Answer:
.45
Step-by-step explanation:
The greatest number can be as large as 81.
<u>Step-by-step explanation:</u>
Given that,
- A set of five different positive integers has a mean of 33 and a median of 40.
- We need to find the set of five different positive integers.
We already know that,
- The term "median" is the middle term which is 40.
- Therefore, if you do not include 0 in positive integers, then the first two positive integers below the median value of 40 to be as low as possible are 1 and 2.
- The median 40 will be the third positive integer of the set.
- Therefore, the fourth positive integer should be the next lowest possible value of 40 which is 41.
With simple algebra you can figure out the last greater number.
-
The set of five different positive integers is given as {1,2,40,41,x}.
- Let, x be the last greater number in the set.
The term "mean" is defined as the sum of all the integers in the set divided by the number of integers in the set.
⇒ Mean = (1+2+40+41+x) / 5
⇒ 33 = (84+x) / 5
⇒ 33×5 = 84 + x
⇒ 165 - 84 = x
⇒ 81 = x
∴ The greatest number can be as large as 81.
Answer:
Shop A = 113 pence
Shop B = 101 pence
Step-by-step explanation:
Given :
Shop A :
5kg for £5.65
Shop B:
2kg for £2.02
Price per kg :
weight / price
100 pence = £1
Shop A :
Price of 1kg :
5.65 / 5 = £1.13 = 113 pence
Shop B:
2.02 / 2 = £1.01 = 1.01 * 100 = 101 pence
Hey there!
To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.
Let the line that we are trying to determine its equation be
and the line that is parallel to
be
.
passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:
⇒Subtitute the values :
![\implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}](https://tex.z-dn.net/?f=%20%5Cimplies%20%5Csf%7Bm%20%3D%20%5Cdfrac%7B%5CDelta%20y%7D%7B%5CDelta%20x%7D%20%3D%20%5Cdfrac%7B%5Cgreen%7B-5%7D%20-%20%5Corange%7B2%7D%7D%7B%5Cred%7B%20%5C%3A%20%5C%3A%203%7D%20-%20%5Cblue%7B9%20%7D%7D%20%3D%20%5Cdfrac%7B%20-%207%7D%7B%20-%206%7D%20%3D%20%5Cboxed%7B%20%5Cbold%7B%5Cdfrac%7B7%7D%7B6%7D%20%7D%7D%7D)
.
Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:
Slope-Intercept Form:
We know that the coordinates of the point (0 , -3) verify the equation since it is on the line
. Now, replace y with -3 and x with 0:
![\implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:](https://tex.z-dn.net/?f=%20%5Cimplies%20%5Csf%7B%5Coverbrace%7B-3%7D%5E%7By%7D%20%3D%20%5Cdfrac%7B7%7D%7B8%7D%20%5Ctimes%20%5Coverbrace%7B0%7D%5E%7Bx%7D%20%2B%20b%7D%20%5C%5C%20%5C%5C%20%5Cimplies%20%5Csf%7B-3%20%3D%200%20%2B%20b%7D%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%5C%20%5C%5C%20%5Cimplies%20%5Csf%7B%5Cboxed%7B%5Cbold%7Bb%20%3D%20-3%7D%7D%20%7D%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20)
Therefore, the equation of the line
is ![\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}](https://tex.z-dn.net/?f=%20%5Cgreen%7B%5Cboxed%7B%5Cred%7B%5Cbold%7B%5Csf%7By%20%3D%20%5Cdfrac%7B7%7D%7B6%7Dx%20-%203%7D%7D%7D%7D%7D%20)
▪️Learn more about finding the equation of a line that is parallel to another one here:
↣brainly.com/question/27497166
Answer:
![\underline{ \underline{ \large{ \pink{ \tt{E \: X \: P \: L \: A \: N \: A \: T \: I \: O \: N}}} }}:](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cunderline%7B%20%5Clarge%7B%20%5Cpink%7B%20%5Ctt%7BE%20%5C%3A%20X%20%5C%3A%20P%20%5C%3A%20L%20%5C%3A%20A%20%5C%3A%20N%20%5C%3A%20A%20%5C%3A%20T%20%5C%3A%20I%20%5C%3A%20O%20%5C%3A%20N%7D%7D%7D%20%7D%7D%3A%20)
✧ We know , Reflection of a point on x - axis remains the x - co-ordinate same but the sign of y - coordinate changes i.e P ( x , y ) ⇢ P' ( x , - y ). So, the image of the point ( 8 , 10 ) under the reflection on x - axis is :
A ( 8 , 10 ) ⇢A' ( 8 , -10 )
☄ Hope I helped! ♡
☃ Have a wonderful day/ night ! ♨
✎
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