The remainder of the polynomial using the remainder theorem and factor theorem is 6.
Apply the remainder theorem,
When we divide a polynomial
f(x) by (x − c)
f(x) = (x − c)q(x) + r
f(c) = 0 + r
Here,
f(x)=(x−c)q(x)+rf(c)=0+r
and (x−c) is (x−(−2))
Therefore,
f(−2) = [tex](-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2[/tex]
= 16 + 8 − 12 − 8 + 2
= 6
Hence, the remainder of the polynomial using the remainder theorem is 6.
Whereas using the factor theorem and doing synthetic division, we get,
x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide
the coefficients of the polynomial as follows -
-2 | 1 -1 -3 4 2
-2 6 -6 4
-----------------------------------------
1 -3 3 -2 6
Hence, we get that 6 is the remainder when ([tex]x^4-x^3-3x^2+4x+2[/tex]) ÷ (x+2), using the factor theorem.
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The complete question is -
Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, [tex]x^4-x^3-3x^2+4x+2[/tex] ÷ (x+2)
Select the correct formula for the polyatomic ion. you can find a list of common polyatomic ions by clicking here. the formula for the ammonium ion: nh3 nh4 am
The chemical formula for ammonium carbonate is (NH₄)₂CO₃. Therefore, option (C) is correct.
When heated, ammonium carbonate, also known as ()2, rapidly breaks down into ammonia and carbon dioxide. It functions as a smelling salt and a leavening agent. Ammonium carbonate, often known as baker's ammonia, was used before baking soda and baking powder as leaveners.
Sal volatile contains ammonium carbonate, and salt of hartshorn when baked emits a strong odour. At standard pressure and temperature, two processes lead to the gradual breakdown of ammonium carbonate. The pure ammonium carbonate sample will combine with different byproducts.
Upon spontaneous dissociation, ammonium carbonate can separate into ammonium bicarbonate and ammonia. which results in the addition of more ammonia, carbon dioxide, and water.
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Answer:
The formula for the ammonium ion: NH4+
The formula for the nitrate ion: NO3–
A chromate ion consists of four oxygen atoms bonded to a chromium atom. It has two extra electrons. The formula of this ion: CrO42–
Heres all three. Hope i helped
NEED HELP ASAP PLEASE THANK YOU!!
Answer:
[tex]\sin(\theta ) = \dfrac{\textrm{opposite}}{\textrm{hypotenuse}}[/tex]
Hence,
[tex]\sin(A) =\dfrac{20}{29}[/tex]
Please help me I’m giving brainlyest
The angles ∠ 5 and ∠ 7 are supplementary angles.
What is supplementary angles?Supplementary angles are those angles that sum up to 180 degrees.
Given is a figure, with two parallel lines and a transversal
In the options,
(∠ 5 and ∠ 8) (∠ 2 and ∠ 3) are vertically opposite angles.
∠ 1 and ∠ 5 are corresponding angles
But ∠ 5 and ∠ 7 are forming linear pair, and we know that, two angles forming linear pairs are supplementary angles,
Hence, The angles ∠ 5 and ∠ 7 are supplementary angles.
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How many solutions does 1/2(6x-2)=2 have
One solution for the equation [tex]\frac{1}{2} (6x - 2) = 2[/tex] is x = 1
What is an equation ?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
According to the given information
The equation given to us is
[tex]\frac{1}{2} (6x - 2) = 2[/tex]
Solving the above equation
We get
3x - 1 = 2
3x = 2 + 1
3x = 3
x = 1
We have only
One solution for the equation [tex]\frac{1}{2} (6x - 2) = 2[/tex] is x = 1
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A salesperson receives a 9.9% commission on her salesIf her total sales for the month are $3600, what is her commission ?
Answer:
$358.4
Step-by-step explanation:
To calculate the salesperson's commission, you can multiply the total sales by the commission rate. In this case, the commission is $3600 * 0.099 = $<<3600*0.099=358.4>>358.4. So the salesperson's commission would be $358.4.
bert is driving along a country road at a constant speed of 30 miles per hour. how long does it take him to travel 50 miles? make sure to convert the answer into hours and minutes. an hour and 30 minutes an hour and 40 minutes an hour and 15 minutes an hour and 50 minutes
The time taken by Bert to travel 50 miles distance with constant speed 30 miles per hour is an hour 40 minutes. So, right answer is option (b).
What is speed ?Speed is defined as the rate at which a particular object able to move or operate. It is a ratio of amount of distance to the time. Speed of object may be fast , slow or constant. The constant speed means there is no increase or decrease in speed during rides.
We have,bert's constant speed=30 miles/hour .
We have to calculate the time taken by Bert to travel 50 miles, i.e distance = 50 miles . Let "t hours " be time taken by Bert to travel 50 miles.
Speed= distance/time
=> time = distance/speed
=> t = 50 miles /30 miles/1 hour
=> t = 5/3 hours
Conversion of hours into minutes :
one hour = 60 minutes
5/3 hour =( 5/3 )× 60 minutes
=> 5/3 hour = 100 minutes = 60 minutes + 40 minutes= 1 hour 40 minutes
So, required time is 1 hour 40 minutes.
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Complete question:
bert is driving along a country road at a constant speed of 30 miles per hour. how long does it take him to travel 50 miles? make sure to convert the answer into hours and minutes.
a)an hour and 30 minutes
b) an hour and 40 minutes
c)an hour and 15 minutes
d)an hour and 50 minutes
Solve the following inequality and plot the answer on the number line shown below.
Answer: n > 3
Step-by-step explanation:
A circle above 3 going right
how many ways are there for eight blue-shirt and five red-shirt to stand in a line so that no two red-shirts stand next to each other?
The total number of ways there are for eight blue-shirt and five red-shirt to stand in a line so that no two red-shirts stand next to each other is 609638400.
What is permutation?A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already ordered, or arranging its members into a sequence or linear order.
Given:
The eight blue-shirt and five red-shirt stands in a line,
Calculate the number of ways as shown below,
The total number of ways = Total no of permutations of blue ones × Total permutation of 9 positions, taken 5 at a time,
N = 8! × 9! / (9 - 5)!
N = 40320 × 362880 /24
N = 609638400
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a university student wishes to explore whether gender (man, woman, trans, non-binary) is associated with agreement (agree, disagree, neutral) to endorse the existence of a social media platform that allows almost all forms of non-violent free speech, with minimal content moderation to censure only the most egregious of posts. of the 47 men polled, 25 agreed and 10 were neutral. of the 50 women polled 14 agreed and 5 were neutral. of the 41 transgendered people polled 18 agreed and 4 were neutral. of the 50 non-binary people, 6 agreed and 12 were neutral. the rest disagreed with such a platform being allowed to exist in our society. the student wishes to test the hypothesis of independence using pearson's chi square test. how many transgendered people (round to the nearest thousandth) would be expected to disagree with such a platform being allowed to exist in our society under the null hypothesis?
The number of transgendered people would be expected to disagree with such a platform being allowed to exist in our society under the null hypothesis is 19.00
What Is a null hypothesis?A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory' veracity. It is sometimes referred to as just "the null," and its symbol is H0.
To determine if a theory regarding markets, investing methods, or economies is correct or wrong, quantitative analysts employ the null hypothesis, often known as the conjecture.
The number of transgendered people would be expected to disagree with such a platform being allowed to exist in our society under the null hypothesis is 19.00
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Solve the word problem below. Enter your answer as a fraction in simplest
terms, using the slash (/) as the fraction bar.
If
of all books at a library are nonfiction and of the nonfiction books are
biographies, then what fraction of the library's books are nonfiction
biographies?
The total number of non-fictional biography books in the library will be equal to 1/5.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the given information in the question,
Let the total number of books is x.
3/5 of total books are non-fiction, then,
3/5 × x = 3/5x
1/3x of them are biographies.
