8. The number of steps needed to get from one floor to the next in a hotel staircase is 14. The ground level is floor 0.
a. Complete the table.
n(floor number)
s(total steps to reach floor)
1
14
2 3 4 5
Answers
Step-by-step explanation:
0 steps to reach floor 0.
a.
floor 0 to floor 1 = floor 0 + 14 = 0 + 14 = 14
floor 1 to floor 2 = floor 1 + 14 = 14 + 14 = 28
floor 2 to floor 3 = floor 2 + 14 = 28 + 14 = 42
floor 3 to floor 4 = floor 3 + 14 = 42 + 14 = 56
floor 4 to floor 5 = floor 4 + 14 = 56 + 14 = 70
b.
when we look at the calculation for the stairs to floor 1, then we see
floor 1 = floor 0 + 14 = 0 + 14 = 14
and for floor 2
floor 2 = floor 1 + 14 = floor 0 + 14 + 14 = 0 + 14 + 14 = 28
and for floor 3
floor 3 = floor 2 + 14 = floor 0 + 14 + 14 + 14 = 42
and so on.
we see
floor n = s(n) = s(0) + 14×n = 0 + 14×n = 14n
s(n) = 14n
Related Questions
College Level Quantitative Reasoning - See Screenshot
Answers
The absolute and relative errors are 0. 8 and 0. 01 respectively.
What is absolute error?Absolute error can be defined as the difference between the inferred or measured value and the actual value of a given quantity.
The formula for absolute error is expressed as;
Absolute error = | VA - VE |
Where;
VA is the actual value = 60. 8 InchesVE is the expected value = 60. 0 InchesSubstitute the values into the formula
Absolute error = | 60. 8 - 60. 0|
Find the difference
Absolute error = | 0. 8|
Absolute error = 0. 8
Relative error = Absolute error/ actual value
Relative error = 0. 8/ 60. 0
Relative error = 0. 01
Thus, the absolute and relative errors are 0. 8 and 0. 01 respectively.
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A college has a financial aid formula that applies to applicants whose family's income is below a certain threshold. The financial aid can be determined by the function f(x)=10000+1000x,f(x)=10000+1000x, where xx is the number of siblings (including half siblings and step siblings) that the applicant has living in their household. Find and interpret the given function values and determine an appropriate domain for the function.
Answers
The numeric values of the function are given and explained as follows:
f(-2) = 8000, meaning a qualifying applicant with -2 siblings would receive a financial aid of $8,000. This interpretation does not make sense in the context of the problem.f(4) = 14,000, meaning a qualifying applicant with 4 siblings would receive a financial aid of $14,000. This interpretation makes sense in the context of the problem.The domain is: {x is a whole number and x ≥ 0}.How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
For this problem, the function is given by:
f(x) = 10000 + 1000x.
In which:
The output f(x) is the financial aid.The input x is the number of siblings in the family.When x = -2, we have that:
f(-2) = 10000 + 1000(-2) = 8000.
Hence:
f(-2) = 8000, meaning a qualifying applicant with -2 siblings would receive a financial aid of $8,000. This interpretation does not make sense in the context of the problem.
When x = 4, we have that:
f(4) = 10000 + 1000(4) = 14,000.
Hence:
f(4) = 14,000, meaning a qualifying applicant with 4 siblings would receive a financial aid of $14,000. This interpretation makes sense in the context of the problem.
The number of siblings is a discrete number, and has to be of at least 0, hence:
The domain is: {x is a whole number and x ≥ 0}.
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help pls i gyg soonn
Answers
Answer:
Step-by-step explanation:
8806
My 10 year old has the following word problem. I am CLUELESS!
Answers
Bob sells cars. His income is based on a graduated scale. If he earns %5 commission for the first $50,000 in scales %8 commission for sales over $50,000, then how much would he earn if his total sales were $95,000
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
A scale drawing of a spider is 5 centimeters long. The actual spider is 10
millimeters long.
a. What is the scale of the drawing?
b. What is the scale factor of the drawing?
c. The spiders mate is 8mm, what size should the drawing for it be in cm? Explain how to decide whether to use the scale or scale factor?
Answers
(a) The scale of the drawing is in centimeters.
(b) The scale factor of the drawing is 5 mm.
(c) The size of the spider's mate drawing should be 4 cm.
Given scale drawing of a spider is 5 cm long.
The actual spider is 10 mm long
(a) The scale of the drawing is in centimeters because the scale drawing of a spider given is in 5 centimeters,
(b) Scale factor:
The scale factor shows by how much the original model has been multiplied or divided by to get the measurements of the drawing.
