Answer:
Step-by-step explanation:
To determine whether the teacher has enough space on the bookshelf for the 60 textbooks, we need to calculate the total space that the textbooks will occupy.
The thickness of each textbook is 2.5cm, so the total thickness of 60 textbooks will be:
60 textbooks * 2.5cm/textbook = 150cm
Therefore, the total space occupied by the textbooks will be 150cm.
The bookshelf is 160cm long, so we need to check whether the length of the bookshelf is greater than or equal to the total space occupied by the textbooks.
160cm >= 150cm
Since the length of the bookshelf is greater than the space occupied by the textbooks, the teacher has enough space on the bookshelf for the 60 textbooks.
I don't know the method to find the equations of the other 2 ides. Can someone please explain step by step how to do this.
The equations of the other two sides are AD: y = -3x + 3 and DC: y = 1/2x - 1/2.
What is point-slope form?
The point-slope form is a way to write the equation of a straight line in algebra. It is used when you know the coordinates of a point on the line and the slope of the line. The point-slope form of a linear equation is:
y - y₁ = m(x - x₁)
where m is the slope of the line, and (x1, y1) are the coordinates of a point on the line.
Since AB and BC are two sides of a parallelogram, they are parallel to each other. Thus, we can use the slope formula to find the slopes of these sides.
Slope of AB:
m = (y₂ - y₁)/(x₂ - x₁)
= (6 - 3)/(6 - 0)
= 3/6
= 1/2
Slope of BC:
m = (y₂ - y₁)/(x₂ - x₁)
= (3 - 6)/(7 - 6)
= -3/1
= -3
Now that we know the slopes of AB and BC, we can use the point-slope form to find the equations of the other two sides.
Equation of AD:
We know that AD is parallel to BC and passes through point A. So, we can use the point-slope form with the slope of BC and point A.
y - y₁ = m(x - x₁)
y - 3 = -3(x - 0)
y - 3 = -3x
y = -3x + 3
Equation of DC:
We know that DC is parallel to AB and passes through point C. So, we can use the point-slope form with the slope of AB and point C.
y - y₁ = m(x - x₁)
y - 3 = 1/2(x - 7)
y - 3 = 1/2x - 7/2
y = 1/2x - 1/2
Therefore, the equations of the other two sides are:
AD: y = -3x + 3
DC: y = 1/2x - 1/2
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The workers' union at a particular university is quite strong. About 96 of all workers employed by the university belong to the workers' union. Recently, the workers went on strike, and now a local TV station plans to interview 4 workers (chosen at random) at the university to get their opinions on the strike. What is the probability that exactly 2 of the workers interviewed are union members?
The probability that exactly 2 of the workers interviewed are union members is approximately 0.044.
To solve this problem, we can use the binomial probability formula, which is:
[tex]P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)[/tex]
where:
n is the sample size (number of workers being interviewed)
k is the number of successes we are interested in (in this case, 2 of the workers being union members)
p is the probability of success (in this case, the probability that a worker is a union member)
(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items (this can be calculated using the formula n! / (k! * (n - k)!))
Plugging in the values, we get:
[tex]P(X = 2) = (4 choose 2) * (0.96)^2 * (1 - 0.96)^(4 - 2)[/tex]
[tex]= (6) * (0.96)^2 * (0.04)^2[/tex]
= 0.04403136
Therefore, the probability that exactly 2 of the workers interviewed are union members is approximately 0.044.
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Jim's favorite hockey player can shoot a hockey puck at a speed of 108 mph what is the speed of the puck in feet per second
Answer:
158.4 ft/sec
Step-by-step explanation:
multiply the speed value by approximately 1.467
[Economics, three part, 100 points]
The graph shows the average total cost (ATC) curve, the marginal cost (MC) curve, the average variable cost (AVC) curve, and the marginal revenue (MR) curve (which is also the market price) for a perfectly competitive firm that produces terrible towels. Answer the three accompanying questions, assuming that the firm is profit-maximizing and does not shut down in the short run.
1) What is the firm's total revenue?
2) What is the firm's total cost?
3) What is the firm's profit? (Enter a negative number for a loss.)
