Answer: 174
Step-by-step explanation: In the first year, the population of 32 goats increases by 71/10032 = 22.72 goats
So the population after 1 year would be 32+22.72 = 54.72 goats
In the second year, the population of 54.72 goats increases by 71/10054.72 = 38.9792 goats
So the population after 2 years would be 54.72+38.9792 = 93.69 goats
It's important to note that the answer provided (93) is the population after one year, not two years. The population after two years would be 174 goats.
help I didn't do this before
Answer:
5 4/9
Step-by-step explanation:
7/9 of 7
= 7/9 × 7
= 7/9 × 7/1
Multiply top×top and bottom×bottom
= 49/9
means 49÷9
9 goes into 49, 5 times. And 9 × 5 is 45. 49 - 45 is 4. So
49÷9 is 5 and 4 leftover.
49 ÷ 9
= 5 4/9
HELP ASP PLEASE THANK YOU Show ur work
Answer: $900
Step-by-step explanation:
Jenny earns $375 when she works 5 hours.
So the money she earns per hour of work can be found by dividing 375 by 5, which is 75.
The question is asking for how much money she earns when she works 12 hours. You can find this by multiplying the amount of money earned per hour of work times 12.
75*12 = 900
Therefore, the answer is $900.
a 95% confidence interval for the true proportion of math students who prefer to use a handheld calculator versus computer software for computations is (0.751, 0.863). is it reasonable to believe more than 75% of math students prefer to use a handheld calculator versus computer software for computations?
It is reasonable to believe that more than 75% of math students prefer to use a handheld calculator versus computer software for computations because the lower bound of the confidence interval, 0.751, is above 0.75.
To determine this:
A 95% confidence interval for a proportion gives us an estimate of the range of values where the true proportion is likely to fall. The interval (0.751, 0.863) means that we are 95% confident that the true proportion of math students who prefer to use a handheld calculator versus computer software for computations falls between 0.751 and 0.863.
Given this information, it is reasonable to believe that more than 75% of math students prefer to use a handheld calculator versus computer software for computations because the lower bound of the confidence interval, 0.751, is above 0.75.
In other words, based on the sample data and the construction of the confidence interval, there is strong evidence that the true proportion of math students who prefer to use a handheld calculator is above 75%.
It's important to note that the confidence interval is only an estimate of the true proportion, and it's possible that the true proportion is not exactly within this interval. However, the 95% confidence level means that if we were to repeat the study many times, in about 95% of the cases, the interval would contain the true proportion.
To learn more about the confidence interval, visit:
brainly.com/question/29680703
#SPJ4
Jim is going to buy donuts for his family. Each donut costs $1.45. If the number of donuts Jim buys is represented using the letter d, which expression represents the total cost?
total cost=1.45d
for example
1.45=1.45(1) if d=1
a company makes wax candles shaped like rectangular prisms. each candle is long, wide, and tall. if the company used of wax, how many candles did they make?
The company made 42 candles from 5040 cm³ of wax.
What is a rectangular prism?Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its shape.
Given the dimensions of the candle, which is in the shape of rectangular prisms
let l be the length, b be width and h be the height,
length = 5 cm
width = 2 cm
height = 12 cm
total wax needed for 1 candle is calculated by the volume of candle,
V = l x b x h
V = 5 x 2 x 12
V = 120 cm³
number of candles made by 5040 cm³ wax
number of candles = 5040/120
number of candles = 42
Hence, 42 candles are made.
Learn more about rectangular prism;
https://brainly.com/question/21308574
#SPJ1
The complete question is,
A company makes wax candles shaped like rectangular prisms. Each candle is 5cm long, 2cm wide, and 12cm tall. If the company used 5040cm3 of wax, how many candles did they make?
PLEASE HELP ASAP!!!!!!!!!
A square with sides 6 inches is shown. If $P$ is a point such that the segment $\overline{PA}$, $\overline{PB}$, $\overline{PC}$ are equal in length, and segment $\overline{PC}$ is perpendicular to segment $\overline{FD}$, what is the area, in square inches, of triangle $APB$
The area of the triangle APB is 6.75 square inches.
We know that PA=PB=PC and that PC is perpendicular to FD. Thus C will be the midpoint of FD.
Draw a perpendicular from P to AB, let the point of intersection be Q.
