Discrete math
Euclidean Algorithm (a) Find the Greatest Common Divisor of 27,720 and 58,212 (b) Find integers r and s so that 27720-5 + 58212.5 = GCD(27720, 58212) =

Answer:

141.6 cm cubed

Step-by-step explanation:

Answer:

23446

76532

12839

09192

29292

Answer:

f(x)=\(\frac{7}{5}\)x-\(\frac{6}{5}\)

Step-by-step explanation:

First put 7x-5y=6 into slope intercept form

y=\(\frac{7}{5}\)x-\(\frac{6}{5}\)

Then put it into f(x) form

Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test).

If the researcher does not reject a null hypothesis that is actually wrong in the population, this is known as a type II error (false-negative). Notwithstanding the fact that type I and type II mistakes cannot be completely prevented, the researcher can lessen their risk by increasing the sample size.

from the question:

Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test). This would result in a lost chance to provide these kids with more swim safety training, perhaps placing them in danger of drowning or other swimming-related mishaps.

Part B: We are unable to reject the null hypothesis since the p-value (0.8438) exceeds the significance level (0.05). This indicates that there is insufficient information to draw the conclusion that less than 40% of children under the age of five can pass a swim test. But, since the test only looked at the alternative hypothesis that the fraction is less than 40%, we cannot draw the conclusion that it is exactly 40%.

Part C: One possible defect in the study is the use of a volunteer sample. The children who volunteered to take the swimming test may not be representative of the entire population of children under 5 in Bloomburg City. For example, parents who are more concerned about their children's swimming abilities may be more likely to volunteer their children for the test, leading to a biased sample. To obtain a more representative sample, a random sample of children under 5 could be selected from the population and asked to take the swimming test.

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Answer:

3.115

Step-by-step explanation:

pi = 405 ÷ 130

= 3.1153846154

upper bound 3.116

lower bound 3.115

Edit : Incorrect Answer

Answer:

Lower Bound = 2.996

Upper bound = 3.244

Step-by-step explanation:

The volume of the solid is  17124 cubic units. To find the volume of the solid, we need to integrate the area of each cross-section perpendicular to the base and parallel to the diameter.

Since these cross-sections are squares. We can find their area by squaring the side length.

Let's call the side length of each square "x". We know that the diameter of the semicircle is 32 (twice the radius of 16), so the side length of each square is also 32.

Now we need to express the volume of the solid as an integral. We can do this by summing the areas of all the infinitesimal squares as we slice the solid perpendicular to the base.

The infinitesimal thickness of each slice is dx. The width of each slice is also dx, since the squares are perpendicular to the base. The height of each slice is the length of the chord of the semicircle that corresponds to the x-coordinate of the slice.

We can use the Pythagorean theorem to find this height. The chord has length 2(sqrt(16^2 - x^2)), so the height is sqrt(16^2 - x^2).

Therefore, the volume of the solid is given by the integral:

V = ∫(0 to 16) of [x^2 * (2sqrt(16^2 - x^2))] dx

Evaluating this integral, we get:

V = (2/3)(16^3)(pi) - (2/3)(16^3)

So the volume of the solid is approximately 17124 cubic units.

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Answer:it’s wrong if so then 5 would’ve been in c’s place

Step-by-step explanation:

Answer:

To the lump sum needed to be invested to receive $10,000 in 10 years at 6.6% interest compounded daily, we can use the present value formula:

PV = FV / (1 + r/n)^(n*t)

where PV is the present value or the initial investment, FV is the future value or the amount we want to end up with, r is the annual interest rate in decimal form, n is the number of times the interest is compounded per year, and t is the time in years.

Plugging in the numbers, we get:

PV = 10000 / (1 + 0.066/365)^(365*10)

= 4874.49

Therefore, the lump sum needed to be invested is about $4,874.49.

Answer: The person above me is correct. Here is a picture if you still dont get it..

Step-by-step explanation:

Attached is a two-way frequency table, to help Hugo organize the results.

A two-way frequency table is a table used to organize and display the relationship between two categorical variables. It is constructed by counting the number of occurrences of each combination of categories and presenting the results in a table format.

1. Identify the categorical variables and list their possible categories.

cat, no cat, dog, no dog

2. Count the number of observations for each combination of categories.

cat = 17

no dog = 20

no cat no dog = 7

3. Organize the counts in a table with the categories of one variable as rows and the categories of the other variable as columns.

          | dog | no dog | total

cat      |        |              |   17  |

no cat |        |     7       |        |

total    |        |     20    |   41  |

4. Fill in the table with the counts of the observed combinations of categories.

cat but no dog = 20 - 7 = 13

both cat and dog = 17 -13 = 4

total no cat = 41 - 17 = 24

total dog = 41 - 20 = 21

dog but no cat = 24 - 7 = 17

          | dog | no dog | total

cat      |   4   |      13     |   17  |

no cat |   17  |     7       |   24  |

total    |   21  |     20    |   41  |

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A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

A probability can be classified as experimental or theoretical, as follows:

Over a small number of trials, these two probabilities can be different, but over a large number of trials, their values get closer.

The dice has eight sides, hence the theoretical probability of rolling a six is given as follows:

1/8 = 0.125 = 12.5%.

(each of the eight sides is equally as likely, and a six is one of these sides).

The experimental probabilities are obtained considering the trials, hence:

(given in the problem).

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In order to know if a triangle is a right triangle on a coordinate plane, you can find the lengths of all three sides of the triangle using the distance formula and apply the Pythagorean theorem.

Find the lengths of the three sides of the triangle using the distance formula.

Once you have the lengths of the sides, check if any of the three sides satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In other words, if a² + b² = c², where c is the longest side, then the triangle is a right triangle.

If one of the sides satisfies the Pythagorean theorem, then the triangle is a right triangle.

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There are a total of 10 possible combinations when selecting two students for the university-wide student committee from the five academic departments.

To determine the number of possible combinations when selecting two students for the university-wide student committee from the five academic departments, we can use the combination formula.

The number of combinations, denoted as C(n, r), represents the number of ways to select r items from a set of n items without regard to the order of selection.

In this case, we have five academic departments, and we want to select two students. Therefore, we can calculate C(5, 2) as follows:

C(5, 2) = 5! / (2! * (5 - 2)!)

= 5! / (2! * 3!)

= (5 * 4 * 3!) / (2! * 3!)

= (5 * 4) / 2

= 10

Therefore, there are 10 possible combinations when selecting two students for the university-wide student committee from the five academic departments.

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Option c. 2

Among the given targets, two targets are correctly described:

Regarding chemical pesticide use, the target is to reduce it by 50% by 2050. This aligns with the vision presented in the Green Food System Strategy.

In terms of chemical fertilizers, the target is to reduce the use of chemical fertilizers produced in Japan from fossil fuels by 30% by 2050. This target is also consistent with the strategy's vision.

The remaining two targets are not correctly described:

The target of expanding the organic market and increasing the ratio of organic farming to arable land to 30% (1 million hectares) by 2050 is not mentioned in the given options.

The target of reducing household food loss by half from the FY2000 level by 2030 is also not mentioned in the given options.

Therefore, the correct answer is option c. 2, as two of the targets are accurately described in the provided options.

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The number is 15.

   2x/3-7=3

   3(2x/3–7)=3×3

   2x-21+21=9+21

   2x/2=30/2

   x=15

Proof

   15×2=30

   30/3=10

   10–7=3

Answer:

A

the tiles add up to x^2 + 4x + 3

(x + 1) (x + 3)

factor it out, and you get x^2 + 4x + 3.

Answer:

First, we write the augmented matrix.

⎡

⎢

⎣

1

−

1

1

2

3

−

1

3

−

2

−

9

|

8

−

2

9

⎤

⎥

⎦

[1−1123−13−2−9 | 8−29]

Next, we perform row operations to obtain row-echelon form.

−

2

R

1

+

R

2

=

R

2

→

⎡

⎢

⎣

1

−

1

1

0

5

−

3

3

−

2

−

9

|

8

−

18

9

⎤

⎥

⎦

−

3

R

1

+

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

5

−

3

0

1

−

12

|

8

−

18

−

15

⎤

⎥

⎦

−2R1+R2=R2→[1−1105−33−2−9|8−189]−3R1+R3=R3→[1−1105−301−12|8−18−15]

The easiest way to obtain a 1 in row 2 of column 1 is to interchange

\displaystyle {R}_{2}

R 2

and

\displaystyle {R}_{3}

R 3

.

Interchange

R

2

and

R

3

→

⎡

⎢

⎣

1

−

1

1

8

0

1

−

12

−

15

0

5

−

3

−

18

⎤

⎥

⎦

InterchangeR2andR3→[1−11801−12−1505−3−18]

Then

−

5

R

2

+

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

1

−

12

0

0

57

|

8

−

15

57

⎤

⎥

⎦

−

1

57

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

1

−

12

0

0

1

|

8

−

15

1

⎤

⎥

⎦

−5R2+R3=R3→[1−1101−120057|8−1557]−157R3=R3→[1−1101−12001|8−151]

The last matrix represents the equivalent system.

x

−

y

+

z

=

8

y

−

12

z

=

−

15

z

=

1

x−y+z=8 y−12z=−15 z=1

Using back-substitution, we obtain the solution as

\displaystyle \left(4,-3,1\right)

(4,−3,1)

Answer:

16 to 9

Step-by-step explanation:

Represent donut with frosting with D1 and donut without frosting with D2.

So, we have:

\(D_1 = 32\)

\(D_2 = 18\)

Required

Find the ratio of D1 to D2

This is calculated as:

\(D_1 : D_2\)

Substitute values for D1 and D2

\(D_1 : D_2 = 32 : 18\)

Divide by 2

\(D_1 : D_2 = 32/2 : 18/2\)

\(D_1 : D_2 = 16 : 9\)

The ratio of donuts with frosting to donuts without is 16 to 9

Answer:

16 to 19

Step-by-step explanation:

The data distribution is skewed to the right. This is because the bars are clustered towards the left side of the histogram and taper off towards the right side.

The histogram of distances students live from school provided in the question shows that the majority of students in Tuan's homeroom live within a short distance of the school, with only a few students living farther away. The distribution is skewed to the right because the bars are clustered towards the left side of the histogram and taper off towards the right side. This indicates that there are fewer students who live farther away from school. A skewed distribution means that the data is not evenly distributed and tends to cluster towards one end. In this case, the distribution is skewed to the right because there are fewer students living farther away from school.

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Complete question is in the image attached below

Answer:

B. skewed.

Step-by-step explanation:

and then the next part is

1

hope this helps :)

Options b, d, and e are the true statements about the substitution method.

b. It is useful to solve the integral ∫2x sin x^2 dx.

d. It utilizes the formula ∫ f(u(x))u'(x) dx = ∫ f(u) du.

e. It is based on the chain rule for derivatives.

The true statements about the substitution method are:

b. It is useful to solve the integral ∫2x sin x^2 dx.

The substitution method is commonly used to simplify integrals and make them easier to evaluate. It can be applied to various types of integrals, including the given example.

d. It utilizes the formula ∫ f(u(x))u'(x) dx = ∫ f(u) du.

The substitution method involves making a substitution in the integral by introducing a new variable. This formula represents the fundamental principle of substitution, where the derivative of the substituted function appears in the integral.

e. It is based on the chain rule for derivatives.

The substitution method is based on the chain rule of derivatives. By making an appropriate substitution, the integral can be transformed into a new form that corresponds to a derivative of a simpler function.

Therefore, options b, d, and e are the true statements about the substitution method.

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According to the question The coefficient of variation for the given data set is 40%.

The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation (SD) by the mean (μ) and expressing the result as a percentage.

The formula for the coefficient of variation is:

\(\[ CV = \left(\frac{SD}{\mu}\right) \times 100 \]\)

In this case, the standard deviation is 4 units and the mean is 10 units. Plugging these values into the formula, we get:

\(\[ CV = \left(\frac{4}{10}\right) \times 100 \]\)

\(\[ CV = 0.4 \times 100 \]\)

\(\[ CV = 40 \]\)

Therefore, the coefficient of variation for the given data set is 40%.

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Answer:

30 × 24 = 720 inches

since there are 12 inches in a foot

720 ÷ 12 = 60

60 feet converted to yards is 20 yards

50 - 20 = 30

they should have 30 yards of string left over

SOLUTION

For 10 days, Mario measured the amount of food that his cat Toby ate each day.

The amount he recorded are shown in the table at the right

Graph the results on the line plot

Amount Toby ate each day for 10 days

Amount of food Days

1/ 4 c 2

3/ 8 c 1

1/ 2 c 3

5/ 8 c 3

3/ 4 c 1

TOTAL AMOUNT OF FOOD TOTAL NUMBER OF DAYS

1/ 4 c + 3/ 8 c + 1/2 c + 5/ 8 c + 3/ 4 c = 5/ 2 c = 2 1/2 c 10

What is the total amount of food Toby ate over the 10 days?

Toby ate 2 1/ 2 c over 10 days.

Answer:

63

Step-by-step explanation:

Ty worked 4 hours ad earned $28. This means that he earned $7 per hour. So, 7 times 9 is equal to 63. Which means that Ty will earns $63 in 9 hours.

Answer:

11/20

Step-by-step explanation:

First, you have to find a common denominator between the two fractions, 4 and 5 can both equal 20 so we change the denominators to 20, 4/5 =16/20 since whatever we multiply on the bottom we multiply on the top, now for 1/4 we change it to 5/20. Now for the question, we subtract since that's what it's asking, so 16/20 - 5/20, 16 - 5 equals 11 and the denominators stay the same so the answer would be 11/20

Answer:

-108 is the correct answer

Step-by-step explanation:

=-9(10+2)

=-90+(-18)

=-90-18

= -108

Answer:

It's D or -108 (✿◠‿◠)

Answer:

Domain: \(0\leq x\leq 6\)

Range: \(\{0, 12, 24, 36, 48, 60, 72\}\)

Step-by-step explanation:

Let \(y\) or \(f(x)\) be equal to the amount of plant food that remains after each day.

\(x\) be the number of days that have passed.

Total amount of plant food used is 72 mm.

Number of days the experiment goes on is 6 days.

Plant food used each day is \(\dfrac{72}{6}=12\ \text{mm}\).

So, the function will be

\(y=f(x)=72-12x\)

at

\(x=0,y=72\)

\(x=1,y=72-12\times 1=60\)

\(x=2,y=72-12\times 2=48\)

\(x=3,72-12\times 3=36\)

\(x=4,72-12\times 4=24\)

\(x=5,72-12\times 5=12\)

\(x=6,72-12\times 6=0\)

Value of \(x\) is the domain which is \(0\leq x\leq 6\).

Value of \(y=f(x)\) is the range which is \(\{0, 12, 24, 36, 48, 60, 72\}\).

range(2,11,2) because range is a tool for defining a range between two numbers and adding a step value.

Range is the difference between the highest and lowest values ​​in a range of numbers. To calculate the range, subtract the smallest number from the largest number in the set.

The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.

range(2,11,2) because range is used to create a range between number and add step value

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Answer:

The solutions will contain an infinite amount of negative numbers.

Step-by-step explanation:

Given x < 0

What does this mean?

First, carefully examine the sign in the inequality. It says less (which is different from less and equal)

Then explain it's meaning.

x < 0 just means that the solutions will contain an infinite amount of negative numbers but NOT zero. This defines the correct answer.

Step-by-step explanation: