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faltersainse [42]
3 years ago
6

Don put $4,000 in a savings account with an interest rate of 4% for three years. If the interest is compounded annually, how muc

h money will he have at the end of the three years?
Mathematics
1 answer:
miskamm [114]3 years ago
4 0

Answer:

$4,499.46

Step-by-step explanation:

We can use the compound interest formula for this problem:

A=P(1+\frac{r}{n} )^{nt}

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, lets change 4% into a decimal:

4% -> \frac{4}{100} -> 0.04

Now lets plug the values into the equation as shown below:

A=4,000(1+\frac{0.04}{1})^{1(3)}

A=4,499.46

Don will have $4,499.46 at the end of the three years.

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A researcher wants to see if a kelp extract helps prevent frost damage on tomato plants. One hundred tomato plants in individual
Anna11 [10]

Answer:

The 95% confidence interval for the true difference in the proportion of tomato plants like these that would experience damage after receiving the kelp treatment and no kelp treatment is -0.2690 < \hat{p}_1-\hat{p}_2 < 0.02901

Step-by-step explanation:

The given data are;

The number of the group 1 plants that exhibited damage = 12

The number of plants in group 1, n₁ = 50

The number of the group 2 plants that exhibited damage = 18

The number of plants in group 2, n₂ = 50

The proportion of group 1 plants that exhibited damage, \hat p_1 = 12/50 = 0.24

The proportion of group 2 plants that exhibited damage, \hat p_2 = 18/50 = 0.36

The z-value at 95% = 1.64

The confidence interval is given by the following formula;

C.I. = \hat{p}_1-\hat{p}_2\pm z^{*}\sqrt{\dfrac{\hat{p}_1\left (1-\hat{p}_1  \right )}{n_{1}}+\dfrac{\hat{p}_2\left (1-\hat{p}_2  \right )}{n_{2}}}

Plugging in the values, we get;

C.I. = 0.24-0.36\pm 1.64 \times \sqrt{\dfrac{0.24\left (1-0.24 \right )}{50}+\dfrac{0.36\left (1-0.36  \right )}{50}}

Therefore, C.I. = -0.2690 < \hat{p}_1-\hat{p}_2 < 0.02901

7 0
3 years ago
A spinner has two equal sections, one green and one orange. The spinner is spun three times, resulting in the sample space S = {
Elina [12.6K]

Solution:

As given , Spinner has two equal Sections, one green and one Orange.

When the Spinner is Spun three times

Total Sample Space  S=  {GGG, GGO, GOG, OGG, GOO, OGO, OOG, OOO}

Random variable X is Selected, which represents number of times orange O' is spun, which is given by

X=0,1,2,3

Probability of an event = \frac{\text{Total favorable outcome}}{\text{Total Possible outcome}}

X=0, Probability of Orange(O), in G G G = \frac{1}{8}

X=1, Probability of Orange(O), in G G O , GOG,and O G G, 3 in total =  \frac{1}{8}

X=2, Probability of Orange(O), in G O O , O GO,and O O G, 3 in total =   \frac{1}{8}

X=3, Probability of Orange(O), in O O O, 1 in all= \frac{1}{8}




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