The principal randomly selected six students to take an aptitude test. Their scores were: 87.4 86.9 89.9 78.3 75.1 70.6 Determine a 90% confidence interval for the mean score for all students. Assume the population is normally distributed. Give the lower limit of the interval as your answer below. Round to two decimal places. (Hint from class: Note that you will need to calculate the sample mean (xbar) and sample standard deviation (s) for this sample data in order to find the confidence interval endpoints. In class I referred to the formula for that -- and erroneously gave the formula for the sample variance instead of the sample standard deviation. The sample standard deviation would be the square root of the sample variance. Formulas for both can be found on the Test formula sheets posted on iLearn among other places.)
Answers
Answer:
79.5688 < µ < 83.1646
Step-by-step explanation:
Sample mean is the sum of all scores, divided the the total number of test takers. In this case, the sample mean is:
(87.4 + 86.9 + 89.9 + 78.3 + 75.1 + 70.6)/6 = 488.2/2 = 81.3667
The sample standard deviation is the square root of the sample variance. See attached photo 1 for calculation of these values...
The sample standard deviation is 3.1856
We need to make a 90% confidence interval for this data. Since n < 30, we will use a t-value. The degrees of freedom is always one less than the sample size so on the t-distribution chart, look under the column for Area under the curve = 0.10, and the row for 5. The t-value you should see is t = 2.015
See attached photo 2 for the construction of the confidence interval
Related Questions
Each month, Kaisorn deposits $50.00 onto her public transportation card. It costs her $2.50 per trip to ride the subway. Thom deposits $40.00 on his public transportation card. It costs him $2.00 per trip to ride the subway. If x represents the number of trips and y represents the amount remaining in each account, which system of equations represents their transportation costs? 50 − 2.5x = y 40 − 2x = y 50 + 2.5x = y 40 + 2x = y 50 − 2.5y = x 40 − 2y = x 50 + 2.5y = x 40 + 2y = x
Answers
Answer:
For Kaisorn: [tex]y=50-2.50x[/tex]
For Thom: [tex]y=40-2x[/tex]
Step-by-step explanation:
Each month, Kaisorn deposits $50.00 onto her public transportation card.
It costs her $2.50 per trip to ride the subway. Means 2.50x
Thom deposits $40.00 on his public transportation card. It costs him $2.00 per trip to ride the subway. Means 2x
Let x represents the number of trips
Let y represents the amount remaining in each account.
Then the system of equations represents their transportation costs are :
For Kaisorn: [tex]y=50-2.50x[/tex]
For Thom: [tex]y=40-2x[/tex]
If a = 5 centimeters, w = 10 centimeters, and h = 6 centimeters, what is the area of the decorative paper he will require?
Answers
Final answer:
The area of decorative paper needed, given the dimensions of length and width, is calculated as 50 square centimeters.
Explanation:
To answer the question about the area of decorative paper required, we need to use the formula for the area of a rectangle which is length times width. However, the given dimensions of a = 5 centimeters, w = 10 centimeters, and h = 6 centimeters seem to describe a box or a prism rather than a flat piece of paper. If the decorative paper is meant to cover the side of the box, then the relevant dimensions are likely length and width, not including the height. Assuming the decorative paper is to cover a flat surface, the formula for the area is A = length × width. Therefore, the required area of decorative paper is A = 5 cm × 10 cm = 50 square centimeters.
What is the trigonometric function's period?
Question 3 options:
pi
2 pi
3 pi
4 pi
Answers
➷ Find the difference from one peak ( highest point) to the next
In this case, it is 2 pi
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➶ Good Luck (:
➶ Have A Great Day ^-^
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Answer:
2 pi
Step-by-step explanation:
Help with this question, please! I need help!
Answers
Answer:
$357Step-by-step explanation:
We have a rectangle measuring 25 feet × 9 feet. Remove from the rectangle two regular hexagons with a side length equal to 2 feet.
The formula of an area of a rectangle:
[tex]A_r=lw[/tex]
l - length, w - width.
