We know that Peyton wants to buy two shirts.
• First shirt cost $24.97.
,• Second shirt cost $13.75.
To do the mental math is ok to round $24.97 to $25, and them sum with $13.75.
However, to get the exact number, Peyton needs to subtract 3 pennies from the last amount $38.75, becuase she rounded before.
Therefore, to find the exact amount she needs to subtract 3 pennies.
A catering service offers 3 appetizers, 7 main courses, and 4 desserts. A customer is to select 2 appetizers, 3 main courses,and 3 desserts for a banquet. In how many ways can this be done?
General category: Mathematics
Sub-category: Probability
Topic: counting techniques
Introduction:
The combination formula C(n,r) shows us the number of ways of picking r unordered outcomes from n possibilities. For n ≥ r ≥ 0, C(n,r) is given by the following formula:
[tex]C(n,r)=\frac{n!}{r!(n\text{ -r})!}[/tex]Explanation:We can use combinations and fundamental counting principles to answer this question.
Let us denote by "a", the number of selection of appetizers. This number can be calculated as follows:
[tex]C(3,2)=\frac{3!}{2!(3\text{ -2})!}=3[/tex]Now, let us denote by "b", the number of selection of main courses. This number can be calculated as follows:
[tex]C(7,3)=\frac{7!}{3!(7\text{ -3})!}=35[/tex]Finally, let us denote by "c", the number of selection of desserts. This number can be calculated as follows:
[tex]C(4,3)=\frac{4!}{3!(4\text{ -3})!}=4[/tex]Now, applying the multiplication principle we get the desired number:
[tex]C(3,2)\cdot C(7,3)\cdot C(4,3)=3\cdot35\cdot4\text{ = 420}[/tex]We can conclude that the correct answer is:
find the slope of the line through each pair of points (3,0) , (-11, -15)
Given:
points (3,0) , (-11, -15)
Required:
Slope
Solution:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{slope}=\frac{-15-0}{-11-3_{}}=\frac{-15}{-14}=\frac{15}{14}[/tex]Answer:
[tex]\text{slope}=\frac{15}{14}[/tex]which question is the odd one out
III + MMM = 3003
L - XXIX = XXI
45 x 2 = 90.00000000000000000000000000000000000000000000000000001
Here the odd one out is 45×2=90.00000000000000000000000000000000000000000000000000001.
What is roman numerals?These are the symbols used in the system of numerical notation. We can convert a natural number to a Roman numeral by modifying the placement of seven symbols. The symbol I stands for 1, V stands for 5, X stands for 10, L stands for 50, C stands for 100, and M stands for 1000. In this system, the numbers are represented by combinations of letters from the Latin alphabet. In roman numerals, alphabets are used to represent fixed positive numbers. There are mainly used by Romans. These are the symbols that are representing the numbers that do not follow the base 10 in the number system.
The numbers III + MMM = 3003 and L - XXIX = XXI are roman numerals but the number 45 × 2 = 90.00000000000000000000000000000000000000000000000000001 is a rational number.
So, the number 45 × 2 is the odd one out.
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What is the range of the function f(x) = |x| + 5? R: {f(x) ∈ ℝ | f(x) < 5} R: {f(x) ∈ ℝ | f(x) ≥ 5} R: {f(x) ∈ ℝ | f(x) > 5} R: {f(x) ∈ ℝ | f(x) ≤ 5}
Given:
[tex]f(x)=|x|+5[/tex]Find-: Range of a function.
Sol:
For |x| is always positive because |x| function is:
[tex]|x|=\begin{cases}-x\text{ at x<0} \\ x\text{ at x>0}\end{cases}[/tex]So the range is:
[tex]\lbrace f(x)\in\Re|f(x)\ge5\rbrace[/tex]How is the function in the following picture graphed on a chart?
Okay, here we have this:
Given the surface area of a sphere is 324ππ sq km, what is the radius of the sphere?
The surface area S of sphere is given by
[tex]S=4\pi r^2[/tex]In our case
[tex]S=324\pi[/tex]Then, we have
[tex]324\pi=4\pi r^2[/tex]By moving 4Pi to the left hand side, we have
[tex]\frac{324\pi}{4\pi}=r^2[/tex]We can cancel Pi out in numerator and denominator, then ,we get
[tex]\begin{gathered} \frac{324}{4}=r^2 \\ 81=r^2 \\ \text{therefore} \\ r=\sqrt[]{81} \end{gathered}[/tex]and the answer is r= 9 kilometers, that is, the radius is 9 km
Charlotte spent $26 at the hair salon. She wants to leave a 12% tip. About how much money should she leave?
We will have the following:
[tex]t=26+(0.12)(26)\Rightarrow t=29.12[/tex]So, she shoulld leave $29.12 in total.
please help, thank you!by the way this is a two-step equation with decimals
Given data:
The given equaion is -0.9p+3.2= -1.7p.
The given equation can be written as,
[tex]\begin{gathered} -\text{0}.9p+3.2=-1.7p \\ 1.7p-0.9p=-3.2 \\ 0.8p=-3.2 \\ p=-4 \end{gathered}[/tex]Thus, the value of p is -4.
A. Make box-and-whisker plots to represent the temperature data for Oakville and Fairview.
B. What conclusions can you make about the temperatures in August in the two cities?
C. Luis finds that the average August temperature in Fairview in 2004 was 73°. How would including this additional data value change the box-and-whisker plot you made in part (a)? Would it change the conclusions you made in part (b)?
Answer:
In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median. The whiskers go from each quartile to the minimum or maximum.
lower air temperature and less precipitation
Graphs that Describe Climate Climographs show monthly average temperatures and precipitation totals on a single graph.
Step-by-step explanation:
please solve it and identify what was wrong in solving it the first time
we have that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
In the triangle ABE
A+B+E=180
substitute given values
60+55+E=180
E=65 degrees
so
mRemember that
m by vertical angles
so
mIn the triangle EDC
msubstitute given values
65+85+D=180
D=30 degreesmSolve: XC - XV. Show your answer as a Roman Numeral. Standard Number 1 5 10 50 100 500 1,000 Roman Numeral 1 V X Х L с D M A) V B) VI C) VIL
To make this substraction, it is better to first convert into standard numbers then make the substraction.
In Romans,
When finding the composition of f (g (x) )substitute f (x) for the x in g (x)multiply f (x) by g (x)substitute g (x) for the x in f (x)
Okay, here we have this:
Considering that the composition of function is formed by taking the outputs of one function and converting them into the inputs of another function. We obtain that, f(g(x)), consists of taking the result obtained by evaluating g (x) and replacing it by x in f (x). Then the correct answer is the third option.
Explain two ways to evaluate 32(13+18)
The given expression is
[tex]32(13+18)[/tex]To evaluate this expression, first, we use the distributive property
[tex]32(13+18)=32\cdot13+32\cdot18=416+576=992[/tex]Therefore, the answer is 992.Liam placed 24 patio pavers as shown below.
A rectangular array shows four patio pavers wide by six patio pavers long. The total length of the side of the rectangle that has four patio pavers is sixty-three and two-tenths inches.
What is the length of a single patio paver?
A.
18.2 in.
B.
15.8 in.
C.
10.53 in.
D.
2.63 in.
4 patio pavers = 63.2 inches
1 patio pavers = 15.8 inches.
The length of one patio paver is 15.8 inches.
What is a rectangle?
A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The total length of the side of the rectangle that has four patio pavers is sixty-three and two-tenths inches.
This means,
Length of the side with 4 patio pavers.
= 63(2/10) inches
= 632/10
= 63.2 inches
Now,
The length of one patio paver.
4 patio pavers = 63.2 inches
Divide both sides by 4.
1 patio pavers = 63.2/4
1 patio pavers = 15.8 inches.
Thus,
The length of one patio paver is 15.8 inches.
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What is the purchase price of a 50-day T-bill with a maturity value of S1,737 that eams an annual interest rate of 2 802% (Assume a 360 day year)The purchase price is (Round to two decimal places)
We need to use the next simple interest formula:
[tex]A=P(1+rt)[/tex]Where
P= Present value
r= annual interest rate in decimal form
T=time in years
A=amount after time
Hence, we have that
A= S1,737
r=2.802%/100=0.02802
t=50/360
P=?
Replacing on the given formula:
[tex]\begin{gathered} 1,737=P(1+0.02802\cdot\frac{50}{360}) \\ P=\frac{1,737}{1+0.02802\cdot\frac{50}{360}} \\ P=1730.27 \end{gathered}[/tex]Hence, the purchase price is $1730.27
Jungle Gym Print On the new jungle gym there are 4 ladders that lead to a landing. From the landing you can get to the big platform by climbing up either the rope or the fireman's pole How many different ways are there to get to the big platform?
Answer: 12 ways
Total number of ladder = 4
Yo can get to the platform either by climbing up the rope or fire mans hope
We have two options to get to the big platform
[tex]\begin{gathered} ^nP_r\text{ = }\frac{n!}{(n\text{ - r)!}} \\ ^4P_2\text{ = }\frac{4!}{(4\text{ - 2)!}} \\ =\text{ }\frac{4!}{2!} \\ \text{= }\frac{4\text{ x 3 x 2 x 1}}{2\text{ x 1}} \\ =\text{ 4 x 3} \\ \text{= 12 ways} \end{gathered}[/tex]Hello I don't know if you can help me with this
we have that
In this problem we have an arithmetic sequence
the general equation is equal to
an=a1+D(n-1)
where
a1 is the first term
D is the common difference
n is the number of terms
so
a1=7
D is the difference between consecutive terms
D=11-7=4
an=7+4(n-1)
change the variables
d=7+4(n-1)
d=7+4n-4
d=4n+3
For n=30
d=4(30)+3
d=123Lyle is a car salesman and is planning to work 5 days this week. His goal is to sell 3 cars per day. How many carsdoes Lyle hope to sell by the end of the week?cars
Firstly, there are 7 days in a week but from the information given, Lyle is planning to work for only 5 days in the week. Since his goal is to sell 3 cars per day, then the total number of cars that he would sell by the end of the week would be
5 * 3 = 15
Lyle would hope to sell 15 cars by the end of the week
Try AgainAt the city museum, child admission is $6.00 and adult admission is $9.20. On Monday, twice as many adult tickets as childtickets were sold, for a total sales of $780.80. How many child tickets were sold that day?
32 child tickets were sold on that day
Explanation:Given:
The cost per child = $6.00
let the number of child tickets = c
The cost per adult ticket = $9.20
let the number of adult tickets = a
To find:
the number of child tickets sold
On Monday:
Adult tickets = 2(children tickets)
a = 2c
Total sales on Monday = $780.80
Total sales = The cost per child (number of child tickets) + The cost per adult (number of adults tickets)
780.80 = 6(c) + 9.2(a)
substitute for a:
780.8 = 6c + 9.2(2c)
780.8 = 6c + 18.4c
780.8 = 24.4c
divide both sides by 24.4:
[tex]\begin{gathered} \frac{780.8}{24.4}\text{ = }\frac{24.4c}{24.4} \\ \\ c\text{ = 32} \end{gathered}[/tex]Hence, 32 child tickets were sold on that day
Given f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity, which of the following is true?
f(x) is decreasing for all x < 6
f(x) is increasing for all x > 6
f(x) is decreasing for all x < 3
f(x) is increasing for all x < 3
Answer: f(x) is increasing for all x < 3
D
Step-by-step explanation: I got the answer right on FLVS
Trust me I got 100%
1. Solve the given system of equations. X + y + z = 9 x - z = 5 X + y = 6the solution is: x = y = and z =
x=8
y=-2
Z=3
Explanation
Step 1
Let
[tex]\begin{gathered} x+y+z=9\text{ Equation (1)} \\ x-z=5\text{ Equation(2)} \\ x+y=6\text{ Equation(3)} \end{gathered}[/tex]Step 2
isolate x from equation (1) , (2) and (3)
[tex]\begin{gathered} x+y+z=9 \\ x=9-y-z\text{ Equation (4)} \end{gathered}[/tex][tex]\begin{gathered} x-z=5 \\ x=5+z\text{ equation (5)} \\ \\ x+y=6 \\ x=6-y\text{ equation(6)} \\ \end{gathered}[/tex]Step 3
combining equation (4) and (5)
[tex]\begin{gathered} 9-y-z=5+z \\ 9-y-2z=5 \\ -y-2z=5-9 \\ -y-2z=-4\text{ Equation(7)} \end{gathered}[/tex]Step 4
[tex]\begin{gathered} x=x \\ \text{equation (5) = equation (6)} \\ 5+z=6-y\text{ equation (8)} \end{gathered}[/tex]Step 5
using equation(7) and (8) find y and z
[tex]\begin{gathered} -y-2z=-4\text{ (7)} \\ 5+z=6-y(8) \\ \text{isolate y from equation (7)} \\ -y=-4+2z \\ y=4-2z \\ \text{replace in equation (8)} \\ 5+z=6-4+2z \\ 5+z=2+2z \\ z-2z=2-5 \\ -z=-3 \\ z=3 \end{gathered}[/tex]replace the value of z= 3 in equation (7) to find y
[tex]\begin{gathered} -y-2z=-4 \\ -y-2\cdot3=-4 \\ -y-6=-4 \\ -6+4=y \\ y=-2 \end{gathered}[/tex]finally, replace the value of y in equation (3) to find x
[tex]\begin{gathered} x+y=6 \\ x-2=6 \\ x=6+2 \\ x=8 \end{gathered}[/tex]I hope this helps you
Multiply (x + x2 + x + 1) (3x2 + 3x-3) (x3 + x2 + x + 1) (3x2 + 3x - 3) = 3x5 6x4 + 3x + 3x2 - 3 (Simplify your answer.)
Problem:
Multiply (x + x2 + x + 1) (3x2 + 3x-3) (x3 + x2 + x + 1) (3x2 + 3x - 3)
Solution:
[tex](x+x^2+x+1)(3x^2+3x-3)(x^3+x^2+x+1)(3x^2+3x-3)[/tex]this is equivalent to:
[tex](2x+x^2+1)(3x^2+3x-3)(x^3+x^2+x+1)(3x^2+3x-3)[/tex]this is equivalent to:
[tex](2x+x^2+1)(x^3+x^2+x+1)(3x^2+3x-3)^2[/tex]this is equivalent to:
[tex]9x^9+45x^8+\text{ 81}x^7+63x^6+18x^5-18x^4-45x^3-27x^2+9x+9[/tex]Then, the correct answer is:
[tex]9x^9+45x^8+\text{ 81}x^7+63x^6+18x^5-18x^4-45x^3-27x^2+9x+9[/tex]How much must be deposited today into the following account in order to have 40,000 in 6 years for a down payment on a house? Assume no additional deposits are made.An account with annual compounding and an APR of 7%how much should be deposited today? $(Do not round until the final answer. Then round to the nearest cent as needed.)
The formula to calculate the compound interest is:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{ Where } \\ A\text{ is the total amount at the end of t years.} \\ P\text{ is the initial amount deposited.} \\ r\text{ is the interest rate.} \\ t\text{ is the time.} \end{gathered}[/tex]From the word problem, we have:
[tex]\begin{gathered} A=40,000 \\ P=? \\ r=7\%=\frac{7}{100}=0.07 \\ n=1\Rightarrow\text{ It was compounded once in a year.} \\ t=6 \end{gathered}[/tex]Then, we can replace the above values in the compound interest formula and solve for P.
