Watch help videoA shipping container will be used to transport several 50-kilogram crates across thecountry by rail. The greatest weight that can be loaded into the container is 24000kilograms. Other shipments weighing 11600 kilograms have already been loaded intothe container. Write and solve an inequality which can be used to determine x, thenumber of 50-kilogram crates that can be loaded into the shipping container.

Answer:

It's false! because 2 3 and 6 do not sum up to each side!

Step-by-step explanation:

Navern's manufacturing cycle efficiency (MCE) for its elevators is: 41.4%

The formula for obtaining the manufacturing cycle efficiency is value-added time divided by the production cycle time * 100. In the data given, the process and inspection times qualify as a value-added time

Process time = 23 days

Inspection time = 13 days

Value added time = 23 + 13 = 36days

The production cycle time = Move time + process time + queue time + inspection time + wait time

= 22 + 12 + 23 + 13 + 17 days

= 87 days

So, the manufacturing efficiency time = 36/87 * 100

= 41.4%

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Answer:

20. A. 357.8 in³

B. 1231.5 yd³

Step-by-step explanation:

20.

A.

Volume of Pyramid : ⅓*base area * height

here,

Base area = area of rectangle=length*breadth =10*8=80in²

Now

Height can be calculated by using Pythagorous theorem

height =\(\sqrt{(slant\: height)^2-(\frac{breadth}{2})^2}\)

height =\(\sqrt{14^2-(\frac{8}{2})^2}=\sqrt{196-16}=\sqrt{180}=13.42 in\)

height =13.4 in

Now

Volume of pyramid = ⅓*base area *height

Volume of Pyramid=⅓*80*13.42

Volume of Pyramid=357.8 in³

B.

Volume of cone = ⅓*area of base* height

Here

slant height=24 yd

height =?

diameter=14yd

radius =14/2=7 yd

Let's find the height:

By using the Pythagorous theorem,

slight height²=radius²+height²

substituting value

25²=7²+height²

height²=25²-7²

height =\(\sqrt{576}\)=24 yd

Now

Area of Base= πr²=π*7²=153.94 yd²

Now

Volume = ⅓*area of base*height =⅓*153.94*24=1231.5 yd³

So,

Volume of cone is 1231.52 yd³.

The reason behind this is that when the negative root goes from the RHS to LHS, its sign gets converted, and it appears like (x + 4).

A 2nd equation in x is known as a quadratic function. Ax2 + bx + c = 0 is the quadratic equations in standard form, wherein there a and b are the coefficient, x is the constant, and c is the constant.

The presence of a non-zero component in the coefficient of x2 (a ≠ 0) is the first prerequisite for an expression to be a quadratic equation.

As per the given information in the question,

The root obtained is -4 or,

We can also write this thing as,

x = -4

So, when -4  will come to the LHS the sign will be converted to positive, and then it can be written as (x + 4).

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Answer: To calculate the simple interest, you can use the formula:

I = Prt

where I is the interest, P is the principal (the amount borrowed), r is the interest rate as a decimal, and t is the time in years.

In this case, P = $4,200, r = 0.03, and t = 6/12 = 0.5 (since the interest is paid over 6 months, which is half of a year). Plugging these values into the formula, we get:

I = Prt = 4,200 * 0.03 * 0.5 = $63

So, Jimena will pay the store $63 in simple interest.

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

To solve this problem, first start setting up the equation.

Start with bob first - this is the easiest. Let x = bob

To get the part for susie - he has $24 more than twice the amount of bob, so his part of the equation would be set up as: 2x + 24

Combine these parts:

x + (2x + 24)

Combined they have $150, so you would set the equation above equal to 150

x + (2x + 24) = 150

Combine like terms:

3x + 24 = 150

Solve the equation for x

3x   +   24   =   150

      -   24         -24

3x               =   126      isolate x by itself on one side of the equation

divide both sides by 3 to get x by itself

3x    =    126

3              3

x    =   42

Now that you have solved for x, you know the amount that bob has... $42

With this information you can substitute 42 for x in the equation that was created for susie

2x + 24   would now by (2*42) + 24  which is $108

So, the amount that bob has is $42 and susie has $108

You can double check your work by adding $42 and $108 together to see if you get $150 (which you do)

Hope this helps!!!

equation and graph attached

The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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Answer: Neither

Step-by-step explanation:

Answer:

A) \(a_{1}\) = 1, \(a_{2}\) = 4

B) \(a_{n}\) = 2\(a_{n-1}\) + 2

C)    \(a_{n} = 2^{n-1} + 2^n -2\\a_{n} = 2^n + 2^{n-1} -2\)

Step-by-step explanation:

For n ≥ 1 ,

S is a set containing 2^n distinct real numbers

an = no of comparisons to be made between pairs of elements of s

A)

\(a_{1}\) = no of comparisons in set (s)

that contains 2 elements = 1

\(a_{2}\) = no of comparisons in set (s) containing 4 = 4

B)  an = 2a\(_{n-1}\) + 2

C) using the recurrence relation

a\(_{n}\) = 2a\(_{n-1}\) + 2

substitute the following values  2,3,4  .......... for n

a\(_{2}\) = 2a\(_{1}\) + 2

a\(_{3}\) = 2a\(_{2}\) + 2 = \(2^{2} a_{1} + 2^{2} + 2\)

a\(_{4}\) = \(2a_{3} + 2 = 2(2^{2}a + 2^{2} + 2 ) + 2\)

    = \(2^{n-1} a_{1} + \frac{2(2^{n-1}-1) }{2-1}\)   ---------------- (x)

since  2^1 + 2^2 + 2^3 + ...... + 2^n-1 =  \(\frac{2(2^{n-1 }-1) }{2-1}\)

applying the sum formula for G.P

\(\frac{a(r^n -1)}{r-1}\)

Note ; a = 2, r =2 , n = n-1

a1 = 1

so equation x becomes

\(a_{n} = 2^{n-1} + 2^n - 2\\a_{n} = 2^n + 2^{n-1} - 2\)

Answer:

It could be 0, is the question multiple choice?

a horizontal line always has a slope of 0, now, for the sake of a silly proof, let's do some rigamarole to get it.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{0}{7 +3} \implies \cfrac{ 0 }{ 10 } \implies \stackrel{ }{\text{\LARGE 0}}\)

The point (2,-4) satisfies y < 3x - 6

For the given triangles:

(1) x = 5.4

(2)  x  =  √23

(3) θ = 25.84 degree

(4)   x = 9.5

(5) n = 41

(1) In the given triangle,

One angle = 16 degree

Perpendicular = x

Hypotenuse    = 20

Since we know that

Sinθ = opposite side of θ/hypotenuse

Therefore,

⇒ sin 16 = x/20

⇒   0.27 = x/20

⇒         x = 5.4

(2)  In the given triangle,

Hypotenuse = 12 km

Base = 11 km

perpendicular = x

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (12)²= (x)² + (11)²

⇒ 144 = (x)² + 121

⇒   x² =  23

Taking square root both sides we get,

Hence,

⇒   x  =  √23

(3) In the given,

Base = 20

Perpendicular = 42

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (Hypotenuse)² =  (42)² + (20)²

⇒ (Hypotenuse)² =  2164

Taking square root both sides,

⇒ (Hypotenuse)  = 46.51

⇒ cosθ = Adjacent/hypotenuse

             = 42/46.51

             = 0.90

Taking inverse of cosθ,

⇒ θ = 25.84 degree

(4) In the given triangle,

One angle = 30 degree

Base = x

Hypotenuse    = 11

Since we know that

cosθ = Adjacent/hypotenuse

Therefore,

⇒ cos 30  = x/11

⇒   √3/2 = x/11

⇒         x = 9.5

(4) In the given triangle,

Base = 40

Perpendicular = 9

Hypotenuse = n

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒  n² = 9² + 40²

⇒  n² = 81 + 1600

⇒  n² = 1681

⇒  n = 41

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The limit of the expression is determined as 0.

