Lee i packing a truck with mall and large filing cabinet. The large cabinet weigh 30 pound, and the mall cabinet weight 20 pound. To optimize the load, the total load weight hould be 1550 pound from a total of 65 cabinet. How many of each ize of cabinet hould Lee pack in the truck?

Answer:

Step-by-step explanation:
Slope is gradient which is, change in y
                                              change in x
so, on the graph, change in y = 10-2.5 = 7.5
                              change in x = 5-0 =5
so, gradient is, 7.5/5
                     = 3/2

Answer:

a. 135 is the correct answer

Step-by-step explanation:

Want to find out what the total degrees is of the octagon.

Octagon = 1080

Divide 1080 by 8

135 degrees per angle

Answer:

Option A is correct

Step-by-step explanation:

Hint :

Sum of angles in Regular Octagon = 1080°.

Simplify :

\(∴z = 135\)

Answer: here you go sir

Step-by-step explanation: I couldn’t put it on here because I had to put certain symbols. Hope this helps!

The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

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In a unit vector notation, the net force on the loop is (3.2×10⁻³ N)​​

Vector:

In math vector is the object containing both magnitude and direction

Given,

In the figure, a long straight wire carries a current i1​=30A  and a rectangular loop carries current i2​=20A. Take the dimensions to be a=1 cm, b = 8cm and L = 30cm.

Here we need to find the unit-vector notation for the net force on the loop due to i1​.

Here let's divide the loop into 4 parts i.e, they are witten as,

=> 1−2 , 2−3 , 3−4 , and 4−1

Then the force F on a wire of length L carrying current I in magnetic field of strength B (constant) is written as,

=> F=L(I×B)

Now, the force on part  2−3  and  4−1  is equal but opposite , hence cancelled, so the remaining are

⟹F2−3​+F4−1​=0

Therefore, Fnet​=F1−2​+F3−4​

Then the value of the net force is

=> (3.2×10⁻³ N)​​

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Answer:

y = (-1/4)x + 2.5

Step-by-step explanation:

-2,3

2,2

Answer:

Hector can fit 210 compact discs into 14 boxes.

The  series \($\sum_{n=0}^{\infty} C_n(x-3)^n$\) converges at x=7, but based on the given information it is not possible to conclude about the convergence at x=10, x=5, or x=0.

The convergence or divergence of a power series depends on the values of x within its interval of convergence. In this case, it is given that the series converges at x=7, which means that the series converges for x values that are closer to 3 (the center of the series) and within the interval of convergence around x=7.

However, the information about the series diverging at x=10 does not provide any direct information about the convergence at other points. It only tells us that the series does not converge at x=10.

Therefore, we cannot make any conclusions about the convergence or divergence of the series at x=5 or x=0 based on the given information.

To determine the convergence at x=10, x=5, or x=0, we would need additional information or tests such as the ratio test or the root test to analyze the behavior of the series at those specific points.

Without further information, we cannot make any definitive statements about the convergence or divergence of the series at x=10, x=5, or x=0.

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Answer:

\(\left(x-10\right)-\left(2x-5\right)^2=-4x^2+21x-35\)

Step-by-step explanation:

As we have to subtract \(\left(2x\:-\:5\right)^2\) from \(\left(x-10\right)\)

so

\(\left(x-10\right)-\left(2x\:-\:5\right)^2\)

solving and simplifying the polynomial in standard form

\(\left(x-10\right)-\left(2x-5\right)^2\)

\(\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\)

\(=x-10-\left(2x-5\right)^2\)

\(=x-10-\left(4x^2-20x+25\right)\)      ∵ \(\left(2x\:-\:5\right)^2=\:4x^2-20x+25\)

\(=x-10-4x^2+20x-25\)

\(=-4x^2+21x-35\)

We know that standard form means that the terms of the expression are ordered from biggest exponent to lowest exponent.

Thus, a simplified polynomial in standard form is:

\(\left(x-10\right)-\left(2x-5\right)^2=-4x^2+21x-35\)

Answer:

3rd and 4th

Step-by-step explanation:

Answer:

∠C and ∠DCB and ∠BCD

Step-by-step explanation:

We can name an angle either using one letter that represents it or use all three letters together.

When we use a single letter to represent or point an angle we must choose the center letter, C in this case.

And when we use all three letter to point an angle we must place the center letter, again C in this case, in the middle

Therefore the angle can be named as

∠C or ∠DCB or ∠BCD

Answer:

The temp at 6P.M. Is -14°C

Step-by-step explanation:

The mean outcome of this experiment with outcomes ranging from 50 to 70 using a uniform random variable is 60.
Step 1: Identify the range of the outcomes.
In this case, the outcomes range from 50 to 70.

Step 2: Calculate the mean of the uniform random variable.
The mean (µ) of a uniform random variable is calculated using the formula:

µ = (a + b) / 2

where a is the minimum outcome value and b is the maximum outcome value.

Step 3: Apply the formula using the given values.
a = 50 (minimum outcome)
b = 70 (maximum outcome)

µ = (50 + 70) / 2
µ = 120 / 2
µ = 60

The mean outcome of this experiment with outcomes ranging from 50 to 70 using a uniform random variable is 60.

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Cycling at a speed of 25 km/h on paved surfaces and 10 km/h on off-road areas, Matthew cycled 41 km in 2 hours.To determine for how long Matthew cycled off-road, we first have to find how long he cycled on paved surfaces and off-road and then subtract the duration on paved surfaces from the total cycling duration of 2 hours.

The time spent cycling on paved surfaces = distance / speed = 28 km / 25 km/h = 1.12 hoursThe time spent cycling off-road = total cycling duration - time spent cycling on paved surfaces= 2 hours - 1.12 hours = 0.88 hours or 52.8 minutes Therefore, Matthew cycled off-road for approximately 53 minutes.

Matthew likes cycling and he cycles partly on paved surfaces and partly off-road, through hilly and wooded areas. Matthew cycles at a speed of 25 km/h on paved surfaces and at 10 km/h on off-road surfaces. The question asks for how long he cycled off-road if he cycled 41 km in 2 hours.We first have to find how long he cycled on paved surfaces and off-road, and then we'll subtract the duration on paved surfaces from the total cycling duration of 2 hours.The time taken to cycle on paved surfaces = distance / speed = 28 km / 25 km/h = 1.12 hours.

The time taken to cycle off-road = total cycling duration - time taken to cycle on paved surfaces= 2 hours - 1.12 hours = 0.88 hours or 52.8 minutesTherefore, Matthew cycled off-road for roughly 53 minutes. He spent more time cycling on paved surfaces, about 68% of the total time. using the given rates of speed, we were able to determine the duration for which Matthew cycled off-road, which was 0.88 hours or approximately 53 minutes.

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Answer:

4th option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - \(\frac{2}{3}\) x + 8 ← is in slope- intercept form

with slope m = - \(\frac{2}{3}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{2}{3} }\) = \(\frac{3}{2}\) , then

y = \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute (- 6, 2 ) into the partial equation

2 = - 9 + c ⇒ c = 2 + 9 = 11

y = \(\frac{3}{2}\) x + 11 ← equation of perpendicular line

Answer:

I miss you

Step-by-step explanation:

The probability that the company will make less than $2m is 0.8 and b) the probability that the company will make less than $1m or at least $2m is 0.7

Here we are given respective probabilities of the revenue a company could make in a year.

a) Here we need to find the probability that it makes a revenue less than $ 2 million

This means that we need t find the probability that it makes revenue

less than $1M + greater than $1 M but less than $2M

= P(A₁) + P(A₂)

= 0.5 + 0.3

= 0.8

b)

The probability that the company will make less than $1M or at least $2M is

P(A₁ U A₃)

= P(A₁) + P(A₃) - P(A₁ ∩ A₃)

Since A₁ and A₃ are clearly mutually exclusive events, P(A₁ ∩ A₃) will be 0.

Hence we get

P(A₁ U A₃) = 0.5 + 0.2

= 0.7

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Complete Question

Assume the following in regard to a company’s annual revenue:

A₁ : Revenue < $1M; P(A₁) = 0.5

A₂ : Revenue > $1M but < $2M; P(A₂) = 0.3

A₃ : Revenue > $2M; P(A₃) = 0.2

a)What is the probability that the company will make less than $2M?

b)What is the probability that the company will make less than $1M or at least $2M

Answer:

9, 20 and 4

Step-by-step explanation:

Swimming only 9

Track only 20

All 3 events

14 did track and field

10 did track and swimming

Those who sis all 14- 10 = 4

The answers are the students do a) swimming only = 9, b)track events only = 20 and c) all three events = 4

A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.

Given that, a school sports team contains 68 students. 33 do field events, 40 do track events, 23 go swimming, 14 do both field and track events. If 15 students do field events only and 10 do both swimming and track events,

Please refer to picture attached

Therefore,

15+a+c+d = 33.......1

b+c+d+e = 40.........2

a+b+d+f = 23..........3

c+d = 14...............4

a+d = 8.............5

b+d = 10.............6

Now, solving for variables,

From 1 and 4,

a = 4

Therefore, from 5,

d = 4

From 6,

b = 6

Put these in eq 3,

f = 9

c = 10

e = 20

Therefore,

Swimming only = 9

Track events = 20

All three = 4

Hence, the answers are the students do a) swimming only = 9, b)track events only = 20 and c) all three events = 4

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The median for the given continuous random variable is m = ±6.65

Let x be a continuous random variable over [a, b] with probability density function f.

Then the median of the x-values is that number m such that integral^ma f(x)dx = 1/2.

Find the median.

Given, f(x) = 1/242x and [0,22].

To find the median, we need to find the number m such that integral^ma f(x)dx = 1/2.

Now, let's calculate the integral,

∫f(x)dx = ∫1/242xdx

= ln|x|/242 + C

Applying the limits,\(∫^m_0 f(x)dx = ∫^0_m f(x)dx\)

∴ln|m|/242 + C

= 1/2 × ∫\(^22_0 f(x)dx\)

= 1/2 × ∫\(^22_0 1/242xdx\)

= 1/2 [ln(22) - ln(0)]/242

Now, we need to find m such that ln|m|/242

= [ln(22) - ln(0)]/484

ln|m| = ln(22) - ln(0.5)

ln|m| = ln(22/0.5)

m = ± √(22/0.5)

[Since the range is given from 0 to 22]

m = ± 6.65

Hence, the median is m = ±6.65

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The quotient of the given complex number is 27/13 - 15/13i.

An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined

Given:

We have to Evaluate the expression.

According to given question we have

Given the division expression

(10 – 4i) ÷ (5 + i).

This can also be expressed as:

10-4i/5+i

On rationalizing, we will have:

10-4i/5+i * 5-i/5-i

50-10i-20i-4(-1)/25-(-1)

50-30i+4/26

54-30i/26

27/13 - 15/13i

Hence, the quotient of the given complex number is 27/13 - 15/13i.

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Answer:

7 is the tenth place and 8 is in the hundredth place.

so it is rounded to 0.78 since 2 is below 5.

Step-by-step explanation:

The value of function f(7) is approximately 14.857.

To find the value of f(7), we can use the information given about f(1), the continuity of f', and the definite integral involving f'.

Let's go step by step:

1. We are given that f(1) = 12. This means that the value of the function f(x) at x = 1 is 12.

2. We are also given that f' is continuous. This implies that f'(x) is continuous for all x in the domain of f'.

3. The definite integral 7 ∫ f'(x) dx from 1 to 7 is equal to 20. This means that the integral of f'(x) over the interval from x = 1 to x = 7 is equal to 20.

Using the Fundamental Theorem of Calculus, we can relate the definite integral to the original function f(x):

∫ f'(x) dx = f(x) + C,

where C is the constant of integration.

Substituting the given information into the equation, we have:

7 ∫ f'(x) dx = 20,

which can be rewritten as:

7 [f(x)] from 1 to 7 = 20.

Now, let's evaluate the definite integral:

7 [f(7) - f(1)] = 20.

Since we know f(1) = 12, we can substitute this value into the equation:

7 [f(7) - 12] = 20.

Expanding the equation:

7f(7) - 84 = 20.

Moving the constant term to the other side:

7f(7) = 20 + 84 = 104.

Finally, divide both sides of the equation by 7:

f(7) = 104/7 = 14.857 (approximately).

Therefore, f(7) has a value of around 14.857.

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There is no sufficient evidence that we can use in order to substantiate the claim of the publisher,

The null hypothesis H0: p = 0.47

The alternative hypothesis is H1: p > 0.47

The question requires us to test the fact that more than 47 percent of the readers have their own personal computer. This is therefore the claim that is to be tested here.

There is no sufficient evidence to substantiate the claim because of the lack of certain details that would have been used to carry out the hypothesis test.

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Answer:

A: yes

B: yes

C: no

D: no

E: no

Hope This Helps!!!

Answer:

s = -2

s = -8

Step-by-step explanation:

negative numbers get smaller and smaller the farther they are from zero

m1 = 5 and m2 = 5

Two lines are said to be parallel if their gradients are equal.

Analysis:

Line L1 is already in the form y = mx +c which is y = 5x + 1

line L2 is not in the form y = mx + c,  so we write it in that form.

2y -10x  + 3 = 0

2y = 10x -3

y = 10x/2 - 3/2

y = 5x + 3 -3/2

the gradient m1 of line L1 is the coefficient of x which is 5.

the gradient m2 of line L2 is the coefficient of x which is 5.

In conclusion, The both lines are parallel since their gradients are equal.

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The derivative of the function y = (2 - x) / (x^3 - 2x^2) with respect to x is given by dx dy​ = -2x.

To find the derivative of the function, we will use the quotient rule, which states that if we have a function of the form f(x) = g(x) / h(x), then the derivative is given by (h(x) * g'(x) - g(x) * h'(x)) / (h(x))^2.  

Applying the quotient rule to the given function, we have g(x) = (2 - x) and h(x) = (x^3 - 2x^2). Taking the derivatives of g(x) and h(x), we get g'(x) = -1 and h'(x) = (3x^2 - 4x).  

Now, substituting these values into the quotient rule formula, we have:

dx dy​ = \([(x^3 - 2x^2) * (-1) - (2 - x) * (3x^2 - 4x)] / (x^3 - 2x^2)^2\)  

Simplifying the expression further, we get:

dx\dy​ =\([-x^3 + 2x^2 + 6x^3 - 8x^2 + 2x - 3x^2 + 4x] / (x^3 - 2x^2)^2\\= [5x^3 - 9x^2 + 6x] / (x^3 - 2x^2)^2\\= -2x\)

Therefore, the derivative of the given function y = (2 - x) / (x^3 - 2x^2) with respect to x is dx dy​ = -2x.

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A correlation coefficient is a statistic that tells us the strength and direction of the linear relationship between two variables.

The correlation coefficient is a measure of the degree of association between two variables. It quantifies how closely the data points align along a straight line. The coefficient can range from -1 to +1, where -1 represents a perfect negative linear relationship, +1 represents a perfect positive linear relationship, and 0 indicates no linear relationship.

The sign of the coefficient indicates the direction of the relationship, while the magnitude indicates the strength. A correlation coefficient of 0 does not necessarily imply the absence of any relationship; it only means that there is no linear association between the variables. It is important to note that correlation does not imply causation, as other factors may be influencing the relationship.

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Answer:

\(4(x - 9)(x - 7)\)

Step-by-step explanation:

...

Answer:

No

Step-by-step explanation:

See take 0.2 for example

In fraction it is 2/100 which can be easily reduced and should be reduced depending on the type of question.

1/50 would be the answer for my example.