Given:
Future Value = $15,000
time (t) = 11 years
rate (r) = 4.4% or 0.044
number of conversions per year (m) = 365
Find: Initial amount or the Principal
Solution:
Formula for Compound Interest is:
[tex]F=P(1+\frac{r}{m})^{mt}[/tex]From that, we can derive the formula for the Principal or the initial amount.
[tex]P=\frac{F}{(1+\frac{r}{m})^{mt}}[/tex]Let's plug in the given data above to the formula of the principal value.
[tex]P=\frac{15,000}{(1+\frac{0.044}{365})^{365\times11}}[/tex]Then, solve for P.
[tex]P=\frac{15,000}{(1.000120548)^{4015}}=\frac{15,000}{1.622504316}\approx9,244.97[/tex]Answer: You must invest $9, 244.97 to the account in order to get $15,000 after 11 years.
A rectangle is 7 times as long as it is wide. The perimeter is 32 feet. Find the dimensions.The length isfeet where the width isfeet.
Let l and w be the length and width of the rectangle, respectively.
Therefore, according to the question,
[tex]\begin{gathered} l=7w \\ and \\ P=32 \\ P=2l+2w \end{gathered}[/tex]Therefore, solving for l and w,
[tex]\begin{gathered} l=7w \\ 2(l+w)=32 \\ \Rightarrow l=7w,l+w=16 \\ \Rightarrow7w+w=16 \\ \Rightarrow w=2 \\ and \\ \Rightarrow l=7*2=14 \end{gathered}[/tex]The answer is length=14ft, width=2ftWhich equation represents a line that is perpendicular to the line passing through (-4,7) and (1,3)?A. y =x + 8B.y =-x + 6C.y =x - 3D. y = -x - 2
If two lines of slopes m1 and m2 are perpendicular, then:
[tex]m_1\cdot m_2=-1[/tex]The slope of a line passing through points (x1, y1) and (x2, y2) is:
[tex]\begin{equation*} m=\frac{y_2-y_1}{x_2-x_1} \end{equation*}[/tex]We are given the points of the first line (-4, 7) and (1, 3). Calculate the slope
[tex]m_1=\frac{3-7}{1+4}=-\frac{4}{5}[/tex]The slope of the perpendicular line is:
[tex]m_2=-\frac{1}{m_1}=-\frac{1}{-\frac{4}{5}}=\frac{5}{4}[/tex]The equation of the perpendicular line has the form:
[tex]y=\frac{5}{4}x+b[/tex]None of the options has the correct answer.
What is the value of z for the equation fraction 1 over 4z = −fraction 7 over 8 + fraction 1 over 8z? −3−737
-7
Explanation
Step 1
given
[tex]\frac{1}{4}z=-\frac{7}{8}+\frac{1}{8}z[/tex]subtrac (1/4)z in both sides
[tex]\begin{gathered} \frac{1}{4}z=-\frac{7}{8}+\frac{1}{8}z \\ \frac{1}{4}z-\frac{1}{4}z=-\frac{7}{8}+\frac{1}{8}z-\frac{1}{4}z \\ 0=-\frac{7}{8}-\frac{1}{8}z \end{gathered}[/tex]Step 2
add 7/8 in both sides
[tex]\begin{gathered} 0=-\frac{7}{8}-\frac{1}{8}z \\ 0+\frac{7}{8}=-\frac{7}{8}-\frac{1}{8}z+\frac{7}{8} \\ \frac{7}{8}=-\frac{1}{8}z \\ \end{gathered}[/tex]finally, multiply both sides by -8 in order to isolate z
[tex]\begin{gathered} \frac{7}{8}=-\frac{1}{8}z \\ \frac{7}{8}*-8=-\frac{1}{8}z*-8 \\ -7=z \end{gathered}[/tex]therefore, the answer is
-7
I hope this helps you
Maggie walks at a constant speed.
Maggie plots points on the coordinate plane below to show amounts of time it takes her to walk
certain distances.
Distance
(km).
The ordered pair which can be plotted according to the given data in graph will be (6,21).
Plotting of point on graph:Plotting an ordered pair on graph of speed and time represents the motion of a particle accelerating from a speed at time 0 , u , to a speed v at time t .
According to given graph we have already plotted points as follows
(2, 7), (4, 15), (5,17)
Now by analysis of the given graph pattern we can conclude that the ordered pair which can be added to the given graph if (6, 21).
