Find the rate. Principle= $50, Interest= $10, Time= 2½ years​

Al-Khwarizmi made significant contributions to the world of mathematics, particularly in the field of algebra. His major accomplishment was the development of algebra as an independent mathematical discipline.

Al-Khwarizmi, a Persian mathematician and scholar, wrote the book titled "Kitab al-Jabr wal-Muqabala," which laid the foundation for modern algebra. In this influential work, he introduced systematic methods for solving linear and quadratic equations. Al-Khwarizmi's algebraic techniques, including the use of variables and equations, greatly advanced mathematical understanding and problem-solving. His work also contributed to the development of algorithms and mathematical notation, such as the concept of the "zero" and the decimal system. Overall, al-Khwarizmi's contributions revolutionized mathematics and had a profound impact on subsequent generations of mathematicians and scientists.

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Answer:

x = 53°

Step-by-step explanation:

alternate exterior angles are equal

Answer:

Step-by-step explanation:

Two lines are parallel.

x = 53  

Alternate exterior angles are equal

Angle BEC is congruent to angle DEC. The student's error lies in assuming that BC + CD = 2BC means that AB = 2BC, which is incorrect. The student concluded that AB = 2BC by incorrectly analyzing the given diagram.

The error can be explained as follows: Since EB is the perpendicular bisector of AD, AB = BD is true.

Angle BEC is congruent to angle DEC, which makes BC = CD true.

If BC + CD is added, it equals BD, which is also equal to AB. Consequently, BC + CD = AB. Also, BC + CD can be written as BC + BC = 2BC.

However, this does not imply that AB = 2BC, as the student incorrectly concluded.

It is because BC and CD are two separate line segments, and just because they have the same length does not imply that they add up to double their length.

So, the student's error lies in assuming that BC + CD = 2BC means that AB = 2BC, which is incorrect.

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The result is assigned tο variable x, sο the value stοred in x is 3.

The value stοred in x can be determined by evaluating the expressiοn οn the right-hand side οf the assignment statement.

Given the statement int x; x = 3 /static_cast<int>(1.5 + 2.4), the expressiοn inside the static_cast is evaluated first:

1.5 + 2.4 = 3.9

Then, the result οf the expressiοn is cast tο an int using static_cast<int>. This perfοrms a static cast, cοnverting the flοating-pοint value tο an integer by truncating the decimal pοrtiοn:

static_cast<int>(3.9) = 3

Finally, the result is assigned tο x, sο the value stοred in x is 3.

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The given series is:[infinity] (−1)n2n 4n(2n)! n = 0The sum of this series can be found as follows:The given series can be written in summation notation as follows:∑ n=0 ∞ (−1)n2n 4n(2n)!

This can be rearranged as follows:∑ n=0 ∞ (−1)n (4n) / [(2n)!]Therefore, this series can be represented as the Maclaurin series of cos 2x, where x = 2 (because the series is represented as 4n instead of 2n).Therefore, the sum of the series is cos (2 × 2) = cos 4.The sum of the given series is cos 4. The given series can be written in summation notation as follows:∑ n=0 ∞ (−1)n2n 4n(2n)!

This can be rearranged as follows:∑ n=0 ∞ (−1)n (4n) / [(2n)!]Therefore, this series can be represented as the Maclaurin series of cos 2x, where x = 2 (because the series is represented as 4n instead of 2n).Therefore, the sum of the series is cos (2 × 2) = cos 4. The sum of the given series is cos 4.

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Answer:

Step-by-step explanation:

The vertex form of an equation of the parabola:  

                                                       f(x) = a(x - h)² + k

the vertex is (7, -4)  ⇒   h = 7,  k = -4

so:

     f(x) = a(x - 7)² + (-4)

    f(x) = a(x - 7)² - 4

The parabola goes through the point (5, 8) ⇒   x=5,  f(x)=8

8 = a(5 - 7)²  - 4

8 = a(-2)²  - 4

+4           +4

12  = 4a

÷4       ÷4

a = 3

It means the equation of the parabola in vertex form:

                               f(x) = 3(x - 7)² - 4

The total distance covered by Amira at the end of her journey as calculated from the data is 9,895 km.

Distance travelled by Amira can be found as,

She travelled 5 hours at the speed of 995km/hour

Distance = speed x time

= 995 x 5

=4,975 km

She travelled  6 hours 15 minutes at the speed of 800km/hour

=800 x 6.15

=4,920 km

Total distance covered =  4,920 + 4,975 = 9,895 km

Therefore, the distance Amira traveled is 9,895 km.

Distance is defined as the difference between the staring point and the ending point of an object. It is a scalar quantity and only has magnitude and no direction.

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Step-by-step explanation:

8m + 20 - 6m - m + 7

We combine 8m and -6m to get 2m. Now we combine 2m and -m to get m.

This gives us:

m + 20 + 7.

We combine 20 and 7 to get 27.

This gives us the answer of

m + 27

Answer:

is that 14 or 1/4?

Step-by-step explanation:

9514 1404 393

Answer:

  A. 15

  B. -3

  C. x

Step-by-step explanation:

C. Since we want different values of g(f(x)), it is convenient to find that first.

  g(f(x)) = g(2x +9) = ((2x +9) -9)/2 = 2x/2

  g(f(x)) = x

__

A. g(f(15)) = 15

__

B. g(f(-3)) = -3

Answer:

z = z

Step-by-step explanation:

first you should combine like terms on the left side of the equation

9z + 7z = 16z

now rewrite

16z-6 = 16z-6

add 6 to both sides

16z = 16z

divide both sides by 16

z = z

Answer:

Both sides are equal. z has no solution. The input is an identity. It is true for all values.

Step-by-step explanation:

9z - 6 + 7z = 16z - 6

16z - 6 = 16z - 6

Both sides are equal. z has no solution. The input is an identity. It is true for all values.

The half-life of an isotope is the time by which there is a 50% probability that decay has occurred if Cobalt-60 has a half-life of 5.27 years then mean time to decay is 7.65 years , standard deviation of the decay time is 3.82 years , the 99th percentile is  36.4 years and  the mean and standard deviation of the total time the experiment will last is 6.61 years.

(a) The mean time to decay can be found using the formula: \(mean = half-life / ln(2)\).

Therefore, for cobalt-60 with a half-life of 5.27 years, the mean time to decay is:

\(mean = 5.27 / ln(2) \approx7.65 years\)

(b) The standard deviation of the decay time can be found using the formula:

standard deviation =    \(half-life /(\ sqrt{(ln(2))}).\)

Therefore, for cobalt-60 with a half-life of 5.27 years, the standard deviation of the decay time is:

standard deviation = \(5.27 / (\sqrt{(ln(2))}) \approx 3.82 years\)

(c) The 99th percentile can be found using the cumulative distribution function (CDF) of the exponential distribution. For cobalt-60 with a half-life of 5.27 years, the CDF is:

\(CDF(t) = 1 - e^{(-t/5.27)}\)

Setting the CDF equal to 0.99 and solving for t, we get:

\(0.99 = 1 - e^{(-t/5.27)}\)

\(e^{(-t/5.27)} = 0.01\)

\(-t/5.27 = ln(0.01)\)

\(t = -5.27 * ln(0.01)\)

\(t\approx 36.4 years\)

Therefore, the 99th percentile of the decay time for cobalt-60 is approximately 36.4 years.

(d) Three cobalt-60 atoms, then the total time the experiment will last is the sum of the decay times of each atom. Since the decay times are independent and identically distributed, the mean and standard deviation of the total time can be calculated by adding the means and variances of each individual decay time.

The mean of the total time is:

\(mean(total) = mean(atom1) + mean(atom2) + mean(atom3)\)

\(mean(total) = 7.65 + 7.65 + 7.65\)

\(mean(total) = 22.95 years\)

The variance of the total time is:

\(variance(total) = variance(atom1) + variance(atom2) + variance(atom3)\)

\(variance(total) = (3.82)^2 + (3.82)^2+ (3.82)^2\)

\(variance(total) \approx43.67 years\)

The standard deviation of the total time is the square root of the variance:

standard deviation(total) \(= \sqrt{(variance(total))}\)

\(standard deviation(total) \approx6.61 years\)

Therefore, the mean and standard deviation of the total time for observing three cobalt-60 atoms until they decay are approximately 22.95 years and 6.61 years, respectively.

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a. The number of washers that can be cut from the sheet is 7500

b. 3050 additional washers could be cut from the metal left over.

a. The area of a washer is πr², where r is the radius of the washer. The radius of the washer is half the diameter, so the radius of this washer is 1 cm / 2 = 0.5 cm. The area of the washer is then π(0.5 cm)² = 0.25π cm².

The sheet of steel is 3 m by 1 m, which is 300 cm by 100 cm. The total area of the sheet is 300 cm * 100 cm

= 30000 cm²

The number of washers that can be cut from the sheet is 30000 cm² / 0.25π cm² = 30000 / (0.25 * 3.14159)

= 7500.

b) If the metal left over was remelted and cast into a sheet of the same thickness and width 1 m, how many additional washers could be cut?

The area of the metal left over is the area of the sheet minus the area of the washers that were cut. The area of the metal left over is 30000 cm² - 7500 cm² = 22500 cm²

The number of additional washers that could be cut from the metal left over is 22500 cm² / 0.25π cm² = 22500 / (0.25 * 3.14159)

= 3050.

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Answer:

\((3x-5)(3x-5)\)

Step-by-step explanation:

\((3x-5)(3x-5)=(3x-5)^2\)

The researcher should consider the following steps when creating the two groups: Random assignment, Pairing students with similar abilities, Controlling for potential confounding variables,

Collecting data and analyzing results.
Random assignment:

To minimize any potential bias, the researcher should randomly assign one student from each pair to receive extra homework problems while the other does not.
Pairing students with similar abilities:

In order to make a valid comparison, the researcher should pair students with similar algebra skills or previous performance in the subject.

This way, any observed differences in the test results are more likely to be due to the extra homework rather than differences in ability.
Controlling for potential confounding variables:

The researcher should control for any other factors that could influence students' algebra test results, such as attendance, study habits, and teacher quality.

After the two-week period, the researcher should collect the test scores of both groups and compare their performance.

This can be done using statistical methods, such as a paired t-test, to determine if there is a significant difference between the groups.

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Answer:

law of detachment

Step-by-step explanation:

The claim that a drug is effective at 1% is not sufficiently supported by the available data.

Participant 1 2 3 4 5 6

Before 185 220 190 158 227 211

After 175 215 195 155 230 207

Difference = Before - After = 10 5 -5 3  -3 4

Participant 7 8 9 10 11 12

Before 260 156 201 300 180 270

After 258 159 201 290 172 272

Difference = Before - After = 2 -3 0 10  8 -2

Participant 13 14 15 16 17 18

Before 293 183 205 151 291 166

After 290 185 200 146 287 166

Difference = Before - After = -7 -2 5 5  4 0

Hypothesis :

H0 : μd = 0

H0 : μd ≠ 0

10+5-5+3-3+4+2-3+10+8-2+3-2+5+5+4+0 = 44

The mean of d, \(d`\) = Σd / n = 44 / 18 = 2.44

The standard deviation, S.d = 4.45 (using calculator)

The test statistic, T : \(d`\) / (S.d/√n)

T = 2.44 / (4.45/√18)

T = 2.44 / 1.0488750

T = 2.326

Degree of freedom, df = n - 1 ; 18 - 1 = 17

P value = 0.0326

α = 0.01

Since P value < α ; we fail to reject H0

So the claim that a drug is effective at 1% is not sufficiently supported by the available data.

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Answer:

f(x) = −2/5x + 1

Step-by-step explanation:

when putting an equation in function notation first you must make sure the equation is in slope-intercept form and then you must rewrite the equation but instead of putting y you will replace it with f(x), or g(x), whichever one you are given directions to put it as.

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The equivalent fraction for the given fraction -11/-4 is -11/(-4) and -11/-4.

Fraction.

Fraction means a number expressed as a quotient, in which a numerator is divided by a denominator.

Given,

Here we have the fraction -11/-4.

Now, we have to find the equivalent fraction of this fraction.

In order to find the equivalent fraction, we have to identify that the given term is reduceable or not.

If it is reduceable, then we have to simplify it to get the equivalent fraction.

But here the given fraction -11/-4 is not reduceable.

So, the next thing we have to do is to find the sign equivalent value for this one.

In the given fraction both the numerator and the denominator are in negative sign.

So, the equivalent fraction, must have both positive or both negative one.

Therefore, the equivalent fraction are -11/(-4) and -11/-4.

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Answer: a

Step-by-step explanation: I did the test

Answer:

The total cost is $6.25

Step-by-step explanation:

3/4 of 1 kilo of rect

4/5 of 1 kilo of square

3/5 of 1 kilo of flower

rect = 3 per kilo

square = 3 per kilo

flower = 3 per kilo

First rectangle beads:

3x = y where x is number of kilos and y is full cost

3(3/4) = y

9/4 = y = 2 1/4 = $2.25

Second square beads:

3x = y where x is number of kilos and y is full cost

3(4/5) = y

12/5 = y = 2 2/5 = $2.20

Third flower beads:

3(x) = y where x is number of kilos and y is full cost

3(3/5) = y

9/5 = y = 1 4/5 = $1.80

Add costs together

1.80 + 2.20 + 2.25 = 6.25

The total cost is $6.25

Answer:

I believe it's an exponential parent function

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

9/36 = 0.25

25% are chocolate.

The nature of roots of quadratic equation x² = -2x + 1 is real and distinct.

The standard form of a quadratic equation is:

ax² + bx + c = 0

The discriminant is defined as:

D = b² - 4ac

Using  the value of discriminant, we can determine the nature of roots of a quadratic equation.

If:

D > 0, the quadratic equation has two distinct real roots or the roots are real and distinct.

D = 0, the quadratic equation has 1 real equal roots or the roots are unique

D < 0, the quadratic equation has complex conjugate roots or the roots are imaginary.

In this case, the quadratic equation is:

x² = -2x + 1

transform it into the standard form:

x² + 2x - 1 = 0

Calculate the discriminant:

D = 2²  - 4 (-1) = 8

Since D > 0, the roots are two distinct real roots.

Your question is incomplete, but most probably your question was:

What is the nature of roots of quadratic equation x² = -2x + 1?

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Answer:

56 rabbits

Step-by-step explanation:

Given that  t represents the time, and weeks, and P(t) is the population of the rabbits and that the population doubles every 6 weeks.

In 126 days, there are

= 126/7

= 18 weeks

It means that the rabbit population will double

= 18/6 times

= 3 times

Since there are currently 7 rabbits at the end of 6 week,

P(6) = 7 * 2

= 14

At the end of 12 weeks

P(12) = 14 * 2 = 28

At the end of 18 weeks

P(18) = 28 * 2 = 56

Hence there will be 56 rabbits at the end of 126 days

Answer:

Probability (not green) = 21 / 29

Step-by-step explanation:

Given:

Number of red marble = 10

Number of green marble = 8

Number of blue marble = 5

Number of white marble = 6

Find:

Probability (not green)

Computation:

Total marble = 10 + 8 + 5 + 6

Total marble = 29

Probability (not green) = 1 - (Probability of green marble))

Probability (not green) = 1 - (8 / 29)

Probability (not green) = 21 / 29

Answer:

I think it might be option 3

Step-by-step explanation:

sorry if I’m wrong

Answer:

8°

Step-by-step explanation:

For exterior angle QRS, angles RPQ and PQR are its remote interior angles.

m<QRS = m<RPQ + m<PQR

4x - 15 = x + 1 + x - 2

2x = 14

x = 7

m<RPQ = x + 1 = 7 + 1 = 8

Answer:

24x^5

Step-by-step explanation:

3 x 8 = 24

x multiplied by x^4 = x^5

(the exponents add to each other when multiplied)