Answer:
5.8
Step-by-step explanation:
The interest rate, to the nearest tenth of a percent, will be 0.05828.
How do you determine the amount of compound interest?If the principal amount is P, the interest rate is R percent per unit time, and the compound interest is left for T units of time, the interest amount gained is:
[tex]\rm CI = P\left(1 +\dfrac{R}{100}\right)^T - P[/tex]
The total is:
[tex]\rm A = CI + PA = P(1 +\dfrac{R}{ 100})T[/tex]
The amount is found as;
[tex]\rm A = P(1+\frac{r}{n})^{nt}\\\\ 540=320 (1+\frac{r}{12} )^{12\times 9}\\\\ (1+\frac{r}{12})^{108}=\frac{540}{320}\\\\ 1+\frac{r}{12}=(\frac{540}{320})^{\frac{14}{108}[/tex]
[tex]\rm 1+ \frac{r}{12}=1.00486\\\\ \frac{r}{12}=0.00486\\\\ r=12 \times 0.0486 \\\\ r=0.05828[/tex]
Hence, the interest rate, to the nearest tenth of a percent, will be 0.05828.
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A random sample of 80 college students showed that 44 had driven a car during the day before the survey was conducted. Suppose that we are interested in forming a 80 percent confidence interval for the proportion of all college students who drove a car the day before the survey was conducted.
Where appropriate, express your answer as a proportion (not a percentage). Round answers to three decimal places.
Answer:
The 80% confidence interval for the proportion of all college students who drove a car the day before the survey was conducted is (0.479, 0.621).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
A random sample of 80 college students showed that 44 had driven a car during the day before the survey was conducted.
This means that [tex]n = 80, \pi = \frac{44}{80} = 0.55[/tex]
80% confidence level
So [tex]\alpha = 0.2[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 - 1.28\sqrt{\frac{0.55*0.45}{80}} = 0.479[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 + 1.28\sqrt{\frac{0.55*0.45}{80}} = 0.621[/tex]
The 80% confidence interval for the proportion of all college students who drove a car the day before the survey was conducted is (0.479, 0.621).
Is the following number rational or irrational?
Pi/5
Choose 1 answer:
Rational
B
Irrational
3/4+1/2= 2. 5/6+1/2= 3. 3/6+1/2= 4.1/6+4/8= 5.7/8+1/4= 6.3/8+1/2=
Answer:
1.) [tex]\frac{5}{4\\}[/tex]
2.) [tex]\frac{4}{3}[/tex]
3.) 1
4.) [tex]\frac{2}{3}[/tex]
5.) [tex]\frac{9}{8}[/tex]
6.) [tex]\frac{7}{8}[/tex]
Step-by-step explanation:
The 2 steps for all of these is to get common denominators and then add and simplify.
1.) 3/4 + 1/2 (common denominator) 3/4 + 2/4 = 5/4
2.) 5/6 + 1/2 (common denominator) 5/6 + 3/6 = 4/3
3.) 3/6 + 1/2 (common denominator) 3/6 + 3/6 = 6/6 (simplify) = 1
4.) 1/6 + 4/8 (common denominator) 8/48 + 24/48 = 32/48 (simplify) = 2/3
5.) 7/8 + 1/4 (common denominator) 7/8 + 2/8 = 9/8
6.) 3/8 + 1/2 (common denominator) 3/8 + 4/8 = 7/8
A 2-column table with 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 3, negative 2, negative 3, 0, 7.
What is the rate of change for the interval between 0 and 2 for the quadratic equation as f(x) = 2x2 + x – 3 represented in the table?
one-fifth
4
5
10
The rate of change for the interval between 0 and 2 for the quadratic equation f(x) = 2x^2 + x - 3, represented in the table, is 6.
To find the rate of change for the interval between 0 and 2 for the quadratic equation f(x) = 2x^2 + x - 3, we can use the values provided in the table.