The three accοmpanying questiοns, assuming that the firm is prοfit-maximizing and dοes nοt shut dοwn in the shοrt run
1)Firm's Tοtal Revenue= $78000
2)Firm's Tοtal Cοst =$128700
3)Firm's Lοss = - $50700
What is wοrd prοblem?Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.
Here in the given graph,
Cοst per unit = $300
Equilibrium quantity = $260 Then,
Firm's Tοtal Revenue = P * Q
=> $300*260 = $78000 (Equilibrium where, MR = MC)
Firm's Tοtal Cοst = Cοst per Unit * equilibrium quantity
=> $495*260 = $128,700
Firm's Lοss = TR - TC
=> $78000 - $128,700 = - $50700
Hence the answers are,
1)Firm's Tοtal Revenue= $78000
2)Firm's Tοtal Cοst =$128700
3)Firm's Lοss = - $50700
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In a Gallup poll conducted nationwide in July 2020, it was found that 63% of a sample of female
adults supported a ban on public smoking.
a) Describe the population parameter of interest in this study.
The population parameter of interest in this study is the proportion or percentage of all female adults in the entire population who support a ban on public smoking. The Gallup poll was conducted to estimate this proportion or percentage by collecting data from a sample of female adults. By using statistical inference methods, the researchers can use the sample data to make inferences about the population parameter with a certain level of confidence.
In a right triangle, sin ( x − 3 ) ∘ (x−3) ∘= cos ( 6 x + 9 ) ∘ (6x+9) ∘ . Find the smaller of the triangle’s two acute angles.
The smaller acute angle of the right triangle is x-3 = 12.6 degrees.
What is Right Triangle?
A triangle in which one angle is 90 degree is called a Right Angled Triangle.
In a right triangle, if one acute angle is x-3 degrees, then the other acute angle is 90-(x-3) = 93-x degrees.
Using the given equation, we have:
sin(x-3) = cos(6x+9)
Taking the sine of both sides:
sin(x-3) = sin(90 - (6x+9)) = sin(81-6x)
Now we have:
sin(x-3) = sin(81-6x)
Since the two angles have the same sine, they must differ by a multiple of 360 degrees. Thus:
x-3 = 81-6x + 360n or x-3 = 6x-81 + 360n
where n is an integer.
Simplifying each equation:
7x = 84 + 360n or 5x = 78 + 360n
Dividing both sides by 7 or 5, respectively:
x = 12 + 51.43n or x = 15.6 + 72n
The first equation gives us values of x that are too large for an acute angle, so we use the second equation:
x = 15.6 + 72n
The smallest such x that satisfies 0 < x < 90 is when n=0, which gives:
x = 15.6 degrees
Therefore, the smaller acute angle of the right triangle is x-3 = 12.6 degrees.
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Find the directional derivative, Duf, of the function at the given point in the direction of vector v. f(x, y) = 2 ln(x2 + y2), (2, 1), v = −1, 2
The directiοnal derivative οf [tex]f(x,y) = 2ln(x^2 + y^2)[/tex] at the pοint (2,1) in the directiοn οf the vectοr v = (-1,2) is 0.
Directiοnal derivative and gradient: what are they?A directiοnal derivative shοws hοw quickly a functiοn changes in any directiοn. A fοrmula that incοrpοrates the gradient can be used tο determine the directiοnal derivative. The gradient οf a functiοn οf mοre than οne variable shοws the directiοn οf greatest change.
We must cοmpute the dοt prοduct οf the gradient οf f at (2,1) with the unit vectοr in the directiοn οf v in οrder tο determine the directiοnal derivative οf the functiοn [tex]f(x,y) = 2ln(x2, + y2)[/tex] at the pοsitiοn (2,1) in the directiοn οf the vectοr v = (-1,2).
Then, we determine f's gradient:
Grad(f) is equal tο [tex](f/x, f/y) = (4x/(x2+y2), 4y/(x2+y2)[/tex]
Hence, the gradient at lοcatiοn (2,1) is as fοllοws:
grad [tex](f)(2,1) = (4(2)/(2^2+1^2), 4(1)/(2^2+1^2)) = (8/5, 4/5)[/tex]
The unit vectοr in the directiοn οf v is then lοcated:
||v|| = √((-1)²+ 2²) = √5\su = v/||v|| = (-1/√5, 2/√5)
We calculate the directiοnal derivative last.
Def = grad(f) (2,1) · u\s= (8/5)(-1/√5) + (4/5)(2/√5)\s= -8/5√5 + 8/5√5\s= 0
Hence, at pοint (2,1) in the directiοn οf the vectοr v = (-1,2), the directiοnal derivative οf f(x,y) = 2ln(x², + y²) is equal tο 0.
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Convert 9kilograms=____milligrams
Answer:
9000000 Milligrams
Step-by-step explanation:
We know that,
1 kilogram = 10^6 Miligram
So, 9 Kilpgrams = 9×10^6 = 9000000 Milligrams
A Bakery allows customers to design and order special cupcakes. There is a single fee of $4 to create the new design and then each special cupcake ordered costs $3.
thy be c matey truth me ARG!!??
Answer:7$
Step-by-step explanation:$4+3$=7$
find the balance in the account: $3,000 principal, earning 3% compounding annually, after 4 years
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.03}{1}\right)^{1\cdot 4}\implies A=3000(1.03)^4 \implies A \approx 3376.53[/tex]
Which graph represents the solution set of the inequality x + 2 greater-than-or-equal-to 6 A number line goes from negative 9 to positive 9. A solid circle appears on positive 3. The number line is shaded from positive 3 through negative 9. A number line goes from negative 9 to positive 9. An open circle appears at positive 3. The number line is shaded from positive 3 through positive 9. A number line goes from negative 9 to positive 9. A closed circle appears at positive 4. The number line is shaded from positive 4 through positive 9. A number line goes from negative 9 to positive 9. An open circle appears at positive 4. The number line is shaded from positive 4 through negative 9.
The shaded area to the right of 4 indicates all values larger than 4 being inequality included in the solution set, while the closed circle at 4 represents the number 4 being included in the solution set.
What is inequality?A relationship between two terms or values which is not equal is known as an inequality in mathematics. Inequality follows imbalances, therefore. In mathematics, an inequality makes a link among two quantities that are not equal. Egality and inequality are different. Use the not similar symbol most frequently when two components are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two parts until only the variables are left, one can solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left & right.
The graph below shows the set of solutions to the inequality where x + 2 is larger than or equal to 6:
From negative 9 to positive 9 is a number line. At positive 4, a closed circle appears. Positive numbers four through nine are shaded on the number line.
This means that the inequality will be satisfied by any value of x larger than or equal to 4. The graph includes the value 4 in the solution set since it has a closed circle there, and because it is shaded to the right of 4, it also includes all values higher than 4.
Here is an illustration of the graph:
|----|----|----|----|----|----|----|----|----|
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
o
---->
4
----]
>
|----|----|----|----|----|----|----|----|----|
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
The shaded area to the right of 4 indicates all values larger than 4 being included in the solution set, while the closed circle at 4 represents the number 4 being included in the solution set.
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The sum of the first two terms of a G.P is 5/2 , and the sum of the first four terms is 65/18. Find the G.P if r>0
Answer:
Common ratio r = [tex]\dfrac{2}{3}[/tex]
Sequence is described by
[tex]a_n = \dfrac{3}{2}\cdot \left(\dfrac{2}{3}\right)^{n-1}\\[/tex]
