Answer:
[tex]\sqrt{128x^8y^3} = 8 x^4 y \sqrt{2y}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{128x^8y^3}[/tex] --- the complete expression
Required
The equivalent expression
We have:
[tex]\sqrt{128x^8y^3}[/tex]
Expand
[tex]\sqrt{128x^8y^3} = \sqrt{128* x^8 * y^3}[/tex]
Further expand
[tex]\sqrt{128x^8y^3} = \sqrt{64 * 2* x^8 * y^2 * y}[/tex]
Rewrite as:
[tex]\sqrt{128x^8y^3} = \sqrt{64 * x^8 * y^2* 2 * y}[/tex]
Split
[tex]\sqrt{128x^8y^3} = \sqrt{64 * x^8 * y^2} * \sqrt{2 * y}[/tex]
Express as:
[tex]\sqrt{128x^8y^3} = (64 * x^8 * y^2)^\frac{1}{2} * \sqrt{2y}[/tex]
Remove bracket
[tex]\sqrt{128x^8y^3} = (64)^\frac{1}{2} * (x^8)^\frac{1}{2} * (y^2)^\frac{1}{2} * \sqrt{2y}[/tex]
[tex]\sqrt{128x^8y^3} = 8 * x^\frac{8}{2} * y^\frac{2}{2} * \sqrt{2y}[/tex]
[tex]\sqrt{128x^8y^3} = 8 * x^4 * y * \sqrt{2y}[/tex]
[tex]\sqrt{128x^8y^3} = 8 x^4 y \sqrt{2y}[/tex]
a 40 foot ladder is leaning against a building and forms a 29.32° angle with the ground. How far away from the building is the base of the latter? Round your answer to the nearest hundred
9514 1404 393
Answer:
34.88 feet
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
We want to find the length of the side adjacent to the measured angle. The hypotenuse is the ladder length.
cos(29.32°) = distance/(40 ft)
distance = (40 ft)cos(29.32°) ≈ 34.876°
The base of the ladder is about 34.88 feet from the building.
_____
Additional comment
It extends about 19.59 feet up the side of the building.
Given the function f(x) = -5x + 2, find the range ofly for x = -1, 0, 1.
O 7, 2, -3
O 7, 2, 3
O-7, -2, 3
0-7, -2, -3
Answer:
A
Step-by-step explanation:
f(-1)=7, f(0)=2, f(1)=-3
The polynomial P is graphed.
5+
P
4+
3
→
-3
-2
-1
1
-2+
-3+
-4-
What is the remainder when P(x) is divided by (x + 2)?
Answer:
-4
Step-by-step explanation:
The remainder when P(x) is divided by (x + 2) is P(-2) which is - 4
I NEED HELP PLEASE!!
sine --> cosecant
csc(x) = 1/sin(x)
cosine --> secant
sec(x) = 1/cos(x)
tangent --> cotangent
cot(x) = 1/tan(x)
Correct Answer: A
Hope this helps!
what function represents exponential decay?
Answer:
There are two types of exponential functions: exponential growth and exponential decay. In the function f (x) = bx when b > 1, the function represents exponential growth. In the function f (x) = bx when 0 < b < 1, the function represents exponential decay.
Step-by-step explanation:
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:
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°.
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).
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)
Triangles ABC and DEF are similar triangles. What are the lengths of the unknown sides?
A)
DF = 39 cm; DE = 15 cm
B)
DF = 48 cm; DE = 52 cm
C)
DF = 65 cm; DE = 25 cm
D)
DF = 52 cm; DE = 48 cm
Answer:
D)
DF = 52
AB = 48
Step-by-step explanation:
Use the two lengths of sides already given.
Divide to find the scale factor:
20 / 5 = 4
Scale factor: 4
Now multiply to find the unknown sides:
13 × 4 = 52
12 × 4 = 48
DF = 52
AB = 48
Hope this helped.
Which of the following expressions is equal to tan205°?
tan55°
tan25°
tan25°
Answer:
the write answer to your question is tan 25 degree
Mr jones rolls a 6 sided cube mumbered 1,2,3,4,5,6, what is the probability he rolls a three.
Answer:1.5
Step-by-step explanation:
(-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
Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 27 dollars and a standard deviation of 9 dollars.
A. What proportion of the bank's Visa cardholders pay more than 29 dollars in interest?
B. What proportion of the bank's Visa cardholders pay more than 35 dollars in interest?
C. What proportion of the bank's Visa cardholders pay less than 14 dollars in interest?
D. What interest payment is exceeded by only 18% of the bank's Visa cardholders?
Answer:
a. 0.4129 = 41.29% of the bank's Visa cardholders pay more than 29 dollars in interest.
b. 0.1867 = 18.67% of the bank's Visa cardholders pay more than 35 dollars in interest.
c. 0.0742 = 7.42% of the bank's Visa cardholders pay less than 14 dollars in interest.
d. An interest payment of $35.2 is exceeded by only 18% of the bank's Visa cardholders.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 27 dollars and a standard deviation of 9 dollars.
This means that [tex]\mu = 27, \sigma = 9[/tex]
A. What proportion of the bank's Visa cardholders pay more than 29 dollars in interest?
This is 1 subtracted by the p-value of Z when X = 29, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{29 - 27}{9}[/tex]
[tex]Z = 0.22[/tex]
[tex]Z = 0.22[/tex] has a p-value of 0.5871.
1 - 0.5871 = 0.4129
0.4129 = 41.29% of the bank's Visa cardholders pay more than 29 dollars in interest.
