Find the annual interest rate. I=$54, P=$900, t=18 months

Answers

Answer 1

well, there are 12 months in a year, so 18 months will then be 18/12 of a year

[tex]\bf ~~~~~~ \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$54\\ P=\textit{original amount deposited}\to& \$900\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{18}{12}\to &\frac{3}{2} \end{cases} \\\\\\ 54=(900)(r)\left( \frac{3}{2} \right)\implies \cfrac{54}{(900)\left( \frac{3}{2} \right)}=r\implies \cfrac{1}{25}=r\implies 0.04=r \\\\\\ r\%=0.04\cdot 100\implies r=\stackrel{\%}{4}[/tex]

Answer 2

Answer:

Step-by-step explanation:

Related Questions

Give the domain and range a. Domain: {-3, 0, 2}, range: {3, 0, -2} b.

Answers

Each point (x, y) is also (domain, range), so the x-values are the domain and the y-values are the range. This answer is A

Final answer:

The domain of a function is the set of all possible input values, while the range is the set of possible output values. In the given example, the function's domain is {-3, 0, 2}, which means the input data will be either -3, 0, or 2. Similarly, the function's range is {3, 0, -2}, which means the output data will be either 3, 0, or -2.

Explanation:

In mathematics, the domain of a function refers to the set of all possible input values (often represented as 'x' values) that the function can accept without producing an undefined result. Similarly, the range of a function refers to the set of all possible output values (often represented as 'y' values) that the function can produce.

To address your examples: for a function with domain {-3, 0, 2} and range {3, 0, -2}, it means all input data ('x' values) will be either -3, 0, or 2; and all output data ('y' values) will be either 3, 0, or -2.

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Fernando evaluated the expression below. What was Fernando’s error?

Answers

C. Fernando incorrectly found the product of -2 and -5

(should be +10 instead of -10)

Answer:

C. Fernando incorrectly found the product of -2 and -5.

Step-by-step explanation:

We have been given an image, which represents work of Fernando's evaluation of an expression. We are asked to find the error in Fernando's work.

[tex]\frac{5(9-5)}{2}+(-2)(-5)+(-3)^2[/tex]

Let us evaluate our given expression using order of operations (PEMDAS).

[tex]\frac{5(4)}{2}+(-2*-5)+9[/tex]

[tex]\frac{20}{2}+10+9[/tex]

[tex]10+10+9[/tex]

[tex]29[/tex]

Since we know that product of two negative numbers is always positive, therefore, the product of negative 2 and negative 5 will be positive 10.

Therefore, Fernando incorrectly found the product of -2 and -5 and option C is the correct choice.

A tourist in ireland wants to visit seven different cities. if the route is randomly selected, what is the probability that the tourist will visit the cities in alphabetical order? round your answer to five decimal places.

Answers

we have that
n----------> number of cities
the probability that the tourist will visit the cities in alphabetical order is (1/n!)

P=(1/n!)
n!-------------> (7*6*5*4*3*2*1)=5040
therefore
1/5040=0.000198-----------> (five decimal places)--------> 0.00020 (0.020%)

the answer is 0.00020 (0.020%)

The probability that the tourist will visit the cities in alphabetical order is 0.00020.

There are a total of 7! ways to visit 7 different cities, but there is only one way to visit them in alphabetical order. So, the probability that the tourist will visit the cities in alphabetical order is:

1/7! = 1/5040 = 0.0002

To five decimal places, the probability is 0.00020.

Here is a step-by-step explanation of the calculation:

We can think of the route as a permutation of 7 letters, with no of the letters being identical.

The number of permutations of 7 letters is 7!.

So, the number of ways to visit the cities in alphabetical order is 1.

The probability that the tourist will visit the cities in alphabetical order is 1/7!.

Here are some additional things to consider:

The probability that the tourist will visit the cities in alphabetical order is very small, because there are many other possible routes.

The probability would be 1 if there were only one city to visit.

The probability would be 0 if there were 7 cities and the tourist had to visit them all in alphabetical order.

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Add the opposite number of 1 1/5 to the sum of the numbers (−8 3/4 ) and (−2 5/6 ).

Answers

Start by finding the sum of (-8 3/4) and (-2 5/6). Find the least common denominator (LCD). 12 is the first thing that both 4 and 6 will evenly divide into, so we convert both fractions to 12ths:

-8 3/4 = -8 9/12 (multiply 4 by 3 to get 12, so multiply the numerator, 3, by 3 as well)
-2 5/6 = -2 10/12 (multiply 6 by 2 to get 12, so multiply the numerator, 5, by 2 as well)
-8 9/12 + -2 10/12 = -10 19/12
We must convert the improper fraction. 12 goes into 19 1 time with 7 left over, so 19/12 = 1 7/12
This means that -10 19/12 = -11 7/12
The opposite of 1 1/5 is -1 1/5. Add this to -11 7/12. Again find the LCD; in this case it is 60.
-1 1/5 = -1 12/60
-11 7/12 = -11 35/60
Adding these two we get -12 47/60.

The result of the sum of the three numbers is: [tex]\frac{-767}{60}[/tex]

The numbers are given as:

Number 1: 1 1/5Number 2: -8 3/4Number 3: -2 5/6

Start by calculating the sum of numbers 2 and 3 as follows:

[tex]Sum = -8\frac 34 -2\frac 56[/tex]

Express the numbers as improper fraction

[tex]Sum = -\frac{35}4 -\frac{17}6[/tex]

Take LCM

[tex]Sum = \frac{-3 \times 35 - 2 \times 17}{12}[/tex]

[tex]Sum = \frac{-139}{12}[/tex]

The opposite of number 1 is: -1 1/5

So, the overall sum is:

[tex]Sum = -1\frac 15 - \frac{139}{12}[/tex]

Express as improper fraction

[tex]Sum = -\frac 65 - \frac{139}{12}[/tex]

Take LCM

[tex]Sum = \frac{-72 - 695}{60}[/tex]

[tex]Sum = \frac{-767}{60}[/tex]

Hence, the result of the sum is: [tex]\frac{-767}{60}[/tex]

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Use two variables k and total to write a for loop to compute the sum of the squares of the first 50 counting numbers, and store this value in total. thus, your code should put 1*1 2*2 3*3 ... 49*49 50*50 into total. use no variables other than k and total.

Answers

I think the question means to "accumulate" or "sum" the individual squares in total. "Store" in computer terms usually means overwriting what's already in total.

With the sens of "summing" or "accumulating", this is one way how it can be coded:

int total=0;
for k=1 to 50 {
total+=k^2;
};
print(total);

Which statement describes the translation of y = −one half (x − 2)2 − 2 from standard position?

Answers

A quadratic in vertex form can be represented as

[tex]y = a(x-h)^{2} +k[/tex]

a represents reflection over the x-axis, and a vertical stretch or compress
- is reflection and a fraction (1/2) represents a compression.

-h represents a shift of that many units to the right (-2 shifts to the right two units)

k represents a shift up or down (-2 is shifting down 2 units_

Reflected over the x-axis, Vertically compressed by a factor of 1/2, shifted 2 units to the right, and shifted 2 units down

Which algebraic expression is equivalent to the expression below?
9(8x + 10) + 9(9 - x)

A. 63x - 171
B. 81x + 171
C. 63x + 9
D. 63x + 171

Answers

9*8x = 72
9* 10 = 90

so far, 72x + 90 + 9(9-x)

9 * 9 = 81
9 * -x = -9x

now, we have: 72x + 90 + 81 -9x

Now we can simplify by combining like terms

72x - 9x = 63x
90 + 81 = 171

63x + 171 is our answer
The answer is B.

Hope I helped!
Let me know if you need anything else!
~ Zoe

23. A glass box shaped like a rectangular prism has width 7 inches, length 9 inches, and height 12 inches. It is being shipped in a larger box with width 10 inches, length 10 inches, and height 15 inches. The space between the glass box and the shipping box will be filled with Styrofoam peanuts. How many cubic inches of space will contain Styrofoam peanuts? Show all work.

Answers

glass box volume = 7 * 9 * 12 = 756 cubic inches
larger box volume = 10 * 10 * 15 = 1,500 cubic inches
Styrofoam peanut volume = 1,500 - 756 = 744 cubic inches

Which algebraic expression represents the phrase “the quotient of negative eight and the sum of a number and three”?

Answers

-8 / (n+3)

Don't need 20 characters

We are going to write the expression step by step.
We have:
the quotient:
() / ()
negative eight:
(-8) / ()
The sum of a number and three:
Let:
x: the number
(-8) / (x + 3)
Answer:
An algebraic expression that represents the phrase is
(-8) / (x + 3)
"The quotient of negative eight and the sum of a number and three"

Antoine wants to convert millimeters into kilometers. Which operation should he choose?

