Answer:
2 1/4
Step-by-step explanation:
first do 4*3/4-4*1/2 because of order order of operations.
12/4-4/2=3-2=1
then do 1^2 because you do exponents before addition.
1^2=1*1=1
5/4+1=5/4+4/4=9/4
9/4=2 1/4
\(\frac{5}{4}+4\left(\frac{3}{4}-\frac{1}{2}\right)^2 =\)
\(\frac{3}{4}-\frac{1}{2} =\frac{3}{4}-\frac{2}{4}=\)
\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}\)
\(=\frac{3-2}{4}\)
\(\mathrm{Subtract\:the\:numbers:}\:3-2=1\)
\(=\frac{1}{4}\)
\(=\frac{5}{4}+4\cdot \frac{1}{4}^2\)
\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{c}^n=\frac{a^n}{c^n}\)
\(=\frac{5}{4}+4\cdot \frac{1}{16}\)
\(\mathrm{Apply\:the\:fraction\:rule}:\quad \:a+\frac{b}{c}=\frac{ac+b}{c}\)
\(=\frac{4\cdot \frac{1}{16}\cdot \:4+5}{4}\)
\(\mathrm{Multiply\:the\:numbers:}\:4\cdot \:4=16\)
\(\frac{16\cdot \frac{1}{16}+5}{4} =\frac{6}{4} =\boxed{\frac{3}{2}}\)
\(\mathrm{I\:hope\:that\:I\:helped\:you\:!}\)
Find the gradient of the line segment between the points (10,-4) and (6,-16).
assume z is a standard normal random variable. then p(1.41 < z < 2.85) equals . a. .4772 b. .3413 c. .8285 d. .0771
The value of P(1.41 < Z < 2.85) is 0.0771.
Hence, the correct answer is d.
A normally distributed random variable with mean μ= 0 and standard deviation σ= 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.
Because the Standard Normal Distribution is a probability distribution, the area under the curve between two points indicates the likelihood that variables will take on a range of values.
The whole area under the curve is one, or one hundred percent.
The mean and variance of a normal distribution are governed by two factors.
A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.
The probability that a standard normal random variable Z is between 1.41 and 2.85 can be found using a standard normal table with a standard normal cumulative distribution function.
The answer is approximate:
P(1.41 < Z < 2.85)
= P(Z < 2.85) - P(Z < 1.41)
= 0.9927 - 0.9185
= 0.0742
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anyone know the answer?
Answer:
It's 15^7/4
Basically just switch what you have for b and c and it'll be right
Research has shown that competent communicators achieve effectiveness by
a. using the same types of behavior in a wide variety of situations.
b. developing large vocabularies.
c. apologizing when they offend others.
d. giving lots of feedback.
e. adjusting their behaviors to the person and situation.
Research has shown that competent communicators achieve effectiveness by adjusting their behaviors to the person and situation (option e).
Effective communication involves being adaptable and responsive to the specific context, individual preferences, and the needs of the situation.
Competent communicators recognize that different people have different communication styles, preferences, and expectations. They understand the importance of tailoring their communication approach to effectively connect and engage with others.
This may involve using appropriate language, tone, non-verbal cues, and listening actively to understand the needs and perspectives of others.
By adapting their behaviors, competent communicators can build rapport, foster understanding, and promote effective communication exchanges. They are mindful of the social and cultural dynamics at play, and they strive to communicate in a way that is respectful, inclusive, and conducive to achieving mutual goals.
In summary, competent communicators understand that effective communication is not a one-size-fits-all approach. They adjust their behaviors to the person and situation, demonstrating flexibility and adaptability in order to enhance communication effectiveness.
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Competent communicators achieve effectiveness mostly by adjusting their behaviors to suit the person they are communicating with and the situation they find themselves in. While other factors, like having a broad vocabulary or giving feedback, play a part in effective communication, the former is considered the most crucial.
Explanation:Research suggests that competent communicators achieve effectiveness mostly through adjusting their behaviors depending on the person they are communicating with and the situation they are in. This is option e. of your question. Communicating effectively involves behaviors like active listening, understanding the other person's point of view, being able to express thoughts and ideas clearly, and being polite and respectful. While a broad vocabulary (option b.) can be useful, it is not as crucial as adapting your behavior to fit the situation. Moreover, giving feedback (option d.) is a part of effective communication but not the sole defining factor. Apologizing when offending others (option c.) is also important but it doesn't necessarily make one a competent communicator. Using the same type of behavior in various situations (option a.) might not always work, as different situations and individuals require different communication styles.
