Answer:
\(\huge\color{Black}\boxed{\colorbox{pink}{Answer♡}}\)
Given ,\(p(x) = ax {}^{3} + 8x {}^{2} + bx + 5 ...(1)\)
Also According to Question ,on dividing polynomial p(x) by ( x + 2 ) , we obtain ( -25 ) as a remainder.
Therefore , putting the value of x as ( x = -2 )
\(p( - 2) = a( - 2) {}^{3} + 8( - 2)^{2} + b( -2) + 5\)
\(p( - 2) = - 8a + 32 - 2b + 5 = - 25 \\ = > - 8a - 2b + 37 = - 25 \\ = > - (8a + 2b) = - (25 + 37) \\ cancelling \: negative \: sign \: at \: both \: sides \\ 8a + 2b = 52 \\ dividing \:both \: sides \: by \: 2 \\ 4a + b = 26...(2)\)
also given that..
when the polynomial p(x) is divided by 2x-1 , it gives 0 as the remainder , i.e. , 2x-1 is a root of p(x)
putting value of x = 1/2 in equation (1)
\(p( \frac{1}{2} ) = a( \frac{1}{2}) {}^{3} + 8( \frac{1}{2} ) {}^{2} + b( \frac{1}{2} ) + 5 = 0 \\ = > \frac{a}{8} + \frac{8}{4} + \frac{b}{2} + 5 = 0 \\ = >taking \: LCM \\ = > \frac{a + 16 + 4b + 40}{8} = 0 \\ = > \frac{a + 4b + 56}{8} = 0 \\ = > a + 4b = - 56...(3)\)
Now , we have equations (2) and (3) as...4a + b = 26... (2)
a + 4b = -56... (3)
multiply equation (2) by 4..16a + 4b = 104...(4)
Solving equations (3) and (4)a + 4b = -56
16a + 4b = 104
- - - ( bc signs are same )solving these equations we get,
-15a = -160
a = -160/-15
a = 32/3
putting value of a in (2) , we get...\(4a + b = 23 \\ 4( \frac{32}{3} ) + b = 23 \\ \frac{128}{3} + b = 23 \\ b = 23 - \frac{128}{3} \\ taking \: LCM \\ b = \frac{69 - 128}{3} \\ = > b = \frac{ -59}{3}\)
hope helpful~
An item costs $390 before tax, and the sales tax is .$11.17 Find the sales tax rate. Write your answer as a percentage.
Answer:
tax rate =
\( \frac{11.17}{390} = 0.2864102564\%\)
Step-by-step explanation:
to find a tax we multiply the price by the tax rate to find the tax value so when we want to find the tax rate we should divide tax value by the price
A train travels 540 miles in 4.5 hours. What is the train's rate in miles per hour?
Answer:
The train travels at 120 miles per hour.
Step-by-step explanation:
All we have to do is divide 540 by 4.5
540 ÷ 4.5 = 120
So the answer is 120 miles per hour.
Hope this helps! :)
答えを書くのを手伝ってください!
P vs NPは何の略ですか?
Answer: あるアルゴリズムが多項式時間で答えを提供できる一般的なクラスの質問は、「クラスP」または単に「P」と呼ばれます。 ...多項式時間で答えを検証できる質問のクラスは、NPと呼ばれ、「非決定論的多項式時間」を表します。
Step-by-step explanation: 恵まれた一日を
Answer: 非決定論的多項式時間
English: nondeterministic polynomial time
HELP ME ASAP!!!!!!!!!
Hello, please do not cheat on classwork on brainly, as this is against the honor code. Please do not continue this activity.
suppose you are good in math and statistics. adding programming to your skill-set will be necessary if you want to be a data scientist.
The appropriate option is "True". Adding programming to your skill-set is essential if you want to be a data scientist. Math and statistics provide a strong foundation for understanding the principles and concepts behind data analysis.
However, to effectively work with data at scale and solve real-world problems, data scientists need to use programming languages and tools.
Here are several reasons why programming is necessary for data scientists:
1. Data Manipulation: Data scientists often work with large and complex datasets that require cleaning, transformation, and manipulation. Programming allows data scientists to automate these tasks and perform them efficiently. Programming languages like Python and R offer extensive libraries and packages for data manipulation, such as Pandas, NumPy, and dplyr.
2. Data Visualization: Communicating insights from data is crucial, and data visualization plays a significant role in this process. Programming enables data scientists to create visualizations and interactive plots to explore and present data effectively. Tools like Matplotlib, Seaborn, ggplot, and Plotly provide powerful visualization capabilities.
3. Machine Learning and Data Modeling: Machine learning is an integral part of data science. Programming skills allow data scientists to implement and apply various machine learning algorithms and models. Libraries like scikit-learn, TensorFlow, and PyTorch provide the necessary tools and frameworks to build and deploy machine learning models.
4. Big Data Processing: With the exponential growth of data, data scientists often encounter big data challenges. Programming languages like Python and tools like Apache Spark enable data scientists to handle and process large-scale datasets efficiently. Knowledge of programming allows data scientists to leverage distributed computing frameworks and techniques to analyze and extract insights from big data.
5. Reproducibility and Collaboration: Programming facilitates reproducibility in data science workflows. By writing code, data scientists can document their analyses, share them with others, and ensure that the results can be reproduced. Programming also enables collaboration among data scientists and allows for version control and code sharing through platforms like GitHub.
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Suppose that a detailed study has revealed that for romance novels the number of pages has mean 364 and standard deviation 47, and that for detective novels the number of pages has mean 404 and standard deviation 173. A reader is going to select at random one romance novel, independently select at random one detective novel, and read both books. What is the standard deviation of the total number of pages the person will read? (A) 14.8 (B) 110.0 (C) 179.3 (D) 220.0 (E) 321.4
The standard deviation of the total number of pages the person will read is approximately 179.3.
To find the standard deviation of the total number of pages the person will read, we need to consider that the number of pages in the romance novel and the number of pages in the detective novel are independent random variables.
The variance of the sum of two independent random variables is equal to the sum of their variances. Therefore, the variance of the total number of pages is the sum of the variances of the romance novel and the detective novel.
For the romance novel:
Mean = 364
Standard Deviation = 47
For the detective novel:
Mean = 404
Standard Deviation = 173
Variance of the total number of pages = Variance of romance novel + Variance of detective novel
Variance = (47^2) + (173^2)
Standard Deviation = √Variance = √(47^2 + 173^2) ≈ 179.3 (rounded to one decimal place)
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find the areas of the shapes
Answer:
both shape together equals 234
Step-by-step explanation:
trapezoid= 14+10/2*4=34
rectangle=10*20=200
An oil can is shaped like a cylinder. The radius of the oil can is 3.5 inches and its height is 10 inches. Which measurement is closest to the volume of the oil can in cubic inches? 109.9 in³ 219.8 in³ 384.8 in³ 1099 in³
Answer:
384.8 cubic inches.
Step-by-step explanation:
Half of the sum of 3x and 4
Answer:
1.5x + 2
Step-by-step explanation:
(3x + 4)/2 = 1.5x + 2
If B is between A and C, AB= x+6, BC= 5x -4, and AC= 12x - 20, then AC=?
Answer:
AC = 24
Step-by-step explanation:
First you want to set up the equation to find what x equals which is AB + BC = AC
12x - 20 = x + 6 + 5x - 4
Then combine like terms and solve.
12x - 20 = x + 6 + 5x - 4
12x - 20 = 6x +2
+20 +20
12x = 6x + 22
-6x -6x
6x = 22
x = 11/3 or 3 2/3
Then plug in x to the AC equation.\
12(11/3) - 20
44-20
AC = 24
Solve please. Correctly
-12 + b + 6 + 8b = -6 - 7b
Answer:
b = 0
Step-by-step explanation:
Answer:
Step-by-step explanation:
simplifies to -6+9b = -6-7b
16b=0
b=0
How do you do 109???
Answer:
F. 1
Step-by-step explanation:
Get 1/7 and 1/6
I would do this by dividing the whole equation by 42
6/42=1/7
7/42=1/6
That means 42/42=1 so the answer is 1
you have 11 art projects that weigh 24 pounds. If you give you mom 7 of your art projects, how much would her box weigh?
The weight for mom's boxes is obtained as 41.41 pounds.
What is weight?
Weight gauges how much gravity is pulling on a body.
The weight formula is provided by -
w = mg
Since weight is a force, it has the same SI unit as a force, which is the Newton (N).
Use a proportion to solve this problem.
Since the weight of the art projects is directly proportional to the number of art projects, we can set up the following proportion -
weight of 11 art projects / 11 = total weight / 24
Solving for the total weight -
total weight = (weight of 11 art projects / 11) x 24
total weight = 2.18 x 24
total weight = 52.32 pounds
So the total weight of the 11 art projects is 24 pounds, and if mom gets 7 of them, 4 art projects will be left weighing a total of -
weight of 4 art projects = (weight of 11 art projects - weight of 7 art projects)
weight of 4 art projects = (24 - (7/11) x 24)
weight of 4 art projects = 10.91 pounds
So, mom would be receiving 7 art projects weighing a total of -
weight of 7 art projects = (total weight - weight of 4 art projects)
weight of 7 art projects = (52.32 - 10.91)
weight of 7 art projects = 41.41 pounds
Therefore, mom's box would weigh 41.41 pounds.
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Rewrite the following equation in slope-intercept form.4x – 3y = -12please show how
The equation of line in slope-intercept form is,
\(y=mx+c\)Here, m is slope of line and c is y-intercept.
Simplify the equation to obtain the slope-intercept form.
\(\begin{gathered} 4x-3y=-12 \\ 4x+12=3y \\ y=\frac{4x}{3}+\frac{12}{3} \\ =\frac{4}{3}x+4 \end{gathered}\)The data in the table above was compiled by a new pet information website from a random survey of users with Basset Hounds and Welsh Corgis. Which statement best compares the height of the two breeds based on the collected data?
An adult Welsh Corgi is always going to be shorter than an adult Basset Hound.
Basset hounds tend to be a little over two inches taller than Welsh Corgis, but have a higher variability in height.
There is no noticeable difference in the height of the two breeds since the Mean Absolute Deviation for each breed is roughly the same.
It is impossible to make a valid conclusion because the sample sizes are too small.
Answer:
An adult Welsh Corgi is always going to be shorter than an adult Basset Hound.
Step-by-step explanation:
That's what I think because the Basset Hound is 13.8 in. in height right? So he's two inches taller if we round up both numbers. Basset hound would be 14 and welsh corgi would be 11....................okay im not sure i give up but it's either
"An adult Welsh Corgi is always going to be shorter than an adult Basset Hound."
"Basset hounds tend to be a little over two inches taller than Welsh Corgis, but have a higher variability in height.
whichever just not the other ones good luck!
Basset hounds tend to be a little over two inches taller than Welsh Corgis, but have a higher variability in height.
What is mean?
Mean is actually the average of all the observations.
What is absolute mean deviation?Basset hounds tend to be a little over two inches taller than Welsh Corgis, but have a higher variability in height.
of a data set is the average distance between each data value and the mean.
How to know which statement best compares the height of the two breeds based on the collected data?According to the problem,
Mean height of Basset hounds is 13.8Mean height of Welsh Corgis is 11.1 Mean absolute deviation of height of Basset hounds is 1.9Mean absolute deviation of height of Welsh Corgis is 1.2Here we can say, the average height of Basset hounds is 13.8 and is highly dispersed in comparison to Welsh Corgis
So, we can say Basset hounds tend to be a little over two inches taller than Welsh Corgis, but have a higher variability in height.
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The Thomson family spends money each month on the expenses shown.
Drag each expense to show whether it is a fixed expense, a variable expense, or if it is neither of these from month to month.
Please help ASAP for 20 Points! and a brainliest!
You are running a fuel economy study. You want
to find out which car can travel a greater distance
on 1 gallon of gas.
a. What is the gas mileage, in miles per gallon,
for the blue car?
b. What is the gas mileage, in miles per gallon,
for the silver car?
c. Which car could travel the greater distance
on 1 gallon of gas?
Thank you!
Answer:
a) gas mileage of blue car: 23.667 miles/gallonb) gas mileage of silver car: 34 miles/gallonc) The silver car would travel a greater distance on 1 gallon than the blue car.Step-by-step explanation:
a) gas mileage of blue car:gas mileage = miles covered/gallons used
but:
miles covered = \(35\frac{1}{2}\)
= 35.5
gallons used = 1\(\frac{1}{2}\)
= 1.5
gas mileage = 35.5/1.5
gas mileage = 23.667 miles/gallon (to 3 decimal places)
b) gas mileage of silver car:gas mileage = miles covered/gallons used
but:
miles covered = \(27\frac{1}{5}\)
= 27.2
gallons used = \(\frac{4}{5}\)
= 0.8
gas mileage = 27.2/0.8
gas mileage = 34 miles/gallon
c)
gas mileage of blue: 23.667 miles/gallon implies the blue car will travel 23.667 miles on 1 gallon
gas mileage of silver: 34 miles/gallon implies the silver car will travel 34 miles on 1 gallon
Hence the silver car would travel a greater distance on 1 gallon than the blue car.
Prescribed: 2 liters 5% Dextrose to infuse in 16 hours. Supplied: Two one-liter bags of 5% Dextrose. Directions: Calculate the flow rate in mL/hr. (Round to the nearest milliliter
Answer:
The flow rate in mL/hr for infusing 2 liters of 5% dextrose over 16 hours is 125 mL/hr.
Step-by-step explanation:
We can use the following formula to calculate the flow rate:
Flow rate (mL/hr) = Volume to be infused (mL) / Time of infusion (hr)
First, we need to convert the total volume of 2 liters to mL:
2 liters = 2000 mL
Next, we can plug in the values:
Flow rate = 2000 mL / 16 hours
Flow rate = 125 mL/hr
Therefore, the flow rate in mL/hr for infusing 2 liters of 5% dextrose over 16 hours is 125 mL/hr.
Melanie and noah are baking a birthday cake for franceca. The recipe call for 3/4 meauring cup and noah ha a 1/8 meauring cup. Which cup hould they ue
They should use 6 cup of Noah's measuring cup
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
Recipe call = 3/4Noah's cup = 1/8Number of cup = ?Calculating the number of cup the should use:
Number of cup = Recipe call / Noah's cup
Number of cup = (3/4) / (1/8)
Number of cup = 3*8 / 4*1
Number of cup = 24/4
Number of cup = 6
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Correctly written question:
Melanie and Noah are baking a birthday cake for Francesca. The recipe call for 3/4 measuring cup and Noah has a 1/8 measuring cup. Which cup should they use?
when determining the size of a fact table, estimating the number of possible values for each dimension associated with the fact table is equivalent to:
When determining the size of a fact table, estimating the number of possible values for each dimension associated with the fact table is equivalent to: determining the number of possible values for each foreign key in the fact table.
The measures, metrics, or facts of a business process are contained in a fact table in data warehousing. In a star or snowflake schema, it sits in the middle, surrounded by dimension tables.
When several fact tables are employed, they are organized according to a fact constellation schema. The two types of columns that make up a fact table are typically those that hold facts and those that serve as a foreign key to dimension tables.
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If we estimate that 10 people can fit in a 5ft by 5ft area, then what would be your estimate of how many people can fit on a basketball court measuring 94ft by 50ft?
Answer:
1,880 people will fit in 94 ft by 50 ft
Step-by-step explanation:
We can estimate this using the area
For 5 ft by 5ft ; 10 people can fit in an area of 5 * 5 = 25 ft^2
In an area of 94 ft by 50 ft, the number of people that can fit will be;
let’s start with the area
Area = 94 * 50 = 4,700 square feet
10 people will fit in 25 square feet
x people in 4,700 square feet
25 * x = 10 * 4700
25x = 47,000
x = 47000/25
x = 1,880 people
Given lines p and q are parallel, find the value of x that makes each diagram true.
In the given diagram the value of x is is 140° and 25° respectively
In the diagram a, when you have 2 parallel lines cut by a transversal, the corresponding angles are equal and the value of x is equal to the corresponding angle as they are vertical angles, vertical opposite angles are equal.
In the diagram b, angle x is equal to the angle that is supplementary to 155° (Sum of supplementary angles is equal to 180°)
180-155=25°
In the given diagram the value of x is 140° in the diagram a and 25° for the diagram b respectively
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Your question is incomplete as the diagram is missing but the above answer might help you out.
Using a) parabolic coordinates and b) cylindrical coordinates, find the differential unit of length, ds2 = dx2 + dy2 + dz2 and the volume element dV = dxdydz.
Parabolic CoordinatesParabolic coordinates are a coordinate system that can be used to define any point in 2D Euclidean space.
In this system, points are defined by two variables u and v. The parabolic coordinates of a point in 2D Euclidean space can be found using the following equations: x = (u^2 - v^2) / 2y = uvIn this coordinate system, the differential unit of length, ds2, can be found using the equation:ds2 = du2 + dv2 + dx2where du2 and dv2 are the differentials of u and v, respectively, and dx2 is the differential of x. Cylindrical CoordinatesCylindrical coordinates are a coordinate system that can be used to define any point in 3D Euclidean space. In this system, points are defined by three variables r, θ, and z.
The cylindrical coordinates of a point in 3D Euclidean space can be found using the following equations: x = r cos(θ)y = r sin(θ)z = zIn this coordinate system, the differential unit of length, ds2, can be found using the equation:ds2 = dr2 + r2 dθ2 + dz2where dr2 and dθ2 are the differentials of r and θ, respectively, and dz2 is the differential of z. The volume element dV can be found using the equation:dV = r dr dθ dz. Using the above explanations, the differential unit of length, ds2, and the volume element dV for parabolic coordinates and cylindrical coordinates are as follows: For Parabolic Coordinates: ds2 = du2 + dv2 + dx2= du2 + dv2 + [(u2 - v2)/2]2dV = dudvdxdydz = [(u2 - v2)/2] dudvdzFor Cylindrical Coordinates: ds2 = dr2 + r2 dθ2 + dz2= dr2 + r2 dθ2 + dz2dV = rdrdθdzThe above explanations provide the main answer, which is the differential unit of length, ds2 and the volume element dV for parabolic coordinates and cylindrical coordinates.
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Find the number of tiles in the 43rd picture
Answer:
1849
Step-by-step explanation:
1 - 1
2 - 4
3 - 9
4 - 16 (drew this one out)
We can see that each of the triangles is the number of the picture squared. So for the 43rd picture we take 43 * 43 = 1849
So the 43rd picture is 1849
the area under the entire probability density curve is equal to___a. 0b. -1c. 1d. [infinity]
The required area under the whole probability density curve is given by option C. 1.
The area under the entire probability density curve is equal to,
As the probability density function (pdf) represents the probability of a continuous random variable.
And continuous random variable taking on a specific value within a certain range.
Since the total probability of all possible outcomes must be equal to 1.
This implies that the area under the entire probability density function (pdf) curve must also be equal to 1.
Therefore, the area under the entire probability density curve function is equal to option c. 1.
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Hailey ran a few laps. D(n)D(n)D, (, n, )models the duration (in seconds) of the time it took for Hailey to run her n^{th}n th n, start superscript, t, h, end superscript lap. nnn 333 777 999 D(n)D(n)D, (, n, )858585 999999 110110110 When did the lap duration increase faster
Question:
Hailey ran a few laps. D(n), models the duration (in seconds) of the time it took for Hailey to run her nth lap. When did the lap duration increase faster?
A. Between the 3rd and 7th lap
B. Between the 7th and 9th lap
C. The lap duration increased at the same rate over both intervals
Answer:
B. Between the 7th and 9th lap
Step-by-step explanation:
Given
See attachment for table
Required
Determine when the lap increases faster
To do this, we simply calculate the rate of change between each lap.
From the attachment, we have:
\(D(3) = 85\)
\(D(7) = 99\)
\(D(9) = 110\)
Rate of change is calculated using:
\(Rate = \frac{D(b) - D(a)}{b - a}\)
For D(3) to D(7), the rate is:
\(Rate = \frac{D(7) - D(3)}{7 - 3}\)
\(Rate = \frac{99 - 85}{7 - 3}\)
\(Rate = \frac{14}{4}\)
\(Rate = 3.5\)
For D(7) to D(9), the rate is:
\(Rate = \frac{D(9) - D(7)}{9 - 7}\)
\(Rate = \frac{110 - 99}{9 - 7}\)
\(Rate = \frac{11}{2}\)
\(Rate = 5.5\)
The rate of change between the 7th and 9th lap is greater than the rate of change between then 3rd and 7th lap .
Hence, (b) is correct
Answer:
B) Between the 7th lap and the 9th lap
Step-by-step explanation:
solve the functions for b I am having many difficulties
From the figure we see that the function in b, only asigns values for the points in -3, -1, 1, 3 and 4 of the x axis.
Then it's domain is
\(\text{Dom}=\lbrace-3,-1,1,3,4\rbrace\)To find the range of the figure in b, we have to see what values does it take in the y axis, we notice that this values are -4, 0, 1, 4 and 5. Hence
\(\text{Range=}\lbrace-4,0,1,4,5\rbrace\)In the case of c. we notice that the lines go on (that's is why it's represented by arrows). We note that if the lines go on, eventually they will take all the values on the x axis. Then
\(\text{Dom=(-}\infty,\infty)\)For the range we notice that it will take all the positive values on the y axis. then
\(\text{Range}=\lbrack0,\infty)\)In the case of the function a, we notice that the function assigns values to every point from -4 to 4 on the x axis. Then we can conclude that the domain is
\(\text{Domain=}\lbrack-4,4\rbrack\)We also notice that the values that y takes are from 0 to 4, therefore
\(\text{Range}=\lbrack0,-4\rbrack\)A 12 sided number cube with the numbers 1 through 12 is rolled.Select from the drop down menu to correctly complete the statement.Rounded to the nearest hundredth, the probability that the number cube lands on a number other than 4 is
of the 32 students in Miss Jenkins class only 8 pass the semester exam what percent of the class did not pass the exam
Answer:
75%
Step-by-step explanation:
8 is 1/4 of 32
so the rest of the students are 3/4 of the class
3/4 is equal to 75%
im losttt
1.4g = 4.2 , solve the equation for g.
a. g=5.2
b. g=3
c. g=2.1
d. g=4
Answer:
g=3
Step-by-step explanation:
all you had to do was divide both sides by 1.4