All the zeros of the polynomial f(x) = x³ - 12x² + 39x - 28 will be 7, 1, and 4.
Given that:
f(x) = x³ - 12x² + 39x - 28
A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
⇒ (x³ - 12x² + 39x - 28) / (x - 7)
⇒ x² - 5x + 4
⇒ x² - 4x - x + 4
⇒ x(x - 4) -1(x - 4)
⇒ (x - 4)(x - 1)
The other roots are given as,
(x - 1)(x - 4) = 0
x = 1, 4
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Which statement about the the slopes of JL and MP are true
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.
What are the properties of similar triangles?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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which of the following language paradigms is based on the mathematical concept of a function?
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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which of the following is false about the margin of error of a confidence interval? as sample size increases, margin of error increases as well. as confidence level increases, margin of error increases as well. as standard deviation of the sample increases, margin of error increases as well.
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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Shandra is going to invest $530 and leave it in an account for 5 years. Assuming the interest is compounded daily, what interest rate, to the nearest hundredth of a percent, would be required in order for Shandra to end up with $700?
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%
Please helppp meeeeee
The length of segment BD is given as follows:
BD = 6.
What is the geometric mean theorem?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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What is the rule for the reflection?
Circle w is dilated ( radius square root of 30) using a scale factor of 2.5 centered at the origin. What is the area of the resulting image?
The area of the resulting image after the dilation is 187.5π square units.To find the area of the resulting image after the dilation, we need to calculate the area of the dilated circle.
The formula for the area of a circle is A = πr^2, where A represents the area and r represents the radius.
Given that the radius of circle w is the square root of 30, we can calculate its area as follows:
Area of circle w = π * (√30)^2 = π * 30 = 30π
Now, we need to apply the dilation with a scale factor of 2.5 to find the area of the resulting image.
The scale factor affects both the radius and the area. When a circle is dilated by a scale factor of k, the new radius becomes k times the original radius. In this case, the new radius is 2.5 * √30.
Area of resulting image = π * (2.5 * √30)^2 = π * (2.5^2 * 30) = π * (6.25 * 30) = 187.5.
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HELP ON TIME LIMIT !!!!!Solve the system of equations. Be sure to check your work. Complete the ordered pair to show your answer.
Y=-2
Y=-x+5
Answer:( , )
what type of sampling is used when it is not possible to select individuals directly from the target population?
Answer:
If a researcher cannot gain access to a target population, snowball sampling procedures can assist in locating subjects. In regard to sampling procedures, if a researcher wants to be able to generalize results to the total population of interest, then a purposeful sampling technique is the best approach.
Answer:
Non-probability sampling
Step-by-step explanation:
Non-probability sampling is a method of selecting units from a population using a subjective method.
John and Jane are married. The probability that John watches a certain television show is 0.7. The probability that Jane watches the show is 0.1. The probability that John watches the show, given that Jane does, is 0.8.
(a) Find the probability that both John and Jane watch the show.
(b) Find the probability that Jane watches the show, given that John does.
(c) Do John and Jane watch the show independently of each other? Yes or no?
(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.
Probability(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:
P(John watches | Jane watches) = 0.8P(Jane watches) = 0.1.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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6 to the power of -4
Answer:
-4,096
Step-by-step explanation:
If you multiply:
4x4x4x4x4x4= 4,096
Then, just make that negative:
-4,069
Hope this helps :3
a farmer collects 78 artichokes and 90 courgettes. How many of the same cards can he form at most? If each artichoke is sold for €0.70 and each courgette for €0.40, how much does he get from the sale of 10 baskets
It’s a GCD(greatest common divisor) problem
The answers are 6 and $151
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! :)}
if martins mass is m kilogram , represent his mass after he gains 7 kilogram
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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A scientist gathers data by weighing different fruits. The weight of each piece of fruit, in pounds, are as follows. 3/8, 1/4, 1/2, 1/2, 1, 1/8, 1/4, 1/2, 1/4, 1, 3/8, 3/8, 5/8
Create a line plot to represent this data set
A line plot for the weight of each piece of fruit, in pounds is shown in the image attached below.
What is a line plot?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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Make a survey of the number of family and non family members living in their house
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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someone pls explain and help :(
Using the tables we can evaluate the given functions to get:
(f + g)(3) = 9(f times g)(-1) = -8f(g(2)) = 8g(f(0)) = 2How to evaluate the given functions?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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sickle-cell disease is a painful disorder of the red blood cells that in the united states affects mostly blacks. to investigate whether drug a can reduce the pain associated with sickle-cell disease, a study by the national institutes of health randomly assigned 150 sickle-cell sufferers to receive the drug. placebos were given to another 150 sickle-cell sufferers. great care was used to ensure that the 300 participants did not know if their pill contained the drug. at the end of the treatment period, the researchers counted the number of episodes of pain reported by each subject. what type of study is this?
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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Interest on $5.255 at 12% for 30 days (use ordinary interest) is: Multiple Choice:
a. $52.55 b. $5,307.55 c. $5.26 d. $5,260.26
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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given f(x)=3x+2 and g(x)= √x-1, determine the following: f(g(x))=
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:
NEED HELP WITH MATH GEOMETRY
The perimeter of parallelogram ABCD is given as follows:
360 units.
What is the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
On a parallelogram, the opposite sides are congruent, hence the equations relating x and y are given as follows:
9x + 68 = 6y + 14.19x = 5y + 1.The solutions to the system are given as follows:
x = 4 and y = 15.
Hence the side lengths are:
Base: 6y + 14 = 6 x 15 + 14 = 104.Height: 19 x 4 = 76.The perimeter is of:
P = 2 x (76 + 104)
P = 360 units.
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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.
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
Which figure is a translation of figure J?
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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if a random sample of size n is taken from a population, then sample mean is approximately normally distributed, if group of answer choices n is at least 30. the population is normally distributed. the population distribution is known. the random sample is unbiased. the random sample is stratified.
The sample mean is approximately normally distributed when a random sample of size n is taken from a population, provided that n is at least 30. This is known as the Central Limit Theorem. It states that as the sample size increases, the distribution of the sample mean approaches a normal distribution, regardless of the population's distribution.
If a random sample of size n is taken from a population, then the sample mean is approximately normally distributed, if the sample size n is at least 30. However, this assumption is valid only when the population is normally distributed, and the population distribution is known. Additionally, it is assumed that the random sample is unbiased, meaning that every member of the population has an equal chance of being selected. If the population is not normally distributed, the sample size may need to be larger than 30 to approximate normality. Stratified sampling can also be used to ensure representation of different subgroups within the population, but it does not affect the assumption of normality or unbiasedness. Overall, ensuring that these assumptions are met can increase the accuracy of statistical inference based on the sample mean.
An unbiased random sample ensures that each member of the population has an equal chance of being selected, and stratified sampling involves dividing the population into homogeneous subgroups and selecting samples from each subgroup. This method can provide more accurate and representative results when analyzing population characteristics.
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Elizabeth goes to a restaurant and the subtotal on the bill was
�
x dollars. A tax of 6% is applied to the bill. Elizabeth decides to leave a tip of 21% on the entire bill (including the tax). Write an expression in terms of
�
x that represents the total amount that Elizabeth paid
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 numbers of tomatoes growing on 7 different tomato plants are 2, 3, 3, 4, 7, 8, and 8. what is the range of this data set?
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 function f(x)= -√√x is shown on the graph.
3+
2-
1+
--5-4-3-2-
H
2 3 4 5
Which statement is correct?
O The range of the graph is all real numbers greater
than or equal to 0.
O The domain of the graph is all real numbers greater
than or equal to 0.
O The range and domain of the graph are the same.
O The domain of the graph is all real numbers.
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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Here are the ingredients needed to make 12 shortcakes.
50g of sugar
200g of butter
200g of flour
10ml of milk.
How many shortcakes does Dan make?
Answer:
He makes 12 shortcakes.
How to calculate the Area of a cylinder
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
can you help me with math
The linear function which represents the total cost is:
c = 11.95 + 48t
How to determine which linear function represents the total cost?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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A right triangle abc is insribed in a circle k(O,r). Find the radius of this circle if m
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°.
