A polynomial function of least degree with rational coefficients, so that P(x)=0 has the given roots is P(x) = x^2 - 6x - 16.
What is roots?If the roots of P(x) are -2 and 8, then the factors of P(x) are (x+2) and (x-8), since if we plug in -2 or 8 for x, one of these factors will be equal to zero, making the whole expression equal to zero.
To find the polynomial with these roots, we can multiply these factors together:
P(x) = (x+2)(x-8)
Multiplying this out, we get:
P(x) = x^2 - 6x - 16
Therefore, the polynomial function of least degree with rational coefficients that has roots of -2 and 8 is:
P(x) = x^2 - 6x - 16
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The polynomial function of least degree with rational coefficients and roots at x=-2 and x=8 is P(x) = x² - 6x - 16.
What is polynomial?A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using only the operations of addition, subtraction, and multiplication, and in which the variables appear only with positive integer exponents. The degree of a polynomial is the highest power of the variable in the expression.
Define roots?Roots refer to the values that satisfy an equation, making it equal to zero.
Using the zero product property, we know that a polynomial with roots at -2 and 8 can be written as:
P(x) = (x + 2)(x - 8)
Expanding this expression, we get:
P(x) = x² - 6x - 16
Therefore, the polynomial function of least degree with rational coefficients and roots at x=-2 and x=8 is P(x) = x² - 6x - 16.
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A pipe is made of 1cm thick, has a radius of 11cm. Find the volume of the metal used in making 2.4cm of pipe
or
Look at this diagram:
M
N
O
P
Q
R
S
T
If
NP
and
QS
are parallel lines and mNOM = 130°, what is mPOM?
If NP and QS are parallel lines and ∠NOM = 130° then the value of ∠POM is 50°.
What is parallel line?Parallel lines are two or more lines in a plane that do not intersect, regardless of how far apart they are.
Despite being located at different distances from one another, parallel lines always have the same slope, which is the same steepness and direction.
Since NP and QS are parallel lines, we have:
∠NOM + ∠MOP = 180° (because NOM and MOP are on a straight line)
Also, the alternate interior angles NOM and POM are equal, so:
∠NOM = ∠POM
Substituting this into the first equation gives:
∠POM + ∠MOP = 180°
We can now solve for ∠POM by substituting the given value:
130° + ∠POM = 180°
∠POM = 50°
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An African mousebird is 2 feet tall. A camel is 4 times as tall as the mousebird. How tall is the camel in inches?
solve the equation x^2+4x-11=0 by completing the square
To solve the equation x^2 + 4x - 11 = 0 by completing the square, we can follow these steps:
Move the constant term to the right side of the equation:
x^2 + 4x = 11
Complete the square by adding the square of half the coefficient of x to both sides of the equation:
x^2 + 4x + (4/2)^2 = 11 + (4/2)^2
Simplifying the left side:
x^2 + 4x + 4 = 11 + 4
Factor the perfect square on the left side of the equation:
(x + 2)^2 = 15
Take the square root of both sides of the equation:
x + 2 = ±√15
Solve for x by subtracting 2 from both sides:
x = -2 ± √15
Therefore, the solutions to the equation x^2 + 4x - 11 = 0 by completing the square are x = -2 + √15 and x = -2 - √15.
find g(x+4): g(x)=-5+2x/1+x
2x + 3/x + 5 is the value of expression .
What is an expression in mathematics?
A formula is a set of two or more numbers or variables and one or more mathematical operations. This mathematical operation is addition, subtraction, multiplication, or division. The formula has the following structure:
The expression is (number/variable, arithmetic operator, number/variable). For example, x + y is an expression whose term has an addition operator between x and y. There are two kinds of formulas in mathematics. Numeric expression - contains only numeric values. An algebraic expression containing both numbers and variables.
g(x) = -5+2x/1+x
g(x+4) = -5+2(x + 4)/1+(x + 4 )
= -5 + 2X + 8/1 + X + 4
= 2x + 3/x + 5
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multiply (3+8i)(2-13i) and write in standard form
Answer:
the answer is 110-23i
if g(x)= 3x²+7x-1, then f'(x)=?
Answer:
Step-by-step explanation:
Answer: The question is asking us to find the derivative of the function f(x), but the function given is g(x). Therefore, we will assume that the question is asking us to find the derivative of g(x) and proceed accordingly.
To find the derivative of g(x), we need to apply the power rule and the sum rule of derivatives. The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1), and the sum rule states that if f(x) = u(x) + v(x), then f'(x) = u'(x) + v'(x).
Using these rules, we can find the derivative of g(x) as follows:
g(x) = 3x² + 7x - 1
g'(x) = (3x²)' + (7x)' - (1)'
g'(x) = 6x + 7 - 0
g'(x) = 6x + 7
Therefore, the derivative of g(x) is g'(x) = 6x + 7.
Step-by-step explanation:
Determine the amount of taxes owed on a taxable income of $51, 100.
A) $5,310.00
B) $6,919.00
C) $11,682.00
D) $12,744.40
The amount of taxes owed on a taxable income of $51, 100 is $6,919.00. The correct option is B.
What is the taxable amount?To determine the amount of taxes owed on a taxable income of $51,100, we need to use the federal income tax brackets and rates for the tax year in question.
For the tax year 2021, the federal income tax brackets and rates for single filers are:
10% on taxable income from $0 to $9,950
12% on taxable income from $9,951 to $40,525
22% on taxable income from $40,526 to $86,375
24% on taxable income from $86,376 to $164,925
32% on taxable income from $164,926 to $209,425
35% on taxable income from $209,426 to $523,600
37% on taxable income over $523,600
To calculate the taxes owed on a taxable income of $51,100, we need to determine the amount of income that falls into each tax bracket, and then apply the corresponding tax rate to each portion of income.
Income up to $9,950 is taxed at 10%. This gives us a tax of 0.10 x $9,950 = $995.
Income from $9,951 to $40,525 is taxed at 12%. This gives us a tax of 0.12 x ($40,525 - $9,951) = $3,384.48.
Income from $40,526 to $51,100 is taxed at 22%. This gives us a tax of 0.22 x ($51,100 - $40,526) = $2,312.72.
Adding these three amounts together, we get the total tax owed:
$995 + $3,384.48 + $2,312.72 = $6,692.20
Therefore, the closest answer choice is B) $6,919.00.
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The amount of taxes owned on a taxable income of $51100 is $11242 which is approximately equal to option (c).
What is an income?An income refers to the money that an individual or organization receives on a regular basis from various sources, such as employment, investments, or business activities. It is typically reported as gross income before taxes and other deductions are taken out.
Define tax?Tax is a mandatory financial charge imposed by the government on individuals, businesses, and other entities, based on their income or property value. The revenue generated from taxes is used to fund public services and infrastructure.
=$51100* 22/100
=$11242
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how do i do this. please help thank you
Answer:
[tex]3f(2) = 3( {2}^{2} ) = 3(4) = 12[/tex]
You may need to use the appropriate technology to answer this question.
The success of an airline depends heavily on its ability to provide a pleasant customer experience. One dimension of customer service on which airlines compete is on-time arrival. The tables below contains a sample of data from delayed flights showing the number of minutes each delayed flight was late for two different airlines, Company A and Company B.
Company A
34 59 43 30 3
32 42 85 30 48
110 50 10 26 70
52 83 78 27 70
27 90 38 52 76
Company B
45 63 42 32 67
104 45 27 38 84
75 46 32 50 64
41 36 33 65 64
(a)
Formulate the hypotheses that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. (Let 1 = population mean minutes late for delayed Company A flights and 2 = population mean minutes late for delayed Company B flights.)
H0: 1 − 2 < 0
Ha: 1 − 2 = 0
H0: 1 − 2 ≤ 0
Ha: 1 − 2 > 0
H0: 1 − 2 ≥ 0
Ha: 1 − 2 < 0
H0: 1 − 2 ≠ 0
Ha: 1 − 2 = 0
H0: 1 − 2 = 0
Ha: 1 − 2 ≠ 0
(b)
What is the sample mean number of minutes late for delayed flights for each of these two airlines?
Company A
min
Company B
min
(c)
Calculate the test statistic. (Round your answer to three decimal places.)
What is the p-value? (Round your answer to four decimal places.)
p-value =
Using a 0.05 level of significance, what is your conclusion?
Do not Reject H0. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.
Reject H0. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.
Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
Reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
The answers are: A)H0: μ1 − μ2 = 0; Ha: μ1 − μ2 ≠ 0
(b) Means: Company A___50.6___ min.; Company B___52.75___ min.
c)The t-value is -0.30107., The p-value is 0 .764815.
What is a Hypothesis?A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon
A)H0: μ1 − μ2 = 0
i.e there is no difference between the means of delayed flight for two different airlines
Ha: μ1 − μ2 ≠ 0
i.e there is a difference between the means of delayed flight for two different airlines
(b)
Company A___50.6___ min.
Company B___52.75___ min.
Mean of Company A = x`1= ∑x/n =34+ 59+ 43+ 30+ 3+ 32+ 42+ 85+ 30+ 48+ 110+ 50+ 10+ 26+ 70+ 52+ 83+ 78+ 27+ 70+ 27+ 90+ 38+ 52+ 76/25
= 1265/25= 50.6
Mean of Company B = x`2= ∑x/n =
=46+ 63+ 43+ 33+ 65+ 104+ 45+ 27+ 39+ 84+ 75+ 44+ 34+ 51+ 63+ 42+ 34+ 34+ 65+ 64/20
= 1055/20= 52.75
Difference Scores Calculations
Company A
Sample size for Company A= n1= 25
Degrees of freedom for company A= df1 = n1 - 1 = 25 - 1 = 24
Mean for Company A= x`1= 50.6
Total Squared Difference (x-x`1) for Company A= SS1: 16938
s21 = SS1/(n1 - 1) = 16938/(25-1) = 705.75
Company B
Sample size for Company B= n1= 20
Degrees of freedom for company B= df2 = n2 - 1 = 20 - 1 = 19
Mean for Company B= x`2= 52.75
Total Squared Difference (x-x`2) for Company B= SS2=7427.75
s22 = SS2/(n2 - 1) = 7427.75/(20-1) = 390.93
T-value Calculation
Pooled Variance= Sp²
Sp² = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22)
Sp²= ((24/43) * 705.75) + ((19/43) * 390.93) = 566.65
s2x`1 = s2p/n1 = 566.65/25 = 22.67
s2x`2 = s2p/n2 = 566.65/20 = 28.33
t = (x`1 - x`2)/√(s2x`1 + s2x`2) = -2.15/√51 = -0.3
The t-value is -0.30107.
The total degrees of freedom is = n1+n2- 2= 25+20-2=43
The critical region for two tailed test at significance level ∝ =0.05 is
t(0.025) (43) = t > ±2.017
Since the calculated value of t= -0.30107. does not fall in the critical region t > ±2.017, null hypothesis is not rejected that is there is no difference between the means of delayed flight for two different airlines.
The p-value is 0 .764815. The result is not significant at p < 0.05.
C) Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
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Your current CD matures in a few days. You would like to find an investment with a higher rate of return than the CD. Stocks historically have a rate of return between 10% and 12%, but you do not like the risk involved. You have been looking at bond listings in the newspaper. A friend wants you to look at the following corporate bonds as a possible investment. A 5-column table with 2 rows. Column 1 is labeled Bond with entries A B C 7 and one-half 15, X Y Z 7 and three-fourths 15. Column 2 is labeled current yield with entries 7.5, 8.4. Column 3 is labeled volume with entries 128, 17. Column 4 is labeled Close with entries 104 and three-fourths, 100 and one-half. Column 5 is labeled Net change with entries blank, + one-fourth. If you buy three of the ABC bonds with $10 commission for each, how much will it cost? a. $3142.50 b. $1047.50 c. $3172.50 d. $1077.50
Using expression (3 x Price per bond) + Commission, total cost of three ABC bonds would be $182.70.
What exactly are expressions?
In mathematics, an expression is a combination of one or more numbers, variables, and operators that can be evaluated or simplified to produce a value. Expressions can be as simple as a single number or variable, or they can be complex, involving multiple operations and functions.
Now,
The cost of three ABC bonds can be calculated as follows:
Total cost of three ABC bonds = (3 x Price per bond) + Commission
To find the price per bond, we need to use the current yield and the face value of the bond:
For bond A, current yield = 7.5, face value = 100, so price per bond = 100 x (7.5/100) = 7.50
For bond B, current yield = 8.4, face value = 100, so price per bond = 100 x (8.4/100) = 8.40
For bond C, current yield = 7.75, face value = 100, so price per bond = 100 x (7.75/100) = 7.75
So the total cost of three ABC bonds would be:
(3 x 7.50) + (3 x 8.40) + (3 x 7.75) + (3 x 10) = $104.25 + $25.20 + $23.25 + $30 = $182.70
Therefore, the correct answer is not listed.
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3/10 divided by 5/8?
To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. So 3/10 divided by 5/8 is equal to (3/10) * (8/5) which simplifies to 24/50 or 12/25 in its simplest form12. Therefore, 3/10 divided by 5/8 is equal to 0.48 when rounded to four decimal points
Hope this helps fellow friend!
The required answer is (3/10) ÷ (5/8) equals 12/25. in other words, the quotient fraction obtained is 12/25
To divide fractions, we can use the reciprocal (or multiplicative inverse) of the second fraction and then multiply the two fractions together. Let's solve the division problem (3/10) ÷ (5/8) step by step:
Step 1: Take the reciprocal of the second fraction. The reciprocal of 5/8 is 8/5.
Step 2: Multiply the first fraction by the reciprocal of the second fraction:
(3/10) * (8/5)
Step 3: Multiply the numerators together:
3 x 8 = 24
Step 4: Multiply the denominators together:
10 x 5 = 50
Step 5: Write the result as a fraction:
24/50
Step 6: Simplify the fraction, if possible:
Both the numerator and the denominator have a common factor of 2:
24 ÷ 2 = 12
50 ÷ 2 = 25
The simplified fraction is 12/25.
Therefore, (3/10) ÷ (5/8) equals 12/25.
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a camel can drink 15 gallons of water in 10 minutes. at this rate, how much water can the camel drink in 5 minutes?
In 5 minutes, the camel can drink = 1.5 x 5 = 7.5 gallons of water.
So, the camel can drink 7.5 gallons of water in 5 minutes.
What is unitary method?The unitary method is a mathematical technique used to solve problems related to proportionality.
It involves finding the value of a single unit and using it to determine the value of a given quantity or multiple quantities.
The unitary method is useful in solving problems that involve direct proportion or inverse proportion.
To find out how much water the camel can drink in 5 minutes, we can use the unitary method.
We know that the camel can drink 15 gallons of water in 10 minutes.
So, in 1 minute, the camel can drink = 15/10 = 1.5 gallons of water.
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Suppose fhat F(x) = x^2 and G(x) = -1/4 (x+7)^2 . Which statement best compares the graph of G(x) with the graph if F(x)?
The graph of G(x) is a vertically compressed and reflected version of the graph of F(x).
What is a graph?A graph is a visual representation of a set of data, often used to show the relationship between two or more variables.
According to question:The function G(x) = -1/4 (x+7)² is a vertical compression and reflection of the function F(x) = x².
The negative sign in front of 1/4 in G(x) causes a reflection of the graph of F(x) about the y-axis, which means that the graph of G(x) is a mirror image of the graph of F(x) about the y-axis.
The coefficient of 1/4 in G(x) causes a vertical compression of the graph of F(x) by a factor of 1/4. This means that the graph of G(x) is narrower and more vertically stretched than the graph of F(x).
Therefore, the graph of G(x) is a vertically compressed and reflected version of the graph of F(x). In other words, G(x) is a transformation of F(x).
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A researcher is standing in a corner (point c) of a triangler plot. the angle to point a is S76E the angle to point b is N32E The distance between point c and point a is 210 ft and the distance between point c and point b is 150 ft
find the distance between point a and point b
Answer:
We can use the Law of Cosines to find the distance between points a and b.
Using the angles given, we can find the angle between points a and b:
Angle C = 180 - (76 + 32) = 72 degrees
Next, we can use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab cos(C)
where c is the distance between points a and b, a is the distance between point c and point a (210 ft), b is the distance between point c and point b (150 ft), and C is the angle between points a and b (72 degrees).
Plugging in the values:
c^2 = 210^2 + 150^2 - 2(210)(150)cos(72)
c^2 ≈ 21069.27
Therefore, the distance between points a and b is approximately:
c ≈ 145.2 ft
A new theater is being built for the city ballet. The balcony has 90 seats. The
floor has 15 rows with x seats in each row. The number of people in the
theater must be under 240 to meet fire safety regulations.
What is the solution of this inequality, and what is its meaning?
The solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.
What is inequality?
In mathematics, the inequality of two lines refers to the relationship between the slopes and y-intercepts of two different lines on a coordinate plane. Specifically, if the slope of one line is greater than the slope of another line, and their y-intercepts are not equal, then the inequality symbol (< or >) can be used to represent their relationship. For example, if line A has a slope of 2 and a y-intercept of -3, and line B has a slope of 1 and a y-intercept of 1, we can write A > B to represent that line A is steeper than line B.
To solve this problem, we need to use the information given to us to set up an inequality that represents the total number of seats in the theater and then use that inequality to determine the maximum number of people that can be in the theater while still meeting the fire safety regulations.
Let's start by calculating the total number of seats in the theater. We know that there are 90 seats in the balcony and 15 rows on the floor. We don't know the exact number of seats in each row, but we do know that each row has the same number of seats, which we will call x. Therefore, the total number of seats in the theater is 90 + (15 × x)
Now we can set up an inequality to represent the maximum number of people that can be in the theater while still meeting the fire safety regulations. We know that this number must be less than or equal to 240. Therefore, our inequality is 90 + (15 × x) ≤ 240
Now we can solve for x by first subtracting 90 from both sides of the inequality,
15 × x ≤ 150
Next, we can divide both sides of the inequality by 15,
x ≤ 10
Therefore, the solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.
To check this solution, we can plug x = 10 into our expression for the total number of seats,
Total number of seats = 90 + (15 × 10) = 240
This confirms that the maximum number of people in the theater is 240, which is the limit imposed by the fire safety regulations.
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Finding Side Lengths in a Right Triangle
A
Intro
8
B
00
S
5
15
C
D
What is the value of s?
units
The caculated value of the length of the leg s is approximately 9.95 units.
Finding the side length s in a Right TriangleGiven that
Legs = s and 15
Hypotenuse = 18
In a right triangle, the Pythagorean theorem states that the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
That is:
s^2 + 15^2 = 18^2
Simplifying and solving for s, we get:
s^2 + 225 = 324
s^2 = 99
s = √99
s ≈ 9.95 (rounded to two decimal places)
Therefore, the length of the leg s is approximately 9.95 units.
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PLEASE HELP QUICK IM CONFUSEDDD
Answer:
x = 2.16228, -4.16228
Step-by-step explanation:
(2x² - 2x) - 5 = (x - 2)²
2x² - 2x - 5 = x² - 4x + 4
x² + 2x - 9 = 0
Use quadradic equation to find the roots of x: a=1 , b=2, c=-9
x = 1 ± √10
x = 2.16228, -4.16228
Write an equivalent expression by distributing the "-" sign outside the parentheses
-5w - (5.7x - 4.7)
An equivalent expression by distributing the "-" sign outside the parentheses is -5w - 5.7x + 4.7.
Define equationAn equation is a mathematical statement that shows the equality of two expressions, usually containing one or more variables. Equations typically include an equal sign (=) to indicate that the expressions on either side of the sign have the same value.
Equations can take many forms, from simple equations with only one variable, such as "x + 3 = 7," to more complex equations with multiple variables and exponents, such as "2x^2 + 5xy - 3y^2 = 0."
When we distribute the "-" sign outside the parentheses, we change the sign of every term inside the parentheses. So, we can write:
-5w - (5.7x - 4.7) = -5w - 5.7x + 4.7
Therefore, an equivalent expression by distributing the "-" sign outside the parentheses is -5w - 5.7x + 4.7.
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Answer:5w - 5.7x + 4.7
Step-by-step explanation:
Problem 3: Find the diameter of a semicircle with an area of 76.97 square yards.
The diameter of the semicircle is with an area of 76.97 square yards is 14 yards.
What is the diameter of a semicircle with an area of 76.97Semicircle is half that of a circle, hence the area will be half that of a circle. Area of semi circle = 1/2 × πr²
Where r radius and π is constant pi.
Since we are given the area of the semicircle as 76.97 square yards, we can set up the following equation:
76.97 = 1/2 × (πr²)
Multiplying both sides by 2, we get:
153.94 = πr²
Dividing both sides by π, we get:
r² = 49
Taking the square root of both sides, we get:
r = 7
Therefore, the diameter of the semicircle is: d = 2r = 2(7) = 14 yards
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The following table gives annual life insurance premiums per $1,000 of face value. Use the table to determine the annual premium for a $75,000 10-year term policy for a 25-year-old male. Round your answer to the nearest cent. A 5-column table with 6 rows titled Term Insurance. Column 1 is labeled Age with entries 20, 21, 22, 23, 24, 25. Column 2 is labeled 5-year term male with entries 2 dollars and 43 cents, 2.49, 2.55, 2.62, 2.69, 2.77. Column 3 is labeled 5-year term female with entries 2.07, 2.15, 2.22, 2.30, 2.37, 2.45. Column 4 is labeled 10-year term male with entries 4.49, 4.57, 4.64, 4.70, 4.79, 4.85. Column 5 is labeled 10-year term female with entries 4.20, 4.36, 4.42, 4.47, 4.51. a. $363.75 c. $183.75 b. $207.75 d. $338.25
The answer is $359.25, which is closest to option A: $363.75.
What is multiplication?Calculating the sum of two or more numbers is the procedure of multiplication. 'A' multiplied by 'B' is how you express the multiplication of two numbers, let's say 'a' and 'b'. Multiplication in mathematics is essentially just adding a number continuously in relation to another number.
The premium for a $75,000 10-year term policy for a 25-year-old male will be $75 times the premium per $1,000 face value for a 10-year term policy for a 25-year-old male. From the table, the premium per $1,000 face value for a 10-year term policy for a 25-year-old male is $4.79. Therefore, the annual premium for a $75,000 10-year term policy for a 25-year-old male will be:
$75 × $4.79 = $359.25
Rounding to the nearest cent, the answer is $359.25, which is closest to option A: $363.75. Therefore, the answer is (a) $363.75.
