Iliana signed up for a store credit card with no annual fee to get a discount of 12.5 percent off her entire first purchase.

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. David invested $220

S_A_V [24]

Answer:

The answer is 23 years.

Step-by-step explanation:

We will use the formula :

$A=P(1+r)^{t}$

Here P = 220

r = 3%

A = 400

Putting these values in the formula we get,

$400=200(1+0.03)^{t}$

$2=1.03^{t}$

Taking log on both sides,

ln(1.03)t=ln 2

$t=\frac{ln(2)}{ln(1.03)}$

t=23.44 or rounding to nearest, t=23 years

The graph of the function can be shown as below.

3 0

2 years ago

Read 2 more answers

A scientist is studying tulips and daffodils. The scientist estimates that there are 150 tulips in the population of 600 tulips

Flauer [41]

Answer: Last Option is correct.

Step-by-step explanation:

Since we have given that

Total number of tulips and daffodils = 600

Number of tulips = 150

Number of daffodils is given by

$600-150\\\\=450$

So, We can get the ratio of tulips to daffodils which is given by

$Tulips:Daffodils\\\\150:450\\\\1:3$

So, we need to choose a random sample of flowers to represent the population.

1) He can choose 50 flowers.

As there are 1:3 of tulip and daffodils flowers but if we divide 50 by 4 it will give a decimal number, so it can't represent the required thing.

2) He can choose 25 tulips and 25 daffodils

As they are divided into 1:1 so, it can't represent the 1:3 tulip to daffodils population.

3) He can choose 15 tulips and 60 daffodils

As it is divided into 1:4 inspite of 1:3.So it can't represent the required population.

4) He can choose 10 tulips and 30 daffodils.

So, Last option which states that he can choose 10 tulips and 30 daffodils as in this case the ratio of tulips to daffodils is 1:3.

Hence, Last Option is correct.

4 0

1 year ago

Read 2 more answers

Darcie wants to crochet a minimum of 3 blankets. Darcie crochets at a rate of 1/15 of a blanket a day. She has 60 days until she

NNADVOKAT [17]

Answer:

The inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal can be given as:

$s\leq 15$

Step-by-step explanation:

The complete question is:

Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways. Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal.

Solution:

Given:

Darcie wants to crochet a minimum of 3 blankets to donate.

Rate at which she crochet = $\frac{1}{15}$ of a blanket per day.

Maximum number of days she has = 60.

To find the number of days Dancie can skip out of 60 days and still reach her goal.

Let $s$ represent the number of days she can skip.

Number of days left to crochet = $(60-s)$ days

At rate of $\frac{1}{15}$ of a blanket per day, number of blankets Dancie can corchet in $(60-s)$ days can be given as :

⇒ $\frac{1}{15}(60-s)$

Simplifying using distribution.

⇒ $(\frac{1}{15}.60)-(\frac{1}{15}.s)$

⇒ $4-\frac{s}{15}$

Dancie needs to crochet a minimum of 3 blankets to reach her goal.

Thus, the inequality can be given as:

$4-\frac{s}{15}\geq 3$

Solving the inequality for $s$

Subtracting 4 both sides.

$4-4-\frac{s}{15}\geq 3-4$

$-\frac{s}{15}\geq -1$

Multiplying both sides by -15.

$-15(-\frac{s}{15})\leq -15(-1)$ [On multiplying by a negative number the sign of inequality reverse]

∴ $s\leq 15$

Thus, Dancie can skip a maximum of 15 days.

5 0

2 years ago

How many distinct pairs of disjoint non-empty subsets of A are there, the union of which is all of A?

Mrac [35]

A = {1, 2, 5, 6, 8}
{1} U {2, 5, 6, 8}
{2} U {1, 5, 6, 8}
{5} U {1, 2, 6, 8}
{6} U {1, 2, 5, 8}
{8} U {1, 2, 5, 6}
{1, 2} U {5, 6, 8}
{1, 5} U {2, 6, 8}
{1, 6} U {2, 5, 8}
{1, 8} U {2, 5, 6}
{1, 2, 5} U {6, 8}
{1, 2, 6} U {5, 8}
{1, 2, 8} U {5, 6}
{1, 5, 6} U {2, 8}
{1, 5, 8} U {2, 6}
{1, 6, 8} U {2, 5}
The answer is 15 distinct pairs of disjoint non-empty subsets.

5 0

2 years ago

According to a Pew Research survey, about 27% of American adults are pessimistic about the future of marriage and the family. Th

IgorLugansk [536]

Answer:

P(X≤5)=0.5357

Step-by-step explanation:

Using the binomial model, the probability that x adults from the sample, are pessimistic about the future is calculated as:

$P(x)=\frac{n!}{x!(n-x)!} *p^{x}*(1-p)^{n-x}$

Where n is the size of the sample and p is the probability that an adult is pessimistic about the future of marriage and family. So, replacing n by 20 and p by 0.27, we get:

$P(x)=\frac{20!}{x!(20-x)!}*0.27^{x}*(1-0.27)^{20-x}$

Now, 25% of 20 people is equal to 5 people, so the probability that, in a sample of 20 American adults, 25% or fewer of the people are pessimistic about the future of marriage and family is equal to calculated the probability that in the sample of 20 adults, 5 people of fewer are pessimistic about the future of marriage and family.

Then, that probability is calculated as:

P(X≤5)= P(1) + P(2) + P(3) + P(4) + P(5)

Where:

$P(0)=\frac{20!}{0!(20-0)!}*0.27^{0}*(1-0.27)^{20-0}=0.0018$

$P(1)=\frac{20!}{1!(20-1)!}*0.27^{1}*(1-0.27)^{20-1}=0.0137$

$P(2)=\frac{20!}{2!(20-2)!}*0.27^{2}*(1-0.27)^{20-2}=0.0480\\P(3)=\frac{20!}{3!(20-3)!}*0.27^{3}*(1-0.27)^{20-3}=0.1065\\P(4)=\frac{20!}{4!(20-4)!}*0.27^{4}*(1-0.27)^{20-4}=0.1675\\P(5)=\frac{20!}{5!(20-5)!}*0.27^{5}*(1-0.27)^{20-5}=0.1982$

Finally, P(X≤5) is equal to:

P(X≤5) = 0.0018+0.0137 + 0.0480 + 0.1065 + 0.1675 + 0.1982

P(X≤5) = 0.5357

3 0

2 years ago