Which of the following is equal to the expression below?
[tex](160*243)^{\frac{1}{5} }[/tex]
A. 80
B. 96
C. [tex]5\sqrt[5]{5}[/tex]
D. [tex]6\sqrt[5]{5}[/tex]
160 = 2 x 2 x 2 x 2 x 2 x 5 = 2^5 x 5
243 = 3 x 3 x 3 x 3 x 3 = 3^5
So
(160 * 243)^1/5
= 5th root of (160 * 243)
= 5th root of (2^5 * 5 * 3^5)
= 2 * 3 * (5th root of 5)
= 6 * (5th root of 5)
Answer is D. 6 * (5th root of 5)
The resultant expression, equivalent to [tex](160*243)^{1/5}[/tex] is Option (D) [tex]6\sqrt[5]{5}[/tex]
Exponents and its properties -An exponent refers to the number of times a number is multiplied by itself. It is represented as a number or letter written above and to the right of a mathematical expression called the base. It indicates that the base is to be raised to a certain power. x is the base and n is the exponent or power.
Represented as [tex]x^{n}[/tex]
What are some of the properties of exponents ?[tex]x*x*x[/tex] ........ upto n times = [tex]x^{n}[/tex][tex](x^{n})^{1/n} = x[/tex][tex](x^{n}*y^{n} )^{1/n} = xy[/tex]How to solve the given exponent problem to get the equivalent expression ?Given expression is [tex](160*243)^{1/5}[/tex].
Now we are separating the expression,
160 = 2*2*2*2*2*5 = [tex]2^{5}*5[/tex]
243 = 3*3*3*3*3 = [tex]3^{5}[/tex]
∴ [tex](160*243)^{1/5}[/tex] = [tex](2^{5}*5*3^{5})^{1/5}[/tex] = [tex]2*3*5^{1/5}[/tex] = [tex]6\sqrt[5]{5}[/tex]
Thus the equivalent expression is Option (C) [tex]6\sqrt[5]{5}[/tex]
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Can someone please help me im struggling with this problem :(
It is given that ABCD is a parallelogram, so AB || DC by the definition of parallelogram. So, ∠1 ≅ ∠2 by the alternate interior angles theorem. It is also given that DC bisects ∠BDE, so ∠2 ≅ ∠3 by the definition of angle bisector. Therefore, ∠1 ≅ ∠3 by the transitive property of congruence (in which ∠1 ≅ ∠2, ∠2 ≅ ∠3, ∴ ∠1 ≅ ∠3 by transitive property of congruence)
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~Rise Above the Ordinary, Senpai
Take away 32 from the product of 6 and a number
Tamara is going to the laundromat. She needs 6 quarters for each of the 4 machines that she is using. How many dollar bills must she insert into the change machine to have enough quarters to do her laundry?
A) 3
B) 4
C) 5
D) 6
E) 7
Your Answer is D.
Simple addition of the value of Quarters can get us the correct answer.
It would take $1.50 to run one machine, and $1.50 x 4 = 6
What is the product of 6+5i and 4+7i?
Enter your answer, in standard form, in the box.
______
The answer to this question is the product is 12i
Answer: The required product is [tex]-11+62i.[/tex]
Step-by-step explanation: We are given to find the product of the following two complex numbers :
[tex]z_1=6+5i,~~~z_2=4+7i.[/tex]
We will be using the following property :
[tex](a+b)(c+d)=a(c+d)+b(c+d).[/tex]
Also, we will use the fact that [tex]i=\sqrt{-1},~~i^2=-1.[/tex]
The product of the given complex numbers is
[tex]z_1z_2\\\\=(6+5i)(4+7i)\\\\=6(4+7i)+5i(4+7i)\\\\=24+42i+20i+35i^2\\\\=24+62i-35\\\\=-11+62i.[/tex]
Thus, the required product is [tex]-11+62i.[/tex]
What is the solution for this inequality?
-4x < 28
A.
x > -7
B.
x < 7
C.
x < -7
D.
x > 7
Joyce makes bracelets that she sells for $1.25 each. If she sells 40 of her bracelets, how much money will she make
1.25x40=50
joyce should make $50
What is [tex]15^{2}[/tex]
Amayo943,
Remember that with exponents you have to multiply the number of exponets by the same number it's in for example: [tex]1^2 = 1 \times 1[/tex] In this case you need to know that:
[tex]15^2 = 15 \times 15[/tex][tex]15 \times 15 = 225[/tex][tex]=225[/tex]Therefore your answer is "225."
Hope this helps!
It costs $100 to be a member of a music club. A member of the club pays $20 per music lesson. A nonmember pay $30 per music lesson. How many music lessons must a member and a nonmember take so the cost for each is the same?
A member and a nonmember must each take 10 music lessons in order for the cost to be the same for both.
Explanation:To find the number of music lessons that must be taken by a member and a nonmember so that the cost for each is the same, we can set up an equation. Let x represent the number of music lessons. For a member, the cost is $100 + $20x, and for a nonmember, the cost is $30x. We can set up the equation:
100 + 20x = 30x
To solve for x, we can subtract 20x from both sides:
100 = 10x
Then, we can divide both sides by 10:
x = 10
Therefore, a member and a nonmember must each take 10 music lessons in order for the cost to be the same for both.
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can you please help me with these two questions?
For this question you are required to determine what is called a slope and y-intercept. To thoroughly explain, a slope is a constant factor while a y intercept is simply a number on the y-axis, for instance (0,1)
In order to determine slope, you would take two ordered pairs and use the following y2 - y1 divided by x2 - x1 to determine slope.
On the first attachment, take two ordered pairs.
-1 - (-3) divided by 1-0
2/1 = 2
m = 2
On the second attachment, use a principle called rise over run to determine the slope.
Using the method above, we “rise” two boxes and “run” one box, therefore the slope for the second attachment would be 2 and if we go down 2 we determine that the y-intercept is 0
Applying the explanation, we determine for the first attachment that the most sufficient answer is y = 2x - 3
The answer for the second attachment is y = 2x
Yolanda used a reconciliation worksheet provided by her bank. Line 5 should equal line 6 at the end of the reconciliation, but it does not. Mega Bank Reconciliation Worksheet Amount 1. Enter the statement closing balance. $ 345 89 2. Enter the sum of any outstanding deposits or credits. $ 0 00 3. Add lines 1 and 2. $ 345 89 4. Enter the sum of any outstanding checks or debits. $ 37 51 5. Subtract line 4 from line 3. $ 308 38 6. Enter your checkbook balance. $ 328 37 Note: Lines 5 and 6 should be equal at the end of the reconciliation. Yolanda wants to first look for a single transaction that could have caused this problem with reconciliation. What is the amount of the transaction that Yolanda should look for in order to find a solution to the problem? A. $17.52 b. $19.99 c. $20.01 d. $37.51
The best answer for the question is B. $19.99
Answer is 19.99 dollars
Explanation:
Let us draw the reconciliatin done by Yolanda linewise
Banking reconciliation Worksheet Amount of Mega
1) Closing balance $ 345 89
2) the sum of any outstanding deposits or credits. 0.00
3) Sum of 1 and 2 345.89
4. sum of any outstanding checks or debits. $ 37 51 5.
5) (3)-(4) $ 308 38
6) checkbook balance. $ 328 37
7) Difference (6)-(5) $ 19.99
SInce difference is exactly 19.99 dollars Yolanda should look for the amount 19.99 dollars to find a solution to the problem i.e. to see the reason for the difference between lines 5 and 6
In 8 minutes,josh was able to type 496 words.What's his typing speed in words per minute
62 words per minute. You would divide 8 from 496 since you need to find out how many words he can type in a minute. Your answer is 62 words per minute.
Hope this helped! :)
Fill in the blank. Given O below, you can conclude that AC is congruent to _____.
A. DF
B. OB
C. AB
D. O
Answer:
A. DF
Step-by-step explanation:
The length of OB is the same as OE, and the angle that AC makes with OB is the same as the angle DF makes with OE. This means the length of both chords, AC and DF, must be the same.
We can conclude that [tex]\boxed{\overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{OB}}} }[/tex]. Option (A) is correct.
Further Explanation:
Given:
The options are as follows,
A. [tex]\overline {{\text{AC}}} {\text{ is congruent to }}\overline {{\text{DF}}}.[/tex]
B. [tex]\overline {{\text{AC}}} {\text{ is congruent to }}\overline {{\text{OB}}}.[/tex]
C. [tex]\overline {{\text{AC}}} {\text{ is congruent to }}\overline {{\text{AB}}}.[/tex]
D. [tex]\overline {{\text{AC}}} {\text{ is congruent to }}\overline {{\text{O}}}.[/tex]
Explanation:
The length of OE is [tex]{\text{OE}} = 7.12{\text{ units}}.[/tex]
The length of OB is [tex]{\text{OB}} = 7.12{\text{ units}}.[/tex]
The length of OB and OE is [tex]7.12{\text{ units}}.[/tex]
AC and FD are the chords of the circle.
OE and OB are the perpendicular bisector of the chords AC and FD respectively.
The length of the perpendicular bisectors of chords is [tex]7.12{\text{ units}.[/tex]
The given chords of the circle are equidistant from the center of the circle.
We can conclude that [tex]\boxed{\overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{OB}}} }[/tex]. Option (A) is correct.
Learn more:
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Circles
Keywords: congruent, fill, blank, conclude, DF, OB, AB, AC, chord, tangent, displacement, two chords, radius, center, circle, equidistant,
The cheerleaders are practicing a dance routine in which all 36 of them need to be in a triangular formation. there will be two more cheerleaders in each row than the previous row. how many rows will be in the formation
If you start with 1 cheerleader in row A, then you'll have 3 cheerleaders in row B (add on 2), and then 5 cheerleaders for row C (add on another 2), etc etc.
Note how: 1+3+5 = 4+5 = 9 which is a perfect square. Also note that 36 is a perfect square.
Rule: The sum of the first positive n odd numbers is going to be equal to n^2. In the example of adding the first three odd numbers (1,3,5), we have n^2 = 3^2 = 9 as the sum
So as you can see, we'll have n = 6 rows because n^2 = 6^2 = 36 and
1+3+5+7+9+11 = 36
which is the sum of the first six positive odd numbers. So we'll have 1 cheerleader in row A, 3 in row B, 5 in row C, 7 in row D, 9 in row E, 11 in row F to have 6 rows total.
To determine the number of rows in the triangular formation, set up an equation and solve for x. The number of rows is 6.
Explanation:To determine the number of rows in the triangular formation, we can set up a series of equations.
Let x be the number of rows.
The first row will have 1 cheerleader, the second row will have 3 cheerleaders, the third row will have 5 cheerleaders, and so on.
We can set up the equation: 1 + 3 + 5 + ... + (2x-1) = 36.
This is the sum of an arithmetic sequence with a common difference of 2. Solving for x, we get x = 6.
Therefore, there will be 6 rows in the formation.
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Select the correct answer from each drop-down menu.
Use the given expression to complete the statements.
5 is a coefficient. A coefficient is a number multiplied by a variable.
(2y+13) is a factor. It can be multiplied by 8 to get an extended answer.
-1 is a constant. A constant is a number that does not change.
Hope this helps!
Answer:
coefficient, factor and constant
Step-by-step explanation:
The given expression is:
[tex]5x-8(3y+13)-1[/tex]
From the given expression , we get
In the first term, [tex]5[/tex] is a coefficient of x (A coefficient is a number multiplied by a variable.).
In the second term, [tex]3y+13[/tex] is the factor (It can be multiplied by 8 to get an extended answer)
In the third term, [tex-1[/tex] is a constant (A constant is a number that does not change)
A cafeteria uses 556 kg of rice each week. The rice comes in bags that hold 13 kg each.
How many bags of rice does the cafeteria use each week?
A. 42
B.42 1/3
C.42 10/13
or
D.43 1/3
Vito owned 120 shares of a stock before tha corporation instituted a 5 for 3 split. Before the split, the stock was selling at 16 a share. Vito now has 200 shares of te stick that is worth about $26.67 each
Vito owned 120 shares of a stock before that corporation instituted a 5 for 3 split. Before the split, the stock was selling at 16 a share. Vito now has 200 shares of the stock that is worth about $26.67 each
Answer =======> False
Post-split number of shares: 5/3 * 120 = 200
post-split price: 3/5 * 16 = $9.60
Hope that helps!!! : )
The given condition is 'False'.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Vito owned 120 shares of a stock before the corporation instituted a 5 for 3 split.
And, Before the split, the stock was selling at 16 a share.
Here,
Vito now has 200 shares of the stock that is worth about $26.67 each
Since, Vito owned 120 shares of a stock before the corporation instituted a 5 for 3 split.
