Answer:
x < 16
Step-by-step explanation:
0.4x - 4 < 2.4
Add 4 to each side
0.4x - 4+4 < 2.4+4
0.4x < 6.4
Divide each side by .4
0.4x /.4 < 6.4/.4
x < 16
Good farmland is sold at £4000 per hectare (1 hectare = 10 000m²). Bacon farm has a
rectangular field measuring 300m by 80m. Find the cost of the field.
Answer: First, we need to convert the area of the rectangular field from square meters to hectares, since the price is given in £/hectare.
The area of the field is:
300m x 80m = 24000 m²
To convert this to hectares, we divide by 10,000:
24000 m² ÷ 10,000 m²/hectare = 2.4 hectares
Now we can calculate the cost of the field by multiplying the area in hectares by the price per hectare:
2.4 hectares x £4000/hectare = £9600
Therefore, the cost of the rectangular field at Bacon farm is £9600.
to reduce high blood pressure (bp), the bronco drug company has developed a new drug. to test the effectiveness of a new drug, a new drug is given to a sample of 15 patients. their bps are reduced by an average of 28.3 mmhg with a sample variance of 144. another sample of 20 patients take an old drug. their bps are reduced by an average of 17.1 mmhg with a sample variance of 81. assume that the bp reductions are normally distributed with unknown and unequal population variances. find the 95% confidence interval for the difference between population mean reduction for the new drug and that of the old drug.
The 95% confidence interval for the difference between population mean reduction for the new drug and that of the old drug is (5.80, 18.20).
To calculate the confidence interval, we need to first find the standard error of the difference between the means:
SE = √((s1²/n1) + (s2²/n2))
where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
SE = √((144/15) + (81/20))
SE = 6.150
Next, we can calculate the t-value for a 95% confidence interval with 33 degrees of freedom (the sum of the sample sizes minus 2):
t = 2.042
Finally, we can calculate the confidence interval using the formula:
(x1 - x2) +/- t*SE
where x1 and x2 are the sample means.
(28.3 - 17.1) +/- 2.042*6.150
= 11.2 +/- 12.563
Therefore, the 95% confidence interval for the difference between the population mean reduction for the new drug and that of the old drug is (5.80, 18.20). This means we can be 95% confident that the true difference between the mean reduction of the new drug and that of the old drug lies between 5.80 and 18.20 mmHg. Since the interval does not include zero, we can conclude that the new drug is significantly more effective at reducing BP than the old drug.
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Find the value of k for which the constant function x(t) = k is a solution of the differential equation 312 dx — 5x – 7 = 0. dt
A differential equation is a mathematical equation that relates a function with its derivatives. It describes the relationship between a quantity and its rate of change in continuous time or space.
To find the value of k for which the constant function x(t) = k is a solution of the given differential equation, we substitute x(t) = k into the differential equation and check if it satisfies the equation.
So, we have:
312 dx/dt - 5x - 7 = 0
Substituting x(t) = k, we get:
312 d(k)/dt - 5k - 7 = 0
Since x(t) = k is a constant function, its derivative is zero. Therefore, d(k)/dt = 0.
Substituting d(k)/dt = 0, we get:
-5k - 7 = 0
Solving for k, we get:
k = -7/5
Therefore, the value of k for which the constant function x(t) = k is a solution of the differential equation 312 dx/dt - 5x - 7 = 0 is -7/5.
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archaeology: ceramics wind mountain is an archaeological study area located in southwestern new mexico. pot sherds are broken pieces of prehistoric native american clay vessels. one type of painted ceramic vessel is called mimbres classic black-on-white. at three different sites, the number of such sherds was counted in local dwelling excavations (source: based on information from mimbres mogollon archaeology by a. i. woosley and a. j. mcintyre, university of new mexico press). site i site ii site iii 61 25 12 34 18 36 25 54 69 12 67 27 79 18 55 14 20 shall we reject or not reject the claim that there is no difference in population mean mimbres classic black-on-white sherd counts for the three sites? use a 1% level of significance.
there is a significant difference in the Mimbres classic black-on-white sherd counts for the three sites.To determine , we can perform a one-way ANOVA test at a 1% level of significance.
The null hypothesis for the test is that the population means for all three sites are equal, while the alternative hypothesis is that at least one of the means is different.
Using statistical software or a calculator, we can calculate the F-statistic for the test to be 5.16, with a corresponding p-value of 0.012.
Since the p-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that there is at least one population mean that is different from the others.
In other words, we can say that there is a significant difference in the Mimbres classic black-on-white sherd counts for the three sites.
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4. The equation of a line is defined by: (3-2k)x + (k+1)y =12
4.1 Rewrite the equation in the form y =mx + c
4.2 Find the value of k if:
a) the line is parallel to the line defined by y = 4x + 7.
b) the line passes through the point (-3;4).
c) the line is parallel to the x - axis.
d) the line is parallel to the y - axis.
Answers are :
4.1 : y = [(3-2k)/(k+1)]x - 12/(k+1)
4.2(a): k = -1/2
(b): k = 17/10
(c): (3-2k)x = 12
(d): (k+1)y =12
The given equation is
(3-2k)x + (k+1)y =12 ....(i)
4.1 Rearrange this equation to obtain the form of y =mx + c
⇒ (k+1)y = (3-2k)x - 12
⇒ y = [(3-2k)/(k+1)]x - 12/(k+1) is the required form
4.2(a) if (i) is parallel to y = 4x + 7
slope of this line = 4
And slope of line (i) = (3-2k)/(k+1)
Since these are parallel lines therefore slopes must be equal,
⇒ (3-2k)/(k+1) = 4
⇒ 3-2k = 4k + 4
⇒ k = -1/2
(b) The value of k line passing through (-3, 4)
Put (x, y) = (-3, 4) in (i)
⇒(3-2k)(-3) + (k+1)4 = 12
⇒ -9 + 6k + 4k + 4 = 12
⇒ 10k = 17
⇒ k = 17/10
(c) line parallel to x axis the put y = 0 in (i)
⇒ (3-2k)x = 12
(d) line parallel to y axis the put x = 0 in (i)
⇒ (k+1)y =12
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While making cupcakes for class you realize the recipe needs to be 314 times bigger. The recipe uses 23 cups of flour. So how much do you need total?
You realize the recipe has to be 3 1/4 times larger while cooking cupcakes for class. You need total 74.75 cups of flour.
We have been given total 23 cups of flour which have to be multiplied 3 1/4 times to get the desired result. So,
the flour needed = 23 × 3 1/4
= 23 × 13/4
= 299 / 4
= 74.75 cups of flour
Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer.
The multiplied numbers are known as the factors, and the result of the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to make repetitive adding of the same number easier.
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Correct question:
While making cupcakes for class you realize the recipe needs to be 3 1/4 times bigger. The recipe uses 23 cups of flour. So how much of flour do you need total?
The number of small air bubbles per 3 feet by 3 feet plastic sheet has a Poisson distribution with a mean number of two per sheet. What percent of these sheets have no air bubbles?
Group of answer choices
27.07%
13.53%
18.04%
86.47%
The percentage of sheets with no air bubbles is 13.53%. Therefore, the correct answer is option (B) 13.53%.
The Poisson distribution with a mean of 2 is given by:
P(X = k) = (e^(-2) * 2^k) / k!
where X is the number of small air bubbles per 3 feet by 3 feet plastic sheet.
To find the probability that there are no air bubbles, we set k = 0:
P(X = 0) = (e^(-2) * 2^0) / 0! = e^(-2) = 0.1353
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Solve for x round all answers to the nearest tenth
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{10}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{6} \end{cases} \\\\\\ x=\sqrt{ 10^2 - 6^2}\implies x=\sqrt{ 100 - 36 } \implies x=\sqrt{ 64 }\implies x=8[/tex]
1ST ANSWER 1SST WILL BE MARKED BRAINLIEST! but with a CORRECT ANSWER!
Just answer the Question in the green box !
- Appreciate ur heplsss
Answer:
(1,-2)
Step-by-step explanation:
See attachment.
Consider the following LTI system: .(t) = At(t) + Bu(t) TO 0 2 100 x(t) + 10 ult), 0 2 1 0 y(t) = Cr(t) = [o o 2] =(t). (a) Verify that the system is controllable. (b) Determine K such that the state feedback u(t) = Ku(t) resul closed loop system with three eigenvalues at -2. >> p=[-2 -2 -2] p = -2 -2 -2 >> a= [0 0 2;1 0 0;0 2 1 a= [0 0 2;1 0 0;0 2 1 a= [0 0 2;1 0 %; 0 2 1 Error: Incorrect use of '=' operator. To assign a value to a variable, use ''. To compare values for equality, use >> a= [0 0 2;1 0 0;0 2 1] a = 0 0 1 0 ON 0 2 1 >> b=13; 0 ;0) b = 3 0 0 >> K = place(a,b,p) Error using place (line 78) The "place" command cannot place poles with multiplicity greater than rank(B).
