Which number can you add to 15 to get a sum of 0? (-10 -15 15 0 )

What is the solution to this inequality? (x | x < 7)

VARVARA [1.3K]

Answer: The answer is at the bottom.

Step-by-step explanation:

Write

x

|

x

|

<

7

as a piecewise.

Tap for more steps...

{

x

2

<

7

x

≥

0

−

x

2

<

7

x

<

0

Solve

x

2

<

7

when

x

≥

0

.

Tap for more steps...

0

≤

x

<

√

7

Solve

−

x

2

<

7

when

x

<

0

.

Tap for more steps...

x

<

0

Find the union of the solutions.

x

<

√

7

The result can be shown in multiple forms.

Inequality Form:

x

<

√

7

Interval Notation:

(

−

∞

,

√

7

)

8 0

2 years ago

The percentage of households in the u.S. With cable television increased from 22.5%in 1980 to 68% in 2000. What was the increase

Arada [10]

Answer: The increase in the percent of household with cable television = 45.5%.

Step-by-step explanation:

Given : The percentage of households in the u.S. With cable television increased from 22.5% in 1980 to 68% in 2000.

i.e. Previous percentage in 1980 = 22.5%

New percentage in 2000= 68%

Now , the increase in percentage = (New percentage) - ( Previous percentage )

= 68% - 22.5%

= 45.5%

Hence, the increase in the percent of household with cable television = 45.5%.

4 0

3 years ago

The data set shows the number of hours per week that each student in a class spends studying at home. What is the shape of the d

AVprozaik [17]

Answer:

The answer is symmetrical

Step-by-step explanation:

x

x x x

x x x x x

x x x x x x x

___________________________

1 2 3 4 5 6 7

4 0

3 years ago

A food-packaging apparatus underfills 10% of the containers. Find the probability that for any particular 10 containers the numb

Maksim231197 [3]

Answer:

a) $P(X = 1) = 0.38742$

b) $P(X = 3) = 0.05740$

c) $P(X = 9) = 0.00000$

d) $P(X \geq 5) = 0.00163$

Step-by-step explanation:

For each container, there are only two possible outcomes. Either it is undefilled, or it is not. This means that we can solve this problem using the binomial probability distribution.

Binomial probability distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem

There are 10 containers, so $n = 10$ .

A food-packaging apparatus underfills 10% of the containers, so $p = 0.1$ .

a) This is P(X = 1)

$P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742$

b) This is P(X = 3)

$P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740$

c) This is P(X = 9)

$P(X = 9) = C_{10,9}.(0.1)^{9}.(0.9)^{1} = 0.00000$

d) This is $P(X \geq 5)$ .

Either the number is lesser than five, or it is five or larger. The sum of the probabilities of each event is decimal 1. So:

$P(X < 5) + P(X \geq 5) = 1$

$P(X \geq 5) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.1)^{0}.(0.9)^{10} = 0.34868$

$P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742$

$P(X = 2) = C_{10,2}.(0.1)^{2}.(0.9)^{8} = 0.1937$

$P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740$

$P(X = 4) = C_{10,4}.(0.1)^{1}.(0.9)^{9} = 0.38742$

So

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.34868 + 0.38742 + 0.19371 + 0.05740 + 0.01116 = 0.99837$

Finally

$P(X \geq 5) = 1 - P(X < 5) = 1 - 0.99837 = 0.00163$

3 0

2 years ago

9 to the second power multiply by 3 to the 6 power =3 to the ? power

GenaCL600 [577]

Answer:

Step-by-step explanation:

$a^{m}$ × $a^{n}$ = $a^{m+n}$

$(a^{m})^{n}$ = $a^{mn}$

~~~~~~~~~~~~~

$9^{2}$ × $3^{6}$ = (3²)² × $3^{6}$ = $3^{2*2+6}$ = $3^{10}$

7 0

3 years ago