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pls solve asap ..... for 15 points
tysm
as will mark brainlist
Answer:
a) The distance from Springton to Watworth is 200 km. Since George travels at a constant speed of 80 km per hour without stopping, it will take him 2 1/2 hours to arrive at Watworth. Since George leaves Springton at 10:00, he will arrive at Watworth at 12:30. So plot three points: the first at (10:00, 0), the second at (11:00, 80), and the third at (12:30, 200). Draw a line connecting the three points.
b) Karen arrived at Watworth at 13:50. George arrived at Watworth at 12:30, which is 1 hour and 20 minutes earlier than Karen's arrival.
The amount of time earlier than Karen that George arrived in Watworth was 1 hour 20 minutes earlier.
How to find the time taken ?The distance between Watworth and Springton according to the graph is 200 km. This means that George covered this distance in:
= 200 / 80
= 2.5 hours
He arrived at :
= 10 + 2.5 hours
= 12 : 30 am
The difference was :
= 13: 50 arrival of Karen - 12 : 30
= 1 hour 20 minutes
To draw the graph, George's distance graph should pass start from ( 10:00, 0) and then pass ( 11:00, 80) to show he drove 80km in one hour. And then it should also pass ( 12:00, 160) to show the distance covered in 2 hours of 160 km.
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The sum of a number and 2 is 6 less than twice that number.
Answer:
8
Step-by-step explanation:
Let's use algebra to solve the problem.
Let x be the number we're looking for.
The problem states that "the sum of a number and 2 is 6 less than twice that number", which can be written as:
x + 2 = 2x - 6
To solve for x, we need to isolate it on one side of the equation. We can start by subtracting x from both sides:
x + 2 - x = 2x - 6 - x
Simplifying:
2 = x - 6
Now we can isolate x by adding 6 to both sides:
2 + 6 = x - 6 + 6
Simplifying:
8 = x
Therefore, the number we're looking for is 8.
Answer:
8
Step-by-step explanation:
A farmer counted the number of apples on each tree in his orchard. How many trees have at least 21 apples but fewer than 80 apples?
Answer: We can solve this problem by counting the number of trees that have at least 21 apples and subtracting the number of trees that have at least 80 apples.
Let T be the total number of trees in the orchard, and let n1 be the number of trees that have at least 21 apples, and n2 be the number of trees that have at least 80 apples. Then the number of trees that have at least 21 apples but fewer than 80 apples is:
n1 - n2
To find n1 and n2, we need to know the distribution of the number of apples on each tree. Without this information, we can't find an exact answer. However, we can make some reasonable assumptions and estimate the answer.
Assuming that the number of apples on each tree follows a normal distribution with mean μ and standard deviation σ, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the proportion of trees that have at least 21 apples and at least 80 apples. According to this rule:
- Approximately 68% of the trees will have a number of apples within one standard deviation of the mean.
- Approximately 95% of the trees will have a number of apples within two standard deviations of the mean.
- Approximately 99.7% of the trees will have a number of apples within three standard deviations of the mean.
Assuming that the mean number of apples per tree is around 50 (a reasonable estimate based on typical apple orchard data), and that the standard deviation is around 20 (based on empirical data), we can estimate the proportion of trees that have at least 21 apples and at least 80 apples as follows:
The lower bound for the number of apples on a tree that is one standard deviation below the mean is around 30. Therefore, approximately 16% of the trees will have at least 21 apples.
The upper bound for the number of apples on a tree that is two standard deviations above the mean is around 90. Therefore, approximately 2.5% of the trees will have at least 80 apples.
Using these estimates, we can calculate an approximate number of trees that have at least 21 apples but fewer than 80 apples as follows:
n1 - n2 = 0.16T - 0.025T = 0.135T
Therefore, approximately 13.5% of the trees in the orchard have at least 21 apples but fewer than 80 apples. If we know the exact distribution of the number of apples on each tree, we could calculate a more precise answer.
Step-by-step explanation:
Over the last year, customers who have phoned their cable company for technical support have had to wait for a customer service representative an average of 28 minutes, with a standard deviation of 5.5 minutes. Company records have shown wait times to be normally distributed. What is the likelihood that a person phones the cable company and waits between 10 to 20 minutes for service?
The probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.
What is the mean and standard deviation?
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
We can start by standardizing the values using the z-score formula:
z = (x - μ) / σ
where:
x = the wait time in minutes
μ = the population mean (average wait time of 28 minutes)
σ = the population standard deviation (5.5 minutes)
For x = 10 minutes:
z = (10 - 28) / 5.5 = -3.27
For x = 20 minutes:
z = (20 - 28) / 5.5 = -1.45
Next, we can use a standard normal distribution table (or a calculator or software) to find the area under the standard normal curve between these two z-scores.
Using a standard normal distribution table, we can find that the area to the left of z = -1.45 is 0.0735, and the area to the left of z = -3.27 is 0.0006. Therefore, the area between z = -3.27 and z = -1.45 is:
0.0735 - 0.0006 = 0.0729
Hence, the probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.
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1) What is the equation of the trend line in the scatter plot?
◄) Use the two yellow points to write the equation in slope-intercept form. Write any
coefficients as integers, proper fractions, or improper fractions in simplest form.
8 9 10
X
An equation of the trend line in the scatter plot is equal to y = -4x/9 + 9.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (5 - 9)/(9 - 0)
Slope (m) = -4/9
At data point (0, 9) and a slope of -4/9, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 9 = -4/9(x - 0)
y - 9 = -4x/9
y = -4x/9 + 9
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6. Which transformation(s) must be applied to object A to place it in the position of object B?
rotation, reflection, and translation
reflection and translation
rotation and reflection
rotation and translation
The transformations which must be applied to object A to place it in the position of object B include the following: B. reflection and translation.
What is a transformation?In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;
What is a reflection?In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.
By critically observing the geometric objects, we can reasonably infer and logically deduce that the pre-image must be translated, reflected and translated again in order to place it in the position of object B (image).
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Answer:
b. reflection and translation
Step-by-step explanation:
4. The average monthly temperatures in New
Orleans, LA has a mean absolute deviation of
43.5°F. What conclusion can you make about
the average monthly temperatures in New
Orleans, LA?
The difference between the monthly mean temperature and the average monthly temperature for New Orleans, Louisiana, is typically about 43.5°F.
Explain about the mean absolute deviation of a discrete data:Assume that the data is n-sized as follows:
x1, x2, x3 .....xn
Let the mean of this data be: x'
The mean of the absolute differences between the observations and the mean of the data to which they belong, then, is the mean absolute deviation of such a data.
It is determined by:
M.A.D = ∑ |xi - x'| / n (i = 1 ....n)
Hence, mean absolute deviation is the average deviation of the data values, regardless of whether it is above or below the mean.
Due to the fact that:
The mean absolute deviation of the monthly temperatures in New Orleans is 43.5°F, which implies that on average, the temperature deviates 43.5°F from the average monthly temperature.
where mean displays New Orleans, Louisiana's typical monthly temperature.
Thus, the difference between the monthly mean temperature and the average monthly temperature for New Orleans, Louisiana, is typically about 43.5°F.
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1245+557-45677/88765×345.865
Answer:
if question is a fraction then -0.001429, if not then 624.0235948
Kate watered all the flowers at a business park. While watering, she noticed the daisies had
been planted in groups of 3 and the lilies had been planted in groups of 12. If Kate watered
the same number of each flower, what is the minimum number of each that she must have
watered?
Katemust have watered at least 12 daisies (in groups of 3) and 12 lilies (in groups of 12).
What is the minimum number of each that she must have watered?To determine the minimum number of each flower Kate must have watered, we need to find the least common multiple (LCM) of 3 and 12.
The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
The multiples of 12 are: 12, 24, 36, 48, 60, ...
We can see that the least common multiple of 3 and 12 is 12, as it is the smallest number that appears in both lists. Therefore, she must have watered at least 12 daisies (in groups of 3) and 12 lilies (in groups of 12).
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