Answer:
a) 0.789, this is the complement of the probability of no repeat offenders; b) 0.411; c) 0.033; d) μ = 1.429; e) σ = 9.58
Step-by-step explanation:
For part a,
The probability that no parolees are repeat offenders is 0.211. This means the probability of at least one is a repeat offender is the complement of this event. To find this probability, subtract from 1:
1-0.211 = 0.789.
For part b,
To find the probability that 2 or more are repeat offenders, add together the probability that 2, 3, 4 or 5 parolees are repeat offenders:
0.216+0.162+0.032+0.001 = 0.411.
For part c,
To find the probability that 4 or more are repeat offenders, add together the probabilities that 4 or 5 parolees are repeat offenders:
0.032+0.001 = 0.033.
For part d,
To find the mean, we multiply each number of parolees by their probability and add them together:
0(0.211)+1(0.378)+2(0.216)+3(0.162)+4(0.032)+5(0.001)
= 0 + 0.378 + 0.432 + 0.486 + 0.128 + 0.005 = 1.429
For part e,
To find the mean, we first subtract each number of parolees and the mean to find the amount of deviation. We then square it and multiply it by its probability. Then we add these values together and find the square root.
First the differences between each value and the mean:
0-1.429 = -1.429;
1-1.429 = -0.429;
2-1.429 = 0.571;
3-1.429 = 1.571;
4-1.429 = 2.571;
5-1.429 = 3.571
Next the differences squared:
(-1.429)^2 = 2.0420
(-0.429)^2 = 0.1840
(0.571)^2 = 0.3260
(1.571)^2 = 2.4680
(2.571)^2 = 6.6100
(3.571)^2 = 12.7520
Next the squares multiplied by the probabilities:
0(2.0420) = 0
1(0.1840) = 0.1840
2(0.3260) = 0.652
3(2.4680) = 7.404
4(6.6100) = 26.44
5(12.7520) = 63.76
Next the sum of these products:
0+0.1840+0.652+0.7404+26.44+63.76 = 91.7764
Lastly the square root:
√(91.7764) = 9.58
Probabilities are used to determine the outcomes of events.
The probability that one or more are repeat offenders is 0.789The probability that two or more are repeat offenders is 0.411The probability that four or more are repeat offenders is 0.033The standard deviation of repeat offenders is 1.093The expected number of repeat offenders is 1.429The table is given as:
[tex]\left[\begin{array}{ccccccc}x &0 &1 &2 &3 &4 &5 &P(x) &0.211 &0.378 &0.216& 0.162 &0.032 &0.001\end{array}\right][/tex]
(a) Probability that one or more are repeat offenders
This is represented as: [tex]P(x \ge 1)[/tex]
Using the complement rule, we have:
[tex]P(x \ge 1) = 1 - P(x = 0)[/tex]
So, we have:
[tex]P(x \ge 1) = 1 - 0.211[/tex]
[tex]P(x \ge 1) = 0.789[/tex]
The probability that one or more are repeat offenders is 0.789
(b) Probability that two or more are repeat offenders
This is represented as: [tex]P(x \ge 2)[/tex]
Using the complement rule, we have:
[tex]P(x \ge 2) = 1 - P(x = 0) - P(x = 1)[/tex]
So, we have:
[tex]P(x \ge 2) = 1 - 0.211 - 0.378[/tex]
[tex]P(x \ge 2) = 0.411[/tex]
The probability that two or more are repeat offenders is 0.411
(c) Probability that four or more are repeat offenders
This is represented as: [tex]P(x \ge 4)[/tex]
So, we have:
[tex]P(x \ge 4) = P(x = 4) + P(x = 5)[/tex]
[tex]P(x \ge 4) = 0.032 + 0.001[/tex]
[tex]P(x \ge 4) = 0.033[/tex]
The probability that four or more are repeat offenders is 0.033
(d) The expected number of repeat offenders
This is calculated as:
[tex]\mu = \sum x \times P(x)[/tex]
So, we have:
[tex]\mu = 0 \times 0.211+ 1\times 0.378 + 2 \times 0.216 + 3 \times 0.162 + 4 \times 0.032 + 5 \times 0.001[/tex]
[tex]\mu = 1.429[/tex]
The expected number of repeat offenders is 1.429
(e) The standard deviation
This is calculated as:
[tex]\sigma= \sqrt{\sum (x^2 \times P(x)) - \mu^2}[/tex]
[tex]\sum (x^2 \times P(x))[/tex] is calculated as:
[tex]\sum (x^2 \times P(x)) = 0^2 \times 0.211+ 1^2 \times 0.378 + 2^2 \times 0.216 + 3^2 \times 0.162 + 4^2 \times 0.032 + 5^2 \times 0.001[/tex]
[tex]\sum (x^2 \times P(x)) = 3.237[/tex]
So, we have:
[tex]\sigma= \sqrt{\sum (x^2 \times P(x)) - \mu^2}[/tex]
[tex]\sigma = \sqrt{3.237 - 1.429^2}[/tex]
[tex]\sigma = \sqrt{1.194959}[/tex]
[tex]\sigma = 1.093[/tex]
The standard deviation of repeat offenders is 1.093
Read more about probability density function at:
https://brainly.com/question/14749588
Write an algebraic expression for "12 less than the quotient of 12 and a number z."
Answer:
Expression is 12 - [tex]\frac{12}{z}[/tex].
Step-by-step explanation:
Given : "12 less than the quotient of 12 and a number z."
To find : Write an algebraic expression .
Solution : We have given 12 less than the quotient of 12 and a number z."
According to question :
Let the quotient = Q
quotient of 12 and a number z.
quotient = [tex]\frac{12}{z}[/tex].
12 less than the quotient of 12 and a number z.
12 - [tex]\frac{12}{z}[/tex].
Therefore, Expression is 12 - [tex]\frac{12}{z}[/tex].
Find the measure of arc KL.
Answer:
The measure of arc KL is [tex]145\°[/tex]
Step-by-step explanation:
we know that
[tex]arc\ JK=arc\ KL=x\°[/tex]
so
[tex]2x+70\°=360\°[/tex] -----> complete circle
solve for x
[tex]2x=360\°-70\°[/tex]
[tex]2x=290\°[/tex]
[tex]x=145\°[/tex]
Evaluate the log without a calculator ( Show your work )
Look at image. That is the problem.
Answer:
8
Step-by-step explanation:
Given in the question a logarithm expression
[tex]125^(log_{5}2)[/tex]
We will use Exponent of Log Rule
[tex]b^(log_{b}k) = k[/tex]
here b = 5
k = 2
Suppose
[tex]125^(log_{5}2) = x[/tex]
take cube root on both sides of this equation
[tex]\sqrt[ 3]{(125^(log_{5}2)}=\sqrt[3]{x}[/tex]
[tex]\sqrt[3]{(125)} ^(log_{5}2)=\sqrt[3]{x}[/tex]
[tex]5^(log_{5}2)}=\sqrt[3]{x}[/tex]
Now according to the rule
2 = ∛x
to remove cube root take cube on both side
x = 8
so [tex]125^(log_{5}2 )[/tex] = 8
What fraction will each person get if 8 friends share 5 apples equally? Enter your answer in the boxes.
Answer:
5/8
Step-by-step explanation:
5/8 is equal to 5 divided by 8 and your dividing 5 so all the friends can have a equal amount. every friend would also get 5/8 of a apple
Every friend would get 5/8 parts of the total apple.
What is fraction?A fraction is a part of a whole number, and a way to split up a number into equal parts.
Given that, 8 friends want to share 5 apples equally. We need to find that what fraction will each person get,
Since, we have 5 apples, which is to be distributed to 8 persons,
To find the same, we will have to, divide 5 apples equally among 8 persons,
Therefore,
If we divide 5 by 8 then the faction of 5/8 of the whole is the part that each of the 8 friends going to have,
Hence, each friend would get 5/8 parts of the total apple.
Learn more about fractions, click;
https://brainly.com/question/10354322
#SPJ2
Liam is a tyre fitter it takes him 56 minutes to fit 4 tyres to a van how long would it take to fit 12 tyres to 3 vans
Answer:
168 minutes, or 2 hours, 48 minutes
Step-by-step explanation:
Set up a proportion and solve.
56 minutes is to 4 tires as 'x' minutes are to 12 tires
becomes
56/4 = x/12 solve for x...
[56(12)]/4 = x (multiply both sides by 12 to get rid of the fraction)
672/4 = x (simplify 52(12) = 672)
168 = x (simplify 672/4 = 168)
Please help me out.......... :)
Answer:
y = 16Step-by-step explanation:
In a parallelogram opposite angles are congruent. Therefore we have the equation:
10y - 29 = 7y +19 add 29 to both sides
10y = 7y + 48 subtract 7y from both sides
3y = 48 divide both sides by 3
y = 16
Kelly paid $54.60 for a bike helmet that was 20% off the original price. What was the original price
The original price of the bike helmet was $68.25, calculated by understanding that the $54.60 Kelly paid represented 80% of the original price after a 20% discount.
Explanation:Kelly paid $54.60 for a bike helmet that was 20% off the original price. To find the original price of the helmet, we need to understand that the price Kelly paid is 80% of the original price, after the discount was applied. Therefore, the equation to find the original price (OP) is:
54.60 = 0.80 × OP
To solve for OP, we divide both sides of the equation by 0.80:
OP = 54.60 / 0.80
OP = $68.25
Thus, the original price of the bike helmet was $68.25.
If you have 3 4/6. Cups of sugar then divided it by 2 cups then added 4.9 cups how many eould you have
Answer:
11/6 or decimal 1.8333... + 4.9 = 6.733333....
Step-by-step explanation:
Simplify the following:
(3 + 2/3)/2
Express 4/6 in its lowest form by cancelling out gcd(4, 6) = 2 from the numerator and denominator. 4/6 = (2×2)/(2×3) = 2/3:
(2/3 + 3)/2
Put 3 + 2/3 over the common denominator 3. 3 + 2/3 = (3×3)/3 + 2/3:
((3×3)/3 + 2/3)/2
3×3 = 9:
(9/3 + 2/3)/2
9/3 + 2/3 = (9 + 2)/3:
((9 + 2)/3)/2
9 + 2 = 11:
(11/3)/2
11/3×1/2 = 11/(3×2):
11/(3×2)
3×2 = 6:
Answer: 11/6 or decimal 1.8333... + 4.9 = 6.733333....
1 liter equals approximately 1.05 quarts. Which BEST approximates the number of liters in 3 quarts?
A) 3 liters
B) 6 liters
C) 9 liters
D) 12 liters
Answer:should be A
Step-by-step explanation:
I dunno
Answer:
it is A i just did it and i got it right so please trust me it is A
Step-by-step explanation:
One letter is selected from the words "conditional probability." What is the probability that an "t" or "a" is chosen?
Answer:
4 out of 22 = 4/22
Step-by-step explanation:
Which two values of x are roots of the polynomial below? x^2-11x+15
Answer: The correct options are
(B) [tex]x=\dfrac{11+\sqrt{61}}{2}.[/tex]
(D) [tex]x=\dfrac{11-\sqrt{61}}{2}.[/tex]
Step-by-step explanation: We are given to select the values of x that are the roots of the following polynomial :
[tex]x^2-11x+15.[/tex]
The quadratic equation formed by the given polynomial will be
[tex]x^2-11x+15=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
we know that
the solution set of a quadratic equation [tex]ax^2+bx+c=0,~~a\neq 0[/tex] is given by
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]
From equation (i), we have
a = 1, b = -11 and c = 15.
Therefore, the roots of equation (i) will be given by
[tex]x=\dfrac{-(-11)\pm\sqrt{(-11)^2-4\times1\times15}}{2\times1}\\\\\\\Rightarrow x=\dfrac{11\pm\sqrt{121-60}}{2}\\\\\\\Rightarrow x=\dfrac{11\pm\sqrt{61}}{2}.[/tex]
Thus, the roots of the given polynomial are
[tex]x=\dfrac{11+\sqrt{61}}{2},~~~~~x=\dfrac{11-\sqrt{61}}{2}.[/tex]
Options (B) and (D) are CORRECT.
Answer:
b and d
Step-by-step explanation:
One of Alberto's zebra danios is 4/3 the lenght of one of his fancy guppies. Which fish is longer?
Answer:
The Zebra Danios!
Step-by-step explanation:
The zebra danios
4/3 is greater than 1, making it an improper fraction. Suppose that fancy guppy's length is x, the danios' length would be 4/3 x, which, since it is an improper fraction, is greater than x.
Mark me brainlest please!
I take half-credit my cousin aswell helped!
If price was $2.00 per gallon and decreased to $1.40 per gallon, how does quantity of gasoline demanded change?
The price and demand are inversely proportional to each other, When the price is less, the demand is higher. When the price is high, the demand is low.
So , as given, the gasoline prices has been decreased from $2.00 per gallon to $1.40 per gallon, so now the demand will increase. The quantity of gasoline that will be in demand will increase.
Answer:
The quantity of gasoline demanded will increase.
Step-by-step explanation:
We are asked to find the change in demand of gasoline, when price of gasoline decreased from $2 per gallon to $1.40.
We know that quantity of a product demanded is inversely proportional to supply of the product.
This means that an increase in price will decrease the quantity demanded, while a decrease in price will increase the demand.
Since the price of gasoline is decreased by $0.60 per gallon, therefore, the quantity of gasoline demanded will increase.
Identify the graph of 9X^2+4xy+5y^2-40=0 and find theta to the nearest degree.
Answer:
The answer is ellipse; 23° to the nearest degree ⇒ answer (d)
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
- 9x² + 4xy + 5y² - 40 = 0
∵ A = 9 , B = 4 , 5 = 5
∴ B² - 4 AC = (4)² - 4(9)(5) = -164 < 0
∴ B² - 4AC < 0
∴ If a conic exists, it will be either a circle or an ellipse.
* To find the type of the graph lets check;
- If A and C are nonzero, have the same sign, and are not
equal to each other, then the graph is an ellipse.
- If A and C are equal and nonzero and have the same
sign, then the graph is a circle.
∵ A and C have same signs and are not equal
∴ The graph is an ellipse
* If we have term xy ⇒ B ≠ 0
∴ The graph is rotate by angle Ф
* To find the angle of rotation use the rule:
- cot(2Ф) = (A - C)/B
∵ A = 9 , B = 4 , C = 5
∴ cot(2Ф) = (9 - 5)/4 = 4/4 = 1
∴ tan(2Ф) = 1
∴ 2Ф = 45°
∴ Ф = 22.5° ≅ 23° to the nearest degree
* The answer is ellipse; with angle of rotation = 23°
M=−8r ^2 +11r−6 T=−7r ^2−9r+14 M+T=
Answer is: −15r ^2 +2r+8
Answer:
[tex]\large\boxed{M+T=-15r^2+2r+8}[/tex]
Step-by-step explanation:
[tex]M=-8r^2+11r-6\\T=-7r^2-9r+14\\\\M+T=?\\\\\text{Substitute:}\\\\M+T=(-8r^2+11r-6)+(-7r^2-9r+14)\\\\M+T=-8r^2+11r-6-7r^2-9r+14\qquad\text{combine like terms}\\\\M+T=(-8r^2-7r^2)+(11r-9r)+(-6+14)\\\\M+T=-15r^2+2r+8[/tex]
The expression that represents M + T is -15r^2 + 2r + 8
The equations for M and T are given as:
[tex]M=-8r^2 +11r -6[/tex]
[tex]T=-7r^2-9r+14[/tex]
The sum of M and T is represented as: M + T
This is then calculated as:
[tex]M+T=-8r^2 +11r -6-7r^2-9r+14[/tex]
Collect like terms
[tex]M+T=-8r^2 -7r^2+11r -9r-6+14[/tex]
Evaluate the like terms
[tex]M + T = -15r^2 + 2r + 8[/tex]
Hence, the expression that represents M + T is -15r^2 + 2r + 8
Read more about algebraic expressions at:
https://brainly.com/question/4344214
London owns a hybrid SUV that can travel 400 miles on a 15-gallon tank of gas. Determine how many miles he can travel on 6 gallons and number 16.
Answer:
Step-by-step explanation:
The imaginary number i is equal to
−1
, which expression is equivalent to −(4 + 3i) + (2 + 2i)?
A) 2 + 2i
B) 2 − i
C) −2 + i
D) −2 − i
Answer:
D
Step-by-step explanation:
An equivalent expression is an expression which is equal to −(4 + 3i) + (2 + 2i). You can expand or simplify an expression to make an equivalent expression. Combine like terms - constants with constants and imaginary with imaginary - to simplify.
−(4 + 3i) + (2 + 2i) = -4 + 2 -3i + 2i = -2 - i
(Q1) Which of the following is true about the function y = 3 • 2x?
Answer: Third option
Step-by-step explanation:
You have the function:
[tex]y=3*2^x[/tex]
Then, if the value of x increases by 1, you obtain:
-Rewrite the function:
[tex]y=3*2^{(x+1)}[/tex]
-Substitute values for x into the function and observe what happen to y. Then:
x=1
[tex]y=3*2^{(1+1)}=12[/tex]
x=2
[tex]y=3*2^{(2+1)}=24[/tex]
x=3
[tex]y=3*2^{(3+1)}=48[/tex]
The value of y is doubled.
Answer:
C=the value of x increases by 1, the value of y will double.
Step-by-step explanation:
The first train leaves the station at 6:15 a m. The second train leaves at 6:55 am. How much does the sec ond train leave the station
Answer: 40
Step-by-step explanation:
second train leaves 40 minutes after
Determine the eccentricity, the type of conic, and the directrix for
r=6/1+2cos theta
Answer:
Choice C is correct
Step-by-step explanation:
The polar equation of the conic section is in standard form. The eccentricity is simply the coefficient of cos theta; thus e = 2
The eccentricity being more than 1 implies the conic section is a hyperbola.
To determine the directrix, divide 6 by 2 to obtain 3. The conic section opens to the left thus;
directrix; x = 3
Answer:
Choice C is correct
El área de una propiedad en metros cuadrados, mide 704/5. Se construye una casa que ocupa 5/6 del área total. La mitad del área restante se utiliza para construir una terraza, cuanta área falta por construir?
Answer:
The area left to build is [tex]\frac{704}{60}\ m^{2}[/tex]
Step-by-step explanation:
The question in English is
The area of a property in square meters, measures 704/5. A house is built that occupies 5/6 of the total area. Half of the remaining area is used to build a terrace, how much area is left to build?
we know that
The total area represent the fraction 6/6
A house represent the fraction 5/6 of the total area
The remaining area represent the fraction (6/6)-(5/6)=1/6 of the total area
If half of the remaining area is used to build a terrace
then
the area of the terrace represent the fraction (1/6)/2=1/12 of the total area
therefore
The area left to build represent the fraction 1/12 of the total area
so
[tex](\frac{1}{12})\frac{704}{5} =\frac{704}{60}\ m^{2}[/tex]
Simplify 27 2
the 2 is tiny so I think it's 27 to the power of 2
Please help 100 points! Will mark Brainliest. Thank You!
HERE'S HOW TO DO IT :)
A composite figure is made up of several simple geometric figures such as triangles, rectangles, squares, circles, and semicircles.
To find the area of a composite figure, separate the figure into simpler shapes whose area can be found. Then add the areas together.
(SEE EXAMPLE ATTACHED)
HERES WHAT WE KNOW ABOUT COMPOSITE FIGURES:
Composite Figures. A figure (or shape) that can be divided into more than one of the basic figures is said to be a composite figure (or shape). For example, figure ABCD is a composite figure as it consists of two basic figures
let me know if i can help more :)
See the attached picture for the answers:
Identify the equation of the translated graph in general form x^2-y^2=8 for T(4,3)
Answer:
B
Step-by-step explanation:
A transformation of T(a,b) in the equation would give this form:
[tex](x-a)^2+(y-b)^2=8[/tex]
So, T(4,3) means translation of 4 units in x and 3 units in y. Thus, we can write:
[tex](x-4)^2+(y-3)^2=8[/tex]
Expanding and rearranging, we get:
[tex](x-4)^2-(y-3)^2-8=0\\x^2-8y+16-y^2+6y-9-8=0\\x^2-y^2-8x+6y-1=0[/tex]
Answer choice B is right.
Answer:
B
x^2-y^2-8x+6y-1=0
Consider the population of all 1-gal cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean μ = 5 ml and standard deviation σ = 0.2 ml is a reasonable model for the distribution of the variable x = amount of red dye in the paint mixture. Use the normal distribution model to calculate the probabilities below. (Round all answers to four decimal places.)
(a) P(x > 5) =
(b) P(x < 5.4)=
(c) P(x lteq.gif 5.4) =
(d) P(4.6 < x < 5.2) =
(e) P(x > 4.5) =
(f) P(x > 4) =
Answer:
A) 0.5000; B) 0.9772; C) 0.9772; D) 0.8185; E) 0.9932; F) 1.0000
Step-by-step explanation:
For each of these, we will use a z score. The formula for a z score is:
[tex]x=\frac{X-\mu}{\sigma}[/tex]
A) Our X is 5, our mean is 5 and our standard deviation is 0.2:
z = (5-5)/(0.2) = 0/0.2 = 0
Using a z table, the value to the left of this, less than, is 0.5000; this means the area to the right of this, greater than, is 1-0.5000 = 0.5000.
B) Our X is 5.4, the mean is 5 and the standard deviation is 0.2:
z = (5.4-5)/0.2 = 0.4/0.2 = 2
Using a z table, the value to the left of this, less than, is 0.9772.
C) The probability for this will be the same as for B; there is no distinction between "less than" and "less than or equal to" in z tables.
D) We find the z score for each of the endpoints of this interval, find the probabilities and subtract them:
z = (4.6-5)/0.2 = -0.4/0.2 = -2; the probability is 0.0228.
z = (5.2-5)/0.2 = 0.2/0.2 = 1; the probability is 0.8413.
The area between them is 0.8413-0.0228 = 0.8185.
E) X is 4.5, the mean is 5 and the standard deviation is 0.2:
z = (4.5-5)/0.2 = -0.5/0.2 = -2.5; the probability less than this is 0.0062. This means the probability greater than this is 1-0.0062 = 0.9938.
F) X is 4, the mean is 5 and the standard deviation is 0.2:
z = (4-5)/0.2 = -1/0.2 = -5. Everything in the z table is larger than this, so the probability is 1.000.
Which type of function correctly describes the exponential function
g(x)=3(4)^x-5
Answer:
See below.
Step-by-step explanation:
This function g(x) = 3(4^x) - 5 is an exponential function since it has a variable as an exponent. It has a initial value of 3 and a multiplicative rate of change of 4. The function itself when x = 0 is y = -2.
What is the volume of this right rectangular prism. 7 feet length 2 feet width and 3.5 feet Height
i think the answer to this problem is49
Answer:
The volume of this right rectangular prism is 49 Cubic feet.
Step-by-step explanation:
Here, the data is given
Lenght (l) = 7 feet
Widht (b) = 2 feet
Height (h) = 3.5 feet
Now, The Volume of rectangular prism
= l × b × h
= 7 × 2 × 3.5 feet
= 7 × 7 feet
= 49 cubic feet
Thus, The volume of this right rectangular prism is 49 Cubic feet.
-TheUnknownScientist
what is the surface area of this square pyramid?
round your answer to the nearest tenth, if necessary.
a. 43.8yd^2
b. 66.6yd^2
c. 105 yd^2
d. 171.6^2
Answer:
c. 105 yd^2.
Step-by-step explanation:
First find the slant height (h) of each of the triangular walls:
tan 60 = h / 3.1
h = 3.1 tan 60
= 5.369 yds.
Area of each side = 3.1* 5.369
= 16.645
Total surface area of the pyramid
= 4 * 16.645 + 6.2^2
= 105.02 yd^2.
A rectangle whose area is 180 square feet has a width that is 3 feet less than the length. Find the dimensions of the rectangle.
Answer:
The length is [tex]15\ ft[/tex]
The width is [tex]12\ ft[/tex]
Step-by-step explanation:
we know that
The area of rectangle is equal to
[tex]A=LW[/tex]
we have
[tex]A=180\ ft^{2}[/tex]
so
[tex]180=LW[/tex] -----> equation A
[tex]W=L-3[/tex] ------> equation B
substitute equation B in equation A and solve for L
[tex]180=L(L-3)[/tex]
[tex]180=L^{2}-3L[/tex]
[tex]L^{2}-3L-180=0[/tex]
using a graphing tool------> solve the quadratic equation
The solution is [tex]L=15\ ft[/tex]
see the attached figure
Find the value of W
[tex]W=15-3=12\ ft[/tex]
To find the dimensions of the rectangle given its area, we set up an equation using the length and width of the rectangle. Solving the equation will give us the dimensions. In this case, the length of the rectangle is 15 feet and the width is 12 feet.
Explanation:To find the dimensions of the rectangle, let's assume the length of the rectangle is L feet. According to the problem, the width is 3 feet less than the length, so the width would be L - 3 feet. The area of the rectangle is given as 180 square feet, so we can set up the equation: L * (L - 3) = 180. Solving this equation will give us the dimensions of the rectangle.
Multiplying the binomials, we get L^2 - 3L = 180. Rearranging the equation, we have L^2 - 3L - 180 = 0. This is a quadratic equation that can be factored. Factoring, we have (L - 15)(L + 12) = 0. We can now solve for L by setting each factor equal to zero: L - 15 = 0 or L + 12 = 0. This gives us two possible solutions for L: L = 15 or L = -12.
Since we cannot have negative dimensions for a rectangle, we discard the negative solution. Therefore, the length of the rectangle is 15 feet. The width can be found by substituting this value back into the equation: Width = 15 - 3 = 12 feet. So, the dimensions of the rectangle are 15 feet by 12 feet.
Learn more about Rectangle dimensions here:https://brainly.com/question/31677552
#SPJ3
Knowing that QPT = ARZ, a congruent side pair is?
Answer:
[tex]\large\boxed{\overline{QT}\cong\overline{AZ}}[/tex]
Step-by-step explanation:
[tex]\triangle QPT\cong\triangle ARZ\\\\\begin{array}{c|c}Q&A\\P&R\\T&Z\end{array}\Rightarrow\begin{array}{ccc}\overline{QP}\cong\overline{AR}\\\overline{PT}\cong\overline{RZ}\\\overline{QT}\cong\overline{AZ}\end{array}[/tex]
Answer:
First option.
Step-by-step explanation:
I drew the triangles to see it better. If two triangles are congruent the sides and the angles have the same length. Also, the order of the vertex is important. I put them as it is enunciated. So, watching the image the congruent sides are:
QT and AZ
QP and AR
PT and RZ
Then, the correct option is the first one.