Step-by-step explanation:
Area ABC=1/2ab×sin C
=1/2 ×20×10 ×Sin C
Sin C =100
If the volume of the expanding cube is increasing at the rate 24 cm3 / min , how fast is its surface area increasing when the surface area is 216 cm2 ?
Answer:
16 cm^2/min
Step-by-step explanation:
dV/dt=24
V=a^3, differentiate with respect to t
dV/dt=3a^2*da/dt, a^2*da/dt=8
S=6a^2, 216=6a^2. a=6. da/dt=(8/36)
dS/dt=12*a*da/dt=12*(8/6)=16 cm^2/min
Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)
2 sin2(θ) = 2 + cos(2θ)
θ=
Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)
cos(2θ) + 7 cos(θ) = 8
θ=
For the first equation, recall that sin²(θ) = (1 - cos(2θ))/2. Then
2 sin²(θ) = 2 + cos(2θ)
1 - cos(2θ) = 2 + cos(2θ)
2 cos(2θ) = -1
cos(2θ) = -1/2
2θ = arccos(-1/2) + 2nπ or 2θ = 2π - arccos(-1/2) + 2nπ
(where n is any integer)
2θ = 2π/3 + 2nπ or 2θ = 4π/3 + 2nπ
θ = π/3 + nπ or θ = 2π/3 + nπ
In the interval [0, 2π), the solutions are θ = π/3, 2π/3, 4π/3, 5π/3.
For the second equation, rearrange the previous identity to arrive at
cos(2θ) = 1 - 2 sin²(θ) = 2 cos²(θ) - 1
Then
cos(2θ) + 7 cos(θ) = 8
2 cos²(θ) - 1 + 7 cos(θ) = 8
2 cos²(θ) + 7 cos(θ) - 9 = 0
(2 cos(θ) + 9) (cos(θ) - 1) = 0
2 cos(θ) + 9 = 0 or cos(θ) - 1 = 0
cos(θ) = -9/2 or cos(θ) = 1
Since |-9/2| > 1, and cos(θ) is bounded between -1 and 1, the first case offers no solutions. This leaves us with
cos(θ) = 1
θ = arccos(1) + 2nπ
θ = 2nπ
so that there is only one solution in [0, 2π), θ = 0.
Which of the following options correctly represents the complete factored
form of the polynomial F(x) = x^3- x2 - 4x-6?
A. F(x) - (x - 3)(x + 1 + I)(x+1- I)
B. F(x) = (x - 3)(x+1+I)(x-1-I)
C. F(x) = (x+3)(x + 1)(x - 1)
D. F(x) - (x+3)(x+1+I)(x +1-I )
The completely factored form for the given algebraic expression is f(x) = (x-3)(x+1+i)(x+1-i).
What is a completely factored polynomial?A completely factored polynomial is a polynomial that can no longer be further simplified. A completely factored polynomial can be expressed as a root of its own equation.
Given that:
f(x) = x³ - x² - 4x - 6
To express this as a factored polynomial using the rational:
f(x) = (x-3)(x²+2x+2)
f(x) = (x-3)(x+1+i)(x+1-i)
Learn more about how to completely factor polynomial here:
https://brainly.com/question/11434122
#SPJ1
I are these orders pairs a function
х,у
0,9
2,8.
4,7
6,6
8,5
10,4
9514 1404 393
Answer:
yes
Step-by-step explanation:
No x-value is repeated, so these ordered pairs do represent a function.
Which best describes the relationship between the lines with equations 2x – 9y = 1 and x + 8y = 6?
A. perpendicular
B. neither perpendicular nor parallel
C. parallel
D. same line
9514 1404 393
Answer:
B. neither perpendicular nor parallel
Step-by-step explanation:
If the lines were perpendicular, the coefficients would be swapped and one negated. (You would have 8x -y = c, or 9x +2y = c in the system.)
If the lines were parallel, the coefficients in the two equations would only differ by a common factor. (Both equations would reduce to 2x -9y = c, or x +8y = c.)
The lines are not the same line (coefficients are different).
So, the only reasonable description is ...
neither perpendicular nor parallel
Please help me with this question
Find the difference between each number:
-11 to -3 is +8
-3 to 5 is +8
The difference is 8
Use the following formula:
Bn = b1 + d(b -1)
Answer: bn = -11 + 8( b-1)
If 6.45% of the battery life of each mobile phone is used in a day by a typical user, for which mobile phone is 1.6125 hours of battery life used in a day?
The table shows the battery life of four different mobile phones. Mobile Phone Battery Life Phone Battery Life (hours) A 20 B 25 C 10 D 18 If 6.45% of the battery life of each mobile phone is used in a day by a typical user, for which mobile phone is 1.6125 hours of battery life used in a day?
B
Should be the answer
Which exponential expression is equivalent to (4x^2 y^3)^2
Answer:
[tex] 16 {x}^{4} {y}^{6} [/tex]
Step-by-step explanation:
[tex](4 {x}^{2} {y}^{3} {)}^{2} [/tex]
➡️ [tex] {4}^{2} \times ( {x}^{2} {)}^{2} \times ( {y}^{3} {)}^{2} [/tex]
➡️ [tex] = 16 {x}^{4} {y}^{6} [/tex] ✅
If p=(3/4)and q=(1/2)find p-2q
Answer:
[tex]p - 2q \\ \frac{3}{4} - 2( \frac{1}{2} ) \\ = \frac{3}{4} - \frac{2}{2} \\ = \frac{3}{4} - 1 \\ = \frac{3 - 4}{4} \\ = \frac{ - 1}{4} \\ = - 0.25[/tex]
I hope I helped you^_^
An adult can lose or gain two pounds of water ina course of a day. Assume that the changes in water weight isuniformly distributed between minus two and plus two pounds in aday. What is the standard deviation of your weight over a day?
Answer:
The standard deviation of your weight over a day is of 1.1547 pounds.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b, and the standard deviation is:
[tex]S = \sqrt{\frac{(b-a)^2}{12}}[/tex]
Assume that the changes in water weight is uniformly distributed between minus two and plus two pounds in a day.
This means that [tex]a = -2, b = 2[/tex]
What is the standard deviation of your weight over a day?
[tex]S = \sqrt{\frac{(2 - (-2))^2}{12}} = \sqrt{\frac{4^2}{12}} = \sqrt{\frac{16}{12}} = 1.1547[/tex]
The standard deviation of your weight over a day is of 1.1547 pounds.
giving brainliest! :)
Answer:
239=5
478=10
956=20
Step-by-step explanation:
Gianna's car can travel 478 mi with 10 gallons of gas
so, 47.8 mi with 1 gallon
by dividing 239 by 47.8 miles/gallon we get the answer 5 miles.
if we multiply 20 gallons by 47.8 mi/gallon #e get the answer 956 miles.
easy weasy
what is square root of 49 over square root of 1250 simplified
im pretty sure its 0.19 because the sqyare root of 49 is 7. the square root of 1250 is 35.35
7/35.35=0.19
Using the identity. (a - b) ²= (a² - 2ab + b²), evaluate 699²
Step-by-step explanation:
hope it helps you.......
[tex]\\ \sf\longmapsto 699^2[/tex]
[tex]\\ \sf\longmapsto (700-1)^2[/tex]
[tex]\\ \sf\longmapsto 700^2-2(700(1)+(1)^2[/tex]
[tex]\\ \sf\longmapsto 490000-1400+1[/tex]
[tex]\\ \sf\longmapsto 488600+1[/tex]
[tex]\\ \sf\longmapsto 488601[/tex]
find the supplement of 158 degrees and 17 minutes
Answer:
supplement of 158 degree
x+158=180
x=180-158
x=22 degree.
Step-by-step explanation:
7 There are five women and six men in a group. From this group a committee of 4 is to be chosen. In how many different ways can a committee be formed that contain at least three women?
Answer:
in three (3) ways a committee can formed
Many freeways have service (or logo) signs that give information on attractions, camping, lodging, food, and gas services prior to off-ramps. These signs typically do not provide information on distances. An article reported that in one investigation, six sites along interstate highways where service signs are posted were selected. For each site, crash data was obtained for a three-year period before distance information was added to the service signs and for a one-year period afterward. The number of crashes per year before and after the sign changes were as follows.
Before 13 22 65 123 56 63
After 14 21 43 84 75 72
1. The article included the statement "A paired t-test was performed to determine whether there was any change in the mean number of crashes before and after the addition of distance information on the signs." Carry out such a test. (Note: The relevant normal probability plot shows a substantial linear pattern.)
a. State and test the appropriate hypotheses. (Use α = 0.05.)
b. Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
t = _____
p-value = _____
c. State the conclusion in the problem context.
A. Fail to reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
B. Reject H0. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
C. Fail to reject H0. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
D. Reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
2. If a seventh site were to be randomly selected among locations bearing service signs, between what values would you predict the difference in the number of crashes to lie? (Use a 95% prediction interval. Round your answers to two decimal places.)
Answer:
Test statistic = 0.63
Pvalue = 0.555
A. Fail to reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
Step-by-step explanation:
Given :
Before 13 22 65 123 56 63
After_ 14 21 43 84 75 72
To perform a paired t test :
H0 : μd = 0
H1 : μd ≠ 0
We obtain the difference between the two dependent sample readings ;
Difference, d = -1, 1, 22, 39, -19, -9
The mean of difference, Xd = Σd/ n = 33/6 = 5.5
The standard deviation, Sd = 21.296 (calculator).
