Answers
The area of the region is equal to the area under the curve y = cos(x) over the interval 0 ≤ x ≤ π/6, given by the integral
[tex]\displaystyle\int_0^{\frac\pi6}\cos(x)\,\mathrm dx = \sin(x)\bigg|_0^{\frac\pi6}=\sin\left(\frac\pi6\right)-\sin(0)=\boxed{\frac12}[/tex]
which follows from
• the fact that d/dx [sin(x)] = cos(x)
• the fundamental theorem of calculus
Related Questions
33) 90÷18-18÷6-6÷3=
Preciso de ajudaaaa
Answers
Answer:
67
Step-by-step explanation:
(90÷18)-(18÷6)-(6÷3)= 72-3-2= 67
HELP ME PLEASE DONT MIND THAT ANSWER DIDNT MEAN THE CLICK IT :(
Answers
Answer:
B)240 sm
Step-by-step explanation
6*4=24 sm
24*10=240 sm
So that means the surface area of that rectangular prism is 240 square meters
Determine the Geometric mean of 18 and 27
Answers
Answer:
The geometric mean of 18 and 27 is 22.045407685
Step-by-step explanation:
I hope this helps and pls mark me brainliest :)
Answer:
22.045407685
Step-by-step explanation:
please please help me I will mark brainlist !!
Answers
Answer:
9. B. 32 millimeters
10. C. 7 inches
11. C. 56.24 millimeters
13. B. 14.13 square feet
Step-by-step explanation:
9. Radius of a circle or any circular shape = ½ of its diameter
Diameter of the disk = 64 millimeters
Radius of the disk = ½(64) = 32 millimeters
10. Width of the cooler = 6 in.
Length = 8 in.
Volume = 336 in.³
Height = ?
Formula for volume of a rectangular prism = L*W*H
Plug in the values
336 = 8*6*H
336 = 48*H
Divide both sides by 48
336/48 = H
H = 7 inches
11. A dime has a circular shape
The circumference of the dime = circumference of a circle = πd
Where,
d = 17.91 millimeters
π = 3.14
Plug in the values
C = 3.14 × 17.91 = 56.2374
≈ 56.24 millimeters (nearest hundredth)
12. Area of the top of the desk = area of semicircle = ½ × πr²
Where,
r = ½(6) = 3 ft
π = 3.14
Plug in the values
Area = ½ × 3.14 × 3² = ½ × 3.14 × 9
Area = 14.13 square feet
Nevaeh’s bag contains 2 red marbles, 3 blue marbles, and 5 green marbles. Nevaeh randomly selects a marble from the bag, records the color, and then puts the marble back in the bag. If she does this 150 times, how many times would she expect to select blue?
A 10 times
B 30 times
C 45 times
D 75 times
Answers
Answer:
30
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
mark me brainlest
24 13
10) Find the midpoint of a line segment AB. A(3, 10) and B (-9,3)
Answers
Answer:
(-3 ;13/2)Step-by-step explanation:
hello :
the midpoint of the line segment is : ((3-9)/2 ;(10+3)/2 )
(-3 ;13/2)
Nancy bought a vase as wedding gift .The cost excluding vat was R250.How much must she pay with VAT inclusive
Answers
Step-by-step explanation:
VAT = 250*15%
VAT = 250*15/100
VAT = 37.5 therefore
total price add VAT =250+37.5
=287.5
Rachel received a monthly raise of $105.25. If this represented a 5.5% increase, what is her monthly salary after the raise?
A. $1,913.64
B. $1,964.13
С. $2,018.89
D. $2.089.18
Answers
Answer:
C
Step-by-step explanation:
105,25:5,5*105.5=2018,89
A store gives customers a markup of 13%. If the store sells a belt for $25, what was the wholesale price paid for the belt by the store?
Answers
Answer:
$22.12
Step-by-step explanation:
Let x be the wholesale price (the price before adding the markup).
The markup is 13%, so 13% of x is added to x.
x + 13%x = $25
x + 0.13x = 25
1.13x = 25
x = 25/1.13
x = 22.12
Please tell me if I got it right
Answers
Answer:
1/9
Step-by-step explanation:
1/3 / 3 = 1/9
she will run 1/9
jog 1/9
and walk 1/9
to check all of them equal 1/3
1/9+1/9+1/9 = 3/9 = 1/3
When driving in England, Brian drove through several speed cameras. On one drive, Brian left his hotel and after 7 minutes he was 2.5 km away and at that moment was measured going 0.5 kpm (kilometers per minute). Later, 18 minutes after he started driving, he was 14.8 km from the hotel and at that moment was measured going 0.8 kpm.
A. Find the linearization at 7 minutes.
B. Find the linearization at 18 minutes.
C. Compute two approximations for Brian's distance from his hotel at 14 minutes, using the linearizations from parts a and b.
D. Which approximation do you think is better? Why?
Answers
Solution :
The formula for the linearization of a function [tex]$f(x)$[/tex] at a point [tex]$x$[/tex] = a is given as
[tex]$L(x)=f(a)+(x-a)f'(a)$[/tex]
Assuming the time is t and the distance travelled is [tex]$f(t)$[/tex], that makes the speed as [tex]$f'(t)$[/tex].
So substituting them in the linearization formula,
A. At t = 7 minutes
f(7) = 2.5 km
f'(7) = 0.5 kpm
∴ [tex]$L_7(t)=f(7)+(t-7)f'(7)$[/tex]
[tex]$=2.5+(t-7)0.5$[/tex]
[tex]$=2.5+0.5t-3.5$[/tex]
[tex]$=0.5t-1$[/tex]
B. At t = 18 minutes
f(18) = 14.8 km
f'(18) = 0.8 kpm
∴ [tex]$L_{18}(t)=f(18)+(t-18)f'(18)$[/tex]
[tex]$=14.8+(t-18)0.8$[/tex]
[tex]$=14.8+0.8t-14.4$[/tex]
[tex]$=0.8t-0.4$[/tex]
C. Substituting the value of t as 14 in both the linearization to determine the position at 14 minutes, we get
[tex]$L_7(14)=0.5(14)-1.0$[/tex]
= 7 - 1
= 6 km
[tex]$L_{18}(14)=0.8(14)+0.4$[/tex]
= 11.2 + 0.4
= 11.6 km
D. According to the linearization at 7, the distance travelled between the 7 minutes and 14 minutes is = 6 km - 2.5 km
= 3.5 km
And between the 14 minutes and 18 minutes is = 14.8 km - 6 km
= 8.8 km
This is an average speed of 0.5 kpm in the first interval and an average speed of 2.2 kpm.
Now, according to the linearization of 18, the distance travelled between the 7 minutes and the 14 minutes is = 11.6 km - 2.5 km
= 9.1 km
And between 14 minutes and 18 minutes is = 14.8 km - 11.6 km
= 3.2 km
This gives an average speed of 1.3 kpm in the first interval and 0.8 kpm in the second interval.
Therefore, the second approximation is the better one since the average speed are closer to the actual readings in the second linearization.
6) A spinner is
divided into 5 sections
lettered A to E. Lena
spins the pointer on
the spinner 25 times.
She records her
results in the table.
Based on these results,
lands on the letter B?
B is 5
Answers
Answer:
1/5
Step-by-step explanation:
there are 5 sections regardless of how many time she rolls it ti does not change the probability of landing on b so it's 1/5
im almost done with this hw. plz help!!! give explanation if you actually know the answer so ik u dont just want points
Answers
Answer:
i belive it is answer B
Step-by-step explanation:
Answer:
I think its B
Step-by-step explanation:
im not sure
In a school of 1200 students, the ratio of
the number of teachers to students is 1 : 15.
After some teachers join the school, the ratio of
the number of teachers to students becomes 3:40.
Find
(i) the initial number of teachers in the school,
(ii) the number of teachers who join the school.
Answers
No. of Teachers joined = 10
Step-by-step explanation:
i)Initial School population,
given 15 units = 1200
1 unit =
[tex]1200 \div 15 \\ = 80[/tex]
Number of teachers (initial) = 1 unit = 80.
ii)take j = number of teachers joining the school.
New teacher population = 80+j
[tex] \frac{3}{43} (1280 + j) = 80 + j \\ \frac{3840}{43} + \frac{3}{43} j = 80 + j \\ j - \frac{3}{43} j = \frac{3840}{43} - 80 \\ \frac{40}{43} j = \frac{400}{43} \\ 40j = 400 \\ j = 400 \div 40 \\ = 10[/tex]
a bag contains 1 red beads,2 yellow beads,2 green beads and 1 blue beads
a bead is chosen at random
a)what is probability that it is green ?
b)what probability that it is green or yellow
Answers
Answer:
a) 2/6 b) 4/6
Step-by-step explanation:
You add the amount of beads: 1+2+2+1= 6
And take the amount of green beads and put it over the total amount so 2/6
For b you do the same but add the green and yellow beads and put that over the total amount 4/6
Answer:
Step-by-step explanation:
a) 2/6 = 1/3
b) green or yellow = (2/6 x 1/5) + (2/6 x 1/5) = 1/15 x 1/15 = 1/225
im not sure if my answers are correct
square root of 27 lies between which two natural numbers?
Answers
Answer:
5,6
Step-by-step explanation:
Answer:
5 and 6
Step-by-step explanation:
5² = 25
6² = 36
Can somebody help please
Answers
The diameter of a cylindrical water tank is 10 ft, and its height is 9 ft. What is the volume of the tank?
Use the value 3.14 for w, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answers
Answer:
225w
Step-by-step explanation:
volume formula: w*r²*9
w*5²*9
25*9w
225w
Answer: V=707
Step-by-step explanation:
help please! need asap
Answers
Answer:
2
Step-by-step explanation:
6×3÷4=2
Hope this helps you
Plz help me on this one.
Answers
Answer: 2
Step-by-step explanation:
Answer:
To find the value of x, add 5 to each side.
x - 5 = 13
+5 +5
x = 18
:)
Pls help I don’t know hot to multiply the last part 8 2
Answers
Answer:
8^2 = 64
Step-by-step explanation:
Hi! Okay, let's get started!
[tex]8^{2}[/tex] is what you need help with right?
So, that equals to 8 x 8.
8 x 8 = 64, so it would be 64
Hope that helps!
-Aphrodite :)
Hailey made the following statement
"It is impossible to build a rectangular prism with a volume of 40 units it one side measures 5 units."
Key
represents
1 cubic unit
Select the two figures below that prove Hailey's statement is false
Answers
Answer:
D
Step-by-step explanation:
the 20% tip on a $8 sandwich
Answers
Answer:
Tip of $1.60
The total is $9.60
Step-by-step explanation:
(20% × $8) + $8
$1.60 + $8
$9.60
Emiliano firmó hoy un pagaré por la cantidad de $ 92.000. la tasa de interés estipulada es un 20% anual
Cuantos dias se necesitan para los intereses de la playa $ 8.000
Answers
Answer:
159 días.
Step-by-step explanation:
Dado que Emiliano firmó hoy un pagaré por la cantidad de $ 92.000 a una tasa de interés estipulada de un 20% anual, para determinar la cantidad de días que se necesitan para que dicho interés genere unos $8.000 se debe realizar el siguiente calculo:
92.000 x 0.2 = X
18.400 = X
18.400 / 365 = 50,41
8.000 / 50,41 = X
158.69 = X
Así, se necesitarán 159 días para que se generen $8.000 en intereses.
what is the present perfect of everybody
Answers
Answer:
Present Perfect Tense Examples
Has lived: She has lived here all her life.
Have written: They have written three letters already.
Have worked: I have worked here since I graduated school.
Has done: He has finished his homework.
Have been: We have been to Canada.
Has forgotten: She has forgotten her folder.
Step-by-step explanation:
QUICK PLEASE HELP!!!
I’LL MARK BRAINLIEST!!!
Answers
Answer:
C) 50
Step-by-step explanation:
50
Answer:
C: 50
Step-by-step explanation:
The inner diamond has congruent sides
Half of the line segment on the left is 25.
The other half of the left line segment is also 25
Together, the left line segment is 50 units
The inner diamond has both 90 degree angles and 18 unit long sides
Thus, we know that both sides are congruent
Finally, the right side is the same length as the left side
The right side is 50 units long
A child weighing 59 lb has a bad infection and is to be given Cefaclor.
The dosage is 15 mg per kg.
The drug will be delivered in an oral suspension with concentration 250 mg/5 mL.
How many mL will she receive?
Round to the nearest whole number.
You will need to convert her weight to kg, using 1 kg = 2.2 lb.
Answers
Answer:
Step-by-step explanation:
59:2,2=26,81
15*26,81:250=1,6086
The authors of a paper concluded that more boys than girls listen to music at high volumes. This conclusion was based on data from independent random samples of 768 boys and 745 girls from a country, age 12 to 19. Of the boys, 397 reported that they almost always listen to music at a high volume setting. Of the girls, 331 reported listening to music at a high volume setting.
Do the sample data support the authors' conclusion that the proportion of the country's boys who listen to music at high volume is greater than this proportion for the country's girls? Test the relevant hypotheses using a 0.01 significance level. (Use a statistical computer package to calculate the P-value. Use μboys − μgirls. Round your test statistic to two decimal places and your P-value to four decimal places.)
Answers
Answer:
Since the calculated value of z= 2.82 does not lie in the critical region the null hypothesis is accepted and it is concluded that the sample data support the authors' conclusion that the proportion of the country's boys who listen to music at high volume is greater than this proportion for the country's girls.
The value of p is 0 .00233. The result is significant at p < 0.10.
Step-by-step explanation:
1) Let the null and alternate hypothesis be
H0: μboys − μgirls > 0
against the claim
Ha: μboys − μgirls ≤ 0
2) The significance level is set at 0.01
3) The critical region is z ≤ ± 1.28
4) The test statistic
Z= p1-p2/ sqrt [pcqc( 1/n1+ 1/n2)]
Here p1= 397/768= 0.5169 and p2= 331/745=0.4429
pc = 397+331/768+745
pc= 0.4811
qc= 1-pc= 1-0.4811=0.5188
5) Calculations
Z= p1-p2/ sqrt [pcqc( 1/n1+ 1/n2)]
z= 0.5169-0.4429/√ 0.4811*0.5188( 1/768+ 1/745)
z= 2.82
6) Conclusion
Since the calculated value of z= 2.82 does not lie in the critical region the null hypothesis is accepted and it is concluded that the sample data support the authors' conclusion that the proportion of the country's boys who listen to music at high volume is greater than this proportion for the country's girls.
7)
The value of p is 0 .00233. The result is significant at p < 0.10.
ZABD and ZDBC are supplementary angles.
What is the measure of x?
X = [?]°
7D
110%
AK
>C
C С
B
Angles are not drawn to scale.
Enter
Answers
Answer:
Measure?
Step-by-step explanation:
Could u like explains more pls?
Answer:
x=70°
Step-by-step explanation:
x+110=180 linear pair
x=180-110=70
Find the slope of the line.