x = ones
y = fives
x+y = 14 total bills
rewrite as x = 14-y
1x +5y = 50
1(14-y) +5y = 50
14-1y +5y = 50
14 +4y = 50
4y = 36
y = 36/4 = 9
x = 14-y = 14-9 = 5
9+5 = 14
9x5 = 45 +5x1 = 50
he had 9 fives and 5 ones
Answer:
There were 5 bills of '1' and 9 bills of '5'.
Step-by-step explanation:
let the number of '1' bill be x
let the number of '5' bill be y.
Total number of bills = 14
x + y = 14 ..[1]
Worth of 14 bills = 50
So,[tex]x\times 1+y\times 5=\$50[/tex]
[tex]x+5y=50[/tex]..[2]
x + y = 14
x = 14 - y
Putting value of x in [2]:
[tex]14- y +5y=50[/tex]
[tex]y=\frac{50-14}{4}=9[/tex]
y = 9
x = 14-y = 14 - 9 = 5
There were 5 bills of '1' and 9 bills of '5'.
The Jonas school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table, where Low represents the fewest days attended and High represents the most days attended for a single student.
School High School M High School N High School P
Low - 128 131 140
High - 180 180 180
Range- 52 49 40
Mean- 141 159 153
Median- 160 154 165
IQR- 55.5 48.5 32.5
σ- 41.5 36.5 31.5
Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justify your answer mathematically. (5 points) Part B: If the school district wants to award the school with the highest average attendance, which school should it choose and why? Justify your answer mathematically. (5 points)
Thank you very much for your help!
The number of hours (H) that a candle will burn increases when the length of the candle (L) increases. Write the correct equation for this scenario, and solve for the number of hours when the length is 2. Length Hours 15 3 20 4
Answer:
H = .2L; H = .4
Step-by-step explanation:
Ue can wash a car in 1 hour. steve can wash a car twice as fast as sue. how long will it take them to wash a car if they work together, but sue starts 30 minutes before steve?
There are 10 runners in race. in how many ways can the first, second and third place finishes occur
A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23/fts. The ball's height h (in feet) after t seconds is given by the following.
h=7+23t-16t^2
Find all values of t for which the ball's height is 15 feet.
Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)
As per quadratic equation, all values of 't' for which the ball's height is 15 feet are 33.25 and (- 31.813).
What is a quadratic equation?"Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x)."
Given, [tex]h = 15[/tex] feet.
Therefore, the quadratic equation for [tex]h = 15[/tex] will be:
A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23 feet per second.
The ball's height h (in feet) after t seconds is:
[tex]h = 7+23t-16t^{2}[/tex]
[tex]15 = 7+23t-16t^{2}[/tex]
⇒ [tex]15-7-23t+16t^{2} = 0[/tex]
⇒ [tex]16t^{2} -23t - 8 = 0[/tex]
⇒ [tex]t = [- (-23)[/tex] ± [tex]\sqrt{(23)^{2} - 4(16)(- 8)}[/tex] ]/(2 × 16)
⇒ [tex]t =[/tex] [23 ± 1041]/32
⇒ [tex]t =[/tex] [23 + 1041]/32, [23 - 1041]/32
⇒ [tex]t =[/tex] 33.25, - 31.813
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Mike wants to make meatloaf. His recipe uses a total of 6 pounds of meat. If he uses a 3 to 1 ratio of beef to pork how much pork will he use? Enter your answer as a mixed number in simplest terms
Mike will use 1 1/2 pounds of pork for his meatloaf recipe, which calls for a 3 to 1 ratio of beef to pork and a total of 6 pounds of meat.
Mike's meatloaf recipe has a total of 6 pounds of meat and uses a 3 to 1 ratio of beef to pork. To find out how much pork he will use, we can express the total amount of meat as the sum of beef and pork parts.
First, we know that there are 3 + 1 = 4 parts in total because of the given ratio. Since the ratio is 3 to 1, for every 4 parts of meat, 1 part is pork. Therefore, we calculate the weight of each part by dividing the total weight by the number of parts:
6 pounds ÷ 4 parts = 1.5 pounds per part
Since one part is pork, Mike will use 1.5 pounds of pork for his meatloaf. Expressed as a mixed number, that's 1 1/2 pounds of pork in simplest terms.
The amount of an ordinary $7,500.00 annuity for 3 years at 12 percent compounded quarterly is
Answer:
$180,997.50.
Step-by-step explanation:
1. On TABLE 14-1 Future Value of $1.00 Ordinary Annuity, select the periods row corresponding to the number of interest periods.
2. Select the rate-per-period column corresponding to the period interest rate.
3. Locate the value in the cell where the periods row intersects the rate-per-period column.
4. Multiply the annuity payment by the table value from step 3.
Future value = annuity payment × table value
FV = $7500.00 * 24.133 = $180,997.50
Which of the following are the coordinates of the vertex of y=3x^2+3?
PLEASE HELP ASAP ILL GIVE BRAINLIEST IF YOURE RIGHT!!
Find the greatest possible error for each measurement.
9 g
a.
1/2 g
b.
1/4 g
c.
1/6 g
d.
1/8 g
gpe = 1/2 of the unit measures
since 9 is a whole number the gpe would be 1/2 g
Solve 2x2 + 5x + 5 = 0. Round solutions to the nearest hundredth.
Rounded to the nearest hundredth, they are:
[tex]\[x_1 \approx -0.63 + 1.35i\][/tex]
[tex]\[x_2 \approx -0.63 - 1.35i\][/tex]
To solve the quadratic equation [tex]\(2x^2 + 5x + 5 = 0\)[/tex], we can use the quadratic formula:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
where [tex]\(a = 2\), \(b = 5\)[/tex], and [tex]\(c = 5\)[/tex].
Substituting the values into the quadratic formula:
[tex]\[x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 2 \cdot 5}}}}{{2 \cdot 2}}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{{25 - 40}}}}{{4}}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{{-15}}}}{{4}}\][/tex]
Since the discriminant [tex](\(b^2 - 4ac\))[/tex] is negative, the solutions will involve imaginary numbers.
Using the imaginary unit [tex]\(i\)[/tex], where [tex]\(i^2 = -1\),[/tex] we can rewrite [tex]\(\sqrt{{-15}}\)[/tex] as [tex]\(i\sqrt{{15}}\):[/tex]
[tex]\[x = \frac{{-5 \pm i\sqrt{{15}}}}{{4}}\][/tex]
So, the solutions to the equation [tex]\(2x^2 + 5x + 5 = 0\)[/tex] are complex numbers. Rounded to the nearest hundredth, they are:
[tex]\[x_1 \approx -0.63 + 1.35i\][/tex]
[tex]\[x_2 \approx -0.63 - 1.35i\][/tex]
These solutions represent the points where the graph of the quadratic equation intersects the x-axis. They lie on the complex plane.
Find the radius of a circle with an area of 615.75 sq kilometers?
area = pi x r^2
615.75 = 3.14 x r^2
r^2 = 615.75/3.14 =196.0987 round to 196.1
r = sqrt(196.1) = 14.00357 round to 14
radius = 14 kilometers
Shyla used a probability simulator to pull 3 colored marbles from a bag and flip a coin 50 times. The results are shown in the tables below:
16 blue
20 green
14 yellow
heads 18
tails 32
Using Shyla's simulation, what is the probability of pulling a blue marble and the coin landing tails up?
Answer:
512/2500
Step-by-step explanation:
If the length of side a is 6 centimeters, the length of side b is 4 centimeters, and the length of side c is 7 centimeters, what is the measure of ? Round your answer to two decimal places.
Answer:
34.77
Step-by-step explanation:
The area of a triangle with sides of length 6 cm, 4 cm, and 7 cm is approximately 11.95 cm² when calculated using Heron's formula and rounded to two decimal places.
The original question appears to be incomplete as there's no clear indication of which measure is being sought for the triangle with sides of length 6 cm, 4 cm, and 7 cm. However, if the goal is to use these sides to determine the area of a triangle, we can use Heron's formula, since the lengths given do not form a right triangle.
First, calculate the semiperimeter (s):
(s) = (a + b + c) / 2
(s) = (6 + 4 + 7) / 2
(s) = 17 / 2
(s) = 8.5 cm
Now, apply Heron's formula which is Area [tex](A) = \sqrt{[ (s)((s)-a)((s)-b)((s)-c) ][/tex]:
[tex]A = \sqrt{[8.5(8.5-6)(8.5-4)(8.5-7)]}\\A = \sqrt{[8.5(2.5)(4.5)(1.5)]}\\A = \sqrt{[8.5 \times 2.5 \times 4.5 \times 1.5]}\\A \approx 11.95 cm^2 after\ calculating\ the\ square\ root[/tex]
Thus the area of the triangle is approximately [tex]11.95 cm^2[/tex] (rounded to two decimal places). Note that the question's original instructions to round to two significant figures would result in an answer of [tex]12 cm^2[/tex].
Which symbol creates a true sentence when x equals 6? 42 + (x – 3)2 __ 28
how many solutions does this system have -3x+6y=10 -3x+6y= -4
A triangle has measurements of 39, 52, and 65 units. Is it a right triangle?
Yes
No
Not enough information to tell
The base of the parallelogram, b, can be found by dividing the area by the height. If the area of the parallelogram is represented by 6x2 + x + 3 and the height is 3x, which represents b, the length of the base
Answer:
[tex]2x+\frac{1}{3}+\frac{1}{x}=Base[/tex]
Step-by-step explanation:
Given: The area of the parallelogram is [tex]6x^2+x+3[/tex] and the height is 3x.
To find: The base of the given parallelogram.
Solution: It is given that The area of the parallelogram is [tex]6x^2+x+3[/tex] and the height is 3x.
Now, area of parallelogram is given as:
[tex]A=b{\times}h[/tex] where b is the base and h is the height of teh gievn parallelogram.
Substituting the given values, we have
[tex]6x^2+x+3=b{\times}3x[/tex]
⇒[tex]\frac{6x^2+x+3}{3x}=Base[/tex]
⇒[tex]\frac{6x^2}{3x}+\frac{x}{3x}+\frac{3}{3x}=Base[/tex]
⇒[tex]2x+\frac{1}{3}+\frac{1}{x}=Base[/tex]
which is the required expression for the base of the given parallelogram.
The length l of a rectangle is 4 inches greater than its width w. The area of the rectangle is 252 square inches.Using the method of completing the square, what are the length and width of the rectangle? Show your work.
Which expression is equivalent to (2x^4y)^3
The equivalent expression to the given expression is [tex]8x^12y^3[/tex].
We have given that,
The expression (2x^4y)^3
We have to determine the,
Which expression is equivalent to (2x^4y)^3
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
The answer is D.
2^3 is 8.
(x^4)^3 is x^12 and y^3 is simply y^3.
Put them together to get the final answer.
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I need help learning how to do these problems some how whenever I do them I always get it wrong please help I have a test Wednesday!
What's the slope of the line that passes through (2,14) and (-1,-1)?
Find the value of two numbers if their sum is 12 and the difference is 4
x+y=12
x-y=4
x=y-4
y-4+y=12
2y-4=12
2y=16
y=8
x=8-4=8
8+4=12
the 2 numbers are 8 & 4
An equilateral triangle and a square have the same perimeter of 12 inches. what is the ratio of the side length of the triangle to the side length of the square? express your answer as a common fraction.
Which has a greater area, a square with sides that are x - 1 units long or a rectangle with a length of x units and a width of x - 2 units?
PLEASE HELP
graph and completely describe the function f (x)= 4^x
I already graphed this on desmos
can someone please help?
Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589.
Which side has an equal measure to BC?
A.DE
B.AB
C.EF
D.DF
PLEASE HELP
In the given diagram, we are given two triangles, triangle ABC and triangle DEF.
And we are given a line or reflection l.
Triangle DEF is the mirror image of triangle ABC.
Therefore, all sides of the triangle ABC would be congruent to sides of triangle DEF.
AB = DF
AC = DE and
BC = EF.
We can see than BC is the smallest side of triangle ABC and EF is the smallest side of triangle DEF.
Therefore, correct option is C option.C.EF. The total cost of gasoline varies directly with the number of gallons purchased. Gas costs $1.77 per gallon. Write a direct variation to model the total cost c for g gallons of gas.
A . c=g/1.77
B. c=1.77g
C. g=1.77c
D. c=g+1.77