Let {₁, 2, 3, 4, 5, 6} be the standard basis in R. Find the length of the vector € = 3ē₁ + 3e₂ - 5ē3 - 3ē4 + 5ē5 + 4e6. ||x||

Answer:

5

Step-by-step explanation:

formula is y=kx where k is constant of variation

then k=15/3=5

Answer:

The rectangular pan will hold more batter

Step-by-step explanation:

To find the volume of a rectangular prism, such as the first cake pan, you need to multiply all of the dimensions. The equation looks like this: "V = l * w * h" substituting the variables with the numbers would make it say "13 * 9 * 2" which would be 234 \(in^{3}\)

To find the volume of a cylinder, the equation is "V=π\(r^{2}\)h". The radius is half the diameter, so "r" would be 4, being half of 8. The substituted equation would read "π\(4^{2}\)2", making the cylinder's volume roughly 100.53 \(in^{3}\)

When you take those two numbers, you are able to see that 234 is bigger than 100.53, therefore making the rectangular pan larger.

Answer:

C) 3

Step-by-step explanation:

This is just a differences of squares:

\((a+b)(a-b)=(a^2-b^2)\\\\(\sqrt{5}+\sqrt{2})(\sqrt{5}-\sqrt{2})=(\sqrt{5}^2-\sqrt{2}^2)=5-2=3\)

Answer:

(c) 3

Step-by-step explanation:

\((\sqrt{5} +\sqrt{2} )(\sqrt{5} -\sqrt{2} )=(\sqrt{5} )^{2} -(\sqrt{2} )^{2} =5-2=3\)

Hope this helps

Answer:

7

Step-by-step explanation:

The average velocity of the particle between t=1.0 s and t=1.5 s is -1.25 m/s.

To find the average velocity of the particle, we need to calculate the displacement of the particle between t=1.0 s and t=1.5 s and divide it by the time interval. The displacement can be obtained by subtracting the initial position from the final position.

Given the equation for position as a function of time: x(t) = (3.5 m/s)t - (5.0 m/s^2)t^2

Let's calculate the displacement at t=1.0 s and t=1.5 s:

At t=1.0 s:

x(1.0) = (3.5 m/s)(1.0 s) - (5.0 m/s^2)(1.0 s)^2

x(1.0) = 3.5 m/s - 5.0 m/s^2 = -1.5 m

At t=1.5 s:

x(1.5) = (3.5 m/s)(1.5 s) - (5.0 m/s^2)(1.5 s)^2

x(1.5) = 5.25 m - 11.25 m = -6.0 m

The displacement between t=1.0 s and t=1.5 s is given by:

Displacement = x(1.5) - x(1.0) = -6.0 m - (-1.5 m) = -4.5 m

The time interval is 1.5 s - 1.0 s = 0.5 s

Average velocity = Displacement / Time interval

Average velocity = -4.5 m / 0.5 s = -9 m/s

Therefore, the average velocity of the particle between t=1.0 s and t=1.5 s is -9 m/s.

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\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 139}}{\left( \cfrac{6}{100} \right)139}\implies 8.34\)

Answer:

1. y=5

2. y=2x-1

3.y=-2x+1

4. y=-(1/2x)+1

Step-by-step explanation:

1. y=y-intercept. y=5.

2. 2x=mx=slope. -1=b=y-intercept

3. 2x=mx=slope. 1=b=y-intercept

4. -(1/2x)=mx=slope. 1=b=y-intercept

-Hope this helped

Answer:

\( y = -\frac{19}{9}x + \frac{5}{3} \)

Step-by-step explanation:

Given:

19x + 9y = 15

Required:

Rewrite in slope-intercept form, y = mx + b

SOLUTION:

19x + 9y = 15

Subtract 19x from both sides

9y = -19x + 15

Divide both sides by 9

y = -19x/9 + 15/9

\( y = -\frac{19}{9}x + \frac{5}{3} \)

Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

The triangle midsegment is a very important concept in geometry, and the triangle midsegment theorem states that the midsegment of a triangle is parallel to the third side and has a length equal to half of the length of the third side

The triangle midsegment theorem states that the midsegment of a triangle is parallel to the third side of the triangle and has a length that is equal to half of the length of the third side.

In this explanation, we will define the midsegment of a triangle and explain the triangle midsegment theorem in more detail.

To begin, let's consider a triangle ABC with midpoints D and E on sides AB and AC respectively. The segment DE is the midsegment of triangle ABC.

According to the triangle midsegment theorem, the length of DE is equal to half the length of the third side of the triangle, BC. Mathematically, this can be represented as follows:

DE = BC/2

In addition to the length, the midsegment of a triangle is also parallel to the third side. This means that if we extend the midsegment, it will eventually intersect the third side of the triangle.

The triangle midsegment theorem states that the midsegment of a triangle is parallel to the third side and also has the same length as half of the third side.

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Among the following statements, the one that best describes a probability distribution is: A list of the outcomes of a random experiment and the probability of each outcome.

A probability distribution is a list of the possible outcomes of a random experiment and the probability of each outcome. It provides a complete description of the possible outcomes and their associated probabilities for an experiment. Probability distributions are used to calculate the likelihood of specific events occurring and to determine the expected value of a random variable.

It lists all possible outcomes of a random experiment and assigns a probability to each outcome. The probabilities assigned to each outcome must add up to 1.

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Answer:

Estimation by inspection is better than trying to determine the line of best fit exactly

i) For a scatter plot : The use of estimation by inspection

ii) For a straight line graph : The exact determination method

Step-by-step explanation:

To create lines of best fit the estimation by inspection is better than trying to determine the line of best fit exactly .

This is because line of best fit only shows the trend of the data and in most cases it doesn't have to start from origin.

Scenarios :

i) For a scatter plot : The use of estimation by inspection

ii) For a straight line graph : The exact determination method

By the concept of unitary method she can run 320 yards  in 2 minutes at the same rate.

The unitary method is a technique used to determine the value of a single unit from the value of many units and the value of multiple units from the value of a single unit. We typically utilize it for math calculations. This approach might be helpful for answering questions on ratio and proportion, algebra, and other subjects. "It is a method where we get the value of a single unit from the value of many units and the value of multiple units from the value of a single unit." bra, geometry, etc. Before determining the value of additional or less items, we must first determine the value of one item by dividing it. There are two categories of unitary approaches.

720 yards = 4.5 minutes

1 minute = 720/4.5

= 160 yards

2 min = 160(2)

= 320 yards

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Answer:

c.

Step-by-step explanation:

\(n \leqslant 1\)

Answer:

312

Step-by-step explanation:

1000x.078=78 interest per year

78 interest x4 years=312 interest after 4 years.

a. Calculate the expected arrival time:

Given: Time range for arrival of elevator during the next 4.7 minutes is equally likely. The expected value of a discrete random variable is calculated by multiplying each possible value by its probability and adding up the products. So, we can calculate the expected value of the elevator arrival time by integrating the value of the probability density function (which is a straight line in this case) over the given interval. The area under the curve of the probability density function over the entire interval of possible values is 1. The expected arrival time (E) of the elevator is given by: E = (1/4.7) ∫(0 to 4.7) tdt= (1/4.7) [t²/2] [from 0 to 4.7]= 2.3596 minutes or 2.36 minutes (rounded to 2 decimal places)Therefore, the expected arrival time is 2.36 minutes.

b. Probability that an elevator arrives in less than 1.8 minutes:

To calculate the probability of an event happening, we need to find the area under the probability density function (pdf) over the given interval (in this case, less than 1.8 minutes). The pdf is a straight line with a slope of 1/4.7, so the equation of the line is: f(t) = (1/4.7) t. The probability of the elevator arriving in less than 1.8 minutes is: P(T < 1.8) = ∫(0 to 1.8) f(t) dt= ∫(0 to 1.8) (1/4.7) t dt= (1/4.7) [t²/2] [from 0 to 1.8]= 0.56765 (rounded to 4 decimal places)Therefore, the probability that an elevator arrives in less than 1.8 minutes is 0.568 (rounded to 3 decimal places).

c. Probability that the wait for an elevator is more than 1.8 minutes: The probability that the wait for an elevator is more than 1.8 minutes is the complement of the probability that it arrives in less than 1.8 minutes. P(T > 1.8) = 1 - P(T < 1.8) = 1 - 0.56765= 0.43235 (rounded to 3 decimal places)Therefore, the probability that the wait for an elevator is more than 1.8 minutes is 0.432 (rounded to 3 decimal places).

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The dimensions of the printed area is \(\frac {10} {12} inches\)

Let's assume the margin width to be 'x'. Then the dimensions of the printed area would be (18-2x) inches by (20-2x) inches.

We know that the area of the printed image is 120 square inches. So, we can set up the equation:

(18-2x) * (20-2x) = 120

Expanding the left side, we get:

\(360 - 76x + 4x^2 = 120\)

Simplifying and rearranging, we get:

\(4x^2 - 76x + 240 = 0\)

Dividing by 4, we get:

\(x^2 - 19x + 60 = 0\)

Factoring the equation, we get:

(x-4) (x-15) = 0

So, the possible values of 'x' are 4 inches and 15 inches.

However, the margin cannot be 15 inches as it would make the dimensions of the printed image negative.

Therefore, the margin width is 4 inches and the dimensions of the printed area are:

\(\frac {(18-2x)} {(20-2x)}\)

= \(\frac {(18-2(4))} {(20-2(4))}\)

= \(\frac {10} {12} inches\).

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Answer:

alternate interior angle tq

According to the question the volume of integration in (x,y,z) space The integral in spherical coordinates becomes :\(\[\int_{0}^{2\pi} \int_{0}^{\frac{\pi}{2}} \int_{0}^{3} \rho^5 \sin(\phi) \cos^2(\phi) \sin(\theta) \, d\rho \, d\phi \, d\theta.\]\)

To evaluate the integral in spherical coordinates, we start by determining the bounds of integration in \($(\rho, \theta, \phi)$\) space based on the volume of integration in \($(x, y, z)$\) space. The given volume is enclosed by the surfaces \(z=0$, $z=\sqrt{9-x^2}$, $z=\sqrt{9-x^2-y^2}$\), and the region defined by

\(x^2 + y^2 + z^2 \leq 1$\).

The spherical coordinates transformation is as follows:

\(\[x = \rho \sin(\phi) \cos(\theta), \quad y = \rho \sin(\phi) \sin(\theta), \quad z = \rho \cos(\phi),\]\)

The bounds of integration in \($(\rho, \theta, \phi)$\) space are determined by the intersection of the given surfaces. The lower bound for \(\phi$ is $0$\), as the volume is bounded by the \($xy$\)-plane. The upper bound for \($\phi$\) is \($\frac{\pi}{2}$\), as the volume is enclosed by the surfaces \(z=0$ and $z=\sqrt{9-x^2}$\).

For \($\theta$\), the bounds are \(0$ to $2\pi$\) since the volume is symmetric around the \($z$\)-axis.

For $\rho$, the bounds can be determined by considering the intersection of the surfaces \(x^2 + y^2 + z^2 = 1$ and $z=\sqrt{9-x^2-y^2}$\). Simplifying the equations, we find \(\rho = 1$ and $\rho = \sqrt{9-\rho^2}$\), which leads to \($\rho = 3$\).

Hence, the integral in spherical coordinates becomes :\(\[\int_{0}^{2\pi} \int_{0}^{\frac{\pi}{2}} \int_{0}^{3} \rho^5 \sin(\phi) \cos^2(\phi) \sin(\theta) \, d\rho \, d\phi \, d\theta.\]\)

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If figure below has surface-area of 72cm², then the area of missing-face is   18 cm²,and the missing-length is 6 cm.

The "total-surface-area" of rectangular-prism is = 72 cm²,

We have to find area of missing face and length of missing edge,

From the figure, we see that "missing-area" denoted by "A" are opposite to each other,

we know that, in "rectangular-prism" the area of "opposite-faces" are equal,

The area of other faces are ⇒ 6 cm², 12 cm² , 6 cm², and  12 cm²,

we also know that "total-surface-area" of prism is = Sum of area of  6 faces,

So, area = 6 + 12 + 6 + 12 + A + A,

We know that,  Area of rectangular prism is 72 cm²,

So, 72 = 6 + 12 + 6 + 12 + A + A,

72 = 36 + 2A,

72 - 36 = 2A,

36 = 2A,

A = 36/2 = 18 cm²,

So, area of single "missing-face" is 18 cm²,

To find the Length of each missing-edge, we use formula for Area of rectangle which is = length × width,

Substituting Area as 18 cm² and width as 3 cm,

We get,

18 = length × 3;

18/3 = length,

length = 6 cm.

Therefore, length of the missing-edge is 6 cm.

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The given question is incomplete, the complete question is

The figure below is a net for a right rectangular prism. It's surface area is 72cm² and the area of some of the faces are filled in bellow.

Find the area of the missing faces and the missing dimension.

Answer:

-60 and -28

Step-by-step explanation:

-60 + 42= -18

CHECK:

-42-18=-60

-56+-28=-84

CHECK:

-84+28=-56

Hope this helps <3 Need thanks? Comment /hearthelp

Answer:

-60

-28

Step-by-step explanation:

x +42 = -18

Subtract 42 from each side

x+42-42 = -18-42

x = -60

-56 +y = -84

Add 56 to each side

y = -84+56

y = -28

The probability of obtaining exactly 3 successes in 5 independent trials of a binomial experiment with a success probability of 0.6 is approximately 0.3456.

To calculate the probability of 3 successes in 5 independent trials of a binomial experiment with a success probability of 0.6, we use the binomial probability formula:

P(x) = (nCx) * p^x * (1-p)^(n-x)

In this case, n = 5, p = 0.6, and x = 3. Substituting these values into the formula:

P(3) = (5C3) * 0.6^3 * (1-0.6)^(5-3)

Calculating the values:

(5C3) = 10 (combining 5 choose 3)

0.6^3 = 0.216 (0.6 raised to the power of 3)

(1-0.6)^(5-3) = 0.16 (0.4 raised to the power of 2)

Substituting these values back into the formula:

P(3) = 10 * 0.216 * 0.16

P(3) = 0.3456 (rounded to four decimal places)

Therefore, the probability of getting exactly 3 successes in 5 independent trials is approximately 0.3456.

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Answer:

27°

Step-by-step explanation:

Angle ABC is 90°

ACB is 63 because it is vertically opposite angle GCJ

Angle CAB is 27° (90-63)

angle x is 27° (vertically opposite CAB)

Answer:

\( \sf \: 104.4\)

Step-by-step explanation:

(7.36)(10)(9)−(6.2)(10)(9)

=(73.6)(9)−(6.2)(10)(9)

=662.4−(6.2)(10)(9)

=662.4−(62)(9)

=662.4−558

=104.4

Answer:

x = 19

Step-by-step explanation:

1 = x - 18

1 + 18 = x

x = 19

Answer:

See below.

Step-by-step explanation:

The answer would be 2 3/4.

The third tick represents 3/4, and this is between 2 and 3.

-hope it helps

Answer:

My guess is 2 3/4

Step-by-step explanation:

Sorry if i'm wrong, if im right can i have brainliest? So explanation is that the plotted point on the number line is c so that will make the numerator is id.k the difference between them the top of the number would be three because c is ploted on c and id.k how to get 4.

The value of the definite integral ∫(-1)¹ x¹⁰⁰ dx is 2/101.

To evaluate the integral S(-1)¹ x¹⁰⁰ dx, we can use the power rule of integration, which states that:

∫ \(x^n dx = (x^(n+1)) / (n+1) + C\), where C is the constant of integration.

Applying this formula, we get:

∫ x¹⁰⁰ dx = (x\(^(100+1)\)) / (100+1) + C

\(= (x^101) / 101 + C\)

To evaluate the definite integral from -1 to 1, we can substitute the limits of integration into the antiderivative and then subtract the result evaluated at the lower limit from the result evaluated at the upper limit:

∫(-1)¹ x¹⁰⁰ dx =\([(1^101)/101\) - \(((-1)^101)/101]\)

= (1/101) - (-1/101)

= 2/101

Therefore, the value of the definite integral ∫(-1)¹ x¹⁰⁰ dx is 2/101.

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