Answers
The approximation of the area of f(x) = x² + 2x, from x = 2 to x = 10, is given as follows:
320 units squared.
How to approximate the area?The area under a curve is approximated using the definite integral of the function that defines the curve within it's bounds.
As it is specified that the area should be approximated using rectangles, a Left Riemann Sum will be used to approximate the area.
First we must obtain the Delta value, which is the difference between the bounds of the integral, divided by the number of intervals, thus, considering four intervals, we have that:
[tex]\Delta_x = \frac{10 - 2}{4} = 2[/tex]
Then the values of x at which the numeric values are calculated are obtained as follows:
[tex]x_i = a + \Delta_x(i - 1)[/tex]
Thus the values of x are of:
[tex]x_1 = 2[/tex][tex]x_2 = 4[/tex][tex]x_3 = 6[/tex][tex]x_4 = 8[/tex]The numeric values are given as follows:
f(2) = 2² + 2(2) = 8.f(4) = 4² + 2(4) = 24.f(6) = 6² + 2(6) = 48.f(8) = 8² + 2(8) = 80.Then the definite integral is obtained as follows:
[tex]\sum_{i = 1}^n \Delta_x f(x_i)[/tex]
Meaning that the result of the integral is of:
2(8 + 24 + 48 + 80) = 320 units squared.
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Related Questions
What is the X intercepts of f(x) =-2x^2 + 10x - 7
Answers
Select the correct answer from each drop-down menu. A graph of quadrilateral 1 with the nodes of (minus 3, 7), (minus 4, 9), (minus 7, 9), and (minus 4, 5). Transformation of quadrilateral 2 with the nodes of (3, minus 4), (3, 6), (8, 2.8), and (7.2, minus 1.9). Quadrilateral 1 and quadrilateral 2 are polygons that can be mapped onto each other using similarity transformations. The transformation that maps quadrilateral 1 onto quadrilateral 2 is a followed by a dilation with a scale factor of .
Answers
This transformation of the polygon ABCD to A'B'C'D' is a by a factor of 2√5.
The coordinates are given as:
First polygon: A (-3, 7), B (-4, 9), C (-7, 9), and D (-4, 5).
Second polygon: A' (3, -4), B'(3, 6), C'(8, 2.8), and D'(7.2, -1.9)
Calculate the distance AB and A'B' using:
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
⇒ AB = √ (-4 + 3)² + (9 - 7)²
⇒ AB = √1 + 4
⇒ AB = √5
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
⇒ A'B' = √ (3 - 3)² + (6 + 4)²
⇒ A'B' = 10
This gives, Divide A'B' by AB to determine the scale factor (k)
k = 10 / √5
k = 2√5
Hence, this transformation is a by a factor of 2√5
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Answer:
Reflection and 2
Step-by-step explanation:
for plato
At Chairs and More, assemblers are paid according to the following differential piece rate scale: 1−25 chairs in a week, $10 each; 26−40 chairs, $13 each; and $17.50 each for every chair over 40. Salina Grant assembled 47 chairs in one week. Find her gross pay.
Answers
Answer:
To find Salina Grant's gross pay, we need to calculate the pay for each range and add them together.
For the first 25 chairs, Salina will be paid $10 for each chair, so her pay for this range is:
25 chairs x $10 per chair = $250
For the next 15 chairs (26-40), Salina will be paid $13 for each chair, so her pay for this range is:
15 chairs x $13 per chair = $195
For the remaining 7 chairs (over 40), Salina will be paid $17.50 for each chair, so her pay for this range is:
7 chairs x $17.50 per chair = $122.50
Adding up all three ranges, Salina's gross pay is:
$250 + $195 + $122.50 = $567.50
Therefore, Salina Grant's gross pay for assembling 47 chairs in one week is $567.50.
Step-by-step explanation:
This month my metro water services bill was $36.34 and my Madison Suburban Utilty District bill was $26.03. My total water bill was $
Answers
Total water bill for the month is $62.37.
It seems that you may have accidentally left out the total amount of your water bill.
The total amount by simply adding the amounts of the individual bills together:
Total water bill =[tex]$36.34 + $26.03[/tex]
= [tex]$62.37[/tex]
You have not provided enough information to determine your total water bill.
