The sides of a square increase in length at a rate of ​m/sec. a. At what rate is the area of the square changing when the sides are m​ long? b. At what rate is the area of the square changing when the sides are m​ long?

The vector parameterization for the line passing through the points (1, 1, -1) and (6, -9, 4) is:

x = 1 + 5t

y = 1 - 10t

z = -1 + 5t

To find a vector parameterization for the line passing through the points (1, 1, -1) and (6, -9, 4), we can use the vector equation of a line:

r = a + t * d

where r is the position vector of any point on the line, a is a known point on the line, t is a parameter, and d is the direction vector of the line.

First, let's find the direction vector d. We can subtract the coordinates of the two points to obtain the direction vector:

d = (6, -9, 4) - (1, 1, -1)

= (5, -10, 5)

Now, we can choose one of the given points, say (1, 1, -1), as our known point a.

Substituting these values into the vector equation, we have:

r = (1, 1, -1) + t * (5, -10, 5)

So, the vector parameterization for the line passing through the points (1, 1, -1) and (6, -9, 4) is:

x = 1 + 5t

y = 1 - 10t

z = -1 + 5t

where t is a real number that can vary to give different points along the line.

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The correct option is (c) O √173. In a right triangle ABC, with right angle C, AB = 13, and BC = 2. We need to find the length of the missing side.

We can use the Pythagorean theorem to find the length of the missing side.Pythagorean Theorem:In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a² + b² = c²

Where a and b are the two legs of the right triangle and c is the hypotenuse of the right triangle. Given AB = 13 and BC = 2, we can find AC by using the Pythagorean Theorem as follows:

AC² = AB² + BC²AC² = 13² + 2²AC² = 169 + 4AC² = 173AC = √173. The length of the missing side, AC, is √173.

Hence, the correct option is (c) O √173.

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Answer:

  16°

Step-by-step explanation:

The trig function tangent relates an acute angle of a right triangle to the measures of the adjacent and opposites sides. Those are the sides given here, so the relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(?) = 14/49 = 2/7

When the tangent of the angle is known, the inverse tangent function can be used to find the angle:

  ? = arctan(2/7) ≈ 16°

The value of "?" is about 16°.

Answer:

the answer for first is 3

second is 4

Answer: 57.8

Step-by-step explanation:48.7 seconds + 49.3 seconds.= 57.8

In a given year, an economy has 10 million unemployed workers and 120 million employed workers. This information provides a snapshot of the labor market and indicates the number of individuals who are currently without jobs and those who are employed.

The information states that in the given year, there are 10 million unemployed workers and 120 million employed workers in the economy. This data provides a measure of the labor market situation at a specific point in time.

Unemployed workers refer to individuals who are actively seeking employment but currently do not have a job. The number of unemployed workers can be an important indicator of the health of an economy and its ability to provide job opportunities.

Employed workers, on the other hand, represent individuals who have jobs and are currently working. The number of employed workers indicates the size of the workforce that is actively contributing to the economy through productive activities.

By knowing the number of unemployed and employed workers, policymakers, economists, and analysts can assess factors such as labor market conditions, unemployment rates, and workforce participation rates. This information is crucial for formulating policies, understanding economic dynamics, and monitoring the overall health and functioning of the economy.

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Answer:

That number rounds to the nearest hundredth to this number: 382.99

Answer:

Step-by-step explanation:

t22 = a + (n- 1)d

t22 = 3 + 21*4

t22 = 3 + 84

t22 = 87

Answer: a constant

Step-by-step explanation:

A constant is a numerical expression like 2, 0,78 etc .

A variable is a alphabetical expression that vary like a,b,c,d,x,y,z.

An expression can consists of both numerical and alphabets and also any arithmetic expression like x, 2abc, 6a+2c etc

A term consist of either numbers and variables multiplied together or only numbers or variable like 2xy, x, 2ab etc.

X is all (a term, a variable , an expression) except a constant because a constant is a numerical expression.

Answer: D, a constant

Step-by-step explanation: A constant is an expression without variables.

The probability that the total sum of all rolls does not exceed 375 is approximately 0.7165

Assuming the die is a fair six-sided die, the possible outcomes for each roll are numbers 1 through 6, each with a probability of 1/6.

Let X be the total sum of all rolls. Then X follows a discrete uniform distribution with parameters n = 104 (number of rolls) and a = 1 (minimum value of each roll). The expected value of X is:

E(X) = n × (a + b) / 2 = 104 × (1 + 6) / 2 = 365

The variance of X is

Var(X) = n × (b - a + 1)^2 / 12 = 104 × 6^2 / 12 = 312

The standard deviation of X is

SD(X) = sqrt(Var(X)) = sqrt(312) = 17.67

To calculate the probability that the total sum of all rolls does not exceed 375, we need to calculate the cumulative distribution function (CDF) of X and evaluate it at 375

P(X <= 375) = F(375)

where F(x) = P(X <= x) is the CDF of X.

