This is an unbiased sampling because there is not a systematically opinion that favors some outcomes over others. So the answer is B
ASSUME THAT THE WAITING TIMES FOR CUSTOMERS AT A POPULAR RESTAURANT BEFORE BEING SEATED ARE NORMALLY DISTRIBUTED WITH A MEAN OF 16 MINUTES AND STANDARD DEVIAITON OF 4 MINUTES.1. IN A RANDOM SAMPLE OF 1000 CUSTOMERS, HOW MANY WAIT 18 MINUTES OR MORE BEFORE BEING SEATED.2. IN A RANDOM SAMPLE OF 500 CUSTOMERS, HOW MANY WAIT LESS THAN 9 MINUTES BEFORE BEING SEATED
Solution.
Calculate the z-score
The formula is shown below
[tex]\begin{gathered} \sigma=4 \\ \mu=16 \\ \end{gathered}[/tex][tex]\begin{gathered} Z_{18}=\frac{18-16}{4}=0.5 \\ P\left(x>0.5\right)=0.30854 \\ n=0.30854\text{ x 1000} \\ n=308.54 \\ n=309(nearest\text{ whole number\rparen} \end{gathered}[/tex]Thus, 309 customers (to nearest whole number) wait 18 minutes or more before being seated
(ii)
[tex]\begin{gathered} Z_9=\frac{9-16}{4} \\ Z_9=-1.75 \\ P\left(x<-1.75\right)=0.040059 \\ n=0.040059\text{ x 500} \\ n=20.03 \\ n=20(nearest\text{ whole number\rparen} \end{gathered}[/tex]Thus, 20 customers (to nearest whole number) wait less than 9 minutes before being seated
Frankie is saving for a new game system that costs $499. His savings account currently holds $150. He plans to deposit $10 a week into the savings account until he has enough to buy the game system.
In how many weeks will Frankie be able to purchase the game system?
Answer:
35 weeks
Step-by-step explanation:
If Frankie already has $150 in his bank account, we can subtract it from the cost of the game.
$499 - $150 = $349
Now we can begin to solve for the number of weeks it will take for Frankie to purchase the game system.
If he needs $349, and he adds $10 every week,
10 weeks would give him $100
5 weeks would give him $50
$100 + $100 + $100 + $50 = $350
10 + 10 + 10 + 5 = 35
It would take Frankie 35 weeks to be able to buy the game system.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.Match each quadratic equation with its solution set.2x^2–8x+5=02x^2-10x-3=02x^2-8x-3=02x^2-9x-1=02x^2-9x+6=0
Solution
For this case we have the following equations:
[tex]2x^2-8x+5=0[/tex]The solutions are:
[tex]x=\frac{4\pm\sqrt[]{6}}{2}[/tex][tex]2x^2-10x-3=0[/tex]Solutions are:
[tex]x=\frac{5\pm\sqrt[]{31}}{2}[/tex][tex]2x^2-8x-3=0[/tex]Solutions are:
[tex]x=\frac{4\pm\sqrt[]{22}}{2}[/tex][tex]2x^2-9x-1=0[/tex]Solutions are:
[tex]x=\frac{9\pm\sqrt[]{89}}{4}[/tex][tex]2x^2-9x+6=0[/tex]Solutions are:
[tex]x=\frac{9\pm\sqrt[]{33}}{4}[/tex]Then final solutions are:
[tex]\frac{9\pm\sqrt[]{33}}{4}\Rightarrow2x^2-9x+6=0[/tex][tex]\frac{4\pm\sqrt[]{6}}{2}\Rightarrow2x^2-8x+5=0[/tex][tex]\frac{9\pm\sqrt[]{89}}{4}\Rightarrow2x^2-9x-1=0[/tex][tex]\frac{4\pm\sqrt[]{22}}{2}\Rightarrow2x^2-8x-3=0[/tex]A card is chosen from a standard deck, thena month of the year is chosen. Find theprobability of getting a face card and June. use the counting principle to find each probability
1) Gathering the data
1 face card out of one deck: 12 /52
1 month of the year: 1/12
2) In Probability, The counting principle says we can multiply two
events
The question, says the probability of getting a face card
We have 12 face cards in a deck so, using the counting principle:
P( face card and June) = 12/52 *1/12 =1/52
Representing fractions as repeating decimalsConvert the fraction to a decimal:5/6
ok
5/6 = 0.833333 or
The line means that number three is repeated till infinty
