Answer:7.293428542
Step-by-step explanation:Calulator :D
Does the MVT apply? Explain why or why not.
y=x^2/4x + 4 ;
[-6, -2]
Hello!
\(\large\boxed{\text{Yes, it does.}}\)
In order to use the MVT, the function must be continuous over the given interval.
\(y = \frac{x^{2} }{4x}+4\)
Simplifies to:
\(y = \frac{x}{4} + 4\)
This is a linear equation that is continuous on the interval (-∞, ∞), which means that it would also be continuous on the interval [-6, -2]. The MVT would apply to this function.
a norman window has the shape of a rectangle surmounted by a semicircle. (thus the diameter of the semicircle is equal to the width of the rectangle.) if the perimeter of the window is 30 ft, find the dimensions of the window so that the greatest possible amount of light is admitted. width of the rectangle ft height of the rectangle
The following measurements will optimize the window's surface area:
Width: 8.4 ft
Height: 4.2 ft
We have a Norman window, where the width of the rectangle and the diameter of the semicircle are equal.
Two of the rectangle's heights, one of its widths, and half of its circumference make up the perimeter.
If w is the semicircle's diameter (and the rectangle's breadth) and h is the other side of the rectangle, we can write the perimeter as follows:
\(P = 2h +w +\frac{\pi w}{2} = 30\)
\(2h + (1 + 0.5\pi )w = 30 \\\\h = \frac{30 - (1+0.5\pi )}{2} \\\\h = 15 - (0.5 + 0.25\pi )w\)
With the perimeter restriction of P=30, we can express h as a function of w.
Now, in order to maximize its value, we can only represent the area as a function of w:
\(A = \frac{A_{c} }{2} + A_{r}\)
\(A = \frac{1}{2}\frac{\pi w^{2} }{4} + hw\\\\ A =\frac{\pi w^{2} }{8} + [ 15 - (\frac{1}{2} -\frac{\pi }{4} )w] w\\\\A = 15w - (\frac{1}{2} +\frac{\pi }{8} )w^{2}\)
To maximize the area, we derive and equal to zero,
\(\frac{dA}{dw} = 15(1) - (\frac{1}{2} -\frac{\pi }{8} )2w = 0\\ \\\frac{dA}{dw} = 15 - ( 1 - \frac{\pi }{8} )w =0\\\\w = \frac{15}{ 1 +\frac{\pi }{4} } = 8.4\)
Now, we can calculate the height as :
\(h = 15 - (0.5 + 0.25 \pi )w = 4.2\)
To read more about areas, visit https://brainly.com/question/17046117
#SPJ4
(-19, 12) , (-9, 1)
slope again
A survey was conducted to determine the percentage ofcollege freshmen that planned to take a math course while in college. The results were given as 75% with a margin oferror of +/- 4%. What does the margin of error of +/- 4%mean?Select one:•4% of the students surveyed refused to participate in the poll.•4% of the students surveyed will most likely change theirminds.• Your guess can be up to 4% wrong and your confidenceinterval will still be correct•4% of the population was not included in the survey.
Recall that the a margin of error ir a way to do calculations under uncertainty. What the margin of error does is guarantee that the given calculation, under uncertainty, will still be valid within that range.
In our example, we are given that the calculation is 75% with a margin of error of 4%. That is, that the process of calculation that the real value would be with a high confidence between 71% and 79%. So, a value of 77% would be still correct, as it is between the admissible ranges.
So, the anwer would be option C.
Prime factorization of 126
HELP IN ALMOST THE NEXT 5 MIN
Answer:
2 × 3^2 × 7
Step-by-step explanation:
hope this works for you :)
Add a term to the expression so tha it becomes a perfect square trinomial. Y^2-13y+
The term that should be added to the expression to make the expression perfect square trinomial is 169/4. The expression then becomes : (y - 13/2)²
What is meant by a perfect square trinomial?
By multiplying a binomial by another binomial, perfect square trinomials—algebraic equations with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of simply two words, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions.
A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is said to be a perfect square.
Given expression y² - 13y + ?
