Factor −3y−18 and choose the correct option.

Calculate the length of diagonals of a square if its own side is 12√2 cm

spin [16.1K]

Answer:

24 cm

Step-by-step explanation:

Let the side be s and diagonal be d.

The relationship between the side and diagonal of a square is:

d = s√2

Substitute the value of s to find d:

d = 12√2 × √2 = 12 × 2 = 24 cm

3 0

2 years ago

Work out the value of x in the following. (See photo)

AfilCa [17]

A) 2^(x+3)= 4^(2x)
make base number the same
2^(x+3)= 2^2 (2x)
set the exponents equal to eachother
x+3=2 (2x)
x+3=4x
-x both sides
3=3x
÷3 both sides
x=1

b) 16^(1/5)×2^(x)=8^(3/4)
make base same number
2^4 (1/5)×2^(x)=2^3 (3/4)
2^(4/5)×2^(x)=2^(9/4)
set exponents
4/5 +x=9/4
-4/5 both sides
x= 29/20

5 0

4 years ago

A simple random sample of size nequals=8181 is obtained from a population with mu equals 77μ=77 and sigma equals 27σ=27. (a) De

ivanzaharov [21]

Answer:

a) $P(\bar X>81.5)=1-0.933=0.067$

b) $P(\bar X$

c) $P(73.4$

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:

$X \sim N(\mu=77,\sigma=27)$

And let $\bar X$ represent the sample mean, the distribution for the sample mean is given by:

$\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})$

On this case $\bar X \sim N(77,\frac{27}{\sqrt{81}})$

Part a

We want this probability:

$P(\bar X>81.5)=1-P(\bar X$

The best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

$P(\bar X >81.5)=1-P(Z$

$P(\bar X>81.5)=1-0.933=0.067$

Part b

We want this probability:

$P(\bar X\leq 69.5)$

If we apply the formula for the z score to our probability we got this:

$P(\bar X \leq 69.5)=P(Z\leq \frac{69.5-77}{\frac{27}{\sqrt{81}}})=P(Z$

$P(\bar X\leq 69.5)=0.0062$

Part c

We are interested on this probability

$P(73.4$

If we apply the Z score formula to our probability we got this:

$P(73.4$

$=P(\frac{73.4-77}{\frac{27}{\sqrt{81}}}$

And we can find this probability on this way:

$P(-1.2$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-1.2$

3 0

4 years ago

Explain what is happening at this step in the solving equation process.

aleksklad [387]

Answer:

1. After solving we get value of x: $\mathbf{x=\frac{6}{11} }$

2. After solving we get value of x: $\mathbf{x=\frac{6}{11} }$

Step-by-step explanation:

We need to Solve the equations.

1. $10 - 6 x = 4 + 5 x$

Step 1: Subtract 5x on both sides

$10 - 6 x-5x = 4 + 5 x-5x\\10-11x=4$

Step 2: Subtract 10 on both sides

$10-11x-10=4-10\\-11x=-6$

Step 3: Divide both sides by -11

$\frac{-11x}{-11}=\frac{-6}{-11}\\x=\frac{6}{11}$

So, after solving we get value of x: $\mathbf{x=\frac{6}{11} }$

2. $7-6x=1+5x$

Step 1: Subtract 5x on both sides

$7 - 6 x-5x = 1 + 5 x-5x\\7-11x=1$

Step 2: Subtract 7 on both sides

$7-11x-7=1-7\\-11x=-6$

Step 3: Divide both sides by -11

$\frac{-11x}{-11}=\frac{-6}{-11}\\x=\frac{6}{11}$

So, after solving we get value of x: $\mathbf{x=\frac{6}{11} }$

5 0

3 years ago

Alexandria wants to go hiking on Saturday. She will consider these conditions when she chooses which of several

kramer

The inequality to find possible <em>distances</em> from Alexandria's home to a park that satisfies the conditions is: 2+D/50≤6 and the distance is 200 miles.

<h3>Inequality</h3>

Minimum distance=(50×2)

Minimum distance=100 miles

Time (T) required to cover the distance (D)

Time=D/50 hours

Inequality is 2+D/50≤6

Hence:

Let solve for Distance (D)

D/55≤6-2

D≤4×50

≤200

Therefore the inequality to find possible <em>distances</em> from Alexandria's home to a park that satisfies the conditions is: 2+D/50≤6 and the distance is 200 miles.

Learn more about inequality here:brainly.com/question/22857154

#SPJ1

5 0

2 years ago