math sceenshot answer math problem

Answer:

Step-by-step explanation: 500

(a) The initial concentration of the solution in the tank is 0.05 kg/L. (b) After 2.5 hours, the amount of salt in the tank remains unchanged at 50 kg. (c) As time approaches infinity, the concentration of salt in the solution remains constant at 0.05 kg/L.

(a) The initial concentration of the solution in the tank can be calculated by dividing the total amount of salt initially present by the total volume of the solution initially.

Total amount of salt initially = 50 kg

Total volume of the solution initially = 1000 L

Concentration of the solution initially = (Total amount of salt initially) / (Total volume of the solution initially)

Concentration of the solution initially = 50 kg / 1000 L = 0.05 kg/L

Therefore, the concentration of the solution in the tank initially is 0.05 kg/L.

(b) Find the amount of salt in the tank after 2.5 hours.

In this case, we need to consider the amount of salt entering and leaving the tank over time.

Amount of salt entering the tank per minute = concentration of the incoming solution × rate of incoming solution

Amount of salt entering the tank per minute = 0.025 kg/L × 10 L/min = 0.25 kg/min

Amount of salt leaving the tank per minute = concentration of the solution in the tank × rate of outgoing solution

Amount of salt leaving the tank per minute = (amount of salt in the tank) / (total volume of the solution in the tank) × 10 L/min

Since the incoming and outgoing rates are equal (10 L/min), the amount of salt in the tank after a certain time remains constant. Let's calculate the amount of salt in the tank after 2.5 hours (150 minutes).

Amount of salt entering the tank in 150 minutes = 0.25 kg/min × 150 min = 37.5 kg

The amount of salt in the tank after 2.5 hours remains the same as the initial amount, as there is no net change in the salt content.

Therefore, the amount of salt in the tank after 2.5 hours is 50 kg.

(c) Find the concentration of salt in the solution in the tank as time approaches infinity.

As time approaches infinity, the concentration of salt in the solution in the tank will be determined by the ratio of the total amount of salt in the tank to the total volume of the solution in the tank.

Total amount of salt in the tank = 50 kg

Total volume of the solution in the tank = 1000 L

Concentration of salt in the solution as time approaches infinity = (Total amount of salt in the tank) / (Total volume of the solution in the tank)

Concentration of salt in the solution as time approaches infinity = 50 kg / 1000 L = 0.05 kg/L

Therefore, as time approaches infinity, the concentration of salt in the solution in the tank will be 0.05 kg/L, the same as the initial concentration.

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Complete question:

A tank contains 50 kg of salt and 1000 L of water. A solution of a concentration 0.025 kg of salt per liter enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the same rate. (a) What is the concentration of our solution in the tank initially? (b) Find the amount of salt in the tank after 2.5 hours. (c) Find the concentration of salt in the solution in the tank as time approaches infinity.

Answer:

(a) 165 m/min

(b) 107.14m/min

Step-by-step explanation:

The slope of the distance time graph gives speed.

Here, the speed of the segment A is

\(v_A= \frac{900-0}{4-0}=225 m/min\)

The speed of segment B is

\(v_B= \frac{1500- 900}{14-4}= 60 m/min\)

(a) The change in speed is

= 225 - 60 = 165 m/min

(b) The average speed is defined as the ratio of total distance to the total time.

So, the average speed is

\(= \frac{1500}{14}= 107.14 m/min\)

Answer:

33 yards

Step-by-step explanation:

To find the number of ribbons that she used to decorate the dresses can be gotten by subtracting the amount of ribbon left from the total amount of ribbon she had.

She bought 100 yards. She has 67 yards left.

Therefore, the amount of ribbon she used for the dresses is:

100 - 67 = 33 yards

By applying algebra, it can be concluded that the number of candies remaining in the bag can be written as c = 150 - 8s, where s is the number of snacking.

Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems

Now we apply algebra to solve the problem:

Tyrone takes 8 pieces of candy each time snacking

After snacking 18 times, 6 pieces of candy remained in the bag

So the totals candies eaten = 8 * 18

                                              = 144 candies

Number of candies in the bag = candies eaten + remaining candies

                                                  = 144 + 6

                                                  = 150 candies

If s denotes the number of snacking, then the total number of candies eaten on s snacking = 8s

if c denotes the number of remaining candies, then:

c = total candies - candies eaten

c = 150 - 8s

Thus the number of candies remaining in the bag can be written as c = 150 - 8s, where s is the number of snacking.

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Answer:

  C, D, E

Step-by-step explanation:

You want to find equations for h and b1 or b2 given the formula for the area of a trapezoid is ...

  A = 1/2h(b1 +b2)

Distributing the factor of 1/2, we get ...

  \(A=h\left(\dfrac{1}{2}b_1+\dfrac{1}{2}b_2\right)\)

Dividing by the coefficient of h, we find ...

  \(\boxed{h=\dfrac{A}{\left(\dfrac{1}{2}b_1+\dfrac{1}{2}b_2\right)}}\qquad\text{matches choice E}\)

Multiplying the original equation by 2 gives us ...

  \(2A=h(b_1+b_2)\)

From here, we can solve for h or b2 as follows:

  \(\boxed{h=\dfrac{2A}{b_1+b_2}}\qquad\text{divide by the coefficient of h; matches D}\\\\\\\\b_1+b_2=\dfrac{2A}{h}\qquad\text{divide by h}\\\\\boxed{b_2=\dfrac{2A}{h}-b_1}\qquad\text{subtract $b_1$; matches C}\)

Answer:she worked 17 hours

Step-by-step explanation: 10×17=170+42=212

Answer:

She worked 16.4 hours

Step-by-step explanation:

Answer:7

Step-by-step explanation:

A stem-and-leaf display is a visual representation of the data that organizes and presents the motor fuel octane ratings in a clear and concise manner

Median: 88.5, Q1: 84.3, Q3: 91.3

i. Stem-and-leaf display for the given data is given below

The stem-and-leaf display is a way to organize and present data in a visual format. In this case, the stem-and-leaf display is constructed for the given data on motor fuel octane ratings.

The stem represents the tens digit of each data point, while the leaf represents the ones digit. The data points are grouped based on their stem values, and the corresponding leaf values are listed next to each stem.

For example, in the stem-and-leaf display:

- The stem "8" corresponds to data points with tens digit 8.

- The leaves "4 8 9 9" indicate that there are four data points with tens digit 8 and ones digit 4, 8, 9, and 9, respectively.

- The stem "9" corresponds to data points with tens digit 9.

- The leaves continue in the same manner for the other stems.

The stem-and-leaf display provides a concise representation of the data distribution, allowing us to easily observe the range and frequency of values.

ii. Median and quartiles of the data:

- Median: The median is the middle value of the dataset when arranged in ascending order. Since the dataset has an odd number of observations (39), the median is the value at the (39 + 1) / 2 = 20th position. The 20th value is 88.5.

- Quartiles: The quartiles divide the dataset into four equal parts. To find the quartiles, we need to determine the positions of the values. The first quartile (Q1) is the value at the (39 + 1) / 4 = 10th position, which is 84.3. The third quartile (Q3) is the value at the (3 * (39 + 1)) / 4 = 30th position, which is 91.3.

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Answer:

B. y = -4. Slope is 0

Step-by-step explanation:

well you can distribute the sqrt(15x) to the (√3x + √5) and then combine the radicals using the product property of radicals: \(\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}\).

\((\sqrt{3x} + \sqrt{5})\sqrt{15x} + 2\sqrt{30}\\(\sqrt{3x} * \sqrt{15x}) + (\sqrt{5} * \sqrt{15x}) + 2\sqrt{30}\\\sqrt{45x^2} + \sqrt{75x} + 2\sqrt{30}\\\)

Now we can simplify the radicals using the same property we used to combine them but instead of combining into one radical we'll separate them into two radicals where one of the radicals simplifies into a number without a radical

\((\sqrt{9} * \sqrt{x^2} * \sqrt{5}) + (\sqrt{25} * \sqrt{3x}) + 2\sqrt{30}\\3x\sqrt{5} + 5\sqrt{3x} + 2\sqrt{30}\)

Answer:

\( x = 5.1 yd \)

Step-by-step Explanation:

Angle of depression is congruent to angle of elevation.

Therefore, angle of elevation of the given figure, which is opposite to x is 25°.

Adjacent length = 11 yd

Opposite length = x

Trigonometric ratio formula for finding x is shown below:

\( tan(25) = \frac{opposite}{adjacent} \)

\( tan(25) = \frac{x}{11} \)

Multiply both sides by 11 to solve for x

\( 11*tan(25) = x \)

\( 5.129 = x \)

\( x = 5.1 yd \) (to the nearest tenth)

Answer:

3/5

Step-by-step explanation:

because in one jar there are total 5 marbles. 2 orange and 3 red. so if he pick randomly then he will 3/5.

The answer is "false". The interval [1, 2] contains all the real numbers between 1 and 2 including the endpoints.

An interval notation is used for representing the continuous set of real values. This is the shortest way of writing inequalities.

Intervals are represented within the brackets such as square brackets or open brackets(parenthesis).

The given interval is [1, 2]

The given statement is - 'the interval [1, 2] contains exactly two numbers - the numbers 1 and 2'

The given statement is 'false'.

This is beacuse, an interval consists set of all the real values in between the two values given.

So, according to the definition, there are not only the end values but also many real values in between them.

Thus, the answer is "false". The interval [1, 2] consists of all the real values between 1 and 2 including 1 and 2.

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Main Answer: The value of f(n) = 16(f(k))^4 when n = 3k.

Supporting Question and Answer:

How can we determine the value of f(n) when n = 3k using the given recurrence relation and initial condition?

By analyzing the given recurrence relation f(n) = 2f(n/3)^4 and the initial condition f(1) = 1, we can recursively calculate the value of f(n) for n = 3k. Using the recurrence relation, we can express f(n) in terms of f(n/3) and apply it iteratively. The value of f(n) when n = 3k is given by f(n) = 16(f(k))^4, where f(1) = 1 is used as the base case.

Body of the Solution:To find the value of f(n) when n = 3k, where f satisfies the recurrence relation f(n) = (2f(n/3))^4 with f(1) = 1, we can use the recurrence relation to recursively calculate the values of f(n).

Given that f(1) = 1, we can calculate the values of f(n) for n = 3, 9, 27, and so on.

f(3) = (2f(3/3))^4

= ((2f(1)))^4

= 2^4(1)^4

= 16

f(9) = (2f(3))^4

= (2(16))^4

= 1048576

f(27) =(2f(9))^4

= (2(1048576))^4

=(2097152)^4

Therefore, f(n) when n = 3k is given by:

f(3K)  =16(f(k))^4

So, f(n) =16(f(k))^4  when n = 3k, where f satisfies the given recurrence relation and f(1) = 1.

Final Answer:Therefore, f(n) =16(f(k))^4 when n = 3k.

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Answer:

2

Step-by-step explanation:

because if 10 is the whole line of the base at the bottom of the trapezoid

and 8 is the whole top 10-8=2

It is true to state that Lin tried to reflect triangle ABC across line t.

She knows something went wrong because the image isn’t congruent to the original figure.

1) Note that  Lin probably understands that the image needs to be the same distance away from the line as the original figure.

2) Lin doesn’t understand that the segments that connect the original figure to the image need to be equidistant to the line.

In mathematics, a reflection is a transformation that flips a figure over a line or plane.

The reflection of a point or shape across a line or plane is the same distance from that line or plane as the original point or shape. This is known as equidistance.

Therefore, reflection and equidistance are closely related in that a reflected point or shape is equidistant from the line or plane of reflection as the original point or shape.

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Answer:

Use the slope −2 and the point (−4,−5) to find the y-intercept.

y=mx+b

⇒−5=(−2×−4)+b

⇒−5=8+b

⇒b=−13

Write the equation in slope intercept form as:

y=mx+b

⇒y=(−2)x−13

Hence, the equation of the line is y=−2x−13.

Answer:

x= 4/5

y= 2/5

Step-by-step explanation:

3x-y=2

2x+y=5

solve them so that they are in y=mx+b form

3x-y-3x=2-3x

-y= -3x+2

y= 3x -2

2x+y -2x= 2-2x

y= -2x+2

now use the substitution method to get your points

3x -2= -2x+2

3x -2+2= -2x+2+2

3x= -2x+4

3x+2x= -2x+4+2x

5x=4

x= 4/5

now substitute x into any of the 2 equations

y= 3x -2

y= 3(4/5) -2

y= 2 2/5 -2

y= 2/5

Hope this helped!

Answer:

PT = 17

Step-by-step explanation:

Since T is the midpoint of PQ, then

PT = TQ , substitute values

4x + 5 = 8x - 7 ( subtract 4x from both sides )

5 = 4x - 7 ( add 7 to both sides )

12 = 4x ( divide both sides by 4 )

3 = x

Thus

PT = 4x + 5 = 4(3) + 5 = 12 + 5 = 17

Answer:

17

Step-by-step explanation:

since T is mid point of PQ

PT=TQ

\(4x + 5 = 8x - 7 \\ 5 + 7 = 8x - 4x \\ 12 = 4x \\ x = 12 \div 4 \\ x = 3 \\ \)

so

\(pt = 4x + 5 \\ = 4(3) + 5 \\ = 12 + 5 \\ pt = 17\)

Part A: The salesperson should expect 1.92 customers until she finds a customer that makes a purchase.

Part B: The probability that a salesperson helps 3 customers until she finds the first person to make a purchase is 11.98%.

The number of customers a salesperson should expect until she finds a customer that makes a purchase can be modeled by a geometric distribution since each customer's decision to make a purchase is independent, and the probability of success (making a purchase) remains constant at 52%.

Part a:

The expected value (E) of a geometric distribution is given by E = 1/p, where 'p' is the probability of success (making a purchase).

In this case, p = 0.52 (52% probability of making a purchase).

E = 1/0.52

= 1.9231

So, the salesperson should expect approximately 1.92 customers until she finds a customer that makes a purchase.

part b:

The probability that a salesperson helps 3 customers until she finds the first person to make a purchase can be calculated using the geometric distribution formula:

\(P(X = k) = (1 - p)^{k-1} \times p\)

Where:

X = the number of trials until the first success (making a purchase)

p = probability of success (making a purchase)

In this case, k = 3 (the salesperson helps 3 customers until the first purchase), and p = 0.52 (probability of making a purchase).

\(P(X = 3) = (1 - 0.52)^{3-1} \times 0.52\)

\(P(X = 3) = (0.48)^2 \times 0.52\)

\(P(X = 3) = 0.2304 \times 0.52\)

\(P(X = 3) = 0.1198\)

Hence, the probability that a salesperson helps 3 customers until she finds the first person to make a purchase is approximately 0.1198 or 11.98%.

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Answer:

Step-by-step explanation:

Answer:

1  1/15

Step-by-step explanation:

you flip the second fraction then multiply straight across

4/5 divided by 3/4

4/5 divided by 4/3

4 x 4 = 16

5 x 3 = 15

16/15

then simplify

1  1/15

hope this helps

Answer:

7(n + 3)

Step-by-step explanation:

let the number be n then add 3 to it , that is n + 3 , now multiply the expression by 7 , that is

7(n + 3)

Answer:

To find the slope of line AB, we use the slope formula:

slope of AB = (yB - yA) / (xB - xA)

where A = (-10, 8) and B = (2, 3).

slope of AB = (3 - 8) / (2 - (-10)) = -5/12

The slope of a line perpendicular to AB will have a negative reciprocal slope, so its slope will be 12/5.

Using the slope-intercept form of the equation of a line:

y = mx + b

where m is the slope and b is the y-intercept, we can find the equation of the line that passes through point X (-5, 10) and has a slope of 12/5.

10 = (12/5)(-5) + b

10 = -24/5 + b

b = 74/5

Therefore, the equation of the line that is perpendicular to AB and passes through point X is:

y = (12/5)x + 74/5

Answer:

Your answer would be 7,600.

Step-by-step explanation:

7,605 rounded to the nearest hundred would be 7,600 because:

The 7 is the thousands.

The 6 is the hundreds.

The 0 is the tens

The 5 is the ones.

So, we need to find which number makes sense to round. Is 605 closer to 600 or 700? 600. So, we have: 7,600

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Money = (1/2×6×7+1/2*3.14*3.5^2)×5.60+150= $375.30

The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to

(1/ ⁸C₂).

As given in the question,

Total number of different toppings = 8

Number of different toppings choose by Rosa's mom randomly = 2

Possibility of choosing sausage and onion (any one) = 1

Total number of outcomes = ⁸C₂

Number of favorable outcomes = 1

Probability of choosing sausage and onion ( exactly ) one topping

= ( Number of favorable outcomes ) / ( Total number of outcomes )

= ( 1/⁸C₂ )

Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).

The above question is incomplete, the complete question is:

A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings

below:

Pepperoni ,Sausage, Chicken ,  Green pepper , Mushroom ,Pineapple, Ham, Onion

Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.

What is the probability that Rosa's mom chooses sausage and onion?

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Answer:

1/8c^2

Step-by-step explanation:

Khan Acadmey