Hello.
y<-1
The sign "<" means "less than"
The solutions of the inequality are less than -1.
For example, -2 is a solution of the inequality (it makes the inequality true)
The numbers that don't make the inequality true are greater than -1.
For example, let's take 3.
3 is greater than -1.
Plug it into the inequality:
3<-1
As we can see, we have a false statement.
Therefore, the answer is:
[tex]\mathrm{Numbers\:greater\:than\:-1\:aren't\:solutions}[/tex]
I hope this helps.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
Zoe invested $5,500 in an account paying an interest rate of 8 1/2% compounded continuously. Aubrey invested $5,500 in an account paying an interest rate of 8 1/4% compounded annually. To the nearest dollar, how much money would Aubrey have in her account when Zoe's money has doubled in value?
Answer:
Audrey will have $10,498.10 when Zoe's money has doubled in value.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra II
Natural Logs and Exponentials
Compounded Continuously Interest Rate Formula: [tex]\displaystyle A = Pe^{rt}[/tex]
P is the principle amountr is the interest ratet is timeCompounded Annually Interest Rate Formula: [tex]\displaystyle A = P(1 + r)^t[/tex]
P is the principle amountr is the interest ratet is timeStep-by-step explanation:
Step 1: Define
Identify.
Zoe:
P = $5,500
r = 0.085
A = 2P
Aubrey:
P = $5,500
r = 0.0825
Step 2: Find Time
Find time elapsed by using Zoe.
Substitute in variables [Compounded Continuously Interest Rate]: [tex]\displaystyle 2P = 5500e^\big{0.085t}[/tex]Substitute in P: [tex]\displaystyle 2(5500) = 5500e^\big{0.085t}[/tex]Simplify: [tex]\displaystyle 2 = e^\big{0.085t}[/tex]Isolate t term: [tex]\displaystyle \ln 2 = 0.085t[/tex]Isolate t: [tex]\displaystyle t = \frac{\ln 2}{0.085}[/tex]So the time it takes for Zoe to get double her money is approximately 8.15467 years.
Step 3: Find Audrey's Money
Substitute in variables [Compounded Annually Interest Rate]: [tex]\displaystyle A = 5500(1 + 0.0825)^\big{\frac{\ln 2}{0.085}}[/tex]Evaluate: [tex]\displaystyle A = 10498.10[/tex]∴ after the elapsed time of approximately 8.15467 years, Zoe would have made double her money valued at $11,000 and Audrey would have made $10,498.10.
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Topic: Algebra II
Unit: Logarithmic Functions
please hurry A side of the triangle below has been extended to form an exterior angle of 133°. Find the value of xx.
Solution:
Note that:
x + 108 + (180 - 133) = 180Simplify the equation to find x.
=> x + 108 + (180 - 133) = 180=> x + 108 + (47) = 180=> x + 155 = 180=> x = 180 - 155 = 25°→ x + 108 + (180 - 133) = 180°
→ x + 108 + (47) = 180°
→ x + 155 = 180°
→ x = 180 - 155 = 25°
Can you guys please help me slove this question? 6w-15w-19=91
Answer:
-12.2 rounded
Step-by-step explanation:
Combine like terms.
Move constants to one side of equal sign
divide
6w-15w-19 =91 combine like terms
-9w-19 = 91 add 19 to both sides
-9w = 110 divide by -9
w = -12.2 repeating or 12.2
Hey guys so I am struggling on this one question and I need your guys help!
6/7 x 2 14/27 = ???
Answer:
[tex]\sf 2\frac{10}{63}[/tex]
steps:
[tex]\sf \frac{6}{7} *2\frac{14}{27}[/tex]
convert into mixed fraction
[tex]\sf \frac{6}{7}\cdot \frac{68}{27}[/tex]
multiply both fractions
[tex]\sf \frac{6\cdot \:68}{7\cdot \:27}[/tex]
simplify the fraction
[tex]\frac{408}{189}[/tex]
final answer in improper fraction
[tex]\sf \frac{136}{63}[/tex]
convert in mixed fraction
[tex]\sf 2\frac{10}{63}[/tex]
Find the values of x and y. Write your answers in simplest form
Answer:
x = 12√3
y = 12
Step-by-step explanation:
=>> x/24 = perpendicular/hypotenuse
=>> x/24 = sin 60°
=>> x/24 = √3/2
=>> x = 24√3/2
=>> x = 12√3
now the value of y
=>> y/24 = cos 60°
=>> y/24 = 1/2
=>> y = 12
If Carly has 3 apples and she eats 2 of them how many apples does she have left
Answer:
SHE HAS ONLY HAS 1 LEFT
Step-by-step explanation:
3 - 2 = 1
I WILL GIVE BRAINLIEST PLEASE ANSWER CORRECTLY Mr. and Mrs. Bailey hope to send their son to college in eleven years. How much money should they invest now at an interest rate of 9% per year, compounded continuously, in order to be able to contribute $7500 to his education? Do not round any intermediate computations, and round your answer to the nearest cent.
Mr. and Mrs. Bailey need to invest $2906.50 for eleven years so as to be able to contribute $7500 their son education.
Compound interestCompound interest is given by:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where A is the final amount, P is principal, r is the rate and n is the times compounded per year, t is the time
Given that t = 11, n = 1, r = 9% = 0.09, A = $7500 . Hence:
[tex]7500=P(1+\frac{0.09}{1} )^{1*11}\\\\P=\$2906.50[/tex]
Mr. and Mrs. Bailey need to invest $2906.50 for eleven years so as to be able to contribute $7500 their son education.
Find out more on Compound interest at: https://brainly.com/question/24924853
Find t′(x) from t(x)=√(−3x−7) using the definition of a derivative.
By definition of the derivative,
[tex]\displaystyle t'(x) = \lim_{h\to0} \frac{t(x+h) - t(x)}h[/tex]
[tex]\displaystyle t'(x) = \lim_{h\to0} \frac{\sqrt{-3(x+h)-7} - \sqrt{-3x-7}}h[/tex]
Rationalize the numerator by multiplying the fraction uniformly by its conjugate:
[tex]\displaystyle t'(x) = \lim_{h\to0} \frac{\sqrt{-3(x+h)-7} - \sqrt{-3x-7}}h \times \dfrac{\sqrt{-3(x+h)-7} + \sqrt{-3x - 7}}{\sqrt{-3(x+h)-7} + \sqrt{-3x - 7}}[/tex]
[tex]\displaystyle t'(x) = \lim_{h\to0} \frac{\left(\sqrt{-3(x+h)-7}\right)^2 - \left(\sqrt{-3x-7}\right)^2}{h \left(\sqrt{-3(x+h)-7} + \sqrt{-3x - 7}\right)}[/tex]
[tex]\displaystyle t'(x) = \lim_{h\to0} \frac{(-3(x+h)-7) - (-3x-7)}{h \left(\sqrt{-3(x+h)-7} + \sqrt{-3x - 7}\right)}[/tex]
[tex]\displaystyle t'(x) = \lim_{h\to0} \frac{-3h}{h \left(\sqrt{-3(x+h)-7} + \sqrt{-3x - 7}\right)}[/tex]
[tex]\displaystyle t'(x) = -3 \lim_{h\to0} \frac1{\sqrt{-3(x+h)-7} + \sqrt{-3x - 7}}[/tex]
The remaining limand is continuous at h = 0, so we can substitute h = 0 directly and get a limit/derivative of
[tex]\displaystyle t'(x) = -\frac3{\sqrt{-3(x+0)-7} + \sqrt{-3x - 7}} = \boxed{-\frac3{2\sqrt{-3x-7}}}[/tex]
HELP PLEASE JUST THIS QUESTION/ ILL GIVE BRAINLIEST IF CORRECT
Answer:
She earned $288 this week
Step-by-step explanation:
x = 12
Work = 2(12) + 8
24 + 8 = 32 hours
Earned = (12) - 3 = 9 per hour
32 × 9 = $288
I hope this helps!
Solve cos theta=- sqrt (3)/2 on [0, 2pi) Write the first solution or lowest on [0, 2pi) . Round to the nearest hundredth .
Answer:
2.62 radians
Step-by-step explanation:
The angle is found from its cosine using the inverse cosine function.
cos(θ) = (-√3)/2
θ = arccos((-√3)/2) = 5π/6 ≈ 2.62 . . . radians
Instructions for a craft project say that the length of a piece of red ribbon should be 7 inches less than the length of a piece of blue ribbon. How long is the blue ribbon if the red ribbon is 12 inches?
Answer:
12 inches of red ribbon + 7 inches
therefore the length of a blue ribbon is = 19 inches
Answer:he right
Step-by-step explanation:
The conditional relative frequency table was generated using data that compares the number of boys and girls who pack their lunch or buy lunch from the cafeteria. A 4-column table with 3 rows. The first column has no label with entries boys, girls, total. The second column is labeled cafeteria with entries 0. 44, 0. 4, 0. 42. The third column is labeled pack with entries 0. 56, 0. 6, 0. 58. The fourth column is labeled total with entries 1. 0, 1. 0, 1. 0. 35 total girls and 50 total boys were surveyed. How many students bought their lunch from the cafeteria? Round to the nearest whole number. Students.
Answer:
734y 87tt795795708 679 ft
Answer:
I don't know
Step-by-step explanation:
Factor x3 x2 x 1 by grouping. What is the resulting expression?.
The factors of the equation [tex]\rm x^3+x^2+x+1\\\\[/tex] are [tex]\rm (x^2 +1)(x +1)[/tex].
What are the factors?
A factor is a number that divides another number leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
Given
The equation is;
[tex]\rm x^3+x^2+x+1[/tex]
The factors of the equation are given by;
[tex]\rm = x^3+x^2+x+1\\\\ = x^2(x +1) + 1( x +1 )\\\\= (x^2 +1)(x +1)[/tex]
Hence, the factors of the equation [tex]\rm x^3+x^2+x+1\\\\[/tex] are [tex]\rm (x^2 +1)(x +1)[/tex].
To know more about factors click the link given below.
https://brainly.com/question/2315299
Jimmy jogged for a total of 6.8 miles last week. How many feet did Jimmy jog last
week? (1 mile - 5,280 feet)
Answer:
35904 ft
Step-by-step explanation:
We can set up an unit converter to find how many feet Jimmy jogged...
[tex]6.8 mi(\frac{5280ft}{1mi})[/tex]
Note that in this case, the miles (units) cancel out leaving us with:
[tex]6.8*5280ft=35904\ ft[/tex]
Solve the proportion for x.
x/15 = x+3/24
Answer:
Step-by-step explanation:
15(x + 3) = 24x
15x + 45 = 24x
45 = 9x
5 = x
1,5,9,13 generalize the pattern by finding the nth term
Answer:
an= a1 +(n-1)*4
Step-by-step explanation:
a1 = 1, a2 =5, a3 = 9, a4= 13,... an= ?
we see that each term is getting bigger so usually that will happen because of addition or multiplication-in our case add 4 to previous term
a1 = 1,
a2 = a1+(2-1) 4 = 1+4 = 5,
a3 = a1 + (3-1)*4 = a1+8 = 1 + 8 = 9,
a4= a1 + (4-1)*4 = a1 + 12 = 1+12= 13,
...
an= a1 +(n-1)*4
Find the value of x in the triangle shown below
Answer:
48 (i might be wrong)
Step-by-step explanation:
180-66-66=48
1. 660
2. 330
3. 275
4. 550
Answer:
330m²Step-by-step explanation:
The area of a trapezoid is found using the formula, A = ½ (a + b) h
so
½(41 + 19) × 11 =
½ 60 × 11 =
30 × 11 =
330 m²
Write 0.0045% as a decimal
Answer:
0.0045%
Step-by-step explanation:
0.0045 is not a fraction so it is a decimal already.
Answer:
0.000045
Step-by-step explanation:
good luck!
These questions are so confusing. Please help. You get 15 points.
Answer:
13,260.22 mm²
Step-by-step explanation:
the area of the shaded region is the area of the larger circle minus the area of the smaller one
to find the area of the larger we will use half of 62 plus 41 as the radius:
Area (larger) = 3.14(72)²
= 16,277.76
Area (smaller) = 3.14(31)²
= 3,017.54
Area (shaded region) is 16277.76 - 3017.54 = 13,260.22 mm²
Find the value of x
Answer:
85 degrees
Step-by-step explanation:
7: 180 - 52 - 43 = 85 degrees
6. It takes one hour longer to fill the empty pool when only the input pipe is open than it takes to empty the filled pool when only the drain pipe is open. It takes 72 hours to empty the filled pool when both pipes are open. How many hours does it take to fill the empty pool when only the input pipe is open
Using the together rate, it is found that it takes 144.5 hours to fill the empty pool when only the input pipe is open.
What is the together rate?It is the sum of each separate rate.
In this problem:
The input's pipe rate is 1/x.The drain's pipe rate is of 1/(x-1).The together rate is of 1/72.Hence:
[tex]\frac{1}{x} + \frac{1}{x - 1} = \frac{1}{72}[/tex]
[tex]\frac{x - 1 + x}{x(x - 1)} = \frac{1}{72}[/tex]
[tex]x^2 - x = 144x - 72[/tex]
[tex]x^2 - 145x + 72 = 0[/tex]
Which is a quadratic equation with coefficients a = 1, b = -145, c = 72, hence:
[tex]\Delta = b^2 - 4ac = (-145)^2 - 4(1)(72) = 20737[/tex]
[tex]x_1 = \frac{145 + \sqrt{20737}}{2} = 144.5[/tex]
[tex]x_2 = \frac{145 - \sqrt{20737}}{2} = -0.5[/tex]
Time is a positive measure, hence, it takes 144.5 hours to fill the empty pool when only the input pipe is open.
More can be learned about the together rate at https://brainly.com/question/25159431
The recipe uses 5/8 oz of simple syrup for 1/4 pint of tea. Find the unit rate in oz per pint
Answer:
The recipe uses 5/8 oz of simple syrup for 1/4 pint of tea. Find the unit rate in oz per pint
Step-by-step explanation:
The recipe uses 5/8 oz of simple syrup for 1/4 pint of tea. Find the unit rate in oz per pint
PLEASE HELP!!!
41. A bag contains 13 red marbles, 12 green marbles and 5 blue marbles. If you mix up the
marbles and pull one out at random, what is the probability that it will be blue? (Answer,
of course, as a fraction in lowest terms.)
Answer:
Number of red marbles = 13
Number of green marbles = 12
Number of blue marbles = 5
Total Number of marbles = 13+12+5
Total Number of Marbles = 30 marbles
[tex] \bf \: probability \: of \: blue \: marbles \: = \frac{number \: of \: blue \: marbles}{total \: number \: of \: marbles} [/tex]
[tex]\sf \dashrightarrow \: probability \: of \: blue \: marble = \frac{5}{30} \\ \\ \sf \dashrightarrow \: probability \: of \: blue \: marble = \cancel \frac{5}{30} \\ \\ \sf \dashrightarrow \: probability \: of \: blue \: marble = \frac{1}{6} [/tex]
So, the probability of blue marbles would be ⅙ .
Answer:
1/6 chance of getting blue
Step-by-step explanation:
find your total (30) that will be your denominator
the number of blue marbles will be your numerator (5)
then simplify 5/30 to 1/6
A sleep study found that the number of hours each person slept was normally
distributed. The study found that the average person slept 8.2 hours with a standard deviation of 0.7 hours.
1. What range of hours of sleep are the 99.7% closest to the mean?
2. The 2.5% of the people who slept the most got more than how many hours
of sleep?
3. The 16% of the people who slept the least got less than how many hours sleep?
Answer:
1. 6.1-10.3
Thats all i know.. hope it helps
The cable company withdraws $67 per month from Denise's checking account
for automatic bill payment. There was $250.75 in Denise's checking account at
the beginning of the year, and no other deductions or additions were made to
the account. How much money is in the account after two months?
Answer: 116.75
Step-by-step explanation: Since $67 is being withdrawn from her checking account EACH month the equation would be $250.75 - 67x.
We already know the value of "x" (2) so we plug that in.
250.75 - 67(2)
Now we multiply and subtract.
250.75 - 134
116.75
Part A. If I wash 24 dogs and used 4 bottles of shampoo, How many dogs can I wash with only 1 bottle of shampoo?
Part B. How many bottles of shampoo should I order if I expect to wash 30 dogs this week?
#2
Dogs=30
Total shampoos=30/6=5What would be the equation of the cannonball’s path if it was launched with the same velocity, but from the ground instead?
The quadratic equation cannonball’s path if it was launched with the same velocity, but from the ground instead would be given by:
[tex]h(t) = -4.9t^2 + 19.8t[/tex]
What is the quadratic equation for the height of a projectile?Considering the gravity, it is modeled by:
[tex]h(t) = -4.9t^2 + v_0t + h_0[/tex]
In which:
[tex]v_0[/tex] is the initial velocity.[tex]h_0[/tex] is the initial height.For this problem, we want:
The same initial velocity, hence [tex]v_0 = 19.8[/tex].Launched from the ground, hence [tex]h_0 = 0[/tex].Then, the equation is:
[tex]h(t) = -4.9t^2 + 19.8t[/tex]
More can be learned about quadratic equations at https://brainly.com/question/24737967
4c divided by 6 + 2a for c= 4 for a =5
Given expression:
[tex] \sf4c \div 6 + 2a[/tex]
Given values:
a = 5c = 4Rule we are going to use:
BODMAS
B = BracketsO = Of OrderD = DivisionM = Multiplication A = AdditionS = SubtractionSolution:
Substitute the variables with their given values and solve using the BODMAS rule[tex] \tt4 \times 4 \div 6 + 2 \times 5[/tex]
[tex] \tt \: \frac{ \cancel4 \times 4}{ \cancel6} + 10[/tex]
[tex] \tt \: \frac{2 \times 4}{3} + 10[/tex]
[tex] \tt \frac{8}{3} + 10[/tex]
[tex] \boxed{ \bf \: \frac{38}{3} }[/tex]
if you want to make 1/3 pound hamburger how many can you make from 2 1/2 pounds of ground beef
Answer:
3
Step-by-step explanation:
2 1/2 pounds is equal to one pound.
If you want to make 1/3 pound hamburgers you can make 3 from 1 pound ground beef.
1/3+1/3+1/3=1
