The linear approximation of f(x) = ln(x) at x = 1 is L(x) = x - 1. Using this approximation, we can estimate ln(1.16) to be approximately 0.16.
The formula for the linear approximation of a function f(x) at a point x = a is given by L(x) = f(a) + f'(a)(x - a), where f'(a) is the derivative of f(x) evaluated at x = a.
In this case, f(x) = ln(x), so f'(x) = 1/x by the derivative of natural logarithm.
We are asked to find the linear approximation of f(x) = ln(x) at x = 1, so a = 1 in the formula.
Plugging in the values, we get L(x) = ln(1) + 1( x - 1) = x - 1.
Now, we can use this linear approximation L(x) = x - 1 to estimate ln(1.16) by plugging in x = 1.16, as given in the question.
L(1.16) = 1.16 - 1 = 0.16, which is our estimated value for ln(1.16) using the linear approximation.
For more questions like Function click the link below:
https://brainly.com/question/16008229
#SPJ11
helppppppp please!!!!!!!
Thus, the height of cone for the given values of circumference an f volume is found as: 4 cm.
Explain about the conical shape:A tri shape that resembles a cone is what is known as a conical shape. A cone has a flat end that gradually taper towards a single point at the top known as the apex. Most commonly, a conical shape's flat end has an oval or circular shape. Conical shapes are on your mind when you imagine an ice cream cone with only a pointed end.
Volume of a cone = 1/3 * π *r²*h
r is the radiush is the height π = 3.14Given that:
circumference c = 6π Volume = 12π
using circumference c = 6π
c = 2πr (for circular base)
6π = 2πr
r = 3 cm
Now, using the volume;
Volume of a cone = 1/3 * π *r²*h
1/3 * π *3²*h = 12π
3h = 12
h = 4 cm
Thus, the height of the cone for the given values of circumference an f volume is found as: 4 cm.
Know more about the conical shape:
https://brainly.com/question/27561023
#SPJ1
Let f be a differentiable function such that f (2) = 4, f(4) = 6, f'(2) = -4, and f'(6) = -3. f 6 . The function g is differentiable and g(x) = f-1(x) for all x. What is the value of g'(4) =
The value of g'(4) is -1/3 if f is a differential function such that f (2) = 4, f(4) = 6, f'(2) = -4, and f'(6) = -3.
First, let's use the information given to find the equation of the tangent line to f at x=2. We know that f(2) = 4 and f'(2) = -4, so the equation of the tangent line at x=2 is
y - 4 = -4(x - 2)
Simplifying, we get
y = -4x + 12
Now let's use the fact that g(x) = f-1(x) for all x. This means that g(f(x)) = x for all x. We want to find g'(4), which is the derivative of g at x=4.
Using the chain rule, we have
g'(4) = [g(f(4))]'
Since f(4) = 6 and g(f(4)) = g(6) (since g(x) = f-1(x)), we can rewrite this as
g'(4) = [g(6)]'
Now we can use the fact that g(x) = f-1(x) to rewrite g(6) as f-1(6)
g'(4) = [f-1(6)]'
Now we need to find the derivative of f-1(x) with respect to x. To do this, we can use the fact that f(f-1(x)) = x for all x. Differentiating both sides with respect to x using the chain rule, we get
f'(f-1(x)) * (f-1)'(x) = 1
Solving for (f-1)'(x), we get
(f-1)'(x) = 1 / f'(f-1(x))
Now we can plug in x=6 and use the information given to find f'(f-1(6)). Since f(4) = 6, we know that f-1(6) = 4. Therefore
f'(f-1(6)) = f'(4)
Using the tangent line equation we found earlier, we know that f(2) = 4 and f'(2) = -4. Therefore, the slope of the line connecting (2,4) and (4,6) is
(6 - 4) / (4 - 2) = 1
Since the line connecting (2,4) and (4,6) is the tangent line to f at x=2, we know that this slope is equal to f'(2). Therefore
f'(4) = f'(f-1(6)) = f'(4)
Now we can plug in x=6 and f'(4) into our expression for (f-1)'(x)
(f-1)'(6) = 1 / f'(4)
Substituting this into our expression for g'(4), we get
g'(4) = [f-1(6)]' = (f-1)'(6) = 1 / f'(4)
Plugging in f'(4) = f'(f-1(6)) = f'(4), we get
g'(4) = 1 / f'(4) = 1 / (-3) = -1/3
Therefore, g'(4) = -1/3.