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 40,000=P(1+\frac{0.07}{1})^{(1)(6)} \\ 40,000=P(1+0.07)^6 \\ 40,000=P(1.07)^6 \\ \text{ Divide by }1.07^6\text{ from both sides} \\ \frac{40,000}{1.07^6}=\frac{P(1.07)^6}{1.07^6} \\ 26,653.69\approx P \\ \text{ The symbol is read 'approximately'.} \end{gathered}[/tex]AnswerYou should deposit today $26,653.69.
Carey creates the table to him determine 75% of 36
The table made is correct, so we conclude that 3/4 is equivalent of 75%. However, we must apply this percentage, or fraction, to the whole number we want to take the percentage of, that is, 36.
The number 27 is the actuall result of taking this percentage.
So, the correct expression would be:
[tex](\frac{3}{4})(36)[/tex]Thus, we need to change the 27 to 36, first alternative.
The initial value of your new car was $20,000. After one year, the value of the car is $18,000.What will the approximate value of the car be in 7 years?$8,000.00O $8,565.94$9,000.00$9,565.94
Answer:
The approximate value of the car after 7 years is;
[tex]\text{ \$9,565.94}[/tex]Explanation:
Given that the initial value of the car is;
[tex]P=\text{ \$20,000}[/tex]after 1 year its new value is;
[tex]\text{ \$18,000}[/tex]The rate of depreciation is;
[tex]r=\frac{18000}{20000}=0.9\text{ per year}[/tex]After 7 years the value of the car can be calculated using the formula;
[tex]F=P(r)^t[/tex]where t equals 7 years.
substituting the values;
[tex]\begin{gathered} F=20000(0.9)^7 \\ F=\text{ \$9,565.94} \end{gathered}[/tex]Therefore, the approximate value of the car after 7 years is;
[tex]\text{ \$9,565.94}[/tex]Solve this system of equations by graphing. First graph the equations, and then type the solution.3x+2y=6y=–5/2x+1
System of equations:
[tex]3x+2y=6[/tex][tex]y=-\frac{5}{2}x+1[/tex]The solution of the system of equations using the graph is the coordinate in which both functions collide:
In our function, this occurs in (-2, 6).
Answer: ( -2, 6 )
Find the equation of the line. Write the equation of the line in standard form Vertical line through (-1,-1)
Solution
We have the following point given (-1, -1)
The equation of a line is given by:
y= mx+b
For this case since we have a vertical line the equation would be:
x= -1
What is your favorite song and why? Does it mean something to you or do you just enjoy the sound of it/the lyrics? Enjoy the points :)
Answer:
Step-by-step explanation:
my favorite song is Sia's unstoppable song. I think it conveys a lot of energy and always while I listen to it I get points and am inspired to do better.
Hello I really need help with this question I’m not understanding it
The subset of the event " The two spins have a sum of 5 " is { (2,3), (3,2), (1,4) and (4,1) }
It is given that the sum of Jae's two spins was 5.
S is the sample space of spinning the spinner twice.
The collection of all the possible outcomes is termed the sample space
Subset: If every element in set A is also an element in set B, then set A is a subset of set B. Set A is therefore contained within set B.
Now, the subset of the event " The two spins have a sum of 5 "
In the spinner, there are 1, 2, 3, and 4.
So, the values that would give us a 5 are (2,3), (3,2), (1,4), and (4,1)
These are the terms that will be in the required subsets,
So, Required subset = { (2,3), (3,2), (1,4) and (4,1) }
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Which of the following is not a solution for x < 8?x = 9x = 4.3x = 7.95x = -3
The expression is given as x < 8.
ExplanationThe expression x less than 8 has values
4.3 , 7.95 , -3.
AnswerHence x=9 is not a solution for x < 8.