A gardener planted some seedlings at equal distances apart along a straight road. The 3rd seedling and the 5th seedling were 9/10 apart. The 2nd seedling and the last seedling were 6 3/4 apart. How many seedlings did he plant?

The distance covered by light in 2 weeks is \(3.6288*10^{14}\) m.

It is given that:-

Speed of light = \(3*10^8 m/s\)

We have to find the distance travelled by the light in 2 weeks.

We know that,

1 week = 7 days

Hence,

2 weeks = 14 days

Also,

1 day = 24 hours

1 hour = 60 minutes

1 min = 60 seconds

Hence, we can write,

1 day = 60*60*24 seconds = 86,400 seconds

14 days = 86400*14 = 12,09,600 seconds

We know that,

Speed = distance/time

Hence,

distance = speed * time

Hence, distance travelled by light in 2 weeks = \(3*10^8*1209600 = 3628800 * 10^8 = 3.6288*10^{14} m\)

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Answer:

x=10/3

Step-by-step explanation:

integral solutions to the equation \($y_1+y_2+y_3+y_4+y_5=24$\).We can use the method of generating functions to find the number of solutions.

The problem requires us to find the number of solutions of the given equation \($x_1+x_2+x_3+x_4+x_5=39$\), such that each \($x_i\geq3$\).

This is a typical problem of finding the number of non-negative The generating function for each\($y_i$ is$$(1+x+x^2+x^3+....)$$\)

The generating function for \($y_1+y_2+y_3+y_4+y_5$\) is the product of the individual generating functions.

\($$(1+x+x^2+x^3+....)^5=\frac{1}{(1-x)^5}$$\)

We can use the formula for the coefficient of\($x^{24}$\) in the above generating function to get the number of non-negative integral solutions to the equation.

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Maria spends $22 on lottery tickets every week and $133 every month on food yearly

This means that in a year

there are 52 weeks and she spends 22 x 52 = $1,144 on Lottery tickets

and there are 12 months in a year, so she spends 133 x 12 = $1,596 on food

The money spent to buy lottery tickets in relation to the money spent on food yearly in percentage is

The solution to the system of equations is x = 7 and y = 3/2.

What is Simultaneous Equation?

Two or more algebraic equations that share variables are said to be simultaneous equations.

1) Rearrange both equations so that one variable is isolated on one side of the equation:

x/2 + y/3 = 4 --> x/2 = 4 - y/3 --> x = 8 - (2/3)y

y/4 - x/3 = 1/6 --> y/4 = 1/6 + x/3 --> y = 2/3 + (4/3)x

2) Substitute the expression for one variable into the other equation:

y = 2/3 + (4/3)x

x/2 + (2/3 + (4/3)x)/3 = 4

3) Simplify and solve for the remaining variable:

x/2 + 2/9 + (4/9)x = 4

5x/9 + 1/9 = 4

5x/9 = 35/9

x = 7

4) Substitute the value of x into one of the original equations and solve for the other variable:

x/2 + y/3 = 4

7/2 + y/3 = 4

y/3 = 1/2

y = 3/2

Therefore, the solution to the system of equations is x = 7 and y = 3/2.

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Answer:

A = 64 m²

Step-by-step explanation:

Step 1: What is the question asking

Step 2: What is known

Step 3: Conversion

Step 4: Answer the question/solve for the area

(a) To find the probability of selecting a blue ball, we need to consider the probabilities from both urns.

The probability of selecting the first urn is 1/2 since there are two urns and one is chosen at random. The probability of selecting a blue ball from the first urn is 6/20 (6 blue balls out of a total of 20 balls).

The probability of selecting the second urn is also 1/2. The probability of selecting a blue ball from the second urn is 12/19 (12 blue balls out of a total of 19 balls).

To find the overall probability of selecting a blue ball, we can use the law of total probability:

P(blue) = P(First Urn) * P(blue | First Urn) + P(Second Urn) * P(blue | Second Urn)

P(blue) = (1/2) * (6/20) + (1/2) * (12/19)

Simplifying the expression, we get:

P(blue) = 0.25 + 0.3158

P(blue) = 0.5658

To convert to a percentage, we multiply by 100:

P(blue) = 56.58%

(b) Given that the chosen ball is blue, we want to find the probability that it came from the first urn.

