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Related Questions
A farmer is building a fence to enclose a rectangular area against an existing wall. Three of the sides will require fencing and the fourth side is a wall that already exists. If the farmer has 148 feet of fencing, what is the largest area the farmer can enclose?
Answers
Answer:
Step-by-step explanation:
There are several things we need to know to solve this: the perimeter formula of a rectangle, the area formula of a rectangle, and how to complete the square to find the answer. First of all, if the farmer has 148 feet of fencing to enclose 3 sides of a rectangle, the perimeter formula we need will include only 3 sides, the 2 widths and the 1 length:
P = 2w + l; solving for l and filling in our length of fencing gives us:
l = 148 - 2w
The area then for this will be:
A = (148 - 2w)(w) which is the same thing as length times width (area for a rectangle). Multiplying that out gives us:
[tex]A=148w-2w^2[/tex]. Let's rearrange that and put it into descending order so we can complete the square on it:
[tex]A=-2w^2+148w[/tex]
The reason we want to complete the square is because the answer that results from that will give us the dimensions of the rectangle (the width and the length) and also the area. Completing the square maximizes (or minimizes) area.
To complete the square, first factor out the -2 since the leading coefficient when you complete the square has to be a +1. When we do that we get:
[tex]A=-2(w^2-74w)[/tex]. Set it equal to 0 so we can factor it:
[tex]-2(w^2-74w)=0[/tex]
The idea now is to take half the linear term (the term stuck to the w), divide it in half, then square that number. Our linear term is 74. Half of 74 is 37, and 37 squared is 1369. So we add 1369 to both sides, the left side first:
[tex]-2(w^2-74w+1369)=...[/tex]
But we didn't just add in 1369. There's a -2 out front there that refuses to be ignored. It's a multiplier. What we ACTUALLY added in was -2 times 1369 which is -2738; therefore:
[tex]-2(w^w-74w+1369)=-2738[/tex]
The left side can be simplified down to a perfect square binomial:
[tex]-2(w-37)^2=-2738[/tex]
Now we'll add over the -2738:
[tex]-2(w-37)^2+2738=y[/tex] and from there determine our answer. The (w-37) term is the width of the rectangle; therefore, the length is 148 - 2(37) which is 74; the total area if the 2738. Completing the square gives us the vertex form of the parabola; the vertex is (37, 2738) where 37 is the width of the rectangle and 2738 is the max area.
2a^2 + 7 + 5b^3
when a = 2 and b= 3
Answers
Answer:
150
Step-by-step explanation:
2(2^2)+7+5(3^3)
2(4)+7+5(27)
8 + 7 + 135= 150
Write the proportion.
8.5 hours is to 3.4 hours as
7.0 hours is to 2.8 hours?
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hope this helps
Which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"
-8
Og+3
8
9+3
-8+g
3
+3
Answers
Answer:
[tex]\dfrac{-8}{x+3}[/tex]
Step-by-step explanation:
We need to find an algebraic expression for the given statement i.e. "the quotient of negative eight and the sum of a number and three".
Let the number be x. Quotient means to divide. It means we need to divide -8 and the sum of x and 3.
So, we can write it as follows :
[tex]\dfrac{-8}{x+3}[/tex]
Hence, this is the required solution.
If each quadrilateral below is rectangle, find the missing measures #5
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13
What is the inverse of when
15
multiplying fractions?
13
A
15
15
B
13
13
C с
13
15
D
15
Answers
Answer:
Step-by-step explanation:
15x13=?
15+15+1=31
so the answer is 31
Mr. Thorbes bought a new journal for his poetry. If the journal normally cost $22 but was on sale for 20% off, how much did Mr. Thorbes save?
Answers
Answer:
He would save $4.40
Step-by-step explanation:
And in total he would pay 17.60
What is the period of f(x) = sin(x)?
Pi over 2
Pi
3 pi over 2
2 pi
Answers
Answer:
2pi
2pi radians are equal to 360 degrees. After this point, the function f(x) = sin(x) repeats its values again. Each cycle is 2pi radians long.
Step-by-step explanation:
Which of the options don’t belong pls look at photo
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Can someone help me? Becks?
Answers
Answer:
Perimeter = 72
Step-by-step explanation:
Notice that the adjacent (next to) lengths by each corner are equal in length.
This occurs when the quadrilateral is circumscribed.