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how many sides does a regular polygon have if one exterior angle measures 30
Answer:
12 sides
Step-by-step explanation:
the sum of the exterior angles of a polygon is 360°
since the polygon is regular then the exterior angles are congruent
number of sides = 360° ÷ 30 = 12
Answer:
12.
Step-by-step explanation:
Please help! I will mark as brainliest IF answer is right. <3
Answer:
hello see my questions and come please
Given that XY is a line segment with the angle a = 48° and c = 59°, work out the value of the angle marked b.
The diagram is not drawn to scale.
Answer:
a+b+c = 180
48+59+b=180
107+b=180
b=180-107
b=73
Answer: b equals to 73 Degrees
Step-by-step explanation:
the statements below reference bank runs (aka banking panics). classify each as true or false. 1. Institutions like Federal Deposit Insurance Corporation (FDIC) decrease the frequency of bank runs. 2. A bank run is when too many of a bank's customers withdraw too much at the same time. 3. A bank run is when many of a bank's customers make large deposits at once 4. A bank run only occurs when a the economy is doing well.
FALSE, Bank runs are usually associated with financial crises or economic instability, which can undermine the public's confidence in banks.
each statement about bank runs as true or false.
"Institutions like the Federal Deposit Insurance Corporation (FDIC) decrease the frequency of bank runs." - This statement is TRUE. The FDIC insures deposits, which helps to maintain confidence among customers and prevent bank runs.
"A bank run is when too many of a bank's customers withdraw too much at the same time." - This statement is TRUE. A bank run occurs when a large number of customers withdraw their deposits simultaneously due to concerns about the bank's solvency.
"A bank run is when many of a bank's customers make large deposits at once." - This statement is FALSE. A bank run is related to withdrawals, not deposits.
"A bank run only occurs when the economy is doing well." - This statement is FALSE. Bank runs are usually associated with financial crises or economic instability, which can undermine the public's confidence in banks.
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You may need to use the appropriate appendix table or technology to answer this question. The following results are for independent random samples taken from two populations. Sample 1 Sample 2 n1 = 20 n2 = 30 x1 = 22.8 x2 = 20.1 s1 = 2.2 s2 = 4.6 (a) What is the point estimate of the difference between the two population means? (Use x1 − x2. ) 2.7 (b) What is the degrees of freedom for the t distribution? (Round your answer down to the nearest integer.) (c) At 95% confidence, what is the margin of error? (Round your answer to one decimal place.) (d) What is the 95% confidence interval for the difference between the two population means? (Use x1 − x2. Round your answers to one decimal place.)
a). The difference between the two population means is estimated at a location to be 2.7.
b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.
c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).
d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.
What is standard deviations?The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.
Using the equation \(x_1-x_2\), we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample
\(1(x_1=22.8)\) and deducting it from the mean of Sample \(2(x_2=20.1)\).
With the use of the equation \(df=n_1+n_2-2\), it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because \(n_1\) = 20 and \(n_2\) = 30.
We must apply the formula to determine the margin of error at 95% confidence \(ME=t*\sqrt[s]{n}\).
The sample standard deviation (s) is equal to the average of \(s_1\) and \(s_2\) (3.4), the t value with 95% confidence is 1.67, and n is equal to the
average of \(n_1\) and \(n_2\) (25). When these values are entered into the formula, we get \(ME=1.67*\sqrt[3.4]{25}=1.7\).
Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means \(CI=x_1-x_2+/-ME\).
The confidence interval's bottom limit in this instance is \(x_1-x_2-ME2.7-1.7=0.0\) and the upper limit is \(x_1+x_2+ME=2.7+1.7=5.4\).
As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.
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Find (a) the mean, (b) the median, and
(c) the mode of the number of verses in
the first eight chapters of Proverbs.
Proverbs 1 23 4 5 6 7 8
Verses 33 22352723352736
(a)
(b)
(c)
Answer:
Mean = 33+ 22+35+27+23+35+27+36 = 238/8 = 29.75
Median = 27+23 = 50/2 = 25
Mode = 35
Range = 36 - 22 = 14
Step-by-step explanation:
Stay Blessed
Solve the system of linear equations in two variables by elimination or substitution.
