The five number summary of the data set for the box plot would be :
Minimum value: 2Q1 : 9Median : 14Q3 : 19Maximum value: 20How to find the five number summary ?First, order the numbers in ascending order:
2, 8, 9, 11, 14, 15, 17, 19, 20
The minimum is the smallest number which is 2. The maximum is the largest number which is 20.
The median is the number in the middle which is 19. The Q1 is the number in the middle of the first half of the numbers which is 9. The Q3 is the number in the middle of the second half which is 19.
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Answer:
min=2
1st quartile= 8.5
median=14
3rd quartile=18
max=20
Step-by-step explanation:
Need help Which of the following is not an expression?
• A. 3x+4 = 7
O B. x+8
ㅇ G0-품
O D. 2x -
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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Please solve this question
Answer:
A.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
id
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.
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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Need help with this homework
Answer:
Step-by-step explanation:
use gauth math it helps with maths
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?
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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Four points are plotted on the number line. Which point best represents 33 1/3% of the distance between zero and one
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 -
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
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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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?
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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100 Points! Geometry question. Photo attached. Determine whether the quadrilateral is a parallelogram. Justify your answer using a theorem. Please show as much work as possible. Thank you!
The prove of the statement is described below.
First of all ,
Labeling the given figure
And draw a diagonal,
In the quadrilateral PQRS,
The side PQ is equal to the side RS.
Therefore,
PQ = RS
And also, the side PQ is parallel to the side RS.
Then,
PQ || RS.
Now, draw the diagonal PR.
We know that a parallelogram's diagonal divides the parallelogram into two congruent triangles.
By the rule of Side-Angle-Side,
we can show that ∆ PQR ≅ ∆ RSP.
Therefore,
The side QR is parallel to PS
Then,
QR || PS.
Hence,
PQRS is a parallelogram.
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on a map, 1 inch equals 8.7 miles. If two cities are 2.5 inches apart on the map, how far are they actually apart?
The distance between the cities is ? miles
Answer:
the distance between the cities is 21.75 miles.
Step-by-step explanation:
1 inch = 8.7 miles.
2.5 inches x 8.7 miles/inch = 21.75 miles
According to the table below, What is the domain of the data
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.
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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Please help answer theses questions
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
Answer these 3 questions if not able to answer all try question 10 thank you
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?
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.
Can someone please answer and provide an explanation for these problems?
(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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mathmatically indication example with solution
A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.
How to solve the equation ?Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.
The equation would be 3 x + 2 = 14.
So we can solve for the equation to be :
3x + 2 - 2 = 14 - 2
3x = 12
3 x / 3 = 12 / 3
x = 4
In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.
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PLEASE HELP ASAP 25 POINTS
Answer:
A) Using Commutative property
Step-by-step explanation:
In step 1, it used distributive property when the number 5 is distributed inside of the equation in the parenthesis.
In Step 4, dividing both sides by 10 to further simplify the equation
In step 2, you combined like terms and it results to the equation in step 3
here is my algebra 13 homework screenshot. can someone please help me quick!!
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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Select all of the following that are quadratic equations. 5 x 2+ 15 x = 0 6 x - 1 = 4 x + 7 x 2 - 4 x = 4 x + 7 2 x - 1 = 0 3 x 2 + 5 x - 7 = 0 x 3 - 2 x 2 + 1 = 0
Answer:
Options A, C and E-----------------------
Quadratic equation has the form of:
ax² + bx + c = 0Analyze the given equations and see which has the same form:
A) 5x² + 15 x = 0, Yes, quadratic equation;B) 6 x - 1 = 4, No, it is a linear equation;C) x + 7x² - 4 x = 4, Yes, quadratic equation;D) x + 72x - 1 = 0, No, it is a linear equationE) 3x² + 5x - 7 = 0, Yes, quadratic equation;F) x³ - 2x² + 1 = 0, No, it is cubic equationHELP ASAP PHOTO INCLUDED
I cannot solve that problem at the moment.
Step-by-step explanation:
But I will help you in the future
[tex]f(x)=\frac{x-3}{x+7}[/tex] find the domain
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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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
The correct answer:
(A) WZ/WX = XW/YW
The sin(n/4)equals ?
A. 0.0137
B. 0.7071
The value of function sin (π/4) is,
⇒ sin π/4 = 0.7071
We have to given that;
The expression is,
⇒ sin π/4
Now, We can simplify the expression as;
⇒ sin π/4
⇒ 1 / √2
⇒ 1 / 1.414
⇒ 0.7071
Thus, The value of function sin (π/4) is,
⇒ sin π/4 = 0.7071
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Find m/ABC.
A. 81°
B. 86°
C. 47°
D. 49.5°
Α.
99°
B
D
94%
C
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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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
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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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
Please help me find the perpendicular height
The perpendicular height of the pyramid is 83.65 cm
How to find the perpendicular height?To find the perpendicular height we can define a right triangle.
The perpendicular height is one leg, and the other leg will be half of the diagonal of the base.
The base is a square whose sidelength is 23cm, then the diagonal is:
D = √( (23cm)² + (23cm)²)
D = 32.527cm
Half of that is
D/2 = 32.527cm/2 = 16.26cm
Now, we know one side of the right triangle and the angle of 79°, for which the known cathetus is adjacent.
The perpendicular height is the opposite cathetus.
Then we can use the relation:
tan(79°) = H/16.26cm
Solving for H, the heigt, we will get.
H = tan(79°)*16.26cm = 83.65 cm
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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.
(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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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
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.