simplify the expression. Write the answer using scientific notation. (4x10^8) ^-2
Given:
[tex](4\times10^8)^{-2}[/tex]Aim:
We need to write the given expression in scientific notation.
Explanation:
[tex]Use\text{ \lparen a}\times b)^n=a^n\times b^n.[/tex][tex](4\times10^8)^{-2}=4^{-2}\times(10^8)^{-2}[/tex][tex]Use\text{ \lparen a}^n)^m=a^{n\times m}.[/tex][tex](4\times10^8)^{-2}=4^{-2}\times10^{-16}[/tex][tex]Use\text{ a}^{-n}=\frac{1}{a^n}[/tex][tex](4\times10^8)^{-2}=\frac{1}{4^2}\times10^{-16}[/tex][tex](4\times10^8)^{-2}=\frac{1}{16}\times10^{-16}[/tex][tex](4\times10^8)^{-2}=0.0625\times10^{-16}[/tex][tex]Use\text{ -16=2-18.}[/tex][tex](4\times10^8)^{-2}=0.0625\times10^{2-18}[/tex][tex](4\times10^8)^{-2}=0.0625\times100\times10^{-18}[/tex][tex](4\times10^8)^{-2}=6.25\times10^{-18}[/tex]Final answer:
[tex](4\times10^8)^{-2}=6.25\times10^{-18}[/tex]Owen, Caden, and Luke played basketball. Owen scored 26 more points than Caden, who scored 68 points. Luke scored half of the total of Owen and Caden's score. How many points did Luke score?
Please give an explanation! Whoever answers first and correctly gets brainlist!!
Answer:
81
Step-by-step explanation:
68+26=94+68=162/2=81
You drive 3 hours to reach the waterpark. Driving home along the same route, you increase your
speed by 20 miles per hour, reducing your drive time by 1 hour. Write and solve an equation to find
how fast you were driving to the waterpark.
The initial speed to the waterpark is 40 miles/hr.
The return speed is 60 miles/hr.
How to find the speed?
Given,
t = 3hr
Return speed = s +20m
Return time = 3 -1 = 2hrs
Solution:
s = d/t
s = d/3
d = 3s----1
s + 20 = d/t - 1
s + 20 = d/3-1
s + 20 = d/2
2s + 40 = d------2
Equating equations 1 and 2,
3s = 2s + 40
s = 40 miles/hr
The initial speed to the waterpark is 40 miles/hr.
Return speed = s +20
= 40+20
= 60 miles/hr
The return speed is 60 miles/hr.
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Postage Stamp A square postage stamp has area 1,260 mm². About how long is each side?
Answer: 35.9166 mm (the square root of 1290)
Step-by-step explanation:
luke ran 3/4 as much as much as he did on thursday then he did on wendsday how many miles did luke run on thrurday
The number of miles that Luke ran on Thursday will be 3 miles.
How to calculate the fraction?From the information given, it was illustrated that Luke ran 4 miles on Wednesday and then ran 3/4 as much as much as he did on Thursday.
It should be noted that the distance that he ran on Thursday will be:
= 3/4 × Distance on Wednesday
= 3/4 × 4
= 3 miles.
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Luke ran 4 miles on Wednesday. Luke ran 3/4 as much as much as he did on thursday than he did on wendsday how many miles did luke run on thrurday
mr.ocampo invested 150,000 at 10% compounded annually. he plans to get this amount for 6 years for his son's college education, how much will he get?
The most appropriate choice for compound interest will be given by -
Mr Ocampo recieves 265734.15
What is compound interest?
If the interest on a certain principal increases over a period of time at a certain rate exponentially rather than linearly, then the interest is called compound interest.
If P is the principal, r is the rate and n is the time in years,
Amount (A) = [tex]P(1 +\frac{r}{100})^n[/tex]
Principal invested by Mr. Ocampo = 150000
Rate = 10%
Time = 6 years
Amount recieved by Mr.Ocampo = [tex]150000(1+\frac{10}{100})^6[/tex]
[tex]150000(1 + \frac{1}{10})^6\\150000(\frac{10+1}{10})^6\\150000(\frac{11}{10})^6[/tex]
265734.15
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5 1 point The following table shows the relationship between the federal taxes owed and the adjusted gross income. Adjusted Gross income Federal tax 16,500 2,475 19,500 2,925 24,000 3,600 Find the tax rate and calculate the amount of federal taxes owed for 31,000. Type your answer... Prbvious
The answer is very simple
The federal tax rate is the relation between federal tax and the adjusted grooss income
[tex]\text{federal tax rate = }\frac{2475}{16500}=0.15[/tex]and the federal tax for 31000 is
[tex]\text{federal tax = 31000}\cdot0.15=4650[/tex]That is the solution.
angela spends $95 to buy 7 cakes for the office party. she cuts each cake into quarters, then cuts each quarter into 3 pieces. if kevin eats 5 pieces of cake during the party, how much did engela spend on just kevins share of the cake
If Angela spent $95 to buy 7 cakes for her office party, and she then cut each cake into quarters and each quarter into further 3 pieces, of which Kevin ate 5 pieces, then Angela had spent $5.65 on just the share of the cake that Kevin had.
As per the question statement, Angela spends $95 to buy 7 cakes for her office party, and she then cuts each cake into quarters and each quarter into further 3 pieces, of which Kevin ate 5 pieces.
We are required to calculate the amount Angela had spent on just the share of the cake that Kevin had.
To solve this question, first let us calculate the total number of pieces, did Angela cut all the 7 pieces of the cake into.
Considering one piece, that it was first cut into a quarter and then each quarter into further 3 pieces, one single piece out of original 7 pieces was cut into a total of [(4 * 3) = 12] pieces.
Therefore, all the 7 original pieces were altogether cut into a total of
[(7 * 12) = 84] pieces.
Now, since Angela spent $95 to buy the original 7 pieces,
Or, Angela actually spent $95 to buy 84 pieces of cake,
Then, 1 piece of the 84 costs $(95/84) = $1.13.
Now, since Kevin ate 5 such pieces of the 84, those 5 pieces cost
$(1.13 * 5) = $5.65.
Therefore, Angela had spent $5.65 on just the share of the cake that Kevin had.
Quarter: In Mathematics, when one whole of anything is divided into 4 equal parts, every part is known as a quarter.To learn more about Quarters, click on the link below.
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helpppp plsssssssss
..........................................
Answer:
D. An infinite number of real solutions
Step-by-step explanation:
3(2x + 1) = 2(3x + 5) - 7
6x + 3 = 6x + 10 - 7
6x + 3 = 6x + 3
I hope this helps!
Eric received a $35.50 gift card for a photo center. He used it to buy prints that cost 6 cents each. The remaining balance, B (in dollars), on the card after buying x prints is given by the following function.
B (x) = 35.50 - 0.06x
What is the remaining balance on the card if Eric bought 40 prints?
Answer:
B(x) = 40.00 - 0.08x
Step-by-step explanation:
Find the slope of the line that passes through the following points: (5,4) (-2,0)
Answer: slope = 4/7
Step-by-step explanation:
you can plug the coordinates into the slope formula. y2 - y2/x2 -x1.
Help with part B please
a) The opposite of the numbers 3, 7.5, and -2(2/3) will be 0.33, 0.133, and -0.375.
b) The sum of the given number and its opposite will be 7.928.
What is an irrational number?It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.
A rational number is a sort of real number that has the form p/q and does not equal zero.
The given number is as,
3, 7.5, and -2(2/3)
a)
The opposite number is obtained as 1 by dividing the given number,
⇒ 1 / 3 = 0.33
⇒ 1 / 7.5 = 0.133
⇒ 1 / -2(2/3) = -0.375
b)
The sum of the given number and its opposite is,
= 3+0.33 + 7.5 + 0.133+ (-2(2/3) ) + (-0.375)
= 7.928
Thus, the opposite of the numbers 3, 7.5, and -2(2/3) will be 0.33, 0.133, and -0.375.and the sum of the given number and its opposite will be 7.928.
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What is the value of this expression when x = -6 and y= 1/2 ?
4(x2 + 3) − 2y
Answer: -37
Step-by-step explanation:
Select the correct answer from each drop-down menu. Consider parallelogram ABCD, where m∠ABC = 135° and the length of diagonal AC is 41 units. A parallelogram ABCD has two diagonals AC and BD, intersects each other at a point E inside it. The length of side AD is 35 units and length of side AB is 7 units. An arc is marked on angle B. Note: figure not drawn to scale Use the figure and given information to complete the statements. m∠BCD = ° The length of segment CD is units. The length of segment AE is units.
The length of segment CD is 7 units. The length of segment AE is 20.5 units. The m∠BCD is 45 degrees.
What is a parallelogram?A parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Given that parallelogram ABCD, has m∠ABC = 135° and the length of diagonal AC is 41 units.
The measure of length of side AD is 35 units and length of side AB is 7 units.
WE know that the opposite side of a parallelogram are same. Thus,
The length of segment CD = AB = 7 units.
Also, the length of diagonal AC = 41 units. Then;
The length of segment AE = 1/2 AC = 41/2 = 20.5 units.
Therefore, m∠BCD + m∠ABC = 180
m∠BCD + 135 = 180
m∠BCD = 180 - 135
m∠BCD = 45 degrees.
Hence, The length of segment CD is 7 units. The length of segment AE is 20.5 units. The m∠BCD is 45 degrees.
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Answer:
45
7
20.5
Step-by-step explanation:
Jeriel is going to invest $640 and leave it in an account for 5 years. Assuming the
interest is compounded annually, what interest rate, to the nearest tenth of a percent,
would be required in order for Jeriel to end up with $760?
Using the compounding formula we can conclude that approximately a 3% of interest rate would be required in order for Jerial to end up with $760.
What is a compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit. It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it so that interest is earned the following period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.So, the principal amount is $640 and the obtained amount is $760.
Compounded annually for 5 years.Then the interest rate will be:
3.497%Rounding off to the nearest tenths: 3%(Refer to the image attached below for calculation)
Therefore, using the compounding formula we can conclude that approximately a 3% of interest rate would be required in order for Jerial to end up with $760.
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the cost of 12 hot dogs and 8 fry portions is £52. The cost of 8 hot dogs and 12 fry portions is £48. What is the total cost of a hot dog and a portion of fries?
Answer:
Hot dogs cost £3 and fry's cost £2.
Total cost £5.
Step-by-step explanation:
Let a hot dog cost £x and a portion of fry's cost £y.
Then:
12x + 8y = 52
8x + 12y = 48
Simplifying these 2 equations we get:
3x + 2y = 13 ---------- (A)
2x + 3y = 12...............(B)
multiply the first equation by 2 and the second by 3:
6x + 4y = 26
6x + 9y = 36
Subtracting:
0 - 5y = -10
y = -10/-5 = 2.
Now, substituting in equation (A):
3x + 2(2) = 13
3x = 9
x = 3.
Suppose it took 19 riders a total of 11 days and 21 hours to ride from New Jersey to Virginia. If they all rode the same number of hours, how many hours did each rider ride?
Answer:
15 hours
Step-by-step explanation:
24 hours= 1 day
11 times 24 = 264
264 + 21 =285
285 dived by 19 = 15
each rider rode 15 hours
You borrow $90,000 for college at an APR of 6.25%. You plan to elect 25-year repayment. How much more must you repay in total if your loan is unsubsidized, as opposed to being subsidized?
Answer:
Step-by-step explanation:
if you have x - 4 and subtract 1 / 4 x + 5 from it the result is
Answer
(3x/4) - 9
[tex]\frac{3x}{4}-9[/tex]Explanation
We are told to subtract (¼x + 5) from (x - 4)
We just simply do this step by step
(x - 4) - (¼x + 5)
[tex]\begin{gathered} (x-4)-(\frac{1}{4}x+5) \\ =x-4-\frac{1}{4}x-5 \\ =x-\frac{x}{4}-4-5 \\ =\frac{4x}{4}-\frac{x}{4}-9 \\ =\frac{4x-x}{4}-9 \\ =\frac{3x}{4}-9 \end{gathered}[/tex]Hope this Helps!!!
I confused on this would be grateful if any one could help
Answer:
126
Step-by-step explanation:
a+b=d
9x being d, 4x being a and 70 being b
4x+70=9x
70=5x
x=14
9(14)=126
What is twelve hundredths as a fraction
ANSWER
[tex]\frac{12}{100}[/tex]EXPLANATION
Now, imagine you are to divide something into 100 equal sections;
the 12th section of those sections is the twelve hundredths.
To represent this as a fraction we have 12/100.
Hence, the twelve hundredths as a fraction is 12/100.
g(x) = x2 − 5x
h(x)= 4x + 4
Find (g ◦ h) (x)
Answer:
(g ◦ h) (x) = 16x² + 12x -4
Step-by-step explanation:
We have
g(x) = x² − 5x
h(x)= 4x + 4
(g ◦ h) (x) = g(h(x))
h(x) = 4x + 4
g(h(x)) = g(4x + 4)
= (4x + 4)² - 5(4x+4) //substitute 4x + 4 wherever there is an s-term in
(4x + 4)² = 16x² + 32x + 16
5(4x + 4) = 20x + 20
(4x + 4)² - 5(4x+4) = 16x² + 32x + 16 -(20x + 20)
= 16x² + 32x + 16 - 20x - 20
= 16x² +(32x - 20x) + (16-20)
= 16x² + 12x -4
Help , stuck on this one .
Answer:
D. -87 + 33i
Step-by-step explanation:
(7 + 5i)(-6 + 9i)
7(-6 + 9i) + 5i(-6 + 9i)
-42 + 63i + -30i + 45i²
-42 + 33i + 45(-1)
-42 + 33i - 45
-87 + 33i
I hope this helps!
I am doing principle rate and time and trying to figure out how to find out what the missing number is whether it be rate time or principle
Generally, the equation representing the simple interest on a deposited amount is;
[tex]I\text{ = }\frac{PRT}{100}[/tex]where ;
I is the simple interest
R is the rate
T is the time
We have other varaints of this formula, depending on the term missing
All we have to is to make the missing term the subject of the equation and input the other given values to get the missing term
We can have the variants of this formula as follows
a) Missing Principal
[tex]P\text{ = }\frac{100I}{RT}[/tex]b) Missing Rate
[tex]R\text{ = }\frac{100I}{PT}[/tex]c) Missing Time
[tex]T\text{ = }\frac{100I}{PR}[/tex]If Sally has 5 apples, 4 oranges, 3 bananas, 2 grapes, and a plum, how many people does it take to screw in a lightbulb?
Some responses are incorrect. They overlooked the fact that we must eventually add up the cost of one banana.
1 Apple = 7
5 + 7 Equals 12 grapes in a bunch.
After substituting the preceding variables, we arrive to the result that 1 banana equals 2 (7 = 1 + 3 bananas). 21 is incorrect
The second equation has 12 grapes, therefore after solving it, we obtain 1 grape = 1.
However, the final equation has 11 grapes, so we end up with (7+11+2)=20.
Eric, counting the grapes was difficult
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complete question:
If Sally has 5 apples, 4 oranges, 3 bananas, 2 grapes, and a plum, how many people does it take to screw in a lightbulb?
the retail price of a television set is $4500. if the buyer pays cash, the price 10% below the retail price. if the set is bought on hire purchasr, the buyer pays a downpayment of $675 and 24 monthly instalments of $212.50.(a) Determine the difference between the hire purchase price and the cash price.(b) Calculate the difference as a percentage of the retail price.
Data:
Retail price: $4500
Pays cash: -10%
hire purshast: $675 + 24(212.50)
-----------------------------------
The cash price is: $40501. Find the 10% of 4500:
[tex]4500\cdot\frac{10}{100}=450[/tex]2. Substract the 10% to the retail price:
[tex]4500-450=4050[/tex]-------------------------------------
Hire purchase price is: $57751. Add 675 and (24*212.50):
[tex]\begin{gathered} 675+(24\cdot212.50) \\ =675+5100 \\ =5775 \end{gathered}[/tex]-----------------------------------------
Difference between hire purchase and cash price is: $1725[tex]5775-4050=1725[/tex]----------------------------
Difference as a percentage of the retail price is: 38.33%As the retail price 4500 is 100% which percent is 1725:
[tex]1725\cdot\frac{100}{4500}=38.33[/tex]4% of a number is what fraction of that number?
First, let's remember how we calculate a percentage:
If we call the number "x", 4% is calculated by dividing x by 100 and then multiplying by 4:
[tex]\frac{x}{100}\times4[/tex]This can also be represented as follows:
[tex]\frac{4}{100}\times x[/tex]Thus, 4% of a number is 4/100 of that number. We can still simplify this result as follows:
[tex]\frac{4}{100}=\frac{1}{25}[/tex]We divide 4 by 4 and get 1, and also divide 100 by 4 and get 25.
Answer: 4% of a number is 1/25 of that number.
Consider the equation 2 (ax+ 3) = 4x- 3 (4x+ 8). For what value of a is there no solution to the equation?
The equation given is,
[tex]2(ax+3)=4x-3(4x+8)[/tex]Solving for a
Expand the terms
[tex]\begin{gathered} 2\times ax+2\times+3=4x-3\times4x-3\times+8 \\ 2ax+6=4x-12x-24 \\ 2ax+6=-8x-24 \end{gathered}[/tex]Comparing the two sides of the equation
[tex]2ax=-8x[/tex]Divide both sides by 2x
[tex]\begin{gathered} \frac{2ax}{2x}=-\frac{8x}{2x} \\ a=-4 \end{gathered}[/tex]Hence, the value of a for which there is no solution to the equation is
[tex]a=-4[/tex]What is the negation of "Everybody loves somebody sometime"
Answer:
Everybody hates somebody sometimes.
Or Not everybody loves somebody sometime
Step-by-step explanation:
a woman can hike 2mph faster down a trail to Archuletta Lake then she can on the return trip uphill. it takes her 2 hours to get to the lake and 4 hours to return. what is her speed hacking down to the late?
Answer:
4 mph
Explanation :
Let us call x, the woman speed as she goes uphill
Now, we know that it took the woman 2 hours to go uphill; therefore, the distance covered is
4* (x)
shortly afterwards, when the woman returns she is walking at x + 2 mph; therefore, the distance she covers is
D = 4 (x +2 )
Since the uphill and the downhill distances ar the same, we have
4x = 2 (x +2 )
4x = 2x + 4
x = 2
Hence, going to the hill, the woman speed is 2 miles per goo