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Question:
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HAVE A BRAINLY DAY!!!! :D

a) To calculate the probability that the tomato plant is alive when Alexa returns from the holiday, we need to consider two scenarios: when Phil remembers to water the plant and when Phil forgets to water the plant.

Let A be the event that the tomato plant is alive and R be the event that Phil remembers to water the plant.

We can use the law of total probability to calculate the probability that the plant is alive:

P(A) = P(A|R) * P(R) + P(A|R') * P(R')

Given:

P(A|R) = 1 - 0.9 = 0.1 (probability of the plant being alive when Phil remembers to water)

P(A|R') = 1 - 0.15 = 0.85 (probability of the plant being alive when Phil forgets to water)

P(R) = 0.8 (probability that Phil remembers to water)

P(R') = 1 - P(R) = 0.2 (probability that Phil forgets to water)

Calculating the probability:

P(A) = (0.1 * 0.8) + (0.85 * 0.2)

= 0.08 + 0.17

= 0.25

Therefore, the probability that the tomato plant is alive when Alexa returns from the holiday is 0.25 or 25%.

b) To calculate the probability that Phil forgot to water the plant given that the plant has died, we can use Bayes' theorem.

Let F be the event that the plant has died.

We want to find P(R'|F), the probability that Phil forgot to water the plant given that the plant has died.

Using Bayes' theorem:

P(R'|F) = (P(F|R') * P(R')) / P(F)

To calculate P(F|R'), we need to consider the probability of the plant dying when Phil forgets to water:

P(F|R') = 0.15

Given:

P(R') = 0.2 (probability that Phil forgets to water)

P(F) = P(F|R) * P(R) + P(F|R') * P(R')

= 0.9 * 0.2 + 1 * 0.8

= 0.18 + 0.8

= 0.98 (probability that the plant dies)

Calculating the probability:

P(R'|F) = (P(F|R') * P(R')) / P(F)

= (0.15 * 0.2) / 0.98

≈ 0.0306

Therefore, the probability that Phil forgot to water the plant given that the plant has died is approximately 0.0306 or 3.06%.

a) The probability that the tomato plant is alive when Alexa returns from the holiday is 0.25 or 25%.

b) The probability that Phil forgot to water the plant given that the plant has died is approximately 0.0306 or 3.06%.

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The difference in their commute distances is 1654 meters.

To compare Mikko's commute distance of 8 km to Jason's commute distance of 6 miles, we need to convert one of the distances to the same unit as the other.

Given that 1 mile is equal to 1609 meters, we can convert Jason's commute distance to kilometers:

6 miles * 1609 meters/mile = 9654 meters

Now we can calculate the difference in their commute distances:

Difference = Mikko's distance - Jason's distance

         = 8 km - 9654 meters

To perform the subtraction, we need to convert Mikko's distance to meters:

8 km * 1000 meters/km = 8000 meters

Now we can calculate the difference:

Difference = 8000 meters - 9654 meters

         = -1654 meters

The negative sign indicates that Jason's commute distance is greater than Mikko's commute distance.

Therefore, their commute distances differ by 1654 metres.

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Answer:

\((a)\ y = 4\ or\ y = -\frac{1}{2}\)

\((b)\ x = 2 \ or\ x = -\frac{1}{4}\)

Step-by-step explanation:

Solving (a)

\(2y^2 - 7y - 4 = 0\)

Expand

\(2y^2 +y - 8y - 4 = 0\)

Expand

\(y(2y + 1) -4(2y + 1) = 0\)

Factor out 2y + 1

\((y -4)(2y + 1) = 0\)

Split

\(y - 4 =0\ or\ 2y + 1 = 0\)

Solve:

\(y = 4\ or\ y = -\frac{1}{2}\)

Solving (b):

\(2(2x)^2 - 7(2x) - 4 = 0\)

Compare the above with the equation in (a)

\(2y^2 - 7y - 4 = 0\)

We have:

\(2x = y\)

So:

\(2x = 4 \ or\ 2x = -\frac{1}{2}\)

Solve for x in both cases

\(x = 2 \ or\ x = -\frac{1}{4}\)

Answer:

c. 2n-6

Step-by-step explanation:

6 less than 2xSteve so 2n-6

The simplified version of (sec a - cosec a) / (sec a + cosec a)  is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Given:

(sec a - cosec a) / (sec a + cosec a)

Multiply the numerator and denominator by (sec a - cosec a)

(sec a - cosec a) / (sec a + cosec a)  × (sec a - cosec a)

(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)

As we know,

\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)

sec² a cosec² a - 2sec a cosec a /  (sec²a - cosec²a)

sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)

cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)

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Answer:

152.6 hours

Step-by-step explanation:

Distance = Speed × Time

Time = Distance/Speed

Santa's sleigh covered a total distance of 5797 kilometres averaging a speed of 38 km/h in snow storm conditions

Hence: Time Santa spent in snow storms is calculated as:

5797km ÷ 38 km/h

= 152.55263158 hours

Approximately = 152.6 hours

Answer:

1: 41

2: 85

3: 95

4: 85

5: 36

6: 49

7: 106

Given data:

The cloth bought by Jakke is C 1 1/2 yards.

The cloth used in the project is P=2/3 yards.

The expression for the cloth left is,

Substitute the given values in the above expression.

Thus, the amount of cloth left is 5/6 yards.

First you will get 4dz

Answer:

B.6

Step-by-step explanation:

Lisa was 48 inches tall when she was younger. She grew 2 1/2 inches per year. Lisa

is now 63 inches tall. How many years did Lisa grow for?

a. 5

b. 6

c. 7

d. 8

2 1/2=5/2

48+(5/2*5)=48+12.5=60.5

48+(5/2*6)=48+15=63

therefore it is answer b

We have proven that the expression (36⁵ - 6⁹)(38⁹ - 38⁸) is divisible by both 30 and 37.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

To prove that the expression (36⁵- 6⁹)(38⁹ - 38⁸) is divisible by 30 and 37, we need to show that it can be written as the product of 30 and 37 with some integer coefficient.

First, let's look at the factorization of 30: 30 = 2 x 3 x 5.

We can see that 6 is a factor of 36, so we can rewrite 36^5 as (6²)⁵. Similarly, we can write 6⁹ as (6²)⁵ x 6³.

Now, let's factor out (6²)⁵ from the first factor in the expression:

(36⁵ - 6⁹) = (6²)⁵ (6⁵ - 6³)

We can factor out 38⁸ from the second factor in the expression:

(38⁹ - 38⁸) = 38⁸ (38 - 1)

So the original expression can be written as:

(36⁵ - 6⁹)(38⁹ - 38⁸) = (6²)⁵ (6⁵ - 6³) 38⁸ (38 - 1)

Now, let's look at the factorization of 37. We can see that 38 - 1 = 37, so we can rewrite the expression as:

(6²)⁵(6⁵ - 6³) 38⁸ (38 - 1) = (2⁵ x 3⁵) (6³) 38⁸ (37)

We can see that the expression contains a factor of 2⁵, a factor of 3⁵, and a factor of 37, so it is divisible by both 30 and 37.

Therefore, we have proven that the expression (36⁵ - 6⁹)(38⁹ - 38⁸) is divisible by both 30 and 37.

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120 ways can the letters in the word spoon be arranged. So, The correct option is d) 120.

The word "spoon" has five letters, and we need to find the number of ways to arrange these letters. This can be done using the permutation formula, which is n!/(n-r)!, where n is the total number of items and r is the number of items being selected. In this case, we have five items and we need to arrange all of them, so r = 5. Therefore, the number of arrangements is 5!/(5-5)! = 5!/0! = 5x4x3x2x1 = 120.

To understand this concept better, consider that the first letter of "spoon" can be any of the five letters. Once we choose a letter for the first position, there are four letters left to choose from for the second position, three for the third position, two for the fourth position, and only one letter left for the fifth position. Multiplying these numbers gives us the total number of arrangements. Therefore, there are 120 ways to arrange the letters in the word "spoon". So the correct answer is d) 120.

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the angle BAD is 75 degrees and  we used the properties of angles in a circle and the tangent-secant theorem to find angle BAD .

To work out angle BAD, we need to use the properties of angles in a circle and the tangent-secant theorem. Here are the steps to solve the problem:

Identify the relevant angles First, we need to draw a diagram to visualize the problem. We have a circle with center O, points A, B, C, and D on the circumference, and tangent ED. Angle ODB is given as 25 degrees. We need to find angle BAD. We can label the angles in the diagram as follows:

Angle AOB = 2x (angle at the center is twice the angle at the circumference)

Angle BCD = x (angles in the same segment are equal)

Angle OBD = 90 degrees (tangent and radius are perpendicular)

Angle OED = 90 degrees (tangent and radius are perpendicular)

Angle ABD = y (we need to find this angle)

Angle BAD = z (we need to find this angle)

Use the sum of angles in a triangle

We notice that triangle ABD is a right triangle, with right angle at B. Therefore, angles ABD and BAD are complementary. That is, ABD + BAD = 90 degrees. Use the tangent-secant theorem

We can use the tangent-secant theorem to find the value of angle ABD. The tangent-secant theorem states that if a tangent and a secant intersect at a point on a circle, then the angle between the tangent and the secant is equal to the half the difference of the intercepted arcs. In our diagram, ED is a tangent, and BD is a secant. Therefore, angle ODB = 25 degrees is half the difference of the intercepted arcs AD and AB. That is, angle ABD = (2x - x)/2 = x/2.

Solve for x

To find x, we can use the fact that the angles in a triangle add up to 180 degrees. Therefore, x + 2x + 90 = 180 (sum of angles in triangle AOB). Solving for x, we get x = 30 degrees.

Find angle ABD and angle BAD

Using the result from step 3, we get ABD = x/2 = 15 degrees. Using the result from step 2, we get BAD = 90 - ABD = 75 degrees.

Therefore, the angle BAD is 75 degrees. In summary, we used the properties of angles in a circle and the tangent-secant theorem to find angle BAD. We noticed that ABD and BAD are complementary, and we used the tangent-secant theorem to find ABD. Then, we solved for x using the fact that the angles in a triangle add up to 180 degrees. Finally, we used the results from steps 2 and 3 to find BAD.

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Ordered pair (0, 6) and  (2, 7)  satisfy both inequalities in the system and are solutions to the system.

To identify the graph that represents the given system of inequalities y > x + 5 and y ≥ 2x + 3, we need to graph the individual inequalities and find the region where they overlap.

When we plot the graph of inequality separately:

    2. y ≥ 2x + 3:

The overlapping shaded region represents the solution to the system of inequalities.

To find two ordered pairs that are solutions to the system, we can choose any points within the overlapping region. Let's select two points:

Ordered pair 1: (0, 6)

Ordered pair 2: (2, 7)

These two points satisfy both inequalities in the system and are solutions to the system.

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The correct question is given below -

Identify the graph that represents the given system of inequalities. Also identify two ordered pairs that are solutions to the system.

y > x + 5

y ≥ 2x + 3

Answer:

y = x² - 3x - 4

Step-by-step explanation:

Given that the x- intercepts are x = - 1 and x = 4, then the corresponding factors are

(x + 1) and (x - 4) and the quadratic is the product of the factors, that is

y = (x + 1)(x - 4) ← expand using FOIL

y = x² - 3x - 4

Answer:

\(10x^2-x+3\) miles.

Step-by-step explanation:

It is given that,

Total length of park trail = \(10x^2+4x+2\) miles

Total length traveled by hiker = \(5x-1\) miles

We need to find the length of trail hiker need to travel to get to the end of the trail.

Required length \(=10x^2+4x+2-(5x-1)\)

               \(=10x^2+4x+2-5x+1\)

               \(=10x^2+(4x-5x)+(2+1)\)

               \(=10x^2-x+3\)

Therefore, hiker need to travel \(10x^2-x+3\) miles to get to the end of the trail.

Answer: a. 3+13n

b. About 3 newspapers

Step-by-step explanation:

a. T=total thickness of newspapers on a skid in inches

T=3+13n

b. 3'=3 ft

1 ft=12 inches

3 ft=3*12 inches

3 ft=36 inches

36=3+13n

13n=33

n=2.54 ==> About 3 newspapers

The 95% confidence interval estimate for the percentage of all adults who want to lose weight is between 48% and 54%

The given information states that a Gallup Poll found 51% of the sample participants responded "yes" when asked if they would like to lose weight. The margin of sampling error is ±3% at a 95% confidence level.

To calculate the 95% confidence interval estimate for the percentage of all adults who want to lose weight, you simply add and subtract the margin of error from the sample percentage.

Lower limit: 51% - 3% = 48%
Upper limit: 51% + 3% = 54%

Therefore, the 95% confidence interval estimate for the percentage of all adults who want to lose weight is between 48% and 54%. This means that if this poll were repeated multiple times under the same conditions, in 95 out of 100 instances, the true percentage of all adults who want to lose weight would fall within this range.

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lol

Step-by-step explanation:

To determine the number of yards Ben will walk in one hour, we need to convert his speed from feet per second to yards per hour.

First, let's convert Ben's speed from feet per second to feet per hour: Speed in feet per hour = Speed in feet per second * 60 seconds * 60 minutes. Speed in feet per hour = 6 ft/s * 60 s * 60 min = 21,600 ft/hour. Next, we need to convert the speed from feet per hour to yards per hour. Since there are 3 feet in a yard: Speed in yards per hour = Speed in feet per hour / 3. Speed in yards per hour = 21,600 ft/hour / 3 = 7,200 yards/hour.

Therefore, Ben will walk 7,200 yards in one hour if he maintains a steady pace of 6 ft per second.

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Answer:

Step-by-step explanation: add 4 to cancel out, dive both sides by 3, y=1.3 repeating

the worker will have earned $231,584.10 from the period of beginning 1962 through the end 1980.

To solve this problem, we can use the formula for the sum of a geometric series:

S = a(1 - rⁿ)/(1 - r)

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, the first term is $8,400 and the common ratio is 1.05 (since the worker's salary increases by 5% each year). We need to find the sum of the series from 1962 to 1980, which is 19 years. So, the total amount that the worker will have earned from the beginning of 1962 through the end of 1980 is:

S = 8,400(1 - 1.05¹⁹)/(1 - 1.05)

S ≈ $231,584.10

Therefore, the worker will have earned approximately $231,584.10 during this period.

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The ratio of 2 1/3 feet to 4 1/2 feet written as a fraction in simplest form is 7/9.

To convert the given ratio into a fraction, we need to divide the first length by the second length. So, 2 1/3 feet divided by 4 1/2 feet can be written as:

(7/3) feet ÷ (9/2) feet
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, we can rewrite the above expression

To simplify the given ratio 2 1/3 feet to 4 1/2 feet as a fraction, we need to divide the first length by the second length. Let's first convert the mixed numbers into improper fractions:
2 1/3 feet = (2x3 + 1)/3 feet = 7/3 feet
4 1/2 feet = (4x2 + 1)/2 feet = 9/2 feet
Now, we can write the ratio as:
(7/3) feet : (9/2) feet
To convert this ratio into a fraction, we can divide the first length by the second length:
(7/3) feet ÷ (9/2) feet
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(7/3) feet x (2/9) feet
We can simplify this expression by canceling out the common factors of 7 and 9:
(7/3) x (2/9) = (7x2)/(3x9) = 14/27
Therefore, the ratio of 2 1/3 feet to 4 1/2 feet written as a fraction in simplest form is 14/27.

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Answer:

277

Step-by-step explanation:

PEMDAS

E: 3^3 (3x3x3) = 27

M: 27x10 = 270

A: 270+7 = 277

Answer:

(10 hours 45 minutes) + (50 minutes) + (30 minutes) =

12 hours 5 minutes

Step-by-step explanation:

the ski club has 20 members. Answer: B. 20 members.

Let's use a proportion to solve for the total number of club members:

11/0.55 = x/1

Simplifying:

x = 11/0.55 = 20

what is number?

A number is a mathematical concept used to represent a quantity or a value. It is an abstract idea that can be represented using symbols or numerals, such as 1, 2, 3, 4, etc. Numbers can be positive, negative, or zero and can be used in various mathematical operations, such as addition, subtraction, multiplication, and division. They are also used to measure, count, and label things in the real world, such as people, objects, time, distance, and more.

what is proportion?

A proportion is an equation that states that two ratios are equivalent. In other words, two fractions are said to be proportional if they have the same ratio of their numerators to their denominators. For example, 2/4 and 6/12 are proportional because they reduce to the same ratio of 1/2. Proportions are commonly used in mathematics, science, and everyday life to solve problems involving ratios and scaling.

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To determine if the new fertilizer is effective, the farmer can use hypothesis testing, specifically a one-sample t-test. This test compares the mean yield of the corn crop using the new fertilizer to the historical mean yield of the corn crop using the old fertilizer.

1. Formulate hypotheses: Set up a null hypothesis (H0) stating that the fertilizer has no effect on yield, and an alternative hypothesis (H1) stating that the fertilizer increases yield.

2. Collect data: The farmer should divide his field into two sections - one with the new fertilizer and one without. He should then measure the corn yield from each section.

3. Determine the test statistic: Calculate the mean yield for each section and find the difference between them.

4. Set a significance level: Choose an acceptable level of Type I error (commonly 5%, represented as α = 0.05).

5. Calculate p-value: Using the appropriate statistical test (e.g., t-test or ANOVA), determine the probability of observing the calculated test statistic or a more extreme value, assuming the null hypothesis is true.

6. Compare p-value to α: If the p-value is less than α, reject the null hypothesis in favor of the alternative hypothesis, indicating that the fertilizer was effective in increasing corn crop yield.

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