/2 + 3(1/2)

= 1/2 + 7/2

= 8/2

= 4

Thus,

There are 14 people in the family.

The total number of cupcakes ordered is 4.

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The complete question is:

Hello, id like to order3 halves of a cupcake for my family plus some extra for my 2 friends.

They'll each want a quarter of a cupcake.

(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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Answer:

A number increased by 9.

Step-by-step explanation:

A number= can be denoted by any letter.

increased= +

by 9= 9

Hope this helps ;) ❤❤❤

To change a decimal to a percentage, we multiply it by 100 and add a percent sign (%).

Therefore, to change 8.28 to a percentage, we multiply it by 100 and get:

8.28 x 100 = 828%

So, 8.28 expressed as a percentage is 828%.

Step-by-step explanation:

The answer is 828%

The decimal 8.28 equals 828%

To convert from decimal to percent, just multiply the decimal value by 100. In this example we have: 8.28 × 100 = 828% ( Which is the answer ).

Which is the answer

Thus the answer to your problem is, 828%

Answer:

x-intercept= 4

y-intercept= 7

Based on the information given, there are a total of 118 solutions.

This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:

x1 + x2 + x3 + y4 = 20

Subject to the following conditions:

0 ≤ x1 < 3

0 ≤ x2 < 4

0 ≤ x3 < 5

0 ≤ y4 < 6

We can solve this problem using the technique of generating functions. The generating function for each variable is:

(1 + x + x^2) for x1

(1 + x + x^2 + x^3) for x2

(1 + x + x^2 + x^3 + x^4) for x3

(1 + x + x^2 + x^3 + x^4 + x^5) for y4

The generating function for the equation is the product of the generating functions for each variable:

(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)

We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118

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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.

Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:

**|**||

then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.

In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).

Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:

C(20+4-1, 4-1) = C(23, 3) = 1771

However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.

Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:

A = A₀ ∩ A₁ ∩ A₂ ∩ A₃

where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.

To find the cardinality of A₀, we use the formula above and obtain:

C(20+4-1, 4-1) = 1771

To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:

C(20-4+3-1, 3-1) = C(18, 2) = 153

Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:

|A| = |A₀| - |A

Step-by-step explanation:

Relative interest refers to the comparison of interest rates between different financial instruments or investment opportunities. It allows individuals or investors to assess and evaluate the attractiveness of various options based on their potential returns.

1. Understand the basic concept: Interest is the cost of borrowing money or the return earned on invested funds. Relative interest involves comparing the interest rates of different financial instruments or investments to determine which one offers a more favorable return.

2. Identify the investment options: Start by identifying the different investment opportunities or financial instruments available. These can include savings accounts, certificates of deposit (CDs), bonds, stocks, or other investment vehicles.

3. Research interest rates: Research and gather information about the current interest rates offered by each investment option. This information can usually be found on financial websites, through financial institutions, or by consulting with a financial advisor.

4. Compare interest rates: Once you have the interest rates for each investment option, compare them side by side. Look for the differences in rates and identify which options offer higher or lower returns.

5. Assess risk and return: Consider the level of risk associated with each investment option. Higher returns often come with higher risk, so it's essential to evaluate the risk-reward tradeoff.

6. Make an informed decision: Based on the comparison of interest rates and the risk-reward assessment, make an informed decision on which investment option aligns with your financial goals and risk tolerance.

Always remember to consider your financial goals, risk tolerance, and consult with a financial advisor if needed.

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Option (b) is the correct answer: Perpendicular segments.

Perpendicular rays, perpendicular segments, perpendicular lines, and parallel lines are important concepts in geometry that describe the relationship between lines and line segments.

1. Perpendicular Rays: Perpendicular rays are two rays that intersect at point and form a right angle (90 degrees) at the point of intersection. The rays extend indefinitely in opposite directions from the point of intersection.

2. Perpendicular Segments: Perpendicular segments are line segments that intersect at a right angle. They share a common endpoint but do not extend indefinitely like rays. The right angle is formed at the point of intersection.

3. Perpendicular Lines: Perpendicular lines are lines that intersect at a right angle. They continue indefinitely in opposite directions and form four right angles at the point of intersection. Perpendicular lines are often denoted by a symbol ⊥.

4. Parallel Lines: Parallel lines are lines that never intersect. They remain equidistant from each other at all points. Parallel lines have the same slope and do not converge or diverge. In Euclidean geometry, parallel lines are denoted by a double vertical line symbol (||).

Understanding these concepts is fundamental in geometry as they help define angles, shapes, and spatial relationships. The properties of perpendicular and parallel lines play a crucial role in various geometric theorems and applications.

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Answer: D

Step-by-step explanation:

20 apples cost $17

100 apples = 100/20 * 17 = D

Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

Answer:

area of ab= trapezium + area of c=rectangle

Step-by-step explanation:

[1÷2(a+b)h] +[l×b]

1÷2(9+14)6 + 6×4

23×3 +24

69+24=93ft=86399.8cm2

Answer: I am pretty sure its what I said

Bruce: x/2 + 4

Angela: 4x + 2

Callie: 4x - 3

Deshawn: x/2 + 3

Let me know If I am correct thank you!

Answer:

Should be

Callie: 4x-3

Angela: 2x+4

Bruce: x/2 + 4

Deshawn: x/2 - 3

Step-by-step explanation:

Hopefully this helps sorry if it’s wrong

Answer and Step-by-step explanation:

116 b.

\(2^{10} = 1024\\2^8 = 256\\\\1024 + 256 = 1280\\\\\\2^5 = 32\\2^3 = 8\\\\32 - 8 = 24\)

1280 × 24 = 30720

30720 ÷ 60 = 512. 512 is the solution; the expression is divisible by 60.

116 c.

\(16^3 = 4096\\8^3 = 512\\\\4096 - 512 = 3584\\\\\\4^3 = 64\\2^3 = 8\\\\64 + 8 = 72\)

3584 × 72 = 258048

258048 ÷ 60 = 4096. 4096 is the solution; the expression is divisible by 63.

116 d.

\(125^2 = 15625\\25^2 = 625\\\\15625 + 625 = 16250\\\\\\5^2 = 25\\\\25 - 1 = 24\)

16250 × 24 = 390000

390,000 ÷ 39 = 10,000. 10,000 is the solution; the expression is divisible by 39.

#teamtrees #PAW (Plant And Water)

Answer:

X=5 y=-3

Step-by-step explanation:

Answer:

2 out of 5 chance of being red

Step-by-step explanation:

Answer: 89.64 kilometers per hour

Step-by-step explanation: Convert 24.9 meters per second into Kilometers per minute by multiplying by 1000 to get 0.0249 kilometers per minute, which gives you 1.494 kilometers per minute. Then, you must convert this to kilometers per hour by multiplying by 60 to get 89.64 kilometers per hour

Kim's test scores indicate that he scored as well as or better than 72% of the test takers, and 28% of the test takers scored better than him. His grade equivalent of 12.1 indicates that he would perform adequately in a twelfth grade science class.

His percentile of 88 indicates that he scored as well as or better than 88% of the test takers. His raw score of 72 does not directly indicate the percentage of questions answered correctly, but it can be assumed that he answered a majority of the questions correctly to achieve his score.

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Step-by-step explanation:

since there is no other information, we have to assume that the prices for student passes and teacher passes are the same.

therefore, the pass price per person is

$737.38 / (44 + 2) = $737.38 / 46 = $16.03

and the lunch costs per student are

$393.36 / 44 = $8.94

altogether,

$16.03 + $8.94 = $24.97

was spent for each student.

(1 , -5) satisfy the inequality y ≤ 3x + 2  but not to y > –2x – 3

According to the question,

It is Given : y ≤ 3x + 2  

y > –2x – 3

We have to find the relationship between the point (1, –5) and the given system of inequalities.

Substituting the point (1,5) in our inequality y ≤ 3x + 2  

=> x = 1

=> y ≤ 3(1) + 2  

=> y ≤  5

=> - 5 ≤ 5

Which is true

Hence point (1, –5)  satisfy y ≤ 3x + 2  

Substituting the point (1,5) in our inequality  y > –2x – 3

x = 1

=> y > -2(1) - 3

=> y > - 5

but - 5 = -5

Hence  point (1, –5)   does not satisfy y > –2x – 3

I've answered the question in general as the given question is incomplete

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Answer:

A

Step-by-step explanation:

An acute angle is an angle that is less than 90 degrees.

Answer:

Step-by-step explanation:

A

f(x) = 4x

To find the inverse of a function, you have to replace every x with an y, as follows:

f(x) = 4y

then, replace f(x) with an x,

x = 4y

and now, isolate y,

x/4 = y

Finally, replace y whit h(x),

h(x) = 1/4x

Sarah's fuel efficiency is approximately 32.91 miles per gallon.

From the question, we are to calculate Sarah's fuel efficiency.

To find Sarah's fuel efficiency in miles per gallon, we need to convert the distance she drove to miles and the amount of gasoline she used to gallons.

From the given information,

1 km = 0.6214 mi

1 gal = 3.8 L

First, let's convert the distance from kilometers to miles:

691.4 km × 0.6214 mi/km = 430.10196 mi

So, Sarah drove a distance of 430.1 miles.

Also,

Convert the amount of gasoline from liters to gallons:

49.7 L ÷ 3.8 L/gal = 13.0789 gal

So, Sarah used 13.0789 gallons of gasoline.

Calculate her fuel efficiency in miles per gallon:

Fuel efficiency = distance ÷ gasoline used

Fuel efficiency = 430.1 mi ÷ 13.0789 gal

Fuel efficiency = 32.9065 mi/gal

Hence, Sarah's fuel efficiency is 32.91 mi/gal

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a) The mean of the data-set is of 2.

b) The range of the data-set is of 4 units, which is of around 4.3 MADs.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:

Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)

Mean = 2.

The range is the difference between the largest observation and the smallest, hence:

4 - 0 = 4.

4/0.93 = 4.3 MADs.

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The sample size for the Gallup poll is 1,627 adults. The 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

To calculate the 95% confidence interval, we need to consider the margin of error. The margin of error is given as 2.5%, which means that we need to account for plus or minus 2.5% around the observed proportion of 22%.

First, let's calculate the margin of error:

Margin of Error = 2.5% of 22% = 0.025 * 22% = 0.0055

Next, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = 22% - Margin of Error = 22% - 0.0055 = 21.995% ≈ 22.0%

Upper Bound = 22% + Margin of Error = 22% + 0.0055 = 22.005% ≈ 22.0%

Therefore, the 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

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By taking the quotient between the total volume and the number of hours, we conclude that she drinks 8 ounces per hour.

We know that Ziba has 4 bottles, each one with 6 ounces, so the total volume of water is:

V = 4*6 ounces = 24 ounces.

We know that she drinks that in 3 hours, so the amount that she drinks each hour is:

24 oz/3 = 8 oz

She drinks 8 ounces of water each hour.

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First, we find x such that:

The only real number that can be a solution for the above equation is 0, therefore x=0.

Now, we complete a t-chart with two points to the right and two points to the left of (0,f(0)):

Answer: The graph of the function is: