Johnny can make 15 pounds of slime in 24 minutes. How
many pounds of slime can he make in 80 minutes?

Answer:

150%

Step-by-step explanation:

6 blocks :) I won’t explain it tho lol

Answer:

\(tan \: g = \frac{14}{25} \)

8 teams will remain in the 4th round of the tournament.

It is given that there are total of 64 teams in the tournament. Each team plays only 1 game per round. The winning team advances to the next round and the losing team gets eliminated and since a game is played between 2 teams, This means for the first round, total number matches are 32 and only 32 teams goes to Round 2.

⇒64 ÷2 = 32

Similarly , for Round 2 there are only 16 matches between 32 teams. If we keep repeating the same process for  Round 3 and Round 4 , we get :

⇒32 ÷ 2 = 16

⇒16 ÷ 2  = 8

Therefore, only 8 teams will remain for the 4th Round of the tournament.

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The equation of a straight line is written as

y = mx + c

Where

m represents slope

c represents y intercept

The given equation is expressed as

3x + y = 3

y = 3 - 3x

y = - 3x + 3

Comparing the above equation with the slope intercept equation,

y intercept = 3

The x intercept is the value of x when y = 0

Putting y = 0 in the equation, it becomes

0 = - 3x + 3

3x = 3

x = 3x/3

x = 1

x intercept = 1

Answer:

3375/13

Step-by-step explanation:

it's found though this equation  \(\frac{84375/25}{325/25}\)

Answer:

\(3375/13\)

Step-by-step explanation:

\(84,375/325\)

Divide the numerator and denominator by 25.

\(3375/13\)

\(=259.615385\)

Answer:

a. 5

b. -5 then 5

c. 5 for both

Step-by-step explanation:

I hope this helps!

Answer:

83 is the answer

Step-by-step explanation:

2*5^2+33

2*25+33

50+33=83

A 13ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of 2 ft/s, then the foot of the ladder will be moving away from the wall at a rate of 4 ft/s when the top is 5 ft above the ground.

This can be determined using the formula Rate = Distance/Time. Since we know that the top of the ladder is slipping down at a rate of 2 ft/s, we can calculate the rate at which the foot of the ladder is moving away from the wall. The distance between the top of the ladder and the foot of the ladder is 8 ft (13 ft - 5 ft). Since the top of the ladder is moving down 2 ft/s, the foot of the ladder must be moving away from the wall at a rate of 4 ft/s.

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Answer:

a. 25/1, likes per follow b. 75,000 likes

Step-by-step explanation:

The slope is the likes per follow, which is 500/20 simplified to 25/1.  To find how many he needs for answer b, you first need to find how many more followers he needs, which is 3000.  You then multiply the number of likes per follow by the number of followers needed, 25x3000.  Dmytryus needs 75000 likes to become Instagram famous.

\(\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)

we're given that Angela formerly had 8 computer games.

★ She got 3 more video games on her birthday.

★ Then she gave away 4 video games.

_____________________________

_____________________________

\(\huge\red{ Solution -}\)

\(8 + 3 - 4 \\ \dashrightarrow \: 11 - 4 \\ \dashrightarrow \: 7\)

hope helpful :D

The standard deviation of the outcome for the given bet is approximately $51.

To obtain this result, we can use the following formula for the standard deviation of a random variable with two possible outcomes (winning or losing in this case):SD = √(p(1-p)w² + p(1-p)l²),where SD is the standard deviation, p is the probability of winning (0.4 in this case), w is the amount won ($50 in this case), and l is the amount lost ($50 in this case).

Plugging in the values, we get:SD = √(0.4(1-0.4)(50²) + 0.6(1-0.6)(-50²))≈ $51

Therefore, the standard deviation of the outcome of the given bet is approximately $51.Explanation:In statistics, the standard deviation is a measure of how spread out the values in a data set are.

A higher standard deviation indicates that the values are more spread out, while a lower standard deviation indicates that the values are more clustered together.

In the context of this problem, we are asked to find the standard deviation of the outcome of a bet. The outcome can either be a win of $50 with a probability of 40% or a loss of $50 with a probability of 60%.

To find the standard deviation of this random variable, we can use the formula:SD = √(p(1-p)w² + p(1-p)l²),where SD is the standard deviation, p is the probability of winning, w is the amount won, and l is the amount lost.

Plugging in the values, we get:SD = √(0.4(1-0.4)(50²) + 0.6(1-0.6)(-50²))≈ $51Therefore, the standard deviation of the outcome of the given bet is approximately $51.

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The derivative for each of the definite integrals using the fundamental theorem of calculus is

a) d/dx ∫ 4x(2(6cos(t)+7)⁴)dt is 4(2(6cos(b)+7)⁴) - 4(2(6cos(a)+7)⁴)

b)  d/dx ∫ x³(4sin(t³−3))dt is 12(b²sin(b³-3) - a²sin(a³-3))

The fundamental theorem of calculus tells us that the derivative of the definite integral of a function f(x) with respect to x is equal to the function evaluated at the upper limit of integration minus the function evaluated at the lower limit of integration. In other words, if we have an integral of the form ∫f(x)dx evaluated from a to b, then

d/dx ∫f(x)dx = f(b) - f(a)

Let's apply this to the first integral, A).

A) d/dx ∫ 4x(2(6cos(t)+7)⁴)dt

We begin by recognizing that the function inside the integral is a function of t, not x. However, we want to take the derivative with respect to x. This means that we need to use the chain rule to differentiate the integrand with respect to x.

Using the chain rule, we have

d/dx [4x(2(6cos(t)+7)⁴)] = 4(2(6cos(t)+7)⁴)(d/dx [4x])

= 4(2(6cos(t)+7)⁴)(4)

= 32(2(6cos(t)+7)⁴)

Now, we can apply the fundamental theorem of calculus. Let's say we are evaluating the integral from a to b. Then,

d/dx ∫ 4x(2(6cos(t)+7)⁴)dt = [4b(2(6cos(t)+7)⁴)] - [4a(2(6cos(t)+7)⁴)]

= 4(2(6cos(b)+7)⁴) - 4(2(6cos(a)+7)⁴)

This is the final answer for A).

Now, let's move on to integral B).

B) d/dx ∫ x³(4sin(t³−3))dt

Again, we need to use the chain rule to differentiate the integrand with respect to x.

d/dx [x³(4sin(t³−3))] = (d/dx [x³])(4sin(t³−3))

= 3x²(4sin(t³−3))

Now, we apply the fundamental theorem of calculus. Let's say we are evaluating the integral from a to b. Then,

d/dx ∫ x³(4sin(t³−3))dt = [3b²(4sin(t³−3))] - [3a²(4sin(t³−3))]

= 12(b²sin(b³-3) - a²sin(a³-3))

This is the final answer for B).

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Answer:

7B + (36 * 4) = 184

Step-by-step explanation:

In a family restaurant there are 36 tables and 7 booths.

Each table can seat 4 people.

Let the number of people who can be seated in a booth be represented by B.

Total seating capacity of the restaurant is 184 people.

Expressing this as an equation:

Among the given options, this relation is expressed in the second option, namely, 7B + (36 * 4) = 184

The value of x will be;

⇒ x = - 3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 8 × 2²ˣ + 4 × 2ˣ × 2 = 1 + 2ˣ

Now,

Since, The expression is,

⇒ 8 × 2²ˣ + 4 × 2ˣ × 2 = 1 + 2ˣ

Solve for x as;

⇒ 8 × 2²ˣ + 8 × 2ˣ = 1 + 2ˣ

⇒ 8 × 2ˣ (2ˣ + 1) = 1 + 2ˣ

⇒ 8 × 2ˣ = (1 + 2ˣ) / (1 + 2ˣ)

⇒ 8 × 2ˣ = 1

⇒ 2ˣ = 1/8

⇒ 2ˣ = 2⁻³

By comparing, we get;

⇒ x = - 3

Thus, The value of x = - 3

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The number of hot water bottles sold is 12.

Let the number of hot water bottles sold be x.

Given that the customer bought 10 times as many thermometers as hot water bottles.

So the number of number of thermometer is = 10x.

Cost of each thermometers is = $2.

So the cost of '10x' number of thermometers is = $2*10x = $20x.

Cost of each hot water bottles = $6.

So the cost of 'x' hot water bottles is = $6x.

So the total sales = $20x + $6x = $26x.

Given that the total sales according to data is $312.

So the equation which best fit this situation is,

26x = 312

x = 312/26 = 12

Hence the number of hot water bottles sold is 12.

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The largest value that f(4) can possibly be is 29.

The mean value theorem states that for a function f(x) that is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), there exists a number c in the open interval (a, b) such that:

f(b) - f(a) = f'(c)(b - a)

In this case, we are given that f(0) = -3 and that f'(x) ≤ 8 for all values of x. To determine how large f(4) can possibly be, we can use the mean value theorem with a = 0 and b = 4:

f(4) - f(0) = f'(c)(4 - 0)

Substituting the given values:

f(4) - (-3) = f'(c)(4)

f(4) + 3 = 4f'(c)

Since f'(x) ≤ 8 for all values of x, we can say that f'(c) ≤ 8. Therefore:

f(4) + 3 ≤ 4f'(c) ≤ 4(8) = 32

Therefore, we have:

f(4) ≤ 32 - 3 = 29

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The probability of getting a face card on the first card is 12/52, and the probability of getting an ace on the second card is 4/52.

Since the two events are independent (because we replace the first card), we can multiply the probabilities to find the probability of both events happening together:

P(getting face card on first card and ace on second card) = P(face card on first card) × P(ace on second card)= (12/52) × (4/52) = 48/2704 = 0.0177.

When you are dealt two cards from a standard deck of 52 cards, there are a certain number of possibilities for each card. For example, if you are trying to find the probability of drawing an ace, there are four aces in the deck, so the probability of drawing an ace on the first card is 4/52, or 1/13. However, if you are trying to find the probability of drawing an ace on the second card after drawing a face card on the first card, the probability is different. In this case, you know that the first card is a face card, which means that there are 12 cards in the deck that could be drawn. Since there are 52 cards in the deck, the probability of drawing a face card on the first card is 12/52, or 3/13. After you replace the first card, there are 52 cards in the deck again, but now there are only four aces because you know that the first card was not an ace. Therefore, the probability of drawing an ace on the second card is 4/52, or 1/13. Since the two events are independent (because you replace the first card), you can multiply the probabilities to find the probability of both events happening together. In this case, the probability is:

P(getting face card on first card and ace on second card) = P(face card on first card) × P(ace on second card)= (12/52) × (4/52) = 48/2704 = 0.0177

In conclusion, the probability of getting a face card on the first card and an ace on the second card is approximately 0.0177, or 1.77%. This means that out of every 100 times you draw two cards from a standard deck of 52 cards, you can expect to get a face card on the first card and an ace on the second card less than two times.

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Random variable and its functions provides a solid foundation for analyzing data, making predictions, performing statistical analyses, and making informed decisions across a wide range of fields and applications.

Knowing the distribution of a random variable and its functions can provide several benefits and insights in various fields, including statistics, probability theory, and data analysis. Here are some of the gains you can achieve by understanding the distribution of a random variable and its functions:

Probability calculations: The distribution of a random variable provides information about the probabilities associated with different outcomes or events. By knowing the distribution, you can calculate probabilities of specific events occurring, determine the likelihood of certain values, and make predictions about the variable's behavior.

Statistical inference: Understanding the distribution of a random variable is crucial for statistical inference. It allows you to perform hypothesis testing, estimate parameters, and construct confidence intervals. With this knowledge, you can make informed decisions and draw conclusions about the population based on the sample data.

Model selection and fitting: In many cases, random variables are assumed to follow specific distributions (e.g., normal, exponential, Poisson). By knowing the distribution, you can select an appropriate model that accurately represents the data. This is particularly important in regression analysis and other modeling techniques.

Data analysis and interpretation: The distribution of a random variable and its functions provide insights into the characteristics and properties of the data. You can examine measures such as the mean, variance, skewness, and kurtosis to understand the central tendency, spread, and shape of the data. This knowledge helps in interpreting the data and drawing meaningful conclusions.

Risk assessment and decision-making: In finance, insurance, and other risk-related fields, understanding the distribution of random variables is crucial. It enables the assessment of potential risks, calculation of expected values and variances, and the determination of optimal strategies. This information aids decision-making and risk management processes.

Simulation and modeling: The distribution of a random variable is often utilized in simulations and modeling exercises. By incorporating the appropriate distribution, you can generate random samples that mimic the behavior of the variable. This allows you to explore various scenarios, assess system performance, and evaluate the impact of different factors.

Overall, understanding the distribution of a random variable and its functions provides a solid foundation for analyzing data, making predictions, performing statistical analyses, and making informed decisions across a wide range of fields and applications.

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Answer:

x= -1

x=1

Step-by-step explanation:

Answer:

height = 15 inches

Step-by-step explanation:

the volume (V) of a cylinder is calculated as

V = Ah ( A is the base area and h the height )

given V = 1650 and A = 110 , then

1650 = 110h ( divide both sides by 110 )

15 = h

To find the probability that a randomly selected newborn baby boy's weight at a local hospital will be less than 4456 grams, we can use the information provided about the normal distribution of weights.

With a mean weight of 3844 grams and a standard deviation of 612 grams, we can calculate the z-score corresponding to the weight of 4456 grams. Using the z-score and the standard normal distribution table, we can determine the probability associated with that z-score. Rounding the answer to four decimal places gives us the desired probability.

To calculate the probability, we first need to standardize the weight of 4456 grams using the z-score formula:

z = (x - μ) / σ

Where:

x = 4456 grams (the weight we want to find the probability for)

μ = 3844 grams (mean weight)

σ = 612 grams (standard deviation)

Substituting the values into the formula, we get:

z = (4456 - 3844) / 612 = 1

Next, we use the standard normal distribution table (z-table) to find the probability associated with a z-score of 1. From the z-table, we find that the corresponding probability is approximately 0.8413.

Therefore, the probability that a randomly selected newborn baby boy's weight will be less than 4456 grams is 0.8413, rounded to four decimal places.

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The probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

To solve this problem, we'll use the M/M/1 queueing model with Poisson arrivals and exponential service times. Let's calculate the required values: (a) Percentage of time Judy is idle: The utilization of the system (ρ) is the ratio of the average service time to the average interarrival time. In this case, the average service time is 10 minutes, and the average interarrival time is 12 minutes. Utilization (ρ) = Average service time / Average interarrival time = 10 / 12 = 5/6 ≈ 0.8333

The percentage of time Judy is idle is given by (1 - ρ) multiplied by 100: Idle percentage = (1 - 0.8333) * 100 ≈ 16.67%. Therefore, Judy is idle approximately 16.67% of the time. (b) Average waiting time for a student:

The average waiting time in a queue (Wq) can be calculated using Little's Law: Wq = Lq / λ, where Lq is the average number of customers in the queue and λ is the arrival rate. In this case, λ (arrival rate) = 1 customer per 12 minutes, and Lq can be calculated using the queuing formula: Lq = ρ^2 / (1 - ρ). Plugging in the values: Lq = (5/6)^2 / (1 - 5/6) = 25/6 ≈ 4.17 customers Wq = Lq / λ = 4.17 / (1/12) = 50 minutes. Therefore, on average, a student spends approximately 50 minutes waiting in line.

(c) Average length of the line: The average number of customers in the system (L) can be calculated using Little's Law: L = λ * W, where W is the average time a customer spends in the system. In this case, λ (arrival rate) = 1 customer per 12 minutes, and W can be calculated as W = Wq + 1/μ, where μ is the service rate (1/10 customers per minute). Plugging in the values: W = 50 + 1/ (1/10) = 50 + 10 = 60 minutes. L = λ * W = (1/12) * 60 = 5 customers. Therefore, on average, the line consists of approximately 5 customers.

(d) Probability of finding at least one student waiting in line: The probability that an arriving student finds at least one other student waiting in line is equal to the probability that the system is not empty. The probability that the system is not empty (P0) can be calculated using the formula: P0 = 1 - ρ, where ρ is the utilization. Plugging in the values:

P0 = 1 - 0.8333 ≈ 0.1667. Therefore, the probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

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Answer:

x + 10 = 24

Step-by-step explanation:

In the figure attached,

There are two external points A and B.

Fro point A two tangents AD and AE have been drawn and From point B tangents BE and BC have been drawn.

Since AD = 10 units,

Therefore, AE = 10 units

(Since tangents drawn from a point to a circle are same in measure, therefore, AD = AE)

Therefore,

BE = AB - AE

Since BE = BC

So BC = AB - AE

       x = 24 - 10

x + 10 = 24

Therefore, (x + 10) = 24 will be the equation to be used to solve for x.

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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Answer:

C) f-1(x) = -9x - 7 the inverse of multiplication is division

He sold four and eight-eighteenths pitchers of lemonade on Saturday, Thus, option C is correct.

Combining an integer (whole number) and a fraction creates a mixed number, which is also referred to as a mixed fraction (part of a whole number).

Given that, Carlos sold two and two-thirds pitchers of lemonade at his lemonade stand i.e.

\(2\dfrac{2}{3}\)

On Saturday, he sold one and four-sixths times as much lemonade as he sold on Friday i.e.

\(1\dfrac{4}{6}\) of \(2\dfrac{2}{3}\)

On solving we get

\(\Rightarrow 1\dfrac{4}{6} \times 2\dfrac{2}{3}\)

\(\Rightarrow \dfrac{10}{6} \times \dfrac{8}{3}\)

\(\Rightarrow \dfrac{80}{18}\)

\(\Rightarrow 4\dfrac{8}{18}\)

Abbreviated as four and eight-eighteenths,

Thus, He sold four and eight-eighteenths pitchers of lemonade on Saturday, Thus, option C is correct.

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(a) The time series plot shows an increasing non-linear trend pattern in the data.

(b) The parameters for the line that minimizes MSE for this time series are:

\(b_o = 2.4376\\b_i = 2.434\)

(a)

t      1    2    3    4    5

\(y_t\)    7  12    8   15   16

Plotting the data points on a graph with time (t) on the x-axis and the observed values (\(y_t\)) on the y-axis, we obtain the following time series plot.

From the time series plot, we can observe an increasing trend in the data. The values of \(y_t\) generally rise over time, indicating a non-linear positive trend pattern.

(b) To find the parameters for the line that minimizes the Mean Squared Error (MSE) for the given time series data, we can use simple linear regression analysis.

The equation for simple linear regression is given by:

\(Y_t = b_o + b_i * t\)

\(\sum Y_t = n * b_o + b_i * \sum t\\\sum Y_t * t = b_o * \sum t + b_i * \sum t^2\)

where n is the number of observations.

Let's calculate the required values:

n = 5 (number of observations)

\(\sum Y_t = 5 + 12 + 8 + 15 + 16 = 56\\\sum t = 1 + 2 + 3 + 3 + 4 + 5 = 18\\\sum Y_t * t = (5 * 1) + (12 * 2) + (8 * 3) + (15 * 3) + (16 * 4) = 117\)

Now, we can substitute these values into the equations:

\(n * b_o + b_i * \sum t = \sum Y_t\\5 * b_o + 18 * b_i = 56 ---(1)\\b_o * \sum t + b_i * \sum t^2 = \sum Y_t * t\\18 * b_o + 30 * b_i = 117 ---(2)\)

To solve this system of equations, we can multiply equation (1) by 18 and equation (2) by 5 to eliminate bo:

\(90 * b_o + 324 * b_i = 1008 ---(3)\\90 * b_o + 150 * b_i = 585 ---(4)\)

Subtracting equation (4) from equation (3):

\(174 * b_i = 423\)

Dividing both sides by 174:

\(b_i = 423 / 174 = 2.434\)

Now, substitute the value of \(b_i\) back into equation (1):

\(5 * b_o + 18 * 2.434 = 56\)

Simplifying:

\(5 * b_o + 43.812 = 56\\5 * b_o = 56 - 43.812\\5 * b_o = 12.188\\b_o = 12.188 / 5 = 2.4376\)

Therefore, the parameters for the line that minimizes the MSE for this time series data are approximately:

\(b_o = 2.4376\\b_i = 2.434\)

So, the equation for the line is:

\(Y_t = 2.4376 + 2.434 * t\)

Complete Question:

Consider the following time series data. t 1 2 3 3 4 5 Yt 5 12 8 15 16

(a) Construct a time series plot. What type of pattern exists in the data?

(b) Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.

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The Net Present Value (NPV) of the investment opportunity cannot be determined based on the given information. None of the provided options is within $26 of the NPV of this investment opportunity.

Net Present Value (NPV) is a financial metric used to assess the profitability of an investment. It represents the difference between the present value of cash inflows and the present value of cash outflows over a specific time period. In order to calculate the NPV, we would need information on the cash flows associated with the investment and the appropriate discount rate. To calculate the NPV of an investment opportunity, we need additional information such as the cash flows associated with the investment, the discount rate, and the time period over which the cash flows occur. Without these details, it is not possible to calculate the NPV accurately. The NPV represents the present value of the expected cash flows from the investment, discounted by the appropriate rate to account for the time value of money.

In this case, since we don't have the necessary data, we cannot determine the NPV and select the correct option from the given choices. It's important to have complete information about the cash flows and discount rate to accurately calculate the NPV and make informed decisions regarding investment opportunities.

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