Answer:
20
Step-by-step explanation:
if we add all these numbers together we get 220
220 divided by 11 is 20
a person invested $330 in an account growing at a rate allowing the money to double every 8 years. Write a function showing the amount of money in the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year, to the nearest hundredth of a percent.
Answer:
The percentage of growth is of 9.05%.
The amount of money in the account after t years is given by [tex]P(t) = 330(1.0905)^t[/tex]
Step-by-step explanation:
Amount of money after t years:
The amount of money in an account after t years is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial deposit and r is the growth rate, as a decimal.
Money doubles every 8 years.
This means that [tex]P(8) = 2P(0)[/tex]. So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]2P(0) = P(0)(1+r)^8[/tex]
[tex](1+r)^8 = 2[/tex]
[tex]\sqrt[8]{(1+r)^8} = \sqrt[8]{2}[/tex]
[tex]1 + r = 2^{\frac{1}{8}}[/tex]
[tex]1 + r = 1.0905[/tex]
[tex]r = 1.0905 - 1[/tex]
[tex]r = 0.0905[/tex]
The percentage of growth is of 0.0905 = 9.05%.
Person invested $330
This means that [tex]P(0) = 330[/tex]
So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 330(1+0.0905)^t[/tex]
[tex]P(t) = 330(1.0905)^t[/tex]
The amount of money in the account after t years is given by [tex]P(t) = 330(1.0905)^t[/tex]
julie wants to invest $3,000 into
a mutual fund that pays 7%
interest for 10 years. suppose
the interest were compounded
monthly instead of annually.
how much would the future
value of the investment
increase?
Answer:
$400
Step-by-step explanation:
The future value of the investment increase will be $6,028.98.
What is compound Interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
Given:
P = $3000
R = 7%
T = 10 years
r = R/100
r = 7/100
r = 0.07 rate per year,
Then solve the equation for A
A = P[tex](1 + r/n)^{nt[/tex]
A = 3,000.00[tex](1 + 0.07/12)^{(12)(10)[/tex]
A = 3,000.00[tex](1 + 0.0058333333333333)^{(120)[/tex]
A = $6,028.98
Hence, the future value will be $6,028.98.
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The rare tweety-birds are decreasing at a rate proportional to the
amount present. On January 1st there are 10,000 tweety-birds.
Fifteen days later, there are only 9,000.
(Problem la, 3 points)
Write a formula for the total amount of birds.
Convert. (13/5) into a mixed number.
Answer:
2 3/5 :)
Step-by-step explanation:
Figure A ~ Figure B
Find the volume of figure A
Answer:
Step-by-step explanation:
The value of a figure dependents from the value of "π"
So, it can be 1374.45 ft³ or 1375 ft³
✏--------------
[tex]Given:- \\\\R_15~ft\\\\R_2=2\\\\v=88[/tex]
[tex]\frac{R_1}{R_2} =\frac{5}{2}[/tex]
[tex]\frac{(R_1)^3}{(R_2)^3} =\frac{v_1}{v_2}[/tex]
[tex]\frac{5^3}{2^3} =\frac{v_1}{88}[/tex]
[tex]8v_1=11,000[/tex]
[tex]v_1=1375ft^3[/tex]
✂ -----------------hope it helps...
have a great day!!
Please help! This is due today!
te amo vato de arriba, ojalá y algún día seas mi novio y me mandes la visa y unos cuantos dólares pa'l frí fayer y comprarme más cosas de marca :"3
en fin... nunca me vas a hacer caso :")
Label 1/4 on the number line. Label 1/2 on the number line .
Answer:
it goes 0 then 1/4 in the first notch 1/2 in the second notch 3/4 in the third notch then the number 1 on the fourth
Step-by-step explanation:
Hope that helps.
(m+2)^2=27
solve by square root property
when i did it i got: m=±√27-4
is that correct?
Answer:
Yes, that's correct
Step-by-step explanation:
-2,4,-8,16... find the 20th term.
