Miguel paid $125 for a stamp collection. He made $25 profit on the stamp collection when he sold it. What was his profit as a percentage of the cost price?.

The greatest common divisor of 6, 14, and 21 is 1, and it can be written as 6(0) 14(0) 21(1).

To find the greatest common divisor (GCD) of 6, 14, and 21 and write it in the form 6r 14s 21t, we can use the Euclidean algorithm.

Step 1: Find the GCD of 6 and 14.
- Divide 14 by 6: 14 ÷ 6 = 2 remainder 2
- Replace 14 with 6 and 6 with 2: Now we have 6 and 2.
- Divide 6 by 2: 6 ÷ 2 = 3 remainder 0
- Since the remainder is 0, the GCD of 6 and 14 is 2.

Step 2: Find the GCD of the result from step 1 (2) and 21.
- Divide 21 by 2: 21 ÷ 2 = 10 remainder 1
- Replace 21 with 2 and 2 with 1: Now we have 2 and 1.
- Divide 2 by 1: 2 ÷ 1 = 2 remainder 0
- Since the remainder is 0, the GCD of 2 and 21 is 1.

Therefore, the GCD of 6, 14, and 21 is 1. In the given form 6r 14s 21t, r would be 0, s would be 0, and t would be 1.

So, the GCD of 6, 14, and 21 is 1, and it can be written as 6(0) 14(0) 21(1).

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Answer:

x=17

y=9

Step-by-step explanation:

set 3x-4=5x-38

-2x=-34

x=17

plug x back into equa.= 47 degrees

180-90(right angle)-47=43

7y-20=43

7y=63

y=9

Answer:

Yes it has infinity of solutions.

Step-by-step explanation:

If you plug in certain numbers it will make the statements true.

Answer:

Infinitely many solutions.

Step-by-step explanation:

Let's solve your system by substitution.

2x+3y=−6;4x+6y=−12

Step: Solve2x+3y=−6for x:

2x+3y=−6

2x+3y+−3y=−6+−3y(Add -3y to both sides)

2x=−3y−6

2x/2 = −3y−6/2

(Divide both sides by 2)

x= −3/2y−3

Step: Substitute −3/2y−3 for x in 4x+6y=−12:

4x+6y=−12 4(−3/2y−3)+6y=−12

−12=−12(Simplify both sides of the equation)

−12+12=−12+12(Add 12 to both sides)

0=0

Answer:

Infinitely many solutions.

Answer:

2(\(x^{2}\)+8x+17)

Step-by-step explanation:

Factor out 2 of the equation.

Answer:

For real numbers: no solution

For complex numbers: \( x = -4 \pm 4i \)

Step-by-step explanation:

2x^2 + 16x + 34 = 0

Divide both sides by 2.

x^2 + 8x + 17 = 0

There are no two numbers whose product is 17 and whose sum is 8, so this polynomial is not factorable.

We can use the quadratic formula.

\( x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

We have a = 1; b = 8; c = 17

\( x = \dfrac{-8 \pm \sqrt{8^2 - 4(1)(17)}}{2(1)} \)

\( x = \dfrac{-8 \pm \sqrt{64 - 68}}{2} \)

\( x = \dfrac{-8 \pm \sqrt{-64}}{2} \)

If you have not learned imaginary or complex numbers, stop here. Since the discriminant is negative, there is no real solution.

If you have learned complex numbers, then we continue.

\( x = \dfrac{-8 \pm 8i}{2} \)

\( x = -4 \pm 4i \)

Answer:

  200 cm²

Step-by-step explanation:

The scale factor for areas of similar figures is the square of the scale factor relating their linear dimensions. For volumes of similar figures, the scale factor is the cube of the linear dimension scale factor. Together, these relations mean the area scale factor is the 2/3 power of the area scale factor.

__

The larger surface area is ...

  (50 cm²) × 8^(2/3) = (50 cm²) ×4 = 200 cm²

_____

Additional comment

The linear dimension scale factor is the cube root, or 1/3 power, of the volume scale factor. The area scale factor is the square of that or the 1/3 power times 2, the 2/3 power.

  sf = ∛(v2/v1) = (v2/v1)^(1/3)

  a2/a1 = sf^2 = ((v2/v1)^(1/3))^2 = (v2/v1)^(2/3)

In this case, we have two partitions: the left partition (27, 56, 46, 57) and the right partition (99, 77, 90).

Given the numbers (27, 56, 46, 57, 99, 77, 90) and pivot=77, the low partition after the partitioning algorithm is completed is (27, 56, 46, 57) and the high partition is (99, 77, 90).

First, to understand the partitioning algorithm in Quicksort, let us define Quicksort:

Quicksort is a sorting algorithm that operates by partitioning an array or list and recursively sorting the sub-arrays or sub-lists produced by partitioning.

Quicksort is one of the fastest sorting algorithms. It is used by many operating systems, libraries, and programming languages.

There are three important steps in the partitioning algorithm of Quicksort:

Choose the pivot element.

Partition the array based on the pivot element.

Recursively sort the two partitions after the partitioning is done.

A low partition and a high partition are formed when partitioning.

The low partition contains all elements lower than the pivot, while the high partition contains all elements higher than the pivot.

For our given numbers (27, 56, 46, 57, 99, 77, 90) and pivot=77, the low partition after the partitioning algorithm is completed is (27, 56, 46, 57), and the high partition is (99, 77, 90).

The partitioning algorithm works as follows:

Choose the pivot element, which is 77.

Partition the array using the pivot element, 77.

Elements less than 77 go to the left partition and elements greater than 77 go to the right partition.27, 56, 46, 57, 90, 99, 77 are the numbers.

Pivot is 77.46 is less than 77. It goes to the left.57 is less than 77. It goes to the left.27 is less than 77. It goes to the left.

90 is greater than 77. It goes to the right.99 is greater than 77. It goes to the right.77 is not considered here because it is the pivot.

Recursively sort the two partitions produced after partitioning.

In this case, we have two partitions: the left partition (27, 56, 46, 57) and the right partition (99, 77, 90).

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-Q->P is proved from the contrapositive of 1.-P->Q.

What is Contrapostive ?

In logic, the contrapositive of a conditional statement of the form "if A, then B" is a statement of the form "if not B, then not A".

Here is a possible formal proof of the contrapositive of 1.-P->Q, which is -Q->P:

-P->Q Premise

Assume -Q Assume for sub proof

Assume -P Assume for subproof

From 2 and 1, we have P Modus tollens (MT)

From 4, we have P and -P Conjunction (CONJ)

From 3 and 5, we have # Contradiction (CONTR)

From 3-6, we have -Q-># Conditional proof (CP)

From 2 and 7, we have P Proof by contradiction (PC)

From 2-8, we have -Q->P Conditional proof (CP)

Therefore, -Q->P is proved from the contrapositive of 1.-P->Q.

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The Chi-square test of variance is appropriate to use.

The correct model from the list to support the hypothesis that the standard deviation of semester units taken by SJSU students is over 4 semester units by sampling the GPAs of 40 SJSU students is the "One sample, Chi-square test of variance. "The Chi-square test of variance is used to determine whether the variance of a population is equal to a specific value. In the Chi-square test of variance, the null hypothesis is that the variance of the population is equal to the specific value or the variance is not greater than the specific value. The Chi-square test of variance is used when the sample is random, the sample is normally distributed, and the variable is measured on a continuous scale. In the given problem, the researcher wants to support the hypothesis that the standard deviation of semester units taken by SJSU students is over 4 semester units.

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Data can be divided on the basis of qualitative nature into two types as follows:

Thus, it is clear that nominal data can not be ranked or ordered but ordinal data are the type of qualitative data that are categorised and then ranked or ordered.

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Answer:

x = 3y + 1

Step-by-step explanation:

You need to find the relationship between x and y before finding the y-intercept.

0-(-1) = 1

1-0 = 1

2-1 = 1

1-(-2) = 3

4-1 = 3

7-4 = 3

As x increases by 1, y increases by 3.

At x = 0, y is already 1. Thus:

x = 3y + 1

Answer:

Slope-intercept For: \(y = 3x + 1\)

Standard Form: \(9x - 3y = -3\)

Point-slope Form: \(y - 4 = 3(x - 1)\)

Step-by-step explanation:

Slope-intercept Form: \(y = mx + b\)

Standard Form: \(Ax + By = C\)

\(\frac{y}{-3x} = \frac{3x}{-3x} + 1\\-3(-3x + y = 1)\\9x -3y = -3\)

Point-slope Form: \(y_2 - y_1 = m (x - x_1)\)

\((1, 4)\\y - 4 = 3 (x - 1)\)

Answer:

n = 7

Explanation:

\(\rightarrow \sf 3 + 5(2 + 7n) = 258\)

apply distributive method: a(b + c) = ab + ac

\(\rightarrow \sf 3 + 10 + 35n = 258\)

simply add the numbers

\(\rightarrow \sf 13 + 35n = 258\)

subtract both sides by 13

\(\rightarrow \sf 13-13 + 35n = 258-13\)

simplify the following

\(\rightarrow \sf 35n = 245\)

divide both sides by 35

\(\rightarrow \sf n = 7\)

Answer:

n = 7

Step-by-step explanation:

1) Subtract 3 from both sides.

5(2 + 7n) = 258 - 3

2) Simplify 258 - 3 to 255.

5(2 + 7n) = 255

3) Divide both sides by 5.

2 + 7n = 255/5

4) Simplify 255/5 to 51.

2 + 7n = 51

5) Subtract 2 from both sides.

7n = 51 - 2

6) Simplify 51 - 2 to 49.

7n = 49

7) Divide both sides by 7.

n = 49/7

8) Simplify 49/7 yo 7.

n = 7

Answer:

Use a proportion::

time/dist = time/distance

t/1.5 = 1/30

t = 1.5/30

t = 15/300

t = 1/20 = 5/100 = 0.05

So A-0.05 is the final answer

Step-by-step explanation:

ik this was 3 yrs ago

If the wheel's radius is 0.08 m, the wheel's angular velocity is 62.5 rad/s. So, correct option is B.

To determine the wheel's angular velocity, we can use the formula that relates linear speed and angular velocity. The formula is:

v = ω * r

where v is the linear speed, ω (omega) is the angular velocity, and r is the radius of the wheel.

Given:

Linear speed (v) = 5.00 m/s

Radius (r) = 0.08 m

Rearranging the formula, we can solve for ω:

ω = v / r

Substituting the given values:

ω = 5.00 m/s / 0.08 m

= 62.5 rad/s

Therefore, the correct answer is b. 62.5 rad/s.

Therefore, the correct answer is b.

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1. The random replacement process ensures that the composition of Windows laptops in the room evolves over time.

The room initially contains 10 Windows laptops, and each month one laptop is randomly selected and replaced. This random replacement process introduces an element of variability and ensures that the composition of the laptops in the room changes over time.

As laptops are replaced, newer models with potentially upgraded features, improved performance, or better specifications may enter the room. This process mimics the natural progression of technology, where older devices are phased out and replaced with newer ones to keep up with advancements in the industry.

The random selection of laptops for replacement also adds an element of chance to the composition of the room. Each month, any of the 10 laptops has an equal probability of being selected, which means that some laptops may be replaced more frequently than others. This can lead to a diverse mix of laptop models within the room, with different generations or configurations represented.

Overall, the monthly random replacement process ensures that the room remains dynamic, with a constantly evolving set of Windows laptops. It allows for the possibility of regularly refreshing the technology and adapting to newer devices as they become available on the market.

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Answer:

mean = 3

Step-by-step explanation:

The mean of a data set is the average of all the elements in the set. This can be calculated using the formula:

\(\text{mean} = \dfrac{\text{sum of elements}}{\text{number of elements}}\)

From the bar graph, we can determine the total number of elements in the data set by counting the number of Xs.

