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Studentka2010 [4]

3 years ago

6

you begin with $25 in savings and $50 in checking, each week you deposit $5 into savings and $10 into checking. after how many w

eeks is the amount in checking twice the amount in savings?

1 answer:

mihalych1998 [28]3 years ago

7 0

The answer to you question is 120$

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David invested $340 in an account paying an interest rate of 2\tfrac{1}{8}2 8 1 % compounded continuously. Natalie invested $3

Nutka1998 [239]

Answer:

$53.83

Step-by-step explanation:

For David

David invested $340 in an account paying an interest rate of 2\tfrac{1}{8}2 8 1 % compounded continuously.

r = 2 1/8% = 17/8% = 2.125% = 0.02125

t = 17 years

P = $340

For Compounded continuously, the formula =

A = Pe^rt

A = Amount Invested after time t

P = Principal

r = interest rate

t = time

A = $340 × e^0.02125 × 17

A = $ 487.94

For Natalie

Natalie invested $340 in an account paying an interest rate of 2\tfrac{3}{4}2 4 3 % compounded quarterly.

r = 2 3/4 % = 11/4% = 2.75% = 0.0275

t = 17 years

P = $340

n = compounded quarterly = 4 times

Hence,

Compound Interest formula =

A = P(1 + r/n)^nt

A = Amount Invested after time t

P = Principal

r = interest rate

n = compounding frequency

t = time

A = $340 (1 + 0.0275/4) ^17 × 4

A = $ 541.77

After 17 years, how much more money would Natalie have in her account than David, to the nearest dollar?

This is calculated as

$541.77 - $ 487.94

= $53.83

Hence, Natalie would have in her account, $53.83 than David

4 0

3 years ago

To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then s

inysia [295]

Answer:

8 inches.

Step-by-step explanation:

From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.

Ab = s ^ 2 = 100

Therefore each side would be:

s = (100) ^ (1/2)

s = 10

So, side of the square base = 10 inches

Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:

Ap = 520/2 = 260

For an area of the square pyramid we have the following equation:

Ap = 2 * x * s + s ^ 2

Where x is the height of each triangular surface and s is the side of the square base

Replacing we have:

260 = 2 * x * 10 + 10 ^ 2

20 * x + 100 = 260

20 * x = 160

x = 160/20

x = 8

Therefore, the value of x is 8 inches.

5 0

3 years ago

A practice law exam has 100 questions, each with 5 possible choices. A student took the exam and received 13 out of 100.If the s

Cloud [144]

Answer:

$z=\frac{13-20}{4}=-1.75$

Assuming:

H0: $\mu \geq 20$

H1: $\mu$

$p_v = P(Z$

Step-by-step explanation:

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest (number of correct answers in the test), on this case we now that:

$X \sim Binom(n=100, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We need to check the conditions in order to use the normal approximation.

$np=100*0.2=20 \geq 10$

$n(1-p)=20*(1-0.2)=16 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=100*0.2=20$

$\sigma=\sqrt{np(1-p)}=\sqrt{100*0.2(1-0.2)}=4$

So we can approximate the random variable X like this:

$X\sim N(\mu =20, \sigma=4)$

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean". The letter $\phi(b)$ is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: $\phi(b)=P(z$

The z score is given by this formula:

$z=\frac{x-\mu}{\sigma}$

If we replace we got:

$z=\frac{13-20}{4}=-1.75$

Let's assume that we conduct the following test:

H0: $\mu \geq 20$

H1: $\mu$

We want to check is the score for the student is significantly less than the expected value using random guessing.

So on this case since we have the statistic we can calculate the p value on this way:

$p_v = P(Z$

5 0

3 years ago

Solve: X=4+(4x-4)

11111nata11111 [884]

Answer:

answer is 10

Step-by-step explanation:

3 0

3 years ago

PLS HELP ME FOR THIS QUESTION

Sergeeva-Olga [200]

Answer: DO you have any options that can help me answer it?

Step-by-step explanation:

6 0

3 years ago