Using the normal approximation to the binomial distribution, we can approximate X as a normal distribution with mean E(X) = 365 and standard deviation SD(X) = 17.67

Z = (X - E(X)) / SD(X)

Z follows a standard normal distribution with mean 0 and standard deviation 1.

P(X <= 375) = P(Z <= (375 - E(X)) / SD(X))

= P(Z <= (375 - 365) / 17.67)

= P(Z <= 0.566)

Using a standard normal distribution table or a calculator, we can find that P(Z <= 0.566) is approximately 0.7165.

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The given question is incomplete, the complete question is :

A die is continuously rolled 104 times. what is the probability that the total sum of all rolls does not exceed 375 ?

Answer:c

Step-by-step explanation:

3*1= 3 3*2=6 and so on

Answer:

\(proj_uw=6.2i-4.2j\)

Step-by-step explanation:

The projection of a vector \(v\) onto a vector \(u\) is defined as the projection of the vector \(v\) on the line that contains the vector \(u\). It can be calculated  using the following formula:

\(proj_uv=\frac{u\cdot v}{||u||^2} u\)

Where:

\(u\cdot v\)

Is the dot product between \(u\) and \(v\) which is given by:

\(u\cdot v= $$\sum_{i=1}^{n} u_iv_i= u_1v_1+u_2v_2+...+u_nv_n$$\)

and:

\(||u||\)

Is the magnitude of vector which can be calculated as follows:

\(||u||=\sqrt{u_1^2+u_2^2+...+u_n^2}\)

In this sense, the projection of vector w onto vector u is:

\(proj_uw=\frac{u\cdot w}{||u||^2} u\)

Where the dot product between \(u\) and \(w\) is:

\(u\cdot w =(9*19)+(-6*15)=171-90=81\)

And the magnitude of \(u\) is:

\(||u||=\sqrt{9^2+(-6)^2} = 3 \sqrt{13}\)

Thus:

\(proj_uw=\frac{u\cdot w}{||u||^2} u=\frac{81}{117} \langle9,-6\rangle=\langle6.23,-4.15\rangle\approx6.2i-4.2j\)

Answer:

A on edge

Step-by-step explanation:

Got it right on quiz (:

Answer:

Step-by-step explanation:

x=-7/5, y=-7

Answer:

30/6 is correct

Step-by-step explanation:

Answer: x = 20

Step-by-step explanation:

We can use the pythagorean theorem:

x^2 + 15^2 = 25^2

x^2 + 225 = 625

We can subtract 225 from both sides:

x^2 = 400

We can take the square root of both sides:

x = 20.

The centripetal force is the force that acts on an object moving in a circular path, directing it towards the center of the circle. option a.

When a car is driving around a curve, the centripetal force is provided by the frictional force between the tires and the road. This force acts inwards, towards the center of the circle, and is responsible for keeping the car moving in a circular path.

The centripetal force is always perpendicular to the direction of motion, so option (b) and (d) can be eliminated.

Additionally, there is no force that acts away from the center of the circle, so option (c) can also be eliminated. Option (e) is not applicable since the question is asking about the direction of the force, not its orientation.

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Answer:

Step-by-step explanation:

16 girls and 18 boys in a class

Total number of students:

Probability of choosing a girl:

Answer:

\(a_{n}\) = 9 - 6n

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = - 3 - 3 = - 9 - (- 3) = - 15 - (- 9) = - 6

This indicates the sequence is arithmetic with explicit formula

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 3 and d = - 6 , thus

\(a_{n}\) = 3 - 6(n - 1) = 3 - 6n + 6 = 9 - 6n

According to the statement the correct answer is option C - yes, the data are distributed evenly around the line of fit.

To determine if a model is a good fit for a data set, one needs to evaluate how closely the data points align with the line of fit. The line of fit represents the best possible straight line that can be drawn through the data points. If the data points are too far from the line of fit or too close to the line of fit, then it is an indication that the model is not a good fit for the data.
Option A states that the data points are too far from the line of fit, indicating that the model is not a good fit for the data. Option B states that the data points are too close to the line of fit, which is not necessarily a good or bad thing as it depends on the level of accuracy required for the analysis. Option C states that the data points are evenly distributed around the line of fit, which indicates that the model is a good fit for the data. Lastly, option D states that the line of fit touches at least one point in the data set, which is not sufficient to determine if the model is a good fit for the entire data set.
Therefore, the correct answer is option C - yes, the data are distributed evenly around the line of fit.

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Answer:

30-4xy+5y^2+10x-22y

Answer:

24 units² and 6 units²

Step-by-step explanation:

shape A

is composed of 2 rectangles , left and right

the rectangle on the left has dimensions 8 by 2

the rectangle on the right has dimensions 4 by 2

total area = (8 × 2) + (4 × 2) = 16 + 8 = 24 units²

shape B is a triangle with area (A) calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the height )

here b = 4 and h = 3 , then

A = \(\frac{1}{2}\) × 4 × 3 = 2 × 3 = 6 units²

Answer:

I think the answer is 2/11.