We can see that there are 11 elements in the data set.

We can also determine the number of Xs for each number of times that a person played mini-golf last summer:

0, 1, 2, (5 × 3), 4, 5, 6

Now, we can plug these values into the above formula to calculate the mean.

\(\text{mean} = \dfrac{0+1+2+5(3) + 4 + 5 + 6}{11}\)

\(\text{mean} = \dfrac{33}{11}\)

\(\boxed{\text{mean} = 3}\)

Answer:

Step-by-step explanation:

2 subtraction symbols equals a plus

so the answer is 9

Answer:

The correct answer is A. the data is skewed to the right, so you have the correct answer chosen already...

Step-by-step explanation:

btw thanks for making this worth more points have a wonderful day!

Answer:

The data is skewed to right already

Step-by-step explanation:

Answer: No

Step-by-step explanation: It is NOT possible because then the division would be incomplete, and even if you did, then you could AT LEAST divide it once more, before ending the problem. I hope this helped!

yes but it would be incomplete

Answer:

The answer is $22.74

Step-by-step explanation:

I think true.

Step-by-step explanation:

You can connect the two long ones with the shorter one.

yes they will because the two longest ones will be at the top and the shortest one can be the base

does that help???

The equation that best represents the set-up is (d) 9^2 + x^2 = 16^2

The complete question is in the image

The value of x is calculated using the following Pythagoras theorem

16^2 = x^2 + 9^2

Rewrite as:

9^2 + x^2 = 16^2

Hence, the equation that best represents the set-up is (d) 9^2 + x^2 = 16^2

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a. The 99% confidence interval for the average body temperature of healthy people is (98.024, 98.476) degrees.  b )   we can conclude that there is evidence to suggest that the average body temperature of healthy people is different from 98.6 degrees.

a) To calculate the 99% confidence interval for the average body temperature of healthy people, we can use the formula:

Confidence interval = mean ± (critical value) * (standard deviation / √n)

Where:

Mean is the sample mean (98.25 degrees)

Standard deviation is the sample standard deviation (0.73 degrees)

n is the sample size (130)

The critical value for a 99% confidence level is 2.61 (obtained from the t-distribution table for a large sample size)

Plugging in the values, we get:

Confidence interval = 98.25 ± (2.61 * (0.73 / √130))

Confidence interval = 98.25 ± 0.226

Confidence interval = (98.024, 98.476)

b) The confidence interval obtained in part (a) does not contain the value 98.6 degrees. Since the accepted average temperature cited by physicians and others is not within the confidence interval, we can conclude that there is evidence to suggest that the average body temperature of healthy people is different from 98.6 degrees. The sample data suggests that the average body temperature is lower than the commonly accepted value.

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Since candy costs $6 per pound, it implies that p pounds of candy costs:

So $6p will be spent on candy.

Since less than $44 will be spent on candy. it follows the required inequality is:

Solve for p in the inequality:

Note that the number of pounds, p should be a positive number hence, the possible number of pounds that can be bought will be non-negative:

(a) Circumference of Earth in kilometers: 40,075.017 km

(b) Surface area of Earth in square kilometers: 510.1 million km^2

(c) Volume of Earth in cubic kilometers: 1.08 trillion km^3

To calculate these values, we use mathematical formulas that relate to the sphere shape of the Earth.

For (a), we use the formula for the circumference of a circle, C = 2 * pi * r, where r is the radius of the Earth in meters (6.37 x 10^6 m). We then convert this result to kilometers by dividing by 1000.

For (b), we use the formula for the surface area of a sphere, A = 4 * pi * r^2, where r is the radius of the Earth. Again, we convert this result to square kilometers.

For (c), we use the formula for the volume of a sphere, V = (4/3) * pi * r^3, where r is the radius of the Earth. We then convert this result to cubic kilometers by dividing by 10^9.

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