3,1,-2,-4,-1, least to greatest

Thus, It takes Jacob a total of hours from San Antonio to Houston and then from Houston to Dallas 7 5/12 hours.

A mixed number combines a proper fraction and a whole number. To express a quantity higher than a but that less than the next whole number, mixed numbers as well as mixed fractions are utilised. Improper fractions can be used to create mixed numbers.

Given that:

Convert the given mixed fraction into proper fractions:

San Antonio to Houston = 3 1/3 hours

                                        = (3*3 + 1)/3 hours

                                        = (9 + 1)/3 hours

                                        = 10/3 hours

Now,

Houston to Dallas = 4 1/12 hours

                              = (4*12 + 1)/12 hours

                              = (48 + 1)/12 hours

                              = 49/12 hours

Total time from San Antonio to Dallas = San Antonio to Houston + Houston to Dallas

Total time from San Antonio to Dallas = 10/3 + 49 / 12

Taking LCM:

Total time from San Antonio to Dallas = (10*4 + 49)/12

Total time from San Antonio to Dallas = (40 + 49)/12

Total time from San Antonio to Dallas = 89/12

Total time from San Antonio to Dallas = 7 5/12 hours

Thus, It takes Jacob a total of hours from San Antonio to Houston and then from Houston to Dallas 7 5/12 hours.

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Answer:64

Step-by-step explanation:

Hope this helped

Answer:

0.7 oz

Step-by-step explanation:

2.25 OZ. + 3.8 OZ. = 6.05 OZ

6.05 oz ÷ 9 = 0.672 oz.

Round to nearest tenth = 0.7 oz

Each paint has 0.7 ounces.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

An artist mixes 2.25 ounces of red paint with 3.8 ounces of white paint.

And, She divides the paint into 9 equal parts.

Now, Total ounces;

2.25 OZ. + 3.8 OZ. = 6.05 OZ

Hence, Each parts of paint;

6.05 ÷ 9 = 0.672 ounces.

After round to nearest tenth = 0.7 ounces.

Thus, Each paint has 0.7 ounces.

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60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

According to the question,

We have the following information:

3 digits integers are to be made from 1,2,3,4 and 5

So, we will use permutation to find the possible number of digits that can be made if we apply all the given conditions.

Now, we have:

Total number of digits = 5

Number of digits to be made = 3

So, we have:

\(^{5} P_{3}\)

Solving this expression:

5*4*3

60

Hence, 60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

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Answer:

In this case the population of interest is the set of all men aged 30 to 87.

In this case the sample is the set of 25,892 men aged 30 to 87.

Step-by-step explanation:

A population is the set of all the data that can be collected and from which a smaller set of data is drawn for further examination. A population may denote to a group of individuals, articles, trials or measurements. A population can thus be called as a collection of information regarding subjects combined together by a common characteristic.

In this case the population of interest is the set of all men aged 30 to 87.

A sample denotes a smaller, controllable form of a larger cluster. It is a subset comprising of the characteristics of a bigger population. Samples are used in statistical experiments when the population under consideration is too large for the test to include all the members.

In this case the sample is the set of 25,892 men aged 30 to 87.

Answer:

The equation is 12 + 1.5w = 26

Step-by-step explanation:

Each week running = 12 miles

He wants to increase the number of miles he runs each week by 1.5 miles until he is running a total of 26 miles each week.

12 + 1.5w = 26

Where,

w = number of weeks to reach his goal

12 + 1.5w = 26

1.5w = 26 - 12

1.5w = 14

Divide both sides by 1.5

w = 14 / 1.5

= 9.33 weeks

Answer:

4

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

x          

 (— -  6) -  2  = 0

  4          

6     6 • 4

   6 =  —  =  —————

        1       4

x - (6 • 4)     x - 24

———————————  =  ——————

     4            4

 (x - 24)    

 ———————— -  2  = 0

    4        

        2     2 • 4

   2 =  —  =  —————

        1       4

(x-24) - (2 • 4)     x - 32

————————————————  =  ——————

       4               4

 x - 32

 ——————  = 0

   4  

x-32

 ———— • 4 = 0 • 4

  4  

x-32

Answer:

f(-3)=-1

f(4)=7

f(-1)=-3

f(12) = -24

Step-by-step explanation:

Piecewise Functions

The piecewise functions define different pieces or subfunctions where the domain is divided into parts according to some conditions on the independent variable.

The pieces of the function are defined as shown below:

\(f(x)=\left\{\begin{matrix}-1 &x\le -2\\ 2x-1 &-2<x\le 4 \\ -3x+8 &x>4 \end{matrix}\right.\)

Let's find the values of:

f(-3). Here the variable x is -3. We have to find the interval where x=-3 belongs. Since -3 ≤ -2:

f(-3)=-1

f(4). The variable x is 4 and it belongs to the second interval, thus

f(4)=2*4-1=7

f(4)=7

f(-1). x = -1. It belongs to the second interval, thus:

f(-1)=2*(-1)-1=-3

f(-1)=-3

f(12). x=12 belongs to the last interval since 12 > 4, thus:

f(12)= -3*12+8 = -36 + 8 = -24

f(12) = -24

Answer:

its 6

Step-by-step explanation:

it will help you cuz i did it right

Answer: 3/2

Step-by-step explanation:

the slope is 3/2 becuaes it is rise over run it connects at (4,1) and (6,4) and to get that you go up 3 and over 2 to the right

Answer:

i think its 3

Step-by-step explanation:

Answer:

It’s option three because both of their domains are all real numbers

Step-by-step explanation:

Answer:

The answer C  earn it

Investment X earns the greater amount of interest over a period of 2 years.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

Let's consider that Ian invests in X, then:

Principle amount, P = $6,000
Time, T = 2 Years

Rate of Interest, R = 4.5% at simple Interest = 0.045

The interest earned is:

Interest = PRT = $6,000 × 0.045 × 2 = $540

Now, consider that Ian invests in Y, then:

Principle amount, P = $6,000
Time, n = 2 Years

Rate of Interest, R = 4% at Compound Interest = 0.04

The interest earned is:

Interest = P(1+R)ⁿ - P

            = $6,000(1+0.04)² - $6,000

            = $489.6

Since $540>$489.6, therefore, Investment X earns the greater amount of interest over a period of 2 years.

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Answer:

Actually the answer is "A"

this is a very strange way to present a problem...

this issue her is that \((x^{a}) ^{b} = x^{a*b}\)

so you need 1/3 * 3 in the answer... none of them have 1/3 * 3

BUT !!!!! 1/3 + 1/3 + 1/3  is the same as  1/3 * 3 So "A" is the solution

Step-by-step explanation:

In quadrant II, the cosine of an angle is negative, while the tangent can be determined using the Pythagorean identity. Therefore, the value of cos(0) in quadrant II is -1, and the given value of tan(0) as -√19/17 is unrelated to the cosine value.

In quadrant II, the x-coordinate (cosine) is negative, while the y-coordinate (sine) is positive. Since angle 0 lies in quadrant II, the cosine value, cos(0), will be negative. Therefore, the value of cos(0) in quadrant II is -1.

On the other hand, the given value of tan(0) as -√19/17 is unrelated to the cosine value. The tangent of an angle is determined using the formula tan(θ) = sin(θ)/cos(θ). However, to find the cosine value, we should focus on the cosine function rather than the tangent.

In conclusion, in quadrant II, the value of cos(0) is -1, while the given value of tan(0) as -√19/17 is not relevant to determining the cosine value.

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Answer: y = -5x+2

Step-by-step explanation:

Slope = \(\frac{rise}{run}\) or \(\frac{y_{2}-y_{1}}{x_{2}-x{1}}\)

therefore, given those two points,

Slope = \(\frac{(-3)-7}{1-(-1)}\)

Slope = \(\frac{-10}{2}\)

Slope = -5

Since the m value is the slope, m = -5

In order to find the b value, just substitute the values in the equation with any of the two points given. I'll use (-1,7) but you can use the other one just fine.

let x =1, y = -3

-3=-5(1)+b

-3 = -5+b

-3+5 = b

b = 2

Plug b in the equation:

y=-5x+2

Answer:

154ft

I took the test. You're Welcome!

Final Answer: \(A\) = \(76.76\) \(in^2\)

Steps/Reasons/Explanation:

We will be trying to find the area of the rectangle. The formula tells us to multiply width times length. This means that we will multiply our length of 15.2 inches by a width of 5.05 inches to find the area of a rectangle.

The final answer would include \(in^2\) because we are multiplying both inches of the length and width to find the area.

Question: What is the area of a rectangle with the length of 15.2 inches and a width of 5.05 in?

Rectangle Area Formula: \(Area\) = \(width\) × \(length\)

\(A\) = \(15.2\) inches × \(5.05\) inches

\(A\) = \(76.76\) \(in^2\)

~I hope I helped you :)~

Answer:

D) y < 1/3x - 1

Step-by-step explanation:

the equation of the line is y= 1/3x-1, then the dark part represents all the values that less than the values of y. The broken line means 'strongly', then the sign should be '<'.

Step-by-step explanation:

there are in total 240 passengers.

out of these 240, there are 150+30=180 passengers that are in holiday.

and 240-180 = 60 passengers are not.

if we pick one passenger then the probability is 180/240 = 3/4 = 0.75 that he/she is on holiday.

remember : desired "events" over total "events".

i)

now we pick 2 passengers.

the probabilty for the first one to be on holiday is again

3/4 or 0.75.

if that event happens, then we have only 179 passengers out of now 239 to be on holiday.

and to pick one out of that pool to be on holiday is then

179/239 = 0.748953975...

and for both events to happen in one scenario we need to multiply both probabilities (it is an "and" relation, while an addition would be for an "exclusive or" relation).

the probabilty that we pick 2 passengers on holiday is

3/4 × 179/239 = 0.561715481... ≈ 0.5617

we cannot simply square the basic probability of 0.75 (0.75² = 0.5625), because that would mean we pick one passenger, then put him back into the crowd, and then pick a second time (with a chance to pick the same person again). like with rolling a die.

but that is not the scenario as I understand it. it is to pick a passenger, then keep that person singled out and pick a second passenger. hence the difference.

ii)

exactly one of the two is in holiday.

that means

either the first one is on holiday and the second one is not, or the the second one is and the first one is not.

now we model this logic statement in probabilty arithmetic.

please note that after the first pull we need to update the numbers for the remaining pool depending on the result of the first pull.

the total remaining is in both cases 239. but either the remaining people on holiday go down to 179 (and not in holiday stays 60), or the remaining people not on holiday go down to 59 (and on holiday stays 180).

so, the first one is on holiday, and the second one is not :

3/4 × 60/239 (remember : "and" relation)

= 3 × 15/239 = 45/239 = 0.188284519...

the first one is not on holiday, and the second one is :

60/240 × 180/239 = 1/4 × 180/239 = 45/239 =

= 0.188284519...

since there is no overlap of the potential events (there is no event that could be in both cases), this is an exclusive or relation, and we can add the probabilities.

so, the probability for exactly one of the picked passengers to be on holiday is

2×0.188284519... = 0.376569038... ≈ 0.3766

The first model of inequality satisfy the problem i.e 2w + 2* 4w ≤ 106

A rectangle is a four-sided, two-dimensional flat shape. The opposite sides of a rectangle's four sides are parallel and equal to one another. It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees. A particular kind of parallelogram that has all of its angles equal is the rectangle. A square is a rectangle with four equally sized sides. Let's now explore the characteristics of the rectangle in this essay.

Rectangles' essential characteristics are as follows:

A rectangle is a parallelogram.

The Perimeter of the rectangle is 2a + 2b where a and b are the two sides

Now , if w is the width of the rectangle then, the length is 4w given in problem.

Perimeter,

2w + 2* 4w

As it is given in the problem

2w + 2* 4w ≤ 106

The first model of inequality satisfy the problem.

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Using the Substitution Rule, we can find the integral of 1/(1+3x)dx. Let's begin by making the substitution u = 1+3x. This allows us to rewrite the integral as ∫1/u du. Differentiating u with respect to x, we get du/dx = 3, or equivalently, dx = du/3. Substituting this into the integral, we have (1/3)∫1/u du.

Now, we can solve the integral ∫1/u du. Integrating 1/u with respect to u gives ln|u|. Hence, the integral becomes (1/3)ln|u| + C, where C is the constant of integration.

To obtain the final answer, we substitute back the value of u, yielding (1/3)ln|1+3x| + C. Therefore, this expression represents the integral of 1/(1+3x)dx using the Substitution Rule.

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Answer: 23/12x = 1.91667x

Step-by-step explanation:

X/2+2x/3+3x/4

1/2x + 2/3x + 3/4x

2:1

Step-by-step explanation:

List all variables

Total people=120

year 11 students=120/2=60

year 10 students=60/3=20

subtract year 10 and 11 students from the total to get the number of year 9 students

year 9 students=120-60-20

=40

year9:year10

40:20

2:1

Value of variable 'n' as per the given condition number of 9 year students : number of 10 year students = n:1 is equals to 2.

" A variable is defined as the quantity which represents the change in value  as per the given condition in a mathematical problem."

