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
solve for x: 7^(3x+7)=7^(-8x-4)
Answer:
x = -1
Step-by-step explanation:
7^(3x+7) = 7^(-8x-4)
First Step: Cancel out like bases.
3x + 7 = -8x - 4
Second Step: Add 8x on both sides.
11x + 7 = -4
Third Step: Subtract 7 on both sides.
11x = -11
Fourth Step: Divide by 11 on both sides.
x = -1
What is the value of the underline digit? 9.521
Answer: one
Step-by-step explanation:
Answer:
Step-by-step explanation:
If 9 was underlined it would be 9 ones
If it was 5, 5 tenths
If it was 2, 2 hundreths
If it was 1, 1 thousandth
Hope this helps:)
I can’t figure out how to find the average.
Answer:
The student needs a minimum score of 81 on the fourth test to ensure a grade of at least a C in the class.
Step-by-step explanation:
Remember what an average is. (Look at the hint at the bottom of the problem.)
To find the average of a set of numbers, add all the numbers and divide by the number of numbers.
For example, if in a class you took 8 tests, the average of the 8 tests is the sum of the 8 scores divided by 8.
In this case, the student took 3 tests and is taking one more, so in the end there will be 4 scores. The number of tests is 4.
We know 3 of the 4 scores. We don't know the fourth score because he has not taken the test yet, so we use a variable to represent the unknown score. Let's call the score of the fourth test x.
To find the average of the 4 scores, we add them and divide the sum by 4.
The three known scores are 63, 62, 74.
The unknown score is x.
Add all 4 scores: 63 + 62 + 74 + x.
Now we divide the sum of the 4 scores by 4 to find the average of the 4 scores.
[tex] \dfrac{63 + 62 + 74 + x}{4} [/tex]
The expression above is the average of the 4 scores. We want the average to be at least 70, so we need the average to be greater than or equal to 70.
We get this inequality.
[tex] \dfrac{63 + 62 + 74 + x}{4} \ge 70 [/tex]
Now we solve the inequality for x.
Add like terms in the numerator.
[tex] \dfrac{199 + x}{4} \ge 70 [/tex]
Multiply both sides by 4.
199 + x = 280
Subtract 199 from both sides.
x = 81
Answer: The student needs a minimum score of 81 on the fourth test to ensure a grade of at least a C in the class.
HELP!!! SHOW WORK PLS!! ITS URGENT
The probability that Chloe is happy given that she has had dinner by 6pm is 0.9. The probability that Chloe is not happy given that she has not had dinner by 6pm is 0.8. Assume that there is a 60% chance that Chloe eats dinner by 6pm on a given day. a) If Chloe is not happy at 6pm, find the probability that she has not had dinner yet. b) If Chloe is happy at 6pm, find the probability that she has already had dinner.
Answer:
a) If Chloe is not happy at 6pm, the probability that she has not had dinner yet =P(B/D)= 0.8
b) If Chloe is happy at 6pm,the probability that she has already had dinner= P(A/C) = 0.9
Step-by-step explanation:
Let A be an event that Chloe is happy given that she has had dinner by 6pm
P(A) = 0.9
Let B be an event that Chloe is not happy given that she has not had dinner by 6pm
P(B) = 0.8.
Let C be an event that Chloe eats dinner by 6pm on a given day
P(C) = 60%=0.6
Let D be an event that Chloe does not eat dinner by 6pm on a given day
P(D) = 1- 60%=1- 0.6= 0.4
This requires conditional probability .
Part a
P(B/D)=P(B∩D)/P(D)
P(B∩D) = 0.8 *0.4=0.32
P(D) = 0.4
P(B/D)=P(B∩D)/P(D)
= 0.32/0.4= 0.8
P(B)= P(B/D)
0.8 is equal to 0.8
This shows that the events are independent.
b)
P(A/C)= P(A∩C)/ P (C) = 0.9*0.6/0.6= 0.9
Which is again equal to probability of event A showing that the events are independent.
graph y = -1/4x + 6
Answer: SEE BELOW
If you need further explanation about how to graph, please let me know.
Hope this helps!! :)
Andrew was making a science project for school. He worked for 6.6 hours the first week, 2.75 hours the second week, and 4.4 hours the third week.
Andrew used the following mental math strategy to find the total number of hours he worked on his project.
Answer:
Step-by-step explanation:
its wierd but 2.22
PLEASE HURRY IM GIVING BRAINLIEST AND 50 POINTS!!! for the function g(x) = x - 2x^2, find g(-3) + 13
Hey there! I'm happy to help!
If we have g(-3) we plug -3 into our function as x.
-3-2(-3)²
-3-2(9)
-3-18
-21
g(-3) is -21, so now we just add 13.
-21+13=-8
The answer is -8.
Have a wonderful day! :D
All lines parallel to y = 5x - 7 have a slope of
Answer:
5
Step-by-step explanation:
[tex]y = 5x - 5 \\ equating \: it \: with \\ y = mx + b \\ slope \: (m) = 5[/tex]
Parallel lines have same slope.
So, slope of required line = 5
Find the measures of angles 1 through 5 in the figure shown.
Its 4 PARTS
The measure of angle ∠1 is 44 degrees and the measure of angle ∠5 is 62 degrees.
What is an angle?Angle is the space between the line or the surface that meets. And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
Angle ∠1 and 46° are complementary angles. Then we have
∠1 + 46° = 90°
∠1 = 44°
Angle ∠1 and ∠3 are vertically opposite angles. Then we have
∠1 = ∠3 = 44°
The sum of all the angles of the triangle is 180 degrees. Then we have
∠3 + 74° + ∠5 = 180°
44° + 74° + ∠5 = 180°
∠5 = 62°
More about the angled link is given below.
https://brainly.com/question/15767203
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how do you compute overtime pay?