B. What proportion of the bank's Visa cardholders pay more than 35 dollars in interest?
This is 1 subtracted by the p-value of Z when X = 35, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 27}{9}[/tex]
[tex]Z = 0.89[/tex]
[tex]Z = 0.89[/tex] has a p-value of 0.8133.
1 - 0.8133 = 0.1867
0.1867 = 18.67% of the bank's Visa cardholders pay more than 35 dollars in interest.
C. What proportion of the bank's Visa cardholders pay less than 14 dollars in interest?
This is the p-value of Z when X = 14. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14 - 27}{9}[/tex]
[tex]Z = -1.445[/tex]
[tex]Z = -1.445[/tex] has a p-value of 0.0742.
0.0742 = 7.42% of the bank's Visa cardholders pay less than 14 dollars in interest.
D. What interest payment is exceeded by only 18% of the bank's Visa cardholders?
This is the 100 - 18 = 82nd percentile, which is X when Z has a p-value of 0.82, so X when Z = 0.915.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.915 = \frac{X - 27}{9}[/tex]
[tex]X - 27 = 0.915*9[/tex]
[tex]X = 35.2[/tex]
An interest payment of $35.2 is exceeded by only 18% of the bank's Visa cardholders.
Kevin's supervisor, Jill, has asked for an update on today's sales, Jill is pretty busy moving back and forth between different store locations. How can Kevin most effectively deliver an update to her ? a) Call with a quick update Ob ) Send a detailed text message c ) Book a one-hour meeting for tomorrow morning d) Send a detailed email
Logan has $1.95 in dimes and quarters in his pocket. He has 2 more dimes than quarters. (Keep in mind that dimes are worth 10c and quarters 25c.)
1. Write an equation that will help you determine the number of quarters.
2. Solve the equation showing all your steps.
3. Tell how many quarters and dimes he has.
Answer:
17 dimes 1 quarter
Step-by-step explanation:
logan has 1.95
step by step explanation:
a dime can not be more than 10 c
and less than 10c
a quarter can not be more than 25c
and less than 25 c
so logan must have 17 dimes and 1 quarter
key = 1 dime = 10c, 1 quarter = 25c
$1.70 + 25c = $1.95
hope this helps!!
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 ^_^
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].
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
find the value of the trigonometric ratio. make sure to simplify the fraction if needed
Answer:
3/5
Step-by-step explanation:
sin=opp/hyp
sinc=24/40=3/5
Use the ratio of a 45-45-90triangle to solve for the variables. Make sure to simplify radicals. Leave your answers as radicals in simplest form.
9514 1404 393
Answer:
m = n = 5
Step-by-step explanation:
The side ratios in a 45°-45°-90° triangle are 1 : 1 : √2. That is, the hypotenuse is √2 times the side length. Here, the hypotenuse is 5√2, so the side length must be 5.
m = n = 5
SOMEONE PLS HELP!!!!
Determine if the function f is an exponential function. If so, identify the base. If not, why not? f(x) = 3x + 1
A) This is a polynomial.
B) The base is x + 1.
C) The base is 3.
D) This is not an exponential function because the variable is in the exponent position.
Answer:
Step-by-step explanation:
Is the function f(x) = 3x+1, f(x) = 3ˣ⁺¹, or f(x) = 3ˣ+1 ?
f(x) = 3x+1 is not an exponential function. It is a straight line.
f(x) = 3ˣ⁺¹ Is an exponential function. The base is 3.
f(x) = 3ˣ+1 is an exponential function. The base is 3.
A clothing manufacturer purchased 50 yd of cotton and 80 yd of wool for a total cost of $1,330. Another purchase, at the same prices, included 75 yd of cotton and 20 yd of wool for a total cost of $895. Find the cost per yard of the cotton and of the wool.
Answer:
The cotton is $9 per yard and the wool is $11 per yard
Step-by-step explanation:
Create a system of equations where c is the cost per yard for the cotton and w is the cost per yard for the wool.
50c + 80w = 1330
75c + 20w = 895
Solve by elimination by multiplying the bottom equation by -4:
50c + 80w = 1330
-300c - 80w = -3580
Add these together and solve for c:
-250c = -2250
c = 9
Plug in 9 as c into one of the equations, and solve for w:
50c + 80w = 1330
50(9) + 80w = 1330
450 + 80w = 1330
80w = 880
w = 11
The cotton is $9 per yard and the wool is $11 per yard.
Find the x- and y-intercept of the line
X+4y=36
Which equation is correct?
1
A. cos x =
sin a
1
B. tan x=
CSC 2
C. sec =
COS
1
D. cot 2 =
sec
SUBMIT
The requried secant function is the reciprocal of the cosine function, i.e., sec x = 1/cos x. Option C is correct.
What are trig ratios?If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
The correct equation is option C: sec x = 1/cos x.
This is because the secant function is the reciprocal of the cosine function, i.e., sec x = 1/cos x.
Learn more about trig ratios here:
https://brainly.com/question/14977354
#SPJ7
[tex]-3x^{2} -4y^{2} -z^{2}+6xy-6x+4z[/tex]
Solve for x
X-8 = -10
A) X = 2
B) X = -2
C) X = 18
D) X = -18
Answer:
x=–2
Step-by-step explanation:
x-8=-10
x=-10-8
x=–2
Answer:
-8= -10
, = -10+8
, = -2
which shape is both a parallelogoram and a rhombus
Answer:
A square can be defined as a rhombus which is also a rectangle and a parellelogram with four congruent sides and four right angles
I hope this helps
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
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
