E
Sam ran 63,756 feet in 70 minutes. What is Sam's rate in
miles per hour? (There are 5,280 feet in one mile.)

9514 1404 393

Answer:

  3

Step-by-step explanation:

Vertical angles share a vertex point, and have opposite rays for sides. In short, they are across the point of intersection from each other. Vertical angles do not have a common side (they are not adjacent).

The first part of the problem is to identify angle NCA. That is shown in red in the attachment. The vertical angle is across the point of intersection. It is angle 3.

We have drawn the number line and included the given points, see attached number line.  

What is the fraction?

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely the numerator, and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.

On the number line above, the decimal values and fractions are labeled as follows:

0.63 is labeled between 0 and 1.

34/100 is labeled at the same point as 0.34, between 0 and 1.

0.02 is labeled between 0 and 1.

7/10 is labeled at the same point as 0.7, between 0 and 1.

Therefore, we have drawn the number line and included the given points, see attached number line.  

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Por definición de probabilidad condicional, la probabilidad de que un paciente sea hombre, dado que finge una enfermedad es 12,5 %.

En primer lugar, debes saber que la Probabilidad es la mayor o menor posibilidad de que ocurra un determinado suceso.

En otras palabras, la probabilidad establece una relación entre el número de sucesos favorables y el número total de sucesos posibles.

La probabilidad condicional P(A|B) es la probabilidad de que ocurra un evento A, sabiendo que también sucede otro evento B. Esto es, es la probabilidad de que ocurra el suceso A si ha ocurrido el suceso B. Se define como:

P(A|B) = P(A∩B)÷ P(B)

En este caso, se llama suceso A al evento de que los pacientes fingen tener una enfermedad (para obtener un certificado médico), mientras que el suceso B será el evento de que los pacientes del consultorio son hombres.

Siendo el suceso A∩B (A intersección B)  cuando A y B ocurren simultáneamente, entonces sabes:

Entonces, la probabilidad de que un paciente finge una enfermedad,  dado que el paciente es un hombre es calculada como:

P(A|B) = P(A∩B)÷ P(B) → P(A∩B)= P(A|B)× P(B)

Reemplazando los valores correspondientes:

P(A∩B)= 0,5× 0,1

Resolviendo:

P(A∩B)=0,05

Finalmente, la probabilidad de que un paciente sea hombre,  dado que finge una enfermedad, es calculada como:

P(B|A) = P(A∩B)÷ P(A)

Reemplazando los valores correspondientes:

P(B|A) = 0,05÷ 0,4

Resolviendo:

P(A∩B)=0,125= 12,5 %

Finalmente, la probabilidad de que un paciente sea hombre, dado que finge una enfermedad es 12,5 %.

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Answer:

See below

Step-by-step explanation:

To find the mean, you take each data point, add them together, and divide it by the number of data points.

Problem 1

Mean of High Temperatures = (65+67+54+52+63+69+75)/7 = 445/7 = between 63 and 64

Problem 2

Mean of Low Temperatures = (61+55+37+29+34+42+54)/7 = 312/7 = between 44 and 45

By elimination, the solution of the system of equations, 5x - y = 4 and 2x - y = 1, is (1 , 1).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

Subtracting the two equations will eliminate the variable y.

5x - y = 4     (equation 1)

2x - y = 1     (equation 2)

3x      = 3

x = 1

Substitute the value of x to any of the two equations and solve for y.

5x - y = 4     (equation 1)

5(1) - y = 4

-y = 4 - 5

-y = -1

y = 1

Hence, the solution of the system of equations is (1 , 1).

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Answer:

n>5

Step-by-step explanation:

move the 20 onto the other side of the > by subtracting 20 on the left side and adding 20 on the right side

now you have

-3n>7n-20

move the 7n onto the other side the same way. subtract 7n from one side and add it to -3n. now you have

4n>20

this is called adding similar terms or inverse operations what ever you wanna call it. Now you divide N by 4. This is because 4n can be simplified to 4×N and the opposite of multiplication is division. you do the same on the other side.

n/4>20/4.

you are left with n>5

Answer:

n<2

Step-by-step explanation:

Subtract 20 from both sides 20-3n-20>7n-20

Simplify -3n>7n-20

Subtract 7n from both sides -3n-7n>7n-20-7n

Simplify again -10n>-20

multiply both sides by -1 (-10n)(-1) < (-20)(-1)

Simplify 10n<20

Divide both sides by 10 Then you get your answer

The inequality that would help Ravi the best to find m, the number of lessons he would need to give in order to buy the guitar will be 27 + 22 m ≥ 129.99.

Cost of guitar that Ravi wants to buy = $ 129.99

The amount of money that he has = $27

The amount of money that he will get per lesson = $ 22

Let the number of lessons given by Ravi be m.

Now, we know that he has to earn $ 129.99 or more to purchase the guitar.

So, the inequality will become:

27 + 22 m ≥ 129.99

Therefore, we get that, the inequality that would help Ravi the best to find m, the number of lessons he would need to give in order to buy the guitar will be 27 + 22 m ≥ 129.99.

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If we standardize both variables what would the regression equation the mortgage amount will be 220.88 and the interest amount will be 7.768.

\(b_1\) = r*\(S_{xy}/S_{xx}\)

= -0.84

\(b_0 = y - b_1x\)

Regression model is used to identify the relation between two variables.In the relation between two variables.

From the given question the regression model fits best to identify the mortgage amount from interest rates.

The interest rate and mortgage both are quantitative values so the regression model is most suitable for this given condition.

Therefore If we standardize both variables what would the regression equation the mortgage amount will be 220.88 and the interest amount will be 7.768.

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Answer: 27/4 or 6 3/4

Step-by-step explanation:

Answer:

8 divided by b

Step-by-step explanation:

"8 over b" is the same as this : \(\frac8b\)

Remember, a fraction is a division problem where the numerator is being divided by the denominator.

8 over b is 8 divided by b

-Chetan K

The probability that the Davis boys will occupy the first two seats in the row, the Jones boys will occupy the next three seats, and the Smith boys will occupy the last four seats is 7.937×\(10^{-4}\).

There are \(\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]\) potential arrangements for the nine boys if we do not make a distinction amongst boys with the same last name. We are curious in the likelihood of a specific one of these configurations.

Probability = \(\frac{1}{\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]}\)

                  = \(\frac{2!3!4!}{9!}\)

                 = 0.0007937

                = 7.937×\(10^{-4}\)

Hence, the probability is 7.937×\(10^{-4}\).

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Answer:

Y-intercept is at 1 and slope of the graph is 2

Step-by-step explanation:

When plotting this equation use the formula y=mx+b. The variable B is the y intercept its where you start your graph. The variable M is the slope and for that you use rise/run.

To graph 2 you would start at 1 because it's the int. And u would go up 2 and right 1 and just follow that pattern

Answer:

10.44y - 12.32

Step-by-step explanation:

Use the distributive property.

4(2.61y − 3.08) =

= 10.44y - 12.32

Answer:

Step-by-step explanation:

boody boody

The total number of sides of a regular polygon with each exterior angle of measure 30 degrees is equal to 12.

Let us consider 'n' be the number of sides of the regular polygon.

Let 'y' be the measure of each of the exterior angle of regular polygon.

y = 30 degrees

Measure of each of the exterior angle of regular polygon 'y'

= ( 360° ) / n

⇒ n = ( 360° / y )

Substitute the value we get,

⇒ n = ( 360° / 30° )

⇒ n = 12

Therefore, the number of sides of a regular polygon with each of the exterior angle 30 degrees is equal to 12.

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The above question is incomplete, the complete question is:

How many sides does a regular polygon have when each exterior angle measures 30 degrees?

The most reasonable range of intervals will depend on the specific characteristics of your data set and the level of granularity you want in your histogram.

The range of data values ​​and the number of data points should be considered when choosing intervals for a histogram to represent your data.

In this particular dataset, the data values ​​range from 22 to 91. You can divide this range into equal intervals. 10, 5, or 2.5 centimeters, depending on the granularity you want in your histogram.

The number of information focuses is generally little at 18 focuses. A great run show of thumb for choosing the number of interims is to require the square root of the number of information focuses.

 In this case, it is approximately 4.24. This can be rounded to 5 or 6 intervals depending on the range selected.

For illustration, in case you select an interim of 10 centimeters, you'll be able to make the taking after the histogram.

20 30 40 50 60 70 80 90

1 shot 1 shot

In this histogram, the first interval contains the values ​​22 and 28, so there is a ball in that interval. The second interval contains the values ​​36, 37, 41, and 54, so there are 4 balls in this interval.

The third interval contains the values ​​57, 58, and 59, so there are 3 balls in this interval. The fourth interval contains the values ​​62, 68, and 76, so there are 3 balls in this interval.

The fifth interval contains the values ​​83, 85, 88, and 89, so there are 4 balls in this interval. The sixth interval contains the values ​​90 and 91, so there are two balls in this interval.

Overall, the most reasonable range of intervals will depend on the specific characteristics of your data set and the level of granularity you want in your histogram.

In general, it is important to choose equally sized intervals to capture a range of data values.  

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Answer:

a. x² + 6x + 9 = -22 + 9

Step-by-step explanation:

they moved the 22 to the right by subtracting it. this leaves a binomial on the left side, which if what you want to solve it.

then they completed the square by dividing b (6) by 2 = 3. then squaring 3 to get 9.

if you added 9 to the left, then you have to add 9 to the right, therefore resulting in -22 + 9.

Answer:

In TTM/Imagine Math it is top left or a.

Step-by-step explanation:

The number of email transmissions (E) is 8300, the number of cellphone calls/texts (C) is 14600, and the number of sat-phone calls (S) is 5200.

Let's denote the number of email transmissions as E, the number of cellphone calls/texts as C, and the number of sat-phone calls as S.

From the given information, we can set up the following equations:

Equation 1: E + C + S = 28100 (Total number of transmissions)

Equation 2: C = E + S + 1100 (Cellphone calls/texts outnumber the combination of email and sat-phone transmissions by 1100)

Now, let's calculate the total number of minutes spent on each type of transmission:

Total minutes spent on email transmissions = 8E

Total minutes spent on cellphone calls/texts = 3C

Total minutes spent on sat-phone calls = 5S

According to the problem, the total average number of minutes spent on all transmissions is 136200, so we can set up the following equation:

Equation 3: 8E + 3C + 5S = 136200

Now we have a system of three equations (Equations 1, 2, and 3) with three unknowns (E, C, and S). We can solve this system of equations to find the values of E, C, and S.

Using Equation 2, we can substitute the value of C in terms of E and S into Equations 1 and 3:

Equation 1: E + (E + S + 1100) + S = 28100

2E + 2S + 1100 = 28100

2E + 2S = 27000   (Equation 4)

Equation 3: 8E + 3(E + S + 1100) + 5S = 136200

8E + 3E + 3S + 3300 + 5S = 136200

11E + 8S = 132900  (Equation 5)

Now we can solve Equations 4 and 5 simultaneously to find the values of E and S. Once we have E and S, we can substitute them back into Equation 2 to find the value of C.

Solving Equations 4 and 5:

Multiply Equation 4 by 11 and Equation 5 by 2 to eliminate the variable E:

22E + 22S = 297000  (Equation 6)

22E + 16S = 265800  (Equation 7)

Subtract Equation 7 from Equation 6 to eliminate E:

(22E - 22E) + (22S - 16S) = 297000 - 265800

6S = 31200

S = 5200

Substitute the value of S back into Equation 4 to find E:

2E + 2(5200) = 27000

2E + 10400 = 27000

2E = 16600

E = 8300

Substitute the values of E and S into Equation 2 to find C:

C = E + S + 1100

C = 8300 + 5200 + 1100

C = 14600

Therefore, the number of email transmissions (E) is 8300, the number of cellphone calls/texts (C) is 14600, and the number of sat-phone calls (S) is 5200.

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Answer:

Step-by-step explanation:

Common ratio is:

The next term is:

The probability of event A or event B occurring, denoted as P(A or B), can be calculated by adding the probabilities of each event and subtracting the probability of both events happening simultaneously.

To calculate P(A or B), we first need to determine the individual probabilities of event A (the six-sided die landing on three) and event B (Abdul rolling doubles). Let's denote the probability of A as P(A) and the probability of B as P(B).

Assuming the die is fair, it has six equally likely outcomes (numbers 1 to 6). The probability of event A, P(A), is the chance of rolling a three, which is 1 out of 6 since there is only one favorable outcome.For event B, rolling doubles, there are six possible outcomes: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). Therefore, the probability of rolling doubles, P(B), is 6 out of 36, or 1 out of 6.

To calculate P(A or B), we need to consider the possibility of both events happening simultaneously. Since event A and event B are independent, we can multiply their probabilities: P(A and B) = P(A) * P(B) = (1/6) * (1/6) = 1/36.Finally, to find P(A or B), we add the probabilities of A and B and subtract the probability of A and B occurring together: P(A or B) = P(A) + P(B) - P(A and B) = 1/6 + 1/6 - 1/36 = 11/36.

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Answer:

See below

Step-by-step explanation:

Rotating CLOCK wise would result in -4,3 becoming  3,4 in the first quadrant

The variable is up against an upper limit. in a maximization problem, a binding less than or equal to (≤)

constraint indicates that the variable associated with the constraint has reached or is at its upper limit. It implies that the variable cannot increase further without violating the constraint.

This constraint acts as a restriction that limits the potential values the variable can take in the optimization problem.

When a constraint is binding, it means that the optimal solution to the problem is achieved when the constraint is satisfied with equality. In the context of a maximization problem,

if a variable is up against an upper limit and the constraint is binding, it suggests that the variable is already maximizing its value within the given constraint.

In contrast, if the constraint is not binding, it means that the variable has not reached its upper limit and has the potential to increase further while still satisfying the constraint. In such cases, the variable can be increased to improve the objective function value and optimize the problem further.

It's important to note that the shadow price, also known as the dual value or marginal value, represents the rate of change of the objective function with respect to a constraint. It indicates the sensitivity of the objective function to changes in the constraint.

The sign of the shadow price is not determined by the direction of the constraint (≤ or ≥), but rather by the problem formulation and the specific constraints and variables involved.

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According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same. The formula for this property can be expressed in real numbers a, b and c. If a × c = b × c.

Property of Equality:

The equivalence property describes the relationship between two equal quantities. If you apply a math operation to one side of the equation, you must also apply it to the other side of the equation to maintain balance.

That is, a property that does not change the truth value of an equation or does not affect the equivalence of two or more quantities is called an equality property. These equality properties help solve various algebraic equations and define equivalence or equilibrium relationships.

Multiplicative Property of Equality:

According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same.

The formula for this property can be expressed as for the real numbers a, b, and c.

If a × b, then, a × c = b × c.

In algebra, the multiplicative property of an equation helps extract unknown terms from an equation. Because multiplication and division are opposites of each other.

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When dealing with the simultaneous occurrence of two events A and B, the probability can be determined by using the probability of one event and the conditional probability of the other event given that the first event has occurred. Both P(A) * P(B|A) and P(B) * P(A|B) are valid ways to calculate this probability.

The concept of probability is fundamental in various fields such as mathematics, statistics, and even in everyday life. The probability of the simultaneous occurrence of two events A and B is a critical concept in probability theory. According to the definition, the probability of A and B occurring at the same time is equal to the probability of A multiplied by the conditional probability of B given that A has occurred. This equation is also valid in the reverse case, where the probability of B and A occurring simultaneously is equal to the probability of B multiplied by the conditional probability of A given that B has occurred.

Understanding the relationship between the probability of two events and their conditional probabilities is essential in predicting the likelihood of these events happening together. In real-life situations, this concept can be used to determine the probability of two events such as the success of a product launch and the corresponding increase in sales. The probability of these two events occurring simultaneously can be predicted by analyzing the probability of the product launch's success and the conditional probability of sales increasing given that the product launch is successful.

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Answer:

Step-by-step explanation:

see the figure below

As O is mid point of rectangle

distance between O to AB and DC is same

also distance between O to AD and BC is same

OP and OQ are perpendiculars so it is straight

and OP divides AB into equal segments as distance between O to AD and BC is same

same goes with OQ

Answer:

Liz is correct

Step-by-step explanation:

Given

See attachment for complete question

Required

Who is correct? Daniel or Liz

From the attached data, we have:

\(Time: 1\frac{3}{4},\ 2\frac{1}{2},\ 2,\ 2\frac{3}{4},\ 1,\ 1\frac{3}{4},\ 1\frac{1}{4},\ 3,3\frac{1}{4},\ 3\frac{3}{4},\ 2,\ 2\)

The total number of students is:

\(n = 12\)

The data that represents  \(2\frac{1}{2}\) or more is:

\(Time: 2\frac{1}{2},\ 2\frac{3}{4},\ 3,3\frac{1}{4},\ 3\frac{3}{4}\)

The frequency of this is 5

The frequency that represents \(2\frac{1}{2}\) or less will be 7

This means that less than half spend \(2\frac{1}{2}\) or more

and more than half spend \(2\frac{1}{2}\) or more

Hence, Daniel is incorrect. Liz is correct

Answer:

The answer is 12,0!

Step-by-step explanation:

Each model should be produced on a weekly basis to maximize net profit is $75,900.

What is Net profit?

In both business and accounting, net income or profit is an entity's revenue less cost of goods sold, costs, depreciation and amortisation, interest, and taxes for a certain accounting period.

As given,

Number of products sold:

T ≥ 1.5G

Maximize Profit Z = 150T + 130G

Labor Constraint:

Labor hours Available:

Production Department:

Number of labor hours available per day = 58 × 7 = 406

Number of days in a week = 5

Number of lobor ours available per week = 406 × 5 = 2030

Assembly Department:

Number of labor hours available per day = 25 × 7 = 175

Number of days in a week = 5

Number of labor hours available per week = 175 × 5 = 875.

Labor hours Required:

Labor hours required for G1 model:

Labor hours required at Production department = 3.5G

Labor hours required at assembly department = 2G

Labor hours required for T1 model:

Labor hours required at Production department = 4T

Labor hours required at Assembly department = 1.5T

Total labor hours required at Production department = 3.5G + 4T

Total labor hours required at Assembly department = 2G + 1.5T.

Constraint:

Labor hours required ≤ Labor hours Available.

Production department Labor constraint

3.5G + 4T ≤ 2030

Assembly department Labor constraint:

2G + 1.5T ≤ 875

The function:

Maximum Profit Z = 150T +130G

Constraint:

3.5G +4T ≤ 2030

2G + 1.5T ≤ 875

T ≥ 1.5G

Suppose that for example:

10.5G +12T = 6090

 16G + 12T = 7000

Solve both equations simultaneously,

5.5G = 7000 - 6090

5.5G = 910

    G = 910/5.5

    G = 363

Since, T > G

Hence,

T = 363,

G = 165

Calculate Profit:

150T + 130G = 150 × 363 + 130 × 165

                     = 54450 + 21450

                     = 75900

Hence, each model should be produced on a weekly basis to maximize net profit is $75,900.

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On solving the provided question, we can say that the probability it is back or female is  55/6 and P( 1 or 6) = 12/7

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

1 gray female, 2 gray males, 2 black male and 2 black males

picked one random kitten

the probability it is back or female is \(^7C_4 + ^6C_3\) = 7!/4!*3! + 6!/3!*3!

= 7*6*5/6+6*5*4/6 = 55/6

A jar contain 7 balls numbered from 1 to seven. You randomly pick a ball. It is numbered 1or 6.

P( 1 or 6) = 12/7

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