Answer:
The y-coordinate is changing by the rate of -70 cm per sec.
Step-by-step explanation:
Given equation,
[tex]y = 7x^2 + 4[/tex]
Differentiating with respect to time (t),
[tex]\frac{dy}{dt}=14x \frac{dx}{dt}[/tex]
We have,
[tex]\frac{dx}{dt}=-5\text{ cm per sec}, x = 1[/tex]
[tex]\frac{dy}{dt} = 14(1)(-5)=-70\text{ cm per sec}[/tex]
It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 55 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo. After one year, 11% of the first group has a second episode and 9% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode? Select the [Rejection Region, Decision to Reject (RH0) or Failure to Reject (FRH0)]
A. [ z < -1.65, RHo]
B. [ z < -1.65 and z > 1.65, FRHo
C. [z > 1.65, FRHo]
D. [z < -1.65 and z > 1.65, FRHo]
E. [z > -1.65 and z < 1.65, RHo]
F. None of the above
Mrs. Andretti is having new drapes made for her living room. The cost of the fabric is $15 per yard. The fee to make and hang the drapes is $250. She uses the expression 15x + 250 to calculate the total cost of the drapes. Mrs. Andretti states that x represents the total cost of the fabric. Is she correct?
Answer: No
Step-by-step explanation:
X does not represent the cost of fabric. X represents the number of yards of fabric used.
15x + 250
Could be read as ($15 × # of yards) + $250
So she has to pay $15 per yard of fabric plus an additional $250 base amount for having them made and hung in the first place.
She could use an additional variable to represent the cost of fabric.
Example: Y
Y= 15x
Cost of fabric is equal to $15 per yard × # of yards.
The equation for the total cost depending on the number of students in Emma's Extreme Sports classes is C = 50 + 20x.
C = 50 + 20x
Where C represents the total cost, 50 is the fee per class, and 20 is the cost per student.
Which point lies on the graph of the line? (5, 8) (1, 6) (–3, 3) (–4, 2)
Answer:
the answer is (-4,2)
Step-by-step explanation:
Answer:
Step-by-step explanation:
the answer is (-4,2)
Please show ALL WORK
WILL MARK BRAINLIEST
Which inequality is graphed below?
y ≥ -2|x - 1| + 3
y ≤ -2|x - 1| + 3
y ≤ -2|x + 1| - 3
y ≥ -2|x + 1| + 3
Answer
The answer
it is y ≥ -2|x + 1| + 3
since the -2 or A controls the negative or positive of an absolute value graph its negative so it's down.
| x+1| if it's like that then you must reverse the sign so it is -1
and for the +3 that controls your vertical line meaning up or down. & in this case it went up so its +3
A pick-up truck with two passengers weighs about 14100 N. In good driving conditions around a curve, the maximum friction with the road is equal to the truck's weight. What is the minimum safe curve radius that the truck could negotiate at 26.2 m/s?
Answer:
r=68.64 m
Step-by-step explanation:
Given that
Weight ,wt= 14100 N
mass m = 1410 kg ( g = 10 m/s²)
Friction force = Weight
Fr= 14100 N
v= 26.2 m/s
Lets take radius of the curve = r
To balance the truck ,radial force should be equal to the friction force
[tex]\dfrac{mv^2}{r}=Fr[/tex]
mv² = Fr x r
1410 x 26.2² = 14100 x r
r=68.64 m
Therefore radius of the curve will be 68.64 m
Answer - r=68.64 m
The minimum safe curve radius that the truck could negotiate at 26.2 m/s in good driving conditions is approximately 78.94 meters. This relies on the principles of centripetal force and friction, and requires converting the weight of the truck into its mass. The resulting radius ensures that the centripetal force, provided by the friction between the tires and the road, is enough to keep the truck on its path.
Explanation:The subject of this question is related to Centripetal Force and Friction in physics. Centripetal force is the net force on an object moving in a circular path and it points towards the center of the circular path. This force keeps the object moving along this path and is provided by the frictional force between the truck's tires and the road.
