Express the confidence interval (0.086 comma 0.130 )in the form of ModifyingAbove p with caret minus Upper E less than p less than ModifyingAbove p with caret plus Upper E.
Answers
Answer:
C.I = 0.108 ± 0.022
Step-by-step explanation:
In this case, we are given a symmetric confidence interval, and the sample proportion p', is derived by finding the average of the two values.
Therefore, the sample proportion will be:
\( p' = \frac{0.086 + 0.130}{2} \)
\( = \frac{0.216}{2} \)
= 0.108
p' = 0.108
To find the margin of error, we have:
M.E = ½ * length of confidence interval
Where length of confidence interval = 0.130 - 0.086
= 0.044
Therefore,
\( M.E = \frac{1}{2} * 0.044 = 0.022 \)
Margin of error = 0.022
The confidence interval is expressed as:
p' ± M.E
= 0.108 ± 0.022
Related Questions
find the area of the region enclosed by one loop of the curve. r = sin(4θ)
Answers
π/16 is the area enclosed by the curve r= sin(4θ)
The given curve is polar curve and hence the area of the polar curve is given by:
Let A be the area of the curve so,
A = \(\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta\)
where a and b is the boundary at which r=0
so after equation r=0
sin(4θ) =0
=> sin(4θ) =0
=> 4θ = 0,π
=> θ = 0, π/4
so a=0 , b= π/4
now
A = \(\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta\) ------(i)
so \(r^2\) = (sin(4θ))^2
=> \(sin^2\)( 4θ )
ans we know that
cos(2α) = 1 - \(2sin^2\)2 α
so \(sin^2\)= (1- cos(8θ) )/2
putting the value of r in the equation (i) we get :-
A = \(\int\limits^b_a {\frac{1}{4} *(1-cos8\theta) } \, d\theta\)
=> 1/4* \(\int\limits^b_a {(1-cos8\theta) } \, d\theta\)
here a=0 and b=π/4
after putting the value and solving the integral
A = π/16
so A is the area enclosed by r=sin(4θ) is π/16
To know more about polar curve click on below link:
brainly.com/question/1094340#
#SPJ4
how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once? how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once, that contain the block cd? how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once, that start with the letter f? how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once, that contain the blocks abc and ef?
Answers
The answer to questions are as follows- a)720 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used once. b)240 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used once, containing the block cd. c)120 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used once, that start with the letter f.d)4 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used once, that contain the blocks abc and ef.
a) To find the number of strings that can be formed using the letters a, b, c, d, e, f with each letter used formerly, we need to find the number of permutations of the letters. This can be set up using the formula for permutations of n objects taken r at a time, which is n!/( n- r)!.
In this case, we've 6 objects and we want to take all 6, so we have
6!/( 6- 6)! = 6! = 720
thus, there are 720 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly.
b) To find the number of strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that contain the block cd, we can treat the block cd as a single object and find the number of permutations of the performing 5 objects( alphabet, e, f, and the block cd). We also multiply this by the number of ways that cd can be arranged within the string( which is 2 since cd can be arranged as cd or dc).
So we have
5! * 2 = 240
thus, there are 240 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, containing the block cd.
c) To find the number of strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that starts with the letter f, we can fix f as the first letter and also find the number of permutations of the remaining 5 objects. This can be set up using the formula for permutations of n objects taken r at a time, which is n!/( n- r)!.
In this case, we've 5 objects and we want to take all 5, so we have
5!/( 5- 5)! = 5! = 120
thus, there are 120 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that start with the letter f.
d) To find the number of strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that contain the blocks alphabet and ef, we can fix alphabet and ef as blocks and find the number of permutations of the remaining 2 objects( d and f). We also multiply this by the number of ways that the blocks can be arranged within the string( which is 2 since alphabet can be before ef or ef can be before the alphabet).
So we have
2 * 2! = 4
thus, there are 4 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that contain the blocks alphabet and ef.
Learn more about permutations;
https://brainly.com/question/28065038
#SPJ4
The correct questions are given below-
a)how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once?
b) how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once, that contain the block cd?
c)how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once, that start with the letter f?
d)how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once, that contain the blocks abc and ef?
Scatter plots
Group of answer choices
1. are not used for revealing patterns.
2. are used to see two numeric variables plotted in comparison
with each other.
3. must lie on straight lines.
4. are used
Answers
The option that correctly describes scatter plots is:
Option 2: are used to see two numeric variables plotted in comparison with each other.
What is the importance of scatter plots?A scatterplot is defined as a type of graph or mathematical graph that uses Cartesian coordinates to show the values of usually two variables in a data set. Additional variables can be displayed if the points are coded
Scatterplots are used to identify possible relationships between changes observed in two different sets of variables. It provides a visual and statistical way to test the strength of the relationship between two variables.
Looking at the given options and comparing with the definition of scatter plots above, it is very clear that only option 2 is correct because they are used to see two numeric variables plotted in comparison with each other.
Read more about Scatter Plots at: https://brainly.com/question/6592115
#SPJ4
Complete question is:
Group of answer choices
1. are not used for revealing patterns.
2. are used to see two numeric variables plotted in comparison with each other.
3. must lie on straight lines.
4. are used to see two categorical variables plotted in comparison with each other.
Which of these is a random sampling technique which is frequently chosen by researchers for its simplicity and its periodic quality?
Answers
Simple random sampling is a frequently chosen for its simplicity and periodicity.
What is frequently ?
Frequently refers to something that happens or occurs often or many times. It is an adverb that describes the regularity of an action or event, indicating that it happens with a high frequency or on a regular basis.
Simple random sampling is a random sampling technique that is frequently chosen by researchers for its simplicity and its periodic quality. This technique involves randomly selecting a sample from a larger population, with each individual in the population having an equal chance of being selected. Simple random sampling is considered to be an unbiased and efficient method for selecting a representative sample, and it is often used as a benchmark for comparing other sampling methods.
Simple random sampling is a frequently chosen for its simplicity and periodicity.
To learn more about frequently visit : brainly.com/question/13305546
#SPJ4
The line representing the equation part of the constraint 7x1 + 4x2 s 28 goes through the following two points a. (4,0) and (7,0) b. (0, 4) and (7,0) c. (4,0) and (0,7) d. (0, 4) and (0,7) e. none of the above
Answers
Point (4,0) and (0,7) (C) were passed through by the line equation of 7x1 + 4x2 = 28.
From the case, we know that:
Line equation: 7x1 + 4x2 = 28
Passed through points?
To answer this question, we can try to find some conditions:
x1 = 0; x2 =?x2 = 0; x1 =?First, we will try to find the valuf f x2 if x1 = 0:
(x1 = 0)
7(0) + 4.x2 = 28
0 + 4.x2 = 28
4.x2 = 28
x2 = 7 --> (0,7)
Next, we try if x2=0, then x1 = ...
(x2 = 0)
7x1 + 4(0) = 28
7x1 = 28
x1 = 4 --> (4,0)
Learn more about Line Equation here: brainly.com/question/29138348
#SPJ4
NEED HELP QUICKLY! PICTURE BELOW!
Answers
Answer:
C
Step-by-step explanation:
Let me know if this is correct!
You have a mortagege of $275,000
after down payment with an interest
rate of 3% for 30 years.
What does P, r,n, and t are equal to?
Answers
Answer:
Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this
Step-by-step explanation:
Andre and Elena are aving money. Andre tart with $100 in hi aving account and add $5 per week. Elena tart with $10 in her aving account and add $20 each week. After four week, who ha more money in their aving account? Explain how you know
Answers
Elena would have more money in her savings account, with a total of $90 compared to Andre's total of $120.
Andre and Elena are saving money. Andre start with $100 in her saving account and add $5 per week. Elena start with $10 in her saving account and add $20 each week.
After four weeks, Elena would have more money in her savings account.Andre adds $5 per week to his savings account, so after 4 weeks, his savings would be: $100 + 4 * $5 = $120
Elena adds $20 per week to her savings account, so after 4 weeks, her savings would be: $10 + 4 * $20 = $90
Therefore, Elena would have more money in her savings account, with a total of $90 compared to Andre's total of $120.
For more such questions on unit of account
https://brainly.com/question/30078783
#SPJ4
Assume the base unit of water is 555 gallons and the cost per unit is $1.74. How much money will be saved in a month by a family who conserves 8000 gallons of water per month?
Answers
1) Gathering the data
555 gallons ----- $ 1.74
2) If 8000 gallons could be spent
If a Family conserves 8000 gallons this family would not have an expense of?
Let's set a proportion for that:
555 g-----$1.74
8000g ---x
555x =13920 Dividing both sides by 555
x=25.08
If a family conserves 8000 gallons of water. They save $25.08 per month assuming that $1.74 is equal to 555 gallons of water.
a simple random sample of 40 items resulted in a sample mean of 25. the population standard deviation is 5. what is the standard error of the mean? (round your answer to two decimal places).
Answers
The standard error of the mean is approximately 0.79 (rounded to two decimal places).
Define standard error ?
The standard error is a statistical term that measures the variability of a sample mean or an estimate of a population parameter from its true value. It is the standard deviation of the sampling distribution of the mean. In simpler terms, the standard error measures how much the sample mean varies from the true population mean. A smaller standard error indicates that the sample mean is more likely to be representative of the population mean, while a larger standard error suggests that the sample mean may not be as reliable.
The formula for the standard error of the mean is:
\(SE = \frac{\sigma }{\sqrt{n}}\)
Where σ is the population standard deviation and n is the sample size.
Substituting the given values:
\(SE =\frac{5}{\sqrt{40}}\)
SE ≈ 0.79
Therefore, the standard error of the mean is approximately 0.79 (rounded to two decimal places).
To learn more about standard deviation from the given link :
https://brainly.com/question/23907081
#SPJ1
If v = 6i - 4j and w = xi + 6j, find all numbers x for which || v + w|| = 2. Select the correct choice and fill in any answer boxes in your choice below. O A. x = B. There is no solution
Answers
The numbers x for which ||v + w|| = 2 are 16 and -167.
When v = 6i - 4j and w = xi + 6j, the numbers x for which ||v + w|| = 2 are given by the expression "||v + w||² = 4".
Explanation: It is known that ||u||² = u·u for any vector u. Thus,||v + w||² = (v + w)·(v + w) = v·v + 2v·w + w·w
Substituting the given values of v and w, we have
||v + w||² = (6i - 4j)·(6i - 4j) + 2(6i - 4j)·(xi + 6j) + (xi + 6j)·(xi + 6j)= 36i·i - 48i·j - 48j·i + 16j·j + 12xi·i + 72xi·j + 72j·i + 36j·j + x²i·i + 12xi·j + 36j·j= (36 + x²)i·i + (144 + 12x)j·i + (72 + 72x)i·j + (52)j·j
The above equation needs to be solved in order to get the values of x such that
||v + w|| = 2:||v + w||² = 4 ⇔ (36 + x²) + (144 + 12x) + 2(72 + 72x) + 52 = 4 ⇔ x² + 86x - 2672 = 0
The solutions for the above quadratic equation are x = 16 and x = -167.
Therefore, the numbers x for which ||v + w|| = 2 are 16 and -167.
Learn more about vectors: https://brainly.com/question/29740341
#SPJ11
For argument ((j→c∧h)∧(¬h))⇒(¬j), either show it is valid via logical equivalence and inference rules, or show it is invalid through a counterexample with truth value assignments of j,c,h.
Answers
The argument ((j→c∧h)∧(¬h))⇒(¬j) is valid using logical equivalence and inference rules.
To prove the argument is valid, follow these steps:
The following logical equivalences hold: j → c ∧ hj ≡ ¬h ∨ ¬cj → ¬h ≡ ¬c ∨ ¬h. Using the logical equivalences, we can then rewrite it as follows:¬h ∨ ¬c ∨ ¬j ≡ ¬(¬h ∨ ¬c ∨ ¬j)Inference rules: To prove the validity of the argument, we will make use of the modus tollens inference rule. The modus tollens rule states that if we have a conditional statement of the form p → q, and we know that q is false, then we can infer that p is false as well. So, (¬j).¬j can be rewritten as j → ⊥, where ⊥ represents a contradiction or falsehood. Hence, we can apply the modus tollens rule to the conditional statement (j → c ∧ h) ∧ ¬h → (¬j), as follows: ¬(j → c ∧ h) ∧ ¬h¬(j → c ∧ h). Using the logical equivalences, we can then further simplify the expression as follows: ¬(¬h ∨ ¬c ∨ ¬j)∧ ¬h¬(¬h ∨ ¬c ∨ ¬j)¬(j → c ∧ h) ∧ ¬h ≡ ¬(¬h ∨ ¬c ∨ ¬j) ∧ ¬h ≡ ¬(j → c ∧ h) ∧ ¬hTherefore, the argument ((j→c∧h)∧(¬h))⇒(¬j) is valid through logical equivalence and inference rules.
Learn more about logical equivalences:
brainly.com/question/13419585
#SPJ11
Which equation illustrates the identity property of multiplication?
A. (a + bi) × c = (ac + bci)
B. (a + bi) × 0 = 0
C. (a + bi) × (c + di) = (c + di) × (a + bi)
D. (a + bi) × 1 = (a + bi)
Answers
Answer:
Step-by-step explanation:
2
Answer: D. (a+bi) times 1 = (a+bi)
Step-by-step explanation: i just took the test on edge2020
Scaled scores on the WISC-V have a mean of ____ and a standard deviation of _____.
a. 10/3
b. 10/5
c. 3/1
d. 100/15
Answers
the correct answer is option a: 10/3, which represents the mean and standard deviation of the scaled scores on the WISC-V.
Scaled scores are used to compare an individual's performance on the WISC-V to the performance of other individuals in the same age group. The scaled scores are derived from raw scores and are standardized to have a mean and standard deviation that are predetermined.The mean of scaled scores on the WISC-V is set to 10. This means that an average performance is represented by a scaled score of 10.
The standard deviation of scaled scores on the WISC-V is set to 3. The standard deviation measures the spread or variability of scores around the mean. A standard deviation of 3 indicates that most scores fall within 3 points above or below the mean of 10.
Learn more about standard deviation here:
https://brainly.com/question/29115611
#SPJ11
you want to order posters to advertise your band. a company charges $109.95 for the first 100 posters and $65 for each additional 100 posters. a. write the equation where $y$ represents the total cost (in dollars) as a function of $x$ , the number (in hundreds) of posters ordered.
Answers
The required question based on number of posters is y = 109.95 + 65x.
The cost of additional posters = 65x, based on the mentioned information.The 100 posters make 1 set. Assuming the total number of posters be x. So, the additional sets will be calculated by the formula = (x - 100)/100.
Now, the equation will be the sum of the cost of first 100 posters and the cost of remaining posters.
y = 109.95 + 65x
Thus, the equation with the total cost (in dollars) as a function of the number (in hundreds) of posters ordered is y = 109.95 + 65x.
Learn more about equations -
https://brainly.com/question/21405634
#SPJ4
solve (-2x) x 8x
its a simple question no equations just solve it its a quadratic expression
Answers
Answer:
-16x²
Step-by-step explanation:
-2x*8x= -16x²
EASYYY!!!PLEASE HELP AND EXPLAIN!!!!POINTS
73 - 24 = 101
Answers
Answer:
z=5
Step-by-step explanation:
1. You will have to rearrange the terms, so the equation would now be z(3)=101+24
2. After that you will calculate the sum to equal z(3)=125
3. You will simplify your answer to z=3^ 125
4. Calculate. Z=5
I hope this helps!
f(x)=-4(x-9)^2+15 in standard form
Answers
Answer:47r64765
Step-by-step explanation:no
question in link below
Answers
Answer:
105
Step-by-step explanation:
2x17=34
17x2.5=42.5
1.5x17=25.5
1/2x2x2x1.5=3
34+42.5+25.5+3=105
Answer Po Ba Ay 11.33?
Step-by-step explanation:
Calc
f(x)=∣x∣
g(x)=∣x−1∣+9
We can think of g as a translated (shifted) version of f
Complete the description of the transformation.
Answers
Answer:
Step-by-step explanation:
There are two transformations, one vertical, one horizontal.
The + 9 part outside the absolute value sign moves the graph up 9 units.
Replacing x with x - 1 moves the graph right 1 unit.
Comment: The horizontal shifts sometimes appear backwards: x - 1 looks like a shift to the left, but it's not.
Example: f(4) = |4| = 4. To get the same output (4) from g(x), you have to use a value for x that is 1 unit larger than 4. g(5) = |5 - 1| = 4.
John left a $3 tip, which was 15% of his bill. How much was his bill?
Answers
Answer:
20$
Step-by-step explanation:
assume x being the bill
x * 15/100 = 3
x = 3 *100/15 = 20
prove that if f is a function from the finiste set x to the finite set y and |x| > |y|, then f is not one to one
Answers
Assume that f is one-to-one, meaning that every element in x maps to a unique element in y. Since |x| > |y|, there must exist at least one element in x that does not have a unique element in y to map to. Therefore, f cannot be one-to-one.
To prove this more formally, we can use the pigeonhole principle. Since |x| > |y|, there are more elements in x than there are elements in y. If f is one-to-one, then each element in x must map to a unique element in y. However, since there are more elements in x than there are in y, there must be at least one element in x that maps to the same element in y as another element in x. This violates the definition of a one-to-one function, and thus f cannot be one-to-one.
In simpler terms, when we have more pigeons (elements in x) than pigeonholes (elements in y), at least one must have more than one pigeon. Similarly, when we have more elements in x than in y, at least one element in x must map to the same element in y as another element in x. Therefore, f cannot be one-to-one.
To learn more about function click here:
brainly.com/question/31957727
#SPJ11
An aerospace company builds a type of cruise missiles. Suppose, on average, the first failure of this type of missiles occurs on the last firing per every 20 successive independent firings. In a successive independent firings of such missiles, if the first failure occurs after at least 10 firings, what's the probability that it occurs after 15 firings? (Round your answer to the nearest ten thousandth.)
Answers
Therefore, the probability that the first failure occurs after 15 firings is approximately 0.085 rounded to the nearest ten-thousandth.
Given that the first failure of a type of missile occurs on the last firing per every 20 successive independent firings. We need to find the probability that the first failure occurs after 15 firings.
Given, The number of firings before the first failure follows geometric distribution with probability of success, p = 1/20 (Since it occurs on the last firing per every 20 successive independent firings)
Let X be the number of firings before the first failure, then X ~ Geometric(p) ⇒ X ~ Geometric(1/20)
Now, we need to find P(X > 15 | X > 10)
Probability of the first failure occurs after at least 10 firings:
\((X > 10) = (1 - p)^{(10 - 1)} * p\)
\(= (19/20)^9 * 1/20\)
= 0.382
For a geometric distribution, P(X > n + k | X > k) = P(X > n), for all n ≥ 0
P(X > 15 | X > 10) = P(X > 5)
\(= (1 - p)^{(5 - 1) }* p\)
\(= (19/20)^4 * 1/20\)
= 0.085
To know more about probability,
https://brainly.com/question/15689512
#SPJ11
A chemist is investigating a new reaction to synthesize barite crystals. She finds that eight grams are synthesized every five minutes. If there are 111 grams of barite after an hour, how many grams of barite did the chemist start with?
possiable answers
0
8
15
71
Answers
Answer:
The answer is 71
What is chemist?
A chemist is a person who specializes in the science of chemistry, which is the study of matter and its properties, structure, composition, behavior, and the changes it undergoes. Chemists are trained in the scientific discipline of chemistry and use their knowledge to study and manipulate matter. This can include anything from the analysis of materials for their chemical makeup, to the development of new products and processes. Chemists can work in a variety of fields, including pharmaceuticals, materials science, biochemistry, research and development, and more. They must be well-versed in the principles and theories of chemistry, as well as in the practical aspects of their work. Through their work, chemists contribute to the advancement and application of science.
To learn more about chemist refer to:
https://brainly.com/question/26313963
#SPJ1
Answer: the answer is 15
Step-by-step explanation:
Part D
The rectangular bases of the treasure box will be cut from wooden planks
4 1/8 feet long and 4 1/8 feet wide. How many planks will Mr. Penny need for his
18 students to each
make one treasure box?
Answers
Answer:
Step-by-step explanation:
it is honors calculus and i’m lost
Answers
The value of k is 2, so correct option is B.
Describe Integration?Integration is a fundamental concept in calculus that involves finding the area under a curve or the accumulation of a quantity over a continuous range. It is the inverse operation of differentiation, and together, they form the basis of calculus.
The process of integration involves finding an antiderivative (or indefinite integral) of a function f(x), which is another function F(x) whose derivative is equal to f(x). The antiderivative is denoted by ∫f(x)dx and is read as "the integral of f(x) with respect to x". The symbol ∫ is called the integral sign, and dx represents the variable of integration.
We have:
(6kx-2k) dx = k^3
Integrating the given expression with limits k and 0, we get:
[3kx² - 2kx]k⁰
= 3k(0)² - 2k(0) - [3k(k)² - 2k(k)]
= 0 + 0 - (3k³ - 2k²)
= -3k³ + 2k²
So, we have:
-3k³ + 2k² = k³
4k³ = 2k²
2k = 4
k = 2
Therefore, the correct option is B 2.
To know more about expression visit:
brainly.com/question/24242989
#SPJ1
A coin is tossed and a card is drawn from a deck containing 1 blue card, 1 green card, and 2 yellow cards.
Which option is the sample space for this event?
O (Heads blue, Heads green, Heads yellow, Tails blue, Tails green, Tails yellow)
O (Heads, Tails, blue, green, yellow 1, yellow 2)
O (Heads blue, Heads green, Heads yellow 1, Heads yellow 2, Tails blue, Tails green, Tails yellow 1, Tails yellow 2)
(Heads Heads, Heads blue, Heads green, Heads yellow 1, Heads yellow 2, Heads Tails, Tails Heads, Tails Tails, Tails
blue, Tails green, Tails yellow 1, Tails yellow 2)
Answers
The sample space for this event is (Heads blue, Heads green, Heads yellow 1, Heads yellow 2, Tails blue, Tails green, Tails yellow 1, Tails yellow 2)
Identifying the sample space for this event?From the question, we have the following parameters that can be used in our computation:
Coin = Head and tail
Card = 1 blue card, 1 green card, and 2 yellow cards
The sample space for this event is derived by taking the head or the tail from the coin and selecting one of the cards
using the above as a guide, we have the following:
The sample space is (Heads blue, Heads green, Heads yellow 1, Heads yellow 2, Tails blue, Tails green, Tails yellow 1, Tails yellow 2)
Read more about sample space at
https://brainly.com/question/2117233
#SPJ1
Solve for y.
y y
—— = ——
P-9 P+9
Answers
9514 1404 393
Answer:
y = 0
Step-by-step explanation:
Subtracting the right side gives ...
\(\dfrac{y}{P-9}-\dfrac{y}{P+9}=0\\\\y\left(\dfrac{(P+9)-(P-9)}{P^2-81}\right)=0\\\\y\left(\dfrac{18}{P^2-81}\right)=0\\\\\boxed{y=0}\)
The factor multiplying y cannot be zero, so y must be zero.
1
2
The formula for the area of a triangle is A = -bh, in which b represents the
length of the base and h represents the height. If a triangle has an area of 140
mm2 and the height is 14 mm, what is the measure of the base?
Answers
Answer:
20mm
Step-by-step explanation:
The problem gives A=140mm^2 and h=14mm
It also gives the equation A=1/2bh
Plug in what you know --> 140=1/2(b)(14)
To solve for b, fist multiply 140 by 2
Now we have 280=14b
Divide by 14, and you get your answer of b=20mm
rotate the triangle below: A(5,3) B(8,10) C(11,3) angle of rotation is 180 centre origin direction is anti- clock wise
Answers
Answer:
see explanation
Step-by-step explanation:
Under a rotation ( clockwise or anticlockwise ) about the origin of 180°
a point (x, y ) → (- y, - x ), thus
A(5, 3 ) → A'(- 3, - 5 )
B(8, 10 ) → B'(- 10, - 8 )
C(11, 3 ) → C'(- 3, - 11 )