Answer: [tex]8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]
Step-by-step explanation:
Consider [tex]\int \cos(x) (8+7 \sin^2(x)) \, dx[/tex]
Substitute t= sinx
then dt = cos x dx
[tex]\int \cos(x) (8+7 \sin^2(x)) \, dx = \int (8+7t^2)dt\\\\ =8t+7(\dfrac{t^3}{3})+C[/tex]
[tex][\int x^ndx=\dfrac{x^{n+1}}{n+1}+C][/tex]
[tex]=8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]
Hence, [tex]\int \cos(x) (8+7 \sin^2(x)) \, dx=8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]
To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35models of Make A and 35 models of Make B. The mean braking distance for Make A is 41feet. Assume the population standard deviation is 4.6 feet.The mean braking distance for Make B is 45feet. Assume the population standard deviation is 4.3 feet.At alphaequals0.10,can the engineer support the claim that the mean braking distances are different for the two makes of automobiles
Answer:
There is sufficient evidence to support the claim.
Step-by-step explanation:
Given
[tex]\alpha = 0.10[/tex]
Make A
[tex]\bar x_1 = 41[/tex]
[tex]\sigma_1= 4.6[/tex]
[tex]n = 35[/tex]
Make B
[tex]\bar x_2 = 45[/tex]
[tex]\sigma_2 = 4.3[/tex]
[tex]n = 35[/tex]
First, we state the null and alternate hypothesis
[tex]H_0 : \mu_1 = \mu_2[/tex]
[tex]H_1 : \mu_1 \ne \mu_2[/tex]
Next, calculate test statistic:
[tex]z = \frac{(\bar x_1 - \bar x_2)-(\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}[/tex]
[tex]z = \frac{(41- 45)-0}{\sqrt{\frac{4.6^2}{35}+\frac{4.3^2}{35}}}[/tex]
[tex]z = \frac{-4}{\sqrt{0.6046+0.5283}}[/tex]
[tex]z = \frac{-4}{\sqrt{1.1329}}[/tex]
[tex]z = \frac{-4}{1.0643}[/tex]
[tex]z = -3.7583[/tex]
The critical value at [tex]\alpha = 0.10[/tex] is: [tex]\±1.282[/tex]
[tex]-3.7583 < -1.282[/tex]
So, we reject [tex]H_0[/tex]
This implies that; there is sufficient evidence to support the claim.
Maurice Luken deposited $3,021 in a savings account that paid 5.5 percent interest
compounded daily. How much interest did he earn in 31 days?
9514 1404 393
Answer:
$14.14
Step-by-step explanation:
The amount of interest earned is ...
I = P((1 +r/365)^n -1) . . . . interest on principal P at annual rate r compounded daily for n days
I = 3021(1 +0.055/365)^31 -1) ≈ 14.14
$14.14 in interest is earned in 31 days.
True or False: x is the same/equal to 1x
Answer:
Yes
Step-by-step explanation:
Because you're multiplying by 1 so it stays the same value
What is the total surface of the pyramid in square centimeters? A: 17.5 B:70 C:140 D:35
Answer:
C:140
Step-by-step explanation:
because 7 x 5 in the tiangle.
If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of two particles are given by the vector functions for t 0. Do the particles collide? If they collide find t. If not enter NONE.
r1(t) = t^2, 8t − 15, t^2
r2(t) = 11t − 30, t^2, 13t − 40
t=
Answer:
Step-by-step explanation:
[tex]r_1(t) = < t^2 , 8t-15,t^2> \\ \\ r_2(t) = < 11t-30, \ t^2 , \ 13t-40> \\ \\ at \ r_1 = r_2 \\ \\ t^2 = 11t - 30 , \ \ \ \ \ \ \ \ \ \ \ \ 8t - 15 = t^2 , \ \ \ \ \ \ \ \ \ t^2 = 13t -40 \\ \\ t^2 - 11t + 30\ \ \ \ \ \ \ \ \ \ \ \ t^2 -8t + 15 , \ \ \ \ \ \ \ \ \ \ \ \ t^2 -13t + 40 \\ \\ t^2 -8t-3t + 30=0 \ \ \ \ \ \ t^2 - 2t -4t + 15=0 \ \ \ \ \ \ t^2 - 1t - 13t + 40 =0[/tex]
[tex](t-6)(t-5) \ \ \ \ \ \ \ \ \ \ \ (t-5)(t-3) \ \ \ \ \ \ \ \ \ \ \ (t-5)(t-8)[/tex]
[tex]\mathbf{The \ common \ value \ of \ t \ = \ 5}[/tex]
Please help, I’ve looked everywhere and haven’t found any answers!
