You get a student loan from the New Mexico Educational Assistance Foundation to pay for your educational expenses this year. Find the interest on the loan if you borrowed $5000 at 5% interest for 1 year

m = 54.8 inches

std = 4.9 inches

We can standarize the variable as:

(X - m)/std

So, the probability of a height randomly choosen is between 51.05 and 54.75 inches is:

P[ 51.05 < X < 54.75]

Standarizing those values:

(51.05 - m)/std = (51.05 - 54.8)/4.9 = -75/98...

(54.75 - m)/std = (51.05 - 54.8)/4.9 = -1/98...

So, the new probability is:

P[ -75/98 < Z < -1/98] = Phi(-1/98) - Phi(-75/98)

Where Z is the new standarized variable.

We can find these Phi values from tables of the standarized normal distributions:

Phi(-1/98) = 0.77796

Phi(-75/98) = 0.49593

So the probability is:

P[ -75/98 < Z < -1/98] = Phi(-1/98) - Phi(-75/98) = 0.77796 - 0.49593

P[ 51.05 < X < 54.75] = 0.28203 = 0.282

And that is the answer

Answer:

The balloon was thrown at a height of 3 feet above the ground.

The balloon reached its maximum height of 6 feet above the ground one second after it was thrown.

The balloon hit the ground 2.414 seconds after it was thrown.

Step-by-step explanation:

Definition of the variables:

The y-intercept tells us the value of y when x is zero. Therefore, it tells us the height of the water balloon above the ground at the time the balloon was thrown.  So the water balloon was 3 feet above the ground when it was thrown.

The vertex (1, 6) is the maximum point of the curve.

Therefore, the balloon reached its maximum height of 6 feet above the ground one second after it was thrown.

The roots are the points at which the curve intersects the x-axis, so when y is zero.  They tell us the time when the balloon's height is zero, so when it is at ground level.  

One of the roots is negative, so as time cannot be negative, the root x = -0.414 can be discounted.  

The other root x = 2.414 tells us that the balloon hit the ground 2.414 seconds after it was thrown.

Answer:

Step-by-step explanation:

given: x-y = 4

x=4+y

given: -10x + y = -58

plug in for x

-10(4 + y) + y = -58

-40 - 10y + y = -58

-9y = -18

y = -18 / -9

y = 2

now plug in 2 for y in the first equation

x-2=4

x=6

There is the solution  x=6, y=2  :)

The given problem can be solved by performing a Fisher's Exact Test on the given data. Using R Studio to answer the question. Discuss.fisher.test(diag(3:4)) # two-sided Fisher's Exact Test for Count Data

data: diag(3:4)

p-value = 0.02857

Alternative hypothesis: true odds ratio is not equal to 1

95 percent confidence interval: 0.9258483 Inf

sample estimates: odds ratio     8 Inf     # strong evidence

We are given the following data in the problem:

Three AUT students and four UoA students are given a problem in statistics.

All three of the AUT students answer the problem correctly, and none of the UoA students answer correctly.

To analyze this data, we will perform a Fisher's Exact Test on the given data. The null hypothesis and alternative hypothesis for the Fisher's exact test are given below:

Null Hypothesis (H0): There is no significant difference between the probability of AUT and UoA students solving the problem correctly.

Alternative Hypothesis (Ha): There is a significant difference between the probability of AUT and UoA students solving the problem correctly.

We can use R Studio to perform Fisher's Exact Test on the given data. The code for the same is given below:

fisher.test(diag(3:4)) # two-sided

The output of the code gives the p-value as 0.02857. The p-value is less than the significance level of 0.05, which indicates strong evidence against the null hypothesis.

From the above discussion, it can be concluded that there is a significant difference between the probability of AUT and UoA students solving the problem correctly. This conclusion is supported by the p-value obtained from the Fisher's Exact Test.

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The inverse of the transpose of matrix A is equal to the transpose of the inverse of matrix A.

To verify that the inverse of A transpose (A^T) is equal to the transpose of the inverse of A (A^-1), we can use the multiplication rule for transposes, which states that (CD)^T = D^T * C^T.

Let's assume that A is an invertible matrix. We want to show that (A^T)^-1 = (A^-1)^T.

First, let's take the inverse of A^T:

(A^T)^-1 * A^T = I,

where I is the identity matrix.

Now, let's take the transpose of both sides:

(A^T)^T * (A^T)^-1 = I^T.

Simplifying the equation:

A^-1 * (A^T)^T = I.

Since the transpose of a transpose is the original matrix, we have:

A^-1 * A^T = I.

Now, let's take the transpose of both sides:

(A^-1 * A^T)^T = I^T.

Using the multiplication rule for transposes, we have:

(A^T)^T * (A^-1)^T = I.

Again, since the transpose of a transpose is the original matrix, we get:

A * (A^-1)^T = I.

Now, let's take the transpose of both sides:

(A * (A^-1)^T)^T = I^T.

Using the multiplication rule for transposes, we have:

((A^-1)^T)^T * A^T = I.

Simplifying further, we get:

A^-1 * A^T = I.

Comparing this with the earlier equation, we see that they are identical. Therefore, we have verified that the inverse of A transpose (A^T) is equal to the transpose of the inverse of A (A^-1).

In conclusion, (A^T)^-1 = (A^-1)^T.

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Answer:

c. greater than 7

Step-by-step explanation:

Answer:uhhh

Step-by-step explanation:

Answer: 3 or 4

Step-by-step explanation:

Answer:

k<=-2

Step-by-step explanation:

-3k≥6

3k<=-6 ==> when dividing by negative numbers switch the sign of the inequality

3k/3<=-6/3

k<=-2

Answer: x = -1

Step-by-step explanation:

90-86 = 4

-4x. =4

x = 4 / -4

x = -1

The numeric value of the function h(x) at x = 4 is given as follows:

8.7.

The quadratic regression equations for each table are given as follows:

To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value, and then apply the remaining calculations.

The function in this problem is defined as follows:

h(x) = 50/(5.5 + 8e^(-0.9x)).

The numeric value that we want to find is of:

h(4).

Hence the lone instance of x is replaced by 4, as follows:

h(4) = 50/(5.5 + 8e^(-0.9x4)) = 8.7.

The standard format of a quadratic regression equation is defined as follows:

y = Ax² + Bx + C.

Hence, for each table in this problem, all the points are inserted into a quadratic regression calculator, and then the values of the parameters A, B and C are given.

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The absolute minimum value of y =-cos(x) - sin(x) on the closed interval [0, π/2] is  \(-\sqrt{2}\)

Consider equation,

y = -cos(x) - sin(x)

Let y = f(x)

Differentiate the function f(x) = -cos(x) - sin(x) with respect to x.

f'(x) = -(-sin(x)) - cos(x)

f'(x) = sin(x) - cos(x)

For f'(x) = 0,

sin(x) - cos(x) = 0

sin(x) = cos(x)

sin(x)/cos(x) = 1

tan(x) = 1                     ..............(tan(θ) = sin(θ)/cos(θ))

x = π/4

For above value of x, the value of function would be,

f(π/4) = -cos(π/4) - sin(π/4)

f(π/4) = \(-\frac{1}{\sqrt{2} } -\frac{1}{\sqrt{2} }\)

f(π/4) = \(-\sqrt{2}\)

f(0) =  -cos(0) - sin(0)

f(0) = -1

And f(π/2) = -cos(π/2) - sin(π/2)

       f(π/2) = -1

So, the minimum value of f(x) is  \(-\sqrt{2}\),  shown in the following graph.

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The probability that none of the patients have broken bones is  0.0352.

What is binomial distribution?

A popular probability distribution known as the binomial distribution simulates the likelihood of getting one of two outcomes given a set of parameters. It totals the number of trials when each trial has an equal chance of producing a particular result. By dividing the quantity of independent trials by the number of successes, one can calculate the value of a binomial.

Let X has binomial distribution with n = 15 and  p = 0.20

The PDF of the distribution can be written as:

P(X=x)  = nCx(p)x (1-p)n-x

Probability for 0 patients have broken bones can be calculated as:

P(x=0) = 15C0(0.20)0 (1-0.20)15-0

P(x=0)  = 0.035184 = 0.0352

Therefore, the probability is  0.0352

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Complete Question

Suppose 20% of all emergency room patients have broken bones. of the next fifteen patients to arrive, what is the probability that none have broken bones?

Answer:

19.4 cubic meter

Step-by-step explanation

Round your answer to the nearest tenth of a cubic centimeter.

Answer:

------------------

Let the amount deposited be x. It is assumed we are talking about simple interest.

After 4 years the interest amount is:

95% of this amount is Rs 4940:

Mrs Majhi deposited Rs 20000.

Mrs. Majhi deposited Rs 20000 in her bank account. This was calculated by first finding the total interest (before tax) and then using the formula for simple interest to determine the principal amount.

The question is based on the concepts of Simple Interest and taxation. We know that Mrs Majhi received Rs 4940 as net interest after 4 years and this amount is 95% of the total interest (since 5% was paid as income tax). The total interest can be calculated as (4940 / 95) * 100 = Rs 5200.

The rate of interest is given as 6.5% per annum. Thus, the money deposited (Principal) by her can be calculated using the formula for simple interest (I = PRT/100), where P is the Principal, R is the rate of interest, and T is the time. Re-arranged to calculate the Principal (P), it becomes P = I / (R*T) = 5200 / (6.5*4) = Rs 20000.

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A: √50x^2 and d: √72x^2 are like radicals.

Like radicals are square roots with the same coefficient outside the radical. For example, √50x^2 and √72x^2 can be simplified to √2 * √25x^2, which makes them like radicals. Simplifying the expressions helps to see if they are alike.

Expressions such as √32x and √18n cannot be simplified to have the same coefficient outside the radical and hence, they are not like radicals.

In conclusion, only √50x^2 and √72x^2 are like radicals after simplification.

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Answer:

A&D

Step-by-step explanation:

Got it right on edge

Answer:

y = 5

Step-by-step explanation:

3y - 2 = 13

We are solving for y, so we want to isolate it.

Add 2 to both sides.

3y = 15

Continue isolating y by dividing both sides by 3.

y = 5

Check your answer by plugging it back into the original equation.

3y - 2 = 13

3(5) - 2 = 13

Multiply.

15 - 2 = 13

Subtract.

13 = 13

Your answer is correct.

Hope this helps!

Answer:

y = 5

Step-by-step explanation:

Get y by itself:

3y - 2 = 13

     +2    +2

3y = 15

Divide by 3:

3y = 13

÷ 3    ÷ 3

y = 5

The end behavior of the graph is that it tends towards negative infinity as x approaches negative infinity, and tends towards positive infinity as x approaches positive infinity.

The end behavior of the graph of f(x) = x5 - 8x4 + 16x3 can be determined by looking at the leading term of the polynomial. The leading term of the polynomial is x5, which is positive for positive values of x and negative for negative values of x. Therefore, as x approaches negative infinity, the graph of f(x) will tend towards negative infinity, and as x approaches positive infinity, the graph of f(x) will tend towards positive infinity. To understand this further, consider what happens when x is very large, either positive or negative. As the absolute value of x increases, the leading term of the polynomial, x5, will have an increasingly large influence on the value of the polynomial, and any other terms will become insignificant. Therefore, for very large values of x, the graph of f(x) will almost entirely reflect the behavior of the leading term, which is to approach negative infinity for negative values of x and positive infinity for positive values of x.

f(x) = x5 - 8x4 + 16x3

When x is very large, either positive or negative:

When x is very large and positive:

f(x) ≈ x5

f(x) → ∞

When x is very large and negative:

f(x) ≈ -x5

f(x) → -∞

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Answer:

42

Step-by-step explanation:

Explanation in image

The set of values for x are 5/3 and 1/3

The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign.

For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5.

This means that there are two set of values for absolute values.

|6x-6|+4=85/3 and 1/3

when |6x-6| is positive

6x - 6 + 4 = 8

6x = 8+6-4

6x = 14-4

6x = 10

x = 10/6 = 5/3

when |6x-6| is negative

-(6x -6) +4 = 8

-6x +6 +4 = 8

-6x = 8 - 10

-6x = -2

x = -2/-6

x = 1/3

Therefore the set of solution for |6x-6|+4=8 are 5/3 and 1/3

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Yes, you can remove a message you've already sent, but there are other options as well. The unsend feature is only compatible with iMessage (iPhone to iPhone).

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Answer: divide by 3.14

Step-by-step explanation:

The surface area of the composite shape is 306cm²

A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes as well.

The surface area of a cube is 6l²

= 6×3²

= 54cm²

The surface area of a triangular prism = 2B +pH

where P is the perimeter of the perimeter of the base and B is the area of the base.

Perimeter of the base = 12+9+3 = 24cm

area of the base = 1/2 bh = 1/2 ×9 × 12 = 54cm²

SA = 2× 54 + 24×6

= 108+144

= 252cm²

Therefore the area of the composite shape is 252+ 54

= 306 cm2

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Answer:

x=-5 x=3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

We can see that:

- Shape B has just been translated down (moving down a couple of squares)

- Shape C has been rotated 90° clockwise

Answer:  90,  and 1600 degrees.2500

Step-by-step explanation:

If the angles are proportional to 3, 4, 5,Then the angle measures are 3x, 4X and 5X

Step-by-step explanation:

Answer:

45  60  75

Step-by-step explanation:

Let's call the angles 3 x , 4 x and 5 x

They must add up to 180 o in a triangle, so:

3 x + 4 x + 5 x = 12 x = 180 → x = 180 / 12 = 15 So the angles are:

3 ⋅ 15 = 45 o 4 ⋅ 15 = 60 o 5 ⋅ 15 = 75 o Check answer:

45 + 60 + 75 = 180

Answer: It’s 3/2(cos(75) + isin(75))

Step-by-step explanation: you multiply 3 and 1/2 first. then add 60 and 15! (edge)

Answer:

A

Step-by-step explanation:

3/2[cos(75º) + i sin (75º)]

The absolute increase in population from 2007 to 2011 is calculated by subtracting the initial population from the final population. Therefore:

Absolute increase = Final population - Initial population
Absolute increase = 5500 - 3450
Absolute increase = 2050 people

the calculation is that the difference between the final and initial population represents the net change in the population over the given time period.

The relative increase, expressed as a percentage, can be calculated by dividing the absolute increase by the initial population and multiplying by 100. Therefore:

Relative increase = (Absolute increase / Initial population) x 100
Relative increase = (2050 / 3450) x 100
Relative increase = 59.42%

The population of the town increased by 2050 people between 2007 and 2011, representing a relative increase of 59.42%.

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