Answer:
418 meters
Step-by-step explanation:
The total distance is 996 meters, hare completed 578 meters. The question asked how much further hare has to run which indicates that this is a subtraction problem.
Equation to solve :996-578=x
x=418
Hope this helps, let me know if I am wrong. Have a good day:)
Find the 97th term of the arithmetic sequence 25, 29, 33, ...25,29,33,...
If the first term is 25 and the common difference is 4. Then the 97th term of the sequence will be 409.
What is a sequence?A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
The sequence is given below.
25, 29, 33, ...., so on
Then the first term is 25. And the common difference is 4.
Then the 97th term will be given as
[tex]\rm a_n = a + (n - 1)d[/tex]
where
n = 97
a = 25
d = 4
Then we have
a₉₇ = 25 + (97 - 1)4
a₉₇ = 25 + 96 x 4
a₉₇ = 25 + 384
a₉₇ = 409
Then the 97th term of the sequence will be 409.
More about the sequence link is given below.
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PLEASE HELP WILL MARL BRAINLIEST
Answer:
3pi/4
Step-by-step explanation:
can't really explain it that well, but I sure hope this helps!! :)
Phu takes out a $2,400 discounted loan using a simple interest rate of 8% for a period of 18 months. What is the effective interest rate, re
Answer:
9.1
Step-by-step explanation:
To calculate the total interest payable, we use the formula
I=P0rt,
and substituting our values yields
I=$2,400×0.08×1812=$288.
Therefore the total amount he receives at loan drawdown is $2,400−$288=$2,112. To calculate the effective interest rate, we use to formula
A=P0(1+ret).
In this instance we have A=$2,400,P0=$2,112 (redefined from the value above) and t=1.5. We substitute into the formula to get
$2,400=$2,112(1+1.5re).
Solve for re.
24002112=1+1.5re
24002112−1=1.5re
24002112−11.5=re
This gives re=0.0909⋯=9.0909…%, which is 9.1%
Help help help help help help
NO LINKS!!!! Exponential Growth and Decay Part 3
Answer:
6. 14.9 years
7. 4.8 years
8. 28.91 years
Step-by-step explanation:
Exponential growth or decay is described by the function ...
y = a·b^t
where 'a' is the initial value, and 'b' is the growth (or decay) factor. The growth (or decay) factor is one added to the growth rate.
__
This equation can be solved for t to get ...
y/a = b^t . . . . . . . divide by a
log(y/a) = t·log(b) . . . . take logarithms
t = log(y/a)/log(b) . . . . divide by the coefficient of t
Note that the time period is in the same units as the growth rate. (If the growth rate is per quarter, then the value of t will be in quarters.)
__
6.The initial value is a=8000; the final value is y=35000; and the growth rate is 10%/4 = 0.025 per quarter. The above equation will give the time period in quarters.
t = log(35000/8000)/log(1+0.025) ≈ 59.77 . . . quarters
Anisha will have $35,000 after 59.77/4 = 14.9 years.
__
7.No loan payment period is given, so we assume that the $43000 represents the repayment of the entire loan. The growth rate is 6% per year. The time required for the loaned amount to accumulate to a value of $43,000 is ...
t = log(43,000/32,500)/log(1 +0.06) ≈ 4.80 . . . years
If the loan period is 4.80 years, Kevin will have paid 43,000 to pay it off.
__
8.The growth rate is 0.024/12 = 0.002 per month. The number of months to achieve the desired balance is ...
t = log(3200/1600)/log(1 +0.024/12) ≈ 346.92 . . . . months
The balance in the account will be $3200 after 346.92/12 = 28.91 years.
_____
Additional comment
As a crude check on the answers, the "rule of 72" can be used. It says the doubling time is approximately 72 divided by the growth rate in percent. That is, a 10% growth rate will cause the value to double in approximately 72/10 = 7.2 years.
In the first problem, the value grows from 8000 to 35000, which represents a little more than 2 doublings (8000 to 16000 and 16000 to 32000). So, it is reasonable to expect the time period to be near 2 times 7.2 years, or 14.4 years. The value of 14.9 years is not unreasonable.
Answer:
Compound interest formula
[tex]\Large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedQuestion 6Given:
A = $35,000P = $8,000r = 10% = 0.1n = 4t = time (in years)[tex]\begin{aligned}8000\left(1+\frac{0.1}{4}\right)^{4t} & = 35000\\(1.025)^{4t} & = \frac{35000}{8000}\\(1.025)^{4t} & = 4.375}\\\ln (1.025)^{4t} & = \ln 4.375\\4t \ln 1.025 & = \ln 4.375\\4t & = \frac{\ln 4.375}{\ln 1.025}\\t & = 0.25\left(\frac{\ln 4.375}{\ln 1.025}\right)\\t & = 14.9427947\end{aligned}[/tex]
Therefore, she will have $35,000 in 15 years.
Question 7Given:
A = $43,000P = $32,500r = 6% = 0.06n = 1t = time (in years)[tex]\begin{aligned}32500\left(1+\frac{0.06}{1}\right)^{1t} & = 43000\\32500(1.06)^{t} & = 43000\\(1.06)^{t} & = \frac{43000}{32500}\\(1.06)^{t} & = \frac{86}{65}\\\ln (1.06)^{t} & = \ln \left(\frac{86}{65}\right)\\t \ln 1.06 & = \ln \left(\frac{86}{65}\right)\\t & = \dfrac{\ln \left(\frac{86}{65}\right)}{\ln 1.06}\\t & = 4.804621116\end{aligned}[/tex]
Therefore, Kevin will have paid $43,000 on the loan in 4 years and 10 months.
Question 8Given:
A = $3,200P = $1,600r = 2.4% = 0.024n = 12t = time (in years)[tex]\begin{aligned}1600\left(1+\frac{0.024}{12}\right)^{12t} & = 3200\\1600(1.002)^{12t} & = 3200\\(1.002)^{12t} & = \frac{3200}{1600}\\(1.002)^{12t} & = 2\\\ln (1.002)^{12t} & = \ln 2\\12t \ln (1.002) & = \ln 2\\12t & = \dfrac{\ln 2}{\ln 1.002}\\t & = \frac{1}{12}\left(\dfrac{\ln 2}{\ln 1.002}\right)\\t & = 28.91000404\end{aligned}[/tex]
The balance of the account will be $3,200 in 28 years and 11 months.
Question 5 of 10
Which of the following rational functions is graphed below?
10+
10
10
1 - 10
X1
X- 4
O A. Fx) = x+1
F
OB. FX) = (x-1(x+4)
(x
O C. FX) = x +
1
- x)
X-
O D. F(X) =
1
(x + 1)(x-4)
x
Answer:
A. is the correct answer tnx to the points
The function f(x) = 1/[(x-1)(x+4)] is a rational function with two vertical asymptotes and one horizontal asymptote, which is graphed below.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
The function f(x) = 1/[(x-1)(x+4)] is a rational function with two vertical asymptotes and one horizontal asymptote.
The vertical asymptotes occur when the denominator, (x-1)(x+4), is equal to zero. This happens when x = 1 or x = -4.
Therefore, the graph will have two vertical asymptotes at x = 1 and x = -4.
The horizontal asymptote can be found by looking at the behavior of the function as x approaches positive or negative infinity. As x gets very large in either direction, the terms (x-1) and (x+4) become insignificant compared to x².
Hence, the correct option is (B) f(x) = 1/[(x-1)(x+4)].
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Find the positive solution for c:
8 2 + 15 2 = c 2
Answer:
15
Step-by-step explanation:
8² + 15² = c²
To find : Value of c
8² = 8 x 8 = 64
15² = 15 x 15 = 225
c² = 225
225 = 15 x 15 = 15²
So,
c² = 15²
c = 15
Select the correct expression.
Select the expression that is equivalent to the expression below.
Answer:
[tex]8\sqrt[3]{-8x^3y^6z^{13}}[/tex]
Step-by-step explanation:
[tex]8\sqrt[3]{-8x^3y^6z^{13}}\\\\=8\sqrt[3]{(-1)^3\cdot2^3\cdot x^3 \cdot y^6 \cdot z^{12} \cdot z}\\\\=8\left[(-1)^3\cdot2^3\cdot x^3 \cdot y^6 \cdot z^{12} \cdot z \right]^{\tfrac 13}\\\\=-8\cdot 2 \cdot x \cdot y^2 \cdot z^4 \cdot z^{\tfrac 13}\\\\=-16xy^2 z^4 \sqrt[3]z[/tex]
12. Which equality represents y=3x^2+2 written in function notation?
Answer:
f(x) = 3x^2 + 2
Step-by-step explanation:
HELP ME ON THIS PLSS Kathy swims at least 6 laps everyday. Write an inequality to show how long Kathy swims each day.
Answer:
x ≥ 6.
Step-by-step explanation:
Given : Kathy swims at least 6 laps every day.
To find: Write an inequality to show how long Kathy swims each day.
Solution : We have given that Kathy swims at least 6 laps every day.
We can see from given statement Kathy can swim 6 laps or greater then 6 laps in a day.
Then we use greater than or equal to sign ( for at least)
Since x ≥ 6.
Therefore, x ≥ 6.
find the area of following quadeilaterals
???????
1. Which of the following are statistical questions? Select all that apply.
a. How many 6th grade students like pizza?
b. Did you go to the beach yesterday?
c. What is the favorite food of all FMS students?
d. What was the high temperature of Florida for each day of the week?
e. How does each student get to school in the morning?
a box in a shape of a rectangle prism has a length of 3 5/8 inches a width of 2 1/2 inches and a height of 4 inches. what is the volume of the box
Answer:
volume is 36.25inches
145/4
Step-by-step explanation:
L= 3 5/8inches
W= 2 1/2inches
H= 4inches
VOLUME = L×W×H
3 5/8 × 2 1/2 × 4 =
29/8 × 5/2 × 4 = 36.25inches
36.25→145/4
Answer these questions for me please i dont have time to go back and figure this out rn
Answer:
Step-by-step explanation:
in 6 years we know that it will be half, because that's what "half life" means
in 3 years it's only loses 1/2 * 1/2 = 1/4 of it's mass
in 1 year it's only loses 1/6 * 1/2 = 1/12 of it's mass
from that we can make the formula that
current weight of radium = Wr
Mass of radium orginal = Mo
year of time = t ( must be in years, not days, months or weeks )
Wr = (1/12)*t* Mo
tony wants to buy a new radio for his car. It cost $350. He wants to purchase it in four months. How much will he have to save each month?
The hanger image below represents a balanced equation.
36
a
a
Find the value of a that makes the equation true.
Answer:
18
Step-by-step explanation:
36 divided by two is 18 therefore 18+18 is 36
A pair of shoes is $50, plus 10% tax. What is the total amount you will pay?
Answer:
$55
Step-by-step explanation:
Given:
A pair of shoes is $50, plus 10% tax.
To Find:
What is the total amount you will pay?
Solve:
Tax = Increase - Add on
Thus,
$50 × 10% = 5
$50 + 5 = $55
Hence, the total amount you will pay is $55.
Kavinsky
Find the exact value of Tan(-420)
Twelve subtracted from twelve times a number is -84. What is the number? A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use x as your variable. The equation is B) Solve your equation in part [A] for x. Answer: 0 =
Answer:
x=-6
Step-by-step explanation:
Let x be the number
A) 12x-12=-84
B) 12x=-72
x=-6
A ----------------- transforms some electrical energy into other forms of energy.
Answer:
A solar panel is the best way to transform electrical energy into other forms of energy
If v₁ = (3,7) and V₂ = (-2,4), then v₁v₂ is equal to which of the following?
A. (-6,28)
B. 34
C. 22
D. (-21,-8)
For the function defined by y = StartFraction 1 Over x squared EndFraction, if x is doubled, what is the effect on y?
a.
y is quartered
c.
y stays the same
b.
y is doubled
d.
y is tripled
Please select the best answer from the choices provided
Answer:
a. y is quartered.
Step-by-step explanation:
y=1/x^2
when x is doubled, the equation becomes:
y=1/(2x)^2=1/(4x^2)
Answer:
If we double x, then the new value of x becomes 2x. So we can find the effect on y by substituting 2x for x in the given function.
y = 1/x^2
When x is replaced by 2x, we get:
y' = 1/(2x)^2
= 1/4x^2
Therefore, y' = (1/4)y
So, if x is doubled, then y is quartered (option a is the correct answer)
5. Apply the law of syllogism to form a new statement based on the following:
R S: If the dog jumps in the lake, then it gets wet.
S T: If the dog gets wet, then it can’t come in the house.
The new statement becomes "If the dog jumps in the lake, then it can't come in the house".
What is the law of syllogism?Legal syllogism is a legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.
We have a statement:
R → S: If the dog jumps in the lake, then it gets wet.
S > T: If the dog gets wet, then it can’t come in the house.
After applying the law of syllogism to form a new statement:
R→T:
If the dog jumps in the lake, then it can't come in the house.
Thus, the new statement becomes "If the dog jumps in the lake, then it can't come in the house".
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A cyclist covers a distance of 90km in 3 hours, what is the average speed?
Answer: I think it's 30km per hour.
Step-by-step explanation:
So first you have to find what speed the cyclist is going per hour. So first I did 90/3 and that gave me 30.
A bag contains 5 green and 3 white balls (the balls are identical in all respect except colour). A ball is drawn at random from the bag without looking into the bag. What is the probability of getting a green ball? Is it more or less than getting a white ball?
Answer:
Probability of getting a green ball is more than that of getting a white ball.
Step-by-step explanation:
There are in all (5+3= 8) outcomes of the experiment. There are 5 outcomes in favour of the event of getting a green ball as there are 5 identical green balls in the bag.
Therefore, P(a green ball) = 5/8
In the same way,P(a white ball) = 3/8
5/8 > 3/8Thus, clearly the probability of getting a green ball is more than that of getting a white ball.
draw the graph of y equals (2) x + 1
Answer + Step-by-step explanation:
y = 2x + 1 represents a linear function then the its graph is a line
To draw the line we have to determine two points that lie on that line
If x = 0 → y = 2(0) + 1 = 1 then the point A(0,1) lies on the line
If x = 2 → y = 2(2) + 1 = 5 then the point B(2,5) lies on the line
Now all we have to do is joining the points A and B with a line
The line AB represents our graph
A person who does not swing from one emotion or another is said to be______.
A. an introvert
B. stable
C. unstable
D. an extrovert
Answer:
Stable. They're solid in they're emotions
Step-by-step explanation:
what is the equation of the line that passes through the point (3,6) and has a slope of -1/3
ASAP PLS
[tex]\Large\texttt{Answer\::}[/tex]
Please consult the "Calculations" section of this ans .
[tex]\Large\texttt{Calculations\::}[/tex]
The information we're given is below :
slope : -1/3Point crossed by the line : (3, 6)As per given information , we can do the following :
Write the line's equation in point slope formPoint - slope form looks like so :
y-y₁=m(x-x₁)
y-6=-1/3(x-3)
y-6=-1/3x+1
y=-1/3x+1+7
y=-1/3x+6
↑ [tex]\small\textsc{EQUATION OF THE LINE}[/tex]
[tex]\small\textit{hope\:helpful~}[/tex]
Alyssa has a points card for a movie theater. She receives 70 rewards points just for signing up. She earns 12.5 points for each visit to the movie theater. She needs 245 points for a free movie ticket. How many visits must Alyssa make to earn a free movie ticket?
let x be the amount of times she visited the movie theater
[tex]70+12.5x=245\\\\12.5x=175\\\\x=14[/tex]
Alyssa needs to make 14 visits to earn a free movie ticket.
This is our y intercept
Rate of pay=12.5This is our slope.
So our equation is
p=12.5v+70Here v is visits
245=12.5v+7012.5v=175v=14visitsFind the value of y for the given value of x. Round to the nearest hundredth.
y = 0.05 − 10 ln x; x = 0.09
Answer:
[tex]y\approx24.129[/tex]
Step-by-step explanation:
[tex]y=0.05-10\ln x;\: x=0.09\\y=0.05-10\ln(0.09)\\y\approx24.129[/tex]
Answer:
24.129
the answer is that and I need 20 characters
