Answer:
Select all the examples of the exponential function
a) y=3x-2
b) y=3^x
c) y=(1/2)^3x
d) y=3x^2
E) y=(1/2)^x
Area under the curve
f(x) = x 2 + 2x
g(x) = x + 2
Answer: The area under the curve refers to the area between the curve of a function and the x-axis. To find the area under the curve of a function, you would typically integrate the function with respect to x and then evaluate the definite integral between a set of limits.
For example, to find the area under the curve of f(x) = x^2 + 2x from x=0 to x=a, we would integrate the function with respect to x,
∫[0,a] (x^2 + 2x) dx = (1/3)x^3 + x^2 evaluated from x=0 to x=a,
Similarly, to find the area under the curve of g(x) = x + 2 from x=0 to x=a, we would integrate the function with respect to x,
∫[0,a] (x + 2) dx = (1/2)x^2 + 2x evaluated from x=0 to x=a
It's important to note that the definite integral is only defined if the function is continuous and has no vertical asymptotes on the interval.
Step-by-step explanation:
Flu is spreading exponentially at a school. The number of new flu patients can be modeled using the
equation F=10e^0. 12d, where d represents the number of days since 10 students had the flu.
(a) How many days will it take for the number of new flu patients to equal 50? Determine your answer
algebraically using the natural logarithm. Round your answer to the nearest day
If the number of flu patients at the school is modelled by the equation [tex]F=10e^{0. 12d}[/tex] , then the number of days that it will take for the number of patients to reach 50 is 13 days .
The Exponential Growth equation is given as : [tex]F=10e^{0. 12d}[/tex] ;
We have to find How many days will it take for the number of new flu patients to equal 50 .
So , we substitute the value [tex]F=50[/tex] in the model equation ;
we get ;
⇒ [tex]50 = 10e^{0. 12d}[/tex] ;
dividing both side by 10 ,
we have ;
⇒ [tex]5=e^{0. 12d}[/tex] ;
taking [tex]\ln[/tex] on both sides ,
⇒ [tex]\ln 5 = 0.12d(\ln e)[/tex] ,....we know that [tex]\ln e = 1[/tex] ;
⇒[tex]d= \frac{\ln 5}{0.12}[/tex] ⇒ 13.41198 ;
≈ 13 days .
Therefore , it will take 13 days for the number of patients to reach 50 .
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a jit system uses kanban cards to authorize movement of incoming parts. in one portion of the system, a work center uses an average of 99 parts per hour while running. the manager has assigned an inefficiency factor of .31 to the center. standard containers are designed to hold 5 dozen parts each. the cycle time for parts containers is about 105 minutes. how many containers are needed? (
The required number of containers are two.
How to solve the problem to number of container?105 minutes per process cycle.
We must first determine the utilization rate of the process in order to determine the number of containers required for the parts. Usage rate is the typical unit utilised each hour.
The scenario specifies that the procedure uses 88 components every hour.
The net cycle time per part per hour is determined as follows: (99/60) x 105 = 173.25
0.31 is the efficiency factor.
We can determine the total number of things Kanban can maintain using the information provided:
= 173.25/(1 - 0.31)
= 119.54
We may calculate the total number of containers required by dividing the container capacity by the entire number of parts after we know how many total pieces will be stored.
Each container can hold 8 dozens, or 96 pieces.
= 119.54
Consequently, two containers are required.
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3 times what equals 5?
Answer: its 1.6667.
Answer:
Step-by-step explanation
3*X=5
X=5/3
X=1.67
a lawn sprinkler located at the corner of a yard rotates through 80 degrees and sprays water of 20 ft. what is the length of the arc of the sector watered?
The length of the arc of the sector watered is 0.89π.
In the given question, a lawn sprinkler located at the corner of a yard rotates through 80 degrees and sprays water of 20 ft.
We have to find the length of the arc of the sector watered.
From the given question,
r = 20 ft, θ = 80 degree
A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends.
The formula for the length of the arc of the sector watered is
L = [tex]\frac{\theta}{360^{o}}\times 2\pi r[/tex]
Now putting the value
L = [tex]\frac{80^{o}}{360^{o}}\times 2\times\pi \times20[/tex]
Now simplifying the length
L = [tex]\frac{320^{o}}{360^{o}}\pi[/tex]
L = 0.89π
Hence, the length of the arc of the sector watered is 0.89π.
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Zell invested $80,000 in two different types of stocks. The first type earned 9% and the second type earned 12%. If the profit on the 12% stocks was $150 more than the profit on the 9% stocks, how much did Zell invest in the 9% stock?
Zell invested $80,000 in two different types of stocks. Solving for x gives us the amount invested in the 9% stock:
x = $45000
What is stock?Generally, Let x be the amount invested in the 9% stock.
Then (80,000 - x) is the amount invested in the 12% stock.
The profit on the 9% stock is 0.09 * x and the profit on the 12% stock is
0.12 * (80,000 - x).
We know that the profit on the 12% stock is $150 more than the profit on the 9% stock.
So we can set up the following equation:
0.12 * (80,000 - x)
= 0.09 * x + 150
x=45000
Therefore, Zell invested $80,000 in two different types of stocks. the amount invested in the 9% stock is $45000
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Answer:
$45,000
Step-by-step explanation:
ange the following polynomial in column and then add 1.(9x+3y)+(5x-4y)
)????????????????????????????????????????????????
Answer:
14x - y
Steps:
(9x + 3y) + (5x - 4y)
Determine the sign:
9x + 3y + 5x - 4y
Combine as terms:
14x - y
I hope it helps you :)
In ΔKLM, k= 1.2 cm, � m∠L=93° and � m∠M=6°. Find the length of I, to the nearest 10th of a centimeter
Using the law of sines, the length of l is: 12.1 cm.
What is the Law of Sines?The Law of Sines is a theorem in triangle geometry that relates the lengths of the sides of a triangle to the sine of its angles. It states that for any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all three sides.
Given the following:
k = 1.2 cm
m<L = 93°
m<M = 6°
m<K = 180 - 93 - 6 = 81°
Using the law of sines, sin K/k = sin L/l:
sin 81/1.2 = sin 93/l
Find l:
(sin 81)(l) = (sin 93)(12)
l = (sin 93)(12)/(sin 81)
l = 12.1 cm
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Jessica is measuring two line segments. The first line segment is 30 cm long while the second line segment is 500 mm long. How long are the two line segments together?A. 80 cmB. 25 cmC. 47 cmD. 49 cm
The length of the two line segments together is 80 cm
Step 1: Convert 500mm into cm.
We know that the value of 1mm is equal to 0.1 cm.
Then, 500mm will be 500mm*0.1 = 50 cm.
Therefore, the second line segment is 50 cm long.
Step 2: Calculate total length.
Let the first line segment be L1= 30 cm long and the second line segment be L2= 50 cm long.
Now, the total length is
L = L1 + L2
Substitute the values L1= 30 cm and L2= 50 cm in L = L1 + L2.
Hence, the length of the two line segments together is 80 cm
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In the diagram, if PW = 12 and PT = 9, find PX.
The length of segment PX in this problem is given as follows:
PX = 9.
How to obtain the length of segment PX?The theorem used to solve this problem is given as follows:
A line parallel to one side of a triangle divides the other two proportionately.
In this problem, all the horizontal lines are parallel, hence the side is divided proportionality, as the resulting triangles in the context of this problem are all similar.
PX is three-fourths of the length of the segment PW = 12, hence it's length is given as follows:
PX = 3 x 12/4
PX = 3 x 3
PX = 9 units.
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In manufacturing, systematic sampling could be used to determine if the machines are operating correctly. Which of the following best describes this type of sampling
According to the given information Every 10th product in the line is selected.
How does systematic sampling work?Systematic sampling is a probabilistic strategy that includes selecting people from the general population at predetermined intervals, such as each 15th people on a list of the population. If the community is set up in a random order, this can replicate the benefits of simple random sampling.
Why is sampling a systematic process?Biased sample sizes and subpar survey results are reduced by systematic sampling. If there is a low chance that data will be manipulated: Data validity may be compromised if researchers rearrange a data set. The best strategy for surveys when there is little likelihood of data manipulation is systematic sampling.
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Help w number 1 please super confused
An equilateral triangle is one that has all three of its sides be in line with one another.A slash mark is used to indicate the congruent sides.Congruent angles are ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
How do you identify congruent angles?An equilateral triangle is one that has all three of its sides be in line with one another.A slash mark is used to indicate the congruent sides.An equilateral triangle always has angles that are 60° in length.
It is referred to as an isosceles triangle when a triangle's two sides are identical. When the corresponding sides and angles of two angles match, the angles are said to be congruent.
When stacked, two angles are also congruent if they match.
If they line up with each other after turning or moving it, then.
Also creating equivalent vertex angles are a parallelogram's diagonals.
Congruent sides - L and X, G and Y, and F and T.
Congruent angles - ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
ΔLGF ≅ ΔXYT
Congruent angles are ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
Congruent sides are L and X, G and Y, and F and T.
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Please Help me out!!
The solution to f(g(h(x))) = [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
f(x) = [tex]x^{4} + 6[/tex]
g(x) = [tex]x-3[/tex]
h(x) = [tex]\sqrt{x}[/tex]
Therefore to find f(g(h(x))),
fogoh(x) = f(g(h(x)))
We first substitute the value of h(x) as above,
f(g([tex]\sqrt{x}[/tex] )) ....... as h(x) = [tex]\sqrt{x}[/tex]
Now, we substitute the value of g(x) where x is [tex]\sqrt{x}[/tex]
f([tex]\sqrt{x} -3[/tex]) ....... as g(x) = [tex]x-3[/tex]
Then we substitute the value of x in f(x) with [tex]\sqrt{x} -3[/tex]
[tex](\sqrt{x} -3)^{4} + 6[/tex]
Now we further solve to find a simpler form of the equation,
[tex](\sqrt{x} -3)^{4} + 6[/tex]
= [tex](x^{2} -12x^{3/2} +54x- 108\sqrt{x} +81) + 6[/tex]
= [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
Therefore, fogoh(x) = f(g(h(x))= [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
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Ishi walked a total of 2 miles on a treadmill. He walked at a constant rate of 4 miles per hour. Which expression shows how long, in minutes, Ishi walked on the treadmill? 2.5 miles : 4 moles/hour x 60 minutes/1 hour 2.5 miles : 4 mmoles/hour x 60 minutes/1 hour 2.5 miles : 4 mom/10 mg x 60 minutes/1 hour 2.5 miles : 4 milem/hour x 60 minutes/1 hour
Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour. To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).
Answer: 2.5 miles : 4 milem/hour x 60 minutes/1 hour
Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.
To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).
Therefore, 2.5 miles / 4 miles/hour x 1 hour = 0.625 hour or 37.5 minutes.
Ishi walked on the treadmill for time 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.
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Which statement is true of table A and table B shown below?
Table A represents a function because there is only one output for
each input value.
Table B represents a function because there is only one output for
each input value.
Table A represents a function because there is only one input for each
output value.
Table B represents a function because there is only one input for each
output value.
Table A represents a function, but Table B does not represent a function.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
A function or mapping is described as a collection of pairs of x and y that are ordered such that given different values of x, there will also be different values of y, or vice versa. For instance, the function x=y+2 yields a different x for every different value of y, while yielding the same x value for every single different value of y. We obtain two distinct x for two distinct ys, thus we can refer to this as a function at that point.
As, each element of X is associated with unique element of Y, so this is a function.
Table A
X Y
3 1
2 0
1 0
As, each element of X is associated with a unique element of Y, so this is a function.
Table B
X Y
3 -2
5 1
5 2
Hence, Table A represents a function, but Table B does not represent a function.
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suppose car gas mileage is normally distributed with a mean of 25 miles per gallon. if 67% of cars get at least 23 miles per gallon, what percentage of cars get less than 30 miles per gallon? a
So, on solving the provided question, we can say that percentage = 1/15 X 100 = 15%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
car gas mileage is normally distributed with a mean of = 25 miles per gallon
67% of cars get at least 23 miles per gallon
percentage of cars get less than 30 miles per gallon
25-23/30
2/30
1/15
percentage = 1/15 X 100 = 15%
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What is the 4 in front of the formula called?
The 4 in front of the formula is called a coefficient.A coefficient is a number that is multiplied by a variable or a constant in an algebraic expression.
In this case, the 4 is being multiplied by the formula, which makes it a coefficient.
A coefficient is a numerical value that is used in an algebraic expression or equation. It is placed in front of a variable or a constant, and it is multiplied by that particular element. The coefficient is used to adjust the value of the expression or equation, and it can be any number, including fractions, negative numbers, and decimals. For example, if a formula were written as 4x + 2 = 10, then the 4 in front of the x is the coefficient. This number is used to adjust the value of the expression, and it can be changed to any other number in order to alter the equation. Coefficients are very useful in mathematics, and they can be used to solve many types of equations and problems.
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10. Your little brother borrows
$5.50 from you. You now have
$20. Which equation shows how
much money you had before you
let your brother borrow money?
Answer:x-5.50=20
Step-by-step explanation:
Can anyone help me answer this question?
In a geometric progression, the first term is 7, the last term 448 and the sum 889. Find
the common ratio.
Answer:
Step-by-step explanation:
Given : In a GP the first term is 7
the last term is 448
and the sum 889
To find : Common ratio ? The number of terms is 7.
The common ratio is 2
Answer:
common ratio (r) = 2
Step-by-step explanation:
solution in picture
A school has a square courtyard and wants to create diagonal walkways. the length of
each side of the courtyard is 25 meters. approximately how long is each walkway?
The length of each side of the courtyard is 25 meters. Then 35.36 meters long is each walkway.
In the given question, a school has a square courtyard and wants to create diagonal walkways.
The length of each side of the courtyard is 25 meters.
We have to find how long is each walkway.
By dividing the square in half to form a right triangle, you can find the solution. The Pythagorean theorem can then be used to find the hypotenuse.
According the Pythagorean Theorem
[tex]a^2+b^2 = c^2[/tex]
[tex](25)^2+(25)^2=c^2[/tex]
Now solving,
625 + 625 = [tex]c^2[/tex]
[tex]c^2[/tex] = 1250
Taking square root on both side, we get
c = 35.36 meters.
Hence, 35.36 meters long is each walkway.
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If h(x) = -x(1 - x), find h(-3).
Answer:
12
Step-by-step explanation:
h(-3)= -(-3)(1-(-3))=
3(4)=12
Convert 17 cm to decimeters
Answer: 1.7
Step-by-step explanation: First, let's see how many decimeters are in 1 cm. To find it, we must divide the cm by 10. So, we can do 17 / 10 or move the decimal one spot left. They should both = 1.7. I hope this helped!
what are the four calculator operations that a student is expected to be able to perform on the ap test?
While some College Board math sections permit all students to use a calculator, other math portion do not. Students can prayer the use of a four-function calculator for use on Non calculator sections.
Four-function calculators are basic calculators that have functions limited to subtraction, addition, multiplication, square roots, division, and percentage.
Four-function calculators can only be used on test portion that need math calculations.
They must be put away during non-mathematical part.
Board policy on use of a calculator may vary by exam. Check by reading calculator rules for the PSAT/NMSQT and PSAT 10 and the SAT or visiting AP Students to read calculator policies for specific AP exams.
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lanie has decided to add strength training to her exercise program. her trainer suggests that she add weight lifting for 5 minutes during her routine for the first week. each week thereafter, she is to increase the weight lifting time by 2 minutes. a) which formula represents this sequential increase in weight lifting time?
23 minutes she will be devoting to weightlifting in week 10.
function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Formula represent the sequential increase in weight lifting time is :
f (n) = 2n + 5
f (n) = 2n + 5
f (10-1) = 2(10-1) + 5
f(9) = 2(9)
f(9) = 18
f(9) = 23
Therefore,23 minutes she will be devoting to weightlifting in week 10.
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what is the maximum of the sinusoidal function? enter your answer in the box.
Answer:
Step-by-step explanation:
B
A right triangle is shown below.
ہو
60%
X
What is the sine of t?
1
The functions sin and cosine, sometimes known as sin() and cos(), show how a right triangle is shaped. Answer is 8.212°.
What does sin t mean in math?The functions sin and cosine, sometimes known as sin() and cos(), show how a right triangle is shaped.
The ratio of the opposite side to the hypotenuse is called sin(), and the ratio of the adjacent side to the hypotenuse is called cos(), when viewed from a vertex with angle.
So, the Pythagorean identity-based formula for sin is sin²x = 1 - cos²x.
Hypotenuse²=base²+perp²
(8)²=(7)²+(perp)²
64=49+(perp)²
64/49=perp²
1.306=perp²
Now taking square root on both sides
Perp=√1.306
Perp=1.142
Sin C=opposite/hypotenuse
Sin =1.142/8
Sin C=0.14285
C=Sin^-1 0.14285
C=8.212°
Answer is 8.212°.
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A bicycle wheel has a radius of 225 mm and has 25 equally spaced spokes. What is the approximate arc length, rounded to the nearest hundredth, between each spoke? Use 3.14 for . Show your work.
The approximate arc length is 56.52mm.
What is arc length in a circle?The central angle that creates the intercepted arc's central angle, or the arc measure, is expressed in degrees. Arc length can be estimated as a percentage of the circle's circumference by multiplying the circle's diameter by the arc length, divided by 360.
The distance between two places along a segment of a curve is known as the arc length.
Given that, the bicycle wheel has a radius (r) = 225 mm
And number of equally spaced spokes (n) = 25
π = 3.14
Perimeter of the bicycle wheel (P) = 2*π*r
Perimeter of the bicycle wheel = 2 * 3.14 * 225 mm
Perimeter of the bicycle wheel = 1413 mm
The arc length = Perimeter of the bicycle wheel (P) / number of spokes (n)
The arc length = 1413 / 25 mm
The arc length = 56.52 mm
The approximate arc length is 56.52mm.
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give the equation of the line in slope intercept form of the line with a slope of -4/3 and that passes through the point (3,-3)
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{4}{3}}(x-\stackrel{x_1}{3}) \implies y +3= -\cfrac{4}{3} (x -3) \\\\\\ y+3=-\cfrac{4}{3}x+4\implies {\Large \begin{array}{llll} y=-\cfrac{4}{3}x+1 \end{array}}[/tex]
question 6 a data analyst at an e-commerce company is working with a spreadsheet containing last month's sales. the most expensive product their company sells costs $49.99, so they want to quickly confirm that all of the data in the sales column is $49.99 or less. what function can they use?
The required function,which best describe the problem is split function.
What is Split function?By designating one of the given string's sub-strings as the delimiter, the split() method can be used to divide a given string or line. The output is the string that comes before and comes after the substring that was supplied as a delimiter.
According to question:a data analyst at an e-commerce company is working with a spreadsheet containing last month's sales.
the most expensive product their company sells costs $49.99, so they want to quickly confirm that all of the data in the sales column is $49.99 or less.
This situation is defined for split function, which is best describe it.
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Wyatt has $780 to spend at a bicycle store for some new gear and biking outfits. assume all prices listed include tax.
he buys a new bicycle for $398.35.
he buys 2 bicycle reflectors for $19.41 each and a pair of bike gloves for $35.27.
he plans to spend some or all of the money he has left to buy new biking outfits for $46.60 each.
write and solve an inequality which can be used to determine oo, the number of outfits wyatt can purchase while staying within his budget.
The inequality which can be used to determine too, the number of outfits Wyatt can purchase while staying within his budget is:
780 ≥ 472.44 + 46.60x
Inequality:
In mathematics, equations are not always balanced on both sides using equal signs. It can also be about "not equal" relationships, such as one being greater than the other or less than the other. In mathematics, an inequality refers to a relationship in which two numbers or other mathematical expressions do not compare equally. These formulas belong to algebra and are called inequalities.
An inequality means that two things are not the same. One of them may be less than, greater than, less than or equal to, greater than or equal to the other.
p ≠ q means p is not equal to qp < q means p is less than qp > q means p is greater than qp ≤ q means p is less than or equal to qp ≥ q means p is greater than or equal to qAccording to the question:
As based on the information,
he can't spent more than $780.
Four cycle reflector cost = 2 × $19.41
= $38.82
Let maximum number of outfit = x
and Cost = 46.60x
and the the pair of glove is for $35.27.
Therefore,
New bicycle + Bicycle reflectors + Biker gloves + Biking Outfit ≤ 780
⇒ $398.35 + $ 38.82 + $ 35.27 + $46.60 x ≤ 780
⇒ 472.44 + $ 46.60x ≤ 780
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