Given:
rate (r) = 5.4% or 0.054 in decimal form
Principal (P) = $3,000
time in years (t) = 3 years
number of conversions per year (m) = 12 (because it says monthly)
Find: future value or maturity value
Solution:
The formula for getting the future value of a compound interest is:
[tex]F=P(1+\frac{r}{m})^{mt}[/tex]Let's plug in the given data to the formula above.
[tex]F=3,000(1+\frac{0.054}{12})^{12\times3}[/tex]Then, solve for F or future value.
[tex]\begin{gathered} F=3,000(1.0045)^{36} \\ F=3,000(1.17532999) \\ F\approx3,526.30 \end{gathered}[/tex]Answer: After 3 years, the deposited money will become $3, 526.30.
Using the following image, solve for CD. 2x - 9 Сс X-9 • E 12 CD |
Answer
CD = 11 units
Explanation
From the image, we can see that
CD = 2x - 9
DE = x - 9
CE = CD + DE
CE = 12
CE = CD + DE
CE = (2x - 9) + (x - 9)
12 = 2x - 9 + x - 9
12 = 3x - 18
We can rewrite this as
3x - 18 = 12
3x = 12 + 18
3x = 30
Divide both sides by 3
(3x/3) = (30/3)
x = 10
CD = 2x - 9 = 2(10) - 9 = 20 - 9 = 11 units
Hope this Helps!!!
Write the expression with a single rational exponent 1/x to the -1 power
Given:
[tex]\frac{1}{x}[/tex]To Determine: The simplified fraction to its rational exponent to the power of -1
Solution
Apply the exponent rule below
[tex]\frac{1}{a^n}=a^{-n}[/tex]Apply the exponent rule above to the given fraction
[tex]\frac{1}{x}=x^{-1}[/tex]Hence, 1/x = x ⁻¹
I will show you the pic .
we have the equation
(2/3)x+5=1
step 1
multiply by 3 both sides
2x+15=3
step 2
subtract 15 both sides
2x=3-15
2x=-12
step 3
divide by 2 both sides
x=-12/2
x=-6Assignment: 5.4 Bellwork Wednesday 2/03 Problem iD: PRABRBYC Rose wants to construct a fence around her garden. The garden is circular in shape with a diameter of 9 ft. What is the length of fencing material she will need to fence around the outside her garden?
The garden is described as having a circular shape. The diameter is 9 feet. The length of fencing material needed to fence around the outside of her garden refers to the perimeter or the circumference of the circular garden.
The circumference of a circle is given as;
[tex]\begin{gathered} \text{Cir}=2\pi r \\ r=\frac{\text{diameter}}{2} \\ r=4.5 \\ \text{Cir}=2\times3.14\times4.5 \\ \text{Cir}=28.26 \end{gathered}[/tex]Therefore, Rose would need 28.26 feet of fencing material
A student is measuring the length of an icicle, y, every hour, x. The icicle is currently 14 inches long and is melting at a rate of 0.9 inches per hour. Find and interpret the slope for this relationship. −0.9; for every additional hour, the length of the icicle decreases by 0.9 inches 0.9; for every additional hour, the length of the icicle increases by 0.9 inches −14; the length of the icicle when the student first measures it 14; the length of the icicle when the student first measures it
The answer is: −0.9; for every additional hour, the length of the icicle decreases by 0.9 inches
( 3y + 1 )( 3y - 1 )Determine each product
It is important to know that a Product is the result of a multiplication.
You have the following expression given in the exercise:
[tex]\mleft(3y+1\mright)\mleft(3y-1\mright)[/tex]Notice that it is the multiplication of two Binomials and it has this form:
[tex](a+b)(a-b)[/tex]By definition:
[tex](a+b)(a-b)=a^2-b^2[/tex]This is called "Difference of two squares".
You can identify that, in this case:
[tex]\begin{gathered} a=3y \\ b=1 \end{gathered}[/tex]Therefore, you get:
[tex]\mleft(3y+1\mright)\mleft(3y-1\mright)=(3y)^2-(1)^2=9y^2-1[/tex]The answer is:
[tex]9y^2-1[/tex]At a carnival, there is a game where you can draw one of 10 balls from a bucket if you pa $16. The balls are numbered from 1 to 10. If the number on the ball is even, you win $22 If the number on the ball is odd, you win nothing. If you play the game, what is the expected profit?
ANSWER
[tex]\text{\$-5}[/tex]EXPLANATION
To find the expected profit, we have to first find the expected payout.
There is a possibility of drawing up to 10 balls, numbered 1 to 10.
There are 5 even balls and 5 odd balls.
We have to find the probabilty of drawing even or odd balls:
=> The probability of drawing an even ball is:
[tex]P(\text{even)}=\frac{5}{10}=\frac{1}{2}[/tex]=> The probability of drawing an odd ball is:
[tex]P(\text{odd)}=\frac{5}{10}=\frac{1}{2}[/tex]The expected payout is the sum of the product of the probability of drawing each ball and the prize of each ball.
That is:
[tex]\begin{gathered} E(X)=\Sigma\mleft\lbrace X\cdot P(X)\mright\rbrace \\ E(X)=(22\cdot\frac{1}{2})+(0\cdot\frac{1}{2}) \\ E(X)=11+0 \\ E(X)=\text{ \$11} \end{gathered}[/tex]The expected profit can be found by subtracting the cost of playing the game from the expected payout:
[tex]\begin{gathered} Exp.Profit=11-16 \\ Exp.Profit=\text{ \$-5} \end{gathered}[/tex]That is the answer.
how much it is -6 1/2 + 12?
In the given fraction, the value of -6 1/2 + 12 is 11/2
Fraction:
The fraction represents the part of a whole. And the fraction is the number is expressed as a quotient, in which the numerator is divided by the denominator.
Given,
Here we have the fraction -6 1/2 + 12.
Now, we need to find the value of this fraction.
To solve this one, first we have to convert the mixed fraction into normal one, then we get,
To convert the mixed fraction fist we have to multiply the denominator by the whole number, then we get
6 x 2 = 12
Then add these value into the numerator, then we get
12 + 1 = 13
So, the fraction is -13/2.
Now, we have to add these two,
=> -13/2 + 12
The fractions have unlike denominators.
First, we have to find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(-13/2, 12/1) = 2
Then we have to multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. Then we get,
=> -13/2 + 24/2
=> 11/2
Therefore, the resulting fraction is 11/2.
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which relation is a function A.(2,3),(1,5),(2,7)B.(-1,5),(-2,6),(-3,7)C.(11,9),(11,5),(9,3)D.(3,8),(0,8),(3,-2)
A function can only have one out put value (y) for every input value (x).
A. (2,3) (2,7)
input value 2 has 2 different output values (3 and 7)
It's not a function.
Same case for C and D.
Correct option . B-
The temperature, in degrees Fahrenheit, of a cup of water placed in a freezer can be modeled by the function f(m)=210(0.94)^m , where m represents the number of minutes after the water was placed in the freezer.
What is the average rate of change from Minute 4 to Minute 11 and how can that rate of change be interpreted?
1. The average rate of change from Minute 4 to Minute 11 is of -8.23 º/min.
2. This means that the temperature decreased from Minute 4 to Minute 11 by an average of 8.23 º/min.
How to obtain the average rate of change of a function?The average rate of change of a function is obtained by the change in the output of the function divided by the change in the input of the function. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
The function in this problem is defined as follows:
f(m) = 210(0.94)^m.
The numeric value of the temperature at Minute 11 is of:
f(11) = 210(0.94)^11 = 106.32º.
The numeric value of the temperature at minute 4 is of:
f(4) = 210(0.94)^4 = 163.96º.
The change in the input is of:
11 - 4 = 7.
Hence the average rate of change is of:
(106.32 - 163.96)/67 = -8.23º min -> decrease of 8.23º each min.
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Match the figure at the right with the number that represents the sum of the interior angles for that figure.
To calculate the sum of the internal angles of a polygon you have to use the following formula:
[tex](n-2)\cdot180º[/tex]Where "n" is the number of sides of the polygon.
So you have to subtract 2 to the number of sides of the polygon and then multiply the result by 180º to determine the sum of the interior angles.
1) The first polygon has n=4 sides. To calculate the sum of its interior angles you have to do as follows:
[tex]\begin{gathered} (n-2)\cdot180º \\ (4-2)\cdot180º \\ 2\cdot180º=360º \end{gathered}[/tex]2) The second polygon has n=5 sides. The sum of its interior angles can be calculated as:
[tex]\begin{gathered} (n-2)\cdot180º \\ (5-2)\cdot180º \\ 3\cdot180º=540º \end{gathered}[/tex]3) The third polygon has n=6 sides. You can calculate the sum of its interior angles as:
[tex]\begin{gathered} (n-2)\cdot180º \\ (6-2)\cdot180º \\ 4\cdot180º=720º \end{gathered}[/tex]4) The fourth polygon has n=7 sides, so you can calculate the sum of its interior angles as:
[tex]\begin{gathered} (n-2)\cdot180º \\ (7-2)\cdot180º \\ 5\cdot180º=900º \end{gathered}[/tex]Find the area under the standard normal distribution curve to the left of z=1.93.
We are given the image of the curve and asked to find the area under the curve to the left of z=1.93.
Since we have been given the z score already all we need to do is look up the z score on a left tailed z-table.
The picture above shows a left-tailed z- table. To find the area under the curve to the left of z=1.93, we look up 1.9 under .03.
From the table, we can therefore see that answer would be
ANSWER=0.97320
Solve the system.x + y + 2z = -1x+ y + 8z = -7(x-9y - 2z = -37
Given the three variable simultaneous equations;
[tex]\begin{gathered} x+y+2z=-1\ldots\ldots.i \\ x+y+8z=-7\ldots\ldots.ii \\ x-9y-2z=-37\ldots\ldots.iii \end{gathered}[/tex]To solve;
let's solve for z by subtracting equation i from ii;
[tex]\begin{gathered} x+y+8z-(x+y+2z)=-7-(-1) \\ x-x+y-y+8z-2z=-7+1 \\ 6z=-6 \\ \frac{6z}{6}=\frac{-6}{6} \\ z=-1 \end{gathered}[/tex]next let's solve for y by subtracting equation i from iii;
[tex]\begin{gathered} x-9y-2z-(x+y+2z)=-37-(-1) \\ x-x-9y-y-2z-2z=-37+1 \\ -10y-4z=-36 \\ \text{ since z=-1} \\ -10y-4(-1)=-36 \\ -10y+4=-36 \\ -10y+4-4=-36-4 \\ -10y=-40 \\ \frac{-10y}{-10}=\frac{-40}{-10} \\ y=4 \end{gathered}[/tex]We have z and y, to get x let us substitute te values of y and z into equation i;
[tex]\begin{gathered} x+y+2z=-1 \\ x+(4)+2(-1)=-1 \\ x+4-2=-1 \\ x+2=-1 \\ x+2-2=-1-2 \\ x=-3 \end{gathered}[/tex]Therefore the values of x, y and z are;
[tex]\begin{gathered} x=-3 \\ y=4 \\ z=-1 \end{gathered}[/tex]Answer is A.
If u = 2i - j; v= -5i + 4j and w = j find 4u (v -w).
Answer:
-40
Explanation:
Given
u = 2i - j; v= -5i + 4j and w = j
Required
4u(v-w)
4u = 4(2i) = 8i
v - w = -5i + 4j - j
v - w = -5i + 3j
Substitute
4u(v-w)
= 8i(-5i+3j)
= -40(i*i) [since i*i = 1]
= -40
Hence the required solution is -40
Higher Order Thinking The bakery had
84 muffins. Ms. Craig bought 5 packs of
6 muffins. Did she purchase an even or an
odd number of muffins? Is the number of
muffins left even or odd? Explain.
shi
Answer:
Even and 54
Step-by-step explanation:
Based on the given conditions, formulate: 84-6x5
Calculate the product or quotient: 84-30
Calculate the sum or difference: 54
Ayako took a trip to the store 4 1/2mi away. If she rode the bus for 3 5/8mi and walked the rest of the way, how far did she have to walk? Express you answer as a simplified fraction or mixed number
Ayako took a trip to the store 4 1/2mi away. If she rode the bus for 3 5/8mi and walked the rest of the way, how far did she have to walk? Express you answer as a simplified fraction or mixed number
we have that
total distance=4 1/2 miles
Let
x ----> number of miles walked
so
4 1/2=3 5/8+x
solve for x
But first, convert mixed number to an improper fraction
4 1/2=4+1/2=9/2
3 5/8=3+5/8=29/8
substitute
9/2=(29/8)+x
x=(9/2)-29/8
the fractions have different denominators
so
Find out an equivalent fraction
9/2=(9/2)*(4/4)=36/8
so
x=(36/8)-29/8
x=7/8
the answer is 7/8 miles2. Find the area: Upload a picture of your work or type it out here 25 cm 123 cm 21 cm
The area of a triangle is represented by the following expression:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ \text{where,} \\ b=\text{base} \\ h=\text{height} \end{gathered}[/tex]With the information given, we know that base is 21cm and height is 23cm, now we can substitute and calculate the area:
[tex]\begin{gathered} A=\frac{21\cdot23}{2} \\ A=\frac{483}{2} \\ A=241.5cm^2 \end{gathered}[/tex]Is a triangle with sides that measure 3 inches, 4 inches, and 5 inches a right triangle?
Solution:
To figure out if a triangle with sides that measure 3 inches, 4 inches, and 5 inches, is a right triangle, we use the Pythagorean theorem.
According to the Pythagorean theorem, the square of the longest side of the triangle (hypotenuse) is equal to the sum of the squares of the other two sides (adjacent and opposite) of a right-triangle.
This implies that
[tex](hypotenuse)^2=(adjacent)^2+(opposite)^2[/tex]In this case, the longest side is 5 inches.
[tex]hypotenuse=5[/tex]Thus,
[tex]\begin{gathered} (hypotenuse)^2=3^2+4^2 \\ =9+16 \\ =25 \\ \end{gathered}[/tex]Since the sum of the squares of the two sides (adjacent and opposite) is exactly equal to the hypotenuse, we can conclude that the triangle is a right triangle.
6200 in standard form
Answer: Six Thousand Two Hundred
Step-by-step explanation:
in a board game players draw cards to move tokens along a path •A card with the number 2 means to move 2 spaces forward •A card with the number -3 means to move 3 spaces backwards , what is most likely the meaning of a card with the number 0
When the player draws a card with a positive number it let him move forward as many spaces as the number of the card, with negatives number the player must move backward, when the player draws a zero card, it means that he can't move his tokens, neither forward or backward, his tokens must stay where they are.
Find the circumference of a circular swimming pool with a diameter of feet. Use as an approximation for . Round your answer to the nearest foot. Enter only the number.
To determine the circumference of any circle we need to use the following formula:
[tex]C=2\cdot\pi\cdot r[/tex]Where r is the radius, which is half of the diameter. For this problem we have a pool with diameter equal to 18 feet, therefore the circumference is:
[tex]\begin{gathered} C=2\cdot3.14\cdot\frac{18}{2}=2\cdot3.14\cdot9 \\ C=56.52\text{ ft} \end{gathered}[/tex]The circumference of the pool is approximately 57 feet.
2.8 -2 3/4 -31/8 2.2 from least to greatest
Express the mixed numbers as decimals and compare:
2.8
-2 3/4
-31/8
2.2
-2 3/4 = -(2x4+3 /4)=11/4 = 2.75
- (31
can you help I dont know how to do it
four segments
[tex]MS,MT,MN,MY[/tex]A ray
[tex]\bar{MY}[/tex]Collinear points
[tex]Y,M,N[/tex]i need help i don’t understand the questions are down below
A picture and a frame are given with dimensions. It is required to find the area of the frame.
To find the area of the frame, subtract the area of the picture from the total area (frame + picture).
Recall the area of a rectangle with a length l and a width w:
[tex]A=l\cdot w[/tex]Substitute l=22 and w=20 into the formula to find the area of the picture:
[tex]A=22\cdot20=440[/tex]Notice that the total length of the picture and frame is l=22+x+x=22+2x, while the total width is w=20+x+x=20+2x.
Substitute these dimensions into the area formula:
[tex]\begin{gathered} A=(22+2x)\cdot(20+2x) \\ A=4x^2+40x+44x+440 \\ \Rightarrow A=4x^2+84x+440 \end{gathered}[/tex]Subtract the areas to find the area of the entire frame:
[tex]\text{ Area of frame}=4x^2+84x+440-440=4x^2+84x+0[/tex]The area of the entire frame is 4x²+84x+0.
First-term is 4x², the second term is 84x, and the third term is 0.
To find the area when x=2, substitute x=2 into the expression for the area:
[tex]4(2)^2+84(2)+0=4(4)+168+0=16+168=184[/tex]The area of the frame when x=2 inches is 184 inches squared.
The perimeter is the sum of the side lengths of the frame given as:
[tex]P=2(l+w)[/tex]Substitute l=22+2x and w=20+2x into the formula:
[tex]P=2(22+2x+20+2x)=2(4x+42)=8x+84[/tex]Substitute x=10 to find the perimeter when x=10:
[tex]P=8(10)+84=80+84=164[/tex]The perimeter is 164 inches.
Answers:
The area of the entire frame is 4x²+84x+0.
First-term is 4x², the second term is 84x, and the third term is 0.
The area of the frame when x=2 inches is 184 inches squared.
The perimeter when x=10 is 164 inches.
Use logarithmic differentiation to find the derivative of y with respect to xy = (10x + 2)^x
Given: An equation-
[tex]y=(10x+2)^x[/tex]Required: To determine the differentiation of y with respect to x.
Explanation: The differentiation of a logarithmic function is-
[tex]\begin{gathered} y=a^x \\ \frac{dy}{dx}=a^x\ln(a) \end{gathered}[/tex]Taking log both sides on the given equation as-
[tex]\begin{gathered} \ln y=\ln(10x+2)^x \\ =x\ln(10x+2) \end{gathered}[/tex]Now, differentiating with respect to x using product rule as-
[tex]\frac{1}{y}\frac{dy}{dx}=\ln(10x+2)\frac{d}{dx}(x)+x\frac{d}{dx}\ln(10x+2)[/tex]Further simplifying as-
[tex]\frac{dy}{dx}=y[\ln(10x+2)+\frac{10x}{10x+2}][/tex]Substituting the value of y as-
[tex]\frac{dy}{dx}=(10x+2)^x[\ln(10x+2)+\frac{10x}{10x+2}][/tex]Final Answer: Option D is correct.
Tommy throws a ball from the balcony of his apartment down to the street. The height of the ball, in meters, is modeled by the function shown in the graph. What's the average rate of change of the height of the ball, in meters per second, while it's in the air?Question options:A) 2∕3B) –2∕3C) –3∕2D) 3∕2
Solution
The average rate of change of the height of the ball is given by
[tex]\frac{f(b)-f(a)}{b-a}[/tex]Here,
[tex]\begin{gathered} a=0 \\ b=10 \\ f(a)=f(0)=15 \\ f(b)=f(10)=0 \end{gathered}[/tex][tex]\begin{gathered} AverageRate=\frac{f(b)-f(a)}{b-a} \\ AverageRate=\frac{0-15}{10-0} \\ AverageRate=\frac{-15}{10} \\ AverageRate=-\frac{3}{2} \end{gathered}[/tex]The average rate is -3/2
Option C
Which pair of functions are inverse functions?()=3+5f(x)=3x+5and()=−3−5g(x)=−3x−5 ()=−+57f(x)=−x+57and()=−7+5g(x)=−7x+5 ()=−3−57f(x)=−3x−57and()=3+57g(x)=3x+57 ()=3−5f(x)=3x−5and()=−53
1) Let's examine the f(x) functions and find the inverse function of f(x), in the first pair of functions:
a) At first, let's swap x for y in the original function
[tex]\begin{gathered} f(x)=3x+5 \\ y=3x+5 \\ x=3y+5 \\ -3y=-x+5 \\ 3y=\text{ x-5} \\ \frac{3y}{3}=\frac{x-5}{3} \\ y=\frac{x-5}{3}\text{ } \\ f^{-1}(x)=\frac{x-5}{3} \end{gathered}[/tex]Note that after swapping x for y, we can isolate y on the left side. So as regards g(x) this is not the inverse function of f(x)
2) Similarly, let's check for f(x)
[tex]\begin{gathered} f(x)=\frac{-x+5}{7} \\ y=\frac{-x+5}{7} \\ x=\frac{-y+5}{7} \\ 7x=-y+5 \\ y=-7x+5 \\ f^{-1}(x)=-7x+5 \end{gathered}[/tex]Note that in this case, we can state that these are inverse functions
[tex]f^{-1}(x)=g(x)[/tex]3) Finally, let's find out the last pair of functions.
[tex]\begin{gathered} f(x)=\frac{-3x-5}{7} \\ y=\frac{-3x-5}{7} \\ x=\frac{-3y-5}{7} \\ 7x=-3y-5 \\ 3y=-7x-5 \\ f^{-1}(x)=\frac{-7x-5}{3} \end{gathered}[/tex]So in this pair, g(x) is not the inverse function of f(x).
4) Hence, the answer is following pair:
[tex]\begin{gathered} f(x)=\frac{-x+5}{7}\text{ } \\ g(x)=f^{-1}(x)=-7x+5 \end{gathered}[/tex]on a family trip mr perers travels 130 miles in two hours at this rate how many miles will he travel in 30 minutes?
Answer:
32.5
Step-by-step explanation:
130 miles divided by 120 minutes (2 hours) then take that number and multiply by 30 minutes
Use the techniques of College Algebra to show how to write an equation for the quadratic graphed below.
x-intercepts: (-3,0) and (1,0). y-intercept: (0,1)
The quadratic equation for the given points x-intercepts: (-3,0) and (1,0). y-intercept: (0,1) is,
f(x) = (-x² - 2x + 3)/3
Given, an equation having
x-intercepts: (-3,0) and (1,0). Also, y-intercept: (0,1)
Now, as we know that the equation is quadratic then, it is clear that the equation will be in the given form :
f(x) = ax² + bx + c
Now, using the given points,
x-intercepts: (-3,0) and (1,0) and y-intercept: (0,1)
we get,
0 = 9a - 3b + c
0 = a + b + c
1 = c
Now, using the value of c, we get
9a - 3b = -1
a + b = -1
On solving the equations, we get
9a - 3b = -1
3a + 3b = -3
On adding both the equations we get,
12a = -4
a = -1/3
Now, using the value of a, we get
-3 - 3b = -1
-2 = 3b
b = -2/3
So, the quadratic equation, be
f(x) = -x²/3 - 2x/3 + 1
On simplifying, we get
f(x) = (-x² - 2x + 3)/3
Hence, the quadratic equation for the given points x-intercepts: (-3,0) and (1,0). y-intercept: (0,1) is,
f(x) = (-x² - 2x + 3)/3
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On a hike, each hiker carries the items shown. Write an expression in simplest form that represents the weight (in pounds) carried by x hikers. sleeping bag: 3.4lb bag: 4.6lb water bottle: 2.2lb
ok
Weight(x) = 3.4x + 4.6x + 2.2x or
W(x) = 3.4x + 4.6x + 2.2x
or
W(x) = 10.2x this is the expression