Since 4.2 is adjacent to the length which makes up the total side 20.
20 – 4.2 = 15.8.
And 15.8 + 4.2 = 20.
(7 + 9) + (9 + 4.2) + (4.2 + 15.8) + (15.8 + 7) =
(16) + (13.2) + (20) + (22.8) =
(16 + 20) + (13.2 + 22.8) =
36 + 36 =
72
A piece of fabric 4 meters long is cut into two pieces. One piece is 1.25 meters long. How much longer is the second piece of fabric?
Answers
Answer:
1.5 meters
Step-by-step explanation:
the fabric is 4 meters long
first piece is 1.25 meters long
second piece will be (4-1.25)=2.75 meters long
therefore the second piece is (2.75-1.25) meters longer
Answer:
1.5 meters
Step-by-step explanation:
4 meters - 1.25 meters=2.75m is the length of the second one.
But when they ask how much longer , I think they want you to compare the two pieces meaning to get the answer you have to take 2.75m-1.25m=1.5m thats how much longer the 2nd fabric is longer than the other one.
hope am right
PLEASEEE HELP PLS ASAPPP GIVING BRAINLIEST!!!!
Answers
Answer:
50 is the answer brainliest?
Step-by-step explanation:
Hauls Vegetable Market has the folloeing vegetables for sale.
Carrots cost 3.50$ per pound
Cucumbers cost 0.69$ per pound
Squash cost 2$ per pound
What will be the ckst for 2 1/2 pounds of carrots and 3/4 pound of squash cost
Answers
Answer:
The cost of 2 1/2 pounds of carrots and 3/4 pound of squash is $ 10.25.
Step-by-step explanation:
Since Hauls Vegetable Market sells carrots that cost $ 3.50 per pound, cucumbers that cost $ 0.69 per pound, and squash that cost $ 2 per pound, to determine what will be the cost for 2 1/2 pounds of carrots and 3/4 pound. of squash the following calculation must be performed:
1/2 = 0.5
3/4 = 0.75
Carrots: 3.50 x 2.5 = 8.75
Squash: 2 x 0.75 = 1.50
8.75 + 1.50 = 10.25
Thus, the cost of 2 1/2 pounds of carrots and 3/4 pound of squash is $ 10.25.
If −6n=−48
then n=
HELP PLEASE
Answers
Answer:
8
Step-by-step explanation:
Calculus helpppppppppppppppp
Answers
Answer:
[tex]\displaystyle y' = \frac{5x^2 + 3}{3(1 + x^2)^\bigg{\frac{2}{3}}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
FunctionsFunction NotationExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Algebra II
Logarithms and Natural LogsLogarithmic Property [Multiplying]: [tex]\displaystyle log(ab) = log(a) + log(b)[/tex]Logarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Calculus
Derivatives
Derivative Notation
Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Logarithmic Derivative: [tex]\displaystyle \frac{d}{dx} [lnu] = \frac{u'}{u}[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x\sqrt[3]{1 + x^2}[/tex]
Step 2: Rewrite
[Equality Property] ln both sides: [tex]\displaystyle lny = ln(x\sqrt[3]{1 + x^2})[/tex]Logarithmic Property [Multiplying]: [tex]\displaystyle lny = ln(x) + ln(\sqrt[3]{1 + x^2})[/tex]Exponential Rule [Root Rewrite]: [tex]\displaystyle lny = ln(x) + ln \bigg[ (1 + x^2)^\bigg{\frac{1}{3}} \bigg][/tex]Logarithmic Property [Exponential]: [tex]\displaystyle lny = ln(x) + \frac{1}{3}ln(1 + x^2)[/tex]Step 3: Differentiate
ln Derivative [Implicit Differentiation]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx} \bigg[ ln(x) + \frac{1}{3}ln(1 + x^2) \bigg][/tex]Rewrite [Derivative Property - Addition]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx}[ln(x)] + \frac{d}{dx} \bigg[ \frac{1}{3}ln(1 + x^2) \bigg][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx}[ln(x)] + \frac{1}{3}\frac{d}{dx}[ln(1 + x^2)][/tex]ln Derivative [Chain Rule]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot \frac{d}{dx}[(1 + x^2)][/tex]Rewrite [Derivative Property - Addition]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot \bigg( \frac{d}{dx}[1] + \frac{d}{dx}[x^2] \bigg)[/tex]Basic Power Rule]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot (2x^{2 - 1})[/tex]Simplify: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot 2x[/tex]Multiply: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{2x}{3(1 + x^2)}[/tex][Multiplication Property of Equality] Isolate y': [tex]\displaystyle y' = y \bigg[ \frac{1}{x} + \frac{2x}{3(1 + x^2)} \bigg][/tex]Substitute in y: [tex]\displaystyle y' = x\sqrt[3]{1 + x^2} \bigg[ \frac{1}{x} + \frac{2x}{3(1 + x^2)} \bigg][/tex][Brackets] Add: [tex]\displaystyle y' = x\sqrt[3]{1 + x^2} \bigg[ \frac{5x^2 + 3}{3x(1 + x^2)} \bigg][/tex]Multiply: [tex]\displaystyle y' = \frac{(5x^2 + 3)\sqrt[3]{1 + x^2}}{3(1 + x^2)}[/tex]Simplify [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{5x^2 + 3}{3(1 + x^2)^\bigg{\frac{2}{3}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Implicit Differentiation
Book: College Calculus 10e
An apartment complex stretched a string of decorative floats diagonally across a
rectangular pool. The width of the pool is 15 ft and the length of the pool is 20 ft.