Substitute l = 25 ft and w = 9 ft:
[tex]A_r=(25)(9)=225\ ft^2[/tex]
The formula of an area of a regular hexagon:
[tex]A_h=6\cdot\dfrac{a^2\sqrt3}{4}[/tex]
a - side
Substitute a = 2 ft:
[tex]A_h=6\cdot\dfrac{2^2\sqrt6}{4}=6\sqrt3\ ft^2[/tex]
The area of the wall:
[tex]A=A_r-2A_h[/tex]
Substitute:
[tex]A=225-2(6\sqrt3)=225-12\sqrt3\approx225-20.785=204.215\ ft^2[/tex]
Paiting the wall costs $1.75 per ft². Calculate:
[tex](\$1.75)(204.215)\approx\$357[/tex]
Bert and Ernie are missing each other and their friend Big Bird They want to meet at Big Bird's nest which is halfway from their apartments. The distance from Bert's apartment to Big Bird's nest (5x + 4) ismiles away while Ernie's apartment to Big Bird's nest is (15x-30) miles away How far are Bert and Ernie's apartments from Big Bird's nest?
Answers
Answer:
The distance between Bert and Ernie's apartments from Big Bird's nest
is 21 miles
Step-by-step explanation:
* Lets change the story problem to an equation to solve the problem
- The information i the story problem is
# The Big Bird's nest is halfway from there apartments
# The distance between Bert's apartment and Big Bird's nest is (5x + 4)
# The distance between Ernie's apartment and Big Bird's nest is (15x - 30)
* Now lets solve
∵ The Big Bird's nest is halfway from there apartments
∴ The distance between Bert's apartment and Big Bird's nest = The
distance between Ernie's apartment and Big Bird's nest
∴ 5x + 4 = 15x - 30
- Collect the variable terms in one side and the numerical terms
in th other side
∴ 15x - 5x = 30 + 4 ⇒ add
∴ 10x = 34
∴ x = 34 ÷ 10 = 3.4
* Now lets find the distance between Bert and Ernie's apartments
from the Big Bird's nest
- We can use any relation to find the distance
∵ The distance = 5x + 4
∵ x = 3.4
∴ The distance = 5(3.4) + 4 = 17 + 4 = 21 miles
You can check the answer by using second equation
∵ The distance = 15x - 30
∵ x = 3.4
∴ The distance = 15(3.4) - 30 = 51 - 30 = 21 miles
Answer:
The distance between Bert and Ernie's apartments from Big Bird's nest
is 21 miles
Step-by-step explanation:
* Lets change the story problem to an equation to solve the problem
- The information i the story problem is
# The Big Bird's nest is halfway from there apartments
# The distance between Bert's apartment and Big Bird's nest is (5x + 4)
# The distance between Ernie's apartment and Big Bird's nest is (15x - 30)
* Now lets solve
∵ The Big Bird's nest is halfway from there apartments
∴ The distance between Bert's apartment and Big Bird's nest = The
distance between Ernie's apartment and Big Bird's nest
∴ 5x + 4 = 15x - 30
- Collect the variable terms in one side and the numerical terms
in th other side
∴ 15x - 5x = 30 + 4 ⇒ add
∴ 10x = 34
∴ x = 34 ÷ 10 = 3.4
* Now lets find the distance between Bert and Ernie's apartments
from the Big Bird's nest
- We can use any relation to find the distance
∵ The distance = 5x + 4
∵ x = 3.4
∴ The distance = 5(3.4) + 4 = 17 + 4 = 21 miles
You can check the answer by using second equation
∵ The distance = 15x - 30
∵ x = 3.4
∴ The distance = 15(3.4) - 30 = 51 - 30 = 21 miles
Will give brainliest!!! Landry took out a cash advance of $ 240 on his credit card. If the bank charges him a $ 3.20 fee and his credit card company charges 3.4 percent of the advance, how much did the advance cost him?
Answers
Answer:
$ 11.36
Step-by-step explanation:
The advance cost him;
3.20 + 3.4% of 240
3.20 + (3.4/100)*240
3.20 + 8.16 = $ 11.36
Identify the equation of the translated graph in general form x^2-y^2=9 for T(-4,2)
Answers
Answer:
B
Step-by-step explanation:
The equation [tex]x^2-y^2=a[/tex] under the translation of T (p,q) will have the form [tex](x-p)^2-(y-q)^2=a[/tex]
Now, using the translation T(-4,2) in the equation given, we can write:
[tex](x+4)^2-(y-2)^2-9=0\\x^2+8x+16-y^2+4y-4-9=0\\x^2-y^2+8x+4y+3=0[/tex]
Looking at the choices, B is the right answer.
Answer:
Looking at the choices, B is the right answer.
The price of a share of stock increases 45.69 over 3 days. What was the average rate of change in its price in dollars per day?
Answers
Answer:
The answer would be 15.23$
Step-by-step explanation:
If you take the over all growth, 45.69, and divide that by the 3 days, you get your average of 15.23 per day
Find the coordinates of the midpoint of a line segment with end points (-3,4) and (7,9)
Answers
Answer: (2, 6.5)
Step-by-step explanation:
[tex]Midpoint_{x,y}=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad \quad=\bigg(\dfrac{-3+7}{2},\dfrac{4+9}{2}\bigg)\\\\\\.\qquad \qquad \quad=\bigg(\dfrac{4}{2},\dfrac{13}{2}\bigg)\\\\\\.\qquad \qquad \quad=\large\boxed{(2,6.5)}[/tex]
PLEASE HELP
In the same circle, chord AB determines a 115° arc and chord AC determines a 43° arc. Find m∠BAC.
(2 answers)
Answers
Answer:
101 or 36 degrees
Step-by-step explanation:
If you add up the measures of the arcs it is 158. That means BC is 202 degrees. Divide it by 2 to find the angle. For the second answer, remember the question did not specify if the arcs were major or minor so you can flip them around.
Answer:
m∠BAC is 101° or 36°.
Step-by-step explanation:
Given,
[tex]m(\widehat{AB})=115^{\circ}[/tex]
[tex]m(\widehat{AC})=43^{\circ}[/tex]
To find : The measurement of angle BAC,
Let O be the center of the circle.
Since, here we have to cases ( shown in diagram ),
In Case 1 :
[tex]m\angle BOC = 360^{\circ}-[m(\widehat{AB})+m(\widehat{AC})][/tex]
[tex]=360^{\circ}-(115^{\circ}+43^{\circ})[/tex]
[tex]=360^{\circ}-158^{\circ}[/tex]
[tex]=202^{\circ}[/tex]
By the central angle theorem,
[tex]m\angle BAC = \frac{m\angle BOC}{2}[/tex]
[tex]=\frac{202^{\circ}}{2}=101^{\circ}[/tex]
In Case 2 :
[tex]m\angle BOC = m(\widehat{AB})-m(\widehat{AC})[/tex]
[tex]=115^{\circ}-43^{\circ}[/tex]
[tex]=72^{\circ}[/tex]
Again by the central angle theorem,
[tex]m\angle BAC = \frac{m\angle BOC}{2}[/tex]
[tex]=\frac{72^{\circ}}{2}=36^{\circ}[/tex]
graph this Function 1: f(x) = −3x2 + 2
Answers
I guess that's f(x) = -3x^2+2
Well :
-3x^2+2=0
-3x^2=-2 / : (-3)
x^2= -2/-3
x^2= 2/3 / sqrt
x= +/ - sqrt(2)/sqrt(3)
We got the zero points.
x ~ +/- 0.81
f(0)= -3(0)^2 + 2
f(0)= 2
Mark three points:
(0.81;0)
(-0.81;0)
(0;2)
Connect with parabolic line and ya got a your graph
A quantity x varies directly with y and inversely with z. Which expression represents the constant of variation, k?
A) xz/y
B) xy/z
C) z/xy
D) y/xz
Answers
[tex]A. \: \frac{xz}{y} [/tex]
EXPLANATION
If quantity x varies directly with y and inversely with z.
The we can write the mathematical statement,
[tex]x\propto \frac{y}{z} [/tex]
We introduce the constant of proportionality k, to obtain,
[tex]x = \frac{ky}{z} [/tex]
We now solve for k, by multiplying through by
[tex] \frac{z}{y} [/tex]
This implies that,
[tex] \frac{xz}{y} = k[/tex]
The correct choice is A.
can someone PLEASE HELP ME ASAP!!!!!
Answers
Answer:
Last choice: 14 = (1/2)x(x - 12)
Step-by-step explanation:
base = x
height = x - 12
area = (1/2)bh
14 = (1/2)x(x - 12)
The answer is C. Thank Me Later ?
Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.
y=-1 tan 1/10 x+4
Answers
Answer:
Reflection across x-axis, horizontal stretch by a factor of 10
and vertical translation up 4 units ⇒ answer (c)
Step-by-step explanation:
* The basic function of tanФ is
# y = tanФ
1- If y = -tanФ ⇒ reflect y over the x-axis
2- If y = tan(-Ф) ⇒ reflect y over the y-axis
3- If y = tan(Ф - k) ⇒ shift y right k units
4- If y = tan(Ф + k) ⇒ shift y left k units
5- If y = tanФ + k ⇒ shift y up k units
6- If y = tanФ - k ⇒ shift y down k units
7- If y = k tanФ ⇒ multiply y-values by k
(k > 1 stretch, 0 < k < 1 compressed vertical)
The scale factor is k
8- If y = tan(kФ) ⇒ divide x-values by k
(k > 1 compressed, 0 < k < 1 stretch horizontal)
The scale factor is 1/k
* Lets solve the problem
∵ y = -tan(1/10)x + 4
* We will use rules number 1 , 5 and 8
∴ Reflect y over the x-axis, shift y up k units and stretch
horizontal by scale factor is 1/k (0 < k < 1)
∴ Reflection across x-axis, horizontal stretch by a factor of 10
and vertical translation up 4 units
Plot each set of points. Choose all that correctly define the quadrilateral in the coordinate plane. A(0, 0), B(0, 5), C(2, 5), D(2, 0) is a rectangle A(?2, 4), B(2, 4), C(4, 2), D(?2. 2) is an isosceles trapezoid A(0, 4), B(4, 1), C(0, ?5), D(?4, 1) is a square A(4, ?3), B(?2, ?3), C(?1, 1), D(5, 1) is a parallelogram
Answers
Answer:
quad
Step-by-step explanation:
Answer: the answers are a and d !!
Step-by-step explanation:
Which graph represents the solution of the system of inequalities?
Answers
You need to rewrite the first equation to solve for y to get y >1+3x
Then graphing the two equations, the bottom right becomes the correct answer.
Solve by using proper methods.
Let's say that we had a 750 coyotes that were decreasing at a rate of 3% per year. How many years would it be until we had only 100 coyotes left? Show your work.
Answers
Answer:
Approximately after 66.15 years, there will be 100 coyotes left
Step-by-step explanation:
We can use the formula [tex]F=P(1+r)^t[/tex] to solve this.
Where
F is the future amount (F=100 coyotes)
P is the initial amount (P=750 coyotes)
r is the rate of decrease per year (which is -3% per year or -0.03)
t is the time in years (which we need to find)
Putting all the information into the formula we solve.
Note: The logarithm formula we will use over here is [tex]ln(a^b)=bln(a)[/tex]
So, we have:
[tex]F=P(1+r)^t\\100=750(1-0.03)^t\\100=750(0.97)^t\\\frac{100}{750}=0.97^t\\\frac{2}{15}=0.97^t\\ln(\frac{2}{15})=ln(0.97^t)\\ln(\frac{2}{15})=tln(0.97)\\t=\frac{ln(\frac{2}{15})}{ln(0.97)}\\t=66.15[/tex]
Hence, after approximately 66.15 years, there will be 100 coyotes left.
Rounding, we will have 66 years
(1Q) Describe how to transform the graph of g(x) = lnx into the graph of f(x)= ln(x-4)+3?
Answers
Answer:
B
Step-by-step explanation:
The correct answer is to go 4 units right (the direction is opposite to the sign) and 3 units up. The up and down direction is the same number as after the function.
Red: Parent Function y = ln(x)
Blue: 4 units right. 3 units up.
Answer: B
Answer:
b
Step-by-step explanation:
he point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = 1/4 (x – 8). What is the slope-intercept form of the equation for this line?
Answers
Answer:
[tex]y=\frac{1}{4}x+2[/tex]
Step-by-step explanation:
The point-slope form of the equation of a line that passes that through points (8, 4) and (0, 2) is given as;
[tex]y-4=\frac{1}{4}(x-8)[/tex]
To find the slope-intercept form of this line, we need to expand the point-slope form.
[tex]y-4=\frac{1}{4}x-2[/tex]
We now solve for y to obtain;
[tex]y=\frac{1}{4}x-2+4[/tex]
We simplify to obtain:
[tex]y=\frac{1}{4}x+2[/tex]
This equation is now in the form;
[tex]y=mx+c[/tex]
This is what we refer to as the slope-intercept form.
This is the manipulated variable in an experiment or study whose presence or degree determines the change in the dependent variable. When graphed this is graphed usually on the horizontal axis.
Answers
Answer:
This is called the independent variable.
Step-by-step explanation:
We know this because it is independent of all outside factors. Additionally, the horizontal axis (also known as the x axis), is the axis known for the independent variable.
Joelle's parents have combined all the candy from her and her three siblings Halloween bags so that the candy can be split evenly amongst the children. Altogether, the kids accumulated 256 pieces. How many pieces does each child receive?
Answers
There are 64 pieces that each child receive.
What is Division?It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.
Here, Joelle's parents have combined all the candy = 256 candy
Total number of Children = 4
Equal division of candy in 4 children = Total Candy/No. of children
= 256 / 4
= 64
Thus, there are 64 pieces that each child receive.
Learn more about Division from:
https://brainly.com/question/21416852
#SPJ2
Final answer:
Each of the four children, including Joelle, will receive 64 pieces of candy after dividing the total of 256 pieces evenly among them.
Explanation:
To find out how many pieces of candy each child receives, we need to divide the total number of pieces by the number of children. Joelle and her three siblings make a group of four children in total. They have accumulated 256 pieces of candy. To divide this evenly, we do the following calculation:
Divide the total number of candies (256) by the number of children (4).
The division gives us the result 64 pieces of candy for each child.
Therefore, each child, including Joelle, will receive 64 pieces of candy.
How do you do this problem?
Answers
Answer:
Step-by-step explanation:
Part A
If it is compounded quarterly, the interest of 1.5 must be cut into a quarter of its present size. 1.5 //4 = 0.375 % per quarter.
In addition, the number of times that payment will be received is
4 quarters * 5 years = 20 quarters.
i = principle (1 + 0.375/100) ^20
i = principle (1 + 0.00375)^20
The principle = 4000 dollars.
i = 4000 * (1.00375)^20
i = 4000 * 1.07773
i = 4310.93
So she's tied up 4000 dollars to make 300 dollars.
Part B
I can't really give you an answer to this because I don't know if the 7% is compounded and over what period of time if it is, or if they mean 7% annually. There's a lot of variation in this question. Most people don't take money out of the market, so if it compounded, the formula would be
New Principle = starting amount (1.07)^4
New Principle = 4000 * 1.07^4
New Principle = 5243.18 so she would make about 4 times as much as the 300 she makes if she puts the money in a bond.
=============
If the interest is simple interest
Gain would be 0.07 * 4000 = 280 dollars.
Over four years = 4*280 = 1120 dollars.
You are going to have to ask your teacher what is intended by this question.
The figures below are similar. the area of the larger trapezoid is 121m^2. Find the area of the smaller trapezoid to the nearest square meter. Please help!
Answers
Answer:
54 square meters
Step-by-step explanation:
Similar figures have corresponding lengths as equal ratios.
Smaller trapezoid's base is given 12 and larger trapezoids base is given 18, so the scale factor is [tex]12k=18\\k=\frac{18}{12}\\k=1.5[/tex]
this means the lengths of larger is 1.5 times lengths of smaller.
In terms of area, the scale factor is squared. Hence the scale factor for area is [tex]k^2=(1.5)^2=2.25[/tex]
this means the area of larger is 2.25 times the area of smaller.
Now, Let area of smaller trapezoid be x so we can say: [tex]x(2.25)=121\\x=\frac{121}{2.25}\\x=53.78[/tex]
to nearest square meter, x = 54 meters squared
(8CQ) Determine whether the series -5+25-125+... is convergent or divergent.
Answers
Answer:
The answer is divergent ⇒ answer (b)
Step-by-step explanation:
* The series is -5 + 25 + -125 + ........
- It is a geometric series with:
- first term a = -5 and common ratio r = 25/-5 = -5
* The difference between the convergent and divergent
in the geometric series is :
- If the geometric series is given by sum = a + a r + a r² + a r³ + ...
* Where a is the first term and r is the common ratio
* If |r| < 1 then the following geometric series converges to a / (1 - r).
- Where a/1 - r is the sum to infinity
* The proof is:
∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number
∴ r^n approach to zero
∴ S = a(1 - 0)/(1 - r) = a/(1 - r)
∴ S∞ = a/1 - r
* If |r| ≥ 1 then the above geometric series diverges
∵ r = -5
∴ IrI = 5
∴ IrI > 1
∴ The series is divergent
There are red and blue balls in a bag. The number of blue balls is 27 and the red balls are 4/ 7 of all balls. What is the total number of balls in the bag?
Answers
➷ We know this:
3/7 = 27
You need to find the value of 1/7
To do this, divide by 3
27/3 = 9
1/7 = 9
Multiply this by 7 to get the total number of balls:
9 x 7 = 63
There are 63 balls.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
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What are the solutions to the system of equations?
(_____ , 2) and ( _____ , _____ )
Answers
Answer:
(1, 2) and (-1, -2)
Step-by-step explanation:
Since y = 2x, the first blank tells you
2x = 2
x = 1
____
Since the variables are squared, a negative solution is as good as a positive solution, so x = -1 and y = -2 will also work.
If A=[tex]\left[\begin{array}{ccc}-4&-3&5\\-5&-4&-2\\-1&-2&-4\end{array}\right][/tex] and B=[tex]\left[\begin{array}{ccc}3&-4&-1\\-5&-5&1\\-1&-3&2\end{array}\right][/tex], find AB.
Answers
It's not C because
[tex](AB)_{1,1}=A_{1,c}B_{r,1}=\begin{bmatrix}-4&-3&5\end{bmatrix}\begin{bmatrix}3\\-5\\-1\end{bmatrix}=-2[/tex]
where [tex](AB)_{1,1}[/tex] denotes the element of [tex]AB[/tex] in row 1, column 1, [tex]A_{1,c}[/tex] denotes the first row of [tex]A[/tex], and [tex]B_{r,1}[/tex] denotes the first column of [tex]B[/tex].
It's not A because
[tex](AB)_{1,2}=A_{1,c}B_{r,2}=\begin{bmatrix}-4&-3&5\end{bmatrix}\begin{bmatrix}-4\\-5\\-3\end{bmatrix}=16[/tex]
It's not D because
[tex](AB)_{2,2}=A_{2,c}B_{r,2}=\begin{bmatrix}-5&-4&-2\end{bmatrix}\begin{bmatrix}-4\\-5\\-3\end{bmatrix}=46[/tex]
So B must be the correct answer (and it is).
Find the measure of the line segment GE. Assume that lines which appear tangent are tangent.
Answers
Answer:
The measure of the line segment GE is [tex]18\ units[/tex]
Step-by-step explanation:
we know that
The Intersecting Secant-Tangent Theorem states that, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment
so
In this problem
[tex]GE*GF=GH^{2}[/tex]
substitute the values
[tex](8+x)(8)=12^{2}[/tex]
solve for x
[tex]8x+64=144[/tex]
[tex]8x=144-64[/tex]
[tex]8x=80[/tex]
[tex]x=10[/tex]
Find the measure of the line segment GE
[tex]GE=8+10=18\ units[/tex]
The string is 120 feet long and stretched taut. The kite string makes an angle of 70° with the ground. How high above the ground is the kite flying. Show Your Work
Answers
Answer:
112.76 feet
Step-by-step explanation:
This is a right triangle trig problem. We have the length of the string which serves as the hypotenuse of the triangle, and we also have the reference angle (the angle the string makes with the ground) and we are looking for the height of the height, which is also the height of the triangle, which is also the side opposite the reference angle. So it's our job now to figure out which trig ratio relates the side opposite the reference angle to the hypotenuse. That's the sin ratio (opposite/hypotenuse). Set it up like this:
[tex]sin(70)=\frac{x}{120}[/tex]
Multiply both sides by 120 and then do the math in degree mode on your calculator. That gives you that x = 112.7631145
Don't know how many decimal places you need, but there you go!
Find the limit if it exists. Picture provided
Answers
Answer:
b. -1
Step-by-step explanation:
When evaluating a limit at a specific value like this, just plug in the number and evaluate.
(2)³ - 3(2)² + 3
8 - 12 + 3
-4 + 3
-1
Answer:
b. [tex]-1[/tex]
Step-by-step explanation:
The given limit is
[tex]\lim_{x \to 2} (x^3-3x^2+3)[/tex]
This is the limit of a polynomial function so we plug in the value of x directly to obtain;
[tex]\lim_{x \to 2} x^3-3x^2+3=(2)^3-3(2)^2+3[/tex]
Evaluate
[tex]\lim_{x \to 2} x^3-3x^2+3=8-12+3[/tex]
This simplifies to
[tex]\lim_{x \to 2} x^3-3x^2+3=-1[/tex]
The correct choice is B.