Answer:
This is the actual steps and answer.
Step-by-step explanation:
\text{Exponential Functions:}
Exponential Functions:
y=ab^x
y=ab
x
a=\text{starting value = }5000
a=starting value = 5000
r=\text{rate = }4\% = 0.04
r=rate = 4%=0.04
\text{Exponential Growth:}
Exponential Growth:
b=1+r=1+0.04=1.04
b=1+r=1+0.04=1.04
\text{Write Exponential Function:}
Write Exponential Function:
y=5000(1.04)^x
y=5000(1.04)
x
Put it all together
\text{Plug in time for x:}
Plug in time for x:
y=5000(1.04)^{7}
y=5000(1.04)
7
y= 6579.6589
y=6579.6589
Evaluate
y\approx 6580
y≈6580
round
The population after 7 years at the rate of 4% growth every year would be 6580.
What is the formula for exponential growth?Exponential growth is a function that grows or decays at a constant percent rate.
The formula used is [tex]y = b(1 + r)^ t[/tex]. where, y is the exponential growth function, b is the initial amount, r rate, and t time interval.
From the information given,
b = 5000
r = 4% = 4/100
= 0.04
t = 7 years
Therefore
[tex]y = b(1 + r)^ t[/tex]
[tex]y = 5000(1 + 0.04)^7[/tex]
[tex]y = 5000(1.04)^7[/tex]
y = 6580
Thus, The population after 7 years at the rate of 4% growth every year would be 6580.
Learn more about exponential growth;
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PLS HELP If g(n) varies inversely with n and g(n) = 6 when n = 2, find the value of n when g(n) = 1.5.
Answer:
g(2)=1.5. Which would be three.
Step-by-step explanation:
You would just plug in n=2 into the equation and then divide it out.
The value of n, when g(n) is 1.5, given that g(n), varies inversely with n and equals 6 when n is 2, we first find the constant of variation k = 12 and then divide k by 1.5 to get n = 8.
If g(n) varies inversely with n, the relationship between g(n) and n can be expressed as g(n) = k/n, where k is a constant. When g(n) = 6 and n = 2, we can find the constant k by multiplying 6 and 2 to get k = 12.
To find the value of n when g(n) = 1.5, we can set up the equation 1.5 = k/n. Using our previously found constant k (12), we substitute it into the equation to get 1.5 = 12/n. Solving for n, we multiply both sides of the equation by n and then divide both sides by 1.5 to get n = 12/1.5, which simplifies to n = 8.
HEEEEEEEEEEEEEEELLLLLLLPPPPPPPPPPP
Probably the third answer is right. If you divide the 9x-6y=12 by 3, it gives you the exact same equation as the 3x-2y=4. They're the same, so they'd overlap.
Mary Jackson gets a student rate of $27.50 a month for health insurance. There is a $200 deductible. She recently received treatment for a covered condition. The bill was $2,350.00. Mary's insurance company provided payment of 80% of the bill less the deductible.
Answer:
the company's payment was $1720
Step-by-step explanation:
Mary's total cost (without the monthly premium) is $630
How do you make 7 1/4 into a decimal
Answer:
7.25
Step-by-step explanation:
We know that 7 equals to 7.0. We also know that 1/4=0.25. So we can add the two together and we get 7.25
Aldrin and Jan are standing at the edge of a huge field. At 2:00 p.m., Aldrin begins to walk along a straight path at a speed of 3 km/h. Two hours later, Jan takes a straight path at a 608 angle to Aldrin’s path, walking at 5 km/h. At what time the two friends be 13km apart?
Answer: After 2:29 hours both Aldrin and Jan will be 13 km apart from each other.
Time at that instant will be : 4:00 pm + 2.29 hours= 6:29 pm
Step-by-step explanation:
According to the figure:
Ab= c = 13 Km
AC = b = [tex]distance= speed\times time =5\times t[/tex]=5t Km
After two hours the distance covered by the Aldrin say till point D :
[tex]distance=speed\times time=3km/hr\times 2 hrs=6 Km[/tex]
Since, we are interested in determining the time at which Aldrin and Jan both 13 Km apart. For that Aldrin Additional distance covered by the Aldrin from point D to B is :
[tex]distance=speed\times time= 3km/hr\times t=3t Km [/tex]
CB= a = CD+DB= 6+3t
We will apply Laws of cosines:
[tex]C^2=A^2+B^2-2AB\times Cos\theta[/tex]
[tex](13)^2=(6+3t)^2+(5t)^2-2(5t)(6+3t)Cos 60^o[/tex]
[tex]19t^2+6t-133=0[/tex]
On solving the the above equation by quadratic formula we get two values of 't'
1) t = 2.49 hours , 2) t = -2.80 hours
Since,time cannot be in negative so we will ignore the negative value of t
t = 2.49 = 2:29 hours ,(0.49 hour=0.49 × 60 min=29.4 min)
After 2.49 hours after the walking of Jan. Both Aldrin and Jan will be 13 km apart from each other.
Time at that instant will be : 4:00 pm + 2:29 hours= 6:29 hour
Given: m || n , <1 is congruent to <3
Prove: p || q
Answer:
A= Angle 1 congruent to angle 2
B= Transitive Property
C= Converse Corresponding angles theorem
Step-by-step explanation:
Graph the image of the given triangle under a dilation with a scale factor of −2 and center of dilation (0, 0) .
Can someone please help me? I just need help with the coordinates. Thanks so much!
Answer:
see attached diagram
Step-by-step explanation:
A dilation with a scale factor of -2 centered at the origin has a rule:
[tex](x,y)\mapsto\left(-2x,-2y\right).[/tex]
Then the image of the triangle ABC is triangle DEF(see attached diagram) with coordinates
[tex]D\left(8,-2);[/tex][tex]E\left(4,4);[/tex][tex]F\left(6,8).[/tex]Answer:
the other answer is correct
Step-by-step explanation:
took test on k12 and that was right
Jane moved from a house with 58 square feet of closet space to an apartment with 29.58 square feet of closet space. What is the percentage decrease of Jane's closet space? A. 96% B. 39% C. 49% D. 51%
Answer:
the answer is D 51 because if you do 29.58 divided by 58 you get .51 which is 51% decreased.
Step-by-step explanation:
every month, omar buys pizzas to serve at a party for his friends. In may, he brought three more than twice the number of pizzas he bought in April. If Omar bought 15 pizzas in may, how many pizzas did he buy in April
Answer:
Step-by-step explanation:
Omar bought 15 pizzas in May.
In May, he bought 3 more than twice the number that he bought in April.
Since we don't know how many he bought in April, let X = the number of April pizzas.
Then, 15 = 2X + 3
Now you can subtract 3 from both sides, then divide both sides by 2 to leave X by itself and discover what it equals.
Final answer:
Omar bought 24 pizzas in April, calculated by setting up an equation based on the information that in May he bought three more than twice the pizzas he got in April.
Explanation:
The question is asking to find the number of pizzas Omar bought in April given that he bought three more than twice the number in May, and he bought 15 pizzas in May. To solve this, we can set up an equation: April Pizzas + 3 = 2 × (April Pizzas) + 2 × 3. Since we know that Omar bought 15 pizzas in May, we substitute 15 for the total number of Pizzas in May, which gives us: April Pizzas + 3 = 30. Subtracting 3 from both sides gives us April Pizzas = 27 - 3, so April Pizzas = 24. Therefore, Omar bought 24 pizzas in April.
Find the value of x in this figure
If PQ is the tangent, then m∠P = 90°.
Therefore we can use the Pythagorean theorem:
[tex]x^2=5^2+12^2\\\\x^2=25+144\\\\x^2=169\to x=\sqrt{169}\\\\\boxed{x=13}[/tex]
Answer: 13Which expression is equivalent to (2x^4 y)^3 PLEASE HURRY!!!
Answer:
8x¹²y³
Step-by-step explanation:
(2x⁴y)³ Cube everything inside parentheses.
= 2² × (x⁴)³ × y³
= 8x¹²y³
The value of y varies directly as x, and y is 10 when x is 5. What is the value of y when x is 4?
Answer:
8.
Step-by-step explanation:
As seen in the pattern y seems to be two times x so 4 x 2 = 8.
Hope that helps
HALP! It's for my Math homework! I will make it a ton of pts!
The gas of your car is 40% full. There are 8 gallons of gas in a tank. What is the capacity of the gas tank?
Thanks in advance!
Step-by-step explanation:
Percentage by which the gas tank of the car is full = 40%
Amount of gas in the gas tank = 8 gallons
capacity of the gas tank = x gallons
40% * x = 8
(40/100) * x = 8
4x/10 = 8
4x = 8 * 10
4x = 80
x = 80/4
Answer = 20 gallons
GEOMETRY QUESTION: PLEASE ANSWER FAST!
Answer:
<A = 30
<B = 150
Step-by-step explanation:
cos<A = AK / ABAK = 4AB = 8Cos<A = 4/8Cos<A = 1/2A = Cos-1(0.5)A = 30 degreesSince BC and and AD are parallel, the interior angles of <A and <B sre supplementary.<A + <B = 18030 + <B = 180<B = 180 - 30<B = 150A basketball is priced at $35.00. If it is on sale for 40% off, what is the final cost?
A basketball priced at $35.00 with a 40% discount would cost $21.00 after the discount.
Explanation:The final price of the basketball can be calculated by first identifying the amount being discounted from the original price. A 40% discount of a $35.00 basketball means you take 40% of 35. Here's how:
0.40 (40% converted to decimal) times $35.00 equals $14.00.
This $14.00 is the discount from the original price. Now, subtract this discount from the original price of the basketball to get the final price: $35.00 - $14.00 equals $21.00.
So, the final cost of the basketball after a 40% discount is $21.00.
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rhianna is planning to redecorator her bedroom with paint and new pillows.she has a buget of $200.the cans of paint she wants cost $32 each and thows pillows are $30 each.Which inquality can rhianna use to find out how many cans of paint,x,and pillow,y,she can afford?
Step-by-step explanation Eeė
find the value of the variable. if your answer is not an interger, leave it in simplest radical form.
Answer:
A
Step-by-step explanation:
using the sine ratio in the right triangle, then
sin 45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{5}[/tex]
multiply both sides by 5
note the exact value of sin 45° = [tex]\frac{\sqrt{2} }{2}[/tex]
x = 5 × sin 45° = 5 × [tex]\frac{\sqrt{2} }{2}[/tex] = [tex]\frac{5\sqrt{2} }{2}[/tex]
Find the value of y when x = 4 in the equation x - 4y = 2 Show your work help
Answer:
y = 0.5
Step-by-step explanation:
plug in x = 4 into the second equation
4 - 4y = 2
Simplify
-4y = -2
y = 0.5
A line passes through the points (-10,-5) and (20,10) what is the equation of the line A. y=5x B.Y=2x C.1/2 x Dy=1/5 x
Answer:
C. y = ½x
Step-by-step explanation:
Step 1. Find the slope of the line
The general equation for a straight line is
y = mx + b
The slope m is
m =(y₂ -y₁)/(x₂/x₁)
Your points are (-10, -5) and (20, 10).
m = [10 – (-5)]/[20 – (-10)] Remove inner parentheses
m = (10+5)/(20 + 10)
m = 15/30
m = ½
===============
Step 2. Find the equation of the line
Substitute the point (20, 10) into the general equation.
10 = ½×20 + b
10 = 10 + b
b = 0
The equation of the line is y = ½x.
The graph shows your line passing through your two points with a slope
m = ½ and a y-intercept at (0, 0).
The basic measure of mass in the metric system is called
Answer:
Grams.
Step-by-step explanation:
Answer:
THE GRAM
Step-by-step explanation:
A steel rod that is 64 feet long must be cut into three pieces to fabricate the supports for a drill press. The longest piece is 3.09 times the shortest and the middle piece is 1.73 times the shortest. How long is each piece? Round nearest foot.
Answer:
let's x be the shortest piece
the middle piece is 1,73 *x
the longest piece is 3,09 x
then if we sum the 3 pieces we will get the steel rod that is 64 feet long
so x+1,73x+3,09x= 5,82x= 64 then x= 10,99 = 11
the shortest piece is 11 feet
the middle piece is 1,73*11=19,03 feet
The longest piece is: 3,09*11= 33,99= 34 feet
Jason's grandparents gave him $500 for his 16 birthday. He put the money in the bark and decided to withdrow $35 each week. I need help with part b, how do I do the table??
Answer:
X Y
0 $500
1 $465
2 $430
3 $395
4 $360
5 $325
6 $290
Step-by-step explanation:
You subtract 35 from the first Y.
is y = |x + 3| a linear function yes or noO
Answer:
Yes
Step-by-step explanation:
Because it passes vertical line test.
Yes, because y = x + 3 is a first degree function which is a linear function. Just ignore the absolute value.
ABC = PQR given ABC = PQR, m<B = 3v + 4, and m<Q = 8v vind m<B ans m<Qm
Answer:
v = 4/5 or 0.8
Step-by-step explanation:
Givens
These two corresponding parts are equal
<B = 3v + 4<Q = 8vEquation
3v + 4 = 8v Subtract 3v from both sides3v - 3v + 4 = 8v - 3v Combine4 = 5v Divide by 54/5 = 5v/5 DivideAnswer
v = 4/5 or v = 0.8
there is a string of green and white lights strung around a mirror for every 6 green lights there are four white lights if there are 30 green lights how many white lights are there
Answer: There are 20 white lights.
Step-by-step explanation:
Given : There is a string of green and white lights strung around a mirror for every 6 green lights there are 4 white lights.
i.e. Ratio of green lights to white lights = 6:4
i.e.
[tex]\dfrac{\text{Number of green lights}}{\text{Number of white lights}}=\dfrac{6}{4}\\\\\Rightarrow\ \dfrac{30}{\text{Number of white lights}}=\dfrac{6}{4}\\\\\Rightarrow\ \text{Number of white lights}=\dfrac{4\times30}{6}=20[/tex]
Hence, there are 20 white lights.
Simplify: 1 ( x − 5 ) − 1 3 ( − 3 x + 12 )
So since 1 multiplied by a number or variable, the number always stays the same we can say that 1(x-5)=x-5. We then, can open the parenthesis for 13*-3x+13*12. The answer for that would be -39x+156. So we then know that x-5-39x+156. We can simplify this until -38x+151.
Hope this helps. <3
A triangle has side lengths of 4, inches, 10 inches, and c inches.
Enter values to write an inequality that describes the possible values for c, the length of the third side of the triangle.
? < c < ?
Answer:
c<4+10
c<14
Step-by-step explanation:
can I get brainliest?
Answer:
6<c<14
Step-by-step explanation:
ben score 56 out of 79 marks in a maths test what is his score as a percentage to 1 decimal place
Answer:
56/79=.7088
The answer is 70.9%
Answer:
70.9%
Step-by-step explanation:
Hope this helps
I need help with number 3, i’m stuck!
Lin Makes $18 per hour. He got a raise. Now Lin makes $22 per hour.What is the percent raise?
Answer:4% raise
Step-by-step explanation: