Which equation best matches the graph shown below ?

Mr Gardener wants to have an annual intrest off 1000. if the annual intrest rate is 5% how much money should he invest

geniusboy [140]

Answer:

$20,000

Step-by-step explanation:

if he invests 20000 he will get 5% of that each year, 5% of 20000=1000 meaning he will have a 1000 yearly interest rate

6 0

2 years ago

Consider a binomial experiment with 15 trials and probability 0.35 of success on a single trial.

DedPeter [7]

Answer:

a

$P(X = 10 ) = 0.0096$

b

$P(X = 10 ) = 0.0085$

c

Option A is correct

Step-by-step explanation:

From the question we are told that

The sample size is n = 15

The probability of success is $p = 0.35$

The number of success we are considering is r = 10

Now the probability of failure is mathematically evaluated as

$q = 1- p$

substituting value

$q = 1- 0.35$

$q = 0.65$

Now using the binomial distribution to find the probability of exactly 10 successes we have that

$P(X = r ) = [\left n } \atop {r}} \right. ] * p^r * q^{n- r}$

substituting values

$P(X = 10 ) = [\left 15 } \atop {10}} \right. ] * p^{10}* q^{15- 10}$

Where $[\left 15 } \atop {10}} \right. ]$ mean 15 combination 10 which is evaluated with a calculator to obtain

$[\left 15 } \atop {10}} \right. ] = 3003$

So

$P(X = 10 ) = 3003 * 0.35 ^{10}* 0.65^{15- 10}$

$P(X = 10 ) = 0.0096$

Now using the normal distribution to approximate the probability of exactly 10 successes, we have that

$P(X = r ) = P( r < X < r )$

Applying continuity correction

$P(X = r ) = P( r -0.5 < X < r +0.5)$

substituting values

$P(X = 10) = P( 10-0.5 < X < 10+0.5)$

$P(X = 10 ) = P( 9.5 < X < 10.5)$

Standardizing

$P(X = r ) = P( \frac{9.5 - \mu }{\sigma } < \frac{X - \mu }{\sigma } < \frac{10.5 - \mu}{\sigma } )$

The where $\mu$ is the mean which is mathematically represented as

$\mu = n * p$

substituting values

$\mu = 15 * 0.35$

$\mu = 5.25$

The standard deviation is evaluated as

$\sigma = \sqrt{n * p * q }$

substituting values

$\sigma = \sqrt{15 * 0.35 * 0.65 }$

$\sigma = 1.8473$

Thus

$P(X = 10 ) = P( \frac{9.5 - 5.25 }{1.8473 } < \frac{X - 5.25 }{1.8473 } < \frac{10.5 - 5.25}{1.8473 } )$

$P(X = 10 ) = P( 2.30 < Z < 2.842 )$

$P(X = 10 ) = P(Z < 2.842 ) - P(Z < 2.30 )$

From the normal distribution table we obtain the $P(Z < 2.841)$ as

$P(Z < 2.841) = 0.99775$

And the $P(Z < 2.30)$

$P(Z < 2.30) = 0.98928$

There value can also be obtained from a probability of z calculator at (Calculator dot net website)

So

$P(X = 10) = 0.99775 - 0.98928$

$P(X = 10 ) = 0.0085$

Looking at the calculated values for question a and b we see that the values are fairly different.

8 0

3 years ago

Convert this number expressed in standard form to scientific notation.<br><br> 28,500,000

tekilochka [14]

Answer:

2.85 × 10^7

Step-by-step explanation:

1.In scientific notation, the whole number before the decimal point shouln't be more than 10(exclude 10) or less than 1(include 1)

2.Count the digits after the decimal point to write the power.

Solution;

1. 2.85( 2 is not less than 1 as well as more than 10).

2.Since there are 7 digits after the decimal point, we should write the power 10^7.

3. Complete answer;

2.85 × 10^ 7

6 0

2 years ago

What two dimensional figure will be created by a horizontal cross section

andre [41]

A.) square pyramid.

8 0

2 years ago

Read 2 more answers

Identify the initial amount a and the growth factor b in the exponential function. f(x) = 620 • 7.8x

Ivanshal [37]

The given is f(x) = 620 · 7.8x

The standard equation for an exponential function is f(x) = Aoe^bx

where:
A is the initial amount
b is the growth factor which is constant
x is any real number

Therefore, the initial amount is 620 and the growth factor is 7.8

8 0

2 years ago

Read 2 more answers