To factor an expression of the form:
[tex]x^2+bx+c[/tex]we find two numbers B and C that fulfills the following properties:
[tex]\begin{gathered} B+C=b \\ BC=c \end{gathered}[/tex]In this case we have b=-4 and c=-12. We can choose B=-6 and C=2. Then we write the expression as:
[tex]x^2-4x-12=x^2-6x+2x-12[/tex]and we factor the common factors in the first two and last terms:
[tex]\begin{gathered} x^2-4x-12=x^2-6x+2x-12 \\ =x(x-6)+2(x-6) \\ =(x+2)(x-6) \end{gathered}[/tex]Therefore:
[tex]x^2-4x-12=(x+2)(x-6)[/tex]P. The Shah family basement floor is shaped like a trapezoid. The basement has sides of and 24 feet and two sides of 21 feet. They are going to carpet the basement. The carpeting will cost $35 per square yard. A. What is the area, in square feet, of the basement foor? Show your work. B. What is the cost to carpet the basement floor? Explain how you found your answer
A.
In order to calculate the area of the trapezoid, we need to calculate its height:
Using the Pythagorean Theorem, we have:
[tex]\begin{gathered} 21^2=h^2+6^2 \\ 441=h^2+36 \\ h^2=441-36 \\ h^2=405 \\ h=20.12 \end{gathered}[/tex]Now, calculating the area:
[tex]\begin{gathered} A=\frac{(B+b)h}{2} \\ A=\frac{(36+24)20.12}{2} \\ A=60\cdot10.06 \\ A=603.6 \end{gathered}[/tex]B.
If each square yard is $35, first let's convert the area from ft² to yd² (1 yard = 3 feet, 1 yd² = 9 ft²):
[tex]A=603.6\text{ ft}^2=\frac{603.6}{9}\text{ yd}^2=67.07[/tex]So the total cost is:
[tex]\text{cost}=67.07\cdot35=2347.45[/tex]So the cost is approximately $2347.45.
In the diagram, RSTU ~ ABC D. Find the ratio of their perimeterA А.24BR18S36TDCThe ratio of their perimeters is
The ratio of the perimeters of two similar shapes is equal to the ratio of their corresponding sides, then, by taking the top sides of these figures we can express the following ratio
18 : 24
by dividing both numbers by 2, we get:
9 : 12
Dividing by 3:
3 : 4
Then the ratio of their perimeters equals 3 : 4
How many -digit even numbers are possible the digit cannot be zero?
Answer:
45,000
Step-by-step explanation:
Hey! Let's help you with your question here!
So, let's think about this logically. The only limit we have here is that the leftmost digit cannot be zero. This makes sense because there would be no five-digit number if the leftmost is zero. In order to find the possible amount of even numbers, we need to take the possible numbers of each digit and have them multiplied to each other to get the total. (I will explain this soon).
First Digit:
Since, the rules state that the leftmost digit cannot be zero, this would be the digit that the rule affects. From here, we can have a possibility of the numbers 1 through 9 here. So, for the first digit, we have the possibility of 9 numbers that can be here.
Second, Third, Fourth Digit:
Now you're probably wondering as to why I've grouped up these 3 digits and not the last or the first one. We'll get to the last one in the next explanation, but we exclude the first digit because the rule that affects the first digit, does not affect these digits nor the last digit. With these 3 digits, we don't have that rule of it cannot be zero, so now our possibilities for what the numbers can be is 0 through 9. If we include 0 as a number too, then we have a possibility of 10 numbers that can be within these digits.
Fifth (Last) Digit:
For this last digit, there is an implicit rule being stated for the last digit. The question asks how many five-digit even numbers are possible if the leftmost digit cannot be zero. This rule affects the last digit only as that allows the whole five-digit number to be even and zero is included in this. So, the even numbers are 0, 2, 4, 6, and 8. In this case, we only have 5 possible numbers to choose from for the very last digit.
Answer Explanation:
Before I begin answering, back in the very first paragraph, I said we need to take the possible numbers of each digit and multiply them altogether to get the total amount of possible values. Why do we do this? This is the idea of possibility combination. We multiply because we are taking in account all of the possible values whereas if we just add, we're only taking in account the maximum possible value of each possibility. So, let's calculate the answer now! For the first digit, we have a possibility of 9 numbers being there (1-9). For the Second, Third, and Fourth digit, we have a possibility of 10 numbers being there (0-9). And finally for the last digit, we have a possibility of only 5 numbers (0, 2, 4, 6, and 8). So, the total possible combination is:
[tex]9*10*10*10*5[/tex]
[tex]=45,000[/tex]
Therefore, we get 45,000 total possible five-digit even numbers where the leftmost digit cannot be zero.
50 gramos de pechuga de un pollo contiene 10.4 g de proteínas, 0.5 g de carbohidratos y 1.6 g de grasas. Los valores medios de energía alimentaria de esas sustancias son de 4.0 kcal/g para las proteínas y los carbohidratos, y de 9.0 kcal/g para las grasas. a) Al jugar baloncesto, una persona representativa consume energía a una potencia de 420 kcal/h. ¿Cuánto tiempo debe jugar para “quemar” esa pechuga?
Tenemos lo siguiente:
Lo primero es calcular las kilocalorías para las proteínas y para los carbohidratos y grasas, de la siguiente día:
[tex]\begin{gathered} \text{Protenas} \\ 10.4\text{ g}\cdot4\frac{\text{ kcal}}{g}=41.6\text{kcal} \\ \text{Carbohidratos} \\ 0.5\text{ g}\cdot4\frac{\text{ kcal}}{g}=2\text{kcal} \\ \text{Grasas} \\ 1.6\text{ g}\cdot9\frac{\text{ kcal}}{g}=14.4\text{kcal} \end{gathered}[/tex]Ahora sumamos todas las kilocalorías y nos queda lo siguiente:
[tex]41.6+2+14.4=58[/tex]Es decir que en total en los 50 gramos de pechuga hay en total de 58 kilocalorías, ahora debemos calcular el tiempo dividiendo el numero de kilocalorías por la cantidad de consumo de kilocalorías al jugar baloncesto
[tex]\frac{58\text{ kcal}}{420\text{ kcal/h}}=0.138\text{ h}[/tex]Es decir que debe jugar 0.138 horas o un total de:
[tex]0.138\text{ h}\cdot\frac{60\text{ min}}{1\text{ h}}=8.28\text{ min}[/tex]Es decir que debe jugar 8.28 minutos
May I please get help with this. For I have tried many times but still could not get the rotation correct
Let us write out the coordinates of the parent image given
Let us name the triangle ABC
[tex]\begin{gathered} A\rightarrow(1,5) \\ B\rightarrow(-3,2) \\ C\rightarrow(-5,4) \end{gathered}[/tex]Therefore, the rule for the rotation 90 degrees counterclockwise about the origin is,
[tex]A(x,y)\rightarrow A^{\prime}(-y,x)[/tex]Let us now obtain the coordinates of the transformed image
[tex]\begin{gathered} A(1,5)\rightarrow A^{\prime}(-5,1) \\ B(-3,2)\rightarrow B^{\prime}(-2,-3) \\ C(-5,4)\rightarrow C^{\prime}(-4,-5) \end{gathered}[/tex]Hence, the coordinates of the transformed image are
[tex]\begin{gathered} A^{\prime}(-5,1) \\ B^{\prime}(-2,-3) \\ C^{\prime}(-4,-5) \end{gathered}[/tex]Let us now plot the transformed image
In one hour, you can earn 350 points in your favorite video game. You already have 1050 points. a) Write an inequality where y is the total number for points and x is the number of hours. b) Your goal is 2450 points. What is the least number of hours to reach this goal?
SOLUTION
The initial points is 1050
The points earned per hour is 350
The total point y earned in x hours is:
[tex]y\ge350x+1050[/tex]Substitute y=2450 into the inequality
[tex]2450\ge350x+1050[/tex]Solve for x
[tex]\begin{gathered} 2450-1050\ge350x \\ 1400\ge350x \\ x\le4 \end{gathered}[/tex]Therefore the lease number of hours is 4.
If X persons are admitted in a hospital during the last five years and Y persons
are recovered out of them during this period then find the average number of
persons admitted in one year.
The average number of persons admitted in one year is X/5.
What is average number?
Average By adding a collection of numbers, dividing by their count, and then summing the results, the arithmetic mean is determined.
If X persons are admitted in last 5 years in a hospital.
Then we get the average value of admitted persons are X/5 per year.
If Y persons are recovered in last 5 years in a hospital.
Then we get the average value of recovered persons are Y/5 per year.
Therefore, the average number of persons admitted in one year is X/5.
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use a combination of inverse operations to solve the following equations.2(x-1) = -6
Given the following question:
[tex]2(x-1)=-6[/tex][tex]\begin{gathered} 2(x-1)=-6 \\ \text{ Divide by two} \\ -6\div2=-3 \\ \frac{2(x-1)}{2}=(x-1) \\ (x-1)=-3 \\ -1+1=0 \\ -3+1=-2 \\ x=-2 \end{gathered}[/tex]Your answer is x = -2.
a machine can stamp 36 bottle caps in 10 seconds copy and complete the table. At this rate, how many bottle caps can the machine stamp in 5 minutes? At this rate, how many minutes will it take to stamp 24,408 bottle caps?
SOLUTION
1. From the question the machine stamps 36 caps in 10 seconds
In 5 minutes it will cap
[tex]\begin{gathered} 5\text{ minutes = 5 }\times\text{ 60 seconds } \\ =300\text{ seconds } \\ 36\text{ }\rightarrow\text{caps in 10 seconds } \\ x\text{ }\rightarrow\text{caps in 300 seconds } \\ \text{cross multiplying we have } \\ 36\times300=10\times x \\ 10800=10x \\ x=\frac{10800}{10} \\ x=1080 \end{gathered}[/tex]So in 5 minutes, it would stamp 1080 bottle caps
2. Minutes it would take to stamp 24,408 bottle caps?
[tex]\begin{gathered} 1080\text{ }\rightarrow\text{caps in 5 minutes } \\ 24,408\rightarrow caps\text{ in }x\text{ minutes } \\ \text{cross multiplying we have } \\ 1080\times x=24,408\times5 \\ 1080x=122040 \\ x=\frac{122040}{1080} \\ x=113\text{ minutes } \end{gathered}[/tex]Hence it would take 113 minutes to stamp 24,408 bottle caps
WW Solve the system by substitution. -10x + 4y = -18 and x= y Submit Answer
Substitute second expression (x=y) in the first expression.
[tex]\begin{gathered} -10x+4y=-18 \\ -10\times y+4y=-18 \\ -6y=-18 \\ y=\frac{-18}{-6} \\ y=3 \end{gathered}[/tex]Substitute the above value of y in the expression number 2.
[tex]\begin{gathered} x=y \\ x=3 \end{gathered}[/tex]Thus, the value of x=3 and the value of y=3.
2-x+ 3-X-4
where a and b are integers.
Work out the value of a and the value of b.
can be written as a single fraction in the form
ax+b
x²-16
Answer:
2-×+3-×-4=0
Step-by-step explanation:
×=1\2
0.5,2`1
Suppose you want to have $ 749,791 for retirement in 13 years. Your account earns 9.5 % interest monthly. How much interest will you earn?$_________ (Round to the nearest DOLLAR)
ANSWER
$530,663
EXPLANATION
The amount the account will have in t years is given by,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where n = 12, t = 13 years, r = 0.095 and A = 749,791. We have to find P,
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]Replace with the values and solve,
[tex]P=\frac{749,791}{(1+\frac{0.095}{12})^{12\cdot13}}\approx219,128[/tex]The interest earned is the difference between the initial deposit P and the final amount A,
[tex]i=A-P=749,791-219,128=530,663[/tex]Hence, the interest earned would be $530,663.
Nguyen deposited $35 in a bank account earning 14% interest, compounded annually. How much interest will he earn in 72 months?
Given:
a.) Nguyen deposited $35 in a bank account.
b.) It earns 14% interest.
To be able to determine how much interest will he earn in 72 months, the following formula will be used for Compound Interest:
[tex]\text{ Interest Earned = P(1 + }\frac{\frac{r}{100}}{n})^{nt}\text{ - P}[/tex]Where,
P = Principal amount
r = Interest rate
n = No. of times the interest is compounded = annually = 1
t = Time in years = 72 months = 72/12 = 6 Years
We get,
[tex]\text{ Intereset Earned = (35)(1 + }\frac{\frac{14}{100}}{1})^{(1)(6)}\text{ - 35}[/tex][tex]\text{ = (35)(1 + }0.14)^6\text{ - 35}[/tex][tex]\text{ = (35)(}1.14)^6\text{ - 35}[/tex][tex]\text{ = (35)(}2.19497262394)^{}\text{ - 35}[/tex][tex]\text{ = 76.82404183776 - 35}[/tex][tex]\text{ = 41.82404183776 }\approx\text{ 41.82}[/tex][tex]\text{ Interest Earned = \$41.82}[/tex]Therefore, the interest he will be earning is $41.82
6 Equations of parallel and perpendicular lines VEB
The equation for line u can be written as y = -x + 1. Line v, which is perpendicular to line
u, includes the point (-3, 2). What is the equation of line v?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answer:
y = 4/9x +10/3
Step-by-step explanation:
You want the slope-intercept equation of the line through point (-3, 2) that is perpendicular to the line y = -9/4x +1.
Slope-intercept equationThe slope-intercept form of the equation for a line is ...
y = mx + b . . . . . . m is the slope, b is the y-intercept
In order to write the desired equation, we need to know the desired slope and the y-intercept that makes the line go through the given point.
SlopeThe slope of the perpendicular line is the opposite reciprocal of the slope of the given line. The given line equation is in slope-intercept form, so the coefficient of x is the slope of it: -9/4.
The slope of the perpendicular line is the opposite reciprocal of this:
m = -1/(-9/4) = 4/9
Y-interceptSolving the slope-intercept form equation for b, we find ...
b = y - mx
Using the values of x and y for the given point, and the slope we just found, we have ...
b = 2 -(4/9)(-3) = 2 +4/3 = 10/3
Desired equationThe slope-intercept equation for a line with slope 4/9 and y-intercept 2/3 is ...
y = 4/9x +10/3
__
Additional comment
It can also be useful to start from the point-slope equation:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
Your line is ...
y -2 = 4/9(x +3) . . . . . . use m=opposite reciprocal of -9/4; (h, k) = (-3, 2)
y = 4/9x +(4/9)(3) +2 = 4/9x +10/3 . . . . . . add 2 and simplify
What are the rotations that will carry this equilateral triangle onto itself?A. 90° counterclockwise rotation about its center PB. 270° counterclockwise rotation about its center PC. 120° counterclockwise rotation about its center PD. 240° clockwise rotation about its center PE. 225 clockwise rotation about its center PF. 200 counterclockwise rotation about its center Prights reserved
Given -
Equilateral Triangle
To Find -
The number of rotations that will carry this equilateral triangle onto itself =?
Step-by-Step Explanation -
We know that in an equilateral triangle each question is of 60°
So,
Since it is a three-sided symmetry So, a rotation of 120° will carry this equilateral triangle onto itself.
Final Answer:
C. 120° counterclockwise rotation about its center P
SOMEONE please help.
The class interval of the median is 1 ≤ x ≤ 2 and the mean of the distribution is 1.8
How to determine the class interval of the median class?From the question, we have
Number of students = 30
This represents the total frequency
So, we have
Total frequency = 30
The median position is then calculated as
Median = (Total frequency + 1)/2
Substitute the known values in the above equation
So, we have
Median = (30 + 1)/2
Evaluate
Median = 15.5th
The 15.5th element is located in the second class
i.e. the class with the interval 1 ≤ x ≤ 2
So, the class interval in this case is 1 ≤ x ≤ 2
The mean of the distributionTo do this, we start by calculating the average of the class interval
This is represented as
0 ≤ x ≤ 1 ⇒ 0.5
1 ≤ x ≤ 2 ⇒ 1.5
2 ≤ x ≤ 3 ⇒ 2.5
3 ≤ x ≤ 4 ⇒ 3.5
So, we have
x f
0.5 6
1.5 13
2.5 7
3.5 4
The mean is calculated as
Mean = ∑fx/∑f
So, we have
Mean = (0.5 * 6 + 1.5 * 13 + 2.5 * 7 + 3.5 * 4)/30
Evaluate
Mean = 1.8
Hence, the mean value is 1.8
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I need help figuring out how to solve the length
We have the parallel sides of the rectangle are equal, therefore:
[tex]\begin{gathered} RS=QP=4x+3 \\ \text{and} \\ SP=RQ=5x \end{gathered}[/tex]The perimeter is the sum of all sides, then:
[tex]RS+QP+SP+RQ=222[/tex]Substitute the given data:
[tex](4x+3)+(4x+3)+5x+5x=222[/tex]And solve for x:
[tex]\begin{gathered} 4x+3+4x+3+5x+5x=222 \\ 18x+6=222 \\ 18x+6-6=222-6 \\ 18x=216 \\ \frac{18x}{18}=\frac{216}{18} \\ x=12 \end{gathered}[/tex]Next, we find the length of side RS:
[tex]RS=4x+3=4(12)+3=48+3=51[/tex]Answer: RS = 51 units
Use the drop-down menus to explain if the two figures below are congruent, similar, or neither. If the figures are similar, state the scale factor I v Figure IJKE congruent to Figure TUVW because rigid motions be used to map Figure IJRL onto Figure TUVW. Figure IJKE dilations similar to Figure TUVW because rigid motions and/or be used to map Figure IJKL onto Figure TUVW.
Figure IJKL is congruent to Figure TUVW because rigid motions can be used to map Figure IJKL onto Figure TUVW
Figure IJKL is similar to Figure TUVW because rigid motions and/or dilations can be used to map Figure IJKL onto Figure TUVW
Since the figures are congruent, the scale factor is 1
Convert: 1200 liters =kiloliters
We have from the question 1200 liters, and we need to convert it into kiloliters.
To find the equivalent in kiloliters to 1200 liters, we can proceed as follows:
1. Find the equivalent between these two measures:
[tex]1\text{ kiloliter=}1000\text{ liters}[/tex]2. Then we have:
[tex]\begin{gathered} 1200liters*\frac{1kiloliter}{1000liters}=\frac{1200}{1000}\frac{liters}{liters}kiloliters=1.2kiloliters \\ \\ \end{gathered}[/tex]Therefore, in summary, we can conclude that 1200 liters are equivalent to 1.2kiloliters.
A park in a subdivision is triangular shaped. Two adjacent sides of the park are 533 feet and 525 feet. The angle between the sides is 53 degrees. To the nearest unit, what is the area of the park in square yards?A. 27,935B. 24,831C. 37,246D. 12,415thank you ! :)
Given:
Length of the two adjacent sides = 533 feet and 525 feet
Angle between the two sides = 53 degrees
Let's find the area of park.
Let's make a sketch representing this situation:
Let's first find the length of the third side.
Apply the cosine rule.
