1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alexandra [31]
3 years ago
10

A mother earned $​8750.00 from royalties on her cookbook. She set aside​ 20% of this for a down payment on a new home. The balan

ce will be used for her​ son's future education. She invests a portion of the money in a bank certificate of deposit​ (CD account) that earns​ 4% and the remainder in a savings bond that earns​ 7%. If the total interest earned after one year is ​$420.00​, how much money was invested at each​ rate?
Mathematics
1 answer:
Masteriza [31]3 years ago
5 0

The problem statement is not clear regarding which money is invested. We will assume it is the 80% of $8750 that is set aside for future education. That amount is

... 0.80 × $8750 = $7000

If x represents the amount invested at 7%, then the total interest earned is

... (7000 -x)×4% + (x)×7% = 420

... 280 +0.03x = 420

... x = 140/0.03 ≈ 4666.67

$4666.67 was invested at 7%.

$2333.33 was invested at 4%.

You might be interested in
How do you round 60.95 to the nearest whole number ? What will it become
Nuetrik [128]
It will become 61
because anything above 0.5 rounds up
5 0
3 years ago
Read 2 more answers
3) Caleb's cellphone says that it is 20% charged. He has 45
ra1l [238]

Answer:

225 minutes

Step-by-step explanation:

45 min = 20% = 20/100

20 x 5 = 100

45 x 5 = 225

3 0
3 years ago
Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o
myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is p = \frac{1}{5} = 0.2

10 questions.

This means that n = 10

A) What is the probability that he will answer all questions correctly?

This is P(X = 10)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so P(X = 0)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

P(X \geq 1) = 1 - P(X = 0)

Since P(X = 0) = 0.1074, from item b.

P(X \geq 1) = 1 - 0.1074 = 0.8926

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264

P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055

P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008

P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001

P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0

P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0

So

P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

8 0
3 years ago
Which of the following expressions are equivalent to 16/5?<br><br> Choose all answers that apply:
In-s [12.5K]

None of the above because it will be 3.2 or -3.2

4 0
3 years ago
Read 2 more answers
F+3.8=9.2 in simplest form
Rom4ik [11]
Just isolate f.. buy getting it alone on one side or the other

7 0
3 years ago
Other questions:
  • What is 95.85 estimated to
    12·2 answers
  • What is the solution set to the equation (2x – 6)(3x – 4) = 0?
    12·2 answers
  • The ratio boy to girl in me.baker social studie class is 2 to 3 if there are 30 total students in class how many girls are in th
    6·1 answer
  • They are not related
    6·1 answer
  • Susanne checks the temperature at 10:00 p.m. she notices that, if the temperature falls by 3 more degrees, it will break the rec
    9·1 answer
  • HIGH SCHOOL LEVEL) <br>SUPER EASY I JUST AM DUMB, PLEASE HELP
    8·1 answer
  • the perimeter of a rectangle is 92m. the length is 10m more than twice the width. find the dimensions
    11·1 answer
  • Please solve 15x+1=10+2x
    6·2 answers
  • Find area of the figure
    10·1 answer
  • A sport jacket that cost the retailer$25 is marked up$10. Write as a fraction the mark up compared to the cost
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!