2x + 4y = 4
2x - y=1
Answer:
x = 0.8 y = 0.6
Step-by-step explanation:
Solve one of the equations for a single variable, I chose the 2nd equation and solved for the variable y and I got y = 2x -1.
Next plug in the value for y into the 1st equation, I got :
2x + 4 ( 2x - 1) = 4
Next solve for x by first distributing the 4 to the (2x-1), this becomes (8x -4) then add like terms and move the -4 to the other side of the equation by addition. I got 10x =8 then I divided 8/10 to solve for x and I got 0.8.
Now plug the value 0.8 in for x in the 2nd equation : 2*(0.8) - y = 1
Then solve for y by subtracting 2*(0.8) or 1.6 from 1 and I got -0.6, lastly divide by -1 to solve for y.
Problem 1. Let A be a finite set and let f : A → P (A) be any function. A. Show that f cannot be surjective. B. Show that f can be injective. C. Give a specific example of A and f such that f is injective.
Problem 2. Let A, B both be subsets of some universal set U. A. Show that (A × B)c = (Ac × B) ∪ (A × Bc) ∪ (Ac × Bc). B. Under which conditions is (A × B)c = Ac × Bc?
Problem 3. Let A = {1, 2}. A. Write out P (A). B. Now write out P (P (A)).
A. Suppose that f is surjective. Then for every subset B of A, there exists an element x in A such that f(x) = B.
Consider the set C = {x ∈ A : x ∉ f(x)}. Since f is surjective, there exists some y ∈ A such that f(y) = C. Now consider two cases:
Case 1: y ∈ C. Then by definition of C, y ∉ f(y) = C, which is a contradiction.
Case 2: y ∉ C. Then by definition of C, y ∈ f(y) = C, which is also a contradiction.
Since both cases lead to contradictions, the assumption that f is surjective must be false.
B. Let A = {1, 2, 3} and define f : A → P(A) by f(1) = {1}, f(2) = {2}, and f(3) = {1, 2}. Then f is injective, since each element of A is assigned a distinct subset of A.
C. Let A = {1, 2} and define f : A → P(A) by f(1) = {1} and f(2) = {2}. Then f is injective, since each element of A is assigned a distinct subset of A.
Problem 2:
A. To show (A × B)c = (Ac × B) ∪ (A × Bc) ∪ (Ac × Bc), we need to show that every element in (A × B)c is in the right-hand side, and vice versa.
Suppose (x, y) is an element of (A × B)c. Then either x ∉ A or y ∉ B. If x ∉ A, then (x, y) is in Ac × Bc. If y ∉ B, then (x, y) is in Ac × B ∪ A × Bc.
Now suppose (x, y) is an element of Ac × Bc. Then x ∉ A and y ∉ B, so (x, y) is not in A × B. Therefore, (x, y) is in (A × B)c.
Similarly, suppose (x, y) is an element of Ac × B ∪ A × Bc. Then either x ∉ A or y ∉ B. If x ∉ A, then (x, y) is in Ac × B ∪ Ac × Bc = (Ac × Bc). If y ∉ B, then (x, y) is in A × Bc ∪ Ac × Bc = (Ac × Bc). Therefore, (x, y) is in (A × B)c.
B. We have (A × B)c = Ac × Bc if and only if every element in (A × B)c is of the form (x, y) where x ∉ A or y ∉ B. This is equivalent to saying that A and B are disjoint.
Problem 3:
A. P(A) = {∅, {1}, {2}, {1, 2}}.
B. P(P(A)) = {∅, {{1}}, {{2}}, {{1, 2}}, {{∅}}, {{1}, {2}}, {{1}, {1, 2}}, {{2}, {1, 2}}, {{1, 2}, {1}, {2}}, {1, 2}}, where we write each subset of P(A) as a set of sets.
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I need this today. Which two integers is 37 square root between?
Answer:
The square root of 37 is approximately 6.0827. To determine which two integers it lies between, we can find the integers that are closest to the square root of 37.
The integer that is smaller than 6.0827 is 6, and the integer that is larger than 6.0827 is 7.
Therefore, the square root of 37 is between the integers 6 and 7.
