Illustrative Mathematics
An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. Using for distance in kilometers and for number of hours, an equation that represents this situation is .
What are two constants of proportionality for the relationship between distance in kilometers and number of hours? What is the relationship between these two values?
Write another equation that relates and in this context.
Answers
1. Two constants of proportionality representing the proportional relationship between distance in kilometers and number of hours are 400 km and 8 hours.
2. The relationship (ratio) between the two values is 50 km per hour or the equation, d = 50t.
3. Another equation that relates distance and time in this context is t = d/50 or 400/50.
What is the constant of proportionality?The constant of proportionality is the ratio relating two given values in a proportional relationship.
Other names for the constant of proportionality include:
Constant rateUnit rateConstant ratioRate of changeConstant of variation.Distance, d = 400 km
Constant speed, t = 8 hours
d = 400/8
d = 50t
Constant of proportionality = 50.
t = d/s
Where d, distance = 400 km and s, speed = 50 km/h
= 400/50
= 8 hours
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Related Questions
Here is a list of numbers:
3 6 9 7 4 6 7 0 7
Find:
a)
the median
b)
the range
C)
the mode
Answers
The mean is 5.4, median is 6, mode is 7 and the range is 9 when the given list of numbers are 3,6,9,7,4,6,7,0,7.
Given that,
The list of numbers are 3,6,9,7,4,6,7,0,7
The mean, median, mode, and range must be determined.
What is mean, median, mode and range?The "mean" is the standard "average," which is calculated by adding up all the numbers and dividing the result by the total number of numbers.
The value that sits in the middle of a set of numbers is known as the "median." Before you can find the median, your numbers must be listed in numerical order from smallest to greatest. This means that you might need to redo your list.
The "mode" value is the one that shows up the most often. There is no mode for the list if no number on the list is repeated.
A list of numbers' "range" is just the range between the largest and lowest values. It conveys "spread," which is the degree to which the values are scattered (or how concentrated they are).
Mean=(3+6+9+7+4+6+7+0+7)/9
Mean = 49/9
Mean = 5.4
Median is 0,3,4,6,6,7,7,7,9
The median is 6
Mode is 7
Range is
Greater number is 9 and the smallest number is 0
Difference is 9-0=9
Range is 9.
Therefore, The mean is 5.4, median is 6, mode is 7 and the range is 9 when the given list of numbers are 3,6,9,7,4,6,7,0,7.
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help with this question please!
Answers
Answer:
A. TPR
B. NM
C. 6
Step-by-step explanation:
1. The triangle NKM matches up with TPR. We also already knew KMN= PRT. So, it was just a matter of aligning the order.
2. If you flip PRT then TR will match with NM
3. 4x-3=21
4x-3+3=21+3
Simplify: 4x=24
4x/4=24/4
x=6
someone please help tysm
Answers
Among the equations and inequality the true expression is 1 / 3 × 9 = 3.
How to solve inequality and equation?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Therefore, let's check the inequality that is true.
Hence,
1 / 4 × 28 > 8
28 / 4 > 8
7 > 8 (false)
1 / 6 × 48 < 5
48 / 6 < 5
8 < 5 (False)
1 / 3 × 9 = 3
9 / 3 = 3
3 = 3(True)
1 / 5 × 25 = 125
25 / 5 = 125
5 ≠ 125(False)
1 / 6 × 24 > 9
24 / 6 > 9
4 > 9 (False)
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Use proportional relationships to solve this mixture problem. The incoming 6th-grade class has a choice between band or choir as an elective. There are four times as many seats in choir as there are in band. How many students can choose band if there is a total of 250 students? 50 students 200 students 124 students 250 students
Answers
The number of students that chose band as an elective is 50
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic
let the total number of seats for choir be x and that for band be y
if there are 4 times as many seats as there in band then mathematically,
x = 4y.--------------------1
If there are 250 students, then, there would be 250 seats for the combined class.
so,
x + y = 250--------------2
substitute x = 4y in equation 2
4y + y = 250
5y = 250
y = 250/5
y = 50
In conclusion, 50 students can choose band.
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The lumber store sells planks in 8 foot pieces. They have an error
tolerance of 4%, What is the minimum length that you can buy
and what is the greatest length you can buy?
