12) Write the equation of the quadratic whose vertex is (-2,3) and a = -3.

Iihhhhhhhhhhhhhhhhhhhhiiiiiiiiiiii

Sever21 [200]

Answer:

hhhhhhhhhhhhhhhhhhhiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

Step-by-step explanation:

8 0

3 years ago

Natalie just rented an apartment for $900 a month. She was told the rent will increase 5.5 %each year. About how much will her r

torisob [31]

Each year the rent is multiplied by (1+0.055), so in 7 years, Natalie's rent will be
.. $900*1.055^7 = $1309.21

6 0

2 years ago

Read 2 more answers

The article "Monte Carlo Simulation—Tool for Better Understanding of LRFD" (J. Structural Engr., 1993: 1586–1599) suggests that

Sedaia [141]

Answer:

a) $P(X$

And we can find this probability using the normal standard distribution or excel and we got:

$P(z$

b) $P(X>40)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-43}{4.5})=P(z>3.78)$

And we can find this probability using the complement rule and normal standard distribution or excel and we got:

$P(z>3.78)=1-P(Z$

c) $z=0.674$

And if we solve for a we got

$a=43 +0.674*4.5=46.033$

So the value of height that separates the bottom 75% of data from the top 25% is 46.033.

Step-by-step explanation:

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".

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(43,4.5)$

Where $\mu=43$ and $\sigma=4.5$

Part a

We are interested on this probability

$P(X$

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

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

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

$P(X$

And we can find this probability using the normal standard distribution or excel and we got:

$P(z$

Part b

$P(X>40)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-43}{4.5})=P(z>3.78)$

And we can find this probability using the complement rule and normal standard distribution or excel and we got:

$P(z>3.78)=1-P(Z$

Part c

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.25$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.674$

And if we solve for a we got

$a=43 +0.674*4.5=46.033$

So the value of height that separates the bottom 75% of data from the top 25% is 46.033.

8 0

2 years ago

An investment of $5,000 is made at a simple annual interest rate of 3%. How much additional money must be invested at a simple a

liubo4ka [24]

Answer: Additional money is $6250.

Step-by-step explanation:

Since we have given that

Amount of investment = $5000

Rate of simple interest = 3%

Let the additional amount of investment be 'x'.

Rate of simple interest = 3.9%

Total annual interest rate on total investment = 3.5%

So, According to question, it would be

$5000\times 0.03+x\times 0.039=(5000+x)\times 0.035\\\\150+0.039x=175+0.035x\\\\0.039x-0.035x=175-150\\\\0.004x=25\\\\x=\dfrac{25}{0.004}\\\\x=\$6250$

Hence, Additional money is $6250.

3 0

3 years ago

The base of an isosceles triangle is 9 and its perimeter 49. The base of a similar isosceles triangle is 14. What is the missing

ratelena [41]

Answer: 76.2

Step-by-step explanation:

Perimetar of isiscales triangle is calculated using equation;

P=b+2a

b=9

P=49

lets find sides of triangle.

P-b=2a

a=(P-b)/2

a=49-9/2

a=40/2=20

If another triangle is similar that means that his base and sides are proportional to first triangle.

Base of first trianlge b₁=9

Base of similar triangle is b₂=14

use proportion to find out side of similar triangle:

b₁:b₂=9:14

a₁:a₂=9:14

a₁=20

20: a₂=9:14

a₂=14*20/9=280/9=31.1

Perimetar of second triangle is:

P₂=b₂+2a₂

P₂=14+2*31.1=14+62.2=76.2

3 0

2 years ago