SOLUTION
The price of the car = $12,000
The depreciate by 10%
[tex]\begin{gathered} \text{ The depreciating value for the first year } \\ 12,000\times(\frac{10}{100})^1 \\ \text{Then} \\ 12,000\times0.1 \end{gathered}[/tex]Then
[tex]12,000-12,00(0.1)[/tex]Then
[tex]\begin{gathered} 12000(1-0.1) \\ 12,000(0.9) \end{gathered}[/tex]For the first year the depreciating value will be
[tex]12,000(0.9)[/tex]Base on the number of years, the exponential equation will be
[tex]\begin{gathered} f(x)=12,000(0.9)^x \\ \text{where } \\ x=\text{ number of years } \end{gathered}[/tex]Therefore
The exponential equation that represent the value of the car is
F(x)=12,000(0.9)^x
The price of the car in 5 yeras will be obtain by substituting x=5 into the equation above
[tex]\begin{gathered} f(x)=12,000(0.9)^x \\ \text{where x=5} \\ f(x)=12,000(0.9)^5=7085.88 \end{gathered}[/tex]The car will worth $7085.88 after 5 years
Similarly, The for 12 years we have x=12
[tex]f(x)=12,000(0.9)^{12}=3389.15[/tex]The car will worth $3389.15 after 12 years
6in 4in 3in 8in 3in 4in area of irregular figures
Daniel opened a small business. His profit for the first month was -$503. If his average profit for months 2-4 was $-421, what was the total profit for months 1-4?Please help me
If Daniel profit for the first month was -$503. If his average profit for months 2-4 was $-421, then $924 was the total profit for months 1-4
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Daniel opened a small business.
Profit for the first month was -$503 five hundred and three
Average profit for months 2-4 was $-421, four hundred and twenty one.
We need to find the total profit for months 1-4
Add profit for 1s month and 2-4 months.
$503+$421
$924
Hence $924 was the total profit for months 1-4
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The maximum grade allowed between two stations in a rapid transit rail system is 3.5%. Between station a and station b which are 290 feet apart, the tracks rise 8 ft. What is the grade of the tracks between these stations ? Round the answer to the nearest tenth of a percent. Does this grade meet the rapid transit rails standards?
Given,
Station A and Station B are 290 feet apart.
Tracks rise 8 feet.
We need to find the slope of the tracks, because the slope of the track is the gradient of the track.
The slope is rise over run.
The rise is "8"
The run is "290"
Hence, the slope is >>>>>
[tex]\frac{8}{290}\approx0.027586[/tex]To convert it to a percentage, we multiply by 100. Thus,
[tex]0.027586\times100\approx2.76\%[/tex]This is within the tolerance range of less than 3.5%.
So, this grade meets the rapid transit rail standards.
AnswerGrade of tracks = 2.8%Yes, it does meet the rapid transit rail standards.Identify the center of the circle defined by the equation (x + 4)² + (y - 1)² = 32
Answer:
The centre of the circle is (-4,1).
Explanation
Given the equation of the circle:
[tex]\mleft(x+4\mright)^2+(y-1)^2=32[/tex]Comparing with the standard form of the equation of a circle:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ Where\; Centre=(h,k) \end{gathered}[/tex]We see that:
[tex]\begin{gathered} x-h=x+4 \\ \implies h=-4 \\ \text{Also:} \\ y-k=y-1 \\ \implies k=1 \end{gathered}[/tex]The centre of the circle is (-4,1).
The function h(x) shown is the result of adding two functions, f(x) and g(x).
Which statement could be used to describe the functions?
The domains of both f(x) and g(x) must be (–∞, ∞).
What is a domain?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).
Here, we concluded that
The domains of both f(x) and g(x) must be (–∞, ∞).
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1593 concert tickets were sold for a total of $22,491. If students paid $11 and nonstudents paid $17, how many student tickets were sold?
765 student tickets were sold
Explanation:Let the number of student tickets be represented by x
Let the number of nonstudent tickets be represented by y
1593 concert tickets were sold
x + y = 1593....................(1)
The total amount made = $22491
Cost of each student ticket = $11
Cost of each nonstudent ticket = $17
This can be interpreted mathematically as:
11x + 17y = 22491...............(2)
Mulitipy equation (1) by 17
17x + 17y = 27081...........(3)
Subtract equation (2) from equation (3)
6x = 4590
x = 4590/6
x = 765
765 student tickets were sold
Factor 2x^2 - 10x - 12.2(x + 2)(x - 3) 2(x - 6)(x + 1)2(x - 1)(x + 6)
The factor is 2(x+1)(x-6).
From the question, we have
2x²-10x-12
=2x²-12x+2x-12
=2x(x-6)+2(x-6)
=(2x+2)(x-6)
=2(x+1)(x-6)
Factors :
The positive integers that can divide a number evenly are known as factors in mathematics. Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied. Each number has a self-referential element. There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are called factors. A factor is therefore another number's divisor.
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Find the value of x. 14 6 / 110° 9 70
We are given a triangle crossed by two parallel lines. The lines are parallel since their corresponding angles are the same. Therefore, from Thale's theorem we have the following relationship:
[tex]\frac{14}{6}=\frac{x}{9}[/tex]Now we solve for "x" by multiplying by 9 on both sides of the equation:
[tex]\frac{14}{6}\times9=x[/tex]Solving the operations we get:
[tex]21=x[/tex]Therefore, x = 21
Write the standard form of the equation of the circle described below. (6,-7) r=9
Solution
Step 1
write out the expression for the equation of a circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where the centers are (h,k)
h = 6
k = -7
r = 9
Step 2
Write out the required equation of the circle using the parameters
[tex]\begin{gathered} \text{The required equation thus is} \\ (x-6)^2+(y-(-7))^2=9^2 \\ (x-6)^2+(y+7)^2=81_{} \end{gathered}[/tex]What is the image of (-8, -1) when it isreflected across the line y=x?A (-1, -8) C (1,8)B(1-1)D8
Give the object with a coordinate (-8,-1)
The transformation of an object with coordinate (x,y) reflected across the line y=x is given by
T(x,y) => (y,x)
So for the question given
If (-8,-1) is reflected across the line y = x
Then
T(-8,-1) => (-1, -8)
Answer = (-1,-8)
Lora rents a car while spending her vacation traveling in Brazil. When she returns the car, she has driven 1350 miles and used about 54 gallons of gas. If gas costs an average of $4.969 per gallon, estimate how much she spent on fuel.
Given:
distance Lora has driven = 1350 miles
amount of gas she used = 54 gallons
cost of gas per gallon = $4.969
The amount she spent o fuel can be calculated using the formula:
[tex]\text{Amount she has spent on fuel = cost per gallon }\times\text{ amount of fuel she has used }[/tex]Substituting we have:
[tex]\begin{gathered} \text{Amount she has spent on fuel = \$5 }\times\text{ 5}5 \\ =\text{ }275 \end{gathered}[/tex]Answer:
Hence, Lora has spent $275 on fuel by estimate
Sandy was shopping and saw that 4lbs of meat costs $8.00. Calculate the unit price for 1 oz of the meat. $____
To answer this question first we convert from lbs to oz.
Recall that:
[tex]1\text{ lb = 16 oz.}[/tex]Therefore,
[tex]4\text{ lbs= 64 oz.}[/tex]Now, since 64 oz cost $8.00, then the cost of 1 oz of meat is:
[tex]\frac{8.00}{64}\text{dollars}\approx0.13\text{ dollars.}[/tex]Answer: $0.13.
in a circle the radius is 11.5 which is the circumference??
The circumference of a circle is the perimeter or external measure.
Given a circle of radius r, the circumference is calculated as:
C=2 π r
The circle has a radius of r=11.5 units
The circumference is:
C=2 π (11.5) = 72.26 units
The circumference is 72.26 units
A ferris Wheel has a radius of 65 feet. What is the circumference of the wheel?
Circumference of the wheel = 408.2 ft
Explanation:radius = 65 ft
Circumference of the wheel = circumference of a circle
Circumference of a circle = 2πr
π = 3.14
Circumference of a circle = 2 × 3.14 × 65
Circumference of a circle = 408.2 ft
Circumference of the wheel = 408.2 ft
Given the function h(x) = x^2 + 3x - 1 determine the average rate of change of the function over the interval -7 ≤ x ≤ 5
Given:
[tex]x^2+3x-1[/tex]Find: average rate of change of the function over the interval -7 ≤ x ≤ 5
Explanation: the average rate of change of the function is
[tex]\begin{gathered} \frac{f(b)-f(a)}{b-a} \\ \end{gathered}[/tex][tex]\begin{gathered} f(b)=f(5)=5^2+15-1 \\ =25+15-1 \\ =39 \\ f(a)=f(-7)=(-7)^2-21-1 \\ =49-22 \\ =27 \end{gathered}[/tex][tex]\frac{f(b)-f(a)}{b-a}=\frac{39-27}{5-(-7)}=\frac{12}{12}=1[/tex]Final answer: the required answer is 1.
Inequality statement for -13,-25,-8
The inequality statement for -13,-25,-8 is -13 > -25 < -8.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
It should be noted that -13 is greater than -25 while -25 is less than -8.
In this case, -13 > -25 < -8.
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If we consider only the cost of gasoline, how much does it cost ( in dollars) to drive each mile ? Round to the nearest cent.
Given:
The cost of gasoline, c=$2.20/gallon.
The car gets x=26 miles per gallon.
The cost to drive each mile if gasoline costs $2.20/gallon is
[tex]\begin{gathered} T=\frac{c}{x} \\ =\frac{\frac{2.20\text{ dollars}}{1\text{ gallon}}}{\frac{26\text{ miles}}{1\text{ gallon}}} \\ =\frac{2.20\text{ dollars}}{1\text{ gallon}}\times\frac{1\text{ gallon}}{26\text{ miles}} \\ =0.08 \end{gathered}[/tex]Therefore, the two fractions for obtaining the solution is,
[tex]\begin{gathered} \frac{2.20\text{ dollars}}{1\text{ gallon}} \\ \frac{1\text{ gallon}}{26\text{ miles}} \end{gathered}[/tex]The cost in dollars to drive each mile is $0.08 per mile (rounded to nearest cent).
a. 10x-6=44b. (x+3)-15=48c. 4(x+6)-10=26d. 3(x+3)-15=48e.Which two equations have the same solution set? Write a sentence explaining how the properties of equality can be used to determine the pair without having to find the solution set for each.
a.
[tex]\begin{gathered} 10x-6=44 \\ 10x=44+6 \\ 10x=50 \\ x=\frac{50}{10} \\ x=5 \end{gathered}[/tex]b.
[tex]\begin{gathered} 9(x+3)-15=48 \\ 9x+27-15=48 \\ 9x+12=48 \\ 9x=36 \\ x=\frac{36}{9} \\ x=4 \end{gathered}[/tex]c.
[tex]\begin{gathered} 4(x+6)-10=26 \\ 4x+24-10=26 \\ 4x+14=26 \\ 4x=26-14 \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]d.
[tex]\begin{gathered} 3(x+3)-15=48 \\ 3x+9-15=48 \\ 3x-6=48 \\ 3x=48+6 \\ 3x=54 \\ x=\frac{54}{3} \\ x=18 \end{gathered}[/tex]The answer in set notation
[tex]x=\mleft\lbrace5,4,3,18\mright\rbrace[/tex]e. Equation b and Equation d have the same solution set . Both of the equations is equals to 48.
A box contains the name of every student in the school. One hundred names are drawn from the box and students are asked their opinion of the new pizza served in the cafeteria. (A) biased or(B) unbiased
This is an unbiased sampling because there is not a systematically opinion that favors some outcomes over others. So the answer is B
if given the function y=-3x+5,what is the output if f(x)=4
To solve this problem, we have to evaluate when f(x) = 4. Remember that y = f(x)
[tex]\begin{gathered} y=-3x+5\rightarrow f(x)=-3x+5 \\ 4=-3x+5 \end{gathered}[/tex]Then, we solve for x
[tex]\begin{gathered} 4-5=-3x \\ -3x=-1 \\ x=-\frac{1}{-3} \\ x=\frac{1}{3} \end{gathered}[/tex]Hence, th
6. Which of the following statements are true? 4 is a perfect cube 8 is a perfect square 100 is a perfect square 35 is a perfect cube
First statement: 4 is NOT a perfect cube, because it cannot be written as the cube of a rational number.
Second statement: 8 is NOT a perfect square because it cannot be written as the square of a rational number.
Third statement: 100 IS a PERFECT square, because ic can be written as 10^2 *the square of the number 10)
Fourth statement: 35 is NOT aperfect cube because it cannot be written as the cube of a rational number.
Therefore the only TRUE statement is the third one:
"100 is a perfect square".
Hello,Can you please help with question 33 on the photo? Thank you
With the help of the given formula, we can find the first four terms of the sequence:
[tex]\begin{gathered} a_1=30 \\ a_2=a_{2-1}-10=a_1-10=20 \\ a_3=a_{3-1}-10=a_2-10=10 \\ a_4=a_{4-1}-10=a_3-10=0 \end{gathered}[/tex]Then, the first four terms of the sequence are 30, 20, 10, 0, ...
Now, as we can see, this is an arithmetic sequence because there is a common difference between each term. The explicit formula of an arithmetic sequence is shown below:
[tex]\begin{gathered} a_n=a_1+d(n-1) \\ \text{ Where} \\ \text{ d is the common difference} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} a_1=30 \\ d=-10 \end{gathered}[/tex][tex]\begin{gathered} a_n=a_1+d(n-1) \\ a_n=30-10(n-1) \\ \text{ Apply the distributive property} \\ a_n=30-10*n-10*-1 \\ a_n=30-10n+10 \\ a_n=-10n+40 \end{gathered}[/tex]Thus, a formula for the general term of the sequence is:
[tex]a_{n}=-10n+40[/tex]Now, we substitute n = 20 in the above formula to find the 20th term of the sequence:
[tex]\begin{gathered} a_{n}=-10n+40 \\ a_{20}=-10(20)+40 \\ a_{20}=-200+40 \\ a_{20}=-160 \end{gathered}[/tex]AnswerA formula for the general term of the sequence is:
[tex]a_{n}=-10n+40[/tex]The 20th term of the sequence is -160.
Earn,deposit, increase and raise all have positive valuesTrue or False
We will have the following:
*Earn: By definition represents a positive value, since you cannot "earn" a negative quantity.
*Deposit: Deposits are "neutral" since they represent the movement of money but not neccesarily an increase, and sometimes it can be also a payment, so it can also be net negative.
*Increase: By definition is a positive value.
*Raise: By definition is a positive value.
So, it is false. Reason:
A deposit represents a net neutral, since it is refering to the movement of money but not it's increase neccesarily, and sometimes is also a negative, since it can be used as payment, thus representing a net negative value.
Use my radians find the amplitude and period of each function then graph
For a function of the form:
[tex]y=acos(b\theta)[/tex]a = amplitude = 2
b = angular frequency = 1/4
The period can be calculated as follows:
[tex]\begin{gathered} T=\frac{2\pi}{b} \\ So: \\ T=\frac{2\pi}{1/4} \\ T=8\pi \end{gathered}[/tex]Now, we can graph the function easily:
Which of the following is the co-function of cos 58 degrees?tan 58°sin 58°cos 32°sin 32°
ANSWER
[tex]\sin 32^o[/tex]EXPLANATION
We want to find the cofunction of the given function.
The cofunction of a cosine function is:
[tex]\cos (\theta)=\sin (90-\theta)[/tex]Therefore, the cofunction of cos(58) is:
[tex]\begin{gathered} \cos (58)=\sin (90-58) \\ \cos (58^o)=\sin (32^o) \end{gathered}[/tex]That is the answer.
find the median of 79,27,24,11,14,11
To get the median of the distribution, we need to re-arrange the data in either ascending or descending order
Re-arranging the data in ascending order, we have
11, 11, 14, 24, 27, 79
There are two numbers that falls in the midle of the distribution, that is 14 and 24
The median = (14 + 24)/2 = 38/2
=19
The answer is 19
For questions 6 – 10, find the unknown side length. number 10
10) Given:
hypotenuse = 20
angle = 45°
To find:
length of s
angle = 45
opposite = side opposite the angle = s
To find the value of s, w will apply sine ratio (SOH)
[tex]sin\text{ 45 = }\frac{opposite}{hypotenuse}[/tex][tex]\begin{gathered} sin\text{ 45 = }\frac{s}{20} \\ s\text{ = 20sin45} \\ sin\text{ 45 = }\frac{\sqrt{2}}{2} \\ \\ s\text{ = 20}\times\frac{\sqrt{2}}{2} \\ s\text{ = 10}\sqrt{2}\text{ \lparen exact answer\rparen} \end{gathered}[/tex][tex]\begin{gathered} s\text{ = 20sin45} \\ s\text{ = 20\lparen0.7071\rparen} \\ s\text{ = 14.142 \lparen decimal approximation\rparen} \end{gathered}[/tex]The following triangles are scaled copies of each other. What is the scale factor? The scale factor is? What is the length of x? What is the length of y?
If we divide corresponding sides, we can obtain the scale factor:
24/6 = 4
Lenght of x
x/8 =4
Solve for x
x=4 (8)
x= 32
Lenght of y:
36/y=4
Solve for y
36/4=y
9=y
Select the correct answer. 3(r + 4) – 2(1 - 1) Which is the simplified form of the expression OA. - 1 OB. 67 101 + 9 O C. 3 Tot + 5 2 76 OD. 15 + 101 Undo Next
We have the expression:
[tex]3(\frac{7}{5}x+4)-2(\frac{3}{2}-\frac{5}{4}x)[/tex]We simplify it as follows:
[tex]\frac{21}{5}x+12-3+\frac{5}{2}x\Rightarrow(\frac{21}{5}x+\frac{5}{2}x)+(12-3)[/tex][tex]\Rightarrow\frac{67}{10}x+9[/tex]From this, we have that the solution is the B option.
Three teachers handed out mathand science textbooks for theirclasses. Two teachers had21 students each, and the lastteacher had 22. How manytextbooks were handed outaltogether?
Given Data:
The number of teachers is, 3.
Two teachers had 21 students each.
The last teacher had 22.
Since, two teachers had 21 students each, the number of textbooks handed out by these two teachers can be calculated as,
[tex]21\times2=42[/tex]Therefore the total number of text books handed out is,
[tex]42+22=64[/tex]Thus, 64 textbooks were handed out altogether.