Answers
The limit for the given piecewise function does not exist(DNE).
4th option is correct.
What is the limit of a function?In mathematics, limits are the points at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend heavily on limits, which are required to determine integrals, derivatives, and continuity. It is applied during the analysis process and always focuses on the function's behavior at a certain time.
Unique real numbers are limits in mathematics.
According to the question,
Left hand limit of the function= -5(3)+4 = -15+4 = -11
Right hand limit of the function= (3)(3)+2 = 11
As the left and right-hand limits are not equal. Thus, the limit of the function does not exist.
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Related Questions
Which expression is equivalent to 8.8x10^9/2.2x10^-3?
A 4 x 10^12
B 4 x 10^6
C 4 x 10^-3
D 4 x 10^-6
Answers
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Answer:
The correct answer:
(A) WZ/WX = XW/YW
Four points are plotted on the number line. Which point best represents 33 1/3% of the distance between zero and one
Answers
The point Y best represents 33 1/3% of the distance between zero and one.
We know that if the mixed fraction a b/c can expressed as improper fraction in below way:
a b/c = (a*c + b)/c
Here the given the mixed fraction is = 33 1/3 = (33*3 + 1)/3 = 100/3
The distance between the point 0 and 1 is given by = 1 - 0 = 1
So the required percentage of the distance = 1*(33 1/3%) = 1*(100/3 %) = 100/(3*100) = 1/3.
From the number line given we can see that the distance between 0 and 1 is divided in to 12 equal parts.
So, 33 1/3% stands at = 12*(1/3) = 4 th parts that is point Y.
Hence the point Y best represents 33 1/3% of the distance between zero and one.
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The question is incomplete. The complete question will be -
The cost of 4 pairs of shorts and 3 sweatshirts is $89. The cost of 9 pairs of shorts and 11 sweatshirts is $247
Enter the cost of one pair of shorts and one sweatshirt
Answers
Need help Which of the following is not an expression?
• A. 3x+4 = 7
O B. x+8
ㅇ G0-품
O D. 2x -
Answers
The answer is A, because it includes an equals sign and a statement of equality.
A. 3x + 4 = 7 is not an expression, but an equation because it includes an equals sign and a statement of equality.
B, C, and D are all expressions. Expression refers to a mathematical phrase that can include numbers, variables, and mathematical operations, but does not contain an equals sign or a statement of equality.
B. x + 8 is a simple expression that includes a variable and a constant.
C. 6 - x/5 is also an expression that involves a constant and a variable, and uses a division operation.
D. 2x-3 is another expression that includes a variable and a constant, and uses a subtraction operation.
Therefore, the answer is A, since it is not an expression.
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Find m/ABC.
A. 81°
B. 86°
C. 47°
D. 49.5°
Α.
99°
B
D
94%
C
Answers
m/ABC=86° (because of the cyclic quadrilaterals). Hence, Option (B) is correct.
A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.
The opposite angles of a cyclic quadrilateral have a total of 180°.
m/ABC + m/ADC = 180°
m/ABC + 94° = 180°
m/ABC = 180° - 94°
m/ABC = 86°
Similarly, one can find m/DCB
m/DAB + m/DCB = 180°
99° + m/DCB = 180°
m/DCB = 180° - 99°
m/DCB = 81°
Hence, m/ABC = 86°
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9*
Giovanni needs to hire a handyman to paint his house. Charles will charge him
$115 up front and $30 per hour. Peter will charge $40 per hour with an $80 flat fee
for paint. After how many hours will the two men charge the same amount to
complete the job?
Answers
The two men will charge the same amount to complete the job after 3.5 hours.
How to determine After how many hours will the two men charge the same amount to complete the job?Let's start with Charles' fee, which is a combination of an upfront fee and an hourly fee. We can represent this as:
C(x) = 115 + 30x
where x is the number of hours Charles works.
For Peter, his fee is a combination of an upfront fee for paint and an hourly fee. We can represent this as:
P(x) = 80 + 40x
where x is the number of hours Peter works.
To find out when the two men will charge the same amount to complete the job, we need to set the two equations equal to each other and solve for x:
115 + 30x = 80 + 40x
Subtracting 30x from both sides: 115 = 80 + 10x
Subtracting 80 from both sides: 35 = 10x
Dividing both sides by 10:
x = 3.5
So, the two men will charge the same amount to complete the job after 3.5 hours.
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Let's say you (a 16-year old) open a savings account with an interest rate of 6% per year and you
aren't adding any additional funds in the future. If you make $80,000 within the year you turn 60, what
is the total amount in your account at 60 years old?
Answers
The total amount in the account when turning 60 years is A = $ 11,13,706.08
Given data ,
A savings account with an interest rate of 6% per year and you aren't adding any additional funds in the future
Now , you make $80,000 within the year you turn 60
So , the number of years = 60 - 16 = 44 years
And , from the compound interest , we get
A = P ( 1 + r/n )ⁿᵇ
On simplifying , we get
Where A is the final amount, P is the initial amount (which is 0 in this case), r is the annual interest rate (6% or 0.06), n is the number of times the interest is compounded per year (let's assume it is compounded monthly, so n=12), t is the time in years (44 years from age 16 to age 60).
A = 80,000 ( 1 + 0.06/12 )¹²ˣ⁴⁴
A = $ 11,13,706.08
Hence , the amount in account is A = $ 11,13,706.08
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Students were asked their favorite ice cream flavor. The results showed that 196 students selected vanilla as their favorite ice cream flavor. This represents 49% of the total number of students surveyed. What was the total number of students surveyed?
I need the answer and explanation!!!
Answers
Answer:
The total number of students surveyed is 400.
Step-by-step explanation:
We want to know that 49% of what number is 196
Let x = the total number of students
.49x = 196 (49% as a decimal is .49) Divide both sides by .49
x = 400
A cyclist covers 5/7 of his route and an additional 40 minutes. He has yet to cover 118 miles less than 0.75 of his route. How long is his route?
Answers
The distance that describes how long his route was is: 168 miles.
How to determine the length of the routeTo determine how long the route was, we need to first represent the entire unknown distance covered by this individual with s.
5/7 s + 40 minutes + (0.75s - 118) = s
5/7s + 75/100s + 40 - 118 = s
5/7s + 75/100s - 78 = s
5/7s + 75/100s - s = 78
325s = 54600
s = 168 miles.
So, the entire distance covered by the cyclist is 168 miles.
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The distance that describes how long his route was is: 168 miles.
How to determine the length of the route.
To determine how long the route was, we need to first represent the entire unknown distance covered by this individual with s.
5/7 s + 40 minutes + (0.75s - 118) = s
5/7s + 75/100s + 40 - 118 = s
5/7s + 75/100s - 78 = s
5/7s + 75/100s - s = 78
325s = 54600
s = 168 miles.
So, the entire distance covered by the cyclist is 168 miles.
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Evaluate the following statement.
( - 179 – 78 ) + 41 - ( - 165 )
Answers
The answer is:
( - 179 – 78 ) + 41 - ( - 165 )
=-51
Answer:
(-257) +41+165
-257+206
-51
Consider the following symbolic logic statement: ¬ (∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y))
a) Translate the statement into English using proper syntax and semantics.
b) Identify and explain any potential ambiguities in the translated statement.
c) Rewrite the statement in a way that eliminates any ambiguities and maintains the original meaning.
Answers
(a). The statement can be translated into English as follows "Not exists x such that P(x) and Q(x), and for all y, if R(y) then P(y)." (b) The rewritten statement explicitly places the negation symbol "¬" only in front of the existential quantifier (∃x). (c). This clarifies that the negation applies to the existence of x such that P(x) and Q(x).
a) Translation into English:
The statement can be translated into English as follows:
"Not exists x such that P(x) and Q(x), and for all y, if R(y) then P(y)."
b) Potential ambiguities in the translated statement:
Ambiguity in the scope of negation: The placement of the negation symbol "¬" might lead to ambiguity. It is not clear whether the negation applies only to the existential quantifier (∃x) or to the entire statement. Specifically, it is unclear if the negation applies to both conjuncts separately or to their conjunction as a whole.
Ambiguity in the scope of quantifiers: The scope of the quantifiers (∃x) and (∀y) is not explicitly defined. It is unclear which variables the quantifiers bind to and how they relate to the predicates P(x), Q(x), R(y), and P(y).
c) Rewritten statement to eliminate ambiguities while maintaining the original meaning:
To eliminate the ambiguities, we can rewrite the statement as follows:
(¬∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y))
The rewritten statement explicitly places the negation symbol "¬" only in front of the existential quantifier (∃x). This clarifies that the negation applies to the existence of x such that P(x) and Q(x). Additionally, parentheses are used to explicitly define the scope of the quantifiers (∃x) and (∀y), making it clear which variables they bind to.
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Cody works at a vehicle rental company. The vehicles available to rent are listed in the table.
What is the ratio of seats to engine cylinders in the truck?
Answers
The Ratio of seats to engine cylinders in the Ford F-150 truck that Cody wants to rent is approximately 0.625.
The ratio of seats to engine cylinders in the Ford F-150 truck that Cody wants to rent can be calculated by dividing the number of seats by the number of engine cylinders. In this case, the Ford F-150 has a seating capacity of 5 passengers and a V8 engine configuration.
To calculate the ratio, we divide the number of seats (5) by the number of engine cylinders (8):
Ratio of seats to engine cylinders = Number of seats / Number of engine cylinders
Ratio of seats to engine cylinders = 5 / 8
Simplifying the ratio, we get:
Ratio of seats to engine cylinders = 0.625
Therefore, the ratio of seats to engine cylinders in the Ford F-150 truck that Cody wants to rent is approximately 0.625.
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Note the full question may be :
Cody works at a vehicle rental company. The vehicles available to rent are listed in the table below:
Vehicle Type | Seats | Engine Cylinders
----------------------------------------------
Car | 5 | 4
SUV | 7 | 6
Truck | 3 | 8
What is the ratio of seats to engine cylinders in the truck?
A. 1:3
B. 3:8
C. 8:3
D. 3:1
Choose the correct option that represents the ratio of seats to engine cylinders in the truck.
Find the values of c guaranteed by the Mean Value Theorem (MVT) for f(x)=……..
Answers
Using the mean value theorem in f(x) = 1/2x² + 7, c = 2√3
What is the mean value theorem?The mean value theorem states that let f be continuous over the closed interval [a,b] and differentiable over the open interval (a,b). Then, there exists at least one point c ∈(a,b) such that f'(c) = [f(b) - f(a)]/(b - a)
To find c using the mean value theoren for f(x) = 1/2x² + 7 over the interval [0, 6], we proceed as follows.
Uisng the mean value theorem, we know that
f'(c) = [f(b) - f(a)]/(b - a)
⇒ f(c) = 1/(b - a)∫ₐᵇ[f(x)
Now over the interval [a, b] = [0,6]
f(c) = 1/(6 - 0)∫₀⁶[f(x)
Now, since f(x) = 1/2x² + 7
Substituting this into the equation, we have that
f(c) = 1/(6 - 0)∫₀⁶[f(x)
f(c) = 1/(6 - 0)∫₀⁶(1/2x² + 7)
f(c) = 1/6∫₀⁶(1/2x² + ∫₀⁶7)
f(c) = 1/6[1/2x³/3 + 7x]₀⁶
f(c) = 1/6[x³/6 + 7x]₀⁶
f(c) = 1/6[6³/6 + 7(6)] - [0³/6 + 7(0)]
f(c) = 1/6[6²+ 42] - [0 + 7(0)]
f(c) = 1/6([36 + 42] - [0 + 0])
f(c) = 1/6(78 - 0)
f(c) = 1/6(78)
f(c) = 13
Now, since f(x) = 1/2x² + 7
f(c) = 1/2c² + 7
1/2c² + 7 = 13
1/2c² = 13 - 7
1/2c² = 6
c² = 2 × 6
c² = 12
c = √12
c = 2√3
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LIGHT The length of the shadow S given by a tower
that is 100 meters high is S = 100/tan θ, where θ
is the angle of inclination of the sun. If the
angle of inclination is 45°, find the length of the shadow.
a. 162 m
b. 62 m
c. 100 m
d. 84 m
Answers
Answer:
c. 100 m
Step-by-step explanation:
You want the length of the shadow of a 100 m tower if the angle of inclination of the sun is 45°.
Isosceles right triangleThe tower and its shadow are modeled as legs of a right triangle. When the acute angle in such a triangle is 45°, the triangle is isosceles and the legs are the same length.
The shadow is the same length as the height of the tower: 100 m.
__
Additional comment
You can check this by using the formula:
S = 100/tan(45°) = 100/1 = 100
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[tex]f(x)=\frac{x-3}{x+7}[/tex] find the domain
Answers
The domain of the function f(x) is all real numbers except x = -7. In interval notation, we can express the domain as (-∞, -7) ∪ (-7, +∞).
To find the domain of the function f(x) = (x - 3)/(x + 7), we need to determine the values of x for which the function is defined.
The function is defined for all values of x except those that make the denominator, x + 7, equal to zero.
Division by zero is undefined in mathematics.
So, we set the denominator equal to zero and solve for x:
x + 7 = 0
x = -7
Hence, the only value that makes the denominator zero is x = -7. Therefore, the domain of the function f(x) is all real numbers except x = -7.
In interval notation, we can express the domain as (-∞, -7) ∪ (-7, +∞).
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Can someone please answer and provide an explanation for these problems?
Answers
(17) The length of the arc is 39.27 in
(18) The length of the arc is 70.7 cm
(19) The area of the sector is 395.84 in²
(20) The area of the sector is 38.5 cm².
What is the area of the sector?The area of each of the sector is calculated by using the following formula;
Area = πr² (θ/360)
Where;
r is the radiusθ is the angle subtended by the sectorThe formula for length of arc is given as;
length of arc = 2πr (θ/360)
(17) The length of the arc is calculated as;
L = 2π (10 in) (225/360)
L = 39.27 in
(18) The length of the arc is calculated as;
L = 2π (15 cm) (270/360)
L = 70.7 cm
(19) The area of the sector is calculated as;
A = π(12)² (315/360)
A = 395.84 in²
(20) The area of the sector is calculated as;
A = π(7)² (90/360)
A = 38.5 cm²
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Please help it’s due today!!!!
Answers
4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.
5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.
How to verify that RSTU is a trapezoid?In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;
RU ║ ST
Slope of side RU = Slope of side ST
Slope of RU = (y₂ - y₁)/(x₂ - x₁)
Slope of RU = (1 + 3)/(5 + 3)
Slope of RU = 4/8
Slope of RU = 0.5.
Slope of RS = (y₂ - y₁)/(x₂ - x₁)
Slope of RS = (-9 + 3)/(-4 + 3)
Slope of RS = -6/-1
Slope of RS = 6.
Slope of ST = (y₂ - y₁)/(x₂ - x₁)
Slope of ST = (-2 - 1)/(10 - 5)
Slope of ST = -3/5
Slope of ST = -0.6.
Slope of UT = (y₂ - y₁)/(x₂ - x₁)
Slope of UT = (-2 + 9)/(10 + 4)
Slope of UT = 7/14
Slope of UT = 0.5.
Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.
Question 5.
In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance RT = √[(-2 + 3)² + (10 + 3)²]
Distance RT = √170 units.
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance US = √[(5 + 4)² + (1 + 9)²]
Distance US = √181 units.
Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.