Answer:

maybe 1/66

Step-by-step explanation:

??? sorry if im wrong

Answer:B

Step-by-step explanation:

Her dexterity improved due to Increased myelination of the central nervous system.

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Answer:

(r o q)(-1) = 20

(q o r)(-1) = -11

Step-by-step explanation:

Given

q(x) = -2x + 1q(x)=−2x+1

r(x) = 2x^2 + 2r(x)=2x2+2

Solving (a): (r o q)(-1)

In function:

(r o q)(x) = r(q(x))

So, first we calculate q(-1)

q(x) = -2x + 1q(x)=−2x+1

q(-1) = -2(-1) + 1q(−1)=−2(−1)+1

q(-1) = 2 + 1q(−1)=2+1

q(-1) = 3q(−1)=3

Next, we calculate r(q(-1))

Substitute 3 for q(-1)in r(q(-1))

r(q(-1)) = r(3)

This gives:

r(x) = 2x^2 + 2r(x)=2x2+2

r(3) = 2(3)^2 + 2r(3)=2(3)2+2

r(-1) = 2*9 + 2r(−1)=2∗9+2

r(-1) = 20r(−1)=20

Hence:

(r o q)(-1) = 20

Solving (b): (q o r)(-1)

So, first we calculate r(-1)

r(x) = 2x^2 + 2r(x)=2x2+2

r(-1) = 2(-1)^2 + 2r(−1)=2(−1)2+2

r(-1) = 2*1 + 2r(−1)=2∗1+2

\begin{gathered}r(-1) = 6\\\end{gathered}r(−1)=6

Next, we calculate r(q(-1))

Substitute 6 for r(-1)in q(r(-1))

q(r(-1)) = q(6)

q(x) = -2x + 1q(x)=−2x+1

q(6) = -2(6) + 1q(6)=−2(6)+1

q(6) =- 12 + 1q(6)=−12+1

q(6) = -11q(6)=−11

Hence:

(q o r)(-1) = -11

120120 Different number of arrangements can be made.

7 identical stuffed dogs

4 identical stuffed cats

3 identical stuffed teddy bears

Total number of objects a toy store managers want

to display = 14.

We know formula to arrange n objects in which p are identical:

There are n!/p! ways to arrange n objects in a row, and p of those ways are exactly the same.

Similarly for this problem we can say:

Different number of arrangements possible.

Here in this question value of n =14 total number of objects.

Total number of arrangements possible for 14 objects is 14! but some objects are duplicate that may be counted more than ones so we have to divide them.

number of arrangements = 14!/ (7!*4!*3!).

by solving this we get

number of arrangements = 120120.

So we can say 120120 Different number of arrangements can be made.

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The multiplicity οf -2 is 1. The multiplicity οf 1+i and 1-i is alsο 1Since the quadratic factοr 13x²+27x+47 has nο real rοοts, it dοes nοt have any multiplicity fοr real numbers such as -2.

The given functiοn is f(x) = 13x³ + 14x² + 12x + 8x + 6x + 8.

Tο find the multiplicity οf each zerο, we need tο first factοrize the pοlynοmial. We can use synthetic divisiοn tο factοrize the pοlynοmial and find its zerοs:

-2 | 13   14   12   8   6   8

 |     -26   24 -72  128 -268

 +----------------------------

   13  -12   36 -64  134 -260

1+i | 13   14    12     8       6      8

   |     13  27i  27+13i  35-7i  41-13i

   +-----------------------------------

   13  27+14i  27-13i  43-7i  47-13i   0

1-i | 13   14    12     8       6      8

   |     13 -27i  27-13i  35+7i  41+13i

   +-----------------------------------

   13  27-14i  27+13i  43+7i  47+13i   0

Hence, the factοrizatiοn οf the given pοlynοmial is:

f(x) = (x+2)(x-1-i)(x-1+i)(13x²+27x+47)

The zerοs οf the pοlynοmial are -2, 1+i, and 1-i.

The multiplicity οf -2 is 1 because it appears as a linear factοr (x+2) in the factοrizatiοn.

The multiplicity οf 1+i and 1-i is alsο 1 each because they appear as linear factοrs (x-1-i) and (x-1+i) in the factοrizatiοn.

Since the quadratic factοr 13x²+27x+47 has nο real rοοts, it dοes nοt have any multiplicity fοr real numbers such as -2.

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Hey there!

1/15 ÷ 8

= 1/15 ÷ 8/1

= 1/15 × 1/8

= 1 × 1 / 15 × 8

= 1 / 120

Therefore, your answer is: 1/120

Good luck on your assignment & enjoy your day!

~Amphirite1040:)

Answer:

its b

Step-by-step explanation:

got it right on edge

The volume of the metal in the cylinderical pipe given the dimensions of the larger and smaller cylinders is 271.30 mm³.

A cylinder is a three-dimensional object. It is a prism with a circular base.

Volume of a cylinder = nr^2h

Where:

The volume of the metal in the cylinderical pipe = 3.14 x 10 x [(8.4/2)² - 6/2)²] = 271.30 mm³

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