Consider a function f(x)=21x2−x+43 on [83,43]. A fixed point iteration is given as xn+1=g(xn), where g(x)=21x2+43, with the starting point x0=83. Show that this scheme is convergent.
The fixed point iteration scheme xn+1 = g(xn) is convergent on the interval [83, 43]. This implies that the iteration scheme xn+1 = g(xn) remains within the interval [83, 43].
To show that the fixed point iteration scheme xn+1 = g(xn) is convergent, we need to prove that it satisfies the conditions for convergence.
First, let's calculate the derivative of g(x):
g'(x) = 2/3x
Since g'(x) exists and is continuous on the interval [83, 43], we can conclude that g(x) is a continuous function on this interval.
Now, let's analyze the behavior of g(x) on the interval [83, 43]:
1. When x > 0, we have g(x) = 21x^2 + 43 > 0.
2. When x < 0, we have g(x) = 21x^2 + 43 > 0.
3. When x = 0, we have g(x) = 43 > 0.
So, g(x) > 0 for all x in [83, 43]. This implies that the iteration scheme xn+1 = g(xn) remains within the interval [83, 43].
Next, let's analyze the behavior of f(x) on the interval [83, 43]:
1. When x > 0, we have f(x) = 21x^2 - x + 43 > 0.
2. When x < 0, we have f(x) = 21x^2 - x + 43 > 0.
3. When x = 0, we have f(x) = 43 > 0.
So, f(x) > 0 for all x in [83, 43].
This implies that f(x) has no fixed points on the interval [83, 43].
Now, let's analyze the behavior of g'(x) on the interval [83, 43]:
1. When x > 0, we have g'(x) = 2/3x > 0.
2. When x < 0, we have g'(x) = 2/3x < 0.
3. When x = 0, we have g'(x) = 0.
Since g'(x) is positive for x > 0 and negative for x < 0, we can conclude that g(x) is monotonically increasing on the interval [83, 43].
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Over time, the value of the property at 397 West Lake Street increased by 275%. If the initial value of the property was P, which expression represents the property’s current value?
Answer:
The expression is 2.75P.
Step-by-step explanation:
If P represents the initial value and the value increases by 275%, then you can say that it is worth 2.75 times as much as the initial value.
What is the prime factorization of 29
Answer:
1x29
Step-by-step explanation:
The prime factorization of 29 is simply 29 as it is prime number.
Prime factorization is the process of expressing a composite number as a product of its prime factors.
It involves breaking down a number into its constituent prime numbers, which are the building blocks of all other positive integers.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Since 29 is a prime number, it cannot be further factored into smaller prime factors.
Therefore, the prime factorization is 29.
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Question 1 of 10
List all the factors of 21 from least to greatest. Enter your answer below,
using a comma to separate each factor.
Answer:
1,3,7,21
Step-by-step explanation:
Tommy is flying his kite one afternoon and notices that he has let out
the entire 130 ft of string. The angle his string makes with the ground
is 48°. How high, to the nearest foot, is his kite at this time?
If Tommy is flying his kite one afternoon and notices that he has let out
the entire 130 ft of string. The height , to the nearest foot, is his kite at this time is : 144 ft.
How to find the height?Given data:
String = 130 ft
Angle = 48°
Let h represent the height
Hence,
Tan48° = h/130
h= 130 tan48°
h = 130 (1.11061251483)
h = 144 ft
Therefore we can conclude that the height is 144ft.
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Which container would most likely have a capacity that is measured in liters? A.Drinking Glass
B.Watering Can
C.Baby Bottle
D.Soup Spoon
the product of a non-zero number and an irrational number is
Answer:
rational
Step-by-step explanation:
Perform the operation
(7x³) + (-2x³ +8x²)
Answer:
x^2(5x+8)
Step-by-step explanation:
1. How many integers are between square root of /5 and square root of /105? Show your work or Explain.
Answer:
10x10 = 100 and 11x11 = 121. Since 100<105<121, 10<square root of 105<11. So the square root of 105 is between 10 and 11.
Step-by-step explanation:
Simplify the expression. 2y−5(y−3)=
Answer:
-3y -15
Step-by-step explanation:
2y - 5(y-3) = 2y -5y - 15
= -3y -15
Your welcome, and feel free to comment if you need have any questions!
The simplified value of the expression, 2y−5(y−3) using the Distributive property is 15- 3y.
Given Expression:
2y−5(y−3)
Using Distributive property
\({\text} a *(b+c) = (a *b) + (a*c)\)
So, applying the Distributive property in the expression 5(y - 3) gives
5(y - 3) = 5y - 15
Substituting the value 5y - 15 in 2y−5(y−3) as
2y−5(y−3) = 2y - (5y-15)
= 2y - 5y + 15
Now, operating the simplified value is
2y−5(y−3) = 15 - 3y
Thus, the simplified expression is -3y + 15.
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The state of a spin 1/2 particle in Sx basis is defined as (Ψ) = c+l + x) + i/√7 l - x) a) Find the amplitude c+ assuming that it is a real number and the state vector is properly defined. b) Find the expectation value . c) Find the uncertainty △SX.
1) The amplitude c+ is c+l
2) The expectation value is 0
3) The uncertainty ΔSX is √(3/7) c+.
Now, we know that any wave function can be written as a linear combination of two spin states (up and down), which can be written as:
Ψ = c+ |+> + c- |->
where c+ and c- are complex constants, and |+> and |-> are the two orthogonal spin states such that Sx|+> = +1/2|+> and Sx|-> = -1/2|->.
Hence, we can write the given wave function as:Ψ = c+|+> + i/√7|->
Now, we know that the given wave function has been defined in Sx basis, and not in the basis of |+> and |->.
Therefore, we need to write |+> and |-> in terms of |l> and |r> (where |l> and |r> are two orthogonal spin states such that Sy|l> = i/2|l> and Sy|r> = -i/2|r>).
Now, |+> can be written as:|+> = 1/√2(|l> + |r>)
Similarly, |-> can be written as:|-> = 1/√2(|l> - |r>)
Therefore, the given wave function can be written as:Ψ = (c+/√2)(|l> + |r>) + i/(√7√2)(|l> - |r>)
Therefore, we can write:c+|l> + i/(√7)|r> = (c+/√2)|+> + i/(√7√2)|->
Comparing the coefficients of |+> and |-> on both sides of the above equation, we get:
c+/√2 = c+l/√2 + i/(√7√2)
Therefore, c+ = c+l
The amplitude c+ is a real number and is equal to c+l
The expectation value of the operator Sx is given by: = <Ψ|Sx|Ψ>
Now, Sx|l> = 1/2|r> and Sx|r> = -1/2|l>
Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= -i/√7(c+l*) + i/√7(c+l)= 2i/√7 Im(c+)
As c+ is a real number, Im(c+) = 0
Therefore, = 0
The uncertainty ΔSX in the state |Ψ> is given by:
ΔSX = √( - 2)
where = <Ψ|Sx2|Ψ>and2 = (<Ψ|Sx|Ψ>)2
Now, Sx2|l> = 1/4|l> and Sx2|r> = 1/4|r>
Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= 1/4(c+l* + c+l) + 1/4(c+l + c+l*) + i/(2√7)(c+l* - c+l) - i/(2√7)(c+l - c+l*)= = 1/4(c+l + c+l*)
Now,2 = (2i/√7)2= 4/7ΔSX = √( - 2)= √(1/4(c+l + c+l*) - 4/7)= √(3/14(c+l + c+l*))= √(3/14 * 2c+)= √(3/7) c+
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Jane wants to make a tent shaped like a square box out of some material and poles she has. She has six square pieces of material to make the four
sides, the roof and the floor of the tent. Each piece of material covers an area of 16 m²
The length of the tent, represented by z, is equal to the square root of the area of material that is used for each side of the tent. The equation below
can be used to find 2, the length of the tent, in meters.
z² = area of material
Determine the maximum length of tent, in meters, Jane can make from the material she has.
The maximum length of the tent from the material is given by A = 4 meters
Given data ,
Let the maximum length of the tent from the material be A
Now , each square piece of material covers an area of 16 m², so six pieces of material will cover a total area of 6 x 16 = 96 m²
Let's assume that the length of the tent is z meters, then the area of each side of the tent will be z² square meters. Since there are four sides, the total area of the sides will be 4z² meters²
The roof and the floor will each require one square piece of material, for a total of 2 x 16 = 32 m²
Therefore, the total area covered by the tent will be 4z² + 32 meters²
We know that the total area covered by the tent cannot exceed the area of the material that Jane has, which is 96 m².
Therefore, we can set up the inequality
4z² + 32 ≤ 96
On simplifying , we get
4z² ≤ 64
Dividing by 4, we get
z² ≤ 16
Taking the square root of both sides, we get
z ≤ 4
Hence , the maximum length of tent that Jane can make from the material she has is 4 meters
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Jean bought 7 packages of sandwich meat.
Each package weighs 23 pound.
Answer:
Total is 23 times 7 which is 161 pounds
Step-by-step explanation:
you do 7 × 23 and u get 161
and thats how you figure it out
5 There are 150 men and 250 women in a crowd.
a What fraction of the crowd are men?
Write your answer in its simplest possible form.
b The ratio of married women to unmarried women is 3 to 2.
How many married women are in the crowd?
C More men arrive. The number of men increases by 20%.
How many men are in the crowd now?
d Some of the women leave.
There are now 60 women in the crowd.
What percentage of the women leave?
Answer:
men=150
women=250
total=400
Step-by-step explanation:
a) fraction of men
men/total=150/400=15/40
men/total =3/8
b)let married be x
so unmarried wil be 250-x
married/unmarried=3/2
x / 250-x =3/2
x =3(250-x)/2
2x =750-3x
5x=750
x=750/5
x =150
married =150
unmarried=250-150=100
c)20% of men will be :20x150
100
: 30
no of men =150+20%
=150+30
=180
d)no. of women decreased=250-60
=190
percentage of women leaved=% x 250
100
190x100/250=%
76 =%
76% women leaved
It took too much time
MARK ME BRAINLIEST THANKS MY ANSWER PLEASE
DO FOLOW
houses cost £150 000 one year ago they now cost £_____this is a 25% increase
i haven't seen this anywhere
Answer:
£150000=100%
125%=125/100×150000
=£187500 is now the cost of a house
I had 125% because the original cost is alway equal to 100%, so if it is increased by 25% then you sum the two percentages up to get your new price
Step-by-step explanation:
The altitude of a triangle is increasing at a rate of 2.5 2.5 centimeters/minute while the area of the triangle is increasing at a rate of 3.5 3.5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 9 9 centimeters and the area is 83 83 square centimeters
Answer:
-4 28/81 cm/min ≈ -4.346 cm/min
Step-by-step explanation:
Differentiating the formula for the area of a triangle gives the relationship between the various rates of change.
A = 1/2bh
A' = 1/2(b'h +bh') . . . . . relation of rates of change
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triangle dimensionsWhen the area is 83 cm², and the height is 9 cm, the base length is ...
83 cm² = 1/2b(9 cm)
b = 166/9 cm
rate of changeFilling in the given values and rates of change, we have ...
3.5 cm²/min = 1/2(b'·(9 cm) +(166/9 cm)(2.5 cm/min))
7 cm²/min -46 1/9 cm²/min = (b')(9 cm)
b' = (-39 1/9 cm²/min)/(9 cm) = -4 28/81 cm/min
The base of the triangle is changing at the rate of -4 28/81 cm/min, about -4.346 cm/min.
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The attachment shows a calculator solution to the problem.
Form a third-degree polynomial function with real coefficients such that 6 plus i and 7 are zeros
the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:
f(x) = (x² - 12x + 37)(x - 7)
To form a third-degree polynomial function with real coefficients such that the complex number 6 + i and the real number 7 are zeros, we can use the fact that complex zeros come in conjugate pairs.
Given that 6 + i is a zero, its conjugate 6 - i will also be a zero. Thus, the zeros of the polynomial are 6 + i, 6 - i, and 7.
To find the polynomial function, we start by forming the factors corresponding to each zero:
(x - (6 + i)) --> This corresponds to the zero 6 + i
(x - (6 - i)) --> This corresponds to the zero 6 - i
(x - 7) --> This corresponds to the zero 7
To simplify the factors, we multiply them out:
(x - (6 + i))(x - (6 - i))(x - 7)
= ((x - 6) - i)((x - 6) + i)(x - 7)
= ((x - 6)² - i²)(x - 7)
= ((x - 6)² + 1)(x - 7)
Expanding the squared term:
= (x² - 12x + 36 + 1)(x - 7)
= (x² - 12x + 37)(x - 7)
Therefore, the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:
f(x) = (x² - 12x + 37)(x - 7)
Learn more about polynomial function here
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