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3 years ago

$9.60 for 4 pounds as a unit rate

Mathematics

1 answer:

Reika [66]3 years ago

4 0

You would divide 9.60 by 4 and you would get 2.40 each pound which would be your unit rate

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What is 5(6.2+z)z=3.8

eduard

if z = 3.8

then

5(6.2 + 3.8)

5(10)

hope this helps

6 0

4 years ago

a $7,000 principal is invested in two accounts, one earning 3% interest and another earning 7% interest. if the total interest f

Ksju [112]

Let the investment in first account be x and this account is earning 3% interest

So Interest on this account is 3% of x = 0.03x

So the investment in second account would be (7000-x) and this account is earning 7% interest

So the interest on this account is 7% of (7000-x) = 0.07*(7000-x)

Given that total interest for the year is $262

So we have

0.03x + 0.07(7000-x) = 262

0.03x - 0.07x + 0.07*7000 = 262

-0,04x + 490 = 262

-0.04x = 262-490

-0.04x = - 228

0.04x = 228x

x = 228/0.04

x = 5700

Therefore Investment in one account s 5700 and the investment in other account is 7000-5700 = 1300

3 0

3 years ago

Read 2 more answers

Evaluate the sum of the following finite geometric series.

rjkz [21]

Answer:

$\large\boxed{\dfrac{156}{125}\approx1.2}$

Step-by-step explanation:

<h3>Method 1:</h3>

$\sum\limits_{n=1}^4\left(\dfrac{1}{5}\right)^{n-1}\\\\for\ n=1\\\\\left(\dfrac{1}{5}\right)^{1-1}=\left(\dfrac{1}{5}\right)^0=1\\\\for\ n=2\\\\\left(\dfrac{1}{5}\right)^{2-1}=\left(\dfrac{1}{5}\right)^1=\dfrac{1}{5}\\\\for\ n=3\\\\\left(\dfrac{1}{5}\right)^{3-1}=\left(\dfrac{1}{5}\right)^2=\dfrac{1}{25}\\\\for\ n=4\\\\\left(\dfrac{1}{5}\right)^{4-1}=\left(\dfrac{1}{5}\right)^3=\dfrac{1}{125}$

$\sum\limits_{n=1}^4\left(\dfrac{1}{5}\right)^{n-1}=1+\dfrac{1}{5}+\dfrac{1}{25}+\dfrac{1}{125}=\dfrac{125}{125}+\dfrac{25}{125}+\dfrac{5}{125}+\dfrac{1}{125}=\dfrac{156}{125}$

<h3>Method 2:</h3>

$\sum\limits_{n=1}^4\left(\dfrac{1}{5}\right)^{n-1}\to a_n=\left(\dfrac{1}{5}\right)^{n-1}\\\\\text{The formula of a sum of terms of a geometric series:}\\\\S_n=a_1\cdot\dfrac{1-r^n}{1-r}\\\\r-\text{common ratio}\to r=\dfrac{a_{n+1}}{a_n}\\\\a_{n+1}=\left(\dfrac{1}{5}\right)^{n+1-1}=\left(\dfrac{1}{5}\right)^n\\\\r=\dfrac{\left(\frac{1}{5}\right)^n}{\left(\frac{1}{5}\right)^{n-1}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\r=\left(\dfrac{1}{5}\right)^{n-(n-1)}=\left(\dfrac{1}{5}\right)^{n-n+1}=\left(\dfrac{1}{5}\right)^1=\dfrac{1}{5}$

$a_1=\left(\dfrac{1}{5}\right)^{1-1}=\left(\dfrac{1}{5}\right)^0=1$

$\text{Substitute}\ a_1=1,\ n=4,\ r=\dfrac{1}{5}:\\\\S_4=1\cdot\dfrac{1-\left(\frac{1}{5}\right)^4}{1-\frac{1}{5}}=\dfrac{1-\frac{1}{625}}{\frac{4}{5}}=\dfrac{624}{625}\cdot\dfrac{5}{4}=\dfrac{156}{125}$

5 0

4 years ago

When two lines are cut by a transversal,if the alternate interior angles are equal in measure then the lines are parallel?

Lerok [7]

Ah what you say is true, yes you've answered your question.

When lines are usually cut by a transversal , the transversal only cuts two parallel lines , therefore any alternate interior angles that you find are equal , the lines are always parallel.

6 0

3 years ago

ANSWER ASAP: New machine has productivity (measured in the number of produced details) 12% greater than the last model. After re

GREYUIT [131]

The total number of produced details increased by 6.4%

suppose the starting number was x.
suppose x=100
100 +12%= 112
112-5%=106.4
106.4-100=6.4
6.4%

4 0

4 years ago

Read 2 more answers