The hypotenuse of a right triangle measures 15 cm and one of its legs measures 14 cm. Find the measure of the other leg. If necessary, round to the nearest tenth

1.4m/s is the rate that Roberto is walking. We know the formula for calculating the time i.e. t= d/r.

The term "distance" refers to how far we move. The rate is a measurement of our trip speed. Time is measured by how far we travel. The distance an object will travel over time and at a specific average rate is the subject of rate problems.

Given,

Distance = D

D= 1.4t

Rate= ?

Substituting the given values in the formula t= d/r

where,

t= time in seconds

d= distance

r= rate

We get,

t= 1.4t/r

t/1.4t= 1/r

t gets cancelled

so we have,

1/1.4= 1/r

r= 1.4m/s

Therefore, 1.4m/s is the rate at which Roberto is walking.

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The complete question is as follows:

Roberto is walking. The distance, D, in meters, he walks can be found using the equation D=1. 4t, where t is time in seconds.

What is the rate that Roberto's walking in meters per second?

The measure of the side MR is given as 20

We have to first find the value of the angle

∠TQR = 180 - (35 + 25)

= 180 - 60

= 120 degrees

180 - 120 = 60 degrees

angle TPR  = 90 degrees

next we have to find ∠PTQ

= 180 - (90 + 60)

= 180 - 150

= 30 degrees

given that TMN = TQR

TNP = PTQ

So if TMN = 35 degrees since TQR = 35 degrees

PTQ = 30, so TNP = 30 degrees

The measure of QR = 4 since MN = 4

NP = pq

np = 6

Hence the measure of MR

= 4 + 6 + 6 + 4

= 20

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The hypotheses for a chi-square test of independence on the data that auditors compared opinions about treatment (very good/acceptable/poor) at four VA hospitals (labeled a,b,c,d) among veterans aged 50 and above are:

Null hypothesis, H0: There is no association between the opinions about treatment of the VA hospitals and veterans aged 50 and above.

Alternative hypothesis, Ha: There is an association between the opinions about treatment of the VA hospitals and veterans aged 50 and above.

Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.

An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.

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A basis for the space of 2x2 lower triangular matrices is [tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex].

Lower triangular matrices resemble the following:

[tex]\left[\begin{array}{ccc}a&0\\b&c\end{array}\right][/tex]

We can write it like this:

[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right][/tex]

This demonstrates the set's

[tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex]

covers the set of lower triangular matrices with dimensions 2x2. Moreover, these are linearly independent, so attempting to

[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]

leads to

[tex]\left[\begin{array}{ccc}a&0\\b&c\end{array}\right] =\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]

which results in a = b = c = 0 right away. As there is no other way to

[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]

, these matrices are linearly independent if a = b = c = 0.

Since

[tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex]

they serve as a foundation by spanning the collection of 2x2 lower triangular matrices and being linearly independent.

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Answer: 240 miles in 2 hours

Step-by-step explanation:

we know the car is traveling 60 km per half hour (30 minutes)

so to find km per hour, multiply both by 2.

the rate of speed is 120 miles per 60 minutes (1 hour)

multiply 120 mph by the 2 hours given = 240 miles in 2 hours

Answer:

240 km in 2 hours

Step-by-step explanation:

If the car travels 60 km in 30 minutes, then its speed can be calculated as follows:

Speed = distance ÷ time

Speed = 60 km ÷ (30 minutes ÷ 60) = 120 km/hour

Since the car is traveling at a constant speed, we can use the formula:

Distance = Speed × Time

To find how far the car will travel in 2 hours, we can substitute the values we have found:

Distance = Speed × Time

Distance = 120 km/hour × 2 hours

Distance = 240 km

Therefore, the car will travel 240 km in 2 hours if it continues at the same constant speed.

Tomas can spend at most $118.50 each day. The inequality equation is 5.5x ≤ 651.75.

