evaluate (-3)^3 x (-5/3)^-4

If the probability that a child being born to them with a certain trait is 0.11 , then the probability that at least four children out of their five children will have that trait  is 0.00067     .

The Binomial Probability is defined as P(X = x) = ⁿCₓ  pˣ  (1 - p)ⁿ⁻ˣ ,

where p is the probability of success and n is number of trials and x is the number of times success occurs .

given that the probability of the child being born with the trait is (p) = 0.11 ,

total number of children of Mr. and Mrs. Doran (n) = 5 ,

So , the probability that at least 4 of the children are born with the trait is represented as P(x ≥ 4) .

which is calculated as ,

P(x ≥ 4) = P(x=4) + P(x=5) ;

P(x ≥ 4) = ⁵C₄ × p⁴ × (1 - 0.11)⁵⁻⁴ + ⁵C₅ × p⁵ × (1 - p)⁵⁻⁵ ;

= ⁵C₄ × (0.11)⁴ × (1 - 0.11)¹ + ⁵C₅ × (0.11)⁵ × (1 - 0.11)⁰

= ⁵C₄ × (0.11)⁴ × (0.89)¹ + ⁵C₅ × (0.11)⁵ × (0.89)⁰

= ⁵C₄ × (0.11)⁴ × (0.89)¹ + ⁵C₅ × (0.11)⁵ × 1

= 0.00065152 + 0.0000161

= 0.00066762

≈ 0.00067

Therefore , the required probability is 0.00067   .

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answer: 0.001 is the correct answer

Answer:

Simplification of algebric expression is \(\frac{x^{2} - 2x^{3}-4 }{x^{2} }\)

Step-by-step explanation:

Simplify any algebric expression means to write an equivalent expression in which all similar terms combined and remove all symbols such as brackets.

The given algebraic equation is \(x^{2} -\frac{4}{x^{2} } +2x\)

now for simplifying it

First of all take L.C.M of \(x^{2}\)

= \(\frac{x^{2} (x^{2}) -4 + 2x(x^{2} )}{x^{2} }\)

We get \(\frac{x^{2} -4+2x^{3}}{x^{2} }\)

Further we can write it as  \(\frac{x^{2} - 2x^{3}-4 }{x^{2} }\)

Simplification of algebric expression is \(\frac{x^{2} - 2x^{3}-4 }{x^{2} }\)

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The surface integral  \((8x 7y z^2)\) over a sphere is equal to 128πy.

The divergence theorem to evaluate the surface integral:

\(\int\limits S (8x 7y z^2) dS = \int\limits V div(8x 7y z^2) dV\)

The divergence of \(8x 7y z^2\) is \(128yz^2\). The volume integral is then:

\(\int\limits V div(8x 7y z^2) dV = \int\limits V 128yz^2 dV\)

The volume of a sphere is\((4/3)\pi r^3\), where r is the radius of the sphere. In this case, the radius of the sphere is 1, so the volume of the sphere is (4/3)π. The integral then becomes:

\(\int\limits V 128yz^2 dV = (4/3)\pi * 128yz^2 = 128\pi y\)

The surface integral is equal to the volume integral, so the answer is 128πy.

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Using the normal distribution, it is found that 2.15% of bedroom apartments in the city cost between $750 and $1,000.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

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

The mean and the standard deviation are given, respectively, by:

\(\mu = 1500, \sigma = 250\)

The proportion of apartments that cost between $750 and $1,000 is given by the p-value of Z when X = 1000 subtracted by the p-value of Z when X = 750, hence:

X = 1000:

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

\(Z = \frac{1000 - 1500}{250}\)

Z = -2

Z = -2 has a p-value of 0.0228.

X = 750:

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

\(Z = \frac{750 - 1500}{250}\)

Z = -3

Z = -3 has a p-value of 0.0013.

0.0228 - 0.0013 = 0.0215.

0.02215 = 2.15% of bedroom apartments in the city cost between $750 and $1,000.

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Answer:

Step-by-step explanation:

700.5

When performing a statistical test, such as the Chi-Square test, the p-value is a crucial component in determining the significance of the data compared to the null hypothesis. The p-value represents the probability of observing the given data, or more extreme results, assuming the null hypothesis is true. In general, a p-value threshold of 0.05 is used to determine statistical significance.

If the calculated p-value is less than or equal to 0.05, it indicates that the observed data significantly differ from what is expected under the null hypothesis. This means that there is a less than 5% chance of obtaining the observed data if the null hypothesis were true. Consequently, researchers often reject the null hypothesis in favor of the alternative hypothesis when the p-value is less than or equal to 0.05.

However, it is essential to note that the choice of the significance level is subjective and may vary depending on the field or specific study. In some cases, a more stringent threshold, such as 0.01, might be required to minimize the chances of false positives, while in other situations, a more lenient threshold, such as 0.10, may be acceptable.

In summary, a p-value of 0.05 or less typically indicates that the data differ significantly from what is expected under the null hypothesis in a statistical test like the Chi-Square test. However, the chosen threshold for significance may vary depending on the specific context and research objectives.

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Answer:

Step-by-step explanation: the answer is 69-123

Answer:

community property addition

A transition mutation is a point mutation that transforms one nucleotide from one type of purine to another (A to G) or from one type of pyrimidine to another (C to T). G and C are substituted for A and T, respectively, and G is a different purine and C is a different pyrimidine.

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The P-value of the test statistic is approximately 0.0445. To determine the P-value, we need to perform a hypothesis test. The null hypothesis (H₀) is that the actual percentage of chips that do not fail is equal to or less than the stated percentage of 73%.

The alternative hypothesis (H₁) is that the actual percentage is greater than 73%.

We can use the normal approximation to the binomial distribution since the sample size is large (1300) and both expected proportions (73% and 74%) are reasonably close. We calculate the test statistic using the formula:

z = (P - p₀) / √[(p₀ * (1 - p₀)) / n]

where P is the sample proportion (74% or 0.74), p₀ is the hypothesized proportion (73% or 0.73), and n is the sample size (1300).

Substituting the values, we get:

z = (0.74 - 0.73) / √[(0.73 * 0.27) / 1300]

Calculating this expression, we find that z is approximately 1.556.

Since we are testing if the actual percentage is more than the stated percentage, we are interested in the right-tailed area under the standard normal curve. We find this area by looking up the z-value in the standard normal distribution table or using statistical software. The corresponding area is approximately 0.0596.

The P-value is the probability of observing a test statistic as extreme as, or more extreme than, the one obtained under the null hypothesis. Since the P-value (0.0596) is less than the significance level of 0.05, we have enough evidence to reject the null hypothesis.

Therefore, there is sufficient evidence at the 0.05 significance level to support the quality control manager's claim that the actual percentage of chips that do not fail in the first 1000 hours is more than the stated percentage.

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Answer:

43

Step-by-step explanation:

250-35(from Monday)=215

215/5=43

Hope this helps!

Answer:

-2/3

Step-by-step explanation:

pick two points

0,5 and 9,-1

Substitute in y2-y1/x2-x1

5+1/0-9

6/-9

-2/3

slope-intercept form

y=-2/3+5

The total number of students who did not have a dog or a cat was 5

Jennifer conducted a survey about the pets of students in her class. In total, 27 students participated in the survey. Among these, 14 students had cats, 12 students had dogs, and 4 students had both cats and dogs.

Jennifer took a survey among the students in her class to know about their pets. The total number of students who took part in the survey was 27. She found that 14 students had cats, 12 students had dogs, and 4 students had both cats and dogs.

Now, we need to calculate the number of students who don't have a dog or a cat. Let's start by calculating the total number of students who had either a dog or a cat.There were 14 students with cats and 12 students with dogs, which means that 26 students had either a cat or a dog.

However, since 4 students had both a cat and a dog, we must subtract this from our total. Therefore, there were 22 students with either a cat or a dog.Now, we need to subtract this from the total number of students who took the survey. That is,27 - 22 = 5 students Therefore, there were 5 students who did not have a dog or a cat.

The total number of students who did not have a dog or a cat was 5.

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To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where:

x1 and x2 are the sample means of the two sheets,

s_p is the pooled standard deviation,

n1 and n2 are the sample sizes.

The pooled standard deviation (s_p) can be calculated using the following formula:

s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

where:

s1 and s2 are the sample standard deviations.

To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.

Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.

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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.

The t-statistic for a paired t-test is calculated as follows:

t = (X1 - X2) / (s / √n)

where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.

Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.

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If no payments are made then the then after 1 year the interest will go by 5% , therefore the amount to be paid will become ,   P + 25 = 525 $.

Principle + 5% of 500

Therefore, the equation becomes ,

Amount = P + 25

To calculate the interest ,

interest = principal × interest rate × term

             = 500 x 5 x 1

              = 2500.

A loan is defined as a thing or money which is borrowed, especially a sum of money that is expected to be paid back with an interest rate which is fixed by both the parties.

Loans are typically taken or granted by by corporations, financial institutions, and governments. They allow for growth in the overall money supply in an economy and open up competition by lending to new businesses.

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Answer:

1,268,620

Step-by-step explanation:

Multiply 1,852×685

Answer:

1268620 meters

Step-by-step explanation:

685x1852= 1268620

Considering the competition, there are already 32 pizza places in the area. The new pizza place will be the 33rd in the vicinity.

The Pretty Pizza Company plans to open a new pizza place. The company has identified a location that is 0.01 (15 blocks) away. The cost per block for constructing the new pizza place is $221. Additionally, there are already 32 existing pizza places in the area.

To calculate the total cost of opening the new pizza place, we multiply the distance by the cost per block:

Total cost = 0.01 (15 blocks) * $221 = $331.50

Considering the competition, there are already 32 pizza places in the area. The new pizza place will be the 33rd in the vicinity.

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Answer:

no it is not possible

Step-by-step explanation:

Meters and seconds are the two units of measurement required to describe speed.

A ball freely falling at 20 m/s will in the next second have a speed of 30 m/s.This is because the speed of a freely falling item rises by 9.8 m/s per second owing to gravity's acceleration. The ball begins at a speed of 20 m/s and adds 9.8 m/s to its initial speed after one second, ending in a final speed of 20 + 9.8 = 29.8 m/s (approx. 30 m/s).

Meters and seconds are the two units of measurement required to describe speed. These units are used to calculate the distance travelled by an item as well as the time it takes to traverse that distance. In this scenario, the ball's speed is measured in metres per second (m/s), which is the distance the ball travels in one second.

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Answer:

2(6.3) + b = 15.7

12.6 + b = 15.7

b = 3.1

The C program for RK 4th order .

C program,

#include<stdio.h>

//differential equation "dy/dx = (y-2*x*y)"

float f(float x, float y)

{

return(y-2*x*y);

}

int main()

{

// Finds value of y for a given x using step size h

int i,n;

float x0,y0,x,h,k1,k2,k3,k4;

printf("Enter the value of x:");

scanf("%f",&x);

//initial value y0 at x0.

printf("Enter the initial value of x & y:");

scanf("%f%f",&x0,&y0);

//step size

printf("Enter the value of h:");

scanf("%f",&h);

//prints the initial value of y at x and step size.

printf("x0=%f\t yo=%f\t h=%f\n",x0,y0,h);

//Count number of iterations using step size or

//step height h

n=(x-x0)/h;

// Iterate for number of iterations

for(i=1;i<=n;i++)

{

//Apply Runge Kutta Formulas to find

//next value of y

k1 = h*f(x0,y0);

k2 = h*f(x0+h/2,y0+k1/2);

k3 = h*f(x0+h/2,y0+k2/2);

k4 = h*f(x0+h,y0+k3);

//Update next value of y

y0 = y0+(k1+2*k2+2*k3+k4)/6;

//Update next value of x

x0=x0+h;

}

//print the value of y at entered value of x.

printf("at x=%f\t,y=%f\n",x,y0);

return 0;

}

Solution of DE,

y' = y - 2xy, y(0) = 1

The task is to find value of unknown function y at a given point x.

Below is the formula used to compute next value yn+1 from previous value yn. The value of n are 0, 1, 2, 3, ….(x – x0)/h.

Here h is step height and xn+1 = x0 + h

\(K_{1} = h f(x_{n} ,y_{n} )\)

\(K_{2} = hf( x_{n} + h/2 , y_{n} + K_{1}/2 )\)

Thus,

\(y_{n+1} = y_{n} + K_{1} / 6 + K_{2} / 3 + K_{3} / 3 + K_{4} / 6 +O(h^{5} )\)

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According to the Empirical Rule (68-95-99.7% Rule), approximately 68% percent of the values will be between 75 and 85.

According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.

\(P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%\)

Here, we had  where mean of distribution of X is \(\mu\) and standard deviation from mean of distribution of X is \(\sigma\).

A distribution of scores on an aptitude test is Normally distributed with a mean of 80 and a standard deviation of 5.

\(\mu=80\\\sigma=5\)

The percentage for the interval of values between 75 and 85 has to be found out. From the 68%, the interval is,

\(P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(80 - 5 < X < 80+ 5) = 68\%\\P(75 < X < 85) = 68\%\)

Thus, according to the Empirical Rule (68-95-99.7% Rule), approximately 68% percent of the values will be between 75 and 85.

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A higher confidence level is associated with a wider confidence interval.

a. The point estimate of µ = (14 + 20 + 21 + 16 + 18 + 19) / 6 = 108 / 6 = 18.

b. For 80% confidence interval for µ, the confidence coefficient is 1 - α = 0.8, so α = 0.2 / 2 = 0.1. From the z-table, we can find the corresponding value of z to be 1.28. The confidence interval can be calculated as follows:

Upper Bound: µ + z*σ / √n = 18 + (1.28)(2.3) / √6 = 21.35

Lower Bound: µ - z*σ / √n = 18 - (1.28)(2.3) / √6 = 14.65

The 80% confidence interval is (14.65, 21.35). For 98% confidence interval for µ, the confidence coefficient is 1 - α = 0.98, so α = 0.01. From the z-table, we can find the corresponding value of z to be 2.33. The confidence interval can be calculated as follows:

Upper Bound: µ + z*σ / √n = 18 + (2.33)(2.3) / √6 = 23.88

Lower Bound: µ - z*σ / √n = 18 - (2.33)(2.3) / √6 = 12.12

The 98% confidence interval is (12.12, 23.88). The 80% and 98% confidence intervals are different because as we move to higher confidence levels, the z-values become larger, which in turn causes the confidence intervals to become wider. Therefore, a higher confidence level is associated with a wider confidence interval.

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Answer:

6/19

Step-by-step explanation:

Answer:

6/19 subtracting 3 each time form the numerator

Step-by-step explanation:

Answer:

y=-4

Step-by-step explanation:

The answer is going to be -4 as when y=-16 x=8.

The profit function made by the cell phone manufacturer is given by -0.09x² -1300x - 750000

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.

The profit function is given as:

Profit = Revenue - Cost

Cost = 2000x + 750000, Revenue = -0.09x² + 700x, hence:

Profit = -0.09x² + 700x - (2000x + 750000) = -0.09x² -1300x - 750000

The profit function made by the cell phone manufacturer is given by -0.09x² -1300x - 750000

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Answer:

(a) the graph is discrete because the number of basketballs cannot exist in fractions

(b) 126 ÷ 14 = 9, 9 basket balls were bought

graph:-

[b] [a]

0 0

1 14

2 28

3 42

4 56

Answer:

discrate

9

0 14 24 38 52

Explanation:

We can model the situation as:

Since P and R have a y-coordinate equal to 0, Q has a y-coordinate 0

Now, to calculate the x-coordinate, we can formulate the following equations:

Rx - Px = 3a

Qx - Px = 2a

Where Rx is the x-coordinate of R, Px is the x-coordinate of P and Qx is the x-coordinate of Q. So, replacing the values:

-12 - 0 = 3a

x - 0 = 2a

Now, solving for a, we get:

-12 - 0 = 3a

-12 = 3a

-12/3 = a

-4 = a

Replacing on the second equation, we get:

x - 0 = 2a

x = 2a

x = 2*(-4)

x = -8

Therefore, the coordinates of Q are (-8, 0)

Answer: (-8, 0)