Lorena is driving a truck that is painting the lines on a new road. The lines she paints are 0.152 meters wide, and she will paint a total length of 5.45 × 105 meters of lines. The shape created by the lines will be a rectangle, and the area will be the product of the length and width.
Approximately what area of the road will Lorena be painting?
5.602 × 10 (5) m2
8.284 × 10 (4) m2
8.698 × 10 (1) m2
8.284 × 10 (5) m2
5.602 × 10 (4) m2
Answers
Answer:
8.284 × 10^4 m^2
Step-by-step explanation:
The area is the product of length and width:
(5.45·10^5 m)·(0.152 m) = 0.8284·10^5 m^2 = 8.284·10^4 m^2
Related Questions
A square cement parking lot is being converted to a nature park. Each side of the parking lot is 100 meters long. The plan is to reduce the side lengths of the lot by 8 meters each year to plant greenery. Which function can be used to calculate the area of the cement parking lot, A, after t years?
Answers
Answer:
[tex]A(t)=(100-8t)^{2}[/tex]
Step-by-step explanation:
Let
t-----> the number of years
A-----> the area of the cement parking lot
we know that
The function that represent this situation is
[tex]A(t)=(100-8t)^{2}[/tex]
Final answer:
The function A(t) = [tex](100-8t)^2[/tex] can be used to calculate the area of the cement parking lot after t years by substituting the side length (100-8t) into the formula for the area of a square.
Explanation:
The function that can be used to calculate the area of the cement parking lot after t years is: A(t) = [tex](100-8t)^2[/tex].
To calculate the area of the square parking lot at any given time t, you substitute the side length (100-8t) into the formula for the area of a square, A = side [tex]length^2[/tex].
For example, after 2 years, the area A(2) would be[tex](100-8(2))^2[/tex] = [tex]84^2[/tex]= 7056 square meters.
Solve the system by using a matrix equation
2x-3y=3
5x-7y=9
Answers
Answer:
The correct answer would be option C
Step-by-step explanation:
If the r-value or correlation coefficient of a data set is 0.827, what is the coefficient of determination to three decimal places?
A. 0.884
B. 0.627
C. 0.684
D. 0.827
Answers
Answer: Option C
[tex]r ^ 2 = 0.684[/tex]
Step-by-step explanation:
The correlation coefficient r is a measure of how strong the relationship between two variables x and y is.
If the value of r is positive then the correlation is positive and that implies that the variable x grows together with the variable y.
If the value of r is negative that means that the correlation is negative and that implies that when the variable x grows then the variable y decreases.
Then for a relationship, the coefficient of determination [tex]r ^ 2[/tex] is a measure of how well the model fit the data or how accurate the model is. While r is closer to 1, better is the precision of the model.
The coefficient of determination [tex]r ^ 2[/tex] for a linear relationship is calculated as the square of the correlation coefficient.
In this problem we have that the correlation coefficient r is
[tex]r = 0.827[/tex]
then the coefficient of determination is:
[tex]r ^ 2 = 0.827 ^ 2[/tex]
[tex]r ^ 2 = 0.684[/tex]
The answer is option C
Determine whether the function is periodic. If it is periodic, find the period.
f(x) = 3 sin 2x + 4 cos 3x
Answers
Answer
a) 2π
Step-by-step explanation:
We can easily solve this question by using a graphing calculator or any plotting tool, to check if it is periodic.
The function is
f(x) = 3*sin(2*x) + 4*cos(3*x)
Which can be seen in the picture below
We can notice that f(x) is periodic. It has periodic amplitudes, and the function has a period T = 6.283 ≈ 2π
The maximum and minimum values are
Max = 6.695
Min = -6.695
Ben fills 42 pints of juice in 12 bottles. Six bottles have a capacity of 3 pints each. The remaining 6 bottles are all of the same capacity. Let b represent the capacity, in pints, of each of the remaining 6 bottles. What is tye capacity of each of the 6 remaining bottles
Answers
Answer:
The capacity of the remaining bottles = 4 pints.
Step-by-step explanation:
6*3 + 6*b = 42
6b = 42 - 18
6b = 24
b = 4.
The required quantity of the remaining 6 bottles is 4 pints.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
Ben fills 42 pints of juice in 12 bottles. Six bottles have a capacity of 3 pints each.
Let b represent the capacity, in pints, of each of the remaining 6 bottles.,
Now,
42 = 3 × 6 + b × 6
42 = 18 + 6b
6b = 42 - 18
b = 24/6
b = 4
Thus, the required quantity of the remaining 6 bottles is 4 pints.
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Rewrite The following expression.
Answers
Answer:
Choice A is correct
Step-by-step explanation:
We have been given the expression;
[tex]x^{\frac{9}{7} }[/tex]
In order to re-write this expression, we shall use some laws of exponents;
[tex]a^{\frac{b}{c} }=(a^{b})^{\frac{1}{c} }[/tex]
Using this law, the expression can be written as;
[tex](x^{9})^{\frac{1}{7}}[/tex]
The next thing we need to remember is that;
[tex]a^{\frac{1}{n} }=\sqrt[n]{a}[/tex]
Therefore, the expression becomes;
[tex]\sqrt[7]{x^{9} }[/tex]
Next,
[tex]x^{9}=x^{7}*x^{2}[/tex]
This implies that;
[tex]\sqrt[7]{x^{9} }=\sqrt[7]{x^{7}*x^{2}}\\=\sqrt[7]{x^{7} }*\sqrt[7]{x^{2} } \\=x\sqrt[7]{x^{2} }[/tex]
ANSWER
A.
[tex]x \sqrt[7]{{x}^{2} } .[/tex]
EXPLANATION
The given expression is
[tex] {x}^{ \frac{9}{7} } [/tex]
We want to rewrite the given expression in radical form:
Recall that:
[tex] {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } [/tex]
This implies that:
[tex] {x}^{ \frac{9}{7} } = \sqrt[7]{ {x}^{9} } [/tex]
[tex]{x}^{ \frac{9}{7} } = \sqrt[7]{ {x}^{7} \times {x}^{2} } [/tex]
Split the radicals.
[tex]{x}^{ \frac{9}{7} } = \sqrt[7]{ {x}^{7} } \times \sqrt[7]{{x}^{2} } [/tex]
This finally simplifies to:
[tex]{x}^{ \frac{9}{7} }=x \sqrt[7]{{x}^{2} } [/tex]
The correct answer is A.
PLEASE HELP!!! NEED ANSWERS TO THESE QUESTIONS..
Answers
Answer:
12. Option A is correct
13. Option A is correct
14. Option C is correct
15. Option D is correct
16. Option A is correct
Step-by-step explanation:
12) Lowest Common Denominator of
[tex]\frac{p+3}{p^2+7p+10} \,\, and \,\, \frac{p+5}{p^2+5p+6}[/tex]
We should find the factors of denominators and then find the LCM of the denominators.Finding LCD is same as finding LCM.
Factors of p^2+7p+10 = p^2 +2p +5p+10 = p(p+2)+5(p+2) = (p+5)(p+2)
Factors of p^2+5p+6 = p^2+2p+3p+6 = p(p+2)+3(p+2) = (p+3) (p+2)
Now, rewriting the above equation with factors and finding the LCM
[tex]\frac{p+3}{(p+5)(p+2)} \,\, and \,\, \frac{p+5}{(p+3)(p+2)}\\[/tex]
LCM of (p+5)(p+2) and (p+3)(p+2) = (p+5)(p+3)(p+2)
The LCD is (p+5)(p+3)(p+2).
So, Option A is correct.
13. Divide
[tex]\frac{40x}{64y} \,\,by\,\, \frac{5x}{8y}[/tex]
by stands for division. The equation can be written as:
[tex]\frac{40x}{64y}\div\frac{5x}{8y}[/tex]
Division sign changed into multiplication, we take reciprocal of second term i.e,
[tex]\frac{40x}{64y}*\frac{8y}{5x}\\\\Solving\\\frac{40x*8y}{64y*5x}\\\\\frac{320xy}{320xy} \\\\1[/tex]
So, Option A is correct.
14. Simplify:
[tex]\frac{x+2}{x^2-6x-16} \div \frac{1}{9x} \\[/tex]
Factors of x^2-6x-16= x^2 -8x +2x -16 = x(x-8)+2(x-8) = (x-8)(x+2)
Putting factors in the above equation and changing division sign with multiplication we get,
[tex]\frac{x+2}{(x-8)(x+2)} * \frac{9x}{1}\\\frac{9x}{x-8}[/tex]
So, Option C is correct.
15. Simplify
[tex]\frac{4}{\frac{1}{4}-\frac{5}{2}}[/tex]
Solving denominator,
Taking LCM of 4 and 2 and subtracting we get
[tex]\frac{4}{\frac{1-(5*2)}{4}}\\\frac{4}{\frac{1-10}{4}}\\\frac{4}{\frac{-9}{4}}\\\frac{4*4}{-9}\\\frac{16}{-9} \,\,or\,\,\\\frac{-16}{9}[/tex]
Option D is correct.
16. Simplify:
[tex]\frac{7x+42}{x^2+13x+42}[/tex]
Making factors of x^2+13x+42= x^2 +6x+7x+42 = x(x+6)+7(x+6) = (x+7)(x+6)
Taking 7 common from numerator and putting factors in denominator we get,
[tex]\frac{7(x+6)}{(x+7)(x+6)}\\\\Cancelling\,\, x+6 \,\, from\,\, numerator \,\, and\,\, \\\\\frac{7}{(x+7)}[/tex]
Option A is correct.
Amber is on a family cell phone plan with 2 other family members. The family gets 720 shared cell phone minutes a month, each family is limited to his or her equal fair share of minutes each month and calls between family members cost zero minutes. How many minutes per day does Amber have to call her friends without going over her monthly minutes if there are 30 days in that month?
Answers
Amber plus 2 family members = 3 total people on the plan.
They share the minutes equally so divide the minutes by 3 to find how many she can use:
720 / 3 = 240 minutes per month.
Now divide the monthly minutes by 30 days:
240 / 30 = 8 minutes per day.
Suppose 15% of the apples picked one afternoon are rotten. The following simulations demonstrate how apples can be randomly chosen and then recorded as rotten or not rotten. Which simulation best models the scenario? Place 20 equally sized pieces of paper in a hat. Of the 20, 3 read "rotten," and the rest read "not rotten". Place 15 equally sized pieces of paper in a hat. Of the 15, 3 read "rotten," and the rest read "not rotten". Place 30 equally sized pieces of paper in a hat. Of the 30, 3 read "rotten," and the rest read "not rotten". Place 12 equally sized pieces of paper in a hat. Of the 12, 3 read "rotten," and the rest read "not rotten".
Answers
Answer:
Place 20 equally sized pieces of paper in a hat. Of the 20, 3 read "rotten," and the rest read "not rotten".
Step-by-step explanation:
Write the quadratic function in the form f(x)=a(x-h)^2+k
Then, give the vertex of its graph.
f(x)=2x^2-20x+51
Answers
Answer:
hello : h =5 and K= 1
Step-by-step explanation:
look this solution :
As per the given quadratic function, the value of the vertex of the graph is written as (5, 1)
A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants, and a ≠ 0. However, the given quadratic function is already expressed in the desired form, f(x) = a(x - h)² + k, which is known as vertex form. In this form, (h, k) represents the coordinates of the vertex of the parabola.
Now, let's rewrite the given quadratic function f(x) = 2x² - 20x + 51 in the vertex form. To achieve this, we'll complete the square:
Step 1: Factor out the leading coefficient 'a' from the x² and x terms. f(x) = 2(x² - 10x) + 51
Step 2: Complete the square inside the parentheses by adding and subtracting the square of half of the coefficient of the x-term (in this case, -10/2 = -5, and (-5)² = 25). f(x) = 2(x² - 10x + 25 - 25) + 51
Step 3: Group the perfect square trinomial and the constant term inside the parentheses. f(x) = 2((x - 5)² - 25) + 51
Step 4: Distribute the leading coefficient 'a' back into the parentheses. f(x) = 2(x - 5)² - 50 + 51
Step 5: Combine the constants. f(x) = 2(x - 5)² + 1
Now, the quadratic function is in the form f(x) = a(x - h)² + k, where a = 2, h = 5, and k = 1.
Therefore, the vertex of the parabola is (h, k) = (5, 1).
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The width of a photograph is 4 inches. Tori measures its width using the two rulers, both of which measure in inches.
Which statement is true about the accuracy and precision of the rulers?
A The measurement found using Ruler 1 is more accurate and more precise.
B The measurement found using Ruler 2 is more accurate and more precise.
C The measurement found using Ruler 1 is more accurate but less precise.
D The measurement found using Ruler 1 is more precise but less accurate.
Answers
Answer:
a
Step-by-step explanation:
plato answer
Answer:
B The measurement found using Ruler 2 is more accurate and more precise.
Step-by-step explanation:
We have to understand the concept here for accuracy and precision.
Accuracy is against some standard. So it is the measured value which is closely against a standard. Accuracy is less if the measured value is deviated from the standard.
Precision is about how closely individually measured values agree with each other. Precision doesn't concern with the standard value.
Now, third concept is significant numbers. It is up to how much decimal numbers an instrument can produce a result.
In ruler 2, you can see that there are more divisions for a whole inch. This means that the ruler 2 can measure more nearly to the standard value, as well as, for repeated measurements, it can give more precised figures due to the ability to read up to more decimal numbers after the decimal point.
Which of these numbers are irrational?
17
, 0,
8
,
22
7
,
81
,
14
A)
17
,
14
B)
8
,
14
C)
17
,
22
7
,
14
D)
17
,
8
,
14
Answers
Answer:
its A
Step-by-step explanation:
Eli bought a jacket that was on sale at 40 percent off. The original price of the jacket was $60.00. How much did Eli pay?
Answers
Answer:
$36.00
Step-by-step explanation:
40% of 60 is 24. Subtract from the origanl amount, you get the price after sale, $36.00. Hope this helps :)
Which is the equation of the porabola with focus of (0,5) and directrix x= -5?
A) x^2 = -5y
B) x^2 = 5y
C)x^2 = 10y
D)x^2 = 20y
Please and thank you!
Answers
the answer is D) x^2 = 20y
A polynomial function has a zero at 4 (multiplicity 3) and 0 (multiplicity 1)
write is standard and simplifed form
Answers
Answer:
Y=3x(x-4)
Step-by-step explanation:
the area of a rectangle is 75 square centimeters the rectangle is 5 centimeters wide how long is the rectangle
Answers
Answer: 15 cm
Step-by-step explanation:
The formula for calculate the area of a rectangle is:
[tex]A=l*w[/tex]
Where "l" is the lenght and "w" is the width.
You know that the area of this rectangle is 75 square centimeters and the width is 5 centimeters. Then, you can substitute these values into the formula [tex]A=l*w[/tex] and solve for the lenght. Then you get:
[tex]75cm^2=l(5cm)\\\\\frac{75cm^2}{5cm}=l\\\\l=15cm[/tex]
Therefore, the lenght of the rectangle is 15 centimeters.
Answer:
15 centimeters.
Step-by-step explanation:
To find the area of a rectangle, you have to multiply the length by the width.
In this case, the width is 5 centimeters.
So, so find the area, you would have to multiply 5 by the length. Let's call the length "x".
The equation to solve this problem would be:
5x - 75
Now we can solve the equation...
Divide both sides by 5...
5x / 5 = 75 / 5
x = 15
Since x is equal to 15, that means that the length is 15, because we said that the length is equal to x.
Length = x = 15
------------------
Hope this helped!
What is the sum of the first 30 terms of this arithmetic sequence?
6, 13, 20, 27, 34, …
Answers
Answer:
3225
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1)d ]
where a is the first term and d the common difference
here a = 6 and
d = 13 - 6 = 20 - 13 = 7, hence
[tex]S_{30}[/tex] = [tex]\frac{30}{2}[/tex][ (2 × 6) + (29 × 7) ]
= 15(12 + 203) = 15 × 215 = 3225
Please help me. I'm still trying to understand parabolas. Find the axis of symmetry of the parabola.
a. y = 0
b. y = –1
c. x = 0
d. x = –1
Answers
I think the answer is b. y= -1
When solving the equation 3n^2 - 15n = 3 by completing the square what is your first step? Options are in the picture.
Answers
[tex]c. \: add \: 15n \: from \: each \: side.[/tex]
WILL GIVE BRAINLIEST
20 POINTS
Answers
Answer:
60
Step-by-step explanation:
If you do 25% + 6 * 10 , it gives you 62.5 and you round that and it's 60.
Answer:
60
Step-by-step explanation:
25% + 6 * 10
=62.5
round 62.5
=60.
Give brainliest plz :'D
Madeline had a pink dress , blue dress , and a yellow dress she has a black pair of shoes and a white pair of shoes how many outfits can she make
Answers
Answer: 6 outfits
Step-by-step explanation:
She can make 6 outfits out of the clothes given.
(p)=pink dress
(b)=blue dress
(y)=yellow dress
(bl)=black shoes
(w)=white shoes
p can combo with bl and w which makes 2 outfits
b can combo with bl and w which makes 2 outfits
y can combo with bl and w which makes 2 outfits
2+2+2=6 outfits
Find the values of x and y.
Answers
x = 90
y = 180 - (90 + 47)
y = 43
the mean (rounded to the nearest tenth if needed) of the following data set is: 110, 142, 120, 180, 151, 110, 159, 173, 173, 144, 110
A. 142.9
B. 157.2
C. 131
D. 146.8
Answers
Answer:
A
Step-by-step explanation:
Add up all of the numbers:
110+142+120+180+ 151+110+159+173+173+144+110 = 1572
Next you divide by how many number there are (there are 11 numbers)
1572 ÷ 11 = 142.9090909
142.9090909 rounded to the nearest tenth is 142.9
Answer:
A. 142.9
Step-by-step explanation:
There are 11 members in the data set, therefore:
The mean = (110+142+120+180+151+110+159+173+173+144+110) / 11
= 1572/11
= 142.9.
Triangle ABC is similar to triangle DEF . The length of AC is 10 cm. The length of BC is 15 cm. The length of DF is 6 cm.
What is the length of EF?
12
6
10
9
Answers
Answer:
9 cm
Step-by-step explanation:
Side lengths of similar triangles are proportional. BC is 1.5 times the length of AC, so EF will be 1.5 times the length of DF:
1.5·6 cm = 9 cm
Two quantities, and are directly proportional. If were tripled, what would happen to ? CLEAR CHECK It would be multiplied by 6. It would be multiplied by 13 . It would depend on the starting value of . It would be tripled. NEXT Reference calculator formulas glossary CLOSE Language ENGLISH CLOSE
Answers
Answer:
you are correct
Step-by-step explanation:
p.s the way you worded this was confusing
What is the ratio for the surface Areas of the rectangular prism’s shown below given that they are similar and that the ratio of the edge Lengths is 8:5
Answers
Answer:
[tex] \frac{ {8}^{2} }{ {5}^{2} } = \frac{64}{25} [/tex]
B) 64:25
Step-by-step explanation:
Ratio of Lengths = a/b
Ratio of Areas = a^2/b^2
Ratio of Volumes = a^3/b^3
PLEASE HELP! TRYING TO FINISH MATH EARLY! PLEASE ACTUALLY ANSWER, AND NOT JUST TAKE THE POINTS! Thank You! ;3
(05.06 MC)
Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
y > −4x − 1
y is less than 3 over 2 times x minus 1
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area.
Part B: Is the point (−1, −1) included in the solution area for the system? Justify your answer mathematically.
Answers
A) the graph is a linear and the slope is negative and positive .
B) (-1,-1) is not a solution because that point does not appear in the shaded region, therefore there is no solution.
:D
Are the two triangles similar? If so, state the reason and the similarity statement.
A. Impossible to determine.
B. The triangles aren't similar.
C. Yes; SSS; ΔAYM ∼ ΔEDC
D. Yes; SAS; ΔAYM ∼ ΔEDC
Answers
Answer:
D. would be your answer
Step-by-step explanation:
Yes, the triangles ΔAYM ∼ ΔEDC by SSS criterion of similarity.
What is similarity of triangles?If the respective angles are congruent and the corresponding sides are proportional, two triangles are said to be similar.
What is SSS similarity of triangles?The two triangles are similar if the three sides of one triangle are proportional to the three sides of the other.
According to SSS criterion of similarity:
CE / AM = ED / AY = CD / MY
3 / 6 = 4 / 8 = 5 / 10
1/2 = 1/2 = 1/2
Hence ΔAYM and ΔEDC are similar by SSS criterion of similarity.
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which of the following best describes the shape of the slice of pizza shown in the figure?
Answers
Answer:
Option D. A sector
Step-by-step explanation:
we know that
A circular sector is the portion of the circle enclosed by two radii and an arc
so
In this problem we have a slice of the pizza enclosed by two radii and an arc
therefore
The shape of the slice is a sector
Answer:
Option C is correct: A Sector
Step-by-step explanation:
A-p-e-x :)
The population of a town can be modeled by the regression equation y = 18,000(1.04x). Which is the best prediction for the population in year 30?
A. 39,440
B. 58,381
C. 68,298
D. 68,298
Answers
Answer:
Hence correct choice is B. 58,381
Step-by-step explanation:
Given equation is [tex]y=18000(1.04)^x[/tex].
There x represents number of years. We need to find about which is the best prediction for the population in year 30.
To find that we will plug x=30 into above formula and simplify
[tex]y=18000(1.04)^x[/tex]
[tex]y=18000(1.04)^{30}[/tex]
[tex]y=18000(3.24339751003)[/tex]
[tex]y=58381.1551805[/tex]
Which is approx 58381
Hence correct choice is B. 58,381.