what is (24^3)^-3 × (40÷4+14)^10 over (fraction bar) (96÷8)+(39÷3-1) ??????
Answers
________________________________
Note:
_______________________________________________
(40 ÷ 4 + 14) ¹⁰ = [ (40 ÷4) + 14 ] ¹⁰ = (10 + 14)¹⁰ = 24¹° ;
(96 ÷ 8) + (39 ÷ 3 −1 ) = (96 ÷ 8) + [ (39 ÷ 3) − 1 ] ;
= 12 + (13 − 1 ) = 12 + 12 = 24 ;
________________________________________________
(24³)⁻³ = 24⁽³ * ⁻³⁾ = 24⁻⁹ ;
___________________________________________
So we can rewrite the problem:
___________________________________________
24⁻⁹ * (24¹⁰ / 24) ;
___________________________________________
Note: " (24¹⁰ / 24) = (24¹⁰ / 24¹) = 24 ⁽¹⁰ ⁻ ¹⁾ = 24 ⁹ ;
___________________________________________
Rewrite the expression:
___________________________________________
24⁻⁹ * 24 ⁹ = 24 ⁽⁻⁹ ⁺ ⁹⁾ = 24⁰ = 1 .
___________________________________________
The answer is: " 1 " .
___________________________________________
Related Questions
Cherries cost $5 for 2 pounds and $7.50 for 3 pounds.
Question:
a. What is the cost per pound?
b. Is it constant?
c. If you were to graph this situation, would you put weight or cost on the x-axis? Which one would you put on the y-axis?
d. Plot the two points described.
e. How much would 5 pounds of cherries cost? What did you do to solve this problem?
Draw your answer below:
Answers
A) 5/2 = 2.50, it costs $2.50 per pound
B) yes because 7.50 / 3 = 2.50 as well
C) weight would be on x-axis and cost on the Y axis
D) draw a graph and put the dots on (2,5) and (3,7.50) and draw a straight line
E) 2.50 *5 = $12.50, multiply cost per pound by pounds.
Someone please help me!
Answers
With the given clues, let the digits of the 5-digit number be: abcde
i) Since, the number consists of 3 different digits, it means that either two of digits are repeated twice each or one of the digit is repeated thrice.
Then the digits could be: abbcc or abccc
ii) Since all digits are even numbers greater than 0, this means that the possible digits are 2, 4, 6 and 8.
iii) Since the value of the ones digit is 1/10 the value of the tens unit, this means that the tens place and the ones place have the same digit.
Thus, the number could be: abbcc
iv) Since the value of the tenth digit is 10 times the value of the 100th digit, this means that the required number has a decimal point and the first two digits after the decimal point are the same.
Thus, the number could be: abb.cc
v) Since the sum of the tenth digit and the hundredth digit gives you the hundreds digit. Recall that the tenth digit and the hundredth digit are the same.
Thus, the possible value for the tenth, hundredth and hundreds digits respectively are: 2, 2, 4 or 4, 4, 8
vi) Since the sum of the tens digit and the ones digit gives you the tenth digit. Recall that the tens digit and the ones digit are the same.
Also, recall that the possible value for the tenth digit from condition (v) is 2 or 4. Then the value of the tens and ones digits is 2 while the value of the tenth digit is 4.
Having applied all the above conditions, therefore, the required 5-digit number is 822.44
Part B:
We know that the number we got in part A above is the only five digit number that satisfy the clues because, there is no other combination of digits that satisfies the given clues.
2a + 4b = d for b
I trying to solve for b.
I don't understand how to isolate the variable.
Answers
we subtract 2a from both sides
2a-2a+4b=d-2a
simplify
4b=d-2a
divide by 4
[tex] \frac{4b}{4} = \frac{d - 2a}{4} [/tex]
simplify
[tex]b = \frac{d - 2a}{4}[/tex]
Is 22/15 less than 14/31?
Is 19/35 greater than 27/19
Is 15/25 greater than 22/44
Is 30/25 less than 29/30
Answers
given that 4,12,x,y,324,972 is a geometric sequence. find the sum of x and y
Answers
The sum of x and y in the given geometric sequence is 144, with x being 36 and y being 108, based on the common ratio of 3.
To solve the problem, we first need to recognize that a geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a constant called the common ratio. We are given a sequence 4, 12, x, y, 324, 972, and we need to find the common ratio and subsequently x and y.
Step-by-Step Solution:
Find the common ratio (r) using two known consecutive terms.
Once r is found, apply it to determine the missing terms x and y.
Calculate the sum of x and y.
Given the sequence 4, 12, x, y, 324, 972, let's use the first two terms to find the common ratio. The ratio of the second term to the first term is 12 / 4 = 3. Thus, the common ratio (r) = 3.
Now, let's find x by multiplying the second term (12) by the common ratio: x = 12 x 3 = 36.
To find y, multiply x by the common ratio: y = 36 x 3 = 108.
The sum of x and y is then: x + y = 36 + 108 = 144.
-9x is greater than or equal to -3(x-4)
Answers
-9x = -3(x-4)
-9x = -3x+4
-6x = 4
x = -4/6
x = -2/3
Now plug -2/3 in for X
-9(-2/3) = 6
-3(-2/3-4) = 2+4 = 6
They are equal to each other.
Nendell saw at a diner if he bought one of each item and spent $7.50, how much did the drink cost
Answers
Burger is $4.46
Fries are $1.47
So the drink is $1.57
Determine the independent variable (__________,y). what word goes in the blank space??
Answers
Which expression would the model be most helpful in solving 5/6
Answers
5/6 divided 1/6, this is the correct answer
In science class Krissy labeled 26 vertebrae bones on a diagram of an adult human Doug labeled 1 bone in the throat and 6 bones of the inner ear for both ears. Most adult humans have 206 bones. Write an equation to solve for the number of bones left in the diagram that need to be labeled
Answers
what is 0.6144 divided by 1.6
Answers
Hoped this helped : )
Explain how you can use a model to find 6x17
Answers
Answer:
The required model is shown below:
Step-by-step explanation:
Consider the provided information.
We need to use partial products model to solve 6×17
The partial product is the product of parts of each factor.
Here Multiplicand is 6 and Multiplier is 17
We can rewrite 17 as 1 ten and 7 ones. i.e 17=10+7
Therefore,
6×17 = 6(10+7)
6×17 = 6×10+6×7 [Distributive property]
6×17 = 60+42 = 102
Hence, the required model is shown below:
I really need help on this.
Answers
(Problem 1.)
Which set of rational numbers is arranged from least to greatest?
−3.5, negative 1 over 4, 2, 1 over 3
−3.5, negative 1 over 4, 1 over 3, 2
2, 1 over 3, negative 1 over 4, −3.5
negative 1 over 4, 1 over 3, 2, −3.5
Answers
The farther left you go on the number line, the less value the number holds.
The farther right you go on the number line, the more value the number holds.
-3.5 is as FAR left as any of these numbers, this means it's the number with the least value. It'll be your first number.
-1/4 is your next one. This is before the -3.5, meaning on the number line, it's a little to the right of the -3.5. So, this'll be your number with the SECOND lowest value.
1/3 is a positive number, meaning it's after the 0, but barely. It's not a whole number, which is why it's a fraction. Even though it's considerably bigger than the other 2 numbers I just listed, it's still pretty low, so this is your number with the THIRD lowest value.
2 is a positive number. It holds the most value, because it is the farthest number out of these to the right of the 0.
Your correct order is B: -3.5, -1/4, 1/3, 2
This is Least to Greatest.
~Hope this helps buddy!
Use the x-values: 1, 2, 3, and 4 to write solutions of the equation y = 14x + 8 as ordered pairs.
Answers
For the equation y = 14x + 8, the ordered pairs with x values of 1, 2, 3, and 4, calculated by substituting these x-values into the equation, are (1,22), (2,36), (3,50), and (4,64).
Explanation:The equation in question is a linear equation, y = 14x + 8 , and you've been asked to use the x-values: 1, 2, 3, and 4 to write the solutions as ordered pairs. To find the corresponding y-values, substitute these x-values one by one into the equation.
For x = 1, y = 14*1 + 8 = 22, so the ordered pair is (1,22) For x = 2, y = 14*2 + 8 = 36, so the ordered pair is (2,36) For x = 3, y = 14*3 + 8 = 50, so the ordered pair is (3,50) For x = 4, y = 14*4 + 8 = 64, so the ordered pair is (4,64)
These points plotted on a graph represent the dependence of y on x.
Learn more about Ordered Pairs here:https://brainly.com/question/30805001
#SPJ12
To determine the solutions of the equation y = 14x + 8 for x-values 1, 2, 3, and 4, each x-value is substituted into the equation to find the corresponding y-values, resulting in ordered pairs (1,22), (2,36), (3,50), and (4,64).
Explanation:To find solutions of the equation y = 14x + 8 using the x-values 1, 2, 3, and 4, we will substitute each x-value into the equation and solve for y to obtain the corresponding y-value.
For x=1: y = 14(1) + 8 = 14 + 8 = 22. The ordered pair is (1, 22).
For x=2: y = 14(2) + 8 = 28 + 8 = 36. The ordered pair is (2, 36).
For x=3: y = 14(3) + 8 = 42 + 8 = 50. The ordered pair is (3, 50).
For x=4: y = 14(4) + 8 = 56 + 8 = 64. The ordered pair is (4, 64).