In this case, the spider is 10 mm long but the drawing length is 5 cm.
Let’s convert both into the same units
5 cm - 50 mm
Original - 10 mm
Painting -50 mm
X - scale factor
50 = X * 10
X = 50/10 = 5 mm
The spider has been multiplied/ enlarged by a scale factor of 5 mm to draw the painting.
(c) Given the spider's mate is 8mm long.
Now for the drawing, we need to choose the scale factor as above to get the perfect measurement.
So, the 8 mm spider has been enlarged by a scale factor of 5 mm to get the size for drawing.
= 8 * 5
= 40 mm
= 4 cm
The size of the drawing should be 4 cm.
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Write the equation of a line perpendicular to 3x - 8y = - 7 that passes through the point (-3,3).
Answers
3y = -8x -27
Solution :
A line equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
Given line: 3x - 8y = -7
-8y = -7 -3x
y=- (-7 -3x)/8
y= 7+3x/8
So, the slope (m1) = 3/8
Let’s consider the slope of the line perpendicular to the given line as m2
Then, m1 x m2 = -1
3/8 x m2 = -1
m2 = -8/3
Now,
The equation of the line perpendicular to the given line and passing through the point (-3, -3) will be
y – y1 = m (x – x1)
y – (-3) = -(8/3) (x – (-3))
y + 3 = (-8/3) (x +3)
3y + 3 = - 8x - 24
3y = -8x -24-3
3y = -8x -27
Thus, the equation of the required line is 3y = -8x -27
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There is exactly 1 pair of parallel sides in the
following shape.
Base=6 base=8 height=5
What is the area of the shape?
Answers
The area of the shape with parallel sides is 35 unit² of trapezoid .
Describe the trapezoid shape?
An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel.A = (1/2) * (a + b)h
Where a, b is the length of the parallel sides and h is the height of the trapezoid.
Given that a = 8, b = 6 and h = 5, hence:
A = (1/2) * (8 + 6) * 5 = 35 unit²
The area of the shape with parallel sides is 35 unit².
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PLEASE CAN SOMEONE ANSWER THIS! Thank you pls
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Answer: draw a parallelogram like figure A and make it the same area of the unlabeled rectangle.
i need help assap dont judge
Answers
Determine the equation of the line described. Put answer in the slope-intercept form, if possible.
Through (9,-9), perpendicular to x = -2
Answers
Step-by-step explanation:
do you have a picture of your work?
and if you have 9.9 in your graph and you get a point it can be valid otherwise it would not help you at all
what is 3 11/12 - 3/4? I have an upcoming test, and I need someone to explain it step-by-step.
Answers
Answer:
3 1/6
Step-by-step explanation:
First, we turn 11/12 and 3/4 to have the same denominator
3/4 x 3 is 9/12
11/12- 9/12 is 2/12
Now we add the extra 3 to 2/12 which is 3 2/12
3 2/12 can be simplified to 3 1/6
How many grams are in 0.0564 mol of sodium?
Answers
Answer:
1.296623028 grams
Step-by-step explanation:
your answer is 1.296623028 grams because you multiply the given number of moles which was 0.0564 by the molar mass to get the grams
x^2+48=14x
Show work please
Answers
Answer:
Step-by-step explanation:
x^2 - 14x = -48
x^2 +48 -14 x
x^2 - 14x - 48 = 0
a = 1
b = -14
c = 48
x=8, x=6
need help due tomorrow too
Answers
Answer: The answer is 7
Step-by-step explanation:
Absolute value is the final amount of spaces it is from 0 so -7 and positive 7 are both 7 spaces from 0 so I claim that 7 is the absolute value making Amanda wrong!
20 push-ups in 2days
Answers
Answer: ok?
Step-by-step explanation:
Write a sequence that has the stated property.
The 1st difference of the sequence can be modeled with the expression 8x-5.
Answers
The sequence that can be modeled by the expression is T(n+1) = Tn + 8x - 5 where n >= 1
How to determine the sequence that can be modeled by the expression?The expression of the first difference is given as
8x - 5
Rewrite properly as
d = 8x - 5
Where the common difference is represented by d
The common difference of an arithmetic sequence is calculated as
d = T2 - T1
So, we have
T2 - T1 = 8x - 5
Add T1 to both sides of the equation
So, we have
T2 = T1 + 8x - 5
Express 2 as 1 + 1
So, we have
T(1+1) = T1 + 8x - 5
Express 1 as n
So, we have
T(n+1) = Tn + 8x - 5 where n >= 1
Hence, the sequence that can be modeled by the expression is T(n+1) = Tn + 8x - 5 where n >= 1
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I need help with question!
Answers
for example here I used (2,-1)(0,1) and used the formula os slope y2-y1/x2-x1
1-(-1)/0-2
=2/-2
=-1
Or you can use (3,-2)(-2,3)
3-(-2)/-2-3
=5/-5
=-1
So the slope is -1
Hope this helped
Jim began a 86-mile bicycle trip to build up stamina for a triathlon competition. Unfortunately, his bicycle chain broke,
so he finished the trip walking. The whole trip took 4 hours. If Jim walks at a rate of 4 miles per hour and rides at 32
miles per hour, find the amount of time he spent on the bicycle.
Answers
The amount of time he spent on the bicycle is; 2.5 hours
How to solve algebra word problems?
The formula that shows the relationship between distance, speed and time is;
distance = velocity * time
Let W = walking time
B = bicycling time
Thus, from the given data we have;
86 = 4W + 32B
W + B = 4
W = 4 - B substitute 6-B for W in 86 = 4W + 32B to get;
86 = 4(4 - B) + 32B
86 = 16 - 4B + 32B
86 = 16 + 28B
70 = 28B
B = 70/28
B = 2.5 hours on the bicycle
W = 4 - 2.5= 1.5 hours walking
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For his birthday, Baldwin got a new drone. According to the box, the drone can fly as fast as 1,100 feet per minute. Baldwin thinks that sounds too fast to be realistic, so he wants to convert the speed to more familiar
Hint: there are 5,280 feet in 1 mile
Answers
In this case you want to convert feet per minute to miles per hour. First convert feet to miles by dividing by 5280 then convert minutes to hours by multiplying by 60.
That will give you 12.5 mph
1. The soccer team is making pizzas for a fundraiser. They put1/4 of a pound of cheese on each pizza. If they have 12 one-pound packages of cheese, how many pizzas can they make? pizzas ?
2. Dan purchased 3 ½ yards of mulch for his garden. Mulch costs $25 a yard. How much did Dan pay for his mulch? $
3. Mr. Hamilton owns 2 ¾ acres of land. He plans to buy 1 and 1/3 more acres. How many acres will he own? Write your answer as an improper fraction. acres
Answers
1) The soccer team can make 48 pizzas using 12 one-pound packages of cheese.
2) The total cost Dan paid for the mulch was $87.50.
3) The number of acres that Mr. Hamilton will own after the planned purchase is 3¹³/₁₂.
How are the values determined?The above values are determined using mathematical operations of addition, division, and multiplication.
For instance, Mr. Hamilton's land increased to 3¹³/₁₂ through the addition of 2¾ and 1¹/₃ acres.
The total cost that Dan paid for the mulch was a multiplication operation.
The number of pizzas the soccer team could make resulted from a division operation.
Data and Calculations:1) Quantity of cheese on each pizza = 1/4 lb
The total quantity of cheese = 12 lb
The number of pizzas to make = 48 (12/1/4) or (12/0.25)
2) The number of yards of mulch purchased = 3¹/₂ yards
Cost of mulch per yard = $25
The total cost for the mulch = $87.50 ($25 x 3¹/₂)
3) Measurement of land owned = 2¾ acres
The planned purchase of additional land = 1¹/₃
The total acres Mr. Hamilton will own = 3¹³/₁₂ (2¾ + 1¹/₃)
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Karen must choose a number between 49 and 95 that is a multiple of 2, 8, and 10. Write all the numbers that she could choose. If there is more than one
number, separate them with commas.
Answers
Answer:
80
Step-by-step explanation:
80 is the only number that is a multiple of ALL 2, 8 and 10
Answer:
the only answer that is a multiple of 2,8 and 10 between 49 and 95, is 80.
Find the equation of the exponential function represented by the table below:
x
0
1
2
3
Y
5
2.5
1.25
0.625
Answers
Answer:
x = r ,r is a whole number
y = 5(.5)^r
y=5(.5)
Step-by-step explanation:
The equation of the exponential function represented by the table given is f(x)=(5)[tex](0.5^{x} )[/tex].
Function:
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
For x=0 for f(0)=(5)[tex](0.5^{0} )[/tex]=5
⇒ x=1 for f(1)=(5)[tex](0.5^{1} )[/tex]=2.5
⇒ x=2 for f(2)=(5)[tex](0.5^{2} )[/tex]=1.25
⇒ x=3 for f(3)=(5)[tex](0.5^{3} )[/tex]= 0.625
Therefore,The equation of the exponential function represented by the table given is f(x)=(5)[tex](0.5^{x} )[/tex].