What is the length of the a diagonal that the floats are stretched across ?
Answers
Answer:
25 feet
Step-by-step explanation:
Use the pythagorean theorem, where the width and length of the pool are the legs of the triangle.
Solve for c, the hypotenuse/diagonal
a² + b² = c²
15² + 20² = c²
225 + 400 = c²
625 = c²
25 = c
So, the length of the diagonal is 25 feet
Can you help I’m in middle school and cant get this!
Answers
12)h=3.75
you have to write the equation for area and then substitute the area and side length. Then you solve the equation using algebra
Help please will mark brainliest!!
Answers
Answer:
5,4 km
Step-by-step explanation:
we know the area and the width.
the formula of the area of a parallelogram is
A = length x width
if we substitute the values that we know, we have
23,1 = x * 4,3
to find x we have to divide the two members by 4,3
x = 23,3/4,3 = 5,4 km
Jason rolls the die 14 times. What is the experimental probability that he will roll a 2
Answers
The experimental probability that Jason will roll a 2 is 3/14.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Given that, Jason rolls the die 14 times.
From the given table,
Number of favorable outcomes = 3
Total number of outcomes = 14
So, the probability = 3/14
Therefore, the experimental probability that Jason will roll a 2 is 3/14.
To learn more about the probability visit:
https://brainly.com/question/11234923.
#SPJ2
A small bar of gold measures 20 mm by 250 mm by 2 mm. One cubic millimeter of gold weighs about
0.0005 ounces. Find the volume in cubic millimeters and the welght in ounces of this small bar of gold.
cubic millimeters and the weight of the bar is
The volume of the bar is
ounce(s).
Answers
Answer: 5 ounces
Step-by-step explanation:
volume is 20*250*2=10000 cubic mm
10,000*0.0005=5
"A driving instructor is investigating whether the time a driver spends in a driverâs education course improves their score on the driverâs test. The instructor randomly selected 10 drivers from a driverâs education course and recorded the number of hours each driver attended the driverâs education course and their corresponding score on the driverâs test. Assuming all conditions for inference are met, which of the following significance tests should be used for the investigation?"
a. A chi-square test of independence
b. A two-sample t-test for a difference between means
c. A two-sample z-test for a difference between proportions
d. A linear regression t-test for slope
e. A matched pairs t-test for a mean difference
Answers
Answer:
e. A matched pairs t-test for a mean difference
Step-by-step explanation:
When the observations from two samples are paired either naturally or by design we find the differences between the two observations of each pair.Treating the differences as a random sample from a normal population with mean ud= u1-u2 and unknwn standard deviation σd we perform one sample t- test on them. This is called the paired difference t- test or a paired t- test.
Suppose 10 young recruits are given a physical training by the Army . Their weights are recorded before and after the training. These observations constitutes natural pairing .
When we eliminate the undesireable sources of variation to take observations in pairs , this is called pairing by design.
wedding planner does some research and finds that approximately 3.5% of the people in the area where a large wedding is to be held are pollotarian. Treat the 300 guests expected at the wedding as a simple random sample from the local population of about 2,000,000. 18) Suppose the wedding planner assumes that 5% of the guests will be pollotarian so she orders 15 pollotarian meals. What is the approximate probability that more than 5% of the guests are pollotarian and therefore she will not have enough pollotarian meals
Answers
Answer:
0.0793 = 7.93% probability that more than 5% of the guests are pollotarian and therefore she will not have enough pollotarian meals
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
3.5% of the people in the area where a large wedding is to be held are pollotarian.
This means that [tex]p = 0.035[/tex]
300 guests
This means that [tex]n = 300[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.035[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.035*0.965}{300}} = 0.0106[/tex]
What is the approximate probability that more than 5% of the guests are pollotarian and therefore she will not have enough pollotarian meals?
This is 1 subtracted by the pvalue of Z when X = 0.05. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.05 - 0.035}{0.0106}[/tex]
[tex]Z = 1.41[/tex]
[tex]Z = 1.41[/tex] has a pvalue of 0.9207
1 - 0.9207 = 0.0793
0.0793 = 7.93% probability that more than 5% of the guests are pollotarian and therefore she will not have enough pollotarian meals
Answer:7.93%
Step-by-step explanation:
Find the area of the trapezoid.
22.2 cm
9.86 cm
8.52 cm
[? ]cm2
Enter the exact answer. Do not round
Answers
Answer:
151.4496
Step-by-step explanation:
it has not been rounded or anything that is the exact answer
Answer: 151.45 (151.4496)
Step-by-step explanation:
Formula: A = (a+b)/2 * h
Base = 22.2
Base = 8.52
Height = 9.86
Do the following:
(22.2+8.52)/2 * 9.86 = 151.4496
someone pls help I'm genuinely confused
I've literally been trying to figure out all three of these for like two hours now but I can't figure it out
Answers
Answer:
the area is 50
Step-by-step explanation:
Answer:
its 0.09637 but round it by urself . please like my answer and brainliest me hshsshhs
Simplify.
Remove all perfect squares from inside the square root. Assume x is positive.
√ 20x^8
Answers
PLEASE HELP:):):):):):):):)
Answers
Answer:
[tex]Area = 8[/tex]
Step-by-step explanation:
Given
The attached figure
Required
Determine the area
The shape is a trapezium. So, the area is:
[tex]Area = \frac{1}{2} *(Sum\ of\ parallel\ sides) * Height[/tex]
From the attached,
The height is 2
The parallel sides are: 2 and 6
So, the area is:
[tex]Area = \frac{1}{2} *(2 + 6) * 2[/tex]
[tex]Area = \frac{1}{2} *8 * 2[/tex]
[tex]Area = 8[/tex]
Hence, the area is 8 units square
Can someone help me please!
Answers
9514 1404 393
Answer:
B, C, E
Step-by-step explanation:
Distributing the minus sign in the given expression results in ...
6x +1 -3x -(-1)
6x +1 -3 +1 . . . . simplify
The two expressions that show the constant terms as +1 - 1 are erroneous. The two constant terms are +1 -(-1) or +1 +1.
The correct expressions are the 2nd, 3rd, and 5th ones (b, c, e).
Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = -16t^2 +16t+480
How long did it take Jason to reach his maximum height?
Answers
Answer:
5 seconds
Step-by-step explanation:
I did the same question a while ago.
Hannah invested $96,000 in an account paying an interest rate of 6\tfrac{1}{2}6 2 1 % compounded quarterly. Evelyn invested $96,000 in an account paying an interest rate of 6\tfrac{1}{4}6 4 1 % compounded monthly. To the nearest hundredth of a year, how much longer would it take for Evelyn's money to double than for Hannah's money to double?
Answers
Answer:
.37 years
Step-by-step explanation:
I did this one in delta math
Please help me I really need it
Answers
Answer:
Angle C
Step-by-step explanation:
By applying sine rule in the given triangle,
[tex]\frac{\text{sinB}}{CD}=\frac{\text{sinC}}{BD}=\frac{\text{sinD}}{BC}[/tex]
[tex]\frac{\text{sinB}}{\text{sinC}}=\frac{\text{CD}}{\text{BD}}[/tex]
Therefore, sides of the given triangle will be in the same ratio as the sine of the angles.
Since, BD > BC > CD
Therefore, Opposite angles of these sides will be in the same ratio.
∠C > ∠D > ∠B
Largest angle of the triangle is angle C.
