Answer:
8n x n x n x n x n x n x n
Step-by-step explanation:
(2n^2)^3 = 8n^ 6
Now just write "n" 6 times and there you go
The given expression without exponents can be written as 8×n×n×n×n×n×n.
The given expression is (2n²)³.
We need to write the given expression without exponents.
What is an exponent?The exponent of a number shows how many times the number is multiplied by itself. For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times.
Now, the given expression can be simplified as follows:
(2n²)³=2³×(n²)³
=2×2×2×[tex]n^{6}[/tex] (∵[tex](a^{m}) ^{n}=a^{m\times n}[/tex])
=8×n×n×n×n×n×n
Therefore, the given expression without exponents can be written as 8×n×n×n×n×n×n.
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A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars form this company have an average gas mileage of 25.5 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set?
Answer:
[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]
The degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]
Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense
Step-by-step explanation:
Information given
[tex]\bar X=25.5[/tex] represent the sample mean
[tex]s=1[/tex] represent the sample standard deviation
[tex]n=8[/tex] sample size
[tex]\mu_o =26[/tex] represent the value to verify
[tex]\alpha=0.06[/tex] represent the significance level
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Hypothesis to est
We want to test if the true mean is at least 26 mpg, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 25.5[/tex]
Alternative hypothesis:[tex]\mu < 25.5[/tex]
The statistic for this case is given by;
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]
The degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]
Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense
Suppose that a large mixing tank initially holds 100 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min. If the concentration of the solution entering is 4 lb/gal, determine a differential equation (in lb/min) for the amount of salt A(t) (in lb) in the tank at time t > 0. (Use A for A(t).)
Answer:
dA/dt = 12 - 2A/(100 + t)
Step-by-step explanation:
The differential equation of this problem is;
dA/dt = R_in - R_out
Where;
R_in is the rate at which salt enters
R_out is the rate at which salt exits
R_in = (concentration of salt in inflow) × (input rate of brine)
We are given;
Concentration of salt in inflow = 4 lb/gal
Input rate of brine = 3 gal/min
Thus;
R_in = 4 × 3 = 12 lb/min
Due to the fact that solution is pumped out at a slower rate, thus it is accumulating at the rate of (3 - 2)gal/min = 1 gal/min
So, after t minutes, there will be (100 + t) gallons in the tank
Therefore;
R_out = (concentration of salt in outflow) × (output rate of brine)
R_out = [A(t)/(100 + t)]lb/gal × 2 gal/min
R_out = 2A(t)/(100 + t) lb/min
So, we substitute the values of R_in and R_out into the Differential equation to get;
dA/dt = 12 - 2A(t)/(100 + t)
Since we are to use A foe A(t), thus the Differential equation is now;
dA/dt = 12 - 2A/(100 + t)
If y = x² + 2x,
find the value of y when x = 5
_____________________________
Hey!!
Solution,
X=5
Now,
y=x^2+2x
=(5)^2+2*5
=25+10
= 35
So the value of y is 35
hope it helps
Good luck on your assignment
___________________________
For the given equation y = x² + 2x, the value of y when x = 5 is, 35
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
An equation, y = x² + 2x
The value of y when x is equal to 5 = ?
after putting value of x in a equation
⇒ y = 5² + 2 × 5
⇒ y = 25 + 10
⇒ y = 35
Hence, the value of y is 35
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The sum of one and the product of 4 and a number x
Answer:
1 + 4x
Step-by-step explanation:
Let's break this down.
"The sum of one" means that something is being added to the number one:
1 +
"and" whatever comes after the word 'and' will be added to the number one
"the product of 4 and a number x" this means that the number four and the variable x are being multiplied:
4x
Put it together:
1 + 4x
Therefore, the expression is 1 + 4x.
What is the area of a rectangle with a base of 23 feet and a height of 6 feet
Answer:
Step-by-step explanation:
Area of rectangle = l × b
= 23 × 6
= 138 feet
hope this helps
plz mark it as brainliest!!!!!!!
What is the indicated missing angle can someone pls help me
Answer:
30
Step-by-step explanation:
Since this is a right triangle, we can use a trig function
cos theta = adjacent/ hypotenuse
cos ? = 52/ 60
Take the inverse cos of each side
cos ^ -1 cos ? = cos ^ -1 ( 52/60)
? =29.92643487
To the nearest degree
? = 30
[tex]answer \\ 30 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
find five rational numbers between ? explain please
Answer:
1.5, 6, 24.7, 384, 404.4, 1,980Step-by-step explanation:
Rational numbers are the result of dividing two integers. Intergers cannot be fractions. So 1.5 is rational but 3/2 is not.
Five rational numbers: 1.5, 6, 24.7, 384, 404.4, 1,980
I'm always happy to help :)
Shanda has 14.7 yards of fabric remaining after
using 8.1 yards to make pillows. How many yards
of fabric did Shanda have before making the
pillows?
Answer:
1-2 yards
Step-by-step explanation:
For most decorative throw pillows you will need 1-2 yards , depending on the size and details you choose to include
1. Ryan budgets $35 a week for lunch for 5 days. What
is his average lunch expense each day?
Answer: $7
Step-by-step explanation:
35/ 5 = 7
Answer:
$7
Step-by-step explanation:
Bc/ 35/5=7
if you flip three fair coins, what is the probability that you’ll get a head on the first flip, a tail on the second flip and another head on the third flip?
Answer: The probability if getting a head on the first flip is 1/2 or 50 percent,the probability of getting a tail on the second flip is also 1/2 and the probability of getting another head on the third flip is 1/2.
Step-by-step explanation:
Answer:
3/8
Step-by-step explanation:
A survey taken in a large statistics class contained the question: "What's the fastest you have driven a car (in miles per hour)?" The five-number summary for the 87 males surveyed is: min = 55, Q1 = 95, Median = 110, Q3 = 120, Max = 155 Should the largest observation in this data set be classified as an outlier? No Yes
Answer:
NO
Step-by-step explanation:
To find out which observation to classify as an outlier, whether the largest or not, a very good approach or way to do this is to apply the 1.5(IQR) rule.
According to the rule, for finding the largest observation in the data that can be classified as an outlier, we would use the formula = Q3 + 1.5(IQR).
Q3 = 120
IQR = Q3 - Q1 = 120 - 95 = 25
Lets's plug these values into Q3 + 1.5(IQR)
We have,
120 + 1.5(25)
= 157.5
Since our max in the observation is given as 155, the largest observation in the data set cannot be set as an outlier because 157.5 which we got from our calculation is higher than the max value we have in the data set.
Our answer is NO.
However, the smallest observation should be set as outlier because:
Q1 - 1.5(IQR) = 95 - (1.5*25) = 57.5, which gives us an outlier that falls within our data range.
Mr. Azu invested an amount at rate of 12% per annum and invested another amount, 580 ghana cedis more than the first at 14% . if Mr. Azu had total accumulated amount of 2,358.60, how much was his total investment?
Answer:
2082.12 was the total invested
Step-by-step explanation:
Let x represent the amount invested at 14%. Then the amount invested at 12% was (x-580). The total accumulated amount was ...
112%(x -580) +114%(x) = 2358.60
2.26x -649.60 = 2358.60
2.26x = 3008.20 . . . add 649.60
x = 1331.06 . . . . . . divide by 2.26
x -580 = 751.06
The total invested was 1331.06 +751.06 = 2082.12 cedis.
__
Check
The investment at 12% was 751.06, so the accumulated amount of that investment was 751.06×1.12 = 841.19.
The investment at 14% was 1331.06, so the accumulated amount of that investment as 1331.06×1.14 = 1517.41.
The accumulated total amount was 841.19 +1517.41 = 2358.60.
What’s the correct answer for this?
Answer:
57°
Step-by-step explanation:
According to theorem, "any two angles in the same segment of the circle are equal"
So,
m<BED = 57°
round 0.004198223 to 3 significant figures
I will give brainliest
Answer:
0.00420 is the answer
Step-by-step explanation:
The definition of sig figs is each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.
The rounding number of 0.004198223 to 3 significant figures is 0.0042
Here,
The number is 0.004198223.
We have to find, 0.004198223 to 3 significant figures.
What is Rounding number?
Rounding means making a number simpler but keeping its value close to what it was.
Here,
The number is 0.004198223.
To find 3 significant figures,
We round a number to three significant figures in the same way that we would round to three decimal places.
Then, We count from the first non-zero digit for three digits. We then round the last digit.
Here, the digit is 9 then it will be round.
We get, the number is;
0.0042
We fill in any remaining places to the right of the decimal point with zeros.
So, The rounding number of 0.004198223 to 3 significant figures is 0.00420
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What’s the correct answer for this question?
Answer:
B:
Step-by-step explanation:
Measure of ARC AFB is 180°
Why?
This is because AB is a diameter.
Customer arrivals at a bank are random and independent; the probability of an arrival in any one-minute period is the same as the probability of an arrival in any other one-minute period. Answer the following questions, assuming a mean arrival rate of three customers per minute.
Required:
a. What is the probability of exactly three arrivals in one-minute period?
b. What is the probability of at least three arrivals in a one-minute period?
Answer:
a)0.2240
b)0.5768
Step-by-step explanation:
Given:
µ=3
Poison probability is given by :
[tex]f_k=\frac{\mu^ke^-^\mu}{k!}[/tex]
a) Evaluating at k=3
[tex]f(3)=\frac{3^3e^-^3}{3!} \approx 0.2240[/tex]
b)Evaluating at k=0,1,2:
[tex]f(0)=\frac{3^0e^-^3}{0!} \approx 0.0498[/tex]
[tex]f(1)=\frac{3^1e^-^3}{1!} \approx 0.1494[/tex]
[tex]f(2)=\frac{3^2e^-^3}{2!} \approx 0.2240[/tex]
Use complement rule:
P(x≥3)= 1 - f(0) - f(1) - f(2)= 1- 0.0498 - 0.1494 - 0.2240 =0.5768
What is the area of the parallelogram With a base of 14 cm and a height of five cm?
Answer:
[tex]70 \: cm^2[/tex]
Step-by-step explanation:
Area of parallelogram.
[tex]A=bh[/tex]
[tex]b \times h[/tex]
[tex]14 \times 5[/tex]
[tex]=70[/tex]
Lesson 10 congruent triangles unit test
Answer:
Step-by-step explanation:
Wheres the question??
A private shipping company will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 108 inches. Suppose you want to mail a box with square sides so that its dimensions are h by h by w and its girth is 2 h plus 2 w. What dimensions will give the box its largest volume?
Answer:
18×18×36
Step-by-step explanation:
According to the Question
108≥ 4h + w
Volume V is given by
V = wh^2
⇒V= (108-4h)h^2
⇒V= 108h^2 - 4h^3
Now differentiating and keeping = 0 we get
V' = 216h - 12h^2 = 0
h = 216/12 = 18
w = 108 - 4×18 = 36
V = 36×18^2 = 11664 from a box of 18×18×36.
what is the solution to this problem
x-17= -5
Hi
X-17 = -5
X = -5+17
X = 12
Answer:
Step-by-step explanation:
I'm pretty sure that you have to add 17 on both sides to keep the final number, not negative.
So like:
x-17=-5
+17 +17
x-0=12
and because 0 is nothing really, x=12
A square has an area of 349.69m2.
Work out the perimeter of the square.
Answer:
[tex]74.8m[/tex]
Step-by-step explanation:
[tex]A=a^2\\P=4a\\P=4\sqrt{A} \\=4*\sqrt{349.69} \\=74.8m[/tex]
Joshua ate 2/6 of his sandwich in the afternoon and 2/6 more for a snack later that day. How much of Joshua’s sandwich is left?
Answer:
1/3 left
Step-by-step explanation:
The total sandwich is 1 or in fraction form 6/6
He ate 2/6
6/6 -2/6 = 4/6
Then he ate 2/6 more
4/6 -2/6 = 2/6
He has 2/6 left
Simplifying
2/6 =1/3
The arrival of customers at a service desk follows a Poisson distribution. If they arrive at a rate of two every five minutes, what is the probability that no customers arrive in a five-minute period?
Answer:
13.53% probability that no customers arrive in a five-minute period
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
They arrive at a rate of two every five minutes
This means that [tex]\mu = 2[/tex]
What is the probability that no customers arrive in a five-minute period?
This is P(X = 0).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]
13.53% probability that no customers arrive in a five-minute period
Display the values of the function in two ways: (a) by sketching the surface zequals=f (x comma y )f(x,y) and (b) by drawing an assortment of level curves in the function's domain. Label each level curve with its function value.
Answer:
(1) f(x,y) = 1-|x|-|y|
(a) 3d figure attached
(b) 2d figure attached
(2) f(x,y) = 6-2x-3y
(a) 3d figure attached
(b) 2d figure attached
Step-by-step explanation:
The Function is not given in the question. Lets solve this for 2 common function for the internet. Hopefully it can solves the given problem
(1) f(x,y) = 1-|x|-|y|
(2) f(x,y) = 6-2x-3y
All the figures are labelled to avoid confusion. (a) part of both functions have 3D sketches. (b) part of both functions have 2d sketches
What is the additive inverse of the complex number 9-4i?
Answer:
[tex] \frac{1}{9 - 4i} [/tex]
I'm not sure
find the arc length of the particle circle
Answer:
Is there a picture or graph or..
Step-by-step explanation:
Step-by-step explanation:
arc length = (radians * radians) . 90° is π/2 radians. Arc length is (π/2×4). So the answer is 2π.
Can someone please help me with this question please
Answer:
Read below.
Step-by-step explanation:
Questions are underlined
Answers are bolded
Which of the following statements is true?
If two polygons are similar then the corresponding sides are proportional and the corresponding angles are proportional.
If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are congruent.
If two polygons are similar, then the corresponding sides are congruent and the corresponding angles are proportional.
None of the choices are correct.
Which of the following sides are corresponding if ΔABC is similar to ΔMNL?
AC and ML, BC and NL, AB and MN is the correct answer but the answer choices are:
AB and MN, BC and NL, AC and ML
AC and MN, BC and NL, AB and ML
AB and ML, BC and NL, AC and MN
None of the choices are correct.
Find the SURFACE AREA of this composite solid.
FINDING THE SURFACE AREA OF A COMPOSITE SOLID
About "Finding the surface area of a composite solid"
Finding the surface area of a composite solid :
A composite solid is made up of two or more solid figures.
To find the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.
Finding the surface area of a composite solid - Examples
Example 1 :
Daniel built the birdhouse shown below. What was the surface area of the birdhouse before the hole was drilled ?
Solution :
Step 1 :
Identify the important information.
• The top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.
• The bottom is a rectangular prism with h = 18 cm. The base is a 30 cm by 24 cm rectangle.
• One face of each prism is not on the surface of the figure.
Step 2 :
Find the surface area of each prism.
Add the areas. Subtract the areas of the parts not on the surface.
Step 3 :
Find the area of the triangular prism.
Perimeter = 17 + 17 + 30 = 64 cm
Base area = (1/2)(30)(8) = 120 sq.cm
Surface area = Ph + 2B
Surface area = 64(24) + 2(120)
Surface area = 1,776 sq.cm
Step 4 :
Find the area of the rectangular prism.
Perimeter = 2(30) + 2(24) = 108 cm
Base area = 30(24) = 720 sq.cm
Surface area = Ph + 2B
Surface area = 108(18) + 2(720)
Surface area = 3,384 sq.cm
Step 5 :
Add. Then subtract twice the areas of the parts not on the surface.
Surface area = 1,776 + 3,384 - 2(720) = 3,720 sq.cm
The surface area before the hole was drilled was 3,720 sq.cm.
The surface area before the hole was drilled was; 3,720 sq.cm.
What is composite solid?A composite solid is made up of two or more solid figures.
To determine the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.
Given that the top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.
The bottom is a rectangular prism with h = 18 cm.
The base is a 30 cm x 24 cm rectangle.
One face of each prism is not on the surface of the figure.
Then the surface area of each prism.
Add the areas. Subtract the areas of the parts not on the surface.
The area of the triangular prism.
Perimeter = 17 + 17 + 30 = 64 cm
Base area = (1/2)(30)(8) = 120 sq.cm
Surface area = Ph + 2B
Surface area = 64(24) + 2(120)
Surface area = 1,776 sq.cm
Now the area of the rectangular prism.
Perimeter = 2(30) + 2(24) = 108 cm
Base area = 30(24) = 720 sq.cm
Surface area = Ph + 2B
Surface area = 108(18) + 2(720)
Surface area = 3,384 sq.cm
Now,
Surface area = 1,776 + 3,384 - 2(720) = 3,720 sq.cm
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Please help. I keep getting this problem wrong . I need help please . I’ll mark you as brainliest if correct . Only answer if you know. Thank you
Answer:
The real number 'a' = 32
The real number 'b' = 0
Step-by-step explanation:
Product of a number of a number and its conjugate = a + bi
The number is = -4 + 4i
Conjugate of this number is = -4 - 4i
Product of the number and it's conjugate
= (-4 + 4i)(-4 - 4i)
= -4(-4 - 4i) + 4i(-4 - 4i) [By distributive property]
= 16 + 16i - 16i - 16i²
= 16 - 16(-1)
= 16 + 16
= 32
a + bi = 32 + (0)i
By comparing both the sides,
a = 32
b = 0
A standard 52-card deck has four 13-card suits: diamonds, hearts, clubs, and spades. The diamonds and hearts are red, and the clubs and spades are black. Each 13-card suit contains cards numbered from 2 to 10, a jack, a queen, a king, and an ace. An experiment consists of drawing 1 card from the standard deck. Find the probability of drawing a black jack of diamonds.
Answer:
0
Step-by-step explanation:
In a suit of 52 cards
The Red Cards are: diamonds and heartsThe Black cards are: clubs and spadesThe experiment consists of drawing 1 card from the standard deck.
Since diamonds are red, there is no black jack of diamonds.
Therefore:
P(drawing a black jack of diamonds)
[tex]=\dfrac{0}{52}\\\\ =0[/tex]
Answers:
In photo below
Explanation:
I got it correct in my test :)