Answers
i) It has been proven that CD/GH = AC/FG by Corresponding Sides of Similar Triangles
ii) △DCB ∼△HGE by the AA criterion of similarity
iii) △DCA ∼△HGF by the AA criterion of similarity
How to solve similar triangles?In △ABC and △FEG, we are told that they are similar and as such we can denote as:
△ABC ∼ △FEG
Thus, we can say that:
∠ACB = ∠EGF (Corresponding angles of similar triangles)
We are told that, CD and GH are bisectors of ∠ACB and ∠EGH respectively and as such we can say that:
∠ACB = 2∠ACD = 2∠BCD
∠EGF = 2∠FGH = 2∠HGE
Thus, by substitution, we can say that:
∠ACD = ∠FGH and ∠DCB = ∠HGE ...................(1)
Similarly:
∠A = ∠F and ∠B = ∠E ...............(2)
With respect to equations 1 and 2 we can establish that:
△ACD ∼ △FGH by the AA criterion of similarity
Similarly, △DCA ∼△HGF
Thus:
CD/GH = AC/FG (Corresponding Sides of Similar Triangles)
Similarly, In △DCB and △HGE, we can also establish that
△DCB ∼△HGE by the AA criterion of similarity
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Related Questions
The space shuttle carries c pounds of cargo, and each piece of cargo weighs 162.68 pounds. Which of the following expressions represents the number of pieces of cargo?
Answers
The expression which represents the number of pieces of cargo is c/162.68 = x, where c is the weight of the cargo in pounds, and x is the number of pieces of cargo.
Given that the space shuttle carries c pounds of cargo, and each piece of cargo weighs 162.68 pounds. We have to determine which of the following expressions represents the number of pieces of cargo.
Let's assume that the number of pieces of cargo be x.
Therefore, the weight of x pieces of cargo will be 162.68x = weight of cargo. The expression which represents the number of pieces of cargo can be written as: c/162.68 = x
This is because the total weight of the cargo is c pounds, and we know that each piece weighs 162.68 pounds.
Therefore, to find the number of pieces, we can divide the total weight by the weight of each piece, which gives us the expression c/162.68 = x, where x is the number of pieces of cargo.
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Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 2 14 9 25
Female 6 4 19 29
Total 8 18 28 54
If one student is chosen at random,
Find the probability that the student was female OR got an "A".
Round answer 4 places after the decimal if needed.
Answers
The answer to four decimal places, the probability is approximately 0.6481.
To find the probability that a randomly chosen student is either female or received an "A," we need to calculate the sum of the probabilities of these two events occurring individually and subtract the probability of both events occurring simultaneously.
Let's start by calculating the probability of selecting a female student. From the given information, we know that there are 29 female students out of a total of 54 students. Therefore, the probability of selecting a female student is 29/54.
Next, we need to determine the probability of selecting a student who received an "A." Looking at the table, we can see that there are a total of 8 students who received an "A" grade out of 54. Hence, the probability of selecting a student who received an "A" is 8/54.
To find the probability of both events occurring, we need to consider the intersection of the two events, which is the set of female students who also received an "A." According to the table, there are 2 female students who received an "A." Therefore, the probability of selecting a female student who received an "A" is 2/54.
Now, we can calculate the probability of selecting a female student OR a student who received an "A" by summing the individual probabilities and subtracting the probability of both events occurring simultaneously:
Probability (Female OR "A") = Probability (Female) + Probability ("A") - Probability (Female AND "A")
= 29/54 + 8/54 - 2/54
= 35/54
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Please help ASAP !! I will give 10 points to the correct answer
Answers
The Rational Roots Theorem indicates that the set of possible rational roots for the polynomial x³ + 5·x² - 8·x - 20 = 0, is the option C
C. ±1, ±2, ±4, ±5, ±10, ±20
What is the Rational Roots Theorem?The Rational Roots Theorem states that if p/q is a rational root of a polynomial with integer coefficients, where p and q have only 1 as their common factor, then p must be a factor of the constant term and q must be a factor of the leading coefficient.
The Rational Root Theorem indicates that where the number p/q is a rational root of the polynomial, then p is a factor of the constant term -20, and q is a factor of leading coefficient 1
The factors of -20 are; ±1, ±2, ±4, ±5, ±10 and ±20
The factors of 1 is; 1
Therefore the possible values of p/q are; ±1, ±2, ±4, ±5, ±10 and ±20
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Please Solve, Thank you!
Answers
For the function g(x) graphed above, the limits should be identified as follows;
a. A. [tex]\lim_{x \to -4} g(x)=0[/tex]
b. A. [tex]\lim_{x \to -3} g(x)=-1[/tex]
c. B. [tex]\lim_{x \to 0} g(x)[/tex] does not exist.
d. B. [tex]\lim_{x \to 0} g(x)[/tex] does not exist.
What is a function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables, graphs, or relations.
Part a.
By critically observing the graph of this function, g(x), we can reasonably infer and logically deduce that as x tends towards negative four, g(x) tends towards positive zero;
[tex]\lim_{x \to -4} g(x)=0[/tex]
Part b.
By critically observing the graph of this function, g(x), we can reasonably infer and logically deduce that as x tends towards negative three, g(x) tends towards negative one;
[tex]\lim_{x \to -3} g(x)=-1[/tex]
Part c and d.
By critically observing the graph of this function, g(x), we can reasonably infer and logically deduce that [tex]\lim_{x \to 0} g(x)[/tex] does not exist because the graph jumps and approaches both −1 and 1 as x → 0.
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HELPPPP!!!!!!!!Fill in the table using this function rule.
Answers
Answer:
This is not the answer but if u have Spanchat you can go to the AI and ask him to fill in the table using this function rule, list x, and then put the equation and he'll give you the table
Step-by-step explanation:
[tex] \huge{ \tt{ \boxed{ \tt{answer}}}}[/tex]
★Refer the attachment mate!! Follow for more★
. Write the equation of a line with a slope of 4 passing through the point (3, 1). Write the
equation in slope-intercept form.
Answers
Answer:
y = 4x - 11
Step-by-step explanation:
The general equation of the slope-intercept form of a line is given by:
y = mx + b, where
(x, y) are any point on the line,m is the slope,and b is the y-intercept.We can find b, the y-intercept of the line, by plugging in 4 for m and (3, 1) for (x, y) in the slope-intercept form:
1 = 4(3) + b
1 = 12 + b
-11 = b
Thus, the y-intercept is -11.
Thus, the equation of the line with a slope of 4 passing through the point (3, 1) in slope-intercept form is y = 4x - 11
The answer is:
y = 4x - 11Work/explanation:
First, we will write the equation in point slope:
[tex]\sf{y-y_1=m(x-x_1)}[/tex]
where m = slope;
(x₁,y₁) is a point on the line.
Plug in the data:
[tex]\sf{y-1=4(x-3)}[/tex]
Simplify
[tex]\sf{y-1=4x-12}[/tex]
Add 1 on each side
[tex]\sf{y=4x-12+1}[/tex]
[tex]\sf{y=4x-11}[/tex]
Hence, the equation is y = 4x - 11.Consider the function h(x)=12x−3 with a restricted domain of {−2, 0, 2, 10} . What is the range of the function? Responses {−2, 0, 2, 10} {−2, 0, 2, 10} all real numbers all real numbers {−4, −3, −2, 2} {−4, −3, −2, 2} the set of integers the set of integers
Answers
The range of the function h(x) with the restricted domain of {-2, 0, 2, 10} is {-27, -3, 21, 117}. Therefore, the correct response is {−27, -3, 21, 117}.
To find the range of the function h(x) = 12x - 3 with the restricted domain of {-2, 0, 2, 10}, we need to evaluate the function for each value in the domain and determine the corresponding range values.
For x = -2:
h(-2) = 12(-2) - 3 = -24 - 3 = -27
For x = 0:
h(0) = 12(0) - 3 = 0 - 3 = -3
For x = 2:
h(2) = 12(2) - 3 = 24 - 3 = 21
For x = 10:
h(10) = 12(10) - 3 = 120 - 3 = 117
The range of the function h(x) with the restricted domain of {-2, 0, 2, 10} is {-27, -3, 21, 117}. Therefore, the correct response is {−27, -3, 21, 117}.
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smerelda simplified a complex fraction. Her work is shown below.
Negative 5 and one-fourth divided by three-halves = negative StartFraction 21 over 4 EndFraction divided by three-halves = (Negative StartFraction 21 over 4 EndFraction) (Three-halves) = Negative StartFraction 24 over 6 EndFraction = negative 4
What errors did Esmerelda make? Select three options.
Esmerelda converted the mixed number to the wrong improper fraction.
Esmerelda added the numerators.
Esmerelda added the denominators.
Esmerelda did not divide –24 by 6 correctly.
Esmerelda did not use the reciprocal of the divisor.
Answers
Answer:
Step-by-step explanation:
ACTUAL ANSWER
(-5¼)/(3/2)
= -{(20+1)/4}/(3/2) //CONVERTING INTO IMPROPER FRACTION
= (-21/4)/(3/2)
= (-21/4) x (2/3) // MULTIPLYING BY RECIPROCAL
= (-21x2)/(4x3)
= -42/12
= -(7x6)/(2x6) TAKING 7 AS COMMON FACTOR
= -7/2
STEPS FOLLOWED BY ESMERELDA
(-5¼)/(3/2)
= -{(20+1)/4}/(3/2)
= -(21/4)/(3/2)
= -(21/4) x (3/2)
= -(21+3)/(4+2)
= - (24/6)
= -4
HENCE THE ERRORS COMMITTED BY HER ARE:-
1. ESMERALDA ADDED THE NUMERATORS
2. ESMERALDA ADDED THE DENOMINATORS
3. ESMERALDA DID NOT USE THE RECIPROCAL OF THE DIVISOE
The Houses of Parliament in Ghyronmia (a hypothetical small country) have two political parties: the Purple Party and the Chartreuse Party.
Answers
The presence of the Purple Party and the Chartreuse Party in the Houses of Parliament in Ghyronmia reflects the diversity of views and opinions in society. It creates a dynamic political environment that encourages debate, discussion, and better decision-making, and ensures that the interests of all sections of society are represented.
In Ghyronmia, a hypothetical small country, the Houses of Parliament have two political parties: the Purple Party and the Chartreuse Party. These two parties may have different political ideologies and values which reflect on their stances on various issues. The presence of different political parties in Parliament creates a dynamic political environment where different ideas are debated and discussed, and this leads to better decision-making and representation of different sections of society.
The Purple Party may represent a certain section of society that values conservatism, tradition, and stability. They may be more inclined to support policies that uphold traditional values, promote law and order, and preserve the status quo. On the other hand, the Chartreuse Party may represent a section of society that values progress, social justice, and reform.
They may be more inclined to support policies that aim to bring about change, promote equality, and challenge the status quo.
The presence of these two parties in Parliament means that different views and opinions are represented, and this creates healthy competition in the political sphere. It also ensures that decisions are not taken without due consideration and debate, and that policies are subject to scrutiny from different angles.
This, in turn, helps to prevent any one party or ideology from dominating the political discourse.
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K
The diagram to the
right illustrates a
hypothetical demand
curve representing the
relationship between
price (in dollars
per unit) and
quantity (in 1,000s of
units per unit of time).
The area of the
triangle shown on the
diagram is $.
(Enter your response
as an integer.)
100
90-
80-
70-67
60-
50-
40-
30-
20-17
10-
D
23
20 30 40 50
60
Quantity (1,000s of units per unit of time)
10
73
70 80 90 100
Answers
Answer:
OK, HERE IS YOUR ANSWER
Step-by-step explanation:
AI-generated answer
We are given a demand curve in the form of a graph, and we are asked to find the area of the triangle shown on the diagram. The formula for finding the area of a triangle is:
Area = 1/2 x base x height
In this case, the base of the triangle is the quantity in thousands of units per unit of time, and the height of the triangle is the price in dollars per unit.
The base of the triangle can be calculated as the difference between the quantities at the two endpoints of the demand curve. From the graph, we can see that the quantity at the left endpoint is 20, and the quantity at the right endpoint is 50. Therefore, the base of the triangle is:
Base = 50 - 20 = 30
The height of the triangle can be calculated as the difference between the prices at the two endpoints of the demand curve. From the graph, we can see that the price at the left endpoint is $90, and the price at the right endpoint is $70. Therefore, the height of the triangle is:
Height = 90 - 70 = 20
Now, we can use the formula to find the area of the triangle:
Area = 1/2 x base x height
Area = 1/2 x 30 x 20
Area = 300
Therefore, the area of the triangle shown on the diagram is $300. Hence, the correct answer is 300.
Mark me as brainliestThe area of the triangle in the demand curve diagram can be found using the formula for the area of a triangle which is 1/2 * base * height. From the points provided, we are able to calculate an area of 2450 dollars.
To answer this question, we need to understand how to calculate the area of a triangle which is represented by the equation: Area = 1/2 * base * height. From the diagram, we can find these values:
Base: The quantity 1,000s of units per unit of time which is the x-axis,
Height: Price per unit (dollars) which is the y-axis.
Assuming that the triangle's points intersect at 10 (on the y-axis) and 70 (on the x-axis) with a hypotenuse ending at 80 on the y-axis. The base would be 70 - 0 = 70, and the height would be 80 - 10 = 70.
Plugging these values into our formula, we get Area = 1/2 * 70 * 70 = 2450 dollars. So the area of the triangle is 2450 dollars.
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The probable question may be:
The diagram to the right illustrates a hypothetical demand curve representing the relationship between price (in dollars per unit) and quantity (in 1,000s of units per unit of time).
The area of the triangle shown on the diagram is $. (Enter your response as an integer.) 100 90- 80- 70-67 60 50- 40 30- 20-17 10- D 23 73 20 30 40 50 60 70 80 90 Quantity (1,000s of units per unit of time) 10 100
What’s the answer please I’m so behind
Answers
Answer:
2
Step-by-step explanation:
3x - 12 is inside the root.
The smallest value of √(3x - 12) is 0.
The greatest value of √(3x - 12) is infinity.
Since the function includes +2, then the range is from 2 to infinity.
Answer: 2
a linear function contains the following points what are the slope and y-interept of this function
Answers
Answer:
Step-by-step explanation:
To find the slope and y-intercept of a linear function, we need to use the formula y = mx + b, where "m" is the slope of the line and "b" is the y-intercept.
Given points in the linear function are not provided in the question, but if you are given two points on a line, you can find the slope of the line by using the slope formula:
slope = (change in y)/(change in x)
Assuming the given points of the linear function are (x1, y1) and (x2, y2), then the slope of the line is:
slope = (y2 - y1)/(x2 - x1)
Once we have the slope of the line, we can use any point on the line and the slope to find the y-intercept, b, using the formula:
y = mx + b
b = y - mx
Therefore, we can find the slope and y-intercept of a linear function, given two points on the line.
If you buy 10 pounds of lettuce for $70, what is the rate which one pound of lettuce costs?
Answers
Answer:
$7/lb
Step-by-step explanation:
$70 / 10 lb = $7/lb
Answer:
$7 per pound of letuce
Step-by-step explanation:
We know
10 pounds = $70
1 pounds = ?
We cross multiply and get:
$7 per pound of letuce
So, the answer is $7 per pound of letuce
Order the following fractions from least to greatest: 11/4, −2, −1/8
Answers
To order the fractions from least to greatest, we need to compare their values. The given fractions are 11/4, -2, and -1/8. The answer of the given question -2, -1/8, 11/4
Let's start by converting the mixed number -2 into a fraction. A mixed number consists of a whole number and a fraction. To convert it to a fraction, we multiply the whole number by the denominator of the fraction part and add the numerator. Then, we place the result over the original denominator. In this case, -2 can be written as -2/1.
Now we have the following fractions: 11/4, -2/1, and -1/8.
To compare these fractions, we can find a common denominator. The least common multiple (LCM) of the denominators 4, 1, and 8 is 8. So, we will rewrite the fractions using 8 as the common denominator:
11/4 = 22/8
-2/1 = -16/8
-1/8 remains the same
Now we have 22/8, -16/8, and -1/8. We can see that -16/8 is the smallest, followed by -1/8, and finally 22/8.
Therefore, in order from least to greatest, the fractions are:
-16/8, -1/8, 22/8
Simplifying further, we have:
-2, -1/8, 11/4
Note that we simplified the fractions, but the order remains the same. The fractions are ordered based on their numerical values, with the least value first and the greatest value last.
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What is the standard form of this function?
f(x) = (x − 2)2 + 6
Answers
Answer:
f(x) = x² - 4x + 10
Step-by-step explanation:
the standard form of a quadratic function is
f(x) = ax² + bx + c ( a ≠ 0 )
given
f(x) = (x - 2)² + 6 ← expand the factor using FOIL
= x² - 4x + 4 + 6 ← collect like terms
= x² - 4x + 10 ← in standard form
Determine the perimeter of a field that has a length of 97 metres and a width of 69 metres
Answers
Answer:
Step-by-step explanation:
2(97+69)=332(m)
What is the slope of the line that contains these points?
x
39
40
41
42
y
36
29
22
15
Answers
Answer:
Slope = -7
Step-by-step explanation:
Take any two points from the table:
(39 , 36) ⇒ x₁ = 39 & y₁ = 36
(41 , 22) ⇒ x₂ = 41 & y₂ = 22
Substitute the points in the below formula:
[tex]\boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{22-36}{41-39}\\\\\\=\dfrac{-14}{2}\\\\=-7[/tex]
What sentence represents the number of points in the problem below?
A test is worth 60 points. Multiple-choice questions are worth 2 points, and
short-answer questions are worth 5 points. If the test has 15 questions, how
many multiple-choice questions are there?
OA. The number of multiple-choice question points times the number
of short-answer question points is 60.
OB. The number of multiple-choice question points plus the number of
short-answer question points is 15.
OC. The number of multiple-choice question points minus the number
of short-answer question points is 15.
OD. The number of multiple-choice question points plus the number of
short-answer question points is 60.
Answers
Answer:
Step-by-step explanation:
The sentence that represents the number of points in the problem is OD. The number of multiple-choice question points plus the number of short-answer question points is 60.
The problem states that the test is worth 60 points, and that multiple-choice questions are worth 2 points each and short-answer questions are worth 5 points each. If the test has 15 questions, then there must be some number of multiple-choice questions and some number of short-answer questions. The total number of points for the multiple-choice questions and the short-answer questions must add up to 60, so the answer is OD.
The other answer choices are incorrect. OA is incorrect because it says that the number of multiple-choice question points times the number of short-answer question points is 60. This is not possible, because the number of points for a question cannot be multiplied by the number of points for another question. OB is incorrect because it says that the number of multiple-choice question points plus the number of short-answer question points is 15. This is not possible, because the total number of points for the test is 60, not 15. OC is incorrect because it says that the number of multiple-choice question points minus the number of short-answer question points is 15. This is not possible, because the number of points for a question cannot be subtracted from the number of points for another question.
Based on a survey, 33% of likely voters would be willing to vote by internet instead of the in-person traditional method of voting. For each of the following, assume that 12 likely voters are randomly selected. Complete parts (a) through (c) below.
a. What is the probability that exactly 9 of those selected would do internet voting? (round to 5 decimal places)
b. If of the selected voters would do internet voting, is 9 significantly high? Why or why not? (round to 5 decimal places)
(A). No, because the probability of or more is ---, which is low.
(B). Yes, because the probability of or more is ---, which is not low.
(C). No, because the probability of or more is ----, which is not low.
(D). Yes, because the probability of or more is ---, which is low.
c. Find the probability that at least one of the selected likely voters would do internet voting. (round to 3 decimal places)
Answers
Answer:
a. 0.00166
b. 0.00200
Overall B is correct because it has the prossibilty of getting more votes. 0.00200
Step-by-step explanation:
Pie chart values
20%. Rice
15%. Others
Pulses. 30%
maize 20%
wheat 15%
Percentage distribution of products in exports of the
given countries.
(a) What is the value (in $ billion) of pulses export
by US? on a billion
(6)
What is the ratio of wheat export of UK to
maize export of IND? 4:10
(e) By what percentage is the maize export of
JAP more than the rice export of AUS?
(d) If the export of AUS is doubled and that of US is
halved but percentage distribution of products of
export remains the same, then find the value of
Export of Rice by US
Export of Pulses by AUS
In USSR, find the ratio of maize export to the
rice export.
Answers
a.) The value of pulses exported by US in billion would be=30 billion.
b.) The ratio of wheat export of UK to maize export of IND would be= 6:5
How to calculate the value of pulses exported?For question a.)
To calculate the pulses, the following steps should be taken as follows:
From the bar chart, the value of pulses in billions = 30 billions.
For question b.)
The ratio of wheat export at UK and maize export at IND would be calculated as follows:
The quantity of wheat export at UK = 24
The quantity of maize export at IND = 20
Therefore, the ratio of wheat to maize = 24:20= 6:5
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When partitioning a line segment, what is the rational form of the ratio 2:3?
Update the answer is: 2/5.
Answers
Answer:
The rational form of the ratio 2:3 is 2/5
Step-by-step explanation:
For those of us who don't know or don't remember what rational means, it just means fraction, and in this case is asking as to convert ratio 2:3 into a fraction.
-First thing is to add the ratio:
2+3=5
-Now, we are going to place 5 as the denominator of the fraction, and we are going to keep the 2 from the ratio (it will always be the first number of our ratio, for example, if the ratio is 6:1 we'd be keeping the 6), and place it on the numerator place:
2:3 = 2/5
-So, that would be pretty much it, by the way, I know that the question was upgraded, but I don't mind to have 5 points more.
Data that does not take numerical form is referred to as: (2)
(1) Continuous data;
(2) Quantitative data;
(3) Qualitative data;
(4) Discrete data.
Answers
( 70 POINTS!! ) In a survey of 2837 adults, 1436 say they have started paying bills online in the last year.
Construct a 99% confidence interval for the population proportion. Interpret the results.
Question
Part 1
A 99% confidence interval for the population proportion is =( ? , ? )
.
(Round to three decimal places as needed.)
Part 2
Interpret your results. Choose the correct answer below.
A. With 99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
B. The endpoints of the given confidence interval show that adults pay bills online 99% of the time.
C. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
Answers
The correct answer is Part 1: The 99% confidence interval for the population proportion is approximately (0.4716, 0.5416).Part 2: With 99% confidence, the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
Part 1:
To construct a 99% confidence interval for the population proportion, we can use the formula:
Confidence Interval = Sample Proportion ± Margin of Error
where the margin of error is determined by the level of confidence and the standard error.
First, let's calculate the sample proportion:
Sample Proportion = (Number of adults who say they have started paying bills online) / (Total number of adults surveyed)
Sample Proportion = 1436 / 2837 ≈ 0.5066 (rounded to four decimal places)
Next, we need to calculate the standard statistics error, which is the measure of the variability in the sample proportion:
Standard Error = sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)
Standard Error = sqrt((0.5066 * (1 - 0.5066)) / 2837) ≈ 0.0136 (rounded to four decimal places)
Now, we can calculate the margin of error:
Margin of Error = Critical Value * Standard Error
The critical value is based on the desired confidence level. For a 99% confidence level, the critical value is approximately 2.576 (obtained from a standard normal distribution table).
Margin of Error = 2.576 * 0.0136 ≈ 0.0350 (rounded to four decimal places)
Finally, we can construct the confidence interval:
Confidence Interval = Sample Proportion ± Margin of Error
Confidence Interval = 0.5066 ± 0.0350
Confidence Interval ≈ (0.4716, 0.5416) (rounded to four decimal places)
Part 2:
The correct interpretation is:
C. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
This means that we are 99% confident that the true proportion of adults who have started paying bills online falls within the range of 0.4716 to 0.5416. The survey results suggest that approximately 47.16% to 54.16% of the population of adults have started paying bills online in the last year.
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If a varies as square root of y, how x is affected when y is increased by 44%
Answers
Answer: 16.7%
Step-by-step explanation:
x/(root y) =x
root y is increased by 44%
x/(44+root y)=16.7%
14 − {7 + 4 · 3 - [(-2)² · 2 - 6]}+ (2² + 6 - 5 · 3) + 3 - (5 - 2³ / 2) =
Answers
Answer: -6
Step-by-step explanation:
1. Evaluate the expressions inside the innermost brackets and braces first:
[tex]\((-2)^2 \cdot 2 - 6 = 4 \cdot 2 - 6 = 8 - 6 = 2\)[/tex]
So, the expression becomes:
[tex]\(14 - \{7 + 4 \cdot 3 - 2\}+ (2^2 + 6 - 5 \cdot 3) + 3 - (5 - 2^3 / 2)\)[/tex]
2. Continue evaluating the expressions inside the braces:
[tex]\(7 + 4 \cdot 3 - 2 = 7 + 12 - 2 = 17\)[/tex]
So, the expression becomes:
[tex]\(14 - 17 + (2^2 + 6 - 5 \cdot 3) + 3 - (5 - 2^3 / 2)\)[/tex]
3. Now, evaluate the expressions inside the parentheses:
[tex]\(2^2 + 6 - 5 \cdot 3 = 4 + 6 - 15 = -5\)[/tex]
[tex]\(5 - 2^3 / 2 = 5 - 8 / 2 = 5 - 4 = 1\)[/tex]
So, the expression becomes:
[tex]\(14 - 17 - 5 + 3 - 1\)[/tex]
4. Finally, perform the remaining operations:
[tex]\(14 - 17 - 5 + 3 - 1 = -3 - 5 + 3 - 1 = -6\)[/tex]
So, the result of the expression is -6.
How to calculate your bi-weekly paycheck based on 20 hour weeks at a rate of $9.00 per hour. Also, You will need to deduct Federal Income Tax (11.9%) , State Income Tax (3.6%), F.I.C.A (7.65%), and professional dues. Lastly you will need to look determine whether or not you will be able to pay your monthly car insurance bill of $200.00?
Answers
To calculate your bi-weekly paycheck, follow these steps:
Step 1: Calculate the gross earnings:
Multiply the number of hours worked per week by the hourly rate.
20 hours/week * $9.00/hour = $180.00/week
Step 2: Calculate the total earnings for two weeks:
Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.
$180.00/week * 2 weeks = $360.00
Step 3: Calculate the deductions:
Calculate each deduction separately and subtract them from the gross earnings.
Federal Income Tax: $360.00 * 11.9% = $42.84
State Income Tax: $360.00 * 3.6% = $12.96
F.I.C.A: $360.00 * 7.65% = $27.54
Professional Dues: Amount varies depending on the specific dues.
Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues
Step 4: Calculate the net earnings:
Subtract the total deductions from the gross earnings.
Net Earnings = Gross Earnings - Total Deductions
Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.
It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.
Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.
For more such questions on gross earning.
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Car A is rated at 32 mi/gal (miles per gallon) for city driving and 30 mi/gal for highway driving. Car B is rated at 29 mi/gal city and 36 mi/gal highway. How many gallons of gas would each vehicle consume for the following amounts of driving? (a) 300 mi of city driving plus 100 mi of highway driving (b) 100 mi of city driving plus 300 mi of highway driving
Answers
(a) For 300 miles of city driving plus 100 miles of highway driving:
For Car A:
City driving: 300 miles / 32 mi/gal = 9.375 gallons
Highway driving: 100 miles / 30 mi/gal = 3.333 gallons
Total gas consumption for Car A: 9.375 gallons + 3.333 gallons = 12.708 gallons
For Car B:
City driving: 300 miles / 29 mi/gal ≈ 10.345 gallons
Highway driving: 100 miles / 36 mi/gal ≈ 2.778 gallons
Total gas consumption for Car B: 10.345 gallons + 2.778 gallons ≈ 13.123 gallons
(b) For 100 miles of city driving plus 300 miles of highway driving:
For Car A:
City driving: 100 miles / 32 mi/gal ≈ 3.125 gallons
Highway driving: 300 miles / 30 mi/gal = 10 gallons
Total gas consumption for Car A: 3.125 gallons + 10 gallons = 13.125 gallons
For Car B:
City driving: 100 miles / 29 mi/gal ≈ 3.448 gallons
Highway driving: 300 miles / 36 mi/gal ≈ 8.333 gallons
Total gas consumption for Car B: 3.448 gallons + 8.333 gallons ≈ 11.781 gallons
Therefore, for the given driving distances, each vehicle would consume approximately:
(a)
Car A: 12.708 gallons
Car B: 13.123 gallons
(b)
Car A: 13.125 gallons
Car B: 11.781 gallons
Calculate the are of rectangle A.you must use area=length×breadth
Answers
The perimeter of the pentagon below is 64 units. Find the length of side PQ.
Write your answer without variables.
Answers
Answer:
PQ=20
Step-by-step explanation:
1) 11+x+2+3x-1+10+2x=64
2) 6x+22=64
3) 6x=42
4) x=7
5) PQ = 3(7)-1 = 20
a. Show that the equation
dy/dx = x²/(1 - y²) is separable, and then find an equation for its integral curves.
b. Solve the initial value problem dy dx dy/dx = (3x² + 4x + 2)/(2(y - 1)) , where y(0) = -1 ,
and determine the interval in which the solution exists.
Answers
Answer:
a. The equation is separable, as we can write it as (1 - y²) dy = x² dx. Integrating both sides, we have (1/2)*ln|1 - y²| = (1/3)*x³ + C, where C is the constant of integration. Solving for y, we get an equation for the integral curves: y = ±sqrt(1 - exp(2/3*x³ + 2C)).
b. Rearranging the equation, we get (2/(y - 1)) dy/dx = (3x² + 4x + 2). This is separable, so integrating both sides, we have 2 ln|y - 1| = x³ + 2x² + 2x + C, where C is the constant of integration. Solving for y, we get y = 1 + Ce^(x³+2x²+2x)/2. Using y(0) = -1, we have -1 = 1 + C, so C = -2. Thus, the solution to the initial value problem is y = 1 - 2e^(x³+2x²+2x)/2. The solution exists for all values of x.