Comparing with the general equation
a = 1
b = -13
For perfect square trinomial
b² = 4ac
(-13)² = 4 * 1 * c
169 = 4c
c = 169/4
So the expression becomes,
y² - 13y + 169/4 = (y - 13/2)²
Therefore the term that should be added to the expression to make the expression perfect square trinomial is 169/4.
To learn more about the perfect square trinomial, follow the link.
https://brainly.com/question/1538726
#SPJ1
Identify complementary angles in the given figure.
Answer:
<6 and <4
Step-by-step explanation:
Complemetary angles are angles that their measure add up to 90 degrees
the angles meet this requirment in this image are angle <6 and angle <4
Find the slope of the tangent line to the curve defined by 4x2+5xy+y4=370
at the point (−9,−1)
Answer:
The slope of the tangent line to the curve at the given point is -11/7.
Step-by-step explanation:
Differentiation is an algebraic process that finds the gradient (slope) of a curve. At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.
Given function:
\(4x^2+5xy+y^4=370\)
To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.
Begin by placing d/dx in front of each term of the equation:
\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)
Differentiate the terms in x only (and constant terms):
\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)
Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:
\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)
Use the product rule to differentiate terms in both x and y.
\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)
\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)
\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)
Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:
\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)
\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)
To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:
\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)
Therefore, slope of the tangent line to the curve at the given point is -11/7.
Which is the correct equation for a line that passes through the points (-2,7) and (2,-5)?
y=3x+5
y=1/3x+3
y= -3x-12
y= -3x+1
Answer:
y= -3x+1
Step-by-step explanation:
x1= -2 x2=2 y1=7 y2=-5
using the formula
(y-y1)/(x-x1)=(y2-y1)/(x2-x1)
(y-7)/(x-(-2))=(-5-7)/(2-(-2))
(y-7)/(x+2)=(-5-7)/(2+2)
(y-7)/(x+2)=(-12)/4
(y-7)/(x+2)=-3
cross multiply
y-7=-3(x+2)
y-7=-3x-6
y=-3x-6+7
y=-3x+1
Solve for R1. Thank you! :)
Answer:
\(\displaystyle R_1 = \frac{R_T\cdot R_2}{R_2 - R_T}\)
Step-by-step explanation:
We are given the equation:
\(\displaystyle \frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}\)
And we want to solve for R₁.
We can multiply everything by the three denominators to remove all fractions:
\(\displaystyle R_TR_1R_2\left(\displaystyle \frac{1}{R_T}\right) = R_TR_1R_2\left(\frac{1}{R_1} + \frac{1}{R_2}\right)\)
Multiply:
\(\displaystyle R_1R_2 = R_TR_2 + R_TR_1\)
Isolate R₁:
\(\displaystyle R_1R_2 - R_1R_T = R_TR_2\)
We can factor:
\(\displaystyle R_1(R_2 - R_T) = R_TR_2\)
And divide. Therefore, in conclusion:
\(\displaystyle R_1 = \frac{R_T\cdot R_2}{R_2 - R_T}\)
Answer:
\(\displaystyle \rm R _{1} = \frac{ R _{T}R _{2} }{R _{2} - R _{T}}\)
Step-by-step explanation:
Just an alternative.
we would like to solve the following equation for \({R_1}\).
\( \displaystyle \rm \frac{1}{R _{T} } = \frac{1}{R _{1} } + \frac{1}{R _{2} } \)
in order to do so,we can simplify the right hand side which yields:
\( \displaystyle \rm \frac{1}{R _{T} } = \frac{R _{2} + R _{1} }{R _{1} R _{2} } \)
Steps, used to simplify the right hand side:
find the LCM of the denominators of the fractions i.e LCM(R_1,R_2)=R_1•R_2divide the LCM by the denominator of every fractionmultiply the result of the division by the numerator of every fractionCross multiplication:
\(\displaystyle \rm R _{1} R _{2}= R _{T}(R _{2} + R _{1} )\)
distribute:
\(\displaystyle \rm R _{1} R _{2}= R _{T}R _{2} + R _{T} R _{1} \)
isolate \(R_1\) to the left hand side and change its sign:
\(\displaystyle \rm R _{1} R _{2} - R _{T}R _{1}= R _{T}R _{2} \)
factor out \(R_1\) from the left hand side expression:
\(\displaystyle \rm R _{1} (R _{2} - R _{T})= R _{T}R _{2} \)
divide both sides by \(R_2-R_T\):
\(\displaystyle \rm \frac{R _{1} (R _{2} - R _{T})}{(R _{2} - R _{T})}= \frac{ R _{T}R _{2} }{(R _{2} - R _{T})}\)
reduce fraction:
\(\displaystyle \rm \boxed{ R _{1} = \frac{ R _{T}R _{2} }{R _{2} - R _{T}}}\)
and we're done!