The test statistic :
T = Xd ÷ (Sd/√n) ; where n = 6
T = 5.5 ÷ (21.296/√6)
T = 5.5 ÷ 8.6940555
T = 0.6326
The Pvalue : Using a Pvalue calculator ;
df = n - 1 = 6 - 1 = 5
Pvalue(0.6326, 5) = 0.5548
Decision region :
Reject H0 ; If Pvalue < α; α = 0.05
Since 0.5548 > 0.05 ; we fail to reject the Null and conclude that the data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
A worker in the automobile industry works an average of 43.7 hours per week. Assume the distribution is normal with a standard deviation of 1.6 hours.
(i) What is the probability that a randomly selected automobile worker works less than 40 hours per week?
(ii) If 15 automobile workers are randomly selected, what is the probability that the sample mean of working time is more than 45 hours per week?
Answer:
The solution is:
(1) 0.0104
(2) 0.0008
Step-by-step explanation:
Given:
Mean,
[tex]\mu = 43.7[/tex]
Standard deviation,
[tex]\sigma = 1.6[/tex]
(1)
⇒ [tex]P(X<40) = P(\frac{x-\mu}{\sigma}<\frac{40-43.7}{1.6} )[/tex]
[tex]=P(z< - 2.3125)[/tex]
[tex]=P(z<-2.31)[/tex]
[tex]=0.0104[/tex]
(2)
As we know,
n = 15
⇒ [tex]P(\bar X > 45)= P(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n} } } >\frac{45-43.7}{\frac{1.6}{\sqrt{15} } } )[/tex]
[tex]=P(z> 3.15)[/tex]
[tex]=1-P(z<3.15)[/tex]
[tex]=1-0.9992[/tex]
[tex]=0.0008[/tex]
A ladder leans against the side of the a house. The ladder is 19 feet long and forms an angle of elevation of 75 degree when leaned against the house. How far away from the house is the ladder? Round your answer to the nearest tenth.
Answer: 18.35259
Hope it helps!
Five trucks are to be transported on a ship. Each one weighs 3200 kg and comes
with 8 tyres which weigh 125 kg each. what is the total weight
Total No of trucks: 5
Weight of trucks: 3200Kg
Total weight of trucks: 3200×5
= 16000kg
Total no of tyres = 5 ×8
= 40
Weight of each tyre = 125kg
Total weight of tyres = 125 × 40
= 5000Kg
The total weight of trucks and tyres: 16000 + 5000
= 21000Kg
Answered by Gauthmath must click thanks and mark brainliest
Find the first six terms of the sequence.
a1=- 6, an= 4 • an-1
Answer:
I think it's 3
Step-by-step explanation:
because an=4 and the question is
an-1
=4-1
=3
The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 45 and a standard deviation of 3. Using the empirical rule, what is the approximate percentage of lightbulb replacement requests numbering between 42 and 45?
Do not enter the percent symbol.
ans = %
Answer:
34%
Step-by-step explanation:
Given that the distribution of daily light bulb request replacement is approximately bell shaped with ;
Mean , μ = 45 ; standard deviation, σ = 3
Using the empirical formula where ;
68% of the distribution is within 1 standard deviation from the mean ;
95% of the distribution is within 2 standard deviation from the mean
Lightbulb replacement numbering between ;
42 and 45
Number of standard deviations from the mean /
Z = (x - μ) / σ
(x - μ) / σ < Z < (x - μ) / σ
(42 - 45) / 3 = -1
This lies between - 1 standard deviation a d the mean :
Hence, the approximate percentage is : 68% / 2 = 34%
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = 6/5x-1
Step-by-step explanation:
We have two points so we can find the slope
(-5,-7) and (5,5)
The slope is
m = ( y2-y1)/(x2-x1)
= ( 5- -7)/( 5 - -5)
= (5+7)/(5+5)
= 12/10
= 6/5
The slope intercept form of a line is
y = mx+b
y = 6/5x+b
Using the point (5,5)
5 = 6/5(5)+b
5=6+b
b=-1
y = 6/5x-1
Suppose g(x) = f( x +2) - 3. Which statement best compares the graph of g(x) with the graph of f(x)? A. The graph of g(x) is shifted 2 units left and 3 units up. B. The graph of g(x) is shifted 2 units right and 3 units down. C. The graph of g(x) is shifted 2 units left and 3 units down. D. The graph of g(x) is shifted 2 units right and 3 units up.
Given:
The function is:
[tex]g(x)=f(x+2)-3[/tex]
To find:
The statement that best compares the graph of g(x) with the graph of f(x).
Solution:
The transformation is defined as
[tex]g(x)=f(x+a)+b[/tex] .... (i)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
We have,
[tex]g(x)=f(x+2)-3[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=2[/tex]
[tex]b=-3[/tex]
Therefore, the graph of g(x) is shifted 2 units left and 3 units down.
Hence, the correct option is C.
A movie theater has a seating capacity of 333. The theater charges $5.00 for children, $7.00 for students,
and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $
2422, How many children, students, and adults attended?
Answer:
182 children, 91 adults, 60 students
Step-by-step explanation:
The quantity of adults is x, then the quantity of children are 2x, the quantity of students is 333-x-2x=333-3x. The charge from all adults is 12x, students gave 7*(333-3x), children gave 5*2x=10x, the sum of all money is 2422
12x+ 7(333-3x)+10x=2422
12x+2331-21x+10x=2422
2331+x=2422
x=91- the amount of adults
1) 91*2=182- the amount of children
333-91-182= 60- the amount of students
What is the value of x that makes l1||l2
A. 35
B. 25
C. 37
D. 18
Answer:
B
Step-by-step explanation:
For l1 and l2 to be parallel, these two angles need to be equal. 3x-15=2x+10, x=25
The graph shows the distribution of lengths of songs (in seconds). The distribution is approximately Normal, with a mean of 227 seconds and a standard deviation of 31 seconds.
A graph titled Song length has length (seconds) on the x-axis, going from 103 to 351 in increments of 31. The highest point of the curve is at 227.
What percentage of songs have lengths that are within 31 seconds of the mean?
34%
68%
95%
99.7%
its everything between 196 and 258 seconds (at max 31secs away from the mean). imagine straight upward lines separating this area from the rest.
34% would be way too low, 95 and above way too much.
only 68% is remotely plausible.
Solve the equation for x 11x=110
A rectangular prism has volume 1,088 ft3 and height 8 ft. What is the area of the base of the prism?
a. 146 ft2
c. 136 ft2
b. 1,080 ft2
d. 1,096 ft2
We know
[tex]\boxed{\sf Volume=Area\:of\:Base\times Height}[/tex]
[tex]\\ \sf\longmapsto Area\:of\:Base=\dfrac{Volume}{Height}[/tex]
[tex]\\ \sf\longmapsto Area\:of\:Base=\dfrac{1088}{8}[/tex]
[tex]\\ \sf\longmapsto Area\;of\:base=136ft^2[/tex]
15. The height and yolume of a cylinder are 4cm and 616cm respectively. Calculate the diameter of the base. (take t = 27 쪽 A. 7cm B. 154cm C. 14cm D. 64cm
Step-by-step explanation:
Given that,
Height of cylinder = 4 cmVolume of cylinder = 616 cm³To find,
Diameter of the base = ?Firstly we'll find the base radius of the cylinder.
[tex]\longmapsto\rm{V_{(Cylinder)} = \pi r^2h}\\[/tex]
According to the question,
[tex]\longmapsto\rm{616= \dfrac{22}{7} \times r^2 \times 4}\\[/tex]
[tex]\longmapsto\rm{616 \times 7 = 22 \times r^2 \times 4}\\[/tex]
[tex]\longmapsto\rm{4312 = 88 \times r^2 }\\[/tex]
[tex]\longmapsto\rm{\cancel{\dfrac{4312}{88}} = r^2 }\\[/tex]
[tex]\longmapsto\rm{49 = r^2 }\\[/tex]
[tex]\longmapsto\rm{\sqrt{49} = r }\\[/tex]
[tex]\longmapsto\rm{7 \; cm = r }\\[/tex]
Now,
[tex]\longmapsto\rm{Diameter = 2r }\\[/tex]
[tex]\longmapsto\rm{Diameter = 2(7 \; cm) }\\[/tex]
[tex]\longmapsto\bf{Diameter = 14 \; cm}\\[/tex]
The required answer is 14 cm.
The central angle in a circle of radius 6 meters has an intercepted arc length of 10 meters. Find the measure of the angle in radians and in degrees
Answer:
The central angle is 5/3 radians or approximately 95.4930°.
Step-by-step explanation:
Recall that arc-length is given by the formula:
[tex]\displaystyle s = r\theta[/tex]
Where s is the arc-length, r is the radius of the circle, and θ is the measure of the central angle, in radians.
Since the intercepted arc-length is 10 meters and the radius is 6 meters:
[tex]\displaystyle (10) = (6)\theta[/tex]
Solve for θ:
[tex]\displaystyle \theta = \frac{5}{3}\text{ rad}[/tex]
The central angle measures 5/3 radians.
Recall that to convert from radians to degrees, we can multiply by 180°/π. Hence:
[tex]\displaystyle \frac{5\text{ rad}}{3} \cdot \frac{180^\circ}{\pi \text{ rad}} = \frac{300}{\pi}^\circ\approx 95.4930^\circ[/tex]
So, the central angle is approximately 95.4930°
