determine if b is in the span of the other given vectors. if so, express b as a linear combination of the other vectors. (if b cannot be written as a linear combination of the other two vectors, enter dne in both answer blanks.) -1 -2 -6
a1 = 3 a2 = -3 b= 9
-1 6 2

Answer:5/3

Step-by-step explanation:

In the following intermediate step, cancel by a common factor of 2 gives 5/3

Answer:

[tex]1\dfrac{2}{3}[/tex]

Step-by-step explanation:

      Use KCF method:

       [tex]\dfrac{5}{6} \ \div \dfrac{1}{2}=\dfrac{5}{6}*\dfrac{2}{1}[/tex]

                   [tex]\sf = \dfrac{5}{3}\\\\= 1\dfrac{2}{3}[/tex]

Here we will have to use the set theory to understand where intersection and union can be used to obtain the results.

a)

Here we need to write an expression for the event that at least one of the events A, B, and C occurs. Hence the event will be of occurrence of

A or B or C

We know that or implies a union of sets hence it will be

(A U B U C)

b)

Here we need to find the occurrence at most one of the events hence we get

[not A and not B and not C]  or [A and not B and not C] or [not A and B and not C] or [not A and not B and C]

the word and implies an intersection hence we get

[not A ∩ not B ∩ not C] U [A ∩ not B ∩ not C] or [not A ∩ B ∩ not C] U [not A ∩ not B ∩ C]

c)

None of the event occurs will imply

[not A ∩ not B ∩ noy C]

d)

This will simply be the opposite of c) hence we will get

A ∩ B ∩ C

e)

Here we will just remove the possibility of non-occurrence of any event from option b) to get

[A ∩ not B ∩ not C] U [not A ∩ B ∩ not C] U [not A ∩ not B ∩ C]

f)

Here we will get

A ∩ B ∩ not C

g)

Here there will be 2 possibilities A occurs and does not occur.

[A ∩ B ∩ C] U [not A ∩ not B ∩ C]

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Answer:

Temperature falls by - 9 degree Celsius

Based on the Alternate Exterior Angles Theorem, the measure of angle 7 is 65 degrees.

The Alternate Exterior Angles Theorem states that if two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent (equal in measure). In other words, the angles on the outside of the lines, on opposite sides of the transversal, have the same measure

Angles 1 and 7 are exterior angles, therefore:

m<7 = m<1

Substitute

m<7 = 65 degrees.

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Answer:

Step-by-step explanation:

To determine the minimum number of students needed, we need to first determine how many newspapers and magazines each student can deliver in total (over 8 hours).

Each student can deliver 35 newspapers + 50 magazines = 85 newspapers + magazines per hour.

In 8 hours, each student can deliver 85 newspapers + magazines/hour * 8 hours = 680 newspapers + magazines.

Now, we can divide the total number of newspapers and magazines to be delivered by the number of newspapers and magazines each student can deliver in 8 hours:

875 newspapers + 1200 magazines = 2075 newspapers + magazines

2075 newspapers + magazines / 680 newspapers + magazines/student = 3 students.

Therefore, the minimum number of students needed to deliver 875 newspapers and 1200 magazines is 3 students.

Answer:

$195

Step-by-step explanation:

First, we need to know the volume of the box, that way we can know how much sand we need to buy.

l x w x h = v            

4 x 4 x 2 = 32

Now we have the volume in feet but we need to convert it into meters.

32 x 0.3048 = 9.7536

Next, we'll multiply the meters by the price so that we'll have the total cost.

9.7536 x 20 = 195.072

Answer:

y=1/4x+7

Step-by-step explanation:

If the y-intercept is (0,7), then the b is +7

the slope is 1/4 which is equal to m

your equation is y=1/4x+7

The Bernoulli differential equation is a nonlinear ordinary differential equation of the form:

dy/dx + P(x)y = Q(x)y^n, where n ≠ 0, 1.

For n = 0 or n = 1, the equation is linear. For other values of n, a common technique to linearize the equation is to make the substitution y = v^(-1/n-1). The resulting equation is:

dv/dx + (P(x) + Q(x)/v^(1/n-1)) * (1/n-1) * v^(1/n-2) * dv/dx = 0.

For the initial value problem given, we have P(x) = -1/x, Q(x) = -5, and n = 2.

We make the substitution y = v^(-1), so v = y^(-1), and dv/dx = -y^(-2)dy/dx. The equation becomes:

-y^(-2)dy/dx + (-1/x - 5y^2) = 0.

We have the initial condition y(1) = 1/5. In terms of v, the initial condition becomes v(1) = 1/(1/5)^2 = 25.

Now, the differential equation is linear, and we can solve it using standard methods, such as separation of variables. To find the solution that satisfies the initial condition, we may use numerical methods such as the Euler method or Runge-Kutta method.

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The probability that the mean profit for the sample was between -2.9 million and 4.5 million is of:

0.0475 = 4.75%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 6.54, \sigma = 10.45, n = 73, s = \frac{10.45}{\sqrt{73}} = 1.22[/tex]

The probability that the mean profit for the sample was between -2.9 million and 4.5 million is the p-value of Z when X = 4.5 subtracted by the p-value of Z when X = -2.9, hence:

X = 4.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (4.5 - 6.54)/1.22

Z = -1.67

Z = -1.67 has a p-value of 0.0475.

X = -2.9:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (-2.9 - 6.54)/1.22

Z = -7.73

Z = -7.73 has a p-value of 0.

Hence:

0.0475 - 0 = 0.0475 = 4.75%.

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Answer:

21 IAMOOOOOOOO

Step-by-step explanation:

Answer:

w = 64

Step-by-step explanation:

A = 6016[tex]m^2[/tex]

l = 94m

A = lw

Sub in all the known values

6016 = (94)(w)

w = [tex]\frac{6016}{94}[/tex]

w = 64

Profit sharing, project bonuses, stock options, warrants, scheduled bonuses (like Christmas and performance-linked), and increased paid vacation time are a few examples of financial incentives.

Financial incentives are used to financially commend employees for doing a great job. Cash or presents having a clear monetary value are examples of monetary rewards and incentives that employers give to their staff.

In addition to employee benefits, leadership and human resources departments offer and create financial incentive programmed to reward employee achievement and motivate team members to surpass their objectives.

Unlike non-monetary incentives, these perks and advantages are provided to employees in addition to their base pay and other benefits.

Therefore, these monetary incentives can take the form of lifestyle budgets, profit-sharing, end-of-year bonuses, spot bonuses, stock options, and end-of-year bonuses.

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Answer:

below

Step-by-step explanation:

The direct distance, d, from starting point is the hypotenuse of a right triangle with two legs of 25 mi and 15 mi

Pythagorean Theorem

d^2 = 25^2 + 15^2

   show d = sqrt(850) = 29.15 mi

The required diameter of the spherical gasoline tank is given as 50 feet.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
The volume of the cylinder = 4/3πr³
4/3πr³ = 65450
r³ = 15625
r = 25 feet

Diameter = 2 × r
              = 2 × 25
              = 50 feet

Thus, the required diameter of the spherical gasoline tank is given as 50 feet.

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The linear function whose graph has slope -4 and passes through the point (5, 2) is f(x) = -4x + 22

Let us assume that f(x) be a required linear function.

We know that an equation of the line passing through point (x₀, y₀) and having slope m is:

(y -  y₀) = m(x - x₀)

Let  (x₀, y₀) = (5, 2) and slope m = -4

So, the equation of the line would be,

(y -  y₀) = m(x - x₀)

(y - 2) = -4(x - 5)

y - 2 = -4x + 20

y -2 + 2 = -4x + 20 + 2

y = -4x + 22

Let y = f(x)

f(x) = -4x + 22

So, the linear function is: f(x) = -4x + 22

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Consider the continuous random variable x that has a uniform distribution over the interval from 40 to 44. The variance of 'x' is approximately C: 1.155.

The variance of a continuous uniform distribution over the interval [a, b] is determined by the formula given as follows:

Var(x) = (b-a)^2 / 12

For the given distribution, a = 40 and b = 44, so the variance is calculated by putting these values into the above formula:

Var(x) = (44 - 40)^2 / 12 = 1.155

Therefore, the variance of 'x' is approximately 1.155

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The length of each edge of the cube : C : 2∛12

Three-dimensional space is quantified by volume.

V= a³ => 96 = a³ => a= ∛96 =2∛12

The length of each edge of the cube : C : 2∛12

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The end behavior of the polynomial 8x^{7}-2x^{5}-4x^{4}+2x^{3}+7x^{2}

is given in graph.

What are polynomials?

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.

Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial.

Now,

Given polynomial is 8x^{7}-2x^{5}-4x^{4}+2x^{3}+7x^{2}.

So, the graph will be dominated by x^7 because it is the highest power.

Hence,

          the end behavior of the function is as shown in graph.

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A simple way to depict sets visually is with a Venn diagram, also called an Euler-Venn diagram. A circle is used for the sets that are being considered, and a rectangle is used as the standard representation.

Consequently, we'll talk about issues with variables two and three in this post.

Let's look at some fundamental Venn diagram formulas for two and three members.

n (A ∪ B) = n (A + B) - n (A ∪ B)

n (A ∪ B ∪ C ) = n(A) + n (B) + n (C) - n (A ∩ B) - n (B  ∩ C) - n (C ∩  A) + n (A  ∩ B  ∩ C)

Then, where n(A) is the quantity of elements in set A, goes on.

You won't need to memorize these formulas once you've understood the notion of a Venn diagram using diagrams.

In this scenario, X is the number of elements that only belong to set A, Y is the number of elements that only belong to set B, and Z is the number of elements that both sets A and B (A + B) contain.

W is the number of objects that are not part of either set A or set B.

n(A) = x + z; n(B) = y + z; n(A B) = z; and n (A B) = x + y + z are all easily deduced from the above diagram.

w = total number of elements = x + y + z.

The Complete Question.

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A hydrogen donor and acceptor must both be present for a hydrogen bond to form.

The key concepts in hydrogen bonding are;

Typically, a strongly electronegative element like N, O, that is covalently connected to a hydrogen bond serves as the donor in a hydrogen bond.

Given that the information is incomplete, the above information shows adequate information about hydrogen bonds.

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The equation of the line passing through the point (0, 8), and having a slope of m = 4 is y = 4x + 8.

The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.

The equation of the line passing through the points (x1, y1), with a slope of m is given by the formula:

(y - y1) = m (x - x1)

Given that the point is (0, 8) and the slope, m = 4.

Substituting the values we have:

(y - y1) = m (x - x1)

y - 8 = 4 (x - 0)

y - 8 = 4x

y = 4x + 8

Hence, the equation of the line passing through the point (0, 8), and having a slope of m = 4 is y = 4x + 8.

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In base ten, 67.315 is exactly 6.7315 tens, is exactly 7 ones, is exactly 3 tenths, is exactly 5 hundredths, is exactly 1 thousandths and is exactly 6 hundreds.

When we break down 67.315 in base ten, we can see that it is composed of:

6 tens because 6*10 = 60

7 ones because 7*1 = 7

3 tenths because 3*0.1 = 0.3

5 hundredths because 5*0.01 = 0.05

1 thousandths because 1*0.001 = 0.001

So, 67.315 is exactly 6.7315 tens, is exactly 7 ones, is exactly 3 tenths, is exactly 5 hundredths, is exactly 1 thousandths and is exactly 6 hundreds.

The answer is cos CAB = 5 × √(10² + h²) in terms of x.

"h" denotes the parallelogram's height.

We know that the base of parallelogram A and B is 10, so the area of parallelogram A and B can be found by:

Area = base * height = 10 * h

Since parallelogram A and B make up a hexagon, their combined area must equal the area of the hexagon:

2 * (10 * h) = 6 * h * a/2

Where a is the length of one of the sides of the hexagon.

Solving for a, we get:

a = 5 * h

Next, let's find the length of DE, which is equal to BC.

We know that the height of parallelogram A is h, and the base is 10.

So, the diagonal of parallelogram A can be found using the Pythagorean theorem:

DA = √(10² + h²)

Since DE = DA, we can substitute DA with DE:

DE = √(10² + h²)

Now we can find cos CAB using the Law of Cosines:

cos CAB = (AB² + BC² - AC²) / 2 * AB * BC

AB = 10

BC = DE = √(10²+ h²)

AC = 10

So,

cos CAB = (10² + (√(10² + h²))² - 10²) / 2 * 10 * √(10² + h²)

= (√(10² + h²))² / 2 * 10 * √(10² + h²)

= 5 × √(10² + h²)

Since h is a variable, we cannot simplify the expression further.

Therefore, cos CAB = 5 × √(10² + h²) in terms of x.

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Answer: if Isaiah gets two thirds than he'll get 293.333333334 but if he gets one third than he will get 146.666666667

Step-by-step explanation:

Answer:

p = - 4

Step-by-step explanation:

- 0.9p + 3.2 = - 1.7p ( add 1.7 to both sides )

0.8p + 3.2 = 0 ( subtract 3.2 from both sides )

0.8p = - 3.2 ( divide both sides by 0.8 )

p = [tex]\frac{-3.2}{0.8}[/tex] = - 4

Answer: p=-4

Step-by-step explanation:

-0.9p+3.2=-1.7p

+0.9p          +0.9p

3.2=-0.8p

32=-8p

p=-4

Answer:

Below

Step-by-step explanation:

1.7 / 130  go/si

1000 si  * 1.7 /130 go/si = 13.08 gm of gold

10 go  /  ( 1.7/130 go/si) = 764.7 gm of  silver  

Answer:

The logistic equation is a differential equation that describes the growth of a population over time. The solution of this equation can be found using separation of variables or other methods of solving differential equations. The general solution for the logistic equation is given by:

y(t) = y_0 * e^(rt) / (1 + (y_0 - 1)e^(rt))

Where y_0 is the initial population size, r is the growth rate, and t is time.

For the specific case given in the question, we have the initial conditions y1(0)=14 and y2(0)=-3. We can use these to find the specific solution for each case.

1(0)=14 => y1(t) = 14e^(rt) / (1 + (14 - 1)e^(rt))

2(0)=−3 => y2(t) = -3e^(rt) / (1 + (-3 - 1)e^(rt))

It is important to note that we can not find the exact value of r without additional information.

Answer:

y(t) = 1 / (1 + (-4e^(-t))

Step-by-step explanation:

The logistic equation is a nonlinear differential equation that describes how a population grows. The solution for the logistic equation is given by y(t) = 1 / (1 + (Ce^(-t)) where C is the constant of integration, which can be determined by the initial conditions.

For the first initial condition, 1(0)=14, we can substitute the initial condition into the solution to get:

y(0) = 1 / (1 + (Ce^(0)) = 1 / (1 + C) = 14

Solving for C, we get C = 13.

So the solution for the first initial condition is:

y(t) = 1 / (1 + (13e^(-t))

For the second initial condition, 2(0)=-3, we can substitute the initial condition into the solution to get:

y(0) = 1 / (1 + (Ce^(0)) = 1 / (1 + C) = -3

Solving for C, we get C = -4.

So the solution for the second initial condition is:

y(t) = 1 / (1 + (-4e^(-t))

The ball reaches a maximum height of 35.375 ft.

s(t) = -16t^2 + 28t + 5

To find the time at which the ball reaches its maximum height, we can take the derivative of the height function with respect to time:

s'(t) = -32t + 28

And then set the derivative equal to zero and solve for t:

-32t + 28 = 0

32t = 28

t = 28/32 = 7/8 sec

So, the ball reaches its maximum height 7/8 seconds after it was thrown.

Next, we can plug this value of t back into the height function to find the maximum height:

s(7/8) = -16 * (7/8)^2 + 28 * (7/8) + 5 = 9.375 + 21 + 5 = 35.375 ft

Therefore, The ball reaches a maximum height of 35.375 ft.

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Answer:

Step-by-step explanation:

The revenue can be modeled by the polynomial function

R

(

t

)

=

−

0.037

t

4

+

1.414

t

3

−

19.777

t

2

+

118.696

t

−

205.332

where R represents the revenue in millions of dollars and t represents the year, with t = 6 corresponding to 2006. Over which intervals is the revenue for the company increasing? Over which intervals is the revenue for the company decreasing? These questions, along with many others, can be answered by examining the graph of the polynomial function. We have already explored the local behavior of quadratics, a special case of polynomials. In this section we will explore the local behavior of polynomials in general.

Multiplicity and Turning Points

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Suppose, for example, we graph the function

f

(

x

)

=

(

x

+

3

)

(

x

−

2

)

2

(

x

+

1

)

3

.

Notice in the figure below that the behavior of the function at each of the x-intercepts is different.

Graph of h(x)=x^3+4x^2+x-6.

The behavior of a graph at an x-intercept can be determined by examining the multiplicity of the zero.

The x-intercept

x

=

−

3

is the solution to the equation

(

x

+

3

)

=

0

. The graph passes directly through the x-intercept at

x

=

−

3

. The factor is linear (has a degree of 1), so the behavior near the intercept is like that of a line; it passes directly through the intercept. We call this a single zero because the zero corresponds to a single factor of the function.

The x-intercept x=2

is the repeated solution to the equation  (x−2)2=0

. The graph touches the axis at the intercept and changes direction. The factor is quadratic (degree 2), so the behavior near the intercept is like that of a quadratic—it bounces off of the horizontal axis at the intercept.

(x−2)2=(x−2)(x−2)