The initial value of the function is 75.
The growth factor or growth rate of the function as a percent is 0.25%
An exponential growth model is defined as :
F(x) = A( 1 + r)^x
Where;
A = Initial amount,
r = rate of increase
x = time
Comparing the exponential growth function with the exponential growth model given;
f(x)=75(1.0025)ˣ
A = 75 = Initial amount
The growth rate of the model expressed as a percentage :
Taking :
(1 + r) = 1.0025
1 + r = 1.0025
r = 1.0025 - 1
r = 0.0025
Expressing r as a percentage:
r = 0.0025×100
= 0.25%
Hence we get the required answers.
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Given the polynomial f(x)= 2x^3-x^24x4
, what i the mallet poitive integer a uch that the intermediate value theorem guarantee a zero exit between 0 and a ?
The smallest positive integer a such that the intermediate value theorem guarantee a zero exist between 0 and 1
given that
polynomial f(x) = 2[tex]x^{3}[/tex] - [tex]x^{2}[/tex]- 4x+4
first derivation of f(x)
f'(x) = 6[tex]x^{2}[/tex] - 2x - 4
= 6[tex]x^{2}[/tex] - 6x +4x -4
= 6x(x-1) + 4(x-1)
= (6x+4)(x-1)
x = -0.6,1
second derivation of f(x)
f''(x) = 12x-2
now substitute x values in f''(x)
x=1
f"(x) = 12(1) - 2 = 12-2= 10
x= -0.61
f"(x) = 12(-0.61) -2 = -7.32-2= -9.32
a=1
the intermediate value theorem guarantee a zero exist between 0 and 1
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Find the value of ? in the figure below
Answer:
Step-by-step explanation:
24
What is the equation in slope intercept form of the line that passes through the y-intercept (0, 1) and has a slope of 4?
Responses
y = 4x - 1
y = 4x - 1
y = 4x - 11
y = 4x - 11
y = 4x + 11
y = 4x + 11
y = 4x + 1
The equation in slope intercept form of the line that passes through the y-intercept (0, 1) and has a slope of 4 is y = 4x + 1
The line is passing through the y intercept = (0, 1)
Here at x = 0, the values of y = 1
Then the y intercept of the line is 1
The slope of the line = 4
The slope of the line is the change in y coordinate with respect to the change in x coordinates of the function
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
x is the x coordinate
y is the y coordinate
Then the equation in the slope intercept form
y =4x + 1
Hence, the equation in slope intercept form of the line that passes through the y-intercept (0, 1) and has a slope of 4 is y = 4x + 1
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Regional erosion occurs at a rate of 2 m per 1,000 years. How much regional erosion will occur over 1,000,000 years? responses 20 m 20 m 200 m 200 m 2,000 m 2,000 m 100,000 m.
The erosion occurs at a rate of 2/1000 m/years. Over 1,000,000 years, the erosion will be 2,000 meters.
Rate is a ratio between one quantity to another quantity. Rate is also a measure of how fast a quantity changes when another quantity changes. For instance, velocity is a rate to measure the change of distance per amount of travelled time.
Suppose we have two quantities: x and y, with rate of change in y per change in x is denoted by dy/dx, then
y = dy/dx · x
In the given problem:
y = length of erosion
t = time
dy/dt = 2 meters / 1000year = 2/1000 meters/year
Then,
y = dy/dt · t
= 2/1000 · 1,000,000 = 2,000 meters
Hence, over 1,000,000 years, the regional erosion = 2,000 meters
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What is the least angle measure by which this figure can be
rotated so that it maps onto itself?
• 45°
•90°
•180°
•360°
The least angle at which given figure maps onto itself is 180°. This can be understand by using magnitude of symmetry.
What is symmetry?
