The table of values below represents a linear function and shows the height of a tree since it was transplanted. What was the height of the tree when it was transplanted?
Answers
The height of the tree when it was transplanted was:
4 feet
Step-by-step explanation:As we could observe that the given table represents a linear function.
The table is given as follows:
Year since it was 4 4.5 5
transplanted
Height (Feet) 12 13 14
We will find the linear function.
Let y denotes height and x denote year since it was transplanted.
We know that any linear function passing through two points (a,b) and (c,d) is given by:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here let (a,b)=(4,12) and (c,d)=(5,14)
Hence, the linear function is calculated as follows:
[tex]y-12=\dfrac{14-12}{5-4}\times (x-4)\\\\\\y-12=2(x-4)\\\\\\y-12=2x-8\\\\\\y=2x-8+12\\\\\\y=2x+4[/tex]
Now the height of tree when it was transplanted is the value of y when x=0
Hence, when x=0 we have:
y=4
Hence, the height was:
4 feet
Related Questions
the sum of partial products is equal to the final product?
Answers
One root of is x = 6. What are all the factors of the function? Use the Remainder Theorem.
Answers
Answer:
C. (x - 6)(x + 4)(x - 2)
Step-by-step explanation:
i just took the test goodluck
Suppose 4 mg of a drug is injected into a person's bloodstream. As the drug is metabolized, the quantity diminishes at the continuous rate of 3% per hour?
Answers
We are told that Q diminishes by 3% every hour.
When t = 0, Q = 4 mg
When t = 1, Q = 4*0.97 mg
When t = 2, Q = 4*(0.97)² mg
By induction,
[tex]Q(t) = 4 (0.97)^{t} \, mg[/tex]
Q'(t) = 0.97Q
Therefore the rate of decrease is 3% per hour.
The person receives an additional dosage when Q falls to 0.50 mg. This happens when
[tex]4(0.97)^{t}=0.5 \\0.97^{t} = 0.125 \\ t \,ln(0.97) = ln(0.125) \\ t = \frac{ln(0.125)}{ln(0.97)} =68.27 \, hrs[/tex]
After the second injection, the mass is now 4.5 mg. Therefore
[tex]Q(t)=4.5(0.97)^{t}[/tex]
When the mass again reaches 0.50 mg, then
[tex]4.5(0.97)^{t}=0.5 \\ 0.97^{t}=0.1111 \\ t \, ln(0.97) = ln(0.1111) \\ t = 72.14 \, hrs[/tex]
Answers:
(a) [tex]Q(t) = 4(0.97)^{t}[/tex]
(b) 3% per hour
(c) 68.3 hours
(d) 72.1 hours
20 children plays a game there are 5 children on each team how many teams play the game write a division sentence to represent the problem
Answers
Final answer:
To find the number of teams playing the game, divide the total number of children by the number of children on each team. In this case, there are 20 children and 5 children on each team, so there are 4 teams playing the game.
Explanation:
To find the number of teams playing the game, you can divide the total number of children by the number of children on each team. In this case, there are 20 children and 5 children on each team. So, the division sentence to represent the problem is:
20 ÷ 5 = 4
Therefore, there are 4 teams playing the game.
Jacob used 1/7 of a liter of water to fill 1/9 of the fish aquarium. How many liters r needed to fill the aquarium?
Answers
Since 1/7 L of water fills 1/9 of the aquarium, 9 times 1/7 will fill the aquarium:
9(1/7) = 9/7 = 1 2/7 L of water will fill the aquarium.
how many liters will it be to fill up the 9/9 of the aquarium?
[tex]\bf \begin{array}{ccll} \stackrel{liters}{water}&\stackrel{fish}{aquarium}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{1}{7}&\frac{1}{9}\\\\ w&\frac{9}{9} \end{array}\implies \cfrac{\frac{1}{7}}{w}=\cfrac{\frac{1}{9}}{\frac{9}{9}}\implies \cfrac{\frac{1}{7}}{\frac{w}{1}}=\cfrac{\frac{1}{9}}{\frac{9}{9}}\implies \cfrac{1}{7}\cdot \cfrac{1}{w}=\cfrac{1}{9}\cdot \cfrac{9}{9} \\\\\\ \cfrac{1}{7w}=\cfrac{1}{9}\implies 9=7w\implies \cfrac{9}{7}=w[/tex]
Solve for Z. Z−4/9−1/3=5/9 Enter your answer in the box. Z=
NEED HELP FAST WILL GIVE BRAINLIEST 15 POINTS
Answers
z -4/9 + 4/9 - 1/3 = 5/9 + 4/9 = 1
z - 1/3 + 1/3 = 1 + 1/3
z= 1 1/3
Answer:
The answer correct answer is, 4/3
Step-by-step explanation:
I am reveiwing this quiz right now!