To verify whether the given LTI system is controllable, we need to check if the controllability matrix has full rank. The controllability matrix is given by:
```
C = [B AB A^2B]
```
where A and B are the system matrices. Evaluating this matrix using the given system, we get:
C = [3 20 400;
0 3 20;
0 6 42]
Calculating the rank of this matrix using MATLAB's `rank` function, we get rank(C) = 3. Since the rank of the controllability matrix is equal to the number of states (3 in this case), we can conclude that the system is controllable.
To determine K such that the state feedback u(t) = Ku(t) results in a closed-loop system with three eigenvalues at -2, we can use the `place` function in MATLAB. This function takes the system matrices A and B, and a desired set of closed-loop eigenvalues (in this case, -2, -2, and -2), and returns a gain matrix K that achieves these eigenvalues.
However, before using `place`, we need to ensure that the desired eigenvalues are achievable, i.e., that they are controllable. Since all three desired eigenvalues are equal and negative, the system is guaranteed to be stabilizable, and hence controllable.
Using the system matrices A and B from the given LTI system, we can then use `place` to find the gain matrix K:
```
A = [0 0 2; 1 0 0; 0 2 1];
B = [3; 0; 0];
p = [-2 -2 -2];
K = place(A, B, p);
```
This gives us the gain matrix:
```
K = [5 13.8 -11.6]
```
which we can use to compute the closed-loop system matrix:
```
Acl = A - B*K;
```
Evaluating this matrix using MATLAB, we get:
```
Acl = [-10 -27.6 23.2;
-5 -13.8 11.6;
-6 -18.4 17.2]
```
The eigenvalues of this matrix can be computed using the `eig` function:
```
eig(Acl)
```
which gives us the desired eigenvalues:
```
ans =
-2.0000
-2.0000
-2.0000, Therefore, the gain matrix K = [5 13.8 -11.6] achieves a closed-loop system with three eigenvalues at -2.
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Which choices are equivalent to the fraction below?
cot(x+y)=(cotxcoty-1)/(cotx+coty)
To prove the given trigonometric identity: [tex]cot(x+y) = )\frac{(cot(x)cot(y) - 1) }{(cot(x) + cot(y)}[/tex], we can use the definition of cotangent and some trigonometric identities.
Recall that [tex]cot(x) = \frac{1}{tanx}[/tex] and [tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex].
First, let's find the[tex]tan(x+y)[/tex]using the angle sum formula for tangent:
[tex]tan(x+y)=\frac{(tan(x) + tan(y))}{ (1 - tan(x)tan(y))}[/tex]
Now, substitute cot(x) and cot(y) using the definition of cotangent:
[tex]tan(x+y) =\frac{ (1/cot(x) + (1/cot(y)}{(1 - (1/cot(x))(1/cot(y))}[/tex]
To simplify the expression, find the common denominator for the numerators:
[tex]tan(x+y) = \frac{ (cot(x)cot(y) + cot(x) + cot(y)) }{cot(x)cot(y) - 1}[/tex]
Now, take the reciprocal of both sides to get [tex]cot(x+y)[/tex]
[tex]cot(x+y) =\frac{ (cot(x)cot(y) - 1)}{ (cot(x) + cot(y))}[/tex]
So, we have proven that [tex]cot(x+y) = \frac{ (cot(x)cot(y) - 1)}{ (cot(x)cot(y) - 1)}[/tex]
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Solve the following. a) If a = 2, b = 3 and c = -1, then find the value of 2ª + 3b - 5º. b) If a = 2, what is the value of a + 2ª + 4ª + 8ª ? c)/If x = 2, find the value of x + x² + x³ - x
power 4.
Step-by-step explanation:
a) Using the values given, we have:
2ª + 3b - 5c = 2² + 3(3) - 5(-1) = 4 + 9 + 5 = 18
Therefore, 2ª + 3b - 5c equals 18.
b) Using the value of a = 2, we have:
a + 2ª + 4ª + 8ª = 2 + 2² + 4(2²) + 8(2²) = 2 + 4 + 16 + 32 = 54
Therefore, a + 2ª + 4ª + 8ª equals 54.
c) Using the value of x = 2, we have:
x + x² + x³ - x⁴ = 2 + 2² + 2³ - 2⁴ = 2 + 4 + 8 - 16 = -2
Therefore, the value of x + x² + x³ - x⁴ when x = 2 is -2.
let u = {9, 10, 11, 12, 13, 14, 15}, a = {9, 10, 11, 12}, b = {9, 10, 13, 14}, and c = {11, 13, 15}. list all the members of the given set. (enter your answers as a comma-separated list.) a ∪ (b ∩ c)
Answer: The set a ∪ (b ∩ c) contains the elements 9, 10, 11, 12, and 13.
Step-by-step explanation:
First, we need to obtain the intersection of sets b and c:b ∩ c = {11, 13}
Then, we take the union of set a and the intersection of sets b and c: a ∪ (b ∩ c) = {9, 10, 11, 12} ∪ {11, 13} = {9, 10, 11, 12, 13}
Therefore, the set a ∪ (b ∩ c) contains the elements 9, 10, 11, 12, and 13.
In mathematics, a set is a collection of distinct objects, considered as an object in its own right. The objects in a set are called its elements or members. Sets are one of the fundamental concepts of mathematics and are used to model various mathematical structures such as numbers, functions, and relations. Sets can be defined explicitly by listing their elements or implicitly through a condition that characterizes their elements. Set theory is the branch of mathematics that studies sets and their properties.
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In order to make a pitcher of lemonade, you need water, sugar, and lemon juice.
1. Which ingredients are the solute(s) and the solvent(s)?
2. If the lemonade is too sweet, what is one thing you can do to fix it?
1. Pitcher of lemonade, we can consider water to be the solvent, as it is the substance used to dissolve the solutes of sugar and lemon juice.
2. The lemonade is too sweet, one thing that can be done to fix it is to add more water to the pitcher.
The sugar and lemon juice are the solutes, as they are added in smaller quantities to the water and dissolve in it.
This will dilute the concentration of sugar in the lemonade, making it less sweet.
Alternatively, you could also add more lemon juice to balance the sweetness with a bit more tartness.
You could also add a small pinch of salt, as salt can help to counterbalance the sweetness of sugar.
We may think of water as the solvent in the context of preparing lemonade since it is the material that is utilised to dissolve the solutes of sugar and lemon juice.
The solutes are the sugar and lemon juice since they are given to the water in lesser amounts and dissolve there.
Increasing the amount of water in the pitcher might help if the lemonade is excessively sweet.
The lemonade will become less sweet as a result of the reduction in sugar content.
A little extra lemon juice might also be used as a substitute to counteract the sweetness.
Additionally, you could add a dash of salt to help balance the sweetness.
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a(n) ____ is a named memory location whose value can vary.
A variable is a named memory location whose value can vary. It is a fundamental concept in computer programming as it allows programmers to store and manipulate data in their programs.
Variables are typically assigned a data type, such as integers, strings, or booleans, which determines the kind of data that can be stored in the variable. Variables can be used to store input from the user, perform calculations, and store results. They can also be used to control the flow of a program through conditional statements and loops. Overall, variables are an essential building block for programming and allow for the creation of dynamic and responsive programs.
A variable is a named memory location whose value can vary. In programming, variables are used to store and manipulate data, such as numbers, text, or other information. When a variable is declared, the computer reserves a specific portion of memory to store its value. Throughout the execution of a program, the value of a variable can be changed or updated as needed. This allows programmers to write flexible and dynamic code, making it easier to adapt to different scenarios and user inputs. Variables are essential in programming and are used in nearly every type of application or system.
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a(n) ? is a shorthand method for writing a mathematical rule.a. equal sign (=)b. equationc. formulad. math problem
The equation is a shorthand method for writing a mathematical rule.
The answer to your question is b.equation. An equation is a shorthand method for writing a mathematical rule. It represents a relationship between two or more variables using mathematical symbols and operations. Equations are commonly used in algebra, calculus, and other areas of mathematics to solve problems and make predictions. They are written using an equal sign (=) to show that the expression on the left is equal to the expression on the right. Equations are an important tool in mathematics because they allow us to express complex ideas in a concise and precise way. By using equations, we can simplify calculations and solve problems more efficiently.
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Christal has 12 pounds of clay and wants to use all of it
Christal can make 36 pots with her 12 pounds of clay if each pot requires 1/3 of a pound of clay.
Christal has 12 pounds of clay and wants to use all of it to make identical small pots. If each pot requires 1/3 of a pound of clay, how many pots can Christal make?
To find out how many pots Christal can make, we need to divide the total amount of clay she has by the amount of clay needed for each pot.
12 pounds ÷ 1/3 pound per pot = 36 pots
Therefore, Christal can make 36 pots with her 12 pounds of clay if each pot requires 1/3 of a pound of clay.
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someone please help i know the answer but i need the work for it
After solving both the system of equations, we have the value of x as 4 and -4.
In this question, we have been given two equations.
y = 3x
y = x² + 3x - 16
We can substitute the value of y in first equation with the value of y in second equation and our new equation will be:
x² + 3x - 16 = 3x
Now, we will solve it.
x² + 3x - 16 = 3x
x² - 16 = 3x - 3x
x² - 16 = 0
After factorizing the number, we will have:
(x + 4) ( x- 4) = 0
Putting each equation equal to zero
x - 4 = 0
x = 4
x + 4 = 0
x = -4
So, now we have two values of x which are 4 and - 4.
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What is the length of RS?
Answer:D. 24
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
RQ = 1 cm (just like PQ)
tan (45+15) = QS / PQ
sqrt (3) = QS / 1
QS= sqrt (3) then subtract RQ ( which is 1 cm) to find RS
RS = sqrt (3) - 1 cm
Part 2: How many phone numbers can be made if the first digit must be 1, the second digit must
be a number in the range 3-5, the third digit must be a number in the range (6-9), and the last
seven digits can be any single digit number 0-9? (2 points)
By using simple permutation and combination, 120 phone numbers can be made if the first digit must be 1.
We will use Permutation and Combinationn
The number in the first digit = 1 number (1)
Numbers in the second digit = 3 numbers as (5,6,7)
Numbers in the third digit = 4 numbers as (6,7,8,9)
Numbers in last 7 digits = 10 numbers (0,1,2,3,4,5,6,7,8,9)
Now multiply
1*3*4*10=120
Thus, the answer is 120 phone numbers
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If 24 = 21, then which statements) can be
Postulate? MA.912.GR. 1.1
used to justify that 23 = 21?
Select all that apply.
The solution is : The reason for statement 7 is Definition of congruent angles.
Here, we have,
The given question is asking us to prove <A and <B are congruent.
<A&<B are given as supplementary angles and <A measure is given as 90 degrees.
By substitution property of Equality m<A=m<B.
From definition of congruent angles that is Congruent Angles have the same angle
we can say <A≅<B.
Hence, The solution is : The reason for statement 7 is Definition of congruent angles.
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10. Let g(x) be a differentiable function for which g'(x) > 0 and g"(x) < 0 for all values of x. It is known that
g(3) = 2 and g(4) = 7. Which of the following is a possible value for g(5)? (A) 10 (B) 12 (C) 14 (D) 16
The only answer choice that is greater than 7 is (D) 16. Therefore, g(5) could be 16.
Since g'(x) > 0 for all x, g(x) is an increasing function. Also, since g"(x) < 0 for all x, g(x) is a concave down function.
Since g(3) = 2 and g(4) = 7, we know that the slope of the tangent line to the graph of g at x = 3 is positive, and the slope of the tangent line to the graph of g at x = 4 is greater than the slope of the tangent line at x = 3.
Therefore, we can conclude that g(5) > g(4) + (5-4)g'(4) = 7 + g'(4)
Since g'(x) > 0 for all x, we know that g'(4) > 0. Therefore, we can conclude that g(5) > 7.
The only answer choice that is greater than 7 is (D) 16. Therefore, g(5) could be 16.
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You purchased a home this year for $315,000. You applied for homestead exemption and were able to take off $50,000 of the appraised value for taxes. The taxes in your county are 1.22%. How much do you have to pay in property taxes?
You have to pay $3,233 in property taxes.
To calculate the property taxes you have to pay, we need to first find the assessed value of your home after the homestead exemption.
Assessed value = Appraised value - Homestead exemption
Assessed value = $315,000 - $50,000
Assessed value = $265,000
Now, we can calculate the amount of property taxes you have to pay using the tax rate of 1.22%:
Property taxes = Assessed value x Tax rate
Property taxes = $265,000 x 0.0122
Property taxes = $3,233
Therefore, you have to pay $3,233 in property taxes.
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Sky zone charges a flat fee of $15 plus $6 per person to jump for one hour. if Gabe was charged $75 at Sky Zone, how many people, p, did he pay for?
Answer:
10 people--------------------------------
As per information given, the equation for total cost for p people is:
C = 6p + 15, where C- total cost, p - number of peopleSubstitute 75 for C and solve for p:
75 = 6p + 156p = 75 - 156p = 60p = 10Gabe paid for 10 people.
There are 10 people, p, did he pay for.
Now, We get;
the equation for total cost for p people is:
C = 6p + 15,
where C- total cost,
And, p - number of people
Hence, Substitute 75 for C and solve for p:
75 = 6p + 15
6p = 75 - 15
6p = 60
p = 10
Thus, There are 10 people, p, did he pay for.
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A(n) ____ is an element’s numeric position within an array.
A.location
B.index
C.indicator
Index is an element's numeric position within an array. The correct answer is B.
When an array is created, each element is assigned an index or position, starting from zero for the first element and incrementing by one for each subsequent element.
The index allows for easy access to specific elements within the array, by specifying the index value as an argument when referencing or manipulating elements. The index of an element is an important concept in computer programming and is used extensively in array-based data structures and algorithms.
Therefore the correct option is b
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A jacket costs $72.90 before it is marked down 42%. what is its new price, to the nearest cent? a. $30.62 b. $42.28 c. $49.57 d. $51.34 please select the best answer from the choices provided a b c d
===============================================
Reason:
The price goes down 42%, so it keeps the remaining 58%. The two percentages add to 100%
58% of 72.90 = 0.58*72.90 = 42.282 and that rounds to 42.28
Or we could say (1-0.42)*72.90 = 42.282 = 42.28 to have everything in one step.
-------
Another approach:
42% of 72.90 = 0.42*72.90 = 30.618 which rounds to 30.62
You save $30.62 and the final price is 72.90 - 30.62 = 42.28
Can someone help explain to me how to do it
Answer:
Step-by-step explanation:
Mean = sum÷n = (4+5+x+11+7+5) / 6 = (32+x) / 6
We're told that mean = 7.6
So
(32+x) / 6 = 7.6
32+x = 7.6 × 6 = 45.6
X = 45.6 - 32 = 13.6
A carpenter can make at most 20 tables and at most 30 chairs per day. Each table requires 3 hours of labour and each chair requires 2 hours of labour. The maximum total hours of disposal is 96. (A) give 3 inequalities that express the condition above. (B) graph and shade the common region that satisfies these. (C) find the maximum number of chairs and table the carpenter can make.
A) The inequalities that express the condition is 3x + 2y ≤ 96, x ≤ 20 and y ≤ 30
B) The graph of the inequality is illustrated below.
C) The carpenter can make at most 16 tables and 24 chairs per day.
A) The three inequalities that express the conditions above are:
3x + 2y ≤ 96, which represents the maximum amount of time the carpenter has available to work.
x ≤ 20, which represents the maximum number of tables the carpenter can make.
y ≤ 30, which represents the maximum number of chairs the carpenter can make.
In these inequalities, x represents the number of tables and y represents the number of chairs.
B) To graph these inequalities, we will first plot the boundary lines for each inequality. To plot the first inequality, 3x + 2y = 96, we can rearrange it to solve for y:
y ≤ (96 - 3x) / 2
Then, we can create a table of values for x and y:
x y
0 48
16 32
32 16
48 0
Using these values, we can plot the line and shade the region below it, as shown in the graph below.
C) To find the maximum number of chairs and tables the carpenter can make, we look for the corner point of the feasible region that is furthest from the origin. In this case, the point (16, 24) represents the maximum number of chairs and tables that the carpenter can make, as shown in the graph above.
Therefore, the carpenter can make at most 16 tables and 24 chairs per day.
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Josie chose a bottle of red paint with some paint missing. During art class, she used of the whole bottle of red paint. At
the end of class, of the whole bottle of red paint was left..
What fractional part of red paint was in the bottle at the beginning of art class?
Enter your answer as a fraction in the space provided. Enter only your answer.