Answers

1km = 1000m

1m = 100m
1000m = 1000 x 100cm
1000m = 100 000cm

1cm = 10 mm
100 000 cm = 100 000 mm x 10mm
100 000 cm = 1000 000 mm

therefore 1km = 1000 000mm

What is 7200 minutes, in days? (Remember, there are 60 minutes in an hour and 24 hours in a day.)

Answers

The answer would be 5 days

Answer:

5 Days is the answer

What is the volume of the cone with diameter 7in and height 9in? Round to the nearest cubic inch

Answers

Diameter = 7 cm
radius = 7÷2 = 3.5
Volume of cone = 1/3 [tex] \pi r^{2} h[/tex]
Volume of cone = 1/3 [tex] \pi 3.5^{2} (9)[/tex] = 115 cubic inches (Answer B)

Frank is constructing the circumscribed circle for △XYZ. He has already used his compass and straightedge to complete the part of the construction shown in the figure.

Which construction could be his next step?

Place the point of the compass on point Y and draw an arc intersecting the two arcs.

Place the point of the compass on point X and draw an arc intersecting the two arcs.

Place the point of the compass on point Z and draw an arc through points X and Y.

Place the point of the compass on one of the arcs and draw an arc through point X.

Answers

circumscribed circle for a triangle is circle where the circumference would cut all the vertices in the triangle
the diagram already has arcs marked from point Y, with the aim of drawing a perpendicular bisector to line XY.

Therefore the next step is to place the compass on point X and draw two arcs which cross the arcs already drawn (second option is the correct answer)

The points at which the 2 arcs meet are connected to each other making a perpendicular bisector that would cut XY perpendicularly.

Next step is to place the compass at Z and draw 2 arcs between Z and Y points, similarly place the compass at Y and draw 2 arcs that would cut the arcs already drawn.

Then connect the two points where the arcs meet and thats the perpendicular bisector of ZY.
The point at which perpendicular bisectors of XY and YZ meet is known as the circumcenter. Place the compass on this point with the radius any of the three points X,Y or Z and draw the circle

Answer:

Place the point of the compass on point X and draw an arc intersecting the two arcs.

Step-by step explanation:

This is to complete the angle bisector.

Given f(x)=3x^2+10x−8 and g(x)=3x^2−2x .

What is (fg)(x)

Answers

the answer for this is C

Answer:

[tex]\frac{x+4}{x} \hspace{8}where\hspace{8}x\neq0,\frac{2}{3}[/tex]

Step-by-step explanation:

The division between functions is defined as:

[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)} ,\hspace{10}g(x)\neq0[/tex]

So:

[tex](\frac{f}{g} )(x)=\frac{3x^2+10x-8}{3x^2-2x}\\ \\Factor\hspace{3}x\hspace{3}out\hspace{3}the\hspace{3}denominator\\\\(\frac{f}{g} )(x)=\frac{3x^2+10x-8}{x(3x-2)}\\\\Factor\hspace{3}the\hspace{3}numerator\\\\(\frac{f}{g} )(x)=\frac{4(3x-2)+x(3x-2)}{x(3x-2)}\\\\Factor\hspace{3}3x-2\hspace{3}from\hspace{3}the\hspace{3}numerator\\\\(\frac{f}{g} )(x)=\frac{(3x-2)(x+4)}{x(3x-2)}=\frac{x+4}{x}[/tex]

Since [tex]g(x) \neq0[/tex] , let's find its roots:

[tex]3x^2-2x=0\\\\Factor\\\\x(3x-2)=0\\\\Split\hspace{3}into\hspace{3}two\hspace{3}equations:\\\\(1):x=0\\(2):3x-2=0[/tex]

For (2)

[tex]3x=2\rightarrow x=\frac{2}{3}[/tex]

Therefore the roots are:

[tex]x=0,\hspace{3}x=\frac{2}{3}[/tex]

Finally the complete answer is:

[tex](\frac{f}{g})(x)= \frac{x+4}{x} \hspace{8}where\hspace{8}x\neq0,\frac{2}{3}[/tex]

It takes Makhaya 75 minutes and 3 paper sheets to complete a writing assignment, and it takes him 15 minutes and 1 paper sheet to complete a math assignment. Makhaya is required to spend more than 300 minutes to complete assignments, and he can use at most 20 paper sheets.
Let W denote the number of writing assignments he completes and M the number of math assignments he completes.

Write an inequality that represents the condition based on the number of minutes.

Write an inequality that represents the condition based on the number of paper sheets.

Answers

Answer:

Part a) [tex]75W+15M > 300\ minutes[/tex]

Part b) [tex]3W+M \leq 20\ paper\ sheets[/tex]

Step-by-step explanation:

Let

W------> the number of writing assignments that Makhaya completes

M-----> the number of math assignments that Makhaya completes

case A) Based on the number of minutes

[tex]75W+15M > 300[/tex] -----> inequality that represent the situation based on the number of minutes

The solution is the shaded area between the positive values of W and M

see the attached figure N 1

case B) Based on the number of paper sheets

[tex]3W+M \leq 20[/tex]-----> inequality that represent the situation based on the number of paper sheets

The solution is the triangular shaded area between the positive values of W and M

see the attached figure N 2

Answer:

First box: 75W+15M>300

Second box: 3W+M≤ 20

Step-by-step explanation:

Did it on Khan

I need help! Really struggling with understanding how to do this

Answers

we have
y>=x+1
y>=4-x

using a graph tool
see the attached figure
the solution is the intersection of both inequalities

1. Use an inequality symbol (<, >, ≥, =) to compare −26 ____ 54

Answers

the answer is less then or <

< because 54 is bigger

An advertisement on a billboard measures 22 ft long and 8 ft high. If the ad is transferred to the side of a bus and is 30 in. Long, how tall is the new ad, to the nearest inch

Answers

the new ad is 10 ft and 11 inches tall, to the nearest inch.

What is Scale?

The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary throughout a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult. This change makes the idea of size significant in two different ways.

Given, An advertisement on a billboard measures 22 ft long and 8 ft high. If the ad is transferred to the side of a bus and is 30 ft. Long.

when the advertisement is 22 ft long then the height is 8 ft.

So,

When the advertisement is 1 ft long then the height is = 8/22 ft.

the advertisement is 1 ft long then the height is = 4/11 ft.

thus,

the advertisement is 30 ft long then the height is = 4/11 * 30 ft.

the advertisement is 30 ft long then the height is = 120/11 ft.

the advertisement is 30 ft long then the height is = 10 ft 11 inches.

Therefore, When the advertisement is 30 ft long then the height is 10 ft 11 inches.

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What is the line of symmetry for the parabola whose equation is y = x2 + 10x + 25? x = -10 x = -5 x = 5

Answers

y = x2 + 10x + 25? x = -10 x = -5 x = 5

Answer:

[tex]y=x^2 + 10x + 25\\\\y=(x+5)^2[/tex]

Used the identity, [tex](a+b)^2=a^2+2ab+b^2[/tex]

The given parabola is of the form , [tex](x+a)^2=y[/tex], having vertex at ,which can be obtained by

x+a=0

x= -a

(-a,0).

So, vertex of the given parabola is , at (-5,0).

The Meaning of term line of symmetry,is that line which divides the parabola in two equal halves.

Drawing the parabola,and finding the line of symmetry,which can be obtained by drawing a line parallel to y axis, passing through (-5,0).

So, the equation of line is : x= -5

Provide a possible situation that the graph shown could represent

Answers

Rapid start of a race - plateau - the decline

I steal the sacred Cheese Puff and run away, I get tired out and take a break, police find me and I run all the way back to return it.

The 12 members in Dante's hiking club shared 176 ounces of trail mix equally. How many ounces of trail mix did each member get?

Answers

176/12 = 14 2/3
so each member receives 14 2/3 ounces of trail mix

Consider the expression 625(5xy)^-3/ (5x)^2 y^7

Answers

625(5xy)^-3/ (5x)^2 y^7

625
= -------------------- / 25x^2y^7
125 x^3y^3

= 5/x^3y^3 / 25x^2y^7
= 5/x^3y^3 * (1/ 25x^2y^7)
= 1 / 5x^5y^10

answer

1
-----------------
5x^5y^10

Answer:

-----------------

5x^5y^10

Step-by-step explanation:

What is the area of a sector with a central angle of 10π/7 radians and a radius of 18.4 m? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.

Answers

Area of sector= \frac{\Theta}{360}\times \Pi \times r^{2}

Area =\frac{10\Pi }{7 }\times \frac{1}{360}\times \Pi \times (18.4)^{2}

Area = \frac{1800 }{7 }\times \frac{1}{360}\times (3.14) \times (18.4)^{2}

So, Area of the given sector= 759.34 square meters.

Answer:

759.34 m²

Step-by-step explanation:

solve f(1) for f(x)=1-5x

f(1)= [?]

Answers

The answer is: "- 4 " .
________________________________________
" f(x) = - 4 " .
________________________________________
Explanation:
________________________________________
Given: " f(x) = 1 – 5x " ; Find: " f(1) " ;

Substitute "1" for values of "x" ;

→ f(1) = 1 – 5(1) = 1 – 5 = - 4 .

The answer is: "- 4 " .
________________________________________
" f(x) = - 4 " .
________________________________________

Joselyn is a manager at a sign-painting company. She has two painters, Allen and Brianne. Allen can complete a large project in 16 hours. Brianne can complete the project in 18 hours. Joselyn wants to know how long it will take them to complete the project together.

Write an equation and solve for the time it takes Allen and Brianne to complete the project together. Explain each step.

Answers

Allen can take 16 hours, while
Brianne can take 18 hours;
Therefore, in 1 hour Allen will complete a fraction of 1/16, while
in 1 hour Brianne will complete a fraction of 1/18
When working together, in 1 hour they will complete a fraction of (1/18+1/16)
= 17/144,
Therefore; to complete the whole project working together, they will take;
144/17 = 8.47 hours

Line segment XY is tangent to circle Z at point U. If the measure of UV is 84, what is the measure of YUV. A. 42 B. 84 C. 96 D. 168

Answers

Answer:

The measure of angle YUV is equal to [tex]m<YUV=42\°[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we have that

[tex]arc\ UV=84\°[/tex] -----> given problem

[tex]m<UZV=84\°[/tex] ------> by central angle

we know that

The triangle UZV is an isosceles triangle

because

[tex]ZU=ZV=radius[/tex]

[tex]m<ZUV=m<ZVU[/tex] -----> bases angle of the isosceles triangle

Remember that

The sum of the internal angles of a triangle is equal to [tex]180\°[/tex]

[tex]m<ZUV+m<ZVU+m<UZV=180\°[/tex]

[tex]2m<ZUV+m<UZV=180\°[/tex]

substitute and solve for m<ZUV

[tex]2m<ZUV+84\°=180\°[/tex]

[tex]m<ZUV=(180\°-84\°)/2=48\°[/tex]

[tex]m<ZUV+m<YUV=90\°[/tex] ------> by complementary angles

solve for m<YUZ

[tex]48\°+m<YUV=90\°[/tex]

[tex]m<YUV=90\°-48\°=42\°[/tex]

Answer: A. 42

Step-by-step explanation: trust i got a 100% on the quiz

In GHI, HI = IHG =3x + 4, and IGH = 2x - 24. What is HIG?

Answers

HIG=16×44=704 its correct okke mmm

HI = GH so GHI is an isosceles triangle

<IGH = <HIG = 2x - 24

as you know sum of interior angles in a triangle = 180
so
2(2x - 24) + 3x + 4 = 180
4x - 48 + 3x + 4 = 180
7x - 44 = 180
7x = 224
x = 32

so
<HIG = <IGH = 2(32) - 24 = 64 - 24 = 40

answer
m<HIG = 40 degrees

Jim's family went on vacation and rented a car. The rental car agency charged $64.75 plus an additional $0.03 for each mile the car was driven. If Jim's family paid a total of $71.14 for the car rental, how many miles did the family drive the car? Explain how you set up an equation to solve this word problem

Answers

$71.14 - $64.75 = $6.39
Each mile = $0.03
$6.39 ÷ $0.03 = 213 miles.

Burt & ernie went to the toy store & saw a total of 51 rubber duckies. they saw twice as many yellow as orange. let y = the # of yellow duckies & r = the # of orange duckies. write a system that could be used to find the total of each color & then solve.

Answers

y +r = 51
y = 2r

There are 34 yellow rubber ducks.
There are 17 orange rubber ducks.

How much will it cost to mail a first-class letter that weighs 2.8 oz?
The rate is $.22 for the first ounce and $.17 for each additional
ounce or fraction of an ounce.
a. $.56
b. $5.60
c. $.53
d. $.39

Answers

Final answer:

The total cost to mail a first-class letter that weighs 2.8 oz is $0.56, which includes $0.22 for the first ounce and $0.34 for the additional weight.

Explanation:

To calculate the cost of mailing a first-class letter that weighs 2.8 oz, you need to know the initial rate for the first ounce and the rate for each additional ounce. According to the given rates, the cost for the first ounce is $0.22, and each additional ounce (or fraction thereof) costs $0.17.

Since the letter weighs 2.8 oz, you have 1.8 oz over the first ounce. Thus, you need to pay for 2 additional ounces.

The total cost = cost for first ounce + cost for additional ounces = $0.22 + 2 x $0.17 = $0.22 + $0.34 = $0.56. Therefore, the correct answer is (a) $.56.

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