Multiply the number of colors by the number of styles
9 x 3 =27 ways
complex vector question.A bolt is tightened by applying a force to one end of a wrench.
The Scalar and Cross Product of Vectors
Given two vectors:
[tex]\begin{gathered} \underline{r_1}=(a,b,c) \\ \underline{r_2}=(d,e,f) \end{gathered}[/tex]The scalar product is defined as:
[tex]\underline{r_1}\cdot\underline{r_2}=ad+be+cf[/tex]The cross product is the result of computing the following determinant:
[tex]\underline{r_1}\times\underline{r_2}=\begin{bmatrix}i & j & {k} \\ {a} & {b} & {c} \\ {d} & {e} & {f}\end{bmatrix}[/tex]Where i, j, and k are the unit vectors in each of the directions x, y, and z, respectively.
This concept will be applied to the following physics problem.
Given a force F= (2, 3, 0) and the distance vector d = (4, 0, 0), the torque is defined by:
[tex]\tau=r\times F[/tex]Calculating:
[tex]\tau=(4,0,0)\times(2,3,0)[/tex][tex]\tau=\begin{bmatrix}{i} & {j} & {k} \\ {4} & {0} & {0} \\ {2} & {3} & {0}\end{bmatrix}[/tex]Calculating the determinant:
[tex]\begin{gathered} \tau=0i+12k+0j-(0k+0j+0i) \\ \tau=0i+0j+12k \end{gathered}[/tex]Expressing in vector form τ = (0, 0, 12) <= should use angle brackets
The magnitude of the torque is:
[tex]\begin{gathered} |\tau|=\sqrt[]{0^2+0^2+12^2} \\ |\tau|=\sqrt[]{144} \\ |\tau|=12 \end{gathered}[/tex]The power P is equal to the scalar product of the torque by the angular velocity w. We are given the angular velocity w = (3, 3, 2), thus:
[tex]\begin{gathered} P=(0,0,12)\cdot(3,3,2) \\ P=0\cdot3+0\cdot3+12\cdot2 \\ P=24 \end{gathered}[/tex]P = 24
If ( a + 3 , b – 1 ) = ( - 2 , 4 ) , then a + b =
Answer: {(1,3),(1,4),(2,3),(2,4)}
Step-by-step explanation:
Step -1: Define the Cartesian product.
Cartesian product: If A and B are two non empty sets, then
Cartesian product A×B is set of all ordered pairs (a,b) such that a∈A and b∈B.
Step -2: Find the Cartesian product of given sets.
We have given,
A={1,2} and B={3,4}
So, A×B={(1,3),(1,4),(2,3),(2,4)}
Hence, option A. {(1,3),(1,4),(2,3),(2,4)} is correct answer.
Find the additive inverse. −31
Answer:
To get the additive inverse of a positive number you put a minus in front of it and to get the additive inverse of a negative number, you remove the minus to make it a positive number.
You paid $600 for a new guitar. Your guitar cost $40 more than twice the cost of your friends guitar. Wright an equation based on this information.
Answer: 600 divided by 2 + 40
Step-by-step explanation:
Answer:
2x + 40 = 600
2x = 560
x = 280.
Your friends guitar costs $280.
Step-by-step explanation:
Set the equation equal to $600, the cost of the new guitar. Let the variable, x, represent the cost of your friends guitar. Since your guitar was + 40 more than double the cost of your friend’s, this can be written as an equation:
2x + 40 = 600
A random sample of 860 births in a state included 423 boys. Construct a 95%
confidence interval estimate of the proportion of boys in all births. It is believed that
among all births, the proportion of boys is 0.513. Do these sample results provide
strong evidence against that belief?
Construct a 95% confidence interval estimate of the proportion of boys in all births.
Using the z-distribution, it is found that the 95% confidence interval is (0.45 , 0.52), and it does not provide strong evidence against that belief.
A confidence interval of proportions is given by:
[tex]\pi[/tex] ± [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
where [tex]\pi[/tex] is the sample proportion, z is the critical value and n is the sample size.
In this problem, we have 95% confidence level, hence [tex]\alpha[/tex] = 0.95, z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2}[/tex] = 0.975, so the critical value is z = 1.96
We have that a random sample of 860 births in a state included 423 boys, hence the parameters are given by:
n = 864, [tex]\pi =\frac{423}{860}[/tex] = 0.49
Then the bounds of the interval are given by:
[tex]\pi[/tex] + [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex] = 0.49 + [tex]1.96\sqrt{\frac{0.49(0.513)}{860} }[/tex] = 0.52
[tex]\pi[/tex] - [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex] = 0.49 - [tex]1.96\sqrt{\frac{0.49(0.513)}{860} }[/tex] = 0.45
The 95% confidence interval estimate of the population of boys in all births is (0.45 , 0.52). Since the interval contains 0.513, it does not provide strong evidence against that belief.
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3) Find the equation of the line:
a) with a gradient of 2 and cutting the y-axis at 7
b) with a gradient of -2 and passing through the point (2;4)
c) passing through the points (2; 3) and (-1; 2)
d) parallel to the x-axis cutting the y-axis at 5
Step-by-step explanation:
this is very much doing the exact same things as the previous question, just with a little bit different numbers.
remember, gradient = slope.
the slope is always the factor of x in the slope-intercept form
y = ax + b
our in the point-slope form
y - y1 = a(x - x1)
"a" is the slope, b is the y-intercept (the y- value when x = 0).
(x1, y1) is a point on the line.
the slope is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
a)
y = 2x + 7
b)
y - 4 = -2(x - 2) = -2x + 4
y = -2x + 8
c)
going from (2, 3) to (-1, 2)
x changes by -3 (from 2 to -1)
y charges by -1 (from 3 to 2)
the slope is -1/-3 = 1/3
we use one of the points, e.g. (2, 3)
y - 3 = (1/3)×(x - 2) = x/3 - 2/3
y = x/3 - 2/3 + 3 = x/3 - 2/3 + 9/3 = x/3 + 7/3
d)
y = 5
this is a horizontal line (parallel to the x-axis) and represents every point on the grid, for which y = 5.
the slope is 0/x = 0, as y never changes at all.
the y- intercept is 5, of course.
Answer:
[tex]\textsf{a) \quad $y=2x+7$}[/tex]
[tex]\textsf{b) \quad $y=-2x+8$}[/tex]
[tex]\textsf{c) \quad $y=\dfrac{1}{3}x+\dfrac{7}{3}$}[/tex]
[tex]\textsf{d) \quad $y=5$}[/tex]
Step-by-step explanation:
Part (a)Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slope.b is the y-intercept.Given values:
Slope = 2y-intercept = 7Substitute the given values into the formula to create the equation of the line:
[tex]\implies y=2x+7[/tex]
---------------------------------------------------------------------------
Part (b)Point-slope form of a linear equation:
[tex]y-y_1=m(x-x_1)[/tex]
where:
m is the slope.(x₁, y₁) is a point on the line.Given:
Slope = -2(x₁, y₁) = (2, 4)Substitute the given values into the formula to create the equation of the line:
[tex]\implies y-4=-2(x-2)[/tex]
[tex]\implies y-4=-2x+4[/tex]
[tex]\implies y=-2x+8[/tex]
---------------------------------------------------------------------------
Part (c)Slope formula:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
where (x₁, y₁) and (x₂, y₂) are points on the line.
Given points:
(x₁, y₁) = (2, 3)(x₂, y₂) = (-1, 2)Substitute the points into the slope formula to calculate the slope of the line:
[tex]\implies m=\dfrac{2-3}{-1-2}=\dfrac{-1}{-3}=\dfrac{1}{3}[/tex]
Substitute the found slope and one of the points into the point-slope formula to create the equation of the line:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-3=\dfrac{1}{3}(x-2)[/tex]
[tex]\implies y-3=\dfrac{1}{3}x-\dfrac{2}{3}[/tex]
[tex]\implies y=\dfrac{1}{3}x+\dfrac{7}{3}[/tex]
---------------------------------------------------------------------------
Part (d)Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slope.b is the y-intercept.If the line is parallel to the x-axis, its slope is zero.
If the line intersects the y-axis at y = 5, then its y-intercept is 5.
Therefore:
m = 0b = 5Substitute the given values into the formula to create the equation of the line:
[tex]\implies y=0x + 5[/tex]
[tex]\implies y=5[/tex]
answer f 1 half 25 y intercept equals 375--g slope 1 half 25 y intercept equal 15H slope equals 25 y intercept equal 375J slope equals negative 25 y intercept equals 15
Answer:
[tex]\begin{gathered} \text{Slope}=-\frac{1}{25} \\ y-\text{intercept}=15 \end{gathered}[/tex]Step-by-step explanation:
Linear functions are represented by the following expression:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]m is the constant rate of change of the function, and it's calculated as the change in y over the change in x:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{14.6-15}{10-0} \\ m=-\frac{1}{25} \end{gathered}[/tex]The y-intercept of a linear function is when the line crosses the y-axis, which means when x=0.
Therefore, the y-intercept of the line is 15.
1. Last year the price of a college textbook(b) was $197. This year the price will be 13% higher. Which expression shows the difference in price from last year to this year? 1. b * 0.13 B. b.1.13 C.b-0.13 D.b - 13
B) b*1.13
1) Since the College textbook's price has been raised up 13%, then we can write:
b(1 +0.13)
b(1.13)
Plugging b = $197 we have:
197(1 +0.13)
197 (1.13)
$222.61
2) So the factor that expresses that difference (13% up) is 1.13
For 1 is equivalent to 100% and 0.13 to 13%
3) Hence, the answer is b* 1.13 calling b that $197.
Make three problem about finding DOMAIN X-intercept Y-intercept Vertical Asymptote Horizontal asymptote
A graph's domain, which is defined as the entire set of input values visible on the x-axis, refers to the set of possible input values. The possible output values are displayed on the y-axis and make up the range.
What is Vertical and Horizontal asymptote?Asymptotes are a distinctive feature of the graphs of rational functions. When a curve is nearing the edges of a coordinate plane, it is said to be asymptote. A rational function's vertical asymptotes happen as its denominator gets closer to zero.
In order to cross a vertical asymptote, a rational function must divide by one, which is impossible. When the x-values increase significantly in size, either positively or negatively, horizontal asymptotes develop. You can pass through horizontal asymptotes.
A vertical asymptote of a graph is a vertical line with the equation x = a, where the graph tends toward positive or negative infinity as the inputs get closer to a.
A graph's horizontal asymptote is a horizontal line, y = b, where the graph moves toward the line as the inputs move toward ∞+ or ∞-.
Three problem about finding DOMAIN, X-intercept, Y-intercept, Vertical Asymptote, Horizontal asymptote
1) Determine the vertical asymptote(s), horizontal or slant asymptote, x-intercept(s), y-intercept, and domain. Then, sketch a graph of the function on the given set of axes. Label all asymptotes and intercepts.
[tex]m(x) = \frac{3x^2 -12}{x^2 -7x + 6}[/tex]
2) Determine the Domain, Y-intercept, x-intercept(s), Vertical Asymptote(s), and Horizontal Asymptote, if the exist: Include the multiplicity of the x-intercepts if the multiplicity is greater than 1. Then graph the ratio function.
[tex]v(x) = \frac{3x - 1}{x^2+5x +6}[/tex]
3) What are the Domain, x-intercept, y-intercept, vertical asymptote and horizontal asymptote of the rational function [tex](x^3-x+12/x^2-3x-4)[/tex]?
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Line BC Is a tangent to circle A at Point B. How would I find the measure of angle BCA? I need more explanation
SOLUTION
Notice that line BA is a radius of the circle.
Since line BC is a tangen then the measure of angle ABC is:
[tex]m\angle ABC=90^{\circ}[/tex]Using Triangle Angle-Sum Theorem, it follows:
[tex]m\angle ABC+m\angle BAC+m\angle BCA=180^{\circ}[/tex]This gives:
[tex]90^{\circ}+57^{\circ}+m\angle BCA=180^{\circ}[/tex]Solving the equation gives:
[tex]\begin{gathered} 147^{\circ}+m\angle BCA=180^{\circ} \\ m\angle BCA=180^{\circ}-147^{\circ} \\ m\angle BCA=33^{\circ} \end{gathered}[/tex]Therefore the required answer is:
[tex]m\angle BCA=33^{\circ}[/tex]List the factors to find the GCF of 24 and 12
Given:
GCF of 24 and 12.
[tex]\begin{gathered} 24=2^3\times3 \\ 12=2^2\times3 \end{gathered}[/tex][tex]\begin{gathered} \text{GCF of 24 and 12=}3\times2^2 \\ \text{GCF of 24 and 12=}12 \end{gathered}[/tex]how to solve 4|x|+|-4|=|-6|
x = 1/2, x = -1/2
Simplify:
4|x| + |-4| = |-6|
4|x| + 4 = 6
4|x| = 2
|x| = 1/2
Solutions:
1) x = 1/2
2) x = -1/2
Which of the following is equivalent to tanблOA. tan 3OB. tan 5OC. tanOD. tanВп3Reset Selection
Okay, here we have this:
Considering the provided expression, we are going to identify to which is equivalent, so we obtain the following:
We obtain that the correct answer is the option C, because:
Please help me, I am happy to contribute and learn .
Explanation:
We are told that the rate at which the pump dumps the pollutant per day to be
[tex]\frac{\sqrt{t}}{15}[/tex]To solve the question, let us assume that t is the number of days
So, to find the amount dumped after 3 days, we will put t =3 into the equation
[tex]\frac{\sqrt{3}}{15}=\frac{1.732}{15}=0.11547[/tex]Therefore, the answer is 0.115
Name two rays that contain the following line segments:• BC• GH
Two rays that contain the given line segment BC is [tex]\overrightarrow {EC}[/tex] and line segment GH is [tex]\overrightarrow {EH}[/tex] .
The length of a line segment is its measurement. Unlike a line that extends continuously, a line segment has a set length and is easy to measure.
The next link in the chain is Ray. It is made up of a line and even a mix of line segments with one terminating end and an eternally extending end.
Due to one of its ends not terminating, its length cannot be determined. Line segments are parts of a line that have two endpoints.
The construction of various shapes, such as triangles, polygons, hexagons, and squares, involves the use of a number of line segments.
From the diagram we can see that the rays EC and EH contains the given line segments. From the Rays the other line segments are BD, CD , GH.
AH is another ray.
Two rays that contain the given line segment BC is [tex]\overrightarrow {EC}[/tex] and line segment GH is [tex]\overrightarrow {EH}[/tex] .
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The office manager orders computer paper every 6 weeks and printer ink cartridges every 8 weeks.
QUESTION: If she places an order for both paper and ink this week, how many weeks will it be until she orders them both in the same week again?
The number of weeks that she orders them both in the same week again is 24 weeks.
How to illustrate the information?From the information, the office manager orders computer paper every 6 weeks and printer ink cartridges every 8 weeks.
The weeks when they will order same will be the least common multiple for 6 and 8. This will be:
6 = 6, 12, 18, 24
8 = 8, 16, 24
The multiple is 24 weeks. This illustrates the information.
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the graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the range of the function.
The graph's range is 0 to M plus or minus 5.5.
Where can I find the function's range?The set of graph output values that make up a function's range.
This means that the set of y values in the graph is the range of a function.
How do you figure out the domain and range?The domain
We can observe the following on the function's graph:
The x values range from zero to seven and a half.
This indicates that the domain is 0=x=7.5.
The range
We can observe the following on the function's graph:
Beginning at 0, the x values go all the way up to 5.5.
In other words, the range is 0 = M = 5.5.
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A price p (in dollars) and demand x (in items) for a product are related by 2x²-5xp + 55p²-23,200.
If the price is increasing at a rate of 3 dollars per month when the price is 20 dollars, find the rate of change of the demand with respect to time. (Round your answer to four
decimal places.)
The monthly rate of change in demand is -$40.7.
How is the rate of change estimated from an equation?The slope of a graphed function is determined using the average rate of change formula. The method for finding the slope is differentiation.
A price-demand relation equation is given.
2x²-5xp + 55p²=23,200.
Differentiate the given equation with time
[tex]\begin{aligned}&4 x \frac{d x}{d t}-5\left(x \frac{d p}{d t}+p \frac{d x}{d t}\right)+110 p \frac{d p}{d t}=0 \\&4 x \frac{d x}{d t}-5 p \frac{d x}{d t}=5 x \frac{d p}{d t}-110 p \frac{d p}{d t} \\&(4 x-5 p) \frac{d x}{d t}=(5 x-110 p) \frac{d p}{d t} \\&\frac{d x}{d t}=\frac{(5x-110 p)}{(4 x-5p)} \frac{d p}{d t}\end{aligned}[/tex]
Put the value of p in the original equation.
For p=20
[tex]2x^{2} -5x\times 20+ 55\times20^{2}=23200\\2x^{2}-100x+22000=23200\\2x^{2}-100x-1200=0\\x^{2}-50x-600=0\\x=60 \text{ or }-10[/tex]
Since the price can not be negative, x=60.
Putting these values in the differential equation.
[tex]\frac{d x}{d t}=\frac{(5 x-110 p)}{(4 x-5 p)} \frac{d p}{d t}\\=\frac{(5\times60-110\times 20)}{(4\times60-5 \times20)} \times3\\=\frac{300-2200}{140}\times3\\ =-40.7[/tex]
So, the monthly rate of change in demand is -$40.7.
The minus sign indicates that demand is decreasing.
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Let theta equals 11 times pi over 12 periodPart A: Determine tan θ using the sum formula. Show all necessary work in the calculation.Part B: Determine cos θ using the difference formula. Show all necessary work in the calculation.
The fisrt part is the divide your angle into two angles, could be 6/12π and 5/12π
[tex]\begin{gathered} A=\frac{4\pi}{12}=\frac{\pi}{3} \\ B=\frac{7\pi}{12} \end{gathered}[/tex]For the sum formula:
[tex]\begin{gathered} \tan (\theta)=\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\cdot\tan B} \\ \tan (A+B)=\frac{1.73-3.73}{1-1.73\cdot(-3.73)} \\ \tan (A+B)=\frac{-2}{7.45}=-0.27 \end{gathered}[/tex]For the difference formula:
[tex]\begin{gathered} A=\frac{1\pi}{12} \\ B=\pi \end{gathered}[/tex][tex]\begin{gathered} \tan (B-A)=\frac{\tan B-\tan A}{1+\tan A\cdot\tan B} \\ \tan (B-A)=\frac{0-0.268}{1+0\cdot0.267} \\ \tan (B-A)=-0.268 \end{gathered}[/tex]Both methods work and result in the same answeer
you and your family are taking a trip to Brazil. You are bringing $175 on the trip. The rate pf currency exchange is 4.65 Real (Brazilian money) per 1 United States dollar. How many Real will you have on the trip?
Answer:
813.75 can you have .75 of a real? if not, then 813
Step-by-step explanation:
175 x 4.65 = 813.75
Evaluate the correlation shown in this scatter plot and then answer the 2 questions below.
How would you describe the direction and strength of this scatter plot? Is it positive or negative? Is it weak, moderately strong, or perfect? (worth 1.5 points)
How did you decide what words to choose to describe this correlation? (worth 1.5 points) 30 POINTS FORR WHO AWNSERS
The given scatter plot points are increasing, indicating a rise in data points, direction oriented to the right and the strength of scatter plot points correlation is moderately strong.
A graph with dots is shown to indicate the relationship between two sets of data.
According to the given scatter plot, the scatter plot points are increasing, indicating a rise in data points, and we may conclude that the correlation is positive.
The scatter plots are now oriented to the right. As a result, we may claim that the correlation is moderately strong.
Thus. the given scatter plot points are increasing, indicating a rise in data points, direction oriented to the right and the strength of scatter plot points correlation is moderately strong.
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Given P(A) = 0.5, P(B) = 0.65 and P(AUB) = 0.75,find P(ANB).
P(A∪B) = P(A) + P(B) - P(A∩B)
where P(A) is the probability of A happening
P(B) is the probability of B happening
P(A∪B) is the probability of A or B happening
P(A∩B) is the probability of A and B happening
P(A) = 0.5, P(B) = 0.65 and P(AUB) = 0.75
.75 = .5+ .65 - P(A∩B)
.75 =1.15 - P(A∩B)
.75 - 1.15 = -P(A∩B)
-.4 = -P(A∩B)
.4 =P(A∩B)
P(A∩B) = .4
8 if x ≤-1
2x if -1 < x <4
-4 - x + 6 if x ≥ 4)
2x=-1+6
2x=5
x=3
so the answer is 3
A new heating and aip constitioner will cost the Benguin fomily $4122,theymake a down payment of 20 percent and finance the remaining amount theyObtain an instaliment loan for 36 months at an APR of 9%A What is the down payment?B What is the amount of the loan?
The cost of the new heating and air conditioner equipment is:
A = $4122
They make a down payment of 20%
A. The down payment is:
[tex]\begin{gathered} DP=\$4122\times\frac{20}{100} \\ \\ DP=\$824.40 \end{gathered}[/tex]B The amount of the loan is the remaining amount after paying the down payment:
L = $4122 - $824.40
L = $3297.60
You roll a 6-sided die two times.What is the probability of rolling a 6 and then rolling a number less than 2?Simplify your answer and write it as a fraction or whole numb
We are asked to determine the probability of rolling a 6 and then rolling a number less than 2. To do that we will use the product rule probabilities since we want to find the probability of two independent events happening:
[tex]P(AandB)=P(A)P(B)[/tex]Where:
[tex]\begin{gathered} A=\text{ rolling a 6} \\ B=\text{ rolling a number less than 2} \end{gathered}[/tex]To determine the probability of rolling a 6 we need to have into account that there are 6 possible outcomes out of which only one is a 6. Therefore, the probability is:
[tex]P(A)=\frac{1}{6}[/tex]To determine the probability of B we need to have into account that in a 6-sided die the numbers that are less than 2 are (1), this means that there is only one number less than 2 out of 6 possible numbers. Therefore, the probability is:
[tex]P(B)=\frac{1}{6}[/tex]Now, we substitute in the product rule:
[tex]P(AandB)=(\frac{1}{6})(\frac{1}{6})[/tex]Solving the product:
[tex]P(AandB)=\frac{1}{36}[/tex]Therefore, the probability is 1/36.
a waffle cone with a height of 6 inches has a volume of 56.52 cubic inches. What's the area
Answer:
28.26 square inches.
Explanation:
Given a waffle cone with the following properties:
• Height = 6 inches
,• Volume = 56.52 cubic inches.
[tex]\text{Volume of a cone}=\frac{1}{3}\pi r^2h[/tex]Note that the base of the cone is a circle and the area of a circle:
[tex]A=\pi r^2[/tex]Substitute the given values:
[tex]\begin{gathered} 56.52=\frac{1}{3}\times\pi\times r^2\times6 \\ 56.52=2\pi r^2 \\ \pi r^2=\frac{56.52}{2} \\ \pi r^2=28.26in^2 \end{gathered}[/tex]The area of the base is 28.26 square inches.
two students determined the value of this expression
these are the steps each student used
analyze the steps and describe any eras made by student p and student q
Answer:
Student P made a mistake at step 1
Student Q made a mistake at step 3
Explanation:
First, let's analyze what are the correct steps to find the value of the expression.
So, the first step is to apply the distributive property:
[tex]\begin{gathered} -2.5(1.4+3.1)+6.9(-4.3) \\ -2.5(1.4)-2.5(3.1)+6.9(-4.3) \\ -3.5-7.75+6.9(-4.3) \end{gathered}[/tex]Then, we need to solve the multiplication of the last term:
[tex]-3.5-7.75-29.67[/tex]Now, we can factorize the sign minus, but we will need to change the signs of all terms:
[tex]-(3.5+7.75+29.67)[/tex]Finally, we can add the term to get:
[tex]\begin{gathered} -(40.92) \\ -40.92 \end{gathered}[/tex]Therefore, the errors made by student P were at step 1, when this student applies the distributive property, he or she made a mistake with the sign of 7.75. This number should be negative. The next steps are correct by taking into account that the error was in the first step, the result will be wrong.
For student Q, we have that everything was correct until step 3, where he or she factorize the minus sign but he or she doesn't change the signs of all signs. After that, the procedure is correct but the answer will be wrong due to the mistake made at step 3.
I need help with 18 I need an answer and a explanation
Mark's height last year was 46 inches.
Mark definitely grows over the past year. Let the height he grew be x.
Then, Mark's new height will be
[tex](46+x)\text{ inches}[/tex]Let us represent Mark's height with M and Peter's height with P.
This means that
[tex]M=46+x\text{ -----------(a)}[/tex]and, from the question, Peter's height is
[tex]P=51\text{ ----------(b)}[/tex]The question says that Mark's height is 3 inches less than Peter's height. This we can write as
[tex]M=P-3\text{ -------------(c)}[/tex]Therefore, if we put Mark's and Peter's ages into equation c, we can find a value for x as follows:
[tex]\begin{gathered} 46+x=51-3 \\ 46+x=48 \end{gathered}[/tex]Since 46 + x = M, then Mark's height is 48 inches
Given g(x) = 1/x^3Explain if the question cannot be solved
Given
[tex]g(x)=\frac{1}{x^3}[/tex]To find:
[tex]\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}g(x)dx[/tex]Explanation:
It is given that,
[tex]g(x)=\frac{1}{x^3}[/tex]That implies,
[tex]\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}g(x)dx[/tex]Apollo Enterprises has been awarded an insurance settlement of $6,000 at the end of each 6 month period for the next 12 years. calculate how much (in $) the insurance company must set aside now at 6% interest compounded semiannually to pay this obligation to Apollo
$12180 the insurance company must set aside now at 6% interest compounded semiannually to pay this obligation to Apollo.
This is a problem from the compound interest system. We can solve this problem by following a few steps.
Apollo Enterprises has been awarded an insurance settlement of $6,000 at the end of each 6-month period for the next 12 years with a 6% interest rate. We have to calculate the total amount after 12 years.
To solve this problem we should know the formula for the compound interest method.
Formula:-
A = P {(1 + r/n)^(n.t)}
Here,
A denotes the final amount, we have to find this.P denotes the initial principal balance which is $6,000r denotes the interest rate which is 6%n denotes the number of times interest is applied per time period which is 12/6 = 2. t denotes the number of time periods elapsed which is 12 years.Now, we can calculate the value of A.
A = 6000 {( 1 + 6/200 )^2.12} = 6000 ( 1 + 6/200 )^24 = 6000 × 2.03 = 12180
Therefore, the total amount after 12 years is $12180
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