Note : - The Question is completed as below and the coordinate plane is attached too.
Maggie walks at a constant speed. Maggie plots points on the coordinate plane below to show amounts of time it takes her to walk certain distances.
Which of the following ordered pairs could Maggie add to the graph?
A. (1,3)
B. (3,10)
C. (6,21)
D. (3,1)
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Can anyone help me with this true or false question
ANSWER
A. True
EXPLANATION
Let the complex number be z = a+ ib, so its complex conjugate is z* = a - ib, where a and b are real numbers. Let's find the product,
The product is,
[tex](a+ib)(a-ib)=a\cdot a-a\operatorname{\cdot}ib+ib\operatorname{\cdot}a-ib\operatorname{\cdot}ib[/tex]Solve the products,
[tex](a+ib)(a-ib)=a^2-iab+iab-i^2b^2[/tex]Simplify: note that the second and third terms are opposites, so they cancel out. Remember that i² is equal to -1,
[tex](a+ib)(a-ib)=a^2+0-(-1)b^2=a^2+b^2[/tex]Since a and b were real numbers, then the sum of their squares is also a real number.
Hence, this statement is true.
Is 21.23 a rational number Show evidence
Answer:
Yes, 21.23 is a rational number.
[tex]21.23=\dfrac{2123}{100}[/tex]
Step-by-step explanation:
Terminating decimal numbers are decimals that have a finite number of decimal places.
A Rational Number is the division of an integer by another integer.
Therefore, 21.23 is a terminating decimal since it has a finite number of decimal places.
Let x be the rational number.
[tex]\implies x=21.23[/tex]
Multiply both sides by 100 so that the right side is an integer:
[tex]\implies 100x=2123[/tex]
Divide both sides by 100:
[tex]\implies x=\dfrac{2123}{100}[/tex]
(This fraction cannot be reduced any further).
Therefore, we have proved that 21.23 is a rational number.
Answer:
It is a rational number.
Step-by-step explanation:
Given value,
→ 21.23
Converting into rational number,
→ (21.23/1) × (100/100)
→ (21.23 × 100)/(1 × 100)
→ 2123/100
Hence, it is a rational number.
Destinee's house is located at (2, 3) on the coordinate grid. El Ticonzito is located at (-4,-2).
If El Ticonzito is the midpoint between Destinee's house and Ana's house, what is the approximate distance between Ana's house and Destinee's house?
A. 6.63 miles
B.
C.
D.
7.50 miles
11.00 miles
10
15.62 miles
The distance between Destinee's house and Anna's house is 15.62 miles
Midpoint of a LineTo find the coordinate of the Anna's house, we can use the formula of midpoint on this. This is given as
[tex]midpoint(x,y) = \frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2}[/tex]
In the question, El Ticonzito's house is at midpoint between Destinee's house and Anna's house.
[tex]midpoint(x,y) = \frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2}\\-4 = \frac{2 + x_1}{2} = -8 = 2 + x_1\\x_1 = -8 - 2 = -10\\\\-2 = \frac{3 + y_1}{2} \\-4 = 3 + y_1\\-4 - 3 = y_1\\y_1 = -7[/tex]
The coordinate's of Anna's point is (-10, -7).
Let's use this to calculate the distance (d) between the two points.
[tex]d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2} \\d = \sqrt{(-10-2)^2 + (-7 - 3)^2} \\d = \sqrt{(-12)^2 + (-10)^2} \\d = \sqrt{244}\\ d = 15.62 miles[/tex]
The distance between the two points is 15.62 miles
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Write the equation of the line (in standard form) that goes through point (5,-1) and is parallel to the equation 3x + 2y = 19.
3x+2y=10 This is the equation of the new line in standard form
Calculate the equation of the line in standard form?Two parallel lines have the same slope, to compute the slope (m) of the equation 3x+2y=19. This can be obtained by converting the equation into slope-intercept form (i.e., y=mx+b, where m is the slope):
by subtracting 3x from both sides, and then simplifying:
3x+2y-3x=19-3x
2y =-3x+19
Then, let's divide both sides by 2, to obtain slope-intercept form:
y = (-3/2)x+(/2) From this, we know that the slope (m) is -3/2
To determine the equation of the line we're being asked to solve for. If we know the slope (in this case m=-3/2) along with any given point on the line ((x0,y0); in this case (4,1)), the equation of the line can be determined as y-y0=m(x-x0)
So substituting, the equation of the line is y-1=(-3/2)(x-5)
We now need to put this into standard form, with both x and y terms on the left side of the equation:
First, distribute the 3/2 on the right side: y-1=(-3/2)x+(3/2)5 or y-1
= (-3/2)x+6
Next, add (3/2)x to both sides, add 1 to both sides, and simplify:
(3/2) x + y = 5
multiply both sides by 2, to eliminate the fraction (3/2): 3x+2y = 10 This is the equation of the new line in standard form
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Find the sector area of the circle. Use 3.14 for the value of pi
Given:
Radius of the cirle = 11 ft
Angle = 150 degrees
π = 3.14
Let's find the area of the sector of the cicle.
To find the area of the sector, apply the formula:
[tex]A=\frac{\theta}{360}\times\pi r^2\text{ }[/tex]Where:
π = 3.13
θ = 150 degrees
r = 11
Thus, we have:
[tex]\begin{gathered} A=\frac{150}{360}\times3.14\times11^2 \\ \\ A=\frac{150}{360}\times3.14\times121 \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} A=0.41667\times3.14\times121 \\ \\ A=158.3ft^2 \end{gathered}[/tex]Therefore, the sector area of the circle is 158.3 square feet.
ANSWER:
158.3 square feet.
b. Alejandro needs 13 yards of wire. How much will he spend on wire?.
Answer:
This is impossible.
Step-by-step explanation:
You didn't give us how much 1 yard is.
Answer: How much is one yard?
Step-by-step explanation:
This is my homework by the way.You can represent the measures of an angle and its complement as x° and (90 -x)° Similarly, you can represent the measures of an angle and its supplement as and (180 -- x)°. Use these expressions to find the measures of the angles described.The measure of an angle is three times the measure of it's supplement.The measure of the supplement of an angle is three times the measure of it's complement.The measure of an angle increased by 20° is equal to the measure of it's complement.
The sum of complemenatry angles = 90
The sum of supplementary angles = 180
Use f(x) =11. f(-8)35x + 11, g(x)=x2-7x, and h(x) = 15 - 9x to evaluate each function.12. g(-2)13.14. 9(5)+g(9)15. 1-216. If f(x) = -7, find x.17. If h(x) = 48, find x.18. Find /(-8c + 2)19. Find g(x-8)
To find f(-8), we just need to replace x by -8 on the function f(x) as:
[tex]\begin{gathered} f(x)=\frac{-3}{2}x+11 \\ f(-8)=\frac{-3}{2}(-8)+11 \\ f(-8)=12+11 \\ f(-8)=23 \end{gathered}[/tex]At the same way g(-2) is equal to:
[tex]\begin{gathered} g(x)=x^2-7x \\ g(-2)=(-2)^2-7\cdot(-2) \\ g(-2)=4+14 \\ g(-2)=16 \end{gathered}[/tex]Finally, h(2/3) is equal to:
[tex]\begin{gathered} h(x)=\left|15-9x\right| \\ h(\frac{2}{3})=\left|15-9\cdot\frac{2}{3}\right| \\ h(\frac{2}{3})=\left|15-6\right| \\ h(\frac{2}{3})=\left|9\right| \\ h(\frac{2}{3})=9 \end{gathered}[/tex]Answers: f(-8) = 23
g(-2) = 16
h(2/3) = 9
Question 15Please answer quickly, i don’t need much explanation and just want this to be done so I can use it as an example
SOLUTION:
Step 1:
In this question Number 15, we are given the following:
Given point Q equals negative 6 radical 3 comma negative 6 in rectangular coordinates, what are the corresponding polar coordinates?
Given the rectangular coordinates of point Q:
[tex]Q(-6\sqrt{3},-6)[/tex]You need to remember that the form from rectangular oordinates to polar coordinates is:
[tex](x,y)\rightarrow(r,\theta)[/tex]By definition:
[tex]\begin{gathered} r=\sqrt{x^2+y^2} \\ \\ \theta=tan^{-1}(\frac{y}{x}) \end{gathered}[/tex]In this case, you can identify that:
[tex]\begin{gathered} x=-6\sqrt{3} \\ y=-6 \end{gathered}[/tex]Then, you can determine that:
[tex]\begin{gathered} r=\sqrt{(-6\sqrt{3})^2+(-6)^2}=12 \\ \\ \theta=tan^{-1}(\frac{-6}{-6\sqrt{3}})=\frac{5\pi}{6} \end{gathered}[/tex]Therefore, the polar coordinates are:
[tex](12,\frac{5\pi}{6})[/tex]Hence, the answer is: Second option.
Jon just received a job offer that will pay him 12% more than what he makes at his current job. If the salary at the new job is 68,000. What is his current salary? Round to the nearest cent.
Let be "x" Jon's current salary.
According to the information given in the exercise, the salary at the new job is 68,000 and this is 12% more than his salary at his current job.
To convert from percent to a Decimal number, you can divide by 100. Then:
[tex]\frac{12}{100}=0.12[/tex]Therefore, knowing that information, you can set up the following equation:
[tex]x+0.12x=68,000[/tex]Now you can solve for "x" in order to find its value:
[tex]\begin{gathered} 1.12x=68,000 \\ \\ x=\frac{68,000}{1.12} \\ \\ x\approx60,714.29 \end{gathered}[/tex]The answer is:
[tex]60,714.29[/tex](1 point) Use the figure below to estimate the indicated derivatives. If a derivative does not exist, enter dne in the answer blank. The graph of f(x) is black and has a sharp corner at x=2. The graph of g(x) is blue.
Let j(x)=g(x)f(x). Find
j'(3)
Applying the quotient rule, the derivative of the given function at x = 3 is of -2/3.
What is the quotient derivative rule?A quotient function is defined as follows:
i(x) = g(x)/f(x)
Applying the quotient rule, the derivative of the function defined above is of:
i'(x) = [g'(x)f(x) - f'(x)g(x)]/f(x)².
Hence, at x = 3, the numeric value of the derivative is given as follows:
i'(3) = [g'(3)f(3) - f'(3)g(3)]/f(3)².
Function f(x) is a linear function with slope of -3/2, hence:
f'(3) = -3/2 (for a linear function, the derivative is constant).f(3) = 3/2 (from the graph).Function g(x) is a linear function with slope of -1/2, hence:
g'(3) = -1/2.g(3) = 1/2.Then the derivative is given as follows:
[tex]g^{\prime}(3) = \frac{-\frac{1}{2} \times \frac{3}{2} - \frac{3}{2} \times \frac{1}{2}}{\left(\frac{3}{2}\right)^2} = -\frac{\frac{6}{4}}{\frac{9}{4}} = -\frac{6}{9} = -\frac{2}{3}[/tex]
Hence the numeric value of the derivative at x = 3 is of -2/3.
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Which experession is equivalent to 4(9+7)
Answer:
64
Step-by-step explanation:
9+7=16
16(4)=64
During a sale, a store offered a 15% discount on a stereo system that originally sold for $400. After the sale the discount price of the stereo system was marked up by 15%. To the nearest whole number, what percent of the original price was the price after mark up
Problem Statement
We are told a store offers 15% discount on the sale of a stereo originally costing $400. After the sale, the new price is marked up by 15%.
We are asked to find what percentage of the original price is the new marked up price.
Method
T
I have a few different questions :) first off I need this domain and range found
ANSWER
[tex]\begin{gathered} \text{Domain: -7 }\leq x\leq3 \\ \text{Range: }-1\text{ }\leq y\leq9 \end{gathered}[/tex]EXPLANATION
We want to find the domain and range of the function.
The domain of a function is the set of all input values of the function. Basically, the set of all x values of a function.
The range of a function is the set of all output values of the function. Basicallly, the set of all y values of a function.
To find the domain of the function, we have to look at the smallest and largest values of x.
The smallest value of x is -7.
The largest value of x is 3.
So, the domain is:
[tex]-7\text{ }\leq x\text{ }\leq3[/tex]To find the range of the function, we have to look at the smallest and largest values of y.
The smallest value of y is -1.
The largest value of y is 9.
So, the range is:
[tex]-1\text{ }\leq y\leq9[/tex]determine whether the given numbers are solutions of the inequality 2t +6 <4-t a 0 b 1 c -3 d 5
The value of t must be less than -2/3, that is, the correct answer must be a negative number, in this case it would be the letter C) -3
Identify the like terms in the expression.12n - 6+p+6n
The like terms in the expression are 12n and 6n
Explanations:Like terms are terms that have the same coefficients and in the same order of degrees.
In the expression:
12n - 6 + p + 6n
The like terms are 12n and 6n
18 of the animals in the shelter arecats. If there are 40 animals in theshelter, what percent of the animalsare cats?
There are 40 animals in the shelter, 18 of that animals are cats.
We need to find the percent of the animals that are cats.
Then, 40 animals represent 100% in the shelter.
We can use the rule of three to find the cat's percent:
Therefore:
40 animals -------------- 100%
18 cats ------------------------ x
x = (18*100)/40
x =45
So, 45 % of the animals are cats.
HELP ASAP!!
Find the product of (x − 6)^2 and is the product a polynomial.
x^2 − 12x + 36; is a polynomial
x^2 − 12x + 36; may or may not be a polynomial
x^2 − 36; is a polynomial
x^2 − 36; may or may not be a polynomial
Answer: Choice A
x^2-12x+36; is a polynomial
===================================================
Explanation:
Use the rule that (A-B)^2 = A^2 - 2AB + B^2 to show (x-6)^2 = x^2-12x+36 is an identity. In this case, A = x and B = 6
You could also use the FOIL rule or the distributive property as two alternatives.
The result is a polynomial because it consists of summing or subtracting various monomials. If we had terms that had say exponents of decimal numbers or negative values, then we wouldn't have a polynomial.
You were using a ladder at your construction job. You started off at ground level and climbed down 10 feet to see the basement. Then you climbed up 20 feet to see the second floor. Finally, you climbed down 9 feet. What is your height relative to ground level?
Answer:
1 foot above the ground, positive 1
Step-by-step explanation:
you start at ground level let's call that 0
you go 10 down 0-10=-10
Now you climb up 20 feet so -10+20=10
Then you finally climb down 9 feet and 10-9=1
So you are one foot above the ground.
5x+10+11x+2=58 please help i’m confused
Answer:
x = [tex]\frac{23}{8}[/tex] or 2 [tex]\frac{7}{8}[/tex]
Step-by-step explanation:
1. Add the numbers
10 + 2 = 12
5x+12+11x = 58
2. Combine like terms
5x + 11x = 16x
16x+12 = 58
3. Subtract 12 from both sides
16x + 12-12 = 58-12
x = [tex]\frac{23}{8}[/tex]
Solve the equation for x. −0.28x − 15.3 = 1.92 x = 61.5 x = −61.5 x = 47.8 x = −47.8
The value of x in the linear equation −0.28x − 15.3 = 1.92 is -61.5 option (B) -61.5 is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The linear equation one variable is:
−0.28x − 15.3 = 1.92
-0.28x = 1.92 + 15.3
-0.28x = 17.22
x = -17.22/0.28
x = -61.5
Thus, the value of x in the linear equation −0.28x − 15.3 = 1.92 is -61.5 option (B) -61.5 is correct.
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Answer:
its B -61.5
Step-by-step explanation:
i attched pictures to show you
If you are selling your house with a local realtor who requires a 5% commission fee, what can you expect to pay the realtor if your house sells for $176,000?
given data:
The cost of house is $176000.
The percentage the house realtor requires is 5%.
That is,
[tex]\begin{gathered} \frac{5}{100}\times176000 \\ =8800 \end{gathered}[/tex]Thus 5% of 176000 is 8800.
Thus, you need to give $8800 to the local realtor.
Given that P(B AND A)=0.07 and P(B|A)=0.20, what is P(A)?
Answer: P A is paranthathesis add
Step-by-step explanation: so frist u do ( + ( = ((
then ((-)))=-)
Math word problem covert into systems of equations
Problem #1
budget rent a car rented a basic car at a daily rate of $45.95 plus 40 cents per mile. Another company rents a basic car for $46.95 plus 20 cents per mile. For what mileage is the cost the same.
Define the variables
Let
x -----> number of miles
y -----> the total cost
we have
budget rent a car
y=40x+45.95 ------> equation 1
Another company
y=20x+46.95 -------> equation 2
Solve the system of equations
equate equation 1 and equation 2
40x+45.95=20x+46.95
solve for x
40x-20x=46.95-45.95
20x=1
x=0.05 miles
therefore
the cost is the same for 0.05 miles6
Mrs. Drake buys 72 peanut butter cups and
64 boxes of Nerds. She wants to make goody
bags for her students for Halloween. Mrs.
Drake wants to make sure that every bag has
the same number of each type of candy.
What is the greatest number of goody bags
she can make?