6. The genetic information of almost
every living thing is stored in a tiny
strand called DNA. Human DNA is
3.4 x 10-8 meter long.
a. Write the length in standard form.
b. How many significant
digits are there in the
measurement?
The la

Answer:

110687192.78951, 6488.47368421, 4214, 0.0464, 0.03626

SIMPLIFIED WAY OF SAYING IT:

Last One to First Box

3rd One to 2nd Box

1st one to 3rd box

2nd one to 4th box

4th one to 5th box

Step-by-step explanation:

(4.3*10^(6))*(9.8*10^(-4)) = 4,214

(2.9*10^7)*(1.6*10^-9) = 0.0464

(4.7*10^3)*(8.6*10^-7)/(3.8*10^-4)*(6.1*10^2) = 6488.47368421

(4.9*10^3)*(7.4*10^-6) = 0.03626

Last one = 110687192.78951

The distance covered is 5 1/2 miles.

The first step is to determine the speed at which Annie walked. Speed is total distance per time.

Speed = distance / time

1/2 ÷ 1/4

1/2 x 4 = 2 miles / hour

Distance covered = time x speed

= 2 x \(2\frac{3}{4}\)

2 x \(\frac{11}{4}\) = \(\frac{11}{2}\) = 5 \(\frac{1}{2}\) miles

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To calculate the area enclosed by the curve r(t)=⟨cos^2(t), cos(t)sin(t)⟩ using Green's Theorem, we can calculate the line integral of the vector field ⟨-y, x⟩ along the curve and divide it by 2.

Green's Theorem states that the line integral of a vector field ⟨P, Q⟩ along a closed curve C is equal to the double integral of the curl of the vector field over the region enclosed by C. In this case, the vector field is ⟨-y, x⟩, and the curve C is defined by r(t)=⟨cos^2(t), cos(t)sin(t)⟩.

We can first calculate the curl of the vector field, which is given by dQ/dx - dP/dy. Here, dQ/dx = 1 and dP/dy = 1. Therefore, the curl is 1 - 1 = 0.

Next, we evaluate the line integral of the vector field ⟨-y, x⟩ along the curve r(t). We parametrize the curve as x = cos^2(t) and y = cos(t)sin(t). The limits of integration for t depend on the range of t that encloses the region. Once we calculate the line integral, we divide it by 2 to find the area enclosed by the curve.

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Answer:

I guess the answer is 9.24

Answer:

52,488

Step-by-step explanation:

First 2187 multiplied by $1 equals $2187

Second 2187 times 3 equals 6561

Third 6561 times 7 equals 52,488

B and C are out because those numbers are too high. A is out for 2 reasons. 1) 5x5 is 25, not 5x3 and 2) a negative times a positive is negative.

So the answer is D

---

hope it helps

To simplify the expression (-5)^3, we need to evaluate the exponent, which means multiplying the base (-5) by itself three times. The correct option is B. -125.

(-5)^3 = (-5) * (-5) * (-5)

Multiplying the negative numbers gives:

(-5) * (-5) * (-5) = 25 * (-5) = -125

Therefore, the simplified expression is -125.

So, when we simplify the expression (-5)^3.The correct option is B. -125.

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Answer:

-4.5

Step-by-step explanation:

3 × 1.5 = 4.5

Negative times positive is negative.

-3 × 1.5 = -4.5

Therefore, √128 lies between 11 and 12 on a number line.

To determine the two numbers between which √128 lies on a number line, we can calculate the square roots of consecutive perfect squares that surround 128.

By calculating the square roots, we can find the two nearest whole numbers that √128 lies between.

Calculating the square roots of perfect squares near 128:

√121 = 11

√144 = 12

Since 128 is greater than 121 and less than 144, √128 lies between √121 and √144 on the number line.

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Answer:

8

Step-by-step explanation:

TRUE. As one performs multiple separate hypothesis tests, the risk of committing a Type I error (rejecting a true null hypothesis) accumulates.

This overall risk is referred to as the experiment-wise alpha level or family-wise error rate (FWER). It represents the probability of making at least one Type I error among all the conducted tests.

