You have $1000 to invest in two different accounts. To save the money you need for college, you need to average 5.7 percent interest. If the two accounts pay 4 percent and 6 percent interest, how much should you invest in each account?
$550 in 4%, $450 in 6%
$300 in 4%, $700 in 6%
$700 in 4%, $300 in 6%
$150 in 4%, $850 in 6%
Answers
Answer:
D
Step-by-step explanation:
that is the solution above
Related Questions
If you have 3/8 of one pie, what does the denominator tells you ?
Answers
Step-by-step explanation:
There was originally 8 pieces of pie.
Answer:
if you have 3/8 of one pie, the denominator tells you that the pie was divided into 8 piece.
For each of the following, assume that the two samples are obtained from populations with the same mean, and calculate how much difference should be expected, on average, between the two sample means. Each sample has n =4 scores with s^2 = 68 for the first sample and s^2 = 76 for the second. (Note: Because the two samples are the same size, the pooled variance is equal to the average of the two sample variances).
a) 4.24.
b) 0.24.
c) 8.48.
d) 6.00.
Next, each sample has n=16 scores with s^2 = 68 for the first sample and s^2 = 76 for the second.
a) 0.12.
b) 2.12.
c) 4.24.
d) 3.00.
Answers
Answer:
d)6.00
d)3.00
Step-by-step explanation:
We are given that
n=4 scores
[tex]S^2_1=68[/tex]
[tex]S^2_2=76[/tex]
We have to find the difference should be expected, on average, between the two sample means.
[tex]S_{M_1-M_2}=\sqrt{\frac{S^2_1}{n_1}+\frac{S^2_2}{n_2}}[/tex]
[tex]n_1=n_2=4[/tex]
Using the formula
[tex]S_{M_1-M_2}=\sqrt{\frac{68}{4}+\frac{76}{4}}[/tex]
[tex]S_{M_1-M_2}=\sqrt{\frac{68+76}{4}}[/tex]
[tex]S_{M_1-M_2}=\sqrt{36}=6[/tex]
Option d is correct.
Now, replace n by 16
[tex]n_1=n_2=16[/tex]
[tex]S_{M_1-M_2}=\sqrt{\frac{68}{16}+\frac{76}{16}}[/tex]
[tex]S_{M_1-M_2}=\sqrt{\frac{68+76}{16}}[/tex]
[tex]S_{M_1-M_2}=\sqrt{9}=3[/tex]
Option d is correct.
Write the range of the function using interval notation.
Answers
Given:
The graph of a function.
To find:
The range of the given function using interval notation.
Solution:
Range: The set of y-values or output values are known as range.
From the given graph, it is clear that the function is defined for [tex]0<x<4[/tex] and the values of the functions lie between -2 and 2, where -2 is excluded and 2 is included.
Range [tex]=\{y|-2<y\leq 2\}[/tex]
The interval notation is:
Range [tex]=(-2,2][/tex]
Therefore, the range of the given function is (-2,2].
Which of the following is not true regarding the flow of information from the adjusted trial balance on the end-of-period spreadsheet?
Answers
The correct statement about the flow of information from the adjusted trial balance on the end-of-period spreadsheet is A. The revenue and expense account balances flow into the income statement.
What is an Adjusted Trial Balance?This refers to the general ledger balance after some changes have been done an account balance such as accrued expenses, depreciation, etc.
Therefore, we can see that from the complete information, the statement that is false about the adjusted trial balance on the end-of-period spreadsheet is option A because the revenue and expense account balances does not flow into the income statement.
The other options from the complete text are:
a. The revenue and expense account balances flow into the income statement.b. The asset and liability account balances flow into the retained earnings statement.c. The revenue and expense account balances flow into the retained earnings statement.d. The retained earnings and dividends account balances flow into the balance sheet.
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A screw manufacturer makes specialized tiny screws that are 15mm long. The manufacturing process does not make every screw exactly 15mm long. The lengths of the screws are normally distributed with mean 15mm and standard deviation 0.04mm. To test for quality control, 36 screws are to be measured. What is the probability that a sample mean is less than 14.99mm?
Answers
Answer:
The probability that a sample mean is less than 14.99mm=0.066808
Step-by-step explanation:
We are given that
Mean,[tex]\mu=15 mm[/tex]
Standard deviation,[tex]\sigma=0.04 mm[/tex]
n=36
We have to find the probability that a sample mean is less than 14.99mm.
