Nelly owns farm land that has an area of 4.2 × 102 acres. Each year, the farm produces 6.72 × 104 bushels of corn. What is the average amount of corn produced per acre represented in scientific notation?
A) 2.82 × 107 bushels per acre
B) 1.6 × 102 bushels per acre
C) 1.6 × 103 bushels per acre
D) 2.82 × 106 bushels per acre
E) 1.6 × 101 bushels per acre
The average amount of corn produced per acre represented in scientific notation can be found using the below formula:
[tex] The \;average\; amount\; of\; corn\; per\; acre=\frac{Bushels \; of\; corn\; produced\; in\; farm}{Area\; of\; farm\; in\; acres} [/tex]
We are given:
[tex] Area \; of\; FARM\; land= 4.2 \times 10^2 \; acres\\ \\ Amount \; of\; corn\; produced=6.72\; \times \; 10^4 \; bushels [/tex]
Substituting the above information in the formula, we get...
[tex] The \; Average\; amount\; of\; corn=\frac{6.72 \times 10^4}{4.2 \times 10^2} \\ \\ \frac{6.72}{4.2} \times \frac{10^4}{10^2}\; =\; 1.6 \times 10^{4-2}\; =\; 1.6 \times 10^2\\ \\ [/tex]
Conclusion:
[tex] The \; Average \; amount\; of \; corn \; is\; 1.6 \times 10^2 \; Bushes\; per\; corn [/tex]
The average amount of corn produced per acre represented in scientific notation is option B)[tex] 1.6 \times 10^2 [/tex]bushels per acre
Le answer is B 1.6 × 102 bushels per acre
The diagonals of an isosceles trapezoid are not congruent. true or false
At the beginning of the day, stock XYZ opened at $3.15. At the end of the day, it closed at $2.87. What is the rate of change of stock XYZ?
Answer:
-8.9%
Step-by-step explanation:
Answer:
The rate of change is - 8.89 %.
Step-by-step explanation:
Given,
The opening price = $ 3.15,
While closing price = $ 2.87,
Now,
[tex]\text{The rate of change}=\frac{\text{closing price-opening price}}{\text{opening price}}\times 100[/tex]
[tex]=\frac{2.87-3.15}{3.15}\times 100[/tex]
[tex]=\frac{-0.28}{3.15}\times 100[/tex]
[tex]=-\frac{28}{3.15}=-8.8889\%\approx -8.89 \%[/tex]
Solve the system of equations using the linear combination method.
{5m+3n=41
3m−6n=9
Enter your answers in the boxes.
m =
n =
Solve the system of equations using the linear combination method.
{6g+8h=40
−6g+2h=−20
Enter your answers in the boxes.
g =
h =
Solve the system of equations using the linear combination method.
{9x+5y=35
2x+5y=0
Enter your answers in the boxes.
x =
y =
Answer:
1. n=2 and m=7
2. g =4 and h =2
3. x=5 and y=-2
Step-by-step explanation:
I took the test
Which property is illustrated by this problem?
53.2 • 1 = 53.2
A. Associative property of multiplication
B. Multiplicative identity
C. Commutative property of multiplication
(02.01 LC) Solve: negative 1 over 2 x + 3 = −x + 7 (5 points) 1 over 2 8 −8 2
Answer:
2 8 -8 2
Step-by-step explanation:
The correct answer is [tex]-\frac{1}{2}x + 3 = -x + 7$ is $x = 8[/tex].
To solve the equation [tex]-\frac{1}{2}x + 3 = -x + 7[/tex], we can follow these steps:
Step 1: Combine like terms on both sides of the equation.
[tex]-\frac{1}{2}x + 3 = -x + 7[/tex]
[tex]\frac{1}{2}x - 3 = x - 7[/tex]
Step 2: Subtract [tex]x[/tex] from both sides to isolate the terms with [tex]x[/tex].
[tex]\frac{1}{2}x - 3 - x = -7[/tex]
[tex]-\frac{1}{2}x - 3 = -7[/tex]
Step 3: Add 3 to both sides to isolate the term with [tex]x[/tex].
[tex]-\frac{1}{2}x = -4[/tex]
Step 4: Multiply both sides by [tex]-2[/tex] to solve for[tex]x[/tex].
[tex]-2 \left(-\frac{1}{2}x\right) = -2(-4)[/tex]
[tex]x = 8[/tex]
Therefore, the solution to the equation [tex]-\frac{1}{2}x + 3 = -x + 7$ is $x = 8[/tex]
I need help please with this math problem
Given: ∠AOB is a central angle and ∠ACB is a circumscribed angle.
Prove: △ACO ≅ △BCO
We are given that angle AOB is a central angle of circle O and that angle ACB is a circumscribed angle of circle O. We see that AO ≅ BO because ____
We also know that AC ≅ BC since ___
Using the reflexive property, we see that ____
Therefore, we conclude that △ACO is congruent to △BCO by the _____
The answers to the dashed parts of the questions to prove that △ACO ≅ △BCO are respectively;
- All radii of the same circle are congruent
- Tangents to a circle that intersect are congruent
- Side CO is congruent to side CO
- SSS congruency theorem
The image of the Triangle and circle has been attached.
Now, from the attached image we can see that;
Point O is the center of the circle and as such AO and BO are both radius of the circle.Thus, it means that AO ≅ BO because; All radii of the same circle are congruent
Since AO and BO are equal, it means that since point C is the intersection point of tangents from points A and B, then we can say that;AC ≅ BC because; tangents to a circle that intersect are congruent.
Reflexive property shows that the length of a side is congruent to itself. Now, in △ACO and △BCO, we see that they share a common side which is CO. Thus, CO is congruent to side CO.We have been able to establish that;
AO ≅ BO
AC ≅ BC
CO ≅ CO
This means all three corresponding sides of both △ACO and △BCO are congruent. Thus, we can conclude that;
△ACO is congruent to △BCO by the "SSS Congruency theorem"
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Answer:
Step-by-step explanation: edge2024
PLEASE SOMEONE HELP!!
IS THE CHOICE I PICKED CORRECT??
IF NOT, PLEASE TELL ME WHICH ONE IT IS??
Rashad draws a figure and divides it into equal parts. Two of the parta are red. The other 4 parts are blue. Rashad saya that 2/4 of the figure is red. What error is he making? Explain. Then write the correct fraction of the figure that is red.
Answer:
Step-by-step explanation:
m ∠ U = (2x−5)° and m ∠W = (x+38)°What is m ∠W?
Question 1 options:
49°
180°
87°
90°
You are working on a proof. You know that A and B are on the perpendicular bisector of CD. What can you conclude? A) AC = BD B) CB = AD C) AC = AD D) AB = CD
Blue and white tiles are used to decorate a wall. The ratio of blue to white tiles is 7:2. There were 180 tiles used in all. How many blue tiles were used?
TIME REMAINING
01:40:32
A flowchart proof
contains a set of sentences explaining the steps needed to reach a conclusion.
uses inductive reasoning to prove a statement.
uses a visual representation of the logical flow of steps needed to reach a conclusion.
contains a table with a logical series of statements and reasons that reach a conclusion.
Answer:
uses a visual representation of the logical flow of steps needed to reach a conclusion.
Step-by-step explanation:
In a flowchart proof, there are boxes for the steps that lead us to the conclusion. Below this are lines for the explanations of those steps.
Each box has an arrow pointing to the next box in the proof.
It helps us visualize the steps necessary to get from the given information to what we're asked to prove.
A flowchart proof contains a set of sentences explaining the steps needed to reach a conclusion uses a visual representation of the logical flow of steps needed to reach a conclusion.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
A flowchart is a picture of the separate steps of a process in sequential order. It is a generic tool that can be adapted for a wide variety of purposes.
A flowchart proof uses a visual representation of the logical flow of steps needed to reach a conclusion. It contains a set of sentences explaining the steps needed to reach a conclusion and uses inductive reasoning to prove a statement.
Hence, A flowchart proof contains a set of sentences explaining the steps needed to reach a conclusion uses a visual representation of the logical flow of steps needed to reach a conclusion.
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An equation was created for the line of best fit from actual enrollment data. It was used to predict the dance studio enrollment values shown in the table below:
Enrollment Month
January February March April May June
Actual 12 14 14 13 16 14
Predicted 8 15 15 12 17 15
Residual 4 −1 −1 1 −1 −1
Analyze the data. Determine whether the equation that produced the predicted values represents a good line of best fit.
No, the equation is not a good fit because the sum of the residuals is a large number.
No, the equation is not a good fit because the residuals are all far from zero.
Yes, the equation is a good fit because the residuals are all far from zero.
Yes, the equation is a good fit because the sum of the residuals is a small number.
Answer: No, the equation is not a good fit because the sum of the residuals is a large number.
Step-by-step explanation:
A residual is the difference on the scatter plot between the actual y-value and the predicted y-value from the regression line equation.
It is the vertical distance from the actual plotted point to the point on the regression line.
The residual is positive then the data point is above the graph.
The sum of the given residual values = [tex]4+(-1)+(-1)+1+(-1)+(-1)=1[/tex]
Since, the sum of the residuals is greater than 0.
Therefore, The equation is not a good fit .
Answer:
A. No, the equation is not a good fit because the sum of the residuals is a large number.
Step-by-step explanation:
Which algebraic expression is equivalent to the expression below? (7x - 15) + 15
a. 7x - 30
b. 7x
c. 105x
d. 7x + 30
Which of the following situations models a geometric sequence? Select all that apply.
Answer:
Options 1, 3, 4.
Step-by-step explanation:
We will check each and every option given here.
1) Amount of cell phone users increases by 33% every year.
Its a geometric sequence because the number of users are increasing exponentially every year.
2) Amount of cakes in bake sale increases by 3 each year the fundraiser is held.
amount of cakes is increasing with a common difference of 3 so it's an arithmetic sequence.
3).Uranium loses half of its weight every 415 years.
Exponential decay in every 415 years. So geometric sequence with a common ratio of 1/2.
4).A family of rabbits doubles in size every 3 months.
Exponential series again so geometric sequence with a common ratio of 2.
5).Car drives at a constant speed of 58 mph.
Its a linear function representing an arithmetic sequence with a common difference of 58 mph.
6). Number of students increases by 122 every year.
An arithmetic sequence with a common difference of 122.
7). Number of pieces of chalk in a class room decreases by 10 throughout the school year.
It's an arithmetic sequence having common difference of 10.
Amount of cell phone users increase by 33% every year. Uranium loses half of its weight every 415 years. A family of rabbits doubles in size every 3 months. Then the correct options are A, C, and D.
What is a geometric sequence and how to find its nth terms?Suppose the initial term of a geometric sequence is a and the term by which we multiply the previous term to get the next term is r.
Then the sequence would look like
a, ar, ar², ar³,..... (till the terms to which it is defined)
Amount of cell phone users increase by 33% every year.
It's a geometric sequence because the number of users is increasing exponentially every year.
Uranium loses half of its weight every 415 years.
Exponential decay every 415 years. So geometric sequence with a common ratio of 1/2.
A family of rabbits doubles in size every 3 months.
Exponential series again so geometric sequence with a common ratio of 2.
Then the correct options are A, C, and D.
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Janna jumped 156in in the long jump competition at the high school track meet . How many feet did Janna jump
The circus is coming to town. Cindy is selling tickets. The first day she sold 8 adult tickets and 5 children tickets for a total of 177.50 in sales. The second day she received $255.00 for 12 adult tickets and 6 children tickets.
Which of these is a simplified form of the equation 8y + 4 = 6 + 2y + 1y?
5y = 2
5y = 10
11y = 2
11y = 10
Answer:
paxx17 is correct.
Step-by-step explanation:
I got the question correct because of them.
The legs of a right triangle measure 4 and 6 inches. The area of the triangle is
5 in.²
12 in.²
24 in.²
Answer:
Area of triangle is 12 in.²
Step-by-step explanation:
we are given that:
The legs of a right triangle measure 4 and 6 inches.
(i.e. height and base of right angled triangle)
We have to find the area of this triangle.
area of triangle=[tex]\dfrac{1}{2}\times base\times height[/tex]
=[tex]\dfrac{1}{2}\times 4\times 6[/tex]
= 12 in.²
Hence, Area of triangle is 12 in.²
What is the algebraic expression for "the difference between seven times a number and three times that number"? 7 - 3 x 7 x - 3 7 x - 3 x
which cream cheese has the lowest price per ounce?
A: $2.59 for 6oz
B: $2.89 for 8 oz
C: $4.29 for 12 oz
D: $5.29 for 14 oz
Answer:the correct answer is $4.29 for 12 oz.
Step-by-step explanation:
The cream cheese which has the lowest price per ounce is the one which is $4.29 for 12 oz. Thus, the correct option is C.
What is Ounce?The ounce is any of the several different units of mass, weight or volume and it is derived almost unchanged from the uncia, unit of measurement.
The ounce is 1/16 avoirdupois pound. This is the United States customary and British imperial ounce. Ounce is primarily used in the United States to measure packaged foods and food portions, areal density of fabric and paper, boxing gloves, and so on, but it is sometimes also used elsewhere in the Anglosphere.
The price for per ounce of different cream cheese will be:
a. 2.59/ 6 = 0.431
b. 2.89/ 8 = 0.361
c. 4.29/ 12 = 0.357
d. 5.29/ 14 = 0.377
Therefore, the cream cheese which has the lowest price per ounce is the one which costs $4.29 for 12 oz.
Therefore, the correct option is C.
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Enter the area of a sector with a central angle of 4π3 radians and a radius of 12.5 cm.
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
What is the area of a sector with a central angle of 5π7 radians and a diameter of 5.6 in.?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
Answer:
The answer is 327.08 i am in k12
Step-by-step explanation:
A cylinder has a base radius of 10cm and a height of 19cm. What is its volume in cubic cm, to the nearest tenths place?
Danielle poured 3/4 gallon of water from a 7/8 gallon bucket. How much water is left in the bucket?
What is the area of this triangle A=bh2
Which expression is equivalent to(3m^-2 n)^-3/6mn^-2? Assume
To simplify the expression (3m⁻² n)⁻³/6mn⁻², follow the steps: apply the negative exponent rule, simplify by multiplying the exponents, and rearrange and combine like terms if necessary.
Explanation:To simplify the expression (3m-2 n)-3/6mn-2 , let's break it down step by step:
Step 1: Apply the negative exponent rule. To do this, we can move any term with a negative exponent from the numerator to the denominator or vice versa. In this case, the term m-2 can be written as 1/m2.
Step 2: Simplify the expression by multiplying the exponents. The exponents in the expression can be added since they have the same base (m).
Step 3: Simplify further by rearranging and combining like terms if necessary.
Putting it all together, the expression is equivalent to (1/3m4n6)1/6mn-2.
Please help if you do not know the answer don’t comment in the answer box just for points
The box plots show the distributions of daily temperatures, in °F, for the month of January for two cities.
Which statements are true about the distributions? Check all that apply.
a. Both distributions are symmetric.
b. Both distributions are skewed right.
c. Both distributions are skewed left.
d. The mean and standard deviation would be the best measures to compare the data.
e. The median and IQR would be the best measures to compare the data.
Hey, the answers are
Both distributions are skewed right.
The median and IQR would be the best measures to compare the data.
That is B and E
What is the area of a sector with a central angle of 5pi/7 radians and a diameter of 5.6 in.? Use 3.14 for pi and round your final answer to the nearest hundredth.