T/F : A determinant of an nÃn matrix can be defined as a sum of multiples of determinants of (nâ1)Ã(nâ1) submatrices.

To determine if the mean launch temperature for flights with o-ring damage is significantly less than for flights with no o-ring damage, we can perform a two-sample t-test with equal variances. Here are the steps:

Step 1: Calculate the sample means and standard deviations for each group:

For flights with o-ring damage:

Sample mean: (43 + 57 + 58 + 63 + 70 + 70 + 75) / 7 = 63.14

Sample standard deviation: 13.42

For flights with no o-ring damage:

Sample mean: (66 + 67 + 67 + 67 + 68 + 69 + 70 + 70 + 72 + 73 + 75 + 76 + 76 + 78 + 79 + 81) / 16 = 72.56

Sample standard deviation: 5.69

Step 2: Calculate the pooled standard deviation:

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

where:

n1 = sample size of flights with o-ring damage = 7

n2 = sample size of flights with no o-ring damage = 16

s1 = sample standard deviation of flights with o-ring damage = 13.42

s2 = sample standard deviation of flights with no o-ring damage = 5.69

s_p = sqrt(((7-1)*13.42^2 + (16-1)*5.69^2) / (7+16-2)) = 9.88

Step 3: Calculate the t-test statistic:

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

where:

x1 = sample mean of flights with o-ring damage = 63.14

x2 = sample mean of flights with no o-ring damage = 72.56

s_p = pooled standard deviation = 9.88

n1 = sample size of flights with o-ring damage = 7

n2 = sample size of flights with no o-ring damage = 16

t = (63.14 - 72.56) / (9.88 * sqrt(1/7 + 1/16)) = -2.70

Step 4: Calculate the degrees of freedom:

df = n1 + n2 - 2 = 7 + 16 - 2 = 21

Step 5: Determine the critical value of t at 5% level of significance and the corresponding p-value:

At 5% level of significance and 21 degrees of freedom, the critical value of t is ±2.08 (from a t-distribution table or calculator).

The p-value for a two-tailed test with t = -2.70 and df = 21 is 0.013 (from a t-distribution table or calculator).

Step 6: Compare the t-test statistic with the critical value and the p-value with the level of significance:

Since the absolute value of the t-test statistic (-2.70) is greater than the critical value of t at 5% level of significance (2.08), we reject the null hypothesis and conclude that there is a significant difference in mean launch temperature between flights with o-ring damage and flights with no o-ring damage.

Moreover, the p-value (0.013) is less than the level of significance (0.05), providing further evidence to reject the null hypothesis.

Therefore, we can say that the mean launch temperature for flights with o-ring damage is significantly less.

Answer:

To find the inverse of g(x) we need to interchange x and y, as follows:

y = 3x - 7

x = 3y -7

3y = x + 7

Step-by-step explanation:

YOUR WELCOME

\(\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}\)

To find g(4), we have to substitute the variable x with 4 on the expression g(x) ~

\(\qquad \sf  \dashrightarrow \: g(x) = 3x - 7\)

\(\qquad \sf  \dashrightarrow \: g(4) = 3(4)- 7\)

\(\qquad \sf  \dashrightarrow \: g(4) = 12- 7\)

\(\qquad \sf  \dashrightarrow \: g(4) =5\)

Answer:

A = 8 and B = -2 and the equation is:

8x - 2y = -24

Step-by-step explanation:

Line intercepts

Any non-horizontal and non-vertical line has two intercepts: The y-intercept is the point where the line crosses the y-axis, and the x-intercept is the point where the line crosses the x-axis, also called the zero or root.

We are given the equation:

Ax+By=-24

The x-intercept is (-3,0). Substituting the values of x and y:

A(-3)+B(0)=-24

Operating:

-3A = -24

Dividing by -3:

A = -24 / (-3) = 8

A = 8

The y-intercept is (0,12). Substituting and using the just-found value of A

8(0)+B(12)=-24

Operating:

12B = -24

Solving:

B = -2

Thus, A = 8 and B = -2 and the equation is:

8x - 2y = -24

Answer:

The first choice

Step-by-step explanation:

7/8 x + 3/4 = -6

6 (x/8) + 3/4 = -6

Answer:

paper and pencil

Step-by-step explanation:

get a paper then a pencil and solve it

-6 × 2 + 6 × 200.

Hope this helps! :D - your friendly neighborhood Jxro!

The values of cos(A) and sin(A) are cos(A) = 0.96 and sin(A) = 0.28

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

The coordinates of C are (0.96, 0.28).

In a unit circle,

(x, y) = (cos, sin)

Using the above as a guide, we have the following:

x = 0.96

y - 0.28

This means that

cos(A) = 0.96

sin(A) = 0.28

Hence, the values of cos(A) and sin(A) are cos(A) = 0.96 and sin(A) = 0.28

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Using the Euler's formula, the number of segments in the pentagonal prism is: 15.

The Euler's formula is given as,  F + V = E + 2, where:

Given that the pentagonal prism has the following dimensions:

Plug in the values into the Euler's formula, F + V = E + 2:

7 + 10 = E + 2

17 - 2 = E

E = 15

Therefore, using the Euler's formula, the number of segments in the pentagonal prism is: 15.

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Answer:

6x2 + 16x = 672

Reorder the terms:

16x + 16x2 = 672

Solving

16x + 16x2 = 672

Solving for variable 'x'.

Reorder the terms:

-672 + 16x + 16x2 = 672 + -672

Combine like terms: 672 + -672 = 0

-672 + 16x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.

16(-42 + x + x2) = 0

Factor a trinomial.

16((-7 + -1x)(6 + -1x)) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying

-7 + -1x = 0

Solving

-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0

0 + -1x = 0 + 7

-1x = 0 + 7

Combine like terms: 0 + 7 = 7

-1x = 7

Divide each side by '-1'.

x = -7

Simplifying

x = -7

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying

6 + -1x = 0

Solving

6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.

6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0

0 + -1x = 0 + -6

-1x = 0 + -6

Combine like terms: 0 + -6 = -6

-1x = -6

Divide each side by '-1'.

x = 6

Simplifying

x = 6

Solution

x = {-7, 6}

Step-by-step explanation:

The given quadratic function models the projectile of the object as it is

launched off the top of the building.

The interpretation of the function values are;

The appropriate domain is 0 ≤ x ≤ 7

Reasons:

The given function for the height of the object is f(x) = -16·x² + 16·x + 672

The domain is given by the values of x for which the value of y ≥ 0

Therefore, when -16·x² + 16·x + 672 = 0, we get;

-16·x² + 16·x + 672 = 0

16·(-x² + x + 42) = 0

-x² + x + 42 = 0

x² - x - 42 = 0

(x - 7)·(x + 6) = 0

x = 7, or x = -6

The minimum value of time, x is 0, which is the x-value at the top of the

building, and when x = 7, the object is on the ground.

Therefore;

The maximum value of f(x) = a·x² + b·x + c, is given at \(x = -\dfrac{b}{2 \cdot a}\)

Therefore;

We have;

\(x = -\dfrac{16}{2 \times (-16)} = \dfrac{1}{2}\)

Which gives;

\(f \left(\frac{1}{2} \right) = -16 \times \left(\dfrac{1}{2} \right)^2 + 16 \times \left(\dfrac{1}{2} \right)+ 672 = 676\)

The height of the building is given when the time, x = 0, as follows;

Height of building, f(0) = -16 × 0² + 16 × 0 + 672 = 672

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Answer:

is the order 2,4,8,10, and then 3?

or is it 2/3, 4/3, 8/3/ 10/3?

Step-by-step explanation:

Answer:

who friendhjcicivigigivigigogogig'g

Answer:

A) \(y = 3x - 4\)

Explanation:

Slope-intercept form is y = mx + b

Answer:

y=70°(base angle of isosceles triangle)

in triangle ABC

70°+x°+y°=180°{sum of interior angle triangle}

70+x+70=180

x=180-140=40°

Step-by-step explanation:

x=40

y=70

Answer:

The function represents the height of the water in the bucket

Step-by-step explanation:

Given

\(f(t) = -t^2 + 4t\)

Required

State what the function represents

From the question, we understand that t represents the time spent while the function illustrates the water level in the bucket.

This implies that f(t) calculates the height of the water in the bucket, given the value of time (t)

Answer:

2^(3/7)

Step-by-step explanation:

For these types of questions, what is inside the root is the numerator, and what is on top is the denominator.

3 is in the root, so it is the numerator

7 is outside the root, so it is the denominator

Therefore, The answer is 2^(3/7)

Answer:

5

Step-by-step explanation:

The number of apples bought by him is 113.

A grouping of variables, symbols, and/or numbers used to represent a mathematical quantity or relationship is known as an expression in mathematics. Expressions might be straightforward with just one number or variable or complex with many terms, operations, and functions.

Let's assume that Sam bought x number of apples.

He bought them at 60 cents each, which means the total cost of buying these apples was:

Cost price = 60x cents

He sold all but 5 of these apples at R1.00 each, which means the total revenue he earned from selling them was:

Revenue = (x - 5) x R1.00 = R(x - 5)

Sam made a profit of R5.00, which means his revenue was more than his cost price by R5.00. We can write this as:

Revenue - Cost price = R5.00

Substituting the values of revenue and cost price from above, we get:

R(x - 5) - 60x = 500 cents

Rearranging and simplifying this equation, we get:

40x = 500 + 5R

Substituting R = R1.00, we get:

40x = 500 + 5 = 505

Solving for x, we get:

x = 12.625

Since Sam cannot buy a fraction of an apple, we round up x to the nearest integer:

x = 13

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The values of x for which f(x) = g(x) are x = (1 + √13) / 2 and x = (1 - √13) / 2

To find the values of x for which f(x) is equal to g(x), we need to set the two functions equal to each other and solve for x.

Setting f(x) equal to g(x):

x^2 - 4 = x - 1

Rearranging the equation:

x^2 - x - 3 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -1, and c = -3. Substituting these values into the quadratic formula:

x = (1 ± √((-1)^2 - 4(1)(-3))) / (2(1))

Simplifying further:

x = (1 ± √(1 + 12)) / 2

x = (1 ± √13) / 2

Therefore, the values of x for which f(x) = g(x) are:

x = (1 + √13) / 2

x = (1 - √13) / 2

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The maximum number of months the computer could be kept so that it is cheaper to rent than to buy is 10 months.

The first step is to determine the month in which the two options would have the same cost. The equation that can be used to determine this value is:

$1890 = $900 + 90t

90t = 1890 - 900

90t = 990

t = 990 / 90

t  = 11 months

The maximum number of months = 11 months - 1 = 10 months

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Answer:14 in 2 days

Step-by-step explanation:

Answer:

\(-13+12p-4=6\left(2p-1\right)\)

\(-13-4=-17\)

\(12p-17=6\left(2p-1\right)\)

\(12p-17=12p-6\)

\(12p-17+17=12p-6+17\)

\(12p=12p+11\)

\(12p-12p=12p+11-12p\)

\(0=11\)

There is No Solution

The radius of the cone is 783.84/√h

A cone is the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex).

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of a cone is expressed as;

V = 1/3πr²h

643072 × 3 = 3.14 × r²h

r²h = 614400

r² = 614400/h

r = 783.84/√h

therefore the radius of the cone is 783.84/√h

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Pareto distribution is a member of a scale family referring fixed values of the shape parameter, it is trivially closed under scale transformations.

The Pareto distribution is a power-law probability distribution used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena. It was initially applied to demonstrate the distribution of wealth in a society, fitting the trend that a large portion of wealth is held by a small fraction of the population. The pareto principle or 80-20 rule states that 80% of outcomes are due to 20% of causes. Pareto distribution is a member of the scale family distribution which is parameterized by a scale parameter. The larger the scale parameter, the more spread out the distribution.

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Answer:

DO you go to a connexus school? I do and i have this same project im trying to find answers to!

Step-by-step explanation:

For the first box the volume, surface area, and cost of materials are 180 cubic inches, 258 square inches, and $12.9, for the second box 192 cubic inches, 224.4 square inches, and $11.22 for the third box 235.61 cubic inches, 227.76 square inches, and $11.38.

It is defined as a three-dimensional space enclosed by an object or thing.

For the first cereal box:

Volume = L×W×H

Here L = 7.5 in, W = 2 in, and H = 12 in

Volume = 7.5×2×12 = 180 cubic inches

Surface area = 2(L×B+B×H+H×L)

= 2(7.5×2+2×12+12×7.5)

= 2(15+24+90)

= 258 square inches

Cost for this cereal box = 258×0.05 = $12.9

For the second cereal box:

\(\rm Volume = \frac{1}{3} bh\)

b is the area and h, is the height of the pyramid.

b = 8×6 = 48 square inches, h = 12 inches

\(\rm Volume = \frac{1}{3} \times48\times12\)

Volume = 192 cubic inches

\(\rm Surface \ area = b+\frac{1}{2} ps\)

p is the perimeter of the base = 2(8+6) = 28 in

Slant height s = 12.6 in

\(\rm Surface \ area = 48+\frac{1}{2} (28)(12.6)\) = 224.4 square inches

Cost of this cereal box = 224.2×0.05 = $11.22

For the third box:

Volume = πr²h

r = 2.5 in and h = 12 in

Volume = π(2.5)²(12) = 235.61 cubic inches

Surface area = 2πr(h+r) = 2π(2.5)(12+2.5) = 227.76 square inches

Cost of this cereal box = 227.76×0.05 = $11.38

Thus, for the first box the volume, surface area, and cost of materials are 180 cubic inches, 258 square inches, and $12.9, for the second box 192 cubic inches, 224.4 square inches, and $11.22 for the third box 235.61 cubic inches, 227.76 square inches, and $11.38.

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Answer: I know two methods of solving both of the sums. One is the method of elimination, the other is method of substitution. You can do any of the given methods which is easier for you. Both methods will be shown below:

1) 5x + y = 9       - - - - (i)
  10x - 7y = - 18 - - - - (ii)

eq. (i) multiplied by 2
   10x + 2y = 18  - - - - (i)
   10x - 7y = - 18 - - - - (ii)       {subtraction of eq. (ii) from eq. (i)}
    0   + 9y = 36
              y = 36/9
              y = 4

From eq. (i),
   5x + y = 9
-> 5x + 4 = 9
-> 5x = 9 - 4
->  x = 5/5
-> x = 1

So, x = 1 and y = 4

2) - 4x + 9y = 9 - - - - (i)
      x - 3y = - 6 - - - - (ii)

eq. (ii) multiplied by 3
    - 4x + 9y = 9 - - - - (i)
     3x - 9y  = - 18 - - (ii)        {addition of eq. (ii) and eq. (i)}
      - x + 0 = - 9
              x  =  9

From eq. (ii),
    x - 3y = - 6
->  9 - 3y = - 6
->  - 3y = -6-9
->  y = -15/-3
->  y = 5

So, x = 9 and y = 5

1) 5x + y = 9       - - - - (i)
  10x - 7y = - 18 - - - - (ii)

eq. (i)

  5x + y = 9
-> y = 9 - 5x

Value of eq. (i) in eq. (ii)
   10x - 7y = - 18
-> 10x - 7(9 - 5x) = - 18
-> 10x - 63 + 35x = - 18
-> 45x = - 18 + 63
-> x = 45/45
-> x =  1

From eq. (i),
   5x + y = 9
-> 5 + y = 9
-> y = 9 - 5
-> y = 4

So, x = 1 and y = 4

2) - 4x + 9y = 9 - - - - (i)
      x - 3y = - 6 - - - - (ii)

eq. (i)
   - 4x + 9y = 9
-> - 4x = 9 - 9y
-> x = (9 - 9y) / -4

Value of eq. (i) in eq. (ii)
      x - 3y = - 6
-> (9 - 9y) / -4  -3y = - 6
-> (9 - 9y + 12y) = - 6 * - 4
-> 3y = 24 - 9
-> y = 15/3
-> y =  5

From eq. (ii)
   x - 3y = - 6
-> x - 3(5) = - 6
-> x - 15 = - 6
-> x = - 6 + 15
-> x = 9

So, x = 9 and y = 5

∩_∩
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┏━∪∪━━━━┓
   hope it helped
┗━━━━━━━┛

Answer:

1 = 51  

2=18    

3=123

4=39

Step-by-step explanation:

Answer:

Step-by-step explanation:

M = {Prime integers between 1 and 11} and N = { factors of 12}. Find:

The members of M

The members of N

M∪N; M = {Prime integers between 1 and 11} and N = { factors of 12}. Find:

The members of M

The members of N

M∪N; M = {Prime integers between 1 and 11} and N = { factors of 12}. Find:

The members of M

The members of N

M∪N; M = {Prime integers between 1 and 11} and N = { factors of 12}. Find:

The members of M

The members of N

M∪N; M = {Prime integers between 1 and 11} and N = { factors of 12}. Find:

The members of M

The members of N

M∪N;

Answer:

Step-by-step explanation:

Sets in full are

Combined set

Common set

The statement "Consistent system of equations has at least one solution, and an inconsistent system has no solution" is true.

In the context of systems of linear equations, a consistent system refers to a system where there exists at least one solution that satisfies all the equations in the system. This means that the equations can be simultaneously satisfied by a set of values for the variables.

On the other hand, an inconsistent system refers to a system of equations that has no solution. This occurs when the equations are contradictory or cannot be satisfied simultaneously by any values for the variables.

Therefore, a consistent system guarantees the existence of at least one solution, while an inconsistent system does not have any solution.

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The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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Answer:

(1, 3 )

Step-by-step explanation:

The solution is at the point of intersection of the 2 lines

The lines intersect at (1, 3 ) , then

solution is (1, 3 )

Answer:

he walked 15 feet in total

Step-by-step explanation:

I'm not sure if u asked a question or not