The inequality is written as 8p ≤ 56. Then the number of pounds of candy will be 7 pounds.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Goran buys candy that costs $8 per pound. He will spend at least $56 on candy.
Let 'p' be the number of pounds of the candy. Then the inequality is given as,
8p ≤ 56
p ≤ 56 / 8
p ≤ 7
The inequality is written as 8p ≤ 56. Then the number of pounds of candy will be 7 pounds.
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Lyla invested $140. She earned a simple interest of 3% per year on the initial investment. If no money was added or removed, what is the amount of money Lyla will earn at the end of two years?
Answer:
8.40
Step-by-step explanation:
Since, the simple interest is,
I= p x r x t
100
Where,
P=Principal
r= rate per periods
t= number of periods
Here, P=140, r=3%, t = 2,
the simple interest will be
I= 140 x 3 x 2
100
= 840
100
=8.40
Rusty Reft, who lives in Territory 5, carries 10/20/5 compulsory liability insurance along with optional collision that has a $300 deductible. Rusty was at fault in an accident that caused $1,400 damage to the other auto and $3,100 damage to his own vehicle. Also, the courts awarded $12,800 and $9,200, respectively, to the two passengers in the other car for personal injuries.
a. How much will the insurance company pay?
b. What is Rusty’s share of the responsibility?
Answer:
A = $2,800 B = $12,600
Step-by-step explanation:
a. How much will the insurance company pay?
The liability insurance will cover the damages to the other car ($1,400) and the personal injury claims ($12,800 + $9,200) up to the limit of $10,000. So the insurance company will pay $10,000.
The collision insurance covers the damage to Rusty's own car, minus the $300 deductible, so the insurance company will pay $3,100 - $300 = $2,800.
Therefore, the insurance company will pay a total of $10,000 + $2,800 = $12,800.
b. What is Rusty’s share of the responsibility?
Rusty is responsible for paying the remaining amount not covered by insurance, which is $1,400 + $3,100 + $12,800 + $9,200 - $12,800 = $12,600.
Therefore, Rusty's share of the responsibility is $12,600.
A company model it net income, in thouand of dollar, with the function f(x) = 9x2 – 54x – 144, where x i the number of unit of it product old. How many unit of it product doe the company need to ell in order for the net income to equal $0?
The company needs to produce 8 units in order for the net income to equal $0
What is factoring?Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.
the equation given can be simplified as:
f(x) = 9x² - 54x - 144.
f(x) = 9(x² - 6x - 16)
Then factoring we have:
f(x) = 9[(x + 2)(x - 8)]
It has a net income equals to 0 when:
f(x) = 0, so the variables are:
x + 2 = 0 -> x = -2
x - 8 = 0 -> x = 8
As the amount of products sold have to be positive the amount of product is 8
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this is due tomorrow pls help
Note that the angle that is vertical to ∠AEB is ∠BEC.
What is a vertical angle?Vertical angles are the angles formed when two lines intersect. The term "vertical" in this context refers to the fact that they share the same Vertex (corner point), rather than the normal connotation of up-down.
Vertical angles of equal measure are always congruent. Both vertical angle pairings (four angles total) always add up to 360 degrees. Angles formed by each pair of vertical angles are referred to as neighboring angles, and they are supplementary (the angles sum up to 180 degrees).
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Peterson Products calculates its pension benefits as follows: Years of service × 1.98% multiplier × Average of last two annual salaries What is Mary’s monthly pension benefit if she worked for Peterson for 28 years and her last two annual salaries were $78,000 and $80,000?
Mary's monthly pension benefit is $3,649.80.
First, we have to find the average salary.
The average is the sum of the salaries divided by the number of salaries.
($78,000 + $80,000)/2 = $79,000
Next, we can find the annual retirement rate.
The annual retirement pension is the product of the average, the rate and the number of years employed.
$79,000 x 1.98% x 28 = $43,797.60
Finally, we can find the monthly retirement pension.
The monthly retirement pension is then the annual retirement pension divided by the number of months in a year.
There are 12 months in a year.
$43,797.60 / 12 = $3,649.80
Therefore, Mary's monthly pension benefit is $3,649.80.
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evaluate the line integral where c is the straight line segment from point to point
The line integral [tex]\int_{c}xds[/tex]where c is the straight line segment from point (1, 2) to point (5, 10) is 12√5.
Using the two-point form of the line, we can compute the equation of the line connecting the points and obtain:
y = 2x
Consider x = t. Now the result is:
y = 2t
We can write C as:
[tex]\vec{r}(t)=t\hat{i}+2t\hat{j}[/tex]
Now, t ranges from t = 1 to t = 5 since x = t and x range from x = 1 to x = 5. When we differentiate the C equation, we obtain:
[tex]\vec{r}'(t)=\hat{i}+2\hat{j}[/tex]
Now finding the magnitude
[tex]|\vec{r}'(t)|=\sqrt{(1)^2+(2)^2}[/tex]
[tex]|\vec{r}'(t)|=\sqrt{1+4}[/tex]
[tex]|\vec{r}'(t)|=\sqrt{5}[/tex]
Now, the integral will be:
I = [tex]\int_{t=1}^5t\:(\sqrt 5)dt[/tex]
I = [tex]\sqrt {5}\int_{t=1}^5tdt[/tex]
Now integrating
I = [tex]\sqrt {5}\left(\frac{t^2}{2}\right)_{t=1}^{5}[/tex]
I = [tex]\sqrt {5}\left(\frac{5^2}{2}-\frac{1^2}{2}\right)[/tex]
I = √5(25/2 - 1/2)
I = √5(12.5 - 0.5)
I = 12√5
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The complete question is:
Evaluate the line integral [tex]\int_{c}xds[/tex]where c is the straight line segment from point (1, 2) to point (5, 10).
problem 3: compute the general solution for: d 2 y dt2 − 2 dy dt − 15y = e 4t
The general solution for given equation is y = c₁e^5t + c₂e^-3t - (1/7)e^4t.
A differential equation is an equation that contains at least one derivative of an unknown function, either an ordinary derivative or a partial derivative. Suppose the rate of change of a function y with respect to x is inversely proportional to y, we express it as dy/dx = k/y.
In calculus, a differential equation is an equation that involves the derivative (derivatives) of the dependent variable with respect to the independent variable (variables). The derivative represents nothing but a rate of change, and the differential equation helps us present a relationship between the changing quantity with respect to the change in another quantity. y=f(x) be a function where y is a dependent variable, f is an unknown function, x is an independent variable.
We have to find the general solution for d²y/dt² - 2 dy/dt - 15y = e^4t
Solving the above ordinary differential equation, we get:
y = c₁e^5t + c₂e^-3t - (1/7)e^4t
Thus, the general solution for given equation is y = c₁e^5t + c₂e^-3t - (1/7)e^4t
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Use the gcf and the distributive property to find the sum of 15+36
Answer: br uh is this even a high school question? anyway, look at the image that i sent you can see the answer there.
better give me brainliest
Step-by-step explanation:
PLS HELP WILL GIVE ALOT OF POINTS DOMAIN AND RANGE
The range of the function lies between -∞<y<∞ and the domain of the function is given by -1<x<3
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: The graph of a function
We know The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
It is clear from the graph that y ∈ (-∞,∞) and x∈ (-1,3)
we know a function is given by y=f(x)
where y is the range values and x is the domain.
Hence, The range of the function lies between -∞<y<∞ and the domain of the function is given by -1<x<3
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I NEED HELP!!!!!!!!!
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Find the missing values of the variables. The diagram is not to scale.
Answer:
y = 64
x = 99
Step-by-step explanation:
180 - 116 = y
y = 64
A parallelogram is 360 degrees.
360 - 72 -125 - 64 = x
x = 99
I hope this helps!
Which function has a percent rate of decrease equal to 5%?
A. F(x) = 3(0. 5)*
B. F(x) = 3(1. 5)
C. F(x) = 3(0. 05)
D. F (x) = 3(0. 95)
E. F(x) = 3(1. 05)
Among the given, the function that has a percent rate of decrease equal to 5% is: F(x) = 3(0.95)
Hence, option (D) is the correct choice.
For (A):
We have,
F(x) = 3(0.5), Here percentage rate decrease = 50%
For (B):
We have,
F(x) = 3(1.5), Here there is percentage rate increase which will be = 50%
For (C):
We have,
F(x) = 3(0.05), Here percentage rate decrease = 95%
For (D)
F(x) = 3(0.95)
Here, percent rate of decrease equal to 5%
This function represents the relationship between input x and the output y where y = 3(0.95^x).
The number 0.95 can be interpreted as 95% of the original value, which means a 5% decrease.
For (A):
We have,
F(x) = 3(1.05), Here there is percentage rate increase which is = 5%
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A random sample of 9th-grade students was asked if they prefer taking notes on a computer or using a pencil. Of the 180 students who were surveyed, 75 said they preferred using the computer. The resulting 99% confidence interval of the proportion of students who prefer taking notes on the computer was (0. 322, 0. 511). The school newspaper ran a story saying that less than half of the body prefers taking notes on a computer. Based on the interval, is the newspaper justified in this statement?
The newspaper's assertion is unjustified. It can be shown that the interval does not contain 0.5 based on the 99% confidence interval of (0.322, 0.511). (which is half).
This indicates that the population parameter (mean, percentage, and standard deviation) is between a and b with x% confidence.
This indicates that at least half of students prefer using a computer to take their notes. Since the interval's lower limit (0.322) is higher than 0.5, there is a 99% likelihood that the actual percentage of students who prefer taking notes on computers is higher than 0.5.
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Find the distance between A and B. Round to the nearest hundredth.
A (-3,-6)
B (-6,1)
Answer: 10.30
Step-by-step explanation:
Distance formula = [tex]\sqrt{(x_{2} +x_{1})^2+(y_{2} +y_{1})^2}[/tex]
A ([tex]x_{1} ,y_{1}[/tex]) = A(-3,-6) so [tex]x_{1} = -2[/tex] and [tex]y_{1} =-6[/tex]
B ([tex]x_{2} ,y_{2}[/tex]) = B(-6, 1) so [tex]x_{2} = -6[/tex] and [tex]y_{2} = 1[/tex]
Plug in the values. You should get [tex]\sqrt{(-6 +-3)^2+(1 +-6)^2}=\sqrt{(-9)^2+(-5)^2}=\sqrt{81+25}=\sqrt{106}[/tex]
≈10.30
How do you convert 200 Kilogram (kg) to Pound (lb)?
The actual weight of a pound is 0.45359237 kilos.
How much in kilogrammes are converted to pounds?To Change the Price Per Pound (Pp) to the Price Per Kilogram (Kg), In order to convert cost per kilogramme to cost per lb, simply multiply the kg price by 2.2046 to get the lb price.In essence, one kilogramme is equivalent to two pounds (there is a longer decimal position, but I abbreviate it to 2.2046).In the fields of mathematics and engineering, converting from kilogrammes to pounds is a frequent operation; fortunately, it is also a simple one. For most conversions, all you need to do is multiply the number of kilogrammes by 2.2 to get the number of pounds.To learn more about Pound (lb) refer to:
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Small market orders copies of a certain magazine for its magazine rack each week. Let X = demand for the magazine, with the following pmf. X 1 2 3 4 5 6 p(x) 1 14 2 14 3 14 3 14 2 14 3 14 Suppose the store owner actually pays $2. 00 for each copy of the magazine and the price to customers is $4. 0. If magazines left at the end of the week have no salvage value, is it better to order three or four copies of the magazine? [Hint: For both three and four copies ordered, express net revenue as a function of demand X, and then compute the expected revenue. ] What is the expected profit if three magazines are ordered? (Round your answer to two decimal places. ) $ 27/7 Incorrect: Your answer is incorrect. What is the expected profit if four magazines are ordered? (Round your answer to two decimal places. ) $ How many magazines should the store owner order
Small market orders copies of a certain magazine for its magazine rack each week. The number of copies to order to generate more revenue is 4.
Let the profit y, the demand for the magazine be x , the number owner ordered k , then we get :
y = 4x - 2m ( m > x)
y = 2m ( m ≤ x)
If m = 3 we get
E (y) = 1/14 (4 - 2x3) + 2/14 (4x2 - 2x3) + 3/14 (2x3) + 3/14 (2x3) + 2/14 (2x3) + 3/14 (2x3)
E(y) = 68/14
If m = 4 get,
E (y) = 1/14 (4 - 2x4) + 2/14 (4x2 - 2x4) + 3/14 (4x3 -2x4) + 3/14 (2x4) + 2/14 (2x4) + 3/14 (2x4)
E(y) = 72/14
E (y)m=4 > E(y)m=3
So order number is 4.
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When u, v are nonzero vectors, then Span{u, v} contains only the line through u and the origin, and the line through v and the origin.
When u, v are nonzero vectors, then Span{u, v} contains only the line through u and the origin, and the line through v and the origin, this statement is false.
The span of two nonzero vectors u and v, Span{u, v}, is the set of all linear combinations of u and v. This set can include not only the lines through u and the origin, and the line through v and the origin, but also all other points on the plane defined by these two lines.
For example, if u = (1, 0) and v = (0, 1), then Span{u, v} would be the set of all points in the x-y plane, since every point in the plane can be represented as a linear combination of u and v.
Therefore, Span{u, v} contains not only the lines through u and the origin, and the line through v and the origin, but all other points on the plane defined by these two lines.
Correct Question :
When u, v are nonzero vectors, then Span{u, v} contains only the line through u and the origin, and the line through v and the origin. True or fasle.
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A pair of gloves are on sale for 20% off
the original price of $4.99. About how
much will a person save buying the
gloves on sale?
Answer: 3.99
Step-by-step explanation:
I dont understand may you please help me
Answer:66
Step-by-step explanation:
336666
8. (6 pts) At a local garden shop, the price of plants includes sales tax. The cost of 4 large plants and 8
medium plants is $40. The cost of 5 large plants and 2 medium plants is $28.
b) Could the cost of one large plant be $5.50 and the cost of one medium plant be $2.25? Justify your
answer.
c)
Determine algebraically both the cost of a large plant and the cost of a medium plant
By solving a system of equations we will see that a large plant costs $4.50 and a medium one $2.75
How to find the costs of the plants?Let's define the variables:
x = cost of a large plant.
y = cost of a medium plant.
We know that " The cost of 4 large plants and 8 medium plants is $40"
4*x + 8*y = 40
And "The cost of 5 large plants and 2 medium plants is $28."
5*x + 2*y = 28
So we have a system of equations:
4*x + 8*y = 40
5*x + 2*y = 28
We can isolate x on the first equation to get:
4x + 8y = 40
4x = 40 - 8y
x = (40 - 8y)/4
x = 10 - 2y
Replacing that in the other equation we will get:
5*(10 - 2y) + 2*y = 28
50 - 10y + 2y = 28
50 - 28 = 8y
22 = 8y
22/8 = y
2.75 = y
And the value of x is:
x = 10 - 2*2.75 = 4.5
Then the cost of a lare plant is $4.5 and the cost of a medium plant is $2.75.
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8-2. Skills Practice. Multiplying a Polynomial by a Monomial.
To multiply a polynomial by a monomial, you must first identify the terms in the polynomial, as well as the factors in the monomial. Once you have identified the components, use the distributive property to multiply each term of the polynomial by the monomial. Then, combine like terms and simplify the resulting polynomial.
For example:
To multiply 3x2 + 2x - 5 by 2x, you would use the distributive property to multiply each term of the polynomial by the monomial: 3x2 * 2x = 6x3, 2x * 2x = 4x2, and -5 * 2x = -10x. The resulting polynomial is 6x3 + 4x2 - 10x.Learn more about Polynomial: https://brainly.com/question/24662212
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The formula for the perimeter of a rectangle is. Part a. Rewrite the formula for the perimeter of a rectangle in terms of the width. In your final answer, include all of your work. Part b. In two or more complete sentences, describe the process you followed while isolating the variable in the equation.
The isolation of variable in the equation will result in the formula - Breadth = (Perimeter - 2length)/2.
As per the known information, the formula of the perimeter of rectangle is -
Perimeter = 2 (length + breadth)
Expanding the formula we get -
Perimeter = 2length + 2breadth
Rewriting in terms of breadth -
2Breadth = Perimeter - 2length
Breadth = (Perimeter - 2length)/2
The process to isolate the variable will require expanding and rewriting the equation with breadth on Left Hand Side of the equation. Now, move the constant on Right Hand Side and you will get the formula.
