Answer:
The number of hours since Vicky took the phone off the charger is the independent quantity, so the variable x should represent it.
Step-by-step explanation:
PLZ PLZ PLZ GIVE ME BRAINLIEST I TOOK THE TUTORIAL AND THIS WAS RIGHT!
Answer:
The rate of change of the function, m, is -5, and the initial value of the function, b, is 100. Substitute the values of m and b in the equation y = mx + b.
The equation of the function that models the phone’s remaining battery life in terms of the number of hours from the time Vicky took it off the charger is y = -5x + 100.
Step-by-step explanation:
Rachel measured the lengths of a random sample of 100 screws. The mean length was 2.9 inches, and the population standard deviation is 0.1 inch. To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be?
Answer:
z = 10
Step-by-step explanation:
The value of the z-statistic is given by:
[tex]z = \frac{X - \mu}{s}[/tex]
In which:
X is the measured value.
[tex]\mu[/tex] is the expected value.
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex] is the standard deviation of the sample. [tex]\sigma[/tex] is the standard deviation of the population.
In this question:
The mean length was 2.9 inches, and the population standard deviation is 0.1 inch.
This means that [tex]\mu = 2.9, \sigma = 0.1[/tex]
Random sample of 100 screws.
This means that n = 100.
To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be?
3 inches, so [tex]X = 3[/tex]
[tex]s = \frac{0.1}{\sqrt{100}} = 0.01[/tex]
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{3 - 2.9}{0.01}[/tex]
[tex]z = 10[/tex]
Answer:
-10
Step-by-step explanation:
If we first note the denominator of fraction numerator sigma over denominator square root of n end fraction equals fraction numerator 0.1 over denominator square root of 100 end fraction equals fraction numerator begin display style 0.1 end style over denominator 10 end fraction equals 0.01
Then, getting the z-score we can note it is z equals fraction numerator x with bar on top minus mu over denominator begin display style 0.01 end style end fraction equals fraction numerator 2.9 minus 3 over denominator 0.01 end fraction equals negative 10
This tells us that 2.9 is 10 standard deviations below the value of 3, which is extremely far away.
The product of an irrational number and a rational number is irrational. Sometimes True Always True Never True
Answer:
Always true
Step-by-step explanation:
If you can't express the number as a ratio of integers, multiplying or dividing it by integers will not make it so you can.
If π is irrational, 2π is also irrational.
It is always true that the product of a rational and an irrational number is irrational.
Answer:
all ways true
Step-by-step explanation:
A cinema can hold 270 people at one performance 5/9 of the seats were occupied of the occupied seats 40% we occupied by concessionary ticket holders
Question:
A cinema can hold 270 people at one performance 5/9 of the seats were occupied of the occupied seats 40% we occupied by concessionary ticket holders.
What is the number of seats occupied by concessionary ticket holders?.
Answer:
60 seats
Step-by-step explanation:
Given
Number of seats = 270
Occupied Seats = 5/9
Concessionary ticket holders = 40% of occupied Seats
Required
The number of seats occupied by concessionary ticket holders
First the number of occupied seat has to be calculated.
[tex]Occupied\ Seats = \frac{5}{9} * 270[/tex]
[tex]Occupied\ Seats = \frac{1350}{9}[/tex]
[tex]Occupied\ Seats = 150[/tex]
Next is to determine the number of seats occupied by concessionary ticket holders.
[tex]Number = 40\%\ of\ occupied\ seats[/tex]
[tex]Number = 40\%\ of\ 150[/tex]
Convert percentage to decimal
[tex]Number = 0.4 * 150[/tex]
[tex]Number = 60[/tex]
Hence, 60 seats were occupied by concessionary ticket holders.
While starting salaries have fallen for college graduates in many of the top hiring fields, there is some good news for business undergraduates with concentrations in accounting and finance (Bloomberg Businessweek, July 1, 2010). According to the National Association of Colleges and Employers’ Summer 2010 Salary Survey, accounting graduates commanded the second highest salary at $50,402, followed by finance graduates at $49,703. Let the standard deviation for accounting and finance graduates be $6,000 and $10,000, respectively.
a. What is the probability that 100 randomly selected accounting graduates will average more than $52,000 in salary?
b. What is the probability that 100 randomly selected finance graduates will average more than $52,000 in salary?
c. Comment on the above probabilities.
Answer:
Step-by-step explanation:
According to the central limit theorem, if independent random samples of size n are repeatedly taken from any population and n is large, the distribution of the sample means will approach a normal distribution. The size of n should be greater than or equal to 30. Given n = 100 for both scenarios, we would apply the formula,
z = (x - µ)/(σ/√n)
a) x is a random variable representing the salaries of accounting graduates. We want to determine P( x > 52000)
From the information given
µ = 50402
σ = 6000
z = (52000 - 50402)/(6000/√100) = 2.66
Looking at the normal distribution table, the probability corresponding to the z score is 0.9961
b) x is a random variable representing the salaries of finance graduates. We want to determine P(x > 52000)
From the information given
µ = 49703
σ = 10000
z = (52000 - 49703)/(10000/√100) = 2.3
Looking at the normal distribution table, the probability corresponding to the z score is 0.9893
c) The probabilities of either jobs paying that amount is high and very close.
What is the quotient 15p^-4q^-6/-20p^-12q^-3 in simplified form?
Answer:
-3p^8/4q^3
Step-by-step explanation:
<3
What kind of graph is characterized by presenting values as coordinate points without any connecting element? a. bar graph b. line graph c. scatter plot d. histogram
Answer:
Option C, Scatter Plot. Hope this helps!
Step-by-step explanation:
Answer:
The answer is C on edge 2020.
Step-by-step explanation:
The stem-and-leaf plot below shows the height of 15 sunflowers grown in the
school garden. The heights are given in inches.
Answer:
30 is not included
Step-by-step explanation:
The way this stem works is that it separates the numbers for better sorting.
Example:
Set that records 11, 12, 24, 28, 32, 32
The stem and leafs would look like
1 1 2
2 4 8
3 2 2
The sampled bold number indicates that 2 and 8 make up 28.
If you look at the plot, there was no 3 and 0 that would make 30. So that does not exist.
Use the graph of f to describe the transformation that results in the graph of g. f(x) = log x; g(x) = 2logx + 6 A.) The graph of g(x) is the graph of f(x) expanded vertically by a factor of 2, and translated 6 unit(s) up. B.) The graph of g(x) is the graph of f(x) reflected in the x-axis, expanded vertically by a factor of 2, and translated 6 unit(s) up. C.) The graph of g(x) is the graph of f(x) expanded vertically by a factor of 2, and translated 6 unit(s) down. D.) The graph of g(x) is the graph of f(x) reflected in the x-axis, expanded vertically by a factor of 2, and translated 6 unit(s) down.
Answer:
A.) The graph of g(x) is the graph of f(x) expanded vertically by a factor of 2, and translated 6 unit(s) up.
Step-by-step explanation:
For vertical expansion by a scale factor of k, the graph of f(x) is transformed to ...
g(x) = k·f(x)
For translation up by k units, f(x) is transformed to ...
g(x) = f(x) +k
___
Comparing the following ...
f(x) = log(x)
g(x) = 2·log(x) +6
We see that a multiplication factor and an addition factor have been applied. That means ...
g(x) is f(x) expanded vertically by a factor of 2, and translated up 6 units.
Answer:
A.) The graph of g(x) is the graph of f(x) expanded vertically by a factor of 2, and translated 6 unit(s) up.
Step-by-step explanation:
For vertical expansion by a scale factor of k, the graph of f(x) is transformed to ...
g(x) = k·f(x)
For translation up by k units, f(x) is transformed to ...
g(x) = f(x) +k
___
Comparing the following ...
f(x) = log(x)
g(x) = 2·log(x) +6
We see that a multiplication factor and an addition factor have been applied. That means ...
g(x) is f(x) expanded vertically by a factor of 2, and translated up 6 units.