The limit of the expression is calculated as follows;

The given expression = lim (x ---> 9) [ ( x - 9 ) / √x - 3)

For the given limit in the expression, we have x maps to 9 or x tends to 9.

When x tends to 9, we will have;

x ---->9 = (9 - 9 ) / (√9 - 3)

= (0)/(-3 - 3)

note: since √x can be negative or positive, we will choose negative so that our solution will not be undefined.

= 0/-6

= 0

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\(\sf \longrightarrow \: \: \lim_{x\to \: 9} \: \: \: \frac{x \: - \: 9}{ \sqrt{x} - 3 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ({ \sqrt{x} \: )}^{2} \: - \: {(3)}^{2} }{ \sqrt{x} - 3 } \\ \)

Now , by using Identity:-

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3)( \sqrt{x} - 3)}{ \sqrt{x} - 3 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3) \cancel{( \sqrt{x} - 3)}}{ \cancel{ \sqrt{x} - 3} } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3)(1)}{1 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{x} + 3)(1) \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{x} + 3)\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{9} + 3)\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \sqrt{9} + 3\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: 3 + 3\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: 6\\ \)

Step-by-step explanation:

Note: The term root and zero are used interchangeably.

Use Descartes Rule of Signs,

For the function, f(x), For every sign change, we have a positive root. If we have at least 2 positive roots, we either have that said number of roots or 2 less number of roots until we reach 0.

For example if we have 8 positive roots, we either have 8,6,4,2, or 0 positive roots

For the function f(-x), For every sign change we have a negative root.. If we have at least 2 negative roots, we either have that said number of roots or 2 less number of roots until we reach 0.

For example, if we have 7 possible roots, we either have 7,5,3,1 possible negative roots.

For g(x), we have 2 sign changes, so 2 positives root or none

\(g( - x) = ( - x) {}^{5} - 2( - x) {}^{3} - ( - x) {}^{2} + 6\)

\(g( - x) = - {x}^{5} + 2 {x}^{3} - {x}^{2} + 6\)

We have 3 sign changes, so we have 3 or 1 negative roots.

The degree of the polynomial tells us the max possible of zeroes. So the total number of zeroes is 5. That will always be the case for this polynomial so fill every row under the total number columns as 5.

The following possible combinations

2 positive zeroes, 3 negative zeroes, 0 imaginary zeroes

2 positive zeroes, 1 negative zeroes, 2 imaginary zeroes

0 positive zeroes, 3 negative zeroes, 2 imaginary zeroes

0 positive zeroes, 1 negative zeroes, 4 imaginary zeroes

line with a slope of 2 and a y interception of -3

Equation of the line:

Use the equation of the line to find a point in the line:

Find the value of y when x= 4

point (4,5)

y-interception gives you the point (0,-3)

Using the points (0,-3) and (4,5) graph the linea: put the points in the plane and draw a line that passes through those points:

Answer:

6/25

Step-by-step explanation:

Less than 13, there is 12 numbers in total

Probability = favourable outcomes/ total outcomes

                 = 12 / 50

                = 6/25 or 0.24 is the probability of selecting numbers less than 13

The time taken to make an amount of $255.45 is 9.75 hours

From the table, we have the following representations:

x=Time

y = Earnings

Using a point from the table, we have

x = 3 and y = 78.60

Express as ratio

This gives

x : y = 3 : 78.60

When the earning is $255.45, we have

x : 255.45 = 3 : 78.60

Express as fraction

x/255.45 = 3/78.60

So, we have

x = 255.45 * 3/78.60

Evaluate

x = 9.75

Hence, it will take 9.75 hours

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Consider a homogeneous machine of four linear equations in five unknowns are all multiples of 1 non-0 solution. Objective is to give an explanation for the gadget have an answer for each viable preference of constants on the proper facets of the equations.

Yes, it's miles true.

Consider the machine as Ax = 0. in which A is 4x5 matrix.

From given dim Nul A=1. Since, the rank theorem states that

The dimensions of the column space and the row space of a mxn matrix A are equal. This not unusual size, the rank of matrix A, additionally equals the number of pivot positions in A and satisfies the equation

rank A+ dim NulA = n

dim NulA =n- rank A

Rank A = 5 - dim Nul A

Rank A = 4

Thus, the measurement of dim Col A = rank A = five

And since Col A is a subspace of R^4, Col A = R^4.

So, every vector b in R^4 also in Col A, and Ax = b, has an answer for all b. Hence, the structures have an answer for every viable preference of constants on the right aspects of the equations.

Answer:

a-1. See part a-1 of the attached excel file for the time series plot.

a-2. The linear trend is not appropriate

b. The quadratic trend equation is y = -0.1618x^2 + 2.889x + 5.7022

c. Revenue in year 11 is 17.90.

Step-by-step explanation:

a-1. Construct a time series plot. Comment on the appropriateness of a linear trend.

Note: See part a-1 of the attached excel file for the time series plot.

a-2. Comment on the appropriateness of a linear trend.

Note: See part a-2 of the attached excel file for the time series plot with a linear trend.

From the time series plot with a linear trend, it can be seen that the movements of the time series plot and the linear trend are not the same. This implies that the linear trend is not appropriate

b. Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast revenue.

Note: See part b of the attached excel file for the quadratic equation trend.

From the quadratic equation trend, we obtained the following quadratic trend equation that can be used to forecast revenue:

y = -0.1618x^2 + 2.889x + 5.7022 ……………. (1)

Where;

y = Revenue

x = Year

c. Using the trend equation developed in part (b), forecast revenue in year 11.

Substituting x = 11 into equation (1), we have:

y = (-0.1618 * 11^2) + (2.889 * 11) + 5.7022 = 17.90

Therefore, revenue in year 11 is 17.90.

Answer:

The circumference of the drive wheel is 10 feet * 3.14 = 31.4 feet.

The circumference of the vat is 18 feet * 3.14 = 56.52 feet.

The total length of belt needed to go around the drive wheel and the vat is 31.4 + 56.52 = 87.92 feet.

Answer:

3x=63

Step-by-step explanation:

3 coins means a coin is x and total expenditure is equal to 63

Answer

Measure the shape yourself and follow the explanation.

Step-by-step explanation:

Measure each side of the Triangles with your ruler. Record it.

For example,

I measured and got 3cm, 3.5cm, 3.5cm.

Multiply by scale factor r 2.

for example, 3cm × 2 = 6cm

3.5cm × 2 = 7.0cm

3.5cm × 2 = 7.0cm

Use your pencil to draw your new numbers to form the new Triangle.

As for the second shape, measure each four sides using ruler

for example, I measured and had 4cm, 6cm, 4cm, 6m.

Multiply by scale factor r 2.

for example, 4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

Use your ruler to measure 1cm, 1.5cm, 1cm and 1.5cm, then to draw your new shape

The time it would take you to run 3.1 miles given the time it takes you to run a mile is 24 minutes 48 seconds.

Multiplication is a mathematical operation that is used to determine the product of a number. The sign used to represent multiplication is ×.

In order to determine the time, multiply 3.1 miles by 8 minutes

3.1 x 8 = 24.8 =  24 minutes 48 seconds.

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**** keep in mind (dy/dx) becomes like a letter itself

5.

x⁴+y⁴=2

Taking the derivative of both sides with respect to x:

4x³ + 4y³ (dy/dx) = 0

4y³ (dy/dx) = -4x³

(dy/dx) = -4x³/4y³

4's cancel out

(dy/dx) = -x³/y³

At (1,-1), we have

(dy/dx) = -x³/y³

(dy/dx) = -(1)³/(-1)³

(dy/dx) = -1/-1

(dy/dx) = 1

7.

y² = 4x

Taking the derivative of both sides with respect to x:

2y (dy/dx) = 4

divide 2y on both sides

(dy/dx) = 4/2y

simplify

(dy/dx) = 2/y

At (1,2), we have

(dy/dx) = 2/y

(dy/dx) = 2/(2)

(dy/dx) = 1

9.

sin y=5x⁴-5

Taking the derivative of both sides with respect to x:

cos y (dy/dx) = 20x³

(dy/dx) = 20x³/cos y

At (1,π), we have (dy/dx) = 20/(-1) = -20.

11.

cos y=x

Taking the derivative of both sides with respect to x:

-sin y (dy/dx) = 1

(dy/dx) = -1/sin y

At (0,π/2), we have (dy/dx) = -1.

6.

x=e^y

Taking the derivative of both sides with respect to x:

1 = e^y (dy/dx)

(dy/dx) = 1/e^y

At (2,In 2), we have (dy/dx) = 1/e^(In 2) = 1/2.

8.

y²+3x= 8

Taking the derivative of both sides with respect to x:

2y (dy/dx) + 3 = 0

(dy/dx) = -3/(2y)

At (1,√5), we have (dy/dx) = -3/(2√5).

10.

√x-2√y = 0

Taking the derivative of both sides with respect to x:

1/(2√x) - 1/√y (dy/dx) = 0

(dy/dx) = √y/(2√x)

At (4,1), we have (dy/dx) = 1/4.

12.

tan xy=x+y

Taking the derivative of both sides with respect to x:

y sec² (xy) (dy/dx) = 1 + y

(dy/dx) = (1 + y)/[y sec² (xy)]

At (0,0), we have (dy/dx) = 1/0, which is undefined.

5-12. Implicit differentiation Carry out the following steps.

a. Use implicit differentiation to find (dy/dx)

b. Find the slope of the curve at the given point.

5. x⁴+y⁴=2 ; (1,-1)

6. y² = 4x ; (1,2)

7. sin y=5x⁴-5 ; (1,π)

8. cos y=x ; (0, (π/2))

9. x=e^y ; (2, In 2)

10. y²+3x= 8 ; (1, √5)

11. √x-2√y = 0 ; (4,1)

12. tan xy=x+y ; (0,0)

ChatGPT

Answer:

(f o h)(-3) = -1

Step-by-step explanation:

(f o h)(x) = -2(-x - 3) - 1

(f o h)(x) = 2x + 6 - 1

(f o h)(x) = 2x + 5

(f o h)(-3) = 2(-3) + 5

(f o h)(-3) = -6 + 5

(f o h)(-3) = -1

Answer:

f(x) = x + 7 and g(x) = x + 3

Step-by-step explanation:

Answer:

i) Consecutive interior angles

ii) Supplementary angles

iii) The two oars are parallel by consecutive interior angles theorem

Step-by-step explanation:

i) m∠1  and m∠2 lie between two line and on the same side of the line passing through the two lines. Therefore, they are consecutive interior angles

ii)x = 10

m∠1 = 6x + 18

= 6(10) + 18

= 60 + 18

= 78

m∠2 = 9x + 12

= 9(10) + 12

= 90 + 12

= 102

m∠1 + m∠2 = 72 + 108 = 180

Since m∠1 and m∠2 add to 180, they are supplementary angles.

iii) The two oars are parallel

consecutive interior angle theorem:

If  a transversal cuts through two line and the consecutive interior angles are supplimentary, then the two lines are parallel

Answer:

x=3

Step-by-step explanation:

3(5x + 7) = 9x + 39

15x + 21 = 9x + 39

15x - 9x = 39 - 21

6x = 18

x = 3