Two functions that satisfy the given condition and are linearly independent on (-∞,∞) are f1(x) = e^(x) and f2(x) = e^(x)
Let's start by recalling the definition of the Wronskian for two functions f1(x) and f2(x):
W(f1,f2)(x) = f1(x)f2'(x) - f1'(x)f2(x)
Given the Wronskian W(f1,f2)(x) = e^(2x), we can try to find functions f1(x) and f2(x) that satisfy this condition. One possible solution is:
f1(x) = e^(x)
f2(x) = e^(x + C)
where C is a constant. We can now calculate the Wronskian of f1(x) and f2(x):
W(f1,f2)(x) = f1(x)f2'(x) - f1'(x)f2(x)
= e^(x) [e^(x + C)]' - [e^(x)]' e^(x + C)
= e^(x) e^(x + C) - e^(x) e^(x + C)
= 0
This means that f1(x) and f2(x) are linearly dependent. However, we can modify our choice of f2(x) by setting C= -x, which gives:
f2(x) = e^(2x - x) = e^(x)
Now we can calculate the Wronskian again:
W(f1,f2)(x) = f1(x)f2'(x) - f1'(x)f2(x)
= e^(x) [e^(x)]' - [e^(x)]' e^(x)
= e^(2x)
Since the Wronskian is non-zero, this means that f1(x) and f2(x) are linearly independent on (-∞,∞).
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The given question is incomplete, the complete question is:
Determine two functions, defined on the interval (−∞,∞), whose Wronskian is given by W(f 1 ,f 2)=e ^2x. Are the functions that you found linearly independent on (−∞,∞)
The point P(-1, 6) is rotated 180° counterclockwise around the origin. What are the coordinates of the resulting point, P'?
The coordinates of the resulting point, P' as required to be determined in the task content is; (1, -6).
What are the coordinates of the image point?It follows from the task content that the coordinates of the image point P' formed when point P(-1, 6) is rotated 180° counterclockwise around the origin is to be determined.
On this note, since a rotation of 180° is such that we have;
(x , y) ======> (-x, -y).
Hence, when point P(-1, 6) is rotated 180° counterclockwise around the origin, the resulting image point, P' has coordinates; (1, -6).
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the library is having a used book sale books cost $3 each or 10 for 25 if you buy 10 how much do you save on each book?
6. According to a survey, 33 out of 120 seventh-graders At Monroe Middle School play an
instrument in the school band. What percent of the seventh-grade students at Monroe
Middle School play in the school band?
A. 27.5%
B. 33.3%
C. 37.5%
D.43.3%
After answering the provided question, we can conclude that As a result, percentage the answer is A. 27.5%.
What is percentage?A percentage is a ratio or number expressed as a percentage of 100 in mathematics. The abbreviations "pct.," "pct," and "pc" are also used on occasion. Despite this, the percentage symbol "%" is commonly used to represent it. The % value is dimensionally empty. In essence, percentages are fractions with a denominator of 100. To indicate that a number is a percentage, a percent sign (%) should be placed next to it. For example, you receive a 75% on an exam if you correctly respond to 75 out of 25 pages (75/100). Divide the result by 100 after dividing the amount by the total when calculating percentages. The percentage is found by multiplying (value/total) by 100%.
To calculate the percentage of Monroe Middle School seventh-graders who participate in the school band, divide the number of students who play an instrument by the total number of seventh-graders and multiply the result by 100.
There are 33 seventh-graders in the school band, and there are 120 seventh-graders in total. Therefore:
percentage = (33 / 120) x 100% % = 27.5%
As a result, the answer is A. 27.5%.
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Ines's younger brother will be home in a half hour. If her garden hose flows at a rate 24 gal/min, does she have enough time to fill the pool before he gets home? Explain.
No, she have not enough time to fill the pool before he gets home. The garden hose with flow rate 24 gal/min will take 40 minutes to complete fill up the tank that is t ~ 40 minutes. So, she cannot complete fill up the pool before he come.
We have, the time in which Ines's younger brother will be home = an half hour = 1/2 hour
water flow rate of garden's hose = 24 gal/min
She want to fill up the pool. From the figure, depth of pool = 3 ft
Width of pool = 10 in.