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A total of 52 microphones are to be purchased. Each microphone costs $548. Estimate the total purchase price by using rounded numbers.
Answers
The total purchase price is $28496 if a total of 52 microphones are to be purchased. Each microphone costs $548.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A total of 52 microphones are to be purchased. Each microphone costs $548.
Let x be the total purchase price
x = 52x548
x = $28496
Thus, the total purchase price is $28496 if a total of 52 microphones are to be purchased. Each microphone costs $548.
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Help help me me me me
Answers
Answer:
(-6, 26),( -4, 8,) (0, -4), (2,2), (8,68)
Step-by-step explanation:
Answer:
(-6, 26),( -4, 8,) (0, -4), (2,2), (8,68)
help me me me me me me me
Answers
The average price per square foot in 2002 was approximately $85.86.
What is a polynomial function?A mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power.
Example: a + bx + cx²
We have,
P(t) = 0.019t³ - 0.287t² + 3.073t + 55.130
Where t = number of years.
From 1992 to 2002 we have,
2002 - 1992 = 10 years
Now,
P(10) = 0.019(10)³ - 0.287(10)² + 3.073(10) + 55.130
P(10) = 19 - 28.7 + 30.73 + 55.130
P(10) = 85.86
Thus the average price per square foot in 2002 was approximately $85.86.
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What is a quadrilateral
Answers
Answer: A quadrilateral is a four-sided figure.
EX: a square, a rectangle, a trapezoid, or a rhombus.
A closed plane figure or figure formed by four nonintersecting line segments which are not on the same line and connected end to end is called quadrilateral.
The candy produced by a company has a sugar level that is normally distributed with a mean of 16.1 grams and a standard deviation of 0.9 grams. The company takes readings of every 10th bar off the production line. The reading points are 17.3, 14.9, 18.3, 16.5, 16.1, 17.4, 19.4. Is the process in control or out of control and why? Use a control chart to answer the question.
It is out of control as the values jump above and below the mean
It is out of control as one of these data points is more than 3 standard deviations from the mean
It is out of control as two of these data points are more than 2 standard deviations from the mean
It is out of control as at least two of three consecutive data points are more than 2 standard deviations from the mean
Answers
The correction option is B, It is out of control as one of these data points is more than 3 standard deviations from the mean.
What is Normal Distribution?The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
Given that the candy produced by a company has a sugar level that is normally distributed with a mean of 16.1 grams and a standard deviation of 0.9 grams. Therefore, the maximum and the minimum weight of the candy can be,
Maximum weight = Mean + 3(Standard deviation)
= μ + 3σ
= 16.1 + 3(0.9)
= 16.1 + 2.7
= 18.8
Minimum weight = Mean - 3(Standard deviation)
= μ - 3σ
= 16.1 - 3(0.9)
= 16.1 - 2.7
= 13.4
Since one of the reading point, 19.4 is more than 3 standard deviations from the mean, therefore, it can be concluded that the process is out of control.
Hence, It is out of control as one of these data points is more than 3 standard deviations from the mean.
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1/4 minus 3/8 in fraction form
Answers
Answer: -1/8 is the answer
Find the values of a and b that make f continuous everywhere.
f(x) =
x2 − 4
x − 2 if x < 2
ax2 − bx + 1 if 2 ≤ x < 3
4x − a + b if x ≥ 3
Answers
The function is a continuous function. Then the value of variables a and b will be 2.5 and 3.5, respectively.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The piecewise function is given below.
[tex]f\left ( \rm x \right ) = \left\{\begin{matrix} \rm \dfrac{x^2 - 4}{x-2} \ or \ x + 2,& \rm x < 2\\ \rm ax^2 - bx + 1, & \rm 2\leq x < 3\\ \rm 4x - a + b, & \rm x \geq 3\end{matrix}\right.[/tex]
At x = 2, the function is continuous, then we have
2 + 2 = a(2²) - 2b + 1
4a - 2b = 3 ...1
At x = 3, the function is continuous, then we have
a(3²) - 3b + 1 = 4(3) - a + b
10a - 4b = 11 ...2
From equations 1 and 2, we have
8a - 10a = 6 - 11
2a = 5
a = 2.5
Then the value of b will be
10(2.5) - 4b = 11
25 - 4b = 11
4b = 14
b = 3.5
The value of the variable a and b will be 2.5 and 3.5, respectively.
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