Find the sale price of the item. Round to two decimal places if necessary.
Original price: $217.90
Markdown: 79%
The sale price is $___
Answers
How do I multiply 8.354 by 11.81?
Answers
Answer is 98.66074
WILL GIVE A BRAINLEST AND 20PTS
Which figures can be precisely defined by using only undefined terms? Check all that apply.
angle
arc
circle
line segment
parallel lines
Answers
Answer:
We can define circle, line segment and parallel lines with the help of undefined terms.
Step-by-step explanation:
The undefined terms in geometry are line, plane and points.
So, we can define line segment, circles and parallel lines with the help of undefined terms.
A line segment is a part of a line that contains two distinct end points.
A circle is defined as a figure with a set of points that are all equidistant from a fixed point called the center.
Parallel lines are lines in a plane that never meet or intersect at any point.
Help please :) ! The dashed triangle is the image of the pre-image solid triangle. What is the scale factor used to create the dilation? Enter your answer in the box.
Answers
Let
x---------> measure of the base of the triangle of the image
y---------> measure of the base of the triangle of the pre-image
sf-------> the scale factor
we know that
the scale factor is equal to
[tex]sf=\frac{x}{y}[/tex]
in this problem we have
[tex]x=6\ units\\y=3\ units[/tex]
Find the scale factor
substitute the values of x and y in the formula above
[tex]sf=\frac{6}{3}=2[/tex]
therefore
the answer is
the scale factor is equal to [tex]2[/tex]
Computer upgrades have a nominal time of 80 minutes. samples of five observations each have been taken, and the results are as listed. sample 1 2 3 4 5 6 79.2 80.5 79.6 78.9 80.5 79.7 78.8 78.7 79.6 79.4 79.6 80.6 80.0 81.0 80.4 79.7 80.4 80.5 78.4 80.4 80.3 79.4 80.8 80.0 81.0 80.1 80.8 80.6 78.8 81.1 factors for three-sigma control limits for formula179.mml and r charts factors for r charts number of observations in subgroup, n factor for formula180.mml chart, a2 lower control limit, d3 upper control limit, d4 2 1.88 0 3.27 3 1.02 0 2.57 4 0.73 0 2.28 5 0.58 0 2.11 6 0.48 0 2.00 7 0.42 0.08 1.92 8 0.37 0.14 1.86 9 0.34 0.18 1.82 10 0.31 0.22 1.78 11 0.29 0.26 1.74 12 0.27 0.28 1.72 13 0.25 0.31 1.69 14 0.24 0.33 1.67 15 0.22 0.35 1.65 16 0.21 0.36 1.64 17 0.20 0.38 1.62 18 0.19 0.39 1.61 19 0.19 0.40 1.60 20 0.18 0.41 1.59
a. using factors from above table, determine upper and lower control limits for mean and range charts. (round your intermediate calculations and final answers to 2 decimal places. leave no cells blank - be certain to enter "0" wherever required.) mean chart range chart ucl 81.06 4.01 lcl 78.86 0.00 g
Answers
The UCL and LCL for the mean and range charts are calculated based on the average and range of the data sets. The table provided in the question provides respective factors for various subgroup sizes. For n=5, the factors are A2=0.58, D3=0 and D4=2.11. Using these we compute UCL and LCL for both charts. Round off to two decimal places and fill '0' in any empty cells.
Explanation:To find the Upper Control Limit (UCL) and Lower Control Limit (LCL) for the mean and range charts, we have to use the r and formula179.mml charts that are provided in your question. We will take the observations in groups of five as mentioned in the question.
Firstly, calculate the average (X-bar) for each of these groups and find the overall average (M) of these five averages.Please find the range (R) for each subgroup and then the average of these ranges (meanR).Referring to the table given in your question, for n=5, the factors are A2=0.58, D3=0 and D4=2.11.The UCL and LCL for the mean chart can be calculated using UCL=M+A2*meanR and LCL=M-A2*meanR, whereas, for the range chart, they are UCL=D4*meanR and LCL=D3*meanRUsing these steps, you can find the upper and lower control limits for both the mean and range charts. Always remember to round off your answers to two decimal places and also, to avoid leaving any cells blank in the excel sheet. If required, fill in '0' in those empty cells. This way, meaningful interpretation of the control charts can be made.
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The upper and lower control limits for the mean chart are 81.06 and 78.86, respectively, while the upper control limit for the range chart is 8.45 and the lower control limit is 0.
To determine the upper and lower control limits for the mean and range charts, we can use the factors provided in the table.
For the mean chart:
- The upper control limit (UCL) is calculated by adding the product of the factor for the mean chart (A2) and the average range (R-bar) to the overall average (X-double-bar). In this case, the A2 factor is 0.73 and the R-bar is 4.01, so the UCL for the mean chart is: 81.06 (rounded to 2 decimal places).
- The lower control limit (LCL) is calculated by subtracting the product of the factor for the mean chart (A2) and the average range (R-bar) from the overall average (X-double-bar). Using the same values, the LCL for the mean chart is: 78.86 (rounded to 2 decimal places).
For the range chart:
- The UCL for the range chart is calculated by multiplying the factor for the range chart (D4) by the average range (R-bar). In this case, the D4 factor is 2.11 and the R-bar is 4.01, so the UCL for the range chart is: 8.45 (rounded to 2 decimal places).
- The LCL for the range chart is always 0 since range values cannot be negative.
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a number is less than 200 and greater than 100 the ones digit is 5 less than 10.the tens digit is 2 more than the ones digit.what is the number
Answers
5 less than 10 is 5.
2 more than 5 is 7
My guess is 157
The correct number is between 100 and 200 would be 175.
Used the concept of number system which states that,
A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols.
Given that,
A number is less than 200 and greater than 100.
Here, the one's digit is 5 less than 10, and the tens digit is 2 more than the one digit.
Since the one's digit is 5 less than 10.
So, the number in one's place is,
10 - 5 = 5
And, the tens digit is 2 more than the one digit.
5 + 2 = 7
Since the number is between 100 and 200.
So, the possible value of a number with the value in one's place 5 and the value in tens place 7 would be,
175
Clearly, the number 175 is between 100 and 200.
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multiply 4xy^3(3×^2y)^2
Answers
Discuss the differences between parametric and non-parametric tests?
Answers
You have 3/8 of a cake. You divide the remaining cake into six equal pieces. What fraction of the original cake is each piece?
Answers
------ = 1/16 of the original
8(6) cake.
Write this in Interval Notation:
4x - 6 ≥ 6x - 20
Answers
What is the value of the expression? 56−(18÷34) as a fraction in simplest form
Answers
Hope this helps! :D
~PutarPotato
The value of the expression [tex]\( 56 - \left( \frac{18}{34} \right) \)[/tex] as a fraction in simplest form is [tex]\( \frac{943}{17} \)[/tex].
To solve the expression, we first perform the division within the parentheses:
[tex]\[ \frac{18}{34} \][/tex]
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[ \frac{18 \div 2}{34 \div 2} = \frac{9}{17} \][/tex]
Now we have:
[tex]\[ 56 - \frac{9}{17} \][/tex]
We need to express the whole number as a fraction with the same denominator as the fraction we are subtracting.
[tex]\[ \frac{56 \times 17}{17} - \frac{9}{17} \][/tex]
[tex]\[ \frac{952}{17} - \frac{9}{17} \][/tex]
[tex]\[ \frac{952 - 9}{17} \][/tex]
[tex]\[ \frac{943}{17} \][/tex]
all quadrilaterals are polygons
Answers
Polygons are figures with straight edges, and any number of sides/vertices.
Quadrilaterals are figures with straight edges, with 4 sides and 4 vertices.
What’s the answer to simply
1
-
2
-
4 it’s a fraction.
Answers
Which equation is equivalent to 1 5/6 - 2/6 = 1 3/6
Answers
Twenty-five bakery customers were surveyed to determine if they like cake or pie. The results are shown in the Venn diagram.
Given that a randomly chosen customer likes cake, what is the probability that the customer also likes pie
A. 2/7
B. 2/5
C. 4/7
D.4/5
Answers
4 of those 14 also like pie.
4/14= 2/7
Final answer: A
From the given Venn diagram. The probability that the customer also likes pie is 2/7.
Given that a randomly chosen customer likes cake
The results are shown in the Venn diagram.
To determine the probability that the customer also likes pie
In total, 14 people liked the cake (10+4).
4 of those 14 also like pie.
What is the formula for probability?The probability of event A is given by the ratio of the no of a favorable outcome in event A divided by the total outcome in a sample space A.
4/14= 2/7
Option A is correct.
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981,657 rounded to nearest ten thousand
Answers
////////////// sorry i need 20 characters
The table below shows the typical hours worked by employees at a company. A salaried employee makes $67,000 per year. Hourly employees get paid $25 per hour, but get $37.50 per hour for each hour over 40 hours. Sun. Mon. Tues. Wed. Thurs. Fri. Sat. 0 10 8 8 7 6.5 4.5 Which of the payment options would you recommend to a new employee? a. Either one. Hourly and salaried employees earn the same amount per week. b. Hourly pay. Hourly employees make more per week than salaried employees. c. Salaried pay. Salaried employees make more per week than hourly employees. d. There is not enough information given to compare weekly earnings.
Answers
Answer:
C should be the correct option
Step-by-step explanation:
Tell me if im wrong :)
We are conducting a test of the hypotheses h0: p = 0.2 ha: p ≠ 0.2 we find a test statistic of z = -1.11. what is the corresponding p-value? give your answer as a proportion between 0 and 1 to 4 decimal places.
Answers
You have a photo that measures 1 in. wide by 3 in. tall. If you want to enlarge the photo so that the height is 18 in., what will the width of the photo be?
A. 98 in.
B. 4 in.
C. 6 in.
D. 108 in.
Answers
6(1)= 6
The answer is C.
Hope this helps!
Find the area bounded by the curve y = x 1/2 + 2, the x-axis, and the lines x = 1 and x = 4 A. 16 B. 10 2/3 C. 7 1/2 D. 28 1/2
Answers
Take the antiderivative: Remember that this what the original function would be if our derivative was x^(1/2) + 2
antiderivative (x ^(1/2) + 2) = (2/3) x^(3/2) + 2x
* To check that this is correct, take the derivative of our anti-derivative and make sure it equals x^(1/2) + 2
To find integral from 1 to 4:
Find anti-derivative at x=4, and subtract from the anti-derivative at x=1
2/3 * 4 ^ (3/2) + 2(4) - (2/3) *1 - 2*1
2/3 (8) + 8 - 2/3 - 2 Collect like terms
2/3 (7) + 6 Express 6 in terms of 2/3
2/3 (7) + 2/3 (9)
2/3 (16) = 32/3 = 10 2/3 Answer is B
12.917 rounded to the nearest ones
Answers
a box of cereal contains 23.4 ounces. It cost $5.49. What is the cost,to the nearest cent, of the cereal per ounce.
Answers
This equals $0.23
The answer is $0.23
Your mid-morning break begins at 10:30 A.M. and lasts for 15 minutes. You work 2 hours and 50 minutes until your lunch break. What time does your lunch break begin?
Answers
because the break takes 15 minutes Which equals 10:45.
2. You then add another 2 hours and 50 minutes of work until your lunch break which makes it 1:35.
3. Your lunch break starts at 1:35
Final answer:
The lunch break begins at 1:20 P.M. after working for 2 hours and 50 minutes from the mid-morning break at 10:30 A.M.
Explanation:
The mid-morning break begins at 10:30 A.M. and lasts for 15 minutes.
You work 2 hours and 50 minutes from 10:30 A.M.
To find the start time of your lunch break, add 2 hours and 50 minutes to 10:30 A.M.
Lunch break begins at 1:20 P.M.
There are 56 trees in an apple orchard. They are arranged in equal rows. There are 8 trees in each row. How many rows of apple trees are there? Which equation can be used to solve this problem?
Answers
Final answer:
In this case, there are 56 trees in the orchard and 8 trees in each row, so there are 7 rows of apple trees in the orchard.
Explanation:
To find the number of rows of apple trees in the orchard, we need to divide the total number of trees by the number of trees in each row.
In this case, there are 56 trees in the orchard and 8 trees in each row.
We can use the equation:
Number of rows = Total number of trees / Number of trees in each row
Plugging in the values:
Number of rows = 56 trees / 8 trees = 7 rows
Therefore, there are 7 rows of apple trees in the orchard.