Spanky, Alfalfa, and Buckwheat sit down to take a geography test that has 12 multiple-choice questions. Each question has three possible answers, of which only one is correct. Alfalfa, as usual, has been spending too much time daydreaming about Darla and has not properly studied for the exam. After looking it over, he discovers that he knows the answers to just five of the questions. So, he answers those questions correctly and randomly guesses on the remaining seven. Afterward, as Miss Crabtree is grading Alfalfa’s exam, she selects one question at random and finds that he answered it correctly. What is the exact probability that Alfalfa actually knew the answer to this question? Answer this question by completing the following parts:a. Carefully construct a correct tree diagram using the letters K for the event that he knows the answer to a question, N for the event that he doesn’t know the answer to a question, and C for the event that he answers a question correctly. Also, label each edge with its exact probability (as either a fraction or a whole number).b. Use the definition of conditional probability to compute the exact value of P(K|C), writing your answer as a fraction in simplified form.

Answer:

  499,153.0 cm^3

Step-by-step explanation:

The volume of a sphere is given by the formula ...

  V = (4/3)πr^3

The volume of a hemisphere will be half that, or ...

  (2/3)πr^3 = (2/3)π(62 cm)^3 = (158885 1/3)π cm^3

  ≈ 499,153.0 cm^3

_____

Comment on this result

We have used a value of pi sufficiently accurate to give the result to 7 significant figures. If you use 3.14, you will get an answer somewhat different from this.

Answer:  499,153.0 cm^3

Answer:

B:4(x)+4(2)

Step-by-step explanation:

(4 × x)+(4 × 2)

You cant do anything in the parentheses so you have to distribute 4

Answer: B:4(x)+4(2)

Step-by-step explanation:

(4 × x)+(4 × 2)

You cant do anything in the parentheses so you have to distribute 4

Step-by-step explanation:

Answer:

3.008 km or 3.0 km

Step-by-step explanation:

According to the Pythagoras theorem:

[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ \therefore \: {a}^{2} = {c}^{2} - {b}^{2} \\ \therefore \: {a}^{2} = {(9.3)}^{2} - {(8.8)}^{2} \\ \therefore \: {a}^{2} = {(9.3 + 8.8)}{(9.3 - 8.8)} \\ \therefore \: {a}^{2} = 18.1 \times 0.5 \\ \therefore \: {a}^{2} = 9.05 \\ \therefore \: {a} = \sqrt{9.05} \\ \therefore \: {a} = 3.00832179 \\ \therefore \: {a} = 3.0 \: km[/tex]

Answer:

Option "B" is the correct answer to the following question.

Step-by-step explanation:

Given:

Rate of annual interest = 0.85%

Find

Value of 0.85% in decimal

Computation:

To convert any percent number into a decimal, we have to divide that number by 100.

So,

Value of 0.85% in decimal = [tex]\frac{0.85}{100}[/tex]

Value of 0.85% in decimal = 0.0085

Note: We have to eliminate the percent symbol from the given number.

Answer:

Check the explanation

Step-by-step explanation:

1) probability for odd or 00 = (18+1)/38 = 0.5

2) expected value can be calculated as follows :

14 * win probability - 13 * lose probability

=14 * (18/38) - 13*(20/38)

= -0.21

Using it's concept, it is found that there is a 0.5 = 50% probability of the marble landing on a 00 or even slot.

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem:

The desired probability is:

[tex]p = \frac{D}{T} = \frac{19}{38} = 0.5[/tex]

0.5 = 50% probability of the marble landing on a 00 or even slot.

A similar problem is given at https://brainly.com/question/15536019

To find the acceleration of an object with a force of 7.92 N and mass of 3.6 kg, use the formula F = ma to calculate the acceleration as 2.2 m/s².

The force acting on the object can be calculated using the formula F = ma, where F is the force, m is the mass, and a is the acceleration.

Given F = 7.92 N and m = 3.6 kg, plug these values into the formula: F = 7.92 N, m = 3.6 kg.

Calculate the acceleration using the formula: a = F/m = 7.92 N / 3.6 kg = 2.2 m/s².

Therefore, the acceleration of the object with a force of 7.92 N and mass of 3.6 kg is 2.2 m/s².

Answer:25

Step-by-step explanation:

Because 5x5 equals 25

Answer:

25 Count by five with your five fingers

Step-by-step explanation:

5x5=25

Answer:

13x + 5x

Step-by-step explanation:

Answer:

Nico

Step-by-step explanation:

We have to convert both to the same units! Think about the units: we have millimeters and centimeters. There are 10 millimeters in a centimeter, so

55 mm = 5.5 cm

We just had to move the decimal point!

Now compare the two measurements in cm. 5.5 and 5.7: which is greater? Look at the tenths place: 5<7, so 5.7 is greater and Nico’s thumb is longer!

Answer:

[tex]t=\frac{282-280}{\frac{38}{\sqrt{89}}}=0.497[/tex]    

Now we can calculate the p value for the test

We are conducting a right tailed test so then the p value is given by:  

[tex]p_v =P(z>0.497)=0.310[/tex]  

Since the p value is higher than the significance level we have enough evidence to conclude that the true mean is not significantly higher than 280 so then the administrator claim is not true

Step-by-step explanation:

Data provided

[tex]\bar X=282[/tex] represent the mean for the assesment test

[tex]\sigma=38[/tex] represent the population deviation

[tex]n=89[/tex] sample size  

[tex]\mu_o =280[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to determine if the mean score for the​ state's eighth graders on this exam is more than 280, so then the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 280[/tex]  

Alternative hypothesis:[tex]\mu > 280[/tex]  

Since we know the population deviation we can use a z test for the true mean and the statistic is given by:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex]  (1)  

Replacing the info given by the problem we got:

[tex]t=\frac{282-280}{\frac{38}{\sqrt{89}}}=0.497[/tex]    

Now we can calculate the p value for the test

We are conducting a right tailed test so then the p value is given by:  

[tex]p_v =P(z>0.497)=0.310[/tex]  

Since the p value is higher than the significance level we have enough evidence to conclude that the true mean is not significantly higher than 280 so then the administrator claim is not true

To determine if there is enough evidence to support the administrator's claim, we need to perform a hypothesis test. By comparing the z-score to the critical value at α=0.05, we can reject the null hypothesis and conclude that there is enough evidence to support the administrator's claim.

To determine if there is enough evidence to support the administrator's claim, we need to perform a hypothesis test. The null hypothesis (H0) is that the mean score for the state's eighth graders is <=280. The alternative hypothesis (Ha) is that the mean score is >280.

To conduct the test, we can calculate the z-score using the formula z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the hypothesized population mean (280), σ is the population standard deviation (38), and n is the sample size (8989). Plug in the given values, we get z = (282 - 280) / (38 / sqrt(8989)) = 3.055.

Next, we compare the z-score to the critical value at α=0.05. For a one-tailed test, the critical value is 1.645. Since 3.055 > 1.645, we reject the null hypothesis and conclude that there is enough evidence to support the administrator's claim that the mean score for the state's eighth graders on this exam is more than 280.

The student's GPA for that term would be 3.16.

Given that;

A student had these grades:

3.9 in a 5 credit Math course

2.4 in a 2 credit Music course

2.7 in a 4 credit Chemistry course

3.1 in a 6 credit Journalism course

Now for the student's GPA for the term, calculate the weighted average of the grades.

First, calculate the total grade points earned by multiplying each grade by the corresponding number of credits:

Grade points for Math course = 3.9 × 5

                                                  = 19.5

Grade points for Music course = 2.4 × 2

                                                   = 4.8

Grade points for Chemistry course = 2.7 × 4

                                                          = 10.8

Grade points for Journalism course = 3.1 × 6

                                                            = 18.6

Hence, the total grade points earned:

Total grade points earned = 19.5 + 4.8 + 10.8 + 18.6

                                            = 53.7

Finally, divide the total grade points earned by the total number of credits:

Total credits = 5 + 2 + 4 + 6

                     = 17

Use the formula;

GPA = Total grade points earned / Total credits

GPA = 53.7 / 17

GPA = 3.16

Therefore, the student's GPA for that term is 3.16.

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To compute a student's GPA, we need to calculate the weighted average of their grades. Multiply each grade by the corresponding number of credits, sum the products, and divide by the total number of credits.

To compute the student's GPA for the term, we need to calculate the weighted average of their grades. The weighted average is calculated by multiplying each grade by the corresponding number of credits and then summing up these products. Finally, we divide the sum by the total number of credits.

For the student in question, let's calculate their GPA:

The student's GPA for that term is 3.16 when rounded to two decimal places.

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Answer:

The repair person did 5 hours of work.

Step-by-step explanation:

155 = 25x + 30

125 = 25x

5 = x

Answer:

5 hours

Step-by-step explanation:

155 less 30 initial = 125 divided by 25 an hour = 5

Answer:

The answer is 8.3 repeating. If you round it the answer is 8.

Answer:

8.3... grams in each cupcake

Step-by-step explanation:

you basically divide 100 by 12

Answer:

The point estimate is 0.391 and the margin of error is 0.042.

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the absolute value of the difference between the point estimate and any of the two bounds.

In this problem, we have that:

Lower bound: 0.349

Upper bound: 0.433

Point estimate:

(0.349+0.433)/2 = 0.391

Margin of error:

|0.391 - 0.433| = |0.391 - 0.349| = 0.042

The point estimate is 0.391 and the margin of error is 0.042.

Final answer:

The midpoint of the confidence interval (0.349, 0.433) provides the point estimate, which is 0.391. The margin of error is calculated by subtracting the point estimate from the upper bound of the interval, resulting in 0.042.

Explanation:

The confidence interval (0.349, 0.433) can be used to find the point estimate and margin of error for the proportion of customers interested in a breakfast menu at a fast food restaurant. To find the point estimate, we take the midpoint of the confidence interval, which is the average of the lower and upper bounds.

Point Estimate = (Lower Bound + Upper Bound) / 2
Point Estimate = (0.349 + 0.433) / 2
Point Estimate = 0.391

To find the margin of error, we subtract the point estimate from either the upper or lower bound of the confidence interval.

Margin of Error = Upper Bound - Point Estimate
Margin of Error = 0.433 - 0.391
Margin of Error = 0.042

Therefore, the point estimate is 0.391 and the margin of error is 0.042 for the proportion of customers interested in the breakfast menu.

Answer:

[tex]\bf a) - 0.0663\\b) - 0.31\\c) - 0.021\\d) - 1 or 100%[/tex]

Step-by-step explanation:

[tex]Let\;p = 69\;\% =0.69[/tex]

[tex]So, p(x)=q^{x-1}p[/tex]     [tex]-(i)[/tex]

a) - The probability which Jeff requires at exactly three advances that is,

Then, put the value of [tex]x=3[/tex] in eq - i

[tex]p(x=3)=(0.31)^{3-1}(0.69)[/tex]

[tex]p(x=3)=0.0663[/tex]

b) - The probability which Jeff requires at least three advances that is,

[tex]p(x\geq1)=1-p[/tex]

Put the value of [tex]p[/tex] in the eq

[tex]p(x\geq 2)=1-0.69=0.31[/tex]

c) - Considering that he has only made four advances, the probability would be that he will require at least three more advances that is.

[tex]p(\frac{x=7}{x\geq 4}) = \frac{p(x=7\;\cap\;x\geq 4)}{p(x\geq 4)}[/tex]

[tex]p(\frac{x=7}{x\geq 4}) = \frac{p(x=7)}{1-p(x\leq 3)}[/tex]

Then, put the value in the eq - i

          [tex]=\frac{(0.31)^{7-1}(0.69)}{1-\sum_{x=1}^{3}(0.31)^{x-1}(0.69)}[/tex]

          [tex]=\frac{0.0006}{1-0.9702}[/tex]   [tex]=0.0201[/tex]

d) - Display that all possibilities actually added up to 100% that is.

[tex]p(x\geq1)=p(x=1)+p(x=2)+p(x=3)...........[/tex]

             [tex]=q^{1-1}p+q^{2-1}p+q^{3-1}p[/tex]

by solving [tex]x=1[/tex] then, we get

            [tex]=\frac{p}{1-q} =\frac{0.69}{1-031}[/tex]

So, we get 1 or 100%.

Answer:

A) 0.0066309 ; B) 0.0961 ; D) Proven

Step-by-step explanation:

Geometric Distribution : X ~ [tex]q^(x-1) . p[/tex]

p = 0.69 ; q = 1- p = 1 - 0.69 = 0.31

A) P (x = 3) = [tex](0.31)^(3-1) (0.69) = 0.31^2 (0.69) = 0.0961(0.69)= 0.0066309[/tex]

B) P (x > 3) = 1 - [ P(x =1) + P(x = 2) ]

[tex]1 - [(0.31)^0 (0.69) + (0.31)^1(0.69)] = 1 - (0.69 + 0.2139) = 1 - 0.9039 = 0.0961[/tex]

D) P (x > 1) = P (x =1) + P (x = 2) + P (x = 3) ...............

= p + pq + pq^2 + pq^3 ........ [Geometric series with a = p , r = q]

Sum of infinite geometric series = a / (1- r)

p / (1-q) = 0.69 / (1-0.31) = 0.69 / 0.69 = 1 {Hence Proven}

Answer:

Maureen's null hypothesis is, H₀: p₁ ≥ p₂.

Step-by-step explanation:

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies wants test whether her goal of shipping 100% orders within 24 hours is achieved or not.

After reviewing the order filling operations at her warehouses she determines that neither the East coast nor the West coast warehouse has achieved the goal. But the East Coast warehouse has consistently out-performed the West Coast warehouse.

To check whether this determination is correct or not Maureen's staff randomly selected 200 orders from the West Coast warehouse (population 1) and 400 orders from the East Coast warehouse (population 2).

Of the 200 orders from the West Coast warehouse, 190 were shipped within 24 hours. And of the 400 orders from the East Coast warehouse, 372  were shipped within 24 hours.

The hypothesis can be defined as follows:

H₀: The proportion of orders that were shipped within 24 hours is not more for East Coast warehouse than for West Coast warehouse, i.e. p₁ ≥ p₂.

Hₐ: The proportion of orders that were shipped within 24 hours is more for East Coast warehouse than for West Coast warehouse, i.e. p₁ < p₂.

Thus, Maureen's null hypothesis is, H₀: p₁ ≥ p₂.

Maureen McIlvoy's null hypothesis would likely be that there is no significant difference in the shipment times of the East Coast and West Coast warehouses. Despite the initial data suggesting better performance at the West Coast, more statistical analysis such as a z-test or t-test would be required to confirm if there is a significant difference.

In this context, Maureen McIlvoy, who is the owner and CEO of a mail order business for wind surfing equipment, is evaluating the efficiency of order fulfilment at her warehouses. Given her goal is to ship 100% of her orders within 24 hours, she is interested in comparing the performance of the East Coast warehouse to the West Coast warehouse.

When conducting such an analysis, a null hypothesis serves as the baseline or default expectation. In this case, Maureen's null hypothesis could possibly be that there's no difference in the performance between the two warehouses in terms of orders shipped within 24 hours, despite the past performance.

With the given data of 190 out of 200 orders shipped on time at the West Coast, and 372 out of 400 orders shipped on time at the East Coast, we can further analyze the percentages of timely shipping - 95% and 93% respectively. Though the West coast performed better in the examined sample, this is not sufficient to reject the null hypothesis that the performances are identical without further statistical testing such as a z-test or t-test.

On the other hand, her alternative hypothesis could state that there is a significant difference in the efficiency of the two warehouses in achieving the 24-hour shipping target.

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Answer:

51 + 29+ 80

Step-by-step explanation:

she got this by adding 51 + 29

Answer:

2.326

Step-by-step explanation:

They are only asking which z-score should you use. To determine find the confidence interval which is 98% or .98.

Subtract this number by 1 and divide by 2.

1-.98=.02/2=.01

Find the correlating z-score for z.01 on the z-score chart which is 2.326

The z-value for a 98% confidence level in statistics, used in constructing confidence intervals, is approximately 2.33 standard deviations away from the mean.

The question falls under the area of statistics, specifically, confidence intervals. In order to find the z-value for a 98% confidence level, we turn to the z-table or use a z-score calculator. The z-value for a 98% confidence level is approximately 2.33. This value represents the number of standard deviations away from the mean that your confidence interval is.

The idea here is that for us to be 98% confident that our interval contains the true population mean or proportion, our interval must extend 2.33 standard deviations on either side of our sample mean or proportion. Thus, in the context of your survey of office managers working overtime, this z-value would be used to calculate your confidence interval for the proportion of all office managers who work overtime.

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Answer:62

Step-by-step explanation:

Answer:

a. Ignacio recibió $9000. Mariela recibió $2400 y Laura, $3600. b. Ignacio y Mariela recibieron [tex] \\ \frac{19}{25}[/tex] del total del premio (diecinueve veinticincoavos) ($11400).

Step-by-step explanation:

Tenemos un total de $15000, que fue el premio del concurso, el cual fue repartido entre tres personas: Ignacio, Mariela y Laura.

Lo que tenemos que hacer es multiplicar cada fracción por la totalidad del premio ($15000), para determinar cuánto recibió cada uno.

Recordemos que para resolver estos casos, la regla general es que sólo tenemos que multiplicar el numerador de la fracción por dicho total ($15000) y luego dividir el producto resultante entre el denominador de la fracción.

De esta manera, procedemos a resolver cada caso.

Lo recibido por Ignacio

Si Ignacio recibió las 3/5 partes del premio: ¿cuánto recibió Ignacio?

Como ya sabemos, la respuesta es multiplicar la fracción por el total del premio. Es decir:

[tex] \\ \frac{3}{5}*15000[/tex]

[tex] \\ \frac{3*15000}{5}[/tex]

[tex] \\ \frac{45000}{5}[/tex]

[tex] \\ 9000[/tex]

Que podemos también resolver de la siguiente manera, considerando que es más fácil dividir 15000 entre 5, por ser 5 un divisor de 15000:

[tex] \\ \frac{15000}{5}*3[/tex]

[tex] \\ 3000*3[/tex]

[tex] \\ 9000[/tex]

Es decir, Ignacio recibió $9000.

Lo recibido por Mariela

Para el caso de Mariela, aplicamos el mismo procedimiento.

Como Mariela recibió las 4/25 (cuatro veinticincoavos) del premio, tenemos entonces:

[tex] \\ \frac{4}{25}*15000[/tex]

[tex] \\ \frac{4*15000}{25}[/tex]

[tex] \\ \frac{60000}{25}[/tex]

[tex] \\ 2400[/tex]

También lo hubiéramos resuelto, sin tener que hacer una multiplicación y división extensas, si consideramos que 15000 y 25 son múltiplos de 5. Por lo tanto:

[tex] \\ \frac{4}{25}*15000[/tex]

[tex] \\ \frac{15000}{25}*4[/tex]

Es decir, dividir 15000 entre 25, y luego multiplicamos por cuatro. Así:

[tex] \\ 600*4[/tex]

[tex] \\ 2400[/tex]

Obteniendo el mismo resultado

De esta manera, Mariela recibió $2400.

Lo recibido por Laura

Laura recibió el resto de lo dejado por Ignacio y Mariela. Podemos resolver ésto de diversas formas. Una de ellas es restar del total del premio la suma de lo recibido por Ignacio y Mariela.

[tex] \\ 15000 - (9000 + 2400)[/tex]

[tex] \\ 15000 - 11400[/tex]

[tex] \\ 3600[/tex]

De esta manera, Laura recibió $3600.

¿Qué parte del premio recibieron Ignacio y Mariela?

En otras palabras, qué parte del premio recibieron Ignacio y Mariela en conjunto, en forma de fracción.

Una manera de resolver esta pregunta es sumando las fracciones que recibió cada uno, es decir, [tex] \\ \frac{3}{5} + \frac{4}{25}[/tex].

Hay varias maneras de sumar ambas fracciones. Una de ellas (la manera más general) es multiplicar el denominador de cada fracción por el numerador de la otra fracción, sumar cada producto obtenido y luego dividirlo entre el producto de los denominadores de cada fracción.

[tex] \\ \frac{3}{5} + \frac{4}{25}[/tex]

[tex] \\ \frac{3*25 + 5*4}{5*25}[/tex]

[tex] \\ \frac{75 + 20}{125}[/tex]

[tex] \\ \frac{95}{125}[/tex]

Podemos observar que 95 y 125 son múltiplos de 5, así que podemos simplificar el numerador y el denominador de la fracción dividiendo a ambos entre 5:

[tex] \\ \frac{95}{125}[/tex]

[tex] \\ \frac{\frac{95}{5}}{\frac{125}{5}}[/tex]

[tex] \\ \frac{19}{25}[/tex]

El número 19 es un número primo y no podemos simplificar más la fracción.

De esta manera, Ignacio y Mariela recibieron [tex] \\ \frac{19}{25}[/tex] del total del premio (diecinueve veinticincoavos), lo cual podemos comprobar si multiplicamos esta fracción por el total del premio y lo comparamos con la suma de los resultados para Ignacio y Mariela:

[tex] \\ \frac{19}{25}*15000[/tex]

[tex] \\ \frac{15000}{25}*19[/tex]

[tex] \\ 600*19[/tex]

[tex] \\ 11400[/tex]

Lo que es igual a la suma de lo recibido por Ignacio ($9000) y Mariela ($2400), es decir $11400.

Laura, por lo tanto recibió [tex] \\ \frac{6}{25}[/tex]

Por cuanto

[tex] \\ \frac{6}{25} + \frac{19}{25} = \frac{6+19}{25} = \frac{25}{25} = 1[/tex]

Es decir, la suma de las fracciones de lo recibido por Ignacio y Mariela más lo que recibió Laura debe sumar la totalidad, es decir, la unidad (1).

Answer:

  (2/9)cis(30°)

Step-by-step explanation:

We can express the two numbers in magnitude∠angle form, then find their ratio.

  |z1| = 3√((-1)² +(√3)²) = 3√4 = 6

  ∠z1 = arctan((3√3)/(-3)) = -arctan(√3) = 120°

  z2 = 27∠90°

So, the ratio is ...

  z1/z2 = (6∠120°)/(27∠90°) = (6/27)∠(120°-90°)

  z1/z2 = (2/9)∠30°

Answer:

lol good luck with that but you add them

Step-by-step explanation:

Answer:

15 small bottles

30 large bottles

Step-by-step explanation:

Let the number of small bottle sold=s

Let the number of large bottle sold=l

She sold all 45 of the hand sanitizer bottles, therefore:

The small bottle sells for $5.00

The large sells for  $12.00

She collected a total of $435

We solve the two equations simultaneously to obtain s and l.

From the first equation, s=45-l

Substitute s=45-l into 5s+12l=435

5(45-l)+12l=435

225-5l+12l=435

7l=435-225

7l=210

Divide both sides by 7

l=30

Recall: s=45-l

Therefore, s=45-30=15

Allanah sold 15 small bottles and 30 large bottles of hand sanitizer.

Answer:

figure to out

Step-by-step explanation:

Answer:

156x-24

Step-by-step explanation:

12*(13x-2)=

12*13x+12*(-2)=

156x-24

Hope this helps!

Answer:

-7x+14y-35

Step-by-step explanation:

Answer:

y=-1/2x+5/2

Step-by-step explanation:

slope intercept form is y=mx+b

add 7x to both sides to get y alone on the left side of the equal sign

divide by 14 to get y alone

gets your answer y=-1/2x+5/2

Answer:

The total area of the figure is 52 in²

Step-by-step explanation:

This figure requires you to find the area of the square and the triangle separately, and then subtract the area of the triangle from the area of the square.

Find the area of the square

l=8in

A=l²

A=8²

A=64 in²

The area of the square is 64 in²

Find the area of the triangle

b=8in

h=3in

A=(bh)/2

A=(8*3)/2

A=24/2

A=12 in²

The area of the triangle is 64 in²

Now we need to subtract the areas

64-12=52 in²

The total area of the figure is 52 in²

Answer:

Sometimes when grouping symbols are use to enclose other grouping symbols, we use braces instead of parentheses or brackets, to make an expression easier to read.

Step-by-step explanation:

To group numbers or variables, brackets and braces are mostly used. Generally, they are used after parentheses. Parentheses are to be used first, then brackets, and then braces: {[( )]}.

However, instead of brackets or braces, sometimes, the use of larger parentheses will be observed.

Answer:

Square brackets will always be used, to enclose or group several arithmetic operations that involve several simultaneous operations, as described in the example.

The bracket generally groups or implies that the most particular or small operations must be performed until finally breaking it down and thus solving the entire general operation.

Step-by-step explanation:

1. When there are no parentheses or square brackets, we do the multiplications and divisions first if there are any. If there are several positive and negative numbers we group them together and then add them together.

2. When there are parentheses, we first make the calculations for the parentheses if there are any, and then to remove the parentheses we apply the rule of signs, sign that is in front of the parenthesis for each sign that is inside.

3. When there are parentheses and square brackets, we make the parentheses first, we remove them applying the rule of signs. Then we make the brackets and remove them applying the rule of signs. Then we make the products and divisions and finally the sums.

The production of black potatoes is 6000 kg, the production of sweet potatoes is 7200 kg, and the total production of both types of potatoes is 13200 kg.

To find the total production of black potatoes and sweet potatoes, we need to multiply the weekly production by the number of weeks (12 weeks).

For black potatoes:

Weekly production = 500 kg

Total production of black potatoes = Weekly production * Number of weeks

= 500 kg/week * 12 weeks

= 6000 kg

For sweet potatoes:

Weekly production = 600 kg

Total production of sweet potatoes = Weekly production * Number of weeks

= 600 kg/week * 12 weeks

= 7200 kg

Now, to find the total production:

Total production = Total production of black potatoes + Total production of sweet potatoes

= 6000 kg + 7200 kg

= 13200 kg

So, the production of black potatoes is 6000 kg, the production of sweet potatoes is 7200 kg, and the total production of both types of potatoes is 13200 kg.

Complete question:

Carlos has a weekly production of 500kg of black potatoes and 600kg of sweet potatoes after 12 weeks. How much will the production of potatoes be? And of sweet potatoes? How much will the total production be?