How long will it take for a $1000 investment to grow to $1500 at an annual rate of 13%, compounded semiannually? Assume that no withdrawals are made. Do
not round any intermediate computations, and round your answer to the nearest hundredth.

Answer:

4.01% probability that the battery will break down during the warranty period

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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 pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 45, \sigma = 12\)

a. What is the probability that the battery will break down during the warranty period

Warranty of 2 years = 24 months. So this is the pvalue of Z when X = 24.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{24 - 45}{12}\)

\(Z = -1.75\)

\(Z = -1.75\) has a pvalue of 0.0401

4.01% probability that the battery will break down during the warranty period

Answer:11

Step-by-step explanation:

Answer:

first answer - you plot 'b' [on the y-axis] first, then use the slope m = c/d to go d units right and then c units up (positive 'c') or down (negative 'c')

Step-by-step explanation:

plot 'b' [on the y-axis] first, then use the slope m = c/d to go d units right and c units up (positive 'a') or down (negative 'a')

It has to be the first answer (in spite of the typo here), because all the others are wrong

The percentage error in the density of metal will be 3.4%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the density of the metal in the handbook is 4.018 g/mL and the measured value of the density is 4.16 g/mL.

The percentage error will be calculated as:-

Percentage = [ ( 4.16 - 4.018 ) / 4.16 ] x 100

Percentage = 0.034x 100

Percentage = 3.4%

Hence, the percentage error will be 3.4% for the densities.

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Answer: p=-1

Step-by-step explanation:

To find the value of p, we can manipulate the right side so that it looks like the left.

We know that \(\sqrt{4}=2\). Therefore, it can be written as 2¹.

\(\frac{1}{4}\) is the same as \(\frac{1}{2^2 }\) because 2²=4. To make it not a fraction, we can flip it and change the exponent. \(\frac{1}{4}=2^-^2\)

Now, we can put them together.

\(2^p=2^1*2^-^2\)         [multiply]

\(2^p=2^-^1\)

Now, we know that p=-1.

Answer:

8700kg

Step-by-step explanation:

b = mass of bricks

l = mass of lorry

b+l = total mass = 11600kg

b = 3l  ==>  l = b/3

substitute: b + b/3 = 11600

multiply every term by 3 to get rid of denominator: 3b + b = 34800

simplify and solve:  4b = 34800  ==>  b = 8700

check:  l = 8700/3 = 2900

2900 + 8700 = 11600?  YES

The algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2).  Option B.

To translate a figure 3 units to the left and 2 units up, we need to adjust the coordinates of the figure accordingly. The algebraic rule that represents this translation can be determined by examining the changes in the x and y coordinates.

When we move a figure to the left, we subtract a certain value from the x coordinates. In this case, we want to move the figure 3 units to the left, so we subtract 3 from the x coordinates.

Similarly, when we move a figure up, we add a certain value to the y coordinates. In this case, we want to move the figure 2 units up, so we add 2 to the y coordinates.

Taking these changes into account, we can conclude that the algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). The x coordinates are shifted by subtracting 3, and the y coordinates are shifted by adding 2. SO Option B is correct.

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Answer:

The expected number of hunters who hit the duck they aim at is 3.6

Step-by-step explanation:

Given;

number of hunters, n = 6

the probability of killing a duck, p = 0.6

The expected number of hunters who hit the duck they aim at?

In binomial distribution, the expected value is equal to the product of the number of trials and the probability of success.

The expected number of hunters who hit the duck they aim at is calculated as follows;

E = np

E = 0.6 x 6

E = 3.6

Therefore, the expected number of hunters who hit the duck they aim at is 3.6

Answer:

86m^2

Step-by-step explanation:

To add these two vectors, we really want to add their comparing parts [-6-22] + [-3 2 1] = [-28] + [-3 2 1] = [-31 2 1]. Thus, option B is correct.

To add two irregular vectors, we essentially break each into parts. We then add the x-parts together. Then we add the y-parts together. At long last, we utilize the Pythagorean hypothesis to track down the resultant and the trig capabilities to track down the course.

A vector amount has two qualities, a size and a heading. While looking at two vector amounts of a similar kind, you need to analyse both the greatness and the course.

Therefore, \(-603]\) We really want to combine the comparative sections of these two vectors, which are \([-6-22] + [-3 2 1] = [-28] + [-3 2 1] = [-31 2 1]\)  .

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Answer:

exact form : 2√3

decimal form : 3.46410161… or 3.46

hope this helps you!

Answer:

The value of the function is \(\sqrt{12}\). Rounded to the nearest hundredth, the answer is 3.46

Step-by-step explanation:

We are given the value of x, so we simply have to evaluate the function:

\(f(x)=\sqrt{x+4}\)

Substitute 8

\(f(8)=\sqrt{8+4}\)

Add in the radical

\(\sqrt{12}\)

The value of the function is sqrt(12).

Rounded to the nearest hundredth: \(3.46\)

Answer: 20 Meters

Step-by-step explanation:

First strand: 2x (twice the length of the shortest strand)

Second strand: 3x (three times the length of the shortest strand)

Third strand: x (the length of the shortest strand)

All the strands: 2x + 3x + x

All the strands: 6x

6x = 120 meters

(DIVIDE BOTH 6 AND 120 BY 6)

x=20

THE LENGTH OF THE SHORTEST STRAND IS 20 METERS

Answer:

Step-by-step explanation:

372 Millimeters

Answer:

2,300 millimeters

Step-by-step explanation:

when you convert 30 centimeters it’s 300 millimeters. When you convert 2 meters it’s 2,000 millimeters so…. That is the correct answer plus I just did the quiz and got it correct with that answer.

The calculated value of x in the circle is 15

From the question, we have the following parameters that can be used in our computation:

The circle and the tangent lines

The sum of angles on the circumference of a circle is 360 degrees

So, the value of x can be calculated using

17x + (180 - 75) = 360

When evaluated, we have

17x = 255

Divide both sides by 17

x = 15

Hence, the value of x is 15

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Answer:

134,784 people

Step-by-step explanation:

Hello!

Let's first find the number of people it can carry on 1 trip. We can do this by multiplying the number of people per coach, by the number of coaches.

The train carries 864 people per trip. We can find the number of people in 156 trips by multiplying 864 by 156.

The train, in full capacity, will carry 134,784 people in 156 trips.

9514 1404 393

Answer:

  1

Step-by-step explanation:

The slope is given by the formula ...

  slope = (y2 -y1)/(x2 -x1)

  slope = (5 -4)/(3 -2) = 1/1 = 1

The slope of MN is 1.

__

Dilation does not change the slope.

Answer:

A

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Answer:

12, 11, 14

Step-by-step explanation:

if we describe x as the second side, we can describe the first side as x + 1 and the third side as x + 3. Since the perimeter is 37, we can sum these polynomials and set them equal to 37, and solve for x.

You can turn a whole number into a division by multiplying with a fraction.

Given:

Turning whole number into a division:

The whole numbers are defined as positive integers including zero. The whole number does not contain any decimal or fractional part. It means that it represents the entire thing without pieces.

The whole number can be converted into division by multiplying it with a fraction value.

Example:

whole number = 5

Turning into division:

= 5 * 1 / 6

= 5/6

whole number = 4

= 4 * 1 / 5

= 4/5

whole number = 15

= 15 * 1/6

= 15/6

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Answer:

Yes

Step-by-step explanation:

The angles are identical, so they are congruent.

Hope I helped! Plz leave a comment and a rating!

The desalination plant can produce \(9.84*10^6\) gallons of water in four days in scientific notation.

We must divide the daily production rate by the number of days in order to get the total volume of water that a desalination plant can generate in four days:

4. days at a rate of \(2.46*10^6\) gallons equals \(9.84*10^6\) gallons.

Hence, in four days, the desalination plant can produce \(9.84 * 10^6\)gallons of water.

Large or small numbers can be conveniently represented using scientific notation, especially when working with measurements in science and engineering. A number is written in scientific notation as a coefficient multiplied by 10 and raised to a power of some exponent. For example, \(2.46*10^6\) denotes 2,460,000, which is 2.46 multiplied by 10 to the power of 6.

The solution in this case is \(9.84*10^6\), or 9,840,000, which is 9.84 multiplied by 10 to the power of 6. Large numbers can be written and compared more easily using this format, and scientific notation rules can be used to conduct computations with them.

In conclusion, the desalination plant has a four-day capacity of \(9.84 * 10^6\) gallons of water production.

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Answer:

We have a binomial probability distribution, in which:

P(X = 0) = 0.064

P(X = 1) = 0.288

P(X = 2) = 0.432

P(X = 3) = 0.216

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it is for domestic travel, or it is for international travel. Flights are independent of each other. So 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.

Let x be the number of requests among the next three requests received that are for domestic flights.

3 flights, and 60% are for domestic travel. This means that \(n = 3, p = 0.6\). The probabilities are given by:

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

\(P(X = 0) = C_{3,0}.(0.6)^{0}.(0.4)^{3} = 0.064\)

\(P(X = 1) = C_{3,1}.(0.6)^{1}.(0.4)^{2} = 0.288\)

\(P(X = 2) = C_{3,2}.(0.6)^{2}.(0.4)^{1} = 0.432\)

\(P(X = 3) = C_{3,3}.(0.6)^{3}.(0.4)^{0} = 0.216\)

Answer: 410

Step-by-step explanation:

Answer:

82

Step-by-step explanation:

4.1*(10*2) is equal to 82 because 10*2 as we all (should) know is 20, and 4.1*20 is 82! I hope this is the answer you wanted!

Answer:

$33

Step-by-step explanation:

Let the amount of money Corey has be $x.

Amount of money Bryce have= $(x +16)

Total amount= $50

$x +$(x +16)= $50

2x +16= 50

2x= 50 -16

2x= 34

Divide both sides by 2:

x= 34 ÷2

x= 17

Amount of money Bryce have

= $(17 +16)

= $33

Answer:

The exponential form of \(\log_{4} 4 = 1\) is \(4 = 4^{1}\).

Step-by-step explanation:

After some research in the web, we find that correct statement is:

Rewrite \(\log_{4} 4 = 1\) in exponential form.

We obtain its exponential form by using the definition of logarithm:

\(4^{\log_{4} 4} = 4^{1}\)

\(4 = 4^{1}\)

Answer: The correct answer is (-1, 2).

Step-by-step explanation: Find how many units the original F point is away from the center. It is 2 units away in terms of x, and 4 units away in terms of y. The x value has to be negative since the initial x point was already negative. -2/2 = -1. Hence, the x value is -1.  4/2 = 2. Hence, the y value is 2.

\(\\ \sf\longmapsto 2x^2=10x\)

\(\\ \sf\longmapsto x^2=\dfrac{10x}{2}\)

\(\\ \sf\longmapsto x^2=5x\)

\(\\ \sf\longmapsto x=5\)