in a significance test of one population mean if vairance of population is unknown but the sample size is 30 or more we use z test why?
The student T distribution would be used since we don't know the population variance (by extension the population standard deviation).
However, if n > 30, then the student T distribution is going to look very similar to the standard normal Z distribution. It won't be a perfect match, but it'll be close enough that it's more simple to use the Z distribution. With the Z distribution, you only have one set of values and you don't have to worry about the degrees of freedom.
El resultado de (6+9i) +(4-5i) es/
?
Answer:
es 362770
Step-by-step explanation:
saque esta imformacion de la calculadora
Answer:
10 + 4i
Step-by-step explanation:
To solve this, just combine the like terms:
\(\sf{(6+9i)+(4-5i)}\)
\(\sf{6+9i+4-5i}\)
\(\sf{6+4+9i-5i}\)
\(\sf{10+4i}\)
Hence, the answer is 10 + 4i
math math math math math math math
The angle m∠JIX is 90 degrees.
How to find angles in line intersection?IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.
IG bisect CIJ. Hence,
m∠CIG ≅ m∠GIJ
Therefore,
m∠CIX = 150 degrees
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
learn more on angles here: brainly.com/question/18854964
#SPJ1
The measure of angle m∠JIX is estimated to be 90⁰.
How to find the angles?You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.
IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.
Frim the given parameters,
IG⊥CIJ.
But; m∠CIG ≅ m∠GIJ
⇒ m∠CIX = 150⁰
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
Learn more about bisecting of angles on https://brainly.com/question/23984603
#SPJ1
Calcula el área y perímetro de un rectángulo que tiene como base (x+y) y altura (x-1).
Answer:
A = x^2 - x + xy - y
P = 4x + 2y - 2
Step-by-step explanation:
\(a = (x + y)(x - 1) \\ a = {x}^{2} - x + xy - y \\ \\ p = 2((x + y) + (x - 1)) \\ p = 2(2x + y + - 1) \\ p = 4x + 2y - 2\)
I hope that is useful for you :)
Helpppppp!!Besides optimism, there are other benefits associated with exercise. A doctor claims the proportion of those who exercise who got sick in the past year is smaller than the proportion of those who do not exercise.
To investigate, an analyst selects independent random samples: 50 adults who exercise regularly and 75 adults who do not exercise regularly. Of those who exercise regularly, 18 got sick in the past year, and of those who do not exercise regularly, 56 got sick in the past year. Do these data provide convincing evidence that these two population proportions differ?
The large count condition is met because all expected counts are greater than 5.
How does this data provide convincing evidence that these two population proportions differ?Now to determine if the data provides convincing evidence that the two population proportions differ, we can conduct a hypothesis test.
Let p1 be the proportion of adults who exercise regularly and got sick in the past year, and p2 be the proportion of adults who do not exercise regularly and got sick in the past year.
The null hypothesis is that the two population proportions are equal: H0: p1 = p2
The alternative hypothesis is that the proportion of those who exercise regularly who got sick in the past year is smaller than the proportion of those who do not exercise regularly: Ha: p1 < p2
We can use a two-sample z-test for proportions to test this hypothesis. The test statistic is given by:
where p_hat is the pooled sample proportion:
p_hat = (x1 + x2) / (n1 + n2)
In this case, we have:
n1 = 50, x1 = 18, n2 = 75, x2 = 56
p_hat = (18 + 56) / (50 + 75) = 0.455
We can also calculate the expected counts using the formula provided:
n1p_hat = 500.455 = 22.75
n1*(1-p_hat) = 500.545 = 27.25
n2p_hat = 750.455 = 34.13
n2(1-p_hat) = 75*0.545 = 40.88
The large counts condition is met because all expected counts are greater than 5.
To calculate the test statistic, we have:
z = (0.18 - 0.747) / sqrt(0.592 * (1 - 0.592) * (1/50 + 1/75)) = -2.36
Using a standard normal table, we find the p-value to be 0.0091 for a one-tailed test. Since the p-value is less than 0.05, we reject the null hypothesis and conclude that there is convincing evidence that the proportion of those who exercise regularly who got sick in the past year is smaller than the proportion of those who do not exercise regularly.
To know more about exercise regularly visit:
https://brainly.com/question/20849410
#SPJ1
Use the number line to find the equivalent decimal and mixed number for givenletter
The equivalent decimal and mixed number for given letter C is,
⇒ C = 8.2 ; 8 2/10
We have to given that,
A number line is shown in image.
Since,
A number lines are the horizontal straight lines in which the integers are placed in equal intervals.
And, All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.
Now, By given number line,
Point C is two point left from point 8.
Hence, The point C is denoted as,
⇒ C = 8.2
⇒ C = 82/10
⇒ C = 8 2/10
Therefore, the equivalent decimal and mixed number for given letter C is,
⇒ C = 8.2 ; 8 2/10
Learn more about the coordinate visit:
https://brainly.com/question/24394007
#SPJ1
To evaluate whether customers enjoy the barista’s new smoothie, a restaurant manager surveys every other customer who orders the new smoothie. The manager determines that customers enjoy the new smoothie. Select all the statements that are true about the sampling method.
The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.
Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:
1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.
2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.
3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.
4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.
5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.
for more such questions on sampling method
https://brainly.com/question/13219833
#SPJ8
1. What is the place value of 7 in 43.0671? A. tenths B. hundredths TA C. thousandths D. ten thousandths
15 X (-25) × (-4) X (10 ) =
please say fast
Answer:
I think it is 15000 but try it
Answer:
15,000
Step-by-step explanation:
Quick maths.
15*-25= -375.
-375*-4= 1,500
1,500*10= 15,000.
Hope this helps! :)
carmela has a deck of 26 alphabet cards. she mixes the cards, places them face down on the table, and turns them over one at a time. what is the probability that the first two cards she turns over are vowel cards (a, e, i, o, u)? 5
The probability that the first two cards Carmela turns over are vowel cards is 2/65.
To calculate the probability of Carmela turning over two vowel cards (A, E, I, O, U) in a row, we'll need to find the probability of each event and then multiply those probabilities.
Step 1: Calculate the probability of the first card being a vowel.
There are 5 vowel cards (A, E, I, O, U) in a deck of 26 alphabet cards.
So, the probability of the first card being a vowel is 5/26.
Step 2: Calculate the probability of the second card being a vowel.
Since the first card was a vowel, there are now 4 vowel cards left and a total of 25 cards left in the deck. So, the probability of the second card being a vowel is 4/25.
Step 3: Multiply the probabilities of each event.
Now, we multiply the probabilities from Step 1 and Step 2:
(5/26) * (4/25) = 20/650
Step 4: Simplify the fraction.
The fraction can be simplified by dividing both the numerator and denominator by 10:
20/650 = 2/65.
For similar question on probability.
https://brainly.com/question/30846562
#SPJ11
Is there anyone here who does Calvert or Odessy?
I was quite behind on my assignments, and, somehow, I go to catch up and they've been completed or something. It says I'm 100% on pace, and I know for a fact that I wasn't. What happened?
what happen is there is a glitch probably
yes this is what happened to me. if u get too far behind they will change the due dates to your "pace" and make it easier for you.
simplify the expression 5×6+6+6–12×2
Answer:
18
Step-by-step explanation:
A company is testing products which
Answer:
Can you please give the entire question
Step-by-step explanation:
I dont understand
James had a large bag of raisins and he ate3/4 of it over the weekend. Monday he decided to share the remaining raisins with 2 friends so that each of 3 of them get a fair share. What portion of the whole bag of raisins did each of friends get
The share of the whole bag of raisins individually of the friends get will be 1/12.
What is Algebra?Algebra is the study of ideational symbols, while logic is the manipulation of all those opinions.
James had a large bag of raisins and he consumed 3/4 of it over the weekend. Then the share of raisins left is given as,
⇒ 1 - 3/4
⇒ 1/4
Monday he determined to share the remaining raisins with 2 friends so that individuals of the 3 of them fetches a fair share. Then the portion of the entire bag of raisins did separately of the friends get will be given as,
⇒ (1/4) / 3
⇒ 1 / (4 x 3)
⇒ 1 / 12
The share of the whole bag of raisins separately among the friends get will be 1/12.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ1
What is the equivalent to the product below when x>_0?
√5x² •√15x²
25000 shares of cumilative preferred 1% stock, $150 par.$56300 first year, dividends per share
Answer: The dividends per share for 25000 shares of cumulative preferred 1% stock, $150 par, with a first-year dividend of $56300 per share, would be $2.252.
To calculate the dividends per share, we need to multiply the number of shares by the dividend rate and the par value.
The dividend rate is 1%, which means that for every $150 of par value, the company will pay $1.50 in dividends per year.
So, for 25000 shares with a par value of $150 each, the total par value would be $3,750,000 ($150 x 25,000).
Multiplying the total par value by the dividend rate gives us the total annual dividend payment:
$3,750,000 x 1% = $37,500
However, we know that in the first year, the company paid a higher dividend of $56,300 per share. Therefore, we need to adjust our calculation to reflect this higher amount.
Dividing the first-year dividend by the par value gives us the first-year dividend rate:
$56,300 / $150 = $375.33
Now we can calculate the dividends per share for subsequent years using this adjusted rate:
$3,750,000 x 0.01 = $37,500
$37,500 / 25000 = $1.50
$1.50 + $0.87533 = $2.252
Therefore, the dividends per share for 25000 shares of cumulative preferred 1% stock with a first-year dividend of $56300 per share would be $2.252.
Hope this helps please give brainleist and smash that like button
Octavia buys a pair of jeans for $20.50 plus 8% tax.
Then she buys a jacket for $32 plus 8% tax.
Answer:
$56.70 all together
Step-by-step explanation:
$22.14 for the jeans
$34.56 for the jacket
$56.7 all together
Take your tax and move the decimal over to the left by 2 spaces
8. becomes .08
take .08 and multiply it by the price so
20.50 x .08= 1.64
and
32 x .08=2.56
the number you get is how much the tax is, $1.64 is 8% of $20.15
take that number and add it to your price
$1.64+$20.50= $22.14
Answer:
$56.70
Step-by-step explanation:
22.14+34.56=$56.70
Pedrobuysawheelbarrowpricedat$86.Shippingandhandlingareanadditional30%oftheprice.HowmuchshippingandhandlingwillPedropay?
The price of the wheelbarrow is $86, and Pedro will need to pay an additional 30% of the price for shipping and handling.
To calculate the shipping and handling cost, we can first find 30% of the price of the wheelbarrow:
30% of $86 = 0.3 x $86 = $25.80
Therefore, Pedro will need to pay $25.80 for shipping and handling.
A truck can be rented from Company A for $100 a day plus $0.30 per mile. Company B charges $50 a day plus $0.80 per mile to rent the same truck. Find the number of miles in a day at which the
rental costs for Company A and Company B are the same.
Atmiles, the rental costs are the same from either company.
Answer:
100 miles
Step-by-step explanation:
Let m be the number of miles.
\(100 + .30m = 50 + .80m\)
\(100 = 50 + .50m\)
\(.50m = 50\)
\(m = 100\)
Answer:
100
Step-by-step explanation:
You can put into a graph such as desmos and see where the lines intersect. the x value of the intersection is the answer you want.
what is 19% of 103?
Answer:
19.57Step-by-step explanation:
When you do 19% of 103
you get 19.57
Hope this helps! <3
Answer: 19% of 103 is 19.57