If each year the population grows by 2.5%, then the "exponential-function" which shows the relationship between "y" and "t" is y = 300,000 × [tex](1.025)^t[/tex].
The "Exponential-Growth" is defined as a type of growth where the rate at which something grows is proportional to its current value. This results in a rapid and increasingly faster growth over time.
The relationship between "y" (population) and "t" (time in years) can be modeled by an "exponential-function" ;
⇒ y = a × [tex](1+r)^{t}[/tex],
where "a" is = initial population, "r" is = annual growth-rate (in decimal), and "t" is = time;
In this case, the "initial-population" is = 300,000, and
The annual growth rate is = 2.5% or 0.025,
So, we can write exponential function as : y = 300,000 × [tex](1+0.025)^{t}[/tex],
Simplifying the expression,
We get,
⇒ y = 300,000 × [tex](1.025)^t[/tex],
Therefore, the required exponential-function is y = 300,000 × [tex](1.025)^t[/tex].
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87,178 time what equals 458,930
Answer: 5.26
Step-by-step explanation:
458,930/87,178 =
5.264 =
5.26
7. You record the heights of two plants each month for 3 months. In what month will Plant A be as tall as Plant B?
Answer:
16
Step-by-step explanation:
starting from month 2, how many more months will A be as tall as B?
A grows at 1.75 in per month
B grows at 1.5in per month
so 7.5+1.75x = 11+1.5x
solve for x
x=14
so from month 2, need to go for another 14 mos.
so at month 16, they'll be same height
After taxes, Jess takes home a salary of J = $5000 every month. She pays P percent of this to her rent and all her fixed bills each month, leaving her with K left. She spends half of K on groceries, leaving her with L left. If she spends 1331 of L on gifts and puts 2552 of L into her savings account, this would leave her with $200 for miscellaneous expenses. What is the value of P?
Using percentage, the correct answer is "The value of P is $3,500 and it corresponds to 70% of her salary".
Define percentage?The denominator of a percentage, also known as a ratio or a fraction, is always 100. For instance, Sam would have received 30 points out of a possible 100 if he had received a 30% on his maths test. In ratio form, it is expressed as 30:100, and in fraction form, as 30/100. Here, "percent" or "percentage" is used to translate the percentage symbol "%." The percent symbol can always be changed to a fraction or decimal equivalent by using the phrase "divided by 100".
First, we need to calculate L.
1/3 or 33.33% of L spend on gift.
2/5 or 40% of L spent on savings.
This would leave her with $200 for miscellaneous expenses:
= 100% - (33.33% + 40%)
= 100% - 73.33%
= 26.67%
So, 26.67% = $200 for miscellaneous expenses
Rule of three, to calculate L.
26.67% is $200.
100% will be:
= (100 X 200) ÷ 26.67
= 20000 ÷ 26.67
= $750
L= $750
Now we going to calculate K.
"K is twice the amount of L".
K = L X 2
K = 750 X 2
K= $1,500
Finally, we going to calculate P.
P = J - K
J = $5,000
K = $1,500
P =$5,000 - $1500
= $3,500
Rule of three
5000 is 100%
3500 will be:
= 3500 x 100 ÷ 5000
= 350000 ÷ 5000
P = 70%
The value of P is $3,500 and it corresponds to 70% of her salary.
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what is 999.09344471 rounded to the nearest square kilometer?
The nearest kilometers to 999.09344471 km is 1000 km.
Given value is 999.09344471 Km.
We have to calculate the round off value to the nearest kilometers. we know that after the decimal if the value of tenth place is 5 or bigger than 5 then we add 1 to the tens place digit, this is the fundamental rule of rounding off.
Now on following this rule from the very right hand side up to the tenth place digit we come to the conclusion that only the value after the decimal (934) is to be rounded off which is (900).
So 999.09344471 km is finally becomes 999.900 km after rounding of to nearest hundredth value.
Again rounding off 999.900 km to nearest km so it becomes 1000 km.
The nearest kilometers to 999.09344471 km is 1000 km.
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The platoon drank 155 liters of water. How many milliliters did the platoon drink?
Answer:
155000 milliliters of water
Step-by-step explanation:
We Know
The platoon drank 155 liters of water.
How many milliliters did the platoon drink?
1 liter = 1000 milliliters
155 liters = 155 x 1000 = 155000 milliliters of water
So, the platoon drank 155000 milliliters of water.
The platoon drank 155,000 milliliters of water.
1 liter = 1000 milliliters
Therefore, 155 liters = 155,000 milliliters
So, the platoon drank 155,000 milliliters of water.
Can someone please help me
Answer:
Step-by-step explanation:
-2 x + 4 =2 x - 4 solve .
Answer:
[tex]\sf{x = 2}[/tex]
Step-by-step explanation:
Question type: solving equations with variables on both sides.
[tex]\textsf{This is a question with variables on both sides, to solve this we need to get the variable x }[/tex]
[tex]\textsf{alone. (getting the x on one side)}[/tex]
--------------------------------------------------------------
[tex]\sf{-2x~+~4~=~2x~-~4[/tex]
Subtract 4 from both sides.
[tex]\sf{-2x~=~2x~-8[/tex]
Subtract 2x from both sides.
[tex]\sf{-4x~=~-8}[/tex]
Divide both sides by -4.
[tex]\bf{x~=~2[/tex]
Therefore, x would be 2.
[tex]-jurii[/tex]
Answer:
x=2
Step-by-step explanation:
From the set {21, 29, 49}, use substitution to determine which value of x makes the equation true. 8(x - 20) = 304 A. 49 B. none of these C. 29 D. 21
Answer:
We can solve this equation by using substitution. We substitute each value of x in the given set and check which one makes the equation true.
Let’s start with A. 8(x - 20) = 304 becomes 8(49 - 20) = 304 which simplifies to 8(29) = 304 which is not true.
Let’s try B. 8(x - 20) = 304 becomes 8(none of these - 20) = 304 which simplifies to 8(-20) = 304 which is not true.
Let’s try C. 8(x - 20) = 304 becomes 8(29 - 20) = 304 which simplifies to 8(9) = 304 which is not true.
Finally, let’s try D. 8(x - 20) = 304 becomes 8(21 - 20) = 304 which simplifies to 8(1) = 304 which is not true.
Therefore, none of these values of x make the equation true
Step-by-step explanation:
Given the function f(x) =3x^2-6x-9 is the point (1,-12) on the graph of f?
Answer: Yes
Step-by-step explanation:
For questions like this, youve been given a value for x, and a value for y.
Plug in and see if it works out!
[tex]3x^2- 6x - 9 = y[/tex]
[tex]3(1)^2- 6(1) - 9 = -12[/tex] ----- Plugging in for x and y
[tex]3 - 6 - 9 = -12[/tex]
[tex]-12 = -12[/tex]
Since -12 is indeed equal to -12, we conclude the statement is true;
In terms of the graph, this translates to, "Yes, the point (1, -12) is on the graph of [tex]y = 3x^2- 6x - 9[/tex]
So your answer is Yes
Clinton and Stacy decided to travel from their home near Austin, Texas, to Yellowstone National Park in their RV.
- The distance from their home to Yellowstone National Park is 1,701 miles.
- On average the RV gets 10.5 miles per gallon.
- On average the cost of a gallon of gasoline is $3.60.
Based on the average gas mileage of their RV and the average cost of gasoline, how much will Clinton and Stacy spend on gasoline for the round trip to Yellowstone National Park and back home?
A. $1,166.40
B. $2,480.63
C. $583.20
D. $64,297.80
this is the total cost for the round trip, the answer is (C) 583.20.
what is round trip ?
A round trip refers to a journey from a starting point to a destination and then back to the starting point. In other words, it involves traveling to a place and then returning to the original location.
In the given question,
To calculate the cost of gasoline for the round trip, we need to first find the total amount of gasoline they will use. We can calculate this by dividing the distance of the trip by the RV's average gas mileage:
Total gasoline used = distance ÷ gas mileage
Total gasoline used = 1,701 miles ÷ 10.5 miles per gallon
Total gasoline used = 162 gallons (rounded to the nearest whole number)
Now, we can find the total cost of gasoline by multiplying the total amount of gasoline used by the average cost of a gallon of gasoline:
Total cost of gasoline = total gasoline used × cost per gallon
Total cost of gasoline = 162 gallons × 3.60 per gallon
Total cost of gasoline = 583.20
Since this is the total cost for the round trip, the answer is (C) 583.20.
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Express the answers in simplest form. If a die is rolled one time, find the probability of (a) Getting a 6. (b) getting an even number (c) number greater than 3 (d) number greater than 0 (E) number greater than 4 and an odd number?
Answer:
a) 1/6
b) 1/2
c) 1/2
d) 1
e) 1/6
Step-by-step explanation:
a)Getting a six
=1/6
b)Gettingan even number =3/6=1/2
c)number greater than 3
=3/6=1/2
d)number greater than 0
=6/6=1
e)number greater than 4 and an odd number
=1/6
Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.
The x y-coordinate plane is given. The curve starts at the point (0, 5), goes down and right, changes direction at the point (2, 0), goes down and left, changes direction at the point (0, −5), goes up and left, changes direction at the point (−2, 0), goes up and right, continuing until it reaches its starting point.
The standard form equation of the ellipse as described in the task content is;
x²/2² + y²/5² = 1What is the standard form equation of the ellipse as described?It is evident from the task content that the standard form equation of the ellipse is to be determined.
Recall, the equation of an ellipse takes the form;
(x - h)²/a² + (y - k)²/b² = 1
where (h, k) is the center and a represents the distance of the center to each vertex on the x-axis and b represents the distance from the center to each vertex on the y-axis.
Therefore, for the given scenario where center is at the origin; the equation of the ellipse is;
x²/2² + y²/5² = 1
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what is the leading coefficient of a third-degree function that has the output of -110 x=3 and has zeros of 14, I, -I
The leading coefficient of a third-degree function that has the output of -110 x=3 and has zeros of 14, I, -I is 10
How to find the leading coefficient of a third-degree functionIf a third-degree function has zeros 14, I, and -I, it can be factored as: f(x) = a(x - 14)(x - I)(x + I)
'a' denotes the leading coefficient.
We may use the knowledge that the function's output is -110 when x = 3 to calculate the value of 'a'.
Substituting x = 3 into the function's factored form yields:
f(3) = a(3 - 14)(3 - I)(3 + I) = -110
When we simplify this equation, we get:
a(-11)(3 - I)(3 + I) = -110
a(-11)(9 - I^2) = -110
a(-11)(9 + 1) = -110 (since I2 = -1)
a(-11)(10) = -110
-110a = -1100
a = 10
Hence , the third-degree function's leading coefficient is 10.
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Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. √5,5i
The polynomial function of lowest degree with rational coefficients P(x) = x⁴ + 20x² - 125
What is a polynomial?A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.
To find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. √5,5i.
Since √5 and 5i are zeros, then their conjugates -√5, and -5i are also zeros.
So,
x = √5,x = 5i.x = -√5,x = -5iSo, the factors of the polynomial are
x - √5,x - 5i.x + √5,x + 5iSo, multiplying the factors together, we get the polynomial.
So, P(x) = (x - √5)(x - 5i)(x + √5)(x + 5i)
= (x - √5)(x + √5)(x - 5i)(x + 5i)
= [x² - (√5)²][x² - (5i)²]
= [x² - 5][x² - (5²i²)]
= [x² - 5][x² - 25(-1))]
= [x² - 5][x² + 25]
Expanding the brackets, we have
= [x² - 5][x² + 25]
= [x² × x² + 25x² - 5x² + 25 × (-5)]
= x⁴ + 20x² - 125
So, P(x) = x⁴ + 20x² - 125
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Find the value of x.
Answer: x=22
Step-by-step explanation:
see image for explanation
calculate the distance that P is :
a. north of Q b.east of Q
The distance of P at north of Q is 34.98 km.
The distance of P at east of Q is 19.39 km.
What is the distance of P?
The distance of P at the given directions is calculated by resolving the vector into vertical and horizontal components.
The distance of P at north of Q is calculated as follows;
Py = d sinθ
Py = 40 km x sin (61)
Py = 34.98 km
The distance of P at east of Q is calculated as follows;
Px = d cosθ
Px = 40 km x cos (61)
Px = 19.39 km
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Comparing Rates of Change Station Cards
Two students are texting.
●
Student A is texting at the rate given in the table.
Number of
Tests Sent
0
1
2
3
4
12
Number of Texts Sent
てん
0
10.
5
10
Student B is texting at the rate given in the graph.
15
20
2 3 4
Minutes
5
7+
What is the different in the texting rate of these two students?
what is student A's rate ?
Student B's rate ?
what is
Answer:
To compare the texting rates of Student A and Student B, we need to calculate their respective rates of change.
For Student A, we can use the formula for the slope of a line:
slope = (change in y) / (change in x)
In this case, the "y" variable represents the number of texts sent, and the "x" variable represents the number of tests sent. Looking at the table, we can see that Student A sent 10.5 texts after sending 1 test, and 10 texts after sending 2 tests. So the change in y is -0.5 (10.5 - 10), and the change in x is 1. Therefore:
slope = (-0.5) / 1 = -0.5
So Student A's texting rate is -0.5 texts per test.
For Student B, we can look at the graph and find the slope of the line connecting any two points. Let's choose the points (2, 15) and (5, 23) because they are easy to read off the graph. The change in y is 8 (23 - 15), and the change in x is 3 (5 - 2). Therefore:
slope = 8 / 3 = 2.67
So Student B's texting rate is 2.67 texts per minute.
To find the difference in their texting rates, we simply subtract:
difference = Student B's rate - Student A's rate
difference = 2.67 - (-0.5) = 3.17
So the difference in their texting rates is 3.17 texts per test.
Step-by-step explanation:
The Dahlia Flower Company has earnings of $3.64 per share. if the benchmark PE for the company is 21, how much will you pay for the stock?
Answer:
Step-by-step explanation:
To calculate the stock price, you can multiply the earnings per share (EPS) by the benchmark PE ratio.
The stock price would be:
$3.64 x 21 = $76.44
So you would pay $76.44 per share for the stock of The Dahlia Flower Company.
how to find 6 rational numbers between 3 and 4?
The six rational numbers between 3 and 4 are: 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6
Listing the rational numbers between 3 and 4To find 6 rational numbers between 3 and 4, we can start by finding the difference between 4 and 3, which is 1.
We can then divide this difference by any number and add it to 3
So that the number will be less than 4 but greater than 3
Now, we can add this gap size successively to 3, starting with the first rational number after 3, to find the six rational numbers between 3 and 4:
3.1, 3.2, 3.3, 3.4, 3.5, 3.6
So, the six rational numbers between 3 and 4 are: 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6
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Please help due in 1 hour
Answer:
Answer is B. 3x^2 +2x - 2.5
Step-by-step explanation:
Just factor out and simplify.
[tex]\frac{0.25x^2*(3x^2+2x-2.5)}{0.25x^2}[/tex]
x cannot be 0 or else the denominator is 0 making the function undefined.
Answer:
it is B
Step-by-step explanation:
An architect is considering bidding for the design of a new museum. The cost of drawing plans and submitting a model is $11,000. The probability of being awarded the bid is 0.2. If the architect is awarded the bid, she will make $180000 minus the $55000 cost for plans and a model.
We can compute the expected value using the given values in the problem such as we have the cost of drawing and submitting the model amounting of $11,000.
We also know that once the project is awarded to them, the anticipated profit is $180,000. Therefore, the expected value is just $180,000 minus $55,000 and the answer is $125,000.
We can compute the expected value using the given values in the problem such as we have the cost of drawing and submitting the model amounting of $11,000.
We also know that once the project is awarded to them, the anticipated profit is $180,000. Therefore, the expected value is just $180,000 minus $55,000 and the answer is $125,000.
The graphs of the functions f(x) = 6x² and g(x) = x + 12 are shown below. Determine the
approximate solution(s) to the given functions. Show or explain your reasoning.
The approximate solution(s) to the given functions are x= -4/3, 3/2.
The given functions are f(x)=6x² and g(x)=x+12.
Set the functions equal to each other, then solve for the variable.
f(x)=g(x)
6x² = x+12
6x²-x-12=0
By splitting middle term we get
6x²-9x+8x-12=0
3x(2x-3)+4(2x-3)=0
(2x-3)(3x+4)=0
2x-3=0 and 3x+4=0
x= -4/3, 3/2
Therefore, the approximate solution(s) to the given functions are x= -4/3, 3/2.
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You are walking from home to a shoe store. You stop for a rest after 1/3 miles. The shoe store is actually 3/4 miles from home. How much farther do you have to walk? Write your answer as a fraction in simplest form.
Answer:
[tex]\frac{5}{12}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] - [tex]\frac{1}{3}[/tex]
[tex]\frac{9}{12}[/tex] - [tex]\frac{4}{12}[/tex] = [tex]\frac{5}{12}[/tex]
Helping in the name of Jesus.
You purchased 96 ounces of fruit. Fruit costs $3 per pound. The cashier says you owe $4,608 for the fruit, but you know that is not correct. Look at the cashier's work and figure out how much you should pay. Explain what the cashier did wrong. 96 x 16 = 1,536 pounds 1,536 pounds x $3 = $4,608
Answer: you pay 18$
Step-by-step explanation:96 ounce×1pound/16ounce×3$/1pound=18$
The amount the cashier charged is incorrect. Based on the given information, the amount of fruit purchased is 96 ounces, which is equivalent to 6 pounds. Therefore, the total cost of the fruit should be 6 pounds x $3 per pound = $18.
The error the cashier made was converting ounces to pounds incorrectly. 96 ounces is equivalent to 6 pounds, not 1,536 pounds. The cashier multiplied 96 by 16 (the number of ounces in a pound) instead of dividing by 16 to get the number of pounds.
simplified version of 3 square root 4x over 5
3√4x/5
the / slash before the 5 is over so you put the 3√4x at the top of the fraction and the 5 at the bottom, so it would be 3√4x divide 5
Find the length of the third side of the right triangle 19, 21 and c
The length of the hypotenuse is 28.3
What is Pythagoras theorem?Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
A right angle triangle is a triangle that has one of it's angles has 90°. And Pythagoras theorem is applied to only right angled triangle.
If a and b are the legs of the triangle and c is the other side(hypotenuse) then,
c² = a²+b²
c² = 19² +21²
c² = 361+441
c² = 802
c = √802
c = 28.3
therefore , if the two legs are 19 and 21, the length of the other side is 28.3
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The length of the hypotenuse is 28.3
What is Pythagoras theorem?Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
A right angle triangle is a triangle that has one of it's angles has 90°. And Pythagoras theorem is applied to only right angled triangle.
If a and b are the legs of the triangle and c is the other side(hypotenuse) then,
c² = a²+b²
c² = 19² +21²
c² = 361+441
c² = 802
c = √802
c = 28.3
therefore , if the two legs are 19 and 21, the length of the other side is 28.3
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Can someone please help me
If tan(a) > 1 where could angle a be on the unit circle?
Option B is correct because the tangent of angle a is greater than 1 when a is between 0 and pi/4. Option G is correct because the tangent of angle a is also greater than 1 when a is between 3pi/4 and pi.
When tan(a) > 1, this means that the tangent of angle a is greater than the length of the adjacent side divided by the length of the opposite side in a right triangle. Since the adjacent and opposite sides of a unit circle have a length of 1, this means that the opposite side of angle a is less than 1.
To determine where angle a could be on the unit circle, we need to find the angles whose tangent is greater than 1. Since tangent is positive in the first and third quadrants, the angles we need to consider are in the first and third quadrants.
In the first quadrant, the angle whose tangent is 1 is pi/4, and the tangent increases as the angle increases. Therefore, angle a could be between 0 and pi/4 (option B).
In the third quadrant, the angle whose tangent is 1 is 5pi/4, and the tangent decreases as the angle increases. Therefore, angle a could also be between 3pi/4 and pi (option G).
Therefore, options B and G are correct, and angles a could be located in the regions described by these options on the unit circle.
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a mean of 589 grams with standard deviation of 16 grams . if you pick 23 fruits at random then 14% of the time their mean weight will be greater than how many grams?
14% of the time the mean weight of 23 fruits will be greater than approximately 594.33 grams.
What is the Central Limit Theorem (CLT)?
According to the CLT, the distribution of sample means from a population with mean μ and standard deviation σ, will be approximately normal with mean μ and standard deviation σ/√n, where n is the sample size.
In this case, the population mean is 589 grams and the population standard deviation is 16 grams. We are picking a sample of 23 fruits at random, so the standard deviation of the sample means will be:
σ/√n = 16/√23 ≈ 3.33
To find the value of x such that 14% of the time the sample mean will be greater than x, we need to find the z-score that corresponds to the 86th percentile of the standard normal distribution. We can use a table or a calculator to find that z-score:
z = invNorm(0.86) ≈ 1.08
The sample mean is normally distributed with a mean of 589 grams and a standard deviation of 3.33 grams. Using the formula for z-score:
z = (x - μ) / (σ / √n)
We can solve for x:
x = z × (σ / √n) + μ
x = 1.08 × (16 / √23) + 589
x ≈ 594.33 grams
Therefore, 14% of the time the mean weight of 23 fruits will be greater than approximately 594.33 grams.
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Lin is tracking the progress of her plant's growth. Today the plant is
5 cm high. The plant grows 1.5 cm per day.
a. Write a linear model that represents the height of the plant after d
days.
(Equation)
b. What will the height of the plant be after 20 days?
Answer:
a. The linear model that represents the height of the plant after d days can be expressed as:
h(d) = 1.5d + 5
where h(d) is the height of the plant in centimeters after d days, and 1.5d represents the growth rate of 1.5 cm per day multiplied by the number of days (d). The constant term 5 represents the initial height of the plant, which is 5 cm.
b. To find the height of the plant after 20 days, we can substitute d = 20 into the linear model:
h(20) = 1.5(20) + 5
= 30 + 5
= 35
So, the height of the plant after 20 days will be 35 cm.
Graph the solution to the inequality |2x + 2) > 6.
The solution to the inequality is all the values of x that are either greater than 2 or less than -4. The required graph of inequality is given below.
What is Inequality :In mathematics, an inequality is a statement that compares two values, often using the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
Inequality graphs show the region of the coordinate plane that satisfies an inequality. The graph of inequality can be determined in a similar way to the graph of an equation, but with some additional steps.
Here we have
The inequality |2x + 2| > 6
To graph the solution to the inequality |2x + 2| > 6,
we can start by rewriting the inequality as two separate inequalities without the absolute value:
2x + 2 > 6 or 2x + 2 < -6
Simplifying these inequalities, we get:
2x > 4 or 2x < -8
x > 2 or x < -4
Therefore,
The solution to the inequality is all the values of x that are either greater than 2 or less than -4. The required graph of inequality is given below.
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