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3 years ago

9

If the ratio of red hair bands to green hair bands is 5 to 9 with a total of 70, how many are green

1 answer:

Eduardwww [97]3 years ago

5 0

$5x-\ red\\9x-\ green\\\\5x+9x=70\\
14x=70\ \ \ | divide\ by\ 14\\\\
x=5\\\\
9x=9*5=45\\\\
There\ are\ 45\ green.$

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What is the sum of the series? 4 ∑k=1 (2k^2−4)

larisa86 [58]

The sum of the series $\sum_{k=1}^{4}\left(2 k^{2}-4\right)$ is 44.

Step-by-step explanation:

The given series is $\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44$

To find the sum of the series, we need to substitute the values for k in the series.

$\sum_{k=1}^{4}\left(2 k^{2}-4\right)=\left[2(1)^{2}-4\right]+\left[2(2)^{2}-4\right]+\left[2(3)^{2}-4\right]+\left[2(4)^{2}-4\right]$

Now, simplifying the square terms, we get,

$[2(1)-4]+[2(4)-4]+[2(9)-4]+[2(16)-4]$

Multiplying the terms,

$[2-4]+[8-4]+[18-4]+[32-4]$

Subtracting the values within the bracket term, we get,

$-2+4+14+28$

Now, adding all the terms, we get the sum of the series,

$\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44$

Thus, the sum of the series is $\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44$

8 0

2 years ago

klasskru [66]

Answer:

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$y=0,\:x=6$

Step-by-step explanation:

Considering the system of the equations

$\begin{bmatrix}2x-7y=12\\ -x+15y=-6\end{bmatrix}$

$\mathrm{Isolate}\:x\:\mathrm{for}\:2x-7y=12$

$2x-7y+7y=12+7y$

$2x=12+7y$

Divide both sides by 2

$\frac{2x}{2}=\frac{12}{2}+\frac{7y}{2}$

$x=\frac{12+7y}{2}$

$\mathrm{Subsititute\:}x=\frac{12+7y}{2}$

$\begin{bmatrix}-\frac{12+7y}{2}+15y=-6\end{bmatrix}$

$-\frac{12+7y}{2}+15y=-6$

$\mathrm{Multiply\:both\:sides\:by\:}2$

$-\frac{12+7y}{2}\cdot \:2+15y\cdot \:2=-6\cdot \:2$

$-\left(12+7y\right)+30y=-12$

$-12+23y=-12$

$-12+23y+12=-12+12$

$23y=0$

$\mathrm{Divide\:both\:sides\:by\:}23$

$\frac{23y}{23}=\frac{0}{23}$

$y=0$

$\mathrm{For\:}x=\frac{12+7y}{2}$

$\mathrm{Subsititute\:}y=0$

$x=\frac{12+7\cdot \:0}{2}$

$x=\frac{12}{2}$

$x=6$

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$y=0,\:x=6$

4 0

3 years ago

I need help asap with number four please help me I'll give points

Nat2105 [25]

Idk what it means, sorry and good luck

6 0

3 years ago

Read 2 more answers

Rajesh invested $30,000 into an account that compounds interest monthly at a rate of 2.16%. He has made arrangements to withdraw

Bond [772]

By Evaluating the Compound Interest, we come to know that Rajesh will have enough money in the account to cover all of the required loan payments.

The Principal Amount(P) = $30,000

Rate of Interest (r) = 2.16 %

Time(t) = 10 years

Number of Times it is Compounded in a year(n) = 12

Now, we have

$A =P(1+\frac{r}{100n}) ^{nt}$

Putting all the values, we evaluate the amount,

$A =30,000(1+\frac{2.16}{100*12}) ^{12*10}\\\\A = 30,000 * 1.240\\A = 37,225.84$

Hence, the Amount after Compound Interest = $37,225.87

Now, The loan amount that he pays = 300 *12*10 = $ 36,000

Yes, he will have enough money in the account to cover all of the required loan payments.

To read more about Compound Interest, visit brainly.com/question/29335425

#SPJ1

5 0

10 months ago

To get an accurate result, a sample size must be

levacccp [35]

At least 30 ..................

8 0

2 years ago