Since the tax on the room is given by the function:
T(x)=0.06x+45
And x(cost in dollars of the room) is given= $120, you just have to subtitue x=120 on the function
T(120)=0.06(120)+4.5
T(120)=7.2+4.5
T(120)=11.7
So, the tax in dollars would be $11.7
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.
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]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
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]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
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.
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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Suppose that the dollar value v () of a certain house that is t years old is given by the following exponential function.v (t) = 637,000 (1.02)^tFind the initial value of the house.s1Does the function represent growth or decay?O growth O decayBy what percent does the value of the house change each year?
Given the function:
[tex]v(t)=637000(1.02)^t[/tex]Where:
v(t) represents the value of the house after t years.
Let's find the following:
• (a). Find the initial value of the house.
Apply the exponential function:
[tex]f(x)=a(b)^x[/tex]Where:
a is the initial value
b is the growth of decay factor.
Here, we have:
a = 637000
b = 1.02
Therefore, the initial value of the house is 637,000 dollars.
• (b). Does the function represent growth or decay?
If b is greater than 1 the function represents a growth function.
If b is less than 1, the function represents a decay function.
Here, we have:
b = 1.02
Therefore, the function represents a growth function.
• (c). By what percent does the value of the house change each year?
Apply the formula:
[tex]f(x)=a(1+r)^x[/tex]Where r is the growth rate.
Thus, to find r, we have:
1 + r = 1.02
r = 1.02 - 1
r = 0.02
The growth rate is 0.02
To convert the rate to percent multiply by 100:
Growth percent = 0.02 x 100 = 2%
Therefore, the value of the house increases by 2% each year.
ANSWER:
• (a). 637000 dollars
,• (b). Growth
,• (c). 2%
ANSWER:
• (a). 637000 dollars
,
• (b). Growth
,
• (c). 2%
Match each function with its graph 1. f (x) =x³+3x²2. f (x) = -x (x-1) (x+2)3. f (x) = -x³+3x²4. f (x) = x (x+1) (x-2)
to understand this graphs you must find the roots on each of the functions.
start by funtion 1.
[tex]\begin{gathered} x^3+3x^2=0 \\ x\cdot(x^2+3x)=0 \\ x=0 \\ (x^2+3x)=0 \\ x(x+3)=0 \\ x=0 \\ x+3=0 \\ x=-3 \end{gathered}[/tex]for function 1 you will need to find a graph that only intercept the x-axis on 0 an -3. In this case it will be the graph A.
Do the same for each function
[tex]\begin{gathered} -x\cdot(x-1)\cdot(x+2) \\ x=0 \\ x-1=0 \\ x=1 \\ x+2=0 \\ x=-2 \end{gathered}[/tex]function 2, the interceptions are 0,1 and -2. Graph C will be the correct one for this function
function 3
[tex]\begin{gathered} -x^3+3x^2=0 \\ x\cdot(-x^2+3x)=0 \\ x=0 \\ (-x^2+3x)=0 \\ x(-x+3)=0 \\ x=0 \\ -x+3=0 \\ x=3 \end{gathered}[/tex]for fuction 3, roots will be 0 and 3, the associated graph will be D
and lastly the roots for function 4.
[tex]\begin{gathered} -x\cdot(x+1)\cdot(x-2) \\ x=0 \\ x+1=0 \\ x=-1 \\ x-2=0 \\ x=2 \end{gathered}[/tex]The associated graph is B.
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
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]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
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
Use the table below to answer the questions. a. Is this a proportional relationship? b. What is the constant of proportionality. X Y-2 6 1 -32 -6
hello
the relationship on the question is a direct proportion. i.e, when x in
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.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.
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:
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]What is the sale price of a $63 sweater if the discount rate is 15%?Round to the nearest cent. Do not put a $ in your answer.
Answer:
Concept:
The formula to calculate the selling price of the sweat will be
[tex]\text{Selling price=original price - discount}[/tex]Step 1:
Calculate the discount price
The discount rate given is
[tex]=15\%[/tex]The discounted price will be
[tex]\begin{gathered} =\frac{15}{100}\times\text{ \$63} \\ =\frac{945}{100} \\ =\text{ \$9.45} \end{gathered}[/tex]Step 2:
Calculate the selling price, we will have
[tex]\begin{gathered} \text{Selling price=original price - discount} \\ \text{Selling price}=63-9.45 \\ \text{Selling price}=53.55 \end{gathered}[/tex]Hence,
The sale price of the sweater will be = $ 53.55
Top side length is 23.4ft. You can use the Pythagorean Theorem or the Cosine ratio or the Sine ration to solve for the remaining side. What is the remaining side (hypotenuse)? Round the answer to one decimal place.
The Hypotenuse = 38.1 feet
Explanations:From the diagram shown:
The adjacent side, A = 30 ft
Let
Let the side facing <38° be represented by B
Let the hypotenuse side be C
The right angle is facing the hypotenuse.
Sum of angles in a triangle = 180°
To calculate the hypotenuse side C, use the sine rule formula below:
[tex]\begin{gathered} \frac{\sin c}{C}=\text{ }\frac{\sin a}{A} \\ \frac{\sin 90}{C}=\text{ }\frac{\sin 52}{30} \\ \frac{1}{C}=\text{ }\frac{0.788}{30} \\ 0.788C\text{ = 30} \\ C\text{ = }\frac{30}{0.788} \\ C=38.1^{} \end{gathered}[/tex]The Hypotenuse = 38.1 feet
Which equation can be used to find 40 percent of 25? 199 25 40 40-1 100x4 400 4044 16 40x4 160 25x4 100 40:4 100=4 10 25
To find percentage is find a quantity smaller than a given number. In this case number is 25, and is required to find 40% of 25.
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
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.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 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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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
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%.
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]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
Function f(x) = |x| is transformed to create function g(x) = |x - 7| + 2.What transformations are performed to function f to get function g?Select each correct answer.Function f is translated 7 units to the left.Function f is translated 7 units down.Function f is translated 2 units up.Function f is translated 7 units to the right.Function f is translated 7 units upFunction f is translated 2 units to the right.Function f is translated 2 units to the left.Function f is translated 2 units down.
We will have the following:
*Function f is translated 7 units rigth.
*Function f is translated 2 units up.