Answer:
a) growth
b) 3%
c) 6 years (since the beginning of the decade)
Step-by-step explanation:
Given:
The population P (in thousands) of Austin, Texas during a recent decade can be approximated by [tex]y=494.29(1.03)^t[/tex] when t is the number of years since the beginning of the decade.
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the y-intercept (or initial value)b is the base (or growth factor)x is the independent variabley is the dependent variableIf [tex]b > 1[/tex] then it is an increasing function
If [tex]0 < b < 1[/tex] then it is a decreasing function
a) The model represents exponential growth as 1.03 > 1
b) The annual percent increase of the population is 3%
1.03 - 1 = 0.03
0.03 x 100 = 3%
c) To estimate when was population about 590,000 set y = 590 and solve for t:
[tex]\implies 590=494.29(1.03)^t[/tex]
[tex]\implies \dfrac{590}{494.29}=(1.03)^t[/tex]
Take natural logs of both sides:
[tex]\implies \ln\left(\dfrac{590}{494.29}\right)=\ln (1.03)^t[/tex]
[tex]\implies \ln\left(\dfrac{590}{494.29}\right)=t\ln (1.03)[/tex]
[tex]\implies t=\dfrac{\ln\left(\dfrac{590}{494.29}\right)}{\ln (1.03)}[/tex]
[tex]\implies t=5.988069001...[/tex]
Therefore the population was about 590,000 6 years since the beginning of the decade.
On a spinner with two equal sections labeled 2 and 3, Josie determines that the probabilities of landing on 2 or 3 are equally likely. How would she express each probability as a decimal?
A 0.05
B 0.1
C 0.5
D 1.0
PLEASE HURRY
What strategies do you use when multiplying decimals? Share your thinking using 2-3 sentences. This is an open-ended question so you can put anything you want but make sure it is correct.
Help help pls pls!!!
Answer:
b
Step-by-step explanation:
eg2022
Kendra is a professional diver. She practices between 80-100 dives before every competition. About how many dives will she practice if she has 12 competitions?
Answer:
She will practice about 960-1200 dives before those competitions in total
Step-by-step explanation:
All you have to do is multiply the number of dives by the number of competitions she has.
Jordan's older brother rode his bike 78 miles in the past 6 days. He rode an equal number of miles each day. Today he rode his bike 2 miles further than he rode on each of the other days.
How many miles did Jordan's brother ride his bike today? Someone please help i need this asap <3 tysm
Answer:
He rode 15 on his bike today.
Step-by-step explanation:
78 / 6 = 13 and 13 + 2 = 15
Answer:
Step-by-step explanation:
f(x) = 10x–4 and g(x) = 1/2 . What is the value of f(g(6))?
To solve f(g(6)):
⇒ we solve for g(6) first
⇒ then plug the value of g(6) into the 'x' position of f(x)
Let's Solve:
Solve for g(6)[tex]g(6) = \frac{1}{2}[/tex]
2. Plug g(6)'s value into f(x)
[tex]f(g(6))=f(\frac{1}{2} )=10(\frac{1}{2} )-4=5-4=1[/tex]
Thus f(g(6))'s value is 1
Answer: 1
Hope that helps!
PLS HEPPP WHAT IS THE ANSWER????
Answer:
Again let's plug in the values.
we get
[tex]8 \frac{1}{8} [/tex]
The group wants to travel from its current location on the map to the South Pole, and then directly back to base camp, passing through their current location. There are 5 people in the group and they expect to travel an average of 10 miles per day. Remember that each person needs 6000 calories per day. Based on your response to item 3, what is the minimum number of calories the group is expected to consume during the entire trip?
the answer to number 3 is 75 miiles
The minimum number of calories the group is expected to consume during the entire trip from current location to southpole and back to camp is 375 kilo calories.
What is Pythagoras theorem?Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
There are total 5 miles in one block and current location to the South Pole there are 5 blocks on map. Thus, the total distance from current location to the South Pole is,
[tex]x=5\times5\\x=25\rm\; miles[/tex]
There are total 12 blocks from current location to the camp on map. Thus, the total distance from current location to the camp is,
[tex]y=12\times5\\y=60\rm\; miles[/tex]
The shortest distance from South Pole to camp is,
[tex]z=\sqrt{25^2+60^2}\\z=\sqrt{4225}\\z=65\rm\; miles[/tex]
Total distance group travel from if it wants to travel from its current location on the map to the South Pole, and then directly back to base camp, passing through their current location is,
[tex]n=65+60\\n=125\rm\; miles[/tex]
The group travel an average of 10 miles per day. Thus, number of days to cover distance,
[tex]\dfrac{125}{10}=12.5\rm\; days[/tex]
There are total 5 people in group and they consume each person needs 6000 calories per day. Thus, total calories,
[tex]C=12.5\times6000\times5\\C=375000 \rm\;C\\C=375 \rm\; kC[/tex]
Thus, the minimum number of calories the group is expected to consume during the entire trip from current location to southpole and back to camp is 375 kilo calories.
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What is the answer
3^12
Answer:
36
Step-by-step explanation:
Answer:
3^12=3*3*3*3*3*3*3*3*3*3*3*3=9*9*9*9*9*9=81*81*81=6561*81=531,441
Step-by-step explanation:
Complete the square to find the
vertex of this parabola.
x² - 12y - 6x + 5 = 0
?]
-H
The graph of an exponential function f passes through (0,1) and (2,4) as shown.
what is the value of f(6)?
The exponential function is given by f(x) = 2ˣ and the value of f(6) is 64
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An exponential funtion is in the form y = abˣ
At point (0, 1):
1 = ab⁰
a = 1
At point (2, 4):
4 = 1(b)²
b = 2
Hence:
f(x) = 2ˣ
Hence f(6):
f(6) = 2⁶ = 64
The exponential function is given by f(x) = 2ˣ and the value of f(6) is 64
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50 PTS!!A right triangle has a leg measuring 16in. And 28in.
What is the length of the hypotenuse?
Round your answer to the nearest tenth.
1)23.0 in.
2)32.2 in.
3)44.0 in.
4)1040.0 in
Answer:
2) 32.2 in (nearest tenth)
Step-by-step explanation:
Pythagoras’ Theorem
[tex]\sf a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = 16 inb = 28 inc = hypotenuseSubstituting these values into the formula and solving for c:
[tex]\implies \sf 16^2+28^2=c^2[/tex]
[tex]\implies \sf 256+784=c^2[/tex]
[tex]\implies \sf c^2=1040[/tex]
[tex]\implies \sf c=\pm\sqrt{1040}[/tex]
[tex]\implies \sf c=\pm 32.2\:in\:(nearest\:tenth)[/tex]
As distance is positive, c = 32.2 in (nearest tenth)
Step-by-step explanation :
Here, A right angled triangle is given with the measure of two sides and we are to find the measure of the third side.
We'll find the measure of third side with the help of the Pythagorean theorem,
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (Hypotenuse {)}^{2}= (Base) {}^{2} + (Perpendicular {)}^{2} }}} \\ \\ [/tex]
Here,
The base (BC) is 16 inThe perpendicular (AB) is 28 inThe hypotenuse is AC.[tex] \: [/tex]
So, substituting the values in the formula we get :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (AC {)}^{2}= (16) {}^{2} + (28 {)}^{2} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (AC {)}^{2}=256 + 784 }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (AC {)}^{2}=1040 }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad AC = \sqrt{1040} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\frak {\qquad AC = 32.24 }}} \\ \\[/tex]
Therefore,
The length of the hypotenuse (AC) is 32.2 in (Rounded to nearest tenth)he quadratic function h(t)=-16.1t^2 + 150 models a balls height, in feet, over time, in seconds, after it is dropped from a 15 story building. From what height, in feet, was the ball dropped? AND After how many seconds, rounded to the nearest hundredth, did the ball hit the ground?
Answer:
The time it takes the ball to hit the ground is 3.05secs
step - by - step explanation:
In order to find height from where ball is dropped, you have to find height or h(t) when time or t is zero.So plug in t=0 into your quadratic equation:h(0) = -16.1(0^2) + 150h(0) = 0 +150h(0) = 150 ft is the height from where ball is dropped. When ball hits the ground, the height is zero. So plug in h(t) = 0 and solve for t.0 = -16.1t^2 + 15016.1 t^2 = 150t^2 = 150/16.1t = sqrt(150/16.1)t = ± 3.05Since time cannot be negative, your answer is positive solution i.e. t = 3.05
This a a vector please help 30 points please brainliest
Answer:
Option #4:
[tex]X=\left[\begin{array}{ccc}10\\24\end{array}\right][/tex]
Step-by-step explanation:
Start With
[tex]\left[\begin{array}{ccc}5&-2\\2&-1\end{array}\right] \left[\begin{array}{ccc}2\\-4\end{array}\right][/tex]
1. Pivot Element
[tex]P_{1} =a_{1,1}=5[/tex]
[tex]\left[\begin{array}{ccc}5&-2\\2&-1\end{array}\right] \left[\begin{array}{ccc}2\\-24\end{array}\right][/tex]
2. Pivot Element Again
[tex]P_{2} =a_{2,2}=-1[/tex]
[tex]\left[\begin{array}{ccc}-1&0\\0&-1\end{array}\right] \left[\begin{array}{ccc}-10\\-24\end{array}\right][/tex]
3. Get x1 and x2 Values
[tex]\left \{ {{(-1)*x_{1}=(-10)} \atop {(-1)*x_{2}=(-24)}} \right.[/tex]
[tex]-x_{2} = (-24)\\x_{2} = 24\\\\-x_{1} = (-10)\\x_{1} = 10\\[/tex]
4. Get Answer
[tex]x_{1}=10\\x_{2}=24\\\\X=\left[\begin{array}{ccc}10\\24\end{array}\right][/tex]
Can someone help me…
Answer:
that’s 700 divided by 0.54 or 700 x 0.54
Step-by-step explanation:
Answer:
that’s 700 divided by 0.54 or 700 x 0.54
Step-by-step explanation:
Area triangle problem! Please help due tonight.
Side length of triangle is ax+9 and base is 4x+b… a=8 b=17
Answer:
218.5
Step-by-step explanation:
Hi brielleha
X = 3/2 = 1.5
4 x 1.5 = 6
B = 17
6 + 17 = 23
A = 8
8 x 1.5 = 12
12 + 9 = 21
6 x 1.5 = 9
9 + 10 =19
19, 21 23
A = 23 x 19
437/2 = 218.5
Which of the following shapes are quadrilaterals?
please help asap I'll make brainliest
Explanation:
A quadrilateral has four sides, and each side is a straight line.
Quad = 4
Lateral = side
This means we go for choices A and C.
Choice B is ruled out because of the curved side on the right.
Choice D is ruled out because it has 5 sides instead of 4.
Find the slant height of a cone of curved surface area 471.3 cm3 and base radius is 10 cm (take pi as 3.142)
Answer:
15
Step-by-step explanation:
471.3 = 3.142×10×H
H= 471.3÷31.42
H=15
what is the value of 1/7x1/7x1/7 so 1/7 to the 3rd power.
Answer:
1/343 = .00291545
Step-by-step explanation:
= 1/(7*7*7) =
The value of the exponential equation is A = ( 1/343 ) = ( 1/7 )³
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = ( 1/7 ) x ( 1/7 ) x ( 1/7 ) be equation (1)
On simplifying the equation , we get
A = ( 1/7 )³
Now , on further simplification , we get
A = ( 1/343 )
And , the value of A = 0.002915
Hence , the exponential equation is A = ( 1/7)³
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For each 15mm of coloured fabric Gavyn uses to make his curtains he also uses 2 cm of white fabric. Express the amount of white fabric to coloured fabric as a ratio in its simplest form
Answer:
Step-by-step explanation:
2cm = 2 * 10 mm
2 cm = 20 mm
for every 15 mm of colored fabric, Gavyn uses 20 cm of white fabric.
The ratio is expressed as white fabric to colored fabric.
Answer: Ratio white to colored = 20 / 15 = 4 / 3
Julian is working two summer jobs, making $8 per hour washing cars and making
$13 per hour tutoring. In a given week, he can work a maximum of 13 total hours and
must earn no less than $130. If a represents the number of hours washing cars and y
represents the number of hours tutoring, write and solve a system of inequalities
graphically and determine one possible solution.
Answer:
Jacob should work minimum of 14 hours washings cars to meet his requirement.
Step-by-step explanation:
Let the number of hours of washing cars be 'x'.
Let the number of hours of landscaping be 'y'.
Given:
Cost for Per hour for washing cars = $10
Cost for per hour Landscaping = $8
Total number of hours of working
Amount to be earned this weekend
So we can say that;
Also,
Amount to be earned this weekend should be greater than or equal to sum of Cost for Per hour for washing cars multiplied by number of hours of washing cars and Cost for per hour Landscaping multiplied by number of hours of landscaping.
framing in equation form we get;
Now Number of hours he worked for landscaping
So we get;
Subtracting both side by 32 we get;
Dividing both side by 10.
Hence Jacob should work minimum of 14 hours washings cars to meet his requirement.
Step-by-step explanation:
I WILL MARK BRAINLIEST
Answer: B
Step-by-step explanation:
Write two different equations with equal solution sets.
Answer:
x + 8 = 13
3x - 2 = 13
The solution set of both equations is {5}.
Step-by-step explanation:
x + 8 = 13
3x - 2 = 13
A triangle has two sides of lengths 5 and 12. What value could the length of
the third side be? Check all that apply.
A. 9
B. 19
C. 5
D. 7
E. 17
F. 11
Answer:
Answer is A and F.
Step-by-step explanation:
To form a triangle the sum of any 2 sides must be greater than the third side.
The answer is not:
B as 5 + 12 < 19
C. as 5+5 < 12
D, as 7 + 5 = 12
E as 5 + 12 = 17
Answer is A and F.
Jason went shopping.
he bought a watch and a pair of trainers for a total price of £53.55
This price includes a 15% loyalty discount.
before the discount, the trainers were priced at £38.
work out the price of the watch before the discount
Answer:
£25
Step-by-step explanation:
100 - 15 = 85
53.55 ÷ 0.85 = 63
63 - 38 = 25
Is the following a statistical question?
In what year did Thomas Jefferson become president of the United States?
it is on ixl
Zoe Swam 25 laps in the pool but this was only 50% of her total swim. How many more laps doe she need to swim?
Answer:
25
Step-by-step explanation:
25
Answer: how many more means subtract so subtract and it will be 25 LLaps
What is the value of x in the equation below?
Answer:
9
Step-by-step explanation:
[tex] \frac{6 + 2x}{4} = 6 \\ 6 + 2x = 6(4) \\ 2x = 24 - 6 \\ x = \frac{18}{2} \\ x = 9[/tex]
What does the slope of the function represent in this situation?
Slope of a function is defined as the rate of change of a function. It determine the unit price of values or amount traveled in unit time.
Slope of a functionSlope of a function is defined as the rate of change of a function. It determine the unit price of values or amount traveled in unit time.
The formula for expressing the slope of a function is given as;
f'(x) = f(b)-f(a)/b-a
a and b are the intervals
The slope can also be expressed as a function of its coordinate (x, y)
Slope = y2-y1/x2-x1
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Answer:
the increase in pressure per meter of depth and the next question is the pressure at the oceans surface
Step-by-step explanation:
edge 2022
how do i answer this question?
Answer:
[tex]f^{-1}[/tex] (59) = 20
Step-by-step explanation:
[tex]f^{-1}[/tex] (x) is the inverse of f(x)
to find the inverse function, let f(x) = y and rearrange to make x the subject.
y = 3x - 1 ( add 1 to both sides )
y + 1 = 3x ( divide both sides by 3 )
[tex]\frac{y+1}{3}[/tex] = x
change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then
[tex]f^{-1}[/tex] (x) = [tex]\frac{x+1}{3}[/tex] , then
[tex]f^{-1}[/tex] (59) = [tex]\frac{59+1}{3}[/tex] = [tex]\frac{60}{3}[/tex] = 20