Answer:
the best interest rate would be a minimum of 3.5% annual interest
Step-by-step explanation:
An inflation rate of 3.5% would mean that the buying power of Lydia's money would decrease by 3.5% every single year. Therefore, the best interest rate would be a minimum of 3.5% annual interest. That way she would at least maintain the same buying power with her money as the day that she first placed it in the account. Any interest rate higher than 3.5% would be even better as Lydia will begin to make a profit from her savings.
A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $14 per linear foot to install and the farmer is not willing to spend more than $7000, find the dimensions for the plot that would enclose the most area. (Enter the dimensions as a comma separated list.)
Answer:
Width = 166.7 ft
Length = 250 ft.
Step-by-step explanation:
From the diagram at the ATTACHMENT
Let us denote the the length of the rectangular area as "x" and
the width of the rectangular area as "y"
Since, cost of the fence on the western side is shared with a neighbor, we can say it is $7 per foot. Otherwise, it is $14 per foot. The northern length is not fenced.
From the question, we know that the cost is not to exceed $7000, therefore we can expressed it as
7y + 14x + 14y = 7000
14x + 21y = 7000
Divide through by 14, we have
(x + 1.5) = 500 ------------- eqn (*)
But the area of the fenced
= A = (x×y) -------------- eqn (**)
Substitute (*) into (**) we have
A = (500 - 1.5y)*y
= 500y - 1.5y²
In other to maximize the Area, we can find the differential of A
A'(y) = 500 - 3y
At A'(y) = 0.
500-3y= 0
3y=500
y= 166.67 ft
From eqn(*)
(x+ 1.5) = 500
x = 500 - 1.5y
500-1.5(166.67)
= 250ft
Therefore, the dimensions for the plot that would enclose the most area are
Width of 166.67 ft and Length = 250 ft.
Jill would like an increase in the hourly wage she receives from the Mathematics Research Center, where she works in the mail room. Her boss gives her an equation to solve, telling her that her raise is the solution to the equation, but only if she can solve it. The equation is x 2- 6x + 9 = 0. What was the amount of her raise per hour? Answer:
Answer:
Jill will receive an increase of $3 per hour
Step-by-step explanation:
The Quadratic Equation
The quadratic equation can be represented in the standard form as:
[tex]ax^2+bx+c=0[/tex]
being a,b, and c are constants.
It can be solved by using the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Jill would like an increase in her hourly wage. The increase will come as the solution for a maths equation.
She must solve the equation:
[tex]x^2-6x+9=0[/tex]
The solution to the equation, or value of x, is the increase in her hourly wage.
Comparing with the general form, we have a=1, b=-6, c=9. Thus, the solutions are:
[tex]\displaystyle x=\frac{-(-6)\pm \sqrt{(-6)^2-4(1)(9)}}{2(1)}[/tex]
[tex]\displaystyle x=\frac{6\pm \sqrt{36-36}}{2}[/tex]
[tex]\displaystyle x=\frac{6\pm \sqrt{0}}{2}[/tex]
The square root is 0, therefore is only one solution:
[tex]\displaystyle x=\frac{6}{2}=3[/tex]
x = 3
Thus, her raise per hour is $3.
Pls anserw the pic attached below
Answer:
[tex]x=38[/tex]
Step-by-step explanation:
[tex]We\ are\ given\ that,\\\angle KLO=134\\\angle OMN= 84\\Hence\ we\ observe\ that,\\\angle KLO\ and\ \angle OLM\ form\ a\ linear\ pair\ and\ hence,\ are\ supplementary.\\Hence,\\\angle KLO\ + \angle OLM=180\\Substituting\ \angle KLO=134,\\134+\angle OLM=180\\\angle OLM=180-134\\\angle OLM=46\\Similarly,[/tex]
[tex]\angle OMN\ and\ \angle OML\ form\ a\ linear\ pair\ and\ hence,\ are\ supplementary.\\Hence,\\\angle OMN\ + \angle OML=180\\Substituting\ \angle OMN=84,\\84+\angle OLM=180\\\angle OLM=180-84\\\angle OLM=96\\[/tex]
[tex]Now\ lets\ consider\ \triangle OML,\\\angle OLM + \angle OML+ \angle LOM=180 [Angle\ Sum\ Property\ Of\ a\ triangle]\\Hence\ substituting\ \angle OLM=46, \angle OML=96, \angle LOM=x\\46+96+x=180\\142+x=180\\x=180-142\\x=38[/tex]
The diagram represents the enlargement of a rectangle by using a scale factor of 6.
A rectangle has a length of 30 feet and width of 6 feet.
What are the dimensions of the original rectangle?
Answer:
lenght of 5 feet and width of 1 feet
Step-by-step explanation:
30/6=5
6/6=1
Answer:
lenght of 5 feet and width of 1 feet
Step-by-step explanation:
30/6=5
6/6=1
Step-by-step explanation: like what that peson said! way to go and good luck on your test!
Please helppppppopppp
Answer:
a..
Step-by-step explanation:
Which of the following is not a solution of the equation y=3x-4?
A. 2,2
B. 0,-4
C. 4,8
D. -1,-1
SOMEONE PLZ HELP ME WIT THIS QUESTION
Answer:
25(x)= 200
Step-by-step explanation:
Total = 200
Per day = 25
x = how many days
25(x)= 200
25(8)= 200
- Sorry i am just a little confused by the question but i hope this helps. Have a great day!
Answer:
x+25=200
Step-by-step explanation:
) Buyers are charged a shipping fee of $4.75 for each scarf order.
Which expression can you use to find the total price of a scarf order?
Answer:
huh can you put the whole question?
Step-by-step explanation:
Put all the answers
Step-by-step explanation:
Find the value of x. Will give brainliest
Answer:
x = 11
Step-by-step explanation:
Angle CAB = 33 degrees (Z-figure)
Angle ACE = 180 degrees (line), therefore angle ACB = 180 - 5x.
Sum of all angles in the triangle should equate to 180 degrees.
Now the sum is of all angles in triangle ABC is:
CAB + ABC + ACB = 33 + (180 - 5x) + 2x = 213 - 3x
So 213 - 3x should equal 180.
213 - 3x = 180 <=> -3x = -33 <=> x = 11
human activities have drastic effects on biomes match the human activities with the biomes they primarily
Refer to - KLMN
2x
M
101
-3
2y
P
y + 3 cm
60°
К.
N
x + 4 cm
mZ1 + m22 =
Answer:
[tex]m∠1 + m∠2 = 180[/tex]
Step-by-step explanation:
[tex]m∠1 = m∠3 \\ m∠2 = m∠4[/tex]
[tex]m∠ 1 = m∠3 \\ 60 = 60[/tex]
[tex]360 - m∠1 + m∠3 = m∠2 + m∠4[/tex]
[tex]360 - 60 + 60 = m∠2 + m∠4[/tex]
[tex]360 - 2(60) = m∠2 + m∠4[/tex]
[tex]360 - 120 = m∠2 + m∠4[/tex]
[tex]240 = m∠2 + m∠4[/tex]
[tex] \frac{240}{2} = m∠2 = m∠4[/tex]
[tex]120 = m∠2 = m∠4[/tex]
[tex]m∠2 = 120 \\ m∠4 = 120[/tex]
[tex]m∠1 = 60 \\ m∠3 = 60[/tex]
[tex]m∠2 = 120 \\ m∠4 = 120[/tex]
[tex]m∠1 + m∠2 + m∠3 + m∠4 { = }^{?} 360[/tex]
[tex]60 + 120 + 60 + 120 { = }^{?} 360[/tex]
[tex]2(60) + 2(120) { = }^{?} 360[/tex]
[tex]120 + 240 { = }^{?} 360[/tex]
[tex]360 = 360[/tex]
[tex]m∠1 + m∠2 [/tex]
[tex]60 + 120 = 180[/tex]
[tex]m∠1 + m∠2 = 180[/tex]
please help!Thank you so much
Answer:
An equation is a math sentence that DOES contain an equals sign (=).
The inverse of addition is subtraction.
The inverse of subtraction is addition.
The inverse of multiplication is division.
The inverse of division is multiplication.
Step-by-step explanation:
I'm sorry if I got the first one incorrect.
Evaluate 15 squared show work
Answer:
225
Step-by-step explanation:
15x15=225
There is a cool trick you can do. Lets take 28 and square it.
First you round the number up. 28 rounded is 30. You rounded up by 2 (30-28=2) so you minus 2 from 28.
You are left with these two numbers, 26 and 30. Add a zero to the 26.
You now have 260 and 3 (you remove 0 on the 30 since you added it to the 26)
Then you multiply by 3.
260x3=780
Then you add the square of the number you rounded up too, which is 2.
You are left with this equation.
(2^2)+780= 784
28x28=784.
This works for numbers below 100 and integers
Factor the polynomial expression 16y4 − 256x12.
Step-by-step explanation:
Using Difference of Squares,
16y⁴ - 256x¹²
= 16(y⁴ - 16x¹²)
= 16(y² + 4x⁶)(y² - 4x⁶)
= 16(y² + 4x⁶)(y + 2x³)(y - 2x³).
Step-by-step explanation:
16y4-256×12=16.(y4-16×12)Find the probability of getting the color crewmate and the hat. Determine the probability for each question and write the code in the box below.
Answer:
Step-by-step explanation:
Probability of an event to occur (P) = [tex]\frac{\text{Favorable event}}{\text{Total outcomes}}[/tex]
1). Probability of getting the red crewmate,
[tex]P_1=\frac{3}{6}=\frac{1}{2}[/tex]
Probability of getting a chef hat,
[tex]P_2[/tex] = [tex]\frac{1}{8}[/tex]
Probability of getting the red crewmate and the chef hat = [tex]P_1\times P_2[/tex]
= [tex]\frac{1}{2}\times \frac{1}{8}[/tex]
= [tex]\frac{1}{16}[/tex]
2). Probability of getting blue crewmate,
[tex]P_1=\frac{2}{6}[/tex]
[tex]=\frac{1}{3}[/tex]
Probability of getting an egg hat,
[tex]P_2=\frac{2}{8}=\frac{1}{4}[/tex]
Probability to get the blue crewmate and an egg hat = [tex]P_1\times P_2[/tex]
= [tex]\frac{1}{3}\times \frac{1}{4}[/tex]
= [tex]\frac{1}{12}[/tex]
3). Probability of getting a green crewmate = [tex]\frac{1}{6}[/tex]
Probability of getting a banana hat = [tex]\frac{3}{8}[/tex]
Probability of getting a green crewmate and banana hat
= [tex]\frac{1}{6}\times \frac{3}{8}[/tex]
= [tex]\frac{1}{16}[/tex]
1
A. (f = g)(x) = 2 - 4
.
true or false
Answer:
=-2
Step-by-step explanation:
x=-(4-2)
Answer:
false
hope this helps
find the answer for 10 + 10
Answer:20
Step-by-step explanation:
At 5:00 p.m., Antonio turned on the oven. While the oven preheated, the temperature in the oven increased from 72°F to 400°F over a 10-minute period. The oven remained at 400°F for 45 minutes until Antonio turned it off. It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m. Which statement best explains whether or not the temperature in the oven is a function of the time?
Answer: It is a function because at any given time the oven was exactly one temperature.
Step-by-step explanation:
It is given that:
At 5:00 p.m., Antonio turned on the oven.
The oven remained at 400°F for 45 minutes until Antonio turned it off.
It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m.
Allison can work up to 35 hours per week. if she works 5 1/2 hours Monday, 6 hours on Tuesday, and 7 3/4 hours on Wednesday, how many more hours can she work during the week
Answer:
15 3/4
Step-by-step explanation:
this is simple addition and subtraction
hey im dum dum what's 45*23455/76?
Answer:
13887.8289474
Step-by-step explanation:
i used a calculator cuz im dum too lol
Answer:
45*23455/76 = 133887.82894736
Ramon earns $1,785 each month and pays $53.80 on electricity. To the nearest tenth of a percent, what percent of Ramon's earnings are spent on electricity each month?
Answer:
3.0%
Step-by-step explanation:
[tex](\frac{53.80}{1785}) * 100 = 3.01[/tex]
Tina's plans to make wooden fences To put heard to triangle art pieces In
How much wood would she need for triangle DFG
Answer:
54 feet.
Step-by-step explanation:
Consider AB and DF. FD is 3 times the size of AB
So if AC = 7 then DG = 3* 7 = 21
The total Perimeter = 15 + 18 + 21 = 54 feet
Answer:
well if the triangle are both equal comparisons just ones a different size then the unknown hunches of the bigger side would probably be 21 so if u add the 15 + 18 + 21 = 54 I think sorry if I'm wrong tho
The governor of state A earns $48,980 more than the governor of state B. If the total of their salaries is $289,660, find the salaries of each
Answer:
Governor of State B: $120,340; Governor of State A: $169,320
Step-by-step explanation:
For the sake of this problem, let's set the salary of State B's governor as x. That would make the salary of State A's governor equal to x+48980. The following lists out how to solve this problem.
Governor B salary + Governor A salary = $48980
x+x+48980=289660
2x+48980=289660
2x=240680
x=120340
120340+48980=169320
I just want ppl to check, extra points too!
Answer:
thats correct
Step-by-step explanation:
i had that on my test and i ot it right
-3(1)+(-3)(-1) =
+()]
-3(1) + (-3)(-1)=-3[0]
-3(1)+(-3)(-1) =
_
+(-3)(-1) =
+
Answer:
³⅜
Step-by-step explanation:
⁴⁵⅖
+⁷⅝×⅖i
I HOPE IT HELP TYSM
Answer:
i dunno
Step-by-step explanation:
1. A certain manufacturing process to build phone batteries results in the production of defective batteries at a rate of 5% (0.05). Suppose that 10 batteries are produced. a. Find the expected number of defective batteries. b. Find the variance and standard deviation in the number of defective batteries. c. Find the probability that at least 1 battery is defective.
Answer:
0.5 ; 0.475 ; 0.689 ; 0.4013
Step-by-step explanation:
Given that:
Rate of production of defective batteries p = 0.05
Number of batteries produced (n) = 10
The expected number of defective batteries = mean = n * p = 10 * 0.05 = 0.5 batteries
Variance of defective batteries :
Var(X) = n * p * q ; q = 1 - p
Hence,
Var(X) = 10 * 0.05 * 0.95 = 0.475
Standard deviation (X) = sqrt(variance) = sqrt(0.475) = 0.689
Probability that atleast 1 battery is defective :
Using the binomial probability function
P(x ≥ 1) = 1 - p(x = 0)
= 1 - q^n
= 1 - 0.95^10
= 1 - 0.59873693923837890625
= 0.40126306076162109375
= 0.4013
HELP WHATS THE ANSWER
Answer:
The answer is 0, hope this helps
hii pls answer as quickly as possible i will give you the brainliest :))
Answer:
sorry
Step-by-step explanation:
I really don't know answer
My head is hurting can you help me
It’s 16 points
Answer:
-6, -4
Step-by-step explanation:
If you flip the shape over the Y axis you can see
find the length of segment cd, given ab is congruent to cd