Using Bayes' theorem, we can calculate:

P(First Urn | blue) = (P(blue | First Urn) * P(First Urn)) / P(blue)

P(First Urn | blue) = (6/20 * 1/2) / 0.5658

P(First Urn | blue) = 0.15 / 0.5658

P(First Urn | blue) ≈ 0.2654

To convert to a percentage, we multiply by 100:

P(First Urn | blue) ≈ 26.54%

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The true average amount of warpage in all such pieces of laminate lies between 0.0609 and 0.0653 inches with 99% confidence.

a) To construct a 99% confidence interval for the average amount of warpage in all such pieces of laminate, we can use the formula:

CI = X ± Z × (s / √n)

where X is the sample mean warpage, Z is the Z-value from the table below, s is the sample standard deviation and n is the number of observations.

The Z-value for a 99% confidence interval is 2.576. (refer the image)

Plugging in the values we get:

0.0631 ± 2.576 × (0.0072 / √45)

= [0.0609, 0.0653]

b) To construct a 90% confidence interval for the average amount of warpage in all such pieces of laminate, we can use the same formula as above but with a different Z-value.

The Z-value for a 90% confidence interval is 1.645.

Plugging in the values we get:

0.0631 ± 1.645 × (0.0072 / √45)

= [0.0618, 0.0644].

c) Because we need to be more positive that our interval contains the genuine population mean as our confidence level rises, the interval for a 99% confidence level is greater than that for a 90% confidence level. This suggests that in order to account for all possible values of the population mean, we must widen our interval.

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The percent needed on the final test is 99.6% in order to earn 93% on all 4 tests combined.

Let x be the percentage of the final test in order to earn 93% on all 4 tests combined.

To solve the problem, we will have to use weighted averages.

It is a method used to determine the mean of a set of data, where each observation has a different weight or frequency.

Let's first find the weighted average of the three tests you have already taken.

Given that you earned scores of 88%, 94%, and 90% on the first three tests, and each test was worth 150 points.

88% of 150 points = 132 points

94% of 150 points = 141 points

90% of 150 points = 135 points

The sum of the points you earned = 132 + 141 + 135 = 408 points

The total possible points = 450 points, which is the sum of 150 points for each of the 3 tests.

So, the weighted average of the first three tests = 408/450 × 100% = 90.67%.

To earn a 93% average on all 4 tests combined, the sum of the total points earned must be 93% of the total possible points.

93% of (450 + 250) = 657 points

The total points earned on the first three tests = 408 points

So, the points required on the final test are 657 - 408 = 249 points.

The final test is worth 250 points, so you need to earn 249/250 × 100% = 99.6%.

Therefore, you need to earn 99.6% on the final test to earn a 93% average on all 4 tests combined.

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Answer:

3/1 is the slope.

Step-by-step explanation:

Slope formula: y2 - y1/x2 - 1

Plugging in the given values, we get:

-9 - (-6)/3-4

-3/-1

Two negatives cancel each other out, so:

3/1 is the slope.

Answer:

124

Step-by-step explanation:

Answer:

C, because it is one unit across

filler filler filler

Answer:

The coordinates of its image are (-4, -3), (-7, -3), (-5, -5), (-2, -5)

Step-by-step explanation:

Let us solve the question

∵ Parallelogram FGHJ has vertices at F (4, 4), G (7, 4), H (5, 2), J (2, 2)

∵ The parallelogram is translated down 7 units

∴ k = 7

→ By using the first rule above, subtract every y-coordinates by 7

∴ F' = (4, 4 - 7) = (4, -3)

∴ G' = (7, 4 - 7) = (7, -3)

∴ H' = (5, 2 - 7) = (5, -5)

∴ J' = (2, 2 - 7) = (2, -5)

∵ The parallelogram is reflected over the y-axis

→ By using the 2nd rule above, change the sign of each x-coordinate

∴ F" = (-4, -3)

∴ G" = (-7, -3)

∴ H" = (-5, -5)

∴ J" = (-2, -5)

∴ The coordinates of its image are (-4, -3), (-7, -3), (-5, -5), (-2, -5)

Answer:

4.4      5.2    7.4    and    2.2

Step-by-step explanation:

The area covered by the pool and the cement walkway is 304  square feet. The width of the walkway would be 5 feet

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Let x be represent the width of the walkway.

The pool measures 25 ft by 10ft . If the walkway must have a uniform width around the entire pool, then the total length of the pool and the walkway =  25+ x + x = 25 + 2x

The total width of the pool and the walkway = 10 + x + x = 10 + 2x

The area covered by the pool and the cement walkway is 304  square feet. This means that;

(25 + 2x)(10 + 2x) = 304

250 + 50x + 20x + 4x^2 = 304

4x^2 + 70x + 250 - 304 = 0

4x^2 + 70x - 54 = 0

x(x + 20) - 5(x + 20) = 0

(x - 5)(x + 20) = 0

x = 5 or x = - 20

Thus The width cannot be negative.

Therefore, the width of the walkway is 5 feet.

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Answer:

The answer is 20

Step-by-step explanation:

0.4 = 40%

0.4 * 50 = 20

Answer:

9/8

Step-by-step explanation:

my work is in the picture. lmk if you'd like me to explain more

Bytaking the quotient between the probabilities we can see that Getting a 17 is three times more likely to get a 18.

If you toss 3 dices with 6 sides each, then the total number of combinations is:

6*6*6 = 216

Now, the outcomes that add up to 18 are:

dice 1, dice 2, dice 3, sum:

6            6         6       , 18

The outcomes that add up to 17 are:

dice 1, dice 2, dice 3, sum:

5           6         6       , 17

6            5         6       , 17

6            6         5       , 17

So the probabilities are:

P(18) = 1/216

P(17) = 3/16

The quotient gives:

P(17)/P(18) = 3

Getting a 17 is 3 times more likely to get a 18.

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Answer:

Bobbi burned the most calories per hour.

Step-by-step explanation:

Ratio

452:2.25

1045:3.5

to simplify the ratios, divide to the unit rate.

452/2.25:2.25/2.25

≈201:1 hour, burned 201 calories in 1 hour

1045/3.5:3.5/3.5

≈299:1 hour, burned 299 calories in 1 hour

299 > 201

Answer:

Bobbi burned the most calories per hour.

Step-by-step explanation:

Ratio

452:2.25

1045:3.5

to simplify the ratios, divide to the unit rate.

452/2.25:2.25/2.25

≈201:1 hour, burned 201 calories in 1 hour

1045/3.5:3.5/3.5

≈299:1 hour, burned 299 calories in 1 hour

299 > 201

Answer:g(x)=x-2+2

Step-by-step explanation:

Kid

Movement plays a crucial role in various aspects of our lives, including physical health, cognitive development, and emotional well-being.

Movement is essential for maintaining physical health and well-being. Regular physical activity helps to strengthen muscles and bones, improve cardiovascular fitness, and maintain a healthy weight. Engaging in activities such as walking, running, swimming, or cycling promotes the overall functioning of the body and reduces the risk of chronic diseases like heart disease, diabetes, and obesity.

Furthermore, movement has a significant impact on cognitive development. Physical activity stimulates the brain and enhances cognitive functions such as memory, attention, and problem-solving skills. Studies have shown that children who engage in regular physical activity tend to perform better academically and have improved cognitive abilities compared to those who lead sedentary lifestyles. Exercise increases blood flow and oxygenation to the brain, promoting neuroplasticity and the growth of new brain cells.

In addition to physical health and cognitive development, movement also plays a crucial role in emotional well-being. Exercise releases endorphins, which are neurotransmitters that help reduce stress and improve mood. Regular physical activity has been linked to lower rates of depression and anxiety, as it provides a natural boost to mental health. Engaging in activities that involve movement, such as dancing, yoga, or team sports, can also enhance social connections and promote a sense of belonging and self-confidence.

In conclusion, movement is vital for our overall well-being. It contributes to physical health, cognitive development, and emotional well-being. By incorporating regular physical activity into our daily routines, we can reap the numerous benefits associated with movement and lead healthier, more fulfilling lives.

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Step-by-step explanation:

when you do an arithmetic operation to functions, you do it for the defining expressions.

so,

(f+g)(x) = (x + 3) + (4x + 4) = x + 3 + 4x + 4 = 5x + 7

(f*g)(x) = (x+3)*(4x+4) = 4x² + 12x + 4x + 12 = 4x² + 16x + 12

= 4(x² + 4x + 3)

(f-g)(4) = (4+3) - (4×4+4) = 7 - (16+4) = 7 - 20 = -13

Answer:

the scale factor of a drawing=1:4

The number of units sold in 2021 = 13,300 units.

The number of units that would have to be sold in 2022 to reach the stockholder's desired profit level = 15,200 units.

Assuming that Cullumber company sells the same number of units in 2022 as it did in 2021, the selling price in order to reach the stockholder's desired profit level = $160.

The net income of a company is its profit function, derived by the formula:

Profit = Sales - Cost.

Sales are the product of the number of units sold and per unit selling price.

Cost is the sum of fixed costs and the product of the number of units produced to the variable cost per unit.

Assuming the number of units sold in 2021 to be x,

we can say sales = $152x, and

cost = ${574800 + 96x}.

Therefore, profit = sales - cost,

or, 170000 = 152x - {574800 + 96x},

or, 170000 = 56x - 574800

or, 56x = 574800 + 170000 = 744800,

or, x = 744800/56 = 13300.

Therefore, the number of units sold in 2021 was 13,300.

In 2022, the desired profit = $170,000 + $106,400 = $276,400.

Assuming the number of units sold in 2022 to be n, at the same unit data and fixed cost, we can say that:

Sales = $152n, and

Cost = ${574800 + 96n}.

Therefore, profit  sales - cost,

or, 276400 = 152n - {574800 + 96n},

or, 276400 = 56n - 574800,

or, 56n = 574800 + 276400 = 851200,

or, n = 851200/56 = 15200.

Therefore, the number of units sold in 2022 should be 15,200 to reach the desired profit of the stakeholders.

When the number of units sold in 2022 is the same as in 2021, that is, the number of units = 13,300, we assume the per unit selling price to be $P.

Now we can say that,

Sales = $13300P.

Costs = ${574800 + 96*13300} = ${574800 + 1276800} = $1851600.

Therefore, profit = sales - cost,

or, 276400 = 13300P - 1851600,

or, 13300P = 1851600 + 276400 = 2128000,

or, P = 2128000/13300 = 160.

Therefore, the new selling price per unit to reach stockholders' desired profit, assuming the number of units sold in 2022 to be the same as in 2021 is $160.

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Answer:

88

Step-by-step explanation: make me brainliest if it is correct

The factors of the polynomial f (x) = x^5 - 7x - 22x³ + 44x² - 104x + 288 that is true for f (9) = 0 are (x - 9) and (x⁴ + 2x³ - 4x² + 8x - 32).

The factor theorem states that: if p(x) is divisible by x - a if and only if p(a)=0.

The polynomial expression x^5 - 7x - 22x³ + 44x² - 104x + 288 and f (9) = 0, then x - 9 = 0 is a factor. Applying long division as follows;

x^5 divided by x equals x⁴

x - 9 multiplied by x⁴ equals x^5 - 9x⁴

subtract x^5 - 9x⁴ from x^5 - 7x - 22x³ + 44x² - 104x + 288 will result to 2x⁴ - 22x³ + 44x² - 104x + 288

2x⁴ divided by x equals 2x³

x - 9 multiplied by 2x³ equals 2x⁴ - 18x³

subtract 2x⁴ - 18x³ from 2x⁴ - 22x³ + 44x² - 104x + 288 will result to -4x³ + 44x² - 104x + 288

-4x³ divided by x equals -4x²

x - 9 multiplied by -4x² equals -4x³ + 36x²

subtract -4x³ + 36x² from -4x³ + 44x² - 104x + 288 will result to 8x² - 104x + 288

8x² divided by x equals 8x

x - 9 multiplied by 8x equals 8x - 72x

subtract 8x - 72x from 8x² - 104x + 288 will result to - 32x + 288.

-32x divided by x equals -32

x - 9 multiplied by -32 equals -32x + 288

subtract -32x + 288 from- 32x + 288 will result to a remainder 0(zero).

We can then conclude the factors (x - 9) and (x⁴ + 2x³ - 4x² + 8x - 32) are the product of linear factors for the polynomial f (x) = x^5 - 7x - 22x³ + 44x² - 104x + 288 that makes it zero.

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MM, MF, FM, and FF where MM stands for two boys, MF stands for one boy and one girl in that order, FM stands for one girl and one boy in that order, and FF stands for two females.

As per the question given,  

The sample space for the gender of the children consists of all possible combinations of the genders of the two children. Assuming that the gender of each child is independent of the other and equally likely to be male or female, the sample space can be represented as:

{MM, MF, FM, FF}

where MM represents two boys, MF represents one boy and one girl in that order, FM represents one girl and one boy in that order, and FF represents two girls.

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Answer:

9030.75

Step-by-step explanation:

5039.16/.558=9030.752688

round to the nearest hundredth

9030.75

i think

We are given three sets of quantum numbers and need to determine the number of electrons that could have these quantum numbers. For n=5, c=2, the maximum number of electrons is 50. For n=6, l=2, ml=-1, the maximum number of electrons is 10.

The quantum numbers specify the energy level (n), the azimuthal quantum number (l), and the magnetic quantum number (ml). By applying the rules for assigning electrons to quantum numbers, we can calculate the maximum number of electrons for each set.

For the set n=, the quantum number n alone does not provide enough information to determine the number of electrons. We need additional quantum numbers such as l and ml to determine the specific electron configuration.

For the set n=5, c=2, the values n=5 and c=2 correspond to the principal quantum number and the azimuthal quantum number, respectively. According to the rules, the maximum number of electrons in a given energy level (n) is given by 2n^2. Therefore, for n=5, the maximum number of electrons is 2(5)^2 = 50.

For the set n=6, l=2, ml=-1, the values n=6, l=2, and ml=-1 correspond to the principal quantum number, azimuthal quantum number, and magnetic quantum number, respectively. The maximum number of electrons in a given energy level (n) and azimuthal quantum number (l) is given by 2(2l+1). Therefore, for n=6 and l=2, the maximum number of electrons is 2(2*2+1) = 10.

In summary, the number of electrons that could have these sets of quantum numbers are as follows:

For n=, the number of electrons cannot be determined without additional information.

For n=5, c=2, the maximum number of electrons is 50.

For n=6, l=2, ml=-1, the maximum number of electrons is 10.

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Answer:

Step-by-step explanation:

You want the remainder of a number when divided by 3 if (1) the sum of digits is 5, and (2) the remainder from division by 9 is 5.

The sum of digits of a 2-digit number will be 5 if that number is one of ...

  {14, 23, 32, 41, 50}

In every case, the remainder when divided by 3 is 2. Effectively, it is the remainder of 5 when that is divided by 2.

In addition to the numbers listed above, 2-digit numbers with a sum of digits of 14 will also have a remainder of 5 when divided by 9. This adds five more numbers to the list:

  {59, 68, 77, 86, 95} . . . . have remainders of 5 when divided by 9

The remainders when divided by 3 are all 2 for these numbers as well.

__

Additional comment

The process of (recursively) summing the digits of a positive integer is called "casting out 9s". It effectively finds the modulo 9 value of the number, with the exception that a sum of 9 corresponds to a modulo 9 value of 0.

Since 9 is divisible by 3, the modulo 3 value of a number will be the modulo 3 value of the modulo 9 value. In other words, if the sum of digits is 5, or the remainder from division by 9 is 5, then the mod 3 value is 5 mod 3 = 2.