In this case, if friction equates to the weight of the truck (14100 N), it will be the centripetal force. The equation for centripetal force is given by:
Fc = mv²/rwhere Fc is the centripetal force, m is the mass of the object, v is the velocity of the object and r is the radius of the circular path. We can arrange this formula to calculate the safe curve radius(r) the truck can negotiate:
r = mv²/FcHowever, in this case, the mass of the truck is given as a force (Weight = 14100 N). So first we need to convert this weight into mass. We can do this by using the formula: Weight = mass (m) × acceleration due to gravity (g). Here, g = 9.8 m/s²:
m = Weight / g = 14100 N / 9.8 m/s² = 1438.78 kgNow we can substitute m = 1438.78 kg, v = 26.2 m/s and Fc = 14100 N into our radius equation to find the minimum safe curve radius for the truck:
r = (1438.78 kg × (26.2 m/s)²) / 14100 N = 78.94 mSo, the minimum safe curve radius that the truck could negotiate at 26.2 m/s in good driving conditions is approximately 78.94 meters.
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A municipality wanting to use integrated waste management methodologies for its citizens would do all of the following EXCEPT: A. pay for each individual's tipping fees at landfills with taxes B. offer curbside recycling to its residents C. attract businesses that utilize source reduction in their manufacturing processes D. offer mulch to its residents at no cost E. maintain a hazardous waste collection site for its residents
Answer:
A. pay for each individuals tipping fee at landfills with taxes
Step-by-step explanation:
Because it is a recyclic methodology .It is a service provide to household for dispose of the waste and recycled it. So as a municipality wanting to waste management so Curbside recycling can be used.
Municipal should attract business that utilize source reduction in their manufacturing.
They should offer much to its resident.
They maintain a hazardous waste collection site for its residents as well.
ASAP PLZ!!! Select the correct answer. Which equation cannot be solved by factoring? A. x2 + 5x − 4 = 0 B. x2 + 6x + 9 = 0 C. x2 + 3x − 4 = 0 D. x2 − x − 6 = 0
Answer:
Step-by-step explanation:
We have four equations here. Let's actually solve them, using factoring if possible and some other method if factoring is not possible.
A) x^2 + 5x + 4 factors into (x + 1)(x + 4), but x^2 + 5x - 4 does not.
B) x^2 + 6x + 9 factors into (x + 3)^2.
C) x^2 + 3x - 4 factors into (x + 4)(x - 1).
D) x^2 - x - 6 factors into (x - 3)(x + 2)
x^2 + 5x - 4 = 0 can be solved, but not by factoring.
ABC is reflected across x = 1 and y = -3. What are the coordinates of the reflection image of A after both reflections?
(-2, -7) (-2, 7) (7, -2) (7, 2)
Answer:
option C) (7, -2)
Step-by-step explanation:
By the graph, the initial coordinates of point A are ( -5, -4)
first reflection along the line x=1, only the x coordinate will change.
the new x coordinate is = x = 7
thus the point becomes (7, -4)
similarly, reflection along y= -3, only the y coordinate will change.
the new y coordinate is = y = -2
thus the final coordinates are (7, -2)
How much is a $26,000 automobile car worth after 1 year if the depreciation is 15% per year
Answer:
The worth of the automobile after an year with 15% depreciation is $22,100.
Step-by-step explanation:
The current cost of the automobile car = $26,000
The percentage of depreciation = 15%
Now, calculating the depreciated amount:
15% of $26,000 = [tex]\frac{15}{100} \times 26,000 = 3,900[/tex]
So, the depreciated amount of the car in the next year = $3,900.
Now, the worth of the car after an year
= CURRENT WORTH - THE DEPRECIATED AMOUNT
= $26,000 - $3,900.
= $22,100
Hence, the worth of the automobile after an year is $22,100.
Enter the equation of the parabola in vertex form that has its vertex at (4,–13) and passes through the point (6,–5).
Answer:
Step-by-step explanation:
If you plot the vertex and the point that it goes through, the point it goes through is above the vertex, so the vertex is a positive one that opens upwards. The general vertex form of a parabola of this type is
[tex]y=a(x-h)^2+k[/tex]
We have the x, y, h, and k. We will plug all those in and solve for a. That looks like this:
[tex]-5=a(6-4)^2-13[/tex] which simplifies to
-5 = 4a - 13 and
8 = 4a so
a = 2
That means that the paraobola in vertex form is
[tex]y=2(x-4)^2-13[/tex]
The students want to make care packages for unhoused people for winter season. They would like to put 5 boxes of tissues into each care package. If they have 450 boxes pack, how many tissue boxes will they need to complete the boxes?
Answer: 50 tissue boxes
Step-by-step explanation:
The students want to make care packages for unhoused people for winter season.
They would like to put 5 boxes of tissues into each care package.
If they have 450 boxes pack, to determine how many tissue boxes that they need to complete the boxes, we will divide the total number of boxes pack that they have by the number of tissues that will go into one pack. It becomes
450/9 = 50
Kyle says 3/5 is equal to 60%. Which statement explains Kyle is correct?
A) Kyle is correct because 3/5 is equivalent to 10/6 .
B) Kyle is correct because 3/5 is equivalent to 60/100 .
C) Kyle is incorrect because 3/5 is less than 1 and 60% is greater than 1.
D) Kyle is incorrect because 3/5 is not a whole number and 60 is a whole number.
Kyle is correct in saying that 3/5 is equal to 60% because 3/5 is equivalent to 60/100.
Explanation:Kyle says that 3/5 is equal to 60%. This statement can be explained by saying that 3/5 is equivalent to 60/100. To convert a fraction to a percentage, you multiply the top number (numerator) by 100 and then divide by the bottom number (denominator). In this case, multiplying 3 by 100 gives you 300, and when you divide 300 by 5, it equals 60. Hence, 3/5 is indeed equivalent to 60%, which makes Kyle's statement correct.
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If the length of a rectangle is given by the expression 2 153 and the width is given by 4 68 , which radical expression represents the perimeter of the rectangle? A) 6 34 B) 14 17 C) 28 17 D) 32 17
Answer:
C) 28√17
Step-by-step explanation:
The perimeter is twice the sum of the two given side lengths, so is ...
P = 2(L +W) = 2(2√153 +4√68)
= 2(6√17 +8√17) = 2(14√17)
P = 28√17 . . . . . matches choice C
_____
This is about simplifying radicals. The applicable rules are ...
√(ab) = (√a)(√b)
√(a²) = |a|
__
153 = 9×17, so √153 = (√9)(√17) = 3√17
68 = 4×17, so √68 = (√4)(√17) = 2√17
_____
Comment on the problem presentation
It would help if there were actually radicals in the radical expressions. We had to guess based on the spacing and the answer choices.
In any event, this problem can be worked with a calculator. Find the perimeter (≈115.45) and see which answer matches that. (That's what I did in order to verify my understanding of what the radical expressions were.)
According to Harper's Index, 55% of all federal inmates are serving time for drug dealing. A random sample of 16 federal inmates is selected.
(a) What is the probability that 11 or more are serving time for drug dealing? (Round your answer to three decimal places.)
(b) What is the probability that 2 or fewer are serving time for drug dealing? (Round your answer to three decimal places.)
(c) What is the expected number of inmates serving time for drug dealing? (Round your answer to one decimal place.)
Answer:
a)[tex]P(X\geq 11) = 0.198[/tex]
b)[tex]P(X\leq 2) = 0.000565[/tex]
c) Mean = 8.8
Step-by-step explanation:
1) Previous concepts
Binomial Distribution is a "discrete probability distribution which is used to calculate the probabilities for the independent trials and for each trial there is only two outcomes success or failure and probability for each success remains constant throughout each trial".
The Binomial distribution is a type of Bernoulli experiment with following properties:
a)There are two possible outcomes; success or failure.
b) Outcomes are independent on preceding result of a trial.
c) The probability of success remains constant throughout the experiment.
d)The number of successes are fixed.
The probability mass function for the Binomial distribution is given by:
[tex]P(X=a)=(nCa)(p)^x (1-p)^{n-x}[/tex]
Where [tex]p[/tex] is the probability of success, n the number of trials and x the number of successes that we want on the n trials.
[tex]X[/tex] represent the number federal inmates that are serving time for drug dealing
[tex]p=0.55[/tex] represent the proportion of federal inmates that are serving time for drug dealing
[tex]n=16[/tex] random sample selected
2) Part a
The random variable X follows this distribution [tex]X \sim Binom(n,p)[/tex]
On this case we want the following probability, and since says greater or equal than 11 we can express like this:
[tex]P(X \geq 11)=P(X=11)+P(x=12)+P(x=13)+P(x=14)+P(x=15)+P(x=16)[/tex]
[tex]P(X=11)=(16C11)(0.55)^{11} (1-0.55)^{5} =0.112[/tex]
[tex]P(X=12)=(16C12)(0.55)^{12} (1-0.55)^{4} =0.0572[/tex]
[tex]P(X=13)=(16C13)(0.55)^{13} (1-0.55)^{3} =0.0215[/tex]
[tex]P(X=14)=(16C14)(0.55)^{14} (1-0.55)^{2} =0.00563[/tex]
[tex]P(X=15)=(16C15)(0.55)^{15} (1-0.55)^{1} =0.000918[/tex]
[tex]P(X=16)=(16C16)(0.55)^{16} (1-0.55)^{0} =0.00007011[/tex]
[tex]P(X \geq 11)=0.112+0.0572+0.0215+0.00563+0.000918+0.00007011=0.198[/tex]
3) Part b
[tex]P(X \leq 2)=P(X=0)+P(x=1)+P(x=2)[/tex]
[tex]P(X=0)=(16C0)(0.55)^{0} (1-0.55)^{16} =0.00000283[/tex]
[tex]P(X=1)=(16C1)(0.55)^{1} (1-0.55)^{15} =0.0000552[/tex]
[tex]P(X=2)=(16C2)(0.55)^{2} (1-0.55)^{14} =0.000507[/tex]
[tex]P(X \leq 2)=0.00000283+0.0000552+0.000507=0.000565[/tex]
4) Part c
The expected value for the binomial distribution is given by the following formula:
[tex] E(X)=np=16*0.55=8.8[/tex]
So then the average number of federal inmates that are serving time for drug dealing on a sample of 16 is approximately 9.
answer correctly / explain a lil.
Which relation could be rewritten using FUNCTION notation?
A) x = 3
B) x + y = 3
C) x + y2 = 3
D) x2 + y2 = 3
Answer:
B) x + y = 3
Step-by-step explanation:
This is a specific way to give details without a detailed written explanation of the function. There will be NO exponents when trying to find out information about something:
[tex]\displaystyle x + y = 3 → y = -x + 3[/tex]
I am joyous to assist you anytime.
In a recent month, 88% of automobile drivers filled their vehicles with regular gasoline, 2% purchased midgrade gas, and 10% bought premium gas. Given that a driver bought regular gas, 28% paid with a credit card; given that they bought midgrade and premium gas, 34% and 42% respectively, paid with a credit card. Suppose we select a customer at random.
a. Draw a tree diagram to represent this situation.
b. What is the probability that an automobile driver filled with regular gasoline AND paid with a credit card?
c. What is the probability that an automobile driver filled with premium gasoline AND did NOT pay with a credit card?
d. What’s the probability that the customer paid with a credit card?
Answer:
b) 0.2464
c) 0.0580
d) 0.2952
Step-by-step explanation:
Probability of those that purchased regular gas = 88% = 0.88
2% purchased mid grade gas
10% purchased premium gad
Given that a driver bought regular gas, 28% paid with credit card
Given that a driver bought mid grade gas, 34% paid with credit card
Given that a driver bought premium gas, 42% paid with credit card
Let R represent drivers that bought regular gas
Let M represent drivers that bought mid grade gas
Let P represent drivers that bought premium gas
Let C represent credit card payment
Let NC represent non-credit card payment
Pr(R) = 88% = 0.88
Pr(M) = 2% = 0.02
Pr(P) = 10% = 0.10
Pr(C|R) = 28%= 0.28
Pr(C|M) = 34%= 0.34
Pr(C|P) = 42%= 0.42
Pr(NC|R) = 1 - 0.28= 0.72
Pr(NC|M) = 1 - 0.34 = 0.66
Pr(NC|P) = 1 - 0.42 = 0.58
Using multiplication rule
Pr(AnB) = Pr(A) * Pr(B|A) = Pr(B) * Pr(A|B)
Using conditional probability,
P(B|A) = Pr(AnB) / Pr(A)
Pr(CnR) = Pr(R) * Pr(C|R)
= 0.88*0.28
= 0.2464
Pr(CnM) = Pr(M) * Pr(C|M)
= 0.02*0.34
= 0.0068
Pr(CnP) = Pr(P) * Pr(C|P)
= 0.10*0.42
= 0.0420
b) the probability that an automobile driver filled with regular gasoline AND paid with a credit card =
Pr(CnR)
= 0.2464
c) the probability that an automobile driver filled with premium gasoline AND did NOT pay with a credit card = Pr(P n NC) = Pr(NC|P) * Pr(P)
= 0.58 * 0.10
= 0.0580
d) The probability of those that paid with credit card is given as
Pr(CnR) + Pr(CnM) + Pr(CnP)
= 0.2464 + 0.0068 + 0.042
= 0.2952
This problem involves calculating different probabilities pertaining to customers' selection of gas type and payment method. These probabilities are found by multiplying corresponding probabilities together for intersecting events, and adding different possibilities together for compound events.
Explanation:The subject of this question is probability, used in Mathematics. Let's solve each part step-by-step:
a. Drawing a tree diagram is a bit tricky in text form, however, it would start with a broad branch representing the initial choice of gas type. This would split into three branches for regular, midgrade, and premium. From each of these, two branches would sprout for the methods of payment: credit card or not credit card. b. The probability that an automobile driver filled with regular gasoline AND paid with a credit card is found by multiplying the probability of each event. So, 0.88 (probability filling with regular gas) * 0.28 (probability of paying with a credit card given that they bought regular gas) = 0.2464 or 24.64%. c. Similarly, the probability that an automobile driver filled with premium gasoline AND did NOT pay with a credit card is calculated as 0.10 (probability filling with premium gas) * 0.58 (probability of not paying with a credit card given that they bought premium gas) = 0.058 or 5.8%. d. The probability a random customer paid with a credit card can be found by adding up the possibilities for each gas type: (0.88 * 0.28) + (0.02 * 0.34) + (0.10 * 0.42) = 0.2464 + 0.0068 + 0.042 = 0.2952 or 29.52%. Learn more about Probability here:https://brainly.com/question/32117953
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An investment of d dollars at k percent simple annual interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?A. (2d)/3
B. (3d)/4
C. (4d)/3
D. (3d)/2
E. (8d)/3
Answer:
easey
Step-by-step explanation:
help me find the equation pls!!
Answer:
y(x) = e^(-2x +3)
Step-by-step explanation:
The graphed line has a "y-intercept" of 3 and a slope of -2, so its equation is ...
ln(y) = -2x +3
Taking antilogs, we get ...
y(x) = e^(-2x +3)
Calvin thinks a certain potato chip maker is putting less product in their personal-sized bags of chips. In the past, these bags contained one ounce of product. Calvin conducted a test of H0:μ=1vs. HA:μ<1. From a random sample of 23 bags of potato chips he calculated a p - value of 0.086 for the sample.
(a) At a 5% level of significance, is there evidence that Calvin is correct? (Type Yes or No):
(b) At a 10% level of significance, is there evidence that he is correct? (Type Yes or No):
Answer:
a) There are no evidence that Calvin is correct.
b) There are evidence that Calvin is correct.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 1 ounce
Sample size, n = 23
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 1\text{ ounce}\\H_A: \mu < 1\text{ ounce}[/tex]
P-value = 0.086
a) Significance level = 5% = 0.05
Since
P-value > Significance level
We fail to reject the null hypothesis and accept it. Thus, the chips bag contain one ounce of product. Thus, there are no evidence that Calvin is correct.
b) Significance level = 10% = 0.10
Since
P-value < Significance level
We reject the null hypothesis and accept the alternate hypothesis. Thus, the chips bag contain less than one ounce of product. Thus, there are evidence that Calvin is correct.
A stone is thrown straight up from the edge of a roof, 775 feet above the ground, at a speed of 16 feet per second. A. Remembering that the acceleration due to gravity is −32ft/sec2, how high is the stone 4 seconds later?
Final answer:
The stone is approximately 583 feet high 4 seconds later.
Explanation:
To find the height of the stone 4 seconds later, we can use the equation of motion for an object in free fall:
h = h0 + v0t + (1/2)gt^2
Where:
h = height at time t
h0 = initial height
v0 = initial velocity
g = acceleration due to gravity
t = time
Substituting the given values:
h = 775 + 16(4) + (1/2)(-32)(4)^2
h = 775 + 64 - 256
h = 583 feet
Therefore, the stone is approximately 583 feet high 4 seconds later.
Traci collects donations for a dance marathon. One group of sponsors will donate a total of $15 for each hour she dances. Another group of sponsors will donate $110 no matter how long she dances. What number of hours should Traci dance if she wants to raise at least $500?
Answer:
she will need to dance for 26 hours
Step-by-step explanation:
500=15(26)+110
Answer:
26 hours
Step-by-step explanation:
One group will donate $15 per hour, while the other is offering a flat sum of $110. She wants $500, so we can set up the equation
15x + 110 = 500 (with x being the number of hours Traci dances). You subtract 110 from 500 to isolate the variable with its coefficient, resulting in
15x = 390 . Then, dividing 390 by 15 to get x by itself, the answer of 26 hours is found.
One of the roots of the equation 2x^2−bx−20=0 is −2.5. Find the other root
Answer:
The answer to your question is x = 4
Step-by-step explanation:
2x² - bx - 20 = 0
One root is -2.5
Process
Get the value of the equation when x = -2.5
2(-2.5)² - b(-2.5) - 20 = 0
2(6.25) + 2.5b - 20 = 0
12.5 + 2.5b - 20 = 0
2.5b = 20 - 12.5
2.5b = 7.5
b = 7.5 / 2.5
b = 3
Then
2x² - 3x - 20 = 0
Factor the polynomial
2 x -20 = -40
2x² -8x + 5x - 20 = 0
2x(x - 4) + 5(x - 4) = 0
(x - 4)(2x + 5) = 0
x₁ - 4 = 0 2x₂ + 5 = 0
x₁ = 4 x₂ = -5/2
x₂ = -2.5
Answer:
The "other" or "second" root is 4.
Step-by-step explanation:
We are told that -2.5 is a root of the equation. The coefficient b of the x term is unknown, and must be determined. Because -2.5 is a root, synthetic division with -2.5 as divisor must return a remainder of zero.
Setting up synthetic division, we arrive at:
-2.5 / 2 -b -20
-5 +12.5 + 2.5b
-------------------------------------
2 -5-b -7.5 + 2.5b
The remainer, -7.5 + 2.5b, must be zero (0). Thus, 2.5b = 7.5, and b = 3.
Then the other factor has the coefficients {2, -5-b}, and because b = 3, this comes out to coefficients {2, -8}.
The other factor is 2x - 8, which, if set equal to 0, yields x = 4. This is the "other root."
Need help with this I am not good in Geometry
Answer:
Step-by-step explanation:
Lines p and line r are parallel. This actually means that they will extend continuously without meeting at a point.
Let us assign an alphabet to an angle to make it easy for reference. The diagram is shown in the attached photo
From the photo,
Angle T is equal to 34 degrees. This is because angle T and 34 degrees are corresponding angles.
Angle G = angle T. This is because angle T is vertically opposite to angle G. Therefore
G = 34 degrees
The angle measurements in the diagram are represented by the following expressions.
Solve for X then find the measurement of ∠A:
∠A = ∠B
6x + 12 = 3x + 63
6x - 3x = 63 - 12
3x = 51
x = 51 ÷ 3
x = 17
6(17) + 12
102 + 12
∠A = 114°
Answer:
114
Step-by-step explanation:
A model rocket has upward velocity v(t) = 10t2 ft/s, t seconds after launch. Use the interval [0, 6] with n = 6 and equal subintervals to compute the following approximations of the distance the rocket traveled. (Round your answers to two decimal places.
(a) Left-hand sum = _____ ft
(b) Right-hand sum = _____ ft
(c) average of the two sums = ______ ft
Answer:
a)550
b)910
c)730
Step-by-step explanation:
The given model is
[tex]v(t) = 10t^2 ft/s[/tex]
Use the interval [0,6], with n=6 rectangles
Then, the interval width is
[tex]\Delta t = \frac{b-a}{n}[/tex]
[tex]\Delta t = \frac{6-0}{6}[/tex]= 1
so, the sub intervals are
[0,1], [1,2], [2,3], [3,4],[4,5],[5,6]
Now evaluating the function values
[tex]f(t_0)= f(0) = 0[/tex]
[tex]f(t_1)= f(1) = 10[/tex]
[tex]f(t_2)= f(2) = 40[/tex]
[tex]f(t_3)= f(3) = 90[/tex]
[tex]f(t_4)= f(4) = 160[/tex]
[tex]f(t_5)= f(5) = 250[/tex]
[tex]f(t_6)= f(6) = 360[/tex]
a) left hand sum is
L_6 = [tex]\Delta t [f(t_0)+ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)][/tex]
=[tex]1 [0+ 10+40+90+160+250][/tex]
= 550
b) right hand sum
R_6 = [tex]\Delta t [ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)+f(t_6)][/tex]
= [tex]1 [10+40+90+160+250+360][/tex]
= 910
c) average of two sums is
[tex]\frac{L_5+R_5}{2}[/tex]
= [tex]\frac{550+910}{2}[/tex]
=730
An electric sale gives a reading equal to the true weight plus a random error that isnormally distributed with mean 0 and standard deviationσ=.1 mg. Suppose that the results of fivesuccessive weightings of the same object are as follows:_______ 3.142, 3.163, 3.155, 3.150, 3.141.(a) Determine a 95 percent confidence interval estimate of the true weight.
(b) Determine a 99 percent confidence interval estimate of the true weight.
Answer:
a) 95% confidence interval estimate of the true weight is (3.026, 3.274)
b) 99% confidence interval estimate of the true weight is (2.944, 3.356)
Step-by-step explanation:
Confidence Interval can be calculated using M±ME where
M is the mean of five successive weightings (3.150)ME is the margin of error from the meanAnd margin of error (ME) can be calculated using the formula
ME=[tex]\frac{t*s}{\sqrt{N} }[/tex] where
t is the corresponding statistic in the given confidence level and degrees of freedom(t-score) s is the standard deviation of the random error (0.1)N is the sample size (5)Using the numbers 95% confidence interval estimate of the true weight is:
3.150±[tex]\frac{2.776*0.1}{\sqrt{5} }[/tex]≈3.150±0.124
And 99% confidence interval estimate of the true weight is:
3.150±[tex]\frac{4.604*0.1}{\sqrt{5} }[/tex]≈3.150±0.206
Are triangles △ABCtriangle, A, B, C and △DEFtriangle, D, E, F similar? To answer, try to map △ABCtriangle, A, B, C onto △DEFtriangle, D, E, F using the interactive widget.
Answer:
From three condition the it is proved that Δ ABC and Δ DEF are similar Triangles .
Step-by-step explanation:
Given as :
To Proof : Triangle Δ ABC and Triangle Δ DEF are similar
There are three methods for two Triangles to be similar
A ) SAS i.e side angle side
B ) AA i.e angle angle
C ) SSS i.e side side side
Now,
A) If two triangle have a pair of equal corresponding angles and sides are proportional then triangle are similar
So, If in Δ ABC and Δ DEF
∠ B = ∠ E
and , [tex]\dfrac{AB}{DE}[/tex] = [tex]\dfrac{BC}{EF}[/tex]
Then Δ ABC [tex]\sim[/tex] Δ DEF
I.e SAS similarity
B ) If two triangles have equal corresponding angles , then triangles are similar .
So, If in Δ ABC and Δ DEF
∠ B = ∠ E and ∠ A = ∠ D
Then Δ ABC [tex]\sim[/tex] Δ DEF
I.e AA similarity
C ) If two triangles have three pairs of corresponding sides proportional then triangles are similar .
So, If in Δ ABC and Δ DEF
[tex]\dfrac{AB}{DE}[/tex] = [tex]\dfrac{BC}{EF}[/tex] = [tex]\dfrac{AC}{DF}[/tex]
Then Δ ABC [tex]\sim[/tex] Δ DEF
I.e SSS similarity
Hence From three condition the it is proved that Δ ABC and Δ DEF are similar Triangles . answer
Answer: Neither
Step-by-step explanation:
Got it wrong bc of the person it top of me but yea
The total surface of the cuboid is 112cm2 find the value of x bottom length 10cm side bottom length 2cm, id prefer just an answer as im about to get an hour detention, thank you
Answer:
The value of x is 3 cm.
Step-by-step explanation:
Given,
Total surface area of cuboid = 112 cm^2
Height of cuboid = 10 cm
Breadth of cuboid = 2 cm
Length of cuboid = x cm
Solution,
Formula for total surface of cuboid = [tex]2\times(length\times breadth +breadth\times height+height\times length)[/tex]
∴[tex]112=2(x\times2+2\times10+10\times x)\\112=2(2x+20+10x)\\112=2(12x+20)\\12x+20=\frac{112}{2}\\12x+20=56\\12x=56-20\\12x=36\\x=\frac{36}{12}=3[/tex]
Thus the length of cuboid is 3 cm.
Help those 3 multiple choice questions correctly and show work please I need it today
Please answer this question correctly I need it today please show work
Answer:
1: C(n) = 2.50 + 16n
2: $66.50
Step-by-step explanation:
Part 1
Each ticket costs $16 per person. If tickets for n persons were purchased, the total cost would be 16n.
There is also a one-time service fee of $2.50 that must be paid. Thus, for n tickets the total cost is
C(n) = 2.50 + 16n
Part 2
For n = 4, the expression evaluates to
C(4) = 2.50 + 16 (4) = $66.50