We have:
[tex]\begin{gathered} a=\sqrt{533^2+525^2-2(533)(525)cos53} \\ \\ a=\sqrt{284089+275625-336805.7777} \\ \\ a=\sqrt{222908.2223} \\ \\ a=472.13\text{ ft} \end{gathered}[/tex]Now, apply the Heron's formula to find the area:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]Where:
a = 472.13
b = 533
c = 525
Let's solve for s:
[tex]\begin{gathered} s=\frac{472.13+533+525}{2} \\ \\ s=\frac{1530.13}{2} \\ \\ s=765.1\text{ } \end{gathered}[/tex]• Therefore, the area will be:
[tex]\begin{gathered} A=\sqrt{765.1(765.1-472.13)(765.2-533)(765.1-525)} \\ \\ A=\sqrt{765.1(292.97)(232.1)(240.1)} \\ \\ A=111738.81\text{ ft}^2 \end{gathered}[/tex]The area in square feet is 111,738.81 square feet.
Now, let's find the area in square yards.
Apply the metrics of measurement.
Where:
1 square yard = 9 square feet
Thus, we have:
111,738.81 square feet =
[tex]\frac{111738.81}{9}=12415.4\approx12415\text{ square yards}[/tex]Therefore, the area of the park in square yards is 12,415 square yards.
ANSWER:
12,415 square yards.
Hi could you help me find out the correct answer to this?
Given:
There are given two triangles.
Explanation:
According to the question:
We need to find the tall of Ariadne.
So,
To find the value, we need to use triangle proportion properties.
So,
Suppose the value of tall is x.
So,
[tex]\frac{x}{6}=\frac{15}{18}[/tex]We need to find the value of x.
Then,
[tex]\begin{gathered} \frac{x}{6}=\frac{15}{18} \\ x\times18=15\times6 \\ x=\frac{15\times6}{18} \\ x=5 \end{gathered}[/tex]Final answer:
Hence, the solution is 5 ft tall.
How many solutions will each equation have?x^2+6x+5
To solve the quadratic equation, factor the expression and then clear x from each of the factors obtained.
[tex]\begin{gathered} x^2+6x+5=0 \\ (x+5)(x+1)=0 \\ x+5=0 \\ x=-5 \\ x+1=0 \\ x=-1 \end{gathered}[/tex]This equation has 2 solutions which are -5 and -1.
There are two machines that produce aluminum cans. The newer machine can produce 5700 cans in 190 minutes. It takesthe older machine 285 minutes to produce that many cans. If the two machines work together, how long will it take them to produce 5700 cans?
114 minutes
Explanation
Step 1
find the rate of production of each machine (cans per minute)
so
a)The newer machine:
[tex]\begin{gathered} rate=\frac{cans\text{ }}{time} \\ rate_1=\frac{5700\text{ cans}}{190\text{ minutes}}=30\text{ }\frac{cans}{minute} \end{gathered}[/tex]b)the older machine:
[tex]\begin{gathered} rate=\frac{cans\text{ }}{time} \\ rate_2=\frac{5700\text{ cans}}{285\text{ minutes}}=20\text{ }\frac{cans}{minute} \end{gathered}[/tex]Step 2
Add the rates together to determine their combined
[tex]\begin{gathered} rate_{total}=rate_1+rate_2 \\ rate_{total}=30\text{ }\frac{cans}{minute}+20\frac{cans}{m\imaginaryI nute} \\ rate_{total}=50\text{ }\frac{cans}{minute} \end{gathered}[/tex]so, the total rate( both machine working ) is 50 cans per minute
Step 3
finally, to find the time to produce 5700 cans, divide the total cans by the rate, so
[tex]\begin{gathered} time=\frac{number\text{ of cans}}{rate} \\ time=\frac{5700\text{ cans}}{50\frac{cans}{minute}}=114minutes \\ time=\text{ 114 minutes} \end{gathered}[/tex]therefore, the answer is 114 minutes
I hope this helps you
Four more than the product of a number and 8 is equal to 3.
Four more than the product of a number and 8 is equal to
Let
x -----> the number
we have that
the algebraic expression is equal to
the product of a number and 8 ------> 8x
so
Four more than the product of a number and 8 is equal to 3
8x+4=3
solve for x
8x=3-4
8x=-1
x=-1/3
therefore
the number is -1/3
HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
Answer:
skill issue
Step-by-step explanation:
skill issue
Evaluate the expression for r = –31, s = 4, and t = –16.
Answer:
st - r = -33
Explanation:
We need to replace r by -31, s by 4 and t by -16, so the expression is equal to
st - r = 4(-16) - (-31)
st - r = - 64 + 31
st - r = -33
So, the answer is
st - r = -33
4.) explain clearly in your own words why the triangles and figure 12.3 to have area 1/2 (b•h) for the given choice of base B and height h
The area of the right angled triangle as well as that of the isosceles triangle is calculated as
Area = 1/2 (b * h)
The explanation is logical, observe the right angled triangle (the one on the left) and you'll see that the length covered by the height (labelled as h) is not the entire width covered by the base (labelled as b) unlike what you have in a rectangle or square. Its only logical to multiply the base by half of the height, otherwise you might end up calculating the area of a rectangle.
That applies to all triangles in general, the area is calculated as
[tex]A=\frac{1}{2}bh[/tex]Which quadrilateral has diagonals that are both congruent and perpendicular?ParallelogramRectangleRhombusSquare
The quadrilateral has diagonals that are both congruent and perpendicular is square.
The correct option is (d)
Answer:
Its A
Step-by-step explanation:
what will the y-intercept be if the graph is proportional?
A graph is proportional if the line intersects at the origin (0, 0)
and the y-intercept will always equal to 0
Since y-intercept is the value of y when x =0, and it passes the origin at x = 0, y= 0.
The answer is 0
A paper airplane contest is being held. The following results are found: 80% of the participants used a triangle shape. The triangle shaped planes only won their trials 16% of the time. The other shaped planes won their trials 36% of the time. Create a tree diagram for this situation: What is the probability that a triangle plane won overall?Out of 100 planes, which shape has the most winners?A winning plane is selected at random, what is the chance it is triangle shaped?
Given:
Percent of participants that used triangles shape = 80% = 0.80
The triangles shaped won their trials 16% of the time = 0.16
The other shaped plane won their trials 36% of the time = 0.36
Thus, we have:
Percent of participants who used other shapes = 100% - 80% = 20% = 0.20
Amount of time the triangle shaped plane lost = 100% - 16% =84% = 0.84
Amount of time the other shaped plane lost = 100% - 36% = 64% = 0.64
Let's solve for the following:
• (a) Create a tree diagram for this situation.
We have the tree diagram below:
• (b) What is the probability that a triangle plane won overall?
To find the probability that a triangle plane won overall, we have:
[tex]P(\text{triangle)}=\frac{0.8\times0.16}{(0.8\times0.16)+(0.2\times0.36)}=\frac{0.128}{0.128+0.072}=0.64[/tex]• (c) Out of 100 planes, which shape has the most winners?
Given that 80% used triangle, the number of planes with triangle shape will be:
0.8 x 100 = 80 planes
Number of planes with other shape:
0.2 x 100 = 20 planes
Number of winners for traingles:
0.16 x 80 = 12.8
Number of winners for other shape:
0.36 x 20 = 7.2
Therefore, the shape with the most winners is the triangle shape.
• (d),. A winning plane is selected at random, what is the chance it is triangle shaped?
To find the probability a winning plane selected at random is triangle shaped, wehave:
[tex]P(\text{triangle)}=\frac{12.8}{12.8+7.2}=\frac{12.8}{20}=0.64[/tex]ANSWER:
(b) 0.64
(c) Triangle shape
(d) 0.64