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%

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.

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]

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.

Answer:

-10

Step-by-step explanation:

Step-by-step explanation:

hope it helps

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

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].

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.

Answer: 5

Step-by-step explanation: I think it is 5

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.

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:

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.

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.

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.

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.

Lauren will get 2/25 because the coin only lands on heads or tail

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.

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

Answer:

39.7

Step-by-step explanation:

Answer:

you simply have to do ide the coefficients and subtract the power

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.

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

Step-by-step explanation:

620 / 17 =36.47058.. ≈ 36.5

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.

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:

Read more about adjusted trial balance here:

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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

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].

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.

To learn more about the zeros of the function visit:

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Answer:

Step-by-step explanation: