Final answer:
To find the price of the jacket, set up a system of equations with the given information and solve for the jacket's price. The final calculated price of the jacket is $46.67.
Explanation:
The total cost of a jacket and a pair of shoes was $99.15. The price of the jacket was $5.81 less than the pair of shoes. Let's denote the price of the jacket as j and the price of the shoes as s. The problem gives us the following system of equations:
1) j + s = $99.15
2) s = j + $5.81
By substituting equation 2 in equation 1, we get:
3) j + (j + $5.81) = $99.15
Simplify and solve for j:
4) 2j + $5.81 = $99.15
5) 2j = $93.34
6) j = $46.67
Therefore, the price of the jacket is $46.67, which is the answer rounded to two decimal places as the student requested.
What is the probability that a randomly selected house with 2 bathrooms has 3 bedrooms?
0.2
0.4
0.6
0.8
[tex] |\Omega|=30\\
|A|=24\\\\
P(A)=\dfrac{24}{30}=\dfrac{4}{5}=0.8 [/tex]
Three girls, Laura, Tammy, and Jeri, can wash the family cars, clean the pool, and mow the lawn in one hour and 20 minutes. If Jeri did all the work, she would take twice as long as Tammy and 2 hours longer than Laura. How long would Tammy take to do the job alone?
3 hrs.
4 hrs.
6 hrs.
The number of hours that Tammy takes to do the job alone will be 4 hours. Then the correct option is B.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Three girls, Laura, Tammy, and Jeri, can wash the family cars, clean the pool, and mow the lawn in one hour and 20 minutes. If Jeri did all the work, she would take twice as long as Tammy and 2 hours longer than Laura.
The equations are given as,
T + J + L = 1 + 20/60
T + J + L = 1.333 ....1
J = 2T ....2
J = 2 + L ....3
The rate for Laura, Tammy, and Jeri will be given as,
Laura DATA:
Time = x hr/job ; Rate = 1/x job/hr
Jeri DATA:
Time = x+2 hr/job ; Rate = 1/(x+2) job/hr
Tammy DATA:
Time = (x+2)/2 hr/job ; Rate = 2/(x+2) job/hr.
Together DATA:
Time = 4/3 hr/job ; Rate = 3/4 job/hr
The equation is given as,
Rate + Rate + Rate = Together rate
1/x + 1/(x+2) + 2/(x+2) = 3/4
Multiply the equation by 4x(x+2) to get:
4(x+2) + 4x + 8x = 3x(x+2)
16x + 8 = 3x^2+6x
3x^2-10x-8 = 0
3x^2-12x+2x-8 = 0
3x(x-4)+2(x-4) = 0
(x-4)(3x+2) = 0
x = 4, - 2/3
The number of hours that Tammy takes to do the job alone will be 4 hours. Then the correct option is B.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
A circle has a radius of 7.2 feet and a central angle aob that measures 112°. what is the area of sector aob? use 3.14 for pi and round your answer to the nearest tenth.
Someone please help me?
In a certain state, each automobile license plate number consists of two letters followed by a four-digit number. to avoid confusion between "o" and zero and between "i" and one, the letters "o" and "i" are not used. how many distinct license plates can be formed in this state?
Which table represents a direct variation function?
x y x y x y
-3 -4.5 -5.5 -3 -3 -7.5
-1 -3.0 -5.5 -1 -1 -2.5
2 -1.5 -5.5 2 2 5.0
5 0.0 -5.5 5 5 12.5
10 1.5 -5.5 10 10 25.0
x y
-5.5 10
-4.5 8
-3.5 6
-2.5 4
-1.5 2
The answer to this question is B Ed
The table that represents a direct variation function is
x y
-3 -7.5
-1 -2.5
2 5.0
5 12.5
10 25.0
How to determine the table?For a table to represents a direct variation, the following must be true
k = y/x
Where k represents the constant of variation
In table 3, we have:
k = 25.0/10 = 12.5/5 = 5.0/2 = -2.5/-1 = -7.5/-3
This gives
k = 2.5
The value of k is the same for all input and output values
Hence, the table that represents a direct variation function is the table 3
Read more about direct variation at:
https://brainly.com/question/6499629
What are three consecutive odd integers that have a sum of 39?
Evaluate the expression
A. arctan ( - \sqrt{3} )
B. Arctan ( - \sqrt{3} )
Pls help i need this asap!
The requried both A and B refer to the same calculation, which is finding the inverse tangent of -√3. The result is -60 degrees or -π/3 radians.
A. The expression "arctan(-√3)" represents the inverse tangent function of the value -√3. The inverse tangent function returns an angle whose tangent is equal to the given value.
To evaluate arctan(-√3), we can use a calculator or reference table that provides trigonometric function values. In this case, the value is approximately -60 degrees or -π/3 radians.
B. The expression "Arctan(-√3)" is the same as "arctan(-√3)" and represents the inverse tangent function of -√3. The uppercase "Arctan" notation is commonly used in mathematical literature and calculators to represent the inverse tangent function.
Learn more about trigonometric functions here:
https://brainly.com/question/1542663
#SPJ6
How would I write #3
Tracy can wallpaper 7 rooms in a new house in 21 hours. together with her trainee they can wallpaper the 7 rooms in 12 hours. how long would it take the trainee working by herself to do the job? round to the nearest tenth.
The recursive rule for a sequence is shown. an=an−1+7 a1=17 what is the explicit rule for this sequence?
The explicit rule for the sequence is [tex]a_n = 10 + 7n[/tex]
The recursive rule is given as:
[tex]a_n=a_{n-1}+7[/tex]
[tex]a_1 = 17[/tex]
The above shows that the sequence is an arithmetic sequence.
Start by calculating a2
We have:
[tex]a_n=a_{n-1}+7[/tex]
Substitute 2 for n
[tex]a_2=a_1+7[/tex]
This gives
[tex]a_2 = 17 + 7[/tex]
[tex]a_2 = 24[/tex]
So, we have:
a1=17
a2 = 24
The common difference (d) is:
d =a2 - a1
d = 24 - 17
d = 7
The explicit rule is then calculated as:
[tex]a_n = a_1 + (n - 1)d[/tex]
This gives
[tex]a_n = 17 + (n - 1) * 7[/tex]
Expand
[tex]a_n = 17 - 7 + 7n[/tex]
[tex]a_n = 10 + 7n[/tex]
Hence, the explicit rule for the sequence is [tex]a_n = 10 + 7n[/tex]
Read more about arithmetic sequence at:
https://brainly.com/question/6561461
Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q. 3 + x - 3x2 = 9 A) (x - 1 6 )2 = 71 36 B) (x - 1 3 )2 = 71 36 C) (x - 1 6 )2 = - 71 36 Eliminate D) (x - 1 3 )2 = - 71 36
Select the equations that are equivalent to the equation y – 2 = 3(x + 6). Select all that apply.
y = 3x + 20
y = 3x + 6
2x - y = -3
3x - y = -20
PLEASE HELP: Question above ☝☝☝
I'm actually pretty sure it's B
Phil is offered a 3-year contract with a law firm. His first year earnings would be $81,000 with an annual raise of 15%.
What would Phil's total earnings be over the term of the contract?
Enter your answer, rounded to two decimal places, in the box.
Phil is offered a 3-year contract with a law firm. His first-year earnings would be $81,000 with an annual raise of 15%. Phil's total earnings would be over the term of the contract is $281272.5.
What is addition?The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
Phil is offered a 3-year contract with a law firm. His first-year earnings would be $81,000 with an annual raise of 15%.
First year
= $81000
Second year
1.15 x ($81000)
= $93150
Third year
1.15 x ($93150)
= $107122.50
Phil's total earnings would be over the term of the contract
= $81000 + $93150 + $107122.50
= 281272.5
Learn more about addition here;
https://brainly.com/question/545875
#SPJ2
The antarctic peninsula is less than 700 miles from what continent
Solve for x in the image below
The value of x in the equation given is 8
Using the equations given for our Calculation;
7/8 - 1/x = 3/4Take the L.C.M of 8 and x ; which is 8x
(7x - 8) / 8x = 3/4
Now we cross multiply;
4(7x - 8) = 3 * 8x
open the bracket
28x - 32 = 24x
28x - 24x = 32
4x = 32
x = 8
Hence, the value of x = 8
Learn more on equations: https://brainly.com/question/2972832
#SPJ2
Which of the following is not an example of like terms? A. 2 and –6 B. 2b and –6b C. 2b and 2 D. 2b^2 and 6b^2
The length of a rectangle is 5 yd less than three times the width, and the area of the rectangle is 28 yd2 . find the dimensions of the rectangle.
The dimensions of the rectangle are width = 4 yds and length = 7 yds.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
We have been given that the length of a rectangle is 5 yds less than three times the width,
The area of the rectangle is 28 yds square.
Let the width of the rectangle is x
So the length of the rectangle = 3x - 5
The area of a rectangle = x × (3x - 5)
28 = 3x² - 5x
3x² - 5x - 28 = 0
(3x + 7)(x - 4) = 0
3x + 7 = 0 and and x - 4 = 0
x = -7/3 and x = 4
Take x = 4 as the width
So the length of the rectangle = 3(4) - 5 = 12 - 5 = 7
Therefore, the dimensions of the rectangle are width = 4 yds and length = 7 yds.
Learn more about the Area of the rectangle here:
brainly.com/question/20693059
#SPJ5
The range of y=1x−2+3 is y=0.
true
false
ind the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2). (answer in slope-intercept form)
what is the classification for this polynomial u^2v^3w?
A.) monomial
B.)binomial
C.)trinomial
The polynomial u^2v^3w is classified as a monomial because it consists of a single algebraic term. Monomials are polynomials with exactly one term, unlike binomials or trinomials which have two or three terms, respectively.
Explanation:The classification for the polynomial u^2v^3w is a monomial. A monomial is a single term algebraic expression with one or more variables raised to a non-negative integer power. Since u^2v^3w consists of a single term without a plus (+) or minus (-) sign connecting it to other terms, it is considered a monomial.
The classification of polynomials is based on the number of terms they contain:
Monomial: A polynomial with one term, such as 3x or -a^4b^2.Binomial: A polynomial with two terms, such as x + y or 3a - 7b.Trinomial: A polynomial with three terms, such as x^2 + 2x + 1 or a^3 - 3a^2b + 2ab^2.Knowing the classification of polynomials helps in understanding how to perform operations such as addition, subtraction, multiplication, and division with them.
Lines that are not in the same plane are called _____ lines. A.perpendicular B.transversal C.skew D.parallel
Lines that are not in the same plane are called skew lines.
What is a line?"A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely."
Given, two lines are not in the same plane.
Here, perpendicular lines, transversal lines, and parallel lines should be in the same plane.
Two lines are called skew lines are two lines if they do not intersect and are not parallel.
Therefore, skew lines are not in the same plane.
Learn more about lines here: https://brainly.com/question/2506929
#SPJ2
Simplify the equation 7.5+N+9.63
Add 7.5+9.63 which would be 17.13
17.13+N
He altitude of a triangle is increasing at a rate of 3000 centimeters/minute while the area of the triangle is increasing at a rate of 3500 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 10000 centimeters and the area is 89000 square centimeters?
what is the volume of the cylinder?
radius=7 height=18
A.126
B.252
C.2268
D.882
Answer:
Option D. [tex]882\pi\ units^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
In this problem we have
[tex]r=7\ units[/tex]
[tex]h=18\ units[/tex]
substitute
[tex]V=\pi (7^{2})(18)=882\pi\ units^{3}[/tex] -----> exact value of the volume
Morgan uses 1/4 of her supply of raisins to make a trail mix and 3/8 of her supply of raisins to make cookies.If Morgan uses 5 pounds of raisins, how many pounds of raisins are in her supply.
In how many ways can 4 blue flags 3 green flags and 2 flags be arranged
You can calculate the number of ways to arrange the flags using the formula for permutations of multi-sets. We substitute the quantities of each flag color into the formula, which yields our answer of 1260 ways to arrange the flags.
Explanation:The question is asking about permutations of different objects— in this case, flags of multiple colors. For such problem, you can use the formula for permutations of multiset:
P(n1, n2, ..., nk) = (n1 + n2 + ... + nk)! / (n1! * n2! * ... * nk!)
Where n1, n2, ..., nk represent the counts of each distinct item (in this case, flag colors).
For our flags, you would substitute n1=4 (blue flags), n2=3 (green flags), and n3=2 (red flags). Applying the formula gives us (4+3+2)! / (4!*3!*2!) = 9! / (4!*3!*2!) = 1260.
So, "there are 1260 ways to arrange 4 blue flags, 3 green flags and 2 red flags that the student has".
Learn more about Permutations here:https://brainly.com/question/23283166
#SPJ12
Find the equation of the line that passes through (-2,5) and is parallel toy= -1/3x+2
You are looking at two different houses. house #1 would have a daily 5-mile commute to work, while house #2 would have a daily 20-mile commute. how much more co2 would you produce annually if you buy house #2? (hint: driving 1 mile produces 1.1 lb of co2 and you work 240 days/year.)
Answer:
B: 3960 lb
Step-by-step explanation:
vhslearning