We know that
[tex]P(\bar{x}<a)=P(Z<\frac{\bar{x}-a}{\frac{\sigma}{\sqrt{n}}})[/tex]
Using the formula
[tex]P(\bar{x}<14.99)=P(Z<\frac{14.99-15}{\frac{0.04}{\sqrt{36}}})[/tex]
[tex]P(\bar{x}<14.99)=P(Z<-1.5)[/tex]
=[tex]1-P(Z\geq -1.5)[/tex]
[tex]=1-0.93319[/tex]
=0.066808
Hence, the probability that a sample mean is less than 14.99mm=0.066808
What conclusion can be determined from the dot plot below?
A dot plot showing five dots above 9, six dots above 10, three dots above 11, and one dot above 12.
The number of observations is 10.
The median of the data set is 10.
The mean of the data set is 15.
The range of the data set is 12.
Answers
A die is rolled 5 times and a 5 or 6 is considered a success. Find the peobability of no success
Answers
Answer:
0.1317 = 13.17% probability of no successes.
Step-by-step explanation:
For each toss, there are only two possible outcomes. Either there is a success, or there is not. The probability of a success on a toss is independent of any other toss, which means that the binomial probability distribution is used 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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A die is rolled 5 times.
This means that [tex]n = 5[/tex]
5 or 6 is considered a success.
2 out of 6 sides are successes, so:
[tex]p = \frac{2}{6} = 0.3333[/tex]
Find the probability of no success:
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.3333)^{0}.(0.6667)^{5} = 0.1317[/tex]
0.1317 = 13.17% probability of no successes.
The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees. If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample
Answers
Answer:
19 beers must be sampled.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees.
This means that [tex]\sigma = 0.26[/tex]
If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample?
This is n for which M = 0.1. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.1 = 1.645\frac{0.26}{\sqrt{n}}[/tex]
[tex]0.1\sqrt{n} = 1.645*0.26[/tex]
[tex]\sqrt{n} = \frac{1.645*0.26}{0.1}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645*0.26}{0.1})^2[/tex]
[tex]n = 18.3[/tex]
Rounding up:
19 beers must be sampled.
A plane flying horizontally at an altitude of 2 miles and a speed of 410 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 5 miles away from the station.
Answers
Answer:
[tex]82\sqrt{21}\text{ or approximately 375.77 miles per hour}[/tex]
Step-by-step explanation:
Please refer to the diagram below. R is the radar station and x is the distance from the station to the plane.
We are given that the plane is flying horizontally at an altitude of two miles and at a speed of 410 mph. And we want to find the rate at which the distance from the plane to the station is increasing when it is five miles away from the station.
In other words, given da/dt = 410 and x = 5, find dx/dt.
From the Pythagorean Theorem:
[tex]a^2+4=x^2[/tex]
Implicitly differentiate both sides with respect to time t. Both a and x are functions of t. Hence:
[tex]\displaystyle 2a\frac{da}{dt}=2x\frac{dx}{dt}[/tex]
Simplify:
[tex]\displaystyle a\frac{da}{dt}=x\frac{dx}{dt}[/tex]
Find a when x = 5:
[tex]a=\sqrt{5^2-2^2}=\sqrt{21}[/tex]
Therefore, dx/dt when da/dt = 410, x = 5, and a = √(21) is:
[tex]\displaystyle \frac{dx}{dt}=\frac{(\sqrt{21})(410)}{5}=82\sqrt{21}\approx 375.77\text{ mph}[/tex]
The rate at which is distance from the plane to the radar station is increasing at a rate of approximately 375.77 miles per hour.
Carin opened a money market account with a deposit of $3,000. This account earns 2% simple interest annually. How many years will it take for her $3,000 deposit to earn $430 in interest, assuming she does not withdraw any of the money?
Answers
Answer:
The correct answer is - 7.166 years
Step-by-step explanation:
Given:
principle amount: 3000
rate of interest: 2%
time?
Interent to get: 430
Formula:
I = P*t*r/100
here p = principle
I = interest
r = rate of intrest and t = time
Solution putting value and deriving Time as formula:
(3000*2*t)/100 = 430
t = 43000/3000*2
= 7.166 years.
Find the area of the geometric figure.
3 yd
3 yd
Traperoid
7 yd
Answers
Step-by-step explanation:
The question isn't clear, so I'll just give you a formula to find the area of trapezoid,
(a+b)*h/2, where a = base side, b = top side, h = height.
So, let's say two sides are 3 yd and 7 yd, and height is 3 yd, so the area becomes,
(3+7)*3/2
= 10*3/2
= 30/2
= 15 yd²
Answered by GAUTHMATH
Estimate 620 / 17 by first rounding each number so that it has only 1 nonzero digit.
no links plz
Answers
Step-by-step explanation:
620 / 17 =36.47058.. ≈ 36.5
PLEASE HELP!!! I have been adding and multiplying many different ways however my answer are wrong. How do I go about solving the perimeter then?
Answers
Answer:
66 m
Step-by-step explanation:
First, lets add up the numbers you know. It should be:
16, 8, 17, and 7.
Add them all up, and you will get:
48.
For the last two sides, subtract 7 from 16 to get 9.
For the last slide, subtract 8 from 17 to get 9.
Add them all up, and get 66.
Which represents can be used to determine the slope of the linear function graphed below
Answers
Lauren flips a coin, spins the spinner, and rolls a standard number cube. Find the probability that the coin will
show heads, the spinner will land on green, and the cube will show an even number.
Answers
Lauren will get 2/25 because the coin only lands on heads or tail
g Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Evaluate logarithmic expressions if possible.
Answers
Answer:
[tex]4\log_bx - \log_by = \log(\frac{x^4}{y})[/tex]
Step-by-step explanation:
Given
[tex]4\log_bx - \log_by[/tex]
Required
Express as a single expression
Using power rule of logarithm, we have:
[tex]n\log m = \log m^n[/tex]
So, we have:
[tex]4\log_bx - \log_by = \log_bx^4 - \log_by[/tex]
Apply quotient rule of logarithm
[tex]4\log_bx - \log_by = \log(\frac{x^4}{y})[/tex]
The following is a list of costs that were incurred in producing book:
a. Insurance on the factory building and equipment
b. Salary of the vice president of finance
c. Hourly wages of printing press operators during production
d. Electricity used to run the presses during the printing of the Book.
e. Sales commissions paid to book representatives for each book sold
f. Paper on which the text is printed
g. Book covers used to bind the pages
h. Straight-line depreciation on an office building
i. Salaries of staff used to develop artwork for the text
j. Glue used to bind pages to cover
Instructions: With respect to the manufacture and sale of this text, classify each cost as either a product cost or a
period cost. Indicate whether each product cost is a direct materials cost, a direct labor cost, or a factory overhead
cost. Indicate whether each period cost is a selling expense or an administrative expense.
Answers
Find the distance between the two points in simplest radical form. (-6,1) and (−8,−4)
Answers
Answer: 5
Step-by-step explanation: I think it is 5
30 students in grade 8 finished their summer packet before August 15.
This was 12% of all the students. How many students are in grade 8?
There are 1,200 people at the beach. If 88% of them went in the water,
how many people DID NOT go in the water?
A $800 T.V. is on sale for 15% off. What is the cost of the T.V.?
You go out to dinner and the bill is $45.12. You want to leave
an 18% tip. How much money should you leave?
Answers
Answer:
1)250 2) 144 3)
Step-by-step explanation:
1) 12/100 = 30/x 2) 1200*0.88
12x=3000 1200-1056
x=250 144
3)800*0.15 4) 45.12*0.18
800-120 45.12+8.12
680 about 53.24
A professor is interested in whether or not college students have a preference (indicated by a satisfaction score) for reading a textbook that has a layout of one column or layout of two columns. In the above experiment, what is the dependent variable
Answers
Answer:
Satisfaction score
Step-by-step explanation:
The dependent variable may be described as the variable which is being measured in a research experiment. In the scenario described above, the dependent variable is the satisfaction score which is used to measure preference for a one or two column textbook. The dependent variable can also seen as the variable which we would like to predict, also called the predicted variable . The predicted variable here is the satisfaction score.
Find the quotient of the following
Answers
Answer:
you simply have to do ide the coefficients and subtract the power
-8(9r - 1) - 9(-8r+2)
Simplest form
Answers
Answer:
-10
Step-by-step explanation:
Step-by-step explanation:
-8(9r-1)-9(-8r+2)-72r+8-72r-18-72r-72r+8-18-144r-10-(144r+10)hope it helps
stay safe healthy and happy...4. Cindy purchased a pair of boots which had a sticker price of $85. Cindy paid $5.95 in sales tax. What was the tax rate on Cindy's purchase?
Answers
To get the tax rate just divide 5.95 by 85 and you get 0.07. The. Convert that to a percentage
Find the factors of function f, and use them to complete this statement. f(x)=2x^(4)-x^(3)-18x^(2)+9x
From left to right, function f has zeros at
Answers
Hello,
[tex]f(x)=2x^4-x^3-18x+9x\\\\=x(2x^3-x^2-18x+9)\\\\=x(x^2(2x-1)-9(2x-1))\\\\=x(2x-1)(x^2-9)\\=x(2x-1)(x-3)(x+3)\\[/tex]
Zeros are : 0; 1/2; -3; 3.
The zeros of the function are -3, 0, 1/2 and 3.
The given function is [tex]f(x)=2x^{4} -x^{3} -18x^{2} +9x[/tex].