1 inch = 0.0833 feet
So, 10 inches = 0.833 feet
outer diameter of pool = 9 ft
so, outer radius of pool = 4.5 ft
Now, inner diameter of pool/tank = outer diameter - 2(width)
= 9 - 2×0.833
= 9 - 1.666 = 7.334
Inner radius of pool = 7.334/2 = 3.667 ft
Water flow rate, Q = 24 gal/min
= 24/7.48 gal ( since 1 ft³ = 7.48 gal)
= 3.20 ft³
Using formula, Q = volume/ time
where t --> time to fill up the pool through hose
Volume of tank/pool = surface area × height (depth)
= π r² × h , where r is inner radius
= π (3.667)² × 3 ft³
= 126.71 ft³
So, Q = 126.71 ft³/t
=> t = 126.71 ft³/3.20 ft³
=> t = 39.59 min
Hence, required time is 39.59 ~ 40 minutes and she cannot complete before he come.
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Complete question:
Ines's younger brother will be home in a half hour. If her garden hose flows at a rate 24 gal/min, does she have enough time to fill the pool before he gets home? See the above figure
Explain. (Hint: 1 ft³ = 7.48 gal)
4. The tree is 15 feet away from the edge of the lake. What is the distance across the lake (water's edge to opposite side)? Justify your decision.
The distance across the lake, given the distance of the tree and Cade would be 14.36 ft.
How to find the distance ?We can use the concept of similar triangles to solve this problem:
(Length of the tree's shadow) / (Distance from the tree to the edge of the lake) = (Length of Cade's shadow) / (Cade's height)
36.2 / 15 = 2.5 / 6.2
Now we can set up another proportion using the length of the tree's shadow and the length of the lake:
(Length of the tree's shadow) / (Length of the lake) = (Distance from the tree to Cade) / (Length of Cade's shadow)
Plugging in the values we know, we get:
36.2 / 15.6 = 15 / 2.5
6.2 * 2.32051282 = 14.36 ft
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The full question is:
The trees shadow is 36.2 feet long. The tree is 15 feet away from the edge of the lake. Cade is 6.2 feet tall and his shadow is 2.5 feet long, his shadow is measured at the exact time the trees shadow reaches the other side of the lake which is 15.6 feet long. What is the distance across the lake (water's edge to opposite side)
The arithmetic mean of 25, 29, and x is 29. Find x.
How do I check what answers I got correct on Edmentum?
Below are few steps given to check what answer you got correct on edmentum.
What is edmentum?
Edmentum is an online learning platform that offers educational software and digital curriculum for K-12 students.
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Edmentum is designed to support student learning and achievement, provide teachers with the tools and resources they need to be successful, and help schools and districts meet their academic goals.
According to given information:To check your answers on Edmentum, you can navigate to the assignment or quiz that you completed and click on the "View Results" button. This will show you a breakdown of your score and which questions you answered correctly or incorrectly.
If you want to review specific questions and their answers, you can click on the individual question numbers to see the question prompt and your response. Depending on how your instructor has set up the assignment or quiz, you may also be able to see the correct answer and an explanation for why it is correct.
If you have trouble finding your results or accessing specific information, you can reach out to your instructor or the Edmentum support team for assistance.
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If my friend went to bed at 1:00am on Friday. Then she woke up at 1:00pm on Friday how many hours of sleep did she get?
If your friend went to bed at 1:00am on Friday and woke up at 1:00pm on Friday, she slept for 12 hours.
To see why, you can count the number of hours between 1:00am and 1:00pm:
1:00am to 2:00am = 1 hour
2:00am to 3:00am = 1 hour
...
11:00am to 12:00pm = 1 hour
12:00pm to 1:00pm = 1 hour
The total number of hours between 1:00am and 1:00pm is 12 hours.
Here is Annie's method to find angle ABC. Explain the mistake that Annie has made. Let angle ABC = 0 8 sin == 10 8= sin-1 8 10 0 = 53.13 (2 dp) Is there more than one possible mistake? Find angle ABC. A 6 cm C 10 cm 8 cm -B
Annie made mistake in her trigonometric ratios. The opposite side of the right triangle should be 6 cm not 8 cm.
How to find the angles of a right angle triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Annie tries to solve the angle ABC of the right triangle. The angle ABC can be found using trigonometric ratios as follows:
where
∅ = angle ABC
Therefore,
sin ∅ = opposite / hypotenuse
sin ∅ = 6 / 10
sin ∅ = 3 / 5
∅ = sin⁻¹ 0.6
∅ = 36.8698976458
∅ = 36.87 degrees
Therefore, she made mistake in her trigonometric ratios.
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6+4
7777777777777777777777777777777777
Answer:
10,
7777777777777777777777777777777777
Step-by-step explanation:
Ida wants to buy a car, but she currently does not have any money. The car she wants costs $2500.
She could borrow $2500 at a weekly interest rate of 1% simple interest and pay the total after 12 months.
What would be the amount of interest (JUST INTEREST) she would owe at the end of 12 months?
Answer:
2200
Step-by-step explanation:
have a good day
An isosceles triangle has an angle that measures 90°. What measures are possible for the other two angles? Choose all that apply.
90 45 75 20
Step-by-step explanation:
All three angels of a triangle have to sum to 180 degrees ....so there is only 90 degrees left for the other two equal-sized angles (isosceles).....they must be 45° each
Can sombody help me with I=prt this is stressing me out .
The result will be the amount of interest earned or paid. Don't stress out too much - with a little practice, you'll become an expert at using this formula!
Sure, I'd be happy to help you with I=prt! This formula is used to calculate simple interest. "I" stands for the interest, "p" stands for the principal (the amount of money borrowed or invested), "r" stands for the interest rate (expressed as a decimal),
and "t" stands for the time period (usually expressed in years). To use the formula, simply multiply the principal by the interest rate and the time period (in years).
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Please explain on how to solve this Question
Answer:
i) ABCDEF has an area of 98m
ii) Flower bed has an area of 6m
iii) The area of the grass is 92m
Hope this helps!
Step-by-step explanation:
The area of a triangle is [tex]\frac{1}{2}[/tex] × L × H
The area for the triangle flower bed will be [tex]\frac{1}{2}[/tex] × 6m × 2m or 6m.
In order to find the entire area of ABCDEF, draw a segment FC to create a trapezoid and a rectangle. The rectangle has an area of 77m ( 7 × 11 ). The trapezoid has a formula of [tex]\frac{1}{2}[/tex] × ( b + b ) × h, this would be [tex]\frac{1}{2}[/tex] × ( 10 + 11 ) × 2.
The trapezoid has an area of 21, this added to the rectangle's area of 77 equals 98m as the total area of the garden.
Subtract the area of the flower bed ( 6 ) from the area of the garden, and you get an area of 92m. This is the area of grass.
I am needing some help
28.26 is the volume of the fig.
What is volume?Each thing in three dimensions takes up some space.
The volume of this area is what is being measured.
The space occupied within an object's borders in three dimensions is referred to as its volume.
It is sometimes referred to as the object's capacity.
Knowing an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.
Hence, 28.26 is the volume of the fig.
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Write the equation of a line perpendicular to y = -4x and passing through the point (12,6).
1. y = -1/4 x + 9
2. y = -1/4 x + 3
3. y = 1/4 x + 9
4. y = 1/4 x + 3
The equation of line perpendicular to y = -4x and passing through the point (12, 6) is y = 1/4 x + 3.
How to determine a line's equation from two points?Using the slope method, determine the slope.
To find the y-intercept (b), use the slope and one of the locations.
You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).
The given equation is y = -4x and we need to find the equation of the line which is passing through the point (12,6).
As y=-4x, therefore compared to the standard equation y = mx, hence the slope of the line is m = -4.
Therefore any line which is perpendicular and has a slope that is the negative reciprocal of the -4 is 1/4.
The modified equation becomes for the line that passes through (12, 6).
y-6 = 1/4 (x-12)
solving this equation we get,
y-6 = 1/4 x - 1/4 * 12
y-6 = 1/4 x - 3
y = 1/4 x -3 + 6
y = 1/4 x + 3
Therefore option 4 is correct, y = 1/4 x + 3
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The tables represent the points earned in each game for a season by two football teams. Saints
21 12 3
3 10 10
14 3 12
28 40 10
17 20 7
Cowboys
10 3 8
6 24 12
21 3 10
28 28 7
7 13 3
Which team had the best overall record for the season? Determine the best measure of center to compare and explain your answer. Cowboys; they have a larger median value of 10 points
Saints; they have a larger median value of 12 points
Cowboys; they have a larger mean value of about 12. 2 points
Saints; they have a larger mean value of about 14 points
The Saints had the best overall record for the season because they had a larger mean value of about 200 points, whereas the Saints had a larger median value of 12 points.
To determine which team had the best overall record for the season, we need to consider the total number of points earned by each team across all games. We can calculate the total points for each team by adding up the points earned in each game.
For the Saints:
Total points = 21+12+3+3+10+10+14+3+12+28+40+10+17+20+7 = 200
For the Cowboys:
Total points = 10+3+8+6+24+12+21+3+10+28+28+7+7+13+3 = 183
Therefore, the Saints earned a total of 200 points, while the Cowboys earned a total of 183 points. Therefore, the Saints had the better overall record for the season.