Step-by-step explanation:
[tex]S_n = \dfrac{a_1(1-r^n)}{1-r}[/tex]
where
r = common ratio
a₁ = first term
Sum of first two terms
[tex]S_2 = \dfrac{a_1(1-r^2)}{1-r}[/tex]
Sum of first four terms:
[tex]S_4 = \dfrac{a_1(1-r^4)}{1-r}[/tex]
[tex]\dfrac{S_4}{S_2} = a_1 \cdot \dfrac{1-r^4}{1-r} \div a_1 \cdot \dfrac{1-r^2}{1-r}\\[/tex]
To divide, flip the divisor and multiply
[tex]\dfrac{S_4}{S_2} =\dfrac{a_1(1-r^4)}{1-r} \times \dfrac{1-r}{a_1(1-r^2)}[/tex]
The a₁ and (1-r) terms cancel out from numerator and denominator leaving
[tex]\dfrac{S_4}{S_2} =\dfrac{1-r^4}{1-r^2} \cdots [1][/tex]
Using the identity
[tex]a^2 - b^2 = (a- b)(a+b)[/tex]
[tex]1- r^4 = 1^4 - r^4 = (1^2 - r^2)(1^2+r^2) = (1-r^2)(1+r^2)[/tex]
Plugging this into equation 1 we get
[tex]\dfrac{S_4}{S_2} =\dfrac{(1-r^{2})(1+r^{2})}{1-r^{2}}[/tex]
The [tex]1- r^2[/tex] terms cancel out leaving:
[tex]\dfrac{S_4}{S_2} =1 + r^2[/tex]
We are given
[tex]S_4 =\dfrac{65}{18}\\\\S_2 = \dfrac{5}{2}[/tex]
[tex]\dfrac{S_4}{S_2} = \dfrac{65}{18} \div \dfrac{5}{2}[/tex]
To divide, flip the denominator [tex]\dfrac{5}{2}[/tex] and multiply
[tex]\dfrac{S_4}{S_2} = \dfrac{65}{18} \times \dfrac{2}{5}\\\\= \dfrac{13}{9}[/tex]
Therefore
[tex]1 + r^2 = \dfrac{13}{9}\\\\r^2 = \dfrac{13}{9} - 1\\\\= \dfrac{13}{9} - \dfrac{9}{9}\\\\= \dfrac{4}{9}[/tex]
[tex]r = \sqrt{\dfrac{4}{9}}\\\\= \dfrac{\sqrt{4}}{\sqrt{9}}\\\\= \dfrac{2}{3}[/tex]
So the common ratio
[tex]r = \dfrac{2}{3}[/tex]
To find the first term we have sum of first two terms = 5/2
[tex]S_2 = \dfrac{a_1(1-r^2)}{(1-r)} = a_1 (1+ r)[/tex]
Plugging in knowns
[tex]\dfrac{5}{2} = a_1(1+\dfrac{2}{3})\\\\= a_1 \cdot \dfrac{5}{3}[/tex]
Multiply both sides by 3/5 to get
[tex]a_1 = \dfrac{5}{2} \times \dfrac{3}{5}\\\\a_1 = \dfrac{3}{2}[/tex]
The nth term of a GP is
[tex]a_n = a_1 \cdot r^{n-1}\\[/tex]
Plugging in the values obtained
[tex]a_n = \dfrac{3}{2}\cdot \left(\dfrac{2}{3}\right)^{n-1}\\[/tex]
I’M STUCK! BRAINLIEST TO WHOEVER CAN GET THIS QUESTION CORRECT!
The two column proof that shows that ΔADC ~ ΔDBC is as shown below.
How to complete the two column proof?A two-column proof is defined as a geometric proof that is said to consist of a list of statements, and the reasons for which those statements are true. The statements are thus listed in a column on the left, with the reasons for which the specific statements can be made are now listed in the right column.
The complete two column proof is expressed as:
Statement 1: ∠ADC is a right angle
Reason 1: Given
Statement 2: DB is perpendicular to AC
Reason 2: Given
Statement 3: ∠DBC is a right angle
Reason 3: Definition of Perpendicular
Statement 4: ∠ADC ≅ ∠DBC
Reason 4: All right angles are congruent
Statement 5: ∠C ≅ ∠C
Reason 5: Reflexive Property of Congruence
Statement 6: ΔADC ~ ΔDBC
Reason 6: AA Similarity
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A triangle has sides with lengths of 19 feet, 59 feet, and 69 feet. Is it a right triangle?
1) What are nonexample of base and exponent in math?
2) What are example and nonexample of coefficient and exponential form?
3)What are example and nonexample of expanded form and standarm form?
4) Lastly, what are example and nonexample of exponent laws?
Answer:
Nonexamples of base and exponent in math would be any mathematical expressions that do not involve raising a base to an exponent. For example, 2 + 3 or √4 do not involve base and exponent.
An example of coefficient and exponential form is 5x², where 5 is the coefficient and x² is the exponential form. A nonexample could be x²/5, which does not have a coefficient in front of the exponential form.
An example of expanded form is 5x + 2, where the expression is fully written out. The standard form of the same expression would be 2 + 5x. A nonexample of expanded form is 2(x + 3), where the expression is not fully written out.
Examples of exponent laws include the product rule (a^m * a^n = a^(m+n)), quotient rule (a^m / a^n = a^(m-n)), and power rule ((a^m)^n = a^(mn)). A nonexample of an exponent law could be the sum of powers rule, which does not exist in traditional exponent laws.
The solutions for all the parts are given below.
What is an exponent?Exponentiation is one of the mathematics operations.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by 'a' times to itself.
So, a is the exponent of m.
1) Non-examples of a base and exponent in math would be: "2 + 3" or "5 - 7" as these are expressions and not a base raised to an exponent.
2) An example of a coefficient and exponential form would be "2x^3" where 2 is the coefficient and x^3 is the exponential form. A nonexample would be "3x + 2" as it is an expression and not in exponential form.
3) An example of an expanded form would be 235 = 2 x 100 + 3 x 10 + 5 x 1, where each digit is multiplied by its corresponding place value. An example of standard form would be 235 written as is, without being broken down into its place values. A nonexample of expanded form would be 235 written as 2 + 3 + 5, as this is not a multiplication of the digits with their place values.
4). Examples of exponent laws include:
Product law: aᵇ x aⁿ = a⁽ᵇ ⁺ⁿ⁾
Quotient law: [tex]a^m / a^n = a^{(m-n)}\\[/tex]
Power law: [tex](a^m)^n = a^{(m \times n)}[/tex]
Negative exponent law: [tex]a^{(-n)} = 1/a^n[/tex]
Zero exponent law: [tex]a^0 = 1[/tex].
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Find the value of x in the isosceles triangle. Round to the nearest tenth if necessary.
The value of x is 15 inches, we find this by Pythagoras theorem and property of isosceles triangle.
What is Pythagoras Theorem?Pythagoras theorem states that sum of square of base and square of perpendicular is equal to square of hypotenuses.
So , it can be formula is given below ,
[tex]perpendicular^{2} + base^{2} = hypotenuse^{2}[/tex]
And In ab isosceles triangle two equal side vertex divide base in two equal parts.
So, here base = 40.
Therefore it is divided in 20-20 inches,
Now putting the formula of Pythagoras theorem, we get
[tex]20^{2} + x^{2} = 25^{2}[/tex]
[tex]x^{2} = 25^{2} - 20^{2}[/tex]
[tex]x^{2} = 225[/tex]
So we get, x = 15 inches.
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True
The following table is a function.
X
y
1
5
-3 2
7 2 6 3
7
-4 5
9
8 4 1
7
1 0
True
False
Given statement: Here's the table with the values organized:
X | Y
-----
1 | 5
-3 | 2
7 | 2
6 | 3
7 | -4
5 | 9
8 | 4
1 | 7
1 | 0
This statement is False.
Because, The table provided is not a function because it does not have a clear and unique output value for each input value.
Since the X values 1 and 7 have multiple Y values, the given table is not a function.
In a function, each input value (X) must have a unique output value (y). However, in the given table, there are some input values, such as X = 7 and X = 1, that have multiple output values. For example, when X = 7, the table provides two output values, 2 and -4. Similarly, when X = 1, the table provides two output values, 5 and 0.
A function is a mathematical relationship between the input and output values, where each input value produces only one unique output value. Functions are used to represent many real-world scenarios, including calculating distances, temperatures, and profits. Therefore, it is crucial to ensure that the provided table represents a function by ensuring that each input value has a unique output value.
In conclusion, the table provided is not a function as it violates the one-to-one mapping between input and output values.
A function must have a clear and unique output value for each input value.
To determine if the given table represents a function, we need to make sure that each input (X value) corresponds to only one output (Y value).
Now let's check for any repeating X values with different Y values:
1 corresponds to both 5 and 7
7 corresponds to both 2 and -4.
False.
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Look at the picture below if you have any questions comment
Answer:
95.522
Step-by-step explanation:
First, we have to find the area of the triangle...
We know that the equation for the area of a triangle is: [tex]\frac{1}{2} lw[/tex]This means that our solution would be: [tex]\frac{1}{2}[/tex] × [tex]8[/tex] × [tex]6[/tex] = [tex]24[/tex]Next, we have to find the area of the sector...
We know that the equation for the area of a circle is: πr²This means that our solution would be: π × 10² = 314As the sector is only 82° so we have to do: 360 ÷ 82 = 4.39024390244So we have to do 314 ÷ 4.39024390244 = 71.5222...(recurring)Now we have to add our results together...
71.5222...(recurring) + 24 = 95.5222...(recurring)Rounded to the nearest hundredth: 95.522Hope this helps, have a lovely day! :)
The grain required to produce 100 L of ethanol can feed a person for a year, Around 49 billion liters more ethanol was produced in US from corn in 2018 than in 2001, how many people could this have fed?
Step-by-step explanation:
Assuming that the grain required to produce 100 liters of ethanol could feed one person for a year, we can calculate the number of people that could have been fed by the additional 49 billion liters of ethanol produced in the US from corn between 2001 and 2018.
First, we need to determine the amount of grain required to produce 1 liter of ethanol. This can vary depending on a number of factors, including the type of grain and the production method, but a commonly cited estimate is that it takes around 1.4 kilograms of corn to produce 1 liter of ethanol.
Therefore, to produce 49 billion liters of ethanol, we would need:
49,000,000,000 liters x 1.4 kg of corn per liter = 68,600,000,000 kg of corn
To convert this to the amount of grain required to feed people, we need to divide by the amount of grain needed to feed one person for a year. Again, this can vary depending on the person's age, sex, and level of activity, but a commonly cited estimate is that an adult needs around 700 kilograms of grain per year.
Therefore, the amount of grain required to feed the number of people who could have been fed by the grain used to produce the additional ethanol is:
68,600,000,000 kg of corn / 700 kg of corn per person per year = 98,000,000 people
So the additional 49 billion liters of ethanol produced in the US from corn between 2001 and 2018 could have fed around 98 million people for a year.
The additional ethanol production from corn in 2018 could have potentially fed 49 billion people
To determine how many people could have been fed with the additional 49 billion liters of ethanol produced in the US from corn in 2018 compared to 2001, we need to calculate the amount of grain saved by producing ethanol instead of using it for direct consumption.
According to the information given, the grain required to produce 100 liters of ethanol can feed a person for a year. Therefore, for each liter of ethanol produced, the grain equivalent can sustain one person for a year.
To find the number of people fed, we can multiply the additional 49 billion liters of ethanol produced by the grain equivalent for each liter:
49 billion liters * 1 person/year per liter = 49 billion people
Hence, the additional ethanol production from corn in 2018 could have potentially fed 49 billion people based on the assumption that the grain used to produce ethanol would have been used for direct consumption instead.
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a square whose side measures 2 centimeters is dilated by a scale factor of 3. what is the difference de tween the area of the dilated square and the original square?
After solving the given problem, we found that the difference between the area of the dilated square and the original square is 32 square centimeters.
The area of the original square with a side length of 2 centimeters can be calculated as:
A = s²
A = 2²
A = 4 square centimeters
When this square is dilated by a scale factor of 3, the new side length will be:
s' = 3s
s' = 3(2)
s' = 6 centimeters
The area of the dilated square can be calculated as:
A' = s'²
A' = 6²
A' = 36 square centimeters
The difference between the area of the dilated square and the original square is:
A' - A = 36 - 4
A' - A = 32 square centimeters
Therefore, the difference between the area of the dilated square and the original square is 32 square centimeters.
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Solve the system
0.2x+y=1.3
2(0.5x-y)=4.6
Answer:
x = 36/7 (or approximately 5.143); y = 19/70 (or approximately 0.271)
Step-by-step explanation:
First, we can distribute the 2 to have both equations look similar:
[tex]2(0.5x-y)=4.6\\x-2y=4.6[/tex]
Now, we can eliminate the ys by multiplying the entire first equation by 2. This will allow us to solve for x.
[tex]2(0.2x+y=1.3)\\\\0.4x+2y=2.6\\x-2y=4.6\\\\1.4x=7.2\\x=\frac{36}{7}\\ x=5.142857143[/tex]
Now, we can plug in 36/7 for x in any of the two equations:
[tex]0.2(\frac{36}{7})+y=1.3\\ \frac{36}{35}+y=1.3\\ y=\frac{19}{70}\\ y=0.2714285714[/tex]
If you use the decimal answers, you can round as much as you need.