These ordered pairs represent solutions for the given linear equation and show the dependence of y on x.
Learn more about Ordered Pairs here:https://brainly.com/question/30805001
#SPJ3
The function f(x) is graphed on the coordinate plane.
What is f(−2) ?
Enter your answer in the box.
f(−2)=
Answers
Answer:
The value of f(-2) is, -2
Step-by-step explanation:
The graph which is shown on the coordinate plane passes through the two points i.e, (2,0) and (0, -1).
First find the equation for this line:
Using Point-Slope form for the equation of line: [tex]y-y_{1}=m(x-x_{1})[/tex] ..[1]
where m is the slope given by ;
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
First find the slope:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-1-0}{0-2}[/tex]
⇒ [tex]m=\frac{-1}{-2} =\frac{1}{2}[/tex]
Now, substitute the value of m=[tex]\frac{1}{2}[/tex] , [tex]x_{1}[/tex]= 2and [tex]y_{1}[/tex]=0 in equation [1];
[tex]y-0=(\frac{1}{2})(x-2)[/tex] or
[tex]y=\frac{1}{2}\cdot (x-2)[/tex]
In this graph x represents the input of the process and Y the output of the process and f the function of the variable x i.e, y=f(x)
∴ [tex]y=f(x)=\frac{1}{2}(x-2)[/tex] ....[2]
now, we put the value of x=-2 inequation [2] to solve for f(-2).
[tex]f(-2)=\frac{1}{2}(-2-2) =\frac{1}{2} \cdot (-4)[/tex]
Simplify we get;
[tex]f(-2)=-2[/tex]
Which two sets of angles are corresponding angles?
∠e and ∠h; ∠f and ∠g
∠e and ∠i; ∠f and ∠h
∠e and ∠g; ∠f and ∠h
∠e and ∠i; ∠f and ∠g
Answers
points A is 5,623m above sea level.points B is below sea level at -1,245m. what is the distance between the two points?
Answers
If you go from point B to sea level, you need to go up 1,6,868 m245 m.
Add the two distances to find the distance between the points.
5,623 m + 1, 245 m = 6,868 m
5623 m + 1245 m = ?
1. Write the ratio in the simplest form. 16:24 (1 point) 1:2 4:3 3:4 2:3
Answers
Any ratio can be simplified into its simplest form by dividing the numerator and denominator by the common factor.
The given ratio is 16:24. To bring the ratio in its simplest form we will look for the factors of 16 and 24 and look for the greatest number that divides both 16 and 24.
The greatest number that divides both 16 and 24 is 8.
16÷8=2
24÷8=3.
The ratio 16:24 in its simplest form is 2:3
The solution for the ratio in the simplest form is, 2 : 3
Given that,
16:24 is the specified ratio.
Now, By finding the largest integer that divides both 16 and 24 and the factors of 16 and 24, we may reduce the ratio to its most basic form.
Hence, 8 splits both 16 and 24 to the maximum possible extent.
So, we get;
16 / 8 = 2
24 / 8 = 3
Thus, the simplest form of the fraction is,
⇒ 16 : 24
⇒ 16 / 24
⇒ 2 / 3
It can be written as,
⇒ 2 : 3
So, the simplest form is,
⇒ 2 : 3
Learn more about the ratio visit:
https://brainly.com/question/12024093
#SPJ6
Joshua has a baseball card collection.84 cards make up 70% of his collection how many cards are in his total collection
Answers
The formula f=n/4+37 estimates the temperature F in degrees Fahrenheit when crickets chirp n times per minute. Use the formula to estimate the temperature when n = 18 chirps/min. Round to the nearest whole number, if necessary. 41 42 37 46
Answers
[tex]f=\dfrac{n}{4}+37\\\\\text{substitute the value of n = 18 to the expression}\\\\f=\dfrac{18}{4}+37=4.5+37=41.5\approx42[/tex]
Answer: f = 42.
By using substitution of value n, temperature F in degree Fahrenheit is 42.
What is substitution method?"The substitution method is a simple way to solve a system of linear equations algebraically and find the solutions of the variables."
Given
Formula to estimate the temperature F in degree Fahrenheit
f = [tex]\frac{n}{4} +37[/tex]
n = 18 chirps/min
Substituting n in the formula
f = [tex]\frac{n}{4} +37[/tex]
⇒ f = [tex]\frac{18}{4}+37[/tex]
⇒ f = 4.5 + 37
⇒ f = 41.5 ≅ 42 (nearest whole number)
Thus, temperature F in degree Fahrenheit is 42.
Learn more about substitution method here
https://brainly.com/question/14619835
#SPJ2
What is 57.15% rounded to the nearest whole percent?
Answers
.15 does not round up because it is less than 50
so 57.15% would round down.
making it 57%
Hope it helped!
The number we would get when we round 57.15% to the nearest whole number is: A. 57%.
What is Nearest Whole Percent?Nearest whole percent means the number has no fractional part of decimal.
Given the number, 57.15%, to round it to the nearest whole number, digits 1 and 5 would be removed since the last number closer to the whole number is less than 5.
Thus, we would have 57%.
Learn more about nearest whole number on:
https://brainly.com/question/1803741
#SPJ2
1/3(9−6m)+1/4(12m−8)
Answers
They are asking you to simplify it. So, let me help you out..
[tex] \frac{1}{3}(9-6m)+ \frac{1}{4}(12m-8) Use the distributive property [/tex]
(1/3)(9) + (1/3)(-6m) + (1/4)(12m) + (1/4)(-8)
=3 - 2m + 3m - 2
= m + 1
Best of luck with your studies!
Answer:
M+1
Step-by-step explanation:
Add the two expressions. 8k + 4 and 3k + 8
Enter your answer in the box.
THE ANSWER IS 11K + 12
Answers
One carpet cleaning cost are shown in the table. The relationship is linear. Find and interpret the rate of change and the initial value for this situation.
Answers
The first costs $125. Supposing we subtract $50 from that, we get $75. So, it sounds like it costs $75 just to get the carpet cleaners to your house.
The rule would then be $75 + $50x, where x : {1, 2, 3, 4, .... }
Let's check this result. Suppose x = 1. Will the charge be $125, as show in the table? $75 + $50(1) = $125. Correct.
Suppose x = 4. Will the charge be $275 as shown in the table?
$75 + $50(4) = $275. YES
There are two containers of milk. There is twice as much milk in the first container as in the second. After using 2 gal. of milk from the second container and 3 gal. of milk from the first container, the second container had 4.5 times less milk than the first. How many gallons of milk were in both containers originally?
Answers
Let us say that:
V1 = initial gallons in first container
V2 = initial gallons in second container
From the problem statement, we can create the equations:
V1 = 2 V2
V1 – 3 = 4.5 (V2 – 2)
Combining the two:
2 V2 – 3 = 4.5 (V2 – 2)
2 V2 – 3 = 4.5 V2 – 9
2.5 V2 = 6
V2 = 2.4 gallons
V1 = 2 V2 = 4.8 gallons
So there are 4.8 gallons in the 1st container while 2.4 gallons in the 2nd container.
malcolm buys a 5/6 pound bag of black beans and a 3/4 pound bag of pinto beans. how many pond of beans does malcolm buy in all
Answers
5/6 + 3/4
5/6 = 10/12
3/4 = 9/12
10/12 + 9/12 = 19/12 = 1 7/12 pounds total
Answer: the answer is 1 7/12 pounds
Step-by-step explanation:
Because 5/6+3/4=1 7/12
Round 846 divided by 11 to the nearest tenth
Answers
Rounded by nearest 10 =
80
A cone has a diameter of 18 units and height of 8 units. What is its volume?
Answers
Answer:
289
Step-by-step explanation:
btw i need the point pls dont use this
Final answer:
The volume of a cone with a diameter of 18 units and height of 8 units is approximately 678.58 cubic units, calculated using the formula V = 1/3πr²h.
Explanation:
The student is asking about the volume of a cone with a given diameter and height. To calculate the volume (V) of a cone, you can use the formula:
V = ⅓πr²h
where π (pi) is approximately 3.14159, r is the radius of the base of the cone, and h is the height of the cone.
The diameter is given as 18 units, so the radius (r) is half of the diameter, which is 9 units. The height (h) is given as 8 units. By substituting these values into the formula, the calculation for the volume is:
V = ⅓π(9 units)²(8 units)
V = ⅓π(81 units²)(8 units)
V = ⅓π(648 units³)
V = 216π units³
When we calculate this using the approximate value of π, the volume is:
V = 216 × 3.14159 units³
V = 678.58464 units³
The volume of the cone is approximately 678.58 cubic units.
Use the distributive property to express 16+48
Answers
Final answer:
The sum of 16 and 48 can be expressed using the distributive property by factoring out the common factor of 16, yielding 16 + 48 = 16(1 + 3).
Explanation:
The question involves using the distributive property, a concept in mathematics, to express the sum of two numbers, specifically the numbers 16 and 48. To apply the distributive property, we look for a common factor that can be factored out. In this case, the common factor of both 16 and 48 is 16. Therefore, we can express the sum as:
16 + 48 = 16(1 + 3)Here, we've factored out the number 16 that is common to both terms in the sum. The distributive property allows us to then multiply 16 by each term inside the parentheses to get back the original expression.
This is an example of how the distributive property can simplify expressions and aid in mental calculations, such as understanding that 48 can be divided evenly by 16, resulting in 3.