1.8.3 practice - functions

11. Find f(2) and f(a+h) when f(x) = 3x^2 + 2x + 4.​

Step-by-step explanation:

you you can use two formulas here either pi d or 2 pi r so when you use pie d which change the radius to diameter by multiplying by two so in this case we will multiply 7 by 2 to get 14 then use the formula so is 22/7 * 14 to get 44

Answer:

Step-by-step explanation:

y=4x-5

put y=3 and x=2

3=4(2)-5

3=8-5

3=3 so the point lies on the line

y=18+2x

put y=17 and x=-1

17=18+2(-1)

17=18-2

17=16

so the point does not lie on the line

Answer:

Question 1:

Point = (x,y) = (2,3)

So, x = 2, y = 3

Let's put this in the equation to check whether it lies on the line or not

=> 3 = 4(2)-5

=> 3 = 8-5

=> 3 = 3

Since LHS = RHS so The point lies on the line

Question 2:

Point = (x,y) = (-1,17)

So, x = -1, y = 17

Let's put this in the equation to check whether it lies on the line or not

=> 17 = 18+2(-1)

=> 17 = 18-2

=> 17 ≠ 16

Since LHS ≠ RHS, So this point doesn't lie on the line.

The stars in order from the closest one to the farthest one are:

0.883, 0.886, 0.89, 1.25

so, the answer is A.

What is a sequence?

A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).

To put the given distances in order from the closest one to the farthest one, we need to arrange them in ascending order.

That means we need to start with the smallest value and move toward the largest value.

Looking at the given distances, we see that the smallest value is 0.883, followed by 0.886, then 0.89, and finally 1.25, which is the largest value.

Putting the given distances in ascending order, we get:

0.883, 0.886, 0.89, 1.25

Therefore, the stars in order from the closest one to the farthest one are:

0.883, 0.886, 0.89, 1.25

so, the answer is A.

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The polar coordinates of (1, -9) are (9.06, -1.47 radians).

To convert from rectangular coordinates to polar coordinates, we can use the following formulas:

r = √(x² + y²)

θ = tan⁻¹(y/x)

where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

In this case, x = 1 and y = -9. Plugging these values into the formulas, we get:

r = √(1² + (-9)²) = √82 ≈ 9.06

θ = tan⁻¹((-9)/1) ≈ -1.47 radians

Therefore, the polar coordinates of (1, -9) are (9.06, -1.47 radians). The distance from the origin to the point is approximately 9.06 units, and the angle between the positive x-axis and the line connecting the origin to the point is approximately -1.47 radians (or approximately -84.26 degrees).

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The point B and C are opposite to each other.

A number line is a mathematical visual representation of numbers on a straight line. The digits on a number line are positioned sequentially at regular intervals throughout its length. It frequently appears horizontally and might go on forever in any direction.

As seen from the number line, point A is one unit left of -1 which is -2. Since each mark is a difference of 1 and to the left is a negative value, point B is midway between -1 and 0 is half of -1 which is -0.5, point C is midway between 0 and 1 is basically half of 1 which is 0.5 and point D is halfway between 1 and 2 is exactly that 1.5

As per the numerical values of the given points, the two that are opposites to each other are points B and C. They both have a value of 0.5 on each end of the number line, one being negative while the other is positive, thus they are opposites of each other.

Therefore, points B and C are opposite to each other.

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The given question is incomplete. Here is the complete question:

Which two points on the number line are opposites? A number line goes from negative 2 to positive 2 in increments of 1. There are 4 equal spaces between each number. Point A is 1 mark to the left of negative 1. Point B is halfway between negative 1 and 0. Point C is halfway between 0 and 1. Point D is halfway between 1 and 2.

The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

The functions for this problem are defined as follows:

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

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Answer:$80.24

Step-by-step explanation:68*0.18(18%)

12.24

68+12.24=$80.24

Answer:

yes it does

Step-by-step explanation:

the x numbers do not repeat

Yes, the given relation is function.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

set of ordered pairs= {(0,4),(2,6),(4,2), (6,2), (8,6)}

As, we know that the function has one input with corresponding one output.

So, we can see from the ordered pair that no input value have repeated and have respective output.

Hence, the relation is function.

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Answer:

Step-by-step explanation:

              Statements                                            Reasons

1). Triangle ABC is isosceles. D is          1). Given

   the midpoint of AC.

2). AD ≅ DC                                            2). Definition of midpoint

3). BA ≅ BC                                             3). Definition of an isosceles

                                                                     triangle.

4). BD exists                                            4). A single line segment can be

                                                                    drawn between any two points.

5). BD ≅ BD                                            5). Reflexive property

6). ΔABD ≅ ΔCBD                                 6). By SSS property of congruence

7). ∠BAC ≅ ∠BCA                                  7). CPCTC

Answer:

The Ballwin Bears are taller on average, and the Aviston Aces have players whose heights are more consistent.

Step-by-step explanation:

for derby dragon;

mean height = 72 inches

standard deviation = 1.2 inches

for aviston aces:

mean height = 70.8

standard deviation = 0.7 inches

for balwin bears;

mean height = 73 inches

standard deviation = 1.0 inches

the mean height of aviston aces < mean height of derby < mean height of balwin bears

So on average the balwin bears are taller.

The standard deviation of derby dragon is > that of balwin bears > aviston aces.

So the more consistent height is that of aviston aces players.

We conclude that after 7/4 years the value of the jet ski is $4,784

The value of the jet ski is given by the exponential equation:

f(t) = 8,500*(0.72)^t

Where t is the time in years, to get the value of the jet ski after 7/4 years, we just need to evaluate the above function in t = 7/4, where evaluating means that we need to replace the variable t by the given number, then we will get:

f(7/4) = 8,500*(0.72)^(7/4) = 4,783.55

If now we need to round it to the nearest dollar, then we round upwards to 4,784

In this way, we conclude that after 7/4 years the value of the jet ski is $4,784

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Answer:

Step-by-step explanation:

18 * 10 - 8 * 4    (remember pemdas)

180 - 32 =

148 cm²

23.45 inches fabric was used on a headband and 9.64 inches fabric was used on a wristband for each player.

No. of players = 29

No. of coaches = 4

Total fabric used for headbands = 773.85 inches

Total no. of people for headbands = 29 + 4

                                                          = 33

Fabric used for headband for 1 person = 773.85/33

                                                                 = 23.45 inches

Total fabric used for wristbands = 279.56 inches

Total no. of people for wristbands = 29

Fabric used for headband for 1 person = 279.56/29

                                                                 = 9.64 inches

Hence, fabric for headband is 23.45 inches and for wristband is 9.64 inches.

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Answer:

The answer is a^6 b^18

Step-by-step explanation:

Objects commonly found in a locality include residential buildings, commercial establishments, public facilities, transportation infrastructure, landmarks, natural features, utilities, street furniture, and vehicles.

The type of objects that can be found in a locality can vary greatly depending on the specific location and its surroundings. Here are some common types of objects that can be found in a locality:

Residential Buildings: Houses, apartments, condominiums, and other types of residential structures are commonly found in localities where people live.

Commercial Establishments: Localities often have various types of commercial establishments such as stores, shops, restaurants, cafes, banks, offices, and shopping centers.

Public Facilities: Localities typically have public facilities such as schools, libraries, hospitals, community centers, parks, playgrounds, and sports facilities.

Transportation Infrastructure: Localities usually have roads, sidewalks, bridges, and public transportation systems like bus stops or train stations.

Landmarks and Monuments: Some localities may have landmarks, historical sites, monuments, or cultural attractions that represent the area's heritage or significance.

Natural Features: Depending on the locality's geographical characteristics, natural features like parks, lakes, rivers, mountains, forests, or beaches can be present.

Utilities: Localities have infrastructure for utilities such as water supply systems, electrical grids, sewage systems, and telecommunications networks.

Street Furniture: Localities often have street furniture like benches, streetlights, waste bins, traffic signs, and public art installations.

Vehicles: Various types of vehicles can be found in a locality, including cars, bicycles, motorcycles, buses, trucks, and possibly other modes of transportation.

It's important to note that the objects present in a locality can significantly differ based on factors such as urban or rural setting, cultural context, economic development, and geographical location.

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Answer:

50 inches, or 4 1/6 feet

Step-by-step explanation:

If one inch is equal to 6 1/4 feet, we can translate this number from feet to inches.

4 1/6 feet = 75 inches.

Now we can take 75 and find out 2/3 of it.

2/3 of 75 is 50.

The answer is 50 inches.

If you want to convert the answer from feet to inches, its simple.

12 × 4 = 48

50 - 48 = 2

2 inches is equal to 1/6 of a foot.

The answer in feet, is 4 1/6 foot.

Answer:

I think it true?

I is correct?

my brainlist answer please. <:(

Answer:

The approximate standard deviation of the sampling distribution of the mean for all samples of size n is \(s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}\)

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean life expectancy of a certain type of light bulb is 945 hours with a standard deviation of 21 hours

This means that \(\mu = 945, \sigma = 21\).

What is the approximate standard deviation of the sampling distribution of the mean for all samples of size n?

\(s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}\)

The approximate standard deviation of the sampling distribution of the mean for all samples of size n is \(s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}\)

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

The total medical expenses for the five people in the car are $3,000 + $3*$500 + $62,000 = $3,000 + $1,500 + $62,000 = $66,500

What does a math word problem entail?

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Since Allen's personal injury protection policy covers each person up to $50,000, the insurance company must pay out $50,000*5 = $250,000 for the five people in the car.

Since the total medical expenses for the five people are $66,500, the insurance company will pay out the total medical expenses for the five people, which is $66,500.

Therefore, the insurance company must pay out $66,500 for these five people.

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Answer: l used to know that

Step-by-step explanation:

Answer:

78.88% probability that this sample proportion is within 0.05 of the population proportion

Step-by-step explanation:

We need to understand the normal probability distribution and the central limit theorem to solve this question.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For proportion p in a sample of size n, we have that \(\mu = p, s = \sqrt{\frac{\pi(1-\pi)}{n}}\)

In this question:

\(p = 0.8, n = 100\)

So

\(\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04\)

What is the probability that this sample proportion is within 0.05 of the population proportion.

This is the pvalue of Z when X = 0.8 + 0.05 = 0.85 subtracted by the pvalue of Z when X = 0.8 - 0.05 = 0.75.

X = 0.85

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.85 - 0.8}{0.04}\)

\(Z = 1.25\)

\(Z = 1.25\) has a pvalue of 0.8944.

X = 0.75

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.75 - 0.8}{0.04}\)

\(Z = -1.25\)

\(Z = -1.25\) has a pvalue of 0.1056.

0.8944 - 0.1056 = 0.7888

78.88% probability that this sample proportion is within 0.05 of the population proportion

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

The cost of the bottle of drink is P4.85. The refund for an empty bottle is 25 thebe.

To express the refund as a percentage of the cost of the drink, we need to convert the refund to the same unit as the cost of the drink.

1 thebe = 0.038 Philippine pesos (as of June 2023)

25 thebe = 0.95 Philippine pesos

Therefore, the refund for an empty bottle is 0.95/4.85 x 100% = 19.59%

So the refund for an empty bottle is 19.59% of the cost of the bottle of drink.

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Answer:

The percent of change in Anna's working hours is 22%, indicating an increase.

Step-by-step explanation:

Step 1: Calculate the difference:

Difference = 36 hours - 28 hours

Difference = 8 hours

Step 2: Calculate the percent change:

Percent Change = (Difference / Original Value) * 100

Percent Change = (8 hours / 36 hours) * 100

Percent Change ≈ 22.22%

Therefore, the percent change in Anna's working hours is approximately 22.22%, representing an increase.

Answer:

120 apples and 100 oranges

Step-by-step explanation:

6/11 x 220 = 120 apples

5/11 x 220 = 100 oranges

Answer:

The product of two numbers is twenty.

Answer:

The product of two numbers is twenty.

Step-by-step explanation: