Find the angle between the vectors u = 5i – 2j and v = 2i + 3j.

Answers

Answer 1

STEP - BY - STEP EXPLANATION

What to find?

The angle between the given vectors.

Given:

u = 5i – 2j and v = 2i + 3j.

To solve the given problem, we will follow the steps below:

Step 1

Write the formula that can be use to solve the above.

[tex]cos\theta=\frac{\vec{a}\vec{.b}}{\vec{|a}\vec{||b}|}[/tex]

Step 2

Determine;

→ →

a. b

[tex]\begin{gathered} \vec{a}\vec{.b}=(5)(2)+(-2)(3) \\ \\ =10-6 \\ \\ =4 \end{gathered}[/tex]

Step 3

Determine;

→ →

|a| and | b|

[tex]\begin{gathered} \vec{|a|}=\sqrt{5^2+(-2)^2} \\ \\ =\sqrt{25+4} \end{gathered}[/tex][tex]=\sqrt{29}[/tex]

[tex]\begin{gathered} \vec{|b|}=\sqrt{2^2+3^2} \\ \\ =\sqrt{4+9} \\ \\ =\sqrt{13} \end{gathered}[/tex]

Step 4

Substitute the values into the formula.

[tex]\begin{gathered} cos\theta=\frac{4}{\sqrt{29}\times\sqrt{13}} \\ \\ =\frac{4}{\sqrt{377}} \end{gathered}[/tex]

Step 5

Take the arc cos of both-side.

[tex]\theta=cos^{-1}(0.20601)[/tex][tex]\theta=78.1\degree[/tex]

ANSWER

θ = 78. 1°


Related Questions

Which Problems can be solved by performing this multiplication 1/5 x 30

Answers

Answer:

c

Step-by-step explanation:

Select from the drop-down menus to correctly complete the statement. The expressions 3.22 1 and 10 – 0.33 . 2 should be joined by

Answers

we have the expressions

3.2^2-1=10.24-1=9.24

10-0.33*2=10-0.66=9.34

therefore

should be joined by a not equal sign to form an inequality

so

9.24 < 9.34

9.24 is less than 9.34

I’ve completed the question.

Would you like me to elaborate on any point?

f the area of the rhombus below is 232 m 2, and diagonal AC = 16 m, find the length of diagonal BD.

Answers

The formula for calculating the area of a rhombus is expressed as

Area = 1/2d1d2

where

d1 and d2 are the lengths of the diagonals

From the information given,

Area = 232

d1 = AC = 16

d2 = BD

Thus,

232 = 1/2 x 16 x BD

232 = 8BD

BD = 232/8

BD = 29

Use the Square Root Property to solve the quadratic equation 36c2−144c+144=−35. If there are multiple answers, list them separated by a comma, e.g. 1,2. If there is no solution, enter ∅.

Answers

The square root property to solve the quadratic equation;

[tex]\begin{gathered} 36c^2-144c+144=-35 \\ 36c^2-144c+144+35=0 \\ 36c^2-144c+179=0 \end{gathered}[/tex]

is given as;

[tex]\begin{gathered} c=\frac{-b\pm\sqrt[]{b^2-4ad}}{2a} \\ \\ \text{Where} \\ a=36 \\ b=-144 \\ d=179 \end{gathered}[/tex][tex]\begin{gathered} c=\frac{-(-144)\pm\sqrt[]{(144)^2-4(36)(179)}}{2(36)} \\ c=\frac{144\pm\sqrt[]{-5040}}{72} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Since,} \\ \sqrt[]{b^2-4ad}<0 \\ \text{Then, th}ere\text{ is no real solution for c} \\ c=\phi \end{gathered}[/tex]

The ratio of the number of adults to the number of students at a field trip has to be 3:8. During a current field trip, there are 190 more students on the trip than there are adults. How many students are attending the field trip? How many adults?
Please put this answer in a easy way (no algebra) use ratios and basic opreations.

Answers

The number of students attending the field trip is 304 and the number of adults is 114.

Calculating number of students and adults attending a field trip

From the question, we are to determine the number of students and adults attending the field trip.

From the given information,

"The ratio of the number of adults to the number of students at a field trip has to be 3:8"

Let the number of students be x and the number of adults be y

Thus,

y/x = 3/8

8y = 3x           ------------- (1)

Also,

There are 190 more students on the trip than there are adults

That is,

x - y = 190

Therefore,

x = 190 + y      -------------- (2)

Substitute into equation

8y = 3x

8y = 3(190 + y)

8y = 570 + 3y

8y - 3y = 570

5y = 570

y = 570/5

y = 114

Thus, the number of adults is 114

Substitute the value of y into equation (2)

x = 190 + y

x = 190 + 114

x = 304

Hence, the number of students is 304

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Rhombus ABCD with vertices A(1,0), B(6,-2), C(8,-7), and D(3,-5); 90° counterclockwise rotation about the origin

Answers

Given data:

The given coordinates of Rhombus are A(1,0), B(6,-2), C(8,-7), and D(3,-5).

The coordinate of a point after 90 degrees counterclockwise rotation is,

[tex](x,\text{ y)}\rightarrow(-y,x)[/tex]

The final coordinate of Rhombus are,

[tex]\begin{gathered} A(1,0)=A^{\prime}(0,\text{ 1)} \\ B(6,\text{ -2)=B'(2, 6)} \\ C(8,\text{ -7)=C'(7},\text{ 8)} \\ D(3,\text{ -5)=D'(5, 3)} \end{gathered}[/tex]

Thus, the final coordinate of Rhombus are A'(0,1), B'(2, 6), C'(7, 8) and D'(5, 3).

Write the quadratic function with the indicated characteristics. The graph passes through the origin and the points (-3, 0) and (-1, 3).

Answers

substituteGiven:-

[tex](0,0),(-3,0)(-1,3)[/tex]

To find the quadratic equation.

So now we use the formula,

[tex]y=ax^2+bx+c[/tex]

So now we subtitute the points and find the value of a,b,c. So we get,

[tex]\begin{gathered} 0=a(0)+b(0)+c \\ c=0 \end{gathered}[/tex]

Also,

[tex]\begin{gathered} 0=a(-3)^2+b(-3)+c \\ 0=9a-3b \end{gathered}[/tex]

Also,

[tex]\begin{gathered} 3=a(-1)^2+b(-1)+0 \\ 3=a-b \end{gathered}[/tex]

So now we simplify both equation. so we get,

[tex]\begin{gathered} 9a-3b=0 \\ 3a-3b=9 \end{gathered}[/tex]

Now we add both the equations. we get,

[tex]\begin{gathered} 6a=-9 \\ a=-\frac{3}{2} \end{gathered}[/tex]

Now we find the value of b, so we get,

[tex]\begin{gathered} a-b=3 \\ -\frac{3}{2}-b=3 \\ -b=3+\frac{3}{2} \\ -b=\frac{9}{2} \\ b=-\frac{9}{2} \end{gathered}[/tex]

So the required values are,

[tex]y=-\frac{3}{2}x^2-\frac{9}{2}x+0[/tex]

What is the difference in elevation between the highest and lowest bodiesof water listed in the table below? Write an equation to show how youfound your answer."Height Above Sea LevelBody ofElevation(in feet)WaterCaspian Sea92Lake Maracaibo0Lake Superior600Lake Victoria3,720

Answers

The highest value is the highest positive integer, which is 3720.

The lowest value is the negative value, -92.

To obtain the difference between the two, subtract -92 from 3720. thus we have the following:

[tex]3720-(-92)[/tex]

Add the additive inverse of -92 to 3720.

[tex]3720-(-92)=3720+92=3812[/tex]

19. The Millers open a savings account for their newborn son with $430. Find the total amount in the account after 3 years if the simple interest rate is 2.5%.

Answers

we get that

[tex]C=430+3\cdot0.025\cdot430=462.25[/tex]

I need help if because I’m not sure if I was right or not

Answers

A trapezium has only 4 sides. This rules out option A

A trapezium has only one pair of parallel sides.

For option c, it is a parallelogram because it has 2 pairs of parallel sides.

For option d, it has no pair of parallel sides.

Thus, the correct option is B

when solving the system below algebraically using the substitution method, which of the following could be an equation you could. create to solve for x?A) x = 3y - 3B) -2x + 6(2x + 11) = 6C) -2x - 6 = - 2x - 11D) -2 (3y - 3) + y = 11

Answers

We have that the solutions of the system are

[tex]x\text{ = -6 and y = -1}[/tex]

So we are going to check which of the answers give that answer, we are going to try with A fisrt

[tex]x\text{ = }3(-1)\text{ }-3\text{ = -6}[/tex]

So with A, the solutions are the same, so we have that the answer is A.

Write A formula that tells the amount of bacteria in the bottle.A if we are given the number of minutes ,t that have passed

Answers

A formula that tells the amount of bacteria in the bottle is Generation time (G) is defined as the time (t) per generation (n is number of generations).

What is the formula for bacteria?The generation time, which is also the bacterial population's doubling time, is used to express the exponential growth rate of a bacterial culture. The time (t) spent on each generation (n = number of generations) is known as the generation time (G).Therefore, generation time calculations (below) arise from the equation G=t/n.The number of germs after t hours is thus given by the function P(t) = 500e1. 3863t.The beginning rate is equal to the slope of the reactant concentration versus time curve at time zero, which is negative.Model of Exponential Growth P(t)=P0(1+r)t. The initial population is P0.

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The ordered pair (8,5) represents a point on the graph of a proportional relationship. Which ordered pair also represents a point on the same graph? A. (5/8, 1) B. (1, 5/8) C. (5,8) D. (1, 8/5)

Answers

Given the ordered pair:

(8, 5)

Let's find the ordered pair that represents a point on the same graph assuming this is a graph of a proportional relationship.

Here, we have:

(x, y) ==> (8, 5)

Since this is a graph of a proportional relationship, let's find the constant of proportionality.

We have:

[tex]K=\frac{y}{x}=\frac{5}{8}[/tex]

This means when x is 1, y is 5/8.

Thus, the ordered pair that also represents a point on the same graph is:

[tex](1,\frac{5}{8})[/tex]

ANSWER:

[tex]\text{ B. (1, }\frac{5}{8})[/tex]

Sample proportions of size ten were taken from a group of students. Students were asked if they wore glasses while watching TV. The proportion that wore glasses while watching TV was recorded. The standard deviation of the data is 0.19 The margin of error can be given by the formula Margin ferror = 2 * s/(sqrt(n)) where s is the standard deviation and n is the sample size . What is the margin of error for the data collected ?

Answers

Margin of error:

[tex]ME=2\times\frac{s}{\sqrt{n}}[/tex]

For the given data collected

[tex]\begin{gathered} s=0.19 \\ n=10 \\ \\ ME=2\times\frac{0.19}{\sqrt{10}}=\frac{0.38}{\sqrt{10}}=0.12 \end{gathered}[/tex]Then, the margin of error is 0.12

Find the area of the composite figure below. Round your answer to the tenths.

Answers

Answer:

54 square units

Explanation:

First, divide the composite figure into common plane shapes as shown below:

Thus, we have two plane shapes:

• A triangle with a base of 10 units and a height of 6 units.

,

• A rectangle with a length of 6 units and a height of 4 units.

Therefore:

[tex]\begin{gathered} \text{ Area of the composite figure}=\text{ Area of the triangle+Area of the rectangle} \\ =\frac{1}{2}bh+lh \\ =(\frac{1}{2}\times10\times6)+(6\times4) \\ =30+24 \\ =54\text{ square units} \end{gathered}[/tex]

The area of the composite figure is 54 square units.

I just need the answer to check my work no explanation needed

Answers

To solve for z, we proceed as follows:

[tex](\frac{1}{4})^{3z-1}=16^{z+2}\times64^{z-2}[/tex]

Now, we simplify the expression on the right-hand side of the equation as follows:

[tex](\frac{1}{4})^{3z-1}=(4^2)^{z+2}\times(4^3)^{z-2}[/tex][tex](\frac{1}{4})^{3z-1}=4^2^{(z+2)}\times4^3^{(z-2)}[/tex][tex](\frac{1}{4})^{3z-1}=4^{2z+4}\times4^{3z-6}[/tex][tex](\frac{1}{4})^{3z-1}=4^{2z+4+3z-6}[/tex][tex](\frac{1}{4})^{3z-1}=4^{5z-2}[/tex]

Now, we simplify the expression on the left-hand side of the equation as follows:

[tex](4^{-1})^{3z-1}=4^{5z-2}[/tex][tex]4^{-1(3z-1)}=4^{5z-2}[/tex][tex]4^{-3z+1}=4^{5z-2}[/tex]

Now, since we have both expressions on the left and right hand sides to have a base of 4, we can simply equate their indices, as follow:

[tex]\begin{gathered} 4^{-3z+1}=4^{5z-2} \\ \Rightarrow-3z+1=5z-2 \\ \end{gathered}[/tex]

Now, we collect like terms:

[tex]-3z-5z=-2-1[/tex][tex]\begin{gathered} -8z=-3 \\ \Rightarrow z=\frac{-3}{-8} \\ \Rightarrow z=\frac{3}{8} \end{gathered}[/tex]

help pls for geometry

Answers

Answer:

ohhh that one is hard but i think is ur mom

Step-by-step explanation:

i wanted to wast y0our time but hopefully you get the answet

Round 2.8962 to the nearest hundredth. Do not write extra zeros.

Answers

To round the number

2.8962 to the nearest hundredth

First check the digit whose place value is hundredth

The digit is 9

You will either round it up or down depending on the next digit immediately after it which is called the decider

If the decider is from 0-4 then we round the number down

If the decider is from 5 -9 then we round the number up

The decider is 6 so we are rounding the number up

2.8962 ≈ 2.90 to the nearest hundredth

When the 9 increases to ten, we can't write 10 down so we write 0 and add 1 to 8 which makes it 9

Answer:

9

Step-by-step explanation:

A chemistry teacher needs to mix a 20% salt solution with a 80% salt solution to make 15 qt of a 40% salt solution. How many quarts of each solution should the teacher mix to get the desired result?20% salt solution qt80% salt solution qt

Answers

Given that the chemistry teacher needs to mix a 20% salt solution with an 80% salt solution to make 15 quarts of a 40% salt solution.

Let be "x" the number of quarts of 20% salt solution the teacher should mix to get the desired result, and "y" the number of quarts of 80% salt solution the teacher should mix to get the desired result.

You can write the following System of Equations using the information provided in the exercise:

[tex]\begin{cases}0.2x+0.8y={(0.4)(15)} \\ x+y=15\end{cases}[/tex][tex]\begin{cases}0.2x+0.8y={6} \\ x+y=15\end{cases}[/tex]

In order to solve the exercise, you can use the Substitution Method:

1. Solve the second equation for "y":

[tex]y=15-x[/tex]

2. Substitute the new equation into the first equation and solve for "x":

[tex]0.2x+0.8(15-x)=6[/tex][tex]0.2x+12-0.8x=6[/tex][tex]\begin{gathered} x=\frac{-6}{-0.6} \\ \\ x=10 \end{gathered}[/tex]

3. Substitute the value into the second original equation and solve for "y":

[tex]\begin{gathered} 10+y=15 \\ y=15-10 \\ y=5 \end{gathered}[/tex]

Hence, the answer is:

• 20% salt solution:

[tex]10\text{ }qt[/tex]

• 80% salt solution:

[tex]5\text{ }qt[/tex]

12) Triangle ABC and A'B'C' are shown on the coordinate plane. Which algebraic representation showshow to find the coordinates of triangle A'B'C'?

Answers

x,y) ---------> (2/3x, 2/3y)

1) For that dilation, we always start from the pre-image. In this case, the ABC is the bigger one

So taking one point of that triangle as an example.

C(9,3)

And one of that image

C'( 6,2)

Dilating from C to C' all other points follow that same rule.

2) This leads us to conclude

Pre image Image

(x,y) ---------> (2/3x, 2/3y)

On March 8, 2017, one U.S. dollar was worth 19.61 Mexican pesos.(a) On that date, how many dollars was 149.23 pesos worth?Round your answer to the nearest hundredth of a dollar.dollars(b) On that date, how many pesos was 63.64 dollars worth?Round your answer to the nearest hundredth of a peso.OPpesosI need help with these two math problems.

Answers

ANSWERS

(a) 7.61 USD

(b) 1247.98 MXN

EXPLANATION

We know that on March 8, 2017, 1 USD was worth 19.61 MXN.

(a) To find how many dollars was 149.23 MXN worth on that date, we have to divide this amount by 19.61,

[tex]149.23\text{ }MXN\cdot\frac{1\text{ }USD}{19.61\text{ }MXN}\approx7.61[/tex]

Hence, 149.23 Mexican pesos were worth 7.61 US dollars.

(b) Now, to find how many Mexican pesos were 63.64 USD worth on that date, we have to multiply it by 19.61 instead,

[tex]63.64\text{ }USD\cdot\frac{19.61\text{ }MXN}{1\text{ }USD}\approx1247.98\text{ }MXN[/tex]

Hence, 63.64 US dollars were worth 1247.98 Mexican pesos.

Line l passes through the points, (6,-14) and (2,-4) . If line m is parallel to line l, the slope of the line m is equal to

Answers

Determine the slope of line l passes through points (6,-14) and (2,-4).

[tex]\begin{gathered} m=\frac{-4-(-14)}{2-6} \\ =\frac{-4+14}{-4} \\ =-\frac{10}{4} \\ =-\frac{5}{2} \end{gathered}[/tex]

The line m is parallel to line l and parallel line have equal slope. So slope of line m is equal to -5/2.

Option 3 is correct.

Staples sells folders in packs of 12 for 4.80. Office max sells ffolders in packs of 17 for 7.50. Which has the better deal

Answers

The first step is to find the unit price of each seller. We were told that Staples sells folders in packs of 12 for 4.80. It means that the price per folder is

4.80/12 = 0.4 per folder

Also, Office max sells folders in packs of 17 for 7.50. It means that the price per pack is

7.50/17 = 0.44

Since the unit rate of Staples is low, then Staples has the better deal

Staples dived $4.80 by 12 $7.50 by 17 and the cheaper price is the better deal. In this case it’s staples at 40 cents whole office max is at 44 cents

Jenny knit a total of 12 centimeters of scarf over 2 nights. How many nights will Jenny have
to spend knitting in order to knit a total of 18 centimeters of scarf? Assume the relationship is
directly proportional.

Answers

As we can assume the relationship is directly proportional, we have to build the proportion and do the cross product. So:

[tex]\begin{gathered} \frac{12cm}{\text{2 nights}}=\frac{18cm}{x\text{ nights}} \\ 12x=2\cdot18 \\ 12x=36 \\ x=\frac{36}{12} \\ x=3 \end{gathered}[/tex]

She needs 3 nights

Determine the direction angle (in degrees) for each vector:• Make sure you're using degrees instead of radians.• If you use a decimal approximation, you must be accurate to at least 3 decimal places.a. (5, 3) has direction angle: 0 =b. (-4,5) has direction angle: 0 =c. (8,-8) has direction angle: 0=d. (-12, -3) has direction angle: 0=

Answers

Explanation

a vectors makes a rigth angle to the x-positve axis , so

so, the x coordinate is adjacent side and the y-coordinate becomes into the opposite side, then we can use a trigonometric function that relates those values,it is

[tex]\begin{gathered} tan\theta=\frac{opposi\text{te side}}{adjacent\text{ side}} \\ tan\theta=\frac{y\text{ coordinate}}{x\text{ coordinate}} \end{gathered}[/tex]

hence

Step 1

a)

let

[tex]\begin{gathered} \langle5,3\rangle, \\ x=5 \\ y=3 \end{gathered}[/tex]

replace and solve for the angle

[tex]\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=\frac{3}{5} \\ \theta=\tan^{-1}(\frac{3}{5}) \\ \theta=30.964° \end{gathered}[/tex]

so,

a)Blank1: 30.964

Step 2

b)

let

[tex]\begin{gathered} \langle-4,5\rangle, \\ x=-4 \\ y=5 \end{gathered}[/tex]

replace and solve for the angle

[tex]\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=\frac{5}{-4} \\ \theta=\tan^{-1}(\frac{5}{-4}) \\ \theta=-51.340\~+180(Iquadrant) \\ \theta=128.660 \\ . \end{gathered}[/tex]

so,

b)Blank2:128.660

Step 3

c)

[tex]\begin{gathered} \langle8,-8\rangle, \\ x=8 \\ y=-8 \end{gathered}[/tex]

replace and solve for the angle

[tex]\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=\frac{-8}{8} \\ \theta=\tan^{-1}(-1) \\ \theta=-45 \end{gathered}[/tex]

so,

c)Blank3:-45 °

Step 4

d)

[tex]\begin{gathered} \langle-12,-3\rangle, \\ x=-12 \\ y=-3 \end{gathered}[/tex]

replace and solve for the angle

[tex]\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=\frac{-3}{-12} \\ \theta=\tan^{-1}(\frac{1}{4}) \\ \theta=14.036 \end{gathered}[/tex]

so,

direction

[tex]\begin{gathered} direcgtion\text{ =}\theta+180=14.036 \\ angle=194.036 \end{gathered}[/tex]

graph

d)Blank4: 194.036

I hope this helps you

hentIf TR = 11 ft, find the length of PS.IfР P.TentR16d ArcsSnd ArcsRound to 2 decimal places.and Arcs

Answers

SOLUTION

This is a length of arc problem.

The formula for finding the length of an arc is:

[tex]\frac{\theta}{360}\times2\pi r[/tex]

r=TR=PT=11ft

[tex]\begin{gathered} \frac{\theta}{360}\times2\pi r \\ r=11ft \\ \theta=164^o \end{gathered}[/tex][tex]\begin{gathered} \frac{164}{360}\times2\pi(11) \\ =\frac{164}{360}\times2\times3.14\times11 \\ =31.4698ft \\ =31.47ft(to\text{ 2 decimal places)} \end{gathered}[/tex]

The final answer is 31.47ft.

Nina and Nathan are creating a budget so they can afford paying all their billsand save to move to a nicer apartment. They decide that the ratio of spendingto saving needs to be 7:3. Last month their bills totaled $3975.20. Theymanaged to save $1,248.00. What was their actual spending ratio? At thisrate, will they meet their goal?

Answers

The ratio of spending to savings needs to be 7:3.

The actual spending ratio is 3,975.20 : 1,248.00.

In order to reach the goal, the actual spending ratio must the lower than the decided spending ratio.

3,975.20 : 1,248.00 < 7:3.

Dividing the ratios:

3.18 < 2.33

Since 2.33 is not greater than 3.18, they will not reach their goal at this rate.

Estimate 52% of 42 right in a whole number

Answers

52% of 42 is 21.84 rounded to the nearest whole number is 22.

What is the percentage?

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

We know 52% of 42 can be numerically expressed as,

(52/100)×42.

= 21.84.

Now, 21.84 rounded to the nearest whole number is 22.

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encuentra la medida de dos angulos complementarios. A=7×+4 y B=4×+9

Answers

Complementary angles mean that they add up to 90.

Thus, we can write:

[tex]\begin{gathered} A+B=90 \\ 7x+4+4x+9=90 \end{gathered}[/tex]

We can use algebra to find x:

[tex]\begin{gathered} 7x+4+4x+9=90 \\ 11x+13=90 \\ 11x=90-13 \\ 11x=77 \\ x=\frac{77}{11} \\ x=7 \end{gathered}[/tex]

To find measure of the individual angles, A and B, we simple plug in 7 into x of the expressions of A and B.

Angle A:

7(7) + 4 = 53 degrees

Angle B:

4(7) + 9 = 37 degrees

Rajesh invested $30,000 into an account that compounds interest monthly at a rate of 2.16%. He has made arrangements to withdraw $300 automatically every month to pay off his 10-year student loan. Will Rajesh have enough money in the account to cover all of the required loan payments? (Round to the nearest tenth of a year.)

Answers

By Evaluating the Compound Interest, we come to know that Rajesh will have enough money in the account to cover all of the required loan payments.

The Principal Amount(P) = $30,000

Rate of Interest (r) = 2.16 %

Time(t) = 10 years

Number of Times it is Compounded in a year(n) = 12

Now, we have

[tex]A =P(1+\frac{r}{100n}) ^{nt}[/tex]

Putting all the values, we evaluate the amount,

[tex]A =30,000(1+\frac{2.16}{100*12}) ^{12*10}\\\\A = 30,000 * 1.240\\A = 37,225.84[/tex]

Hence, the Amount after Compound Interest = $37,225.87

Now, The loan amount that he pays = 300 *12*10 = $ 36,000

Yes, he will have enough money in the account to cover all of the required loan payments.

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D (x - 4) B . In the figure shown, what is the value of x? C E 19 A F The piston diameter of a certain hand pump is inch. The manager determines that the diameters are normally distributed, with a mean of inch and a standard deviation of inch. After recalibrating the production machine, the manager randomly selects pistons and determines that the standard deviation is inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the level of significance?. Which of the following inferences best explains why none of the animals steal the harvest? order the numbers -7,7,1 and -1 from least to greatest. Convert each equation to slope-intercept form. Then label the slope & y-intercept. 1) Which of the following is not true about vectors.a) Must have magnitude and direction.b) When doing math with vectors, we can usually treat the x and y components independently.c) If several vectors are added together, their order does not matter.d) The magnitude of a vector is the sum of the magnitude of its x and y components.2) Explain briefly your argument or reasoning. How to calculate the volume of this shape?(1 litre = 1000 cm^3) The average price of a new home in a neighborhood in thousands of dollars (f(x)) is related to the number of years since the neighborhood was built (x) in the function: Use the graph of the function to describe its domain.A. The domain is the average price of homes in a new neighborhood, which is represented by all real numbers from 0 to 100B. The domain is the average price of homes in a new neighborhood, which is represented by all real numbers from 0 to infinity C. The domain is the number of years since the neighborhood was built, which is represented by all real numbers from zero to infinityD. The domain is the number of years since the neighborhood was built, which is represented by all real numbers from 0 to 100l Which of the following is a factor of x + 343?x-7x - 14x + 49x + 7x +49x+7 Lionfish are considered an invasive species, with an annual growth rate of 69%. A scientist estimates there are 9,000 lionfish in a certain bay after the first year. A bag contains 6 green balls and 4 yellow balls. What is the probability that two balls picked randomly are both of the same color? identify the term in experimentation -2X write the expanded form of the expression : 7(2x + y) Explain how both nucleic acids and proteins are polymers. be sure to describe the monomers that make up the polymers. CAN YOU HELP?I was asked by my teacher to do a project where I ask two people to do a five sentence paragraph about something they're passionate about. Instructions are down below. /Write one paragraph (minimum five sentences) about something you really feel strongly about. What is something in your life you feel passionate about? It can be a hobby, an idea, or anything else that you feel drives you! A graph shows three linear relationships but different y y-intercepts the following slopes line1: 1 / 5 line 2: 3/5 line 3: 6 / 5 write an equation for each line type your answers in the boxes below Producing all postage stamps, currency, and coinageManaging government accounts and the United States public debtEnforcing Federal finance and tax lawsAll of these are duties of what Executive Department of the U.S. Government?.A StateB commerceCommerceC JusticeD Treasury Reread this section from Act I, Scene III of Macbeth to determine a possible theme in the play, as revealed by foreshadowing. Then answer the follow-up questions.Part AWhich of the following statements best identifies an event foreshadowed in the passage and a possible theme it suggests?A) Banquos son will kill Macbeths; fate will eventually have its way.B) Banquo will not be king but will be better off than Macbeth, who will; power can have a destructive effect.C) Macbeth and Banquo will fight over the crown; friendship is often forgotten in the struggle for power.D) Macbeth and Banquo have gone mad; war and conflict can lead to mental as well as physical damage.Part BWhich of the following lines from the passage best supports your answer in Part A?A) FIRST WITCH: Lesser than Macbeth, and greater.B) THIRD WITCH: Thou shalt get kings, though thou be noneC) BANQUO: Were such things here as we do speak about? Or have we eaten on the insane root That takes the reason prisoner?D) BANQUO: You shall be king. Why did Sir Syed Ahmad Khan think that education was very important for Muslims? Nora needs help to manage her time better. What would you suggest? A. She should delegate all her work. B. She should stop attending staff meetings. C. She should keep her work area organized. D. She should put in more hours at the workplace.