Answer:
I think the answer of this question is,
Step-by-step explanation:
The 20th term may be 1048576
f(x)= -2x^2+3x-7, calculate the average rate of change on the interval [1, 1+h]
Answer:
[tex]Rate = -2h-1[/tex]
Step-by-step explanation:
Given
[tex]f(x) = -2x^2 + 3x - 7[/tex]
[tex]Interval: [1,1+h][/tex]
Required
The average rate of change
This is calculated as:
[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]
Where:
[tex][a,b] = [1,1+h][/tex]
So, we have:
[tex]Rate = \frac{f(1+h) - f(1)}{1+h - 1}[/tex]
[tex]Rate = \frac{f(1+h) - f(1)}{h}[/tex]
Calculate f(1+h) and f(1)
[tex]f(x) = -2x^2 + 3x - 7[/tex]
[tex]f(1) = -2 * 1^2 + 3 * 1 - 7 = -6[/tex]
[tex]f(1+h) = -2 * (1+h)^2 + 3 * (1+h) - 7[/tex]
Evaluate squares and open bracket
[tex]f(1+h) = -2 * (1+h+h+h^2) + 3+3h - 7[/tex]
[tex]f(1+h) = -2-2h-2h-2h^2 + 3+3h - 7[/tex]
[tex]f(1+h) = -2-4h-2h^2 + 3+3h - 7[/tex]
Collect like terms
[tex]f(1+h) = -2h^2-4h +3h-2+ 3 - 7[/tex]
[tex]f(1+h) = -2h^2-h-6[/tex]
So, we have:
[tex]Rate = \frac{f(1+h) - f(1)}{h}[/tex]
[tex]Rate = \frac{-2h^2-h-6 - -6}{h}[/tex]
[tex]Rate = \frac{-2h^2-h-6 +6}{h}[/tex]
[tex]Rate = \frac{-2h^2-h}{h}[/tex]
Factorize the numerator
[tex]Rate = \frac{h(-2h-1)}{h}[/tex]
Divide
[tex]Rate = -2h-1[/tex]
Find an equation of the line that bisects the acute angle formed by the graphs of negative 5X plus 7Y +4 equals zero and 7X minus 5Y +6 equals zero
Answer:
Step-by-step explanation:
x+ y = 0
and
-2x + 5y + 2 = 0
Step-by-step explanation:
given line
3x+5y+2=0
5x+3y-2=0
solution
when two line bisect each other then line equation of bisector is express as
1
and here
A1 = 3
B1 = 5
C1 = 2
and
A2 = 5
B2 = 3
C2 = -2
so now put value in equation 1 we get
solve it we get
-2x + 5y + 2 = 0 1
and
3x+5y+2 = - ( 5x+3y-2 )
solve it we get
8x + 8y = 0
x + y = 0 2
Answer: D -12x +12y -2 =0
Step-by-step explanation:
Edge 2021
NEED HELP WITH THIS QUESTION
girl name are April, may, June, what is the name the mother?
mary is the 4th childs nam,e
3.
At time t = 0 years, a forest preserve has a population of 1500
deer. If the rate of growth of the population is modeled by
R(t) = 2000e0.231 deer per year, what is the population at time
t=3.
The population of deer at time t=3 years is approximately 4128 deer.
What is an exponential function?An exponential function is a mathematical function of the form [tex]f(x) = a^x[/tex], where a is a positive constant called the base, and x is the input variable. The exponent x represents the power to which the base a is raised.
The rate of growth of the deer population is given by the function [tex]R(t) = 2000e^{(0.231t)}[/tex], where t is the time in years since t=0.
To find the population at time t=3, we need to evaluate R(3) using the given function:
[tex]R(3) = 2000e^{(0.231\times 3)[/tex]
[tex]R(3) = 2000e^{0.693}[/tex]
R(3) ≈ 4127.72
Therefore, the population of deer at time t=3 years is approximately 4128 deer.
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Solve 5.408 − 1.07
pls answer
Answer: 4.338
Step-by-step explanation: Calculator
A group of 80 people who had been diagnosed as prediabetic because of high blood glucose levels volunteered to participate in a study designed to investigate the use of cinnamon to reduce blood glucose to a normal level. Of the 80 people, 40 were randomly assigned to take a cinnamon tablet each day and the other 40 were assigned to take a placebo each day. The people did not know which tablet they were taking. Their blood glucose levels were measured at the end of one month. The results showed that 14 people in the cinnamon group and 10 people in the placebo group had normal blood glucose levels. For people similar to those in the study, do the data provide convincing statistical evidence that the proportion who would be classified as normal after one month of taking cinnamon is greater than the proportion who would be classified as normal after one month of not taking cinnamon?
a. No conclusion can be made about the use of cinnamon because the people in the stuey were volunteers
b. There is convincing statistical evidence at the level of 0.01
c. There is convincing statistical evidence at the level of 0.05 but not at the ver.01
d. There is convincing statistical evidence at the level of 0.10 any reason
e. There is not convincing statistical evidence
Answer:
E
Step-by-step explanation:
AP Classroom says so.
The data doesn't provide convincing statistical evidence for considered proportion comparison. We deduce that: Option E: There is not convincing statistical evidence
How to form the hypotheses?There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.
Null hypothesis is the one which researchers try to disprove.
How to calculate the value of z-test statistic for two sample proportions?Suppose we have:
[tex]\hat{p}_1[/tex] = first sample's proportion[tex]n_1[/tex] = first sample's size[tex]\hat{p}_2[/tex] = second sample's proportion[tex]n_2[/tex] = first sample's size[tex]\hat{p}[/tex] = overall proportionThen, we get:
[tex]Z = \dfrac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p}_1 )(\dfrac{1}{n_1} + \dfrac{1}{n_2}) }}[/tex]
If the level of significance = [tex]\alpha[/tex]critical value of Z is: [tex]Z_{\alpha/2}[/tex], and if [tex]Z > Z_{\alpha/2}[/tex]null hypothesis, else if [tex]Z_{\alpha/2} > Z[/tex] then we cannot reject it.
For this case, we want to know if the data provides convincing statistical evidence that the proportion who would be classified as normal after one month of taking cinnamon is greater than the proportion who would be classified as normal after one month of not taking cinnamon.
Thus, we get our hypotheses as:
Null hypotheses: They don't provide convincing evidence (and thus, cinnamon had no improvement on the proportion), and thus:
[tex]H_0: \hat{p}_1 \leq \hat{p}_2[/tex]
Alternate hypothesis: Data provides convincing evidence (that the use of cinnamon made increment in considered proportion), and thus:
[tex]H_a: \hat{p}_1 > \hat{p}_2[/tex]
The test is single tailed.
For this case, we have:
[tex]x_1[/tex] = quantity of intended object found in first sample = 14 (of those who take cinnamon tablets each day)[tex]n_1[/tex] = first sample's size = 40[tex]\hat{p}_1 = x_1/n_1 = 14/40 =0.35[/tex] [tex]x_2[/tex] = quantity of intended object found in second sample = 10 (of those who take placebo each day)[tex]n_2[/tex] = second sample's size = 40[tex]\hat{p}_2 = x_2/n_2 = 10/40 =0.25[/tex][tex]\hat{p}[/tex] overall proportion = [tex](x_1 + x_2)/(n_1 + n_2) = (10 + 14)/80 = 0.3[/tex]Thus, we get:
[tex]Z = \dfrac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p}_1 )(\dfrac{1}{n_1} + \dfrac{1}{n_2}) }} =\dfrac{0.35 - 0.25}{\sqrt{0.3(0.7 )(\dfrac{1}{40} + \dfrac{1}{40}) }} \approx 0.976[/tex]
At 0.01 level of significance ([tex]\alpha = 0.01 = 1\%[/tex]), we get the critical value of Z from z-tables as:
[tex]Z_{\alpha/2} = 2.576[/tex]
Since [tex]Z_{\alpha/2} > Z[/tex] , we cannot reject the null hypothesis, and thus, deduce that there is not convincing statistical evidence at the level of 0.01
At 0.05 level of significance ([tex]\alpha = 0.05 = 5\%[/tex]), we get the critical value of Z from z-tables as:
[tex]Z_{\alpha/2} = 1.96[/tex]
Since [tex]Z_{\alpha/2} > Z[/tex] , we cannot reject the null hypothesis, and thus, deduce that there is not convincing statistical evidence at the level of 0.05
At 0.10 level of significance ([tex]\alpha = 0.10 = 10\%[/tex]), we get the critical value of Z from z-tables as:
[tex]Z_{\alpha/2} = 1.645[/tex]
Since [tex]Z_{\alpha/2} > Z[/tex] , we cannot reject the null hypothesis, and thus, deduce that there is not convincing statistical evidence at the level of 0.10
Remember that the conclusions can be made even if they were volunteers since that doesn't make it wrong as volunteers are randomly coming out people from real population.
Thus, we deduce that: Option E: There is not convincing statistical evidence
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I need help ASAP!!!!!! Plzzzzzzzzzzz!!!!!!
Answer:
The second graph, the extreme v
Step-by-step explanation:
We know that y=4x passes through 4 on 1. When absolute valued, we add the graph y=-4x. This gives us the graph second to the right.
By the way, can you follow me?
Thanks
I can Multiply a 11x6 matric by a 6x7 matrix. The resulting matrix will be ??? Can somebody help me
Answer:
The resulting matrix will be 11 * 7
Step-by-step explanation:
Given
Matrices 11 * 6 multiplied by 6 * 7
Required
The dimension of the resulting matrix
When a matrix a * b is multiplies by a matrix b * c, the resulting matrix will be: a * c
In this case:
[tex]a * b = > 11 * 6[/tex]
[tex]b * c => 6 * 7[/tex]
So, the resulting matrix will be:
[tex]a * c => 11 * 7[/tex]
What is the equation of the exponential function??
Anthony's mom bought a new Prius in 2018 that cost
$28,000. She looked up the current value and saw that
it was only $22,000 after two years! She is worried
about how much her car will be worth in 3 more years.
What is the exponential equation?
1
How much will the car be worth in 3 years?
Submit
Answer:
$19500Step-by-step explanation:
Let the depreciation rate is x per year, then we have:
28000*x² = 22000x² = 22000/28000x² = 0.7857x = √0.7857 x = 0.8864Exponential function for this case is:
V(t) = 28000*0.8864^t, where V(t) - future value, t- number of yearsValue of the car after 3 years:
V(3) = 28000*0.8864^3 V(3) = 19500determine if the sequence below is arithmetic or geometric and determine the common difference/ ratio in simplest form 5,15,45,...
Answer:
It's geometric and common difference is 3
Step-by-step explanation:
15/5=3
45/15=3
Answer:
its geometric and the common ratio is 3
Step-by-step explanation:
The Pacheco family has a monthly income of $ 7,300 . They have monthly fixed expenses of $ 3,280 . In July, they had monthly variable expenses of $ 2,620 . They have annual expenses totaling $ 14,000 . Assuming annual expenses are paid off at an equal rate monthly, what was the Pacheco’s cash flow for July?
Answer:
Positive 233
Step-by-step explanation:
7300-3280-2620-1167(14000/12)=233.
Write the equation for the function g(x), which can be described as a
vertical shift 13 units up from the function f(x) = In x –1
Answer:
Step-by-step explanation:
When you shift up or down, the function gets added to or subtracted from the expression on the right of the y value. Put in simpler language, for this question, the equation becomes.
g(x) = f(x) + 13
And the solution is
g(x) = ln(x) - 1 + 13
g(x) = ln(x) + 12
ARITHMETIC SEQUENCES, what comes next after -2/25? I will Mark you as BRAINLIEST pls help
Answer:
26/5
Step-by-step explanation:
an=a1+(n-1)d
d is common difference
so,
2/5- (-2)=12/5
putting values in above formula
=-2+(4-1)(12/5)
=-2+3(12/5)
=-2+(36/5)
=26/5
Question 1(Multiple Choice Worth 2 points)
(10.03 MC)
Select the sentence that correctly uses a prepositional phrase.
Andy in her backpack has extra supplies.
Around the corner. Belle spotted a lost dog.
Through her binoculars, Kathryn spotted a hawk.
Mika wore under her hiking boots thick wool sock
Answer:
i think the answer is c but im soo sorry if im wrong
Step-by-step explanation:
PLZ HELP ILL MARK BRAINLIST!!!
Answer:
So, your answer would be 226.08 cubic meters of dirt.
Step-by-step explanation:
:D
i will mark brainliest please help
A- less than -5
B- less than or equal to -5
C- Greater than -5
D- Greater than or equal to -5
Using formula B=p(1+r)5
=$1000(1+0.05)5
1000(1.05)5
1000(1.2762815625)
total=1276.28
using formula above, calculate balance if interest is compounded annually. $800.00 at 4% interest for 2 years
how did I get the (1.2762815625)
multiplying what numbers?
Answer:
45.5
Step-by-step explanation: NUN
4) Divide x^4 – 14x^2 + 45 by (x - 3)
Answer:
Ok 9-8=1 times 2 = 2
Step-by-step explanation:
Answer:
x^3−5x+3x^2−15
Step-by-step explanation:
Common math
If you know the answer your a genius at math^
Answer: I think its B
Step-by-step explanation: hoped this helped :)
What is the sum of just the fraction parts of 1 5/8 and 1 6/8?
Answer:
Just the fraction parts: 11/8 or 1 3/8
Step-by-step explanation:
1 5/8 + 1 6/8 = 3 3/8
Hopefully this helps :3 sorry if wrong :( Plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3
-Bee~