two rectangles are similar. the first has a width of 4 meters and a length of 15 meters. the second has a width of 12 meters. what is the area of the second rectangle?

Answer:

The concept of "difference of squares" is a special case in factoring where you have a quadratic expression that can be written as the difference of two perfect squares. Specifically, it takes the form of (a^2 - b^2), where 'a' and 'b' represent any real numbers or algebraic expressions.

Let's consider an example to help explain this concept. Suppose we have the expression x^2 - 9. Notice that x^2 is a perfect square because it can be written as (x * x). Similarly, 9 is a perfect square because it can be written as (3 * 3). So, we can rewrite the expression as (x^2 - 3^2), where '3' represents the square root of 9.

Now, according to the special case rule for difference of squares, we can factor this expression by recognizing that it is the difference between two perfect squares. The rule states that (a^2 - b^2) can be factored as (a + b) * (a - b).

Applying this rule to our example, we can factor x^2 - 9 as follows:

x^2 - 9 = (x + 3) * (x - 3).

Here, (x + 3) represents the sum of the square root of x^2 and the square root of 9, while (x - 3) represents the difference between them.

To summarize, the concept of difference of squares refers to a special case in factoring where a quadratic expression can be expressed as the difference between two perfect squares. By applying the special case rule (a^2 - b^2) = (a + b) * (a - b), we can factor such expressions easily.

Step-by-step explanation:

The difference of squares is a special case in factoring quadratic expressions, where we subtract the square of one term from the square of another term. The special case rule for factoring a difference of squares is (a²- b²) = (a + b)(a - b). An example is given to illustrate the process of factoring a difference of squares.

The concept of difference of squares is a special case in factoring where a quadratic expression is a result of subtracting the square of one term from the square of another term. It can be expressed in the form (a² - b²), where 'a' and 'b' are algebraic terms. To factor a difference of squares, we use the special case rule: (a² - b²) = (a + b)(a - b).

For example, let's consider the expression x² - 4. In this case, 'a' is x and 'b' is 2. We apply the special case rule: (x² - 4) = (x + 2)(x - 2). This means that the quadratic expression x² - 4 can be factored as the product of (x + 2) and (x - 2).

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Answer:

the answer is 9

Step-by-step explanation:

x=9 and w=9 making it 18, so if x=9 then v=7 because 7+9=16

Answer:

m(DE) = 90°

Step-by-step explanation:

Since both circles are equal, therefore, their radius would be equal too.

m<S = 180 - right angle (angles on a straight line)

m<S = 180 - 90 = 90°

m<R = m<S (congruent triangles)

m<R = 90°

m<R = m(DE) (central angle = intercepted arc based on the central angle theorem)

Substitute

90° = m(DE)

m(DE) = 90°

(6x^3-4x+5)-(3x^3-5x^2+6x-2)

Step 1

Let's subtract the number with power x^3

6x^3-3x^3=3x^3

Answer:

the formula is base time height times 1/2 its really easy use desmos calculater:))))

Step-by-step explanation:

inConsider the h(x) as the parental function

To determine the function g(x), there were two transformations performed to the parental function.

-First, they added 1 to the x-term, which results on a horizontal translation of one unit to the left

-Second, there were subtracted 8 units to the function, which results in a vertical translation down:

So the function g(x) has the same shape as function h(x) but its vertex is on the coordinates (-1,-8)

The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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The ordered pairs which make the open sentence true are:

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an algebraic expression based on any of the following arguments:

For this exercise, you should evaluate each of the given expressions to determine which inequalities is true when the ordered pairs are substituted. This ultimately implies that, you would have to substitute the ordered pairs into each of the given algebraic expressions and then evaluate.

When ordered pairs = (3, 6), we have:

3x + y < 14

3(3) + 6 < 14

9 + 6 < 14

15 < 14 (False).

When ordered pairs = (7, -7), we have:

3x + y < 14

3(7) + (-7) < 14

21 - 7 < 14

14 < 14 (False).

When ordered pairs = (6, 0), we have:

3x + y < 14

3(6) + 0 < 14

18 - 0 < 14

18 < 14 (False).

When ordered pairs = (-1, 6), we have:

3x + y < 14

3(-1) + 6 < 14

-3 + 6 < 14

3 < 14 (True).

When ordered pairs = (4, -1), we have:

3x + y < 14

3(4) + (-1) < 14

12 - 1 < 14

11 < 14 (True).

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Answer:

x = 20

Step-by-step explanation:

15/9 = x/12

180 = 9x

x = 20

Answer:

The equation is 12x+1.88 = 14.84

It solves to x = 1.08

This means one bottle of juice costs $1.08

==========================================================

Work Shown:

x = cost of one bottle of juice

12x = cost of a 12-pack of juice

12x+1.88 = add on the cost of the chips

12x+1.88 = 14.84 is the equation to set up

----------

Let's solve for x

12x+1.88 = 14.84

12x = 14.84-1.88

12x = 12.96

x = 12.96/12

x = 1.08 is the cost of one bottle of juice

Answer:

Each juice bottle is $1.08

Step-by-step explanation:

$14.84 (total before tax) - $1.88 (cost of bag of chips) = $12.96

$12.69 / 12 (bottles of juice bottles) = $1.08

Each juice bottle is $1.08

Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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Nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.

What is the pigeon-hole approach?
According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m. For instance, if one possesses three gloves but none of them are ambidextrous or reversible, then there must be at least two right-handed gloves or at least two left-handed gloves since there are three items but only two categories of handedness. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.

The standard 52 deck has 4 suits of 13 cards each, thus as per n pigeons need to be extracted from p = 4 pigeon-holes; as per established literature above.
∴ [(n - 1) / p] + 1 = 3 ⇒ [(n - 1) / 4] + 1 = 3 ⇒ n - 1 = 8 ⇒ n = 8 + 1 ⇒ n = 9
Therefore, nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.

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Answer:

\(1290\) calories

Step-by-step explanation:

Given: The racer moves at \(13.1\) miles per hour expends energy at a rate of \(645\) calories per hour.

To find: Energy in calories, required to complete a marathon race \(26.2\) miles at this pace.

Solution: We have,

The racer moves at \(13.1\) miles per hour.

The racer expends energy at a rate of \(645\) calories per hour.

So, energy expended while moving \(13.1\) miles \(=645\) calories.

Now, energy expended while moving \(1\) mile \(=\frac{645}{13.1}\) calories.

So, energy expended while moving \(26.2\) miles \(=\frac{645}{13.1}\times 26.2=645\times 2=1290\) calories.

Hence, \(1290\) calories of energy is required to complete a marathon race \(26.2\) miles at this pace.

The wheelchair-marathon racer would need 1290 calories to complete the marathon race.

Speed is the ratio of distance travelled to total time taken. It is given by:

Speed = distance / time

The speed of the racer is 13.1 miles per hour. To complete a 26.2 miles:

13.1 = 26.2 / t

t = 2 hours.

The racer expends energy at a rate of 645 calories per hour, for 2 hours:

Amount of calories = 645 calories per hour * 2 hours = 1290 calories

The wheelchair-marathon racer would need 1290 calories to complete the marathon race.

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The probability that there will be fewer than 3 with no DMF teeth in a sample of 20 children is 0.287. The probability that there will be exactly 5 with no DMF teeth in a sample of 20 children is 0.224.

(a) In a sample of 20 children, the number of children with no DMF teeth follows a binomial distribution with n = 20 and p = 0.25. The probability that there will be fewer than 3 with no DMF teeth is given by:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

where X is the number of children with no DMF teeth in the sample.

P(X = k) = (nCk) pk (1-p)n-k

where nCk represents the number of ways to choose k children out of n total children.