To compare the central tendency of the points earned by each team, we can use either the mean or the median. However, in this case, the median is a better measure of center because it is less sensitive to extreme values than the mean.
Calculating the median for each team:
For the Saints:
Arrange the points earned in ascending order: 3 3 7 10 10 12 12 14 17 20 21 28 40
The median value is the middle value, which is 12.
For the Cowboys:
Arrange the points earned in ascending order: 3 3 6 7 8 10 10 12 13 21 24 28
The median value is the middle value, which is 10.
Therefore, the Cowboys have a median value of 10 points, while the Saints have a median value of 12 points. However, as we already determined, the Saints had a better overall record for the season based on the total points earned.
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Gizmo
Helpp pleaseee
25 points!!
Model reef can sustain 20% net fishing because the species didn’t increase as much as it did with the other net fishing method.
Explanation:
What is reef fishing ?
Reef fishing is commonly called “Bottom Bouncing” where anglers using heavy 60-100lb handline and rod techniques to target such prized eating fish as Coral Trout, Red Emperor and Nannygai.
What is net fishing ?
A fishing net is a net used for fishing. Nets are devices made from fibers woven in a grid-like structure. Some fishing nets are also called fish traps, for example fyke nets.
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you have been asked to design a can shaped like right circular cylinder that can hold a volume of 432⇡-cm3. what dimensions of the can (radius and height) will use the least amount of material?
The dimensions of the can that use the least amount of material are a radius of approximately 4.38 cm and a height of approximately 3.11 cm.
To design a can that uses the least amount of material, we want to minimize its surface area. Since the can is shaped like a right circular cylinder, its surface area is given by:
A = 2πr² + 2πrh
where r is the radius of the base of the cylinder and h is its height.
We also know that the volume of the can is given by:
V = πr²h
We can use these equations to express h in terms of r, and then substitute this expression for h into the equation for surface area. Then we can differentiate the resulting equation with respect to r, set it equal to zero, and solve for r to find the value of r that minimizes surface area.
First, we solve for h in terms of r by rearranging the equation for volume:
h = V/(πr²)
Substituting this expression for h into the equation for surface area, we get:
A = 2πr² + 2πr(V/(πr²))
A = 2πr² + 2V/r
To minimize A, we differentiate with respect to r:
dA/dr = 4πr - 2V/r²
Setting this expression equal to zero and solving for r, we get:
4πr = 2V/r²
r³ = V/(2π)
Substituting the given value for V, we get:
r³ = 432/2π
r ≈ 4.38 cm
Now we can use the expression for h in terms of r to find the corresponding height:
h = V/(πr²) ≈ 3.11 cm
Therefore, the dimensions of the can that use the least amount of material are a radius of approximately 4.38 cm and a height of approximately 3.11 cm.
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Circumference=14.4
Area =?
Answer:
[tex]a = \frac{1296}{5\pi} [/tex]
Step-by-step explanation:
Given:
C = 14,4 (circumference)
Find: A - ? (area)
Let's start by writing down both circumference and area formulas:
[tex]c = 2\pi \times r[/tex]
[tex]a = \pi \times {r}^{2} [/tex]
We can find the radius (r) from the 1st formula:
[tex]r = \frac{c}{2\pi} = \frac{14.4}{2\pi} =14 \frac{4}{10} \times \frac{1}{2\pi} = \frac{144}{10} \times \frac{1}{2\pi} = \frac{144}{20\pi} = \frac{36}{5\pi} [/tex]
Now, that we know the length of the radius, we can find the area:
[tex]a = \pi \times( { \frac{36}{5\pi} })^{2} = \frac{1296}{25 {\pi}^{2} } \times \frac{\pi}{1} = \frac{1296}{25\pi} [/tex]
If a + c = 4.98 and b + c = 6.48, what is the value of b^2+bc-ab-ca?
A) 7.47
B) 8.16
C) 9.08
D) 9.72
E) None of the preceding
Answer:
it is option no d at least
cuz it is what it is
⚠️URGENT !!! ⚠️Bonjour, pouvez-vous m'aider a resoudre ce problème ?
Énoncé :
Paul roule avec son vélo à la vitesse constante de 8,3m/s (30km/h) pendant une durée égale à 120 secondes.
Question :
Quelle durée mettra-t-il à cette vitesse pour parcourir 3km ?
Merci d'avance,
Bonne journée.
PS : est-il possible de mettre me calcul pour que je comprenne mieux?
bonjour,
a) on pourrait faire un produit en croix
8,3 m ----> 1s
combien de m en ----> 120s
120*8,3= 996m en 120s
soit 0,996 km (on décale de 3 rangs vers la gauche)
il parcoure donc 996m en 120secondes
b) pour parcourir 3km, de même faisons un produit en croix
(3 km = 3000m)
8,3 m ---> 1s
3000m ----> combien de secondes ?
3000*1/8,3= environ 361,45 secondes
transformons les en heures, minutes
361,45/60 = 6,02 minutes
0,02*60= 1,2
donc pour parcourir 3km, à cette vitesse, il mettra environ 6 minutes et 1 seconde.
c) posons un produit en croix :
vitesse en km/h
15km ----> 25 min
? -----> 60 min (1h)
60*15/25= 36
donc il a une vitesse de 36km/h
vitesse en km/mn
15km ----> 25 min
?km ------> 1 min
1*15/25 =0,6 km/mn
voilà j'espère t'avoir aidé
si t'as des questions n'hésite pas
Naomi went shopping for a new pair of sneakers because of a sale. The store was offering a 10% discount. What number should she multiply the prices on the tags by to find the price she would have to pay, before tax, in one step?
She should multiply the prices on the tags by 0.9 to find the price she would have to pay, before tax, after the 10% discount.
To find the price Naomi would have to pay for her new sneakers after the 10% discount, she needs to multiply the original price on the tag by a factor that reflects the discount.
Since the discount is 10%, the factor by which she should multiply the original price is 1 minus 10% or 0.9. This is because the final price is equal to the original price minus the discount, which is 10% of the original price, or 0.1 times the original price.
So, if the price on the tag is $100, the price Naomi would have to pay, before tax, after the 10% discount would be:
$100 * 0.9 = $90
This means that she would save $10, which is 10% of the original price.
In general, if the original price on the tag is P, the price Naomi would have to pay, before tax, after the 10% discount would be:
P * 0.9 = 0.9P
Therefore, she should multiply the prices on the tags by 0.9 to find the price she would have to pay, before tax, after the 10% discount.
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These are the steps Brittany took to find the difference, but she made a mistake. Select the step at which Brittany made her first mistake. Then select the correct difference in simplest form. Select all the correct locations on the image.
Answer:
Step-by-step explanation:
Help me asap please
Answer:
4
Step-by-step explanation:
because it median, so it number was the middle of the total
as we know there is total of 9
and we count to 5
so it 4 letters
Answer:
4
Step-by-step explanation:
arranging the name lengths from smallest to largest we have; 3,3,3,3,4,5,7,7,9
From the set of numbers,4 appears at the middle hence the median name length.
Find the image matrix for quadrilateral ABCD
after the composite transformation.
A(−10, 0), B(−8, 6), C(−3, 7), and D(0, 3)
Rotation: 270º
Reflection: y = -x
The required transformed coordinates of the quadrilateral as:A'(-10, 0),B'(-8, -6),C'(-3, -7), D'(0, -3).
How to find the image matrix for quadrilateral ABCD?The image matrix for the composite transformation of a rotation of 270º and a reflection over the line y=-x can be found by multiplying the transformation matrices for each operation.
The rotation matrix for 270º counterclockwise can be represented as:
[tex]$R_{270} = \begin{bmatrix}0 & -1 \1 & 0\end{bmatrix}$[/tex]
The reflection over the line y=-x can be represented as:
[tex]$F_{y=-x} = \begin{bmatrix}0 & -1 \-1 & 0\end{bmatrix}$[/tex]
To find the composite transformation matrix, we multiply the two matrices:
[tex]$M = F_{y=-x} \cdot R_{270} = \begin{bmatrix}0 & -1 \-1 & 0\end{bmatrix} \cdot \begin{bmatrix}0 & -1 \1 & 0\end{bmatrix} = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix}$[/tex]
To apply this transformation to the coordinates of the quadrilateral ABCD, we write each point as a column vector:
[tex]$A = \begin{bmatrix}-10 \0\end{bmatrix}$[/tex],
[tex]$B = \begin{bmatrix}-8 \6\end{bmatrix}$[/tex],
[tex]$C = \begin{bmatrix}-3 \7\end{bmatrix}$[/tex],
and
[tex]$D = \begin{bmatrix}0 \3\end{bmatrix}$[/tex]
We can then apply the composite transformation matrix M to each of these vectors:
[tex]$A' = M \cdot A = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix} \cdot \begin{bmatrix}-10 \0\end{bmatrix} = \begin{bmatrix}-10 \0\end{bmatrix}$[/tex]
[tex]$B' = M \cdot B = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix} \cdot \begin{bmatrix}-8 \6\end{bmatrix} = \begin{bmatrix}-8 \-6\end{bmatrix}$[/tex]
[tex]$C' = M \cdot C = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix} \cdot \begin{bmatrix}-3 \7\end{bmatrix} = \begin{bmatrix}-3 \-7\end{bmatrix}$[/tex]
[tex]$D' = M \cdot D = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix} \cdot \begin{bmatrix}0 \3\end{bmatrix} = \begin{bmatrix}0 \-3\end{bmatrix}$[/tex]
We can then write the transformed coordinates of the quadrilateral as:
A'(-10, 0),
B'(-8, -6),
C'(-3, -7),
D'(0, -3)
Therefore, the image matrix of quadrilateral ABCD after the composite transformation is:
[tex]$ \begin{bmatrix}-10 & -8 & -3 & 0 \0 & -6 & -7 & -3\end{bmatrix}$[/tex]
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A scientist has three small jars of chemicals to use for an experiment jar one has a mass of 0.62 g jar to has a mass of 1.431 g jar three has a mass of 0.5 g what is the total mass of jars in grams complete the chart Each box
According to the question we can conclude that the total mass of the jars is 2.561 g.
Explain law of mass conversion?The mass is the amount of matter in an object. It is measured in grams, kg, ect. According to the law of conservation, mass in such an isolated system may only be changed through one form to another and cannot be created or destroyed.
To find the total mass of the jars, we simply need to add up the masses of jar one, jar two, and jar three:
Total mass of jars = mass of jar one + mass of jar two + mass of jar three
Total mass of jars = 0.62 g + 1.431 g + 0.5 g
Total mass of jars = 2.561 g
So the total mass of the jars is 2.561 g.
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In analyzing hits by certain bombs in a war, an area was partitioned into 561 regions, each with an area of 0.75 km2. A total of 525 bombs hit the combined area of 561 regions. Assume that we want to find the probability that a randomly selected region had exactly four hits. In applying the Poisson probability distribution formula, P(x)=
μx•e−μ
x!, identify the values of μ, x, and e. Also, briefly describe what each of those symbols represents.
Answer:
x is the number of successes
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
There is a 17.18% probability that a randomly selected region had exactly two hits.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X=x)=\dfrac{e^{-\mu}\times\mu^x}{(x)!}[/tex]
In which
x is the number of successes
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
In this problem we have that:
A total of 525 bombs hit the combined area of 561 regions. So the mean hits per region is:
[tex]P=\dfrac{525}{561}=0.9358[/tex]
Assume that we want to find the probability that a randomly selected region had exactly two hits.
This is P(X = 2).
[tex]P(X=x)=\dfrac{e^{-\mu}\times\mu^x}{(x)!}[/tex]
[tex]P(X=2)=\dfrac{e^{-0.9358}\times(0.9358)^2}{(2)!}=0.1718[/tex]
There is a 17.18% probability that a randomly selected region had exactly two hits.
select all the lines that intersect y=3
v
To identify which lines intersect the line y = 3, you would need to provide a list of lines to choose from. In general, any line that is not parallel to y = 3 will intersect it. Lines parallel to y = 3 will have equations of the form y = c, where c is a constant value different from 3.
Gumballs cost $0. 50 each, and jawbreakers cost $0. 30 each. Bob has $3. 00 to spend on candy.
Create an inequality that represents the number of gumballs and jawbreakers Bob can buy
This inequality states that the total cost of buying x gumballs and y jawbreakers must be less than or equal to $3.00.
Let x be the number of gumballs that Bob buys, and let y be the number of jawbreakers that Bob buys.
The cost of buying x gumballs is $0.50 times x, or 0.50x. The cost of buying y jawbreakers is $0.30 times y, or 0.30y.
Bob has $3.00 to spend on candy, so we can write an inequality to represent the total cost of buying both types of candy:
0.50x + 0.30y ≤ 3.00
This inequality states that the total cost of buying x gumballs and y jawbreakers must be less than or equal to $3.00.
Note that this inequality assumes that Bob spends all of his money on candy. If Bob wants to save some money or spend it on something else, the inequality would need to be modified accordingly.
To know more about inequality, visit: brainly.com/question/30228778
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