One inlet pipe can fill an empty pool in 9 hours, and a drain can empty the pool in 15 hours. how long will it take the pipe to fill the pool if the drain is left open?

The length of y of the triangle is y = 9√2 units

Given data ,

Let the Triangle be ΔABC , such that

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

On simplifying , we get

From the trigonometric relations , we get

sin θ = opposite / hypotenuse

sin 45° = 9 / y

Multiply by y on both sides , we get

y = 9 / sin 45°

On simplifying , we get

y = 9√2 units

Hence , the length is y = 9√2 units

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Answer:

use midpoint formula

(5,-1)

Answer:

It would take 17 hours to get to the cabin.

Explanation:

1054 / 62 = 17

Answer:

Hours:         Elevation:

0                  3000

2                  2000

5                  500

Step-by-step explanation:

Time is always placed on the x (horizontal) axis, and the dependent variable on the y. Just find the number given and find the corresponding value to go with it! Hope this helps :)

The monthly payment and total cost for the bank loan are $180.55 and $2,166.60, respectively.

To calculate the monthly payments and total cost, we'll assume that the interest is calculated using the simple interest method for the bank loan and the add-on method for the store loan. For the bank loan: Principal amount (cost of sofa, table, and chairs) = $1,980; Interest rate = 13% per year; Repayment period = 1 year (12 months). Monthly interest rate = 13% / 12 = 1.0833%; Number of months = 12. Using the formula for calculating monthly payments on a simple interest loan: Monthly payment = (Principal amount + (Principal amount * Monthly interest rate * Number of months)) / Number of months. Substituting the values into the formula: Monthly payment = (1980 + (1980 * 0.010833 * 12)) / 12; Monthly payment ≈ $180.55; Total cost = Monthly payment * Number of months = $180.55 * 12 = $2,166.60. For the store loan:Principal amount (cost of sofa, table, and chairs) = $1,980; Interest rate = 11% per year; Repayment period = 1 year (12 months). Using the add-on method, the interest is simply added to the principal amount. Interest = Principal amount * Interest rate  = $1,980 * 0.11 = $217.80. Total amount to be repaid = Principal amount + Interest = $1,980 + $217.80 = $2,197.80. Monthly payment = Total amount / Number of months = $2,197.80 / 12 ≈ $183.15.

Therefore, the monthly payment and total cost for the bank loan are $180.55 and $2,166.60, respectively. On the other hand, the monthly payment and total cost for the store loan (using the add-on method) are $183.15 and $2,197.80, respectively. The bank payment and total cost are lower even though the stated interest rate is higher because the bank loan uses the simple interest method, which calculates interest based on the remaining balance after each payment. This results in lower interest charges over time. On the other hand, the add-on method used by the store loan calculates the interest based on the original principal amount, resulting in higher interest charges. Despite the higher stated interest rate, the bank loan's lower interest charges lead to lower monthly payments and a lower total cost compared to the store loan.

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The Excel function used when deciding to reject or fail to reject the null hypothesis is the T.TEST function.

This function is used to calculate the probability of obtaining the observed results or more extreme results, assuming that the null hypothesis is true. If the probability, also known as the p-value, is less than the significance level, typically 0.05, the null hypothesis is rejected, and it is concluded that there is sufficient evidence to support the alternative hypothesis.

Otherwise, if the p-value is greater than the significance level, the null hypothesis is not rejected, and it is concluded that there is not enough evidence to support the alternative hypothesis.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming that the null hypothesis is true. If the p-value is less than or equal to the level of significance (alpha) chosen for the test, typically 0.05 or 0.01, then the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than the chosen alpha level, then the null hypothesis is not rejected.

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What is a Matrix?

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital applications as well.

A)

\(\left[\begin{array}{cccc}$3.15& $3.79& $2.99&$3.49 \\$2.99& $2.89& $2.79 &$3.29\\ $3.74 &$2.98& $2.89& $2.99\end{array}\right]_{3 x 4}\)

B)

\(\left[\begin{array}{c}5*5\\4*5\\5*1\\4*5\end{array}\right]_{4x1}\)

C)

A x B = C

\(\left[\begin{array}{cccc}$3.15& $3.79& $2.99&$3.49 \\$2.99& $2.89& $2.79 &$3.29\\ $3.74 &$2.98& $2.89& $2.99\end{array}\right]_{3 x 4}\)  X    \(\left[\begin{array}{c}5*5\\4*5\\5*1\\4*5\end{array}\right]_{4x1}\)

=

\(\left[\begin{array}{c}183.46\\159.66\\179.51\end{array}\right]_{3x1}\)

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Answer:

ewan ko po pero yan yung alam ko4.3%

I hope its help

Answer:

Petter Sydow : A producer of division.

Step-by-step explanation:

Answer: Johann Heinrich Rahn

It was introduced by the Swiss mathematician, Johann Heinrich Rahn, in his work Teutsche Algebra (1659). This symbol was not much of a success in his home country of Switzerland or in Europe. But however, it was in both the Britain and also the USA.

Answer:4(2x + 1) = 12x + 3 - 4x +1=0

Step-by-step explanation:

group like terms =4(2x+1)=12x-4x+3+1

add similar elements=4(2x+1)=8x+3+1

add the numbers=4(2x+1)=8x+4

expand=8x+4=8x+4

subtract 4 from both sides 8x+4-4=8x+4-4

simplify=8x=8x

subtract 8x  both sides=0  

Answer:

A and C are discrete, B and D are continuous

Step-by-step explanation:

A is continuous because the temperature of the air can be any possible temperature and every possible number in between.

B is discrete because the cost can only be an exact amount of money. It couldn't be 88.7 centers, for example.

C is continuous because the distance includes every possible measurement between 0 and the total number of miles.

D is the same as B.

Answer:

200+50x

Step-by-step explanation:

If Han's cell phone plan costs $200, Han will have to pay $200 at the start, and since Han has to pay $50 dollars each month, and x = months, we can create 50x for $50 each month. Put both of these together, and we get 200+50x.

The results for several randomly selected employees are given below \(Y = 11.7 + 1.02x.\)

Below, we will discover the road equation, dissociation for each the management's conduct and fulfillment.

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Domain of function =  {-3 , -4}

Range of function =  {4 , -1 , -4}

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

Given,

points on graph of a function are

(-3 , 4) , (-3 , -1) , (-4 , -4)

Range is set of y-values,

Range = {4 , -1 , -4}

Domain is set of x - values

Domain = {-3 , -4}

Hence, Domain and range of function are {-3 , -4} and {4 , -1, -4} respectively.

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Answer:

x=1, y = -3

Step-by-step explanation:

2x -y=-11

6x + y = 3​

Add the two equations together

2x -y=-11

6x + y = 3​

--------------------

8x  = 8

Divide by 8

8x/8 = 8/8

x= 1

Now find y

6x+y = 3

6(1) +y = 3

6+y =3

Subtract 6 from each side

6+y-6 = 3-6

y = -3

The velocity function v(t) for the train traveling along a horizontal line is v(t) = 24t^2 - 6t + 2.

To get the velocity function v(t) for a train traveling along a horizontal line according to the position function s(t) = 8t^3 - 3t^2 + 2t + 4, you'll need to take the derivative of the position function with respect to time t.
Step 1: Differentiate the position function s(t) with respect to time t.
v(t) = ds(t)/dt = d(8t^3 - 3t^2 + 2t + 4)/dt
Step 2: Apply the power rule to each term.
v(t) = 3(8t^2) - 2(3t) + 2
Step 3: Simplify the expression.
v(t) = 24t^2 - 6t + 2
So, the velocity function v(t) for the train traveling along a horizontal line is v(t) = 24t^2 - 6t + 2.

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Answer:

24 and 135

Step-by-step explanation:

let x and y represent the numbers

x=15+5y

x-y=111

making x the subject in equation 2

x=111+y put into eqn 1

111+y=15+5y

-4y=-96 y=24

x=15+5(24)

x=135

Numbers which represents the given condition are \(24\)and \(135\).

" Number is defined as the count of the given quantity as per the given condition."

According to the question,

\('x'\) represents the first number

As per the condition we have,

Second number \(= 5x + 15\)

Substitute the numbers in the given condition we get,

\(5x+15-x=111\)

Simplify it to get the value of \('x'\)

\(4x + 15 = 111\\\\\implies 4x = 96\\\\\implies x = 24\)

Substitute the value of \('x'\) to get second number,

\(5 (24) +15\\\\= 135\)

Hence , numbers which represents the given condition are \(24\)and \(135\).

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Answer:

x = 6

y = 24

z = there is no z?

Step-by-step explanation:

All angles of a polygon add up to 360 degrees

The 2 parellel lines on top and bottom mean that there are 2 right angles on the left side

3y + 18 = 90

3y = 72

y = 24

15x + 30 + 10x = 180

25x = 150

x = 6

Answer:

a no association b non liner c liner d liner

Answer:

A) No association
B) Nonlinear
C) Linear
D) Nonlinear

Step-by-step explanation:

Linear Relationship: A linear relationship is one in which the scatter plot resembles a straight line. When one variable increases, the other variable increases or decreases proportionally.

Nonlinear Relationship: A nonlinear relationship is one in which the scatter plot does not resemble a straight line. It could resemble a curve or it could not resemble anything at all. A proportional increase or decrease in one variable does not result in a proportional rise or decrease in the other variable.

No Association: a graph of data showing discrete (individual) points of data that are not connected.

Using these definitions we can conclude whether the graphs are linear, nonlinear, or no association.

The values for \(\theta (0 \le \theta \le 2\pi)\) that satisfy the equation are\(\dfrac{4\pi} {3}, \dfrac{5\pi} {3}\). The correct option is a.

The trigonometric function \(sin \theta\)  is a continuous and periodic function. The relationship between the sides and the angles of the right angle triangle are denoted by trigonometric functions.

The values for\(\theta (0 \le \theta \le 2\pi)\)  that satisfy the equation are calculated as:

\(3sin \theta = sin\theta \sqrt{3}\)

This can be solved as:

\(3sin \theta = sin\theta \sqrt{3}\)

Subtract \(sin \theta\) from both sides of the equation:

\(2sin\theta = -\sqrt{3}\)

Divide both sides by 2:

\(sin\theta = -\sqrt\dfrac{3}{2}}\)

From the unit circle or trigonometric ratios, we know that \(sin \theta\) that corresponds to two angles are \(\dfrac{\pi}{3}\) and \(\dfrac{5\pi}{3}\).

Therefore, the values for\(\theta (0 \le \theta \le 2\pi)\) that satisfy the equation are \(\dfrac{4\pi} {3}, \dfrac{5\pi} {3}\)

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The solution to the trigonometric equation 3sinθ = sinθ - √3 for values of theta between 0 and 2π is θ = π/3 , 5π/3 (option d).

First, let's start by consolidating the trigonometric equation on one side. So, 3sinθ - sinθ = √3. This simplifies to 2sinθ = √3.

Now, we can divide both sides by 2 to solve for sinθ, so sinθ = √3/2.

Looking at the unit circle, the values of theta (0≤θ≤2π) that make sinθ = √3/2 are π/3 and 5π/3. Therefore, the solution to the equation 3sinθ = sinθ - √3 within the given domain is θ = π/3 , 5π/3.

This corresponds to option (d) in the given multiple choice responses.

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The quiz scores of Rich Borne's Chemistry 101 students are as follows: 24, 31, 47, 29, 31, 16, 48, 41, 50, 54, 37, 22, 54, 38, 7, and 16.the performance of Rich Borne's Chemistry 101 students on the quiz

To analyze this data, we can calculate various descriptive statistics such as the mean, median, mode, range, and standard deviation. The mean (average) score can be obtained by summing up all the scores and dividing by the total number of scores. The median represents the middle value when the scores are arranged in ascending order. The mode refers to the most frequently occurring score. The range is the difference between the highest and lowest scores, indicating the spread of the data. The standard deviation measures the variability or dispersion of the scores around the mean.

By calculating these descriptive statistics, we can gain insights into the performance of Rich Borne's Chemistry 101 students on the quiz and understand the central tendency and variability of their scores.

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Answer:

B. 5

Step-by-step explanation:

Step 1: Rewrite the equation a bit

\(\frac{7^\frac{3}{4}}{7^\frac{x}{8}}=\sqrt[8]{7}\\7^\frac{3}{4}^-^\frac{x}{8}=7^\frac{1}{8}\)

Step 2: Place a logarithm base 7 on both sides

\(7^\frac{3}{4}^-^\frac{x}{8}=7^\frac{1}{8}\\log_77^\frac{3}{4}^-^\frac{x}{8}=log_77^\frac{1}{8}\\(\frac{3}{4}-\frac{x}{8})log_77=\frac{1}{8}log_77\\(\frac{3}{4}-\frac{x}{8})1=\frac{1}{8}1\\\frac{3}{4}-\frac{x}{8}=\frac{1}{8}\)

Step 3: Solve for x

\(\frac{3}{4}-\frac{x}{8}=\frac{1}{8}\\\frac{6}{8}-\frac{x}{8}=\frac{1}{8}\\-\frac{x}{8}=-\frac{5}{8}\\\frac{x}{8}=\frac{5}{8}\\x=5\)

Neat exponent question :)

Answer:

A. is correct

Step-by-step explanation:

20 + 16 = 36 obviously

The equation 3000=150(1+. 025/12)^(12t) can be solved using logarithm  functions. The value of t can be found by isolating it on one side of the equation. After simplification, the final answer is approximately 4.37 years.

To solve the equation, begin by dividing both sides by 150:

3000/150 = (1 + 0.025/12)^(12t)

Simplify the left-hand side:

20 = (1.002083)^12t

Take the logarithm of both sides using the natural logarithm (ln):

ln(20) = ln[(1.002083)^12t]

Use the logarithm rule to bring down the exponent:

ln(20) = 12t ln(1.002083)

Divide both sides by ln(1.002083):

t = ln(20) / [12 ln(1.002083)]

Using a calculator, the final answer is approximately 4.37 years. Therefore, after 4.37 years, an initial investment of $150 at a monthly interest rate of 2.5% would grow to $3000.

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Step-by-step explanation:

x+ 172= 180-x

x+ 172= 180-x2x= 8

x+ 172= 180-x2x= 8x= 4°

180-4= 176

the angle is 4° and the measure of the other angle is 176°

Answer:

8

Step-by-step explanation:

The statement is true:

"Students are different in recognizing France versus Great Britain, and this difference is statistically significant."

The statement indicates that there is a statistically significant difference between the students' ability to recognize France and Great Britain on the geography test.

This suggests that the students' performance in identifying these two countries differs.

The other statements are not true:

This statement assumes that there is dependence between the observations, but there is no information provided to support this claim.

The z-test can be valid for comparing proportions if certain assumptions are met.

The values can be 0 or 1: This statement describes a binary outcome where students are represented by tickets, and their ability to pick France and Great Britain is represented by values of 0 or 1.

However, the given information does not explicitly mention a box model or the assignment of values to students.

It describes a geography test given to a sample of high-school students, where the focus is on their ability to identify two countries on an outline map.

There is no mention of a treatment, control group, or random assignment to different conditions.

Therefore, only the statement indicating a statistically significant difference in recognizing France versus Great Britain is true based on the given information.

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The probability that represents the likelihood of a single event occurring by itself is called marginal probability.

Marginal probability refers to the probability of an individual event happening independently without considering any other events. It focuses on a single variable or outcome without considering the relationship or dependencies with other variables.

To calculate marginal probability, you divide the number of times the specific event occurs by the total number of observations. For example, if you have a bag of marbles with different colors and you want to find the marginal probability of drawing a red marble, you would count the number of red marbles and divide it by the total number of marbles in the bag.

Marginal probability is often used when working with categorical variables or when studying the probability of a single event without considering any other variables or conditions. It provides a fundamental understanding of the likelihood of an event occurring in isolation, independent of any other factors.

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9514 1404 393

Answer:

  No

Step-by-step explanation:

If the relationship were proportional, the ratio of y to x would be a constant.

  y/x = 3/1 ≠ 7/3

x and y are not proportional.