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Irina18 [472]
3 years ago
12

1. Calculate the simple interest over an amount of N$ 2500 that is invested for 3 years and 6 months at a rate of 7% pa.​

Mathematics
1 answer:
Umnica [9.8K]3 years ago
3 0

Answer:

N$  612.5

Step by step explaination:

Given,

Principal or'P'=N$2500

Time or'n'=3 years & 6 months or 3.5 years

Rate of profit or 'r'=7% or 7/100

Profit or 'I'=?

_____________________________________

We know,

I=P*n*r

I=2500*3.5*7/100

I=612.5

So,simple interest is N$  612.5.

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Q
Luda [366]

Answer:

x = 10

Step-by-step explanation:

Q  is the midpoint of PR: PQ = QR

4x + 5 = 2x + 25

2x = 20

x = 10

3 0
2 years ago
Automobile license plates in Massachusetts usually consist of three digits followed by three letters. The first digit is never z
Serga [27]

Answer:

1,58,18,400

Step-by-step explanation:

1st digit can have the values 1-9 (9 distinct values)

2nd digit can have the values 0-9 (10 distinct values)

3rd digit can have the values 0-9 (10 distinct values)

1st letter can have the value A-Z (26 distinct values)

2nd letter can have the value A-Z (26 distinct values)

3rd letter can have the value A-Z (26 distinct values)

Total number of different plates possible = 9*10*10*26*26*26

=1,58,18,400

3 0
2 years ago
Solve for x. -3(x+n)=x
marusya05 [52]

Answer:

x = 3/4 n

Step-by-step explanation:

-3(x+n)=x

Distribute

-3x-3n = x

Add 3x to each side

-3x-3n+3x= x+3x

3n = 4x

Divide by 4

3/4n = 3x/3

3/4 n = x

3 0
3 years ago
An engineer on the ground is looking at the top of a building. The angle of elevation to the top of a buliding. The angle of ele
Marysya12 [62]

\tan( \alpha )  \:  =  \:  \frac{h}{b}
\alpha  \:  =  \:  {22}^{0}
h \:  =  \: 450 \: ft
Therefore,
b \:  =  \: h \cot( \alpha )
b \:  =  \: 450  \: ft \:  \times  \:  \cot( {22}^{0} )
b = 450 ft × 2.47508685
b = 1,113.78908 ft
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6 0
2 years ago
An insurance company selected a random sample of 500 clients under 18 years of age and found that 180 of them had had an acciden
Butoxors [25]

Answer:

a) The pooled proportion is p=0.3.

b) P-value = 0.000078

c) Lower bound = 0.0556

d) Upper bound = 0.1644

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the accident proportions differ between the two age groups .

Then, the null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0

The significance level is 0.05.

The sample 1, of size n1=500 has a proportion of p1=0.36.

p_1=X_1/n_1=180/500=0.36

The sample 2, of size n2=600 has a proportion of p2=0.25.

p_1=X_1/n_1=150/600=0.25.

The difference between proportions is (p1-p2)=0.11.

p_d=p_1-p_2=0.36-0.25=0.11

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{180+150}{500+600}=\dfrac{330}{1100}=0.3

The standard error for the difference between proportions can now be calculated as:

The estimated standard error of the difference between means is computed using the formula:

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.3*0.7}{500}+\dfrac{0.3*0.7}{600}}\\\\\\s_{p1-p2}=\sqrt{0.00042+0.00035}=\sqrt{0.00077}=0.0277

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.11-0}{0.0277}=\dfrac{0.11}{0.0277}=3.964

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

P-value=2\cdot P(t>3.964)=0.000078

As the P-value (0.000078) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is  enough evidence to support the claim that the accident proportions differ between the two age groups.

If we want to calculate the bounds of a 95% confidence interval, we start by calculating the margin of error.

For a 95% CI, the critical value for z is z=1.96.

Then, the margin of error is:

MOE=z \cdot s_{p1-p2}=1.96\cdot 0.0277=0.0544

Then, the lower and upper bounds of the confidence interval are:

LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.11-0.0544=0.05561\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.11+0.0544=0.16439

The  95% confidence interval for the population mean is (0.0556, 0.1644).

5 0
3 years ago
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