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krok68 [10]
3 years ago
12

A savings account accrues interest at a rate of 3.0% yearly. If someone opens an account with $2,500, how much money would the a

ccount have after 4 years?
Mathematics
1 answer:
Dmitriy789 [7]3 years ago
5 0
To answer the question above we first need to know how much is the interest per year. In equation, 3% of $2500 is 75. 75 per year in 4 years is 300. So add $300 to the principal amount, the money after 4 years would be $2800.
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Determine if the lines r1(t) = <3, 0, 2> + t <1, 2, −2> and r2(s) = <0, 1, −1> + s <4, 1, 1> intersect,
Temka [501]

Answer:

Yes lines are intersecting, point of intersection is <4,2,0>.

Step-by-step explanation:

Given parametric equations of line are:

r_{1}(t) =  + t  \\ r_{1}(t) = \\ r_{1}(t) = ---(1)

r_{2}(s) =  + s \\ r_{2}(s) = \\ r_{2}(s) = ---(2)\\

If lines are intersecting then parametric coordinates of (1) are equal to (2)

3+t=4s---(A)\\2t=1+s---(B)\\2-2t=s-1---(C)\\

Considering A and B to find values of t and s

From A

t=4s-3---(D)

Putting in (B)

2(4s-3)=1+s

8s-6=1+s

7s=7

s=1

Then

t=4-3

t=1

If lines are intersecting then these values of s and t must satisfy (C)

2-2(1)=1-1

0=0

This shows lines are intersecting.

At this value of t, (1) becomes

r_{1}(1) = \\=

Putting s=1 in (2)

r_{2}(1)=4, 1+1,-1+1>\\=

Point of intersection is <4,2,0>.

4 0
3 years ago
Which set of expressions represents three consecutive integers?
Svetlanka [38]
D, as it increases by one
4 0
3 years ago
Write a real-life word problem that corresponds to the equation below.
ella [17]

The real life problem that corresponds to the equation will be "The area of a farmer's square garden is 144 square feet. What is the length of the garden?"

<h3>How to solve the equation</h3>

A real-life word problem that corresponds to the equation x² = 144 will be that the area of a farmer's square garden is 144 square feet. What is the length of the garden?

In this case, the length of the garden will be the square root of 144. This will be calculated thus:

x² = 144

x = ✓144

x = 12

Therefore, the length of the garden is 12 feet.

Learn more about equations on:

brainly.com/question/13763238

7 0
3 years ago
An Italian restaurant offers small, medium and large calzones. The choices of filings are cheese, sausage, spinach, or vegetable
larisa86 [58]

Answer:

A) 12 toppings.

Step-by-step explanation:

That would be the answer if there are no combinations of toppings.

You would simply take the number of sizes (3) and the number of toppings (4) and multiply them together to get 12 combinations.

8 0
3 years ago
Researchers are interested if a school breakfast program leads to taller children. Assume that the population of all 5 year-old
DedPeter [7]

Answer:

39-1.96\frac{1}{\sqrt{25}}=38.608    

39+1.96\frac{1}{\sqrt{25}}=39.392    

So on this case the 95% confidence interval would be given by (38.608;39.392)    

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

\bar X=39 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=1 represent the population standard deviation

n=25 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

The margin of error is given by:

ME= z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96

And replacing we got:

ME= 1.96 *\frac{1}{\sqrt{25}}= 0.392

Now we have everything in order to replace into formula (1):

39-1.96\frac{1}{\sqrt{25}}=38.608    

39+1.96\frac{1}{\sqrt{25}}=39.392    

So on this case the 95% confidence interval would be given by (38.608;39.392)    

7 0
3 years ago
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