Can anyone find the first and second derivative for #26?? I’m gonna go crazy pls help
The first derivative of y is: y' = [4tan(πt)sec(πt) - πsec²(πt)]/(π³) and
The second derivative of y is: y'' = [4sec(πt)(π²sec²(πt) - 3πtan(πt))]/(π⁴)
What are first and second derivative?The first derivative of a function represents the rate of change or slope of the function. The second derivative represents the rate of change of the first derivative or the curvature of the function.
To find the first derivative of y, we use the quotient rule:
y = [tan(πt)/π²] + [4 sec(πt)/π²]
y' = [π²(sec²(πt)) - 2tan(πt)sec(πt)]/(π⁴) + [4πsec(πt)tan(πt)]/(π⁴)
Simplifying this expression, we get:
y' = [(πsec(πt))(4tan(πt) - πsec(πt))]/(π⁴)
y' = [4πtan(πt)sec(πt) - π²(sec²(πt))]/(π⁴)
To find the second derivative of y, we again use the quotient rule:
y'' = [(π³(sec³(πt)) - 12πtan(πt)sec²(πt)) - 2π(4tan(πt)sec(πt) - πsec²(πt))(πsec(πt))]/(π⁶)
Simplifying this expression, we get:
y'' = [(4πsec(πt))(π²(sec²(πt) - 3tan(πt)))]/(π⁶)
y'' = [4sec(πt)(π²sec²(πt) - 3πtan(πt))]/(π⁴)
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The retail price at the department store is calculated by increasing the wholesale price by 40%. That is, the retail price is calculated by adding 40% of the selling price to the selling price as well. a) What is the retail price of a piece of clothing if its wholesale price is $300? b) What is the selling price of a pair of jeans if its retail price is $77?
Using the given information, we calculated the following prices:
a) The retail price is $420
b) The wholesale price is $55
What are retail and wholesale prices?
The processes of wholesale and retail are essentially distinct from one another because they entail the transfer of commodities from manufacturing to distribution. Purchasing products and selling them to clients constitute retail.
Retailers pay wholesale pricing to producers or distributors. Then, the shop charges customers a higher price—the retail price—for the identical product. Wholesale pricing is what you charge retailers who buy things in large amounts. With wholesale pricing, products are sold for more money than it costs to produce them in order to generate a profit.
The final selling price that retailers decide to charge customers is known as the retail price. In retail pricing, the customer is everything.
Let,
The retail price = x
The wholesale price = y
Then,
x = y + 0.4y = 1.4y
a) When y = $300
x = 1.4 * 300 = $420
b) When x = $77
77 = 1.4y
y = 77/1.4 = $55
Therefore using the given information, we calculated the following prices:
a) The retail price is $420
b) The wholesale price is $55
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Determine a series of transformations that would map polygon ABCDE onto polygon
A'B'C'D'E'?
The sequence of transformations is:
Reflection over the x-axis.Reflection over the y-axis.Translation of 3 units to the right.How to find the series of transformations?Let's only follow the coordinates of one of the vertices to identify the transformations, we clearly have a reflection over a vertical line and a reflection over a horizontal line, so first let's apply thes two.
Vertex A starts at (1, -4)
First a reflection over the x-axis will change the sign of the y-component, then we get:
A₁ = (1, 4)
Then a reflection over the y-axis changes the sign of the x-component to:
A₂ = (-1, 4)
Finally we have a translation, we can see that:
A' = (2, 4).
Then we have a translation (a, b) such that:
(-1 + a, 4 + b) = (2, 4)
So we can see that a = 3 and b = 0, then we have a translation of 3 units to the right.
That is the sequence of transformations.
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I just need the table
1) The nth term if the sequences are (a) 9a-7 (b) 13-6a
How to determine the sequence?A sequence is a list of numbers or objects in a special order.1 It is an enumerated collection of objects in which repetitions are allowed and order matters.