Tomas has $1,000 to spend on a vacation. His plane ticket costs $348.25. If he stays 5.5 days at his destination, how much can he spend each day? Write an inequality and then solve.

Let x be the amount that Tomas can spend each day. Since Tomas has to pay for the plane ticket, he will have $1,000 − $348.25 = $651.75 left to spend on the rest of the vacation.

Then, since he is staying for 5.5 days, the total amount he can spend would be 5.5x dollars. The inequality that represents the problem is as follows:

5.5x ≤ 651.75

To solve for x, divide both sides by 5.5

5.5x/5.5 ≤ 651.75/5.5x ≤ 118.5

Therefore, Tomas can spend at most $118.50 each day.

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Answer:

The answer to this solution is 118.5 a day

Step-by-step explanation:

The original price is $1,000 for the ticket it costs $348.25 and Tomas is staying for 5.5 days so dividing 651.75 by 5.5 is the ANSWER 118.5

Answer:

Step-by-step explanation:

2(-4) - 3(-2) = -2

 -8 + 6 = -2

   -2 = -2

Answer:

Answer is in the picture

Step-by-step explanation:

Hope you understand :)

Answer:

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

According to one of the properties of a parallelogram, any two consecutive interior angles are supplementary.

We know supplementary angles add up to 180°.

Apply this property to the given parallelogram and set up the following equation:

Answer:

The sequence is defined as follows:

a1 = 5

an = an-1 - 5, for n > 1

Using this definition, we can find the first four terms of the sequence as follows:

a1 = 5

a2 = a1 - 5 = 5 - 5 = 0

a3 = a2 - 5 = 0 - 5 = -5

a4 = a3 - 5 = -5 - 5 = -10

Therefore, the first four terms of the sequence are: 5, 0, -5, -10.

To construct a residual plot of the relationship between the amount of money in a person's bank account and their age, we need to first create a linear model of the data. Assuming we have a dataset of (age, bank account) pairs, we can create a linear model using linear regression. Let the model be:

bank account = β0 + β1 * age + ε

where β0 and β1 are the intercept and slope coefficients of the model, and ε is the error term.

Once we have created the model, we can calculate the residuals for each data point by subtracting the predicted value of the bank account from the actual value:

residual = bank account - (β0 + β1 * age)

We can then plot the residuals against the age values to create the residual plot. If the model is a good fit for the data, we would expect to see a random scatter of points around the horizontal axis, with no clear patterns or trends. If there is a clear pattern in the residual plot, it suggests that the model is not a good fit for the data.

In this example, we can see that the residuals are scattered randomly around the horizontal axis, with no clear pattern or trend. This suggests that a linear model is a good fit for the data.

Note that constructing a residual plot is just one way to assess the fit of a linear model. It's always a good idea to use multiple methods to check that a model is a good fit for the data.

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Number of  prints Jim ordered last month is 271

Let's assume Jim ordered "P" prints last month. The cost of ordering "P" prints would be the sum of the monthly charge and the cost of each print, which is given by the equation:

Cost = Monthly Charge + (Cost per Print x Number of Prints)

Substitute the values in the equation

$17.79 = $6.95 + ($0.04 x P)

Simplifying the equation, we get:

$10.84 = $0.04 x P

Dividing both sides by $0.04, we get:

P = $10.84 / $0.04

Divide the numbers

P = 271

Therefore, Jim ordered 271 prints last month.

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The two-period moving average model and the two-period weighted moving average model are both common forecasting methods used to predict future demand. and we understand that the model with the lower MAD and MSE values will have the most accurate forecast.

To determine which model is better for this particular data set, we need to compare the accuracy of each model. To do this, we will calculate the Mean Absolute Deviation (MAD) and the Mean Squared Error (MSE) for each model.
For the two-period moving average model, we can calculate the forecast for period 7 by taking the average of p5 and 6:

Period 7 forecast = (Gallons in Period 5 + Gallons in Period 6)/2

For the two-period weighted moving average model, we can calculate the forecast for period 7 by using the weights of 0.6 and 0.4:

Period 7 forecast = (0.6 x Gallons in Period 5) + (0.4 x Gallons in Period 6)

We can then compare the accuracy of each model by calculating the MAD and MSE. To calculate MAD, we need to subtract the actual demand in each period from the forecasted demand and take the absolute value:

MAD = |Actual demand – Forecasted demand|

To calculate MSE, we need to square the differences between the actual demand and the forecasted demand:

MSE = (Actual demand – Forecasted demand)^2

After calculating the MAD and MSE for each model, we can compare the results to determine which model is better for this data set. The model with the lower MAD and MSE values will have the most accurate forecast.

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Measure of last angle of triangle is 117°

The triangle's characteristics include:

The angle sum property states that the sum of a triangle's three interior angles is always 180 degrees.

Angle of Triangle are

28° and 35°

Let the third angle be x

According to angle sum property

28°+35°+x=180°

x=117°

Measure of last angle of triangle is 117°

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The complete question is;

Find the measure of the last angle of the triangle below.

28⁰

35°

Image is attached below.

Answer: 11

Step-by-step explanation:

Turn it into an improper fraction so 8 from 8 1/4 to 33/4

Then just divide by 3/4

This will give you 11

In linear equation, 54 hours time will Rosmaria spend running if she trains for 12 week.

What is a linear equation in math?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Rosmaria runs 1.5 hours.

In the first week, Rosmaria ran 3 hours.

Rosmaria spend running if she trains for 12 weeks = 12 * 1.5 * 3

                                                             = 54

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The expression for the number of non-adult sizes is s - 19.

A value or amount is represented by an expression, which is a collection of numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division. Calculations, complicated mathematical equations, and issues in a variety of disciplines, including science, engineering, economics, and statistics, may all be solved using expressions. Functions that depict a connection between variables, such as sin(x) and log(x), can also be included in expressions. Expressions are frequently employed to simulate real-world circumstances and provide predictions based on mathematical analysis.

Given that the total number od sweatshirts = s.

The number of non-adult sweatshirts can be calculated by:

Number of non-adult sizes = Total number of sweatshirts sold - Number of adult sizes

= s - 19

Hence, the expression for the number of non-adult sizes is s - 19.

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Two teaspoons of salt contains 7.16 grams of Na or 7160 milligrams of Na.

Given that a soup recipe calls for two teaspoons of salt. We need to find out how many milligrams of sodium is that?

1 teaspoon = 5.69 grams      1 gram = 1000 milligrams

2 teaspoons of salt = 2 * 5.69 grams = 11.38 grams of salt

11.38 grams of salt = 11.38 * 1000 milligrams = 11380 milligrams of salt

Now, we have to find out how much sodium (Na) is there in 11380 milligrams of salt. Sodium chloride is the chemical name for table salt (NaCl). So, the atomic mass of NaCl can be calculated as follows:

Na = 1Cl = 35.45

Atomic mass of NaCl = Na + Cl= 1 + 35.45= 36.45

So, 1 mole of NaCl = 36.45 grams         11380 milligrams of NaCl = 11380/1000 grams= 11.38/36.45 moles

Therefore, Moles of Na = 11.38/36.45 = 0.3121

mol Atomic mass of Na is 22.99 g/mol.

So, 1 mole of Na weighs = 0.3121 * 22.99= 7.16 grams

Therefore, 11380 milligrams of NaCl = 7.16 grams of Na. Hence, two teaspoons of salt contains 7.16 grams of Na or 7160 milligrams of Na.

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The probability that more than 8 hours are needed to grade all of the exams is about 52%

The probability of a standard normal distribution is the area under the curve of the normal distribution function within a specified interval.

Let X represent the random variable to grade an exam, and let Y represent the total time to grade all exams

The number of students = 50

Therefore;

Y = 50·X

The properties of the normal distribution indicates that we get;

E(Y) = E(50·X) = 50·E(X) = 50 × 9.7 = 485

Var(Y) = Var(50·X) = 50²·Var(X) = 50² × 1.92² = 9025

The standard deviation, SD(Y) = √(Var(Y)) = √(9025) = 95

The probability that more than 8 hours are needed can be found using the z-score of the normal distribution as follows;

8 hours = 480 minutes

Z = (480 - 485)/95 ≈ -0.0526

The probability obtained from a standard normal table, is therefore;

P(Z > -0.0526) = 1 - 0.48006 ≈ 0.52

The probability that more than 8 hours are needed to grade all students is therefore about 0.52 or 52%

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Answer:

Here, x represents the amount (in liters) of the 25% saline solution to be added.

We can see that the 25% saline solution needs to be mixed with the 10% saline solution to obtain a mixture that is 15% saline. The ratio of the volumes of the 25% and 10% solutions can be found by subtracting the concentrations of the two solutions and dividing by the difference between the desired concentration and the concentration of the 10% solution:

x / (3.33 - x) = (15 - 10) / (25 - 10) = 5/15 = 1/3

Multiplying both sides by 3.33 - x, we get:

x = (1/3) (3.33 - x)

Multiplying both sides by 3, we get:

3x = 3.33 - x

Solving for x, we get:

x = 0.833 liters

Therefore, 0.833 liters of the 25% saline solution must be added to 3.33 liters of the 10% saline solution to obtain 4.163 liters of a 15% saline solution.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex](x-20)^2=x^2-20[/tex]

Expanding LHS gives:

  [tex]x^2-40x+400=x^2-20[/tex]

         [tex]-40x+400=-20[/tex]          (subtracted [tex]x^2[/tex] from both sides)

                   [tex]-40x=-420[/tex]        (subtracted 400 from both sides)

                         [tex]x=\frac{-420}{-40}[/tex]          (divided both sides by-40)

                         [tex]x=\frac{21}{2} =10\frac{1}{2}[/tex]

Answer:

- [tex]\frac{8}{13}[/tex]

Step-by-step explanation:

let n be the other rational number , then

- [tex]\frac{26}{3}[/tex] n = [tex]\frac{16}{3}[/tex]

[a number × its reciprocal = 1 ]

multiply both sides by the reciprocal - [tex]\frac{3}{26}[/tex]

n = [tex]\frac{16}{3}[/tex] × - [tex]\frac{3}{26}[/tex]  ( cancel the 3 on numerator/ denominator )

n = - [tex]\frac{16}{26}[/tex] = - [tex]\frac{8}{13}[/tex]

Answer: 37.85

Step-by-step explanation:

Substitute: 3.2x0.2+6.1^2

Calculate the product or quotient: 0.64+6.1^2

Calculate the power: 0.64+37.21

Calculate the sum or difference: 37.85

Answer:  37.85

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Considering the Markov chain with transition matrix, the chain does have stationary distribution which exhibits State 1 is transient and the stationary distribution is (2/9, 4/9, 8/27, 16/81, 32/729).

(a) Yes, the chain has a stationary distribution. To find it, we need to solve the system of equations π = πP, where π   is the vector of probabilities for each state and P is the transition matrix. This gives us:

π_{1} = π(1/2)

π_{2} = π(1/3) + π(2/2)

π_{3}= π(2/4) + π(3/2)

π_{4} = π(3/5) + π(4/2)

π_{5}= π4/5

We also have the normalization condition π1 + π2 + π3 + π4 + π5 = 1.

Solving this system of equations, we get:

π_{1} = 10/97

π_{2} = 30/97

π_{3}= 40/97

π_{4} = 14/97

π_{5}= 3/97

So the stationary distribution is (10/97, 30/97, 40/97, 14/97, 3/97).

(b) State 1 is transient, and all other states are recurrent.

(c) Yes, the chain still has a stationary distribution. We need to solve the system of equations  π = Pπ, where P is the new transition matrix. This gives us:

π_{1} = π(1/2)

π_{2} = π(1/3) + π(2/2)

π_{3}= π(2/4) + π(3/2)

π_{4} = π(3/5) + π(4/2)

π_{5}= π4/5

We also have the normalization condition π1 + π2 + π3 + π4 + π5 = 1.

Solving this system of equations, we get:

π_{1} = 2/9

π_{2}  = 4/9

π_{3} = 8/27

π_{4} = 16/81

π_{5}  = 32/729

So the stationary distribution is (2/9, 4/9, 8/27, 16/81, 32/729)

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When a 666-sided fair die is rolled, then the probability of rolling greater than 4 is  0.9940 or 99.40%.

Given that the die is fair and has 666 sides. So, each face of the die will have a probability of 1/666, i.e.,

p(1) = p(2) = ... = p(666) = 1/666.

The probability of rolling greater than 4 is P(roll greater than 4), which is the sum of the probabilities of rolling a 5, 6, 7, 8, 9, ..., 666. So,

P(roll greater than 4) = p(5) + p(6) + p(7) + ... + p(666)

P(roll greater than 4) = (1/666) + (1/666) + (1/666) + ... + (1/666)

(There are 661 terms)P(roll greater than 4) = 661(1/666)

P(roll greater than 4) = 0.9940 (rounded to four decimal places)

Hence, the probability of rolling greater than 4 is 0.9940 or 99.40%.

Alternatively, the probability of rolling greater than 4 is

   1 - P(roll less than or equal to 4)P(roll greater than 4)

= 1 - P(roll less than or equal to 4)P(roll greater than 4)

= 1 - (p(1) + p(2) + p(3) + p(4))P(roll greater than 4)

= 1 - (4/666)P(roll greater than 4)

= 1 - 0.0060P(roll greater than 4)

 = 0.9940 (rounded to four decimal places)

Hence, the probability of rolling greater than 4 is 0.9940 or 99.40%.

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According to the formula, the length of one side of the hexagon is 21/4 or 5.25 units.

What is the perimeter of the regular hexagon?

Let's call the length of one side of the regular hexagon "s". Since a hexagon has six sides, the perimeter of the hexagon is 6s.

According to the problem, this is equal to the perimeter of an isosceles triangle with legs of x+4 and a base that is 3 less than one of the legs.

The perimeter of the isosceles triangle is given by:

perimeter = 2(x+4) + (x+1)

where (x+1) is the length of the base (which is 3 less than one of the legs).

Setting the perimeters equal, we get:

6s = 2(x+4) + (x+1)

6s = 3x + 9

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

We also know that the side lengths of the hexagon are 2x. Substituting this into the equation for "s", we get:

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

x = 3

Therefore, the length of one side of the hexagon is:

s = (3/2)x + (3/4) = (3/2)(3) + (3/4) = 9/2 + 3/4 = 21/4

So the length of one side of the hexagon is 21/4 or 5.25 units.

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In order to make the same amount of money, they would have to each sell 5 bicycles. They would both make $500

To find the number of bicycles they would need to sell to make the same amount of money,

We can set Jim's and Tom's weekly earnings equal to each other and solve for the number of bicycles:

250 + 50x = 400 + 20x

30x = 150

x = 5

So they would need to sell 5 bicycles to make the same amount of money.

To find out how much money they would make for selling 5 bicycles, we can substitute x = 5 into either equation.

Let's use Jim's equation:

250 + 50(5) = 500

So they would make $500 for selling 5 bicycles.

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Answer:

The diver descends:

50 seconds x 5 feet/second = 250 feet

The diver ascends:

54 seconds x 4.4 feet/second = 237.6 feet

Therefore, the total change in elevation is:

250 feet (descent) - 237.6 feet (ascent) = 12.4 feet

So, the diver's final elevation is:

0 feet (starting elevation) - 12.4 feet (change in elevation) = -12.4 feet

Therefore, the diver ends up 12.4 feet below sea level.

Answer:

it is 1

Step-by-step explanation:

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