Can the relationship in Monday’s table be described by a constant unit rate? ExplainCan the relationship in Tuesday’s table be described by a constant unit rate? Explain
Answers
Step 1
We will consider the Time(min) and distance (km) covered by Ken on his bike on Monday from the table given
From the Monday table
1) The time increases by a constant unit of 20 mins as seen below
\(\begin{gathered} 40\text{ -20 = 20 mins} \\ 60-40\text{ = 20 mins} \\ 80-60=\text{ 20 mins} \\ 100\text{ -80 = 20 mins} \end{gathered}\)2) The distance however, does not increase by a constant unit as seen below
\(\begin{gathered} 10\text{ - 5= 5km} \\ 12-\text{ 10= 2 km} \\ 14-12\text{ = 2km} \\ 16-14=\text{ 2km} \end{gathered}\)Therefore, the relationship in Monday's table cannot be described by a constant unit rate since the time and distance individually do not increase by a constant unit.
Step 2
From Tuesday's table, we can deduce that
1) The time increases by a constant unit of 20 mins
\(\begin{gathered} 40\text{ -20 = 20 mins} \\ 60-40\text{ = 20 mins} \\ 80-60=\text{ 20 mins} \\ 100\text{ -80 = 20 mins} \end{gathered}\)2) The distance increases by a constant unit of 4km as seen below
\(\begin{gathered} 8-4=4\operatorname{km} \\ 12-8=4\operatorname{km} \\ 16-12=4\operatorname{km} \\ 20-16=\text{ 4km} \end{gathered}\)Since, both the time and distance individually increases by a constant unit, we can therefore conclude that the relationship in Tuesday's table can be described by a constant unit rate.
Related Questions
A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 7 freshmen, 9 sophomores, 7 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen?
Answers
There are 3457440 ways combination in which this dance committee can be formed.
What is permutation and combination?
A set of items can be divided into subsets in two different ways: combination and permutation. The subset's components can be listed in any order when combined. The components of the subset are arranged in a particular order in a permutation.
2 freshmen out of 7 freshmen can be chosen in ⁷C₂ ways.
3 sophomores out of 9 sophomores can be chosen in ⁹C₃ ways.
4 juniors out of 7 juniors can be chosen in ⁷C₄ ways.
5 seniors out of 8 seniors can be chosen in ⁸C₅ ways.
⁷C₂ × ⁹C₃ × ⁷C₄ × ⁸C₅ ways, the dance committee of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors can be chosen.
= 7!/(7-2)!2! × 9!/(9-3)!3! × 7!/(7-4)!4! × 8!/(8-5)!5!
= 7!/5!2! × 9!/6!3! × 7!/3!4! × 8!/3!5!
= 21×84×35×56.
= 3457440 ways.
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Sandra is looking to buy two dozen decorative doughnuts for a party. She is considering two local bakers. She looks Up bakers online to find how much each one charges. Here are the advertisements she saw online. Ms. Spellings Donut Shop Try out this week's special! All decorative donuts are on sale for $1.62 each with an $8 boxing fee! Phil'd Up Doughnuts Baxing fee included in price! Decorative Price Doughnuts 2 $S 4 $13 6 $17 8 $21 $25 12 $29 two 10 12a. What is the rate of change and the boxing fee for each doughnut shop? 126. 11 the total cost is Sandra's biggest concern, who should she buy from? Why?
Answers
Answer:
Step-by-step explanation:
The temperature t is at least 75
Answers
Answer:
t ≥ 75
Step-by-step explanation:
"at least 75" means 75 or higher.
The temperature is equal to 75 or greater than 75.
t ≥ 75
An airplane compartment can hold thirty-six pieces of luggage. If a small plane had sixteen compartments, how many pieces of luggage could they hold
Answers
Which is the value of this expression when m-3 and n=-5
Answers
Answer:
1/8
Step-by-step explanation:
(6m^-1n^0)^-3 =
= (6 × 1/3 × (-5)^0)^-3
= (6/3)^-3
= 2^-3
= 1/2^3
= 1/8
Write an equation of the direct variation that includes the point (-10,-17)
A. y = 10/17 x
B. y = -1/17 x
C. y = 1 7/10 x
D. y =- 1 7/10 x
Answers
Answer:
C
Step-by-step explanation:
The answer should be y= 17/10x
Please help what is the slope of the line?
Answers
Answer:
-5/4
Step-by-step explanation:
Let \((x_1,y_1)=(-4,4)\) and \((x_2,y_2)=(0,-1)\). The slope of the line would be:
\(\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{0-(-4)}=\frac{-5}{4}=-\frac{5}{4}\)
Answer: -5/4
Step-by-step explanation:
To find the slope between two points, you can use the formula:
Slope = (y2 - y1)/(x2 - x1)
Using the points (0, -1) and (-4, 4), we can substitute the coordinates into the formula:
slope = (4 - (-1))/(-4 - 0)
slope = (4 + 1)/(-4)
slope = 5/-4
Therefore, the slope between the two points is -5/4.
Find the intercepts and the vertical and horizontal asymptotes
Answers
The x and y-intercepts of the rational function are; (-3, 0) and (0, -3/25).
The vertical asymptotes of the function are; x = ± 5.
The horizontal asymptotes of the function is f(x) = 0.
What are the intercepts?For x-intercept; let f (x) = 0;
0 = (x + 3) / (x² - 25)
x + 3 = 0; x = -3 or (-3, 0).
For the y-intercept; let x = 0.
f (0) = (0 + 3) / (0² - 25)
= -3/25 or (0, -3/25).
For the vertical asymptotes;
x² - 25 = 0
x² = 25
x = ±5.
For the horizontal asymptote;
Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is; f (x) = 0.
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Question 3 (25 points) Calculating a binomial probability PROBLEM: See the preceding alternate example. Should the player be surprised if fewer than 2 of the rolls result in snake eyes? Calculate an appropriate probability to support your answer.
Answers
The probability that fewer than 2 rolls result in snake eyes is approximately equal to 0.492.
To calculate the probability that fewer than 2 rolls result in snake eyes, we need to calculate the probability that exactly 0 rolls and the probability that exactly 1 roll result in snake eyes, and then sum these probabilities.
The probability that exactly 0 rolls result in snake eyes is given by the binomial probability formula:
P(exactly 0 rolls) = (n choose k) * p^k * (1-p)^(n-k)
Where:
n = the number of rolls
k = the number of successful rolls (in this case, 0)
p = the probability of success on a single roll (in this case, 1/6, since there is a 1/6 probability of rolling snake eyes on a single roll)
Plugging in the values, we get:
P(exactly 0 rolls) = (5 choose 0) * (1/6)^0 * (5/6)^5 = 0.164
The probability that exactly 1 roll results in snake eyes can be calculated in a similar manner:
P(exactly 1 roll) = (5 choose 1) * (1/6)^1 * (5/6)^4 = 0.328
To get the probability that fewer than 2 rolls result in snake eyes, we sum these probabilities:
P(fewer than 2 rolls) = P(exactly 0 rolls) + P(exactly 1 roll) = 0.164 + 0.328 = 0.492
Therefore, it would not be surprising if fewer than 2 rolls result in snake eyes.
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Complete Question:
Question 2 (25 points) Calculating a binomial probability PROBLEM: When rolling two fair six-sided dice, getting a pair of ls is called "snake eyes." The probability of getting "snake eyes" on any roll is 1/36. Suppose that a game player rolls the two dice 80 times. Let X = the number of rolls that result in "snake cyes." Find P(X = 2). Interpret this value in context If two dice are rolled 80 times, then there is a 27.089% chance that we get a pair of snake eyes. Question 3 (25 points) Calculating a binomial probability PROBLEM: See the preceding alternate example. Should the player be surprised if fewer than 2 of the rolls result in snake eyes? Calculate an appropriate probability to support your answer.
A train travels at 100 miles per hour. Write an equation that compares the time (t) with the distance (d).
t = 100d
d = 100t
d = t + 100
t = d + 100
Answers
Answer: d = 100t
Hope this helps!
Answer:
d = 100 * t
Step-by-step explanation:
d
------------
S l t
distance = d
time = t
speed = 100miles/h
d = 100 * t
Tres multiplicaciones de seis factores:una en la que el resultado sea positivo,otra en la que sea negativo,y una cuyo resultado sea 0
Answers
Answer:
Vamos a inventa tres multiplicaciones de seis factores en la que el resultado sea positivo, es decir un número mayor que cero, en la otra negativo, es decir, un número menor que cero y por último otra multiplicación que de como resultado el cero "0".
Primero recordemos que:
Los factores son los números que se multiplican.
Seis factores serían 6 números.
Multiplicación con resultado positivo, es decir mayor a 0:
2×3×4×2×1×5=240
Multiplicación con resultado negativo, es decir menor a 0:
-4×2×5×2×1×10= -400
Multiplicación con resultado cero:
2×4×6×7×11×0=0
Step-by-step explanation:
Brainliest please
HELP PLEASE! ASAP !
These 2 questions !
Answers
Answer: 9 is true, 10 is false
Step-by-step explanation:
The key to these problems is to make sure the sequence of the letters is equal: 10 would be correct if they said DF ≅XZ
Select the two values of x that are roots of this equation. 2x^2-11x+15=0
Answers
Hey there! :)
Answer:
x = 5/2 and 3.
Step-by-step explanation:
Factor the equation. Find numbers that will sum up to -11 involving the coefficient of 2, and that multiply into 15.
2x² - 11x + 15 = 0
(2x - 5)(x - 3) = 0
Use the Zero Product Property to solve for the roots of this equation:
2x - 5 = 0
2x = 5
x = 5/2
----------
x - 3 = 0
x = 3.
Therefore, the two values of x that are roots of this equation are:
x = 5/2 and 3.
━━━━━━━☆☆━━━━━━━
▹ Answer
x₁ = 5/2
x₂ = 3
▹ Step-by-Step Explanation
2x² - 11x + 15 = 0
2x² - 5x - 6x + 15 = 0
x(2x - 5) - 6x + 15 = 0
x(2x - 5) - 3(2x - 5) = 0
(2x - 5) * (x - 3) = 0
2x - 5 = 0
x - 3 = 0
x₁ = 5/2
x - 3 = 0 → x₂ = 3
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
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Mr. green has a garden. Of the 40 seeds he planted, 35% were vegetable seeds. How many vegetable seeds did he plant
Answers
Answer:
14
Step-by-step explanation:
35% of 40 is 14
Answer:
I believe the answer is 14
Step-by-step explanation:
35% of 40 is 14
"Of" means multiply so I did 0.35 * 40
A baker uses 5.5 pounds (lb) of flour daily.
Part A
How many ounces of flour will the baker use in two weeks? (1 lb = 16 oz)
The baker uses
Part B
The baker’s recipe for a loaf of bread calls for 12 ounces of flour. If he uses all of his flour to make loaves of bread, how many full loaves can he bake in two weeks?
The baker can make
full loaves of bread in two weeks.
Answers
Answer:
Part A:
The baker uses 5.5 pounds of flour daily, which is equal to 5.5 x 16 = 88 ounces of flour daily.
In two weeks (14 days), the baker will use 88 x 14 = 1232 ounces of flour.
Therefore, the baker will use 1232 ounces of flour in two weeks.
Part B:
If the baker uses 12 ounces of flour to make one loaf of bread, then the number of loaves he can make with 1232 ounces of flour is:
1232/12 = 102.67
However, the baker cannot make a fraction of a loaf, so he can only make 102 full loaves of bread.
Therefore, the baker can make 102 full loaves of bread in two weeks.
What is the solution to this equation? (1/27)^2-x=9^3x
Answers
Answer:
= 1/532170
Step-by-step explanation:
components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). the first inspector detects 87% of all defectives that are present, and the second inspector does likewise. at least one inspector does not detect a defect on 26% of all defective components. what is the probability that the following occur?
Answers
The probability that a defective component will be detected only by the first inspector is 0.19
The probability that a defective component will be detected by exactly one of the two inspectors is 0.38
The probability that all three defective components in a batch escape detection by both inspectors is 0.
It is given that The first inspector detects 81% of all defectives that are present, and the second inspector does likewise.
Therefore P(A)=P(B)=81%=0.81
At least one inspector does not detect a defect on 38% of all defective components.
Therefore, bar P(A∩B)=0.38
As we know:
bar P(A∩B)=1-P(A∩B)=0.38
P(A∩B)=1-0.38=0.62
A defective component will be detected only by the first inspector.
P(A∩barB)=P(A)-P(A∩B)
=0.81-0.62
P(A∩barB)=0.19
The probability that a defective component will be detected only by the first inspector is 0.19
Part (B) A defective component will be detected by exactly one of the two inspectors.
This can be written as: P(A∩barB)+P(barA∩B)
As we know:
P(barA∩B)=P(B)-P(A∩B) and P(A∩bar B)=P(A)-P(A∩B)
Substitute the respective values we get:
P(A∩ barB)+P(bar A∩B)=P(A)+P(B)-2P(A∩B)
=0.81+0.81-2(0.62)
=1.62-1.24
P(A∩ barB)+P(bar A∩B)=0.38
The probability that a defective component will be detected by exactly one of the two inspectors is 0.38
Part (C) All three defective components in a batch escape detection by both inspectors
This can be written as: P(bar A∪ bar B)-P(bar A∩B)-P(A∩ barB)
As we know bar P(A∩B)=P(bar A∪ bar B)=0.38
From part (B): P(bar A∩B)+P(A∩bar B)=0.38
This can be written as:
P(bar A∪ bar B)-P(bar A∩B)-P(A∩bar B)=0.38-0.38=0
The probability that all three defective components in a batch escape detection by both inspectors is 0
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Which value makes the equation 4x = 36 true?
x=8
x=9
x=10
x=12
Answers
This is because 4 multiplied by 9 = 36
Write 0.000073 in scientific notation
Answers
Answer:
7.3x10^-7
Step-by-step explanation:
you move the decimal to the right 7 times.
Hope this helps.
Answer:
\(10^-^5\) \(*73\)
Step-by-step explanation:
So in 0.000073, 7 is the fifth digit in the term so we can write it as \(10^-^5\) * 73
or 10 to power of negative 5 multiplied by 73.
What is the reference angle for the angle with the measure 2x/3
Answers
The reference angle for the angle with the measure 2x/3 is 54⁰
How to determine the reference angle?You should understand that a reference angle is the acute angle to a given angle.
The given angle is 2x/3
We should understand that since the angle has the variable x
= x + 2x/3 = 90⁰
Simplifying the fraction to have
(3x+2x)/3 = 90
Cross and multiply we have 5x=270⁰
Making x the subject
x= 270/5
x=54⁰
Therefore, the reference angle with the measure 2x/3 is = 54⁰
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What is the area of the parallelogram?
Answers
Answer:
35
Step-by-step explanation:
The formula for solving the area of parrelelograms is B(base) times H(height).
the height here is 5 and the base is 7 so the area is 35.
PLEASE HELP ASAP !!! WILL MARK BRAINLIEST TO WHOEVER ANSWERS CORRECTLY
Answers
Answer:
See below.
Step-by-step explanation:
Alternate Interior Angles - 1
Alternate Exterior Angles - 2
Corresponding Angles - 4
Same-side Exterior Angles - 5
Same-side Interior Angles - 3
Answer:38292
A
Step-by-step explanation:w
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Two sides of a rectangular garden are 3 meters long. The area of the garden is 18 square meters. How long are the other two sides? What is the perimeter of the garden?
Answers
The length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.
According to the question,
We have the following information:
Two sides of a rectangular garden are 3 meters long. The area of the garden is 18 square meters.
We know that the following formula is used to find the area of rectangle:
Length*width = 18
Length*3 = 18
Length = 18/3
Length of the rectangular garden = 6 meters
Now, perimeter of the rectangular garden:
2(length+width)
2(6+3)
2*9
18 meters
Hence, the length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.
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Continuous Functions
Answers
Some of the graphs are continuous graphs while some are discontinuous graphs
How to determine the domain, range and the function type?Continuous graphs are graph that there is a y value for all x values
On the other hand, some graphs can be discontinuous graphs. This is so because there have holes or jumps or gaps on the coordinate plane
Also, the domain and the range of a relation are the set of input and output values of that relation, respectively
Using the above as a guide, we have:
Graph a
Continuous? YesDomain: -∝ < x < ∝Range: y >= 0Graph b
Continuous? NoDomain: x < 2 and x > 2Range: y < 7 and y > 7Graph c
Continuous? YesDomain: -∝ < x < ∝Range: y >= 1Graph d
Continuous? NoDomain: -∝ < x < ∝Range: y <= 1 and y > 4Graph e
Continuous? NoDomain: x < 3 and x > 3Range: -∝ < y < ∝Graph f
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Does anyone know how to solve this with steps?
Find the savings plan balance after 19 months with an APR of 11% and monthly payments of $250.
Answers
To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.
The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.
The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.
$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:
$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow
A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow
A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$
Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).
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The figure consists of a quarter circle and a parallelogram. What is the area of the composite figure? Use 3.14 for 10,
Round to the nearest whole number,
14 in
14 in.
15 in
Suom
Save and Exit
thandro
Answers
Help help help please please
Answers
Answer:
\(4^6\)
Step-by-step explanation:
We have a simple formula to follow:
\(a^{b} * a^d = a^{b+d}\)
So the new equations is:
\(4^{-3+9} = 4^6\)
The answer is \(4^6\)
-Chetan K
Answer:
4^6
Step-by-step explanation:
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Is the point (4,11) a solution to the following system of equations? How do you know?
y=2x+14
y=3x−5
Answers
Nathan earned $63 for working 7 1/2 hours.. How much does Nathan earn per hour?
0 $8.40
O $7.20
$8.90
O $9.50
Answers
Answer:
$8.40
Step-by-step explanation:
We have to find the unit rate, so our equation is:
63 ÷ 7 1/2 = 8 2/5 or 8.4
So Nathan earns $8.40 per hour
Please help me with this! worth 30 points!!
Answers
Answer:
A. yes
b. No
c. YEs
d.No
Step-by-step explanation: