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Using compound interest, it is found that:

a) A(8) = 2389.66

b) t = 31.15

c) P = 1870.85

Compound interest:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In this problem:

Item a:

[tex]P = 2000[/tex], hence:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(8) = 2000\left(1 + \frac{0.0225}{1}\right)^{8}[/tex]

[tex]A(8) = 2389.66[/tex]

Item b:

[tex]A(t) = 4000[/tex], hence:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]4000 = 2000\left(1 + \frac{0.0225}{1}\right)^{t}[/tex]

[tex](1.0225)^t = 2[/tex]

[tex]\log{(1.0225)^t} = \log{2}[/tex]

[tex]t\log{1.0225} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{\log{1.0225}}[/tex]

[tex]t = 31.15[/tex]

Item c:

[tex]A(3) = 2000[/tex], hence:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]2000 = P\left(1 + \frac{0.0225}{1}\right)^{3}[/tex]

[tex]P = \frac{2000}{(1.0225)^3}[/tex]

[tex]P = 1870.85[/tex]

A similar problem is given at https://brainly.com/question/24850750

The least prime greater than 17 that is the sum of four different prime numbers is 23

The least prime that is the sum of four different prime numbers is 17

That is, 17 = 2 + 3 + 5 + 7

Prime numbers greater than 17 are 23, 29, 31. 37, 41,........

Prime numbers less than 17 are 2, 3, 5, 7, 11, 13

How can we combine the prime numbers 2, 3, 5, 7, 11, and 13 to give the least prime number greater than 17

The only possible combination is:

2  +  3  +  7  +  11   =  23

Therefore, the least prime greater than 17 that is the sum of four different prime numbers is 23

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Answer:

Its AD||CD

Step-by-step explanation:

Answer:

4=4x

Step-by-step explanation:

the formula y=mx+b

corresponds to y=slope+y intercept

all proportional relationships start on the origin so the y-intercept is always 0

the fact that the equation y = 4x doesn't have an intercept shows its proportional this can go with any similar equation like y = 4.5x

Answer:

9m^2

Step-by-step explanation:

Area of triangle = 1/2 ×base×height

=1/2(2/3m ×27m)

Area of triangle =9m^2

Answer:

7

Step-by-step explanation:

5/45 = 3/2x+13

Answer:

charles 4 years

adam 20 years

Step-by-step explanation:

charles present = x

adams present age 5x

8 years later

charles x+8

adam 5x+8

ATQ

x+8+5x+8=10x

4x=16

x=4

5x=20

Using the trigonometry ratio and Pythagorean Theorem, the value of b in the triangle is: 4.

Recall:

Given the trigonometry ratio of sin A = 3/5

Recall that, sin ∅ = opp/hyp (SOH)

Thus, this means that, in sin A = 3/5,

Thus, find the value of b by applying the Pythagorean theorem.

[tex]b = \sqrt{c^2 - a^2}[/tex] (Pythagorean Theorem)

[tex]b = \sqrt{5^2 - 3^2}\\\\\mathbf{b = 4}[/tex]

Therefore, using the trigonometry ratio and Pythagorean Theorem, the value of b in the triangle is: 4.

Learn more about Trigonometry ratios on:

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Answer:

The slope of this line is y=3x-3

Step-by-step explanation:

(I'm not sure but is the line on the point(1,0)? or is it past that point?)

Answer:

a) 8cm

b) 19.8cm

Step-by-step explanation:

The key to these types of questions is to keep proportions in mind.

To solve the first question, you want to find the proportion of the smaller triangle to the bigger triangle. The length of AE is 6cm, but the length of AD is (6+4) = 10cm. So the proportion of the bigger triangle to the smaller triangle is 10/6. So to find the lengths of the sides of the bigger triangle, we want to keep this number in mind.

The BE side is parallel to CD, so we have to use length of BE multiplied by the proportion in order to get the length of CD.

CD = 4.8 * (10/6) = 8

CD = 8cm

For the second question, you use the same concept to find all the other side lengths. The only one you need left for the shape EBCD is side BC. Do the same thing you did before, take the length of the side of the smaller triangle that corresponds with side AC on the bigger triangle. In this case, it's AB, which is 4.5cm. Multiply this by 10/6 to get AC.

AC = 4.5 * (10/6) = 7.5

AC = 7.5

But we're not done. We just found the length of AC, but we need the length of BC to calculate the perimeter. To do this, we want to take the length of AC - the length of AB.

7.5 - 4.5 = 3

So the length of BC is 3cm. Now, to find the perimeter, just add all the sides of EBCD together.

4.8 + 4 + 8 + 3 = 19.8cm.

Hope this helps.

Answer:

a) CD = 8 cm

b) Perimeter of EBCD is 19.8 centimeters

Step-by-step explanation:

For this question, you can assume that ΔABE and ΔACD are similar. That's proven by BE ║ CD, but that's not directly relevant to the question so I won't explain it unless you would like me to.

In 2 similar triangles, all corresponding angles are congruent and all corresponding sides have the same scale factor.

For example, in ΔABC and ΔXYZ:

[tex]\frac{AB}{XY} =\frac{AC}{XZ} =\frac{BC}{YZ}[/tex]

Using those relationships, you can solve for any side in one triangle given the corresponding side in the other triangle.

A)

In the given triangles ΔABE and ΔACD, CD corresponds to BE, so:

[tex]\frac{CD}{BE} =\frac{AD}{AE}[/tex]

where AD is just 6 + 4 = 10.

[tex]\frac{CD}{4.8} =\frac{10}{6} \\\\\frac{CD}{4.8} =1.6667\\\\CD=8[/tex]

CD = 8cm

B)

Doing the same thing as above, now find the length of AC:

[tex]\frac{AC}{AB} =\frac{AD}{AE} \\\\\frac{AC}{4.5} =\frac{10}{6}\\\\\frac{AC}{4.5} =1.6667\\\\AC=7.5[/tex]

Now, to find BC:

[tex]BC=AC-AB\\BC=7.5-4.5\\BC=3[/tex]

Finally, add up the sides to find the perimeter of EBCD:

[tex]4.8+3+8+4\\19.8[/tex]

Perimeter of EBCD is 19.8 centimeters

The height of the board is an illustration of Pythagoras theorem

The ramp will rise 10.3 inches from the ground

The angle of elevation is given as:

[tex]\mathbf{\theta = 19^o}[/tex]

The length of the board is given as:

[tex]\mathbf{l = 30}[/tex]

The height h is calculated using the following tangent ratio

[tex]\mathbf{tan(\theta) = \frac{Opposite}{Adjacent}}[/tex]

So, we have:

[tex]\mathbf{tan(19) = \frac{h}{l}}[/tex]

This gives

[tex]\mathbf{tan(19) = \frac{h}{30}}[/tex]

Make h the subject

[tex]\mathbf{h = 30 \times tan(19)}[/tex]

[tex]\mathbf{h = 10.3}[/tex]

Hence, the ramp will rise 10.3 inches from the ground

Read more about heights at:

https://brainly.com/question/15138986

Answer:

y = 2x - (3/2)

standard equation is

y = mx + c

c is the y intercept

m is the gradient/slope

so

2 is the slope (m)

Answer:

Slope = 2

Step-by-step explanation:

Our equation: y = 2x - 3/2

=> Given equation: y = mx + b

Now, let's compare:

=> y = mx + b = y = 2x - 3/2

=> We can tell that the slope is m, which is 2.

Hoped this helped.

Answer:

45 degree is an acute Angle

Step-by-step explanation:

Please mark as brain list

Answer:

So you can convert e.g. 1 cup of rice or rice flour into grams or ounces etc. easily. Other even more exotic rice varieties converters menu page. You may enter whole numbers, decimals or fractions

Step-by-step explanation:

Answer:21.9FM

Step-by-step explanation:

Answer:

53 po ang tamang sagot po

Answer:

8(×2)+8(×+4)-(4×+9)

Answer:

The larger number is 96.

Step-by-step explanation:

[tex]let \: the \: two \: numbers \: be \: a \: and \: b \\ a + b = 110 \\ let \: a \: be \: the \: larger \: number \\ a = 7b - 2 \\ we \: can \: get \: the \: value \: of \: b \: by \: substituting \: the \: value \: above \: for \: a \: in \: eq \: 1 \\ 7b - 2 + b = 110 \\ 8b - 2 = 110 \\ 8b = 110 + 2 \\ 8b = 112 \\ b = \frac{112}{8} \\b = 14\\ calculate \:the \: value \: of \: a \: using \: the \: equation \: above \\ a + b = 110 \\ a = 110 - 14 \\ a = 96 \\ hence \: the \: large \: number \: is \: 96[/tex]

Answer:

they are not congruent

Step-by-step explanation:

Answer:

The slope of the line is [tex]\frac{9}{2}[/tex] (nine over two)

Step-by-step explanation

Have a nice day

Answer:

In order for a limit to exist, the function has to approach a particular value. In the case shown above, the arrows on the function indicate that the the function becomes infinitely large. Since the function doesn't approach a particular value, the limit does not exist.

Step-by-step explanation:

Answer:

PX : XQ = 2 : 5

Step-by-step explanation:

Since RX is perpendicular to PQ , then

Δ RPX and Δ RQX are right triangle

Calculate PX and XQ using Pythagoras' identity in the right triangles

PX² = 20² - 16² = 400 - 256 = 144 ( take square root of both sides )

PX = [tex]\sqrt{144}[/tex] = 12

Similarly

XQ² = 34² - 16² = 1156 - 256 = 900 ( take square root of both sides )

XQ = [tex]\sqrt{900}[/tex] = 30

Then

PX : XQ = 12 : 30 = 2 : 5 ( in simplest form )

Answer:

37%

Step-by-step explanation:

10% of 600 students is 60 students surveyed and 22 people chose bears. So to find the percent out of 60 just divide 22 by 60

22/60=.36666

move the decimal to get about 37%

hope this helps

Answer:

sure!

Step-by-step explanation:

if you're just wondering How to, then here you are. in order to add fractions, you first must make sure your two fractions in the equation have like denominators (if youre unsure, the bottom number in a fraction), so they just need to be the same before you can add them. Take 1/2 + 2/3 for example, both 2 and 3 can go into 6, so you can make them both fractions of 6. in order to change the bottom part of the fraction, you need to change the top part too. in the case of 1/2, you will multiply the 2 by 3, so also multiply the 1 by 3. then you have 3/6. for 2/3 you will multiply the 3 by 2, so you must also multiply the 2 by 2, you will get 4/6. Now we have 3/6 + 4/6. Do not change the denominator and simply add across the top. Now you'll have 7/6, or 1 1/6. Multiplying fractions is much much simpler. The denominators don't need to be the same, so you just multiply straight across. Multiply first numerator by second numerator, and first denominator by second denominator. using the 1/2 and 2/3 example again, you have 1/2 * 2/3. so you'll first multiply 1 * 2, and make that the numerator. You have 2/-. Then the same with the denominator, 2 * 3, giving you 2/6. (Or, you can simplify to 1/3.) hope this helps, let me know if you have more questions. :)

Answer:

A slope in math is basically rise/run on a coordinate plane. If you have the trend line given and a few values given on the 'x' coordinate and the 'y' coordinate, you can find the slope using rise/run.

Hoped this helped.

The true statement is

The survey results are most at risk for under coverage.

Survey methodology is an area of applied statistics that focuses on human-research surveys. It examines the sampling of discrete groups from a population and related methods for gathering survey data, such as creating questionnaires and techniques for boosting response rates and accuracy.

We have,

A school board is interested in whether high school students would like to shift the school day forward by 30 minutes.

As, It would be biassed to just survey kids who participate in extracurricular activities because they would be excluding the opinions of many other students.

Thus, the survey results are most at risk for under coverage.

Learn more about Survey here:

https://brainly.com/question/17373064

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