When multiple hypothesis tests are performed simultaneously or sequentially, the individual alpha levels (typically set at 0.05) for each test may no longer be appropriate. This is because if we conduct, for example, 20 separate tests with an alpha level of 0.05 for each test, the cumulative chance of committing at least one Type I error can be much higher than the desired 5%.

To control the experiment-wise error rate, various multiple comparison procedures and adjustments can be employed, such as the Bonferroni correction or the Holm-Bonferroni method. These methods aim to maintain a desired level of significance for the entire set of tests, reducing the risk of accumulating Type I errors.

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The value of x is 2 and the value of y is 3 when we have y = -x/2+4 and y = 2x-1.

According to the question,

We have the following equations:

y = -x/2+4 and y = 2x-1

Now, we can equate the right hand side of both the equations because on the left hand side of both the equations we have y:

2x-1 = -x/2+4

Now, taking the least common factor of 2 and 1:

2x-1 = (-x+8)/2

Now, using the cross multiplication method:

2(2x-1) = -x+8

4x-2 = -x+8

Moving -x from the right hand side to the left hand side:

4x+x = 8+2

5x = 10

x = 10/5

x = 2

Putting this value of x in y:

y = -2x+1

y = -2*2+1

y = -4+1

y = -3

Hence, the value of x is 2 and the value of y is -3 when we have  y = -x/2+4 and y = 2x-1.

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Answer: The probability that the sample mean is between 74 and 76 is approximately 0.7924.

Step-by-step explanation:

We can use the central limit theorem to approximate the sampling distribution of the sample means as normal with a mean of 75 and a standard deviation of 5/√40 = 0.79.

1. To find the probability that the sample mean is less than 74, we need to standardize the sample mean using the formula:

Z = (X - μ) / (σ / √n)

where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

Z = (74 - 75) / (5 / √40) = -1.26

Using a standard normal table or calculator, we find that the probability of a standard normal random variable being less than -1.26 is 0.1038.

Therefore, the probability that the sample mean is less than 74 is approximately 0.1038.

2. To find the probability that the sample mean is between 74 and 76, we need to standardize both sample means using the formula above and find the probability that Z lies between two values.

Substituting the given values for 74, we get:

Z1 = (74 - 75) / (5 / √40) = -1.26

Substituting the given values for 76, we get:

Z2 = (76 - 75) / (5 / √40) = 1.26

Using a standard normal table or calculator, we find that the probability of a standard normal random variable being less than -1.26 is 0.1038, and the probability of it being less than 1.26 is 0.8962.

Therefore, the probability of a standard normal random variable being between -1.26 and 1.26 is:

0.8962 - 0.1038 = 0.7924

Therefore, the probability that the sample mean is between 74 and 76 is approximately 0.7924.

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Answer:

Step-by-step explanation:

SOLVING

================================================================

6=-2(7-c)

Use distribution to multiply -2 by parenthesis

6=-14+2c

Add to both sides 14

20=2c

Divide 2 into both sides

10=c

5(h-4)=8

Use distribution to multiply 5 by the parenthesis

5h-20=8

Add to both sides 20

5h=28

Divide 5 into both sides

\(h=\frac{28}{5}\)

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We will find the sum of 3+ 1 1/2 with help of a

9y - 7 = 29

=> 9y = 29 + 7 [Transferring 7 to R.H.S.]

=> 9y = 36

=> y = 36/9 [Transferring 9 to R.H.S.]

=> y = 4

Hence proved.

Answer:

Here

Step-by-step explanation:

The average rate of change per hour in the temperature is 0.83 degrees.

To find the average rate of change per hour, we need to divide the total change in temperature by the number of hours over which the temperature changed.

The temperature rose by 5 degrees from 6:00 am to 12:00 pm, which is a period of 6 hours.

Therefore, the average rate of change per hour can be calculated as follows:

average rate of change per hour = total change in temperature / number of hours

So, we have

average rate of change per hour = 5 degrees / 6 hours

average rate of change per hour = 0.83 degrees/hour (rounded to two decimal places)

So, the average rate of change per hour is 0.83 degrees.

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To determine the decision rule for rejecting the null hypothesis (H₀: μ1 = μ2) and conclude if the mean score for Group 1 is significantly lower than Group 2, we will perform a two-sample t-test with a significance level (α) of 0.05. Since the problem states that the population variances are equal and the populations are normally distributed, we can proceed with the pooled variance t-test.
Step 3: Determine the decision rule for rejecting the null hypothesis H₀.
First, we need to calculate the degrees of freedom (df). For a pooled variance t-test, df = (n1 - 1) + (n2 - 1), where n1 and n2 are the sample sizes for Group 1 and Group 2, respectively.
\(df = (10 - 1) + (15 - 1) = 9 + 14 = 23\)
Next, we need to find the critical t-value. Since we are testing for a significantly lower mean score in Group 1, we are conducting a one-tailed t-test with α = 0.05 and df = 23.
Using a t-table or calculator, we find the critical t-value to be approximately -1.714.
Thus, the decision rule for rejecting the null hypothesis H₀ is: if the calculated t-value is less than -1.714, we reject H₀ and conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2.

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Answer:

  2.76×10^-3 m/s²

Step-by-step explanation:

You want to know the acceleration of the moon toward the Earth, given its distance is 3.8×10^8 meters, Earth's mass is 5.98×10^24 kg, and the gravitational constant is 6.673×10^-11 N·m²/kg².

The acceleration of one body by another is ...

  a = GM/r²

where G is the gravitational constant, M is the body creating the gravitational field, and r is the distance between the masses.

  a = (6.673×10^-11)(5.98×10^24)/(3.8×10^8)² N/kg

  a = (6.673·5.98/3.8²)×10^(-11+24-16) m/s² ≈ 2.76×10^-3 m/s²

maybe try using the 2 and dropping the decimal

The sample tensile strength of fiber specimens will be greater than 75.75 psi in 43.25 percent of cases.

Z-score: Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean. Standard deviation is essentially a reflection of the amount of variability within a given data set.

given that a synthetic fiber used in manufacturing carpet has a tensile strength that is normally distributed with a mean 75.5 psi and standard deviation 3.5 psi

z = (raw score - mean) / (sample standard deviation - standard deviation)

n = 6; mean=75.5 psi; standard deviation=3.5 psi.

For (greater than) > 75.75,

z = (75.75 - 75.5) / (3.5 ÷√6) = 0.17

P(z > 0.17) = 1 - P(z < 0.17) = 1 - 0.5675 = 43.25%

The sample tensile strength of fiber specimens will be greater than 75.75 psi in 43.25 percent of cases.

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Answer:

\(A=11.7\ m^2\)

Step-by-step explanation:

Given that,

Central angle, \(\theta=160^{\circ}\)

Diameter,d = 5.8 m

Radius, r = 2.9 m

We need to find the area of sector. The formula for the area of sector is given by :

\(A=\dfrac{\theta}{360}\times \pi r^2\\\\=\dfrac{160}{360}\times 3.14\times 2.9^2\\\\=11.7\ m^2\)

So, the area of a sector is equal to \(11.7\ m^2\).

Answer:

  $50,000 in stocks

  $40,000 in bonds

  $25,000 in CDs

Step-by-step explanation:

Let c represent the amount invested in CDs. Then the amount invested in bonds is (c+15000) and the amount invested in stocks is (115000 -c -(c+15000)) = (100000 -2c). The total interest earned is ...

  0.04c +0.053(c +15000) +0.062(100,000 -2c) = 6220

  -0.031c +795 +6200 = 6220

  -0.031c = -775 . . . . . . . . . . . . . . . subtract the left-side constants

  c = 25000 . . . . . . . . . . divide by the coefficient of c

  c+15000 = 40000 . . . . bonds

  100000 -2c = 50000 . . . . . stocks

Maricopa Success invested ...

  $50,000 in stocks

  $40,000 in bonds

  $25,000 in CDs

Answer:

$14.77

Step-by-step explanation:

Answer:

E. n=4

Step-by-step explanation:

"compounded quarterly" meaning 4.

Option E is correct. The amount Mayra deposited into the account quarterly is $1,146.35 where the value of n is 4

In order to get the amount compounded quarterly, we will use the compounded interest formula as shown:

A = P(1+r/n)^nt where:

A is the amount after 5 years = $6000

r is the rate (in %) = 6% = 0.06

n is the compounding time =  1/4 (quarterly)

t is the time taken (in years) = 5 years

Required

Amount invested quarterly.

First, we need to get the amount initially invested

Substitute the given values into the formula;

6000 = P(1+0.06(4))^{5/4)}

6000 = P(1+0.24)^1.25

6000 = P (1.24)^1.25

6000 = 1.3085P

P = 6000/1.3085

P = $4,585.40

The amount initially deposited will be $4,585.40

The amount deposited quarterly = P/n where n = 4

Amount deposited quarterly = $4,585.40/4

Amount deposited quarterly = $1,146.35

Therefore the amount Mayra deposited into the account quarterly is $1,146.35 where the value of n is 4.

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Answer: D. Mrs. Bell has the lower interest rate, because both decimals have a 4 in the ones place, and 1 the third is less than 2 tenths.

Answer:

D

Step-by-step explanation:

take the natural logarithm of both sides:

Divide both sides by ln(12):

By the principle of mathematical induction, we will show that the algorithm to compute the sum of the cubes of the first n positive integers returns the correct value for every positive integer input.

To prove that the algorithm to compute the sum of the cubes of the first n positive integers returns the correct value for every positive integer input using induction, we will need to show two things:

1. Base case: The algorithm returns the correct value for n = 1.

Base case: When n = 1, the algorithm returns 1^3, which is the correct value for the sum of the cubes of the first positive integer. Therefore, the base case is true.

2. Inductive step: Assume that the algorithm returns the correct value for some positive integer k, and show that it also returns the correct value for k + 1.

Inductive step: Assume that the algorithm returns the correct value for some positive integer k, i.e., SumCube(k) returns 1^3 + 2^3 + ... + k^3.

We need to show that the algorithm also returns the correct value for k + 1, i.e., SumCube(k + 1) returns 1^3 + 2^3 + ... + (k + 1)^3.

Using the recursive definition of the algorithm, we have:

SumCube(k + 1) = (k + 1)^3 + SumCube(k)

By the induction hypothesis, we know that SumCube(k) returns the correct value, so we can substitute it into the above equation to get:

SumCube(k + 1) = (k + 1)^3 + (1^3 + 2^3 + ... + k^3)

Expanding (k + 1)^3, we get:

SumCube(k + 1) = k^3 + 3k^2 + 3k + 1 + (1^3 + 2^3 + ... + k^3)

Simplifying the right-hand side, we get:

SumCube(k + 1) = 1^3 + 2^3 + ... + k^3 + (k^3 + 3k^2 + 3k + 1)

We recognize the last term as (k + 1)^3, so we can substitute it in to get:

SumCube(k + 1) = 1^3 + 2^3 + ... + k^3 + (k + 1)^3

which is the correct value for the sum of the cubes of the first (k + 1) positive integers. Therefore, the inductive step is true.

By the principle of mathematical induction, we have shown that the algorithm to compute the sum of the cubes of the first n positive integers returns the correct value for every positive integer input.

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Answer: 58.33%

Step-by-step explanation:

So, Liz flipped the coin a total of 60 times

Let this be the denominator.

Probability of coin landing up: 35/60

Probability of coin landing down: 24/60

We need the probability of the coin landing up.

So, convert 35/60 into a percentage

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 1003560 × 100100= (35 × 10060) × 1100 = 58.33/100

So, the probability is 58.33%

Answer:

\(x\)∈{\(\frac{\sqrt{129} +33}{60} ,\frac{-\sqrt{129}+33 }{60} )\)

Step-by-step explanation:

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