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3 years ago

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Solve the equation 32=2m-6

1 answer:

ollegr [7]3 years ago

5 0

32 = 2m - 6
Add 6 to both sides
38 = 2m
Divide 2 to each side
19 = m

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A garden supply store sells two types of lawn mowers. Total ales of mowers for the year were $8379.70. The total number of mower

Anestetic [448]

Answer:

The number of small mowers are 19 and the large mowers are 11.

Step-by-step explanation:

Given:

A garden supply store sells two types of lawn mowers. Total sales of mowers for the year were $8379.70. The total number of mowers sold the 30. The small mower cost $249.99 and the large mower costs $329.99.

Now, to find the number of each type of mower sold.

Let the number of small mower be $x.$

And the number of large mower be $y.$

So, total number of mowers are:

$x+y=30$

$x=30-y\ \ \ ....(1)$

Now, the total sales of mowers are:

$249.99(x)+329.99(y)=8379.70$

Substituting the value of $x$ from equation (1) we get:

$249.99(30-y)+329.99y=8379.70$

$7499.7-249.99y+329.99y=8379.70$

$7499.7+80y=8379.70$

<em>Subtracting both sides by 7499.7 we get:</em>

$80y=880$

<em>Dividing both sides by 80 we get:</em>

$y=11.$

The number of large mower = 11.

Now, to get the number of small mowers we substitute the value of $y$ in equation ( 1 ):

$x=30-y\\x=30-11\\x=19.$

The number of small mower = 19.

Therefore, the number of small mowers are 19 and the large mowers are 11.

6 0

3 years ago

Simplify this equation<br> -5x+7>22

Lana71 [14]

Answer:

<h2>x < - 3</h2>

Step-by-step explanation:

$- 5x + 7 > 22$

Move 7 to the other side of the inequality

$- 5x > 22 - 7 \\ - 5x > 15$

Divide both sides by - 5

$\frac{ - 5x}{5} > - \frac{15}{5} \\ x > - 3$

Reverse the sign

We have the final answer as

<h3>x < - 3</h3>

Hope this helps you

4 0

2 years ago

Abi invest€500 for 4 years in a bank account pays simple interest at a rate of 2.3% per year work out the total amount of the in

timofeeve [1]

Answer:

46euros

Step-by-step explanation:

Formula- I=P*R/100*T

P=principal amount R=rate T=time

Compute the values given in the question to this formula

So, it would be-

I= 500*0.023*4

I= 46euros

And that's all!

7 0

3 years ago

What's 17⁄12 as a mixed number? <br><br> A. 1 5⁄12<br> B. 1 12⁄7<br> C. 1 7⁄12<br> D. 7 1⁄2

Tju [1.3M]

Answer:

A

Step-by-step explanation:

17 / 12

(12 + 5) / 12

12/12 + 5/12

1 5/12

8 0

3 years ago

The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x

RoseWind [281]

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.

<em>Firstly we will calculate the general probability that of P(a < X < b) </em>

P(a < X < b) = $\int_{a}^{b} \frac{2}{x^{3}} dx$ = $2\int_{a}^{b} x^{-3} dx$

= $2[ \frac{x^{-3+1} }{-3+1}]^{b}_a dx$ { Because $\int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a$ }

= $2[ \frac{x^{-2} }{-2}]^{b}_a$ = $\frac{2}{-2} [ x^{-2} ]^{b}_a$

= $-1 [ b^{-2} - a^{-2} ]$ = $\frac{1}{a^{2} } - \frac{1}{b^{2} }$

a) Now P(X < 5) = P(1 < X < 5) {because x > 1 }

Comparing with general probability we get,

P(1 < X < 5) = $\frac{1}{1^{2} } - \frac{1}{5^{2} }$ = $1 - \frac{1}{25}$ = 0.96 .

b) P(X > 8) = P(8 < X < ∞) = 1/ $8^{2}$ - 1/∞ = 1/64 - 0 = 0.016

c) P(6 < X < 10) = $\frac{1}{6^{2} } - \frac{1}{10^{2} }$ = $\frac{1}{36} - \frac{1}{100 }$ = 0.018 .

d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)

= $(\frac{1}{1^{2} } - \frac{1}{6^{2} })$ + (1/ $10^{2}$ - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982

e) We have to find x such that P(X < x) = 0.75 ;

⇒ P(1 < X < x) = 0.75

⇒ $\frac{1}{1^{2} } - \frac{1}{x^{2} }$ = 0.75

⇒ $\frac{1} {x^{2} }$ = 1 - 0.75 = 0.25

⇒ $x^{2}$ = $\frac{1}{0.25}$ ⇒ $x^{2}$ = 4 ⇒ x = $2$

Therefore, value of x such that P(X < x) = 0.75 is 2.

8 0

3 years ago