In common parlance, the term "symmetry" describes a sense of lovely proportion and balance. A more precise definition of "symmetry" can be found in mathematics, where it typically refers to an object that is unaffected by certain transformations like translation, reflection, rotation, or scaling. Although these two interpretations of "symmetry" can occasionally be distinguished from one another, they are intricately linked and are therefore discussed jointly in this article. Aspects of mathematical symmetry can be seen in abstract objects like theoretical models, language, and music, as well as in the passage of time, as a spatial relationship, through geometric transformations, and in other types of functional transformations.
A figure in the plane has rotational symmetry if the figure can be mapped into itself by a rotation between 0° to 360° about the center of figure.
The given figure has one line of symmetry,
figure is divided into two parts that can overlap
angle will be = 360/2=180° .
So, the smallest angle is 180°.
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A sequence of patterns is made from circular tiles and square tiles
Here are the first three patterns in the sequence.
ooo
a b
000
pattern number 1 pattern number 2
pattern number 3
a) How many square tiles are needed to make pattern number 7?
b) How many circular tiles are needed to make pattern number 20?
c) When the pattern number is odd, the total number of tiles (square
and circular) needed to make the pattern
A will always be even B will always be odd C could be even or odd
(2)
(2)
(2)
a) 49 square tiles are needed to make pattern number 7
b) 84 circular tiles are needed to make pattern number 20
c) When the pattern number is odd, the total number of tiles (square
and circular) needed to make the pattern is B) always odd
What is meant by sequence?A sequence in mathematics is an enumerated collection of objects in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the sequence is defined as the number of elements (which could be infinite). Unlike a set, the same elements can appear multiple times in a sequence at different positions, and the order does matter. Formally, a sequence can be defined as a function from natural numbers (the sequence's positions) to the elements at each position. The concept of a sequence can be extended to include an indexed family, which is defined as a function from an arbitrary index set.
a) Squares tiles needed for 7 pattern =n²
n²=7²
n²=49
b) Circular tiles for 20th pattern=4(n+1)
=4(20+1)
=4(21)
=84
c) Total tiles(square and circle)
=n²+4(n+1)
for n=odd (let n=1,3,5)
n=1; 1+4(1+1)=9
n=2; 9+4(3+1)=25
n=5; 25+4(5+1)=49
Therefore, It is always odd
So, the answer is option B
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Gary is buying a $1,250 computer on an installment plan. He makes a down payment of $150. He has to make monthly payments of 48.25 for 2 1/2 years. What is the total finance charge?
Answer:
Step-by-step explanation:
Down payment = $150
Monthly Payment = $48.5
Buyer price = $1250
Number of months = 30 (2 1/2 years)
The total amount of monthly payments = Monthly payments × Number of months
= 48.5 × 30
= 1447.50
The total cost = Total amount of monthly payments + Down payments
= 1447.50 + 150
= 1597.50
Finance charge = Total cost - Buyer price
= 1597.50 - 1250
= 347.50
Find the value of x
Transversal angles, interior exterior angles, parallel
Answer:
115°
Step-by-step explanation:
They are the same angle because we know the lines are parallel.
Answer:
115°
Step-by-step explanation:
alternate exterior, they're the same
a) Factorise x^2+ 5x + 6
Step-by-step explanation:
[tex] {x}^{2} + 5x + 6[/tex]
[tex] {x}^{2} + 6x - x + 6[/tex]
[tex]x(x + 6) - 1(x + 6)[/tex]
[tex](x - 1)(x + 6)[/tex]
Miranda buys 5.1 pounds of avocados at the local store. How much does
one pound of the fruit cost if she is billed $16.83 for the purchase?
The cost of one pound is $3.3 or the rate of per pound fruits is $3.3.
What is meaning of one pound?
Pound is an unit to measure mass of an object. The plural form of pound is pounds.
What is the unitary method?
The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given that Miranda buys 5.1 pounds of avocados at the local store. The cost of the fruits is $16.83.
Apply unitary method to calculate the cost of 1 pound:
The cost 5.1 pounds fruit is $16.83.
The cost 1 pound fruit is $16.83/5.1 = $3.3.
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what is the answer to 365 x 240?
Answer:87,600
Step-by-step explanation:
Find negative absolute value of negative three fifths.
−3.5
negative three fifths
three fifths
3.5
-4 is the absolute value of -3.5 and three fifths.
What is Expression?An expression is combination of variables, numbers and operators.
negative absolute value of negative three fifths.
−3.5-3/5
Three fifths means three by five
-3.5-3/5
(-5(3.5)-3)/5
Minus seventeen point five minus three divided by five
-17.5-3/5
Minus twenty point five divided by five
-20.5/5
Minus four point one
-4.1
-4
Hence -4 is the absolute value of -3.5 and three fifths.
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Why is the product of two rational numbers always rational?
Select from the drop-down menus to correctly complete the proof.
Let ab and cd represent two rational numbers. This means a, b, c, and d are
Choose...
, and
Choose...
. The product of the numbers is acbd, where bd is not 0. Because integers are closed under
Choose...
, acbd is the ratio of two integers, making it a rational number. Integers or rational numbers.
The product of two rational numbers is always rational because (ac/bd) is the ratio of two integers, making it a rational number.
We need to prove that the product of two rational numbers is always rational. A rational number is a number that can be stated as the quotient or fraction of two integers : a numerator and a non-zero denominator.
Let us consider two rational numbers, a/b and c/d. The variables "a", "b", "c", and "d" all represent integers. The denominators "b" and "d" are non-zero. Let the product of these two rational numbers be represented by "P".
P = (a/b)×(c/d)
P = (a×c)/(b×d)
The numerator is again an integer. The denominator is also a non-zero integer. Hence, the product is a rational number.
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pls help sjajgdjsiaysgdhwiudhh
Answer:
scalene acute
Step-by-step explanation:
scalene = 2 sides are the same and one is different
acute = all three angles are smaller than 90
Find the Error A student found the slope of one segment on a line to be 4 and the slope of another segment on the same line to be 8/2. He concludes that the slope is different at different points on the line. Correct his thinking.
The slopes are similar in each segment of the line because the ratios, 8/2 and 4/1 are similar.
What is the slope of the triangle?The first step to understanding slope of a line is that; it represents the rate of change in the vertical axis to that in the horizontal axis.
Consequently, it follows that the slope of the first segment can be computed by drawing a triangle with vertical side length of 4 and a horizontal side length of 1.
Hence, the slope of the first segment (from the triangle is) 4 / 1.
Also, for the second segment; a triangle with vertical length; 8 and a horizontal length, 2. Hence, the slope of the segment is; 8 / 2.
Ultimately, since the ratios, 8 / 2 and 4 / 1 are similar, it follows that the two triangles are similar and consequently, the slope is same in each segment of the line.
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The perimeter of an isosceles triangle is 48 inches. Each leg is 6 inches less than two times the base.
Find the length of each side of the triangle.
The length of two same sides of isosceles triangle is 18 inches and the third side of the triangle is 12 inches.
According to the question,
We have the following information:
The perimeter of an isosceles triangle is 48 inches. Each leg is 6 inches less than two times the base.
We know that in an isosceles triangle two sides are equal.
Let's take the base of the triangle to be x inches.
Other sides = (2x-6) inches
So, we have the following expression:
2x-6+2x-6+x = 48
5x-12 = 48
5x = 48+12
5x = 60
x = 60/5
x = 12 inches
Now, the other two sides of triangle:
2*12-6
24-6
18 inches
Hence, the length of two same sides of isosceles triangle is 18 inches and the third side of the triangle is 12 inches.
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a boat travels 12 miles up the river in the same amount of time it takes to travel 32 miles down the same river. if the current is 5 miles per hour, what is the speed of the boat in still water?
Answer:
11 mi/h
Step-by-step explanation:
You want the speed of the boat when it travels 12 miles upstream against a current of 5 mph in the same time it travels 32 miles downstream with the current.
TimeThe relation between time, speed, and distance is ...
time = distance/speed
If b represents the speed of the boat, the times upstream and downstream are the same, so we have ...
(12 mi)/(b -5) = (32 mi)/(b+5)
Multiplying by the product of the denominators gives ...
12(b+5) = 32(b-5) . . . . . . also divided by "mi"
12b +60 = 32b -160 . . . . multiply by (b+5)(b-5)
220 = 20b . . . . . . . . . . . . add 160 -12b
11 = b . . . . . . . . . . . . . . . . . divide by 20
The speed of the boat in still water is 11 miles per hour.
__
Additional comment
Each trip took 2 hours.
a hammer get 300miles on 20 gallons of gas. How many miles can it cover on 50 gallons of gas
Answer:
750 miles
Step-by-step explanation:
20 gallons -------------- 300 miles
1 gallon ---------------- 300/20 = 15 miles
50 gallons -------------- 15x50 = 750 miles
how do you graph x=6
Answer: it’s a vertical line going through the point (6,0)
Step-by-step explanation: this is because when you only have an x value the line is going to be vertical line through the x value on that axis
kent spent 5/6 hour washing dishes on Monday as shown on the number line . kent washed dishes for the same amount of time on Tuesday and Wednesday. much time did kent spend washing dishes during those 3 days
Answer:150 minutes easy?
Step-by-step explanation:
A local farmer had a mouse problem in his barn. He estimated there were about 800
mice to start with. He adopted some cats and noticed that the number of mice was
decreasing by 8%/wk. The graph models the number of mice x weeks after the
farmer adopted the cats.
Identify and interpret the key features of the exponential function modeled in terms
of this situation!
Answer: try a c and e
Step-by-step explanation:
For this exponential
function,
what is the output value (y),
when the input value (x) is O?
y = 12.5x
*it’s not 1*
After solving the exponential function y = 12.5ˣ, the value of y = 1.
What is an exponential function?The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0.
The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
So, the exponential function:
y = 12.5ˣ
We know that x is 0.
The exponential function rule states that when the power is 0, the answer is always 1.
y = 12.5ˣ
y = 12.5⁰
y = 1
Therefore, after solving the exponential function y = 12.5ˣ, the value of y = 1.
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Correct question:
For this exponential function, what is the output value (y), when the input value (x) is O?
y = 12.5ˣ
|x-3| = |9-2x| solve the following question
Answer:
x = 4 or x = 6
Step-by-step explanation:
to solve the inequality
solve both
x - 3 = 9 - 2x OR x - 3 = - (9 - 2x)
x - 3 = 9 - 2x ( add 2x to both sides )
3x - 3 = 9 ( add 3 to both sides )
3x = 12 ( divide both sides by 3 )
x = 4
OR
x - 3 = - (9 - 2x)
x - 3 = - 9 + 2x ( subtract 2x from both sides )
- x - 3 = - 9 ( add 3 to both sides )
- x = - 6 ( multiply both sides by - 1 )
x = 6
5.8, 6.328, 5.8042, 5.84 order these numbers from least to greatest
Answer:
Step-by-step explanation:
5.8, 5.8042, 5.84, 6.328
f a certain cannon is fired from a height of 9.3 meters above the ground, at a certain angle, the height of the cannonball above the ground, h, in meters, at time, t, in seconds, is found by the function h(t) = - 4.9t^2 + 30.5t + 9.3. Find the time it takes for the cannonball to strike the ground.
The amount of time it takes for the cannonball to strike the ground is equal to 6.516 seconds.
How to determine the amount of time?Based on the information provided, we can logically deduce that the height (h) in meters, of this cannonball during above the ground is related to time by the following function:
h(t) = - 4.9t² + 30.5t + 9.3.
Generally speaking, the height of this cannonball would be equal to zero (0) when it strikes the ground. Therefore, we would equate the height function to zero (0):
0 = - 4.9t² + 30.5t + 9.3.
4.9t² - 30.5t - 9.3 = 0
Next, we would solve the quadratic equation by using the quadratic formula:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-(-30.5)\; \pm \;\sqrt{(-30.5)^2 - 4(4.9)(-9.3)}}{2(4.9)}\\\\x = \frac{30.5\; \pm \;\sqrt{930.25\; + \;182.28}}{9.8}\\\\x = \frac{30.5\; \pm \;\sqrt{1112.53}}{9.8}[/tex]
Time, x = (30.5 ± 33.3546)/9.8
Time, x = (30.5 + 33.3546)/9.8
Time, x = 63.8546/9.8
Time, x = 6.516 seconds.
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I need help please!!!!
Answer: -10/6
Step-by-step explanation:
Using the Slope Formula which is, [tex]\frac{y_{2} -y_1}{x_2-x_1}[/tex] you can substitute the numbers. This leads to [tex]\frac{-1 -9}{-1-(-7)}[/tex] which will get you, [tex]\frac{-10}{6}[/tex].
A concession stand serves hot dogs and
hamburgers at a ratio of 3 to 2. Based on this
ratio, how many hamburgers will be served if
there are a total of 60 hot dogs served? Use a
tape diagram to model your thinking.
Using ratios we know that 40 hamburgers will be served.
What are ratios?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.So, a number of hamburgers that will be served are:
The ratio of hotdogs and hamburgers = 3:2The total number of hotdogs served is 60.So, the number of hamburgers will be:
3/60 = 2/x3x = 60×23x = 120x = 120/3x = 40Therefore, using ratios we know that 40 hamburgers will be served.
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Correct question:
A concession stand serves hot dogs and hamburgers at a ratio of 3 to 2. Based on this ratio, how many hamburgers will be served if there are a total of 60 hot dogs served?
love = what? what will happen to the rest couples
Answer: love=an intense feeling of deep affection
Step-by-step explanation:
A 9-member team plans to run a 4-mile relay race. Distance markers are placed on the racecourse every 0.25 mile. a. Place an X on the number line at the approximate locations where the relay exchanges will take place. b. Will any of the relay exchanges take place at any of the 0.25-mile markers? If so, which one(s)? List the locations of all of the exchanges in decimal form.
Relay exchanges will not take place at any of the 0.25-mile markers
The calculated relay exchanges are
0.44440.88891.33331.77782.22222.66673.11113.55564How to find the relay exchangesThe number of team members which is 9 is equal to the number of relay exchanges in the 4-mile race.
This will result to the relay exchanges occurring at every 4/9, and repeated addition of 4/9 will give the other points, and the list is
4/9, 8/9, 4/3, 16/9, 20/9, 8/3, 20/9, 32/9, and 4 in fraction
In decimal form this will be listed in four decimal place
0.4444
0.8889
1.3333
1.7778
2.2222
2.6667
3.1111
3.5556
4
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You operate a theme park and want to use the temperature outside and the day of the week to predict how many people will be in attendance each day. While testing this model, you also want to see if the relationship between temperature and theme park visitors will be curvilinear. You decide not to test for interactions. How many betas will be in your model aside from the y-intercept?.
Three betas will be in our model aside from the y-intercept.
In the given question, we have to find how many betas will be in your model aside from the y-intercept.
You operate a theme park and want to use the temperature outside and the day of the week to predict how many people will be in attendance each day.
While testing this model, you also want to see if the relationship between temperature and theme park visitors will be curvilinear.
You decide not to test for interactions.
From the given question,
We have y intercept that means our model well be
[tex]y=\beta_{0}+x_{1}\beta _{2}+x_{2}\beta _{2}+x_{1}x_{2}\beta _{12}[/tex]
where [tex]\beta _{1}[/tex] is for temperature and [tex]\beta _{2}[/tex] is day of the week.
3 betas are there aside intercept of y.
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