I don't understand word problems and if I get the same lady don't leave me I left you because I was finished and I gave you a good rating so please don't leave
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The mechanic charges $24 per hour. Also, labour was charged for 1 3/4 hours. Therefore, the total labour cost is,
[tex]L=24\times1\frac{3}{4}=24\times\frac{7}{4}=42[/tex]Now, the total bill is,
[tex]T=42+9+12+4.79=67.79[/tex]Therefore, the total bill is $67.79.
Related Questions
Determine an equation for the pictured graph. Write your answer in factored form.
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Ok, we need to find a suitable equation for that graph and write it in factored formed. With this information what we can imply is that said equation is a polynomial one:
[tex]f_{(x)}=a\cdot(x-r_1)^A(x-r_2)^B\ldots[/tex]Where the r terms are the roots or zeros of the function which are the x-values for which y=0. In a graph these points correspond to the x-intercepts. In this case we have two x-intercepts which means that we have two different roots:
[tex]\begin{gathered} r_1=-1 \\ r_2=2 \end{gathered}[/tex]Now as stated in the factored formula I wrote before the terms (x-r) have exponents A and B. To find those exponents you'll need to use the graph. If in a x-intercept the graph of the function changes its sign then the exponent of that root is an odd number. If the sign stays the same then the exponent of that root is an even number.
The function pass from negative to positive values in x=2 so for that root the exponent is an odd number (we are gonna use 1):
[tex](x-2)^1=(x-2)[/tex]In the other x-intercept, x=-1, the function is negative at both sides of that point so its exponent has to be an even number (we are gonna use 2):
[tex](x-(-1))^2=(x+1)^2[/tex]So now we have that:
[tex]f_{(x)}=a\cdot(x+1)^2(x-2)[/tex]We just need to find the value of a. If you look at the graph you can see that it has a y-intercept in y=-2. This means that:
[tex]f_{(0)}=-2[/tex]So:
[tex]f_{(0)}=a\cdot(0+1)^2(0-2)^{}=a\cdot1\cdot(-2)^{}=-2a=-2[/tex]Then:
[tex]a=\frac{-2}{-2}=1[/tex]So the final factored form of the equation is:
[tex]y=(x+1)^2(x-2)[/tex]What is the time in years according to the giver graph
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If the population is 2 thousand people, this corresponds to the value of 2 on the y-axis. If we look where is the graph defined when y = 2, we can see that the graph passes through the point (2,2). Therefore, the time in years for 2 thousand people is 2 years
What place value is the 6 in out of 3.4689
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3.4689
Number six is 2 places after the decimal point.
That is the hundredths place.
So 6 is in the hundredths place.
A = P + PRT/100 make p the subject from the formula
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Answer
[tex]\begin{gathered} \text{Given relation: A }=P+\frac{PRT}{100} \\ \text{Multiply both sides by100} \\ 100A=100P+100(\frac{PRT}{100}) \\ 100A=100P+\text{PRT} \\ 100P+\text{PRT}=100A \\ P(100+RT)=100A \\ \text{Divide both sides by (100+RT)} \\ P=\frac{100A}{100+RT} \end{gathered}[/tex]Estimation Suppose the original quantity is $30 and the new quantity is $39. Estimate the percentchange. Is this an example of a percent increase or a percent decrease?Which of these is the best estimate for the percent change?OA. 100%OB. 90%OC. 30%OD. 60%
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STEP - BY - STEP EXPLANATION
What to find?
Percentage change.
Given:
original quantity = $30
New quantity = $39
Step 1
Recall the formula for percentage change.
[tex]\text{ \% change=}\frac{new\text{ quantity-original quantity}}{original\text{ quantity}}\times100\text{ \%}[/tex]Step 2
Substitute the values.
[tex]\text{ \% change=}\frac{39-30}{30}\times100\text{ \%}[/tex][tex]=\frac{9}{30}\times100^\text{ \%}[/tex][tex]=30\text{ \%}[/tex]Hence, we have a 30% percentage increase.
ANSWER
C. 30%
Use the sum-to-product identities to rewrite the following expression in terms containing only firstpowers of tangent.sin7x + sin5xcos 7x + cos5x
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We have to rewrite the expression using sum-to-product identities.
The expression is:
[tex]\frac{\sin7x+\sin5x}{\cos7x+\cos5x}[/tex]We will then use this identity:
[tex]\sin a+\sin b=2\sin (\frac{a+b}{2})\cos (\frac{a-b}{2})[/tex]and this identity:
[tex]\cos a+\cos b=2\cos (\frac{a+b}{2})\cos (\frac{a-b}{2})[/tex]We can apply it to our expression as:
[tex]\begin{gathered} \frac{\sin7x+\sin5x}{\cos7x+\cos5x}=\frac{2\cdot\sin (\frac{7x+5x}{2})\cos (\frac{7x-5x}{2})}{2\cdot\cos (\frac{7x+5x}{2})\cos (\frac{7x-5x}{2})} \\ \frac{\sin7x+\sin5x}{\cos7x+\cos5x}=\frac{\sin (\frac{12x}{2})}{\cos (\frac{12x}{2})} \\ \frac{\sin7x+\sin5x}{\cos7x+\cos5x}=\frac{\sin (6x)}{\cos (6x)} \\ \frac{\sin7x+\sin5x}{\cos7x+\cos5x}=\tan (6x) \end{gathered}[/tex]Answer: the expression is equal to tan(6x)
what angle is formed between the ground and the baseball bat?
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Since the triangle in the diagram is a right triangle, we can use the trigonometric function cosine to solve this problem.
The cosine of an angle x is defined as follows:
[tex]\cos x=\frac{\text{adjacent side}}{\text{hypotenuse}}[/tex]First, we have to find the adjacent side to the angle x:
And then, find the hypotenuse of the triangle, which will be the side opposite to the 90° angle:
[tex]\begin{gathered} \text{adjacent side=15in} \\ \text{hypotenuse}=32in \end{gathered}[/tex]Thus, we substitute this in the definition of the cosine of x:
[tex]\cos x=\frac{15in}{32in}[/tex]And to solve for x, we use the inverse cosine:
[tex]x=\cos ^{-1}(\frac{15}{32})[/tex]The result is:
[tex]x=62.05[/tex]Answer: 62.05°
Please help to solve 4x - 8 = 14
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Adding 8 to the given equation we get:
[tex]\begin{gathered} 4x-8+8=14+8, \\ 4x=22. \end{gathered}[/tex]Dividing the above equation by 4 we get:
[tex]\begin{gathered} \frac{4x}{4}=\frac{22}{4}, \\ x=\frac{11}{2}\text{.} \end{gathered}[/tex]Answer:
[tex]x=\frac{11}{2}\text{.}[/tex]Which expression is NOT equivalent to the value 64? A) 2 to the 6th power B) 2 to the 4th x 4 C) 2to the 3rd x 4 to the 2nd D) 4 to the 3rd power?
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WE need to find which expression is not equivalent to the value 64.
A) 2 to the 6th power = 2^6 = 2 * 2 * 2 * 2 * 2 * 2 = 64
B) 2 to the 4th x 4 = 2 * 2 * 2 * 2 * 4 = 16 * 4 = 64
C) 2to the 3rd x 4 to the 2nd = 2 * 2 * 2 * 4 * 4 = 8 * 16 = 128
D) 4 to the 3rd power = 4 * 4 * 4 = 64
So, the options that is not equivalent to 64 is option c) 2to the 3rd x 4 to the 2nd
3) Place the following in order from least to greatest.2/3, 1/5, 3/8, 4/5, 5/6A. 1/5, 318, 4/5, 2/3, 5/6B. 5/6, 2/3, 3/8, 1/5, 4/5C 1/5, 3/8, 2/3, 4/5, 5/6D. Not here
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hello
to solve this question, we need to rearrange the numbers from the lowest to the highest
1/5, 3/8, 2/3, 4/5, 5/6
this arrangement corresponds to option C
car rental agency advertised renting car for $27.95 per day and $0.28 per mile. If Brad rents this car for 3 days, how many whole miles can he drive on a $150 Budget? miles (Round down to the nearest whole mile.)
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Let x represent the number of miles
For 3 days rent, he will pay = 3 x $26.95 = $80.85
The number miles = $0.31 × x
Thus
[tex]80.85+0.31x=100[/tex][tex]\begin{gathered} 0.31x=100-80,85 \\ 0.31x=19.15 \\ x=\frac{19.15}{0.31} \\ x=61.77 \end{gathered}[/tex]Hence, the whole miles can he drive on a $100 Budget is 61 miles
What number increased by 57% results in the value of 50.24?
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ANSWER
32
EXPLANATION
Let the number we are looking for be x.
It is increased by 57% to result in 50.24.
An increase by 57% means that 57% of the number (x) is added to x.
That is:
[tex]\begin{gathered} (57\text{ \% of x) + x = 50.24} \\ \Rightarrow(\frac{57}{100}\cdot x)\text{ + x = 50.24} \\ 0.57x\text{ + x = 50.24} \\ 1.57x\text{ = 50.24} \\ \text{Divide through by 1.57:} \\ x\text{ = }\frac{50.24}{1.57} \\ x\text{ = }32 \end{gathered}[/tex]The number is 32.
What would the next 2 terms be: 1.5, 0.75, 0, -0.75
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The formula for an arithmetic sequence is given as;
[tex]\text{nth}=a+(n-1)d[/tex]The 5th term would be;
[tex]\begin{gathered} 5th=1.5+(5-1)(-0.75) \\ 5th=1.5+(4)(-0.75) \\ 5th=1.5-3 \\ 5th=-1.5 \end{gathered}[/tex]The 6th term would be;
[tex]\begin{gathered} 6th=1.5+(6-1)(-0.75) \\ 6th=1.5+(5)(-0.75) \\ 6th=1.5-3.75 \\ 6th=-2.25 \end{gathered}[/tex]Decide if the two lines y =1/5x + 3 and y = 5x – 2 are parallel, perpendicular, or neither. Explain your answer.
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The given equation of lines are:
[tex]y=\frac{1}{5}x+3;\; y=5x-2[/tex]Notice that the equations of the lines are given in the slope-intercept form y=mx+c, where m is the slope and c is the y-intercept.
Comparing with the given equation, it follows that the slopes of the given lines are:
[tex]m_1=\frac{1}{5};\; m_2=5[/tex]Recall that the slopes of perpendicular lines are negative reciprocals of each other.
Recall also that the slopes of parallel lines are equal.
Notice that the slopes of the given lines, 1/5 and 5 are just reciprocals of each other.
Hence, they are neither perpendicular lines nor parallel lines because their slopes are reciprocals of each other.
Answer:
Th
solve the given expression for b.ab=x
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Given the expression:
[tex]ab=x[/tex]To solve the given expression for b, divide both sides of the equation by "a", the variable beside "b".
[tex]\begin{gathered} \frac{ab}{a}=\frac{x}{a} \\ b=\frac{x}{a} \end{gathered}[/tex]Thus, the result is:
[tex]b=\frac{x}{a}[/tex]I need this problem for my prep guide explained and answered
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The standard form of the equation of a hyperbola with
center (h, k) and transverse axis parallel to the y-axis is
[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]The coordinates of the foci are
[tex](h,k\pm c)[/tex]Where c is
[tex]c^2=a^2+b^2[/tex]Since the given equation is
[tex]\frac{(y-1)^2}{9}-\frac{(x-3)^2}{16}=1[/tex]Compare it with the form above, then
[tex]\begin{gathered} h=3 \\ k=1 \\ a^2=9 \\ b^2=16 \end{gathered}[/tex]Let us find c by using the rule above
[tex]\begin{gathered} c^2=9+16 \\ c^2=25 \\ c=\pm\sqrt[]{25} \\ c=\pm5 \end{gathered}[/tex]Substitute the values of h, k, c in the coordinates of the foci above
[tex]\begin{gathered} (3,1+5),(3,1-5) \\ (3,6),(3,-4) \end{gathered}[/tex]The coordinates of the foci are (3,6) and (3,-4)
hi how are you, will u pls help me. is my answer right?
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The correct answer is 26 points.
Explanation:
[tex]\text{Mean}=\frac{\text{ sum of observations}}{\text{ number of observations}}=\frac{21+25+36+16+32}{5}=\frac{130}{5}=26[/tex]Graph the hyperbola and label the intercepts. y²/36-x²/25=1
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We want to graph the hyperbola;
[tex]\frac{y^2}{36}-\frac{x^2}{25}=1[/tex]This is the hyperbola, as you can see, it has y-intercepts (0,6) and (0,-6)
1. Use the diagram below to answer the following questions. a) Name all segments parallel to XT.
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We observe the segment XT is a vertical line segment
Then, all the vertical segments are parallel to XT
Those segments are:
SW
VZ
UY
is this figure defined W,X,Y and Z a rhombus? justify your answer
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Step 1: Write out the formula for finding the distance d between two points (x1,y1) and (x2,y2)
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \end{gathered}[/tex]Step 2: Find the distance between the vertices of the figure
The distance d1 between vertices X(6,-5) and Y(11,-5) is 11-6 = 5 units.
The distance d2 between vertices Y(11,-5) and Z(11,-10) is -5 -- 10 = 5 units.
The distance d3 between vertices Z(11,-10) and W(6,-10) is 11 - 6 = 5 units.
The distance d4 between vertices W(6,-10) and X(6,-5) is -5 -- 10 = 5 units.
Hence all the sides of the figure are congruent
Step 3: Write out the formula for finding the gradient m of the line joining two points (x1,y1) and (x2,y2).
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step 4: Check if side XY is Parallel to side WZ
Let m1 be the gradient of XY. Then
[tex]m1=\frac{-5--5}{11-6}=\frac{0}{5}=0_{}[/tex]Let m2 be the gradient of WZ. Then
[tex]m2=\frac{-10--10}{11-6}=\frac{0}{5}=0_{}[/tex]Hence XY is parallel to WZ ( and they are parallel to the x-axis)
Step 5: Check if side XW is Parallel to side YZ
Let m1 be the gradient of XW. Then
[tex]m1=\frac{-10--5}{6-6}=\frac{-5}{0}=\text{undefined}[/tex]Let m2 be the gradient of YZ. Then
[tex]m2=\frac{-10--5}{11-11}=\frac{-5}{0}=\text{ undefined}[/tex]Hence XY is parallel to YZ ( and they are parallel to the y-axis)
Therefore,
WXYZ is a rhombus. Based on the coordinates opposite sides are parallel and all the sides are congruent
The second option
Use the formula s=rwt to find the value of the missing variable. S= pi/11 m, r=5 m, t= 8 sec
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Answer:
w = π/440
Explanation:
The formula is:
[tex]s=r\cdot w\cdot t[/tex]Then, replacing s = π/11, r = 5 and t by 8, we get:
[tex]\frac{\pi}{11}=5\cdot w\cdot8[/tex]So, to solve for w, we first need to multiply 5 by 8:
[tex]\frac{\pi}{11}=40\cdot w[/tex]Finally, divide both sides by 40:
[tex]\begin{gathered} \frac{\pi}{11}\cdot\frac{1}{40}=\frac{40\cdot w}{40} \\ \frac{\pi}{440}=w \end{gathered}[/tex]So, the missing variable is w = π/440
describe a situation where it would be beneficial to round decimals to the nearest Dollar explain why you would use rounding
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Problem
describe a situation where it would be beneficial to round decimals to the nearest Dollar explain why you would use rounding
Solution
For this case we can conclude that one possible answer is:
when we sold a product and we round the amount sold to the nearest dollar, that could be a benefecial situation for the person who sold the product on this case
Marco says mom has sent him to the store to buy apples and oranges she gives Marco instructions to buy 4 pounds of apples and 4 as many pounds of oranges as possible he also has to spend exactly $9.11 of 1 pound of apples cost $1.29 and 1 lb of oranges cost 79 cents how many pounds of oranges will Marcos be able to buy use the equation below to find your answer $1.29 (4) +0.79x=9.11
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To find how many pounds of oranges Marco can buy we need to solve the equation given:
[tex]\begin{gathered} 1.29(4)+0.79x=9.11 \\ 5.16+0.79x=9.11 \\ 0.79x=9.11-5.16 \\ \text{0}.79x=3.95 \\ x=\frac{3.95}{0.79} \\ x=5 \end{gathered}[/tex]Therefore Marco bought 5 pounds of oranges.
I don't understand Matrices at all, most of the questions are about adding and subtracting them
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To add matrixes, we have to add the terms in the same column and row. As an example, we have to do it as follows:
Row 1, Column 1:
[tex]-1+7=6[/tex]Row 1, Column 2:
[tex]6-11=-5[/tex]Row 2, Column 1:
[tex]-2+(-3)=-5[/tex]Row 2, Column 2:
[tex]2-1=1[/tex]Row 3, Column 1:
[tex]4+9=13[/tex]Row 3, Column 2:
[tex]9+(-3)=6[/tex]Answer:
Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary. Hint: Use the Pythagorean Theorem
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The distance between two points on the plane is given by the formula below
[tex]\begin{gathered} A=(x_1,y_1),B=(x_2,y_2) \\ \Rightarrow d(A,B)=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2} \end{gathered}[/tex]Therefore, in our case,
[tex]A=(-1,-3),B=(5,2)[/tex]Thus,
[tex]\begin{gathered} \Rightarrow d(A,B)=\sqrt[]{(-1-5)^2+(-3-2)^2}=\sqrt[]{6^2+5^2}=\sqrt[]{36+25}=\sqrt[]{61} \\ \Rightarrow d(A,B)=\sqrt[]{61} \end{gathered}[/tex]Therefore, the answer is sqrt(61)
In general,
[tex]-(-n)=n[/tex]Remember that
[tex]-n=(-1)\cdot n[/tex]Therefore,
[tex]\begin{gathered} a-(-n)=a+(-1)(-n)=a+(-1)(-1\cdot n)=a+(-1)^2\cdot n=a+1\cdot n=a+n \\ \Rightarrow a-(-n)=a+n \end{gathered}[/tex]Graph the system x+y=8 and 6x+3y=36
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Let's conside the first equation x+y=8
Since it is an equation with degree 1, it is a straight line. So 2 coordinates are enough to plot a graph.
To plot a grpah, let's take, x=0,1
If x=0
[tex]\begin{gathered} x+y=8 \\ 0+y=8 \\ y=8 \end{gathered}[/tex]So, the coordinate is (0,8)
If x=1
[tex]\begin{gathered} 1+y=8 \\ y=8-1 \\ y=7 \end{gathered}[/tex]So, the coordinated is (1,7)
Let's plot the graph.
Let's take the second equation
6x+3y=36
If x=0
[tex]\begin{gathered} 6x+3y=36 \\ 0+3(y)=36 \\ y=\frac{36}{3} \\ y=9 \end{gathered}[/tex]Hence the y coordinated is (0,9)
If x=1
[tex]\begin{gathered} 6x+3y=36 \\ 6(1)+3y=36 \\ 3y=36-6 \\ y=\frac{30}{10} \\ y=10 \end{gathered}[/tex]Hence the coordinate is (1,10)
Let's plot the graph
Hence both the graphs are plotted.
EACHFroh A BOARD THAT1) To pieces Of W00D SINCHES LONG HAVE BEEN CUT15 25 INCHES LONG, KAAT IS THELENGTH OF THE REMAINING PART OF THE BOARDX55 25- (2x 54)
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Answer:
Explanation:
25 - ( 2 x 5(1
Lucia bought a table and some chairs at a furniture store.The equation that models this situation is y= 40x + 55, where y is the amountof money she spent and x is the number of chairs she bought.What does the -intercept mean in this situation?
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the y -intercept means the price of the table(55)
Explanation
Step 1
a)let
x represent the numbers of chairs she bought
y represents the total money
so, we can set the equation to check the the y-intercept means
total money=cost of charis +cost of table
she pays only one time,and x times the cost of each chair
so
[tex]\begin{gathered} total\text{ cost = cost of chairs+cost of table} \\ y=40x+55 \end{gathered}[/tex]therefore
[tex]\begin{gathered} total\text{ cost of the charis=40x} \\ cost\text{ of the table = 55} \end{gathered}[/tex]the y intercept is the value for x=0, in this case, the cost of zero chairs and the table, so
the y -intercept means the price of the table ($55)
I hope this helps you
you and your four friends plan a surprise party interview contribute to the same amount of money for food write an algebraic expression for the total amount of money contributed for food evaluate your expression if each person contributed $5.25
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since there are in total 5 persons in the group (you and four friends) then the expression will be 5m, where m is the amount of money that will contribute each friend.
if each friend contributes 5.25 dollar then the total amount of money will be (5)x(5.25)=26.25 dollars
Kylie went to a store on three different days. She spent $6 on the first day, $14 on the second day, and x on the third day. If the mean amount that Kylie spent at the store was $16 per day, what is the value of x? O $10 O $16 O $22 O $28
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We know that
• She spent $6 on the first day, $14 on the second day, and ,x, on the third day.
,• The mean is $16 per day.
To solve this problem, we have to use the formula for the mean.
[tex]\bar{x}=\frac{\Sigma(x_i)}{N}[/tex]In words, we have to sum all the money spent and then we divide it by the total number of days. Also, the mean is 16.
[tex]16=\frac{6+14+x}{3}[/tex]Now, we solve for x. First, we multiply each side by 3.
[tex]\begin{gathered} 16\cdot3=\frac{6+14+x}{3}\cdot3 \\ 48=6+14+x \\ 48=20+x \end{gathered}[/tex]Then, we subtract 20 on each side.
[tex]\begin{gathered} 48-20=20-20+x \\ x=28 \end{gathered}[/tex]Therefore, the value of x is 28.