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Virty [35]
2 years ago
5

H(n) = 3^n+3; Find h (3n)

Mathematics
1 answer:
olya-2409 [2.1K]2 years ago
5 0

Answer:

The option which you chose is absolutely right.

Step-by-step explanation:

h(n) = 3^ n + 3

h(3n) = 3 ^3n + 3

Hope it will help :)

You might be interested in
Twice the greater of two consecutive odd intergers is 13 less than three times the lesser. Find the intergers ​
erastova [34]

Answer:

\large\boxed{15, 16}

Step-by-step explanation:

2 consecutive integers represented as variables:

x, x + 1

Greater one: x + 1

Lesser one: x

Write as an equation

2(Greater) + 13 = 3(Lesser)

Substitute in known values

2(x + 1) + 13 = 3(x)

Multiply

2x + 2 + 13 = 3x

Subtract 2x from both sides of the equation

2 + 13 = x

Add 2 + 13 to simplify

x = 15

Lesser = x = 15

Greater = x + 1 = 15 + 1 = 16

\large\boxed{15, 16}

Hope this helps :)

3 0
3 years ago
Suppose that from the past experience a professor knows that the test score of a student taking his final examination is a rando
DENIUS [597]

Answer:

n=13.167^2 =173.369 and if we round up to the nearest integer we got n =174

Step-by-step explanation:

Previous concepts

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

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".

Let X the random variable who represents the test score of a student taking his final examination. We know from the problem that the distribution for the random variable X is given by:

X\sim N(\mu =73,\sigma =10.5)

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

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

Solution to the problem

We want to find the value of n that satisfy this condition:

P(71.5 < \bar X

And we can use the z score formula given by:

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

And we have this:

P(\frac{71.5-73}{\frac{10.5}{\sqrt{n}}} < Z

And we can express this like this:

P(-0.14286 \sqrt{n} < Z< 0.14286 \sqrt{n} )=0.94

And by properties of the normal distribution we can express this like this:

P(-0.14286 \sqrt{n} < Z< 0.14286 \sqrt{n} )=1-2P(Z

If we solve for P(Z we got:

P(Z

Now we can find a quantile on the normal standard distribution that accumulates 0.03 of the area on the left tail and this value is: z=-1.881

And using this we have this equality:

-1.881 = -0.14286 \sqrt{n}

If we solve for \sqrt{n} we got:

\sqrt{n} = \frac{-1.881}{-0.14286}=13.167

And then n=13.167^2 =173.369 and if we round up to the nearest integer we got n =174

6 0
3 years ago
The results of a survey asking 500 people about their favorite ice cream flavor are shown in the table.
brilliants [131]

chocolate:  experimental 100 theoretical 165

vanilla: experimental 100 theoretical 135

Mint chip: experimental 100 theoretical 100

banana:experimental 100 theoretical 30

<em>BRAINLYEST PLZ PLZ PLEASE </em>

7 0
3 years ago
Find the surface area of a cylinder with a diameter of 4 cm, and a height of
4vir4ik [10]

Answer:

125.66

Step-by-step explanation:

3 0
3 years ago
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 50 feet cubed. A cylinder with height h a
Arada [10]

Answer:

Volume of the sphere is 66.67r/h

Step-by-step explanation:

Hello,

Volume of a sphere = ⁴/₃πr³

Volume of a cylinder = πr²h

The volume of the cylinder = 50ft³

But the cylinder and sphere both have the same radius and height

Volume of a cylinder = πr²h

50 = πr²h

Make r² the subject of formula

r² = 50/πh

Volume of a sphere = ⁴/₃πr³

Put r² into the volume of a sphere

Volume of a sphere = ⁴/₃π(50/πh)r

Volume of a sphere = ⁴/₃ × 50r/h

Volume of a sphere = ²⁰⁰/₃ r/h

Volume of a sphere = 66.67r/h

The volume of the sphere is 66.67r/h

7 0
3 years ago
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