First, let's calculate the values of f(x) for x = 0 and x = 2:
For x = 0: f(0) = 2(0)^2 + 0 - 3 = -3
For x = 2: f(2) = 2(2)^2 + 2 - 3 = 9
Now, we can find the rate of change by calculating the difference in the values of f(x) divided by the difference in x for the interval [0, 2]:
Rate of change = (f(2) - f(0)) / (2 - 0)
Substituting the values we found:
Rate of change = (9 - (-3)) / (2 - 0)
= (9 + 3) / 2
= 12 / 2
= 6
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You pick a card at random.
6 7 8
What is P(odd)?
Write your answer as a fraction or whole number.
Answer:
1/3
Step-by-step explanation:
1/3
The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. (Assume both planets are aligned with the sun and are on the same side of the sun.)
Answer:
t = 42857.14 h
Step-by-step explanation:
Given that,
The speed of space shuttle, v = 28000 km/h
We know that, the distance between the Saturn and the Earth is 1,200,000,000 km.
Let t be the time.
As we know, speed = distance/time
So,
[tex]t=\dfrac{d}{v}\\\\t=\dfrac{1,200,000,000}{28000}\\\\t=42857.14\ h[/tex]
So, the required time is equal to 42857.14 hours.
What is the value of x in the equation 4(2x + 12) = 0? (1 point)
Question 18 options:
1)
−8
2)
−6
3)
6
4)
8
Answer:
4 (2x + 12) = 0
8x + 48 = 0
8x = - 48
x = -48/8
x = - 6 (option 2)
Service calls arriving at an electric company follow a Poisson distribution with an average arrival rate of 5656 per hour. Find the average and standard deviation of the number of service calls in a 1515-minute period. Round your answer to three decimal places, if necessary.
Answer:
The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval. The variance is the same as the mean.
Average rate of 56 calls per hour:
This means that [tex]\mu = 56n[/tex], in which n is the number of hours.
Find the average and standard deviation of the number of service calls in a 15-minute period.
15 minute is one fourth of a hour, which means that [tex]n = \frac{1}{4}[/tex]. So
[tex]\mu = 56n = \frac{56}{4} = 14[/tex]
The variance is also 14, which means that the standard deviation is [tex]\sqrt{14} = 3.74[/tex]
The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.
The family is hiking in the mountains at a rate of 6 miles every 3 hours
How long would it take the family to hike 7.5 miles?
(Hint: You will have a decimal or fraction in your final answer!)
Answer:
Time = 3 hours & 45 minutesStep-by-step explanation:
Distance = 6 miles
Time = 3 hours
Speed = Distance ÷ Time
Speed = 6 ÷ 3
Speed = 2 miles/hour
....................................................
Speed = 2 miles/hour
Distance = 7.5 miles
Time = Distance ÷ Speed
Time = 7.5 ÷ 2
Time = 3.75 hours
3.75 hours = 3 hours & 45 minutes
Answer:
Step-by-step explanation:
Time taken to travel 6 miles = 3 hours
Time taken to travel 1 mile = 3 ÷ 6 = [tex]\frac{3}{6}=\frac{1}{2} hour[/tex] = 30 minutes
Time taken to travel 7.5 miles = 30 * 7.5 = 225 minutes = 3.45 hours
Please solve this problem
I really need help!
Mercury is 3.6 x 10^6 miles from the sun. Pluto is 3.6 x 10^9 miles from the sun. how many times farther from the sun is pluto than mercury? Answer written in scientific notation.
Thank you!
Answer:
[tex]3.6 * 10^{3} \\\\[/tex]
Step-by-step explanation:
The length of a rectangle is 3 inches more than three times it's width. Write an equation relating the length, “, of the rectangle to its width, w.
Cyclone cleared leaves from the same number of yards each day for 5 days. Then on day 6, he cleared the leaves from 8 more yards. He cleared 133 yards in all.How many yards did Cyclone clear the first day?
Answer:
20.83 yard
Step-by-step explanation:
Calculate Cubic Yards
Calculate your area
Calculate your volume: Multiply area times the depth to get volume in cubic feet
Calculate your cubic yards: Divide cubic feet by 27 to convert to cubic yards and this is your answer
Where ft2 = square foot, ft3 = cubic foot, yd3 = cubic yard
Total yards = 5[x] + x + 8
Solve
133 = 6x + 8
6x = 125
x = 20.83 yard
Therefore, the Cyclone cleared 20.83 yards on the first day.
If one side of a regular decagon is 4 cm, how long is each of the other sides?
Answer:
4cm
Step-by-step explanation:
A decagon has 10 sides that are probably equal. one of the sides is 4cm.The remaining 9sides = 9×4 = 36cmeach sides are 4cm.Each of the other sides of the regular decagon is (√19/4) cm long, or approximately 1.861 cm to three decimal places.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
A regular decagon is a polygon with ten sides of equal length and ten angles of equal measure.
To find the length of each of the other sides, we can use the fact that a regular decagon can be divided into ten congruent isosceles triangles.
The isosceles triangle can be split into two right triangles by drawing an altitude from the vertex opposite the base to the midpoint of the base.
Let's call the length of one of the equal sides of the isosceles triangle "s", and let's call the length of the altitude "h".
Then we can use the Pythagorean theorem to find the length of the other side:
s² = h² + (s/2)²
We can solve for "h" in terms of "s" as follows:
h² = s² - (s/2)²
h² = (4s²)/4 - s²/4
h² = (15s²)/16
h = (s√15)/4
Since the altitude divides the isosceles triangle into two congruent right triangles, each with a hypotenuse of "s",
We can use the Pythagorean theorem again to find the length of each of the other sides of the regular decagon:
s² = h² + (s/2)²
s² = [(s√15)/4]² + (s/2)²
s² = (15s²)/16 + (s²)/4
s² = (15s² + 4s²)/16
s^2 = (19s²)/16
s = √(19/16) s
s = (√19/4) cm
Therefore,
Each of the other sides of the regular decagon is (√19/4) cm long, or approximately 1.861 cm to three decimal places.
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What does n equal?
EASY
Answer:
n=8/11
Step-by-step explanation:
Answer:
C) n=8/11
Step-by-step explanation:
3/4n=6/11
n=6/11÷3/4
invert and multiply
n=6/11x4/3
n=24/33
n=8/11
the total cost of. $220 meal with 25% tip.
Answer:
275
Step-by-step explanation:
Answer:
Total Cost = $275
Step-by-step explanation:
25% = 0.25
Multiply $220 by 0.25 to get 25% of $220.
0.25 × $220 = $55
Now add $220 and $55 to get the total cost.
$220 + $55 = $275
Please help I don’t understand
Answer:
6:5
Step-by-step explanation:
Step 1: we need to match the b portions of each ration, use a lcm calculator, we see that the least common factor of 1 and 2 is 2
Step 2: For our a:b ratio of 3:1 we need to multiply each portion of the ration by 2 divided by 1 is 2
2 times 3:2 times 1 = 6: 2 our new a b ratio
Step 3: for our bc ratio of 2: 5 we need to multiply each portion of the ratio by 2 divided by 2 equals 1
1 times 2: 1 times 5 = 2:5 our new b:c ratio
since the b portions of each ratio match, we just take a: c = 6:5
GOOD LUCK!
11 divided by 3 2/3 with step by step explination
Answer:
3
Step-by-step explanation:
11/1 divided by 11/3
keep change flip to get:
11/1 x 3/11
and multiply to get:
33/11
Simplify to get:
3/1 or 3
Answer:
3
Step-by-step explanation:
step one is to make the fraction into a unbalanced fraction
step two is to make it a proper fraction by switching the values (I am talking about 2 2/3s so you know)
Then remove the greatest common factor, so 11, and only three remains
Find the missing sides
Answer: x =1/2
y = [tex]\sqrt{3}[/tex]/2
Step-by-step explanation:
Factor by removing a common
1. 3a +9ab
Answer:
3a(1+3b)
Step-by-step explanation:
First step is to find the greatest common factor between these two terms, which is 3a. Next you'll need to divide the two terms by that factor, which would give you what would be in the parenthesis, placed the factor in front to signify the multiplication of those terms and voila, you got the fully factored form.
I need help with math
* Question Completion Status:
QUESTION 3
Find the measure of the unknown angle of the triangle.
18
122
find the difference between 3/4 and 5/10
Answer:
The answer would be 1/4. I explained below if you don't get how you get the answer. Good luck!
Step-by-step explanation:
1. Find the LCM of 4 and 10
4, 8, 12, 16, 20
10, 20
The LCM of 4 and 10 is 20.
2. Divide 4 and 10 by 20.
20 ÷ 4 = 5
20 ÷ 10 = 2
3. Multiply the numbers by the answer you got in step 2.
3 x 5 = 15
5 x 2 = 10
4. Put it together.(example:number you got in step 3/20)
15/20
10/20
5. Subtract
15/20 - 10/20 = 5/20
You get the answer of 5/20 or 1/4. I would write 1/4 though.
Find f. f ''(x) = −2 + 36x − 12x2, f(0) = 8, f '(0) = 18 f(x) =
Answer
its confusing
Step-by-step explanation:
An official for a national dog show studies the characteristics of one breed of dog, the Dandie Dinmont Terrier. Two common measurements are the height and weight of the dog, and the official would like to develop a model that would be helpful in predicting weight based on a given height. The official first makes a scatterplot that relates height and weight, then another that compares the logs of each measurement.
A graph titled Dandie Dinmont Terrier height versus weight has height (inches) on the x-axis, and weight (pounds) on the y-axis. The points curve up.
A graph titled Dandie Dinmont Terrier log height versus log weight has log (height) on the x-axis, and log (weight) on the y-axis. The points curve up.
Based on the graphs, which type of model is likely appropriate for predicting weight from height?
A linear model is appropriate because the graph of the transformed data is roughly linear.
A power model is appropriate because the scatterplot of height versus weight appears curved.
A power model could be appropriate because the scatterplot of log height versus log weight is roughly linear. The next step is to look at the residual plot.
An exponential model is appropriate because the scatterplot of log height versus log weight has a stronger linear relationship than the scatterplot of the non-transformed data.
Based on the graphs provided its is seen that, a power model could be appropriate because the scatter plot of log height versus log weight is roughly linear. Therefore, option C is the correct answer.
Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
Based on the graphs provided its is seen that, a power model could be appropriate because the scatter plot of log height versus log weight is roughly linear. The next step is to look at the residual plot.
Therefore, option C is the correct answer.
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Please Help! SCAMMERS WILL BE REPORTED. Use Gauss-Jordan elimination to solve the following linear system
-4x + 4y + 5z = 9
-2x + 2y + z = 3
-4x + 5y = 4
Answer:
This is possible and the answer is (-1,0,1)
Step-by-step explanation:
It’s difficult to write out matrices here.
I apologize!
you earn $9.15 per hour painting a fence. It takes 6.75 hours to paint the fence. did you make enough money. how much money do you have left.
Answer:
$61.76
Step-by-step explanation:
So I can't answer how much do you have left or did you make enough money, but I can calculate the money you made. Since it's $9.15 per hour and you worked 6.75, you simply multiply the numbers together. The money you made was $61.76.
Help please picture inserted
The measure of an angle is 47º. What is the measure of its complementary angle?
Answer:
137 degrees since it says 47
Step-by-step explanation:
The model represents the percentage of family households in the 2012 census. What percent of households were not considered families?
A:75%
B:65%
C:65%
D:35%
also it's not c I got it wrong