Answer:
10/16=5/8
6+6+4=16
The probability is 5/8
Three numbers are in the ratio of 1:2:4. If 3 is added to the first and 8 is subtracted from the third, the new numbers will be the first and third terms of an A.P., whose second term is the second number. Find the original numbers.
9514 1404 393
Answer:
5, 10, 20
Step-by-step explanation:
Suppose the three numbers are x, 2x, and 4x. Then they have the required ratios. After the transformation, we have ...
((x+3) +(4x -8))/2 = 2x . . . . . 2nd term is average of 1st and 3rd
5x -5 = 4x ⇒ x = 5
The original numbers are 5, 10, 20.
_____
After the adjustment, the arithmetic sequence is 8, 10, 12.
Find the arclength of the curve r(t) = ⟨ 10sqrt(2)t , e^(10t) , e^(−10t)⟩, 0≤t≤1
Answer:
[tex]\displaystyle AL = 2sinh(10)[/tex]
General Formulas and Concepts:
Pre-Calculus
Hyperbolic FunctionsCalculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Exponential Differentiation
Integration
IntegralsIntegration Constant CDefinite IntegralsParametric Integration
Vector Value Functions
Vector IntegrationArc Length Formula [Vector]: [tex]\displaystyle AL = \int\limits^b_a {\sqrt{[i'(t)]^2 + [j'(t)]^2 + [k'(t)]^2}} \, dt[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \vec{r}(t) = <10\sqrt{2}t , e^{10t} , e^{-10t} >[/tex]
Interval [0, 1]
Step 2: Find Arclength
Rewrite vector value function: [tex]\displaystyle r(t) = 10\sqrt{2}t \textbf i + e^{10t} \textbf j + e^{-10t} \textbf k[/tex]Substitute in variables [Arc Length Formula - Vector]: [tex]\displaystyle AL = \int\limits^1_0 {\sqrt{\bigg[\frac{d}{dt}[10\sqrt{2}t \textbf i]\bigg]^2 + \bigg[\frac{d}{dt}[e^{10t} \textbf j]\bigg]^2 + \bigg[\frac{d}{dt}[e^{-10t} \textbf k ]\bigg]^2}} \, dt[/tex][Integrand] Differentiate [Respective Differentiation Rules]: [tex]\displaystyle AL = \int\limits^1_0 {\sqrt{[10\sqrt{2} \textbf i]^2 + [10e^{10t} \textbf j]^2 + [-10e^{-10t} \textbf k]^2}} \, dt[/tex][Integrand] Simplify: [tex]\displaystyle AL = \int\limits^1_0 {\sqrt{200 \textbf i + 100e^{20x} \textbf j + 100e^{-20x} \textbf k}} \, dt[/tex][Integral] Evaluate: [tex]\displaystyle AL = 2sinh(10)[/tex]Topic: AP Calculus BC (Calculus I + II)
Unit: Vector Value Functions
Book: College Calculus 10e
Bearings And Vectors • The bearing of X from Y is 045 and the bearing of Z from Yis 145, where X, Y and Z are three points in the plane. If Y is equidistant from X and Z, find the bearing of Z from X.
9514 1404 393
Answer:
185°
Step-by-step explanation:
The triangle internal angle at Y is 145° -45° = 100°. Since the triangle is isosceles, the internal angles at X and Z are both (180° -100°)/2 = 40°. Then the bearing of Z from X is the bearing of Y from X less the internal angle at X:
(45° +180°) -40° = 185°.
Z from X is 185°.
10x^3 - 25x^2 + 20
How to factor this
5(2x^2-x-2)(x-2)
Step-by-step
Answer: [tex]5(\frac{10x^3}{5}+\frac{-25x^2}{5}+\frac{20}{5}) \\\\5(2x^3-5x^2+4)\\\\5(2x^2-x-2)(x-2)[/tex]
If y varies directly as x, and x = 4 when y = 20, find y when x = 18.
Step-by-step explanation:
y=Kx
20=4k
k=5
when x=18
y=18 x 5
y=90
CAN YOU GUYS PLEASE HELP ME? THANK YOU!
Answer:
60
step by step explanitation
Which two statements are true
In how many ways can 10 people be divided into three groups with 2, 3, and 5 people respectively?
Answer:
2100
Step-by-step explanation:
In how many ways can a group of 10 people be divided into three groups consisting of 2,3, and 5 people?
First, you need to choose 4 people to fill the first group.
The number of ways is (104) which equals to 210.
Then, pick 3 more people out of the remaining 6 to be in the second group. And then, pick 3 more out of the remaining 3.
However, we need to divide it by 2, since we don’t really care on the order of selection of group.
(63)(33)/2=10
So, there are 210 x 10 = 2100 ways
Answer:
hmmm I read JeremyBrooks answer... I think that it might be different...
i think it is 2520
of the 10 you first choose 2
10 choose 2 = 45 ways
in each of the 45 "chooses" you now
pick a group of 3 of the 8 left
8 choose 3 = that is 56
of the five people left you choose 5
5 choose 5 = 1
so the possibilities are 45*56 * 1 = 2520
Step-by-step explanation:
Help me plz plz help me with this question
Answer:
6 97/100 bags
Step-by-step explanation:
4 1/10 ⋅ 1 7/10 = ?
41/10 ⋅ 17/10 = 697/100
697/100 = 6 97/100
6 97/100 bags
Answer:
697/100 bags
or
6 97/100 bags
Step-by-step explanation:
it is fractions. just plain and simple.
when you eat a pizza slice, it is usually one of 8 slices that make the whole pizza. 1/8 or one 8th. meaning that the whole thing is 8/8 or eight 8ths.
the same for 10ths or any other fractions.
4 1/10 bags = 41/10 bags
1 7/10 times = 17/10 times
and now we multiply fractions, as 17/10 times is similar to 2 times or 3 times something - we multiply by this factor.
41/10 × 17/10
as we learned in early elementary school : numerators (top part of the fraction) are multiplied with each other, and denominators (bottom part) are multiplied with each other. and then we simplify the result as much as possible.
41/10 × 17/10 = (41×17) / (10×10) = 697/100
no simplification is possible, sadly.
but that means he used almost 7 bags of hot dog buns.
exactly 6 full bags and 97/100 of the 7th bag.
so, either
697/100 bags
or
6 97/100 bags
or as alternative (not wanted here in this example but just FYI)
6.97 bags
Colin stacks 3 snowballs on top of each other to make a snowman. The snowballs are \dfrac7{10} \text{ meter} 10 7 meterstart fraction, 7, divided by, 10, end fraction, start text, space, m, e, t, e, r, end text, \dfrac12 \text{ meter} 2 1 meterstart fraction, 1, divided by, 2, end fraction, start text, space, m, e, t, e, r, end text, and 38 \text{ centimeters}38 centimeters38, start text, space, c, e, n, t, i, m, e, t, e, r, s, end text tall. What is the total height of the snowman in centimeters?
Answer:
[tex]Total = 158cm[/tex]
Step-by-step explanation:
Given
[tex]x: \dfrac7{10}m, \dfrac12m,38cm[/tex]
See comment
Required
The total height
This is calculated as:
[tex]Total = \sum x[/tex]
So, we have:
[tex]Total = \dfrac7{10}m+ \dfrac12m+38cm[/tex]
Express m as cm
[tex]Total = \dfrac7{10}cm * 100+ \dfrac12cm * 100+38cm[/tex]
[tex]Total = 70cm + 50cm + 38cm[/tex]
Take LCM
[tex]Total = 158cm[/tex]
Answer: ♔158 centimeters.☯ Trust me it is correct. ヾ(•ω•`)o
If f (x) = 8X, then f (3) =
O 24
O 64
O 512
O 4,096
What is the measure of 7 shown in the diagram below?
110°
O A. 74.5°
B. 32°
X
O C. 71°
Z
D. 35.5°
Answer:
c
Step-by-step explanation:
Answer:
the correct choice is B
Step-by-step explanation:
Could you guys answer this for me by 12am!
Answer:
-3
Step-by-step explanation:
Slope is y2 - y1 / x1 - x2.
So, let's take two random points; I have chosen (0, 3) and (2, -3).
Excellent. Let's calculate the slope.
Slope = (-3 - 3) / (2 - 0) = -6 / 2 = -3.
Hope this helps!
An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 127 brakes using Compound 1 yields an average brake life of 42,814 miles. A sample of 163 brakes using Compound 2 yields an average brake life of 37,197 miles. Assume that the population standard deviation for Compound 1 is 1819 miles, while the population standard deviation for Compound 2 is 1401 miles. Determine the 98% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.
Step 1 of 3 is Point estimate so 42,814 - 37,197 = 5,617
Step 2 of 3 :
Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.
Step 3 of 3:
Construct the 98% confidence interval. Round your answers to the nearest whole number. (lower and upper endpoint)
Answer:
The point estimate is 5,617.
The margin of error of a confidence interval for the difference between the two population means is 454.18386 .
The 98% confidence interval for the difference between the two population means is (5163, 6071).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Compound 1:
127 brakes, average brake life of 42,814 miles, population standard deviation of 1819 miles. This means that:
[tex]\mu_1 = 42814[/tex]
[tex]s_1 = \frac{1819}{\sqrt{127}} = 161.41[/tex]
Compound 2:
163 brakes, average brake life of 37,197 miles, population standard deviation of 1401 miles. This means that:
[tex]\mu_2 = 37197[/tex]
[tex]s_2 = \frac{1401}{\sqrt{163}} = 109.73[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 42814 - 37197 = 5617[/tex]
The point estimate is 5,617.
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{161.41^2 + 109.73^2} = 195.18[/tex]
Confidence interval
The confidence interval is:
[tex]\mu \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = zs[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
Margin of error:
[tex]M = zs = 195.18*2.327 = 454.18386 [/tex]
The margin of error of a confidence interval for the difference between the two population means is 454.18386 .
For the confidence interval, as we round to the nearest whole number, we round it 454. So
The lower bound of the interval is:
[tex]\mu - zs = \mu - M = 5617 - 454 = 5163[/tex]
The upper bound of the interval is:
[tex]\mu + zs = \mu + M = 5617 + 454 = 6071[/tex]
The 98% confidence interval for the difference between the two population means is (5163, 6071).
the diameter of a circle is 8 cm what is its area?
A = πr^2 and d = 2r.
So r = 8/2 = 4 cm.
Now use the first formula
A = π(4 cm)^2 = 50.265 cm^2
An amount of $700 was invested at 7% for 7 months what is the interest? Round your answer to your nearest cent.
Answer:
$343
step by step explanation: interest=PRT/100
:I=700×7×7/100
:I=$343.
Given:
Principal, P = $700
Rate of interest, R = 7% = 0.07
Time period, T = 7 months (it is considered as a monthly investment)
∴ Simple Interest, SI = PRT
SI = 700 × 0.07 × 7
SI = $343
What is straightforward interest and model?
Straightforward Simple Interest is the strategy for working out the premium sum for a specific chief measure of cash at some pace of revenue. For instance, when an individual takes credit of Rs. 5000, at a pace of 10 p.a. for a very long time, the individual's advantage for quite some time will be S.I. on the acquired cash.
Straightforward recipes generally start with an equivalent sign (=), trailed by constants that are numeric qualities and computation administrators like in addition to (+), short (- ), asterisk(*), or forward cut (/) signs.
Learn more about Simple Interest here
https://brainly.com/question/2294792
#SPJ2
Can someone let me know if this is right? Show work.
Answer:
I'd be estimatining the answer between 29-31.
Draw a line of best fit. It will be easier to make the estimation.
8x=3x²-1 plz help me show your work
Answer:
Step-by-step explanation:
3 times 8= 24 • 24 = 576 - 1 =575
or
3•8=24•2=48-1=47
not sure
Answer:
The answer is [tex]x=\frac{4(+-)\sqrt{19} }{3}[/tex] in exact form or [tex]x=2.7863[/tex], [tex]x=-0.1196[/tex] in decimal form.
Step-by-step explanation:
To solve this equation, start by moving all expression to the left side of the equation, which will include subtracting [tex]3x^2[/tex] and adding 1 to both sides of the equation. The equation will look like [tex]8x-3x^2+1=0[/tex].
Then, use the quadratic formula to find the solutions to the equation. The quadratic formula looks like [tex]\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex].
For this problem, the quadratic variables are as follows:
[tex]a=-3\\b=8\\c=1[/tex]
The next step is to substitute the values [tex]a=-3[/tex], [tex]b=8[/tex], and [tex]c=1[/tex] into the quadratic formula and solve for x. The quadratic formula will look like [tex]\frac{-8(+-)\sqrt{8^2-4(-3)(1)} }{2*-3}[/tex]. To simplify the equation, start by simplifying the numerator, which will look like [tex]x=\frac{-8(+-)2\sqrt{19} }{2*-3}[/tex]. Then, multiply 2 by -3 and simplify the equation, which will look like [tex]x=\frac{4(+-)\sqrt{19} }{3}[/tex]. The final answer is [tex]x=\frac{4(+-)\sqrt{19} }{3}[/tex] in exact form. In decimal form, the final answer is [tex]x=2.7863[/tex], [tex]x=-0.1196[/tex].