If all else remains constant and the values of two variables move in the same direction it indicates a Group of answer choices negative slope relationship. inverse slope relationship. the values of the two variables will move in the same direction then move in opposite directions. positive slope relationship.
Answer:
positive slope relationship.
Step-by-step explanation:
When two variables move in the same direction, they are positively related. An increase in one variable would lead to an increase in the other variable.
For example, price and quantity supplied are positively correlated. An increase in price, leads to an increase in quantity supplied and a decrease in price leads to a decrease in quantity supplied.
Please check the attached image for a positively correlated curve
Solve 1-4 to be mark brainiest and show your work!
Answer:
Hope you understand not to sure but that's what I got
Find the slope of the line passing through each of the following pairs of points and draw the graph of the line.
(6, −7), (6, 1)
Answer: undefined; vertical line
Step-by-step explanation:
To find the slope, you use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
[tex]m=\frac{1-(-7)}{6-6} =\frac{8}{0}[/tex]
The slope is undefined because you cannot divide anything by 0.
The graph of the line is a vertical line at x=6. We know this because the points are both at x=6, with different y-values.
Express (x-4)^2 as a trinomial in standard form
Answer:
x² - 8x + 16
Step-by-step explanation:
Step 1: Write out expression
(x - 4)²
Step 2: Expand
(x - 4)(x - 4)
Step 3: FOIL
x² - 4x - 4x + 16
Step 4: Combine like terms
x² - 8x + 16
what is the median 9 7 6 10 3 4 6
What is the y-intercept of:
y = x2 - 6x + 5
Answer:
the y intercept is (0,5)
Step-by-step explanation:
Factor x3 – 7x2 – 5x + 35 by grouping. What is the resulting expression? o
(x2 – 7)(x - 5)
(x2 – 7)(x + 5) •
(x2 – 5)(x – 7)
(x2 + 5)(x – 7)
Answer: C
.................................................................
The expression is a polynomial expression, and the factored expression of x³ - 7x² - 5x + 35 is (x² - 5)(x - 7)
How to factor the expression?The expression is given as:
x³ - 7x² - 5x + 35
Factorize the expression
x²(x - 7) - 5(x - 7)
Factor out x - 7 in the expression
(x² - 5)(x - 7)
The above expression cannot be further factorized.
Hence, the factored expression of x³ - 7x² - 5x + 35 is (x² - 5)(x - 7)
Read more about factorized expression at:
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Today only, a table is being sold at a 26% discount. The sale price is $481.
What was the price yesterday?
Answer:
The price yesterday was 650
Step-by-step explanation:
X is the price yesterday
There is a 26% discount
That means today we pay 100 -26 = 74 %
x* 74% = 481
.74x = 481
Divide each side by .74
.74x/.74 = 481/.74
x = 650
The price yesterday was 650
Which of the following is/are units of velocity? Can select more than one answer A) m/s B) m/s^2 C) km/hr D) km/hr/s E) m/s/s
Answer:
The answer to your question is m/s which is the A
Answer:
m/s is the answer
Step-by-step explanation:
because
velocity = displacement/time =meter/second
that is m/s
Point V is on line segment UW, given VW = x + 7, UW = 3x - 9, and UV = 8, determine the numerical length of UW
Answer:
The numerical length of UW is 27
Step-by-step explanation:
(8x/2)^3 whats the answer??????
Answer:
(8x)^(2/3
Step-by-step explanation:
what the facters of 18
☽------------❀-------------☾
Hi there!
~
[tex]1, 2, 3, 6, 9, 18[/tex]
The factor pairs of 18 are:
[tex]1 \times 18 = 18\\2 \times 9 = 18\\3 \times 6 = 18[/tex]
❀Hope this helped you!❀
☽------------❀-------------☾
Answer:
1, 2, 3, 6, 9, 18
Step-by-step explanation:
1*18=18
2*9=18
3*6=18
There are no other factors, Hope this helps!!
the statement formed when an equal sign is placed between two expressions is called
Answer: An equation
Step-by-step explanation: In math a equal sign put in between two expressions is called an equation. :)
Calculate the average speed between 160 s to 200 s
[tex]v=(0-150)/(200-160)=-150/40=-3,75[/tex]Answer:
-3,75
Step-by-step explanation:
Velocity is the derivative of time displacement
The geometric meaning of the derivative-tangent of the angle of inclination of the tangent to the function.
Find the unknown length y in the pair of similar triangles.
Step-by-step explanation:
If 2 triangles are similar then the ratio of any 2 sides of one triangles will be equal to the ratio of any 2 sides of the another triangle.
So,
[tex] \frac{30}{8} = \frac{20}{y} [/tex]
Cross-multiplying the denominators gives,
[tex]30y = 160[/tex]
[tex] = > y = \frac{160}{30} = \frac{16}{3} [/tex]
Is 9.4 rational or irrational :p, please help
Answer:
i think its rational.
Step-by-step explanation:
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
What are the coordinates of the vertices of AA'B'C' after each movement?
Answer:
The answer is in the picture attached.
Step-by-step explanation:
Edmentum Sample Answer
Answer:
Step-by-step explanation:
(1-,1, (2,0), ( 3,-2 )
(-4, 2),(-3,3),(2,1)
(-3,-3), (-2,-2), (-1,4)
Solve for x and check: 1/2x - 3 =25
Answer:
14
Step-by-step explanation:
Step 1:
1/2x - 3 = 25
Step 2:
1/2x = 28
Answer:
x = 14
Hope This Helps :)