Which statement is TRUE for f(x)= x³+4x²+x-6?

The cost of one calzone given the information in the table is $8.75 (first option).

The first step is to form a system of equation to represent the information in the question:

16p + 12c = 269 equation 1

20p + 8c = 275 equation 2

Where:

p =cost of pizzas bought

c = cost of calzones bought

The elimination method would be used to determine the cost of one calzone.

Multiply equation 1 by 5 and equation 2 by 4

80p + 60c = 1345 equation 3

80p + 32c = 1100 equation 4

Subtract equation 4 from equation 3

28c = 245

Divide both sides of the equation by 28

c = 245 / 28

c = $8.75

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Answer:

10208

Step-by-step explanation:

116x88=10208

The system of equation to calculate the number of apples and oranges is given by x + y = 15 and 0.5x + 0.65y = 9 .

The number of apples is x and the number of oranges is y .

Total number of fruits bought is 15.

Hence we can write the equation for the number of fruits as:

x + y = 15

This is our first equation of the system.

Now each apple costs $ 0.5 , cost of x apples = 0.5x

Now each orange costs $0.65 , cost of y apples = 0.65y

Total cost is 9 apples.

Hence total cost can be represented by 0.5x + 0.65y = 9

Therefore the system of equations to represent the above situation is given by:

x + y = 15

0.5x + 0.65y = 9 .

A system of equations, often known as a set of simultaneous equations or an equation system, is a finite type of linear problem for which common solutions have been identified.

A system of equations can be classified similarly to a single equation. In everyday life, equation systems are utilised to model problems when the unknown values can be represented as variables.

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Answer:

Step-by-step explanation:

o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex ...

Answer:

y=-8 or y=8

Step-by-step explanation:

First you swap the sides of the question:

y^2=64

then you simplify the equation and take the square root of both sides of the equation and remember to use both positive and negative roots:

y= + 8 (make sure the "+" has the line under it that looks like this _)

Then you separate the solution and write the solutions, with a + sign and - sign, which gives you your solution:

y=-8

y=8

or

y1=-8 , y2=8

Answer:The Council of Trent 

Step-by-step: explanationwas the formal Roman Catholic reply to the doctrinal challenges of the Protestant Reformation. It served to define Catholic doctrine and made sweeping decrees on self-reform, helping to revitalize the Roman Catholic Church in the face of Protestant expansion.

:

Answer:

E

Step-by-step explanation:

Since rectangle have 90 degree angles, Angle D is a 90 degree angle.

Side CD is 3

AD is 4

We found both of those using the definition of rectangle.

[tex] \tan(x) = \frac{opp}{adj} [/tex]

[tex] \tan(x) = \frac{4}{3} [/tex]

E is correct

The answer to this Question based on donations is 40 and 85

What is a donation?

Giving things to poor and needy people is called donating things and this word thing can contain anything from money to household things etc

Here music club has made ticket sales and donations are collected but both are different amounts for 2 weeks

hence we can add them to get total expense

On adding ticket sales and donations for 2 weeks we get 23t + 50 + 17t + 35

= 40t + 85 where t represents price for one ticket

Hence our answer is just coefficients that are 40 and 85 respetively

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The example of stratified sampling is a health educator wanted to study the sleeping habits of the undergraduate students in her study.

For her study, the researcher chose a simple random sample of size 150 from each of the classes (150 freshmen, 150 sophomores, 150 juniors, and 150 seniors) for a total of 600 sampled students. a poll asked a random sample of 1,112 adults whether they believe that the use of marijuana for medical reasons should be legalized.

Sampling:

In statistics, quality assurance, and research methodologies, sampling is the selection of a subset of individuals (statistical sample) from a statistical population in order to estimate characteristics of the population as a whole. A statistician tries to collect a representative sample of the population in question. Sampling is less costly than measuring the entire population, provides faster data collection, and can provide insight when the entire population cannot be measured.

Stratified Sampling:

When the population embraces a number of distinct categories, the frame can be organized by these categories into separate "strata." Each stratum is then sampled as an independent sub-population, out of which individual elements can be randomly selected. The ratio of the size of this random selection (or sample) to the size of the population is called a sampling fraction. There are several potential benefits to stratified sampling.

There are, however, some potential drawbacks to using stratified sampling.

First, identifying strata and implementing such an approach can increase the cost and complexity of sample selection, as well as leading to increased complexity of population estimates.

Second, when examining multiple criteria, stratifying variables may be related to some, but not to others, further complicating the design, and potentially reducing the utility of the strata.

Finally, in some cases (such as designs with a large number of strata, or those with a specified minimum sample size per group), stratified sampling can potentially require a larger sample than would other methods (although in most cases, the required sample size would be no larger than would be required for simple random sampling).

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System utilization is 0.26 or 20%

System utilization is the action of using something, i.e., making practical and effective use of it. Put simply; the term refers to the use of something or the process of using it effectively. In the supply chain industry, utilization may also refer to the percentage of available time that a machine, device, warehouse, or employee is actively is working.

We can also use the term for a fraction of the available time that a system is operating.

In a warehouse, space is essential, so warehouse space utilization measures the efficiency with which the warehouse uses its inventory storage capacity. Low values for this KPI may suggest that the warehouse is too large, inventory is being stored in improper places, demand forecasting is not accurate or that inventory replenishment processes are slow.

given that:

a single-bay car wash with a poission arrival rate and an exponential service time has cars arriving at an average of 8 minutes apart with an average service time of 4 minutes

System utilization(ρ) = λ(arrival rate)/μ(service rate)

arriving rate = 8min ⇒ λ = 4/hr

service rate = 4min ⇒ μ = 15/hr

System utilization(ρ) = λ/μ

System utilization(ρ) = 4/15 = 0.26

System utilization is 0.26 or 20%

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Answer: 965cm =9.65 meters

Step-by-step explanation:

Answer:  B. 278%

Step-by-step explanation:

The area of the circle formula is area = pi times r^2

Let's find the area of Circle X.

3.14 times 5^2 = 78.5

Let's find the area of Circle Y

3.14 times 3^2 = 28.26

Now take 78.5 divided by 28.26, then times 100% = 277.7% or ground up to 278%

So the answer is B. 278%

Answer:

- 1/2 × 8 = -4

-1/2 × -2 = 1

- 1/2 × 6/7 = - 3/7

B. -4 + 1 - 3/7x

D. -3-3/7x

The square root of the given expression√49 is equal to ±7.

As given in the question,

Given expression is equal to √49.

Let the square root of 49 be equal to the variable x we get,

x = √49

Write factors of 49 in form of prime numbers we get,

49 = 7 × 7

⇒ x = √ 7 × 7

⇒ x = √7²

Apply law of exponent ( mᵃ )ᵇ = mᵃᵇ we get,

here m = 7 , a = 2 and b = 1/2

⇒ x = ( 7² )^1/2

⇒ x = ( 7 )^( 2 × 1/2 )

⇒ x = ( 7 ) ¹

Any number raise to one is equal to number itself.

⇒ x = 7

Therefore, the square root of the given expression √49 is given by 7.

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The new height after the increase is 207cm

Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. To calculate the percentage we need to have the initial value and the increased (new) value. In other words, we can say that percentage increase is a measure of percent change which gives the extent to which a quantity gains magnitude.

therefore %increase =( final value- initial value)/initial value ×100

let the final height of bush be x

15= (x-180)/180 ×100

2700= 100x-18000

collect like terms

2700+18000=100x

100x= 20700

divide both sides by 100

x= 20700/100

x= 207cm

therefore the new height of the bush is 207cm

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Answer: 2/13

Step-by-step explanation:

There are 4 queen (Q) & 4 king (K) cards in a standard deck of 52 cards . Therefore,required probability of drawing a queen or a king = P(QUK) = P(Q) + P(K) = 4/52 + 4/52 = 2/13 .

The volume of Ms. Armstrong's toolbox is 3,375 cm³.

Cube: A cube is a three-dimensional object with six square faces that are equal. Each of the six square faces of the cube has the same dimensions.

The total number of cubic units that a cube occupies in a three-dimensional space is its volume. A cube is a three-dimensional shape with eight vertices, twelve edges, and six faces. As a result, the space enclosed by a cube's six faces is its volume.

mathematically,

Volume = side³

because Armstrong has a 15-inch toolbox side.

Volume = 15³

Volume = 3,375

hence, Ms. Armstrong's toolbox has a volume of 3,375 cm3.

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The value of x in the expression -2.5(4x - 4) = - 6 is 4/3.

There are three types of basic arithmetic laws of operation.

Commutative law for addition and multiplication states,

a + b = b + a.

a×b = b×a.

Distributive law states,

a(b ± c) = ab ± ac.

Associative law states,

a + (b + c) = (a + b) + c.

Given, -2.5(4x - 4) = - 6.

∴ - 2.5(4x) - 2.5(-4) = - 5.

- 12x + 10 = - 6.

- 12x = - 16.

12x = 16.

x = 16/12.

x = 4/3.

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By using the formula of standard deviation, it can be calculated that

Standard deviation = 2.52

What is standard deviation?

At first it is important to know about variance.

Variance is the sum of the square of deviation from mean divided by the number of observations

Square root of variance gives standard deviation.

Here the data set is

3, 5, 6, 6, 9, 1

Mean = [tex]\frac{3 + 5 + 6 + 6 + 9 + 1}{6} = \frac{30}{6}[/tex] = 5

Variance = [tex]\frac{(3 - 5)^2 + (5 - 5)^2+(6 - 5)^2 + (6 - 5)^2 + (9 - 5)^2 + (1 - 5)^2}{6}[/tex]

                = [tex]\frac{4 + 0 +1+1+16+16}{6}[/tex]

                = [tex]\frac{38}{6}[/tex]

                = 6.33

Standard deviation = [tex]\sqrt{6.33}[/tex]

                                = 2.52

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Volume of the sphere V is 2304π units³ when in the picture we have a sphere with radius 12 cm.

Given that,

In the picture we have a sphere with radius 12 cm.

We have to find what is the volume of the sphere of the picture.

We know that,

The volume of the sphere formula is V = 4/3πr³.

Here,

π is 3.14

r is 12

Volume of the sphere V = 4/3πr³

Volume of the sphere V = 4/3(π)(12)³

Volume of the sphere V = 4/3(π)(1728)

Volume of the sphere V = 2304π

Therefore, Volume of the sphere V is 2304π units³ when in the picture we have a sphere with radius 12 cm.

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Answer: No

Step-by-step explanation:

Parallel lines have the same slope. However, the slopes of the lines with the given equations are -3 and 3, respectively.

Since the slopes are not the same, the lines are not parallel.

The product is less than 67,124 because the number 50,343 is less that the number 67,124.

The product is greater than 12,400 because the number 14,800 is greater than 12,400.

What is product?

A mathematical expression that specifies the objects to be multiplied, known as a factor, produces a product. For instance, the product of x and is c dot, and the product of 6 and 5 is 30.

First to multiply 67124 x 3/4

Here 67124 x 3 = 201372

⇒201372/4 = 50343

Hence, the product is less than 67,124 because the number 50,343 is less that the number 67,124.

Now to multiply 12,400 x 1 1/5

First to convert [tex]1\frac{1}{5}[/tex] into a fraction.

[tex]1\frac{1}{5} = \frac{5+1}{5} = \frac{6}{5}[/tex]

Now,

12,400 x 6/5 = 74,400/5 = 14800

Hence, the product is greater than 12,400 because the number 14,800 is greater than 12,400.

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The equivalent expression is 2.3 raised to the fifteenth power divided by 0.9 raised to the twelfth power.

What analogous expressions are there?

Expressions that perform the same operations but differ in appearance are said to be equivalent.

There is the phrase;

{ (2. 3)^5/ (0. 9)^4 }^3

multiply by the denominator's inverse power.

(2. 3^5 × 0. 9^-4)^3

broaden the bracket

2.3 × 0. 9 ^5 +(-4) (-4)

{2.3 × 0. 9 ^ 1}^3

The phrase can be written as follows:

{ (2. 3)^5× 3/ (0. 9)^4× 3}

{ (2. 3)^15/ (0. 9)^4 }^12

Thus, 2.3 raised to the fifteenth power divided by 0.9 raised to the twelfth power is the equivalent formula.

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Answer:

  (c)  20

Step-by-step explanation:

You want to find x, given that the external angle adjacent to a base angle of an isosceles triangle is (5x +12)°, and the other base angle is marked (3x +8)°.

The base angles of an isosceles triangle are congruent, so the other base angle is congruent to the marked base angle.

The external angle and the adjacent base angle are a linear pair, hence supplementary.

  (5x +12)° +(3x +8)° = 180°

  8x +20 = 180 . . . . . . . divide by °, collect terms

  8x = 160 . . . . . . subtract 20

  x = 20 . . . . . divide by 8

The total pressure of a mixture of two gases is the finalized value of the summation of the total pressure of each of the gases.

The total pressure of a mixture of two gases can be expressed in the form of an equation, as below,

Total Pressure = Pressure of Gas 1 + Pressure of Gas 2

It is noteworthy to be mentioned that the partial pressure of an individual gas is completely in contrast to that of the individual pressure of a gas. It can be expressed in the form of an equation, as below,

Partial Pressure = Total Pressure of Gas x Mole Fraction of Gas

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Thus , option a)human brains evolved to notice how often things occur, not how likely they are to occur is correct

Probability theory deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is expressed as a number between 0 and 1, with 1 typically signifying certainty and 0 typically signifying impossibility.

Here,

According to the hypothesis of the frequency format, humans may process information more effectively when it is given as frequencies rather than probabilities. Possibly, this is the reason

Because human brains have evolved to perceive frequency rather than likelihood of events.

Thus , option a)human brains evolved to notice how often things occur, not how likely they are to occur is correct.

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Answer:q

Step-by-step explanation: If you want an answer you have to give us the data

The values of a, b and c if the root x = 3 ± 2i  are 1, -6 and 13

From the question, we have the following parameters that can be used in our computation:

x=3\pm2ix=3±2i

y = ax2 +bx+c

Rewrite the above expressions properly

So, we have the following representation

x = 3 ± 2i

y = ax² + bx + c

This means that

x₁ = 3 + 2i

x₂ = 3 - 2i

The quadratic equation is then calculated as

y = (x - x₁) * (x - x₂)

Substitute the known values in the above equation, so, we have the following representation

y = (x - (3 + 2i)) * (x - (3 - 2i))

This gives

y = ((x - 3) + 2i) * ((x - 3 - 2i)

Apply the difference of two squares

y = (x - 3)² + 4

Expand the bracket

y = x² - 6x + 9 + 4

Evaluate

y = x² - 6x + 13

Hence, the values of a, b and c are 1, -6 and 13

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Answer: 72 meters

Step-by-step explanation: The formula for the area of a square is

Length x Width = Area. The width is 6. Double of six is 12. 12 x 6 =72.

Answer:

x²(4+x)

Step-by-step explanation:

4x²+x³

Both of these terms have a common factor of x² :

x²(4+x)

This is our final answer

Hope this helped and have a good day