Therefore,

P(X = 0) = (20C0) 0.25⁰ (0.75)²⁰

P(X = 0) = 0.019

P(X = 1) = (20C1) 0.25¹ (0.75)¹⁹

P(X = 1) = 0.086

P(X = 2) = (20C2) 0.25² (0.75)¹⁸

P(X = 2) = 0.182

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.019 + 0.086 + 0.182

P(X < 3) = 0.287

Therefore, the probability that there will be fewer than 3 with no DMF teeth in a sample of 20 children is 0.287.

(b) The probability that there will be exactly 5 with no DMF teeth is given by:

P(X = 5) = (20C5) 0.25⁵ (0.75)¹⁵

where X is the number of children with no DMF teeth in the sample.

Therefore,

P(X = 5) = (20C5) 0.25⁵ (0.75)¹⁵

P(X = 5) = 0.224

Therefore, the probability that there will be exactly 5 with no DMF teeth in a sample of 20 children is 0.224.

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A negative exponent means that you should take the reciprocal of the base and use the positive exponent:
5^(-4) = 1 / 5^4.So, the answer is: C. 1 / 5^4

To solve this problem, use the properties of exponents. Specifically, when multiplying numbers with the same base, you add the exponents. In this case, the base is 5, and the exponents are 3 and -7.

5^3 × 5^(-7) = 5^(3 + (-7))

Now, add the exponents:

3 + (-7) = -4

So, the expression becomes:

5^(-4)

A negative exponent means that you should take the reciprocal of the base and use the positive exponent:

5^(-4) = 1 / 5^4

So, the answer is:

C. 1 / 5^4.

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Answer:

w=1.14m-19.4

Step-by-step explanation:

m = months, the cat loses 1.14lbs per month. plus the cat started with 19.4 pounds. each month 1.14 is being subtracted from 19.4

Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=5 so y would = 3

In a case whereby Ken and Hamid run around a track where it take Ken 80 seconds to complete a lap It take Hamid 60 seconds to complete a lap. the number of  laps they will each have run when they next meet on the start line is that Ken will have run 3 laps and Hamid will have run 4.

The LCM of 80 nd 60 seconnds can be written as 240,  however when 240 seconds go then they will both be at the start line.

So the lap that  Ken will covered in 240s = 240/80 = 3laps

So the lap that  Hamid will covered in 240s = 240/60 = 4laps

Therefore, we can come into conclusion that Ken will have to run   3laps  where Hamid will have run  4Laps.

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Approximately 32% of students scored above 86 on the university exam.

To determine the percentage of students who score above 86, we can use the 68-95-99.7 rule, also known as the empirical rule or the three-sigma rule.

According to this rule, in a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Given that the mean is 78 and the standard deviation is 8, we can calculate the z-score for 86 using the formula:

z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

z = (86 - 78) / 8 = 1

Since 86 is one standard deviation above the mean, we know that approximately 68% of students scored below 86. Therefore, the percentage of students who score above 86 can be estimated as 100% - 68% = 32%.

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A)the mass of $700 billion worth of gold is approximately 24,822,695,035.5 grams. B)The actual length will depend on the exact density of gold and the accuracy of the provided values.

A) In order to calculate the mass of $700 billion worth of gold, we need to convert the dollar value into grams.

To do this, we first need to determine the price of gold per gram. Given that gold was worth $800 per ounce ($28.20 per gram), we can use this conversion factor to calculate the mass.

$800 per ounce is equivalent to $28.20 per gram. Therefore, 1 gram of gold is worth $28.20.

Next, we can divide the total dollar value ($700 billion) by the value of 1 gram of gold ($28.20) to find the mass in grams.

$700 billion / $28.20 per gram = 24,822,695,035.5 grams

So, the mass of $700 billion worth of gold is approximately 24,822,695,035.5 grams.

B)Moving on to the second part of the question, if this amount of gold were in the shape of a cube, we need to calculate the length of each side of the cube.

To find the length, we can use the formula for the volume of a cube, which is side length cubed. Since we know the mass of the gold (24,822,695,035.5 grams), we need to calculate the side length.

Let's assume the density of gold is 19.32 grams per cubic centimeter (g/cm³). By dividing the mass of the gold (24,822,695,035.5 grams) by the density (19.32 g/cm³), we can find the volume of the gold in cubic centimeters.

Volume = Mass / Density = 24,822,695,035.5 g / 19.32 g/cm³

By solving this equation, we can find the volume of the gold.

Finally, we can use the volume of the gold to calculate the length of each side of the cube by taking the cube root of the volume.

This will give us the length of each side of the cube formed by the given amount of gold.

The actual length will depend on the exact density of gold and the accuracy of the provided values. The above calculation is an example based on the given information.

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The amount paid back when the loan is paid in full at the end of that period will be $77,546.3.

Given that:

Principal, P = $35,000

Rate, r = 7.5% or 0.075

Time, n = 11 years

The amount (A) is calculated as,

A = P(1 + r)ⁿ

If the loan is paid in full at the end of that period, then the amount paid back is calculated as,

A = $35,000 x (1 + 0.075)¹¹

A = $35,000 x (1.075)¹¹

A = $35,000 x 2.2156

A = $77,546.3

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Answer:

If the area is four, the radius would be two.

Step-by-step explanation:

Remember that the radius is always half of the area! I hope this help.

Answer:

Press down the brake firmly and smoothly. ...

Don't brake and swerve the car at the same time. ...

Avoid using your transmission for quick stops. ...

Focus on where you want to go, not what you want to avoid.

The amount of brown sugar called for in the recipe is 1134.0 grams, tenths of a gram rounded up. By dividing 40 ounces by the conversion value of 28.35 grams per ounce, you can calculate this and get 1134.0 grams.

Rounding to the closest tenth of a gram is necessary to convert 40 ounces to grams. To do this, multiply the weight in ounces by the conversion factor of 28.35 (1 ounce = 28.35 grams).

Therefore, 40 ounces of brown sugar are equivalent to:

40 ounces x 28.35 grams per ounce = 1134 grams

Because 1 gram only roughly equates to 0.04 ounces, it is vital to keep in mind that this is an estimation. This conversion factor may change based on the situation and the material being measured.

Hence, The amount of brown sugar required for the recipe is roughly 1134 grams.

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Arlene buys a phone case and charging cord for 15% off

Discount on case and cord = 15%

Original cost of case = $18

Total discount amount = $4.20

Let the original cost of charging cord = x

So, Arlene buys a phone case and charging cord for 15% off = 15% of cost of cord and case

15% of cord and case = 15% of (x + 18)

as the discount amonut ins $18

15% of cord and case = 15% of (x + 18)

15% of cord and case = 4.20

15% of (x + 18) = 4.20

So, the expression is : 15(x + 18) = 420

Simplify the expression for x :

15(x + 18) = 420

15x + 270 = 420

15x = 420 - 270

15x = 150

x = 150/15

x = 10

So, the cost of charging cord is $10

Answer : equation : 15(x + 18) = 420

$10

Okay, here we have this:

Considering the provided formula and information, we are going to calculate the requested percent of college freshmen in 2010, so we obtain the following:

So since x corresponds to the number of years after 1980, in this case we will replace x with 30, since it is 30 years after 1980, we have:

p=4x/5+25

Replacing:

p=4(30)/5+25

p=120/5+25

p=24+25

p=49

So, as we can see, the model assumes that in 2010 the percentage was 49%, and the real one is 47%. It means that the model overestimates the real value by 2%.

Answer:

\(\sqrt{40}\) or 6.32

Step-by-step explanation:

We can find the distance between two points by using this formula

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

where the x and y values are derived from the given points

The points given are ( -2 , 5 ) and ( 4 , 3 )

So we plug in the x and y values of those coordinates into the distance formula

\(\sqrt{(4-(-2)^2+(3-5)^2} \\4-(-2)=6\\3-5=-2\\d=\sqrt{6^2+-2^2} \\6^2=36\\-2^2=4\\36+4=40\\d=\sqrt{40}\)

or 6.32

Answer:

1 /5

Step-by-step explanation: