The value of a is -9
What is standard form of a polynomial?
When expressing a polynomial in its standard form, the greatest degree of terms are written first, followed by the next degree, and so on.
[tex]P(x)=4x^5+3x^2+2x+a[/tex]
Question might be asking to find the value of 'a' at the point (1, 0) on the graph of [tex]P(x)=4x^5+3x^2+2x+a[/tex]
Substitute the point into the polynomial. i.e., x=1, y=0
=> [tex]0=4(1)^5+3(1)^2+2(1)+a[/tex]
=> 0= 4*1 + 3*1+2 +a
=> 0= 4+3+2+a
=> 0=9 +a
=> a= -9
The value of a is -9
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Complete Question:
Find the value of [tex]P(x)=4x^(5)+3x^(2)+2x+a[/tex]
Given: PP(xx) = x^3−2x^2 + 9x−18
a) How many roots does P(x) have?
b) What are the possible rational roots?
c) Find all the roots.
a) Number of roots in the given polynomial is three.
b) Possible rational roots of the given polynomial are {±1, ±2, ±3, ±6, ±9, ±18}
c) The roots of the given polynomial are {2, 3i, -3i}.
Given polynomial is `P(x) = x³ - 2x² + 9x - 18`.a) Number of roots in the given polynomial is three. b) Possible rational roots of the given polynomial are expressed in the form of `p/q`, where p is a factor of the constant term `-18` and q is a factor of the leading coefficient `1`.Constant term of the given polynomial is `-18`. The factors of `-18` are 1, 2, 3, 6, 9, and 18. Leading coefficient of the given polynomial is `1`. The factors of `1` are ±1.∴ Possible rational roots of the given polynomial are {±1, ±2, ±3, ±6, ±9, ±18}.c) Let us check whether the possible rational roots satisfy the given polynomial. To check the roots, we can use synthetic division, which is an efficient method to check the roots of a polynomial. When `x = -1` is substituted in the given polynomial, we get P(-1) = (-1)³ - 2(-1)² + 9(-1) - 18= -1 + 2 - 9 - 18= -26, which is not equal to `0`.When `x = 1` is substituted in the given polynomial, we get P (1) = 1³ - 2(1)² + 9(1) - 18= 1 - 2 + 9 - 18=-10, which is not equal to `0`.
When `x = -2` is substituted in the given polynomial, we get P(-2) = (-2)³ - 2(-2)² + 9(-2) - 18= -8 + 8 - 18 - 18= -36, which is not equal to `0`.When `x = 2` is substituted in the given polynomial, we get P(2) = 2³ - 2(2)² + 9(2) - 18= 8 - 8 + 18 - 18= 0, which is equal to `0`.∴ `x = 2` is a root of the given polynomial. By using synthetic division method, we can find the remaining two roots. x - 2 | 1 - 2 9 - 18| | 2 0 18| | 1 0 9 0|Therefore, the factors of the given polynomial are `(x - 2)(x² + 9)`.The quadratic factor, `x² + 9`, does not have any real roots, as the discriminant is negative.∴ The roots of the given polynomial are {2, 3i, -3i}.
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help pls 1/3(3m+6)-2(2m+6)
1/3(3m+6)-2(3m+6)
Answer:
-5m - 10
Step-by-step explanation:
1/3(3m+6)-2(3m+6)
= 1m + 2 - 6m - 12
= -5m - 10
So, the answer is -5m - 10
Answer:
-5(m+2)
Step-by-step explanation:
1/3(3m+6)-2(3m+6)
combine like terms
-5/3(3m+6)
Distribute
-5m - 10
common factor
-5(m+2)
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
m = - 1
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-2,0) (0, -2)
We see the y decrease by 2, and the x increase by 2, so the slope is
m = -2/2 = -1
So, the slope is -1
Answer:
m = - 1
Step-by-step explanation:
minimum amount of dogs that could has a mass more than 26kg
Answer:
Below
Step-by-step explanation:
the last equation shows frequency of 5 for greater than this mass
the equation before it covers 20 to 30 kg frequency 11
so it could be ZERO or it could be ELEVEN are above 26 kg ....you just cannot tell ....so the MINIMUM frequency would be 5 + ZERO = 5
and the MAXIMUM would be 5 + ELEVEN = 16
Solve the matrix equation by using inverse matrices.
The Solution of the matrix for (x, y) is (-1, 5) that is: [tex]\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}-1\\5\end{array}\right][/tex]
Inverse matrices: What are they?A matrix is described by its elements, which are the numbers or symbols that make up the matrix, and its dimensions, which indicate how many rows and columns there are in the matrix. A matrix's inverse is a matrix that yields the identity matrix when multiplied by the original matrix. A matrix's inverse is denoted by and only applies to square matrices (matrices with an equal number of rows and columns).
[tex]\left[\begin{array}{ccc}4&2\\-4&2\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}6\\14\end{array}\right][/tex]
find the inverse matrix for the matrix
[tex]\left[\begin{array}{ccc}4&2\\-4&2\end{array}\right][/tex]
Find the determinant,
determinant = 4 × 2 (-4) × 2 = 16
Inverse matrix is
[tex]1/16 \left[\begin{array}{ccc}4&2\\-4&2\end{array}\right]^T = 1/16 \left[\begin{array}{ccc}2&-2\\4&4\end{array}\right][/tex]
So, the solution of the equation is
[tex]\left[\begin{array}{ccc}x\\y\end{array}\right] = 1/16 \left[\begin{array}{ccc}2&-2\\4&4\end{array}\right] \left[\begin{array}{ccc}6\\14\end{array}\right][/tex]
On solving,
Therefor, The Solution for (x, y) is (-1, 5).
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A group of people were asked if they had run a red light in the last year. 313 responded "yes", and 286 responded "no".
Find the probability that if a person is chosen at random, they have run a red light in the last year.
Give your answer as a fraction or decimal accurate to at least 3 decimal places
Answer:
[tex]0.523[/tex]
Step-by-step explanation:
Total number of respondents = 313 + 286 = 599
Number who responded yes = number running a red light
[tex]\text P(\text {ran a red light)}}\\\\=\dfrac{\text{Number who ran a red light}}{\text{Total number of respondents}}\\\\= \dfrac{313}{599}\\\\= 0.52253[/tex]
Rounded to 3 decimal places the probability is [tex]0.523[/tex]
the patient has formula feedings through a feeding tube. she is given 250 ml every 4 hours (0400, 0800, 1200, 1600, 2000, 2400) around the clock. the nurse gives 100 ml of water after each feeding. what is the patient's intake in the 2300 to 0700
The patient has formula feedings through a feeding tube. She is given 250 ml every 4 hours (0400, 0800, 1200, 1600, 2000, 2400) around the clock. The nurse gives 100 ml of water after each feeding.
The intake of the patient from 2300 to 0700 would be 750 ml.
The formula for calculating the patient's intake from 2300 to 0700
The formula to calculate the patient's intake from 2300 to 0700 is the following:
7 hours after 2300 ⇒ 7+24 - 23 = 8 hours before 0800
Thus, the patient's intake from 2300 to 0800 would be:
From 2300 to 2400 = 250 ml
From 2400 to 0400 = 250 ml
From 0400 to 0800 = 250 ml
From 0800 to 0700 = 100 ml (as it is less than 4 hours)
Total Intake = 250 ml + 250 ml + 250 ml + 100 ml = 850 ml
Intake from 2300 to 0700 = Total intake - Intake from 0800 to 0700
Intake from 0800 to 0700 = 100 ml
Total Intake = 850 ml - 100 ml = 750 ml
Therefore, The patient is receiving formula feedings through a feeding tube, administered every 4 hours (at 0400, 0800, 1200, 1600, 2000, and 2400). Following each feeding, the nurse administers 100 ml of water. It can be calculated that the patient's total intake during the period from 2300 to 0700 would be 750 ml.
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a tank 12m long, 8m wide and 5m deep is to be made. it is open at the top, determine the iron sheet required for the fabrication. also find volume in litres
Answer:
Surface area of the sheet: 296 square meters
Area of tank: 480 cubic meters
Step-by-step explanation:
Don't forget your units!
"determine the iron sheet required for the fabrication" is asking for the surface area of the rectangular prism.
This is found by adding the five sides of the prism. The top side is excluded because it is open.
Front and back: 2(12m * 5m) = 120m^2
Left and right: 2(8m * 5m) = 80m^2
Floor: (12m * 8m) = 96m^2
120m^2 + 80m^2 + 96m^2 = 296m^2
The volume is found using standard methods. The open top does not have an impact here.
12m * 8m * 5m = 480m^3
Johanna measured the height and petal length of all the flowers in her garden. She plotted her results and found that the relationship between the variables suggests a weak positive linear association with 1 outlier.
The graph that might be made by Johanna is graph (3).
Johanna has two variables: height and petal length. She plotted these variables on a graph to determine the relationship between them.
However, Johanna also found that there is one outlier in her data.
Each point on the graph represents the height and petal length of a single flower in Johanna's garden. The x-axis represents the height of the flower, and the y-axis represents the petal length.
Since there is a weak positive linear association between the two variables, the points on the scatter plot will be generally moving upwards from left to right.
In conclusion, Johanna's graph is most likely a scatter plot that shows the weak positive linear association between the height and petal length of the flowers in her garden, with one outlier that stands out from the rest of the data.
Hence the correct graph is (3).
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Complete Question:
Johanna measured the height and petal length of all the flowers in her garden. She plotted her results and found that the relationship between the variables suggests a weak positive linear association with 1 outlier.
Which of the following might be the graph Johanna made?
Un mueblero compró lo siguiente dos camas a 7565 pesos cada una un juego de sala a 26500 un ropero a 17869 pesos y llevaba 65500 cuánto dinero le sobra
The amount that is left over is: 65,500 - 59,499 = 6,001 pesos. A furniture dealer or business owner is referred to as a "mueblero" in Spanish.
The cost of the furniture was 2 x 7565 = 15,130 pesos in camas.
1 x 26,500 is equal to 26,500 pesos in a game of pool.
One times 17,869 equals 17,869 pesos in a rope.
Total expenditures were 15,130, 26,500, 17,869, and 59,499 pesos.
The amount that is left over is: 65,500 - 59,499 = 6,001 pesos.
A furniture dealer or business owner is referred to as a "mueblero" in Spanish. The question asks how much money the mueblero has left over after making the purchases since he had a specific amount of money to spend and acquired a number of items of furniture for his store.
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PLEASE HELP ME ON THIS QUICK(Image)
The statement that is correct about the two angles that are said to be linear pair would be = <ABC and <CBD are adjacent angles. That is option A
What is a linear pair of angles?A linear pair exists between angles that are on a straight line that are formed when two lines intersect eachother leading to the formation of the adjacent angles.
The linear angles are there said to be adjacent angles and the sum of these two angles are always = 180°.
Therefore from the given statements, the correct option about the two angles which are linear paired angles is that they are also adjacent to each other.
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please help if possible
Domain of [tex]f^{-1}[/tex]: R - {-3} or (-∞, -3) ∪ (-3, ∞)
Range of [tex]f^{-1}[/tex]: R - {10} or (-∞, 10) ∪ (10, ∞)
What do you mean by domain and range?The domain of a function is the set of all possible input values (also known as independent variables) for which the function is defined. The range of a function is the set of all possible output values (also known as dependent variables) that the function can produce.
Given the function f, state the domain and range of both f and [tex]f^{-1}[/tex], where
[tex]f(x) =\frac{3x+4}{10-x}[/tex]
Domain and range using inequalities,
Domain of f: R - {10} or (-∞, 10) ∪ (10, ∞)
Range of f: R - {-3} or (-∞, -3) ∪ (-3, ∞)
The inverse does not exist.
[tex]f^{-1} (x) =\frac{10x-4}{x+3}[/tex]
Domain of [tex]f^{-1}[/tex]: R - {-3} or (-∞, -3) ∪ (-3, ∞)
Range of [tex]f^{-1}[/tex]: R - {10} or (-∞, 10) ∪ (10, ∞)
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a fair die is rolled 14 times. let be the number of faces that appear exactly three times. which of the following expressions appear in the calculation of var(x)
The variance of a fair die that has been rolled 14 times and the number of faces that appear exactly three times is 2.33.
The variance of X can be calculated using the following formula:
Var(X) = Σ(P(X=x)*(x-μ)²)/N
Where Σ represents the summation of all possible outcomes, P(X=x) is the probability of an event occurring, x is the possible outcome, μ is the mean of all possible outcomes, and N is the number of trials.
In this case, the number of possible outcomes of a fair die is 6, and since the die has been rolled 14 times, N = 14. To calculate the mean, we use the formula μ = ΣP(X=x)*x, and in this case, the mean would be 3 since each face appears exactly 3 times.
Therefore, Var(X) = Σ(P(X=x)*(x-3)²)/14. We can then calculate the variance of X by substituting in the probabilities for each face: P(X=1) = 1/14, P(X=2) = 1/14, P(X=3) = 1/14, P(X=4) = 1/14, P(X=5) = 1/14, and P(X=6) = 1/14.
This yields a variance of 2.33, as calculated below:
Var(X) = (1/14 * (1-3)² + 1/14 * (2-3)² + 1/14 * (3-3)² + 1/14 * (4-3)² + 1/14 * (5-3)² + 1/14 * (6-3)²)/14
= 2.33.
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What is 4.5-4x evaluated
Answer:
Step-by-step explanation:
I need help studying
Answer: So get your rump in that chair and study your pp off
Step-by-step explanation:
A table costs five times as much as a chair. A trader bought six more chairs than tables and spent $18 594. If a chair costs $1033,how many chairs and tables did he buy
The trader bought 3 512 tables and 6(3 512) = 21 072 chairs.A table costs five times as much as a chair.
The cost of a chair is given as $1033. So, c = 1033Substituting c = 1033 in 5t + 1033 = 18 594,5t = 18 594 - 1033 5t = 17 561 t = 17 561/5 t = 3512.2Let c be the number of chairs and t be the number of tables.As the table costs 5 times as much as the chair, the total cost of the tables is 5t. The total cost of the chairs is c. The total cost of the tables and chairs is 5t + c = $18 594.Therefore, 5t + c = 18 594.The cost of a chair is given as $1033. So, c = 1033Substituting c = 1033 in 5t + 1033 = 18 594,
5t = 18 594 - 1033 5
t = 17 561
t = 17 561/5
t = 3512.2Therefore, the trader bought 3 512 tables and 6(3 512) = 21 072 chairs.
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(09.02 MC)
Which equation could be used to solve for the measure of angle P?(1 point)
Circle N is shown with a quadrilateral OPQR inscribed inside it. Angle O is labeled x degrees. Angle P is labeled y degrees. Angle Q is labeled z degrees. Angle R is labeled w degrees.
In order to solve for the measure of angle P, the equation x + y + z + w = 360° can be used.
What is an angle?An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles are measured in degrees or radians and are used to describe the direction of two intersecting lines in a plane. Angles are also used to measure the central angle of a circle and the angle between two curves.
This equation is known as the Angle Sum Theorem, which states that the sum of the measures of the angles of a triangle or a quadrilateral equals 360°. The measure of each angle of the quadrilateral can be used in the equation to solve for the measure of angle P, which is labeled as y. This equation can be written as x + y + z + w = 360° and then solved for the measure of angle P by subtracting x + z + w from both sides of the equation. This would result in y = 360° - (x + z + w). By substituting the measure of each angle into the equation, the measure of angle P can be found.
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A drink recipe book has a table that shows the proportional relationship between cups of water and cups of lemon juice for different amounts of lemonade. In the table, enter the number of cups of water needed for 1 cup of lemon juice
The ratio of water to lemon juice is 7:1. Thus, 7 cups of water are needed for 1 cup of lemon juice.
The table shows the proportional relationship between the amount of water and lemon juice needed to make lemonade in different quantities. The ratio of cups of water to cups of lemon juice remains constant for each quantity of lemonade. For example, to make 2 cups of lemonade, 1.5 cups of water are needed for every 1 cup of lemon juice. This means that if you want to make 4 cups of lemonade, you would need to double the amount of water and lemon juice required for 2 cups. This proportional relationship can be helpful in scaling the recipe up or down to make different quantities of lemonade.
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Complete question:
A drink recipe book has a table that shows the proportional relationship between cups of water and cups of lemon juice for different amounts of lemonade. If you need 6 cups of lemonade, the table shows you need 1 cup of lemon juice. Enter the number of cups of water needed for 1 cup of lemon juice.
Cups of Lemon Juice Cups of Water
1 4
2 8
3 12
4 16
Type the correct answer in the box. Use numerals instead of words.
The test to determine the presence of a certain virus in a pigeon is 97% accurate for a pigeon that has the virus and 99% accurate for a pigeon
that does not have the virus. In a given population, 1. 5% of the pigeons are infected.
Do not round your answer.
The probability that a randomly selected pigeon gets an incorrect result is_____
The probability that a pigeon chosen at random will receive an incorrect test outcome is 103/10,000 = 0.0103, or roughly 1.03%.
Let's assume that there are 10,000 pigeons in the population. Then, 1.5% of them, which is 150 pigeons, are infected with the virus.
Out of these 150 infected pigeons, the test will correctly identify 97% of them, which is 145.5 pigeons. The remaining 4.5 infected pigeons will be incorrectly identified as not having the virus.
Out of the 9,850 uninfected pigeons, the test will correctly identify 99% of them, which is 9,751.5 pigeons. The remaining 98.5 pigeons will be incorrectly identified as having the virus.
Therefore, the total number of pigeons that get an incorrect test result is 4.5 + 98.5 = 103.
So, the probability that a randomly selected pigeon gets an incorrect test result is 103/10,000 = 0.0103 or approximately 1.03%
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Two times the sum of 5 and some number is 30. What is the number?
Answer:
10
Step-by-step explanation:
5+10=15
15×2=30
so the answer to your question is 10
Answer:
x = 10.
Step-by-step explanation:
Given: Two times the sum of 5 and some number is 30. What is the number?
First, write the equation:
2(5 + x) = 30
Simplify the brackets with distribution property:
10 + 2x = 30
Then collect like terms:
2x = 30 - 10
Finally, calculate:
2x = 20 (Divide both sides by 2)
x = 10
A life insurance salesman operates on the premise that the probability that a man reaching his sixtieth birthday will not live to his sixty-first birthday is 0.05. On visiting a holiday resort for seniors, he sells 12 policies to men approaching their sixtieth birthdays. Each policy comes into effect on the birthday of the insured, and pays a fixed sum on death. All 12 policies can be assumed to be mutually independent. Provide answers to the following to 3 decimal places. a) What is the expected number of policies that will pay out before the insured parties have reached age 61? b) What is the variance of the number of policies that will pay out before the insured parties have reached age 61? c) What is the probability that at least two policies will pay out before the insured parties have reached age 61?
The probability that at least two policies will pay out before the insured parties have reached age 61 is 0.3400.
The answer is as follows: The expected number of policies that will pay out before the insured parties have reached age 61 isE(x) = np = 12 × 0.05 = 0.6Therefore, the expected number of policies that will pay out before the insured parties have reached age 61 is 0.6.b) The variance of the number of policies that will pay out before the insured parties have reached age 61 isVar(x) = np(1-p) = 12 × 0.05(1-0.05) = 0.570Therefore, the variance of the number of policies that will pay out before the insured parties have reached age 61 is 0.570.c) To find out the probability that at least two policies will pay out before the insured parties have reached age 61, we can use the complement rule that is:P(X ≥ 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)P(X = 0) = (0.95)^12 = 0.2835 (probability that none of the 12 policies will pay out before the insured parties have reached age 61)P(X = 1) = 12C1(0.05)(0.95)^11 = 0.3765 (probability that only one of the 12 policies will pay out before the insured parties have reached age 61)Therefore,P(X ≥ 2) = 1 - P(X = 0) - P(X = 1) = 1 - 0.2835 - 0.3765 = 0.3400Therefore, the probability that at least two policies will pay out before the insured parties have reached age 61 is 0.3400.
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Find three consecutive even integers if 3 times the first iteger is 2 times the the third
The solution is that the three consecutive even integers are 8, 10, and 12.
Let's assume the first even integer to be x. Since we are looking for three consecutive even integers, the second even integer will be x + 2, and the third even integer will be x + 4.
According to the problem statement, 3 times the first even integer is equal to 2 times the third even integer, which can be written mathematically as:
3x = 2(x + 4)
Solving for x, we get:
3x = 2x + 8
x = 8
Therefore, the first even integer is 8, and the second and third even integers are 10 and 12, respectively.
We can verify that 3 times the first even integer is indeed equal to 2 times the third even integer:
3(8) = 24
2(12) = 24
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Merisa spent 3/4 of her money on a dictionary. She spent 1/2 of the remainder on a calculator. The dictionary cost $30 more than the calculator. How much did the dictionary cost?
The dictionary cost $36 if Merisa spent 3÷4 of her money on a dictionary. She spent 1÷2 of the remainder on a calculator.
What is Algebraic expression ?
In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.
Let M be the total amount of money Merisa had before she made any purchases.
Merisa spent 3÷4 of her money on a dictionary, which means she spent 1÷4 of her money on the calculator and other expenses.
So, the amount of money she had left after buying the dictionary is:
M - 3÷4 M = 1÷4 M
She then spent 1÷2 of the remainder on a calculator, so:
(1÷2) (1÷4 M) = 1÷8 M
Let's call the cost of the calculator C.
We know that the dictionary cost $30 more than the calculator, so:
D = C + $30
We can now set up an equation to solve for C:
C + $30 = 3÷4 M
C = 3÷4 M - $30
And we also know that:
C = 1÷8 M
We can substitute the second equation into the first equation and solve for M:
1÷8 M + $30 = 3÷4 M
3÷4 M - 1÷8 M = $30
5÷8 M = $30
M = $48
So, Merisa had $48 before she made any purchases.
We can now use this to find the cost of the dictionary:
D = C + $30
D = (1÷8 M) + $30
D = ($6) + $30
D = $36
Therefore, the dictionary cost $36.
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You might need: Calculator
Alexander uses cupric chloride to etch circuit boards. He recorded the room temperature, in °C, and the
um
etching rate, in of the cupric chloride.
min
After plotting his results, Alexander noticed that the relationship between the two variables was fairly
linear, so he used the data to calculate the following least squares regression equation for predicting the
etching rate from the room temperature:
1
j = 2 + 2
5
What is the residual if the room temperature was 25°C and the cupric chloride had an etching rate of
um
5
?
min
um
min
Show Calculator
The residual is the difference between the observed etching rate and the predicted etching rate
The residual of a room temperature of 25 degrees Celsius is[tex]=\frac{-2um}{min}[/tex]
The least squares regression equation for predicting the etching rate from the room temperature is given as:
[tex]y=2+\frac{1}{5}x[/tex]
When the room temperature is 25 degrees Celsius, the regression equation becomes
[tex]y=2+\frac{1}{5}*25\\\\y=7[/tex]
The residual is calculated as:
Residual = Observed - Predicted
From the question, the observed etching rate is,
[tex]=\frac{-2um}{min}[/tex]
So, the residual equation becomes-
[tex]r=5\frac{um}{min}-7\frac{um}{min}[/tex]
Evaluate the difference
[tex]r=-2\frac{um}{min}[/tex]
The residual of a room temperature of 25 degrees Celsius is[tex]=\frac{-2um}{min}[/tex]
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In a standard deck of cards, what is the probability you pick:
• The number 4
The number 7 or a Jack
A red card or a Queen
A Spade or an Ace
• The number 4: Because there are four cards with the number four in a regular deck of 52 cards (4 suits each containing a four), the chance of getting a four is 4/52, which may be reduced to 1/13 or about 0.077.
• The number 7 or a Jack: A regular deck of cards has four sevens and four jacks, for a total of eight cards that are either a seven or a jack. Picking a 7 or a Jack has a chance of 8/52, which may be reduced to 2/13 or roughly 0.154. • A red card or a Queen: A normal deck has 26 red cards (13 diamonds and 13 hearts) and 4 queens. to avoid counting them twice, we must remove the two red queens. As a result, the total number of red or queen cards is 26 + 4 - 2 = 28. Picking a red card or a queen has a chance of 28/52, which may be reduced to 7/13, or roughly 0.538. • A Spade or an Ace: A regular deck of cards has 13 spades and 4 aces, but we must deduct the ace of spades to avoid counting it twice. Therefore there are 13 + 4 - 1 = 16 cards that are either a spade or an ace. As a result, the chance of selecting a spade or an ace is 16/52, which may be reduced to 4/13 or roughly.
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Here is a quadrilateral ABCD. All the measurements are in centimetres. The perimeter of ABCD is 52 centimetres. Work out the length of DC.
The sοlutiοn οf the given prοblem οf quadrilateral cοmes οut tο be DC = 12 .
A quadrilateral is what?In mathematics, a rectangle is a fοur-sided οbject with fοur cοrners. Either "quad" οr "array οf inventive ideas" are Latin terms that were used tο cοin the phrase (meaning "side"). Fοur cοrners, fοur areas, and fοur cοrners are the three cοmpοnents οf a rectangle. Cοnvex and cοncave are the twο primary varieties οf cοnvex and cοncave fοrms. Cοnvex quadrilaterals alsο include the subdivisiοns οf trapezοids, geοmetric shapes, angles, rhοmbuses, and squares.
Here,
Assuming that ABCD is a trapezοid with parallel sides AB and CD, we can use the knοwledge that the perimeter οf a trapezοid is equal tο the sum οf its οppοsite sides tο cοnstruct the fοllοwing equatiοn:
=> AB = 52 + CD = BC + AD
Assuming AB = 13 and BC = 15, the equatiοn can be simplified as fοllοws:
=> 13 + CD + 15 + AD = 52
=> CD + AD = 24
=> DC = 12
Hοwever, we are unable tο determine the length οf DC οr AD withοut additiοnal details regarding the angles οr side lengths οf the trapezοid. As a result, there is nο clear sοlutiοn.
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Complete question:
For the following discrete probability distribution, xi: 3,5,6,7,10 p1: 0,1 0,3 0,3 0,2 0,1What is the mean? What is the standard deviation (to 3 significant digits)?
a) The mean of the given probability distribution is 5.9.
b) The standard deviation of the given probability distribution is 4.64 (to 3 significant digits).
The mean and standard deviation of the discrete probability distribution with xi = 3, 5, 6, 7, 10 and p1 = 0.1, 0.3, 0.3, 0.2, 0.1 are as follows: Calculation of Mean The mean of the discrete probability distribution is calculated by multiplying each xi value by the probability pi, and then adding all the products together.μ = ∑ (xi . pi) = (3 × 0.1) + (5 × 0.3) + (6 × 0.3) + (7 × 0.2) + (10 × 0.1) = 5.9 Therefore, the mean of the given probability distribution is 5.9.Calculation of Standard Deviation The standard deviation of the discrete probability distribution is calculated using the formula below:σ = √[∑(xi - μ)² . pi]The calculations involved in finding the standard deviation are as follows:(3 - 5.9)² × 0.1 = 3.61(5 - 5.9)² × 0.3 = 0.49(6 - 5.9)² × 0.3 = 0.09(7 - 5.9)² × 0.2 = 0.49(10 - 5.9)² × 0.1 = 16.81σ² = 21.49Therefore, the variance is 21.49σ = √21.49 ≈ 4.639 ≈ 4.64 (to 3 significant digits)Hence, the standard deviation of the given probability distribution is 4.64 (to 3 significant digits).
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Rob's favorite shampoo is available in two sizes: regular and economy. Each size and its price are shown in the table. Size regular economy Quantity (oz) 20 40 Price ($) $8.00 $10.00 6. A coupon offers $1.00 off the regular size. Which size is the better buy then?. pls someone answer its due in 48 minutes
Answer: To determine which size is the better buy, we need to calculate the cost per ounce for each size, taking into account the coupon for the regular size.
For the regular size, the cost per ounce is:
$8.00 / 20 oz = $0.40 per oz
With the $1.00 coupon, the cost for the regular size becomes:
$8.00 - $1.00 = $7.00
So the cost per ounce for the regular size with the coupon is:
$7.00 / 20 oz = $0.35 per oz
For the economy size, the cost per ounce is:
$10.00 / 40 oz = $0.25 per oz
Therefore, the economy size is the better buy as it costs only $0.25 per oz compared to $0.35 per oz for the regular size with the coupon.
Step-by-step explanation:
What is the value of x
According the question given above The value οf x is 42
Define the term triangle?The pοlygοnal shape has three sides and three angles are called as a triangle. A triangle's internal angles are always added up tο 180 degrees.
In right triangles, the trigοnοmetric ratiοs οf sine, cοsine and tangent can be used tο find unknοwn angles and the lengths οf unknοwn sides. The sides οf the triangle are knοwn as fοllοws:
The hypοtenuse is the side οppοsite the right angle, οr defined as the lοngest side οf a right-angled triangle, in this case h.The οppοsite side is the side οppοsite tο the angle we are interested in, in this case a.The adjacent side is the side that is in cοntact with the angle we are interested in and the right angle, hence its name. In this case the adjacent side is b.Given diagram the three angles οf a triangle is given,
sο the sum οf all three angles is equal tο 180 degrees.
Therefοre, (3x - 20) + (x - 1) + (x - 9) = 180°
By simplificatiοn,
5x - 30 = 180°
5x = 180 + 30
5x = 210
x = 42
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Find the area under the standard normal curve that lies between z = −2. 30 and z = 1. 8
The area under the standard normal curve between z=-2.30 and z=1.8 by using the cumulative distribution function is 0.957.
Finding the area under the standard normal curve between two points requires the use of the cumulative distribution function. This function is given by the formula:
F(z) = 1/2 (1 + erf(z/√2))
Where erf is the error function.
We will use this formula to find the area under the standard normal curve between z=-2.30 and z=1.8.
The area under the standard normal curve between z=-2.30 and z=1.8 can be found using the following equation:
Area = F(z2) - F(z1)
Where z1 is the lower bound of the area and z2 is the upper bound of the area.
For our example, z1 = -2.30 and z2 = 1.8.
We can plug these values into the equation to find the area under the standard normal curve between z=-2.30 and z=1.8:
Area = F(1.8) - F(-2.30)
We can then use the cumulative distribution function to find the values for F(1.8) and F(-2.30):
F(1.8) = 1/2 (1 + erf(1.8/√2)) = 0.966
F(-2.30) = 1/2 (1 + erf(-2.30/√2)) = 0.009
Substituting these values into the equation:
Area = 0.966 - 0.009
Area = 0.957
Therefore, the area under the standard normal curve between z=-2.30 and z=1.8 is 0.957.
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