A county is planning to expand its train service. To better understand the current service, the county planner looked at which train stations are along or not along various train lines
Solution
(a)
5 stations are along the orange line
(b)
8 stations
Suppose Albers Elementary School has 26 teachers and Bothel Elementary School has 14 teachers. If thetotal number of teachers at Albers and Bothel combined is 27, how many teachers teach at both schools
Given:
Albers Elementary School has 26 teachers
Bothel Elementary School has 14 teachers
And the total number of teachers at Albers and Bothel combined is 27
Note, there a number of teachers working at both schools
We will let the following:
The number of teachers at Albers = x
The number of teachers at Bothel = y
The number of teachers at both = z
So, we can write the following system of equations:
x + z = 26 ⇒ (1)
y + z = 14 ⇒ (2)
x + y + z = 27 ⇒ (3)
Solving the system of equations to find x, y, and z
From (1) ⇒ x = 26 - z
From (2) ⇒ y = 14 - z
Substitute with (x) and (y) into equation (3)
[tex]\begin{gathered} (26-z)+(14-z)+z=27 \\ -z-z+z=27-14-26 \\ -z=-13 \\ z=13 \end{gathered}[/tex]So, the answer will be
The number of teachers teach at both schools = 13
One equation from a system of two linear equations is graphed on the coordinate grid. 51 46 5 4 3 2 1 6 x -1 -21 The second equation in the system of linear equations has a slope of 3 and passes through the point (2,-5). What is the solution to the system of equations? th
First, we need to find the equation for the two equations.
The equation graphed has a y-intercept of 3 and a slope of
[tex]m=\frac{-6}{3}=-3[/tex]therefore, the equation of the line is
[tex]\boxed{y=-\frac{1}{2}x+3.}[/tex]For the second equation, we know what it has a slope of 3; therefore it can be written as
[tex]y=3x+b[/tex]Now, we also know that this equation passes through the point y = -5, x = 2; therefore,
[tex]-5=3(2)+b[/tex]which gives
[tex]-5=6+b[/tex][tex]b=-11[/tex]Hence, the equation of the line is
[tex]\boxed{y=3x-11}[/tex]Now we have the equations
[tex]\begin{gathered} y=-\frac{1}{2}x+3 \\ y=3x-11 \end{gathered}[/tex]equating them gives
[tex]-\frac{1}{2}x+3=3x-11[/tex]adding 11 to both sides gives
[tex]-\frac{1}{2}x+14=3x[/tex]adding 1/2 x to both sides gives
[tex]14=\frac{7}{2}x[/tex]Finally, dividing both sides by 7/2 gives
[tex]\boxed{x=4\text{.}}[/tex]The corresponding value of y is found by substituting the above value into one of the equations
[tex]y=-\frac{1}{2}(4)+3[/tex][tex]y=1[/tex]Hence, the solution to the system is
[tex](4,1)_{}[/tex]I tried everything I could to answer this question but I couldn’t get it
We need to use some properties of the kyte:
· The opposite obtuse angles are equal. In the figure, this means ∠WZY = ∠WXY
· The large diagonal bisects the angles ∠ZWX and ∠XYZ
56 ask us to find m∠XYZ. We can note that the angles ∠ZXY and ∠XZY are congruent. And we know that the interior angles of the triangle XYZ add to 180º.
m∠VXY = m∠VZY = 58º
Then:
[tex]\begin{gathered} m∠ZXY+m∠XZY+m∠XYZ=180º \\ 58º+58º+m∠XYZ=180º \\ m∠XYZ=64º \end{gathered}[/tex]The answer to 56. is 64º
57 ask us to find m∠ZWV, we can use the second property listed above. The large diagonal bisects the angle ∠ZWX. Since we know ∠ZWX = 50º, then:
[tex]\begin{gathered} m∠ZWV=\frac{1}{2}\cdot m∠ZWX \\ . \\ m∠ZWV=\frac{1}{2}\cdot50º=25º \end{gathered}[/tex]The answer to 57 is 25º
58 ask us to find m∠VZW. We know that the sum of all internal angles of a kite (or any quadrilateral), is 360º.
We know:
m∠ZWX = 50º
m∠WZY = m∠WXY
m∠XYZ = 64º
Then:
[tex]\begin{gathered} m∠ZWX+m∠WZY+m∠WXY+m∠XYZ=360º \\ 50º+2m∠WZY+64º=360º \\ 2m∠WZY=360º-114º \\ m∠WZY=\frac{1}{2}\cdot246º \\ m∠WZY=123º \end{gathered}[/tex]And:
[tex]m∠WZY=m∠VZW+m∠VZY[/tex]Now replace the known values of m∠WZY = 123º and m∠VZY = 58º:
[tex]\begin{gathered} 123º=m∠VZW+58º \\ m∠VZW=123º-58º=65º \end{gathered}[/tex]The answer to 58 is 65º
59 ask us to find m∠WZY, we sis it in 58 to find m∠VZW.
The answer to 59 is 123º
Match the steps to put them in the correct order of something. You will not use all of the options.
SOLUTION
[tex]\begin{gathered} Given \\ 2h+9=21 \end{gathered}[/tex][tex]\begin{gathered} Step\text{ 1:} \\ Subtract\text{ 9 from both sides} \\ 2h+9-9=21-9 \\ 2h=12 \end{gathered}[/tex][tex]\begin{gathered} Step\text{ }2: \\ Divide\text{ both sides by 2} \\ \frac{2h}{2}=\frac{12}{2} \\ h=6 \end{gathered}[/tex][tex]\begin{gathered} Final\text{ answer:} \\ h=6 \end{gathered}[/tex]six fifths, eight ninths, 0.5, forty percent?
Answer:
I'm assuming this is a greatest to least, but in case it was not, I put least to greatest, too.
Step-by-step explanation:
Greatest to least:
6/5, 8/9, 0.5, 40%
Least to greatest:
40%, 0.5, 8/9, 6/5
Hope this helps!
22. QRST is a rectangle. If RU = 3x - 6 and UT = x + 9, find x and the length of QS.RUx= 5QS =TS
We are given two lengths of the rectangle:
RU=3x-6
UT=x+9
These two lengths are shown in the following diagram:
Since this is a rectangle, the lengths of RU and UT must be equal:
[tex]RU=UT[/tex]Thus
[tex]3x-6=x+9[/tex]We need to solve this equation for x.
We start by subtracting x to both sides of the equation:
[tex]\begin{gathered} 3x-x-6=9 \\ 2x-6=9 \end{gathered}[/tex]Now, add 6 to both sides:
[tex]\begin{gathered} 2x=9+6 \\ 2x=15 \end{gathered}[/tex]Finally, divide both sides by 2:
[tex]\begin{gathered} \frac{2x}{2}=\frac{15}{2} \\ x=7.5 \end{gathered}[/tex]We have the value of x: x=7.5
Now we have to find the length of QS. Since QS and RT are diagonals of the same rectangle, they have to be equal:
[tex]RT=QS[/tex]This means that we can find RT by adding RU and UT, and the result will be equal to QS:
[tex]QS=RU+TU[/tex]substituting the given expressions for RU and TU:
[tex]QS=3x-6+x+9[/tex]And now, substitute x=7.5 and solve for QS:
[tex]QS=3(7.5)-6+7.5+9[/tex][tex]\begin{gathered} QS=22.5-6+7.5+9 \\ QS=33 \end{gathered}[/tex]Answer:
x=7.5 and QS=33
I WILL GIVE BRAINLIEST
Juan bought three and three-fourths pounds of pineapple and three and three-eighths pounds of strawberries for a fruit salad. After eating one and fifteen-sixteenths pounds of the fruit salad, how much was left?
five and three-sixteenths pounds
five and three-eighths pounds
five and nine-sixteenths pounds
seven and twenty-one sixteenths pounds
Salad was left (A) Five and three-sixteenths pounds.
Fraction is the comparison between numbers or mathematical quantities.
Given that, Juan bought pineapple of = (3 + 3/4) pounds = 15/4 pounds
Juan bought strawberries of = (3 + 3/8) pounds = 27/8 pounds
So now the amount total fruit salad = 15/4 + 27/8 = (30+27)/8 = 57/8 pounds
Juan eats = (1+15/16) = 31/16 pounds
Now salad left = 57/8 - 31/16 = (114-31)/16 = 83/16 = (5+3/16) pounds
Hence the correct option is (A).
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what is 7.950•100? and how to do it?
This problem uses the symbol •, which is another symbol to denote multiplication. Also, we are multiplying a decimal to 100. When multiplying such number, we move the decimal place to the right by two since we are multiplying the decimal by 100.
For this problem, we have
[tex]7.950\cdot100[/tex]We are multiplying 7.950 by 100. This means that we move the decimal point two times to the right. Hence, 7.950 multiplied by 100 will yield
[tex]7.950\cdot100=795.0[/tex]Answer: 795.0
use the graph of y=-x/3 -1 determine which of the ordered pairs of the solution to the equation select all correct answers
Given:
[tex]y=-\frac{x}{3}-1[/tex]We have the graph below:
To determine the correct ordered pairs, let's solve for each of them.
a) (x, y) ==> (0, -1)
From the equation, substitute 0 for x and -1 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -1=-\frac{0}{3}-1 \\ \\ -1=0-1 \\ \\ -1=-1 \\ \\ \text{Therefore (0, -1) is a solution} \end{gathered}[/tex]b) (x, y) ==> (3, -2)
Substitute 3 for x and -2 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -2=-\frac{3}{3}-1 \\ \\ -2=-1-1 \\ \\ -2=-2 \\ \\ (3,\text{ -2) is a solution} \end{gathered}[/tex]c) (x, y) ==> (3, -5)
Substitute 3 for x and -5 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -5=-\frac{3}{3}-1 \\ \\ -5=-1-1 \\ \\ -5=-2 \\ \\ (3,\text{ -5) is not a solution} \end{gathered}[/tex]d) (0, -5)
Substitute 0 for x and -5 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -5=-\frac{0}{3}-1 \\ \\ -5=0-1 \\ \\ -5=-1 \\ \\ (0,\text{ -5) is not a solution} \end{gathered}[/tex]e) (x, y) ==> (-3, 0)
Substitute -3 for x and 0 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ 0=-\frac{-3}{3}-1 \\ \\ 0=1-1 \\ \\ 0=0 \\ \\ \text{The ordered pair (-3, 0) is a solution} \end{gathered}[/tex]ANSWER:
(0, -1)
(3, -2)
(-3, 0)
After watching some fish 40 feet below the surface of the water, a scuba diver went up 15 feet to explore a coral reef Use a number line to help you create an equation that shows the location of the coral reef in relation to the water's surface. mo Interpret the sum in the context of the problem A. The equation is -40 (-16) 28 The coral reef is 5 feet belo the water's surface
First he was 40 feet below surface, so he was at -40 feet
The he went up 15, so now he is -40 + 15 = -25, that means 25 feet below surface
So the right equation is D and for the line:
You TryWrite an equation for each of the following,then solve for the variable.20 is the same as the sum of 4 and g.
Given statement:
20 is the same as the sum of 4 and g
Let us break down the statement into parts and then write the equation
the sum of 4 and g:
[tex]\text{= 4 + g}[/tex]This sum is equal to 20:
[tex]4\text{ + g = 20}[/tex]Hence, the equation is:
[tex]4\text{ + g = 20}[/tex]Solving for the variable:
[tex]\begin{gathered} \text{Collect like terms} \\ g\text{ = 20 -4} \\ g\text{ = 16} \end{gathered}[/tex]Answer Summary
[tex]\begin{gathered} \text{equation: 4 + g = 20} \\ g\text{ = 16} \end{gathered}[/tex]The equation m = 5b represents the time in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b).
Determine the constant of proportionality.
10
5
1
one fifth
The constant of proportionality for the equation m = 5b is 5.
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 4 is an equation.
We have,
The equation m = 5b represents the time in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b).
Now,
The equation:
m = 5b can be written as m ∝ b
m ∝ b
m = 5b
Where 5 is the constant of proportionality.
Thus,
The constant of proportionality for the equation m = 5b is 5.
Option B is the correct answer.
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Answer: 5
Equation of a Proportional Relationship
m = 5b
the 5 represents the constant of proportionality
the m represents the dependent variable, or y-coordinate in an ordered pair
the b represents the independent variable, or x-coordinate in an ordered pair
write a multiplication equation for the area of the square with side lengths of 1 meter
Area of a square is expressed using the formula;
A = L^2
L is the side length of the square
From the question, we are given;
L = 1 meter
The multiplication equation for the area of the square will be;
A = 1 meter * 1 meter
A = 1m^2
Find x and y without a calculator! No Desmos! Make sure that this one is on your work that you are uploading.
Given:
Given the system of equations:
[tex]\begin{gathered} y=4x \\ 2x+3y=-28 \end{gathered}[/tex]Required: Values of x and y
Explanation:
Substitute 4x for y into the equation 2x + 3y = -28.
[tex]\begin{gathered} 2x+3\cdot4x=-28 \\ 14x=-28 \\ x=-2 \end{gathered}[/tex]Plug the obtained value of y into y = 4x.
[tex]\begin{gathered} y=4(-2) \\ =-8 \end{gathered}[/tex]Solution is (x, y) = (-2, -8).
Final Answer: Solution is (-2, -8).
Solve by graphing. If the radioactive half-life of a substance is 20 days, and there are 5 grams of it initally. When will the amount left be 2 grams? Round to the nearest tenth of a day. Be sure to label your answer.
The exercise describes an exponential decay, you can express this using the general form:
[tex]y=ab^x[/tex]Where
a is the initial amount
b is the decay factor
x is the time intervals
y is the amount after x time intervals
The half-life of a substance indicates the time it takes for the amount to decrease by half.
If the initial amount is a=5 grams, the half-life indicates that after x=20 days, the amount will be
y= 5/2 = 2.5 grams.
You can replace these values on the formula above to obtain an expression where the decay factor will be the only unknown:
[tex]\begin{gathered} y=ab^x \\ 2.5=5b^{20} \end{gathered}[/tex]To solve for b, first, divide both sides of the equation by 5:
[tex]\begin{gathered} \frac{2.5}{5}=\frac{5b^{20}}{5} \\ 0.5=b^{20} \end{gathered}[/tex]Then apply the square root with index 20 to both sides of the equal sign no reach the value of b:
[tex]\begin{gathered} \sqrt[20]{0.5}=\sqrt[20]{b^{20}} \\ b=0.97 \end{gathered}[/tex]Now that you know the value of the decay factor, you can determine how much time it will take for the substance to decrease to 2grams.
The expression for the exponential decay in this case is:
[tex]y=5\cdot0.97^x[/tex]For y=2grams:
[tex]2=5\cdot0.97^x[/tex]Now, you have to solve the expression for x:
-Divide both sides by 5:
[tex]\begin{gathered} \frac{2}{5}=\frac{5\cdot0.97^x}{5} \\ 0.4=0.97^x \end{gathered}[/tex]-Apply the logarithm to both sides of the equal sign:
[tex]\begin{gathered} \log (0.4)=\log (0.97^x) \\ \log (0.4)=x\log (0.97) \end{gathered}[/tex]-Divide both sides by the logarithm of 0.97 to determine the value of x:
[tex]\begin{gathered} \frac{\log(0.4)}{\log(0.97)}=\frac{x\log (0.97)}{\log (0.97)} \\ x=30.08\approx30.1 \end{gathered}[/tex]It will take approximately 30.10 days to have 2 grams of substance left.
у 10 8 P 4 2 0 2 6 8 10 Which ordered pair represents the location of point P on the coordinate plane? a (5,6) b (6,5) (6,7) d (7,6)
The ordered pair that represents the location of point P is (6,5)
Explanation:
In order to determine the position of point P, we will need to trace its position to the x axis and also trace its position to the y axis.
Tracing its position to the x axis, we find it corresponds to 6 units
Tracing its position to the y axis, we find it corresponds to 5 units.
This because each line represents 1 units. After the 4 units, the next line is 5 units.
Using the coordinates (x,y):
The ordered pair that represents the location of point P is (6,5)
i need the answer i can’t figure it out and my teacher won’t help
Solution:
From the given question, we have
To solve for the ramp angle from the ground, we use trigonometric ratios.
Thus, we have
[tex]\sin\theta=\frac{opposite}{hypotenuse}[/tex]This gives
[tex]\begin{gathered} \sin\theta=\frac{11.5}{175} \\ \Rightarrow\sin\theta=0.06571 \\ take\text{ the sine inverse of both sides} \\ \sin^{-1}(\sin\theta)=\sin^{-1}(0.06571) \\ \theta=3.77^{\circ\:} \\ \therefore \\ \theta\approx3.8\degree(nearest\text{ tenth\rparen} \end{gathered}[/tex]Hence, to the nearest tenth, the ramp angle is
[tex]3.8\degree[/tex]Fergus gets paid $5.25 an hour with time-and-a-half for overtime(over 40 hours). How much did he earn one week when he worked 48hours?a. $63.04b. $190.90c. $210d. $273.04
The correct answer is d. $273
Fergus worked 48 hours in the week. This means that for 40 hours he was paid $5.25 per hour; And for 8 hours he was paid 150% of the normal (150% is one and a half time)
Then for the regular paid hours:
$5.25 per hour by 40 hours => 5.25*40= $210
Now for the 8 remaining hours we need to calculate how much Fergus is paid by hour.
Then 50% of $5.25 is the same as 5.25 divided by 2: 5.25/2 = $2.625
Then the 150% is equal to 100% + 50%. The 100% is $5.25 and the 50% is $2.625
5.25 + 2.625 = $7.875
This is what Fergus gets paid for every overtime hour. This week he worked 8 overtime hours.
Then, $7.875 * 8 = $63
Now the total earning of the week is equal to $210 + $63 = $273 and that's option D.
Part AWhat is the mass in grams of 17.96 mL of acetone?Express your answer to four significant figures and include the appropriate units.mass = Value and UnitsPart BWhat is the volume in milliliters of 7.40 g of acetone?Express your answer to three significant figures and include the appropriate units.V = Value and Units
Part A:
Ans: Mass=14.11 g.
Given:
The volume of acetone, V=17.96 mL.
We know, the density of acetone, D=0.7857 g/mL.
The mass in grams of acetone is,
[tex]\begin{gathered} M=VD \\ =17.96\text{ mL}\times0.7857\text{ g/mL} \\ =14.11\text{ g} \end{gathered}[/tex]Therefore, mass of acetone in grasm rounded upto four significant figures is 14.11 g.
Mass=14.11 g.
Part B:
Ans: V=9.42 mL
Given
The mass of acetone, M=7.4 g.
We know, the density of acetone, D=0.7857 g/mL.
The volume in mL of acetone is,
[tex]\begin{gathered} V=\frac{M}{D} \\ =\frac{7.40\text{ g}}{0.7857\text{ g/mL}} \\ =9.42\text{ mL} \end{gathered}[/tex]Therefore, voulme of acetone in mL rounded upto three significant figures is 9.42 mL.
Volume, V=9.42 mL
10. Do the ratios -2:1,-4: 2 and - 6:3 represent a proportional relationship? O No, the ratios do not represent a proportional relationship because, when graphed, the line passes through the origin but is not straight. No, the ratios do not represent a proportional relationship because, when graphed, the line is not straight, and it does pass through the origin. Yes, the ratios represent a proportional relationship because, when graphed, the line passes through the origin and is a straight line. No, the ratios do not represent a proportional relationship because, when graphed, the line is straight, but it does not pass through the origin.
Solution
For this case we have the following proportions:
-2:1 = -2
-4:2 = -2
-6:3 = -2
If we plot the relationship we got something like this
And then we can conclude that the answer is:
Yes the ratios represent a proportional relationship because when graphed the line passes through the origin and is a straight line
6ft 3ft 8ft 16ft area of irregular figures
Solution.
From the figure given we will have to find the
(Area of A) + (The Area of B)
STEP 1 :
For figure B
b = 3
h = 6
[tex]\begin{gathered} \text{Area of A = }\frac{1}{2}\times b\times h \\ \text{ = }\frac{1}{2}\times3\times6 \\ \text{ = }\frac{18}{2}\text{ = 9} \end{gathered}[/tex]Step 2:
For Figure A
L = 16
b = 8ft
Area of B = L x B
= 16 x 8
= 128
STEP 3
Area of A + Area of B
128 + 9 = 137 square feet
Three vertices of parallelogram JKLM are J(1, 4), K(5, 3), and L(6,-3). Find the coordinates ofvertex M.The coordinates are MOD.
Given data:
The coordinate of first vertex is J(1, 4).
The coordinate of second vertex is K(5, 3).
The coordinate of third vertex is L(6,-3).
Assume the coordinate of M is (x, y).
The diagonal of the parallelogram intersect at the mid point, the mid point of the diagonal JL is,
[tex]\begin{gathered} a=\frac{1+6}{2} \\ =\frac{7}{2} \\ b=\frac{4-3}{2} \\ =\frac{1}{2} \end{gathered}[/tex]This is also the mid point of KM diagonal.
[tex]\begin{gathered} \frac{7}{2}=\frac{x+5}{2} \\ x=2 \\ \frac{1}{2}=\frac{y+3}{2} \\ y=-2 \end{gathered}[/tex]Thus, the coordinate of M is (2, -2).
can you explain step by step how to solve this?
Remember that
the area of a parallelogram is equal to
A=b*h
in this problem
b=35 cm
h=44 cm
substitute
A=35*44
A=1,540 cm2Find out the perimeter
P=2*(35)+2*(47)
P=164 cmProblem N 2
we know that
the length of the wall is 170 inches
step 1
Find out the dimensions of the diagonal of the square
Applying the Pythagorean Theorem
d^2=12^2+12^2
d^2=2*12^2
[tex]d=12\sqrt[\square]{2}\text{ in}[/tex]Divide the length of the wall by the length of the diagonal
[tex]\frac{170}{12\sqrt[\square]{2}}=10.02[/tex]therefore
I need 11 (1/2 tiles)Note I rounded up because with 10 (1/2 tiles) the length is less than 170 inchesNeed help Which expression is equivalent to the given expression?(ab^2)^3/b^OA.a3/bOB.a3boc.a4/bOD.a3
Given the expression:
[tex]\frac{(ab^2)^3}{b^5}[/tex]We will use the following rules to modify the given expression:
[tex]\begin{gathered} (a^{m)n}=a^{mn} \\ \frac{a^m}{a^n}=a^{m-n} \end{gathered}[/tex]So, the answer will be as follows:
[tex]\frac{(ab^2)^3}{b^5}=\frac{a^3b^6}{b^5}=a^3b^{6-5}=a^3b[/tex]So, the answer will be option ⇒ B. a³b
