Yes, this series converges. We can check using the integral test; we have
![\displaystyle\frac1{25}+\frac1{36}+\frac1{49}+\cdots=\sum_{n=5}^\infty\frac1{n^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac1%7B25%7D%2B%5Cfrac1%7B36%7D%2B%5Cfrac1%7B49%7D%2B%5Ccdots%3D%5Csum_%7Bn%3D5%7D%5E%5Cinfty%5Cfrac1%7Bn%5E2%7D)
and
![\displaystyle\sum_{n=5}^\infty\frac1{n^2}\le\int_5^\infty\frac{\mathrm dx}{x^2}=\frac15](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bn%3D5%7D%5E%5Cinfty%5Cfrac1%7Bn%5E2%7D%5Cle%5Cint_5%5E%5Cinfty%5Cfrac%7B%5Cmathrm%20dx%7D%7Bx%5E2%7D%3D%5Cfrac15)
Answer:
x=3
Step-by-step explanation:
![\frac{x}{9} =\frac{8}{21+x}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B9%7D%20%3D%5Cfrac%7B8%7D%7B21%2Bx%7D)
x²+21x-72=0
(x-3)(x+24)=0
x=3 or x=-24(rejected)
∴x=3
![\text{Let the coordinate of the point be P(x,y)}.\\ \\ \text{this point is 3/8 of the way from }A(-8,-9)\text{ to }B(24,-1).\\ \text{so this point is divide the line joining AB in a ratio }3:5\\ \\ \text{by the division ratio, we know that if a point P divides }A(x_1,y_1)\text{ and }B(x_2,y_2)\\ \text{in a ratio m:n, then we have}](https://tex.z-dn.net/?f=%20%5Ctext%7BLet%20the%20coordinate%20of%20the%20point%20be%20P%28x%2Cy%29%7D.%5C%5C%0A%5C%5C%0A%5Ctext%7Bthis%20point%20is%203%2F8%20of%20the%20way%20from%20%7DA%28-8%2C-9%29%5Ctext%7B%20to%20%7DB%2824%2C-1%29.%5C%5C%0A%5Ctext%7Bso%20this%20point%20is%20divide%20the%20line%20joining%20AB%20in%20a%20ratio%20%7D3%3A5%5C%5C%0A%5C%5C%0A%5Ctext%7Bby%20the%20division%20ratio%2C%20we%20know%20that%20if%20a%20point%20P%20divides%20%7DA%28x_1%2Cy_1%29%5Ctext%7B%20and%20%7DB%28x_2%2Cy_2%29%5C%5C%0A%5Ctext%7Bin%20a%20ratio%20m%3An%2C%20then%20we%20have%7D%20)
![P=\left ( \frac{mx_2+nx_1}{m+n}, \ \frac{my_2+ny_1}{m+n} \right )\\ \\ \text{so using this, the coordinates of the required point are:}\\ \\ P=\left ( \frac{3(24)+5(-8)}{3+5}, \ \frac{3(-1)+5(-9)}{3+5} \right )\\ \\ \Rightarrow P=\left ( \frac{32}{8}, \ \frac{-48}{8} \right )\\ \\ \Rightarrow P=(4, -6)](https://tex.z-dn.net/?f=%20P%3D%5Cleft%20%28%20%5Cfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%2C%20%5C%20%5Cfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%20%5Cright%20%29%5C%5C%0A%5C%5C%0A%5Ctext%7Bso%20using%20this%2C%20the%20coordinates%20of%20the%20required%20point%20are%3A%7D%5C%5C%0A%5C%5C%0AP%3D%5Cleft%20%28%20%5Cfrac%7B3%2824%29%2B5%28-8%29%7D%7B3%2B5%7D%2C%20%5C%20%5Cfrac%7B3%28-1%29%2B5%28-9%29%7D%7B3%2B5%7D%20%5Cright%20%29%5C%5C%0A%5C%5C%0A%5CRightarrow%20P%3D%5Cleft%20%28%20%5Cfrac%7B32%7D%7B8%7D%2C%20%5C%20%5Cfrac%7B-48%7D%7B8%7D%20%5Cright%20%29%5C%5C%0A%5C%5C%0A%5CRightarrow%20P%3D%284%2C%20-6%29%20)
Hence the coordinate of the point that is 3/8 of the way from A to B is: (4, -6)
The following dataset represents the math test scores for a class of 20 students. 90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80
neonofarm [45]
Answer:
yes
Step-by-step explanation:
The mode is the measure of the central tendency for the given data set. The mode represents the highest frequency of the number
Since in the given data set as we can see that the 100 would be appeared 6 times
So this represent that the mode is 100
So here the mode would be the good measure