According to the question,

Total number of students in school = 120

As per the conditions given we have,

Number of 11 year students = \(\frac{120}{2}\)

                                               = 60 people

Number of 11year students = 3 × ( Number of 10 year students)

⇒Number of 10 year students = \(\frac{Number of 11 year students}{3}\)

                                                   = \(\frac{60}{3}\)

                                                   = 20 people

Number of (11year + 10year +  9year ) students  = 120  

⇒ 60 + 20 + Number of 9 year students =120                                        

⇒Number of 9 year students = 120 - 80

                                                 = 40 people

Substitute the value in the given condition  to get the value of the variable we get,

Number of 9 year students : Number of 10 year students = n:1

⇒40 : 20 = n: 1

⇒n = 2

Hence, value of variable 'n' as per the given condition number of 9 year students : number of 10 year students = n:1 is equals to 2.

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The value of z in the solution set is approximately -8.33 for the determinant of the matrix of coefficients is −3, Option E is the correct answer.

To solve the system of equations, we can use the method of determinants. The value of z can be determined by finding the determinant of the matrix of coefficients.

The given system of equations can be represented as:

| 1 3 1 | | x | | -2 |

| 2 5 1 | × | y | = | -5 |

| 1 2 3 | | z | | 0 |

The determinant of the matrix of coefficients is -3, which is non-zero. This means that the system of equations has a unique solution.

To find the value of z, we need to calculate the determinant of the matrix obtained by replacing the z-column with the constants column:

| 1 3 -2 |

| 2 5 -5 |

| 1 2 0 |

Using the rule of determinants for a 3x3 matrix, we can calculate the determinant:

Det = (1 × (50 - -52)) - (3 × (20 - -51)) + (-2 × (2 × -5 - 51))

= (1(0 + 10)) - (3 × (0 + 5)) + (-2 × (-10 - 5))

= (110) - (35) + (-2 × -15)

= 10 - 15 + 30

= 25

Since the determinant is non-zero, the system has a unique solution. To find the value of z, we divide the determinant of the matrix obtained by replacing the z-column with the constants column by the determinant of the matrix of coefficients:

z = Detz / Det

= 25 / -3

= -8.33

Therefore, the value of z in the solution set is approximately -8.33.

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The question is -

Given the system of equations x + 3y + z = -2

                                                   2x + 5y + z = -5

                                                   x+ 2y + 3z = 0

The determinant of the matrix of coefficients is -3. The value of z in the solution set is:

(a) z=−2/3

(b) z=5/3

(c) z=4/3

(d) z=−2

(e) None of the above

Constant 'k' has the value in the form of factored after factorization, the provided polynomial equation is 2.

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).

The factor of a polynomial is the terms in linear or equation form, which are when multiplied together, give the original polynomial equation as result.

The given polynomial equation in the problem is,

\(8x^3 +6x^2 - 32x - 24\)

The factor of the polynomial equation are given as,

\(2(x+ k)(x - k)(4x +3)\)

First find out the factors to compare and find the value of k.The above equation has the unknown variable x and the highest power of this unknown variable is 3.

Take out the highest common factor 2, which can divide each term of the above equation (8, 6, -32, -24). Thus,

\(2(x+ k)(x - k)(4x +3)=2(4x^3 +3x^2 - 16x - 12)\)

Take out the highest common factor to make the groups as,

\(2(x+ k)(x - k)(4x +3)=2(x^2(4x +3) - 4(4x + 3))\\2(x+ k)(x - k)(4x +3)=2(4x +3) (x^2 -4)\\2(x+ k)(x - k)(4x +3)=2(4x +3) (x^2 -2^2)\)

Use the property of difference of the square for the (x²-2²) term as,

\(2(x+ k)(x - k)(4x +3)=2(4x +3) (x +2)(x-2)\\2(x+ k)(x - k)(4x +3)=2(x +2)(x-2)(4x +3)\)

On comparing the two equation, we get the value of k as 3. Thus, the value of the constant 'k' in the factored form factorization the provided polynomial equation is 2.

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Answer:

C

Step-by-step explanation:

The probability distribution for the duration of a service call is a discrete uniform distribution with X taking on values of 1, 2, 3, or 4 hours with equal probability of 0.25 for each value.

Since the different types of malfunctions occur at the same frequency, the probability of each type of malfunction is equal to 1/4.

Let X be the duration of a service call in hours. Then, the probability distribution for X can be represented by the following :

X P(X)

1 0.25

2 0.25

3 0.25

4 0.25

Here, P(X) represents the probability of the service call taking X hours to complete. Since the probabilities for each duration are equal, this is a discrete uniform distribution.

To verify that this is a probability distribution, we can check that the probabilities sum to 1:

0.25 + 0.25 + 0.25 + 0.25 = 1

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Complete question is:

A technician services mailing machines at companies in the phoenix area. depending on the type of malfunction, the service call can take one, two , three , or four hours. the different types of malfunctions occur at the same frequency. if required, round your answers to two decimal places. a. develop a probability distribution for the duration of a service call.