The value of the limit of the function given when the value of x tends to zero is 0
What is a limit of a function?The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular inputs.
Given the function limit below;
lim x→0 [1 − cos(2x) /x]
Substitute the value of x into the expression to have;
f(0) = 1-cos2(0)/0
f(0) = 1-1/0
f(0) = 0/0 (ind)
Apply the L'hospital rule to have:
lim x→0 [ − (-2sin2x)) /1]
Substitute the value of x into the result
f(0) = 2sin2(0)/1
f(0) = 2(0)
f(0) = 0
Hence the value of the limit of the function given when the value of x tends to zero is 0
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A pattern has 2 blue triangles to every 10 yellow triangles. What is the ratio of blue triangles to all triangles?
Answer:
2 : 12
Step-by-step explanation:
There are 2 blue triangles, so 2 will come first. It's then followed by the sum of blue and yellow, which is 2 + 10, which is 12. So, the ratio is 2 : 12.
Brainliest, please :)
As an introduction to probability, a student asked to roll a fair, six sided number cube seven times the results of those seven rolls are shown below 1,4,4,4,4,6,5 what is the standard deviation of the data?
Using it's concept, the standard deviation of the data is of 3.742.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.For this data-set, the mean is:
M = (1 + 4 + 4 + 4 + 4 + 6 + 5)/7 = 4.
Hence the standard deviation is:
[tex]S = \sqrt{\frac{(1 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (6 - 4)^2 + (5 - 4)^2}{7}} = 3.742[/tex]
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An article in the British Medical Journal [“Comparison of Treatment of Renal Calculi by Operative Surgery, Percutaneous Nephrolithotomy, and Extra-Corporeal Shock Wave Lithotrips,” (1986, Vol. 292, pp. 879–882)] found that percutaneous nephrolithotomy (PN) had a success rate in removing kidney stones of 289 out of 350 patients. The traditional method was 78% effective.
(a) Is there evidence that the success rate for PN is greater than the historical success rate? Find the P-value.
(b) Explain how the question in part (a) could be answered with a confidence interval.
The Success rate of (PN) had 82.57% which is greater than traditional method's success rate.
According to the statement
we have given that the percutaneous nephrolithotomy (PN) had a success rate in removing kidney stones of 289 out of 350 patients. And
The traditional method was 78% effective.
we have to show that the success rate for PN is greater than the historical success rate then
we use the percentage formula to find the success rate of the new method. So,
(a) Total patients = 350
Success rate in number of patient = 289
Percentage of success rate = (289/350)*100
Then after calculating
Percentage of success rate = 82.57%
It is clear that the outcome success rate is 82.57% which is greater than traditional method.
(b) we have a 95% confidence that the success rate of new method is higher than the older method from a confidence interval of 2.262 and 3.67
So, The Success rate of (PN) had 82.57% which is greater than traditional method's success rate.
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15v - 2v + 29 = 5v - 27
Answer:
v=-7
Step-by-step explanation:
13v-5v=-27-29
8v=-56
v=-56/8=-7
The estimated population of Los Angeles in 2019 was 3,979,576. Its area is 469 square miles. What is the population density of Los Angeles, in people per square mile?
Given that, the estimated population of Los Angeles in 2019 was 3,979,576 and its area is 469 square miles, the population density of Los Angeles is 8486 people per square miles.
What is the population density of Los Angeles, in people per square mile?Population density simply the measurement of population per unit area.
It is expressed as;
Population density = Number of people / Area
Given the data in question;
Number of people in Los Angeles N = 3,979,576 peopleArea of Los Angeles A = 469 square milesPopulation density = ?We substitute the given values into the above equation.
Population density = Number of people / Area
Population density = 3,979,576 people / 469 square miles
Population density = 8485.23667 ≈ 8486 people per square miles
Given that, the estimated population of Los Angeles in 2019 was 3,979,576 and its area is 469 square miles, the population density of Los Angeles is 8486 people per square miles.
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The following are the ages (years) of 5 people in a room:
14
,
16
,
16
,
13
,
A person enters the room.
The mean age of the 6 people is now 21.
What is the age of the person who entered the room?
Answer:
67 years old. (you only gave 4 people and missed out one person)
Step-by-step explanation:
take all the ages first and put the unknown (age of the person who entered the room) as x.
14, 16, 16, 13, x
all of these numbers added to together would be:
59 + x
Because the question is talking about the mean age, to find mean:
add all the values in the data (ages) and divide by the total number of values on the list. (in your case would be 6 people (following your question) but you gave only 5 people including the x).
then (59 + x) / 6 = 21
21 x 6 = 126
126 = 59 + x
x = 67
12. The brakes on a vehicle can slow it down at a rate of 15m/s 2. Remember that slowing down is also a rate of change of speed. If this vehicle is travelling at 40 m/s how long would it take the brakes to bring the vehicle to a standstill? Show all steps and formulae used
Step-by-step explanation:
there are several formulas that could play a role.
but in our case, where we have velocities and the deceleration, we are going to use
fV = iV + at
fV = final velocity (0 on our case)
iV = initial velocity (40 m/s in our case)
a = acceleration (-15 m/s² in our case)
t is the time it takes to reach fV.
0 = 40 + (-15)t = 40 - 15t
15t = 40
3t = 8
t = 8/3 = 2.666666666... seconds
so, it takes 2.6666666... or 2 2/3 seconds to bring the vehicle to a standstill.
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180
The true options regarding the triangle diagram are;
m∠5 + m∠6 = 180°
m∠2+ m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
How to prove congruent angles?We see the attached image showing ΔABC with Exterior angles as;
∠ 1 , ∠ 4 ,and ∠ 6
Now, the exterior angle property of triangles states that; An exterior angle of a triangle is equal to the sum of the opposite interior angles.
For Exterior ∠1 we have;
∠1 = ∠5 + ∠3 (Exterior angle Property of Triangle)
Similarly,
For Exterior ∠ 4 we have;
∠4 = ∠5 + ∠2 (Exterior angle Property of Triangle)
For Exterior ∠6 we have;
∠6 = ∠2 + ∠3 (Exterior angle Property of Triangle)
From Triangle Sum Property, we know that the sum of the measures of angles in a triangle is equal to 180°. Thus;
m∠2 + m∠3 + m∠5 = 180° (Triangle Sum Property)
Linear Pair of angles states that the measure of a straight angle is 180° and as such a linear pair of angles must add up to 180°. Thus;
m∠5 + m∠6 = 180° (Linear Pair)
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answers for these? pls
Answer:
6a. 13.5m
6b. 12.4m
Step-by-step explanation:
We can use trig identities to solve these problems because each triangle is a right triangle.
6a. Find the measure of the hypotenuse.
Using the angle in the top corner, which is defined as 66 degrees and its adjacent side, we can find the hypotenuse. Remember that the hypotenuse is the longest side, which in this case would be AB. The adjacent side is the side next to the angle that is not the hypotenuse, in this case it would be AC, which is shown to be 5.5m.
The trig identity cos(x) is defined as adjacent/hypotenuse, or the value of the adjacent side divided by the value of the hypotenuse, where x is the degrees of the angle.
So we can set up the equation:
cos(x)=adj/hyp
If we know that x=66 (the degree of the angle) and adj=5.5m, we can substitute this into the equation. Let c represent the hypotenuse.
cos(66)=5.5/c
Then we can multiply by c:
c*cos(66)=5.5
Then divide by cos(66):
c=5.5/cos(66)
Use a calculator to estimate that c approximately equals 13.5m when rounded to the nearest tenth (remember to use degree mode because our angle is measured in degrees).
6b. Find the measure of side a.
Side a is the side opposite to angle A. This can also be known as side CB or the bottom of the triangle.
Method 1: Use trig identity tan(x)tan(x)=opp/adj
Remember x=66 and adj=5.5m. Let a represent the opposite side. Plug in these values into the equation:
tan(66)=a/5.5
Multiply both sides by 5.5:
a=tan(66)*5.5
Use a calculator to estimate that a approximately equals 12.4m when rounded to the nearest tenth (remember to use degree mode because our angle is measured in degrees).
Method 2 (I would recommend method 1, however because you are basing this answer off of the first answer, and in a test or a quiz, you might not be sure if your first answer was correct):
Use Pythagorean Theorem:
a^2+b^2=c^2
c, or the hypotenuse is 13.5m as found in out last problem, and b, the adjacent side is 5.5m which was a given. Substitute these values into the equation:
a^2+5.5^2=13.5^2
a^2+30.25=182.25
a^2=152a=sqrt(152) which rounds to 12.3m, which is almost the same as Method 1, however our answers are different because we used a rounded value of b, rather than the approximate.
According to the tables used by insurance companies, a 47-year old woman has a 0.179% chance of passing away during the coming year. An insurance company charges $204 for a life insurance policy that pays a $100,000 death benefit. What is the expected value for the person buying the insurance?
The expected value for the person buying the insurance is -25.
How the expected value is calculated?The expected value is the average gain or loss of an event if the event is repeated a number of times.
Expected value = ∑xP(x)
Calculation:It is given that,
The probability of a 47-year-old woman passing away during the coming year is 0.179% = 0.00179
The death benefit = $100,000 - $204 = $99,796
The loss from living = -204
Then the expected value = 99796(0.00179) + (-204)(0.99821) = -25
Therefore, the expected value for the person buying the insurance is -25.
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A random sample of vehicle mileage expectancies has a sample mean of x¯=169,200 miles and sample standard deviation of s=19,400 miles. Use the Empirical Rule to estimate the percentage of vehicle mileage expectancies that are more than 188,600 miles. Round your answer to the nearest whole number (percent).
The percentage of vehicle mileage expectancies that are more than 188,600 miles is 93%
How to determine the percentage?The given parameters are:
Mean = 169200
Standard deviation = 19400
x = 188600
Calculate the z value using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
So, we have:
[tex]z = \frac{188600 - 169200}{19400}[/tex]
Evaluate
z = 1
Using the Empirical Rule, we have:
P(x > 188600) = P(z > 1.5)
From z table of probability, we have:
P(x > 188600) = 0.93319
Express as percentage
P(x > 188600) = 93.319%
Approximate
P(x > 188600) = 93%
Hence, the percentage of vehicle mileage expectancies that are more than 188,600 miles is 93%
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Which choice is equivalent to the quotient shown here for acceptable values of x?
The expression [tex]\sqrt{\frac{5}{x-1} }[/tex] is equivalent to the given quotient.
Option A is correct.
When we divide one number by another, the result is a quotient. Although a quotient can be greater than the divisor, it will never be greater than the dividend.
In mathematics, the outcome of dividing a number by any divisor is known as the quotient. It refers to how many times the dividend contains the divisor.
After the division has been done, the quotient is obtained. This signifies that the quotient is the result of dividing a dividend by a divisor.
According to the question,
[tex]\sqrt{25(x-1)}[/tex] ÷ [tex]\sqrt{5(x-1)^{2} }[/tex] = 5[tex]\sqrt{x-1}[/tex] ÷ (x-1)[tex]\sqrt{5}[/tex]
= [tex]\sqrt{\frac{5}{x-1} }[/tex]
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Triangle PQR is rotated, translated, and dilated to obtain triangle P'Q'R' as shown. An Image of triangle PQR and PQR prime are displayed. The Triangle PQR intersects P at (minus 2, 0.5), R at (minus 2, minus 2.5) and Q at (0, minus 1.5). Similarly P, R, Q prime at (1.5,minus 1.5), (1.5,3), and (minus 1.5,1.5). Which statement about the two figures is correct? A. The two figures are similar because each angle measure of the image is times the corresponding angle measure of the preimage and all the pairs of corresponding sides are congruent. B. The two figures are similar because each angle measure of the image is times the corresponding angle measure of the preimage and all the pairs of corresponding sides are congruent. C. The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent. D. The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent.
The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent.
How to determine the true statements?The transformations are given as:
RotationTranslationDilationRotation and translation would preserve the lengths and the angles of the triangles. Because they are rigid transformations.
Dilation would only preserve the angle of the triangles. Because it is a nonrigid transformation.
The above means that the angles of triangle PQR and triangle P'Q'R' are congruent
Hence, the true statement is (d)
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Emma throws an object upwards from a hill
The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A non linear function is a function whose graph is not linear or can be represented by a straight line.
The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.
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Which of the following inequalities matches the graph?
-8 -0
O x>4
O x<4
O y> 4
O y<4
1
Answer:
it matches with equation c
Which is the graph of the function f(x)=√x?
The graph is shown in the attached image.
Select the correct answer.
What is the range of the function shown in the graph?
keeping in mind that the range is vertical values covered by the function, Check the picture below.
3
3
4
Possible inputs for the quadratic when the
output is 3 are
(Note: Fill in the least input first)
or
[tex]x {}^{(1)} = - 3 \: \: \: \: \: \: x {}^{(2)} = - 1[/tex]
The teenager from the question above rejoins the group and another teenager is picked at random.
What is the probability that the teenager picked at random is male and their favourite hobby is playing video games? You can simplify this fraction if you wish
Using it's concept, the probability that the teenager picked at random is male and their favorite hobby is playing video games is:
[tex]\frac{1}{16}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching this problem on the internet, it is found that out of 32 teenagers, 2 are males who prefer playing videogames, hence the probability is:
[tex]p = \frac{2}{32} = \frac{1}{16}[/tex]
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After defeating the fire breathing dragon, the knight decides
to celebrate his victory with a celebratory goblet made out of Dragon Alloy #17, which is 36% gold, 9% silver, and 55% magic steel. The dwarves have Dragon Alloy #11, which is 36% gold, 28% magic steel, and the rest silver. They also have Dragon Alloy #15, which is 36% gold and 64% magic steel. How many grams of each
alloy should the dwarves combine to get 1 kg of Dragon Alloy #17?
250 grams of dragon alloy #11 and 750 grams of dragon alloy #35 is needed to make 1000 grams (1 kg) of Dragon alloy #17.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of alloy #11 and y represent the amount of alloy #15, hence:
(0.36x) + (y * 0.36) = 1(0.36) (1)
Also:
0.28x + 0.64y = 1(0.55) (2)
From both equations:
x = 0.25, y = 0.75
250 grams of dragon alloy #11 and 750 grams of dragon alloy #35 is needed to make 1000 grams (1 kg) of Dragon alloy #17.
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If DAB = 80°, then DAC =
Answer:
80
Step-by-step explanation:
DAB =DAC...........
Find the area of the trapezoid. 15ft 10ft 20ft
Answer: 175 ft squared
Step-by-step explanation: A= a + b / 2h= 20 + 152 · 10 = 175
Explain the difference between using area and volume with 2-D and 3-D figures.
The difference between Area and Volume lies in the fact that the former relates to plane shapes while the latter takes the concept of solid shapes into account.
What is the difference between Area and Volume?The distinctive characteristic of area is the space occupied by a two-dimensional, 2D flat object in a plane while Volume on the other hand is defined as the space covered by a three-dimensional, solid object. The area is quantised in square units while the volume is quantised in cubic units.
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write the expression as the sine or cosine of an angle
pi/5 cos pi/2+sin pi/2\cos pi/5
The given expression as a sine function is [tex]sin(\frac{\pi}{5} +\frac{\pi}{2} )[/tex]
The addition formula for trigonometryThe given expression is:
[tex]sin(\frac{\pi}{5})cos(\frac{\pi}{2} ) + cos(\frac{\pi}{5})sin(\frac{\pi}{2} )[/tex]
Note that:
[tex]sin(A+B)=sinAcosB+cosAsinB[/tex]
Applying the addition principle to the given expression, we have:
[tex]sin(\frac{\pi}{5})cos(\frac{\pi}{2} ) + cos(\frac{\pi}{5})sin(\frac{\pi}{2} )=sin(\frac{\pi}{5} +\frac{\pi}{2} )[/tex]
Therefore, the given expression as a sine function is [tex]sin(\frac{\pi}{5} +\frac{\pi}{2} )[/tex]
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Pls help me I'm stuck
The measure of the angle BAM is approximately 40.894°.
What is the angle withing a rectangle?
In this problem we proceed to draw the figure representing the entire figure and labeling all known lengths, both from statement and derived from Pythagorean theorem. Since the angle BAM is part of a right triangle, then we can apply the following trigonometric function:
[tex]\tan \theta = \frac{BM}{AB}[/tex]
[tex]\tan \theta = \frac{\frac{\sqrt{3}}{2}\cdot x }{x}[/tex]
[tex]\tan \theta = \frac{\sqrt{3}}{2}[/tex]
θ ≈ 40.894°
The measure of the angle BAM is approximately 40.894°.
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An H0-scale model railroad engine is 9 inches long. The H0 scale is 87 feet to 1 foot. How long is a real engine?
The real engine is 65.25 feet long
How to determine the length?The scale is given as:
Scale = 87 feet to 1 foot
The scale length is given as
Scale length = 9 inches
Convert inches to feet
Scale length = 9/12 feet
The actual length is then calculated as:
Actual = 87 * 9/12 feet
Evaluate
Actual = 65.25 feet
Hence, the real engine is 65.25 feet long
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Refer to the figure below.
BED and CEA are
angles.
A
C
E
D
B
Answer:
both two
Step-by-step explanation:
because it is in alphabetical order
Value of x after the statement "if P(x) then x 1" is executed where P(x): > 1
and x = 0 when the statement is reached:
The values of x after the statement are:
b) If x=1, then the statement P(1)="1>1" is false, and thus the value of x is equal to 1 after the statement "P(x) then x := 1".c) If x=2, then the statement P(2)="2>1" is true, and thus the value of x is equal to 1 after the statement "if P(x) then x := 1".What is Discrete Mathematics?This refers to the field of mathematics that studies mathematical structures and views them as discrete, rather than continuous and they include integers, statements, etc.
Therefore, if we consider the statement "if P(x) then x:=1" which is equivalent to "if x>1 then x:=1", then we can see that If x=1, then the statement P(1)="1>1" is false
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14) Noah needs a car to get to his new job each day. He figures he can afford to pay $120 each month. Since he
is not looking at a new car, his bank will only give him a 4-year loan at 9.20 percent interest. Given these
parameters, what is the most Noah can borrow? Give answer to nearest hundred dollars.
O a.) $4600
Ob.) $4800
Oc.) $4900
O d.) $5000
Answer: $4600
Step-by-step explanation:
The method in which all the elements of the set are written within brackets is called
Answer:
The set can be defined by listing all its elements, separated by commas and enclosed within braces. This is called the roster method.
Step-by-step explanation:
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