Answer:
Part 1) The exponential function is [tex]y=140,000(1.05)^x[/tex]
Part 2) [tex]305,602\ people[/tex]
Step-by-step explanation:
Part 1) Write an exponential function
we know that
The exponential growth function is given by the formula
[tex]y=a(1+r)^x[/tex]
where
y is the population
x is the number of years
a is the initial population
r is the rate of change
we have
[tex]a=140,000\ people\\r=5\%=5/100=0.05[/tex]
substitute
[tex]y=140,000(1+0.05)^x[/tex]
[tex]y=140,000(1.05)^x[/tex]
Part 2) How much will the population be after 16 years?
For x=16 years
substitute the value of x in the exponential function
[tex]y=140,000(1.05)^{16}=305,602\ people[/tex]
An exponential function to model the population growth of 5% per year from an initial population of 140,000 after 16 years is y = 140,000(1 + 0.05)^x. After substituting x with 16, you calculate the growth and multiply by the initial population to find the population size after 16 years.
Explanation:To model the population growth in this scenario, we use an exponential growth function. The formula for exponential growth is y = P(1 + r)^t, where y is the final amount, P is the initial principal balance, r is the rate of interest, and t is the number of time periods the interest is applied. In this case, the population P is 140,000, the growth rate 'r' is 5% (or 0.05 when expressed as a decimal), and the number of years 't' is 16.
The exponential function in terms of 'x' (where 'x' represents the number of years) will be: y = 140,000(1 + 0.05)^x.
After plugging in 't' as 16 years, we calculate the population after 16 years as follows: y = 140,000(1 + 0.05)^16. Now we calculate the growth factor (1 + 0.05)^16 and multiply this by the initial population of 140,000 to determine the population after 16 years.
Haley's age is 6 years less than half her mother's
age. If Haley is 16 years old, what is an equation
that can be used to determine her mother's age?
Answer: (16+6)2=y
Step-by-step explanation: Hailey is six years younger than half her mother age, and she is 16. You add six to 16, and get 22. Multiply that by 2 and get 44.
Write the percent of free space on the computer as a decimal.
Volume Capacity Free Space % Free Space
(C:) 200 GB 150 GB 75%
Answer:
0.75
Step-by-step explanation:
Final answer:
To convert 75% to a decimal, divide 75 by 100 to get 0.75. This conversion is necessary to express the percent of free space on a computer in decimal form.
Explanation:
To convert the percent of free space on the computer to a decimal, you can follow these steps:
Take the percent value, which in this case is 75%.Write this percentage as a fraction with a denominator of 100, so 75% becomes ⅔.Divide the numerator by the denominator: 75 ÷ 100 = 0.75.The decimal equivalent of 75% is 0.75. This means that 75% of the computer's storage capacity is free space.
Noah says to find 20% of a number he divides the number by 5. Does Noah method always work?
Answer:
Yes because 20 percent of anything, including 0, multiplied by 5 is 100 percent
Step-by-step explanation:
Answer: yes
Step-by-step explanation:
it does work because 5x4= 20 and if you divide 20% by 5 you get 4. You can also do 20% Divided by 2 you get 100.
What type of triangle can a right triangle be?
Answer:
it could be a isosceles triangle.
Step-by-step explanation:
A right triangle can also be an isosceles triangle.
Final answer:
A right triangle, which always has a 90-degree angle, can be either Scalene if all sides are different lengths, or Isosceles if two sides are equal. The classification depends on the lengths of the sides. Additionally, right triangles are fundamental to the application of the Pythagorean theorem.
Explanation:
A right triangle is a type of triangle that has one angle measuring exactly 90 degrees. Despite always having this right angle, right triangles can vary in the lengths of their other sides and the measures of their other angles. So, a right triangle can also be classified based on its side lengths:
If all three sides of a right triangle have different lengths, it is a Scalene right triangle.If two sides of a right triangle (the legs) are of equal length, it is known as an Isosceles right triangle, and this also implies that the two non-right angles are equal, each being 45 degrees.Therefore, the type of right triangle depends on the specific side lengths and can be either Scalene or Isosceles. The understanding of right triangles also extends to concepts such as the Pythagorean theorem, which relates the lengths of the sides of a right triangle, stating that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Write an equation in Slope-intercept form for the line that is perpendicular to the line y = 2x - 5 that passes through the given point (4,-2).
Answer:
y = (-1/2)x
Step-by-step explanation:
The slope of the given line is 2, the perpendicular line wil have a reciprocal slope given by -1/2 (add a minus sign, move the slope to the denominator).
So all that's left to calculate is the offset b of a line
y = -1/2 x + b
such that it passes through (4,-2). Filling in that point gives:
-2 = -1/2*4 + b
so b = 0!
y = -1/2x is the answer
Line perpendicular to y = 2x - 5 is y = (-1/2)x.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know perpendicular lines have slopes that are negative reciprocal of each other.
The given line y = 2x - 5, has a slope of 2.
So, the given line will have a slope of (-1/2) passing through point (4,-2).
∴ - 2 = (-1/2)(4) + b.
- 2 = - 2 + b.
b = 0.
∴ y = (-1/2)x is our required line.
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plz help im in 5th grade 20 times 2
Answer:
40
Step-by-step explanation:
20
x 2
0x2=0
2x2=4
you have to take the bottom 2 in the ones place
then you have to multiply that by 0
last you have to multiply both 2's
and you have your answer
Solve the linear inequality.
5x-3(x+1)<7
The solution to the inequality 5x-3(x+1)<7 is x<5.
Step-by-step explanation:
Given inequality is;
5x-3(x+1)<7
Solving the inequality
[tex]5x-3x-3<7[/tex]
Adding 3 on both sides both sides of inequality
[tex]5x-3x-3+3<7+3\\2x<10[/tex]
Dividing both sides of inequality by 2
[tex]\frac{2x}{2}<\frac{10}{2}\\\\x<5[/tex]
The solution to the inequality 5x-3(x+1)<7 is x<5.
Keywords: inequality, division
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Do you guys now how to estimate 69.58.
Answer:
The answer is 70 if it's to whole number but if it's just rounding to the tenth spot it's 69.6
Step-by-step explanation:
It's 70 because if the tenth spot(the number after the decimal) is 5 or higher you add one on the one spot so that's why it's 70
Estimates are typically whole numbers.
To estimate an answer, you would take whatever numbers you are trying to add/subtract/multiply/divide ect. and round them to the nearest whole number then complete said action with them.
Example: 3.99 + 33.85 + 31.74
3.99 is closest to 4
33.85 is closest to 34
and 31.74 is closest to 32
Then, we would add up all the numbers: 4 + 34 + 32 = 70
70 is very close to 69.58, therefore 70 is a good estimate.
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What is the value of x in the equation 0.6x = 0.4 − 0.2x?
0.5
1
1.5
3
Answer:
x=0.5
Step-by-step explanation:
6x=4-2x
8x=4
x=1/2
Answer:
0.5
Step-by-step explanation:
You solve it as a 2-step equation.
0.6x=0.4-0.2x
Isolate the variables ((add 0.2x to both sides since that it how you get rid of it at the right))
Your equation should now be
0.8x=0.4
Divide both sides by 0.8 in order to get x by itself
x=0.5
What is the name of a shape with its length, width, and height all equal?
Answer:
cube
Step-by-step explanation:
Janelle ate 82% of the pie. What fraction of the pie remained
A distribution data has a maximum value of 96, a median value of 56.5, and a minimum of 23. Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth.
Answer:
The standard deviation estimate by the Range Rule of Thumb = 18.3
Step-by-step explanation:
i) maximum = 96
ii) minimum = 23
iii) standard deviation [tex]\approx[/tex] [tex]\frac{(maximum\hspace{0.1cm} - \hspace{0.1cm} minimum)}{4} = \frac{96 - 23}{4} = \frac{73}{4} = 18.25[/tex]
The standard deviation estimate by the Range Rule of Thumb = 18.3
Is this equation an infinite solution, no solution, or one solution?? 36-7x=-7(x-5) is
Answer:
no solution
Step-by-step explanation:
36-7x=-7(x-5)
first what we have to do is do the multiplications
36 - 7x = -7x + 35
we add 7x from both sides
36 - 7x + 7x = - 7x + 7x + 35
36 = 35
we subtract 36 from both sides
36 - 36 = 35 - 36
0 = -1
This means that the system has no solution
if we look at the equation at the beginning we can realize since we have the same term on both sides "-7x" and a term without x on each side, this means that we can never find a value of x that meets the conditions
Solve the equation 0.5p-3.45=-1.2
Answer:
4.5
Step-by-step explanation:
The equation above is such that we find the value of p. Therefore, it is calculated thus:
0.5p - 3.45 = -1.2
Add 3.45 to both sides of the equation
0.5p - 3.45 + 3.45 = -1.2 + 3.45
0.5p = 2.25
Divide both sides by 0.5
0.5p/ 0.5 = 2.25/0.5
p = 4.5
Answer: The answer is 4.5
Step-by-step explanation:
0.5p - 3.45 = -1.2
So basically, you take everything on the left of the equal sign (0.5p-3.45) then since the sign is telling you to subtract, you use the inverse operation, so you would add 0.5 to the 3.45 and to the -1.2. So when you add the 0.5 to the 3.45, it cancels out, and when you add it to the -1.2, you should get 2.25. Then now that your done adding, your expression should be: 0.5p = 2.25. Then, now that you have 0.5p = 2.25, and there is no sign, multiplication is expected, but since were using the inverse operation, were dividing. So, 0.5p divided by 0.5 cancels out, and then you divide the 2.25 by 0.5 and you should get 4.5 after dividing. So, your final answer should be p = 4.5.
Hope this helps!!
Our car has a 15-gallon gas tank. A lower grade of gasoline costs $2.96 per gallon. The premium grade gasoline costs
$3.15 per gallon. There are three gallons left in your gas tank. What is the difference in the cost of filling your tank between the two grades
of gasoline?
a) $2.05
b) 52.28
c) $35.52
d) $44.40
Answer:
The correct option is b.) $2.28
Step-by-step explanation:
i) the gas tank is of 15 gallons
ii) there are three gallons left in the gas tank
iii) therefore the tank has to be filled with 15 - 3 = 12 gallons
iv) lower grade of gasoline costs $2.96 per gallon
v) the upper grade of gasoline costs $3.15 per gallon
vi) the cost of filling the tank with the lower grade gasoline
= 12 [tex]\times[/tex] 2.96 = $35.52.
vii) the cost of filling the tank with the lower grade gasoline
= 12 [tex]\times[/tex] 3.15 = $37.80
viii) therefore the difference in the cost of filling your tank between the two grades
= $37.80 - $35.52 = $2.28
Therefore the correct option is b.) $2.28
Final answer:
The difference in the cost of filling the 15-gallon gas tank between the two grades of gasoline is $2.28.
Explanation:
Firstly, let's calculate how many gallons are needed to fill the car's tank completely, since it currently has 3 gallons left in a 15-gallon tank. This means the car requires 15 - 3 = 12 gallons of gasoline to be filled up.
Next, we calculate the cost to fill up the car with the lower grade gasoline that costs $2.96 per gallon. The cost for 12 gallons would be 12 x $2.96 = $35.52.
Then, we calculate the cost to fill up the car with the premium gasoline that costs $3.15 per gallon. The cost for 12 gallons would be 12 x $3.15 = $37.80.
Finally, to find the difference in cost between the two grades of gasoline, we subtract the lower cost from the higher cost: $37.80 - $35.52 = $2.28. Hence, the difference in cost is $2.28, so the correct answer is option (b).
Included angle between WA and AS
Answer:
I believe the answer is angle A.
Step-by-step explanation:
I think it is angle A because INCLUDED angle between WA AS and only angle a is included in both. Hope this helps.
Answer:
< AStep-by-step explanation:
3x squared minus 7x minus 34 is less than or equal to -10x + 2
Answer:
x =-2 or 0
Step-by-step explanation:
Factoring 7x2+3x-34
The first term is, 7x2 its coefficient is 7 .
The middle term is, +3x its coefficient is 3 .
The last term, "the constant", is -34
Step-1 : Multiply the coefficient of the first term by the constant 7 • -34 = -238
Step-2 : Find two factors of -238 whose sum equals the coefficient of the middle term, which is 3 .
-238 + 1 = -237
-119 + 2 = -117
-34 + 7 = -27
-17 + 14 = -3
-14 + 17 = 3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -14 and 17
7x2 - 14x + 17x - 34
Step-4 : Add up the first 2 terms, pulling out like factors :
7x • (x-2)
Add up the last 2 terms, pulling out common factors :
17 • (x-2)
Step-5 : Add up the four terms of step 4 :
(7x+17) • (x-2)
Which is the desired factorization
(x - 2) • (7x + 17) = 0
How many hours did you sleep each day this month
10 hours, none more, none less
:
The basketball team is ordering hats for its members. Each hat costs $8. The fee to ship any size order of hats is $6. Let h equal the number of hats ordered and c equal the total cost.
The equation that I think you are looking for is:
c = 8h + 6
which of the following phrases would represent this expression x/3
Answer:
x is divided by 3
Step-by-step explanation:
Factor completely. x2−2x−24 Enter your answer in the box.
Answer:
x = -4
x = 6
Step-by-step explanation:
x² - 2x -24 = 0
x² - 6x + 4x - 24 = 0
x ( x - 6 ) + 4 ( x - 6) = 0
x + 4 and x- 6
so either of them is zero so values if x are
X = -4
X = 6
The Answer is (x+4) (x-6). I just took the test
-3/4 / (-8/5) write in simplest form
Answer:
Ans = 15/32
Step-by-step explanation:
-3/4 / (-8/5)
= -3/4 ÷ (-8/5)
= -3/4 * -5/8
= 15/32 (- * - = +)
The safe load for a certain horizontal beam used to hold up part of a building varies inversely as the length between the
supports.
True
False
The statement is true.
Answer: Option 1.
Explanation:
An horizontal beam is constantly flat and has a consistent cross-segment. Notwithstanding normal shaft parameters, bar has the accompanying properties: Direction. A flat shaft might be situated either along the worldwide X-hub or worldwide Y-pivot.
A horizontal beam is used to hold a building up right and to give the support to the building. But the length of the horizontal beam differs in an inverse way between the supports.
Which expression is not equivalent to cos 150°
A) sin 240 degrees
B) cos 210 degrees
C)cos 60 degrees
D) -sin 60 degrees
Answer:
cos 60° isn't equivalent
Step-by-step explanation:
cos 60°=1/2
The expression that is not equivalent to cos 150° is option C, cos 60 degrees, because it lies in the first quadrant where cosine is positive, unlike cos 150° which is negative.
The expression that is not equivalent to cos 150° is C) cos 60 degrees. The cosine function is positive in the first and fourth quadrants and negative in the second and third quadrants. Since 150° lies in the second quadrant, cos 150° is negative. Now, if we look at the provided options, sin 240° is essentially -sin(240° - 180°), which equals -sin 60°; this is the same as cos(180° - 240°), which equals cos(330°) or cos(−30°), and therefore, equivalent to cos 150°.
Similarly, cos 210° is also in the third quadrant where cosine is negative; this is the same as -cos(210° - 180°), which equals -cos 30° which also equals -sin 60°. Therefore, this is equivalent to cos 150° as well. In contrast, cos 60° lies in the first quadrant where cosine is positive, which does not match the sign of cos 150°. Lastly, -sin 60° is simply the negative of sin 60° and since sin 60° = cos 30°, it matches the value of cos 150° in terms of magnitude but is opposite in sign, thus it is equivalent to cos 150°.
Therefore, option C, cos 60 degrees, is not equivalent to cos 150°.
A bag holds 11 beads. 7 are red, the rest are white. Two beads are taken at random from the bag. What is the probability that one bead of each colour is taken? You must show your working.
Got 2/4 marks for 14/55
Answer:
28/55
Step-by-step explanation:
The probability of taking a red bead first and a white bead second is:
P(red, white) = (7/11) (4/10)
P(red, white) = 14/55
The probability of taking a white bead first and a red bead second is:
P(white, red) = (4/11) (7/10)
P(white, red) = 14/55
So the probability that one bead of each color is taken is:
P = P(red, white) or P(white, red)
P = 14/55 + 14/55
P = 28/55
Answer:
56/110=14/55
Step-by-step explanation:
you get 4 marks!
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if 48 men have ration for 16 days how long will the food last if a reinforcement of 16 men arrived
Step-by-step explanation:This is a simple question.
The food that lasts for 48 men for 16 days is 48 × 16 = 768 units.
Now because of 16 additional members i.e. a total of 64 men the food will last for:
768÷64 = 12 days. Answer.
Final answer:
The ration that would have lasted for 16 days for 48 men will now last for 12 days when an additional 16 men are added to the group, making it a total of 64 men.
Explanation:
The question concerns a problem in ration proportion related to the consumption of food by a group of men. Initially, 48 men have enough rations for 16 days. If 16 more men join this group, the total number of men becomes 48 + 16 = 64 men. We need to calculate how long the rations will last for the increased group.
We can consider this as a problem of inverse proportion where more men would consume the same amount of food in lesser time. The original group of 48 men could last 16 days, so we can set up the following proportion: 48 men × 16 days = 64 men × X days. Solving for X gives us X = (48 men × 16 days) / 64 men, which simplifies to X = 12 days. Therefore, the food would last for 12 days for 64 men.
Find the total surface area of the figure.
A. 150.7 ft sq.
B. 402.1 ft sq
C. 301.5 ft sq
D. 288.4 ft sq
Answer:
Answer is B
surface area for a cylinder : 2 (pi) r h + 2 (pi) r^2
r= 4
h= 12
2 (pi) x 4 x 12 + 2 (pi) × 4^2
= 402 .1
Answer:
it is B
Step-by-step explanation:
An architect is making a floor plan for an apartment. The floor plan will include a Great Room with a length of 30 feet and a width of 20 feet. On her floor plan, 1/4 inch will represent 1 foot of the room’s actual width. What will be the width of the Great Room, in inches, on her floor plan?
Answer:
5 inches
Step-by-step explanation:
we know that
The scale drawing is
[tex]\frac{1}{4}\ in : 1\ ft[/tex]
using proportion find out the width of the great room on her plan
[tex]\frac{(1/4)}{1}\ \frac{in}{ft}=\frac{x}{20}\ \frac{in}{ft}\\\\x=20(1/4)\\\\x=5\ in[/tex]
Answer:
5 inches
Step-by-step explanation:
Hope this helped!!
Which expression is equivalent to 5(8z)
Answer:
answer is 40z
Step-by-step explanation:
multiply the numbers and keep the variable the same
Most bees have a body temperature of 35* Celsius. When they sleep, it can drop by up to 2* celsius. What's their range in body temperature written as an inequality with the variable t?
33°≤ t ≤ 35°
Step-by-step explanation:
The body temperature of a bee is given as 35°
When it sleeps, it drops by 2°
The sleeping temperature is therefore : 35°-2°=33°
The rage of body temperature is : 33°-35°
If t is body temperature then the rage in body temperature is;
33°≤ t ≤ 35°
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Keywords : body, temperature, sleep,drop,range, variable
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