If f(x)=3x^2-2 and g(x)=2x+4, Find (f-g)(x). Explain your process

Which one of the following is NOT equivalent to 3/4?

16/24 = 2/3

15/20 = 3/4

6/8 = 2/3

24/32 = 3/4

Answer: 16/24 and 24/32 are not equivalent to 3/4

Step-by-step explanation:

Equivalent fractions represent the same value, even though they look different.

Here, when we convert every fraction to its simplest form, we can verify if they are equal.

(16/24) ÷ (8/8) = 2/3

(15/20) ÷ (5/5) = 3/4

(6/8) ÷ (2/2) = 3/4

(24/32) ÷ (4/4) = 6/7

As the simplest forms of 16/24 and 24/32 are not 3/4, they are not equivalent fractions of 3/4.

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Answer:

\(2x^3+x^2-8x-4=(2x+1)(x+2)(x-2)\)

Step-by-step explanation:

Let's collect \(x^2\) between the first two terms, and -4 between the last two:

\(2x^3+x^2-8x-4=x^2(2x+1) -4 (2x+1)\)

At this point you should see there is a common factor\(2x+1\)between both terms, then let's collect that:

\(2x^3+x^2-8x-4=x^2(2x+1) -4 (2x+1) = (2x+1)(x^2-4)\)

Final step is recognizing a difference of squares (x and 2) in the second bracket, to end up our work!

\(2x^3+x^2-8x-4=x^2(2x+1) -4 (2x+1) = (2x+1)(x^2-4) =(2x+1)(x+2)(x-2)\)

Step-by-step explanation:

\(f(x) = {2}^{3} + {x}^{2} - 8x - 4\)

\( {x}^{2} (2x + 1) - 2(2x + 1) = 0\)

\((2x + 1)( {x}^{2} - 2)\)

\(x = \frac{ - 1}{2} \\ x = \sqrt{2} \)

hope it's helpful

Price chart :

Item Price per pound

Dark Roast Coffee $7.50

Pumpkin Spice Coffee $10.50

Breakfast Tea $23.50

Answer:

Step-by-step explanation:

4

Maximum amount to spend ≤ 65

Cost of dark roast coffee = $7.50

2 dark roast coffee= $7.50 * 2 = $15

Pumpkin Spice + dark roast ≤ amount to spend

Let pumpkin spice = x

Cost of pumpkin spice = $10.50

Dark Roast Coffee = y

10.50x + 2* 7.50 ≤ 65

10.50x + 15 ≤ 65

10.50x ≤ 65 - 15

10.50x ≤50

x ≤50 / 10.50

x ≤ 4.76

Number of pumpkin spice coffee that can be purchased is 4.

Therefore, there are 900 four-digit numbers that are multiples of 5.

To find the number of 4-digit numbers that are multiples of 5, we need to determine the range of numbers and then count how many of them meet the criteria.

The range of 4-digit numbers is from 1000 to 9999 (inclusive).

To be a multiple of 5, a number must end with either 0 or 5. Therefore, we need to count the number of possibilities for the other three digits.

For the first digit, any digit from 1 to 9 (excluding 0) is possible, giving us 9 options.

For the second and third digits, any digit from 0 to 9 (including 0) is possible, giving us 10 options each.

Multiplying these options together, we get:

9 * 10 * 10 = 900

Therefore, there are 900 four-digit numbers that are multiples of 5.

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Answer:

The blue container ways 15 more pounds.

Step-by-step explanation:

Subtract 5 from 20 and it gives you 15.

20- 5= 15

Answer:

Step-by-step explanation:

Answer:

1/4 or 0.25

Step-by-step explanation:

I think it is 1/4

1/3+1/4+1/6=0.75(3/4)

so there is another 1/4, so it is 1/4(0.25)

The measure of the central angle d is 90 degrees

According to the problem, the areas of the regions created by the central angles are in the ratios 1/3, 1/4, and 1/6. This can be expressed as:

a/A = 1/3

b/A = 1/4

c/A = 1/6

Since the sum of the areas of the regions must equal the total area of the circle, we can write:

a/A + b/A + c/A + d/A = 1

Substituting the given ratios, we have:

1/3 + 1/4 + 1/6 + d/A = 1

(4 + 3 + 2)/12 + d/A = 1

9/12 + d/A = 1

3/4 + d/A = 1

Subtracting 3/4 from both sides:

d/A = 1 - 3/4

d/A = 1/4

Since the central angle d represents a fraction of the total circle area equal to 1/4, we can conclude that its measure in degrees is also 1/4 of the total number of degrees in a circle, which is 360 degrees.

Therefore, the measure of the central angle d is:

d = (1/4) * 360

d = 90 degrees

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Using a t-distribution table, here with 46 degrees of freedom (n-1), the critical value for a two-tailed test with a level of significance of α = 0.10 is ±2.575. Therefore, we reject H0 if the standardized test statistic is greater than 2.575 or less than -2.575. The correct answer is D. Reject H0 if the standardized test statistic is greater than 2.575 or less than -2.575.

To determine whether to reject H0, we need to calculate the standardized test statistic using the formula (sample mean - hypothesized mean) / (standard deviation / square root of sample size). Since the null hypothesis is that μ = 3.5, the sample mean and standard deviation must be used to calculate the standardized test statistic.
Assuming a normal distribution, with a sample size of n=47 and a level of significance of α = 0.10, we can use a two-tailed test with a critical value of ±1.645. However, since we are testing for μ ≠ 3.5, this is a two-tailed test, and we need to use a critical value that accounts for both tails.

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The product of vectors a and b is approximately 5.292.

To find the product of two vectors a and b, we need to use the dot product formula which is a · b = |a| |b| cosθ, where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.
In this case, we are given that |a| = 2 and |b| = 7, and the angle between a and b is 2/3. We can use this information to find cosθ as follows:
cosθ = cos(2/3) ≈ 0.378
Now, we can substitute the values into the formula:
a · b = |a| |b| cosθ
a · b = 2 * 7 * 0.378
a · b ≈ 5.292
Therefore, the product of vectors a and b is approximately 5.292.

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The equation allows us to chart the tree's development over time and forecast its ultimate height.

A function is a mathematical formula that allots each input from one set, known as the domain, to precisely one output from another set, known as the range. A function can be used to model relationships between variables, answer issues, and make predictions. It can be represented by an equation, a graph, a table, or a verbal description. Numerous branches of mathematics, as well as disciplines like physics, engineering, finance, and computer science, make extensive use of functions. Typical instances of functions include: When a function is graphed, it always changes at the same rate and forms a straight line. They are frequently used to simulate relationships between two variables that are related linearly, such as time and location.

given

After d days, Alani created the following algorithm to measure the height of the banana tree:

h = d + 8

Since this function is linear, the banana tree's development will remain constant over time. According to the calculation, the tree starts out at a height of 8 units, and it increases by 1 unit per day after that.

We can enter a figure for d (the number of days) and solve for h using this equation (the height of the tree after d days). For instance, we can enter d = 10 into the calculation to get the height of the tree after 10 days:

h = 10 + 8

h = 18

Therefore, the altitude of the banana plant after 10 days would just be 18 units. This equation allows us to chart the tree's development over time and forecast its ultimate height.

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Depends if your dividing or Times

Step-by-step explanation: So,

I want to say it would be 1 But there is a Off And on question (Try Dividing )

Using concepts of Errors and Measurement, we got 252cm³ will be  the maximum error in volume of sphere.

We know that volume(V) of sphere is given by  =\(\frac{4.\pi .r^{3} }{3}\),where r is the radius of the volume.

If the error in the measured value of r is denoted by then the corresponding error in the calculated value of Volume is , which can be approximated by the differentiating the volume with respect to radius.

When r = 20 and dr = 0.05, this becomes:

d(V)/dr = 4×π×r²

=>d(V)=(4×π×r²)×dr

On putting the values,

=>d(V)=4×π×(20²)×(0.05)

=>d(V)=4×3.14×400×0.05

=>d(V)=252

Hence, the maximum error is 252cm³ in calculating the volume of sphere if we use the given radius.

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a. The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b. The probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c. Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

a) The three characteristics of this scenario that indicate we are working with Bernoulli trials are:

The experiment consists of a fixed number of trials (eight shots).

Each trial (shot) has two possible outcomes: hitting the target or missing the target.

The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b) To find the probability of hitting the 6th target (considered as a single trial), we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the binomial coefficient or number of ways to choose k successes out of n trials,

p is the probability of success in a single trial, and

n is the total number of trials.

In this case, k = 1 (hitting the target once), p = 0.88, and n = 1. Therefore, the probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c) To find the probability that the first time hitting the target is not until the 4th shot, we need to consider the complementary event. The complementary event is hitting the target before the 4th shot.

P(not hitting until the 4th shot) = P(hitting on the 4th shot or later) = 1 - P(hitting on or before the 3rd shot)

The probability of hitting on or before the 3rd shot is the sum of the probabilities of hitting on the 1st, 2nd, and 3rd shots:

P(hitting on or before the 3rd shot) = P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

Calculate these probabilities and sum them up to find P(hitting on or before the 3rd shot), and then subtract from 1 to find the desired probability.

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Answer:

\( \huge \orange { \boxed{x = \frac{c - k}{12} }}\)

Step-by-step explanation:

12x + k = c

Step 1: transfer k on right side

12x = c - k

Step 2: Divide both side by 12

\( \frac{12x}{12} = \frac{c - k}{12} \\ \huge \red{ \boxed{x = \frac{c - k}{12} }}\)

When X denote the number of times that the executive will be late to the office in the next 60 working days. Determining  \(P \quad 5 \leq X \leq 10\) is 0.6822.

As per the details share in the above question are as follow,

Let us consider,

\(\lambda=4\) days per 30 working day.

\($X=$\) no.of times that executive will be late to the office in next 60 working days.

Here each day is independent.

Rate of arriving late at office is constant.

Late day of occurrence is Random process.

\(& P(x)=\frac{e^{-\lambda t}(\lambda t)^x}{x !} \\& P(x)=\frac{e^{-\frac{4}{30} \times 60}\left(\frac{4}{30} \times 60\right)^x}{x !}=\frac{e^{-8}(8)^x}{x !}\)

Now consider the probability,

\(& =p(5 \leq x \leq 10) \\& =\frac{e^{-8}(8)^5}{5 !}+\frac{e^{-8}(8)^6}{6 !}+\cdots+\frac{e^{-8}(8)^{10}}{10 !}\)

=0.0916+0.1222+0.1396+0.1396+0.1241+0.0993

=0.6822

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Note the correct question is

On experience, it is found that an executive is late for office on four days out of 30 working days. Let X denote the number of times that the executive will be late to the office in the next 60 working days. Determine \(P \quad 5 \leq X \leq 10\).

Answer:

7

Step-by-step explanation:

-42

-----------

-2-4

Complete the bottom part of the fraction first

-2-4 = -6

-42

-----

-6

Divide

7

Answer:

48pq².

Step-by-step explanation:

(4pq+3q)² - (4pq - 3q)²​

This is the difference of 2 squares so we can use the identity

a^2 - b^2 = (a - b)(a + b):

(4pq+3q)² - (4pq - 3q)²​

= (4pq + 3q - (4pq - 3q)(4pq + 3q + (4pq - 3q)

= (4pq + 3q - 4pq + 3q)(4pq + 3q + 4pq - 3q)

= 6q * 8pq

= 48pq².

Answer:

48pq²

Step-by-step explanation:

As we know,

(a + b)² = a² + 2ab + b²

and

(a – b)² = a² – 2ab + b²

So,

(4pq+3q)² - (4pq - 3q)²​

= [(4pq)² + 2 X 4pq² X 3q + (3q)²] – [(4pq)² -  2 X 4pq² X 3q + (3q)²]

= (16p²q² + 24pq²+ 9q²) – (16p²q² – 24pq²+ 9q²)

= 16p²q²+ 24pq²+ 9q² – 16p²q²+ 24pq² – 9q²

= 24pq² + 24pq²

= 48pq²

Answer:

Heyyy. Glad to see someone from malaysia taking add maths hete. Hope this helps

Answer:

=(x-7)(x+2)

Step-by-step explanation:

Answer:

\(x {}^{2} - 5x - 14 \\ = x {}^{2} - (7 - 2)x - 14 \\ = x {}^{2} - 7x + 2x - 14 \\ = x(x - 7) + 2(x - 7) \\ = (x - 7)(x + 2)\)

Thank you ☺️☺️

Answer: $2,550

Step-by-step explanation:

I’m not 100% sure what this question is asking.

But if it’s asking “how much money does he earn in total if he mows for 25 days and if he earns $102 each day”, then that would be your answer.

Since there is 25 days, and he earns $102 each day, you would multiply 25 by 102.

Then your answer (his total amount of money earned once he has mowed for 25 days) would be: $2,550.

Answer:

prime

Step-by-step explanation:

3x^2 + 5x + 1

it can't be factorizes with rational numbers

Answer:

Prime

Step-by-step explanation:

3x^2 + 5x + 1

3x^2  factors in to 3x and x

1 factors into 1 and 1

( 3x   + 1) ( x+1)

We need to verify the middle is 5

3x+1x = 4x

so this is not true

We cannot factor this so it is prime

89 degrees

Triangles will always have 180 degrees. This means that given 2 angles, we can find the missing measurement.

Setting Up an Equation

To help us solve for the unknown angle, a, we can set up an algebraic equation. To make this equation remember that all 3 internal angles sum to 180.

This is only one equation that you could set up to represent this situation.

Solving For a

Now that we have an equation we can begin to solve it. First, combine like terms that are on the same side of the equation.

Next, subtract 91 from both sides.

To check our answer we can plug it back into the original equation.

This means that the missing angle must be 89 degrees.

The number of sides the regular polygon has is: B. 8.

A polygon with an n-side have a sum of interior angles which can be determined using the formula: (n - 2)180, where n is the number of sides of the regular polygon.

Thus, to find the measure of each interior angle of the polygon, we have: interior angle of a polygon = sum of interior angles ÷ number of sides.

Given the following information about the regular polygon:

Interior angle of the regular polygon = 135 degrees.

Plug this into the given formula for finding the interior angle of a polygon:

135 = (n - 2)180/n

Multiply n by both sides of the equation

135 × n = (n - 2)180/n × n

135n = (n - 2)180

Open the bracket

135n = 180n - 360

Subtract both sides by 180n

135n - 180n = 180n - 360 - 180n

-45n = -360

Divide both sides by -45

-45n/-45 = -360/-45

n = 8

Thus, the number of sides that the regular polygon has is: B. 8 sides.

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Answer: 4,875.05

Step-by-step explanation:

I took the quiz

Answer:

d

Step-by-step explanation:

Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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Answer:

The correct choice is (A)

Answer:  

A.

an=100 · (0.64)n−1a subscript n baseline equals 100 times left parenthesis 0.64 right parenthesis superscript n minus 1 baseline; about 10.74 cm

Step-by-step explanation:  I got it off of the internet

Step 1 of 1

In geometric sequence, the ratio between two consecutive terms is constant. This ration is called the common ratio.

Consider the following sequence:

Thus the common ratio of the sequence is .

...............................................................................................................................................

You drop a handball from a height of 1 meter. Each curved path has 64% of the height of the previous path.   A. A(n)= 100*(0.64)^n-1

Answer:

13

Step-by-step explanation:

A confidence interval for the mean is said to be symmetrical around the population mean. Symmetry means that the central tendency measures are equally positioned about the middle of the interval.

When constructing a confidence interval, the interval width on either side of the point estimate is equal (assuming a symmetric distribution). The critical values, the margin of error, and the point estimate are all equidistant from the midpoint of the interval.

This is why a confidence interval for the mean is said to be symmetrical around the population mean. Therefore, a confidence interval for the mean is symmetrical around the population mean as long as the population is normally distributed.

Also, it is worth noting that a confidence interval can only be symmetrical if the sample size is large enough. In the case of a smaller sample size, the distribution of the confidence interval may not be entirely symmetrical and may skew to the left or right. The larger the sample size, the more symmetrical the distribution will be.

A confidence interval is typically expressed in a specific range, such as 95 percent, which means that the population mean is expected to fall within that range 95 percent of the time. In conclusion, the symmetry of a confidence interval around the population mean is important for statistical inference because it ensures that the confidence level is maintained.

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