[tex]100^{\frac{-3}{ 2} }[/tex] can be simplified into 0.001.
Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.
Prime factorization of 100 = 5 x 5 x 2 x 2 = [tex]10^{2}[/tex]
According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.
i.e.,[tex](x^{m} )^{n} = x^{mn}[/tex]
According to the given condition,
∴ [tex]100^{\frac{-3}{2} }[/tex] = [tex](10^{2})^{\frac{-3}{2} }[/tex]
Applying the law of indices mentioned above,
[tex]100^{\frac{-3}{2} }[/tex] = [tex](10^{2 X}^{\frac{-3}{2} })[/tex]
= [tex]10^{-3}[/tex] = 0.001.
Thus, [tex]100^{\frac{-3}{2} }[/tex] can be simplified into 0.001.
To learn more about laws of indices, refer to this link:
brainly.com/question/27432311
#SPJ4
Estimate the mean lifetime of a bulb.
Give your answer rounded to 2 DP
?hours
The mean lifetime of a bulb is 31. 57
What is mean?Mean can be defined as the average of a given set of values or elements.
The formula for the mean of a given set of values is expressed as;
Mean = sum of the occurrence of the values/ number of values
Or
Mean = sum of terms/number of terms
From the information given, the frequency of the lifetime of the bulbs were given as;
34, 31, 94, 40 , 0 , 17, 5
The sum of the terms is given as:
= 34 + 31 + 94 + 40 + 0 + 17 + 5
= 221
The number of terms = 7
Substitute into the formula
Mean = 221/ 7
Mean = 31. 571
In 2 decimal place
Mean = 31. 57
Thus, the mean lifetime of a bulb is 31. 57
Learn more about mean here:
https://brainly.com/question/1136789
#SPJ1
mr. fullingham has 75 geese and 125 turkeys. what is the ratio of te number of geese to the total number of birds in simplest terms
help plss
Which table represents a linear function?
Michael is doing an underwater handstand. His feet are sticking up 0.5 meters above the surface
hands are 1.8 meters directly below his feet.
of the water. Michael's
What is the position of Michael's hands relative to the surface of the water?
Answer:
Step-by-step explanation:
Answer:
michael is doing an underwater handstand . His feet are sticking up 0.5 meter above the surface handsare 1.8 meters directly below his feet of the water
michael handsrelative to the surface of the water
Step-by-step explanation:
Pleas look at screenshot
Two interior decorating teams are competing in a kitchen remodel competition. their remodels are graded on the following categories, each worth 18 points; time to complete, design, and total cost. time to complete is worth 75% of their final score, design is 15%, and total cost is 10%. whoever has the largest final score wins $150,000. suppose team a received 15 points for time to complete, 9 points for design, and 14 points for total cost. suppose team b received 17 points for time to complete, 7 points for design, and 13 points for total cost. using technology, determine which team won the competition. team a won by 1.9 points. team a won by 1.1 points. team b won by 1.9 points. team b won by 1.1 points.
Answer:
team b by 1.1
Step-by-step explanation:
everything else was wrong when i did it
Tickets to a sporting event cost $125 each. What's a reasonable domain and range.
The domain and the range of a function is the set of input and output values of the function.
The domain is the set of all whole numbers.
The range is the set of all whole numbers.
Let the number of tickets be x, and the revenue be y.
So, the revenue function will be:
y = 125
The number of tickets cannot be less than 0.
So, the domain of the revenue function is
domain=0,∞
The above means that, the domain is the set of all whole numbers
Similarly, the revenue cannot be less than 0.
So, the range of the revenue function is
range = 0,∞
The above means that, the range is also the set of all whole numbers (in multiples of 125).
to know more about range and domain;
visit;brainly.com/question/28135761
#SPJ9
John calculates an arc length involving a circle with a radius of 9 inches. The associated central angle has a measure of radians. John's work is shown
Answer:
Step 3, computed the radius multiply by the center angle
Step-by-step explanation:
{arc-length: a * r}
arc-lenght= 3\pi * 9 = 27pi inches. John made his first error in sept 3, he listes the correct equations, but he should have computed the radius by the center angle
Answer:
Step-by-step explanation:
The blue dot is at what value on the number line -16 to -10
Which translation takes y=|x| to y=|x+3|-1 ?
(A) 3 units right, 1 unit down (C) 3 units left, 1 unit down
(B) 3 units right, 1 unit up (D) 3 units left, 1 unit up
The translation is given by option (C)3 units left ,1 unit down.
A translation occurs when you a graph is moved either horizontally or vertically. That is to say, each point on the parent graph gets translated in one of four directions: left, right, up, or down. There is usually addition or subtraction involved in translation.
Let us consider the function y=|x+3|-1 which is translated from the parent function of y=|x|.
The following steps are followed for the translation of the function:
There is an horizontal shift to the left of the parent function about 3 units .There is a vertical shift downwards of 1 unit.The translation can be seen in the attached graphical representation of the two functions.
The blue line represents the translated function while the red line represents the parent function.
Therefore the translation required for the function y=|x+3|-1 from y=|x| is 3 units left and one unit down .
To learn more about translation of a function visit:
https://brainly.com/question/12463306
#SPJ4
Notes:
For semiannual premiums, use 51% of the annual rate.
For quarterly premiums, use 26% of the annual rate.
For monthly premiums, use 9% of the annual rate.
For females, use the age of a male three years younger.
Will C. Lowe wishes to purchase an ordinary whole life insurance policy with a face value of $50,000. What will his annual premium be, if his age for insurance purposes is thirty-one?
(Use a thousands comma where applicable.)
The annual insurance premium that Will C. Lowe will be paying is $ 766.5
What is insurance premium?Insurance premium is annual, quarterly, semi annual or monthly payments that has to be paid accordingly to keep our insurance policy active.
Annual insurance premium can be calculated by multiplying the face value per $1000 of the policy by the rate of the insurance of policy.
Given is that Will C. Lowe is 31 year old male who wants to buy a ordinary whole life insurance policy with a face value of $50,000.
From the table we can see that rate of insurance for a 31 year old male for a ordinary whole life insurance policy is 15.33
Then annual premium = (face value per $1000)*(rate of insurance)
= $ (50,000/1000)*(15.33) = $766.5
Therefore, the annual insurance premium that Will C. Lowe will be paying is $766.5
Also, learn more about the insurance premium from the link below:
https://brainly.com/question/13724529
#SPJ1
Please help!!
Solve for a:
b(a + f) = M
Use the Change of Base Formula. What is the value of each expression?
b. log₄18
The value of the given expression that is log₄ 18 = 2.084
A logarithm operation can be rewritten as a fraction of logarithms with a new base using the change of base formula.
Example: logₐ b = (logₓ b) / logₓ a)
Therefore, log₄ 18 = (log₁₀ 18) / (log₁₀ 4).....eq(i)
We know, log₁₀ 4 = 0.602
We can write log₁₀ 18 as log₁₀(2x9).
Using the product rule of logarithms, log₁₀ 18 = log₁₀2 + log₁₀9log₁₀ 18 = 0.301 + 0.954log₁₀ 18 = 1.255
Substituting the value of log₁₀ 18 = 1.255 in eq(i) we get,
log₄ 18 = 1.255/0.602log₄ 18 = 2.084
The final answer to the question is log₄18 = 2.084 using the change of base formula.
Learn more about the change of base formula here https://brainly.com/question/23753980
#SPJ4
Are the lines paraellel, perpendicular, or neither? b) line 1 : y+1/3x=4 line 2 y=3x-2
If the point (x, y) is in Quadrant III, which of the following must be true?
