Miranda found 4 pieces of an ancient ceramic bowl.

Solve the inequality 4x+3<3x+6

Sveta_85 [38]

Answer:

x<3

Step-by-step explanation:

Move all terms containing

x

to the left side of the inequality.

Tap for more steps...

x

+

3

<

6

Move all terms not containing

x

to the right side of the inequality.

Tap for more steps...

x

<

3

The result can be shown in multiple forms.

Inequality Form:

x

<

3

Interval Notation:

(

−

∞

,

3

)

7 0

4 years ago

Expanding brackets (x + 3)(x + 10)

Katarina [22]

Answer:

x² + 13x + 30

Step-by-step explanation:

(x + 3) (x + 10)

Expand the brackets.

x(x + 10) + 3(x + 10)

x² + 10x + 3x + 30

Add like terms.

x² + 13x + 30

6 0

3 years ago

Read 2 more answers

What is the perimeter of ABC with vertices at A (-11,4) B(-7,8) and C (-4,4)

Alborosie

Answer:

Step-by-step explanation:

Using the distance formula,

$AB=\sqrt{(-11-(-7))^{2}+(4-8)^{2}}=\sqrt{16+16}=4\sqrt{2}\\AC=\sqrt{(-11-(-4))^{2}+(4-4)^{2}}=7\\BC=\sqrt{(-7-(-5))^{2}+(8-4)^{2}}=\sqrt{4+16}=2\sqrt{5}\\\\$

So the perimeter is $4\sqrt{2}+7+2\sqrt{5}$

3 0

2 years ago

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in t

andreyandreev [35.5K]

Answer:

The test statistic is c. 2.00

The p-value is a. 0.0456

At the 5% level, you b. reject the null hypothesis

Step-by-step explanation:

We want to test to determine whether or not the mean waiting time of all customers is significantly different than 3 minutes.

This means that the mean and the alternate hypothesis are:

Null: $H_{0} = 3$

Alternate: $H_{a} = 3$

The test-statistic is given by:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

Sample of 100 customers.

This means that $n = 100$

3 tested at the null hypothesis

This means that $\mu = 3$

The average length of time it took the customers in the sample to check out was 3.1 minutes.

This means that $X = 3.1$

The population standard deviation is known at 0.5 minutes.

This means that $\sigma = 0.5$

Value of the test-statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{3.1 - 3}{\frac{0.5}{\sqrt{100}}}$

$z = 2$

The test statistic is z = 2.

The p-value is

Mean different than 3, so the pvalue is 2 multiplied by 1 subtracted by the pvalue of Z when z = 2.

z = 2 has a pvalue of 0.9772

2*(1 - 0.9772) = 2*0.0228 = 0.0456

At the 5% level

0.0456 < 0.05, which means that the null hypothesis is rejected.

7 0

3 years ago

1. what two things need to be true in order to add/subtract two radicals ?

Novay_Z [31]

Answer: 1. To add or subtract radicals, the indices and what is inside the radical (called the radicand) must be exactly the same. If the indices and radicands are the same, then add or subtract the terms in front of each like radical. If the indices or radicands are not the same, then you can not add or subtract the radicals.2.The index tells you how many of a kind you need to put together to be able to move that number or variable from inside the radical to outside the radical. For example, if the index is 2 (a square root), then you need two of a kind to move from inside the radical to outside the radical.3.When factoring a trinomial in the form x2 + bx + c, consider the following tips. Look at the c term first. o If the c term is a positive number, then the factors of c will both be positive or both be negative. In other words, r and s will have the same sign.

Step-by-step explanation:

6 0

3 years ago