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Un fabricante de bombillas gana 0,60€ por cada bombilla que sale de fábrica pero pierde 0,80€ por cada una que sale defectuosa. Un determinado día en el que fabrico 2.100 bombillas obtuvo un beneficio de 966€. ¿Cuántas bombillas de cada tipo fabricó?
Answers
The manufacturer made 1,890 non-defective light bulbs and 210 defective light bulbs.
How many defective and non-defective light bulbs was made?Let represent number of non-defective light bulbs with x
Let represent number of defective light bulbs with y.
The profit from selling non-defective light bulbs is €0.60x
The loss from selling defective light bulbs is €0.80y.
Given that the manufacturer made a profit of €966, we can form the equation:
0.60x - 0.80y = 966 ---(1)
The total number of light bulbs produced is 2,100, so we have:
x + y = 2,100 ---(2)
To solve this, we will use method of elimination.
We multiply equation (2) by 0.60.
0.60x + 0.60y = 1,260 ---(3)
Now, subtract equation (3) from equation (1):
0.60x - 0.60x - 0.80y - 0.60y = 966 - 1,260
-1.40y = -294
y = -294 / -1.40
y = 210
Substituting value of y into equation (2):
x + 210 = 2,100
x = 2,100 - 210
x = 1,890.
Translated question:
A light bulb manufacturer earns €0.60 for each bulb that leaves the factory but loses €0.80 for each one that is defective. On a certain day when he manufactured 2,100 light bulbs, he made a profit of €966. How many light bulbs of each type did he make?
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Given circle E with diameter CD and radius EA. AB is tangent to E at A. If AB=34 and EB=38, solve for EA. Round to the nearest tenth if necessary
Answers
The value of side EA is,
EA = 16.9
We have to given that;
Circle E with diameter CD and radius EA.
And, AB is tangent to E at A.
Here, AB = 34 and EB = 38
Hence, By using Pythagoras theorem we get;
AB² + AE² = EB²
34² + AE² = 38²
1156 + AE² = 1444
AE² = 1444 - 1156
AE² = 288
AE = √288
AE = 16.9
Thus, The value of side EA is,
EA = 16.9
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A young artist went to an art shop to buy a canvas. There were many sizes from which to choose. Some were standard sizes and some were custom-made. She wanted her next piece to incorporate the Golden Ratio, so she decided to buy the canvas whose dimensions most closely matched the Golden Rectangle. Here are the sizes that were available:
24" x 36"
24" x 40"
10" x 16"
26" x 16"
20" x 12"
Which canvas should the artist buy? Show your work.
Answers
The artist should buy the canvas with dimensions 26" x 16" as it most closely matches the Golden Rectangle.
To determine which canvas size most closely matches the Golden Rectangle, we need to calculate the aspect ratios of the available options and compare them to the Golden Ratio.
The Golden Ratio is approximately 1.618. A rectangle is considered to be a Golden Rectangle if its aspect ratio (width divided by height) is equal to the Golden Ratio.
Let's calculate the aspect ratios for each canvas size:
Canvas 1: 24" x 36"
Aspect ratio = 24 / 36 = 0.67
Canvas 2: 24" x 40"
Aspect ratio = 24 / 40 = 0.6
Canvas 3: 10" x 16"
Aspect ratio = 10 / 16 = 0.625
Canvas 4: 26" x 16"
Aspect ratio = 26 / 16 = 1.625
Canvas 5: 20" x 12"
Aspect ratio = 20 / 12 = 1.667
Now, let's compare the aspect ratios of the available options with the Golden Ratio (1.618) to see which one is closest:
Canvas 1: |0.67 - 1.618| = 0.948
Canvas 2: |0.6 - 1.618| = 1.018
Canvas 3: |0.625 - 1.618| = 0.993
Canvas 4: |1.625 - 1.618| = 0.007
Canvas 5: |1.667 - 1.618| = 0.049
The canvas with the aspect ratio closest to the Golden Ratio is Canvas 4: 26" x 16". Its aspect ratio of 1.625 is only 0.007 away from the Golden Ratio.
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here is my algebra 13 homework screenshot. can someone please help me quick!!
Answers
The slope of the graph f(x) = (1/3)x + 4 is less than the slope of g(x) = 4x-1
f(x) = 1/3 x + 4
g(x) = 4x - 1
The equation of line is given by y = mx +c
On comparing both equation with y = mx + c
m is the slope of the line and c is the intercept of the equation
Let the slope of f(x) is m₁
In f(x) =1/3 x + 4
m₁ = 1/3 = 0.33
Let the slope of g(x) is m₂
In g(x) = 4x - 1
m₂ = 4
m₁ < m₂
slope of f(x) is less than slope of g(x)
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Please solve this question
Answers
Answer:
A.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
id
Please help answer theses questions
Answers
Answer:
Question 6 : True
Question 7: False
Step-by-step explanation:
To find g(f(x)) given f(x) and g(x), substitute the expression for f(x) for every x in g(x)
f(x) = 2x
g(x) = x²
g(f(x) = (2x)² = 4x²
So True
f(x) = x² + x
g(x) = 2x + 1
g(f(x)) = 2(x² + x) + 1 = 2x² + 2x + 1
So False
According to the table below, What is the domain of the data
Answers
Domain: {15, 17, 19, 21, 23}
Step-by-step explanation:The domain describes the x-values within a function.
Inputs
In a function, the inputs are the values that are plugged into a function, and the outputs are the resulting values. This means that the inputs represent the x-values and the outputs are the y-values. Since this is a function, each of the inputs has one output. So, each input is unique. We can use the input values to find the domain.
Domain
The domain of a data set is the x-values. Each x-value is one part of the domain. The domain is written as a list of values in numerical order with braces surrounding the values. Since the inputs represent the x-values, we can use the input values as the domain values. This means that the domain of the data is {15, 17, 19, 21, 23}.
Consider a sample with six observations of 16, 11, 13, 22, 15, and 19. Compute the z-score for each observation.
Answers
The z-scores for the observations 16, 11, 13, 22, 15, and 19 are approximately 0, -1.37, -0.82, 1.64, -0.27, and 0.82, respectively.
To compute the z-scores for each observation in the sample, we need to first calculate the mean and standard deviation of the data set.
Given the sample with observations: 16, 11, 13, 22, 15, and 19.
Calculate the mean (μ):
Add up all the observations and divide by the total number of observations.
Mean (μ) = (16 + 11 + 13 + 22 + 15 + 19) / 6 = 96 / 6 = 16.
Calculate the standard deviation (σ):
Subtract the mean from each observation.
Deviation = Observation - Mean
Square each deviation.
Squared Deviation = Deviation²
Calculate the average of the squared deviations.
Average Squared Deviation = (Squared Deviation1 + Squared Deviation2 + ... + Squared Deviation6) / 6
Take the square root of the average squared deviation.
Standard Deviation (σ) = √(Average Squared Deviation)
Let's calculate each step:
Deviation1 = 16 - 16 = 0
Deviation2 = 11 - 16 = -5
Deviation3 = 13 - 16 = -3
Deviation4 = 22 - 16 = 6
Deviation5 = 15 - 16 = -1
Deviation6 = 19 - 16 = 3
Squared Deviation1 = 0² = 0
Squared Deviation2 = (-5)² = 25
Squared Deviation3 = (-3)² = 9
Squared Deviation4 = 6² = 36
Squared Deviation5 = (-1)² = 1
Squared Deviation6 = 3² = 9
Average Squared Deviation = (0 + 25 + 9 + 36 + 1 + 9) / 6 = 80 / 6 = 13.33
Standard Deviation (σ) = √13.33 ≈ 3.65
Now that we have the mean (μ = 16) and standard deviation (σ ≈ 3.65), we can calculate the z-score for each observation.
The z-score (Z) for an observation (X) is calculated using the formula:
Z = (X - μ) / σ
Let's calculate the z-scores for each observation:
Z1 = (16 - 16) / 3.65 = 0 / 3.65 = 0
Z2 = (11 - 16) / 3.65 = -5 / 3.65 ≈ -1.37
Z3 = (13 - 16) / 3.65 = -3 / 3.65 ≈ -0.82
Z4 = (22 - 16) / 3.65 = 6 / 3.65 ≈ 1.64
Z5 = (15 - 16) / 3.65 = -1 / 3.65 ≈ -0.27
Z6 = (19 - 16) / 3.65 = 3 / 3.65 ≈ 0.82
So, the z-scores for the observations 16, 11, 13, 22, 15, and 19 are approximately 0, -1.37, -0.82, 1.64, -0.27, and 0.82, respectively.
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What is the volume of this figure?
Enter your answer in the box.
ft³
Three-dimensional figure formed by placing two rectangular prisms together to form an L shape where the bottom of the L is on the left and the top of the L extends to the right. The wider part of the L has a width of 3 feet. The other part of the L has a width of 2 feet. The total length of the L is 7 feet, and the length of the narrower part of the L is 6 feet. The height connecting the L shaped bases is 5 feet.
Answers
The volume of the rectangular prism in this problem is given as follows:
99 ft³.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:
Volume = length x width x height.
The figure in this problem can be divided into two prisms, with dimensions given as follows:
3 ft, 5 ft and 7 - 6 = 1 ft.6 ft, 2 ft and 7 ft.Hence the volume of the prism is given as follows:
V = 3 x 5 x 1 + 6 x 2 x 7
V = 99 ft³.
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What can be interpreted from the scatter plot above
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The thing that can be interpreted from the scatter plot above is A. There is a negative association between number of hours of daily TV viewing and math quiz scores.
How to explain the scatterplotAs per given scatter plot, If the number of hour of daily TV viewing increases then the math quiz scores are decreases.
Hence, the number of hour of daily TV viewing and math quiz scores varies inversely.
Therefore, There is a negative ath association between number of hour of daily TV viewing and math quiz scores
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Percy's Desserts made a batch of fresh scones with 5/8 of a pound of butter and 1/2 of a
pound of sugar. How much more butter than sugar was used?
Write your answer as a fraction or as a whole or mixed number.
pounds
Answers
Answer:
Step-by-step explanation:
To find the difference between the amount of butter and sugar used, we need to subtract the weight of sugar from the weight of butter.
The weight of butter used is 5/8 pounds, and the weight of sugar used is 1/2 pounds. To subtract these fractions, we need to find a common denominator.
The common denominator for 8 and 2 is 8, so we can rewrite the fractions as follows:
5/8 pounds of butter
4/8 pounds of sugar
Now we can subtract the weight of sugar from the weight of butter:
5/8 - 4/8 = 1/8
Therefore, Percy's Desserts used 1/8 pound more butter than sugar.
Answer: Percy's Desserts used 1/8 pounds more butter than sugar in their batch of fresh scones.
Step-by-step explanation:
1. Identify the quantities of butter and sugar used: Percy's Desserts used 5/8 of a pound of butter and 1/2 of a pound of sugar.
2. Convert the quantities to a common denominator: To compare these quantities, we need to express them with a common denominator. The least common denominator of 8 and 2 is 8. So, we express 1/2 as 4/8.
3. Subtract the quantity of sugar from the quantity of butter: Now that both quantities are expressed in eighths of a pound, we can subtract them: 5/8 - 4/8 = 1/8.
4. Convert the result back to a decimal: 1/8 of a pound is equivalent to 0.125 pounds.
So, Percy's Desserts used 0.125 pounds more butter than sugar in their batch of fresh scones.
Find the y-intercept of the line 12x - 18y = -24.
Answers
Answer:
Therefore, the y-intercept of the line is (0, 4/3).
Step-by-step explanation:
To find the y-intercept of the line 12x - 18y = -24, we need to set x = 0 and solve for y.
12(0) - 18y = -24
Simplifying, we get:
-18y = -24
Dividing both sides by -18:
y = 4/3
Therefore, the y-intercept of the line is (0, 4/3).