The given sequences are
1) (a) 2,11,20,...
the first term a= 2, the common difference d = 11-2 =9
The nth term is given as
Tn = a + (n-1)d
Tn = 2 + (n-1)*9
Opening the brackets to get
2 + 9n -9
Rearrange to have
9n -7
(b) the sequence is 7,1,-5,...
a = 7 ,
d= 1-7 = -6
Tn = a + (n-1)d
Tn = 7 + (n - 1)-6
Tn = 7 + -6n +6
Tn = 7+6 -6n
Tn = 13 -6n
2) Remember for every Fibonacci sequence
1st+2nd=3rd
2nd+3rd=4th
3rd+4th=5th
4th+5th=6th
Remember for every arithmetic Progression
Tn = a + (n-1)d
For every Geometric Progression,
Tn = arⁿ⁻¹
First five terms Next three terms Name of sequence(A,G,F,Q)
10,6,2,-2,-6 -10,-14,-18 arithmetic
2,8,32,126512 2048, 8192,32768 Geometric
20,13,33,46,79 125,204,329 Fibonacci
200,100,50,25,12.5 6.25, 3.125, 1.5625 Geometric
46,39,32,25,18, 11,4 , -3 Arithmetic
-2,,2,0,2,2,4 6,10,16 Fibonacci
3,6,10,15, 21 28,35,42 Arithmetic
25,15,0,-20,-45, -80,-125,-175 Arithmetic
2,5,7,12,19 31,50,81 Fibonacci
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Find the length of BC
bc=√{ac²-ab²}
bc=√{16²-11²}
bc=√{256-121}
bc=√{135}
bc=11.62
Please help! I need the answer to the whole of the question!
A coffe costs x pence. A teas costs 20pence less than coffe.
a) write an expression in term of x ___pence
b) write an expression in the terms of x, for the total cost of 3 coffees and 2 teas
Answer:
x+3+3
Step-by-step explanation:
So bassicly you have to add everything up ad then divide by 1
Consider the right triangle below:
The length of the missing leg, AC= meters
Round your answer to the nearest tenth.
Note: Figure not drawn to scale and all the measurements are in meters.
What is the perimeter of triangle ABC
Suppose you borrow $5000 at a 21% annual interest rate, compounded monthly (1.75% each month). At the end
of each month, you make a $325 payment.
Use this information to complete the table below. Round to the nearest cent as needed.
Month
1
2
3
4
5
Prior Balance
$
$5000
$4520.84
Question Help: Video
1.75% Interest
on Prior Balance
S
$74.81
Monthly Payment
$325
$325
$325
$325
Ending Balance
$
S
$5000
$4520.84
Answer:
Step-by-step explanation:
To fill in the table, we can use the following steps:
Calculate the interest for each month, which is the prior balance multiplied by the monthly interest rate (1.75%).
Subtract the monthly interest from the prior balance to get the new balance before the monthly payment.
Subtract the monthly payment from the new balance to get the ending balance.
Month Prior 1.75% Interest on Monthly Ending
Balance Prior Balance Payment Balance
1 $5000 $87.50 $325 $4762.50
2 $4762.50 $83.39 $325 $4520.84
3 $4520.84 $79.06 $325 $4276.90
4 $4276.90 $74.50 $325 $4029.23
5 $4029.23 $69.69 $325 $3777.87
Therefore, after 5 months of making $325 payments, the remaining balance on the loan is $3777.87.
Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.
Answer: Let's assume that the speed of the plane in still air is represented by p and the speed of the wind is represented by w.
When the plane is flying with the tailwind, its speed relative to the ground is the sum of its speed in still air and the speed of the wind, or (p + w). Similarly, when the plane is flying against the wind, its speed relative to the ground is the difference between its speed in still air and the speed of the wind, or (p - w).
We can set up two equations based on the given information:
(p + w) = 158 (1) (when flying with the tailwind)
(p - w) = 112 (2) (when flying against the wind)
To solve for p and w, we can add equations (1) and (2):
2p = 270
p = 135
So the speed of the plane in still air is 135 km/h.
We can then substitute this value of p into equation (1) to solve for w:
(p + w) = 158
(135 + w) = 158
w = 23
So the speed of the wind is 23 km/h.
Therefore, the plane flies at 135 km/h in still air and the wind blows at 23 km/h.
Step-by-step explanation: