Answers
Using a proportional relationship, it is found that the unit rate of change is of 9.
The relation d = 9t is graphed at the end of the answer.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, we have d as a function of t, hence the relationship is:
d = kt.
When t increases by 0.2, d increases by 1.8, hence the constant is given as follows:
k = d/t = 1.8/0.2 = 9
The relation d = 9t is graphed at the end of the answer.
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Related Questions
Geometry: fill in the blanks (ASAP! It’s urgent)
Answers
a. altitude = CE
b. bisector = BD
c. exterior angle = ∠ABE
d. median = CF
e. remote interior angles = ∠BCE and ∠CEB
GeometryFrom the question, we are to fill in the blanks
In ΔBCE, we have that ∠BCE is a right angle
Thus,
a. altitude = CE
Also, we have that
∠EBD ≅ ∠CBD
Thus, BD is a bisector
b. bisector = BD
The exterior angle of the triangle is ∠ABE
c. exterior angle = ∠ABE
From the given information,
BF ≅ EF
∴ F is the midpoint of BE
NOTE: Median is a line segment joining the vertex of one side of the triangle to the midpoint of its opposite side.
The median of the triangle is CF
d. median = CF
The remote interior angles of the triangle are ∠BCE and ∠CEB
e. remote interior angles = ∠BCE and ∠CEB
Hence,
a. altitude = CE
b. bisector = BD
c. exterior angle = ∠ABE
d. median = CF
e. remote interior angles = ∠BCE and ∠CEB
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A lampshade made from a piece of sheet plastic has a radius of the inner circle to be 7cm and that of the outer circle is 28cm. if its arc subtends an angle of 315 degree at the center, what is the area of the plastic used to form the lampshade
Answers
The area of the plastic used to form the lampshade is 2021.25 square centimeters
How to determine the area of the plastic used to form the lampshade?The given parameters in the question are:
Outer radius, R = 28 cm
Inner radius, r = 7 cm
Angle, ∅ = 315
The area of the plastic used to form the lampshade is calculated using the following area of sector formula
A = ∅/360 * π(R² - r²)
Substitute the known values in the above equation
A = 315/360 * 22/7 * (28² - 7²)
Evaluate the exponents
A = 315/360 * 22/7 * (784 - 49)
Evaluate the difference
A = 315/360 * 22/7 * 735
Evaluate the product
A = 2021.25
Hence, the area of the plastic used to form the lampshade is 2021.25 square centimeters
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50 points!!!
Someone help pls, I can’t understand it and it’s due tomorrow :c
Answers
[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}[/tex]
[tex]\star\:{\underline{\underline{\sf{\purple{Solution:}}}}}[/tex]
❍ Arrange the given data in order either in ascending order or descending order.
2, 3, 4, 7, 9, 11
❍ Number of terms in data [n] = 6 which is even.
As we know,
[tex]\star \: \sf Median_{(when \: n \: is \: even)} = {\underline{\boxed{\sf{\purple{ \dfrac{ { \bigg (\dfrac{n}{2} \bigg)}^{th}term +{ \bigg( \dfrac{n}{2} + 1 \bigg)}^{th} term } {2} }}}}}[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ { \bigg (\dfrac{6}{2} \bigg)}^{th}term +{ \bigg( \dfrac{6}{2} + 1 \bigg)}^{th} term } {2} }[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \dfrac{6 + 2}{2} \bigg)}^{th} term } {2} }[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \cancel{ \dfrac{8}{2}} \bigg)}^{th} term } {2} }[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ 4}^{th} term } {2} }[/tex]
• Putting,
3rd term as 4 and the 4th term as 7.
[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 4 + 7 } {2} }[/tex]
[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 11} {2} }[/tex]
[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} = \purple{5.5}[/tex]
[tex]\\[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}[/tex]
[tex]\star\:{\underline{\underline{\sf{\red{Solution:}}}}}[/tex]
❍ Arrange the given data in order either in ascending order or descending order.
1, 2, 3, 4, 5, 6, 7
❍ Number of terms in data [n] = 7 which is odd.
As we know,
[tex]\star \: \sf Median_{(when \: n \: is \: odd)} = {\underline{\boxed{\sf{\red{ { \bigg( \frac{n + 1}{2} \bigg)}^{th} term}}}}}[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: odd)} = {{ \bigg(\dfrac{ 7 + 1 } {2} \bigg) }}^{th} term[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: odd)} = { \bigg(\cancel{\dfrac{8}{2}} \bigg)}^{th} term[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: odd)} ={ 4}^{th} term[/tex]
• Putting,
4th term as 4.
[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: odd)} = \red{ 4}[/tex]
[tex]\\[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 3 :}}}}}}[/tex]
[tex]\star\:{\underline{\underline{\sf{\green{Solution:}}}}}[/tex]
The frequency distribution table for calculations of mean :
[tex]\begin{gathered}\begin{array}{|c|c|c|c|c|c|c|} \hline \rm x_{i} &\rm 3&\rm 1&\rm 7&\rm 4&\rm 6&\rm 2 \rm \\ \hline\rm f_{i} &\rm 4&\rm 6&\rm 2&\rm 2 & \rm 1&\rm 1 \\ \hline \rm f_{i}x_{i} &\rm 12&\rm 6&\rm 14&\rm 8&\rm 6&\rm \rm 2 \\ \hline \end{array} \\ \end{gathered} [/tex]
☆ Calculating the [tex]\sum f_{i}[/tex]
[tex] \implies 4 + 6 + 2 + 2 + 1 + 1[/tex]
[tex] \implies 16[/tex]
☆ Calculating the [tex]\sum f_{i}x_{i}[/tex]
[tex] \implies 12 + 6 + 14 + 8 + 6 + 2[/tex]
[tex]\implies 48[/tex]
As we know,
Mean by direct method :
[tex] \: \: \boxed{\green{{ { \overline{x} \: = \sf \dfrac{ \sum \: f_{i}x_{i}}{ \sum \: f_{i}}}}}}[/tex]
here,
• [tex]\sum f_{i}[/tex] = 16
• [tex]\sum f_{i}x_{i}[/tex] = 48
By putting the values we get,
[tex]\sf \longrightarrow \overline{x} \: = \: \dfrac{48}{16}[/tex]
[tex]\sf \longrightarrow \overline{x} \: = \green{3}[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{Note\: :}}}}}}[/tex]
• Swipe to see the full answer.
[tex]\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}[/tex]
The following figure is made of 2 triangles.
9
5
A
Figure
Triangle A
Triangle B
Whole figure
7
B
Find the area of each part of the figure and the whole figure.
Area (square units)
Answers
area is 1/2 times base times height
triangle A
1/2 times 7 times 9
answer 31.5
Triangle B
1/2 times 7 times 5
answer 17.5
Triangle A: 31.5 units squared
Triangle B: 17.5 unites squared
But you really should start memorizing formulas
Select the correct answer from the drop-down menu. consider the equations y = |x − 1| and y = 3x 2. the approximate solution of this system of equations is .
Answers
The approximate solution of this system of equations is
(x,y)=(-0.25,1.25)
What is an equation?Equation is defined as the state of being equal and is often shown as a math expression with equal values on either side, or refers to a problem where many things need to be taken into account.
Given that,
y = |x − 1| and y = 3x+2
y = |x − 1|
= (x-1) , for (x-1)>0 or x>1
and
y = -(x-1) , for(x-1)<0 or x<1
y = -x+1
Now, For x>1
y = x-1 ......(1)
y = 3x+2 ......(2)
Solving for x by equaliting's method:
3x+2 = x-1
→ 3x-x = -1-2
→ 2x = -3
→ x = -3/2
→ x = -1.5 which is <1.
For x<1
y = -x+1 ......(1)
y = 3x+2 ......(2)
Solving for x by equaliting's method:
3x+2 = -x+1
→ 3x+x = 1-2
→ 4x = -1
→ x = -1/4
→ x= -0.25 which is <1.
substitute the value of x = -0.25 in equation 1 for x<1.
y = -x+1
= -(-0.25)+1
y = 1.25
Hence, The approximate solution of this system of equations is
(x,y)=(-1/4,5/4)=(-0.25,1.25).
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Kwame must earn more than 16 1616 stars per day to get a prize from the classroom treasure box. Write an inequality that describes S SS, the number of stars Kwame must earn per day to get a prize from the classroom treasure box.
Answers
The inequality that describes the number of stars S that Kwame must earn per day to get a prize from the classroom treasure box is: S > 16.
What is the inequality that models this situation?The number of stars that he earns is represented by the variable S. He must earn more than 16 stars to earn a prize from the classroom treasure box, hence the inequality that represents the desired amount is given as follows:
S > 16.
Which is read as:
S is greater than 16, which is derived from the Fact that Kwame must earn more than 16 stars per day to get a prize, as stated in the problem.
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A group of 65 baseball players were surveyed about which hand they favor for batting. The data from the survey are shown in the Venn diagram.
Determine the value for each variable in the two-way table.
a =
b =
c =
d =
e =
Answers
The value of each variable in the two-way table is:
a = 7
b = 31
c = 28
d = 13
e = 65
What are the value of the variables?A Venn diagram uses circles that overlap each other to show logical relationships between two or more sets of items. A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns.
The following have to be established:
a player can either be male or female
a player favors either the left or the right
a = females that favor the left. Looking at the Venn diagram, this number is 7.
b = total number of females : 24 + 7 = 31
c = males that favor the right = total number of males - males that favor the left
34 - 6 = 28
d = Total number of people who favor the left = 7 + 6 = 13
Total number of baseball players = 65
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I need help cancelling units. please help
Answers
Hello and Good Morning/Afternoon:
Let's take this problem step by step:
Let's write out the equation we would hypothetically use to convert 410 kilometers to meters:
[tex]410 kilometers * \frac{1000 meters}{1 kilometers}[/tex]
Let's see if there are any errors:
there are 1000 meters in 1 kilometerwhen converting kilometer --> meter⇒ we want to get rid of the kilometer symbol
⇒ which is done in this problem
[tex]410 kilometers * \frac{1000 meters}{1 kilometers}=\frac{410 kilometers}{1 kilometers}*1000 meters = 410000meters[/tex]
Thus the answer is true
Answer: True
Hope that helps!
If you were a travel agent and a client asked about the daily cost of renting a condominium on maui, what average would you use? explain.
Answers
The average mean cost used for the condominium on maui is 132.5
According to the statement
we have given that the some data values and we have to find the mean of the data and tell the how much expensive is condominium on maui.
So, The given data set is
89 50 68 60 375 55 500 60 50 250 45 45 125 235 1 40 350 65 60 120
So, For this purpose we know that the
Average Mean is a middle point or something (as a place, time, number, or rate) that falls at or near a middle point
Formula to calculate mean is sum of terms / total number of terms.
So,
Mean = 89+ 50+ 68+ 60+ 375+ 55+ 500+ 60+ 50+ 250+ 45+ 45+ 125+ 235+ 1+ 40+ 350+ 65+ 60+ 120 / 20
Mean = 2643 / 20
Mean = 132.5
So, The average mean cost used for the condominium on maui is 132.5
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Maui Vacation How expensive is Maui? If you want a vacation rental condominium
(up to four people), visit a Maui tourism web site. The Maui News gave the following costs in dollars per day for a random sample of condominiums located throughout the island of Maui.
89 50 68 60 375 55 500 60 50 250 45 45 125 235 1 40 350 65 60 120
what average mean would you use?
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Four out of 5 students passed the entrance exam. On the same trend, if 252 students got passing mark, how many students took the examination?
Answers
Answer:
315 students
Step-by-step explanation:
Based on the question, we can deduce:
[tex] \frac{4}{5} = 80percent \: passing \: rate[/tex]
Next we can find out the total number of students who sat for the examination.
80% = 252
[tex]1percent \: = \frac{252}{80} \\ 100 \: percent = \frac{252}{80} \times 100 = 315 \: students [/tex]
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answers
Answer:
○ [tex]F = \frac{S + 24}{3}[/tex]
Step-by-step explanation:
We know that:
[tex]S = 3F -24[/tex],
where F is the length of the foot of a person, and S is their shoe size.
To solve for the length of a person's foot, we have to rearrange the given equation to make F the subject:
[tex]S = 3F -24[/tex]
⇒ [tex]S + 24 = 3F[/tex] [adding 24 to both sides]
⇒ [tex]\frac{S + 24}{3} = F[/tex] [dividing both sides by3]
⇒ [tex]F = \frac{S + 24}{3}[/tex] [swapping the sides]
Jacob is cutting a tile in the shape of a parallelogram. two opposite angles have measures of (6n − 70)° and (2n 10)°. what are the two different angle measures of the parallelogram-shaped tile?
Answers
The measures of the two different angles are 70° and 110°.
What is angle in parallelogram ?
A parallelogram is a flat 2d shape which has four angles. The opposite interior angles are equal. The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees. Hence, the sum of the interior angles of a parallelogram is 360 degrees.Thus from the given question, we have:
(6n − 70)° + (2n + 10)° = 180°
8n - 60 = 180° + 60
8n = 240
n = 240/8
n = 30°
So that,
i. (6n − 70)° = (6[30] − 70)°
= 180 - 70
= 110°
ii. (2n + 10)° = (2[30] + 10)°
= 60 + 10
= 70°
Therefore, the measures of the two different angles are 70° and 110°.
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How would you find the area or perimeter of this shape?
Answers
The perimeter of a given shape implies the sum of all its sides. While the area of a given shape is the total value of space it would cover on a 2-dimensional plane.
The perimeter of the shape is 104 cm.
The area of the shape is 640 [tex]cm^{2}[/tex].
The perimeter of a given shape implies the sum of all its length of sides., such that the value of each individual side is summed to a total value.
The area of a given shape is the total value of space it would cover on a 2-dimensional plane. The area of shapes depends on the type of shape.
In the given question, the given shape has 12 sides. Some of these sides can sum up to a given length as shown in the diagram.
So that;
perimeter = 2 + 32 + 10 + 10 + 2 + 32 + 8 + 8
= 104 cm
Thus, the perimeter of the shape is 104 cm
ii. The area of the shape = length x width
= 32 x 20
= 640 [tex]cm^{2}[/tex]
Therefore, the area of the given shape is 640 [tex]cm^{2}[/tex].
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200 σ j=1 2j( j 3) describe the steps to evaluate the summation. what is the sum?
Answers
The sum of the equation is = 5494000.
What does summation mean in math?The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.
Briefing:Distribute 2j to (j+3).
Rewrite the summation as the sum of two individual summations.
Evaluate each summation using properties or formulas from the lesson.
The lower index is 1, so any properties can be used.
The sum is 5,494,000.
Calculation according to the statement:[tex]\sum_{j=1}^{200} 2 j(j+3)[/tex]
simplifying them we get:
[tex]\sum_{j=1}^{200} 2 j^{2}+6 j[/tex]
Split the summation into smaller summations that fit the summation rules.
[tex]\sum_{j=1}^{200} 2 j^{2}+6 j=2 \sum_{j=1}^{200} j^{2}+6 \sum_{j=1}^{200} j[/tex]
[tex]\text { Evaluate } 2 \sum_{j=1}^{200} j^{2}[/tex]
The formula for the summation of a polynomial with degree 2
is:
[tex]\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}[/tex]
Substitute the values into the formula and make sure to multiply by the front term.
[tex](2)$$\left(\frac{200(200+1)(2 \cdot 200+1)}{6}\right)$$[/tex]
we get: 5373400
Evaluating same as above : [tex]6 \sum_{j=1}^{200} j[/tex]
we get: 120600
Add the results of the summations.
5373400 + 120600
= 5494000
The sum of the equation is = 5494000.
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I really don't know what to do for this question! :( help?
Answers
The amount of money she should deposit is 6131.14 dollars.
How to find the compound interest ?The amount she should deposit can be found as follows:
[tex]p = \frac{A}{(1+\frac{r}{n} )^{nt} }[/tex]
where
A = amount to depositr = raten = number of timest = timep = principalTherefore,
p = [tex]\frac{20000}{(1+\frac{0.12}{4}{} )^{40} }[/tex]
[tex]p=\frac{20000}{(1+0.03)^{40} }[/tex]
[tex]p = \frac{20000}{1.03^{40} }[/tex]
[tex]p=\frac{20000}{3.262037792}[/tex]
Hence,
p = $6,131.14
Therefore, she should deposit 6131.14 dollars.
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Which of the following measurements would be MOST likely to have a negative exponent in scientific notation?
a. The distance the Earth is from the sun in meters.
b. The length of a needle in millimeters
c. The length of a football field in inches.
d. The length of an amoeba in meters.
Answers
The measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.
Given four measurements:
The distance the Earth is from the sun in meters.The length of a needle in millimetersThe length of a football field in inches.The length of an amoeba in meters.We are required to choose one measurement which would most likely to have a negative exponent in scientific notation.
A negative exponent is defined as the multiplicative inverse of the base,raised to the power which is of the opposite sign of tthe given power.It is expressed as [tex]e^{-x}[/tex].
We know that exponent shows continuous growth or continuous decay.
Among all the measurement the measurement which is most likely to have a negative exponent in scientific notation is the length of an amoeba in meters because among all the option amoeba can grow continously or decay continuously.
Hence the measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.
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The height of an equilateral triangle is 4 startroot 3 endroot. what is the perimeter of the equilateral triangle?
Answers
Answer:
perimeter = 24
Step-by-step explanation:
formula:
In an equilateral triangle with sides of lengths ‘a’
The height of the triangle is equal to :
[tex]= \frac{\sqrt{3} }{2} a[/tex]
……………………………………………
Calculating ‘a’ :
We have to solve the equation:
[tex]4\sqrt{3} =\frac{\sqrt{3} }{2} a[/tex]
[tex]\Longleftrightarrow 4=\frac{1 }{2} a[/tex]
[tex]\Longleftrightarrow a = 8[/tex]
Calculating the perimeter:
= 3a
= 3 × 8
= 24
How do you graph x < 5 on a number line and is the circle open or not? Where's the number line going? Thanks!
Answers
The inequality sign < means "less than." If there is a line underneath the inequality sign that means "less than or equal to."
To graph x < 5, we first need to understand what the inequality is saying. In this case, x must be less than 5. So, a number that will make this inequality true will be less than, but not equal to, 5.
Start by putting an open circle on the number 5. An open circle indicates that 5 is not a value that works in this inequality. Then, we know that our values that make this inequality true are less than 5, so we'll draw an arrow from the circle to the left as numbers to the left of 5 are less than it.
Hope this helps!
Exponential Growth
Find f(4), where f(x) = 3x.
Answers
f(x) = 3^x
f(4) = 3^4
f(4) = 3 * 3 * 3 * 3
f(4) = 9 * 9
f(4) = 81
Hope this helps!
Find the value of x
a. 13 b. 14/5 c. 5 d. 8
Answers
Answer:
C. 5
Step-by-step explanation:
The product of chord segment lengths is the same for the two crossing chords.
ApplicationOne chord has segment lengths 4 and 10; the other has segment lengths x and 8.
(4)(10) = (x)(8)
40/8 = x = 5 . . . . . . . divide by the coefficient of x
The value of x is 5, making option C the right choice, using the chord theorem.
The chord theorem, also known as the intersecting chords theorem, is a statement in basic geometry that explains the relationship between the four line segments formed by two intersecting chords inside of a circle. According to this statement, the products of the line segment lengths on each chord are equal.
In the question, we are asked to find the value of x.
Using the chord property, we know that:
8*x = 4*10,
or, 8x = 40,
or, x = 40/8,
or, x = 5.
Thus, the value of x is 5, making option C the right choice, using the chord theorem.
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Graph Y equals |x|-5
Answers
Answer:
graph C
Step-by-step explanation:
when X= 0
Y ---> -5
so , answer is graph C
Answer:
c
Step-by-step explanation:
the graph of | x | has its vertex at the origin and has shape V
the graph of | x | - 5 is the graph of | x | translated 5 units vertically down.
That is graph c represents | x | - 5
greatest common factor of 6,12, and 21
Answers
Answer:
3
Step-by-step explanation:
[tex]6=2 \times 3 \\ \\ 12=3 \times 2^2 \\ \\ 21=3 \times 7[/tex]
Please help me fast
Determine an exact value for the expression and include a complete solution
(sin 225°) ² - cos 330° cos 240°
Answers
Answer:
1.187991
Step-by-step explanation:
sin^2(225)−(cos(330))(cos(240))
=(−0.930095)2−(cos(330))(cos(240))
=0.865076−(cos(330))(cos(240))
=0.865076−−0.991199(cos(240))
=0.865076−(−0.991199)(0.325781)
=0.865076−(−0.322914)
=1.187991
What is the maximum value of the transformed function, y = -3cos (2x - 8) + 5
A. 3 units
B. 5 units
C. 8 units
D. 11 units
Answers
Answer:
C. 8 units.
Step-by-step explanation:
The maximum value of the cosine ( cos) function is 1
So, for y = 3cos(2x - 8) + 5
Maximum value is 3 *1 + 5 = 8.
y = -3cos(2x - 8) + 5 is the above graph reflected in the y axis so the maximum value is also 8.
Jenny packaged 108 eggs in 9 cartons. Write this statement as a ratio
Answers
108:9
108/9 (simplest form = 12)
108 eggs to 9 cartons
I hope that this is what you were looking for!
Answer:
12:1
Step-by-step explanation:
each pack contains 12 eggs
108/9 = 12
Hope this helps
Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→[infinity] (5x − ln(x))
Answers
The limit of lim x→[infinity] (5x − ln(x)) by using L'hospital rule is ∞.
According to the given question.
We have to find the limit of [tex]\lim_{x \to \infty} 5x - lnx[/tex]
As we know that L'hospital rule is a theorem which provides a technique to evaluate limits of indeterminate forms.
And the formual for L'hospital rule is
[tex]\lim_{x \to \ c} \frac{f_{x} }{g_{x} } = \lim_{x \to \ c} \frac{f^{'}( x)}{g^{'} (x)}[/tex]
[tex]\lim_{x \to \infty} 5x - lnx[/tex] can be written as
[tex]\lim_{x \to \infty} 5x - lnx\\= \lim_{x \to \infty} x(5 - \frac{lnx}{x})[/tex]
If we put the value of limit in lnx/x we get an indeterminate form ∞/∞.
Therefore, [tex]\lim_{x \to \infty} \frac{lnx}{x} = \frac{\frac{1}{x} }{1}[/tex]
[tex]\implies \lim_{x \to \infty} \frac{1}{x} = 0[/tex] (as x tends to infinity 1/x tends to 0)
So,
[tex]\lim_{x \to \infty} 5x - lnx\\= \lim_{x \to \infty} x(5 - \frac{lnx}{x})[/tex]
[tex]= \lim_{x \to \infty}x(5 -0)[/tex]
[tex]= \lim_{n \to \infty} 5x \\= \infty[/tex](as x tends to ∞ 5x also tends to infinity)
Therefore, the limit of lim x→[infinity] (5x − ln(x)) by using L'hospital rule is ∞.
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please help 20 points!!!!!
hree students want to estimate the mean backpack weight of their schoolmates. To do this, they each randomly chose 8 schoolmates and weighed their backpacks. The samples are shown in the table. (a)Fill in the sample means in the table. Do not round your answers. Sample Backpack weight (in pounds) Sample mean 1 3, 7, 8, 3, 7, 9, 6, 8 2 8, 6, 4, 7, 9, 4, 6, 7 3 9, 4, 5, 8, 7, 5, 9, 6
(b)Use the table to calculate the range of the sample means. Rangeofsamplemeans:
(c)The students are going to use the sample means to estimate the mean backpack weight of their schoolmates. Select all the true statements below.
A single sample mean will tend to be a worse estimate than the mean of the sample means.
The mean of the sample means will tend to be a worse estimate than a single sample mean.
The closer the range of the sample means is to 0, the less confident they can be in their estimate.
The farther the range of the sample means is from 0, the less confident they can be in their estimate.
Answers
Three students want to estimate the mean backpack weight of their schoolmates. To do this, they each randomly chose 8 schoolmates and weighed their backpacks. Then as per the given sample data,
(a) The sample means of the backpacks are: 6.375,6.375,6.625
(b) Range of sample means: 0.25
(c)The true statement is: The closer the range of the sample means is to 0, the less confident they can be in their estimate.
For the first sample, mean= 6.375
For the second sample, mean= 6.375
For the third sample, mean= 6.625
Range of sample means=Maximum Mean- Minimum Mean
= 6.625 - 6.375
= 0.25
The students will estimate the average backpack weight of their classmates using sample means, the true statement is:
The closer the range of the sample means is to 0, the more confident they can be in their estimate.
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yvette uses 6 grams of tea leaves to make 24 fluid ounces of tea. last week she made 288 fluid ounces of tea. how many grams of tea leaves did yvette use to make tea last week
Answers
72 grams tea is needed to prepare 288 fluid ounces of tea.
According to the statement
we have given that the yvette uses 6 grams of tea leaves to make 24 fluid ounces of tea.
And we have to find that the how much grams of tea uses to make 288 fluid ounces of tea.
So, For this purpose,
the given terms are:
6 grams tea = 24 fluid ounces of tea
Now, we use division method
1 gram of tea = 4 fluid ounces of tea
It means
4 fluid ounces of tea prepared by 1 gram of tea.
then
288 fluid tea prepared = ?
So,
288 fluid tea prepared by grams of tea = 288/4
288 fluid tea prepared by grams of tea = 72.
So, 72 grams tea is needed.
So, 72 grams tea is needed to prepare 288 fluid ounces of tea.
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Mr. Ahmed has 31 students in his class. There are 14 boys and 17 girls.
The ratio
describes the part-to-whole relationship for boys.
The ratio
describes the part-to-whole relationship for girls.
Answers
We get, the ratio of the part-to-whole relationship for boys is 14/31.
And since there are 17 girls
We get, the ratio of the part-to-whole relationship for girls is 17/31.
The daily high temperature of Elk Creek drops by 1.2°C every day. What is the net change in the daily high temperature after two calendar weeks?
Answers
[tex]1.2 \: degrees \: drop \: a \: day \\ 14 \: days \: in \: two \: weeks \\ net \: change = 14 \times 1.2 = 16.8 \: deg[/tex]