You invested $23,000 in two accounts paying 6% and 7% annual interest, respectively. If the total interest earned for the year was $1560, how much was invested at each rate?
Answer:
$ 18,000 was invested at 7%, and $ 5,000 was invested at 6%.
Step-by-step explanation:
Given that I invested $ 23,000 in two accounts paying 6% and 7% annual interest, respectively, and the total interest earned for the year was $ 1,560, to determine how much was invested at each rate, the following calculation must be performed:
23,000 x 0.07 + 0 x 0.06 = 1,610
22,000 x 0.07 x 1,000 x 0.06 = 1,600
21,000 x 0.07 x 2,000 x 0.06 = 1,590
20,000 x 0.07 x 3,000 x 0.06 = 1,580
19,000 x 0.07 x 4,000 x 0.06 = 1,570
18,000 x 0.07 x 5,000 x 0.06 = 1,560
Thus, $ 18,000 was invested at 7%, and $ 5,000 was invested at 6%.
The half life of a certain tranquilizer in the bloodstream is 36 hours. How long will it take for the drug to decay to 87% of the original dose? Use the exponential decay model to solve.
Finding the Decay constant(λ):
λ = 0.693 / (half-life)
we are given that the half-life is 36 hours
λ = 0.693 / (36)
λ = 0.01925 /hour
Time taken for 87% decay:
Since decay is first-order, we will use the formula:
[tex]t = \frac{2.303}{decay constant}log(\frac{A_0}{A} )[/tex]
Where A₀ is the initial amount and A is the final amount
Let the initial amount be 100 mg,
the final amount will be 87% of 100
Final amount = 100*87/100 = 87 mg
Replacing the values in the equation:
[tex]t = \frac{2.303}{0.01925}log(\frac{100}{87} )[/tex]
[tex]t = \frac{2.303}{0.01925}*0.06[/tex]
t = 7.18 hours
We used 'hours' as the unit because the unit of the decay constant is '/hour'
Therefore, the drug will decay to 87% of initial dosage after 7.18 hours
Select all of the values for x that would make the inequality 2 x > 10 true.
a 1
b 3
c 5
d 8
e30
Answer:
d 8
e 30
Step-by-step explanation:
x must be greater than 5
Answer: D E
Step-by-step explanation:
2(8) > 10
2(30) > 10
Both greater than
pls help the teacher said it’s not 14 I don’t know
Answer:
let no be x
by the question
2x-5=9
2x=9+5
x=14/2=7
the secret no is 7.
HEEEEEEEEEELLLLLLLLLLP
Solve the problem:
Kiram has 5 ziploc bags. He puts an equal number of marbles (X).Then he realized that he
needed to add 2 more marbles for each bag. If the total number of marbles is 30 how many
marbles in each bag?
Answer:
6?
Step-by-step explanation:
I guessed dont trust the answer
write the number pattern by writing the next number of 100, 90, 80, 70
Answer:
60
Step-by-step explanation:
Goes down by ten everytime.
Answer: 60
Step-by-step explanation:
You are taking away 10 each time.
A bookshelf measures 1 yard long by 12 inches wide by 2 feet high. What is the volume of the bookshelf in cubic inches?
Answer:
72 cubic inches
Step-by-step explanation:
I not sure.
Find the area of the composite figure.
If you answer I'll give you branliest :)))(
Answer:
252cm²
Step-by-step explanation:
This figure consists of 2 trapeziums.
Area of a trapezium= (The sum of the parallel side/2)× height
Explanation:
[(16+20)÷2]×7
[36÷2]×7
18×7
126cm²
Since the 2 trapezium have the same value we will just multiply the answer by 2.
126×2
252cm²
Hope this helps:)
Write an equation for the quadratic graphed below
x-intercepts: (-1,0) and (2,0). y-intercept: (0,-3)
Answer:
Step-by-step explanation:
LOL The graph doesn’t match the y intercept :)
Anyway
If we have point (0,-3) we have a quadratic of
y=ax^2+bx-3 we are given points (-1,0) and (2,0) so
a-b-3=0 and 4a+2b-3=0
4a+2b-3+2(a-b-3)=0
4a+2b-3+2a-2b-6=0
6a-9=0
6a=9
a=1.5, since a-b=3
1.5-b=3
b=-1.5
y=1.5x^2-1.5x-3
Answer:
1/2(x + 1)(x - 2)
Step-by-step explanation:
The x intercepts are -1 and 2, so the intercept form for this is y = a(x+1)(x-2).
We then by plug in the y intercept (0,-3)
-3 = a(0+1)(0-2)
1 * -2 = -2
-3 = -2a
division
-3/-2 = 3/2 which is 1.5
a = 1.5
y = 1.5(x+1)(x-2)
25. Which equation is not proportional? *
Oy=2x-3
Oy=150x
Oy=1/2x
YE 7
Hi there! Your answer is y = 2x-3
Please see an explanation for a better and clear understanding to your problem.
Any questions about my answer and explanation can be asked through comments! :)
Step-by-step explanation:
For an easy understanding to "proportional equation", It is basically an equation that is in form of y = mx + b where b = 0. Therefore, when b = 0 - Our new equation would be y = mx.
Other choices are in form of y = mx while the first choice isn't in the form of y = mx.
To be a proportional function or equation, the equation must be in the form of y = mx only.
The question asks which equation Is not proportional. Hence, the answer is the first choice.
Hope this helps!
what is the value of a?
Answer:
9\sqrt{2}
Step-by-step explanation:
this is a 30-60-90 triangle so
the side opposite of 30 is x and the opposite side of 60 is x[tex]\sqrt{2}[/tex]. then the side opposite 90 is 2x.
so if 9=x then a=x\sqrt{2}
9\sqrt{2} is the side length of a
Hope that helps :)
4) The measure of unknown angle x is.
Researchers interested in lead exposure due to car exhaust sampled the blood of 52 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a primarily urban environment. The blood samples of these officers had an average lead concentration of 122.31 µg/l and a SD of 38.75 µg/l; a previous study of individuals from a nearby suburb, with no history of exposure, found an average blood level concentration of 35 µg/l.
Required:
a. Write down the hypotheses that would be appropriate for testing if the police officers appear to have been exposed to a higher concentration of lead.
b. Explicitly state and check all conditions necessary for inference on these data.
c. Test the hypothesis that the downtown police officers have a higher lead exposure than the group in the previous study. Interpret your results in context.
d. Based on your preceding result, without performing a calculation, would a 99% confidence interval for the average blood concentration level of police officers contain 35 ug/l?
Step-by-step explanation:
n = 52
x bar = 122.31
standard deviation sd = 38.75
1. the hypothesis:
null hypothesis
h0: μ ≤ 35
alternative hypothesis
h1: μ > 35
2.
we have been given the sd of the sample but not that of the population. so what we are supposed to use here is the t test and not the z test. the following conditions have to be met.
population has to be normalsample size has to be more than 30. we have sample size = 52 in this question.3.
= [tex]\frac{122.31-35}{38.75/\sqrt{52} }[/tex]
= 87.31/5.37
= 16.26
using the T distribution function in excel, the p value was calculated and found to be approximately equal to 0.
TDIST(16.26, 51, 1)
since p value is very small we reject the null and accept the alternate hypothesis.
4. from the result above the answer to this question is yes
Help me and J give brainlest
Answer:
27
Step-by-step explanation:
First multiply 7 times 2 according to pemdas. Then add 10+3+14. The final answer would be 27.
Answer:
ya its 27 make sure u use pemdas but ya its 27
factor 3a^5-18a^3+6a^2, I know the answer is 3a^2(a^3-6a+2) but I am so lost on how to get the factor of 3a^2..How in the world do you get the exponent for the factor
Answer:
[tex]\huge\boxed{3a^2(a^3-6a+2)}[/tex]
Step-by-step explanation:
[tex]\sf 3a^5-18a^3+6a^2\\\\HCF = 3a^2\\\\Take \ 3a^2 \ common\\\\= 3a^2(a^3-6a+2)\\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807the farmer has a field of 300m.he want to fence it with 4 rounded barbed wire . what is the total length of wire he requires
Answer:
1,200 meters.
Step-by-step explanation:
Given that the farmer has a field of 300 meters and he wants to fence it with 4 rounded barbed wire, to determine what is the total length of wire he requires, the following calculation must be performed:
300 x 4 = X
1,200 = X
Thus, the farmer needs 1,200 meters of barbed wire to be able to fence his entire field.
WALLAI HELP ME THIS IS HARD HELP ME PLEASE
Answer:
3,-1 I hope it is a right answers
Step-by-step explanation:
( 3,1 )
please mark as brilliant
Elizabeth has a book collection. Her biographies are 42 pages each. Her fiction books are 50 pages each. She has 3 biographies and 6 fiction books. How many pages do the books have altogether?
express 75 as a product of three factors
Simplify the expression:
6(20 + 1)
=
Answer:
120+6
Step-by-step explanation:
Using distributive property 6times 20 is 120 and 6 times 1 is 6 so 120+6
I really need help with this. Can anyone help me please?
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.
3,-2+2i
Thank you!
Answer:
f(x) = x³ + x² - 4x - 24Step-by-step explanation:
Since one of zero's is complex number, its conjugate should also be a zero of the given polynomial.
The conjugate of -2 + 2i is -2 - 2iThe polynomial is going to be:
f(x) = (x - a)(x - b)(x - c) with minimum of degree 3, with zero's a, b and c.Substitute zero's:
f(x) = (x - 3)(x - (-2 + 2i))(x - (-2 - 2i)) = (x - 3)(x² - x (-2 + 2i -2 - 2i) + (-2 + 2i)(-2 - 2i)) = (x - 3)(x² + 4x + 8) = x³ + x² - 4x - 24Consider A is a set and B is another set, if Au B=A n B, then
Select one:
O A = B
O A = Null
O A = U
OB = Null
Answer:
A = B
Step-by-step explanation:
The correct option is;
A = B
Check:
A = {2,3,4}
B = {2,3,4}
Au B = A n B = {2,3,4}
A or B cannot be null.
check
A = {2,3,4}
B = {}
Au B = {2,3,4}
A n B = {}
Original amount: 27
End amount: 38.61
Increase or decrease
Answer:
increase
Step-by-step explanation:
11.61 was added to 27
Answer for brainliest
Answer:
b
Step-by-step explanation:
Answer:
Y = 2x. it is given
now , 2x + 2y = 30
now putting y = 2x ,. in ( 2x + 2y) = 30
hence ,.2x + 4x = 30
6x = 30
x= 5
now ,y= 2x
y = 10
Find m∠ABC in the picture. (it's not solving for x.)
Answer:
The answer would be 6º
Step-by-step explanation:
first we know that a straight lin is always 180º
so since we know that the angle outside of the triangle is 110º we can do 180º -110º
then we get the measuerment for angle C :70º
since we dont know the measurements of the other angles but know that a full triangle is equal to 180º we make this equation
2+6x+12x+70=180
then we solve
72+18x=180
-72 -72
18x=108
/18 /18
x=6
then we plug in the x value to find the angle measurement
2+6(6)
2+36
38º
your answer is m<CAB is 38º
Please help! It’s super easy and I’ll reward you brainiest
If a day of the week is randomly selected, what's the probability that the day contains the letter "a" in its name?
Round your answer to four decimal places (if necessary).
Answer:
1
Step-by-step explanation:
monday, tuesday, wednesday, thursday, friday, saturday, and sunday all have "a" in it so it has a 100% probability
Answer:
There would be a 100% chance.
Step-by-step explanation:
All the days of the week end with -day. The word day has an 'a' in it.
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Therefore, it will be certain that you will pick a day that has an 'a' in it's name.
Hope this helps!
Fruit-O-Rama sells dried pineapple for $0.25 per ounce. Mags spent a total of $2.65 on pineapple. How many ounces did she buy
Answer:
2.65/.25= 10.6oz
............
Answer:
10.6 Ounces
Step-by-step explanation:
Each ounce of dried pineapple costs $0.25
Divide $2.65 by $0.25
2.65/0.25=10.6
Mags bought 10.6 oz.
As a farmer, one of your responsibilities is to plow the field to prepare it for planting. On day 1, you plowed of the field. On day 2, you plowed of the field.
How much more of the field did you plow on day 1 than on day 2?
a.1/16
b.1/12
c.5/24
d.13/24
Answer:
you plowed more of the field on day 2 than on day one because minus equals
Step-by-step explanation: