Recall that the side length of the square was 14 units long. What is the base area of the prism?

Diameter of cylinder base - 19.8
base area of cylinder - 307.8
volume of cylinder - 9.234

A linear combination of the values of a1 = (1,-2,0), a2 = (0,1,2), and a3 = (5,-6,8) with the corresponding weights is b = (2,-1,6).

We may construct a system of equations using the coefficients of the linear combination and the elements a1, a2, and a3 to determine whether b is a linear combination of a1, a2, and a3.

It is possible to write the equation for a linear combination of the type b = k1a1 + k2a2 + k3a3 in the following way:

b = k1 × (1,-2,0) + k2 × (0,1,2) + k3 × (5,-6,8) (5,-6,8)

So,

x = k1 + 5k3

y = -2k1 + k2 - 6k3

z = 2k2 + 8k3

From b =, we know the values of x, y, and z. (2,-1,6)

Thus, we can construct the equations in the following system:

x = k1 + 5k3 = 2

y = -2k1 + k2 - 6k3 = -1

z = 2k2 + 8k3 = 6

To determine the values of k1, k2, and k3, we can solve the system of equations using techniques like substitution or elimination.

k1 = 1, k2 = 3, k3 = 1

As a result, we can write b as a linear combination of the variables a1, a2, and a3 with the respective weights of (1, 3, and 1) for k1, k2, and k3.

b = 1a1 + 3a2 + 1 × a3

This indicates that b is a linear combination of the three variables a1, a2, and a3 with the weights (1, 1, and 3, respectively).

The Complete Question  linear combination.

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Answer: Kayak Central

Step-by-step explanation:

Surf Bargains is 31.54 for 2 hours, if you want to find the hourly cost your going to do 31.54/2= 15.76 So Surf Bargains is 15.76 per hour.

Kayak Central you will do the same thing, 43.96/3.5= 12.56 per hour.

This means kayak central offers the lowest rate of $12.56 per hour.

Answer:

3/20

Step-by-step explanation:

3/20 is .15 in the simplest fraction form

The amount of square inches of the log that the furniture maker sanded in terms of π is; 288π in²

The formula for volume of a cylinder is;

V = πr²h

where;

V is volume

h is height

r is radius

Now, we have the parameters as;

r = 2 in

V = 96π in³

Thus;

96π = π(2)²h

h = 96/4

h = 24 in

Formula for surface area of a cylinder is;

S.A =  2πr²h +  2πrh

S.A = 2(π(2)²*24) + 2(π * 2 * 24)

S.A = 192π + 96π

S.A = 288π in²

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The total cost function C is  T(x) =  0.000001x³ - 0.03x² + 200x + 15,000, the total profit function P is P(x) = 0.000001x³ - 0.01x² + 50x + 15,000 and the profit for the company if 1,900 units are produced and sold each week is $80,759

The term function in math is  written as  a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.

Here we have given that the division of Chapman Corporation manufactures a pager.

Here we also know that the weekly fixed cost for the division is $15,000, and the variable cost for producing x pagers/week in dollars is represented by the function V(x).

Then the function is written as,

=> V(x)= 0.000001x³ - 0.01x² + 50x.

Here we have given that company realizes a revenue in dollars from the sale of x pagers/week represented by the function R(x).

Then the function is written as,

=> R(x)= -0.02x² + 150x Where the value of x lies between (0<x<7500)

Then the total cost is calculated as,

=> T(x) = Total Cost + fixed cost + variable cost

Then apply the values on it, then we get,

=> T(x) = 15,000 + 0.000001x³ - 0.01x² + 50x - 0.02x² + 150x

=> T(x) =  0.000001x³ - 0.03x² + 200x + 15,000

And the total profit function is written as,

=> P(x) = 0.000001x³ - 0.03x² + 200x + 15,000 - (-0.02x² + 150x)

=> P(x) = 0.000001x³ - 0.01x² + 50x + 15,000

If the is the profit for the company if 1,900 units are produced and sold each week, then the profit is calculated as,

=> P(1900) = 0.000001(1900)³ - 0.01(1900)² + 50(1900) + 15,000

=> P(1900) = 80759

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Answer:

Step-by-step explanation:

I think anyone needs to care about the school bus, it's just a bus, and maybe the people inside are like you, so relax, keep calm on a school bus

In the 30-60-90 triangle below, side s has a length of 4 and side q has a length of [tex]4\sqrt{3}[/tex] (Option E).

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem. The Pythagorean Theorem says (hypotenuse)²= (leg1)²+(leg2)². And the main trigonometric ratios are: sin (x) , cos  (x) and tan  (x) .

The question asks the value of sides s and q of the given right triangle. If you have the value of the hypotenuse and all angles of the triangle, you can solve this exercise by applying the trigonometric ratios. See below.

[tex]sin 30\° = \frac{opposite \; leg}{hypotenuse}\\ \\ \frac{1}{2}=\frac{s}{8} \\ \\ 2s=8\\ \\ s=4[/tex]

[tex]cos 30\° = \frac{adjacent\; leg}{hypotenuse}\\ \\ \frac{\sqrt{3} }{2}=\frac{q}{8} \\ \\ 2q=8\sqrt{3} \\ \\ q=4\sqrt{3}[/tex]

Therefore, the solution to this question is the letter E.

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The correct answer is D. the proportion of boxes with broken glass is greater than 0.08.

The p-value is 0.001 which is less than the significance level of α = 0.01; therefore, the null hypothesis (H0: p = 0.08) can be rejected. We can conclude that there is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.

To calculate the p-value, we can use the formula: p-value = P(x ≥ X|H0)

Where X is the sample mean, and H0 is the null hypothesis that the proportion of boxes with broken glass is equal to 0.08.

Using this formula, we get: p-value = P(x ≥X|H0) = P(x ≥ 0.08) = 0.001

Since the p-value is less than the significance level of 0.01, the null hypothesis can be rejected and we can conclude that there is convincing evidence that the proportion of boxes with broken glass is greater than 0.08.

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He has 255.17 more in debits than in credits. Thus, option D is correct.

Debits and credits in double-entry bookkeeping are entries made in account ledgers to reflect changes in value brought on by business transactions. A debit entry, not a credit entry, is used to show the amount of money that has been transferred into or out of an account. Value is exchanged with each transaction from credited to debited accounts.

Let's call B the amount in credit that Ignatius had, and C the amount in debits that Ignatius had during the month.

We know that the initial amount in his account was 124.82, while the final balance was 659.27.

Final amount = the initial amount + amount of credits - the amount of debits

$255.17= $255.17 (B-C)

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The trigonometric function that represent the equation in the graph is y = sin(x + π/2).

The key components visible on the graph are:

y = π/2  is the midpoint.

We can conclude that the correct answer is either b or d.

at x = 0, f(x) = 0.

Function y = sin(x + π/2)

Therefore the correct answer is option d that is y = sin(x + /2) is the trigonometric function that represents the equation in the graph.

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We can see that height is the dependent variable and age is independent.

Therefore the graph of the relation, if connected, is a line segment parallel to the x-axis.

If we prove it with the vertical line test it will pass the test. Hence we can state it is a function.

The domain is:

The range is:

the star of the mentioned, figure is attached below.

What is a star?

A polygon, which is a form with many sides, is a type of star. In fact, five-pointed stars are categorised as decagons or polygons with ten sides, although the number of sides changes depending on the number of points on the star, such as six, ten, etc. An equilateral and equiangular polygon that self-intersects is referred to as a regular star shape or regular star polygon. It was made by connecting the vertices of a straightforward, regular, n-sided polygon to one another in a nonadjacent direction until the original vertices were once again reached.

How are stars with five points made?

All stars are formed by lines at particular angles. The basic pattern is as follows in the case of five-pointed stars, which are the most prevalent:

Use lines of the same length and rotate 135° each time.

Hence the star of the mentioned figure is attached below.

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The artist needs 78,835.2 cm² of metal to make the sculpture.

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On a variable ratio schedule, reinforcement is given for the next correct response after varying numbers of responses have been made.

What is variable ?

A variable is a value or quantity that can change or take on different values in a given context or system. In mathematics and science, variables are often used to represent unknown or changing values in an equation or model. In programming, a variable is a named container or storage location that holds a value that can be modified during the execution of a program.

On a variable ratio schedule, reinforcement is given for the group of correct responses that occur after varying amounts of time have passed. This means that the reinforcement is not given after a fixed number of responses or after a fixed amount of time has passed. Instead, the reinforcement is given after a varying number of correct responses have been made, making it unpredictable for the individual or organism being reinforced. This type of schedule is often used in gambling and other situations where the reinforcement is desired to be unpredictable and maintain the individual's interest or motivation.

On a variable ratio schedule, reinforcement is given for the next correct response after varying numbers of responses have been made.

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Answer:

1st and 2nd ones

Step-by-step explanation:

39 + 3(17) = 90 degrees

Supplementary angles add up to 180

Answer: (-2) + 22 + (-30) = (-10)

Step-by-step explanation:

I'm not too sure, I hope this works

The binomial distribution has one possible outcome, success, and two possible outcomes, failure. In contrast, the Poisson distribution has an infinite number of potential outcomes.

The distribution of binary data from a finite sample is described by the binomial distribution. As a result, it provides the likelihood that r events will occur in n trials. The distribution of binary data from an infinite sample is described by the Poisson distribution. It provides the likelihood that r events will occur in a population. Two discrete probability distributions are the Poisson distribution and the Binomial distribution.

In discrete trials, the binomial distribution counts discrete occurrences. In a continuous domain, the poisson distribution counts discrete occurrences. The poisson should ideally only be used when success could happen anywhere in a domain.

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Answer: 4(u−2)−3u=2(u−6)

Step-by-step explanation:

The equation of the plane is:-6x + 0y + 6z - 18 = 0

The equation of a plane containing a point P(x1, y1, z1) and a line defined by x = x0 + at, y = y0 + bt, z = z0 + ct, is given by:

Ax + By + Cz + D = 0

Where:

A = (y1 - y0)a - (x1 - x0)b

B = (z1 - z0)a - (x1 - x0)c

C = (z1 - z0)b - (y1 - y0)c

D = -(A*x1 + B*y1 + C*z1)

Plugging in the given values, we have:

A = (1 - 5)3 - (1 - 3)5 = -6

B = (3 - 1)3 - (1 - 3)2 = 0

C = (3 - 1)5 - (1 - 5)2 = 6

D = -(-6*1 + 0*1 + 6*3) = -18

Therefore, the equation of the plane is:

-6x + 0y + 6z - 18 = 0

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The cost per ounce of a container of gochujang at the market can be calculated using the equation of the line of best fit.

The line of best fit is given by the equation y = 0.14x + 1.3, where y is the cost of the container and x is the amount of sauce in the container (in ounces). To calculate the approximate cost per ounce of a container of gochujang, we can use this equation. We set y = 1, since we want the cost of one ounce of sauce. The equation of this line is y = 0.25x + 3.2, where x is the amount of sauce in the container and y is the cost of the container. To find the cost per ounce, we need to divide the y-intercept, 3.2, by the slope, 0.25. This gives us 12.8. Therefore, the approximate cost per ounce of a container of gochujang at the market is $12.8.

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The given two triangles are similar to each other by the postulate called SAS.

What is triangle ?

Triangle can be defined as in which it consists of three sides, three angles and sum of the three angles are 180 degrees always.

Given,

The triangles are RST and UVT

So

From the given figure we can say that,

RT = TU

RS = VU

As two sides are already equal and vertically opposite angles are always equal .

so we can say that By postulates SAS we can say that they are similar to each other.

Hence, The given two triangles are similar to each other by the postulate called SAS.

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Answer: 22 minutes

Step-by-step explanation: m + 2m + m + 7 = 4m + 7

4m + 7 = 50

4m = 44

m = 11

2m = 11 x 2 = 22 minutes

The probability that you select a gold marble is, 1/21.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

A bag contains 2 gold marbles, 10 silver marbles, and 30 black marbles.

Here, Number of gold marbles = 2

And, Number of total marbles = 2 + 10 + 30

                                              = 42

Hence, The probability that you select a gold marble is,

⇒ Number of gold marbles / Total number of marbles

⇒ 2 / 42

⇒ 1 / 21

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Answer:

6% = $4000

Step-by-step explanation:

6%x + 7%(8500 - x) [tex]\geq[/tex] 555

0.06x + 0.07(8500 - x) [tex]\geq[/tex] 555

0.06x + 595 - 0.07x [tex]\geq[/tex] 555

-0.01x + 595 [tex]\geq[/tex] 555

-0.01x [tex]\geq[/tex] -40

x [tex]\leq[/tex] 4000

Answer:

Step-by-step explanation:40

41

+

9

i

41

The amount of time that it took for Abby to meet Betty is given as follows:

2 minutes.

The quadratic function giving Abby's distance from home is defined as follows:

s(t) = -100t² + 400t.

The coefficients of the function are given as follows:

a = -100, b = 400.

The vertex of the quadratic function is the turning point of the graph, that is, the moment that Abby meet Betty.

The t-coordinate of the vertex is given as follows:

t = -b/2a

t = -400/-200

t = 2 minutes.

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