Express 2^40 × 4^30 in the form 2^n
Answer:
[tex]2^{100}[/tex]
Step-by-step explanation:
Given expression:
[tex]2^{40} \times 4^{30}[/tex]
Rewrite 4 as 2²:
[tex]\implies 2^{40} \times (2^2)^{30}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 2^{40} \times 2^{(2\times30)}[/tex]
[tex]\implies 2^{40} \times 2^{60}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies 2^{(40+60)}[/tex]
[tex]\implies 2^{100}[/tex]
Therefore, n = 100.
05.05
The sample space for tossing a coin 3 times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
Determine P(2 tails).
12.5%
37.5%
50%
75%
The value of P(2 tails) is 37.5%, the correct option is B.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
We are given that;
The sample space= {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Now,
The sample space for tossing a coin 3 times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}, where H represents heads and T represents tails.
To determine P(2 tails), we need to count the number of outcomes in which there are 2 tails, and divide that by the total number of outcomes:
Number of outcomes with 2 tails: There are three outcomes with 2 tails: TTH, THT, and HTT.
Total number of outcomes: There are eight outcomes in total.
P(2 tails) = number of outcomes with 2 tails / total number of outcomes = 3/8 = 0.375, which is equivalent to 37.5%.
Therefore, the probability the answer will be 37.5%.
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Terry used a total of 52 inches of ribbon to make 6 decorations. He used the same amount of ribbon for each decoration. How much ribbon did Terry use for each decoration?
Answer:52 x 6=312
Step-by-step explanation:
Terry used 52 inches of ribbon for the same amount. He's multiplying. Hope this helped.
ms. wilson draws a model of the factorization of a polynomial with integer factors. her model is partially complete. which equation is represented by ms. wilson’s model? n2 3n 40
n²+13n+40,
This is why;
Observe only the right side. The number is (n+8)(n+5).
Let's elaborate on that using FOIL.
F = When we multiply the first two terms, n and n, we obtain n².
O = outer instructs us to multiply n by 5 to get n*5 or 5n from the outer terms.
I = inner instructs us to multiply the inner expressions 8 by 8 and n by n to obtain 8n.
Since 8 and 5 are multiplied by L, we obtain 8*5 = 40.
Add up the outcomes: n²+5n+8n+40 = n²+13n+40
Observe how the phrase is a little bit simplified by the combination of the like terms (5n and 8n).
This demonstrates how (n+8)(n+5) becomes n²+13n+40, becoming the correct response. For all values of n, none of the other options are valid equations;
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graph: y + 2 = 2 (x + 3)
what the answer to
1 4/5 x 5/6
Answer:
7/3
Step-by-step explanation:
14/5×5/6
=14/6
=7/3
Berto has $12 to put gas in his car. If gas costs $3.75 per gallon, which ordered pair relating number of gallons of gas, x, to the total cost of the gas, y, includes the greatest amount of gas Berto can buy?
(
,
)
The ordered pair for the greatest amount he can buy is (3.2, 12)
How to find the greatest cost of gas?He has $12 to put gas in his car. The gas costs $3.75 per gallon.
Therefore,
x = number of gallons of gasy = total cost of the gas.Hence, the total amount he has to spend is 12 dollars.
Therefore,
y = 3.75x
where
y = 12 dollars
Therefore,
12 = 3.75x
divide both sides by 3.75
12 / 3.75 = 3.75x / 3.75
x = 3.2
Therefore, the ordered pair for the greatest amount he can buy is (3.2, 12)
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Which is a reasonable first step that can be used to solve the equation 2 (x + 6) = 3 (x minus 4) + 5?
Group of answer choices
Distribute 2 to (x + 6) and 3 to (x – 4).
Apply the subtraction property of equality to move the 6 from the left side of the equation to the right side.
Combine like terms, 3 and 5, on the right side of the equation.
Distribute 2 to x on the left side of the equation and 3 to x on the right side of the equation.
Answer:
x = 19
Step-by-step explanation:
I think you are on the right track. Below is the way I would approach it:
1. Expland the brackets
2. Collect like terms
3. Make x the subject
Let me know if you want the working out. Hope this helps.
Martin scores 10% of the points in a game if this represents 10 point how many points were scored in total
Answer:
10 OR 100. Read the explanation for details.
Step-by-step explanation:
If Martin scored 10%, and this represents 10 points, that means that martin scored 10 points. If he is talking about ALL the points in total then there are 100 points because 10% is 1/10, and if each 1/10th is 10 points, if you multiply that by 10 you get
100.
On a coordinate plane, point P is at (negative 4, 3). a. (–4, 3) b. (–3, 4) c. (3, –4) d. (4, –3) Group of answer choices
option (A) ( - 4 , 3 ) is the correct option to represent the coordinate of point P at ( negative 4, 3 ).
We are given the coordinate of the point as:
(negative 4, 3)
the negative means a minus ( - ) sign.
So, the coordinate of point P can also be written as:
( - 4 , 3 )
So, we get that:
Option (A) ( - 4 , 3 ) is the correct option.
Therefore, we get that, option (A) ( - 4 , 3 ) is the correct option to represent the coordinate of point P at ( negative 4, 3 ).
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Dan earns £9.20 per hour. How much will he earn for 8 hours work?
Answer:
£73.6
Step-by-step explanation:
Earnings per hour ( means for one hour of work he earns)= £9.20
total no of hours he works for = 8
so,in 8 hours he will earn
9.20× 8=£73.6
In the figure QRST, point Q has coordinates (2, -3). If you translate the figure 4 units left and 3 units down, what are the coordinates of the translated point Q'?
Answer:
Q' (- 2, - 6 )
Step-by-step explanation:
a translation of 4 units left is in the x- direction and means subtract 4 from the x- coordinate.
a translation of 3 units down is in the y- direction and means subtract 3 from the y- coordinate.
Q (2, - 3 ) → Q' (2 - 4, - 3 - 3 ) → Q' (- 2, - 6 )
1. Write the following sentence using mathematical symbols.
Twice x, plus 10, is the same as - 5.
The sentence can be represented as 2x+10=-5, with x = -7.5
Given that twice the value of x plus 10 is equals to -5
Mathematical symbols are used to perform various operations. The symbols make it easier to refer Mathematical quantities. It is interesting to note that Mathematics is completely based on numbers and symbols. The math symbols not only refer to different quantities but also represent the relationship between two quantities. All mathematical symbols are mainly used to perform mathematical operations under various concepts.
• Helps in denoting quantities
• Establishes relationships between quantities
• Helps to identify the type of operation
2(x)+10=-5
2(x)=-15
x=-15/2
x=-7.5
Hence, The sentence can be represented as 2x+10=-5, with x = -7.5
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*First to answer rightfully will get brainliest. NO LINKS are allowed. Thank you.
Please help with the following question:
You just got back from a trip to
Florida for the school break and
you still have $225 in U.S.
currency. Today, the bank rate is
C$1.04 for US$1. How much in
Canadian funds will you get for
your U.S. currency?
se polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the following exercise. find the following sums without using a calculator or a formula
The sums of series using Polya's four-step problem-solving strategy in (a), (b) and (c) are 79800, 150975, and 1560 respectively.
(a) Let S = 1 + 2 + 3 + … + 398 + 399Write the series in reverse order and then add both series.S = 1 + 2 + 3 + … + 398 + 399S = 399 + 398 + … + 2 + 12S = 400 + 400 + … + 400 + 4002S = 400 x 399S = (400 X 399 ) / 2 = 200x399 = 79800(b) Let S = 1 + 2 + 3 + … + 548 + 549Write the series in reverse order and then add both series.S = 549 + 548 + … + 2 + 12S = 550 + 550 + … + 550 + 5502S = 550 x 549S = (550x549 ) / 2 = 275x549 = 150975(c) Let S = 2 + 4 + 6 + 8 + … + 72 + 74 + 76 + 78Write the series in reverse order and then add both series.S = 2 + 4 + 6 + … + 72 + 74 + 76 + 78S = 78 + 76 + 74 + … + 6 + 4 + 22S = 80 + 80 + … + 80 + 802S = 80 x 39S = (80 X 39 ) / 2 = 40 x 39 = 1560a sequence is, more or less speaking, a description of the operation of adding infinitely many quantities, one after the opposite, to a given starting quantity. The examine of series is a chief part of calculus and its generalization, mathematical evaluation. series are utilized in maximum areas of mathematics, even for reading finite structures (which includes in combinatorics) thru producing features.
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Answer:
?
Step-by-step explanation:
2. compare the histogram at 5 bins and at 25 bins. what does the narrower bin width reveal that the wider bin width obscures?
Answer: skewed left
Step-by-step explanation:
a distribution with two peaks: one at $30,000 and the other at $40,000
I need help. somebodysolve this. i think the answer is 8
(2x +20)y X=10 y=5
Answer:
If there is divide sign between (2x+20) and y, then the answer is 8 but if there's multiplication sign between (2x+20) and y, then the answer is 200.
Benjamin's credit card has an APR of 19%, calculated on the previous monthly
balance, and a minimum payment of 2%, starting the month after the first
purchase. His credit card record for the last 7 months is shown in the table
below.
End of
month
2
3
5
6
7
Previous
balance
$0.00
$2400.00
$2390.00
$2380.04
$2370.12
$2360.25
$2350.41
New
charges
$2400.00
$0.00
$0.00
$0.00
$0.00
$0.00
$0.00
Payment Finance
received
charges
$0.00
$0.00
OA. $59.38
OB. $47.01
OC. $285.01
OD. $225.64
$48.00
$47.80
$47.60
$47.40
$47.20
$47.01
$38.00
$37.84
$37.68
$37.53
$37.37
$37.21
Principal
paid
$0.00
$10.00
$9.96
$9.92
$9.88
$9.83
$9.79
New
balance
$2400.00
$2390.00
$2380.04
$2370.12
$2360 25
$2350.41
$2340.62
What is the total amount that Benjamin has made in payments over the 7
months?
If Benjamin's credit card has an APR of 19%, calculated on the previous monthly balance, and a minimum payment of 2%, starting the month after the first purchase. the total amount that Benjamin has made in payments over the 7 months is: $285.01.
Total amount made in paymentTo determine the total amount that Benjamin has made in payments over the 7 months we would need to add up or sum up all the Payment Finance received charges for the first six months.
Now let calculate the total amount that Benjamin made in payment.
Hence,
Total amount made in payment=$48.00+$47.80+$47.60+$47.40+$47.20+$47.01
Total amount made in payment =$285.01
Therefore if Benjamin's credit card has an APR of 19%, calculated on the previous monthly balance, and a minimum payment of 2%, starting the month after the first purchase. the total amount that Benjamin has made in payments over the 7 months is: $285.01.
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Help needed with geometry.
Answer:
d
Step-by-step explanation:
Answer: d
what is the monthly difference in median income for a male versus a female when both have a bachelor's degree
Answer: $1,372
Step-by-step explanation:
If using the Labor Statistics Document
A men’s median weekly earning with Bachelor’s degree only is $1,384 * 4 weeks = $5,536
A women’s medium weekly earning with a Bachelor’s degree only is $1,041 * 4 weeks = $4,164
Subtract $5,536 - $4,164 = $1,372
The full sentences are:
The typical monthly salary for women with bachelor's degrees is $3,020.
The typical annual salary for a guy with an associate's degree is $36,432.
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Every month has four weeks.
The median monthly income is thus:
Earnings = 4 * $755
Earnings = $3020
As a result, the typical monthly salary for women with bachelor's degrees is $3,020.
The median annual income:
A man with an associate's degree makes $759 each week.
A month has four weeks, while a year has twelve months.
Hence, the annual median income is:
Earnings = 4 x 12 x $759
Earnings = $36,432
Thus, the typical annual salary for a guy with an associate's degree is $36,432.
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Complete question:
3. What is your monthly median income if you are a female with a bachelor's degree? _____
4. What is your yearly median income if you are a male with an associates degree? _____
Complete the explanation to identify the set of numbers that best describes the situation.
the amount of water in a glass as it evaporates
The amount can be any
number less than 0
, thus it is a
rational
number.
Ria has these two cubes.
The side length of the smaller cube is x cm.
The side length of the larger cube is twice the side length of the
smaller cube.
Write an expression for the side length of the larger cube in
terms of x.
Answer:
2x
Step-by-step explanation:
side length of smaller cube = x
side length of larger cube is two times the side length of smaller cube.
Therefore side length of larger cube = 2x
up
A water tap is leaking at the rate of 25 mL every 20 seconds. How many litres of
water are wasted each day?
[3 marks]
Answer: 108 liters
Step-by-step explanation: There are 86,400 seconds in a 24-hour day. If 25 mL leak every 20 seconds, divide 86,400 by 20 (4,320), then multiply by 25 (108,000). There is 1,000 mL for every liter, so divide 108,000 by 1,000, and you will get 108 liters.
You are solving a measurement problem where the numbers 4.0286 × 109 and 3.1 × 10−4 are divided. How many significant digits should the quotient have?
The quotient will have 2 significant figures.
The digits in the number , that contribute to the degree of accuracy can be defined as Significant Figures.
For Example ; 2.096 has 4 significant Figures
0.069 has 2 significant figures.
Rule Of Significant for Multiplication & Division :
Rule says in multiplication or division , the final result should retain as many significant figures as there are in the original number with the least significant figures.
In the given question
4.0286 × 10⁹ = 5 significant figures
3.1 × 10⁻⁴ = 2 significant figures
The quotient on dividing the numbers is 1.2995 x 10¹³ will have 2 significant figures as the least significant from 5 and 2 is 2.
Therefore , the quotient will have 2 significant figures.
The given question is incomplete , the complete question is
You are solving a measurement problem where the numbers 4.0286×10⁹ and 3.1×10⁻⁴ are divided. How many significant digits should the quotient have?
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I need help please help me if u can
here is the answer
Step-by-step explanation:
it is just changing decimals to normal numbers.
proof that the span of two noncollinear vectors is the plane containing the origin and the heads of the vectors.
The Span of two noncollinear vectors is the plane containing the origin and the heads of the vectors.
Linear Span of vectors can be represented as
let [tex]x_{1} and x_{2}[/tex] be two non collinear vectors its span be written as [tex]x=a_{1} x_{1} +a_{2} x_{2}[/tex] where [tex]a_{1}, a_{2}[/tex] are arbitrary scalars.
Subspace of vectors : a subset A of a vector space V is called a subspace of V if A is itself a vector space under scalar multiplication and addition defined on V.
The Span of two vectors is a vector space containing two vectors. Hence the span is also a vector space . It is sufficient to notice that any two independent vectors from subspace can be the basis.
Zero vector is the linear combination of these basis vector.
hence it is not possible to have a span of two non collinear vectors that does not contain origin .
Therefore, The span of two noncollinear vectors is the plane containing the origin and the heads of the vectors.
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4+801542/85*994567789
Answer:9,378,727,447,079.929
Step-by-step explanation:
Answer:
9.37414075 13 squared digit I don’t remember what it is called for that number so yea
Step-by-step explanation:
8011542/84 is 94257.43529 (already added 4) and 94257.43529 is about 9.37414075 13 squared digit I don’t remember what it is called for that number but that is the answer
Muse synthetic division to find the quotient and remainder when 3x^4 +19x^3+22x^2-6x+4 is divided by x+2
Answer: 3x^3 +13x^2 -4x +2 +0/(x+2)
Step-by-step explanation:
-2: 3 19 22 -6 4=
-6 -26 8 -4
3 13 -4 2 0 ==> 3x^3 +13x^2 -4x +2 +0/(x+2)
Quotient: 3x^3 +13x^2 -4x +2
Remainder: 0
Write 10 algebraic expressions and then solve them!
(This is kinda easy and also I'll make brainliest answer to someone who answered correctly,clear and detailed!)
Answer: done
x + 3 = 0
subtract 3 on both sides
x = -3
x +4 = -3
subtract 4 on both sides
x = -7
3x = 0
divide 3 on both sides
x = 0
5x = 2
divide 5 on both sides
x = 2/5
x - 4 = 0
add 4 on both sides
x = 4
5x - 4 = 0
add 4 on both sides then divide both sides by 5
x = 4/5
2x + 4 = 5
subtract both sides by 4 then divide both sides by 2
x = 1/2
2x^2 = 9
square root both sides then divide both sides by 2
x = 3/2
5x - 1 = 2
add both sides by 1 then divide both sides by 5
x = 3/5
x + 3 = 65
subtract both sides by 3
x = 62