What are the zeros of a function?Zeros of a function are the points where the graph of the function meets the X-axis i.e., at the solutions of f(x) = 0.
Now, factorise the given function, that is f(x)=x(2x³-x²-18x+9).
=x[x²(2x-1)-9x(2x-1)]
=x(2x-1)(x²-9)
=x(2x-1)(x+3)(x-3)
= -3, 0, 1/2, 3
Therefore, the zeros of the function are -3, 0, 1/2 and 3.
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A shipment of 50 precision parts including 4 that are defective is sent to an assembly plant. The quality control division selects 10 at random for testing and rejects the entire shipment if 1 or more are found defective. What is the probability this shipment passes inspection?
Answers
Answer:
0.3968 = 39.68% probability this shipment passes inspection.
Step-by-step explanation:
The parts are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
50 parts means that [tex]N = 50[/tex]
4 defective means that [tex]k = 4[/tex]
10 are chosen, which means that [tex]n = 10[/tex]
What is the probability this shipment passes inspection?
Probability that none is defective, so:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,50,10,4) = \frac{C_{4,0}*C_{46,10}}{C_{50,10}} = 0.3968[/tex]
0.3968 = 39.68% probability this shipment passes inspection.
Okay, let's calculate the year end adjustment for overhead. Based on the data below, determine the amount of the year end adjustment to cost of goods sold due to over or under allocated manufacturing overhead during the year
Answers
Answer:
the adjustment made to the cost of goods sold is -$2,014
Step-by-step explanation:
The computation of the adjustment made to the cost of goods sold is given below:
Total actual overhead expenses $110,822
Less: Total overheads allocated -$112,836
Adjustment made to the cost of goods sold -$2,014
Hence, the adjustment made to the cost of goods sold is -$2,014
The same should be considered
In orders an ice cream cone filled to the top with ice cream, with 1 perfectly round scoop of ice cream on top. The cone and the scoop of ice cream both have a radius of 1.8 inches, and the height of the cone is 4.5 inches. What is the total volume of ice cream ian receives?
A. 24.4
B. 39.7
C. 3.4
D. 15.3
Answers
Answer:
39.7
Step-by-step explanation:
how do you write in numerals
Answers
Answer:
Basic numbersNumbers up to nine should always be written in words, anything higher than nine can be written in numerals. Alternatively, some guides suggest that if you can write the number in two words or fewer then use words rather than number.hope it's helpful for u !! stay safe ...Step-by-step explanation:
1 : a conventional symbol that represents a number. 2 numerals plural : numbers that designate by year a school or college class and that are awarded for distinction in an extracurricular activity. Other Words from numeral Synonyms Example Sentences Learn More About numeral.A numeral is a symbol or name that stands for a number. Examples: 3, 49 and twelve are all numerals. So the number is an idea, the numeral is how we write it.hope it helps.stay safe healthy and happy...Christian and Tanae both leave Disneyland at the same time. Christian travels north at 65 mph. Tanae travels south at 55 mph. How long will it take them to be 540 miles apart? Which of the following equations would you use to solve this word problem?
65t + 55(t − 1) = 540.
65t + 55t = 540.
65t + 55(t + 1) = 540.
None of these choices are correct.
Answers
Answer:
Step-by-step explanation:
B looks like it would work.
You add speeds * time when you are travelling in opposite directions.
I don't know why you would add or subtract 1 as in A and C
120 * t = 540
t = 540/120
t = 4.5 hours.
So after 4.5 hours they are 540 miles apart.
Answer:
b
Step-by-step explanation:
The average height of a current NBA player is 79 inches with a standard deviation of 3.4 inches. A random sample of 35 current NBA players is taken. What is the probability that the mean height of the 35 NBA players will be more than 80 inches?
Answers
Answer:
0.0409 = 4.09% probability that the mean height of the 35 NBA players will be more than 80 inches.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The average height of a current NBA player is 79 inches with a standard deviation of 3.4 inches.
This means that [tex]\mu = 79, \sigma = 3.4[/tex]
A random sample of 35 current NBA players is taken.
This means that [tex]n = 35, s = \frac{3.4}{\sqrt{35}}[/tex]
What is the probability that the mean height of the 35 NBA players will be more than 80 inches?
This is 1 subtracted by the p-value of Z when X = 80. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{80 - 79}{\frac{3.4}{\sqrt{35}}}[/tex]
[tex]Z = 1.74[/tex]
[tex]Z = 1.74[/tex] has a p-value of 0.9591
1 - 0.9591 = 0.0409
0.0409 = 4.09% probability that the mean height of the 35 NBA players will be more than 80 inches.