x < 0 and y>0
x < 0 andy<0
Submit
x > 0 and y>0
x > 0 and y < 0
Answer: x < 0 and y < 0
Step-by-step explanation:
quadrant three is here
|
II | I
|
--------------------|-------------------
|
III | IV
|
here /\
so, the x is to the left which is negative, and the y is down which is negative. x is less than zero, and y is less than zero
1 Find the value of 5 x
(a) 500
(b) 50
(c) 5000
(d) 5
2 Find the product of 3.6 x 100
(a) 36
(b) 360
(c) 0.36
(d) 0.0036
3 The additive inverse of is ------------
(a) -1
(b)
(c) -5
(d) 1
4 Find the mode of the data 4, 3, 5, 11, 4, 7, 5, 4, 3
(a) 4
(b) 3
(c) 5
(d) 7
5 Write the base of
(a) p
(b) 10
(c) 1
(d) 0
6 Find the value of
(a) 2
(b) 6
(c) 3
7 Write the value of 5
(a) 3
(b) 0
(c) 1
(d) 15
8 Find the value of
(a) 100000
(b) 10000
(c) 100
(d) 10
9 Find the range of the following observations 48, 62, 78, 12, 96, 34, 25
(a) 84
(b) 78
(c) 80
(d) 69
10 ------- is the multiplicative inverse of 60
(a) 60,
(b) -60
(c) 1
11 The value of (
(a) -1
(b) 1
(c) 8
(d) -8
12 3.45 × -1000 is-------------
(a) -3450
(b) -345
(c) 0
(d) 3450
13 Number of edges of the cylinder is ----------------
(a) 8
(b) 6
(c) 2
(d) 4
14 Number of faces in a cube is -------------
(a) 12
(b) 8
(c) 6
(d) 10
SECTION – B
II. Solve the problems ( 11 x 2 = 22 )
15 Write four rational numbers equivalent to
16 Find the value of the following
3365 x 164 – 2365 x 164
17 Evaluate of 105
18 Divide the following
(a) 168.96 8
(b) 505 ÷ 100
19 Express 15625 as a power of 5
20 Multiply the following
(a) 4.9 x 0.005
(b) 0.0016 x 625
21 Find the value of
22 Find the mean of the data 3.2, 4.8, 18.9, 7.8, 10.3
23 The median weight of the data set 16, 5, 11, 19, x, 4 is 9 . Find the value of
24 The distance between the sun and the Jupiter is 778,500,000,000 m . Express it in standard form.
25 A rectangular garden has an area of 25.3 and a width of 4.4 m . What is the length of the garden.
SECTION C
III. Solve the problem with proper steps ( 8 X 3 = 24)
26 Arrange the rational numbers in descending order
, , , and
27 The mean of 8numbers is 27. Find the sum of these 10 numbers.
28 Find 10 rational numbers between -2 and -3
29 Simplify and express in the exponential form using laws of exponents.
30 Represent on a number line
31 A rectangular garden has a length m and a width of m . What is the perimeter of the garden ?
32 Find the value of
33 Find value using properties
(19 × 5) + (19 × 21)
SECTION - D
IV. Solve the problems with proper steps ( 5 X 4 = 20 )
34 From a ribbon of length 7 m , Shreya used 4 m of ribbon . How much ribbon is left ?
35 The product of two numbers is 173.502. If one of them is 18.9, then find the other number ?
36 Express each of the following as a product of powers of prime numbers
(a) 1296
(b) 625
37 The scores that two gymnastic and Josh obtained in six events of parallel bars were as follows
Asif : 8.1, 9.6, 9.2 , 7.5, 9.4, 9.0,
Josh : 9.3, 9.5, 8.0, 9.1, 7.8, 8.5
(a) Find the mean score of Asif
(b) Find the mean score of Josh
(c) Whose performance was better.
38 The table shows the favourite pets of 40 children in a class . Draw Bar graph for this data.
PETS DOG CAT RABBIT FISH
NUMBER OF
CHILDREN
14 8 10 8
I will mark as brainliest
The solution to all parts is shown below.
What is Mean of data?Simply dividing the total number of values in a data set by the sum of all of the values yields it. The calculation can be performed on unprocessed data or data that has been combined into a frequency table.
1. The value of 5 in 2875 is 5.
2. The product is 360
3. Additive inverse is -1
4. Mode = 4
9. Range = 96 - 12 = 84
10. 1/60
12. -3.45 x -1000 = 3450
13. Number of edges of the cylinder is 2.
14. Faces = 6
16. 3365 x 164 – 2365 x 164
= 164( 3365 - 2365)
= 1640
17. (a) 168.96 /8 = 21.12
(b) 505 ÷ 100 = 50.5
18. 15625 = [tex]5^6[/tex]
19. Mean = 45/5= 9
21. 778,500,000,000 m = 7.7785 x [tex]10^{11[/tex] m
22. length of the garden = 25.3 / 4.4 = 5.75 m
Learn more about Mean of Data here:
https://brainly.com/question/30891252
#SPJ5
DIG DEEPER A three-dimensional printing pen uses heated plastic to create three-dimensional objects. A kit comes with one 3D-printing pen and p packages of plastic. An art club purchases 6 identical kits for (180+58.5p) dollars. Write an expression that represents the cost of one kit.
Answer:
Step-by-step explanation:
mdcmmmm
Given f(x) = 3x + 3, write a new function if the y-intercept is increased by two units.
Answer:
f(x) = 3x + 5
Step-by-step explanation:
Because if the y-intercept is increased by two units in the slope formula where b is the y-intercept, then the answer is 3x + 5.
c rounded to the nearest 10 is 640.
d rounded to the nearest 10 is 420.
what are the lower and upper bounds of c + d?
The bounds of C is 635 - 644
The bounds of D is 415 - 424
The lower bounds of C + D can be found by adding 635 + 415, which is 1050
The upper bounds of C + D can be found by adding 644 + 424, which is 1068
So, the lower bounds of C + D is 1050 and the upper bounds is 1068
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
The upper bound is 1068 and the lower bound is 1050
What is the upper bound and lower bound of a number?The lower bound is the smallest value that would round up to the estimated value. The upper bound is the smallest value that would round up to the next estimated value.
Given here, c rounded to the nearest 10 is 640 and d rounded to the nearest 10 is 420. Then we have the minimum and maximum value as
Min C = 635 and Max C = 644 & Min D=415 and Max D = 424
Therefore the upper bound for c+d = 644+424
= 1068
And the lower bound for c+d = 635+415
=1050
Hence The upper bound is 1068 and the lower bound is 1050
Learn more about lower and upper bound here:
https://brainly.com/question/22965427
#SPJ2
How much will a person pay for 5.5 pounds of bananas at a price of $1.66 per pound?
...
The person pay $9.13 for 5.5 pounds of bananas .
The unit method is a method of finding the value of one unit and then finding the value of the required number of units."It's a way to get a single unit value from a multiple unit value and a multiple unit value from a single unit value." or should find a lesser value. To do this, you must first find the value of one thing by division, and then find the value of more or less by multiplication. For simplicity, we always write the computed side on the right and the known side on the left.It is given that $1.66 per pound of bananas .
1 pound of banana cost = $1.66
5.5 pounds of banana cost will be [tex]=5.5\times1.66[/tex]
[tex]=\$9.13[/tex]
Learn more about unitary method here :
https://brainly.com/question/24587372
#SPJ9
Determine whether the function has line symmetry.
Nope, the domain is not centered at any point, let along that this is a linear function.
Suppose that A and B are points on the number line.
If AB=9 and A lies at 7, where could B be located?
If there is more than one location, separate them with commas.
On the number line, if 'A' lies at 7 then 'B' could lie at -2, 16.
What is a number line?
A number line can be stretched in either direction indefinitely and is commonly displayed horizontally.
The numerals on the number line grow as one goes from left to right and drop as one moves from right to left.
Given, AB = 9 and 'A' lies at 7
So, basically 'B' can be at -2 on the number line which makes the distance between 'A' and 'B' 9 units. The same is possible for B at 16 on the number line.
To know more about number line, click on the link
https://brainly.com/question/24644930
#SPJ1
Which expression is NOT equivalent to ⁶√16 ²?
(A) (16 r²)¹/₆ (B) 4 r¹/₃ (C) (4 r)¹/₃ (D) ∛4 r}
The correct option is (B) [tex]4 r^\frac{1}{3}[/tex]
The exponential expression [tex]4 r^\frac{1}{3}[/tex] is not equivalent to ⁶√16r².
