Answer:
[tex]\left \{ {{n+q=28} \atop {n(0.05)+q(0.25)=4}} \right.[/tex]
And the pair [tex](n,q)=(15,13)[/tex] is the solution.
Step-by-step explanation:
We know that Yolanda paid for her movie ticket using 28 coins. She only paid with nickels and quarters.
We also know that the ticket cost $4.
We need to form a linear equation system that solves this problem.
We have the following variables :
n : number of nickels
q : number of quarters
We know that she used 28 coins ⇒ the number of nickels plus the number of quarters must be equal to 28.
We have our first equation :
[tex]n+q=28[/tex] (I)
For the second equation we need to use the ticket price information.
We know that the ticket cost $4 and she only paid with nickels and quarters.
Therefore we can write the following equation that relates the variable ''n'' and the variable ''q'' :
[tex]n(0.05)+q(0.25)=4[/tex] (II)
This equation represents that the number of nickels ''n'' per its value plus the number of quarters ''q'' per its value is equal to $4 that it is the value of the movie ticket.
With (I) and (II) we form the linear equation system :
[tex]\left \{ {{n+q=28} \atop {n(0.05)+q(0.25)=4}} \right.[/tex]
This linear equation system can be used to find the value of ''n'' and ''q''.
For example, in equation (I)
[tex]n+q=28[/tex]
we can solve it in terms of ''n'' :
[tex]n=28-q[/tex] (III)
If we use (III) in (II) :
[tex](28-q)(0.05)+q(0.25)=4[/tex]
[tex]1.4-(0.05)q+(0.25)q=4[/tex]
[tex]q(0.2)=2.6[/tex]
[tex]q=\frac{2.6}{0.2}=13[/tex]
[tex]q=13[/tex]
Now replacing this value of q in (III) :
[tex]n=28-13=15[/tex]
[tex]n=15[/tex]
We find that Yoland used 15 nickels and 13 quarters to paid the movie ticket .
(50 points)
What is the product of -2x^3+x-5 and x^3-3x-4?
Is the product of -2x^3+x-5 and x^3-3x-4 equal to the product of x^3-3x-4 and -2x^3+x-5 explain your answer.
Answer:Yes, the products are equal because of commutativity. To find the product, use distributive law. Just simplify the below:
-2x^3(x^3-3x-4) + x(x^3-3x-4) - 5(x^3-3x-4)
Step-by-step explanation:
How to multiply fractions by a number with an exponent?
Solve the system shown.
A $6,000.00 principal earns 8% annual interest, compounded semiannually (twice per year). After 35 years, what is the balance in the account?
A. $22,800.00
B. $39,600.00
C. $88,712.07
D. $93,429.71
Answer:
After 35 years balance in the account = $93429.71
Explanation:
We will applying the compound interest formula.
A = [tex] P(1 +\frac{r}{n})^{nt} [/tex]
Where,
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years
Given that,
P = $6000
r = 8% = [tex] \frac{8}{100} [/tex] = 0.08
n = 2 (because of twice in a year)
t = 35 years
[tex] A= 6000(1 + \frac{0.08}{2}) ^{2*35} [/tex]
A = 6000[tex] (1.04)^{70} [/tex]
A= $93429.71 (Option D)
PLEASE HELP!!!! POINTS^^^^^^
1.) Kayla wants to find the distance, AB, across a river. She walks along the edge of the river 75 ft and marks point C. Then she walks 100 ft further and marks point D. She turns 90° and walks until her final location and marks point E. Point E, point A, and point C are collinear.
2.) Can Kayla conclude that ∆ABC and ∆EDC are similar? Why or why not?
3.) Suppose DE= 175 ft. What can Kayla conclude about AB? Explain. Don’t forget to label your answer.
1 - yes 100 and 75 are both collinear both are the same line.
2 - She can conclude that there both similar because the both go the same direction and both same shape.
3 - AB would equal 150 because the other one was 100 and the other angle was 25 down. So AB would equal 150.
Hope I helped
Please help me I have no idea what to do.
A large frog eats 500 flies a day. How many flies does a frog eat in a 365-day year?
can some one help me with this?:
A python curls up to touch the tip of its own tail with its nose, forming the shape of a circle. The python is 2.6pi meters long.
What is the radius r of the circle that the python forms?
Over what interval is the growth rate of the function decreasing?
Force exerted by the ball on the kickers foot.
15 is what percent of 40?
Pls Show Work
Thx
in the figure below,angle y and angle x from vertical angles.angle y forms a straight line with 80° angle and the 60° angle
Quiz: Area of Rectangles Assessment items A rectangle is 13 yards long and 23 yards wide. What is the area of the rectangle? Enter your answer in the box as a fraction in simplest form. $$ yd2 Assessment navigation
Quiz: Area of Rectangles Assessment items A rectangle is 13 yards long and 23 yards wide. What is the area of the rectangle? Enter your answer in the box as a fraction in simplest form. $$ yd2 Assessment navigation
Length of rectangle=13yards
Width of rectangle=23yards
The formula for, Area of rectangle= length*width
So, Area=13*23[tex] yards^{2} [/tex]
As, 13 multiplied by 23 is 299
So, Area=299[tex] yards^{2} [/tex]
To represent in fractions, Area=[tex] \frac{299}{1}yards^{2} [/tex]
Area=299[tex] yd^{2} [/tex]
Is 67.714813 rational or irrational?
Given that (7,-4) is on the graph of f(x), find the corresponding point for the function f(x+4)
Final answer:
To find the corresponding point of a function after transformation, substitute the given point into the transformed function.
Explanation:
Given: (7, -4) is on the graph of f(x).
To find: The corresponding point for the function f(x+4).
Solution:
Substitute x+4 into the function f(x) to get the new function f(x+4).
Substitute x=3 into f(x+4) to find the corresponding point.
Therefore, the corresponding point for f(x+4) is (3, -4).
Decide whether the data table represents a linear function or an exponential function PLEASE!
Answer:
D
Step-by-step explanation:
300 pounds of oranges were purchased at $0.24 per pound. The desired markup is 50% based on selling price, but 21% spoilage is expected. What should the selling price per pound be? (Round your answer to the nearest cent)
The selling price per pound, considering 50% markup and 21% spoilage, should be approximately $2.74, rounded to nearest cent.
To find the selling price per pound, we need to consider the cost, the desired markup, and the expected spoilage.
First, let's calculate the total cost of the oranges:
Total cost = Quantity * Cost per pound
Total cost = 300 pounds * $0.24/pound
Total cost = $72
Next, let's calculate the selling price per pound with the desired markup:
Markup based on selling price = 50%
Let's denote the selling price per pound as S.
[tex]\[S = \frac{{\text{Total cost}}}{{1 - \text{Markup}}} \times (1 + \text{Markup})\]\[S = \frac{{72}}{{1 - 0.50}} \times (1 + 0.50)\]\[S = \frac{{72}}{{0.50}} \times 1.50\]\[S = 144 \times 1.50\]\[S = 216\][/tex]
So, the selling price per pound, without considering spoilage, should be $2.16.
However, since 21% spoilage is expected, we need to adjust the selling price per pound to account for the expected loss.
[tex]\[S_{\text{adjusted}} = \frac{{S}}{{1 - \text{Spoilage}}} = \frac{{2.16}}{{1 - 0.21}} = \frac{{2.16}}{{0.79}} \approx 2.738\][/tex]
Rounding to the nearest cent, the selling price per pound, accounting for expected spoilage and desired markup, should be approximately $2.74.
55.9 is what percent of 545.8? Click to select the correct answer. Round answer to the nearest whole number.
55.9 is approximately 10% of 545.8. To calculate this, divide 55.9 by 545.8 and then multiply by 100 to get the percentage, and round to the nearest whole number as per the precision of the given values.
Explanation:To find what percent 55.9 is of 545.8, we use the formula for percentage: Percentage = (Part / Whole) × 100. Plugging in the numbers, we get:
Percentage = (55.9 / 545.8) × 100
Executing the division first (as per order of operations), we have:
Percentage = 0.1024 × 100
Now, multiplying by 100 to convert to a percentage:
Percentage = 10.24%
Rounding this to the nearest whole number, we get 10%. Because the question requires following proper rounding rules based on significant figures, we consider the least precise number provided - 55.9 (tenths place) - when determining the final answer. Therefore, we round the percentage to the tenths place to coincide with the precision of the given values.
help me please asap ill mark brainliest nd plz be correct
What is the solution to the proportion? Start Fraction 3 y minus 8 over 12 End fraction equals start fraction y over 5 End Fraction?
Answer:
1.78
Step-by-step explanation:
To solve for x we need to cross multiply it
We have = sign in between the fractions so we cross multiply it
9*x = 2* 8
9x = 16
Now we divide by 9 on both sides
so x= 1.7777777778
When we round to two decimal places then
x= 1.78
please helm me
A circular piece of metal has a radius of 3.5 meters.
The metal sells for $3.25 per square meter.
What is the total cost of the circular piece of metal?
A.
$11.38
B.
$38.47
C.
$71.44
D.
$125.01,
Answer:
The answer would be $125.01
Step-by-step explanation:
I took the test.
What statement is true about the polynomial
insert <,>,or = or make the sentence true.sqrt(3)__sqrt(7)
Look at the table below showing an example of a checkbook ledger. Malcolm has several receipts from recent transactions that he entered in his records. The receipts include an ATM receipt for an $80.00 deposit, a grocery store receipt for $25.50, and a paycheck deposit slip for $650.00. When he finishes entering his transactions, Malcolm realizes that his balance is incorrect. Assuming that Malcolm had no beginning balance, what should his correct balance be? $624.50 $704.50 $755.50 $784.50
Answer:
I just took this quiz and the answer is B:$704.50
Step-by-step explanation:
Edg 2022
each blade on a windmill is in the shape of a triangle with a base of 7 feet and a height of 4 ft if there are four blades on the windmill what is the total area of the blades
The total area of the blades is the area of a triangle multiplied by 4.
We have then:
[tex] A = (4) * (1/2) * (b) * (h)
[/tex]
Where,
b: base of the blades
h: height of the blades
Substituting values we have:
[tex] A = (4) * (1/2) * (7) * (4)
[/tex]
Doing the calculation we have that the area of the blades is given by:
[tex] A = 56 feet ^ 2
[/tex]
Answer:
The total area of the blades is:
[tex] A = 56 feet ^ 2 [/tex]
Each blade on a windmill is in the shape of a triangle with a base of 7 feet and a height of 4 ft if there are four blades on the windmill what is the total area of the blades
Total area of blades= Sum of areas of all blades
=Sum of areas of four blades
As, all blades have same dimension
SO, Total area of blades=4*Area of one blade
As, shape of blade is triangle, Area of triangle=[tex] \frac{1}{2} [/tex]*base*height
Total Area of blades =4* [tex] \frac{1}{2} [/tex] * base * height
Total Area of blades =4* [tex] \frac{1}{2} [/tex] * 7 * 4
Total Area of blades =4* [tex] \frac{1}{2} [/tex] * 28
Total Area of blades =4* 14
Total Area of blades =56 square feet
Students on the CARE Team are selling puppies, yes, puppies! They earn $0.40 on each puppy they sell. Their goal is to earn more than $327. Choose the inequality to find the fewest number of puppies they can sell and still reach their goal. Also indicate what that number would be.
Elijah played in a golf tournament. For the first three days he averaged a score of -2. On the fourth day he shot a +2. What was his average for all four days?
one face of a cube an area of 49 square centimeters. what is the volume of the cube
Roderick wants to draw a circle for which the numerical value of the circumference is greater than the value of the area. Which lengths could he use for the radius? Check all that apply.
Answer:
The length of the radius must be less than [tex]2[/tex]
[tex]\frac{1}{2},1,1.5[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
where r is the radius of the circle
In this problem we have that
[tex]C > A[/tex]
Substitute
[tex]2\pi r > \pi r^{2}[/tex]
Simplify
[tex]2r > r^{2}[/tex]
[tex]2> r[/tex] ------> rewrite
[tex] r< 2\ units [/tex]
The length of the radius must be less than [tex]2[/tex]
the answer is
[tex]\frac{1}{2},1,1.5[/tex]
Roderick select the length of radius, for keeping the value of circumference of the circle greater than the value of its area, should be 1/2,1 and 1.5. Thus the option A, B and C is the correct option.
What is circumference and area of the circle?Circumference of the circle is the length of its boundary. It can given as,
[tex]P=2\pi r[/tex]
The area of the circle is the space occupied by it. It can be given as,
[tex]A=\pi r^2[/tex]
Given information-
Roderick wants to draw a circle.
The circumference of the circle must be greater than the area of the circle.
The circumference of the circle having radius equal to [tex]r[/tex] units can be given as,
[tex]P=2\pi r[/tex]
The area of the circle having radius equal to [tex]r[/tex] units can be given as,
[tex]A=\pi r^2[/tex]
Now as Roderick wants to draw a circle in which, the circumference of the circle must be greater than the area of the circle. Thus,
[tex]P>A[/tex]
Put the values as,
[tex]2\pi r>\pi r^2\\2r>r^2\\2>r[/tex]
Thus the value of the radius of Roderick circle must be less than the number 2.
Number 1/2 , 1, and 1.5 is less than the number two.
Thus, Roderick select the length of radius, for keeping the value of circumference of the circle greater than the value of its area, should be 1/2,1 and 1.5. Thus the option A, B and C is the correct option.
Learn more about the circumference and area of the circle here;
https://brainly.com/question/402655
Why might algebra tiles not be a good tool to use to factor x^2 + 18x + 80? Explain.
Sample Response: Algebra tiles would not be a good tool to use to factor the trinomial because you would need to drag an x-squared tile, 18 x-tiles, and 80 plus tiles. That is a total of 99 tiles. It would take a lot of time to drag that many tiles on the board and there might not be enough space to hold all of them. You would also need to determine how to arrange all those tiles to make a rectangle. Since 80 is a multiple of 10, you might recognize that 10 and 8 are the factors that add to 18, which would give you the values to use in the X method.