Hence, Post split number of shares = 5/3 × 120
= 200
So, Post split price = 3/5 × 16 = $9.60
Thus, The given condition is false.
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What type of number cannot be written as a fraction p and q where p and q are interfere and q is not equal to zero?
The definition of a rational number is that it can be written in form [tex]\frac{p}{q}[/tex]. If it cannot be written in that form then it is not a rational number (which makes it an irrational number)
Answer: irrational number
Which is the simplified form of p to the power 0
Answer:
the correct option is D : 1
Step-by-step explanation:
Lenny has $74. He spent $24 on video games, and $21 at the grocery store. How much does lenny have left? $
If you spend money, you have less money than before. Subtraction is the operation that describes this "taking quantities away".
So, you start with 74$. You spend 24$, so we have to subtract 24:
[tex] 74-24 = 50 [/tex]
Then, you spend 21$. So, we have to subtract again:
[tex] 50-21 = 29 [/tex]
So, you're left with 29$ after you buy the video game and the groceries.
A store sells 18 costumes per day in the 5 days before Halloween. How many costumes do they sell in this time period?
They sell 18 costumes per day, times 5 days.
So,
18 costumes per day * 5 days
18*5 =90
Final answer:
To find the total number of costumes sold, multiply the daily sales of 18 costumes by the 5 days before Halloween, which equals 90 costumes.
Explanation:
If a store sells 18 costumes per day during the 5 days before Halloween, we can calculate the total number of costumes sold by multiplying the daily sales by the number of days.
Here is the calculation:
Determine the number of costumes sold per day: 18 costumes.Multiply this number by the number of days: 18 costumes/day × 5 days = 90 costumes.Therefore, the store sells a total of 90 costumes in the 5 days before Halloween.
This calculation method provides a straightforward way to determine the overall sales volume for the specified period, making it accessible for analysis and planning. The systematic breakdown into steps, including the identification of daily sales and multiplication by the number of days, enhances transparency in understanding the final result. Such clear and concise procedures contribute to effective business forecasting and logistical decision-making during peak periods like Halloween.
Terry sees an offer about a refurbished phone which is 35% off the original price the new price is £78 how much was the phone before the discounted price
part/whole=0.65
78/whole=0.65
whole =78/0.65 =120 £
Answer:
The price before discount would be $120
Step-by-step explanation:
The actual price of the phone is 100%-35% = 65% of the original price of the phone.
So by rule of three
If 65% of the price is $78, the total price of the phone would be:
[tex]Total price = \frac{74}{0,65} \\\\Total price = 120[/tex]
Sal has a small bag of candy containing three green candies and two red candies. While waiting for the bus, he ate two candies out of the bag, one after the other, without looking. What is the probability that both candies were the same color?
A.
2/5
B.
3/100
C.
8/25
D.
3/5
Answer:
A. 2/5
Step-by-step explanation:
3/5*2/4+2/5*1/4
6/20+2/20
8/20 = 2/5
Answer:
Option A
Step-by-step explanation:
Given that Sal has a small bag of candy containing three green candies and two red candies.
He ate two candies one after the other.
The probability that both candies were the same color has to be calculated.
The probability that both candies were the same color = P(both are red or both are green)
= P(both are red)+P(both are green)
Total no of ways to draw 2 candies out of 5 = 5C2 = 5(4)/2 = 10
No of ways of drawing 2 red candies = 2C2 =1
No of ways of drawing 2 green candies = 3C2 =3
Hence required prob =(1+3)/10 = 2/5
In 2015 there were approximately 33,500 firearm fatalities. How many deaths per hour
A grocer is going to sort 13.5 pounds of candy weighing 0.75 each. How much candy will be left over? 0 pounds, 0.38 pounds, 0.50pounds, 10.13 pounds
0 pounds
divide 13.5 by 0.75
[tex]\frac{13.5}{0.75}[/tex] = 18 with no remainder
Andre earns $165 for each digital projector that she sells if she works five days a week for 11 hours each day and sales 12 digital projectors a week on average what is her average hourly wage
Answer: Hi!
Andre earns $165 for each digital projector that she sells.
We know that she works 11 hours per day, 5 days per week and that she sells 12 digital projectors a week. We want to know the average hourly wage.
First, we need to know how much she wins in the week. This is the number of digital projectors sold multiplied by the profit for each one:
12*$165 = $1980
And now we need to see how the amount of hours that she works each week, this is 11 hours per day and 5 days per week, then she works 11*5 = 55 hours per week.
Now we can divide the earns per week by the number of hours that she works each week, and obtain the average hourly wage:
$1980/55 = $36
So Andre wins an average of $36 per hour.
A café sold 1,400 beverages in one month. If 60% of those beverages were coffee, how many coffees did the café sell in the month
Number of beverages sold by cafe= 1,400
Number of beverages which were coffee= 60 % of number of beverages sold.
So, number of coffees that the café sell in the month= 60 % of 1400
[tex]=\frac{60}{100}\times 1,400\\\\= 60 \times 14\\\\=840[/tex]
Keep in mind, x % of y is , [tex]\frac{x y}{100}[/tex]
Number of Coffees that cafe sell in month= 840
Tobias dropped a tennis ball from a height of 60 meters. The time in seconds it takes for the ball to fall is 60 feet is 0.25 √60. Find three sets of approximations for the amount of time it will take. Then determine how long it will take for the ball to hit the ground.
Answer:-1)The three sets of approximation of time will be
Time taken to fall tennis ball from height of 60 m =35.41014 s ≈35.410 s (to the nearest thousandth)
≈35.41s (to the nearest hundredth)
≈35.5 seconds(to the nearest tenth)
2)Time by the ball to hit the ground =35.5 seconds
Step-by-step explanation:
Time taken to fall tennis ball from height of 60 feet = 0.25 √60 s
So,time taken to fall tennis ball from height of 1 foot =0.25√60 divided by 60=[tex]\frac{0.25\sqrt{60} }{60}s[/tex]
We know that 1 m = 0.3048 foot
⇒60 m =60×0.3048=18.288 feet
therefore, Time taken to fall tennis ball from height of 60 m = 18.288 ×time taken to fall tennis ball from height of 1 foot=[tex]\frac{0.25\sqrt{60} }{60}\cdot18.288=35.41014\ s[/tex]
∴Time taken to fall tennis ball from height of 60 m =35.41014 s ≈35.410 s (to the nearest thousandth)
≈35.41s (to the nearest hundredth)
≈35.5 seconds(to the nearest tenth)
The time it will take for a tennis ball dropped from a height of 60 meters to reach the ground can be calculated using the equation t = 0.25 √h. Three sets of approximations were determined for heights of 30m, 45m and 60m, with the final time for the 60m drop being approximately 1.94 seconds.
Explanation:
The time it takes for the tennis ball to hit the ground can be calculated using the equation t = 0.25 √h, with 't' being time and 'h' being height. Inserting the given height of 60 meters into this equation will reveal how long it takes for the tennis ball to hit the ground.
Approximation set 1: If h = 30 m, t = 0.25 √30 = 1.37 sec Approximation set 2: If h = 45 m, t = 0.25 √45 = 1.68 sec Approximation set 3: If h = 60 m, t = 0.25 √60 = 1.94 sec
From these calculations, it can be determined that the time it will take for the tennis ball dropped from a height of 60 meters to hit the ground is "approximately 1.94 seconds".
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Four times the difference of a number and 5 is the same as 5 increased by four times the number plus five times the number
The value of expression is,
x = - 5
Here;
The written expression is;
''Four times the difference of a number and 5 is the same as 5 increased by four times the number plus five times the number.''
We have to solve this expression.
What is Mathematical expression?
The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.
Now,
Let a number is 'x'.
Then, The mathematical expression is written as;
4* ( x - 5 ) = 5 + (4*x) + (5*x)
We can solve as;
4* ( x - 5 ) = 5 + (4*x) + (5*x)
4x - 20 = 5 + 4x + 5x
- 20 - 5 = 4x + 5x - 4x
- 25 = 5x
x = -5
Hence, The value of expression is,
x = - 5
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What are the like terms of 10a+4b+3a-15b
The like terms in the expression are 10a and 3a, as well as 4b and -15b.
We have,
The like terms of the expression 10a + 4b + 3a - 15b are the terms that have the same variable(s) raised to the same power(s).
In this case, the like terms are:
10a and 3a (both have the variable 'a')
4b and -15b (both have the variable 'b')
Thus,
The like terms in the expression are 10a and 3a, as well as 4b and -15b.
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