Answer:
b=18
Step-by-step explanation:
b+17=35
-17 -17
b=18
3. [W] Consider the following data from NASA about the density of the sun. • When you are 10% of the way out from the center of the sun (use x = 0.1), the density is approximately 82.9619 g/cm3 . • When you are 20% of the way out of the sun, the density is approximately 38.7504 g/cm3 . • When you are 70% of the way out of the sun, the density is approximately 1.7819 g/cm3 . • When you are 80% of the way out of the sun, the density is approximately 1.9824 g/cm3 . • When you are 90% of the way out of the sun, the density is approximately 0.7859 g/cm3 . We want to use this data to find a quartic (4th degree) interpolating polynomial for the density of the sun throughout. y = Ax4 + Bx3 + Cx2 + Dx + E (a) Set up this problem as a system of linear equations. (b) Find the quartic polynomial that goes through these data points. (c) Use this polynomial to approximate the density 50% of the way out of the sun.
Answer:
a)
A(0.1)^4 + B(0.1)^3 + C(0.1)^2 + D(0.1) + E = 82.9619 ----------1
A(0.2)^4 + B(0.2)^3 + C(0.2)^2 + D(0.2) + E = 38.7504 -------2
A(0.7)^4 + B(0.7)^3 + C(0.7)^2 + D(0.7) + E = 1.7819 ----------3
A(0.8)^4 + B(0.8)^3 + C(0.8)^2 + D(0.8) + E = 1.9824 ----------4
A(0.9)^4 + B(0.9)^3 + C(0.9)^2 + D(0.9) + E = 0.7859 ----------5
b) y = 519x^4 - 1630x^3 + 1844x^2 - 889x + 155
c) 0.1875
Step-by-step explanation:
a)
Let y = Ax^4 + Bx^3 + Cx^2 + Dx + E
Setting up the problem as a system of linear equations
when x=(10%)=0.1, y = 82.9619
therefore
A(0.1)^4 + B(0.1)^3 + C(0.1)^2 + D(0.1) + E = 82.9619 ----------1
when x=(20%)=0.2, y = 38.7504
A(0.2)^4 + B(0.2)^3 + C(0.2)^2 + D(0.2) + E = 38.7504 -------2
when x=(70%)=0.7, y = 1.7819
A(0.7)^4 + B(0.7)^3 + C(0.7)^2 + D(0.7) + E = 1.7819 ----------3
when x=(80%)=0.8, y = 1.9824
A(0.8)^4 + B(0.8)^3 + C(0.8)^2 + D(0.8) + E = 1.9824 ----------4
when x=(90%)=0.9, y = 0.7859
A(0.9)^4 + B(0.9)^3 + C(0.9)^2 + D(0.9) + E = 0.7859 ----------5
b)
Find the quartic polynomial that goes through these data points
Now to find the values ( A,B,C,D,E)
[MATRIX]
║A║ ║ (0.1)^4 (0.1)^3 (0.1)^2 (0.1) 1 ║^-1 ║ 82.9619 ║
║B║ ║ (0.2)^4 (0.2)^3 (0.2)^2 (0.2) 1 ║ ║ 38.7504 ║
║C║ = ║ (0.7)^4 (0.7)^3 (0.7)^2 (0.7) 1 ║ ║ 1.7819 ║
║D║ ║ (0.8)^4 (0.8)^3 (0.8)^2 (0.8) 1 ║ ║ 1.9824 ║
║E║ ║ (0.9)^4 (0.9)^3 (0.9)^2 (0.9) 1 ║ ║ 0.7859 ║
║A║ ║ 29.7619 -47.619 166.667 -238.095 89.2857 ║ ║ 82.9619║
║B║ ║ -77.381 119.048 -333.333 452.381 -160.714 ║ ║ 38.7504║
║C║ = ║ 71.131 -102.381 208.333 -269.048 91.9643 ║ ║ 1.7819 ║
║D║ ║ -26.369 33.0952 -41.6667 52.619 -17.6786 ║ ║ 1.9824 ║
║E║ ║ 3.00 -2.4 -2.4 -3.00 -1.00 ║ ║ 0.7859 ║
║A║ ║ 519 ║
║B║ ║ -1630║
║C║ = ║ 1844 ║ , y = 519x^4 - 1630x^3 + 1844x^2 - 889x + 155
║D║ ║ -889 ║
║E║ ║ 155 ║
c)
approximate the density 50% of the way out of the sun
so at 50% (0.5) x=0.5
we substitute
y = 519(0.5)^4 - 1630(0.5)^3 + 1844(0.5)^2 - 889(0.5) + 155
= 0.1875
6. Laura has $322 in her checking account. She bought a pair of jeans for $32. Then, she
bought a pair of boots for $47. What is the current balance of Laura's checking account?
Answer:
243
Step-by-step explanation:
Jacob makes $3600 a month, he spends 40% of his income on his mortgage. How much money does he spends? A. $400 B. $1440 C. $440 D. $820
Answer:
the answer is b- 1440
Step-by-step explanation:
hope this helps
Answer:
b
Step-by-step explanation:
5x2x_=90
A-9 B-10. C-80. D-83
Can some one ☝️ plz help me
Just add 7 to all x-coordinates and subtract 9 from all y-coordinates.
S' = -3 + 7 = 4 and 6 - 9 = -3 therefore S'(4, -3)
T' = 0 + 7 = 7 and 7 - 9 = -2 therefore T'(7, -2)
U' = 1 + 7 = 8 and 4 - 9 = -5 therefore U'(8, -5)
V' = -5 + 7 = 2 and 2 - 9 = -7 therefore V'(2, -7)
what is f(0) ?
12 only
2 and 3 only
-2 , -1, 1 and 2 only
-2,-1, 1, 2 and 12
plzzzz help
Answer: it's 12 only
Step-by-step explanation:
whats the answer of 23,869 in long division
----------
038 -38-------------
08 -8----------
90 -90TOTAL ANS; 1194.45THE REASON WHY THE 9 TURNED INTO 90 WAS BECAUSE: 9 CAN NOT BE DIVISIBLE BY TWO SO I HAD TO ADD A 0 AND REPLACE THE symbol (.)IN THE ANSWER.I HOPE IT HELPED YOU.DON'T HESITATE TO ASK FOR FURTHUR EXPLANATION.HELP ME FIND HIM (MY LOST LOVE).THANK YOU.# THE BEAUTIFUL EMPRESS!!
How do you change a percent to a decimal? What is 6 1/2% as a decimal?
0.065
To convert a percent to a decimal, you move the decimal point to the left two times
Answer: 0.065
Step-by-step explanation:
When we divide 50 by 100 we get 0.5 (a decimal number). So, to convert from percent to decimal: divide by 100, and remove the percent symbol. So for 6.5% divided by 100=0.065
In the 2019 NBA Eastern Conference semi‐finals, Philadelphia 76ers (PHI) played the (eventual 2019 NBA Champion) Toronto Raptors (TOR) in a best‐of‐7 series where the first team to win 4 games wins the series. Assume that the outcome of each game is independent. (a) Assuming that either team has a win probability of 0.5, what is the probability that after the first 4 games, the teams would be tied 2‐2? Clearly show all your steps.
Answer: 0.375
Step-by-step explanation:
Given the following :
Both teams have an equal probability of winning = 0.5
Find the probability that both teams are tied after 4 games, that is 2-2 ( this means each team has exactly 2 successes and 2 losses).
This problem can be modeled using a binomial probability :
P(x) = nCx * p^x * (1-p)^(n-x)
x = number of successes = 2
P = probability of success = 0.5
(1-p) = probability of failure = 0.5
n = number of trials = 4
P(x = 2 ) = 4C2 * 0.5² * 0.5^(4-2)
P(x = 2) = 6 * 0.5² * 0.5²
P(x = 2) = 6 * 0.25 * 0.25
P(x = 2) = 0.375
line g has a slope of 9/5. line h is perpendicular to g. what is the slop of line h?
Answer:
-5/9
Step-by-step explanation:
Note. If the line is parallel, then the slope is shared. If the line is perpendicular (directly opposite), it means to flip the sign as well as the fraction.
The slope of line g is 9/5. This means that the slope of line h, (which is perpendicular to line g), would be the opposite, or -5/9
-5/9 is your answer.