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Two athletes practice for a marathon by running back and forth on an 11-mile course. They start running simultaneously, one at a speed 2 mph faster than the other's speed. How fast does each run if they meet 1 hour 6 minutes after starting? (The faster runner is already returning at this point. ) How far from the starting point do the runners meet? The speed of the faster runner is mph. The speed of the slower runner is mph. The distance from the starting point is miles
The speed distance of the faster runner is 8 mph, and the speed of the slower runner is (8 - 2) = 6 mph.
The speed of the faster runner is 8 mph.
The speed of the slower runner is 6 mph.
The distance from the starting point is 5.5 miles.We can use the formula d = rt, where d is the total distance, r is the rate (speed) and t is the time taken to cover the distance.
Let us assume that the speed of the faster runner is x mph. Then, the speed of the slower runner is (x-2) mph.
Since the two runners meet 1 hour 6 minutes after starting, the total time taken is 1 hour 6 minutes = 66 minutes.
Thus, the total distance covered = (x * 66) + (x - 2) * 66 = 132x - 132
But, the total distance covered is 11 miles, so
132x - 132 = 11
Solving for x, we get
x = 8 mph
Therefore, the speed of the faster runner is 8 mph, and the speed of the slower runner is (8 - 2) = 6 mph.
Since they meet 1 hour 6 minutes after starting, they have travelled a total distance of (8 * 66) + (6 * 66) = 5.5 miles. Therefore, the distance from the starting point at which they meet is 5.5 miles.
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I need help ASAP. I can’t figure out the answer can someone give it or explain the answer?
1.5 cm is the data range. The number sequence "4, 6, 9, 3, 7" is an example where the lowest value is 3 and the highest is 9. The range is therefore 9 3 = 6. Just like that!
What is meant by data range?In statistics, the range of your data is the range between the lowest and greatest values of the distribution. It acts as a typical sign of unpredictable behavior.Measurements of variability provide descriptive statistics for your data set's summary, together with measures of central tendency. In a list or collection of numbers, the range is the difference between the lowest and highest integers. Place all the numbers in order before attempting to determine the range. The lowest number is then subtracted (subtracted) from the greatest number. The range is the range of values, i.e., the range between the lowest and highest values. The lowest value is 3 and the highest is 9 in the example number sequence "4, 6, 9, 3, 7." As a result, the range is 9 3 = 6. Simple as that!Q3 - Q1 is the interquartile range (IQR).
The third quartile (Q3) of the box plot is the data value that exactly matches the end of the box's edge (7 cm).
The data value exactly at the box's outside edge (5.5 cm) is the first quartile (Q1).
Range between quartiles (IQR): 7 - 5.5 = 1.5 cm
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Can anyone help me solve this?
On the right side, we can just simplify the expression to 1+tanθ+cotθ
The Identity equationYes, this is true.
The left side of the equation can be simplified to 1, which is equal to the right side.
Left side:
(cotθ/1-tanθ)+(tanθ/1-cotθ)
= (cotθ + tanθ)/(1 - tanθ - cotθ)
= (tanθ + cotθ)/(1 - tanθ - cotθ)
= 1/(1 - tanθ - cotθ)
= 1
Right side:
1 + tanθ + cotθ = 1
To prove that this equation is true for any value of θ, we must first expand and simplify each side of the equation. On the left side, we can express the fraction as a product of two terms, giving us (cotθ*(1-tanθ))+(tanθ*(1-cotθ)).We can then factor out cotθ and tanθ, giving us (cotθ*(1-tanθ+1-cotθ))+(tanθ*(1-cotθ+1-tanθ)).We can then combine the terms that are being multiplied by each side to get (cotθ+tanθ)*(1-tanθ-cotθ). Since the brackets are equal to 0, this simplifies to 0*(1-tanθ-cotθ), which is equal to 0.To learn more about Identity equation refer to:
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Answer:
See proof below
Step-by-step explanation:
(Please excuse any typos and point them out to me. It is a pain typing in LateX)
We are asked to prove:
[tex]\dfrac{\cot\theta}{1-\text{\ensuremath{\tan\theta}}}+\dfrac{\tan\theta}{1-\cot\theta}=1+\tan\theta+\cot\theta[/tex]
Since
[tex]\tan\theta =\dfrac {\sin\theta}{\cos\theta}\\\\\cot\theta = \dfrac {\cos\theta}{\sin\theta}\\\\[/tex]
the left side becomes
[tex]\dfrac{\cos\theta/\sin\theta}{1-\sin\theta/\cos\theta}+ \dfrac{{\sin\theta/\cos\theta}}{1-\cos\theta/\sin\theta} \cdots \cdots \cdots(1)[/tex]
For ease of expressing this let
[tex]a = \sin\theta\\b = \cos\theta\\[/tex]
Substituting the above in expression (1) gets us
[tex]\dfrac{b/a}{1- a/b} + \dfrac{a/b}{1-b/a}[/tex]
Let's take the individual terms and simplify each
[tex]\dfrac{b/a}{1- a/b} = \dfrac{b}{a}\cdot \dfrac{1}{1-\dfrac{a}{b}}[/tex]
[tex]\dfrac{1}{1-\dfrac{a}{b}}= \dfrac{1}{\dfrac{b-a}{b}}=\dfrac{b}{b-a}[/tex]
Therefore
[tex]\dfrac{b}{a}\cdot\dfrac{b}{b-a} = \dfrac{b^2}{a(b-a)}[/tex]
For the second term we get
[tex]\dfrac{a/b}{1-b/a} = \dfrac{a^2}{b(a-b)}[/tex]
Noting that (a - b) = - (b - a)
the entire expression becomes
[tex]\dfrac{b^2}{a(b-a)} = - \dfrac{a^2}{b(b-a)}[/tex]
Multiply this expression throughout by the LCM which is
[tex]ab(b-a)[/tex]
[tex]\dfrac{b^2 \cdot b - {a^2}\cdot a}{ab(b-a)}\\\\= \dfrac{b^3 - a^3}{ab(b-a)}\cdots\cdots(2)\\[/tex]
(b -a) cancels in numerator and denominator on both sides giving
For the numerator we have the identity
[tex]b^3 - a^3 = (b-a)(b^2 + ab + b^2)[/tex]
So the expression in (2) becomes
[tex]\dfrac{(b-a)(b^2 + ab + a^2)}{ab(b-a)}\\\\\textrm{(b-a) cancels from the numerator and denominator}\\\\[/tex]
This leaves us with:
[tex]\dfrac{(b^2 + ab + a^2)}{ab}[/tex]
Substituting for a = sinθ and b = cosθ we get
[tex]\dfrac{\cos^2\theta + \sin^2\theta+ \cos\theta\sin\theta}{\sin\theta\cos\theta}[/tex]
Divide each term in the numerator by [tex]\sin\theta \cos\theta[/tex]
==> [tex]\dfrac{cos^2\theta}{\sin\theta\cos\theta} + \dfrac{\sin^2\theta}{\sin\theta\cos\theta}+ \dfrac{\sin\theta\cos\theta}{\sin\theta\cos\theta}}[/tex]
==> [tex]\dfrac{\cos\theta}{\sin\theta} + \dfrac{\sin\theta}{\cos\theta} + 1[/tex]
[tex]\cot\theta + \tan\theta + 1\\== > 1 + \tan\theta + \cot\theta[/tex]
Hence PROVED
-5x+15
5x-25
4a+13
5x-25
The value of the equations if they are zero each are: 3, 5, -13/4 and 5
What is an equation?By definition, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =
The given equations are
-5x+15=0
-5x = -15
Making x the subject of the relation we have
x=3
2) 5x-25 = 0
Collecting like terms
5x=25
Making x the subject
x=5
3) 4a+13=0
4a = -13
Making a the subject of the relation
a=-13/4
4) 5x-25=0
Collecting like terms
5x=25
Making x the subject of the relation
x=5
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The CEO of the Wild Widget Company has decided to invest $360, 000 in his Michigan facgory. His economic analysts have noted that the output of this factory is modeled by the function Q : (0,[infinity])^2 → R given by Q(KL)-60K^-1/3L^2/3 where K denotes the amount (in thousands of dollars) spent on capital equipment and L represents the amount (also in thousands of dollars) spent on labor. (a) How should the CEO allocate the $360, 000 between labor and equipment? (b) Show that
aQ/aK=aQ/aL
at the point (K, L) found in part (a)
xplanation:
a b c your way out the picture
The CEO should allocate $144,000 to labor and $216,000 to capital equipment.
How should the CEO allocate the $360, 000 between labor and equipment?Step-by-step explanation given below
The CEO should allocate $144,000 to labor and $216,000 to capital equipment. This allocation maximizes the output of the factory, which can be found by taking the partial derivatives of the function Q with respect to K and L and setting them equal to 0.
Partial derivative of Q with respect to K = -20K^-4/3L^2/3 = 0
20K^-4/3L^2/3 = 0
K^4/3L^2/3 = 20
K = (20L^2/3)^1/4
Partial derivative of Q with respect to L = -40K^-1/3L^-1/3 = 0
40K^-1/3L^-1/3 = 0
K/L = 40
K = 40L
Solving for K and L, we get:
K = (20*L^2/3)^1/4
L = 40K
Substituting K into the equation for L, we get:
L = (40*(20L^2/3)^1/4)
L = 80(20L^2/3)^1/4
L^3/4 = 160L^2/3
L^3 = 1280L^2
L^2 = 1280L
L = 1280
Substituting L into the equation for K, we get:
K = (20*1280^2/3)^1/4
K = (307200/3)^1/4
K = 144
Therefore, the CEO should allocate $144,000 to labor and $216,000 to capital equipment.
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Jayden is going to invest $97,000 and leave it in an account for 16 years. Assuming the interest is compounded annually, what interest rate, to the nearest hundredth of a percent, would be required in order for Jayden to end up with $143,000?
An interest rate of 2.5 % is required to obtained a current capital of $ 143,000 after a period of 16 years.
How to find the interest rate of a deposit
In this problem we find that Jayden deposits an amount of money for a period of 16 years and such account is under composite interest, that is, that the account increases its capital continously in time. Compound interest model is shown:
C' = C · (1 + r / 100)ˣ
Where:
C - Initial capital, in monetary units.C' - Current capital, in monetary units. r - Interest rate, in percentage.x - Number of periods, in years.If we know that C = 97,000, C' = 143,000 and x = 16, then the interest rate is:
143,000 = 97,000 · (1 + r / 100)¹⁶
143 / 97 = (1 + r / 100)¹⁶
1.025 = 1 + r / 100
0.025 = r / 100
r = 2.5
The needed interest rate needed for a capital of $ 143,000 after a period of 16 years is equal to 2.5 %.
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How to rotate a triangle 270 degrees counterclockwise?
Rotating a triangle 270 degrees counterclockwise is the same as rotating a figure 90 degrees clockwise. The solution has been obtained using the concept of rotation.
What is rotation?
A rotation in mathematics is a transformation that revolves a shape around a fixed point.
We have a specific rule that we can use to do this that is based on the fact that a 270° anticlockwise rotation is the same as a 90° clockwise rotation. One such rotation is to rotate a triangle 270° anticlockwise.
On a graph, we can rotate a triangle 270° anticlockwise by passing each of its vertices through the transformation shown below:
Change the x and y coordinates after multiplying the x coordinate by a negative number.
Consequently, (x,y) becomes (y,-x).
Hence, this way we can rotate a triangle 270 degrees counterclockwise.
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The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown.
f(x) = 4(x2 + 12x) + 10
(twelve-halves) squared = 36
What is the function written in vertex form?
f(x) = 4(x + 6)2 + 10
f(x) = 4(x + 6)2 – 26
f(x) = 4(x + 6)2 – 134
f(x) = 4(x + 6)2 + 154
The function written in vertex form is:
f(x) = 4(x + 6)² - 26
Option B is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 4(x² + 12x) + 10
Now,
f(x) = 4(x² + 12x) + 10
f(x) = 4 (x² + 2 x (x) x 6 + 36) - 36 + 10
f(x) = 4(x + 6)² - 26
Thus,
f(x) = 4(x + 6)² - 26 is the function in vertex form.
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Answer:
B is correct
Step-by-step explanation:
The base of the parallelogram-like figure is half the circumference of the circle, or b= 1/2 (2pir)= pir. Therefore, the area of the figure will be A=
The formula for the area of the parallelogram-like figure is A = πr
What is parallelogram?parallelogram can be defined as a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
bh, where h is the height of the parallelogram-like figure.
Therefore, The formula for the area of the parallelogram-like figure is A = πr.
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