Ms. Burke invested $23,000 in two accounts, one yielding 4% interest and the other yielding 10%. If she received a total of $1,280 in interest at the end of the year, how much did she invest in each account?

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

On the planet of Mercury, 4-year-olds average 3.2 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.7 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day.

a. In words, define the random variable X

b. What is X ~N(,)

c. Find the probability that the child spends less than 2 hours per day unsupervised.

d. What percent of the children spend over 12 hours per day unsupervised?

Given Information:  

Mean = μ = 3.2 hours  

Standard deviation = σ = 1.7 hours  

Required Information:  

a. In words, define the random variable X

b. X ~N(,) = ?

c. P(X < 2) = ?

d. P(X > 12) = ?

Answer:  

a) X is the number of hours in a day that a 4-year-old child spends being unsupervised.

b) X ~N(μ,σ) = X ~N(3.2, 1.7)

c) P(X < 2) = 23.88%

d) P(X > 12) = 0%

Explanation:  

a)

Let X is the number of hours in a day that a 4-year-old child spends being unsupervised.

b)

X ~N(μ,σ) = X ~N(3.2, 1.7)

Where 3.2 is the average number of hours that 4-year-old child spends being unsupervised and 1.7 is the standard deviation.

c)

We want to find out the probability that a child spends less than 2 hours per day unsupervised.

P(X < 2) = P(Z < (x - μ)/σ)

P(X < 2) = P(Z < (2 - 3.2)/1.7)

P(X < 2) = P(Z < (- 1.2)/1.7)

P(X < 2) = P(Z < -0.71)

The z-score corresponding to -0.71 is 0.2388

P(X < 2) = 0.2388

P(X < 2) = 23.88%

Therefore, the probability that a child spends less than 2 hours per day unsupervised is 23.88%

d)

We want to find out the probability that a child spends over 12 hours per day unsupervised.

P(X > 12) = 1 - P(X < 12 )

P(X > 12) = 1 - P(X < (x - μ)/σ)

P(X > 12) = 1 - P(X < (12 - 3.2)/1.7)

P(X > 12) = 1 - P(X < 8.8/1.7)

P(X > 12) = 1 - P(X < 5.18)

The z-score corresponding to 5.18 is 1

P(X > 12) = 1 - 1

P(X > 12) = 0

Therefore, the probability that a child spends over 12 hours per day unsupervised is 0%

The question discusses unsupervised hours of Mercurian children and it's a statistics problem involving normal distribution where the average unsupervised time is 3.2 hours with a standard deviation of 1.7 hours.

This question is related to statistics, specifically about normal distribution. The mean unsupervised time for 4-year-olds on Mercury is 3.2 hours, with a standard deviation of 1.7 hours. If we randomly survey a 4-year-old Mercurian child living in a rural area, the time they likely spend alone, denoted as X, will range according to this distribution.

Normal distributions can be defined by two parameters: the mean (μ) and the standard deviation (σ). In this case, μ = 3.2 hours and σ = 1.7 hours. Therefore, we can say that the time X spent by this sampled child alone is normally distributed with these parameters.

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Answer:

47.5% of lightbulb replacement requests numbering between 63 and 83

Step-by-step explanation:

The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 63

Standard deviation = 10

What is the approximate percentage of lightbulb replacement requests numbering between 63 and 83

63 is the mean

83 = 63 + 2*20

So 83 is two standard deviations above the mean.

The normal distribution is symmetric, so 50% of the measures are above the mean and 50% below the mean.

Of those above the mean, 95% are within 2 standard deviations of the mean.

So

0.5*95% = 47.5%

47.5% of lightbulb replacement requests numbering between 63 and 83

1+3+5+7+...+999 =

= 1+2+3+4+...+500

     +1+2+3+...+499

= 2·(1+2+3+...+499) + 500

= 2·(499·500)/2 + 500

= 499·500 + 500

= 500·(499 + 1)

= 500·500

= 250.000

To find the sum of the series 1 + 3 + 5 + 7 + ... + 999, we recognize this is the sum of the first 500 odd numbers. Using the property that the sum of the first n odd numbers is n², we find the sum to be 500², which is 250000.

Summation of Odd Numbers:

To find the sum of the series 1 + 3 + 5 + 7 + ... + 999 using Gauss's method, we first recognize that this sequence is a series of the first 500 odd numbers.

An interesting property to note is that the sum of the first n odd numbers is n².

For example:

→ 1 = 1 (which is 1¹)

→ 1 + 3 = 4 (which is 2²)

→ 1 + 3 + 5 = 9 (which is 3³)

And so on...

In general, the [tex]n_{th[/tex] odd number can be expressed as 2n - 1.

For 999, to find its position in the series, note that 999 is the 500th odd number (since 2*500 - 1 = 999).

Thus, the sum of the first 500 odd numbers is:

→ Sum = 500²

           = 250000

→ So, the sum of the series 1 + 3 + 5 + 7 + ... + 999 is 250000.

Answer and explanation:

Here is code:

credit = int(input("Enter credits : "))

if credit < 7:

print("You are a Freshman")

elif credit >= 7 and credit < 16:

print("You are a Sophomore")

elif credit >= 16 and credit < 26:

print("You are a Junior")

elif credit >= 26:

print("You are a Senior")

Output: check image

To calculate a student's class standing, use conditional statements to determine the appropriate class based on the number of credits earned.

To write a program that calculates a student's class standing based on the number of credits earned, you can use conditional statements. Here's a step-by-step explanation:

Take the input of the number of credits earned from the user.

Use conditional statements (if, else if) to check the number of credits and assign the appropriate class standing.

If the number of credits is less than 7, then the student is a Freshman. If it is at least 7 and less than 16, then the student is a Sophomore.

If it is at least 16 and less than 26, then the student is a Junior. Otherwise, the student is a Senior.

Display the class standing to the user.

Here's an example pseudocode:

credits = input('Enter the number of credits earned: ')

if credits < 7:

   print('Class Standing: Freshman')

elif credits < 16:

   print('Class Standing: Sophomore')

elif credits < 26:

   print('Class Standing: Junior')

else:

   print('Class Standing: Senior')

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Answer:

x = 42

Step-by-step explanation:

The two angles are complementary so the add to 90 degrees.

x+48 = 90

Subtract 48 from each side

x+48-48=90-48

x = 42

Answer:

The angle x°=42.

Step-by-step explanation:

∠PQS equals 90° because it's a right angle (denoted with the square on the bottom).

∠PQS = ∠PQR + ∠RQS

So, ∠RQS = ∠PQS - ∠PQR where ∠PQR = 48°

Plug in the Values:

∠RQS = 90° - 48° = 42°

Answer:

43.62% probability that it will take more than an additional 34 minutes

Step-by-step explanation:

To solve this question, we need to understand the exponential distribution and the conditional probability formula.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Conditional probability formula:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Taking more than 24 minutes.

Event B: Taking ore than 24+34 = 58 minutes.

P(A)

More than 24, use the exponential distribution.

Mean of 41, so [tex]m = 41, \mu = \frac{1}{41} = 0.0244[/tex]

[tex]P(A) = P(X > 24) = e^{-0.0244*24} = 0.5568[/tex]

Intersection:

More than 24 and more than 58, the intersection is more than 58. So

[tex]P(A \cap B) = P(X > 58) = e^{-0.0244*58} = 0.2429[/tex]

Then:

[tex]P(B|A) = \frac{0.2429}{0.5568} = 0.4362[/tex]

43.62% probability that it will take more than an additional 34 minutes

If you have $100, you can calculate the number of Euros by plugging x = 100 into the f(x) function: f(100) = 0.8167 * 100 = 81.67 Euros. Therefore, with $100, you can buy 81.67 Euros.

If you possess 50 Euros, you can determine the number of yen by substituting x = 50 into the g(x) function: g(50) = 145.8038 * 50 = 7290.19 yen. Hence, with 50 Euros, you can buy 7290.19 yen.

Traders engage in foreign currency trading to potentially profit from fluctuations in currency values. In this example, the exchange rates are as follows: 1 U.S. dollar buys 0.8167 Euros, and 1 Euro buys 145.8038 yen. We are asked to define two functions: f(x) represents the number of Euros you can buy with x dollars, and g(x) represents the number of yen you can buy with x Euros.

1. To determine the number of Euros you can buy with x dollars, multiply the exchange rate between dollars and Euros by x. In this case, the exchange rate is 0.8167 Euros per dollar. Therefore, the function f(x) is f(x) = 0.8167x.

2. To find the number of yen you can buy with x Euros, multiply the exchange rate between Euros and yen by x. In this case, the exchange rate is 145.8038 yen per Euro. The function g(x) is g(x) = 145.8038x.

For example:

- If you have $100, you can calculate the number of Euros by plugging x = 100 into the f(x) function: f(100) = 0.8167 * 100 = 81.67 Euros. Therefore, with $100, you can buy 81.67 Euros.

- If you possess 50 Euros, you can determine the number of yen by substituting x = 50 into the g(x) function: g(50) = 145.8038 * 50 = 7290.19 yen. Hence, with 50 Euros, you can buy 7290.19 yen.

These functions enable traders to evaluate the quantity of foreign currency they can acquire or exchange based on the prevailing exchange rates.

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Answer:

-2,4

Step-by-step explanation:

i just did it

Answer:

-2,4

Step-by-step explanation:

i just did it on ed 2020

Final answer:

The incorrect statement about the normal distribution is that its distribution function generally has a bell shape when graphed. This shape relates to the probability density function, not the cumulative distribution function, which actually has an S-shaped curve.

Explanation:

When we discuss the properties of a normal distribution, we are dealing with a continuous probability distribution that is widely used across many fields. The statement in question is identifying characteristics of the cumulative distribution function (CDF) of a normal distribution. The correct attributes of this function are that it ranges from 0 to 1, it increases as the quantity increases, and it returns the probability that the outcome from the normal distribution is a certain quantity or lower. However, the statement that the distribution function generally has a bell shape when graphed is incorrect regarding the CDF. The bell shape is a characteristic of the probability density function (PDF) and not the CDF, which increases from 0 to 1 in an S-shaped curve.

The standard normal distribution, which is a special case of the normal distribution with a mean (μ) of zero and a standard deviation (σ) of one, is used for a variety of applications in psychology, business, engineering, and other fields. Understanding the properties of the normal distribution — particularly the standard normal distribution — is crucial for interpreting data and using statistical methods.

It is also important to note that the integral of the normal distribution across its entirety (from ∞ to ∞) is equal to one. This area under the curve represents the total probability of all outcomes and justifies why the CDF ranges from 0 at the minimum to 1 at the maximum end of the distribution.

Answer:

Account B

Step-by-step explanation:

The answer is 15.66

Answer:

15.66

Step-by-step explanation:

[tex]18\% \: of \: 87 \\ \\ = \frac{18}{100} \times 87 \\ \\ = 0.18 \times 87 \\ \\ = 15.66 \\ [/tex]

Answer:

17,19,23

that the prime number

Answer:

A prime number is a number whose only factors are one and itself

Prime numbers between 15 and 25:

17, 19, 23

Answer:

61 degrees

Step-by-step explanation:

87+32=119

180 (total degrees for triangle)-119=67 degrees

Answer:

Step-by-step explanation:

From the information given we know that

[tex]p \equiv 0 \,\,\,\, \text{mod(3)}\\p \equiv 1 \,\,\,\, \text{mod(5)}\\p \equiv 2 \,\,\,\, \text{mod(7)}\\[/tex]

And we know as well that

[tex]p \equiv x \,\,\,\, \text{mod(11)}\\p \equiv x \,\,\,\, \text{mod(13)}[/tex]

Remember what that the Chinese reminder theorem states.

Theorem:

Let  p,q be coprimes, then the system of equations

[tex]x \equiv a \,\,\,\, mod(p)\\x \equiv b \,\,\,\, mod(q)[/tex]

has a unique solution [tex]mod(pq)[/tex].

Now, if you read the proof of the theorem you will notice that  if

[tex]q_1 = q^{-1} \,\, mod(p) , p_1 = p^{-1} \,\,mod(q)[/tex]

the the solution looks like this.

[tex]x = aqq_1 + bpp_1[/tex]

Now. you can easily generalize what I just stated for multiple equations and you will see that if you apply the theorem for this case it is straightforward that

[tex]p \equiv 0*35*[35^{-1}]_3+1*21*[21^{-1}]_5+2*15[15^{-1}]_7 \,\,\,\,\,\,\,\, mod(3*5*7)\\p \equiv 1*21*1+2*15*1 \,\,\,\,\,\,\,\,mod(105) \\p \equiv 1*21*1+2*15*1 \,\,\,\,\,\,\,\, \\p \equiv 51[/tex]

Therefore, Alice is in room 51.

(b)

Using the Chinese reminder theorem you need less than 2 erasures. The process is very similar.

Answer:

Step-by-step explanation:

From the information given we know that

And we know as well that

Remember what that the Chinese reminder theorem states.

Theorem:

Let  p,q be coprimes, then the system of equations

has a unique solution .

Now, if you read the proof of the theorem you will notice that  if

the the solution looks like this.

Now. you can easily generalize what I just stated for multiple equations and you will see that if you apply the theorem for this case it is straightforward that

Therefore, Alice is in room 51.

(b)

Using the Chinese reminder theorem you need less than 2 erasures. The process is very similar.

Step-by-step explanation:

Answer:

f(2x+1)sin(9[tex]F(2x+1)sin(90.9292)\pi[/tex]- 4.3784)

Step-by-step explanation:

The number of bald eagles is 26.

Answer:

Among 4.1 and 4.009 The greater one is 4.1

Hope it will help.

Given:

Given that the radius of the circle is 12 cm.

The length of the rectangle is 11 cm.

The width of the rectangle is 5 cm.

We need to determine the area of the shaded region.

Area of the rectangle:

The area of the rectangle can be determined using the formula,

[tex]A_1=length \times width[/tex]

Substituting the values, we have;

[tex]A_1=11\times 5[/tex]

[tex]A_1=55 \ cm^2[/tex]

Thus, the area of the rectangle is 55 square cm.

Area of the circle:

The area of the circle can be determined using the formula,

[tex]A_2=\pi r^2[/tex]

Substituting r = 12, we have;

[tex]A_2= (3.14)(12)^2[/tex]

[tex]A_2=452.16 \ cm^2[/tex]

Thus, the area of the circle is 452.16 square cm.

Area of the shaded region:

The area of the shaded region can be determined by subtracting the area of the rectangle from the area of the circle.

Thus, we have;

Area = Area of the circle - Area of the rectangle.

Substituting the values, we have;

[tex]Area=452.16-55[/tex]

[tex]Area=397.16 \ cm^2[/tex]

Thus, the area of the shaded region is 397.16 square cm.

Answer:

y=6

Step-by-step explanation:

3=9-y

y+3=9

y=6

Answer:

y=6

Step-by-step explanation:

3=9-y

3-9 = -y

-6 = -y

y=6

Answer:

The scale factor is 1/2

Step-by-step explanation:

we know that

A dilation is a non rigid transformation that produces similar figures

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ---> the scale factor

x ---> the area after dilation

y ---> the original area

[tex]z^2=\frac{x}{y}[/tex]

we have

[tex]x=25\ cm^2\\y=100\ cm^2[/tex]

substitute

[tex]z^2=\frac{25}{100}[/tex]

[tex]z^2=\frac{1}{4}[/tex]

[tex]z=\frac{1}{2}[/tex]

Final answer:

The standard deviation used to calculate the test statistic for the one-sample z-test, when investigating the proportion of people in Norway with A positive blood type against the U.S. proportion, is 0.0392.

Explanation:

To calculate the standard deviation used to calculate the test statistic for a one-sample z-test in this scenario, where we are testing whether the proportion of people in Norway with a blood type of A positive is different from that in the United States, we use the formula for the standard deviation of a proportion, which is  [tex]\(\sqrt{\frac{p(1-p)}{n}}\)[/tex], where p is the proportion in the population (0.36 in this case, representing 36%), and n is the sample size (150 in this case).

Plugging in the values: [tex]\(\sqrt{\frac{0.36(1-0.36)}{150}}\) = \(\sqrt{\frac{0.36(0.64)}{150}}\) = \(\sqrt{\frac{0.2304}{150}}\) = \(\sqrt{0.001536}\) = 0.0392.[/tex]

So, the standard deviation used to calculate the test statistic for this hypothesis test is 0.0392.

The standard deviation used to calculate the test statistic for the one-sample z-test is approximately 0.0379.

To determine the standard deviation for the one-sample z-test, we use the formula for the standard deviation of a sample proportion, which is given by:

[tex]\[ \sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}} \][/tex]

 Given that the population proportion p of people with A positive blood type in the United States is 0.36, and the sample size n from Norway is 150, we can plug these values into the formula:

[tex]\[ \sigma_{\hat{p}} = \sqrt{\frac{0.36(1-0.36)}{150}} \][/tex]

[tex]\[ \sigma_{\hat{p}} = \sqrt{\frac{0.36 \times 0.64}{150}} \][/tex]

[tex]\[ \sigma_{\hat{p}} \approx 0.0379 \][/tex]

Therefore, the standard deviation used in the calculation of the test statistic for the one-sample z-test is approximately 0.0379.

Step-by-step explanation:

Given, the face of a clock is divided into 12 equal parts.

Angle of each part = [tex]\frac{360}{12}[/tex] = 30°

(i) When one hand points at 2 and the other points at 4, this is can be divided into two parts, 2 to 3 and 3 to 4.

The angle formed = 2 (30) = 60°

Option (i) is correct

(ii) The circumference of the clock is ,

Circumference of circle = 2πr,

where r is the radius = 6 and π = 3.14.

Substituting the values in the formula, we get

Circumference of circle = 37.68.

Option (ii) is wrong.

(iii) With one hand at 5 and the other at 10, this is 5 parts

The angle formed= 30(5) = 150°.  

The arc length =[tex]\frac{150}{360}[/tex](37.68) = 15.7

Option (iii) is correct

(iv) When one hand points at 1 and the other points at 9, this is 4 parts,

30(4) = 120°.  T

Option (iv) is wrong

(v) The length of the minor arc from 11 to 2, this is 3 parts

3(30) = 90°  

minor arc from 7 to 10 is 3(30) = 90°  

Option (v) is correct

Answer: options 1,3,5

Answer:

V = 18.75

Method: First find the area of the pyramid on top, then find the area of the rectangular prism below.

V of the pyramid = 3.75 ft³

V of the rectangular prism = 15 ft³

3.75 + 15 = 18.75

Hope this helped!!  :)

First, find the volume of the pyramid on top:

(2.5 * 3 * 1.5) / 3 = 3.25

Then, find the volume of the rectangular prism:

2.5 * 3 * 2 = 15

Add the two volumes together:

3.25 + 15 = 18.25

To explain: you found the volume of each separate part and added it together.

Answer:

False

Step-by-step explanation:

Substitute 22 in for b

16 < b - 8

16 < 22 - 8

16 < 14

False, 14 is not greater than 16

The solution:

16 < b - 8

Add 8 to both sides

24 < b

Answer:

I don't know you're options but the answer could be 30.

Answer:

The answer is B

Step-by-step explanation:

the question states that they are similar, so B is automatically an option. It's 8 times because the radius and height are being doubled. Logically there are more factors to be A and E.

B. The two cans are similar figures, and the volume of the new can is 8 times the volume of the old can.

Answer:

41.25$

Step-by-step explanation:

Answer:

41.25

Step-by-step explanation:

55/4=13.75

So 13.75 is 25% of 55

So then you would do 55-13.75

Because that is 25% off

The final answer would be $41.25 for the sale price.

Answer:

Tyler ran 2030 meters. Jennifer ran 2386. Together they ran 4416 meters.

Step-by-step explanation:

Turn the km to m then add them together to get Tyler's distance. From Tyler's distance add what Jennifer ran more of to Tyler's to get Jennifer's distance. Then add together what they ran to get the total amount of meters they ran.

Answer:586

Step-by-step explanation:

Answer:

  C.  all real numbers except 3/4

Step-by-step explanation:

f(x) and g(x) are both defined for all real numbers. However, the ratio f/g will be undefined where g(x) = 0. That occurs when ...

  4x -3 = 0

  4x = 3 . . . . . add 3

  x = 3/4 . . . . . divide by 4

The value of x = 3/4 makes f/g undefined, so must be excluded from the domain.