Answer:
$0.26
Step-by-step explanation:
To find the unit price, divide the cost by the amount you have.
$2.86/11 = $0.26
The unit price is $0.26.
The half-life of radioactive iodine is 60 days. How much of a 50-mg sample will be left in 40 days? Round your answer to the nearest tenth.
Answer:
Remaining amount of the element = 31.5 mg
Step-by-step explanation:
Half life of radioactive Iodine is [tex](T_{\frac{1}{2}})[/tex] = 60 days
Formula to get the remaining element after t days is,
[tex]N=N_0(e)^{\lambda.t}[/tex]
Where [tex]\lambda[/tex] = decay constant of the radioactive element
t = duration of the decay (in days)
[tex]N_0[/tex] = Initial amount of the element
N = final amount after decay
For half life period 't' = 60 days
[tex]\frac{N_0}{2}=N_0(e)^{\lambda\times 60}[/tex]
[tex]e^{60\lambda}=0.5[/tex]
[tex]ln(e^{60\lambda})=ln(0.5)[/tex]
[tex]60\lambda =-0.069315[/tex]
[tex]\lambda=-0.0115524[/tex]
Remaining amount of the element after 40 hours,
N = [tex]50(e^{40\lambda} )[/tex]
= [tex]50(e)^{-(0.0115524)\times 40}[/tex]
= 50(0.62996)
= 31.49
≈ 31.5 mg
Therefore, remaining amount of the element after 40 days is 31.5 mg.
Answer:
In 40 days, there would be approximately 31.5 mg remaining.
Step-by-step explanation:
Monica’s school band held a car wash to raise money for a trip to a parade in New York City. After washing 125 cars, they made $775 from a combination of $5.00 quick washes and $8.00 premium washes. This system of equations models the situation. x + y =125 5x + 8y = 775
Answer:
The number of car they did quick wash is 75 and the number of car they did premium washes is 50 .
Step-by-step explanation:
The number of cars they washed is equals to 125 cars. They made a total of $775 from the wash. The wash is in two category the quick washes which is $5 and the premium washes which is $8.
Let
number of car for quick washes = x
number of car for premium washes = y
Base on the equation given below
x + y =125 .........(i)
5x + 8y = 775 .......(ii)
Let us find x and y
from equation (i)
y = 125 - x
inserting the value of y in equation (ii)
5x + 8(125 - x) = 775
5x + 1000 - 8x = 775
-3x = -225
divide both sides by -3
x = -225/-3
x = 75
insert the value of x in equation (i)
75 + y =125
y = 125 -75
y = 50
The number of car they did quick wash is 75 and the number of car they did premium washes is 50 .
Answer:
The Answer is A
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Point C is on the graph of the function y = x2 – 3. Its x-coordinate is 4. Which ordered pair gives the location of point C? A.(4, 42 – 3) B.(4, 2 + 3) C.(42, 42 – 3) D.(4, 42)
Answer:
B (4, 2+3)
Step-by-step explanation:
To do this you fill in x with 4 so the equation becomes y = (4)2 - 3
You then solve to y = 8 - 3
then 8 - 3 is 5.
Making the coordinates (4, 5) and in this case with the answers (4, 2+3)
Answer:
A. (4, 4^2 – 3)
Find the critical point of the given function and then determine whether it is a local maximum, local minimum, or saddle point.
Answer:
critical point of the given function f(x,y) = x²+y²+2xy is from line y = -x is the critical point of the function f(x0,y0) = 0
and it local minimum.
Step-by-step explanation:
Let the given function be;
f(x,y) = x²+y²+2xy
From above function, we can locate relative minima, maxima and the saddle point
f(x,y) = x²+y²+2xy = (x+y)²
df/dx = 2x+2y = 0 ---- (1)
df/dy =2y+2x = 0 ---- (2)
From eqn 1 and 2 above,
The arbitrary point (x0,y0) from line y = -x is the critical point of the function f(x0,y0) = 0
Then, from f(x,y) >= 0 for arbitrary (x,y) € R^n, the arbitrary point from the line x = -y is local minima of the function f.
Find the solution(s) of the system of equations: x2 + y2 = 8 y = x – 4 options: (–2,–6) (2,–2) and (–2,–6) (2,–2) No solutions
Answer: x=2 y=-2
(2,-2) one solution
Step-by-step explanation:
Solve by substitution
[tex]\begin{bmatrix}x^2+y^2=8\\ y=x-4\end{bmatrix}[/tex]
[tex]\mathrm{Subsititute\:}y=x-4[/tex]
[tex]\begin{bmatrix}x^2+\left(x-4\right)^2=8\end{bmatrix}[/tex]
[tex]2x^2-8x+16=8[/tex]
[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:2x^2-8x+16=8:\quad x=2[/tex]
[tex]\mathrm{For\:}y=x-4[/tex]
[tex]\mathrm{Subsititute\:}x=2[/tex]
[tex]y=2-4[/tex] [tex]2-4=-2[/tex]
[tex]y=-2[/tex]
[tex]The\:solutions\:to\:the\:system\:of\:equations\:are[/tex]
[tex]x=2,\:y=-2[/tex]
The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.
a. Determine the amount to be financed.15a. _______________
b. Determine the installment price.b. _________________
c. Determine the finance charge.c. _________________
Answer:
see details below
Step-by-step explanation:
The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.
a. Determine the amount to be financed.15a. ___$23450____________
29450 - 6000 = 23450
b. Determine the installment price.b. ___$792,22______________
"monthly payment of $792.22"
c. Determine the finance charge.c. __$5069.92_______________
A = 792.22
n = 36
finance charge = total paid - amount to be financed
= 36*792.22 - 23450
= 5069.92
A graph shows an x- and y-axis. The data line is in the shape of a "vee." The begins above the x-axis and to the left of the y-axis, extends below the x-axis to a point on the y-axis, and ascends above the x-axis to the right of the y-axis. Which statement describes the relationship between x and y? As x increases, y decreases. As x increases, y increases. As x increases, y increases and then decreases. As x increases, y decreases and then increases.
Answer:
As x increases, y decreases and then increases
Step-by-step explanation:
You need only understand your own description of the graph:
begins above the x-axis, extends below the x-axis, and ascends above the x-axis
This is a description of decreasing, then increasing:
As x increases, y decreases and then increases
Answer:
C. As x increases, y increases and then decreases.
Step-by-step explanation:
Just took the Unit Test and got it correct on Edge.
Assume that y varies directly with
x, then solve.
If y=2when x=, find y when x=1
y =
PLZ IM ON THE CLOCK!!!!! A sports memorabilia store makes $6 profit on each football it sells and $5.50 profit on each baseball it sells. In a typical month, it sells between 35 and 45 footballs and between 40 and 55 baseballs. The store can stock no more than 80 balls total during a single month. What is the maximum profit the store can make from selling footballs and baseballs in a typical month? $457.50 $460.00 $462.50 $572.50
Answer:
460
Step-by-step explanation:
Answer:
460
Step-by-step explanation:
In order to sustain itself in its cold habitat, a Siberian tiger requires 25 pounds of meat per day.
How much meat would seven Siberian tigers need for the month of April?
Select one:
a. 750 pounds
b. 175 pounds
c. 5425 pounds
d. 5250 pounds
Answer:
the answer is 750 because there are 30 days in the month of april and you just need to multiply it by how much meat they need to have per day.
Step-by-step explanation:
30 x 25 = 750
what is 1 plus 90876543579645968765443223456789009876543212345678909876543
Answer: 9.0876544e+58
Step-by-step explanation:
Answer:
90876543579645968765443223456789009876543212345678909876544
Step-by-step explanation:
90876543579645968765443223456789009876543212345678909876543
+
1
=
90876543579645968765443223456789009876543212345678909876544
Susan and Mark are given the same amount of money. Mark spends $5 and susan spends $20. If Mark now has twice as much money as Susan , how many dollars did they each have originally ?
so amnt of money is x
x - 5 is Mark's remaining amnt
x - 20 is Susan's remaining amount
x - 5 = 2( x - 20) as he has twice the amnt of Susan
x - 5 = 2x - 40
40 - 5 = 2x - x
35 = x
the original amnt is $35
solve and give answer in surd form
√7 /1+1/√2
Answer:
Step-by-step explanation:
√7 /1 + 1/√2
= √7 + √2 / 2
What is the cost of a $1, 200 washing machine after a discount of ⅕ the original price?
Answer:
$960
Step-by-step explanation:
A shortcut method.
If you get a discount of 1/5, then that means you would end up paying 4/5 of the whole cost. That means all you have to do then is plug in what it costs, which in this case is 1200, and then multiply it by 4/5, so you end up with $960.
Answer:
$960
Step-by-step explanation:
1200*1/5 = 240
1200 - 240 = $960
Would appreciate brainliest!! But it's ok if not
Let A = {H, T} be the set of outcomes when a coin is tossed, and let B = {1, 2, 3, 4, 5, 6} be the set of outcomes when a die is rolled. The set of outcomes when a coin is tossed twice. Write the set in terms of A and/or B. A ∩ B A × A A × B A ∪ B List the elements of the set.
Answer:it is 6 trust
Step-by-step explanation:yah know
Fill in the blank. A _______ variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.
Answer:
Random variable
Step-by-step explanation:
The reason it is a random variable is because a, the definition fits, and b you can use context clues as well, such as 'determined by chance' which is another example of random! So, the answer is random, because random variables are determined by chance. Hope this helped.
Answer:
"A random variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure."
A random variable is distinct on the off chance that it takes on a countable number of quantities.
Look at this triangle work out length AB
Answer:
2√137
Step-by-step explanation:
To find AB, we can use the Pythagorean Theorem (a² + b² = c²). In this case, a = 22, b = 8 and we're solving for c, therefore:
22² + 8² = c²
484 + 64 = c²
548 = c²
c = ± √548 = ± 2√137
c = -2√137 is an extraneous solution because the length of a side of a triangle cannot be negative, therefore, the answer is 2√137.
PLEASE HELP ASAP!!!!Write the ratio as a fraction in lowest terms. 9 pounds to 36 pounds.(50 points!!)
Answer:
1/4
Step-by-step explanation:
9 lbs
---------
36 lbs
We can write this because the units are the same
Divide the top and bottom by 9
9/9
----------
36 /9
1/4
Answer:
1/4
Step-by-step explanation:
9 pounds
36 pounds
Ratios are written as x:y, fractions are written as x/y.
9:36 as a fraction will be 9/36
Simplify the fraction.
1/4
From al-Khowarizmi's Algebra: Ten dinar is divided equally among a group of men so that when 6 more men are added to their number and 40 dinar is divided equally among them, then each receives as much as he did previously. Find the original number of men.
Answer:
The original number of men is 2
Step-by-step explanation:
Let the number of men be x
The amount each of the men will receive from the ten dinar since they all received equal amounts will be 10/x
Now, adding 6 more men, we have a total of x + 6 men now
Now we share 40 dinar amongst the x + 6 men and each will receive 10/x as received before
Mathematically;
40/x + 6 = 10/x
x(40) = 10(x + 6)
40x = 10x + 60
40x -10x = 60
30x = 60
x = 60/30
x = 2
There were originally 2 men
At an assembly, 180 students sit in 9 equal rows. How many students sit in each row?
Answer:
20 students per row
Step-by-step explanation:
person per each row=180/9=20
Answer:
20
Step-by-step explanation:
Take the number of students and divide by the number of students
180/9
20
There are 20 students in each row
Which expression is equivalent to 486 – 9 + 6 + 33 × 2?
Answer:
549
Step-by-step explanation:
Remember PEMDAS (this is the order of operations).
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
So, lets do multiplication first.
33*2 = 66
So, our new expression is 486 - 9 + 6 + 66.
Remember that addition and subtraction are reversible.
486 - 9 = 477
477 + 6 = 483
483 + 66 = 549
Answer:
404
Step-by-step explanation:
P-parenthesis
E-exponents
M-multiplication
D-division
A-addition
S-subtraction
486-9+6+33*2
486-9+6+66
486-81=404
Which of the following triangles can be proven similar through AA?
A)
B)
C)
D)
Answer:
The options that have two angles, which are A and D prove both triangles to be similar.
Step-by-step explanation:
The postulate AA is exactly what it sounds like, and you can find the two angles, which will prove the similarity of two triangles sharing those two angles.
The reason being is if two angles are the same between the two triangles, the third can't be different.
A construction crew is lengthening a road. The road started with a length of 56 miles, and the crew is adding 3 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D. Then use this equation to find the total length of the road after the crew has worked 33 days.
Answer:
Below
Step-by-step explanation:
The initial length of the road was 56. 56 is the y-intercept assuming that the graph of this function is a line.
so the equation is:
y= mx+56
m is the slope of the function wich is by how much the function grows.
By analogy, m is the distance added to the road each day.
● y= 3x+56
X is the number of days.
■■■■■■■■■■■■■■■■■■■■■■■■■■
To find the length of the road after 33 days, replace x by 33.
y= 3*33+56 = 155
So after 33 days the road is 155 miles.
Solve the equation and give the solution 6x – 3y = 3 –2x + 6y = 14
Answer:
x=3.9 or 39/10 and y=3.13333 or 47/15
Step-by-step explanation:
Since both expressions (6x-3y) and (3-2x+6y) are equal to 14, separate the equations:
6x-3y=14 and 3-2x+6y=14
Simplify the equations
6x-3y=14 and -2x+6y=11
Now, line the equations up and pick a variable (either x or y) to eliminate
6x-3y=14
-2x+6y=11
In this case, let's eliminate y first. To do so make the y values in both equations the same but with opposite signs. Make both be 6y but one is +6y and the other -6y
Multiply (6x-3y=14) by 2 to get:
12x-6y=28
Line the equations up and add or subtract the terms accordingly
12x-6y=28
-2x+6y=11
This becomes:
10x+0y=39
Isolate for x
x= 39/10 or x= 3.9
Now substitute the x value into either of the original equations
6x-3y=14
6(3.9)- 3y=14
Isolate for y
23.4-14=3y
3y= 9.4
y= 3.1333 (repeating) or y= 47/15
Answer: x = 39/10, y = 94/30
Step-by-step explanation:
6x - 3y = 3 - 2x + 6y,
Now solving this becomes
6x + 2x -3y - 6y = 3
8x - 9y = 3 ------------------- 1
3 - 2x + 6y. = 14
-2x + 6y = 14 - 3
-2x. + 6y = 11
Now multiply both side by -1
2x. - 6y = -11 ----------------- 2
Solve equations 1 & 2 together
8x - 9y. = 3
2x - 6y = -11
Using elimination method
Multiply equation 1 through by 2 ,and equation 2 be multiplied by 8
16x - 18y = 6
-16x - 48y = -88 ------------------------- n, now subtract
30y = 94
Therefore. y = 94/30.
Now substitute for y in equation 2
2x - 6y = -11
2x - 6(94/30) = -11
2x - 94/5 = -11
Now multiply through by 5
10x - 94 = -55
10x = -55 + 94
10x = 39
x = 39/10
Find the measures of the angles in the figure.
Answer:
[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]
which agrees with the first answer in the list of possible options.
Step-by-step explanation:
We can use the fact that the addition of all four internal angles of a quadrilateral must render [tex]360^o[/tex]. Then we can create the following equation and solve for the unknown "h":
[tex]2h+2h+h+h = 360^o\\6h=360^o\\h=60^o[/tex]
Therefore the angles of this quadrilateral are:
[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]
Answer:60,60,120,120
Step-by-step explanation:All qualdrilaterals equal to 360, so if you add all of the different numbers you should get 360
A cube 4 units on each side is composed of 64 unit cubes. Two faces of the larger cube that share an edge are painted blue, and the cube is disassembled into 64 unit cubes. Two of the unit cubes are selected uniformly at random. What is the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces?
Answer:
P = 0.0714
Step-by-step explanation:
If two faces of the larger cube that share and edge are painted blue, it means that 28 of the 64 unit cubes are painted in at least one side and 36 cubes have no painting faces.
Additionally, from the 28 cubes painted only 4 have exactly two painted faces.
Then, to calculate the number of ways in which we can select x elements from a group of n, we can use the following equation:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces is:
[tex]P=\frac{4C1*36C1}{64C2}=0.0714[/tex]
Because there are 64C2 ways to select 2 cubes from the 64, and from that, there are 4C1*36C1 ways to select one cube with exactly two painted faces and one cube with no painted faces.
Please help. What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?
Answer:
y = 3x + 4
Step-by-step explanation:
We can use the equation y = mx + b to find the equation:
Plug in the slope and the point into the equation, and we can find b:
-5 = 3(-3) + b
-5 = -9 + b
4 = b
Now, we can plug in the slope and y-intercept into the equation:
y = 3x + 4 will be our equation
23. Stacie is a resident at the medical facility where you work. You are asked to chart the amount of solid food that she consumes. For the noon meal, today, she ate 1/2 of a 3-ounce serving of meatloaf, 3/4 of her 3-ounce serving of mashed potatoes, and 1/3 of a 2-ounce serving of green beans. Show, in decimal form, how many ounces of solid food that Stacie consumed. Round two decimal places for final answer.
Answer:
4.42 ounces
Step-by-step explanation:
Given:
The solid food Stacie has eaten in the noon meal:
1. [tex]\frac{1}2[/tex] of a 3-ounce serving of meatloaf.
2. [tex]\frac{3}4[/tex] of her 3-ounce serving of mashed potatoes
3. [tex]\frac{1}3[/tex] of a 2-ounce serving of green beans
To find:
How many ounces of solid food was consumed by Stacie (upto 2 decimal places) ?
Solution:
Let us convert the given fractions to decimal form upto 2 decimal places:
1. [tex]\frac{1}{2}\ of\ 3\ ounces[/tex] [tex]= \frac{1}{2}\times 3 =1.50\ ounces[/tex] meatloaf .
2. [tex]\frac{3}{4}\ of\ 3\ ounces[/tex] [tex]= \frac{3}{4}\times 3 =2.25\ ounces[/tex] mashed potatoes .
3. [tex]\frac{1}{3}\ of\ 2\ ounces[/tex] [tex]= \frac{1}{3}\times 2 =0.67\ ounces[/tex] green beans.
Let us add the above 3 quantities to get total solid food consumed.
Total solid food consumed = 1.50 + 2.25 +0.67 = 4.42 ounces.
So, the answer is 4.42 ounces.
A study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed. The sample average age was 24.2 with a standard deviation of 3.7. The p-value is
Answer:
The p-value is 2.1%.
Step-by-step explanation:
We are given that a study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed.
The sample average age was 24.2 with a standard deviation of 3.7.
Let [tex]\mu[/tex] = true average age a "child" moves permanently out of his parents' home in the United States.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 23 {means that the average age a "child" moves permanently out of his parents' home in the United States is at most 23}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 23 {means that the average age a "child" moves permanently out of his parents' home in the United States is greater than 23}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average age = 24.2
s = sample standard deviation =3.7
n = sample of U.S. Adults = 43
So, the test statistics = [tex]\frac{24.2-23}{\frac{3.7}{\sqrt{43} } }[/tex] ~ [tex]t_4_2[/tex]
= 2.127
The value of t-test statistics is 2.127.
Now, the p-value of the test statistics is given by;
P-value = P( [tex]t_4_2[/tex] > 2.127) = 0.021 or 2.1%
Ash Lee bought a new Brunswick boat for $17,000. He made a $2,500 down payment on it. The bank's loan was for 60 months. Finance charges totaled $4,900. His monthly payment is:
Answer: $323.33
Step-by-step explanation:
($17,000 + $4,900 - $2,500) ÷ 60 months = $323.33 per month
↓ ↓ ↓
price finance down payment