Answer:
The function is continuous at x = 36
Step-by-step explanation:
From the question we are told that
The function is [tex]f(x) = x * \sqrt{ \frac{x}{ (x-6) ^2 } }[/tex]
The point at which continuity is tested is x = 1
Now from the definition of continuity ,
At function is continuous at k if only
[tex]\lim_{x \to k}f(x) = f(k)[/tex]
So
[tex]\lim_{x \to 36}f(x) = \lim_{n \to 36}[x * \sqrt{ \frac{x}{ (x-6) ^2 } }][/tex]
[tex]= 36 * \sqrt{ \frac{36}{ (36-6) ^2 } }[/tex]
[tex]= 7.2[/tex]
Now
[tex]f(36) = 36 * \sqrt{ \frac{36}{ (36-6) ^2 } }[/tex]
[tex]f(36) = 7.2[/tex]
So the given function is continuous at x = 36
because
[tex]\lim_{x \to 36}f(x) = f(36)[/tex]
Ben and Cam are scuba diving. Ben is 15.8 meters below the
surface of the water. Cam is 4.2 meters above Ben. What is Cam's
position relative to the surface of the water?
=======================================================
Explanation:
Check out the diagram below.
Draw a vertical number line with 0 at the center. The positive values are above it, while the negative values are below it.
Between -15 and -16, closer to -16, plot the value -15.8 to indicate Ben's position. I have done so as the point B.
We move 4.2 units up to arrive at Cam's position
-15.8 + 4.2 = -11.6
So Cam is 11.6 meters below the surface of the water.
Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0,0):
Answer:
It rotated 180 degrees
Step-by-step explanation:
If you use this image and paste in on to google docs you will be able to rotate the image. Use this tool so that your can identify the amount of degrees.
If the Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0,0) then the angle of rotation is option (c) 180 degrees
What is Quadrilateral?
In geometry a quadrilateral is a four-sided polygon, having four edges and four corners
What is Angle of rotation?The angle of rotation is a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle.
Given,
Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0,0)
Consider the coordinates of D and D'
D(2,3) and D'(-2,-3)
Connect D and D'
∠D0D' = 180 Degrees
Hence, If the Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0,0) then the angle of rotation is option (c) 180 degrees
Learn more about Quadrilateral and Angle of rotation here
https://brainly.com/question/17106452
#SPJ2
The length and width of a rectangle are measured as 58 cm and 45 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.
Answer:
Error in calculated area = [tex]\pm 10.3 cm^2[/tex]
Step-by-step explanation:
x = 58 cm
y = 45 cm
A = x*y
delta A
= delta (x*y)
= y delta x + x delta y (neglecting small qty delta x * delta y = 0.01)
= 45(0.1) + 58(0.1)
= 103(0.1)
= 10.3 cm^2
Find the 50th term in the sequence 16, 7, -2, …
This is an arithmetic sequence because the difference
between the terms in the sequence remain constant.
In other words, we subtract 9 from one term to get the next.
So we start off with the explicit formula, shown below in yellow.
"n" will be the number of terms in the sequence,
a1 will be the first term in the sequence,
and d will be the common difference.
Now substitute these in like I have below.
You will get -425 as an answer.
A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true? A. ABCD is a parallelogram with non-perpendicular adjacent sides. B. ABCD is a trapezoid with only one pair of parallel sides. C. ABCD is a rectangle with non-congruent adjacent sides. D. ABCD is a rhombus with non-perpendicular adjacent sides.
Hey There!!
The answer to this is: A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true?" Line BC is parallel to line AD because their slopes is equal i.e. (0 - 0) / (7 - 2) = (5 - 5) / (8 - 3) which gives 0 / 5 = 0 / 5 giving that 0 = 0. We check whether line AB is parallel to line CD. Slope of line AB is given by (0 - 5) / (2 - 3) = -5 / -1 = 5. Slope of line CD is given by (5 - 0) / (8 - 7) = 5 / 1 = 5 We have been able to prove that the opposite sides of the quadrilateral are parallel which means that the quadrilateral is not a trapezoid. Next we check whether the length of the sides are equal. Length of line AB is given by sqrt[(0 - 5)^2 + (2 - 3)^2] = sqrt[(-5)^2 + (-1)^2] = sqrt(25 + 1) = sqrt(26) Length of line BC is given by sqrt[(0 - 0)^2 + (7 - 2)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Length of line CD is given by sqrt[(5 - 0)^2 + (8 - 7)^2] = sqrt[5^2 + 1^2] = sqrt(25 + 1) = sqrt(26) Length of line DA is given by sqrt[(5 - 5)^2 + (8 - 3)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Thus, the length of the sides of the quadrilateral are not equal but opposite sides are equal which means that the quadrilateral is not a rhombus. Finally, we check whether adjacent lines are perpendicular. Recall the for perpendicular lines, the product of their slopes is equal to -1. Slope of line AB = 5 while slope of line BC = 0. The product of their slopes = 5 x 0 = 0 which is not -1, thus the adjacent sides of the quadrilateral are not perpendicular which means that the quadrilateral is not a rectangle. Therefore, ABCD is a parallelogram with non-perpendicular adjacent sides. Thus, For (option A).
Hope It Helped!~ ♡
ItsNobody~ ☆
Answer:
A. ABCD is a parallelogram with non-perpendicular adjacent sides.
Hope this helps!
Step-by-step explanation:
In an examination, 40% of the candidates failed. The number candidates who failed was 160. How many candidates passed the examination?
Answer:
240 candidates
Step-by-step explanation:
40% candidates failed, i. e. out of every 100 candidates 40 failed.
40 failed ----------------------------- 100 total students
1 failed --------------------------------100/40 total students, given 160 failed therefore
160 failed ----------------------------(100/40) x 160 total students
Total students = (100/40) x 160 = 400
Number of candidates passed = (total candidates) - (total candidates failed)
= 400 - 160 = 240 candidates
Define “constant value”
A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants.
I need help with this question.
Answer:
Complement = 15 Degrees
Supplement = 105 Degrees
Step-by-step explanation:
The complement of an angle refers to the measure that will make the angle 90 degrees. So, the complement of 75 would be 15, since 90 - 75 = 15.
The supplement of an angle refers to the measure that will make the angle 180 degrees. So, the supplement of 75 would be 105, since 180-75 = 105.
Cheers.
What number is equivalent to 9 1/2?
Answer:
the answer is going to be 2/4
22 tons is equivalent to ______ kilograms.
Answer:
20000 kg
Step-by-step explanation:
Recall that 1 kg = 2.2 lb approximately. Then:
22 tons 1 kg 2000 lb
------------ * ------------ * -------------- = 20000 kg
1 2.2 lb 1 ton
The radar system beeps once every second. How many times will it beep in 3 days?
Answer:
259200
Step-by-step explanation:
so there are 86400 in one day. multiply by 3.
Answer:
259200
Step-by-step explanation:
60x24x3x60=
3. Simplify the following
a)[(116)3 x 114]x 1212
Answer:
48082464 is the answer
Step-by-step explanation:
=[(116)3×114] × 1212
=[348×114] × 1212
=39672 × 1212
=48082464 is the answer
hope it will help :)
Hey There!!
All you really need To do is: Divide [(116)] 3 x 114] x 1212) ( 20 + 51 + 43) ÷ 7
Hope It Helped!~ ♡
ItsNobody~ ☆
Suppose you have a bag with the following in it: 5 one dollar bills, 4 fives, 3 tens, 5 twenties, and 3 fifties. Assuming the experiment requires drawing one bill from the bag at random, complete the probability distribution for this experiment.
Required:
What is the probability of drawing 9 dollars or less in a single draw?
Answer:
(a) Probility Distribution
Outcome probability
$1 5/15 = 1/3
$5 4/15
$10 3/15 = 1/5
$20 5/15 = 1/3
(b) P($9 or less) = 3/5
Step-by-step explanation:
(a) Probility Distribution
Outcome probability
$1 5/15 = 1/3
$5 4/15
$10 3/15 = 1/5
$20 5/15 = 1/3
Any other denomination
0
(b)
ways to draw $9 or less in a single draw
P($1) = 1/3
P($5) = 4/15
P($9 or less) = P($1) + P($5) = 1/3 + 4/15 = 9/15 = 3/5
Graph the function f(x) = 18(0.8)
[tex]f(x)=18(0.8)=14.4[/tex]
is a constant function, so it will be a straight line parallel to x axis and passing through y axis at $14.4$
normal population has a mean of 63 and a standard deviation of 13. You select a random sample of 25. Compute the probability that the sample mean is: (Round your z values to 2 decimal places and final answers to 4 decimal places): Greater than 65.
Answer:
0.2207
Step-by-step explanation:
Here, we want to find the probability that the sample mean is greater than 25.
What we use here is the z-scores statistic
Mathematically;
z-score = (x-mean)/SD/√n
From the question;
x = 65, mean = 63, SD = 13 and n = 25
Plugging these values in the z-score equation, we have
Z-score = (65-63)/13/√25 = 2/13/5 = 0.77
So the probability we want to calculate is ;
P(z > 0.77)
This can be obtained from the standard normal distribution table
Thus;
P(z > 0.77) = 0.22065 which is 0.2207 to 4 d.p
T= 2pi times the sqrt of l/g (l=2.0m; g= 10m/s^2
Answer:
v (m/s) a(m/s2). √. ½. 0. ¼. √. -¼. Movimiento circular y M.A.S. Un punto se mueve ... como la que se ilustra en la figura, llamada onda cuadrada. ... Movimiento Armónico Simple I. Una partícula cuya masa es de 1 g vibra con movimiento ... Multiplicando por el Periodo de oscilación del sistema T (con ... distancia de 10 m?
Step-by-sv (m/s) a(m/s2). √. ½. 0. ¼. √. -¼. Movimiento circular y M.A.S. Un punto se mueve ... como la que se ilustra en la figura, llamada onda cuadrada. ... Movimiento Armónico Simple I. Una partícula cuya masa es de 1 g vibra con movimiento ... Multiplicando por el Periodo de oscilación del sistema T (con ... distancia de 10 m?tep explanation:
Which of the following is -32(5x-7)(x+8)/-4(x+8)(5x-7) simplified? A.8/(x+8) B.8 C.4 D.4/(5x-7)
Answer:
work is shown and pictured
What is the solution to this system of linear equations?
y-x = 6
y + x = -10
(-2,-8)
(-8.-2)
(6.-10)
(-10.6)
Answer:
The correct answer is A
Step-by-step explanation:
Answer:
(-8, -2)
Step-by-step explanation:
y-x = 6
y + x = -10
Add the two equations together to eliminate x
y-x = 6
y + x = -10
--------------------
2y = -4
Divide by 2
2y/2 = -4/2
y = -2
Now find x
y+x = -10
-2+x = -10
x = -8
Find the slope of the line that passes through the points (1, -4) and (3,-1)
Hi there! :)
Answer:
[tex]\huge\boxed{m = \frac{3}{2}}[/tex]
Find the slope using the slope formula:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in the coordinates of each point:
[tex]m = \frac{-1 - (-4)}{3 - 1}[/tex]
Simplify:
[tex]m = \frac{3}{2}[/tex]
Therefore, the slope of the line is 3/2.
Answer:
3/2
Step-by-step explanation:
The slope is given by
m = (y2-y1)/(x2-x1)
= ( -1 - -4)/(3-1)
= ( -1+4)/(2)
= ( 3/2)
Can u pls help I don’t understand I’ll give u 15 points
Answer: [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
This is a multiplication problem. You are multiplying [tex]\frac{1}{3}[/tex] by 4. This also means 4 divided by 3. They are both the same.
Find the value of the test statistic z using . The claim is that the proportion of adults who smoked a cigarette in the past week is less than , and the sample statistics include n subjects with saying that they smoked a cigarette in the past week.
Correct question is;
The claim is that the proportion of adults who smoked a cigarette in the past week is less than 0.35, and the sample statistics include n = 1168 subjects with 385 saying that they smoked a cigarette in the past week. Find the value of the test statistic
Answer:
Test statistic is z = -1.46
Step-by-step explanation:
Let's first of all define the hypotheses:
Null hypothesis:
H0: p = 0.35, i.e 35% in the sample of 1,168 adults have smoked cigarettes in the previous week.
Alternative hypothesis:
Ha: p < 0.35, i.e less than 35% in the sample of 1,168 adults have smoked cigarette in the previous week.
The sample size is, n = 1,168 while the number of adults who smoked in the previous week would be; x = 385
Therefore, the sample proportion of adults who smoked in the previous week would be calculated as;
p^ = x/n = 385/1168 ≈ 0.3296
Now, from Central Limit Theorem for large samples, The sampling distribution of the sample proportion p^, will have a mean of μ = p = 0.35
Formula for standard deviation is;
σ = √[p (1 – p)/n]
σ = √(0.35 × (1 – 0.35)/1168)
σ = √0.0001947774
σ = 0.014
Formula for test statistic is;
z = (p^ - p)/σ
z = (0.3296 - 0.35)/0.014
z = - 1.46
If mL DOC = 44º and m2 COB = 80°,
find the measure of the indicated arc
in circle o.
С
o
B.
mDEB = ?
Answer:
236°
Step-by-step explanation:
The circumference of a circle is 360° since <DOC is given as 44° and <COB is given as 80° and the center angles are equal to the arc it sees the the measure of arc DEB would be 360 - 44 - 80 = 236°
Evaluate x^2 − 4x + 5, when x = − 3
Answer:
[tex]\huge\boxed{26}[/tex]
Step-by-step explanation:
[tex]\sf x^2-4x+5\\Given \ that \ x = -3\\(-3)^2-4(-3)+5\\9+12+5\\26[/tex]
Answer:
[tex] \boxed{26}[/tex]
Step-by-step explanation:
[tex] \mathsf{ {x}^{2} - 4x + 5}[/tex]
[tex] \mathrm{Plug \: the \: value \: of \: x}[/tex]
⇒[tex] {( - 3)}^{2} - 4 \times(- 3 )+ 5[/tex]
[tex] \mathrm{Evaluate \: the \: power}[/tex]
⇒[tex] \mathsf{9 - 4 \times(- 3 ) + 5}[/tex]
[tex] \mathrm{Multiply \: the \: numbers}[/tex]
⇒[tex] \mathsf{9 + 12 + 5}[/tex]
[tex] \mathrm{Add the numbers}[/tex]
⇒[tex] \mathsf{26}[/tex]
Hope I helped!
Best regards!
The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information.
Store's Card Major Credit Card
Sample size 64 49
Sample mean $140 $125
Population standard deviation $10 $8
A point estimate for the difference between the means is:________
a. 18
b. 265
c. 15
d. 2
if y = 2√x÷ 1–x', show that dy÷dx = x+1 ÷ √x(1–x)²
Answer: see proof below
Step-by-step explanation:
Use the Quotient rule for derivatives:
[tex]\text{If}\ y=\dfrac{a}{b}\quad \text{then}\ y'=\dfrac{a'b-ab'}{b^2}[/tex]
Given: [tex]y=\dfrac{2\sqrtx}{1-x}[/tex]
[tex]\sqrtx[/tex][tex]a=2\sqrt x\qquad \rightarrow \qquad a'=\dfrac{1}{\sqrt x}\\\\b=1-x\qquad \rightarrow \qquad b'=-1[/tex]
[tex]y'=\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)}{(1-x)^2}\\\\\\.\quad =\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)\bigg(\dfrac{\sqrt x}{\sqrt x}\bigg)}{(1-x)^2}\\\\\\.\quad =\dfrac{1-x+2x}{\sqrt x(1-x)^2}\\\\\\.\quad =\dfrac{x+1}{\sqrt x(1-x)^2}[/tex]
LHS = RHS: [tex]\dfrac{x+1}{\sqrt x(1-x)^2}=\dfrac{x+1}{\sqrt x(1-x)^2}\qquad \checkmark[/tex]
Point E lies within rectangle ABCD. If AE = 6, BE = 7, and CE = 8, what is the length of DE?
Answer:
[tex]\sqrt{51}[/tex] units.
Step-by-step explanation:
Point E is inside a rectangle ABCD.
Please refer to the attached image for the given statement and dimensions.
Given that:
Sides AE = 6 units
BE = 7 units and
CE = 8 units
To find:
DE = ?
Solution:
For a point E inside the rectangle the following property hold true:
[tex]AE^2+CE^2=BE^2+DE^2[/tex]
Putting the given values to find the value of DE:
[tex]6^2+8^2=7^2+DE^2\\\Rightarrow 26+64=49+DE^2\\\Rightarrow DE^2=100-49\\\Rightarrow DE^2=51\\\Rightarrow \bold{DE = \sqrt{51}\ units}[/tex]
Cybil flips a coin and rolls a fair number cube at the same time. What is the probability that she will toss tails and roll a number less than 3? A. 1/6 B. 1/3 C. 2/5 D. 1/2 Please include ALL work! <3
[tex]|\Omega|=2\cdot6=12\\|A|=1\cdot2=2\\\\P(A)=\dfrac{2}{12}=\dfrac{1}{6}[/tex]
Rob sent an email survey to 2,000 cell phone owners asking about their satisfaction with their current plan. Only 256 people returned the survey and they were predominately 18-24 years old.
Which of the following statements is true?
Rob is ignoring the assumption that all survey participants will want to act independently.
The survey likely has bias because the people who could not answer differ from those who did answer.
Rob included too many people on the survey list, affecting the data collected.
The survey suffers from census issues because only 256 people responded.
Answer:
option B
everyone has different opinions about different things, since we only recorded the survey of a fourth of the total people, the survey will definitely have bias since the people who dont have to answer survey will not be able to record their opinions
A line is an undefined termi because it
Answer:
Goes on forever.
Step-by-step explanation:
Marco is investigating some of the business models of SureSpin, one of Faster Fidget's top competitors.
He has learned that they model their cost of production for one type of spinner with the function C(x) =13,450 + 1.28x, where x is the number of spinners produced. Interpret the model to complete the
statement.
Type the correct answer in each box. Use numerals instead of words. Based on the model, the fixed cost of production is $?
Answer:
$13,450
Step-by-step explanation:
The fixed cost of production is $13,450, this is because a fixed cost of production is the amount of cost that does not change with an increase or decrease in the amount of the goods or services produced. Fixed cost of production are paid by companies. It is one of the two component of the total cost of goods or services along with the variable cost.
In regard to the information given in the question, no matter how many spinners the company produces, the fixed cost will remain the same.
Assuming x is the variable cost which signifies the number of spinners produced, this literally implies that the cost to produce each spinner is $1.28 and the fixed cost which is independent of the production is $13,450.
Hence, the fixed cost of production is $13,450.