Then, the number of non-fictional biographies are,
3/5 × 1/3
=1/5
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You can spend at most $6 at the market. Apples cost $0.44 each, and pears cost $0.85 each. Let x be the number of apples and let y be the number of pears. Write an inequality that represents the numbers of apples and pears you can buy.
Answer:
0.44x + 0.85y <= 6
Step-by-step explanation:
We can write the total cost of the apples as 0.44x, and the total cost of the pears as 0.85y. Since the total cost cannot exceed $6, we can write the following inequality:
0.44x + 0.85y <= 6
This inequality represents the numbers of apples and pears you can buy at the market, given that you can spend at most $6.
Answer:
0.44x + 0.85y ≤ 6
Step-by-step explanation:
To represent the number of apples and pears you can buy, you can use the following inequality: 0.44x + 0.85y ≤ 6. This inequality states that the total cost of the apples and pears, which is 0.44x + 0.85y, must be less than or equal to $6. This means that you cannot spend more than $6 at the market, and the number of apples and pears you can buy is limited by this budget constraint.
Given the growth rate of 205%, what is
the growth factor?
If you take 3 away from 100 every minute how long does it take to get to 0
Answer:
100÷3 = 33.33, so 33.33 minutes
\frac{x}{y} x^2+2*x-6/x+1
The division of the polynomial x^2 + 2*x - 6 by (x + 1), using the long division method of dividing polynomials is x + 1 - 7/(x + 1)
What is the long division method?The long division method allows the division of large numbers (which is the dividend) into the number of groups of the divisor and a remainder which is a value less than the expressed value of the divisor.
The expression \_f_rac{x}{y} x^2 + 2*x - 6/x + 1 can be presented as follows;
[tex]\dfrac{x^2+2\cdot x-6}{x + 1}[/tex]The long division showing the steps can be obtained using code found online as follows;
[tex]\begin{array}{*1r {\arraycolsep}{\arraycolsep} *{11}l} & && x + 1 \\\cline{4-3}& &x+1& \longdiv {) x^2 +2\cdot x - 6& & & & & \\ & & & x^2 +x \\\cline{4-} && &\ \ \ x -6& \\ & & \ \ \ & \ \ \ x +1 \\\cline{4-} & & & \ \ \ \ \ \ \ -7 & \\ \cline{4-} \end{array}[/tex]
The remainder of the long division is -7, therefore, we get;
[tex]\dfrac{x^2+2\cdot x-6}{x + 1} = x + 1 - \dfrac{7}{x+1}[/tex]
The value of the expression, \_f_rac{x}{y} x^2 + 2*x - 6/x + 1 following the long division is; x + 1 - 7/(x + 1)
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2x+5/x+2>_ x-1/x-2
Which shows all the critical points for the inequality
O x= -2, x = 1, and x = 2
Ox=-6 and x = 2
Ox=-4 and x = 2
Ox=2
The critical points for the inequality (2x+5/x+2>_ x-1/x-2), are x = -2 and x = 2. Option A
What are the critical points?Generally, To find the critical points for the inequality, you need to set the expression on the left side of the inequality equal to zero and solve for x. This will give you the values of x where the inequality changes direction.
In this case, the inequality is:
2x + 5/(x + 2) > 0
To find the critical points, you can set the expression on the left side equal to zero and solve for x:
0 = 2x + 5/(x + 2)
0 = 2x + 5 - 5/(x + 2)
0 = 2x - 5 + 5/(x + 2)
0 = 2x - 5 + 5(x + 2)/(x + 2)
0 = 2x - 5 + 5x + 10
0 = 7x - 15
x = -2, x = 2
Therefore, the critical points for the inequality are x = -2 and x = 2.
It is not correct to say that the critical points are x = -6 and x = 2, x = -4 and x = 2, or x = 2. These values do not correspond to any points where the inequality changes direction.
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Answer: B -6 and x=2
Step-by-step explanation: for edgen.
A certain amount of money wa divided between jaya and jyoti in the ratio 3:4. If jaya recieved R2700,then how much wa the total amount
By setting up the equation and solving we get the total amount of money was 1800.
What is ratio?A ratio is a way of comparing two or more quantities. It is expressed as a fraction or a decimal, and it represents the relative sizes of the quantities being compared.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. An equation typically consists of two expressions separated by an equals sign (=), and it states that the expressions are equal in value.
we can set up the following equation:
(2700 / X) = (3 / 4)
We can solve this equation for X by multiplying both sides by X:
2700 = (3 / 4) * X
2700 = (3 / 4) * X
5400 = 3X
X = 5400 / 3
X = 1800
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A metal i made up of copper and zinc in the ratio 3:2 by volume. 1cm cube of copper ha a ma of 8. 9g and 1cm cube of zinc ha a ma of 7. 1g. Find the ma of 100cm cube of the metal
When metal is composed of copper and zinc in a 3:2 by volume ratio, the mass of metal in a 100cm cube is 1600g.
What is proportion?A percentage is a component, piece, or amount that is compared to a total. It might be 0 or 1, or any number between 0 and 1. It can be stated numerically or as a percentage. In official statistics, one example would be the proportion of the Canadian population residing in a certain province. The population percentage is marked by the letter p, whereas the sample proportion is denoted by the letter p. Thus, p=0.43 if 43% of individuals visiting a business make a purchase before leaving. If 78 customers out of 200 enter the store and make a purchase, p=78200=0.39.
Here,
1/8.9=100/x
x=890g
1/7.1=100/x
x=710g
Total mass of metal=890+710
=1600g
The mass of metal in 100cm cube is 1600g when metal is made up of copper and zinc in the ratio 3:2 by volume.
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Please help me with this
The order of the side lengths from least to greatest is; GH< IH< FG< GI< FH.
What is the order of the side lengths from least to greatest?
As with other closed geometric figures, the shortest side length is opposite the smallest angle measure while the longest side length, is opposite the greatest angle measure.
Hence, it follows from the statement above that the order of side lengths is; GH< IH< FG< GI< FH.
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Jacob i aving to buy an electronic tablet that cot $380 including tax and ha aved $150
The required Inequality is $12x + $150 ≥ $380 where x is the minimum number of lawns Jacob will need to mow in order to buy the ticket. The solution of inequation is x ≥ 19.2 ~ 19.
What is an Inequality?An inequality is a mathematical expression in which both sides are not equal. Unlike equations, inequalities compare two values. Equal signs between are replaced by less than (or less than and equal), greater than (or greater than and equal ) sign.
How to solve an Inequality?When solving an inequality:
We can add the same quantity to each side We can subtract the same quantity from each side. We can multiply or divide each side by the same positive quantity . If we multiply or divide each side by a negative quantity, the inequality symbol must be reversed.We have, total cost of electronic ticket i.e with all taxes = $380
Saved cost = $150
Cost of one mowing lawn = $12
let "x" be the number of lawns mowed by Jacob for earning the rest of money .
Total cost of x mowed lawns by Jacob।
= $12x .
Now, $12x + $150 ≥ $380 --(*)
This is the required Inequality and x is minimum number of lawns which Jacob have to mowed .
The solution of above Inequality,
Substracts 150 from both sides in (*)
12 x + 150 - 150 ≥ 380 - 150
=> 12x ≥ 230
dividing by positive 12 both sides we get,
=> x/12 ≥ 230/12
=> x ≥ 19.16
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Complete question:
Jacob is saving to buy an electronic ticket that costs $380 including tax and has saved $150. Jared plans to earn the rest of the money by mowing lawns and will charge $12 for each lawn he mows. Write an inequality to find x, the minimum number of lawns Jacob will need to mow in order to buy the ticket. Show how to solve the inequality and what is solution.
Enter the letter of the graphed function.
a. y = (x + 2)(x - 1)³(x-3)
b. y = (x + 2)(x - 1)(x-3)³
c. y = (x + 2)(x - 1)²(x - 3)²
d. y = (x - 1)(x-3)²(x + 2)²
e. y = (x + 2)²(x-1)²(x-3)
10
Answer:
d. y = (x - 1)(x-3)²(x + 2)²
Step-by-step explanation:
When there is a local max or local min on the x-intercept, then the function on the x-intercept is raised to an even power.
At x=3 and x=-2, the function goes up then down, or down then up.
If the function goes through an x-intercept when there is no local max or local min on the x-intercept, then the function on the x-intercept is raised to an odd power.
At x=1, the function goes through the x-intercept.
Hence, d is the answer.
The equation y=(1/4)x relate proportional quantitie x and y. What i the value of x when y i 7
To solve for x when y is given, we can use the given equation y=(1/4)x.By multiplying both sides of the equation by 4.x=28, we may find the value of x.
To solve for x when y is given, we can use the given equation y=(1/4)x. By multiplying both sides of the equation by 4.x=28, we may find the value of x. This gives us the equation 4y=x. Then, we can substitute the given value of y, 7, into the equation. This gives us 4(7)=x. Simplifying this equation gives us 28=x, which is the value of x when y is 7.
y=(1/4)x
4y=x
4(7)=x
28=x
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Mr. Green mowed 2 5 of hi lawn. Hi on mowed 1 3 of it. Who mowed mot of the lawn? How much of the lawn till need to be mowed? Solve thi on paper. Then check your work on Zearn. Who mowed mot of the lawn? i greater than o mowed mot of the lawn
Mr. Green mowed more of the lawn. 2/5 of the lawn still needs to be mowed, according to the concept of proportion or ratio.
To get this answer, we can first set up a proportion or ratio to compare how much of the lawn each person mowed. Mr. Green mowed 2/5 of his lawn and his son mowed 1/3 of it.
2/5 = x/1, We can then cross multiply to solve for x.
2x = 5/3 x = 5/6 Since 5/6 is greater than 1/3, this means that Mr. Green mowed more of the lawn than his son. This means that 2/5 of the lawn still needs to be mowed.
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i need help past due
Answer:
Unit price 12.16 for 4.07 pounds is $2.99 per pound
Unit price 14.99 for 5.11 pounds is $2.93 per pound
The best deal is the 14.99 per 4.11 pounds
Step-by-step explanation:
Unit price 12.16/4.07 = 2.99 rounded to the nearest cent
Unit price 14.99/5.11 = 2.93 rounded to the nearest cent.
Answer:
1) $2.99
2)$2.93
The better buy is the 4.07 pound bag
Step-by-step explanation:
To find the unit price you find the cost per pound
$12.16 : 4.07
? : 1
4.07x = 12.16
x = 2.98771499
$2.99
$14.99 : 5.11
? : 1
5.11x = 14.99
x= 2.9334638
if the residuals violate the assumption of normality, we expect that a. the sample was not taken randomly. b. confidence intervals may be unreliable. c. least squares formulas will fail. d. the residuals will not sum to zero.
The assumption of normality is important for valid results. If the residuals do not follow a normal distribution, then confidence intervals may not be accurate and should not be trusted.
The assumption of normality is a key element of statistical analysis. It suggests that a dataset follows a normal bell-shaped curve, which is important for reliable results. If the residuals of a dataset do not follow a normal distribution, then the assumptions of statistical techniques such as confidence intervals, least-squares formulas, and sample randomness, may be unreliable. This means that the results of any statistical analysis will be affected and not be as accurate as they could be. In this case, confidence intervals may be particularly unreliable since they rely on the assumption that the data is normally distributed. Therefore, if the residuals do not follow a normal distribution, it is important to investigate further to ensure the accuracy of the results.
example;
The mean of the data is 8.3 and the standard deviation is 4.2.
We can calculate the z-score for any given value by subtracting the mean from the value and then dividing by the standard deviation.
if the value is 16, then the z-score would be:
z = (16 - 8.3) / 4.2 = 2.33.
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HI I NEED SOME HELP ON THIS QUESTION, THANK YOU VERY MUCH !
A line has a slope of –1/9 and includes the points (6,z) and (–3,5). What is the value of z?
Applying the formula for the slope of a line, the value of x = 4.
What is the Slope of a Line?To find the slope of a line, the following formula or equation can be employed:
Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
Given the following points, (6, z) and (-3, 5) lies on a line that has a slope of -1/9, to find the value of z, follow the steps below:
Let (6, z) be represented as [tex](x_1, y_1)[/tex]
Let (-3, 5) be represented as [tex](x_2, y_2)[/tex].
m = -1/9
Plug in the values:
-1/9 = (5 - z) / (-3 - 6)
-1/9 = (5 - z) / -9
Cross multiply:
-1 × -9 = (5 - z) × 9
9 = 45 - 9z
9 - 45 = -9z
-36 = -9z
Divide both sides by -9:
-36/-9 = -9z/-9
4 = z
z = 4
The value of z is: 4.
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Which congruence criterion do you use in the following? Given : EB = DB AE = BC ∠A = ∠C = 90° ∆ABE = ∆CDBSSS
SAS
RHS
ASA
By RHS congruence criterion, since it is given that EB=BD, AE=CB, ∠A=∠C=90°
RHS Congruence Property:
Two right triangles are congruent if the hypotenuse and one side of the first triangle are respectively equal to the hypotenuse and one side of the second.
If the length of the hypotenuse and one side of one triangle is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent.
ΔABE ≅ ΔACD
The hypotenuse and one side of a right-angled triangle are respectively equal to the hypotenuse and one side of another right-angled triangle.
Therefore,
ΔABE≅ΔCDB.
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Percentage increase and decrease problems
Your wages increase by 11%.
They used to be £10 p/h what is
your new wage?
Your new football s boots are reduced
by 17% in the sale. They used to cost
£35, what is the new price?
Claire improves her further distance
for running by 19%. She used to be
able to run km. How far can she run
now?
The new wage is £11.1
The new price of the boot is £29.05Her improved distance is 1.19xWhat is your new wage?From the question, we have the following parameters that can be used in our computation:
Old wage = £10
Increase = 11%
The new wage is calculated as
New wage = Old wage * (1 + Old wage)
Substitute the known values in the above equation, so, we have the following representation
New wage = £10 * (1 + 11%)
So, we have
New wage = £11.1
What is the new price?From the question, we have the following parameters that can be used in our computation:
Old price = £35
Decrease = 17%
The new price is calculated as
New price = Old price * (1 - Decrease)
Substitute the known values in the above equation, so, we have the following representation
New price = £35 * (1 -17%)
So, we have
New price = £29.05
How far can she run now?Here, we have
Old distance = x
Improvement = 19%
The new price is calculated as
New distance = Old distance * (1 + Improvement)
Substitute the known values in the above equation, so, we have the following representation
New distance = x * (1 + 19%)
So, we have
New distance = 1.19x
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The prices paid for a model of a new car are approximately normally distributed with a mean of $17,000 and a standard deviation of $500.
The price that is 3 standard deviations above the mean is $__
The price that is 2 standard deviations below the mean is $__
The percentage of buyers who paid between $16,500 and $17,500 is %__
The percentage of buyers who paid between $17,000 and $18,000 is %___
The percentage of buyers who paid less than $16,000 is %__
Answer:
Step-by-step explanation:
they are telling you the standard deviation , it's 500
then they ask, what's 3 times that. It's kinda obvious, when I put it in words like that so i'll let you do that math. 17,000 + (3*500) = ?
b)
17000 - (2*500) = ?
c)
This is the bell curve numbers of 1 deviation, it's 68%, if you don't recall
d)
it will be 1/2 of the 2nd deviation, or 95% * 0.5 = 47.5%
e)
this is the tiny amount outside of the main part of the 2 deviation on the bell curve.
5% is outside of the 2nd deviation. so it's half of that or 2.5%
Understand?????
:/
Which expression is equivalent to 4 +(4x(5-2) divided by 2
Answer:
Step-by-step explanation:
1) Do what's in the parentheses first. (5 - 2 = 3)
2) 4x times 3 = 12x
3) 12x + 4
If you can’t see the last part, it’s a 10.
Answer:
I don't know what is the answer