A house is worth $350,000 when purchased. It was worth $335,000 after the first year and $320,000 after the 2nd year.
So, the difference between initial cost and the cost after one year =
335,000 - 350,000 = -15,000
The difference between the cost after one year and after 2 years =
320,000 - 335,000 = -15,000
As the common difference is constant
so, the cost represents Arithmetic sequence
the first term is 330,000 and the common difference is -15,000
The general form of the sequence is a + d(n - 1)
where a is the first term and d is the common difference and n the number of term
so, a = 335,000 and d = -15,000
so, the general form will be = 335,000 - 15,000(n-1)
So, the value of the house after 5 years = 335,000 - 15,000 * (5-1) = 275,000
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1. Geometric or Arithmetic and Why?
Arithmetic
2. Complete a table that shows the value of the house for 5 years.
For 5 years:
first year = $335,000
second year = $320,000
third year = $305,000
fourth year = $290,000
fifth year = $275,000
3. Write an explicit and recursive formula for the sequence.
The formula will be : 335,000 - 15,000(n-1)
4. What is the value of the house after you have lived in it for 10 years?
After 10 years;
the value of the house = 335,000 - 15,000 * (10-1)
= 335,000 - 15,000 * 9 = $200,000
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Julia rides her bike 14 miles in 2 hours. If she rides at a constant speed, select the answers below that are equivalent ratiosto the speed she rides. Select all ratios that are equivalent,
Divide the distance over the total time to find the distance Julia rides in one hour:
[tex]\frac{14\text{ miles}}{2\text{ hours}}=7\text{ miles per hour}[/tex]Do the same for each option to find whether or not they represent the same speed:
A)
[tex]\frac{35\text{ miles}}{6\text{ hours}}=5.83\text{ miles per hour}[/tex]B)
[tex]\frac{7\text{ miles}}{1\text{ hour}}=7\text{ miles per hour}[/tex]C)
[tex]\frac{28\text{ miles}}{4\text{ hours}}=7\text{ miles per hour}[/tex]D)
[tex]\frac{42\text{ miles}}{7\text{ hours}}=6\text{ miles per hour}[/tex]Therefore, only options B and C represent the same ratio.
write an equation in slope intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.(0,0); y=-7x + 5y =
Slope intercept form:
y= mx+ b
Where:
m= slope
b= y-intercept
For: y=-7x+5
m= -7
Perpendicular lines have negative inverse slopes.
Negative inverse of -7 = 1/7
So far we have
y= 1/7x + b
Replace (x,y) fo the given point (0,0) and solve for b:
0= 1/7(0) + b
b= 0
Final equation:
y= 1/7x
Given:• ABCD is a parallelogram.• DE=3z-3• EB=2+11• EC = 5x + 7What is the value of x?44.507
To answer this question, we need to recall that: "the diagonals of a parallelogram bisect each other"
Thus, we can say that:
[tex]DE=EB[/tex]And since: DE = 3x - 3 , and EB = x + 11, we have tha:
[tex]\begin{gathered} DE=EB \\ \Rightarrow3x-3=x+11 \end{gathered}[/tex]we now solve the above equation to find x, as follows:
[tex]\begin{gathered} \Rightarrow3x-3=x+11 \\ \Rightarrow3x-x=11+3 \\ \Rightarrow2x=14 \\ \Rightarrow x=\frac{14}{2}=7 \\ \Rightarrow x=7 \end{gathered}[/tex]Therefore, the correct answer is: option D
determine the fractional value of each division problem 5 divide 95 divide 22 divide 10
Given:
5 divide 9
5 divide 2
2 divide 10
Required:
Find the fractional value of each division problem.
Explanation:
Fractional numbers are numbers that are written in the form of a numerator and denominator.
5 divide 9
[tex]5\div9=\frac{5}{9}[/tex]5 divide 2
[tex]5\div2=\frac{5}{2}[/tex]2 divide 10
[tex]\begin{gathered} 2\div10=\frac{2}{10} \\ =\frac{1}{5} \end{gathered}[/tex]Final Answer:
The fractional value of each division problem is
5 divide 9
[tex]=\frac{5}{9}[/tex]5 divide 2
[tex]=\frac{5}{2}[/tex]2 divide 10
[tex]\begin{gathered} =\frac{2}{10} \\ =\frac{1}{5} \end{gathered}[/tex]Factor 3x² + 10x + 8 using earmuff method.
To factor the above quadratic equation using Earmuff Method, here are the steps:
1. Multiply the numerical coefficient of the degree 2 with the constant term.
[tex]3\times8=24[/tex]2. Find the factors of 24 that when added will result to the middle term 10.
1 and 24 = 25
2 and 12 = 14
3 and 8 = 11
6 and 4 = 10
Upon going over the factors, we will find that 6 and 4 are factors of 24 and results to 10 when added.
3. Add "x" on the factors 6 and 4. We will get 6x and 4x.
4. Replace 10x in the original equation with 6x and 4x.
[tex]3x^2+6x+4x+8[/tex]5. Separate the equation into two groups.
[tex](3x^2+6x)+(4x+8)[/tex]6. Factor each group.
[tex]3x(x+2)+4(x+2)_{}[/tex]7. Since (x + 2) is a common factor, we can rewrite the equation into:
[tex](3x+4)(x+2)[/tex]Hence, the factors of the quadratic equation are (3x + 4) and (x + 2).
Another way of factoring quadratic equation is what we call Slide and Divide Method. Here are the steps.
[tex]3x^2+10x+8[/tex]1. Slide the numerical coefficient of the degree 2 to the constant term by multiplying them. The equation becomes:
[tex]\begin{gathered} 3\times8=24 \\ x^2+10x+24 \end{gathered}[/tex]2. Find the factors of 24 that results to 10 when added. In the previous method, we already found out that 6 and 4 are factors of 24 that results to 10 upon adding. So, we can say that the factors of the new equation we got in step 1 is:
[tex](x+6)(x+4)[/tex]3. Since we slide "3" to the constant term, divide the factors 6 and 4 by 3.
[tex]\begin{gathered} =(x+\frac{6}{3})(x+\frac{4}{3}) \\ =(x+2)(x+\frac{4}{3}) \end{gathered}[/tex]4. Since we can't have a fraction as a factor, slide back the denominator 3 to the term x in the same factor.
[tex](x+2)(3x+4)_{}[/tex]Similarly, we got the same factors of the given quadratic equation and these are (x + 2) and (3x + 4).
I'm reviewing for a final. Can u please help me solve the following
The direction of the resultant vector is approximately 320°.
We have three vectors. The magnitudes of the vectors t, u, and v are 7, 10, and 15, respectively. The angles of the vectors t, u, and v are 240°, 30°, and 310°, respectively. We have to find the angle of the resultant vector of the sum of all three vectors. To add all the three vectors, we need to split the vectors into their horizontal and vertical components. The horizontal components are 7cos(240°), 10cos(30°), and 15cos(310°). The vertical components are 7sin(240°), 10sin(30°), and 15sin(310°).
Let the horizontal and vertical components of the resultant vector be denoted by H and V, respectively. The horizontal component is H = 7cos(240°) + 10cos(30°) + 15cos(310°) = 7*(-0.5) + 10*(0.866) + 15*(0.643) = -3.5 + 8.66 + 9.645 = 14.805. The vertical component is V = 7sin(240°) + 10sin(30°) + 15sin(310°) = 7*(-0.866) + 10*(0.5) + 15*(-0.766) = -6.062 + 5 - 11.49 = -12.552. The angle of the resultant vector can be calculated by the ratio of the components as tan(θ) = V/H = -12.552/14.805 = -0.848. So, the angle "θ" is approximately equal to 320°.
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A construction crew is lengthening a road that originally measured 43 miles.The crew is adding 1 mile to the road each day. Let L be the length in brackets in miles after the days over construction right in equation relating L to D then use this equation to find the length of the road after 15 days
The original measurement is 43 miles.
The rate is 1 mile each day.
Use this information, we can express the following
[tex]L=1\cdot D+43[/tex]So, for 15 days, we have
[tex]L=1\cdot15+43=15+43=58[/tex]Hence, after 58 days, the length of the road will be 58 miles.distance is a direct variation of time if the distance
Explanation
In order to be able to predict the time, it will take to cover 220 miles, we will have to get the relationship
The relationship between distance and the time can be obtained as follow:
When the distance is 80 miles, the time taken is 2 hours
So when the distance is 220 miles, the time taken will be
[tex]x=\frac{220\times2}{80}=5.5[/tex]Therefore, it will take 5.5 hours to cover a distance of 220 miles
Therefore, the answer is 5.5 hours
Hi there! I have a probability quiz this week and I grabbed some problems from my worksheet. This one in particular has me stumped:At a car park there are 100 vehicles, 60 of which are cars, 30 are vans and the remainder are lorries. If every vehicle is equally likely to leave, find the probability of:a) a van leaving first.b) a lorry leaving first.c) a car leaving second if either a lorry or van had left first.Can you help??
Explanation
In the question, we are given that;
[tex]\begin{gathered} \text{Number of vehicles = 100} \\ \text{Number of cars =60} \\ Number\text{ of vans =30} \\ \text{Number of lorries =10} \end{gathered}[/tex]Since each of the vehicles is equally likely to leave;
Part A
[tex]Pr(van)=\frac{\text{number of vans}}{Total\text{ number of vehicles}}=\frac{30}{100}=0.3[/tex]Answer: 0.3
Part B
[tex]Pr(\text{lorry)}=\frac{number\text{ of lorries}}{\text{Total number of vehicles}}=\frac{10}{100}=0.1[/tex]Answer: 0.1
Part C
First we find the probability of a lorry or van leaving
[tex]Pr(\text{Lorry or van) = }pr(lorry)+pr(Van)=0.1+0.3=0.4\text{ or }\frac{4}{10}[/tex]Next, we find the probability of a car; but remember that one of either a lorry or van has left the car park already, so the total number of vehicles will reduce by 1
[tex]Pr(car)=\frac{60}{99}=\frac{20}{33}[/tex]Therefore, the probability of a car leaving second if either a lorry or van had left first is
[tex]Pr((\text{lorry or van) and car)) }=\frac{4}{10}\times\frac{20}{33}=\frac{8}{33}[/tex]Answer:
[tex]\frac{8}{33}[/tex]3. Determine - f(a) for f(x) =2x/x-1 and simplify.
Substitute a for x
[tex]-f\text{ (x ) = - f (a) = - }\frac{2a}{a-1}[/tex]Determine - f(a) for f(x) =2x/x-1 and simplify.
Thus, the solution becomes:
[tex]-\frac{2a}{a-1}\text{ or }\frac{2a}{1-a}[/tex]c) How would you describe the correlation in the data? Explain your reasoning.
Answer: Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect.
If your car gets 32 miles per gallon, how much does it cost you to drive 30 miles when gasoline costs $2.55 per gallon?
32 miles ---------> 1 gallon
30 miles--------------> xgallons
Solving for x:
32/30 = 1/x
x = 30/32 = 0.9375 gallons
1 gallon ------>$2.55
0.9375 gallons----->$y
1/0.9375 = 2.55/y
Solving for y:
y = 2.55*0.9375 = $2.390625
It will cost $2.390625
Which of the following transformations, when performed on Figure Q, will result in Figure R?A.) a reflection over the y-axis followed by a translation of 1 unit to the rightB.) a translation of 7 units to the rightC.) a rotation of 270 degrees counterclockwise about the originD.) a rotation of 90 degrees clockwise about the origin
Given:
Given that a figure Q and its transformation R.
Required:
To choose the correct transformation of the given figure.
Explanation:
The figure R is 7 unit right to the figure Q.
Therefore the option B is correct.
Final Answer:
(B) A translation of 7 units to the right.
For a given geometric sequence, the common ratio, r, is equal to -3, and the 11th term, a₁, is equal to 11. Find the value of the 13thterm, a13. If applicable, write your answer as a fraction.a13
Given:
Common ratio=-3
11th term=11
To determine the 13th term, we first note the geometric sequence formula:
[tex]a_n=ar^{n-1}[/tex]where:
a=1st term
n=nth term
Since the 11th term is 11, we can solve the first term by following the process as shown below:
[tex]\begin{gathered} a_{n}=ar^{n-1} \\ a_{11}=a(-3)^{11-1} \\ 11=a(-3)^{10} \\ Simplify \\ a=\frac{11}{59049} \end{gathered}[/tex]Next, we plug in a=11/59049 when n=13:
[tex]\begin{gathered} a_{n}=ar^{n-1} \\ a_{13}=(\frac{11}{59049})(-3)^{13-1} \\ Calculate \\ a_{13}=99 \end{gathered}[/tex]Therefore, the answer is: 99
A right triangle has legs that are 5 cm and 7 cm long what is the length of the hypotenuse 1.√122.√243.√74 4.√144
Answer:
3. √74
Explanation:
By the Pythagorean theorem, the length of the hypotenuse can be calculated as:
[tex]c=\sqrt[]{a^2+b^2}[/tex]Where c is the hypotenuse and a and b are the lengths of the legs.
So, replacing a by 5 and b by 7, we get:
[tex]\begin{gathered} c=\sqrt[]{5^2+7^2} \\ c=\sqrt[]{25+49} \\ c=\sqrt[]{74} \end{gathered}[/tex]Therefore, the answer is 3. √74
2. A common formula in physics is shown below. my2 FE a) Solve for m in terms of F, v, and r. b) Solve for v in terms of F, m, and r.
1)
a) Solving for m, is isolating the m variable on the left side like this
[tex]\begin{gathered} F=\frac{mv^2}{r}\text{ } \\ mv^2=Fr\text{ } \\ m=\frac{Fr}{v^2} \\ \end{gathered}[/tex]We need to Cross multiply like a ratio, and then divide both sides by v²
Now we can solve for m.
b) Similarly, let's now solve for v, in terms of F, m and r
[tex]undefined[/tex]I’m not sure how to solve it please help me!
ANSWER:
33.5%
STEP-BY-STEP EXPLANATION:
We have the amount in 2003 in 5799 fish and in 2014 there are there are 1943 less fish.
The percentage of change would be the difference in fish between these years divided by the initial amount of fish, just like this:
[tex]\begin{gathered} p=\frac{5799-(5799-1943)}{5799}\cdot100 \\ \\ p=\:\frac{1943}{5799}\cdot100\: \\ \\ p=33.505\cong33.5\% \end{gathered}[/tex]This means that the percentage of change is negative since the population has decreased by 33.5%.
How do you write 476 in scientific notation?
Answer:
[tex]undefined[/tex]How to write 476 in scientific notation.
To write a number in scientific notation, express the number in the form:
[tex]m\text{ }\times10^n[/tex]Where m is a number that has a unit place value. (That is a number less than 10 but greater than 1)
In the case of 476, you put a point after 4, you would see that there are two digits after 4 ( 7 and 6)
The scientific notation of 476 is therefore:
[tex]4.76\times10^2[/tex]For his long distance phone service, David pays a $7 monthly fee plus 7 cents per mintue. Last month, David's long distance bill was $13.93. For how many minutes was David billed?
For the long-distance service, David pays a monthly fee of $7 plus 7 cents per minute.
Let "d" represent the minutes the call lasted, and "c" the total cost of the bill, then you can express the total cost of the bill using the following expression:
[tex]c=7+0.07d[/tex]If the total cost of the bill was c=13.93, to determine the number of minutes David was billed for, you have to replace input this value in the equation and solve it for d
[tex]\begin{gathered} c=7+0.07d \\ 13.93=7+0.07d \end{gathered}[/tex]Pass 7 to the other side of the equation by applying the opposite operation
[tex]\begin{gathered} 13.93-7=7-7+0.07d \\ 6.93=0.07d \end{gathered}[/tex]And divide both sides by 0.07 to determine the value of d
[tex]\begin{gathered} \frac{6.93}{0.07}=\frac{0.07}{0.07}d \\ d=99 \end{gathered}[/tex]David was billed for 99minutes.
Tank (#1) Capacitybarrels per Ft: 62.50Barrels per inch: 5.21.Convert Barrels to Feet, and inches with the information given.If you deposited 190 barrels of water into tank #1. What would be the total amount deposited (feet) and (inches).*remember there are only 12 inches in a foot*
To answer this question, we have to convert the given amount of barrels to feet and to inches using the conversion factors shown.
Barrels to feet:
[tex]190barrels\cdot\frac{1ft}{62.50barrel}=3.04ft[/tex]Barrels to inches:
[tex]190barrels\cdot\frac{1in}{5.21barrel}=36.47in[/tex]It means that the total amount deposited would be 3.04 ft or 36.47 in.
what is the probability of drawing a heart from a standard deck of cards
Answer:
1/4
Step-by-step explanation:
In total, there are 4 suits of cards: spades, clubs, hearts, and diamonds.
This way, the probability of drawing a heart from a standard deck of cards is:
[tex]\frac{1}{4}[/tex]I need help knowing the range of this function. the graph of it is[tex]y = {x}^{2} - 2x - 8[/tex]
Given the function:
[tex]y=x^2-2x-8[/tex]Let's determine the range of the function using the graph.
The range of a function is the set of all possible y-values which define the function.
From the graph shown, the value of y starts from the vertex at y = -9 and goes upward.
Therefore, the range of the function is all values of y greater than or equal to -9.
{y|y ≥ - 9}
Hence, in interval notation is:
[tex][-9,\infty)[/tex]ANSWER:
[tex][-9,\infty)[/tex]Simplify the result if possible assume all variables represent positive real numbers
The function [tex]log_{b} \sqrt[3]{(\frac{x^{8} }{y^{9} z^{6} })}[/tex] is simplified to be [tex]8/3log_{b}x-3log_{b}y-2log_{b}z[/tex]
How to simplify the functionThe function is simplified using the laws of logarithm
[tex]log_{b} \sqrt[3]{(\frac{x^{8} }{y^{9} z^{6} })}[/tex]
[tex]= log_{b}(\frac{x^{8} }{y^{9} z^{6} })^{1/3}[/tex]
[tex]= log_{b}(\frac{x^{8/3} }{y^{9/3} z^{6/3} })[/tex]
[tex]= log_{b}(\frac{x^{8/3} }{y^{3} z^{2} })[/tex]
Applying the quotient rule
[tex]= log_{b}x^{8/3}-log_{b}( y^{3} z^{2})[/tex]
Applying the product rule
[tex]= log_{b}x^{8/3}-(log_{b}y^{3}+log_{b}z^{2})[/tex]
expanding the parenthesis
[tex]= log_{b}x^{8/3}-log_{b}y^{3}-log_{b}z^{2}[/tex]
Applying the exponential rule
[tex]= 8/3log_{b}x-3log_{b}y-2log_{b}z[/tex]
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Below is the graph of =y3x.Translate it to become the graph of =y+3−x41.
The Solution:
Given:
[tex]y=3^x[/tex]Required:
To translate it to become:
[tex]y=3^{x-4}+1[/tex]The Transformations:
A horizontal shift of 4 units to the right.
A vertical shift of 1 unit up.
Below is th graph:
Marc sold 457 tickets for the school play. Studen tickets cost $2 and adult tickets cost $3. Marc's sales totaled $1161. How many adult tickets and how many student tickets did Marc sell? 210 adult, 247 student b. 247 adult, 210 student 215 adult, 242 student d. 242 adult, 215 student
The given situation can be written as a system of equations. Based on the given information you have:
x + y = 457
2x + 3y = 1161
where x is the number of student tickets and y is the number of y tickets.
In order to determine the values of x and y, proceed as follow:
- multiply the first equation by -2:
(x + y = 457)(-2)
-2x - 2y = -914
- then, add the previous equation to the second equation of the system:
-2x - 2y = -914
2x + 3y = 1161
y = 247
- next, replace the previous value of y into the first equationof the system, and solve for x:
x + y = 457
x + 247 = 457
x = 457 - 247
x = 210
Hence, the number of student tickest sold was 210, and adult tickets sold was 247
Nate claims that cat that the catfish is closer to the surface of the water then either the bird or the bone is to the ground level do you agree with his claim
It is important to know that the gound level is zero, so the bone is closer to the ground level because -4.5 is closer than -12.5 or 4.5.
Hence, Nate is wrong.At a charity fundraiser, some guests will be randomly selected to receive a gift. The probability of receiving a gift is 5 over 18. Find the odds in favor of receiving a gift.
Odds in favor of receiving a gift = 5/13
Explanation:The probability of receiving a gift, P(R) = 5/18
Probability of not receiving a gift, P(nR) = 1 - 5/18 = 13/18
The odds in favor of receiving a gift is calculated below:
[tex]Odds(R)=\frac{P(R)}{P(nR)}[/tex]Therefore:
[tex]\begin{gathered} Odds(R)=\frac{5}{18}\div\frac{13}{18} \\ \\ Odds(R)=\frac{5}{18}\times\frac{18}{13} \\ \\ Odds(R)=\frac{5}{13} \end{gathered}[/tex]Odds in favor of receiving a gift = 5/13
If the area of square 2 is 225 units?, andthe perimeter of square 1 is 100 units, what isthe area of square 3?
Step 1. Find the length of the side of square 2.
Since square 2 has an area of:
[tex]\text{area}=225units^2[/tex]We can calculate the length of its sides (all sides in a square are equal) with the following formula that relates the area of a square "a", which the length of its side "l":
[tex]a=l^2[/tex]Solving this equation for the length "l" by taking the square root of both sides:
[tex]\sqrt[]{a}=l[/tex]Substituting the area of square 2 to find the length of the side of square 2:
[tex]\begin{gathered} \sqrt[]{225}=l \\ 15=l \end{gathered}[/tex]The length of square 2 is 15 units:
Step 2. Find the length of the side of square 1.
We are told that the perimeter of square 1 is 100 units:
[tex]p=100\text{units}[/tex]Here, "p" represents the perimeter.
Now we use the formula that relates the perimeter "p" to the length of the side of the square "l":
[tex]p=4l[/tex]And since we need to find "l" we solve that equation for "l" by dividing both sides by 4:
[tex]\frac{p}{4}=l[/tex]Substituting the value of the perimeter to find l:
[tex]\begin{gathered} \frac{100}{4}=l \\ \\ 25=l \end{gathered}[/tex]The length of the side of square 1 is 25 units:
Step 3. Find the length of the side of square 3.
Since we are asked for the area of square 3, first we need to calculate the length of its side, and we find it by using the Pythagorean Theorem in the triangle that is in the middle of the squares.
I will label the values as follows for reference:
25 is the hypotenuse of the triangle which is represented by "c"
15 is one of the legs of the triangle which is represented by "b"
and the missing length of the side of square 3 will be the second leg of the triangle "a". The following image shows this better:
The Pythagorean theorem is as follows:
[tex]a^2+b^2=c^2[/tex]Since the letter we need is a, we solve for it:
[tex]\begin{gathered} a^2=c^2-b^2 \\ a=\sqrt[]{c^2-b^2} \end{gathered}[/tex]Now, substitute the values c and b that we previously defined:
[tex]a=\sqrt[]{(25)^2-(15)^2}[/tex]Solving the operations:
[tex]a=\sqrt[]{625-225}[/tex][tex]\begin{gathered} a=\sqrt[]{400} \\ a=20 \end{gathered}[/tex]We have found the length of the side of square 3: 20 units.
Step 4. Calculate the are of square 3 using the area formula for a square:
[tex]a=l^2[/tex]Where "l" is the length of the side of the square, in this case, 20 units:
[tex]a=(20units)^2[/tex][tex]a=400units^2[/tex]Answer:
[tex]400units^2[/tex]in the diagram below, line CD and BC intersect at a. Which of the following rigid motions could be used to show that
The only rigid motion that could be used to show that angle BAE is congruent to the angle DAC is D.
Because if we do the rotation of 180° clockwise about A we will obtain the same Figure.
This is the original figure
As we can see making the rotation we obtain same figure
Steve made a business trip of 200.5 miles. He averaged 51 mph for the first part of the trip and 62 mph for the second part. If the trip took 3.5 hours, how long did hetravel at each rate?
Let t = time traveled at 51 mph
The total time is given as 3.5 hours
So (3.5- t )= time traveled at 62 mph
We are going to use the distance formula:
distance = speed* time
51t + 62(3.5-t) = 200.5
51t + 62*3.5 - 62*t = 200.5
51t + 217 - 62t = 200.5
Solve the equal terms
51t - 62t = 200.5 - 217
-11t = -16.5
t = -16.5/-11
t = 1.5
Then he took 1.5 at 51mph
and (3.5- t ) = (3.5-1.5) = 2h at 62 mph
To confirm these results, find the actual speed of each speed:
speed* time = distance
51*1.5 = 76.5miles
62*2. = 124 miles
76.5miles + 124 miles = 200.5miles