Part A
A rectangular prism measures 7 1/2cm by 12 cm by 15 1/2cm.
Calculate the number of cubes with edge length 1/2 cm that fit in this prism
cubes____

Answer:

Angle A = 83.59° (2 d.p.)

Angle C = 56.41° (2 d.p.)

Side a = 193.25 (2 d.p.)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]

Given:

Substitute the given values into the Sine Rule formula:

[tex]\implies \dfrac{\sin A}{a}=\dfrac{\sin 40^{\circ}}{125}=\dfrac{\sin C}{162}[/tex]

Solve for angle C:

[tex]\implies \dfrac{\sin 40^{\circ}}{125}=\dfrac{\sin C}{162}[/tex]

[tex]\implies \sin C=\dfrac{162\sin 40^{\circ}}{125}[/tex]

[tex]\implies C=\sin^{-1}\left(\dfrac{162\sin 40^{\circ}}{125}\right)[/tex]

[tex]\implies C=56.4136175...^{\circ}[/tex]

Interior angles of a triangle sum to 180°. Therefore:

[tex]\implies A+B+C = 180^{\circ}[/tex]

[tex]\implies A = 180^{\circ}-B-C[/tex]

[tex]\implies A = 180^{\circ}-40^{\circ}-56.4136175...^{\circ}[/tex]

[tex]\implies A = 83.5863824...^{\circ}[/tex]

Finally, to find a, substitute the found angles and sides into the Sine Rule and solve for a:

[tex]\implies \dfrac{\sin A}{a}=\dfrac{\sin B}{b}[/tex]

[tex]\implies \dfrac{\sin 83.5863824...^{\circ}}{a}=\dfrac{\sin 40^{\circ}}{125}[/tex]

[tex]\implies a=\dfrac{125\sin 83.5863824...^{\circ}}{\sin 40^{\circ}}[/tex]

[tex]\implies a=193.248396...[/tex]

Answer:

The coupon that gives $14 rebate off $75 gives a lower price

Step-by-step explanation:

Let's figure out what percentage of $75 the $14 rebate coupon is

If this percentage is greater than 15% then the $14 rebate coupon gives a better discount; if not the 15% discount offers a better buy

To find what % $14 is of the $75 cost of printer, divide 14 by 75 and multiply by 100 to convert to %:

[tex]\dfrac{14}{75} \times 100 = 18.67\%\\\\[/tex]

Since 18.67% is greater than 15%, getting $14 off $75 will give a lower price

The graph of the quadratic function, y = -x² + 8·x - 15, created with MS Excel is attached.

The  roots are; (3, 0) and (5, 0)

The location of the vertex of a parabola is; (4, 1)

A parabola is a curve formed uy the path of an object that moves such that the distance of the object from a fixed point is the same as the distance of the point from a fixed line.

The specified function is f(x) = -x² + 8·x - 15

The equation is a quadratic equation, and the shape of the graph of the function is a parabola.

The points that can be used to graph tjhe function, obtained using MS Excel are;

x  [tex]{}[/tex]    f(x)

2  [tex]{}[/tex]    -3

3  [tex]{}[/tex]    0

4  [tex]{}[/tex]    1

5  [tex]{}[/tex]    0

6  [tex]{}[/tex]    -3

The roots are the x-intercept of the graph, which are the points the graph intersects the x-axis, which are the points where, y = 0.

The roots obtained from the values in the above table are; (3, 0), and (5, 0)

The vertex point is the highest point on the graph. The heighest point or vertex is the point where the y-value is maximum

From the table and the attached graph, the vertex is the point (4, 1)

The vertex of the parabola, obtained using the graph is (4, 1)

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Answer:

14.115

Step-by-step explanation:

Recall Trapezoidal Rule

[tex]\displaystyle \int\limits^b_a {f(x)} \, dx=\frac{1}{2}\biggr(\frac{b-a}{n}\biggr)\biggr[f(x_0)+2\bigr(f(x_1)+f(x_2)+\text{... }+f(x_{n-1})\bigr)+f(x_n)\biggr][/tex]

Make necessary substitutions and evaluate

[tex]\displaystyle \int\limits^5_1 {\sqrt{x^2+3}} \, dx=\frac{1}{2}\biggr(\frac{5-1}{4}\biggr)\biggr[2+2\bigr(\sqrt{7}+\sqrt{12}+\sqrt{19}\bigr)+\sqrt{28}\biggr]\approx14.115[/tex]

Note that the actual value of the integral is [tex]\displaystyle \int\limits^5_1 {\sqrt{x^2+3}} \, dx\approx14.078[/tex], so we can see how accurate the Trapezoidal rule is with just a few equal partions.

We use the concepts of continuity and differentiability to prove that a continuous function of order 3 is continuous of order 1 after being differentiated twice.

Let us assume the function x³ as the function of order 3. We know that its 1st derivative will be 3x² and its 2nd derivative will be, 6x. Now, let's check both of their continuities at any point "a" on the function. By putting a limit x tending to a to the function

= lim (x³) = a³

  x→a

and putting a directly to the equation i.e, f(a) = a³ therefore, x³ is a continuous function at a. Similarly, by putting a limit x tending to a to the function

= lim (6x) = 6a

  x→a

and putting a directly to the equation i.e, f(a) = 6(a) therefore, 6x is also a continuous function at a. Hence we can say that the continuous function of order 3 is continuous of order 1 after being differentiated twice.

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Answer for the "different" question: The distance between -4.5 and 3.5 is 8.

Answer for the "same" questions:

O Add -4.5 and 3.5: -4.5 + 3.5 = -1

O What is -4.5 increased by 3.5: -4.5 + 3.5 = -1

Find the sum of -4.5 and 3.5: -4.5 + 3.5 = -1

Answer: What is the distance between -4.5 and 3.5?

Step-by-step explanation:

         The distance between -4.5 and 3.5 and will be different than all the others because the distance it's asking for the distance between the absolute values, not adding them together.

          Find "both" answers.

➜ Answer for the "different" question:

           What is the distance between -4.5 and 3.5? = 4.5 + 3.5 = 8

➜ Answer for the "same" questions:

           Add -4.5 and 3.5 = -4.5 + 3.5 = -1

Answer:

5.92

Step-by-step explanation:

Set up a proportion

cups/mg = cups/mg

[tex]\frac{1.5}{148}[/tex] = [tex]\frac{6}{x}[/tex]

1.5 x 4 = 6,

so 1.48 x 4 = 5.92

The class width of the histogram is 5

A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width called the class width.

The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most common type of histogram.

The class width is plotted in the x - direction. this is the difference between the two consecutive values in the boundary.

class width = 100.5 - 95.5 = 5

class width = 85.5 - 80.5 = 5

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Answer:

44 boxes

Step-by-step explanation:

You have to find 20% of 20.
20% = 1/5

1/5 of 20 is 4

So next year she will buy 24 boxes

If you add them together, she will have 44 boxes in all

Answer: Add −9b and 2b. −7b + 2n −4

Answer: -2 i think

Step-by-step explanation:

(5-4)-3*(5-4)

1-3*1

1-3=-2

Answer:

The value is 0

The simplified expression is

3• (5 - 4) -3 (5 - 4)

Step-by-step explanation:

Tom's monthly mortgage repayment will be an amount of $1,144.41.

To calculate Tom's monthly mortgage repayment, we can use the formula:

[tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n -1 ][/tex]

Where:

M = monthly repayment

P = the principal amount (loan amount) = $300,000 - $30,000 = $270,000

i = monthly interest rate = 2%/12 = 0.02/12 = 0.0017

n = number of months = 25 years x 12 months/year = 300 months

Plugging in the values:

M = $270,000 [ 0.0017(1 + 0.0017)³⁰⁰ ] / [ (1 + 0.0017)³⁰⁰ – 1 ]

M = $1,144.41

Thus, his monthly mortgage repayment will be $1,144.41.

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Answer: 9/80

Step-by-step explanation:

1/8 = 10/80

1/10 = 8/80

9/80 is fraction between 1/8 and 1/10

Have A Good Day :)

When Kayla was instructed to rewrite the polynomial expression x2 + 6x + 9, she wrote [tex]x^2+2 x-3+3^2=(x+3)^2[/tex].

Factor [tex]$ x^2+6 x+9: \quad(x+3)^2$[/tex]

[tex]$$x^2+6 x+9$$[/tex]

Rephrase in the manner of [tex]$a^2+2 a b+b^2$[/tex] :

[tex]$9=3^2$[/tex]

[tex]$6 x=2 x \cdot 3$\\$=x^2+2 x \cdot 3+3^2$[/tex]

Using the Perfect Square Formula : [tex]$\quad a^2+2 a b+b^2=(a+b)^2$[/tex]

[tex]$$\begin{aligned}& x^2+2 x-3+3^2=(x+3)^2 \\& =(x+3)^2\end{aligned}$$[/tex]

An expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables is said to be a polynomial. Variables, which are sometimes known as indeterminates, and coefficients make up a polynomial. x2 4x + 7 is an illustration of a polynomial of one uncertain x.

An expression with a single or a number of terms is referred to as a polynomial. The words "polynomial" and "nomial," which are two distinct phrases, are the origins of the term. Nominal is another word for many, while poly is another word for many. An algebraic expression with two or more algebraic terms is referred to as a polynomial.

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The in-house production  amount costs per foot of cables A, B, and C are $6, $8, and $10, respectively.

1. The question states that a company produces three types of cables, A, B, and C.

2. The in-house production amount costs for each type of cable is given in the question. The cost per foot of cable A is $6, the cost per foot of cable B is $8, and the cost per foot of cable C is $10.

The company produces three types of cables, A, B, and C, and each type of cable has a different in-house production cost. Cable A has a cost per foot of $6, cable B has a cost per foot of $8, and cable C has a cost per foot of $10. This means that if the company produces 100 feet of cable A, the in-house production cost would be $600, whereas if they produce 100 feet of cable B, the in-house production cost would be $800, and if they produce 100 feet of cable C, the in-house production cost would be $1000.

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Answer:

   C

Step-by-step explanation:

2.52/4 =0.63/1

The probability of rolling two ones in a row is equal to P = 1/36

We want to find the probability of rolling two ones in a row.

Remember that a dice has 6 sides, so the probability of randomly rolling a 1 is just:

p = 1/6

And if we want to do that two times then we need to have that probability twice:

q = 1/6

And the joint probability (probability of rolling two ones) is equal to the product between the individual ones:

P = p*q = (1/6)*(1/6)

P = 1/36

That is the probability.

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The number of handshakes altogether exists 45.

In mathematics, there are two alternative methods for dividing up a collection of components into subsets: combination and permutation. The subset's components can be arranged in any sequence when used together. The components of the subset are arranged in a particular order in a permutation.

A combination in mathematics is a choice of elements from a set with distinct members, where the order of the choices is irrelevant.

Combinations are a mathematical method for calculating the number of alternative arrangements in a collection of objects where the order of the selection is irrelevant. You are free to choose any combination of the things.

Given:

Number of people in the conference = 10

Each person shakes hands with others.

The total number of handshakes [tex]$={ }^n \mathrm{C}_2$[/tex]

Total number of handshakes [tex]$={ }^{10} C_2=(10 \times 9) / 2=45$[/tex] handshakes.

The complete question is:

At the end of a meeting all the ten people present shake hands with each other once. The number of handshakes altogether is

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your solution

4+13x=57

x=53÷4 = 13.25

If a bag has orange marbles, the number of red marbles it will contain would be also the same as the number of orange marbles.

The Dante's Marble Company sells bags of marbles that contains different types of marbles such as both the red and the orange marbles I'm a particular order.

In a bag of marbles, every red marbles = every orange marbles.

Therefore the number of red marbles found in a bag will be the same amount of orange marbles found in the same bag.

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A. No accidents occur in one week. Probability = 0.0113

B. 10 or more accidents occur in a week. Probability = 0.0018

C. One accident occurs today. Probability =0.2122

A. No accidents occur in one week.

Probability = e^(-4.7)

= e^(-4.7)

= 0.0113

B. 10 or more accidents occur in a week.

Probability = 1 - e^(-4.7)(1 + 4.7 + (4.7^2)/2 + (4.7^3)/6 + (4.7^4)/24 + (4.7^5)/120)

= 1 - e^(-4.7)(1 + 4.7 + 22.09 + 100.521 + 470.4724 + 2,054.085)

= 1 - e^(-4.7)(3,648.78)

= 1 - 0.0050

= 0.0018

C. One accident occurs today.

Probability = 4.7e^(-4.7)

= 4.7e^(-4.7)

= 0.2122

The probability of no accidents occurring in one week is 0.0113, the probability of 10 or more accidents occurring in one week is 0.0018, and the probability of one accident occurring today is 0.2122. These probabilities are calculated using the Poisson distribution with a mean of 4.7 accidents per week.

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Answer:

D or 12.8

Step-by-step explanation:

Distance (d) = √(-2 - 8)2 + (9 - 1)2

= √(-10)2 + (8)2

= √164

= 2√41

= 12.806248474866

Answer:

Hello

Hi 2√41 approximately equals to 12.8, good luck and please see the file below for the answer.

It is D.

The equation of the straight line would be -

y = 4x + 5.

Given is that a line y = mx + 5 that passes through the point (1, 6) and is parallel to y = 4x + 6.

       y = mx + c

Equation of the line is -

y = mx + 5

It is parallel to -

y = 4x + 6

Then -

m = 4  {slopes of || lines are equal)

So, we get the equation as -

y = 4x + 5

Therefore, the equation of the straight line would be -

y = 4x + 5.

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Answer:

this is a little typical

A) r(t) =[tex]c_{1}[/tex]×e^(∧×t)[tex]v_{1}[/tex]+ [tex]c_{2}[/tex] × e^(∧²×t)[tex]v_2[/tex]  ; B) r(t) = X×e^(∧×t)c ; C) [tex]r_1[/tex](t) = [tex]c_{1}[/tex](-1×[tex]e^{3t}[/tex])×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) -4×[tex]e^{3t}[/tex], [tex]r_2[/tex](t) =  [tex]c_2[/tex](-1×[tex]e^{3t}[/tex]×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) + 4i×[tex]e^{3t}[/tex].

A) The solution to the linear equation in eigenvalue/eigenvector form:

r(t) = [tex]c_{1}[/tex]×e^(∧×t)[tex]v_{1}[/tex]+ [tex]c_{2}[/tex] × e^(∧²×t)[tex]v_2[/tex]

B) The solution to the linear equation in fundamental matrix form:

 r(t) = X×e^(∧×t)c

C) As two equations: The solution to the linear system can also be written as two equations as follows:

 [tex]r_1[/tex](t) = [tex]c_1[/tex] ×e^(∧²×t)[tex]v_1[/tex] = [tex]c_{1}[/tex](-1×[tex]e^{3t}[/tex])×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) -4×[tex]e^{3t}[/tex]

 [tex]r_2[/tex](t) = [tex]c_2[/tex]×e^(∧² ×t)[tex]v_2[/tex] = [tex]c_2[/tex](-1×[tex]e^{3t}[/tex]×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) + 4i×[tex]e^{3t}[/tex]

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Answer: 125

Step-by-step explanation: product of 5 and 75 = 5*75 = 375 divided by 3 which is 375/3 = 125.

The correct answer is C), because it is possible to create an economic model describing the relationship between fertilizer usage and yield.

The economic model would take into account the nonlinear relationship, which is shown in the graph. Specifically, the slope of the curve between one and two tons of fertilizer is approximately 2 (change in yield divided by change in fertilizer usage). This means that for every ton of fertilizer used, the yield increases by two (change in yield / change in fertilizer usage = 2). Although using more than three tons of fertilizer has minimal effect on yield, the economic model would still take this into account and provide a more accurate representation of the relationship between the two variables.

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The speed when the object and dropped from a height of 350 feet and takes exactly 5 seconds is 70 feet per seconds.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity

In this situation, when dropped from a height of 350 feet, it takes exactly 5 seconds for the stone to hit the ground.

The speed will be:

= Distance / Time

= 350 / 5

= 70 feet per seconds

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Complete question

A moving object travels 350 feet in 5 seconds assuming that the object travels at a constant speed , When dropped from a height of 350 feet , It takes exactly 5 seconds for the stone to hit the ground. Calculate the speed.

The quadratic equation whose roots are -1 and 6 and the leading coefficient is 4 is written in the form

The roots of a quadratic equation is the value of x when y is zero hence we have the equation

x = -1 and x = 6

(x + 1)(x - 6)

with the  leading coefficient of 4

4(x + 1)(x - 6)

expanding will result to

= 4(x² - 6x + x - 6)

= 4(x² - 5x - 6)

= 4x² - 20x - 25

The quadratic equation is 4x² - 20x - 25

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