Step-by-step explanation:
I just used this and I got it correct
Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1m to catch rainwater off his roof. He has a full 2 litres tin of paint in his store and decides to paint the tank (not the base). If he uses 250 ml to cover 1 m2, will he have enough paint to cover the tank with one layer of paint? [take π=3.142]
Answer:
Tublu has more than enough paint to cover the tank surface in one layer coating
Step-by-step explanation:
Height of the cylinder = 1.4 m
diameter of the cylinder = 1.1 m
total volume of paint available = 2 litres
It takes 250 ml to cover 1 m^2 of the tank body
Since only the body is to be painted, we find the perimeter of the circle formed by the body of the tank.
perimeter of the circle formed by the body of the tank = [tex]\pi d[/tex]
==> 3.142 x 1.1 = 3.456 m
This perimeter, if spread out, will form a rectangle with a height of 1.4 m from the base.
The area of the rectangle that will be formed = (perimeter of the cylinder body) x ( height of the cylinder)
==> 3.456 x 1.4 = 4.838 m^2
This is the area that needs to be painted.
Converting the paint volume,
250 ml = 0.25 litres
To paint the above calculated are, we will need 4.838 x 0.25 = 1.21 litres of paint, (of course, excluding the base)
The volume of paint available = 2 litres
volume of paint needed = 1.21 litres
Tublu has more than enough paint to cover the tank surface in one layer coating
Solve the following quadratic equation using the quadratic formula. Separate multiple answers with a comma if necessary. −6x^2+1=−2x
Answer:
Step-by-step explanation:
Hello,
We just need to apply the formula using the discriminant
[tex]-6x^2-2x+1=0\\\\\Delta = b^2-4ac = (-2)^2-*4(-6)*1=4+24=28[/tex]
so we have two distinct real solutions
[tex]x_1=\dfrac{2+\sqrt{28}}{2*(-6)}=\dfrac{2+2\sqrt{7}}{2*(-6)}=-\dfrac{\sqrt{7}+1}{6} \\\\ and \\\\x_2=\dfrac{\sqrt{7}-1}{6}[/tex]
Hope this helps
The figure shows eight congruent triangles made by dividing a square that has an area of 64 cm2. What is the area of ABH? A. 20 cm2 B. 16 cm2 C. 8 cm2 D. 6 cm2 E. 4 cm2
Answer:
the answer is C.
Step-by-step explanation:
64 ÷ 8 = 8
Answer:
c- 8cm squared
Step-by-step explanation:
plato
Need help plz someone help me solved this problem! I will mark you as brainiest !
Answer:
see explanation
Step-by-step explanation:
Given
f(x) = 60 × [tex]16^{x}[/tex]
x = 1 → f(1) = 60 × 16 = 960 ← bacteria present after 1 day
x = 2 → f(2) = 60 × 16² = 15360 ← bacteria present after 2 days
x = 3 → f(3) = 60 × 16³ = 245760 ← bacteria present after 3 days
Adam must fly home to city A from a business meeting in city B. One flight option flies directly to city A from B, a distance of about 456.2456.2 miles. A second flight option flies first to city C and then connects to A. The bearing from B to C is N2929degrees°E, and the bearing from B to A is N59.759.7degrees°E. The bearing from A to B is S59.759.7degrees°W, and the bearing from A to C is N78.978.9degrees°W. How many more frequent flyer miles will Adam receive if he takes the connecting flight rather than the direct flight? Adam would receive nothing more frequent flyer miles.
Answer:
105.6 miles
Step-by-step explanation:
The bearing from B to C is N29°EThe bearing from B to A is N59.7°E. The bearing from A to B is S59.7°WThe bearing from A to C is N78.9°W. Distance from A to B = 456.2 milesIn the diagram
The angle at B = 59.7°-29°=30.7°
The angle at A =180°-(78.9°+59.7°)=41.4°
Using the sum of angles in a triangle, Angle C = 107.9°
Applying the Law of Sines
[tex]\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\\b=\dfrac{c}{\sin C} \times \sin B\\\\=\dfrac{456.2}{\sin 107.9^\circ} \times \sin 30.7^\circ\\\\AC=b=244.76$ miles[/tex]
Similarly
[tex]\dfrac{a}{\sin A}=\dfrac{c}{\sin C}\\a=\dfrac{c}{\sin C} \times \sin A\\\\=\dfrac{456.2}{\sin 107.9^\circ} \times \sin 41.4^\circ\\\\BC=a=317.04$ miles[/tex]
Therefore:
AC+BC=244.76+317.04 =561.8 miles
Difference
561.8 - 456.2 =105.6 miles
Therefore, Adam would receive 105.6 miles more frequent flyer miles.
7
Which statement best describes the relationship
between storage space and number of music files?
As the number of files remains constant, the storage
space used decreases.
As the number of files remains constant, the storage
space used increases.
As the number of files increases, the storage space
used decreases.
Wh
As the number of files increases, the storage space
used increases.
Answer:
The answer is "As the number of files increases, the storage space used decreases."
Step-by-step explanation:
When the music files are put into storage they take up space, this causes the storage space to decrease.
Answer:
As the number of files increases, the storage space used increases.
A rectangular park is 8 miles long and 6 miles wide. How long is a pedestrian route that runs diagonally across the park?
Hey there! :)
Answer:
10 miles.
Step-by-step explanation:
To solve for the diagonal side, we can simply visualize the sides of the rectangle as sides of a right triangle with the diagonal being the hypotenuse.
We can use the Pythagorean Theorem (a² + b² = c²), where:
a = length of short leg
b = length of long leg
c = length of the diagonal
Solve:
c² = a² + b²
c² = 6² + 8²
c² = 36 + 64
c² = 100
c = 10 miles. This is the length of the pedestrian route.
Answer:
10 milesSolution,
Hypotenuse (h) = R
Perpendicular (p) = 8 miles
Base (b) = 6 miles
Now,
Using Pythagoras theorem:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
Plugging the values:
[tex] {r}^{2} = {(8)}^{2} + {(6)}^{2} [/tex]
Calculate:
[tex] {r}^{2} = 64 + 36[/tex]
[tex] {r}^{2} = 100[/tex]
[tex]r = \sqrt{100} [/tex]
[tex]r = 10 \: miles[/tex]
Length of route = 10 miles
Hope this helps...
Good luck on your assignment...
I NEED HELP PLEASE, THANKS! :)
Hey there! :)
Answer:
d ≈ 3.49 units
Step-by-step explanation:
Use the distance formula for polar coordinates to determine the distance:
[tex]d = \sqrt{r_{1} ^{2}+r_{2} ^{2}-2r_{1}r_{2}cos(0_{1}- 0_{2} ) }[/tex] (The '0' is supposed to be theta)
Plug in the values given in the question. Convert radians to degrees to simplify the process.
217π/180 = 217°
-23π/36 = -115°.
Therefore:
[tex]d = \sqrt{7 ^{2}+5 ^{2}-2(7)(5)cos(217-(-115) ) }[/tex]
Begin simplifying:
[tex]d = \sqrt{74-70cos(332) }[/tex]
[tex]d = \sqrt{74-61.81 }[/tex]
Solve:
[tex]d = \sqrt{12.19 }[/tex]
d ≈ 3.49 units
Question 8 of 10
If f(x) = 5x – 2 and g(x) = 2x + 1, find (f+g)(x).
O A. 4x-3
O B. 3x - 1
C. 7x-1
O D. 7x-3
SUBM
Answer:
7x-1
Step-by-step explanation:
f(x)+g(x)5x-2+(2x+1) 5x-2+2x+17x-1The solution is : If f(x) = 5x – 2 and g(x) = 2x + 1, then the value of (f+g)(x) is : 7x-1.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
given that,
If f(x) = 5x – 2 and g(x) = 2x + 1,
now, we have to find (f+g)(x).
so, we have,
f(x) = 5x – 2
and g(x) = 2x + 1
now,
(f+g)(x)
=f(x)+g(x)
=5x-2+(2x+1)
=5x-2+2x+1
=7x-1
Hence, The solution is : If f(x) = 5x – 2 and g(x) = 2x + 1, then the value of (f+g)(x) is : 7x-1.
To learn more on function click:
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If x = 2, then 2x = 4
Answer:
4 = 4
Step-by-step explanation:
=> 2x = 4
Putting x = 2
=> 2(2) = 4
=> 4 = 4
Answer:
TrueSolution,
X= 2
Now,
2x=4
plugging the value of X,
2*2= 4
4 = 4 ( hence it is true)
(01.03 MC) Find the value of the following expression.
Answer:
[tex]\frac{16}{9}[/tex].
Step-by-step explanation:
[tex](2^8*3^{-5}*6^0)^{-2}*(\frac{3^{-2}}{2^3})^4*2^{28}\\ (2^8*\frac{1}{3^5}*1)^{-2}*\frac{\frac{1}{3^8} }{\frac{2^{12}}{1} }*2^{28} \\ (\frac{2^8}{3^5})^{-2} * \frac{1}{2^8*3^{12}} *2^{28}\\ \frac{1}{\frac{2^8*2}{3^{5*2}} } * \frac{1}{2^8*3^{12}} *2^{28}\\ \frac{\frac{1}{1} }{\frac{2^{16}}{3^{10}} } * \frac{1}{2^8*3^{12}} *2^{28}\\ \frac{3^{10}}{2^{16}} * \frac{1}{2^8*3^{12}} *2^{28}\\ \frac{2^{28}}{2^{24}*3^2} = \frac{2^4}{3^2}=\frac{16}{9}[/tex]
Write an expression that is divisible by 7. Use it to find two three-digit numbers numbers divisible by 7.
Answer:
7x+7 is obviously divisible by 7.
put in any value high enough and you can find the two three digit numbers.
Step-by-step explanation:
Two three-digit numbers divisible by 7 are 98 and 105.
Two three-digit numbers divisible by 7 are 98 and 105.To create an expression that is divisible by 7, we can use the property that the difference between two numbers is divisible by 7 if the numbers themselves are divisible by 7.
Let's represent a three-digit number divisible by 7 as "7k" where k is an integer. To find two three-digit numbers divisible by 7, we can use the following expression:
7k - 7
For example, if we substitute k = 15, we get:
7(15) - 7 = 105 - 7 = 98
So, the first three-digit number divisible by 7 is 98.
Similarly, for the second three-digit number, let's substitute k = 16:
7(16) - 7 = 112 - 7 = 105
Therefore, the two three-digit numbers divisible by 7 are 98 and 105.
To know more about divisible, refer here:
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[tex]2x + 3y < 45[/tex]
Answer:
Hello!
~~~~~~~~~~~~~~~``
Simplifying
2x + 3y = 45
Solving
2x + 3y = 45
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3y' to each side of the equation.
2x + 3y + -3y = 45 + -3y
Combine like terms: 3y + -3y = 0
2x + 0 = 45 + -3y
2x = 45 + -3y
Divide each side by '2'.
x = 22.5 + -1.5y
Simplifying
x = 22.5 + -1.5y
Hope this helped you! Brainliest would be nice.
Good Morning can I get some help please?
Answer:
5x + 10 = 25
Subtract 10 on each side to make x alone
5x = 15
divide by 5 on each side
x=3 so x=3
3x + 12 = 48
48-12=36
3x=36
divide by 3
x=12
4x + 8 = 16
4x = 8
x=2
2x + 15=25
2x=10
x=5
5x + 20 = 50
5x=30
x=6
hope this helps
1. 3
2.12
3.2
4.5
5.6
Step-by-step explanation:
Answer:
x = 3x = 12x = 2x = 5x = 6Step by step explanation
First:
Move the constant to the Right Hand Side and change its signCalculate the differenceDivideCalculateSolution,
1. 5x + 10 = 25
Move constant to the R.H.S and change its sign:
5x = 25 - 10
Calculate the difference
5x = 15
Divide both sides by 5
5x/5 = 15/5
calculate
X = 3
2. 3x + 12 = 48
or, 3x = 48 - 12
or, 3x = 36
or, 3x/x = 36/3
x = 12
3. 4x + 8 = 16
or, 4x = 16 - 8
or, 4x = 8
or, 4x/x = 8/4
x = 2
4. 2x + 15 = 25
or, 2x = 25 - 15
or, 2x = 10
or, 2x/x= 10/2
x = 5
5. 5x + 20 = 50
or, 5x = 50-20
or, 5x = 30
or, 5x/x = 30/5
x = 6
Hope this helps...
Good luck on your assignment...
someone help please, already tried 168 says its wrong??
Answer:
245 might be the answer
Step-by-step explanation:
(7*7*10)/2
If <10 and <15 are congruent, which lines are parallel? A.lines b and c B.lines c and d C.lines a and b D.No lines are parallel. - Refer to second picture. Given the information in the diagram, determine if M ll N If so, give the theorem or postulate used to support your conclusion. A.yes; converse of the consecutive interior angles theorem B.yes; converse of the alternate interior angles theorem C.yes; converse of the corresponding angles postulate D.no
Problem 1
Answer: C. lines a and bExplanation: Circle or highlight the angles 10 and 15. They are alternate interior angles with line d being the transversal cut. It might help to try to erase line c to picture the transversal line d better. With d as the transversal, and angles 10 and 15 congruent, this must mean lines a and b are parallel by the alternate interior angle theorem converse.
==============================================
Problem 2
Answer: D. noExplanation: The angles at the top are 32 degrees, 90 degrees, and x degrees which is the missing unmarked angle at the top (all three angles are below line m). The three angles must add to 180 to form a straight angle
32+90+x = 180
x+122 = 180
x = 180-122
x = 58
The missing angle is 58 degrees. This is very close to 57 degrees at the bottom. Though we do not have an exact match. This means lines m and n are not parallel. The alternate interior angles must be congruent for m and n to be parallel, as stated earlier in problem 1.
What is the square root of 64y16?
4y4
4y8
8y4
8y8
Answer: 8y⁸
Step-by-step explanation:
To find the square root of the expression, you want to find the square root of each term.
The square root of 64 is 8. You can write y¹⁶ as (y⁸)². We can pull out this 2 from the square root because it cancels out with the square root. Therefore, the answer is 8y⁸.
IS this table linear?? Can someone please explain???? What would the weight be if the number of weeks in the fitness program was 0???
Answer:
not linearsomewhere between 184 and 186 (maybe)Step-by-step explanation:
As you show, the weight differences are different for the same week differences, so the table is not linear. A graph (attached) can also show you the table is not linear.
__
The highest rate of weight loss shown in the table is 7 lbs in 3 weeks, or 4 2/3 pounds in 2 weeks. The lowest rate of weight loss shown in the table is 5 lbs in 3 weeks, or 3 1/3 pounds in 2 weeks. Based on the rates shown in the table, we might expect the starting weight to be between 3 1/3 and 4 2/3 pounds more than the first table value:
Week 0 weight: between 184 1/3 and 185 2/3 lbs, estimated.
_____
A "line of best fit" for the data has a y-intercept of about 185 pounds, which is the midpoint between our two estimates above.
Find all solutions of the given system of equations and check your answer graphically. HINT [See Examples 2–5.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x).) 3x + 2y = 20 2x + 3y = 20 (x, y) = (No Response)
Answer:
( x, y ) = ( -20, 20 )
Step-by-step explanation:
Given data
Y = y(x)
3x + 2y = 20 ---------- equation 1
2x + 3y = 20 ---------- equation 2
find (x, y )
solving equation 1 and equation 2
3x + 2y = 20 * 2 = 6x + 2y = 40 --------- EQUATION 3
2x + 3y = 20 * 3 = 6x + 3y = 60 --------- EQUATION 4
cancelling out ( x )
Add both equation 3 and equation 4
5y = 100. hence y = 100/5 = 20
back to equation equation 2
2x + 3(20) = 20
2x = - 40
x = -20
attached is the graph to check the answer
Assume that adults have IQ scores that are normally distributed with a mean of 104 and a standard deviation of 15. Find the third quartile Upper Q 3 , which is the IQ score separating the top 25% from the others. Click to view page 1 of the table. LOADING... Click to view page 2 of the table. LOADING... The third quartile, Upper Q 3 , is nothing . (Round to one decimal place as needed.)
Answer:
z = (X-Mean)/SD
X = Mean + (z*SD)
The z value which separates the bottom 75% (100%-25%) from the top 25% is + 0.6745
Therefore, Q3 = X = 107 + (0.6745*16) = 117.8
Step-by-step explanation:
The function f(x) = x^2+4 is defined over the interval (-2,2). If the interval is dived into n equal parts what is the height of the right endpoint of the kth rectangle?
Answer:
Option (A).
Step-by-step explanation:
The function f(x) = x² + 4 is defined over the interval (-2, 2)
Total number of equal parts between this interval = 5
If the interval is divided into n equal parts, height of the right endpoint of each rectangle = [tex]\frac{5}{n}[/tex]
Height of the endpoint of the k rectangles = [tex]k.\frac{5}{n}[/tex]
Therefore, height of the endpoint of the kth rectangle = Height of first rectangle + height of k rectangles
= -2 + [tex]k.\frac{5}{n}[/tex]
Option (A). will be the answer.
The height of the right endpoint of the kth rectangle h = -2 + k (5/n)
What is the height?The height is a vertical distance between two points. In the case of the triangle, the height will be the distance between the base and the top vertex of the triangle.
The function f(x) = x² + 4 is defined over the interval) (-2, 2 )
Total number of equal parts between this interval = 5
If the interval is divided into n equal parts, the height of the right endpoint of each rectangle = (5/n)
Height of the endpoint of the k rectangles = k (5/n)
The height of the endpoint of the kth rectangle:-
= Height of first rectangle + height of k rectangles
= -2 + k ( 5/n )
Therefore the height of the right endpoint of the kth rectangle h = -2 + k (5/n)
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If sin y° = a/6 and tan y° = a/b what is the value of sec y°
Answer:
[tex]sec\ y = \frac{6}{b}[/tex]
Step-by-step explanation:
Given
[tex]sin\ y = \frac{a}{6}[/tex]
[tex]tan\ y = \frac{a}{b}[/tex]
Required
sec y
From trigonometry;
[tex]sec\ \theta = tan\ \theta\ /\ sin\ \theta[/tex]
Substitute y for θ
[tex]sec\ y= tan\ y\ /\ sin\ y[/tex]
Substitute values for tan y and sin y
sec y = a/b ÷ a/6
[tex]sec\ y= \frac{a}{b} /\ \frac{a}{6}[/tex]
[tex]sec\ y= \frac{a}{b} *\ \frac{6}{a}[/tex]
[tex]sec\ y= \frac{6 * a}{a *b}[/tex]
[tex]sec\ y= \frac{6 a}{ab}[/tex]
Divide numerator and denominator by a
[tex]sec\ y= \frac{6}{b}[/tex]
Hence, the value of sec y is
[tex]sec\ y= \frac{6}{b}[/tex]