f(x) = 3x² + 4x – 6
g(x) = 6x3 – 5x2 – 2
Find (f – g)(a).

1. The man must work 9.6 hours per day to complete the job in 10 days.

2. Average price of the 11 brands is P259.45.

3. Mr Macapagal's car covered 14.62 kilometers on a liter of gasoline.

1. Let x be the number of hours per day that the man must work to complete the job in 10 days. We can set up a proportion based on the amount of work to be done:

8 hours/day x 12 days = x hours/day x 10 days

Simplifying this proportion, we get:

96 = 10x

x = 9.6

Therefore, the man must work 9.6 hours per day to complete the job in 10 days.

2. The total cost of the 9 brands of ice cream is:

9 x P254 = P2286

The total cost of the 11 brands of ice cream is:

9 x P254 + P282 + P292 = P2854

The average price of the 11 brands of ice cream is:

P2854 / 11 = P259.45

Therefore, the resulting average price of the 11 brands is P259.45.

3. To find the kilometers covered by Mr. Macapagal's car on a liter of gasoline, we can divide the total distance covered by the amount of gasoline consumed:

175.45 km / 12 L = 14.62 km/L

Therefore, Mr Macapagal's car covered 14.62 kilometers on a liter of gasoline.

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The area of the given sector for the following parameter in which radius and central angle are given is = 165.792 sq .

What about sector?

A sector refers to a region of a circle that is bounded by two radii and an arc of the circle between them. The two radii of the sector form an angle at the center of the circle, and the length of the arc between them determines the size of the sector. The area of a sector can be calculated using the formula A =(θ/360)\(\pi r^2\) , where θ is the central angle of the sector in degrees, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14159. Sectors are often used in geometry and trigonometry to calculate the area and other properties of circular shapes.

Define central angle:

A central angle is an angle that is formed by two radii of a circle that share a common endpoint at the center of the circle. A central angle's measurement is the same as the circumference of the circle's path that it intercepts.  In other words, if a central angle has a measure of x degrees, then the arc intercepted by that angle on the circumference of the circle will also have a measure of x degrees.

According to the given information:

The area of the sector = /\(360^{o}\) (\(r^{2}\))

⇒ Where  = \(132^{o}\) and radius = 12

⇒ Area of the sector = \(\frac{132^{o} }{360^{o} }\) x \(\pi r^{2}\)

⇒ Area of the sector = 0.366 x 3.14 x 144

                                   = 165.792 sq .

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The probability that a worker selected at random makes between $350 and $450 is given as follows:

68%.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

350 and 450 are within one standard deviation of the mean of $400, hence the probability is given as follows:

68%.

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The probability that a worker selected at random makes between $350 and $450 is approximately 0.6827.

To calculate this probability, we need to use the concept of the standard normal distribution. Firstly, we convert the given values into z-scores, which measure the number of standard deviations an individual value is from the mean.

To find the z-score for $350, we subtract the mean ($400) from $350 and divide the result by the standard deviation ($50). The z-score is -1.

Next, we find the z-score for $450. By following the same process, we obtain a z-score of +1.

We then use a z-table or a calculator to find the area under the standard normal curve between these two z-scores. The area between -1 and +1 is approximately 0.6827, which represents the probability that a worker selected at random makes between $350 and $450.

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The number of machines to minimize the unit cost is 110 and minimum cost is 10,389 .

What is Quadratic Equation?

Quadratic equation can be defined as the equation which is in the form of ax^2 +bx +x = 0.

where a,b,c are constants.

Given ,

The standard form of a quadratic is given by:

ax^2 + bx + c

So for our function, we can say,

a = 0.1

b = -22

c = 11599

We can find the vertex (x-coordinate where minimum value occurs) by the formula -b/2a

So,

= -(-22) / 2*0.1

=22/0.2

= 110

Plugging this value into original function would give us the minimum (unit cost):

C(x) = 0.1 x ^2 - 22x +11599

C(x) = 0.1(110*110) - 22(110)+11599

C(x) = 110(11-22) + 11,599

C(x) = -11(110) + 11599

C(x) = -1210 + 11599

C(x) = 10,389

Hence , The number of machines to minimize the unit cost is 110 and minimum cost is 10,389 .

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There are 2024 ways in which the instructor can choose 3 students from a class of 24 students for the field trip.

A combination is a mathematical technique for calculating the number of possible arrangements in a set of items where the order of the selection is unimportant.You can choose the items in any order in combinations.

Permutations and combinations are often confused. In permutations, however, the order of the selected items is critical. For example, the arrangements ab and ba are equal in combinations (considered as one arrangement), but different in permutations.

There is a way you can calculate combinations using a formula. This formula is:

\(nC_r = \frac{n! }{ r!(n-r)! }\)

where

n = total no. of items;

r = items selected for the combination;

"!" is the factorial

Given,

Total number of students in class , n = 24

Number of students selected, r = 3

So, the number of ways that 3 students can be selected from 24 students is

\(24C_3=\frac{24 !}{3!(24-3) !}\\\\=\frac{24 !}{3!*21 !}\\\\=\frac{3!*24*23*22*21 !}{3!*21 !}\\\\=\frac{24*23*22}{3*2*1}\\\\=2024\)

Hence, the students can be selected in 2024 ways for the field trip.

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The variance of X is 195.

We can use the following equations to solve the problem:

Var(X) = E(X^2) - [E(X)]^2

E(X*) = E(X) + 13

We are given that E(X) = 1, Var(X^2) = 5, and E(X*) = 14.

Substituting E(X*) into the equation for E(X), we get E(X) + 13 = 14, which gives E(X) = 1.

Using the equation for Var(X^2), we can find E(X^2) as follows:

Var(X^2) = E(X^2) - [E(X)]^2

5 = E(X^2) - 1

E(X^2) = 6

Substituting these values into the equation for Var(X), we get:

Var(X) = E(X^2) - [E(X)]^2

Var(X) = 6 - 1^2

Var(X) = 5

Therefore, the variance of X is 195.

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Answer:

150 students

Step-by-step explanation:

1300 - 700 = 600

600 x .25 = 150  (25% = 0.25)

The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

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Answer:

50 yards.

Step-by-step explanation:

Since we know that 5 yards can make 2 costumes, we can divide 5/2 to find 2.5 yards are needed to make one costume. Then you can multiply 2.5*20 to get 50 yards needed for 20 costumes. Hope this helps :)

A negative exponent means that you should take the reciprocal of the base and use the positive exponent:
5^(-4) = 1 / 5^4.So, the answer is: C. 1 / 5^4

To solve this problem, use the properties of exponents. Specifically, when multiplying numbers with the same base, you add the exponents. In this case, the base is 5, and the exponents are 3 and -7.

5^3 × 5^(-7) = 5^(3 + (-7))

Now, add the exponents:

3 + (-7) = -4

So, the expression becomes:

5^(-4)

A negative exponent means that you should take the reciprocal of the base and use the positive exponent:

5^(-4) = 1 / 5^4

So, the answer is:

C. 1 / 5^4.

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Answer:

2

Step-by-step explanation:

Degree is the highest power of a term

I hope im right!

Answer:

2

Step-by-step explanation:

hello :

the degree of x2 - 17x + 2x - 5.00 is : 2

Answer:

Step-by-step explanation:

Answer:

Please refer to the attachment

Hope it helps

Pls mark me as the brainliest

Thank you

Answer:

decay

Step-by-step explanation:

The function is in the form

y = a (b)^x

a is the initial value and b is the growth or decay factor

When b < 1  it is decay

When b > 1 it is growth

Since b = .93 it is decay

Answer:

14.60

Step-by-step explanation:

Note that there are 100 centimeters in 1 meter. The plant is 13 meters tall, and grows 8 centimeter every month. It is asking you for 20 months worth (x = 20) of growth.

First, solve for the amount of centimeters total in 20 months:

8 centimeter per month x 20 months = 160 centimeters per 20 months.

Remember, there are 100 centimeters in every meter. Therefore:

160 centimeter/ 100 centimeters per meter = 1.60 meters.

Add the growth to the original height:

13.00 + 1.60 = 14.60

14.60 meters is your answer.

~

Answer:

  42 feet

Step-by-step explanation:

The length of fence is equal to the perimeter of the shape. That can be found by adding the lengths of the edges.

__

Clockwise from the upper left corner, the sum of edge lengths is ...

  2 +6 + 3 + 6 + 2 + 7 + 1 + 1 + 5 + 1 + 1 + 7 . . . . feet

  = 8 + 9 + 9 + 2 + 6 + 8 . . . . added pairwise

  = 17 + 11 + 14

  = 28 + 14 = 42 . . . feet

42 feet of fence is needed to go around the garden

Given:

The scale factor of the actual sports utility vehicle to the toy model is 50:1.

Actual length = 7 feet

Actual width = 5 feet

To find:

The length and width of the toy model.

Solution:

a. Let l be the length of the toy model, then

\(\dfrac{\text{Actual length}}{\text{Length of the toy model}}=\dfrac{50}{1}\)

\(\dfrac{7}{l}=\dfrac{50}{1}\)

\(7=50l\)

\(\dfrac{7}{50}=l\)

\(0.14=l\)

Therefore, the length of the toy model is 0.14 feet.

b. Let w be the width of the toy model, then

\(\dfrac{\text{Actual width}}{\text{Width of the toy model}}=\dfrac{50}{1}\)

\(\dfrac{5}{w}=\dfrac{50}{1}\)

\(5=50w\)

\(\dfrac{5}{50}=w\)

\(0.10=w\)

Therefore, the width of the toy model is 0.10 feet.

There is a 34% chance that the randomly purchased item from the manufacturer will last longer than 8 years.

The question is asking for the probability that a randomly purchased item from a manufacturer will last longer than 8 years. To answer this question, we must use the normal distribution formula and find the area under the curve between 8 and infinity.

The formula for the normal distribution is as follows:

\(1/(\sigma\sqrt{2\pi}) e^{-((x-\mu)^2)2\sigma^2}\)

Where μ is the mean and σ is the standard deviation.

In this problem, μ = 6.5 years and σ = 0.8 years.

Using the formula, the probability of the randomly purchased item lasting longer than 8 years is 0.34.

To calculate the probability, we use the z-score formula, which is \((x-\mu)/\sigma\). Plugging in 8-6.5/0.8 gives us a z-score of 1.875.

Using the z-table, we can find the area under the curve, which is 0.34. This means that the probability of the randomly purchased item lasting longer than 8 years is 0.34.

Therefore, the answer to the question is that there is a 34% chance that the randomly purchased item from the manufacturer will last longer than 8 years.

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Answer:

y = 8

Step-by-step explanation:

The equation of a line parallel to the x- axis has equation

y = c

where c is the value of the y- coordinates the line passes through.

Then

y = 8 ← is equation of line parallel to the x- axis

Answer:

Yes, the lines on the graph at 3 and -3 a part  of the solution,

Step-by-step explanation:

The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.

Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.

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Answer:

(4, 5)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define systems

3x + 3y = 27

x - 3y = -11

Step 2: Solve for x

Step 3: Solve for y

the answer Is 0.24

Step-by-step explanation:

2.1 times 4.4 is

9.24

3.6 divided by 0.4 is

9

9.24 - 9

= 0.24

Remeber guys, we need to use pemdos. In this case we need to do 1. Multiplication

2. Division

3. Subtraction

We cannot do subtraction or division first. We need to go by order.

Answer: \(4 \frac{4}{9}\)

Step-by-step explanation:

By using the formula for area of triangle using coordinates, the following results are obtained

13) Area of triangle = \(\frac{15}{2} \ sq. units\)

14) Area of triangle = \(\frac{49}{2} \ sq. units\)

What is area of triangle?

Area of a triangle is the total space taken by the triangle. If the coordinates of triangle are \((x_1, y_1), (x_2, _2) \ and \ (x_3, y_3)\), then area of triangle is calculated by the formula

Area of triangle = \(\frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|\)

13) The given coordinates are E (3, 1), F(3, -2) and G(-2, 2)

Area of triangle =

\(\frac{1}{2}|3(-2-2) + 3(2-1) + (-2)(1 -(-2))|\\\\\frac{1}{2}|3(-4) + 3(1) -2(3)|\\\\\frac{1}{2}|-12 + 3 - 6|\\\\\frac{1}{2}|-15|\\\\\frac{15}{2} \ sq. units\)

14) The given coordinates are E (-3, 4), F(4, 4) and G(3, -3)

Area of triangle =

\(\frac{1}{2}|(-3)(4-(-3)) + 4(-3-4) + 3(4-4)|\\\\\frac{1}{2}|(-3)(7)+4(-7)+3(0)]\\\\\frac{1}{2}|-21-28+0|\\\\\frac{1}{2}|-49|\\\\\frac{49}{2} \ sq. units\)

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Answer:

hope it helps.........

The percentage that is less than the average number of shoppers in the original store at any time is 60%.

Little's law is a fundamental principle in queueing theory that relates the average number of customers in a stable system to the average time that a customer spends in the system.

The law states that the average number of customers N in the system is equal to the average rate of customer arrivals r multiplied by the average time W that a customer spends in the system:

Here we have

For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes.

=> Number of shoppers per minute = 1.5    

=> Rate of shoppers per minute = 1.5

The manager estimates that each shopper stays in the store for an average of 12 minutes.

Hence, by Little’s law, the number of shoppers N = r × t

=> Number of shoppers = (1.5) × 12 = 18  

Let the estimated average number of shoppers in the original store at any time be 45.    

So, the number of shoppers is (45 - 18) less than the original i.e 27

Percentage  [ 27/45 ] × 100 = 60%  

Therefore,

The percentage that is less than the average number of shoppers in the original store at any time is 60%.

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The final exponential expression in fractional form for "the eighth root of fifty-seven to the sixth degree" is 57^(3/4).

To express the given description as a symbolic expression and then convert it into an exponential expression in fractional form, we'll follow these steps:

Step 1: Symbolic Expression

The description states "the eighth root of fifty-seven to the sixth degree." Let's denote this as √[57]^(1/8)^6.

Step 2: Removing Radical

To eliminate the radical (√), we can rewrite it as a fractional exponent. The numerator of the fractional exponent corresponds to the power (6) applied to the base, and the denominator corresponds to the index of the root (8).

So, the expression becomes (57^(1/8))^6.

Step 3: Simplifying Exponents

To simplify the exponent, we multiply the powers:

(57^((1/8)*6))

Simplifying further:

(57^(6/8))

Step 4: Fractional Form

The exponent 6/8 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:

(57^(3/4))

Therefore, the final exponential expression in fractional form for "the eighth root of fifty-seven to the sixth degree" is 57^(3/4).

This means that we raise 57 to the power of 3/4 to represent the original description. The fraction 3/4 indicates taking the eighth root of 57 and then raising it to the sixth power.

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