Factorise the following

[tex]4x {}^{3} - 6x { }^{2} + 8x[/tex]
​

Answer:

He makes 12 shortcakes.

The calculated value of x in the similar shapes given that abcd ∼ efgh is 15

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

abcd ∼ efgh

By the corresponding ratio of similar shapes, we have the following equation

AB/AD = EF/EH

Using the above as a guide, we have the following:

8/14 = (x - 3)/(x + 6)

Cross multiply the equation

This gives

8(x + 6) = 14(x - 3)

When solved for x, we have

x = 15

Hence, the value of x in the shapes is 15

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The equation of a regression line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope m is given as 1.885.

The y-intercept b can be found using the formula b = y_mean - m * x_mean, where x_mean and y_mean are the means of the x-coordinates and y-coordinates of the data points, respectively. Plugging in the given values, we get:

b = 12.318 - 1.885 * 3.448 b ≈ 5.819

So the y-value of the y-intercept of the line to three decimal places is approximately 5.819. The correct answer is D. 5.819.

Answer:

-4,096

Step-by-step explanation:

If you multiply:

4x4x4x4x4x4= 4,096

Then, just make that negative:

-4,069

Hope this helps :3

The language paradigm that is based on the mathematical concept of a function is the functional programming paradigm.

In functional programming functions are treated as first-class citizens means that they can be passed as arguments to other functions returned as values from functions and assigned to variables.

This is similar to mathematical functions are used in algebra and calculus.

Functional programming emphasizes on the use of pure functions are functions that produce output only based on their input and do not have any side effects.

This helps in writing code that is easier to reason about and test.

Functional programming languages such as Haskell Lisp and OCaml are based on this paradigm and provide built-in support for functions as first-class citizens.

Object-oriented programming (OOP) is based on the concept of objects encapsulate data and behavior.

Imperative programming is based on a sequence of statements that change the state of the program declarative programming focuses on what the program should achieve rather than how to achieve it.

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The interest on $5.255 at 12% for 30 days using ordinary interest can be calculated using the formula:I = PRT,Where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period.

Here, P = $5.255, R = 12% = 0.12 (as a decimal), and T = 30/365 = 0.08219 (in years, as the time is given in days).

So,

I = 5.255 x 0.12 x 0.08219 = $0.0518

Rounding to two decimal places, the interest on $5.255 at 12% for 30 days using ordinary interest is $5.26. Therefore, the correct answer is option (c).

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Answer:

because if you substitute 0.5 for x you get zero as a result

Step-by-step explanation:

ABCD IS A KITE. (4x-2)cm A B AB= (4x-2) cm Jasper says that x could be 0.5 (a) Explain why Jasper cannot be correct.​

I answer for what I understand, the question is not clear

because if you substitute 0.5 for x you get zero as a result

(4x - 2) =

4 × 0.5 - 2 =

2 - 2 = 0

The length of a pregnancy from conception to birth follows a normal distribution with a mean (μ) of 272 days and a standard deviation (σ) of 9 days. To find the percentage of pregnancies that are full-term, we need to calculate the probability of a pregnancy lasting between 252 and 298 days.

First, convert the days into z-scores:

z1 = (252 - μ) / σ = (252 - 272) / 9 ≈ -2.22
z2 = (298 - μ) / σ = (298 - 272) / 9 ≈ 2.89

Next, use a standard normal distribution table to find the probabilities corresponding to the z-scores:

P(z1) ≈ 0.0132
P(z2) ≈ 0.9981

To find the percentage of pregnancies that are full-term, subtract the lower probability from the higher probability:

Percentage = (P(z2) - P(z1)) × 100% = (0.9981 - 0.0132) × 100% ≈ 98.49%

Approximately 98.49% of pregnancies are full-term, lasting between 252 and 298 days.

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The total amount Elizabeth paid can be expressed as 1.27x, where x is the subtotal on the bill.

    To calculate the total amount, first, we need to add the tax to the subtotal, which gives us 1.06x. Then, we need to add the tip to the entire amount, which is 21% of the sum of the subtotal and the tax. This can be expressed as 0.21(1.06x) = 0.22386x. Finally, we add the tip to the subtotal and the tax, which gives us 1.06x + 0.22386x = 1.28386x. This is the same as multiplying the subtotal by 1.27, which gives us the expression 1.27x. Therefore, the total amount Elizabeth paid is 1.27 times the subtotal on the bill.

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The margin of error of a confidence interval is affected by multiple factors, including sample size, confidence level, and standard deviation. Understanding these relationships is essential for making accurate and reliable statistical inferences.

The margin of error of a confidence interval is a measure of the range of values within which the true population parameter is likely to lie. It reflects the amount of sampling error in the estimation process and is influenced by several factors.
Regarding the question, it is false that as sample size increases, the margin of error increases as well. In fact, the opposite is true. As the sample size increases, the margin of error decreases, since larger samples provide more information and reduce the uncertainty in the estimation. This relationship is inversely proportional and can be quantified by the formula: margin of error = z* (standard deviation / sqrt(n)), where z* is the critical value for the desired confidence level, n is the sample size, and standard deviation is the variability of the population.
On the other hand, it is true that as confidence level increases, the margin of error increases as well. This is because a higher confidence level requires a wider interval to capture a larger proportion of the population values, which results in a larger margin of error. For instance, a 99% confidence interval will be wider than a 95% confidence interval for the same sample size and standard deviation.
Finally, it is also true that as standard deviation of the sample increases, the margin of error increases as well. This is because a larger standard deviation implies a greater variability in the population and more uncertainty in the estimation, which requires a wider interval to account for the potential values. Thus, a larger standard deviation leads to a larger margin of error for the same sample size and confidence level.

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Answer:

Surface area of cylinder = 2 π r ² +2 π r h

Step-by-step explanation:

Surface area of cylinder =

area of both circle ends + area of curved surface

= 2 π r ² +2 π r h

A survey was conducted to determine the number of family and non-family members living in their house. The results showed that out of 100 households surveyed, an average of 3.5 family members and 1.2 non-family members were living in each household.

Explanation:

The survey was conducted by randomly selecting 100 households in a particular area and asking them how many family and non-family members were living in their house. The results were then tabulated to determine the average number of family and non-family members per household.

The results showed that on average, each household had 3.5 family members and 1.2 non-family members living in their house. This information can be useful for various purposes, such as city planning, resource allocation, and understanding social dynamics within a community.

It's important to note that the results of this survey may not be representative of all households in the area, as the sample size is relatively small. Additionally, the definition of "family member" may vary from household to household, which could impact the results. Nevertheless, this survey provides some insight into the demographics of households in the area and can be used as a starting point for further research.

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(a) The probability that both John and Jane watch the show is 0.07.

(b) The probability that Jane watches the show, given that John does, is 0.11

(c) No. John and Jane do not watch the show independently of each other.

(a) The probability that both John and Jane watch the show is given by the product of their individual probabilities:

P(John and Jane watch) = P(John watches) x P(Jane watches)

     = 0.7 x 0.1

     = 0.07.

(b) The probability that Jane watches the show, given that John does, is given by Bayes' theorem:

P(Jane watches | John watches) = P(John watches | Jane watches) x P(Jane watches) / P(John watches)

From the information given, we know that:

To find P(John watches), we can use the law of total probability:

P(John watches) = P(John watches | Jane watches) * P(Jane watches) + P(John watches | not Jane watches) * P(not Jane watches)

           = (0.8 x 0.1) + (0.7 x 0.9)

           = 0.71

Therefore,

P(Jane watches | John watches) = 0.8 x 0.1 / 0.71 = 0.1127

(c) John and Jane do not watch the show independently of each other, since the probability that John watches the show changes depending on whether or not Jane watches it. In other words, the events "John watches the show" and "Jane watches the show" are dependent events.

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The linear function which represents the total cost is:

c = 11.95 + 48t

The general form of linear function is:

c = mt + b

where m is the cost per ticket

b is the service fee ($11.95)

Total cost of 4 tickets = $203.95

Cost of 4 tickets without service fee =  $203.95 - $11.95 = $192

Cost per ticket (m) =  $192/4 = 48

Thus, the linear function which represents the total cost will be:

c = 48t + 11.95

c = 11.95 + 48t  (When rearranged)

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The length of segment BD is given as follows:

BD = 6.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

BD.

The bases for this problem are given as follows:

3 and 12.

Hence the length of segment BD is obtained as follows:

(BD)² = 3 x 12

(BD)² = 36

BD = 6 -> taking the square root.

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Answer:To find f(g(x)), we first substitute g(x) into the expression for f(x), then simplify:

f(g(x)) = f(√x-1)

= 3(√x-1) + 2   (substitute √x-1 for x in the expression for f(x))

= 3√x - 3 + 2

= 3√x - 1

Therefore, f(g(x)) = 3√x - 1.

Step-by-step explanation:

a

(4.5, 0) and (5, 0)

The x-intercept of the parabola represents the point where the parabola graph intersects the x-axis. In other words, these are the x values where the y coordinate is 0.

Using the information given, we can observe that the parabola falls from the left, passes through the point (3, 2), reaches the minimum point, then rises to the right and passes through the point (6, 2) .

Since the parabola intersects the x-axis at the x-intercept, we can conclude that the x-intercept is the point where the y-coordinate is 0. In this case, x values of 4.5 and 5 will have a y coordinate of zero. So the x-intercepts of the parabola are (4,5,0) and (5,0). 

Figure L is a translation of Figure J.

Option B is the correct answer.

We have,

Translation refers to the movement of an object in a certain direction without changing its shape, size, or orientation.

In other words,

The object is shifted or moved from one location to another in a straight line while maintaining its properties such as length, angles, and size.

Now,

Translation will give the same shape and size.

So,

Figure J has the same shape and size as Figure L.

Thus,

Figure L is a translation of Figure J.

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Answer:

range = 6

Step-by-step explanation:

the range is the difference between the maximum and minimum values in the data set.

maximum = 8 and minimum = 2 , then

range = 8 - 2 = 6

The radius of given circle would be 18 cm.

Given that a right △ABC is inscribed in circle k(O, r) and m ∠C = 90°, AC = 18 cm, m ∠B = 30°.

We are asked to find the radius of the circle.

Draw a diagram that represent the given scenario. [check the attached diagram]

AB is diameter of circle O and it a hypotenuse of triangle ABC.

We will use sine of the angle to find side AB.

Sin x = AC/AB

Sin 30° = 18 / AB

AB = 36

So, the radius = 18 cm.

Therefore, the radius of given circle would be 18 cm.

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The complete question is =

A right △ABC is inscribed in circle k(O, r). Find the radius of this circle if:

m∠C = 90°, AC = 18 cm, m∠B = 30°.

Using the tables we can evaluate the given functions to get:

Here we have two tables for the functions f(x) and g(x), first we want to find the sum:

(f + g)(3) = f(3) + g(3)

Using the table we can see that:

f(3) = 8

g(3) = 1

Then:

(f + g)(3) = 8 + 1 = 9

For the second one we have:

(f times g)(-1) = f(-1)×g(-1)

Where:

f(-1)= -2

g(-1) = 4

Then we will get (f times  g)(-1) = -2*4 = -8

Now we have the compositions:

f(g(2))

and g(2) = 3, then:

f(g(2)) = f(3) = 8

Finally:

g(f(0))

Where f(0) = 0

Then:

g(f(0)) = g(0) = 2

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If Martin's mass is initially m kilograms, his mass after gaining 7 kilograms would be:

m + 7 kilograms.

In the question, it's given that Martin's initial mass is m kilograms. This means that he weighs m kilograms at some point in time.

If Martin gains 7 kilograms, we need to add 7 to his initial mass to get his new mass. The formula for this is:

Martin's new mass = Martin's initial mass + the mass he gained

Martin's new mass = m + 7

So if Martin's initial mass is m kilograms, his mass after gaining 7 kilograms would be m + 7 kilograms. This means that he would weigh m + 7 kilograms at this point in time.

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Answer: 5.56%

Step-by-step explanation:

Compound interest formula:

A = P(1 + r/n)^nt

A = final amount

P = principle amount (original amount of money)

r = interest rate

n = number of times interest in compounded per year

t = time

Step 1:

Fill in the formula

A = 700 (she ends up with this amount of money)

P = 530 (she started with this)

r = ?

n = 365 (it is compounded 365 times per year, or once a day)

t = 5 (she left the money in the account for 5 years)

700 = 530(1 + r/365)^365(5)

Step 2:

Solve the equation for r. You will get 0.055644...

Convert this to a percent and you get the final answer of 5.56%

The domain and the range of the given function will be same and all the real numbers.

Given is a function f(x)= -√√x we need to see the range and the domain of the function,

Since the function is a root function, so the range and the domain will be all real numbers and hence equal.

Hence the domain and the range of the given function will be same and all the real numbers.

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The correct statement is: The range and domain of the graph are the same.

The function f(x) = -√-x is a valid function for all real numbers.

When x is negative, -x is positive and √-x is an imaginary number, which is then multiplied by -1 to make the function real.

Therefore, the range of the graph is all real numbers.

Thus, The range and domain of the graph are the same.

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A statement about the the slopes of JL and MP that is true include the following: A. The slope of JL is the same as the slope of MP because △JKL is similar to △MNP.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar and the slopes of side JL and side MP are equal;

Slope of side MP = NP/MN

Slope of side JL = KL/JK

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Answer: How Much Does the Farmer Get From the Sale of 10 Baskets?

Step-by-step explanation:  If the greatest common divisor of 78 artichokes and 90 courgettes is 6, then the farmer can form at most 6 baskets with the same number of artichokes and courgettes. Therefore, the answer is $6.

If each artichoke is sold for €0.70 and each courgette is sold for €0.40, then the revenue from one basket is (0.70 * 6) + (0.40 * 6) = €6.60. The revenue from 10 baskets is 10 * €6.60 = €66.

Converting this to USD at the current exchange rate of 1 EUR = 1.18 USD, the revenue from 10 baskets is approximately $78.

{Hope This Helps! :)}

A line plot for the weight of each piece of fruit, in pounds is shown in the image attached below.

In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

In this scenario and exercise, we would use an online graphing calculator to graphically represent the weight of each piece of fruit, in pounds on a line plot as shown in the image attached below.

In conclusion, we can reasonably infer and logically deduce that the data set is skewed.

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The key features include random assignment of participants into two groups (drug A and placebo), administration of the drug or placebo without participants knowing which one they received, and comparison of outcomes (number of pain episodes) between the groups at the end of the treatment period.

This is a randomized controlled trial (RCT). An RCT is a type of research study where participants are randomly assigned to receive either the treatment (drug) or a placebo, and then the outcomes of both groups are compared. In this case, the study was conducted by the National Institutes of Health to investigate whether drug A can reduce the pain associated with sickle-cell disease. 150 sickle-cell sufferers were randomly assigned to receive the drug and another 150 were given placebos. The researchers took great care to ensure that the participants did not know whether they were receiving the drug or the placebo. At the end of the treatment period, the number of episodes of pain reported by each subject was counted. This study is important in helping researchers and healthcare professionals understand the effectiveness of the drug in reducing the pain associated with sickle-cell disease.

This study is a double-blind randomized controlled trial (RCT).

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