A turboprop plane flying with the wind flew 1,200 mi in 4 h. Flying against the wind, the plane required 5 h to travel the same distance. Find the rate of the wind and the rate of the plane in calm air.
Answer:
30 and 270 respectively
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*4=1200 and (x-y)*5=1200. Solving it, we get x=270 and y=30
Use the given conditions to write an equation for each line in point-slope form and slope-intercept form.
Slope= 1/3, passing through the origin.
Answer:
y = 1/3x y - 0 = 1/3 (x - 0)
Step-by-step explanation:
slope intercept: y = 1/3x
point slope: y - 0 = 1/3 (x - 0)
Samuel had 12 red marbles , 15 blue marbles , and 13 green marbles . Which fraction represents the number of red marbles he has
Answer:
12/40 or simplified it would be 3/10
Step-by-step explanation:
Please answer I’m struggling
Step-by-step explanation:
Question 7.[tex] \frac{{(3 + u)}^{2} }{8} [/tex]
[When u = 5]
[tex] = \frac{{(3 + 5)}^{2} }{8} [/tex]
[tex] = \frac{ {(8)}^{2} }{8} [/tex]
[tex] = \frac{8 \times 8}{8} [/tex]
= 8 (Ans)
Question 8.-2(a - 7)
(Using Distributive property)
= - 2 × a -2 × (-7)
= -2a + 14 (Ans)
Answer:
7. 8
8. -2a+14
Step-by-step explanation:
(Excuse this form of the expression)
7.
u = 5
(3 + u)²
---------
8
Plug in
(3 + 5)²
---------
8
(8)²
---------
8
64
---- = 8
8
8.
-2(a - 7)
Multiply -2 with each number in the parenthesis
-2a + 14
Find the value of x round to the nearest tenth.
9514 1404 393
Answer:
117.9°
Step-by-step explanation:
Solving the Law of Cosines equation for C, we get ...
C = arccos((a² +b² -c²)/(2ab))
Filling in the values from the figure, we find the angle X to be ...
X = arccos((y² +z² -x²)/(2yz)) = arccos((55² +50² -90²)/(2·55·50))
X = arccos(-2575/5500) ≈ 117.9°
Which three relations are functions? Select all correct answers
Answer:
the 3rd, 4th, and 5th one
Step-by-step explanation:
Answer:
Step-by-step explanation:
:)
Can someone do #4 and #5
Answer:
First, find two points on the graph:
(x₁, y₁) = (0, 2)(x₂, y₂) = (2, 8)Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{8-2}{2-0} =\frac{6}{2}=3[/tex]
16 + (-3) = 16 - 3 = 13
9)[{(-90) + (-5)}2-10].2 I need help ASAP please please due Monday show work
Ans; [{(-90) + (-5)} 2-10] ×2 —> [{-90-5}2-10]×2 —> [{-95}2-10]×2 —> [-190-10]×2 —> [–200] ×2 —> = –400
I hope I helped you ^_^
Please help!
Answers
A,B,C and D
The information is already in the chart
( ignore the charts below question 2.)
I believe the answer is B!
Hope this helped you! Please follow my account, thanks!
(-1)×(-1)×(-1)×(2m+1) times where m is a natural number,is equal to?
1. 1
2.-1
3.1 or-1
4.None
Answer:
(2). -1
Step-by-step explanation:
The given parameter can be represented as:
[tex](-1)^{2m + 1}[/tex]
See comment for correct question
Required
The end result
From the question, we understand that m is a natural number
This means that:
[tex]2m + 1 \to[/tex] odd number
So:
[tex](-1)^{2m + 1} = -1[/tex] --- i.e. -1 to the power of an odd number will give -1
Hence; (2) is correct
g (x) = f ( x + 1).
graph
The two rectangles have the same perimeters, find the value of x.
Answer:
x = 8ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Answer:
x=4
Step-by-step explanation:
2x-2+x+2x-2+x=3+7+3+7
6x-4=20
6x=24
x=4