You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.
To find your total water bill, you simply need to add the two bills together.
So, the total amount you owe for water this month would be:
Total water bill = [tex]$36.34 + $26.03[/tex]
= [tex]$62.37[/tex]
It appears that you may have forgotten to include the full amount of your water bill by accident.
Simple addition of the separate bill amounts yields the following sum:
Water bill total = [tex]$36.34 + $26.03[/tex]
= [tex]$62.37[/tex]
Your total water bill cannot be calculated because not enough information has been given.
Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.
You just need to combine the two invoices together to get your total water bill.
As a result, this month's total water bill for you would be:
Water bill total = [tex]$36.34 + $26.03[/tex]
= [tex]$62.37[/tex]
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A track coach recorded the time it took for each of her athletes to run a mile. She plans to display the results with a histogram. Which of the following will it show? Select all that apply. (please help as soon as possible. thanks :))
Answers
The histogram will show the distribution of the athletes' mile running times. It will provide a visual representation of the frequency or count of athletes falling within different time intervals.
1. Determine the time intervals or "bins" for the histogram. For example, you might have bins of 5-second intervals, such as 0-5 seconds, 5-10 seconds, and so on.
2. Count the number of athletes who fall within each bin. For instance, if three athletes completed the mile in the 0-5 second bin, and five athletes completed it in the 5-10 second bin, record those counts.
3. Plot the bins on the x-axis of the histogram and the corresponding frequency or count on the y-axis.
4. Draw rectangles (or bars) on the histogram, with the height of each bar representing the frequency or count of athletes within each bin.
5. Label the axes and add a title to the histogram for clarity.
The resulting histogram will provide a visual representation of how the athletes' mile running times are distributed, allowing you to observe any patterns or trends.
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Consider the following symbolic logic statement: ¬ (∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y))
a) Translate the statement into English using proper syntax and semantics.
b) Identify and explain any potential ambiguities in the translated statement.
c) Rewrite the statement in a way that eliminates any ambiguities and maintains the original meaning.
Answers
a) The given symbolic logic statement can be translated into English as follows:
"Not exists x such that (P(x) and Q(x)), and for all y, if R(y) then P(y)."
b) Potential ambiguities in the translated statement:
The scope of the negation symbol "¬" is not explicitly defined. It can be interpreted as applying only to the first part of the statement or to the entire statement.
The scope of the quantifiers (∃x) and (∀y) is not explicitly defined. It is unclear which parts of the statement they apply to.
c) To eliminate ambiguities while maintaining the original meaning, the statement can be rewritten as follows:
"(∀x)(¬(P(x) ∧ Q(x))) ∧ (∀y)(R(y) → P(y))"
How to explain the informationIn the revised statement: The negation symbol "¬" applies to the entire first part of the statement, indicating that there does not exist any x for which both P(x) and Q(x) are true.
The quantifiers (∀x) and (∀y) explicitly indicate that the following predicates apply universally to all values of x and y.
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Dana had to pay her friend $900, 3 months ago and she has to pay $580 in 3 months. If her friend was charging her an interest rate of 1.50% per month, what single payment would settle both payments today?
Answers
Dana had to pay her friend $900, 3 months ago, and she has to pay $580 in 3 months. If her friend was charging her an interest rate of 1.50% per month. $1499.45, single payment would settle both payments today.
Given:
The principal of a loan is the original sum borrowed.The interest rate per period is known as rate.The loan's duration is expressed in terms of time.Simple interest = Principal × Rate × Time
Simple interest = $900 × 0.015 × 3
Simple interest = $40.50
Present Value = Future Value / (1 + Rate x Time)
Present Value = $580 / (1 + 0.015 × 3)
Present Value = $580 / 1.045
Present Value = $558.95
Total amount $580 loan is $558.95.
Total amount owed = $940.50 + $558.95
Total amount owed = $1499.45
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Which represents "5 subtracted from 3 times p"? A. 5 - 3p B. (5 - 3)p C. 3p - 5 D. p3 - 5
Answers
The algebraic expression for the sentence "5 subtracted from 3 times p" is given as follows:
A. 5 - 3p.
How to obtain the algebraic expression?
The sentence in the context of this problem is defined as follows:
"5 subtracted from 3 times p"
The expression that represents 3 times p is given as follows:
3p.
(that is, 3 and p are multiplied).
Then 5 subtracted from 3 times p means that the number 5 subtracts the above expression, hence the expression is given as follows:
5 - 3p.
Meaning that option A gives the correct answer in the context of this problem.
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Kenya wants to open a savings account at a bank. The bank offers a savings account that pays
out 8% annual interest. If Kenya wants at least $7,000 in his account after 15 years, how much does
Kenya need to put in the account initially?
Answers
Kenya needs to initially put in the amount of $2,208.2in the account to have at least $7,000 after 15 years.
We can use the formula for compound interest:
A = P(1 + r/n)ⁿ
where A is the amount of money in the account after t years, P is the initial principal, r is the annual interest rate (as a decimal), and n is the number of times per year the interest is compounded.
Here, we want to find P, so we can rearrange the formula as:
P = A / (1 + r/n)ⁿ
We are given that r = 0.08 (8% interest) and n = 1 (interest is compounded annually).
We also know that A = $7,000 and t = 15 years.
So we can plug in these values and solve for P:
P = 7000 / (1 + 0.08/1)¹⁵
P = 7000 / (1.08)¹⁵
P ≈ $2,208.2
Therefore, Kenya needs to initially put in approximately $2,208.2in the account to have at least $7,000 after 15 years.
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NO LINKS!!!! URGENT HELP PLEASE!!!!!
Find the area of ΔABC
5. B= 141°, a = 7, c = 8
6. C=70°, a=30, b= 24
7. A = 100°, b = 20, c = 25
Answers
Answer:
5) 17.62 units² (2 d.p.)
6) 338.29 units² (2 d.p.)
7) 246.20 units² (2 d.p.)
Step-by-step explanation:
To find the area of a triangle given two sides and the included angle, use the Sine Rule (Area of a Triangle) formula:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Sine Rule (Area of a triangle)}\\\\$A=\dfrac{1}{2}ab \sin C$\\\\\\where: \\ \phantom{ww}$\bullet$ $a$ and $b$ are adjacent sides. \\ \phantom{ww}$\bullet$ $C$ is the includ\:\!ed angle.\\\end{minipage}}[/tex]
[tex]\hrulefill[/tex]
Question 5Given values:
a = 7c = 8B = 141°The two sides of the triangle are 'a' and 'c', and the included angle is 'B'.
Substitute the given values into the formula and solve for area:
[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} ac \sin B\\\\&=\dfrac{1}{2} \cdot 7 \cdot 8 \cdot \sin 141^{\circ}\\\\&= 28 \sin 141^{\circ}\\\\& = 17.6209709...\\\\&= 17.62\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Question 6Given values:
a = 30b = 24C = 70°The two sides of the triangle are 'a' and 'b', and the included angle is 'C'.
Substitute the given values into the formula and solve for area:
[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} ab \sin C\\\\&=\dfrac{1}{2} \cdot 30\cdot 24 \cdot \sin 70^{\circ}\\\\&= 360\sin 70^{\circ}\\\\&= 338.289343...\\\\& = 338.29\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Question 7Given values:
b = 20c = 25A = 100°The two sides of the triangle are 'b' and 'c', and the included angle is 'A'.
Substitute the given values into the formula and solve for area:
[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} bc \sin A\\\\&=\dfrac{1}{2} \cdot 20 \cdot 25 \cdot \sin 100^{\circ}\\\\&= 250 \sin 100^{\circ}\\\\&= 246.201938...\\\\& = 246.20\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]
Triangle ABC is shown. Use the graph to answer the question.
triangle ABC on a coordinate plane with vertices at 1 comma negative 2, 9 comma negative 2, 5 comma 2
Determine the coordinates of the image if triangle ABC is translated 5 units down.
A′(−4, −2), B′(4, −2), C′(0, 2)
A′(1, −7), B′(9, −7), C′(5, −3)
A′(1, 3), B′(9, 3), C′(5, 7)
A′(6, −2), B′(14, −2), C′(10, 2)
Answers
If triangle ABC is translated 5 units down, the coordinates of the image vertices are A′(1, −7), B′(9, −7), C′(5, −3).
The correct option among the given choices is A′(1, −7), B′(9, −7), C′(5, −3).
To determine the coordinates of the image if triangle ABC is translated 5 units down, we need to subtract 5 from the y-coordinate of each vertex of the triangle.
The given vertices of triangle ABC are A(1, -2), B(9, -2), and C(5, 2).
To translate the triangle 5 units down, we subtract 5 from the y-coordinate of each vertex.
The new coordinates of the vertices after the translation are:
A': (1, -2 - 5) = (1, -7)
B': (9, -2 - 5) = (9, -7)
C': (5, 2 - 5) = (5, -3)
Therefore, the correct option among the given choices is A′(1, −7), B′(9, −7), C′(5, −3).
In summary, if triangle ABC is translated 5 units down, the coordinates of the image vertices are A′(1, −7), B′(9, −7), C′(5, −3).
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Brandon has 4 cups of powdered sugar. He sprinkles 1/10 of the sugar onto a plate of brownies and sprinkles the rest onto a plate of lemon cookies. How much sugar does Brandon sprinkle on the brownies?
Answers
Based on the fraction of the sugar sprinkled on the Brownies, Brandon sprinkles 0.4 cups of sugar on the brownies
How much sugar does Brandon sprinkle on the brownies?The amount of sugar sprinkled on the Brownies by Brandon is determined as follows:
Data given:
Brandon sprinkles 1/10 of the sugar onto the plate of brownies
Since he has 4 cups of powdered sugar in total
The amount of sugar he sprinkles on the brownies can be calculated as:
amount of sugar = fraction of sugar sprinkled * total amount of sugarThe amount of sugar he sprinkles on the brownies = 1/10 * 4 cups
The amount of sugar he sprinkles on the brownies = 0.4 cups
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Based on the picture above, what is the solution to the system of equations?
Type a response
Answers
Step-by-step explanation:
The 'solution ' is the point where the two lines intersect : ( 0,-1)
Which point would be a solution to the system of linear inequalities shown below?
Answers
Answer:
(-2, 10)
Step-by-step explanation:
You want the point that would be a solution to the inequalities ...
y ≥ 5/2x +2y ≥ -4x -7GraphIt can be useful to graph the inequalities, or develop a mental picture of what the graph would look like. Both boundary line slopes are fairly steep, and the lines cross in the third quadrant. The V-shaped space above that intersection is the solution space.
The attachment shows the point (-2, 10) is a solution.
Try the answersFrom the shape and location of the solution space, we can eliminate the choices ...
(-8, 2) — too close to the x-axis in the far left part of the 2nd quadrant
(10, -3) — no part of the 4th quadrant is in the solution space
General formIt can work nicely to rewrite the inequalities as a comparison to zero.
5x -2y +4 ≤ 0 . . . . . the first inequality in general form
point (-2, 10): 5(-2) -2(10) +4 = -10 -20 +4 = -26 ≤ 0 . . . a solution
point (4, 9): 5(4) -2(9) +4 = 20 -18 +4 = 6 > 0 . . . . . . . not a solution
4x +y +7 ≥ 0 . . . . . . the second inequality in general form
point (-2, 10): 4(-2) +(10) +7 = -8 +10 +7 = 9 ≥ 0 . . . . . . a solution
point (4, 9): don't need to test (already known not a solution)
Point (-2, 10) is a solution.
__
Additional comment
We chose the use of "general form" inequalities for evaluating answer choices because ...
the arithmetic is mainly with positive integers (no fractions)the comparison to zero does not require a lot of mental effort<95141404393>
3. How does the percentage of people who would borrow from some financial institution compare to
the percentage of people who would borrow from friends or family?
Answers
The percentage of people borrowing from financial institutions generally exceeds borrowing from friends or family due to formality, legal protection, larger loan amounts, privacy, expertise, and long-term implications.
The percentage of people who would borrow from a financial institution compared to the percentage of people who would borrow from friends or family can vary depending on various factors such as cultural norms, economic conditions, individual preferences, and access to financial services. However, in general, borrowing from financial institutions is often more common and prevalent than borrowing from friends or family for several reasons.
Formality and Legal Protection: Borrowing from financial institutions offers a more formal and legally protected process. When individuals borrow from a financial institution, they enter into a contractual agreement that outlines the terms and conditions of the loan. This agreement provides a legal framework that protects both the borrower and the lender. In contrast, borrowing from friends or family often lacks the same level of formality and legal protection, which can lead to ambiguity and strain personal relationships.
Access to Larger Loan Amounts: Financial institutions typically have more capital and resources to lend larger amounts of money compared to friends or family members. If someone requires a substantial loan, such as for purchasing a home or starting a business, they are more likely to turn to a financial institution. These institutions have processes in place to evaluate creditworthiness, collateral, and other factors, allowing them to provide loans that meet the borrower's specific needs.
Privacy and Independence: Borrowing from a financial institution offers a level of privacy and independence that may be preferred by individuals. Some people might feel uncomfortable disclosing personal financial details or discussing their financial challenges with friends or family. Financial institutions provide a professional environment where individuals can maintain privacy and retain control over their financial matters.
Expertise and Financial Advice: Financial institutions employ professionals with expertise in lending and financial management. When borrowing from a financial institution, borrowers can benefit from the advice and guidance of these professionals. They can help borrowers understand the terms of the loan, explore different options, and make informed financial decisions. Friends and family members may not possess the same level of financial knowledge or experience, limiting their ability to provide comprehensive advice.
Long-Term Implications: Borrowing from friends or family can have long-term implications for personal relationships. Financial transactions have the potential to create tension, conflicts, or misunderstandings among individuals, especially if there are difficulties in repaying the borrowed amount. Relying on financial institutions can help maintain healthy personal relationships, as the borrowing and lending processes are conducted on a professional level, minimizing the emotional and relational strain that can arise from borrowing from loved ones.
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helpppppppppp meeeeee please
Answers
Answer: D. <4 and <7
Step-by-step explanation:
Consecutive means one after the other
Interior means within the parallel lines
So we are looking for 2 to angles inside the parallelel lines that are 1 after the other on the same side
D. <4 and <7
This exercise uses the normal probability density function and requires the use of either technology or a table of values of the standard normal distribution. The cash operating expenses of the regional phone companies during the first half of 1994 were distributed about a mean of $29.96 per access line per month, with a standard deviation of $2.25. Company A's operating expenses were $28.00 per access line per month. Assuming a normal distribution of operating expenses, estimate the percentage of regional phone companies whose operating expenses were closer to the mean than the operating expenses of Company A were to the mean. (Round your answer to two decimal places.)
Answers
The probability of the values of X that are less than 21 is 0.97725.
We have,
The term "standard deviation" refers to a measurement of the data's dispersion from the mean.
A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Given:
u = 20
and SD = 2.25
To find P(X < 21)
So, P(X < 21 )
= 1 - P(X > 21)
Now, P(X > 21)
= P(Z > [(21–20)/2.25]
= P( Z > 1/2.25)
= P(Z > 0.444)
= 0.02275
So, the required probability = P(Z < 21) = 1 - 0.02275= 0.97725
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complete question:
Let X be a normally distributed random variable with a mean of 20 and a standard deviation of 2.25. Using Excel, find the proportion of the values of X that are less than 21.
Please help me anwser this
Answers
The values are given as:
a. Mean = 19
Median = 20
Mode = 22
Standard deviation = 7.2
Range = 24
b. Mean = 75
Median = 80
Mode = 90
Standard deviation = 16
Range = 100
What the measures of central tendency?The three measures of central tendency include;
MeanModeMedianThe measures of dispersions are;
Rangeinterquartile range standard deviationFrom the information given, if 4 is added to all the measures, we get;
Mean = 15 + 4 = 19
Median = 16 + 4 = 20
Mode = 18 + 4 = 22
Standard deviation = 3.2 + 4 = 7.2
Range = 20 + 4 = 24
If the values are multiplied by 5
Mean = 15(5) = 75
Median = 16(5) = 80
Mode = 18(5) = 90
Standard deviation = 3.2(5) = 16
Range = 20(5) = 100
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30 POINTS, MULTIPLE CHOICE, TIME SENSITIVE!!
Select the correct answer.
Use a graphing tool to solve the equation for x.
-4x-1= 5x + 4
Answers
Answer: x= —5/9
Step-by-step explanation:
Which graph represents the solution to the following problem? y < |x+3|
Answers
The graph that shows the solution set of the inequality is the second one.
Which graph represents the solution set of the inequality?Here we have the following inequality:
y < |x + 3|
Notice that we have the symbol "<", then we know that the graph of the absolute value must be with dashed lines (because the points that lie on the graph aren't solutions).
Also, y is smaller than that, then the shaded region must be below the graph.
With that in mind, we conclude that the correct option is the second one.
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Bill checked out 5 books from the library. Hazel checked out b fewer books than Bill. Choose the expression that shows the number of books Hazel checked out.
Answers
The solution is : (5-b ) is the expression that shows the number of books Hazel checked out.
Here, we have,
given that,
Bill checked out 5 books from the library.
Hazel checked out b fewer books than Bill.
now, we have to find the expression that shows the number of books Hazel checked out.
let,
that shows the number of books Hazel checked out = x
so, we have,
that shows the number of books Hazel checked out = b fewer books than Bill.
as, Bill checked out 5 books from the library.
so, we get,
the number of books Hazel checked out = 5 - b
so, we have,
x = 5-b
Hence, The solution is : (5-b ) is the expression that shows the number of books Hazel checked out.
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50 Points! Multiple choice algebra question. Photo attached.
Answers
The period of the function is given as follows:
C) 4.
How to obtain the period of the function?A periodic function is a function that has the behavior repeating in intervals over the domain.
Then the period of the function is defined as the difference between two points in which the function has the same behavior.
The function in this problem has the behavior repeating at these following points:
x = 0, x = 4, x = 8, ...
Hence the period is given as follows:
4 - 0 = 8 - 4 = 4.
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Solve the system of equations :-)
Thank you
Answers
4x - y + 3z = 12 ...(1)
2x + 9z = -5 ...(2)
x + 4y + 6z = -32 ...(3)
From equation (2), we can express x in terms of z:
2x = -9z - 5
x = (-9z - 5) / 2 ...(4)
Substitute equation (4) into equations (1) and (3):
From equation (1):
4((-9z - 5) / 2) - y + 3z = 12
-18z - 10 - y + 3z = 12
-15z - y = 22 ...(5)
From equation (3):
((-9z - 5) / 2) + 4y + 6z = -32
-9z - 5 + 8y + 12z = -64
3z + 8y = -59 ...(6)
Now we have a system of two equations in terms of y and z.
To solve the system, let's multiply equation (5) by 3 and equation (6) by 15 to eliminate z:
-45z - 3y = 66 ...(7)
45z + 120y = -885 ...(8)
Add equations (7) and (8):
-3y + 120y = 66 - 885
117y = -819
y = -7
Substitute y = -7 into equation (7):
-45z - 3(-7) = 66
-45z + 21 = 66
-45z = 45
z = -1
Substitute y = -7 and z = -1 into equation (4):
x = (-9(-1) - 5) / 2
x = (9 - 5) / 2
x = 2
Therefore, the solution to the system of equations is:
x = 2
y = -7
z = -1
I need help please with this question
Answers
The approximation of [tex]\sqrt{44}[/tex], to the hundredths place, is given as follows:
[tex]\sqrt{44} = 6.63[/tex]
How to estimate a non-exact square root?The estimate of a non-exact square root of x is done finding two numbers, as follows:
The greatest number less than x that is a perfect square, which we call a.The smallest number greater than x that is a perfect square, which we call b.For this problem, we want to estimate the root to the hundredth's place, hence the number that we must compare is:
44 x 10^4 = 440000.
(as each 10² is equivalent to the square root of a decimal digit).
Then the numbers are:
663² = 439569 < 440000.664² = 440896 > 440000.Hence the square root is approximated as follows:
663/100 = 6.63.
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HELP PLS !% POINTS!!
Answers
Answer:
149 sq. ft
Step-by-step explanation:
For the triangle:
Base = 16-9 = 7 ft
Area of Triangle = 1/2 of b.h
= 1/2 of 7 * 6
= 21 sq. ft
Area of Rectangle = l.b
= 5 * 16
= 128 sq. ft
Total Area = 149 sq. ft
8. For positive real numbers a, b, and c, the expressions albici and Vabac are equivalent. What are the values
of p, q, and r?
Answers
Answer:
Step-by-step explanation:
To find the values of p, q, and r in the expression albici = Vabac, we need to equate the corresponding parts on both sides.
From the given equation, we have:
p * (a * b) * (c * i) = q * (a * b * a * c)
Comparing the exponents of a, b, and c on both sides, we get:
p = q * a^2
1 = q * c
To determine the value of r, we can use the fact that albici and Vabac are equivalent. The radical symbol (√) represents taking the square root.
√(a * b * c * i) = √(a * b * a * c)
This implies that:
√(a * b * c * i) = √(a^2 * b * c)
Comparing the exponents of a, b, and c on both sides, we get:
1/2 = 2 * p * q * r
Combining all the equations, we have:
p = q * a^2
1 = q * c
1/2 = 2 * p * q * r
To find the specific values of p, q, and r, we need additional information or equations involving a, b, and c. Without more context or equations, it is not possible to determine the exact values of p, q, and r.
Find the simple interest owed if $340 is borrowed at 6.6% for 9 years
Answers
The simple interest owed on a $340 loan at 6.6% interest for 9 years is $201.96.
How to find simple interest?The simple interest formula is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given that:
Principal P = $340
Interest Rate r = 6.6%
Time t = 9 years
First convert the interest rate from percent to decimal:
Rate = r/100
Rate = 6.6/100
Rate = 0.066
Now, plug the values into the above formula and solve for interest.
I = P × r × t
I = $340 × 0.066 × 9
I = $201.96
Therefore, the simple interest is $201.96.
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Exam the following data set.
{8,19,11,20,2,14,17,9,15}
Which answer shows the five number summary that could be used to create a box plot for this data?
Answers
The five number summary of the data set for the box plot would be :
Minimum value: 2Q1 : 9Median : 14Q3 : 19Maximum value: 20How to find the five number summary ?First, order the numbers in ascending order:
2, 8, 9, 11, 14, 15, 17, 19, 20
The minimum is the smallest number which is 2. The maximum is the largest number which is 20.
The median is the number in the middle which is 19. The Q1 is the number in the middle of the first half of the numbers which is 9. The Q3 is the number in the middle of the second half which is 19.
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Answer:
min=2
1st quartile= 8.5
median=14
3rd quartile=18
max=20
Step-by-step explanation:
Hii please answer i would appreciate it thankssss
Answers
a) The triangles are congruent by the AAA criterion.
b) The triangles are congruent by the SAS criterion.
a) In the first triangle the interior angles are 40 degrees and 30 degrees.
The other interior angle would be 180 - (40 + 30) = 110 degrees.
As per the diagram, the triangles have equal proportionate-sized side lengths.
Therefore, the triangles are congruent by the AAA criterion.
b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.
Therefore, the triangles are congruent by the SAS criterion.
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1. Drag the cards so that each number sentence is true. (You will have one card left over.)
2. Describe your thinking.
Answers
The numbers arranged in the correct order are:
-3 = -3
-3 < | -1 |
0 < | 1 |
2 > | 0 |
3 > | 1 |
We have,
-3 = -3:
This is a true statement because -3 is indeed equal to -3.
-3 < | -1 |:
This is also a true statement.
The absolute value of -1 is 1, so we are comparing -3 and 1.
Since -3 is less than 1, the inequality is true.
0 < | 1 |:
Again, this is a true statement.
The absolute value of 1 is 1, so we are comparing 0 and 1.
Since 0 is less than 1, the inequality holds true.
2 > | 0 |:
This is also a true statement.
The absolute value of 0 is 0, so we are comparing 2 and 0.
Since 2 is greater than 0, the inequality is true.
3 > | 1 |:
Once again, this is a true statement.
The absolute value of 1 is 1, so we are comparing 3 and 1.
Since 3 is greater than 1, the inequality holds true.
Therefore,
By arranging the given numbers in this order: -3, -3, -1, 0, 1, 2, 3, all of the number sentences become true.
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