Answer:
m = 4 + (2n)/(3)
Step-by-step explanation:
Move all terms that contain m to the right side and solve it.
9
On a field trip, there are 3 adults for every 45 students. Which graph models a relationship with
the same unit rate?
А
с
101
9
10
9
8
7
7
6
5
4
b
6.
5
4
3
2
3
2
1
0
30
60
90 120 150
30
60 90 120 156
B
D
10T
9
8
10
9
6
5
Answer:
I believe the answer is C
Definition the value of a number regardless of its sign Definition
What is the answer to
2x squared?
Answer:
it’s just 2x^2
it’s not factorable
Can someone please help meeee I’m desperateeee
Answer:
Step-by-step explanation:
1)(-3x+10)(50-x)=180
-4x+60=180
-4x=120
x=-30
2)6x+2+2x=90
8x=88
x=11
larger angle: 68°
3) a=3x°
4)(7x-5)=-2x+22
9x=27
x=3
DBE=16°
5)(x-39)=2x-59)
x=20
The number line is 0 to 1 true or false 2/8 is close to 0
Answer:
True
Step-by-step explanation:
from the scale 0-1, 2/8 is closer to 0 because you round 2 down to 0, which gives you 0.
A container has 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, put it back in the container and draw another marble. What is the probability of pulling out a yellow marble, followed by a blue marble?
The square pyramid has a base area of 144 square centimeters and a height of 12 centimeters. Find the volume.
Step-by-step explanation:
the answer is 576 cubic centimetre.
Answer:
Its 576 cubic centimeters
Step-by-step explanation:
4
Which of the following is a function?
А
B
C
D
Answer:
B)
Step-by-step explanation:
A function is when every input has one output.
Easiest way is to do the "vertical line test" and "horizonal line test."
Basically you draw a vertical line and a horizontal line.
If either line passes through more than one point, then it is not a function.
The only one that passes them is B, the line.
Answer:
B
Step-by-step explanation:
A function is when every input has one output.
Easiest way is to do the "vertical line test" and "horizonal line test."
Basically you draw a vertical line and a horizontal line.
If either line passes through more than one point, then it is not a function.
The only one that passes them is B, the line.
POV: you procrasiant a lot and dont pay attention on online school and ur failing ur classes, so now ur on brainly, just me?
also someone pls answer my other question will make brainliest!
Answer:
its true i cant pay attention in class cuz its boring but im
not failing it thank god
Answer:
sameeee but im currently not failing, lets hope it stays like that ;-;
Step-by-step explanation:
im smart
Stuck on this problem, can't find 3x
Answer:
x equals 10, angle measure is 30°
Step-by-step explanation:
By using the Vertical Angles Theorem which states that opposite angles formed by 2 intersecting lines are congruent we can find that the measure of the angle with 3x is equal to the measure of it's opposite angle or 30°. Using this we can make an equation that can find us our answer.
3x = 30
Divide both sides by 3
3x/3 = 30/3
x = 10
What is the value of 8+(7+1)^2÷4(1/2)^4
Will Mark Brainliest
^=exponents
Answer:
264
Step-by-step explanation:
8+(7+1)^2 / 4(1/2)^4
8+ 8^2 / 4(1/2)^4
8+64/4(1/16)
8+64 / 1/4
8 + (64*4)
8+256
264
tell what place the digit is in for the following number 14,632.708
4
0
7
Answer:
4 is in the one thousands place. The 0 is in the hundredths place. The 7 is in the tenths place.
For each ordered pair determine if it is a solution to 7x+5y=9
(-4,-3)
(-3,6)
(5,0)
(2,-1)
Figure A is a scale image of Figure B. Figure A: 7.2 , 4. Figure B: 3 , x. What is the value of x
Answer: 5.4
Step-by-step explanation:
Answer:
5.2
Step-by-step explanation:
what is the simplified expression of 6h +(-7.1d)-15+4d-3.4h
Answer:
6h+ (-7.1d) -15+4d-3.4h
Step-by-step explanation:
Find cos (P)
Q
74
70
P
24
R
A.
37
12
В.
35
37
C.
12
Answer:
cos P = 71.09
Step-by-step explanation:
cos = [tex]\frac{adajcent}{hypotenuse}[/tex]
cos P = [tex]\frac{24}{74}[/tex]
cos P = 0.324
cos-1 of 0.324 is 71.09
cos P = 71.09
Kylee bought a backpack at Tilly's for $32. The same backpack is on sale today for $24. What is the percent
of change? Round your answer to the nearest tenth.
Answer:
25
Step-by-step explanation:
PLEASE HELP
determine the intercepts of the line
x intercept (__ , __)
y intercept (__ , __)
Answer:
i think y=2 and x=-7
Step-by-step explanation:
A researcher found that 55% of families in the United States have one child under the age of 21, 22% have two children under the age of 21, 15% have three children under the age of 21, 5% have 4 children under the age of 21and 3% have 5 or more children under the age of 21. If a family is selected at random, what is the probability the family has at least 3 children under the age of 21? (Express your answer as a percent, Please include the % symbol.)
Answer:
23% probability the family has at least 3 children under the age of 21.
Step-by-step explanation:
If a family is selected at random, what is the probability the family has at least 3 children under the age of 21?
15% have three children under the age of 21
5% have 4 children under the age of 21
3% have 5 or more children under the age of 21.
So:
15% + 5% + 3% = 23%
23% probability the family has at least 3 children under the age of 21.
Alice has $90 to spend on
new clothes. She wants to buy
some shirts for $20 each. If
she has a coupon for $10 off
her total purchase, how many
shirts can she buy?
Answer:
5
step by step explanation:
if she gets $10 off of her purchase that means she would have a little extra money to another shirt
In ΔGHI, i = 64 inches, g = 91 inches and ∠H=134°. Find the length of h, to the nearest inch.
Answer:
143
Step-by-step explanation:
delta math
The length of h, to the nearest inch. is 57.4 inch.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
Here, given that,
In ΔGHI, i = 64 inches, g = 91 inches and ∠H=134°
Now. we know that,
a sinA =b sinB =c sinC
We get,
length of h = 57.4 inch.
hence, The length of h, to the nearest inch. is 57.4 inch.
To learn more on triangle click:
brainly.com/question/29126067
#SPJ2
A rock is thrown upward from the top of a high cliff overlooking the ocean at a speed of 96 feet per second . The rock's height above ocean can be modeled by the equation H(t) = - 16t ^ 2 + 96t + 112 . How long will it take seconds for the rock to hit the ocean? Do not include units in your answer.
Answer:
7
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
In this question:
The height of the rock after t seconds is given by the following equation:
[tex]H(t) = -16t^2 + 96t + 112[/tex]
How long will it take in seconds for the rock to hit the ocean?
This is t for which:
[tex]H(t) = 0[/tex]
So
[tex]-16t^2 + 96t + 112 = 0[/tex]
Simplifying by -16
[tex]t^2 - 6t - 7 = 0[/tex]
So a quadratic equation with [tex]a = 1, b = -6, c = -7[/tex]
[tex]\Delta = b^{2} - 4ac = (-6)^2 - 4*1*(-7) = 36 + 28 = 64[/tex]
[tex]t_{1} = \frac{-(-6) + \sqrt{64}}{2*1} = 7[/tex]
[tex]t_{2} = \frac{-(-6) - \sqrt{64}}{2*1} = -1[/tex]
Since time is a positive measure, it will take 6 seconds for the rock to hit the ocean, and the answer is 7.
which set of measurements would NOT creat a triangle?
A) 3in,8in,6in
B) 14in,6in,20in
C)11in,12in,22in
D)9in,8in,16in
Combine like terms
x + 10x-30= -8
Answer: x=2
Isolate the variable by dividing each side by the factors that don't contain variables.