To know more about differentiable function here
https://brainly.com/question/22549106
#SPJ4
The captain of the baseball team hit a homerun 1 out of every 6 at-bats. What is the probability that the captain will hit a homerun on his next 2 at-bats?
Determine which simulation models the situation. Select Yes if the simulation can be used to model the situation or No if the simulation cannot be used to model the situation.
Yes No
OO
Using a six-sided number cube to model the situation, assign the number 1 to represent the captain hitting a homerun and the number 2 to represent not hitting a homerun.
Using a stre-sided number cube to model the situation, assign the number 1 to represent the captain hitting a homerun and the numbers 2 to 6 to represent not hitting a homerun
Using a coin flip to model the situation, assign heads to represent the captain hitting a homerun and tails for not hitting a homerun
O
Using a random number generator between 1 and 60 to model the situation, assign the numbers 1 to 10 to represent the captain hitting a homerun and the numbers 11 to 60 to represent not hitting a homerun.
The probability of the captain hitting a home run in his next two at-bats is 1/36, and the best simulations to model the situation are using a six-sided number cube or a random number generator between 1 and 60.
Determine the probability that the captain will hit a home run in his next two at-bats and find the best simulation to model the situation.
The probability of the captain hitting a home run in one at-bat is 1/6. To find the probability of hitting a home run in two consecutive at-bats, you can multiply the individual probabilities:
Probability = (1/6) * (1/6) = 1/36
Now let's evaluate the provided simulations:
1. Using a six-sided number cube: Yes, this can be used to model the situation because the probability of hitting a home run (1/6) and not hitting a home run (5/6) can be represented accurately by the numbers 1 and 2-6, respectively.
2. Using a three-sided number cube: No, this cannot be used to model the situation because the probability distribution is not accurately represented with only three sides.
3. Using a coin flip: No, this cannot be used to model the situation because the probability distribution is not accurately represented with only two outcomes (heads and tails).
4. Using a random number generator between 1 and 60: Yes, this can be used to model the situation because the probability of hitting a home run (1/6) and not hitting a home run (5/6) can be represented accurately by the numbers 1-10 and 11-60, respectively.
Learn more about random numbers: https://brainly.com/question/29609783
#SPJ11
Lan shuffles a standard deck of 52 playing cards and turns over the first four cards, one at a time. He records the
number of aces he observes.
Have the conditions for a binomial setting been met for this scenario?
O Yes, a success is "ace. "
O Yes, all four conditions in BINS have been met.
No, we do not know how many aces will occur in those first four cards.
O No, the cards are not being replaced, so the independence condition is not met.
Next
Submit
Save and Exit
Mark this and return
The binomial conditions are not met as the cards are not being replaced, so the independence condition is not met. So, the correct answer is D).
The conditions for a binomial setting are
there are a fixed number of trials,
the trials are independent,
there are only two possible outcomes (success or failure),
the probability of success is constant for each trial.
In this scenario, the first two conditions are met as Lan is turning over the first four cards and they are independent events. The third condition is also met as the success is defined as observing an ace and the failure is observing any other card.
However, the fourth condition is not met as the probability of success changes for each trial. After the first card is turned over, the probability of observing an ace changes for the second trial. Therefore, the scenario does not meet all the conditions for a binomial setting. So, the correct option is D).
To know more about conditions for a binomial:
https://brainly.com/question/30100278
#SPJ4
Find the equation of the tangent line of y=xlog(x) at the point(1,0).
The equation of the tangent line is y = x - 1.
To find the equation of the tangent line of y=xlog(x) at the point (1,0), we will first need to find the derivative of the function y=xlog(x) with respect to x.
Step 1: Find the derivative of y=xlog(x) with respect to x.
Using the product rule, (uv)' = u'v + uv', where u=x and v=log(x).
u' = derivative of x with respect to x = 1
v' = derivative of log(x) with respect to x = 1/x
Now, apply the product rule:
y' = u'v + uv' = 1*log(x) + x*(1/x) = log(x) + 1
Step 2: Find the slope of the tangent line at the point (1,0).
Evaluate y' at x=1:
y'(1) = log(1) + 1 = 0 + 1 = 1
The slope of the tangent line at (1,0) is 1.
Step 3: Find the equation of the tangent line.
We will use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the point (1,0) and m is the slope (1).
y - 0 = 1(x - 1)
y = x - 1
The equation of the tangent line of y=xlog(x) at the point (1,0) is y = x - 1.
Tangent linehttps://brainly.com/question/3074597
#SPJ11
Evelyn has a coupon that will reduce her grocery bill by 8%. If c represents the cost of Evelyn's groceries, which expression represents Evelyn's grocery bill?
a) c-0. 08
b) c+0. 92
c) 0. 08c
d) 0. 92c
Therefore, the correct answer is option (b) c + 0.92.
What is The expression that represents Evelyn's grocery bill?The expression that represents Evelyn's grocery bill after the 8% discount is:
c - 0.08c
This can be simplified as:
0.92c
Therefore, the correct answer is option (b) c + 0.92.
Learn more about Evelyn's grocery bill
brainly.com/question/15252985
#SPJ11
The expression that represents Evelyn's grocery bill after the coupon is applied is 0.92c. Therefore, the correct option is D.
If Evelyn has a coupon that will reduce her grocery bill by 8% and c represents the cost of her groceries, the expression that represents Evelyn's grocery bill after using the coupon is 0.92c. It is determined as follows.
1. The coupon reduces the bill by 8%, which means Evelyn will pay 100% - 8% = 92% of the original cost.
2. Convert the percentage to a decimal: 92% = 0.92
3. Multiply the original cost (c) by the decimal: 0.92c
So, the correct answer is option D: 0.92c.
Learn more about Cost:
https://brainly.com/question/19104371
#SPJ11
67 Solve for the value of x. 6x+16 12x+2 8
Answer:
x=9
Step-by-step explanation:
These 2 angles are both on a straight line, meaning that the total angle sum is 180°.
We can write an equation:
180=(6x+16)+(12x+2)
combine like terms
180=18x+18
subtract 18 from both sides
162=18x
divide both sides by 18
9=x
Hope this helps! :)
Debnil has 6 teaspoons of salt. The ratio of teaspoons to tablespoons is 3 to 1. How many tablespoons of salt does Debnil have?
Answer: Debnil has 2 Tablespoons of salt.
Step-by-step explanation:
3/1 is the ratio for teaspoons to tablespoons.
Substitute the 1 with the 6. What is six divided by three? 2.
On the same coordinate plane, mark all points (x,y) such that (A) y=x-2, (B) y=-x-2, (C) y=|x|-2
The marked points are (-2,-4), (-2,-1), (0,-2), (2,-1), and (2,-4), under the condition that they are on the same coordinate plane having (A) y=x-2, (B) y=-x-2, (C) y=|x|-2.
In the given graph points on the coordinate plane, we have to plot the points (x,y)
Here
x = horizontal axis
y = vertical axis.
In the given point A, y=x-2, we can continue at the origin (0,0) and move 2 units go down on the y-axis and 2 units right on the x-axis to plot point A at (2,0).
In the given point B, y=-x-2, we can continue at the origin (0,0) and transfer 2 units down on the y-axis and 2 units left on the x-axis to plot point B at (-2,0).
In the given point C, y=|x|-2, we can continue plotting two points for this equation.
When x is considered negative, we can procees at the origin (0,0) and transfer 2 units down on the y-axis and 2 units left on the x-axis to plot point C at (-2,0).
When x is positive, we can start at the origin (0,0) and move 2 units down on the y-axis and 2 units right on the x-axis to plot point C at (2,0).
Then, all points (x,y) such that (A) y=x-2, (B) y=-x-2, (C) y=|x|-2 are (-2,-4), (-2,-1), (0,-2), (2,-1), and (2,-4).
To learn more about coordinate plane
https://brainly.com/question/29765572
#SPJ4
A teacher writes the following product on the board:
(372) (675) =18k7
Ana says that 3k2 is a factor of 18k7
Felipe says that 18k? is divisible by 372
Who is correct?
In the equation , Felipe is correct.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given equation is (372) (675) =18k7.
We know that the factor is a number that divides the another number and leaves no reminder .
If we divide 18k7 by 372 the we get remainder 675. So 372 is not factor of 18k7.
But 372 is divides the number 18k7.
Hence Felipe is correct.
To learn more about equation refer the below link
https://brainly.com/question/29336774
#SPJ4
What is the molarity of a solution made by adding 116. 0 g of NaCl to 2. 00 L of water?
The molarity of the solution is approximately 0.9925 M.
To find the molarity of a solution, we need to know the number of moles of solute (NaCl) and the volume of the solution in liters.
First, let's calculate the number of moles of NaCl:
Number of moles of NaCl = Mass of NaCl / Molar mass of NaCl
The molar mass of NaCl is 58.44 g/mol (sodium has a molar mass of 22.99 g/mol and chlorine has a molar mass of 35.45 g/mol).
Number of moles of NaCl = 116.0 g / 58.44 g/mol = 1.985 moles
Next, let's calculate the volume of the solution in liters:
Volume of solution = 2.00 L
Finally, let's calculate the molarity of the solution:
Molarity = Number of moles of solute / Volume of solution
Molarity = 1.985 moles / 2.00 L = 0.9925 M
Therefore, the molarity of the solution is approximately 0.9925 M.
Learn more about molarity,
https://brainly.com/question/30404105
#SPJ11
To build a triangular shaped raised bed frame for her tomato plants, chris has three pieces of lumber whose length are 4 feet 5 feet and 9 feet. can chris build her planter? explain
Chris cannot build the triangular raised bed frame with the given lumber.
How can Chris build a triangular raised bed frame?To determine if Chris can build her triangular raised bed frame, we need to check if the length of any one of the lumber pieces is greater than the sum of the other two. If this condition is not met, the pieces can be used to build the frame.
Let's check:
4 + 5 = 9 (no)
4 + 9 = 13 (no)
5 + 9 = 14 (yes)
Since the length of the 5-foot and 9-foot lumber pieces add up to be greater than the 4-foot piece, Chris can build her triangular raised bed frame. She can use the 4-foot and 5-foot pieces for the two shorter sides of the triangle and the 9-foot piece for the longer side.
Learn more about bed frame
brainly.com/question/19969346
#SPJ11
2
How much water will a cone hold that has a diameter of 6 inches and a height of 21 inches.
Use 3. 14 for 7 and round your answer to the nearest whole number.
A 66 cubic inches
B 198 cubic inches
C) 594 cubic inches
D 2374 cubic inches
The cone will hold approximately 198 cubic inches of water. The correct answer is option B.
To find how much water a cone with a diameter of 6 inches and a height of 21 inches will hold, we need to calculate the volume of the cone. We can use the formula for the volume of a cone: V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
1. Since the diameter is 6 inches, the radius (r) is half of that: r = 6/2 = 3 inches.
2. The height (h) is given as 21 inches.
3. Use 3.14 for π.
Now, plug the values into the formula:
V = (1/3) * 3.14 * (3^2) * 21
4. Calculate the square of the radius: 3^2 = 9
5. Multiply the values: (1/3) * 3.14 * 9 * 21 ≈ 197.64
6. Round the answer to the nearest whole number: 198 cubic inches.
To learn more about volume
https://brainly.com/question/27710307
#SPJ11
JAMIE SPUN THE SPINNER SHOWN 30 TIMES AND RECORDED THE FREQUENCY OF
EACH RESULT IN THE TABLE BELOW. USE THE TABLE TO COMPLETE THE STATEMENTS
IN THE ORANGE
If Jamie spins the spinner 60 times, we can predict 20 red, 10 blue, 20 green, and 10 yellow outcomes
How to solveFirst, calculate the probability of each color by dividing the frequency by 30 spins.
Red: 10/30 = 1/3
Blue: 5/30 = 1/6
Green: 10/30 = 1/3
Yellow: 5/30 = 1/6
Now, predict the frequency of each color if Jamie spins the spinner 60 times.
Red: (1/3) * 60 = 20
Blue: (1/6) * 60 = 10
Green: (1/3) * 60 = 20
Yellow: (1/6) * 60 = 10
So, if Jamie spins the spinner 60 times, we can predict 20 red, 10 blue, 20 green, and 10 yellow outcomes
Read more about frequency table here:
https://brainly.com/question/28035330
#SPJ1
The Complete Question:
Jamie spun a spinner with 4 colors - red, blue, green, and yellow - 30 times and recorded the frequency of each result in the table below. Use the table to determine the probability of each color and predict the frequency of each color if Jamie spins the spinner 60 times.
Table:
Red - 10
Blue - 5
Green - 10
Yellow - 5
a population of 100 individuals is undergoing exponential growth with a population doubling time of 1 year. what size will this population be in 2 years?
The size of the population of 100 individuals which are undergoing exponential growth is equal to 400.
Population is undergoing exponential growth,
Use the formula of exponential ,
Nt = N0 × e^(rt)
Where,
Nt is the population size at time t
N0 is the initial population size
e is the mathematical constant, approximately 2.71828
r is the growth rate
If the population doubling time is 1 year,
Use the following formula to calculate the growth rate,
r = log(2) / t
Where t is the doubling time,
log(2) is the natural logarithm of 2 = approximately 0.693.
⇒ r = log(2) / 1 year
= 0.693 / year
Plug in the values,
Nt = N0 × e^(rt)
⇒Nt = 100 × e^(0.693 × 2)
Population size in 't' = 2 years.
Nt = 100 × e^1.386
⇒Nt = 100 × 3.998
⇒Nt = 100 ×4.000
⇒ Nt = 400
Therefore, the population will be 400 individuals in 2 years if it continues to undergo exponential growth with a population doubling time of 1 year.
Learn more about exponential here
brainly.com/question/31295441
#SPJ4
9) The profit from a business is described by the function P(x) = -3x² + 12x + 75, where xis the number of items made, in thousands, and P(x) is the profit in dollars. How many items will maximize the profit? А 1,000 4,000 B 2. 000 D 6,000
The number of items that will maximize the profit is 2000. Thus, the correct answer is option c.
To calculate the maximum profit that can be earned we have to differentiate the equation and find the value of x
dP/dx = 1/dx (-3x² + 12x + 75)
= -6x + 12
Calculating dP/dx = 0
0 = -6x + 12
6x = 12
x = 2
Next, we calculate the next differential of the equation:
It comes out to be -6
Since it is smaller than zero, the value of x calculated is the maxima.
The maxima = 2
Thus, the item that will maximize the profit comes out to be 2000 as x is the number of items made in thousand.
Learn more about Maxima:
https://brainly.com/question/29502088
#SPJ4
The derivative of the function ds/dt of the function s = (tan² t - sec² t)⁵ is ...
The derivative of s with respect to t is:
ds/dt = 10(sec² t - tan t) * (tan² t - sec² t)⁴
How to find the derivative of the function?To find the derivative of s with respect to t, we will use the chain rule and the power rule of differentiation.
Let u = (tan² t - sec² t). Then, s = u⁵.
Using the chain rule, we have:
ds/dt = (du/dt) * (ds/du)
Now, we need to find du/dt and ds/du.
Using the chain rule again, we have:
du/dt = d/dt(tan² t - sec² t) = 2tan t * sec² t - 2sec t * tan t * sec t = 2sec² t * (tan t - sec t)
To find ds/du, we can simply apply the power rule:
ds/du = 5u⁴
Substituting these into the original equation for ds/dt, we get:
ds/dt = (2sec² t * (tan t - sec t)) * (5(tan² t - sec² t)⁴)
Therefore, the derivative of s with respect to t is:
ds/dt = 10(sec² t - tan t) * (tan² t - sec² t)⁴
Learn more about derivative of function
brainly.com/question/25752367
#SPJ11
In 2015, there were roughly 1 X 10^6 high school football players and 2 X 10^3 professional football players in the United States. About how many times more high school football players are there? Explain how you know
There are approximately 500 times more high school football players than professional football players in the United States.
How to determine ratio of football players?To determine how many times more high school football players there are than professional football players in the United States, we need to divide the number of high school players by the number of professional players:
1 x 10⁶ / 2 x 10³ = 500
Therefore, there are approximately 500 times more high school football players than professional football players in the United States.
We can determine this by dividing the two numbers and finding the ratio of high school players to professional players. The result tells us how many times greater the number of high school players is than the number of professional players. In this case, the ratio is 500:1, which means that for every professional football player, there are 500 high school football players.
Learn more about football players
brainly.com/question/18883243
#SPJ11
how many paths are there from point (0,0) to (90,160) if every step increments one coordinate and leaves the other unchanged and you want the path to go through (80,70)?
There are 4.097 x [tex]10^43[/tex] paths from (0,0) to (90,160) that pass through (80,70).
To calculate the number of paths from (0,0) to (90,160) while passing through (80,70), we need to break down the problem into smaller steps.
First, we can calculate the number of paths from (0,0) to (80,70) and then
multiply that by the number of paths from (80,70) to (90,160).
To go from (0,0) to (80,70), we need to take 80 steps to the right and 70 steps up, which gives us a total of 150 steps. The order in which we take these steps doesn't matter, so we can think of it as choosing 70 steps out of 150 to be up. This can be calculated using the binomial coefficient, which gives us (150 choose 70) = 2.364 x [tex]10^43[/tex]
To go from (80,70) to (90,160), we need to take 10 steps to the right and 90 steps up, which gives us a total of 100 steps. Using the same method as above, the number of paths from (80,70) to (90,160) is (100 choose 10) = 17,310,309.
Multiplying these two values together, we get the total number of paths from (0,0) to (90,160) that pass through (80,70):
(2.364 x 10^34) x (17,310,309) = 4.097 x [tex]10^43[/tex]
Therefore, there are 4.097 x [tex]10^43[/tex] paths from (0,0) to (90,160) that pass through (80,70).
Learn more about binomial coefficient,
https://brainly.com/question/31229700
#SPJ4
A cylinder has volume 108 cm? What is the volume of a cone with the same
radius and height? Use 3. 14 for it and be sure to add units to your answer.
The volume of the cone with the same radius and height as the cylinder is 36 cm³.
To find the volume of a cone with the same radius and height as the cylinder, we first need to find the radius and height of the cylinder.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
We are given that the volume of the cylinder is 108 cm^3.
So, 108 = πr^2h
To solve for r and h, we need more information. However, we can use the fact that the cone has the same radius and height as the cylinder to our advantage.
The formula for the volume of a cone is V = (1/3)πr^2h.
Since the cone has the same radius and height as the cylinder, we can substitute the values of r and h from the cylinder into the cone formula.
V = (1/3)π( r^2 )(h)
V = (1/3)π( r^2 )(108/π)
V = (1/3)( r^2 )(108)
V = 36( r^2 )
Therefore, the volume of the cone with the same radius and height as the cylinder is 36 cm³
More on volume: https://brainly.com/question/29184704
#SPJ11
FRANK IS DESIGNING 30-KILOMETERS TRAIL RUN WATER WILL BE GIVEN TO THE RUNNERS 4000 OW MANY WATER STATIONS WILL THERE BE
Based on the above, Frank will need to have about 533 water stations per kilometer for the 30-kilometer trail run.
What is the water stations?If each runner is said to have about 250 milliliters (0.25 liters) of water per station and there are said to be 4000 liters of water available in total, we have to calculate the total number of water stations by:
4000 liters of water ÷ 0.25 liters of water per station
= 16000 stations
we have 30-kilometer run, we have to divide the total number of stations by the distance and it will be:
16000 stations ÷ 30 kilometers
= 533.33 stations per kilometer
Therefore, about 533 water stations per kilometer for the 30-kilometer trail run is needed by Frank.
Learn more about water stations from
https://brainly.com/question/6905953
#SPJ1
see full question below
frank is designing a 30-kilometers trail run water that will be given to runners. if 4000 liters of water is available, each runner was given about 250 milliliters (0.25 liters) of water per station. how many water stations will there be 30-kilometer run.
I have no congruent sides. One of my angles has a measure of 100 degrees. Answer with drawing of the triangle
I am a(n and triangle
You are an scalene triangle.
How can you identify the type of triangle when given the information that it has no congruent sides and one angle measuring 100 degrees?You are a scalene triangle.
A scalene triangle is a type of triangle where all three sides have different lengths, and no two angles are congruent. In this case, you mentioned that one of the angles has a measure of 100 degrees.
Here's a simple diagram of a scalene triangle to help illustrate:
\
\
\
\
\
\
In the diagram, the angles are not drawn to scale, but it represents a scalene triangle where one angle measures 100 degrees. The sides of the triangle would have different lengths, distinguishing it from an equilateral or isosceles triangle where at least two sides are congruent.
Learn more about triangle
brainly.com/question/2773823
#SPJ11
Help please asap need help.
The surface areas of the pyramids are listed below:
125 in² 304 ft² 420 yd² 57 yd² 336 in² 104 ft²How to determine the surface area of the square pyramid
In this problem we find six cases of square pyramids, whose surface areas shall be found by means of the following formulas:
A = 4 · 0.5 · b · s + b²
Where:
b - Base sides - Slant heightA - Surface areaNow we proceed to determine the surface area of the square pyramid:
Case 1:
A = 4 · 0.5 · (5 in) · (10 in) + (5 in)²
A = 125 in²
Case 2:
A = 4 · 0.5 · (8 ft) · (15 ft) + (8 ft)²
A = 304 ft²
Case 3:
A = 4 · 0.5 · (10 yd) · (16 yd) + (10 yd)²
A = 420 yd²
Case 4:
A = 4 · 0.5 · (3 yd) · (8 yd) + (3 yd)²
A = 57 yd²
Case 5:
A = 4 · 0.5 · (8 in) · (17 in) + (8 in)²
A = 336 in²
Case 6:
A = 4 · 0.5 · (4 ft) · (11 ft) + (4 ft)²
A = 104 ft²
To learn more on surface areas: https://brainly.com/question/29298005
#SPJ1
write a real-world example that could be solved by useing the the inequality 4x + 8 greater than 32. Then solve the inequality.
1. 8 added to four times the product of 4 and a number is greater than 32
1. x = 6
How to determine the valueIt is important to know that inequalities are expressions showing unequal comparison between number, expressions, or variables.
From the information given, we have that;
4x + 8 greater than 32.
This is represented as;
4x + 8 > 32
collect the like terms, we get
4x > 32 - 8
subtract the values
4x> 24
Divide both sides by the coefficient of x which is 4, we have;
x > 24/4
x > 6
Learn about inequalities at: https://brainly.com/question/25275758
#SPJ1
A wheatfarmer is converting to com because he believes that com is a more lucrative crop. It is not feasible for him to convert all his creace to com at onceHe is farming 100 acres of com in the current year and is increasing that number by 30 acres per year. As he becomes more experienced in growing com his output increas. He currently harvests 130 buhof com per acre. But the yield be increasing by buhol per acre per year. When both the increasing berage and the increasing yield are considered, how rapidly Withe total number of but of corn currently increasing bushes per year
The rate at which the total number of bushels of corn currently increases per year depends on the value of "b", which represents the annual increase in yield per acre. If the yield per acre is not increasing (i.e., b = 0), then the rate of increase is a constant 1300 bushels per year.
Let's call the total number of acres the farmer is farming in corn in a given year as "a". We know that initially, a = 100 acres, and that it increases by 30 acres per year. So, in general:
a = 100 + 30t
where "t" is the number of years since the farmer started converting to corn.
Now, let's call the yield in bushels per acre in a given year as "y". We know that initially, y = 130 bushels per acre, and that it increases by "b" bushels per acre per year. So, in general:
y = 130 + bt
Finally, we can calculate the total number of bushels of corn produced in a given year by multiplying the number of acres by the yield per acre:
bushels per year = a * y
Substituting the expressions we have for "a" and "y", we get:
bushels per year = (100 + 30t) * (130 + bt)
Expanding this expression, we get:
bushels per year = 13000 + 1300t + 3900bt + 30tb
Now we can differentiate this expression with respect to time to find how rapidly the total number of bushels of corn currently increases per year:
d(bushels per year)/dt = 1300 + 3900b + 30b
Simplifying, we get:
d(bushels per year)/dt = 1300 + 3930b
So the rate at which the total number of bushels of corn currently increases per year depends on the value of "b", which represents the annual increase in yield per acre. If the yield per acre is not increasing (i.e., b = 0), then the rate of increase is a constant 1300 bushels per year. If the yield per acre is increasing, then the rate of increase will be greater than 1300 bushels per year, and the rate of increase will depend on the value of "b".
To learn more about bushels of corn visit: https://brainly.com/question/13223409
#SPJ11
PLEASE HELP MEE
4 thumb drives and 1 compact disk have a total capacity of 18 gigabytes. 3 compact disks and 4 thumb drives have a total capacity of 22 gigabytes. Find the capacity of 1 thumb drive (x) and the capacity of 1 compact disk (y)
The capacity of 1 thumb drive is 4 gigabytes and the capacity of 1 compact disk is 2 gigabytes.
What is the capacity of 1 thumb drive and 1 compact disk?The first step is to form the system of equations that represent the information in the question:
4x + y = 18 equation 1
4x + 3y = 22 equation 2
The elimination method would be used to determined the required values.
Subtract equation 1 from equation 2
2y = 4
y = 4/2
y = 2
Substitute for y in equation 1: 4x + 2 = 18
4x = 18 - 2
4x = 16
x = 16/4
x = 4
To learn more about simultaneous equations, please check: brainly.com/question/25875552
#SPJ1
HELP ME PLEASE ANYBODY I NEED IT URGENTLY
I also have to show my work
Thank you.
Ms. Redmon gave her theater students an assignment to memorize a dramatic monologue to present to the rest of the class. The graph shows the times, rounded to the nearest half minute, of the first 10 monologues presented.
A number line going from 0.5 to 5. 0 dots are above 0.5 0 dots are above 1. 2 dots area above 1.5. 1 dot is above 2. 3 dots are above 2.5. 1 dot is above 3. 2 dots are above 3.5. 1 dot is above 4. 0 dots are above 2.5. 0 dots are above 5.
The next student presents a monologue that is about 0.5 minutes long. What effect will this have on the graph?
The median will decrease.
The mean will decrease.
The median will increase.
The mean will increase.
The effect of the student presenting such a monologue would be B. The mean will decrease.
How to find the effect ?Order the data points:
1. 5, 1. 5, 2, 2. 5, 2. 5, 2. 5, 3, 3. 5, 3. 5, 4
Find the mean ;
= (1. 5 + 1. 5 + 2 + 2. 5 + 2. 5 + 2. 5 + 3 + 3. 5 + 3. 5 + 4) / 10
= 27 / 10
= 2. 7
Then find the new mean after the student presents the monologue:
= ( 0. 5 + 1. 5 + 1. 5 + 2 + 2. 5 + 2. 5 + 2. 5 + 3 + 3. 5 + 3. 5 + 4) / 11
= 2. 5
The mean therefore reduced.
Find out more on median at https://brainly.com/question/13221365
#SPJ1
Answer:
b
Step-by-step explanation:
If |x+5|=, what are the possible values of x
The possible values of x that satisfy the equation |x+5| = c are x = c - 5 and x = -c - 5.
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
Assuming you meant to write |x+5|= some value, I can give you a general method to solve equations involving absolute values.
If |a| = b, then either a = b or a = -b. Thus, to solve the equation |x+5| = c, where c is some given value, we can split it into two cases:
Case 1: x+5 = c
Solving for x, we get x = c - 5.
Case 2: -(x+5) = c
Solving for x, we get x = -c - 5.
So, the possible values of x that satisfy the equation |x+5| = c are x = c - 5 and x = -c - 5.
To learn more about algebra from the given link:
https://brainly.com/question/24875240
#SPJ4
What is a minimum monthly payment?
To prevent loan or credit card payment default, borrowers must make a minimum monthly payment.
What is a minimum monthly payment?Based on the outstanding debt amount, this payment includes interest and other fees along with portions of principal. The lender/creditor typically sets these payments to ensure progress towards paying off existing debt.
However, by making just minimum payments, borrowers may end up shelling out significantly more in added interest over the lifetime of the debt. Furthermore, prolonging the repayment time is another possible outcome to such a practice; hence, it remains crucial to determine suitable ways of meeting higher than expected monthly payments on debts.
Read more on monthly payment here:https://brainly.com/question/29475683
#SPJ1