Answers
The minimum length that you can buy is 7.68 foot and the greatest length that you can buy is 8.32 foot
The length of the planks that lumber stores sell = 8 foot
The error tolerance of the plank = 4%
Then the 4% of the length 8 is
= 8 × (4/100)
Divide the terms
= 8 × 0.04
Multiply the terms
= 0.32
Therefore the error tolerance will be ±0.32
The minimum length that you can buy = 8 - 0.32
= 7.68 foot
The greatest length that you can buy = 8 + 0.32
= 8.32 foot
Hence, the minimum length that you can buy is 7.68 foot and the greatest length that you can buy is 8.32 foot
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How does the graph of g(x) = (x − 4)3 + 5 compare to the parent function f(x) = x3?
Answers
The graph of g(x) = (x-4)3+5 compare to the parent function f(x) is g(x) is shifted 4 units to right and 5 units up.
What is transformation of function?
Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the function f (x) = x 2 + 3 is obtained by just moving the graph of g (x) = x 2 by 3 units up.
Given,
function g(x) = (x − 4)3 + 5 and compares to function f(x) = x3,
The graph of g(x) = (x-4)3+5 compare to the parent function f(x) is g(x) is shifted 4 units to right and 5 units up.
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Mr. Walters receives a dividend every 5 months and a royalty check every 6 months. He
received both payments in May 2019. When is the next time he would receive both
payments in the same month?
Answers
AS per the combination method, Mr. Walters receive both payments in the same month in the 6th time.
Combination method:
A way of adding equations together in such a way that the variables are set aside, one by one is called as combination.
Given,
Mr. Walters receives a dividend every 5 months and a royalty check every 6 months. He received both payments in May 2019.
Here we need to find the next time he would receive both payments in the same month.
While looking into the given question we have identified he following things,
Dividend payment = 5 months
Royalty payment = 6 months
Both payment received = May 2019.
So, according to the combination method,
The value of n = 6 and the value of x = 5
So, the next time he would receive both payments in the same month is
=> 6 C 5 = 6! / 5! (6 - 5)!
Which results the value as 6.
Therefore, on 6th time from this payment he will receive both in the same month.
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The reflection of (-2,-2) is ...
The reflection of (-1,1) is...
please help meeeeeeeeeee
Answers
The reflection of (-2, -2) and (-1, 1) are
preimage image
(-2, -2) (-4, -2)
(-1, 1) (-5, 1)
What is reflection?Reflection is one of the movements in transformation that involve creation of mirror image
Transformation rule for reflection over x-axis at origin (0, 0)) is
(x, y) → (x, -y)
Transformation rule for reflection over line y-axis at origin (0, 0)) is
(x, y) → (-x, y)
The reflection to be done is over line x = -3
However, reflection over line x = -3 which is (-3, 0) is done as follows
from -2 to -3 = -2 - -3 = 1 unit
reflecting 1 unit over x = -3
-3 - 1 = -4
(-4, -2)
(-2, -2) ⇒ (-2 - -3, -2) ⇒ (1, -2) ⇒ (-3 - 1, -2) → (-4, -2)
from -1 to -3 = -1 - -3 = 2 units
reflecting 2 units over x = -3
-3 - 2 = -5
(-5, 1)
(-1, 1) ⇒ (-1 - -3, 1) ⇒ (2, 1) ⇒ (-3 - 2, 1) → (-5, 1)
The calculation is simply saying put
(-2, -2) this point is just before the reflection line, the image will formed at the point just after the reflection line -3 which is -4 hence (-4, -2)
(-1, 1) this point is a line before the reflection line, the mirror image will be formed skipping a line (-4) to get to -5 hence the point (-5, 1)
the y coordinate is constant for both situations
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Is this column graph skewed or symmetrical?? and if skewed what way?
Answers
Answer:
skewed to the right
Step-by-step explanation:
look at the graph
divide it in half
if both the sides are not equal then it is skewed
then to find out which way it is skewed look which side has more.
If two dice are rolled one time, find the probability of getting these results. Show all possible combinations. Express the probability as a fraction of 36
A 3 on one die or on both dice
A sum greater than or equal to 10
Answers
Step-by-step explanation:
any particular result with 2 dice has a probability of
1/6 × 1/6 = 1/36
a 3 on one die or both simply means at least one 3.
so, if all the 36 different outcomes we are looking at
3 1
3 2
3 3
3 4
3 5
3 6
1 3
2 3
4 3
5 3
6 3
the 3 3 combination can be counted only once !
so, we have 11 desired outcomes out of the possible 36.
so, the probability of getting at least one 3 is
11/36
the sum of at least 10 means the corresponding cases
4 6
5 5
5 6
6 4
6 5
6 6
in this case we don't need to turn this around, because it would be exactly the same outcomes again, and we don't want to count them twice.
so, we have 6 desired outcomes of the 36.
the probability of that is
6/36 = 1/6
Divide.
5.3696
0.001
Answers
The length of the vector that represents z₁ = 6-8i is 10 because √6² + (-8)² = √√100 = 10.
a.
Find at least seven other complex numbers that can be represented as vectors that have length 10.
Answers
The vectors having length of 10 units are,
-6 + 8i , 10 , 10i , -10 , -10i , 3 + 9i , -3 + 9i
We have to find the seven complex numbers that have the length of 10 units.
So, the vectors having length of 10 units are,
1) -6 + 8i
2) 10
3) 10i
4) -10
5) -10i
6) 3 + 9i
7) -3 + 9i
Hence, the vectors having length of 10 units are,
-6 + 8i , 10 , 10i , -10 , -10i , 3 + 9i , -3 + 9i
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Banerjee Company began its operations in September of the current year. During September, the company paid wages of $23,400. For the last quarter of the year, the taxable wages paid amounted to $64,700. None of the employees was paid more than $7,000 this year. a. Is Banerjee Company liable for FUTA tax this year? Yes b. If your answer to part a above is "Yes", what is the net FUTA tax for the year? Round your answer to the nearest cent.
Answers
Banerjee Company is liable for FUTA tax this year and the net FUTA tax for the year is $528.60.
How to find the net FUTA tax?a. Yes. Banerjee Company liable for FUTA tax this year.
b. FUTA tax
FUTA tax =0.6%
Hence,
Net FUTA tax = (Wages paid × tax rate ) +(Taxable wages × Tax rate)
Net FUTA tax = ($23,400 × 0.6%) + ($64,700 ×0.6%)
Net FUTA tax = $140.40 + $388.30
Net FUTA tax =$528.60
Therefore $528.60 is the Net FUTA tax.
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A house mover towed a historic Victorian home 45 miles to locate it on a new site. On his return, without the heavy house in tow, his average speed was 30mph faster and the trip was 2 hours shorter. How fast did he drive in each direction?
Answers
The required speed is 45 mph in each direction.
What is speed?
The definition of speed is a measurement of how quickly an object's location changes in any direction. Speed is defined as the ratio of distance to the amount of time it took to cover that distance.
We know that distance=rate*time
d=rt
45=rt
45=(r+30)(t-2)
rt=(r+30)(t-2)
This shows,
rt=rt+30t-2r-60
0=30t-2r-60
if 45=rt, then r=45/t
substitute in the equation
0=30t-2(45/t)-60
multiply both sides by t
0=30t²-90-60t
on solving this quadratic equation, we get t= 3 s, t=-1 s
consider positive value
t=3 hours
45=rt
45=r*3
r=45/3 =15 mph to new site
r+30=15+30=45 mph returning
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40 POINTS PLS ANSWER FAST
Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle. Which congruence theorem can be used to prove that the triangles are congruent?
AAS
SSS
SAS
HL
Answers
Since the congruent angle is a right angle and it is not included, the two congruent sides of the triangles must include their hypotenuses and one of their legs.The triangles would be congruent by the hypotenuse leg theorem, which states that if the hypotenuse and one leg of a right triangle is congruent to the hypotenuse and a leg of another right triangle, the triangles are congruent.Answer:hypotenuse leg theorem
Which is more, 6 liters or 6,001 milliliters?
Answers
Answer: 6,001 milliliters
Step-by-step explanation: 6 Liter translates to 6,000 milliliters, which is 1 less than 6,001 milliliters.
Answer:
I believe 6 liters is more.
In triangle XYZ, m∠Z = (2m − 12)° and the exterior angle to ∠Z measures (3m + 7)°. Determine the value of m.
m = 42
m = 37
m = 19
m = 2.6
Answers
Answer:
m = 37
Step-by-step explanation:
The interior and corresponding exterior angle of a triangle are always supplementary.
Therefore, we can set the sum of the two given angle measures to 180°:
[tex](2m-12) \textdegree + (3m+7) \textdegree = 180 \textdegree[/tex]
and solve algebraically for m.
[tex]2m-12 + 3m+7 = 180[/tex]
[tex](2m + 3m) + (-12+7) = 180[/tex]
[tex]5m-12+7 = 180[/tex]
[tex]5m - 5 = 180[/tex]
[tex]5m = 185[/tex]
[tex]m=37[/tex]
The value of m is 37.
What is Linear pair?When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.
Given:
m ∠Z = (2m − 12)° and exterior angle ∠Z =(3m + 7)°.
int. m <Z + ext. <Z= 180
2m - 12 + 3m + 7 = 180
5m - 5 = 180
5m = 185
m = 185/ 5
m = 37
Hence, the value of m is 37.
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if parallel lines are cut by transversal then there interior angles on the same side of the transversal are blank.
Answers
Anlges on the same side of the transversal add up to 180 degrees.
What is Transversal?
A transversal is a line in geometry that connects two lines in the same plane at two separate places. Transversals help determine if two or more lines in the Euclidean plane are parallel.
Solution:
Using the property of Lineaar Pair Angle the Interior Angles on the same side of the Transversal add up to 180 degrees.
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two groups of hikers left camp at the same time. each traveled at a constant rate
group A covered 3/4 mile in 1/2 hour
It took Group B 3/4 hour to travel 1/3 mile
Answers
The group that travels faster when groups of hikers left camp at the same time and each traveled at a constant rate is group B.
How to calculate the rate?From the information, two groups of hikers left camp at the same time. each traveled at a constant rate.
Since group A covered 3/4 mile in 1/2 hour, the speed will be:
= Distance / Time
= 3/4 ÷ 1/2
= 1.5 miles per hour.
It took Group B 3/4 hour to travel 1/3 mile. The speed will be:
= Distance / Time
= 3/4 ÷ 1/3
= 2.25 miles per hour.
Group B had a faster speed.
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Complete question
Two groups of hikers left camp at the same time. each traveled at a constant rate
group A covered 3/4 mile in 1/2 hour
It took Group B 3/4 hour to travel 1/3 mile
Which group so travelling at a faster rate?
Subtract using the number line -2 -(+7)
Answers
The answer is -9.
-2 -(+7) = -2 -7
-2 -7 = -9
Find the retail price of each item. Round to two decimal places when necessary.
Cost of oil change: $18.00
Markup: 70%
Answers
well, we know the price is $18, now, if we jack it up by 70%, well, what's 70% of 18?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{70\% of 18}}{\left( \cfrac{70}{100} \right)18}\implies 12.6~\hfill \underset{price}{\stackrel{18~~ + ~~12.6}{\text{\LARGE 30.60}}}[/tex]
50 points to whoever answers!!
Answers
Answer:
create a line between (0,0) and (1,3)
the unit rate is 3/2 or 1.5
Step-by-step explanation:
pls mark
A pendant of gold alloy weighs 15/32 troy ounces. How many pendants can a jeweler make
from 5 5/8 troy ounces of gold alloy?
Solve the problem mathematically by finding the quotient.
Answers
The Jeweler makes the number of Pendants from the total weight of gold alloy = 12
The Jeweler has the total weight of gold alloy = 5 [tex]\frac{5}{8}[/tex] = 45/8 troy ounces.
Weight of a single gold alloy pendant = 15/32 troy ounces.
Jeweler makes the number of Pendants from the total weight of gold alloy = 45/8 ÷ 15/32.
Dividing Fractions by Fractions
We just learned how to divide fractions by taking the reciprocal. Now, let us see the method of dividing fractions by fractions with an example. Have a look at the formula of the division of a fraction by fraction given below. If x/y is divided by a/b, this implies,
x/y ÷ a/b
⇒ x/y × b/a (reciprocal of a/b is b/a)
⇒ xb/ya
Now, if we need to divide: 5/8 ÷ 15/16, we will substitute the values of the given numerators and denominators.
45/8 ÷ 15/32 = 45/8 × 32/15 = 12
∴ The value of 45/8 ÷ 15/32 = 12.
Hence the Jeweler makes the number of Pendants from the total weight of gold alloy = 12
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The sum of the speed of the two trains is 723.5 miles per hour. if the speed of the first train is 4.5 mph faster than that of the second train, find the speeds of each
Answers
The speed of first train is 364 miles per hour and the speed of second train is 359.5 miles per hour .
In the question,
it is given that ,
the sum of speed of two trains = 723.5 miles per hour
let the speed of the first train = x miles per hour
let the speed of the second train = y miles per hour ,
also given that , the speed of the first train is 4.5 mph faster than that of the second train , which means
x = y + 4.5 .
the sum is 723.5 ,
so , the equation is
x + y = 723.5
y + 4.5 + y = 723.5
2y + 4.5 = 723.5
2y = 719
y = 719/2
y = 359.5
So , x = 359.5 + 4.5 = 364 .
Therefore , The speed of first train is 364 miles per hour and the speed of second train is 359.5 miles per hour .
The given question is incomplete , the complete question is
The sum of the speed of the two trains is 723.5 miles per hour. if the speed of the first train is 4.5 mph faster than that of the second train, find the speeds of each train ?
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In 2017, the library was able to record 4907 borrow books. By December of the same year, the library has 6 times its January record. The library’s December record is ?
Answers
The library’s December record is 29442
Mathematical Operations:Mathematical operations are Operators which emphasize particular actions like adding, subtracting, adding multiple times, dividing, etc.
There are 4 basic operations in mathematics as given below.
1. Addition => (+)
2. Subtraction => (-)
3. Division => (÷)
4. Multiplication => (x)
Here we have
In 2017 the library was able to record 4907 borrowed books
By December of the same year, the library has 6 times its January record.
[ Here we use Multiplication to find the December record ]
The December record = 6 times of January record
⇒ 6 × January record
⇒ 6 × 4907
⇒ 29442
Therefore,
The library’s December record is 29442
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IXL Please Help Fast!
Answers
Answer:
y = 1/2 x + 3/2
Step-by-step explanation:
A perpendicular slope is the opposite reciprocal, so it is 1/2
2 = 1/2(1) + b To solve for b
2 = 1/2 + b Subtract 1/2 from both sides
1 1/2 = b
y = 1/2 x + 3/2
The graph of y = f(x) is graphed below. What is the end behavior of f(x)?
Answers
as x -> -infinity, y -> -infinity and as x-> infinity, y-> infinity
So, last option is correct
Which of the following traits do histograms, Pareto charts, and scatter plots have in common?
a) They are all bar charts.
b) They are all visual tools to display data.
c) They all show change over time.
d) All of the above.
Answers
The correct option is option (B) .
In other words Histograms , Pareto charts and scatter plots have a common thing that they are all visual tools to display data.
Histogram :
It show continuous data in ordered rectangular columns. There are usually no gaps between columns.
Histograms show the frequency distribution (shape) of a data set.To graphically summarize large datasets.Scatterplot :
A scatterplot is an x-y plot that shows the relationship between two variables. Used to plot data points on vertical and horizontal axes.
Predicts the behavior of the dependent variable based on the scale of the independent variable. If you just want to visualize the correlation between two large datasets without considering hours.Pareto Chart :
A Pareto chart is a common tool used by manufacturers to analyze quality and defect data, providing a quick visual representation of the frequency and cumulative percentage of occurrences of a particular problem.
A Pareto chart is a combination of a bar chart and a line chart.Hence , all of three have a common thing that is they visualize tools to represent the data
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Evaluate the expression.
−5 × (−8 − 6 ÷ −3)
Answers
Answer:
=30
Step-by-step explanation:
-5×(-8-6÷-3)-5×(-8+2)........as -6÷-3=2-5×-630I need help with this please help me
Answers
Answer:
m∠1 = 126°
m∠2 = 154°
Step-by-step explanation:
First, find the measure of angle that is supplementary to ∠1. (I will call it ∠A)
We know that the measures of the interior angles of a triangle add to 180°.
Therefore,
m∠A + 96° + 30° = 180°
m∠A + 96° = 150°
m∠A = 54°
From this value, we can solve for m∠1, since it is supplementary to ∠A:
m∠A + m∠1 = 180°
54° + m∠1 = 180°
m∠1 = 126°
To solve for ∠2, we must first solve for the adjacent supplementary angle that I have named ∠B.
First, the measures of the interior angles of a triangle add to 180°:
28° + m∠1 + m∠B = 180°
28° + 126° + m∠B = 180°
m∠B = 26°
Finally, we can solve for m∠2 because it is supplementary to ∠B.
m∠B + m∠2 = 180°
26° + m∠2 = 180°
m∠2 = 154°