~
x+x/7+1/11(x+x/7)=60
Answer:
5 yes or good i'm not good morning guys
Answer:x= 48.126
Step-by-step explanation:
HELP PLEASE
If y varies directly with x and y = 26 when x = 8, write the equation that represents this direct variation relationship
Oy - 4x + 13
Oy=13x +4
Answer: y= 13 over 4x
Step-by-step explanation: trust me king
HELPP!! Find the x with the details in this picture ^
Answer:
y≈5.56
Step-by-step explanation:
[tex]\angle KLM=136\\\\\angle KLN=47\\\\\angle NLM=16y\\\\\angle KLM=\angle KLN+\angleNLM\\\\136=47+16y\\\\136-47=16y\\\\136-36-11=16y\\\\100-11=16y\\\\89=16y\\\\y=\frac{89}{16}\\\\y=5.5625[/tex]
Answer:
y = 5.56
Step-by-step explanation:
Use the total, measure KLN = 136⁰ and subtract measure KLN = 47 from measure KLM. Then do 89/16 = 5.5625. Then round to the hundredths, 5.56.
[136 - 47 = 89]
[89 / 16 = 5.5625]
[Round to 5.56]
Cost of wood is $9.50. How much would it cost Matt to buy 2 1/2 metres?
Answer:
23.75
Step-by-step explanation:
how this helped bye I would appreciated if u liked my comment tho
The cost of 2 1/2 meters of wood is $23.75
How to determine the cost of 2 1/2 meters?The given parameters are:
Unit rate = $9.50 per minutesNumber of meters = 2 1/2 metersThe total cost is then calculated as:
Total = 9.50 * 2 1/2
Evaluate the product
Total = 23.75
Hence, the cost of 2 1/2 meters of wood is $23.75
Read more about rates at:
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1-89. On graph paper, draw the quadrilateral with vertices A(–1, 3), B(4, 3), C(–1, –2), and D(4, –2). a. What kind of quadrilateral is this?
Answer:
it is a square
because
as we can see in the graph the
distance from A to B is 5 cm
distance from B to C is 5 cm
distance from C to D is 5 cm
distance from D to A is 5 cm
please mark me as the brainliest I really need it
16.2=2.7(h=1) solve for h
Answer:
h = 5Step-by-step explanation:
[tex]16.2=2.7(h+1)\\\\2.7\left(h+1\right)=16.2\\\\\mathrm{Multiply\:both\:sides\:by\:}10\\2.7\left(h+1\right)\cdot \:10=16.2\cdot \:10\\\\Refine\\27\left(h+1\right)=162\\\\\mathrm{Divide\:both\:sides\:by\:}27\\\frac{27\left(h+1\right)}{27}=\frac{162}{27}\\\\Simplify\\h+1=6\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\h+1-1=6-1\\\\Simplify\\h=5[/tex]
Solve. 4 11/16 ÷1 1/4 ? 2 1/8 2 1/4 3 7/16 3 3/4
Answer:
3 1/4
Step-by-step explanation:
4 1/16÷1 1/4=
65/16÷5/4=
65/16*4/5=
260/80=
3 20/80=
3 1/4
Jane's penny bank is 1/3 full. After she adds 480 pennies, it is 7/9 full. How many pennies can Jane's bank hold?
answer
980
Step-by-step explanation:
7/9-1/3=480
4/9=480
9/9=?
9/9×9/4×4809/1×120= 980Answer:
1080
Step-by-step explanation:
We take x to be the number of pennies in the bank at first which filled the bank by a ¹/3
¹/3=×
⁷/9=×+480
⅓ multiply by 3 with both the numerator and denominator to get 3/9
7/9-3/9=4/9
4/9=480
If 4/9=480 what of 9/9
9/9×480÷4/9
Reciprocate 4/9
9/9×480×9/4=1080
Which equation represents a direct linear variation?
y=1x
y = x2
y = x + 2
y=12x
(Number 4)help...plzz
You intend to estimate a population mean μ with the following sample. 78.4, 85.3, 50, 68.4, 59.4, 73.7, 73.2, 47.4, 40.5
You believe the population is normally distributed.
Find the 99.5% confidence interval.
The answer must be done as an open-interval accurate to 2 decimal places.
Answer:
(17.75, 110.32)
Step-by-step explanation:
The sample mean is 64.03, and the standard deviation is 15.43.
The population is normally distributed, so 99.5% confidence is ±3 standard deviations.
The confidence interval is therefore:
(64.03 − 3 × 15.43, 64.03 + 3 × 15.43)
(17.75, 110.32)
The 99.5% confidence interval will be equal to (17.75, 110.32).
What is Probability?Probability is calculated as the proportion of favorable events to all potential scenarios of an event. The proportion of positive results, or x, for an experiment with 'n' outcomes can be expressed.
As per the given data provided by the question,
With a standard deviation of 15.43 and a sample mean of 64.03, respectively.
Since the population has normally distributed, 99.5% probability lies within a range of three standard deviations.
Consequently, the confidence interval is:
= (64.03 − 3 × 15.43, 64.03 + 3 × 15.43)
= (17.75, 110.32), this is up to 2 decimal places.
To know more about Probability:
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-56.5 as a mixed number
Answer:
-56 1/2
Step-by-step explanation:
Answer:
-5.6
Step-by-step explanation:
Aretailer is having a promotional sale for 35% off all items. There is a 7% sales tax added to the price. Which
represents the situation, where x is the original cost of the item(s)?
Answer:
.65x(1.07) = 0.6955x
Step-by-step explanation:
HELPPPPPP ASAP . Which triangle represents the reflection ABC across the y-axis ?
Answer:
The answer above me is wrong, it is C, red triangle.
Step-by-step explanation:
Got it right on a school test.
The red triangle represents the reflection ABC across the y-axis. Option C is correct.
What is geometric transformation?It is described as the modification of both the geometric body's coordinates and form. A two-dimensional transformation is another name for it. Geometric transformations allow for the rotation, translation, reflection, and glide translation of the geometry.
We have to find the triangle that represents the reflection ABC across the y-axis.
A flip is a term for a reflection in geometry. The form is mirrored in a reflection. The line of reflection is a line across which an image will reflect. Every point in a figure is said to mirror the other figure if and only if it is equally spaced from every corresponding point in the other figure.
Since the green and blue triangles are equidistant from the y-axis. The red triangle will represent the reflection ABC across the y-axis
Thus, option C is correct.
Learn more about the geometric transformation here:
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Help with writing the set from an interval notation.
Answer:
(-oo, 1) U (1, 3) U (3, oo)
Step-by-step explanation:
We have a line with two arrowheads. The arrow heads show us that the numbers in the set continue forever in the negative direction past -5 and in the positive direction past 5. In this case, the set consists of all real numbers except 1 and 3 since they have open circles.
That means the set is from negative infinity to 1, from 1 to 3, from 3 to positive infinity, but leaving out 1 and 3.
Remember that a regular parentheses symbols, ( and ), do not include the number near them and are used for open circles.
Square brackets, [ and ], do include the number near them and are used for closed circles.
Also, infinity and negative infinity are not numbers, so we always use regular parentheses when dealing with infinity or negative infinity.
We need the union of three sets:
from negative infinity to 1, from 1 to 3, from 3 to positive infinity
Answer: (-oo, 1) U (1, 3) U (3, oo)
Find AB if (-9,2) and B(5,-4)
Answer 1,-8
Step-by-step explanation:
9+x=10
x=1
2+y=-6
y=-8
B= 1,-8
George Foster had a batting
average of .323 one season. Pete
Roses' average was .306 that same
season. How much better was
George Foster's average?
Answer:
.17 better average
Step-by-step explanation:
.323 - .306 = .17
Subtract.
-4 - 2
Plz help:((
Answer:
The answer is -4-2 = -6
Answer:
-6 is the answer hope that helps
If UV=5x, VW = 8x - 17, and UW = 11x+11, what is UW
Answer:
UW=165
Step-by-step explanation:
UV + VW =UW
5x + 8x-17= 11x +11
13x - 17 = 11x + 11
Subtract 11x and add 17 to both sides:
2x= 28
Divide 2 both sides:
x=14
Plug in x to the equation of UW:
11 (14) +11
165
2.1 If an event has a probability that is greater than 0.4, what does it mean?
2.2 What is meant when two events are said to be mutually exclusive?
Answer:
Step-by-step explanation:
1) i think for the first question any probability greater than 0.4 has more likelihood that it will happen
2) mutually exclusive events are ones that cannot occur at the same time as it's impossible e.g. a single coin toss cannot result in you getting heads and tails