We know that CQ = DB = 6 inches
That is PC + PQ = 6 inches
PQ = (6 - PC) inches
Consider triangle APQ, it is a right angled triangle, right angled at Q. So using Pythagorean theorem
PA² = PQ² + AQ²
PA² = (6 - PC)² + (AB/2)²
PA² = (6 - PA)² + (6/2)²
PA² = 36 - 12PA + PA² + 9
12PA = 45
PA = 3.75
So PA = PB = PC = 3.75 inches
Also PQ = 6 - PC = 2.25 inches
The area of a triangle can be found by using the formula:
area = (base * height) / 2.
In this case, the base, AB is equal to the length of the side of the square, which is 6 inches, and the height is equal to PQ. So the area of triangle APB is
= (6*2.25)/2
= 6.75 square inches.
To know more on area
https://brainly.com/question/19305981
#SPJ4
in 2003 the exchange rate between the United States and Canada was three Canadian dollars to two US Dollars Cindy has 78 US dollars to exchange when she visits Canada how many Canadian dollars could she get in exchange?
Cindy gets 117 Canadian dollars as exchange.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that in 2003 the exchange rate between the United States and Canada was three Canadian dollars to two US Dollars
Cindy has 78 US dollars to exchange when she visits Canada
We need to find the number of Canadian dollars could she get in exchange
Let the unknown value be x
Formulate a proportion
3/2=x/78
Apply cross multiplication
3×78=2x
234=2x
Divide both sides by 2
x=117
Hence, Cindy gets 117 Canadian dollars as exchange.
To learn more on Ratios click:
https://brainly.com/question/13419413
#SPJ5
When do scientists use math in an experiment? How do you know?
Scientists use math in experiments when they make measurements, analyze quantitative data, and make predictions based on this data.
This is known because Math is an integral part of Science which is why both subjects ( Science and Math ) are considered STEM subjects.
How do scientists use math ?Scientists use math in an experiment to make measurements, analyze data, and make predictions.
For example, scientists use math to make precise measurements of physical quantities such as length, weight, and temperature. They also use math to perform calculations such as determining the concentration of a substance in a solution or the rate of a chemical reaction.
Scientists also use mathematical models and statistical analysis to analyze data and make predictions about the outcome of an experiment. They use mathematical equations to describe the relationships between different variables and to test hypotheses. They also use statistical techniques to determine the significance of their results and to make inferences about a larger population from a smaller sample of data.
Find out more on math and science at https://brainly.com/question/14473572
#SPJ1
how do I solve this?
Answer:
x = 13
Step-by-step explanation:
to solve this question you must know that angles in a triangle add up to 180 degrees
therefor 180 = 43 + 62 + (7x-16)
solve for x
180 = 43 + 62 + (7x-16)
180 = 105 + (7x-16)
Now, we can subtract 105 from both sides to get
75 = 7x-16
Next, we can add 16 to both sides to get
91 = 7x
Finally, we can divide both sides by 7 to get
x = 91/7
x = 13
So the value of x that satisfies the equation is 13
Answer:
x = 13
Step-by-step explanation:
Interior angles of a triangle sum to 180°. Therefore:
[tex]\implies 62^{\circ}+43^{\circ}+(7x-16)^{\circ}=180^{\circ}[/tex]
[tex]\implies 62+43+(7x-16)=180[/tex]
[tex]\implies 105+7x-16=180[/tex]
[tex]\implies 7x+89=180[/tex]
[tex]\implies 7x+89-89=180-89[/tex]
[tex]\implies 7x=91[/tex]
[tex]\implies 7x \div 7=91 \div 7[/tex]
[tex]\implies x=13[/tex]
Graph y=15x+3
.
ANYONE PLEASE ASAP LIKE LITERALLY ASAP PLEASE
there you go
to solve it you flip the equation to 15x+3=y
then add -3 to both sides and you get 15x=y-3 then divide both sides by 15 and you get x=1/15y+-1/15
5. The sum of two numbers is 15. The difference between five times the first number and Three times the second number is 19. Find the two numbers.
The first number will be 8 and the second number will be 7.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The sum of the two numbers is 15. The difference between five times the first number and Three times the second number is 19.
Let the first number be 'x' and the second number be 'y'. Then the equations are given as,
x + y = 15 ...1
5x - 3y = 19 ...2
From equations 1 and 2, then we have
5x - 3(15 - x) = 19
5x - 45 + 3x = 19
8x = 64
x = 8
Then the value of the variable 'y' is given as,
8 + y = 15
y = 15 - 8
y = 7
The first number will be 8 and the second number will be 7.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ1
The equation of line s is y= 3 5 x+ 2 5. Line t, which is parallel to line s, includes the point (2,1). What is the equation of line t? write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
The equation is y = 3x/5 - 1/5.
Based on the position of two lines: m = 3/5
Write the equation of linear function
Substitute: 1 = 3/5 * 2 + b
Rearrange unknown terms to the left side of the equation: -b = 3/5 * 2 -1
Write as a single fraction:
Find common denominator and write the numerators above common denominator: -b = (3*2)/5 - 1
Calculate the sum or difference: -b = (6 - 5 )/5
Divide both sides of the equation by the coefficient of variable: b = -1/5
Substitute: y = 3x/5 - 1/5
Find the required form: y = 3x/5 - 1/5.
To learn more about equation here:
https://brainly.com/question/29657988
#SPJ4
a golf course has 18 holes. a guidebook provided to golfers includes useful information about each hole. the individuals in this data set are shown below. a 4-column table with 6 rows. column 1 is labeled hole number with entries 1, 2, 3, 4, 5, 6. column 2 is labeled yards with entries 312, 530, 147, 350, 410, 185. column 3 is labeled bunkers with entries 2, 5, 1, 0, 2, 1. column 4 is labeled difficulty level with entries moderate, moderate, easy, moderate, hard, moderate. which of the variables in the data set is a categorical variable? hole number yards bunker difficulty level
The variable "difficulty level" in the data set is a categorical variable.
What is variable in math?A variable in math is a symbol or letter that is used to represent a number or set of numbers in an equation or expression. Variables can be anything such as x, y, a, b, c, etc. Variables are used to represent unknown values or values that can change. They allow equations and expressions to be flexible and can help make problem-solving easier.
Categorical variables are those that have discrete categories or labels, such as "moderate", "easy", and "hard". They are usually qualitative in nature and do not have numerical values. In this case, the difficulty level of each hole is indicated by a label, which can be used to classify the hole accordingly.
To know more about variables click-
https://brainly.com/question/25223322
#SPJ4
Answer:
difficulty level
Step-by-step explanation:
took the test
A region satisfies the inequalities 1 ≤ x ≤ 5 and 2 ≤ y ≤a. What value of a would give the region an area of 24 square units?
Answer:
a = 8
Step-by-step explanation:
The following inequalities will form a rectangle. Hence, the area of a rectangle is [tex]\displaystyle{A=\Delta x \cdot \Delta y}[/tex]
In this case, [tex]\Delta x[/tex] = 5-1 which is 4, and [tex]\Delta y[/tex] = a - 2. Substitute in:
[tex]\displaystyle{24 = 4\cdot (a-2)}[/tex]
Now solve the equation for a-term:
[tex]\displaystyle{24=4a-8}\\\\\displaystyle{24+8=4a}\\\\\displaystyle{32=4a}\\\\\displaystyle{8=a}[/tex]
Therefore, the value of a is 8 to make the region have an area of 24 square units.
Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Answer: 25.0
Step-by-step explanation:
[tex]\frac{x}{\sin 65^{\circ}}=\frac{22}{\sin 53^{\circ}}\\\\x=\frac{22 \sin 65^{\circ}}{\sin 53^{\circ}}\\\\x \approx 25.0[/tex]
the washington family and the bennett family each used their sprinklers last summer. the water output rate for the washington family's sprinkler was per hour. the water output rate for the bennett family's sprinkler was per hour. the families used their sprinklers for a combined total of hours, resulting in a total water output of . how long was each sprinkler used?
30 hours of use by the Washington family sprinkler and 35 hours of use by the Bennett family sprinkler.
We can find how long was each sprinkler used by substitution method.
Let W = hours of use by the Washington family
65 - W = hours of use by the Bennett family
According to the question we get
15W + 40(65 -W) = 1850
15W + 2600 - 40W = 1850
-25W = -750
W = 30
Now, put the value of W in 65 - W to calculate the hours used by the Bennett family
65 - W = 65 - 30 = 35
Thus, the amount of time used for sprinklers by the Washington family and the Bennett family is 30 hours and 35 hours, respectively.
--The given question is incomplete, the complete question is
"The Washington family and the Bennett family each used their sprinklers last summer. The water output rate for the Washington family's sprinkler was 15L per hour. The water output rate for the Bennett family's sprinkler was 40L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1850L. How long was each sprinkler used?"--
To know more about substitution method, we get
https://brainly.com/question/21117330
#SPJ4
William invested 5000 dollars in an account that earns 3. 5% interest compounded annually the formula for compound intrest is A(t) = P(1 + i) ^t. How much did william have in his account after 4 years
The amount William will have in his account after 4 years is $5737.50.
The formula for compound interest is
A(t) = P(1 + i)^t
where A(t) is the final amount in the account after t years, P is the initial principal or the amount invested, i is the annual interest rate, and t is the number of years.
In this case, P = 5000 dollars, i = 3.5% (expressed as a decimal), and t = 4 years.
So, to find the final amount in the account after 4 years, we can plug these values into the formula:
A(4) = 5000(1 + 0.035)^4
To calculate this we can use a calculator or use the exponential function, in this case, we get:
A(4) = 5000(1.035)^4
= 5000(1.1475)
= 5737.50
To know more on compound interest
https://brainly.com/question/13155407
#SPJ4
Find a second equation for the system so it has infinitely many solutions. Simplify fractions and write in the form a/b
Answer: [tex]4y=-3x+16[/tex]
Step-by-step explanation:
For there to be infinitely many solutions, the equations must represent the same graph.
The points [tex](0,4)[/tex] and [tex](4,1)[/tex] lie on the line. So, the slope is [tex]\frac{4-1}{0-4}=-\frac{3}{4}[/tex]. As the [tex]y[/tex]-intercept is [tex](0,4)[/tex], the equation is [tex]y=-\frac{3}{4}x+4[/tex].
Multiplying both sides by [tex]4[/tex] yields [tex]4y=-3x+16[/tex].
If we changed the 2 to a 5 in the domain restriction , what would happen to the graph?
It depends on the specific context and the nature of the graph. Without more information about the domain restriction and the graph, it is difficult to say exactly what effect changing the 2 to a 5 would have. However, in general, changing a value in a domain restriction would affect the range of possible input values for the graph and could potentially change the overall shape or behavior of the graph.
a. Mia's solution is below. Is she correct? Explain.
Mia's Solution
7TH
GRADE
8TH
GRADE
9 rectangles = 270 students
1 rectangle = 30 students
7+h=1100=11
8+4=75
There are 4 30 7th grade students or 120
There are 5 30 8th grade students or 150 students
Based on the given linear equations, the number of 7th-grade students and 8th-grade students is 120 students and 150 students respectively. Hence, Mia's solution is correct.
What is the value of h in the linear equation?The value of h in the given linear equation is determined as follows:
9 rectangles = 270 students
1 rectangle = 30 students
7 + h = 11
h = 11 - 7
h = 4
The number of 7th-grade students and 8th-grade students is then determined as follows:
7th-grade students:
4 * 30 = 120 students
8th-grade students:
5 * 30 = 150 students
Learn more about linear equations at: https://brainly.com/question/28732353
#SPJ1
[I WILL GIVE BRAINLIEST] This shape is made up of one half-circle attached to an equilateral triangle with side lengths of 8 inches. You can use 3.14 as an approximation for π. What is the approximate perimeter of the entire shape?
The solution is, The perimeter is 37inches.
How to find the perimeter of a figure?The perimeter of a figure is the sum of the whole sides of the figure.
Therefore, the perimeter of the entire shape can be calculated as follows:
The shape is made of one half-circle attached to an equilateral triangle
Therefore,
circumference of the semi-circle = πr
r = 8 / 2 = 4 inches
circumference of the semi-circle = 4π
Hence,
perimeter of the shape = 8+8+8+4π
perimeter of the shape = 24+ 4(3.14)
perimeter of the shape = 24 + 12.56
= 36.56
Therefore, perimeter of the shape = 37 inches (approx)
To learn more about perimeter from the given link:
brainly.com/question/5550237
#SPJ1
Please help! Find the measure of 7
Answer:
The measure of 7 is 118 degrees.
Step-by-step explanation:
You use the straight line with the 62 degree angle on it to solve.
The line is equal to 180 degrees so you subtract 62 from 180.
180-62=118
That gives you the answer of 118 degrees :)
In the diagram, each of the three identical circles touch the other two. The circumference of each circle is 36. What is the perimeter of the shaded region?
The perimeter of the shaded region is 18 units.
The circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line, then the length of that line will be the circle's circumference.
The result of the lengths of the sides is the perimeter of any polygon. In the case of a triangle: Perimeter = Sum of the three sides.
If we connect the centers of the circles, this will form an equilateral triangle.
The two sides of this triangle meeting at any vertex will pass through the points of tangency where one circle meets the other two, these two tangent points form the endpoints of one side of the shaded region.
Since the vertex angle of the triangle = 60°, then the arc formed by one side of the shaded region
= 1/6 the circumference of the circle
= 1/6 × 36
= 6 units
So, the perimeter of the shaded region is 3 times this
= 3 × 6
= 18 units
Therefore, the perimeter of the shaded region is 18 units.
To learn more about circle visit : brainly.com/question/11833983
#SPJ4
find the exact length of the curve. x = y4/8 + 1/4y2 , 1 ≤ y ≤ 2
The curve's approximate length is 33/16, as mentioned throughout the paragraph.
With an example, what is a curve?Curved shapes are those composed entirely of curves. A curved form, such as a circle, an ellipse, a parabola, or an arc, can be two-dimensional. Three-dimensional objects like sphere, cones, and cylinders can also have curved forms. A curved line is one that is not straight. A curve results from a point that is not moving in a straight line.
We'll use the following formula to get the angle of a function:
[tex]\begin{aligned}& L=\int d s \\& d s=\sqrt{1+\left(\frac{d x}{d y}\right)^2} d y\end{aligned}[/tex]
Let's now calculate x's derivative:
[tex]\begin{aligned}& \frac{d x}{d y}=\frac{4}{8} y^3-\frac{2}{4} \frac{1}{y^3} \\& =\frac{1}{2}\left(y^3-\frac{1}{y^3}\right)\end{aligned}[/tex]
Okay, now enter this into the ds formula to obtain:
[tex]d s=\sqrt{1+\frac{1}{4}\left(y^3-\frac{1}{y^3}\right)^2}[/tex]
Observe that:
[tex]\begin{aligned}& 1+\frac{1}{4}\left(y^3-\frac{1}{y^3}\right)^2=1+\frac{1}{4} y^6-\frac{1}{2}+\frac{1}{4 y^6} \\& =\left(\frac{1}{2} y^3+\frac{1}{2} y^{-3}\right)^2\end{aligned}[/tex]
The integral will now be easier to understand:
[tex]\begin{aligned}& L=\int_1^2 \sqrt{\left(\frac{1}{2} y^3+\frac{1}{2} y^{-3}\right)^2} d y=\int_1^2 \frac{1}{2} y^3+\frac{1}{2} y^{-3} d y \\& =\left[\frac{1}{8} y^4-\frac{1}{4} y^{-2}\right]_2^1 \\& =\frac{33}{16}\end{aligned}[/tex]
To know more about Curve visit:
https://brainly.com/question/27958086
#SPJ4
The complete question is-
Find the exact length of the curve:
[tex]x=\frac{y^4}{8}+\frac{1}{4 y^2}, 1 \leq y \leq 2[/tex]
Triangle $ABC$ has vertices $A(0, 8)$, $B(2, 0)$, $C(8, 0)$. A line through $B$ cuts the area of $\triangle ABC$ in half; find the sum of the slope and $y$-intercept of this line.
By applying a linear equation, it is concluded that the slope of the line is 2 and the y-intercept is -4
A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is y = mx + k, where m is the slope of the line and k is the y-intercept.
First, we draw a triangle ABC whose vertices are A(0, 8), B(2, 0),C(8, 0)
Then we determine point D as the midpoint of AC, so D(4,4)
Now we use B(2,0) and D(4,4) to determine slope of the line (m):
m = (y₂-y₁) / (x₂-x₁)
= (4-0) / (4-2)
= 4/2
= 2
To find the y-intercept of the line, we pick one of the points on the line. Let's say we pick point (6,8). Then we put those values into the equation:
y = mx + k
8 = 2*6 + k
8 = 12 + k
k = -4
Thus the y-intercept of the line is - 4
To learn more about linear equations, click here: https://brainly.com/question/20596809
#SPJ4
what is the geometric mean of 12 and 7
Given
let the value of geometric mean be a and b
a=12
b=7
we know that,
Geometic mean(G.M)=√ab
=√12×7
=√84
=9.16
the geometric mean of 12 and 7 is 9.16
a ladder 26 feet long is leaning against the wall of a house (see the figure below). the base of the ladder is pulled away from the wall at a rate of 3 feet per second. how fast is the top of the ladder moving down the wall when its base is 10 feet from the wall?
The rate at which the top of the ladder is moving down the wall = 9 feet/second.
This is a problem of right triangle similarity.
We can use the Pythagorean theorem to find the height of the ladder, which is the hypotenuse of a right triangle.
We can use the relationship between similar triangles to find the rate at which the top of the ladder is moving down the wall.
Let x be the distance of the base of the ladder from the wall.
We know that the ladder is 26 feet long, so the height of the ladder is the square root of (26^2 - x^2).
We know that the base of the ladder is moving away from the wall at a rate of 3 feet per second.
So, the rate at which the top of the ladder is moving down the wall is (3 feet/second) * (height of ladder / x)
When x = 10 feet, the height of the ladder is the square root of (26^2 - 10^2) = the square root of (676) = 26 feet.
So, the rate at which the top of the ladder is moving down the wall is (3 feet/second) * (26 feet / 10 feet) = 9 feet/second.
To learn more about heights and distances visit: brainly.com/question/15939509
#SPJ4
Find the z-score for the value 93, when the mean is 100 and the standard deviation is 3.
The z-score for the value 93, when the mean is 100 and the standard deviation is 3 is solved to be
2.3How to solve for z scoreZ scores is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of the parameters
mean, μ = 100
standard deviation, σ = 3
sample score, X = 93
z score for the score of 93
z = (X - μ) / σ
substituting into the formula
z = (93 - 100) / 3
= -7 / 3
= -2.333
Hence we can say that the z score is 2.333
Learn more about Z scores at:
https://brainly.com/question/28940355
#SPJ1
Let $f$ and $g$ be functions defined on a domain $A$. Prove that if $f$ is bounded, and $\displaystyle\lim_{x \rightarrow c} g(x)
If [tex]$f$[/tex]is bounded and [tex]$\displaystyle\lim_{x \rightarrow c} g(x)$[/tex] exists, then the limit of function[tex]$f(x)g(x)$[/tex]as [tex]$x$[/tex] approaches domain[tex]$c$[/tex]also exists and is equal to [tex]$Lf(c)$[/tex]
Let [tex]$M$[/tex]be an upper bound of [tex]$f$[/tex] on the domain . Since [tex]$\displaystyle\lim_{x \rightarrow c} g(x)$[/tex] exists, there exists a number [tex]$L$[/tex] such that for all [tex]$\epsilon > 0$[/tex] there exists a [tex]$\delta > 0$[/tex] such that for [tex]$x \in A$[/tex] with [tex]$0 < |x - c| < \delta |g(x) - L| < \epsilon[/tex].
Now let [tex]\epsilon > 0Then $|f(x)g(x) - Lf(x)| = |f(x)||g(x) - L| < M\epsilon[/tex]
for all [tex]x \in A$ with $0 < |x - c| < \delta$[/tex]. So [tex]\displaystyle\lim_{x \rightarrow c} f(x)g(x)$ exists and is equal to $Lf(c)[/tex]
If [tex]$f$[/tex] is bounded and [tex]$\displaystyle\lim_{x \rightarrow c} g(x)$[/tex] exists, then the limit of [tex]f(x)g(x)$[/tex]as [tex]$x$[/tex]approaches[tex]$c$[/tex]also exists and is equal to [tex]$Lf(c)$[/tex].
The complete question is:
Let [tex]$f$[/tex] and [tex]$g$[/tex] be functions defined on a domain[tex]$A$[/tex]. Prove that if [tex]$f$[/tex] is bounded, and [tex]$\displaystyle\lim_{x \rightarrow c} g(x)$[/tex]exists, then [tex]$\displaystyle\lim_{x \rightarrow c} f(x)g(x)$[/tex] exists.
Learn more about domain here
https://brainly.com/question/13113489
#SPJ4
