Find the particular solution determined by the given condition. ds/dt = 16t^2 + 9t - 6; s = 120 when t = 0 The particular solution that satisfies the given condition is s =

Answer:

Only the mean increased.

Step-by-step explanation:

The mean is the total divided by the number of scores, and since adding 21 will increase the total score significantly, the mean increases.

The median is still 7.

Answer:

48 degrees

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

If one angle is 132 degrees, the other must be 48 degrees.

75% of the population has an IQ greater than 89.95.

(a)What percentage of people have an IQ lower than 91?The given distribution is the normal distribution, with the mean 100 and standard deviation 15. It is required to calculate the percentage of people having an IQ score lower than 91.

To calculate the percentage of people having an IQ score lower than 91, standardize the given IQ score of 91 using the formula of z-score.z=(x−μ)/σwherez is the standardized score,x is the raw score,μ is the mean, andσ is the standard deviation.

The values can be substituted as follows.z=(91−100)/15=−0.6Now, find the probability of having a z-score less than or equal to -0.6 using the standard normal distribution table.

The value in the table is 0.2743, which means the probability of having a z-score less than or equal to -0.6 is 0.2743.Thus, 27.43% of people have an IQ score lower than 91.

(a) 27.43% of people have an IQ lower than 91.(b)Fill in the blank. 75% of the population have an IQ that is greater than X.

In order to find X, the z-score can be calculated using the formula of z-score.z=(x−μ)/σwherez is the standardized score,x is the raw score,μ is the mean, andσ is the standard deviation.

The z-score for the given problem can be calculated as follows:z = (x - μ)/σ (standardized score formula)z = (x - 100)/15 (values substituted)To find the value of x for which 75% of the population have an IQ greater than x, we need to determine the z-score that corresponds to the 25th percentile.

This is because 75% of the population is above the 25th percentile and below the 100th percentile.Using a standard normal distribution table, we can find the z-score that corresponds to the 25th percentile. The z-score is approximately -0.67.

Now that we have the z-score, we can solve for x as follows.-0.67 = (x - 100)/15 (substitute z-score)-10.05 = x - 100 (multiply both sides by 15)-89.95 = x

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(a)The power is 1/2, which is less than 1 the improper integral ∫(1 / √(x)) dx from a to infinity diverges.

b)The value of the integral of ∫(1 / √(x)) dx from 1 to infinity is ln(√2 + 1).

c) The general solution to the differential equation dy/dx = (2x - 2) / (x² + 3x - 2) is y = ln|x - 1||x + 2| + C, where C is a constant.

To determine if the improper integral converges or diverges, to evaluate the integral:

∫(1 / √(x)) dx from a to infinity

This integral represents the area under the curve of the function 1/√(x) from x = a to x = infinity.

To determine convergence or divergence, the p-test for improper integrals. For the p-test, the power of x in the denominator, which is 1/2.

If the power is greater than 1, the integral converges. If the power is less than or equal to 1, the integral diverges.

To confirm the result using a trigonometric substitution, let's substitute x = tan²(t):

√(x) = √(tan²(t)) = tan(t)

dx = 2tan(t)sec²(t) dt

substitute these values into the integral:

∫(1 / √(x)) dx = ∫(1 / tan(t))(2tan(t)sec²(t)) dt

= ∫2sec(t) dt

To determine the limits of integration. Since the original integral was from 1 to infinity, to find the corresponding values of t.

When x = 1, tan²(t) = 1, which implies tan(t) = ±1. the positive value because dealing with positive values of x.

tan(t) = 1 when t = π/4

The integral with the appropriate limits:

∫(1 / √(x)) dx = ∫2sec(t) dt from t = 0 to t = π/4

Evaluating the integral:

∫2sec(t) dt = 2ln|sec(t) + tan(t)| from t = 0 to t = π/4

Plugging in the limits:

2ln|sec(π/4) + tan(π/4)| - 2ln|sec(0) + tan(0)|

ln(√2 + 1) - ln(1)

ln(√2 + 1)

The given differential equation is:

dy/dx = (2x - 2) / (x^2 + 3x - 2)

To find the general solution,  by factoring the denominator:

dy/dx = (2x - 2) / [(x - 1)(x + 2)]

decompose the fraction into partial fractions:

dy/dx = A/(x - 1) + B/(x + 2)

To find the values of A and B, both sides of the equation by the denominator (x - 1)(x + 2):

2x - 2 = A(x + 2) + B(x - 1)

Expanding the right side and collecting like terms:

2x - 2 = Ax + 2A + Bx - B

Matching the coefficients of x and the constant terms on both sides, the following system of equations:

A + B = 2 (coefficient of x)

2A - B = -2 (constant term)

Solving this system of equations,  A = 1 and B = 1.

Substituting these values back into the partial fraction decomposition:

dy/dx = 1/(x - 1) + 1/(x + 2)

integrate both sides with respect to x:

∫ dy = ∫ (1/(x - 1) + 1/(x + 2)) dx

Integrating each term separately:

y = ln|x - 1| + ln|x + 2| + C

Combining the logarithmic terms using properties of logarithms:

y = ln|x - 1||x + 2| + C

This is the general solution to the given differential equation.

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Answer:

It increases by 2.5

Step-by-step explanation:

yeah

Answer:

65,760

Step-by-step explanation:

move decimal over two places to make a percent a decimal so .37

then multiply that times the 48000 to get 17,760 and then add that to the original 48000 to get 65,760

Answer:

If the radius is 6mm, the diameter is 12mm.

If the diameter is 22 ft, the radius is 11 ft.

Step-by-step explanation:

1st one) When you try to find the diameter of any circle, and you already have the radius, you need to multiply it by two (double it)

6 x 2 = 12mm

2nd one) Then to do the opposite, you need to divide the diameter by 2.

22/2 = 11 ft

Hope this helped :)

Answer:

c ) 2480 cm²

Step-by-step explanation:

Surface Area of a Triangular prism =

S = bh + lb + 2ls

b = 30cm

h = 8cm

s = 17 cm

l = 35cm

The surface area = 30cm × 8 cm + 35 × 30 cm + 2(35 × 17)

= 240 cm² + 1050 cm² + 1190 cm²

= 2480 cm²

Option c is the correct option

Answer:

$42.84

Step-by-step explanation:

P = 85 * 6 = 510

Formula:

I = Prt

Given:

P = 510

r = 2.1% or 0.021

t = 4

Work:

I = Prt

I = 510(0.021)(4)

I = 42.84

Answer:

True

Step-by-step explanation:

It pases vertical line test but does not have an inverse

Answer:

$1.40

Step-by-step explanation:

4 quarters

1 quarter = 25 cents

Therefore, 4 quarters = 1/25 x 4/x

multiply 4 by 25, since 1 quarter = 25 cents

4 x 25 = 100

4 quarters = 100 cents

which equals $1

8 nickels

1 nickle = 5 cents

Therefore, 8 nickles = 1/5 x 8/x

multipy 8 by 5, since 1 nickel = 5cents

8 x 5 = 40

8 nickels = 40 cents

So add both 40 cents and 100 cents, which equals 140 cents.

But you still have to change the cents to dollars.

Which is 100 cents = $1

Add 40 cents

= $1.40

Answer:

yo is your math class teacher named wicker? I think I'm ur classmate lol

Answer:

A would be the answer I would choose

Answer:

16 = 3x

Step-by-step explanation:

It is an equilateral triangle. The formula for the perimeter of an equilateral triangle is P = 3a.

3X IS ANSWER AND IT IS SIMPLE BECAUSE P= 3X

There is no polynomial attached ; considering the hypothetival

Answer:

x³ = leading term.

2 = leading Coefficient

1 = constant term.

Step-by-step explanation:

Considering an hypothetical situation ;

For any polynomial such as 2x³ + 3x + 1

The polynomial is represented as : ax³ + bx + c

Where a = leading Coefficient ;

x³ = leading term

c = constant term

Therefore ;

The leading term in this hypothetical question is :

x³ = leading term.

2 = leading Coefficient

1 = constant term.

Answer:

True.

Step-by-step explanation:

given equation: (tan x - 1)/(tan x + 1) = (1 - cot x)/(1 + cot x)

1. manipulate the right side by using trigonometric identities

(tan(x) - 1)/(tan(x) + 1) = (-cos(x) + sin(x))/(cos(x) + sin(x))

2. manipulate the right side by using trigonometric identities

(-cos(x) + sin(x))/(cos(x) + sin(x)) = (-cos(x) + sin(x))/(cos(x) + sin(x))

Both sides of the equation are now equal -> (tan x - 1)/(tan x + 1) = (1 - cot x)/(1 + cot x) is true.

Answer:

The triangle is isosceles.

Step-by-step explanation:

This means that one angle's sine is the same as the other's cosine.

Answer:

94.25 feet.

Step-by-step explanation:

Answer:

The general solution to the given linear system is x = 3z - 1, y = -z + 1, where z is a free variable. This means that the solution consists of infinitely many points that lie on a straight line in three-dimensional space.

To solve the linear system, we can use the method of elimination or Gaussian elimination. Here, we'll use Gaussian elimination to find the general solution.

We start by writing the augmented matrix of the system:

[1 1 -2 | 0]

[2 2 3 | 1]

[3 3 1 | 7]

To simplify the matrix, we perform row operations to create zeros in the first column below the first entry. We subtract twice the first row from the second row and subtract three times the first row from the third row:

[1 1 -2 | 0]

[0 0 7 | 1]

[0 0 7 | 7]

Next, we divide the second and third rows by 7 to create leading ones:

[1 1 -2 | 0]

[0 0 1 | 1/7]

[0 0 1 | 1]

Now, we perform row operations to create zeros in the second column below the second entry. We subtract the third row from the second row:

[1 1 -2 | 0]

[0 0 1 | 1/7]

[0 0 0 | 0]

From the last row, we can see that 0z = 0, which means that z is a free variable. We can assign a parameter to z, say t, and solve for x and y in terms of t. From the first row, we have x + y - 2z = 0. Plugging in the values for x and y, we get x = 3z - 1 and y = -z + 1. Therefore, the general solution to the linear system is x = 3z - 1, y = -z + 1, where z is a free variable.

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The confidence coefficient for a 98% confidence interval is 2.33, indicating the number of standard deviations away from the mean.

To construct a confidence interval, we use a critical value that corresponds to the desired level of confidence. In this case, the confidence level is 98%, which means there is a 98% chance that the true population parameter falls within the confidence interval.

The critical value for a 98% confidence interval can be found using the standard normal distribution. Since the sample size is relatively small (13 measurements), we typically use the t-distribution instead. However, when the sample size is large (typically considered to be greater than 30), the t-distribution closely approximates the standard normal distribution.

For a 98% confidence level, the critical value is 2.33. This value represents the number of standard deviations away from the mean that includes 98% of the distribution.

Therefore, the correct answer is (D) 2.33 as the confidence coefficient for a 98% confidence interval.

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Answer: 80

Step-by-step explanation:

The number of ways to arrange the 11 donors in line is 11!. 11! = 39,916,800.

The donors can be in line in different ways.

To calculate the number of distinguishable ways, we can use the concept of permutations. Since all the donors are distinct (different blood types), we need to find the total number of permutations of these donors.

The total number of donors is 4 (type O+), 4 (type A+), and 3 (type B+), giving a total of 11 donors.

The number of ways to arrange these donors in line can be calculated using the formula for permutations. The formula for permutations of n objects taken all at a time is n!.

Therefore, the number of ways to arrange the 11 donors in line is 11!.

Calculating 11!, we get:

11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 39,916,800.

Hence, the donors can be in line in 39,916,800 different ways.

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Answer: 91 centimeters

Step-by-step explanation:

Answer:

91

Step-by-step explanation:

68+23=91

we need a sample size of at least 248 to have a probability of 0.8664 that the sample mean is within 0.8 of the population mean.

Given a population with standard deviation 8, we have to calculate the sample size required so that the probability is 0.8664 that the sample mean is within 0.8 of the population mean.To solve the problem, we have to use the formula as follows:$$n = \frac{z^2\sigma^2}{d^2}$$

Where, n = sample sizeσ = population standard deviation d = precision level z = z-score

So, z can be found using the standard normal table. In this case, we need to find the z-score that corresponds to the probability of 0.8664 plus half of the remaining probability of 1 - 0.8664, which is equal to 0.0668.Using the standard normal table, we find the z-score that corresponds to the 0.9334 probability, which is 1.48 (approximately).Now, we can substitute all the values into the formula and solve for n.$$n = \frac{z^2\sigma^2}{d^2}$$$$n = \frac{(1.48)^2 \cdot 8^2}{(0.8)^2}$$$$n = 247.15$$

Therefore, we need a sample size of at least 248 to have a probability of 0.8664 that the sample mean is within 0.8 of the population mean.

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The needed sample size is given as follows:

n = 250.

We first must use the z-score formula, as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).

The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

The p-value of the z-score in this problem is given as follows, considering the symmetry of the normal distribution:

0.5 + 0.8864/2 = 0.9432.

Hence the z-score is given as follows:

z = 1.58.

Then the sample size is obtained as follows:

[tex]1.58 = \frac{0.8}{\frac{8}{\sqrt{n}}}[/tex]

[tex]\sqrt{n} = 15.8[/tex]

n = 15.8²

n = 250.

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Answer:

55

Step-by-step explanation:

Answer:

#4 is B

#5 is also B

Step-by-step explanation:

i big brain

Answer:

4. b) [tex]4x^2-20xy+25y^2[/tex]

5. b) [tex]x^2+14x+49[/tex]

Step-by-step explanation:

4. [tex](2x-5y)^2[/tex]

First, one must rewrite the exponential equation as a multiplication problem,

[tex](2x-5y)(2x-5y)[/tex]

Now distribute, multiply every term in one of the parenthesis by every term in the other parenthesis,

[tex]=(2x-5y)(2x-5y)\\\\=(2x)(2x)+(2x)(-5y)+(-5y)(2x)+(-5y)(-5y)[/tex]

Now simplify the given expression,

[tex]=(2x)(2x)+(2x)(-5y)+(-5y)(2x)+(-5y)(-5y)\\\\=4x^2-10xy-10xy+25y^2[/tex]

Combine like terms,

[tex]=4x^2-20xy+25y^2[/tex]

5.[tex](x+7)^2[/tex]

To solve this problem, one should follow the same series of steps as they did to solve the last expression. First, rewrite the exponential expression as a multiplication problem.

[tex](x+7)(x+7)[/tex]

Now distribute, multiply every term in one of the parenthesis by every term in the other parenthesis,

[tex]=(x)(x)+(7)(x)+(7)(x)+(7)(7)[/tex]

Simplify the expression,

[tex]=(x)(x)+(7)(x)+(7)(x)+(7)(7)\\\\=x^2 + 7x + 7x + 49[/tex]

Finally, combine like terms,

[tex]=x^2+14x+49[/tex]

Answer:

lets divide the figure into two parts.

triangle base=2ft+2ft+6ft

triangle base=10ft

area of triangle = 1/2×base×height

area of triangle = 1/2×10ft×12ft

area of triangle =60ft²

area of square=side²

area of square=(6ft)²

area of square=36ft²

The value of e varies based on A. Oe=b - Pb e = 0 Oe=AtAb would be  (AT A)-1 AT b.

The given projection matrix is P = A(AT A)-1A".

We have been asked to find the value of e if A is invertible. Let's proceed further and solve this problem. First, we need to find the product of A and its transpose, i.e., AT A.A.T.A = [a11 a12 ... a1n] [a21 a22 ... a2n] ... [an1 an2 ... ann] = [Σ(ai1)(aj1) Σ(ai1)(aj2) ... Σ(ai1)(ajn)] [Σ(ai2)(aj1) Σ(ai2)(aj2) ... Σ(ai2)(ajn)] ... [Σ(ain)(aj1) Σ(ain)(aj2) ... Σ(ain)(ajn)]

The inverse of AT A is (AT A)-1. Thus, (AT A)-1 AT A = I.Where I is the identity matrix. So we get P = A(AT A)-1 A".

Now, the value of e can be calculated as: Oe = b - Pe = b - A(AT A)-1 A" b = A x (AT A)-1 x AT b

This is the expression for the solution of the least square problem and if A is invertible, we can find the solution by directly calculating A-1 x b which is nothing but e. Thus, the value of e is e = A-1b.

Substituting the given expression of e, we get e = (AT A)-1 AT b.

Thus, the correct answer is e = (AT A)-1 AT b.

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