What is exponential expression ?In, mathematics a exponential function or exponential expression is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the exponential function can be written as [tex]a^x[/tex] .Or we can say that there is always has something power something rule in case of exponents.
where, a is the base expression of function
x = exponent of expression
According to question,
the expression,[tex]\sqrt[6]{16r^2}[/tex] can be written in following ways:
Case 1 : if we simplify the expression using fractional method ,
then, [tex]\sqrt[6]{16r^2}[/tex] = [tex]({16r^2})^{\frac{1}{6}} = (4r)^\frac{2}{6 } = (4r)^\frac{1}{3 }[/tex]
i.e. option (A) and (C) are satisfying the expression
Case 2 : if we simplify the equation exponentially ,
then, [tex]\sqrt[6]{16r^2} = 3\sqrt{4r}[/tex]
i.e. option (D) is satisfying the expression
Hence, the expression is not equivalent to ⁶√16r² is option B.
To know more detail about exponential equations, visit :
brainly.com/question/28278137
#SPJ4
If z=30 when x=3 and y=2 , write the function that models the relationship.
z varies directly with x and inversely with y .
z = 20 x/y is the variation of equation.
How to write the function that models the relationship?A relationship between a set of values for one variable and a set of values for other variables is known as a variation.
One of the most fundamental concepts in mathematics is the idea of a function, in part because functions are a useful tool for describing and illuminating patterns.
given that
z=30 when x=3 and y=2
z varies directly with x that means z is directly proportional to x.
z = kx .................(1)
z varies inversely with y means z is inversely proportional to y.
z = k 1/y ................(2)
both equation 1 and 2
z = k x/y
k = zy/x
now, find the value of k using given information.
k = 30(2)/3
k = 60/3
k = 20
now,
z = k x/y
z = 20 x/y
This is the variation of equation.
Learn more about variation equations from here:
https://brainly.com/question/13998680
#SPJ4
3xy+5x+2+3y+x+4 answer
The equivalent expression of the expression given as 3xy + 5x + 2 + 3y + x + 4 is 3xy + 6x + 3y + 6
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
3xy + 5x + 2 + 3y + x + 4
Collect the like terms in the above expression
So, we have
3xy + 5x + 2 + 3y + x + 4 = 3xy + 5x + x + 3y + 4+ 2
Evaluate the like terms in the above expression
So, we have
3xy + 5x + 2 + 3y + x + 4 = 3xy + 6x + 3y + 6
Hence, the equivalent expression of the expression given as 3xy + 5x + 2 + 3y + x + 4 is 3xy + 6x + 3y + 6
Read more about expression at
https://brainly.com/question/12470265
#SPJ1
8 over 3 / 3 simplified
Answer:
8
Step-by-step explanation:
if you mean 8/ (3/3), Then you get 8 because 3/3 = 1 and 8/1 is 8. Also if you put that equation into a calculator then you get 8
1. Solve for x:
1/3x = -26
What are the solution(s) of 2(x+3)²/₃=8 ?
The solution is 5
Rewriting the expression -
2(x+3)²/₃=8
Divide Left Hand Side and Right Hand Side of the equation -
(2(x+3)²/₃)÷2 = 8÷2
Performing division to find the solution
(x+3)²/₃ = 4
Taking cube on both sides of the equation
((x+3)²/₃)³ = 4³
The exponent on Left Hand Side will be multiplied cancelling 3, as it is common in both numerator and denominator
(x + 3)² = 64
Now, taking square root on both sides of equation
√(x + 3)² = √64
Solving the square root on both sides of equation
x + 3 = 8
Shifting 3 to Right Hand Side of the equation
x = 8 - 3
Performing subtraction
x = 5
Hence, the solution of equation is 5
Learn more about calculations to find solution -
brainly.com/question/12063720
https://brainly.com/question/28476926
#SPJ4
The value of the perimeter of the figure is equal to the value of the area. Find the value of X.
The value of x if the value of the perimeter of the figure is equal to the value of the area is 1.5
Area and perimeter of rectangleLength of the rectangle = 6 inWidth of the rectangle = 2x inArea of rectangle = perimeter of rectangle
Length × width = 2(length + width)
6 × 2x = 2(6 + 2x)
12x = 12 + 4x
collect like terms12x - 4x = 12
8x = 12
divide both sides by 8x = 12 / 8
x = 1.5
So,
Width of the rectangle = 2x in
= 2(1.5)
= 3 in
Therefore, the length and width of the given rectangle is 6 in and 3 in respectively
Read more about rectangle:
https://brainly.com/question/13048427
#SPJ1