if the null space of a 7 × 9 matrix is 3-dimensional, find rank a, dim row a, and dim col a.

Answer: ($2100+96d) + ($2755+116d)

               = $4855+212d

The standard error of the distribution of sample proportions is 0.032.

option C is the correct answer.

The standard error of the distribution of sample proportions is calculated as follows;

S.E = √(p (1 - p)) / n)

where;

The standard error of the distribution of sample proportions is calculated as;

S.E = √ ( 0.1 (1 - 0.1 ) / 90 )

S.E = 0.032

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Your question has been heard loud and clear

Passive voice

The matter will be looked into by him.

Thankyou

Answer:

0.976 or 97.6%

Step-by-step explanation:

To calculate the frequency of the recessive allele, we need to use the information provided about the frequency of the dominant trait.

Let's assume that the particular dominant trait is determined by a single gene with two alleles: the dominant allele (A) and the recessive allele (a).

Given that 45 out of 1,000 babies are born with the dominant trait, we can infer that the remaining babies (1,000 - 45 = 955) do not have the dominant trait and can be considered as the recessive trait carriers.

The frequency of the recessive allele (q) can be calculated using the Hardy-Weinberg equation:

q = sqrt((Recessive individuals) / (Total individuals))

In this case, the total number of individuals is 1,000, and the number of recessive individuals is 955.

q = sqrt(955 / 1,000)

Using a calculator, we can find the value:

q ≈ 0.976

Therefore, the frequency of the recessive allele is approximately 0.976 or 97.6%.

To find the Maclaurin series for the function f(x) = 12e^x cos(x), we can use the known Maclaurin series expansions for e^x and cos(x), and then multiply the series together.

The Maclaurin series expansion for e^x is:

e^x = 1 + x + (x^2)/2! + (x^3)/3! + ...

The Maclaurin series expansion for cos(x) is:

cos(x) = 1 - (x^2)/2! + (x^4)/4! - ...

Multiplying the two series together term by term, we get:

f(x) = 12e^x cos(x)

= 12(1 + x + (x^2)/2! + (x^3)/3! + ...)(1 - (x^2)/2! + (x^4)/4! - ...)

Expanding the product and collecting like terms, we obtain:

f(x) = 12(1 - (x^2)/2! + (x^4)/4! - ...) + 12(x - (x^3)/2! + (x^5)/4! - ...) + 12((x^2)/2! - (x^4)/4! + (x^6)/6! - ...) + ...

Simplifying, we can write the first three nonzero terms of the series as:

f(x) = 12 + 12x - 4x^3 + ...

Therefore, the first three nonzero terms in the Maclaurin series for f(x) = 12e^x cos(x) are 12, 12x, and -4x^3

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Answer: The missing values represented by x and y are 8 and 20, that is;

(x, y) = (8, 20)

Step-by-step explanation: The function y = 16 + 0.5x is a linear equation that can be solved graphically. This means the values of both variables x and y can be found on different points along the straight line graph.

The ordered pairs simply means for every value of x, there is a corresponding value of y.

The 2-column table has values for x and y which all satisfy the equation y = 16 + 0.5x. Taking the first row for example, the pair is given as (-4, 14).

This means when x equals negative 4, y equals 14.

Where y = 16 + 0.5x

y = 16 + 0.5(-4)

y = 16 + (-2)

y = 16 - 2

y = 14

Therefore the first pair, just like the other four pairs all satisfy the equation.

Hence, looking at the options given, we can determine which satisfies the equation

(option 1) When x = 0

y = 16 + 0.5(0)

y = 16 + 0

y = 16

(0, 16)

(option 2) When x = 5

y = 16 + 0.5(5)

y = 16 + 2.5

y = 18.5

(5, 18.5)

(option 3) When x = 8

y = 16 + 0.5(8)

y = 16 + 4

y = 20

(8, 20)

From our calculations, the third option (8, 20)  is the correct ordered pair that would fill in the missing values x and y.

Answer:

The missing values represented by x and y are 8 and 20, that is;

(x, y) = (8, 20)

Step-by-step explanation:

It is proved that if f has a zero at 0 and if Ref(z) > 0 for every ze aD(0; 1), then f has a pole in D(0; 1).

The problem is based on Complex Analysis.

Let U CC be a region containing D(0; 1) and let f be a meromorphic function on U, which has no zeros and no poles on aD(0; 1).

If f has a zero at 0 and if Ref(z) > 0 for every ze aD(0; 1), we need to prove that f has a pole in D(0; 1).

We know that f is meromorphic function on U and we are given that it has a zero at 0. So, we can write the Laurent expansion of f around 0 as: f(z) = anzn+ ... + a1z + a0 + b1z + ... where an ≠ 0 and the expansion is valid in a deleted neighborhood of z=0. This implies that f(z) has a pole of order m at 0 where m is the largest non-negative integer such that am ≠ 0.

Suppose that m = 0 and f(z) has a removable singularity at 0 then by Riemann’s theorem f(z) is bounded in some deleted neighborhood of z = 0 which implies that Ref(z) ≤ M, a contradiction to Ref(z) > 0 for every ze aD(0; 1).

Hence, f(z) has a pole at 0. Therefore, f has a pole in D(0; 1). Hence, we have proved that if f has a zero at 0 and if Ref(z) > 0 for every ze aD(0; 1), then f has a pole in D(0; 1).

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Uncle Makhosi needs approximately 1.56 kilograms of butter.

To determine the amount of butter in kilograms, we'll use the conversion rate of 1 kg = 2.25 pounds.

First, we need to convert 3 and a half pounds to a decimal form. Since half a pound is equal to 0.5 pounds, we can express 3 and a half pounds as 3.5 pounds.

Next, we'll use the conversion rate to calculate the equivalent weight of 3.5 pounds in kilograms:

3.5 pounds * (1 kg / 2.25 pounds) = 1.56 kilograms (rounded to two decimal places).

To summarize, based on the given conversion rate of 1 kg = 2.25 pounds, Uncle Makhosi requires approximately 1.56 kilograms of butter to fulfill his 3 and a half pound requirement. This conversion can be useful when dealing with different units of measurement, allowing us to easily switch between kilograms and pounds.

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By finding the slopes of the two segments we can see that the segments are not parallel nor perpendicular.

The slope for a segment whose endpoints are:

(x₁, y₁) and (x₂, y₂) is:

slope = (y₂ - y₁)/(x₂ - x₁)

Two segments are:

Segment AB has endpoints (-1, -1) and (1, 5), so the slope is:

s = (5 + 1)/(1 + 1) = 3

For segment CD the endpoints are (1, 2) and (5, 4), so the slope is:

s' = (4 - 2)/(5 - 1) = 2/4 = 1/2

So the slopes are different and their product is obviously not -1, then the lines are neither parallel nor perpendicular.

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Answer:

16

Step-by-step explanation:

75% is the same as 0.75, or 75/100, or 3/4, so all you have to do is multiply 20 by 3/4 to get your answer of 16!

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

hmmm now, if we look at the coordinates above, well, notice, the y-coordinates are the same -2, that means is a horizontal line, and thus it has an slope of "0", now, we can just go through the rigamarole of rise/run and get the same thing.

\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-2)}}} \implies \cfrac{-2 +2}{3 +2} \implies \cfrac{ 0 }{ 5 } \implies \text{\LARGE 0}\)

Answer:

330 television set

Step-by-step explanation:

Last month production = 880 television sets

This month production = 1,210 television sets

The increase in production from last month to this month = This month production - Last month production

= 1,210 - 880

= 330

The increase in production from last month to this month = 330 television set

As per linear equation, the increase in production of television of the factory is 330.

A linear equation is an equation where the variable has the highest power of 1.

Given, a factory produced 880 television sets last month.

This month, the same factory produced 1,210 television sets.

Therefore, the increase in production of television of the factory is

\(= (1210-880)\\= 330\)

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The two expressions that are equivalent to sin(θ) are sin²(θ) and 1 - cos²(θ). These expressions represent different trigonometric identities that relate the sine function to other trigonometric functions.

The given expression sin(θ) can be rewritten in two equivalent forms: sin²(θ) and 1 - cos²(θ).

sin²(θ): This expression represents the square of the sine function. It means taking the sine of θ and squaring the result. The square of the sine function is equivalent to multiplying sin(θ) by itself, which matches the given expression sin(θ).

1 - cos²(θ): This expression is based on a trigonometric identity known as the Pythagorean identity, which states that sin²(θ) + cos²(θ) = 1. By rearranging the equation, we can isolate sin²(θ) as 1 - cos²(θ). Therefore, this expression is also equivalent to sin(θ).

These equivalent expressions arise from the fundamental relationships among trigonometric functions and their identities. By manipulating these identities, we can derive various equivalent forms of a given trigonometric expression, as seen with sin(θ).

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The conjecture that describes the pattern in the sequence is current term is 2 added to the previous term and the next term is 10

The sequence is given as:

0, 2, 4, 6, 8

In the above sequence, we can see that each current term is 2 added to the previous term

i.e.

Tn = 2 + Tn-1

Using the above conjecture, we have

Next term = 8 + 2

Evaluate

Next term = 10

Hence, the conjecture that describes the pattern in the sequence is current term is 2 added to the previous term and the next term is 10

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To determine the amount of wrapping paper needed to wrap a cylindrical gift with a diameter of 8 meters and a height three times the radius, we need to find the surface area of the cylinder.

The diameter is 8 meters, so the radius (r) is half of that, which is 4 meters. The height (h) is three times the radius, so it is 3 * 4 = 12 meters.

The surface area of a cylinder is given by the formula: A = 2πr(h + r)

Plugging in the values, we get: A = 2 * π * 4 * (12 + 4) = 2 * π * 4 * 16 = 128π square meters.

So, it would take approximately 128π square meters of wrapping paper to wrap the cylindrical gift.

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Answer:

it's the first one.

LETTER "A"

Answer:

Step-by-step explanation:

tis A

The area of the region inside the rose r = 6sin(30°) and outside the circle r = 3 is 9π square units.

To find the region inside the rose r = 6sin(30°) and outside the circle r = 3, we need to set up the integral for the area of this region.

First, let's determine the limits of integration for the angle θ. The rose curve completes one full rotation for θ ranging from 0 to 2π (360°). So, we will integrate with respect to θ from 0 to 2π.

The area element in polar coordinates is given by dA = (1/2) r^2 dθ. In this case, the region lies between two curves, so the integral for the area is:

A = ∫[0 to 2π] [(1/2)\((6sin(30))^2 - (1/2) (3)^2\)] dθ

Simplifying the expression:

A = ∫[0 to 2π] [(1/2) (36sin^2(30°) - 9)] dθ

Now we can evaluate this integral to find the area of the region inside the rose and outside the circle.To evaluate the integral for the area of the region inside the rose r = 6sin(30°) and outside the circle r = 3, we will integrate the expression:

A = ∫[0 to 2π] [(1/2) (36sin^2(30°) - 9)] dθ

First, let's simplify the expression inside the integral:

A = ∫[0 to 2π] [(1/2) (36(1/2) - 9)] dθ

= ∫[0 to 2π] [(1/2) (18 - 9)] dθ

= ∫[0 to 2π] (1/2) (9) dθ

= (1/2) (9) ∫[0 to 2π] dθ

= (1/2) (9) [θ] from 0 to 2π

= (1/2) (9) (2π - 0)

= (1/2) (9) (2π)

= 9π

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Answer:

Explanation:

sum of the power of 2x^2y=2+1=3

sum of the power of 4x^5=5

sum of the power of 6xy^3=1+3=4

Highest power=5

Therefore, The degree of given polynomial is 5.

Hope this helps...

Good luck on your assignment..

Answer:

4296 kg

Step-by-step explanation:

40/100 = x/7160

716 times 6 is 4296

Answer: C on edge

Step-by-step explanation:

The rectangular form of the parametric equations x = 4cos(t) – 3 and y = 5sin(t) + 2 is shown in the option third, option third is correct.

A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.

The missing options are in the attached picture please refer to the picture.

We have two parametric equations:

x = 4cos(t) – 3 and

y = 5sin(t) + 2

From the options plug x and y values in the equation:

\(\rm \dfrac{(x+3)^2}{16}+\dfrac{(y-2)^2}{25}=1\\\)

\(\rm \dfrac{(4cos(t)-3+3)^2}{16}+\dfrac{(5sin(t)+2-2)^2}{25}=1\\\)

\(\rm \dfrac{(4cos(t))^2}{16}+\dfrac{(5sin(t))^2}{25}=1\\\)

cos²t + sin²t = 1  (true)

Thus, the rectangular form of the parametric equations x = 4cos(t) – 3 and y = 5sin(t) + 2 is shown in the option third, option third is correct.

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The weight of each beef will be 6⁴

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

From the information, in a butcher shop, each slab of beef weighs 6^7 pounds and there are 6^3 containers filled with beef, the weight of each beef will be:

= Total pounds / Container

= 6^7 / 6^3.

= 6^(7 - 3).

= 6^4

The weight is 6⁴.

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Answer:

4

Step-by-step explanation:

u divide 14 by 2 and then subtract 3

hope this helps!

Answer:

About 31.8%

Step-by-step explanation:

56/175 would get you your answer.

but i'm a bit rusty on how to do this

The equation of the line passing through the points (18, -5) and (-4, 13) in slope-intercept form is \(y = -\frac{9}{11}x + \frac{107}{11}\), the equation of the line with x-intercept 107/0 and a slope of 0 is y = 0.

The equation of line in slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

a)

To determine the equation of the line passing through the points (18, -5) and (-4, 13).

First, we find the slope m:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\\ \\m = \frac{13 -(-5)}{-4 - 18} \\\\m = \frac{13 + 5}{-4 - 18} \\\\m = \frac{18}{-22} \\\\m = -\frac{9}{11}\)

Now, plug the slope m = -9/11 and point (18, -5) into the point-slope form and simplify:

( y - y₁ ) = m( x - x₁ )

\(y - (-5) = -\frac{9}{11}( x - 18 )\\ \\y + 5 = -\frac{9}{11}x + \frac{162}{11} \\\\y = -\frac{9}{11}x + \frac{162}{11} - 5\\\\y = -\frac{9}{11}x + \frac{107}{11}\)

The equation of the line is \(y = -\frac{9}{11}x + \frac{107}{11}\).

b)

To find the equation of the line that has the same x-intercept as the line above, but has a slope of 0.

First, we find the x-intercept:

\(y = -\frac{9}{11}x + \frac{107}{11}\\\\0 = -\frac{9}{11}x + \frac{107}{11}\\\\\frac{9}{11}x = \frac{107}{11}\\\\x = \frac{9}{11} / \frac{107}{11}\\\\x = \frac{107}{9}\)

Now, a line of slope of 0 is a horizontal line regardless of the x-intercept:

y = 0

Therefore, the equation of the line with x-intercept 107/0 and a slope of 0 is y = 0.

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Step-by-step explanation:

since sqrt(25)×sqrt(25) = 25, then x can be any number, because x = x in all cases. and then both sides of the equation are always equal, no matter what value we give x, as long as x is a factor in both sides.

sqrt(25)×x×sqrt(25) = 25x

is always true for every x.

if the question would be

sqrt(25)×x×sqrt(25) = 25

then the answer can only be x = 1. because for every other value of x the equality is destroyed.

Answer:

See below

Step-by-step explanation:

g (h(6))   :

   h (6) =  3 ( 6^2) + 2 = 110

   then g (110) =   sqrt (110)

h (g(5))

    g(5) = sqrt 5

        then h( sqrt5) = 3 ( sqrt5)^2 + 2 = 17

An inertial frame is a non-accelerating reference frame, while a non-inertial frame is accelerating or rotating. The principal axes of a rigid body are the axes of maximum, minimum, and intermediate moments of inertia.

An inertial frame is a reference frame that obeys Newton's first law of motion, where objects at rest stay at rest and objects in motion continue moving at a constant velocity unless acted upon by external forces. In contrast, a non-inertial frame experiences acceleration or rotation, causing deviations from the laws of Newtonian physics.

An example of an inertial frame is a spaceship moving at a constant speed in outer space, while a car accelerating or a spinning amusement park ride represent non-inertial frames.

The principal axes of a rigid body are three perpendicular axes passing through its center of mass. Along these axes, the moments of inertia of the body take their maximum, minimum, and intermediate values. The principal axes determine the body's orientation and rotational behavior.

Understanding the distinction between inertial and non-inertial frames and the concept of principal axes provides a foundation for analyzing motion and rotational dynamics in different physical scenarios.

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