Ask question

Ask question

All categories

3 years ago

15

Jack's age is three years more than twice his younger brother Jimmy's age If the sum of their ages is at most 18 find the greate

st age that Jimmy could be.

1 answer:

UNO [17]3 years ago

6 0

J + 3 + 2j ≤ 18
3j + 3 ≤ 18
3j ≤ 15
j ≤ 5
jimmy's age is 5 years or less

You might be interested in

11B. Long Beach Towing Company charges $40 plus $5 per mile to

gavmur [86]

Answer:

The charges will be the same after 10 miles.

Step-by-step explanation:

Long Beach Towing Company:

Charges $40 plus $5 per mile. So after x miles, the charge will be of:

$L(x) = 40 + 5x$

Five-Star Towing Company:

Chargers of $70 plus $2 per mile. So after x miles, the charge will be of:

$F(x) = 70 + 2x$

After how many miles the charges for the two companied will be the same?

This is x for which:

$L(x) = F(x)$

So

$40 + 5x = 70 + 2x$

$5x - 2x = 70 - 40$

$3x = 30$

$x = \frac{30}{3}$

$x = 10$

The charges will be the same after 10 miles.

5 0

2 years ago

Find g(x), where g(x) is the reflection across the y-axis of f(x)=x.

3241004551 [841]

X➝-x by reflection, so g(x)=-x

7 0

2 years ago

Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

Phantasy [73]

Answer:

$y=-2.95836 x +234.56159$

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479$

$\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694$

$\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897$

$\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226$

$\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22$

And the slope would be:

$m=-\frac{-4152.222}{1403.556}=-2.95836$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222$

$\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111$

And we can find the intercept using this:

$b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159$

So the line would be given by:

$y=-2.95836 x +234.56159$

7 0

2 years ago

What is the next term of AP : √2, √8, √18, .......?

solmaris [256]

Answer:

$\sqrt {32}$

Step-by-step explanation:

Next term of the given AP can be obtained by adding common difference (d) in the last term $\sqrt {18}$

$d = \sqrt{18} - \sqrt{8} = 3 \sqrt{2} - 2 \sqrt{2} = \sqrt{2} \\ next \: term = \sqrt{18} + \sqrt{2} \\ = 3 \sqrt{2} + \sqrt{2} \\ = 4 \sqrt{2} \\ = \sqrt{ {4}^{2} \times 2 } \\ = \sqrt{16 \times 2} \\ \huge \red{ \boxed{next \: term = \sqrt{32} }}$

8 0

2 years ago

A rectangular lawn is 2 m longer than it is wide.

PtichkaEL [24]

Let's breadth be x

Length be x+2

ATQ

$\\ \sf\longmapsto x(x+2)=21$

$\\ \sf\longmapsto x^2+2x=21$

Use completing the square method

$\\ \sf\longmapsto 4(x^2+2x)=4(21)$

$\\ \sf\longmapsto 4x^2+8x=84$

$\\ \sf\longmapsto (2x)^2+2(2x)(2)=84$

$\\ \sf\longmapsto (2x)^2+2(2x)(2)+2^2=2^2+84$

$\\ \sf\longmapsto (2x+2)^2=88$

$\\ \sf\longmapsto 2x+2=\pm\sqrt{88}$

As it's dimensions we will take positive

$\\ \sf\longmapsto 2x+2\approx 9.7$

$\\ \sf\longmapsto 2x=9.7-2=7.7$

$\\ \sf\longmapsto x=3.8$

x+2=3.8+2=5.8

Now

$\\ \sf\longmapsto Perimeter=2(L+B)$

$\\ \sf\longmapsto perimeter=2(3.8+5.8)$

$\\ \sf\longmapsto perimeter=2(9.6)$

$\\ \sf\longmapsto Perimeter=19.2m$

Length of 1 strip=13m

Total strips

$\\ \sf\longmapsto \dfrac{19.2}{13}$

$\\ \sf\longmapsto 1.47strips$

She needs 2 strips

3 0

2 years ago

Read 2 more answers