Given:
There are given that the Jotham needs 12 litters of 20% alcohol solution.
Explanation:
Let x be the volume of the 50% solution needed
Then,
The volume of the 10% solution to mix is:
[tex](12-x)[/tex]Then,
The equation to find x is:
[tex]0.50x+0.10\times(12-x)=0.20\times12[/tex]That means,
It say that the volume of the pure alcohol in ingredients is equal to the volume of pure alcohol.
Then,
From the above equation, calculate the value of x
So,
[tex]\begin{gathered} 0.50x+0.10\times(12-x)=0.20\times12 \\ 0.50x+0.10\cdot12-0.10x=0.20\cdot12 \\ 0.40x+0.10\cdot12=0.20\cdot12 \\ 0.40x=0.20\cdot12-0.10\cdot12 \\ x=\frac{12(0.1)}{0.40} \\ x=3 \end{gathered}[/tex]Final answer:
For the 50%, there are 3 litters solution and for the 10%,
[tex]\begin{gathered} 12-x=12-3 \\ =9 \end{gathered}[/tex]Hence, 3 liters of the 50% solution and 9 liters of the 10% solution.
The hotel room tax in Junction City is calculated using the function T(x) =0.06x + 4.5, where x = the cost in dollars of the room and T(x) = the tax in dollars. What is the tax on a room that costs $120?
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
Complete the statements about the following numbers: 2/7, 0.1, 0.9, 6/8. Use the + and - buttons to change how many ticks are displayed. The number represents the amount of even segments between 0 and 1. The point closest to the benchmark 1 is at The point closest to the benchmark O is at How would you order these fractions and decimals from least to greatest? Click or tap and drag to move the dot along the number line. 1 B 2 2 +
To solve the exercise it is easier to convert all the given points to decimals. So,
[tex]\frac{2}{7}=0.23[/tex][tex]\frac{6}{8}=0.75[/tex]Then,
*The point closest to the benchmark 1 is at 0.9.
*The point closest to the benchmark 0 is 0.1.
*Ordering these points from least to greatest you have:
[tex]\begin{gathered} 0.1 \\ 0.23=\frac{2}{7} \\ 0.75=\frac{6}{8} \\ 0.9 \end{gathered}[/tex]
"Radon: The Problem No One Wants to Face" is the title of an article appearing in Consumer Reports. Radon is a gas emitted from the ground that can collect in houses and buildings. At
certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (PCI/L). A radon level of 4 pci/L is considered "acceptable." Radon levels in a house vary
from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pcI/L).
1.9 2.8 5.7 4.8 1.9 8.6 3.9 7.3
(a) Find the mean, median, and mode. (Round your answers to two decimal places.)
mean
median
mode
(b) Find the sample standard deviation, coefficient of variation, and range. (Round your answers to two decimal places.)
S
CV
range
(c) Based on the data, would you recommend radon mitigation in this house? Explain.
O Yes, since the average value is over "acceptable" ranges, although the median value is not.
O Yes, since the median value is over "acceptable" ranges, although the mean value is not.
O No, since the average and median values are both under "acceptable" ranges.
O Yes, since the average and median values
are both over "acceptable"
ranges.
a) The mean of the data set is 4.61
The median of the data set is 4.35
The mode of the data set is 1.9
b) Sample standard deviation is 2.58
Coefficient of Variation is 55.96
Range is 6.7
Given,
The data set;
1.9, 2.8, 5.7, 4.8, 1.9, 8.6, 3.9, 7.3
a) We have to find the mean, median and mode
Mean = (1.9 + 2.8 + 5.7 + 4.8 + 1.9 + 8.6 + 3.9 + 7.3) / 8 = 36.9/8 = 4.61Median;Order the data first;
1.9, 1.9, 2.8, 3.9, 4.8, 5.7, 7.3, 8.6
Now,
The data is of even number, so;
Median = [(n/2) + (n/2 + 1)] / 2
Here,
n/2 = 8/2 = 4th term
n/2 + 1 = 5th term
Then,
Median = (3.9 + 4.8) / 2 = 8.7/2 = 4.35
Mode;The mode of the given data is 1.9
b) Sample Standard DeviationHere it is the formula to calculate it:
x = √(∑(xi - x)²/n-1))
sₓ = √(46.85/7) ≈ 2.58
Coefficient of VariationCV is the quotient between sample Standard deviation over Mean and it is used to make comparisons.
CV = sₓ/x × 100 = 2.58/4.61 x 100 = 55.96
RangeThe difference between the highest and the lowest value of this sample
8.6 - 1.9=6.7
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Find the measure of a positive angle and a negative angle that are coterminal with 100° sketch of three angles labeling clearly with directional arrows.
Coterminal angles are different angles that have the same terminal side.
A positive angle has one turn more around so it has a measure of 100°+360° = 460°.
A negative angle will have a measure that is represented in clockwise rotation and be equal to 100° - 360° = -260°.
We can sketch an angle of measure 100°, a positive coterminal angle and a negative coterminal angle as:
What is the product of the complex numbers below?(3 - 2i)(1 + 7i)A.-11 + 19iB.17 + 19iC.-11 - 23iD.17 - 23i
Solution:
Given:
[tex](3-2i)(1+7i)[/tex]To find the product, we multiply the terms in the second parentheses by each term in the first parentheses.
Thus, we have
[tex]\begin{gathered} 3(1+7i)-2i(1+7i) \\ open\text{ parentheses,} \\ 3+21i-2i-14i^2 \\ but\text{ i}^2=-1 \\ thus,\text{ we have} \\ 3+21i-2i-14(-1) \\ collect\text{ like terms,} \\ (3+14)+i(21-2) \\ \Rightarrow17+19i \end{gathered}[/tex]Hence, the product of the complex numbers is
[tex]17+19i[/tex]The correct option is B
Suppose that you decide to buy a car for $32,635, including taxes and license fees. You saved $9,000 for a down payment and can get a four year car loan at 6.31%. Find the monthly payment and the total interest for the loan. Equation below.
SOLUTION:
Step 1:
In this question, we are given the following:
Suppose that you decide to buy a car for $32,635, including taxes and license fees.
You saved $9,000 for a down payment and can get a four-year car loan at 6.31%.
Find the monthly payment and the total interest for the loan.
Step 2:
In this question, we are given:
Cost of the car = $ 32, 635
Down payment = $ 9000
Principal on the Car loan = $ ( 32,635 - 9,000 ) = $ 23, 635
Rate = 6. 31%
Using the PMI Formulae, we have that:
If the measures of the angles of a triangle arerepresented by 2x, 3x - 15, and 7x +15, the triangleis1) an isosceles triangle2) a right triangle3) an acute triangle4) an equiangular triangle
Answer
Option 1 is correct.
The triangle is an isosceles triangle.
Explanation
Noting that the sum of angles in a triangle is 180°.
We can solve for each of the angles in this triangle to obtain the type of triangle it is.
The angles of the triangle are 2x, (3x - 15) and (7x + 15)
2x + 3x - 15 + 7x + 15 = 180°
2x + 3x + 7x - 15 + 15 = 180°
12x = 180°
Divide both sides by 12
(12x/12) = (180°/12)
x = 15°
We can then solve for the measures of the three angles now
2x = 2 (15°) = 30°
3x - 15 = 3 (15°) - 15° = 45° - 15° = 30°
7x + 15 = 7 (15°) + 15° = 105° + 15° = 120°
So, the angles of the triangle are 30°, 30° and 120°
A tringle that has two of its angles equal to each other is called an isosceles triangle.
Hope this Helps!!!
find the constamt of proportionality (r) in the equation y=rx
To find the constant of proportionality of the equation y = rx, from the values of the given table, just calculate the quotient r = y/x, where x and y can be any pair of values of the table.
For x = 3 and y = 30:
r = 30/3
r = 10
Hence, the constant of proportionality is
r = 10
A and B are mutually exclusive events P(A) =0.60 and P(B)=0.30 what is P (A or B)
We know that for any number of mutually exclusive events, we have the formula:
[tex]P(A_1\cup A_2\cup A_3\cup\ldots)=P(A_1)+P(A_2)+P(A_3)+\cdots[/tex]In this case, we have that P(A)=0.60 and P(B)=0.30, then:
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)=0.60+0.30=0.90 \\ P(A\cup B)=0.90 \end{gathered}[/tex]Therefore, P(A or B) =0.90
The results of a survey show that the percent of adults in a certain town who want to add bike lanes to amajor roadway is in the interval (0.57, 0.65) (9 points)(a) What is the point estimate for the percent who want to add the bike lanes?(b) What is the poll's margin of error?(c) If the town's adult population is 31,526, what is the best estimate for the number of people whowould support the bike lanes?
If we know the confidence interval for the proportion, the point estimate will be at the center of this interval.
Then, we can calculate the point estimate p as the average between the boundaries of the interval:
[tex]p=\frac{0.57+0.65}{2}=\frac{1.22}{2}=0.61[/tex]The margin of error can be calculated, knowing the interval, as half the difference between the upper boundary and the lower boundary of the interval:
[tex]\text{MOE}=\frac{UB-LB}{2}=\frac{0.65-0.57}{2}=\frac{0.08}{2}=0.04[/tex]The margin of error is 0.04. This margin of error is also the absolute difference between any boundary of the interval and the point estimate.
If the town's population is 31,526, the best estimate for the number of people who
would support the bike lanes is to use the point estimate as the proportion:
[tex]X=p\cdot N=0.61\cdot31526\approx19231[/tex]Answer:
a) The point estimate is p=0.61
b) The margin of error is MOE = 0.04
c) The best estimate is X=19231
Hello, May I please get some assistance with this homework question? I posted an image below. Question A has already been answered, but do need help with the other questions. Q2 (part b)
ANSWER
• (g o f)(x) = ,16x² + 24x + 9
,• B., the domain of g o f is all real numbers
EXPLANATION
The composition is,
[tex](g\circ f)(x)=g(f(x))[/tex]This means that, to find the composition, we have to replace x with f(x) in the function g(x),
[tex]g(f(x))=(f(x))^2[/tex]Now, replace f(x) with its expression,
[tex]g(f(x))=(4x+3)^2[/tex]We can expand this binomial squared to write it in standard form. The composition is,
[tex](g\circ f)(x)=16x^2+24x+9[/tex]As we can see, this is a polynomial function. Therefore, the domain is all real numbers.
Find the starting value and the base for the exponential function f(x)=kb^x that passes through the two points:(0,3) and (2,12).The starting value k is: AnswerThe base b is: Answer
The exponential equation given is,
[tex]f(x)=kb^x[/tex]Given the points
[tex](0,3)\text{ and (2,12)}[/tex]Therefore, the values for k and b will be resolved graphically.
Let us now plot the graph using a graphical calculator
From the graph,
[tex]\begin{gathered} y_1=f(x) \\ a=k=3 \\ b=2 \end{gathered}[/tex]Final answers
[tex]\begin{gathered} k=3 \\ b=2 \end{gathered}[/tex]Can you please help me with this , choices (Add,divided,exponent, multiply, square roots, subtract and N/A)
a) in term
b)subtraction
c) N/A
d) 4
Explanation
a term is a single mathematical expression , it can be a number, a variable or a combination, the terms are separated by the symbols + or -
for example:
in
[tex]ax^2+bx+c[/tex]there are 3 expression , so
Step 1
check the expression
[tex]\frac{6(5-3)^3}{12}[/tex]it has only a term ( a fractions)
so
a)the number of terms is : 1
Step 2
b)first thing to do to term 1
PEMDAS means the order of operations for mathematical expressions involving more than one operation. It stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.so
we need to P ( break the parenthesis)
to do that,
do the SUBTRACTION
[tex]\begin{gathered} \frac{6(5-3)^3}{12} \\ \frac{6(5-3)^3}{12}=\frac{6(2)^3}{12} \\ \frac{6\cdot2^3}{12} \end{gathered}[/tex]
Step 3
c) as there is not term 2
N/A
Step 4
simplify the expression: folloing the PEMDAS order
[tex]\begin{gathered} \frac{6\cdot2^3}{12}\text{ } \\ \text{Exponents} \\ \frac{6\cdot2^3}{12}\text{ =}\frac{6\cdot8}{12}\text{ } \\ \text{ Mulitiplication} \\ \frac{6\cdot8}{12}\text{ =}\frac{48}{12} \\ \text{Division} \\ \frac{48}{12}=4 \\ 4 \end{gathered}[/tex]so
d) 4
i hope this helps you
3x - 4y = 10Add a Com6x + y = 38andMediac-9% +12y = -30Save9x - 3y = 48These systems are said to be equivalent. Both of the equations in the secondsystem came from the first system somehow,Two questions: How was the first equation is the second system formed fromthe first system? And how was the second equation in the second systemformed from the first system?
First solution
[tex]\begin{gathered} \text{The first equation in the second system (Equation 2.1),} \\ \text{was formed by multiplying (Equation 1.1) by -3} \end{gathered}[/tex][tex]\begin{gathered} \text{proof:} \\ -3\text{ (3x - 4y= 10) = -9x + 12y = -30} \end{gathered}[/tex]Second solution
The second equation in the second system (Equation 2.2) was formed by adding both equations in the first system.
That is;
(Equation 2.2) = (Equation 1.1) + (Equation 1.2)
[tex]\begin{gathered} \text{proof:} \\ 3x\text{ -4y = 10 } \\ +\text{ 6x + y = 38} \\ (3x+6x)\text{ + (-4y+y) = 10+38} \\ 9x\text{ -3y = 48} \end{gathered}[/tex]If a person travels 3.5 miles in 30 minutes, what is their speed i miles per hour
Given:-
If a person travels 3.5 miles in 30 minutes.
To find their speed in miles per hour.
So now we solve using the formula,
[tex]\text{Distance}=\text{speed}\times time[/tex]Substituting the known values. we get,
[tex]3.5=\text{Speed}\times\frac{1}{2}[/tex]Now we solve for speed. so we get,
[tex]\begin{gathered} \text{speed}=3.5\times2 \\ \text{speed}=7 \end{gathered}[/tex]So the required speed is 7miles/hr.
23 pointsThe length of a rectangular box is 1 inch longer than twice the width (x).The height is 5 inches.which is the volume (y) function
y = 5x ( 2x + 1)
Explanations:Let the width of the rectangular box be x
Let the length be L
Let the height be H
Let the volume be y
The length of the rectangular box is 1 inch longer than twice the width (x)
L = 2x + 1
The Height is 5 inch
H = 5
The volume of a rectangular box is:
Volume = Length x Width x Height
y = LHx
y = (2x + 1) (5) (x)
y = 5x (2x + 1)
*1. If the variable x represents the total number of COVID-19 deaths in the United States since March 1,I 2020, what do the following expressions represent?a. X - 100,000
The expression represents the number of COVID deaths since March 1 2020 minus 100,000 deaths.
3.2 Hangalakani works as a builder for 6,5 hours per day excluding 30 minutes tea break 1 hour lunch. He starts working at 07:30 am 2.1 Determine the time of the day Hangalakani leaves work for home 312.2 Hangalakani calculated that 245,37 bags of cement are required for the job His manager states that they need to purchase 246 bags Explain why the manager's statement is correct.
Hangalakani leaves his work for home at 3.30 PM .
Hangalakani starts his work at 7.30 am.
He works for 6.5 hours.
He then takes a lunch break for 1 hour .
He then takes tea break for about 30 minutes = 0.5 hour
Total time spent at work = 6.5 + 1 + 0. 5 = 8 hours.
So if he starts work at 7.30 then he will end at
7.30 am + 8 hours = 3.30 pm in the afternoon .
Now the manager says that they need 246 bags while Hangalakani calculated they need 245.37 bags of cement.
The manager is correct because bags of cement are not sold as a part or decimal . The number of bags that can be bought must be a whole number.
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Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.She needs to find the approximate surface area of the attic, including the walls, floor, andceiling. The attic is in the shape of a triangular prism. Linda draws the net and writesthe expression below to represent the surface area of the attic. Are Linda's net andexpression correct?15 ft45 ft25 ft40 ft25 ft25 ft25 ft- 15 ft45 ft40 ft15 ftExpression for Surface Area of Attic:45 (40 + 25 + 25) + ] (40 x 15)
We can formulate an expression for the surface area of the attic like this:
The area of a triangle is given by the following formula:
[tex]A=\frac{b\times h}{2}[/tex]Where b is the base and h is the height of the triangle.
The area of a rectangle is given by the following formula:
[tex]A=w\times l[/tex]Where w is the width and l is the length of the rectangle.
In this case, the attic has three rectangular faces, all of them have a width of 45 ft. two of them have a length of 25 ft and one has a width of 40 ft, then we can calculate the areas of these faces like this:
[tex]\begin{gathered} A1=45\times40 \\ A2=45\times25 \\ A3=45\times25 \end{gathered}[/tex]By summing up these areas, we get the area of the rectangular faces:
[tex]A=45\times40+45\times25+45\times25[/tex]From this expression, we can factor 45 to get:
[tex]A=45\times(40+25+25)[/tex]For the two triangular faces, their height equals 15 ft and the length of the bases equals 40 ft, then their areas are:
[tex]\begin{gathered} A1=\frac{15\times40}{2} \\ A2=\frac{15\times40}{2} \end{gathered}[/tex]By summing them up, we get the area of the triangular faces:
[tex]A=\frac{15\times40}{2}+\frac{15\times40}{2}=15\times40[/tex]By summing the area of the rectangular faces and the area of the triangular faces, we get the expression to calculate the total surface area of the attic, like this:
[tex]A=45(40+25+25)+40\times15=4650[/tex]Then, the net Linda draw is correct. The first term of Linda's expression 45(40+25+25) is correct. The second term of Linda's equation missing a factor of 2. The surface area of Linda's attic is 4650 square feet
Add Solve: n + 7 = 31
Answer:
n = 24
Explanation:
The initial expression is:
n + 7 = 31
So, to solve the equation, we need to subtract 7 from both sides:
n + 7 - 7 = 31 - 7
n = 24
Therefore, the solution is n = 24
Kathy wants to buy a condominium selling for $96,000. The taxes on the property are $1300 per year, and homeowners' insurance is $336 per year. Kathy's gross monthly income is $4000. She haher van. The bank is requiring 20% down and is charging a 9.5% interest rate with no points. Her bank will approve a loan that has a total monthly mortgage payment of principal, interest, property tthan or equal to 28% of her adjusted monthly income. Complete parts a) through h) below.a) Determine the required down payment.The required down payment is $b) Determine 28% of her adjusted monthly income.28% of her adjusted monthly income is $(Round to the nearest cent as needed.)c) Determine the monthly payments of principal and interest for a 25-year loan.The monthly payment of principal and interest for a 25-year loan is $(Round to the nearest cent as needed.)d) Determine her monthly payment, including homeowners' insurance and taxes.Her total monthly payment, including homeowners' insurance and taxes is $(Round to the nearest cent needed.) Does Kathy qualify for the loan?0 YesO No
a) the cost of the house is 96000 and the down paidment is the 20% so we can use a rule of 3 to solve it so:
[tex]\begin{gathered} 96000\to100 \\ x\to20 \end{gathered}[/tex]so the equation will be:
[tex]\begin{gathered} x=\frac{96000\cdot20}{100} \\ x=19200 \end{gathered}[/tex]b) her income is $4000 so the 28% will be:
[tex]\begin{gathered} 4000\to100 \\ x\to28 \end{gathered}[/tex]so the equation will be:
[tex]\begin{gathered} x=\frac{4000\cdot28}{100} \\ x=1120 \end{gathered}[/tex]c) the equation that models a loan is:
[tex]C=\frac{P\cdot(0.095\cdot(1+0.095)^n)}{(1+0.095)^{25}-1}[/tex]So we replace the princeiple and find monthly paidment.
[tex]\begin{gathered} C=\frac{76800\cdot(0.095\cdot(1.095)^{25}}{8.67} \\ C=\frac{76800\cdot0.92}{8.67} \\ C=\frac{70540.30}{8.67} \\ C=8136.14 \\ C\approx8136 \end{gathered}[/tex]d)The total monthly paidment will be:
[tex]\begin{gathered} T=8136+\frac{1300}{12}+\frac{336}{12} \\ T=8136+108.33+28 \\ T=8272.33 \\ T\approx8272 \end{gathered}[/tex]SOo the answer is NO she can't afort to buy this house
A train travels 165 km in 1.5 hours.
How far will the train travel in 2.2 hours if it maintains the same speed?
[tex]\huge\red{\mid{\underline{\overline{\textbf{EQUATION AND ANSWER}}}\mid}}[/tex]
_________________
Let's solve this equation using rates,
_________________DefinitionsUnit Rate - A unit rate means a rate for one of something.
Cross Multiplication - In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.
_________________
Now that we understand the definition we can further solve this equation
[tex]\large\red{\mid{\underline{\overline{\textbf{Values}}}\mid}}[/tex]
[tex]165[/tex] [tex]km[/tex] ⇒ [tex]1.5[/tex] [tex]hr[/tex]
[tex]x\\[/tex] [tex]km[/tex] ⇒ [tex]2.2[/tex] [tex]hr[/tex]
Now we will use cross-multiplication to solve this equation
[tex]\large\red{\mid{\underline{\overline{\textbf{Equtation}}}\mid}}[/tex]
[tex]165 \cdot 2.2\\x\cdot1.5[/tex]
Once solving this equation we get
[tex]1.5x=363[/tex] [tex]km[/tex]
Divide both sides by [tex]1.5[/tex]
[tex]x=242[/tex] [tex]km[/tex]
[tex]\large\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}[/tex]
A train travels 165 km in 1.5 hours. How far will the train travel in 2.2 hours if it maintains the same speed?The train would've traveled a total of 242 km in 2.2 hours.
Have a good day!Evaluate the function when x= -2,0, and 5 h(x)= -2x+9
Given:
a function is given as h(x) = -2x + 9
Find:
we have to evaluate the function at x = -2 , 0 and 5.
Explanation:
when x = -2
h(-2) = -2(-2) + 9 = 4 + 9 = 13
when x = 0
h(0) = -2(0) + 9 = 0 + 9 = 9
when x = 5
h(5) = -2(5) + 9 = - 10 + 9 = -1
Therefore, the values of given function h(x) are 13, 9 , -1 at x = -2, 0 , 5 respectively.
How do I find all possible rational zeros in a polynomial function?f(x) = x^4-2x^3-4x^2+2x+3
The factors are 1 , -1 twice and 3
Here, we want to find the rational roots of;
[tex]f(x)\text{= }x^4-2x^3-4x^2+2x+3[/tex]We can start here by trying out simple numbers if we cannot factorize the polynomial at a go
The given polynomial here can be factorized
We can express it as;
[tex]x^4-2x^3-4x^2+2x+3\text{ = (}x-1)(x+1)^2(x-3)[/tex]So what we have here is to simply equate individual linear factor to zero
Thus, we have the factors as;
1 , -1 twice and 3
i need help with question 36 (make sure to read the the information above the graph)
Given:
[tex]\begin{gathered} x+2y>6 \\ -2x+3y\leq6 \end{gathered}[/tex]Required:
To solve the given inequality by graphing.
Explanation:
The graph of the above inequality is,
Now, the solution is shaded in the graph.
Final Answer:
The solution by using the graph is,
WILL GIVE BRAINLYEST 100 POINTS !!!! A student is painting a brick for his teacher to use as a doorstop in the classroom. He is only painting the front of the brick. The vertices of the face are (−6, 2), (−6, −7), (6, 2), and (6, −7). What is the area, in square inches, of the painted face of the brick?
144 in2
108 in2
72 in2
42 in2
The area, in square inches, of the painted face of the brick is; 144 in²
How to find the area of a square with coordinates?The area of a square is given by;
A = L²
where;
L is the length of the side of the square
The sides of a square all have the same length, and as such we just need to find the length of one side.
The length of the side of the square here is the distance between two vertices, which can be calculated as
L = √[(x₂ - x₁)² + (y₂ - y₁)²]
However, to avoid long process, since it is a square, we can use subtraction of coordinates to get the side length which is gotten by using the first 3 coordinates;
Horizontal length = (6 + 6) = 12
Thus;
Area = L² = 12² = 144 in²
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A painter has three partially filled paint cans. One contains1 7/8 gallons, the second contains1 1/5 gallons, and the third contains1 3/4 gallons. Which answer is closest to the total amount of paint?
Explanation
Step 1
convet the mixed numbers into simple fractions
remember
[tex]a\frac{b}{c}=\frac{(a\cdot c)+b}{c}[/tex]then
[tex]\begin{gathered} 1\text{ }\frac{7}{8}=\frac{(1\cdot8+7)}{8}=\frac{15}{8} \\ 1\frac{1}{5}=\frac{(1\cdot5+1)}{5}=\frac{6}{5} \\ 1\frac{3}{4}=\frac{(1\cdot4+3)}{4}=\frac{7}{4} \end{gathered}[/tex]Step 2
now, make the sum to find the total amount
[tex]\begin{gathered} \text{total amount= }\frac{15}{8}+\frac{6}{5}+\frac{7}{4} \\ \text{total amount=}\frac{(15\cdot5\cdot4)+(6\cdot8\cdot4)+(7\cdot5\cdot8)}{160} \\ \text{total amount=}\frac{300+192+280}{160} \\ \text{total amount=}\frac{772}{160} \\ \text{total amount=}\frac{193}{40} \end{gathered}[/tex]I hope this helps you
The exit is exactly half way between the Ferris wheel and where you parked your car. Give the coordinates of your parking spot.
GIven data :
The coordinates of ferris wheel is, (2,7).
The coordinates of exit is (4,0).
they have given exactly half way so let us use the midpoint formula,
the mid point formula is,
[tex](\frac{x_1+x_2}{2},\frac{y_1,y_2}{2})\ldots(1)[/tex]take the coordinates as
[tex]\begin{gathered} (x_1,y_1)=(2,7) \\ (x_2,y_2)=(4,0) \end{gathered}[/tex]let us subsitute in eqiuation (1),
[tex]\begin{gathered} (\frac{2+4_{}}{2},\frac{7_{}+0_{}}{2}) \\ (\frac{6}{2},\frac{7}{2}) \\ (3,3.5) \end{gathered}[/tex]thus the coordinates of parking spot is (3,3.5).
Johann uses 42 +7 to represent the number of players who are on teams.Explain what 42÷7 means. Enter a number in each box.
Johann uses 42 +7 to represent the number of players who are on teams.
Explain what 42÷7 means.
_______________________________
42 +7 = the number of players who are on teams
42 = he number of players who are on teams minus 7
42 players
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Dividing by 7 (the number of player per group)
Each team has 7 players
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Convert percent to decimal 51.2% =
Let's begin by identifying key information given to us:
51.2% = 51.2/100
[tex]\begin{gathered} 51.2\text{ \%}=\frac{51.2}{100} \\ \Rightarrow0.512 \end{gathered}[/tex]