Answers
Answer:
x = 9
Step-by-step explanation:
using the rule of indices
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]5^{x}[/tex] = [tex]\frac{5^{8} }{5^{-1} }[/tex] = [tex]5^{(8-(-1))}[/tex] = [tex]5^{(8+1)}[/tex] = [tex]5^{9}[/tex]
since bases on both sides are equal, both 5 , then equate indices
x = 9
Related Questions
There are 60 members in the school glee club. The glee club needs to raise at least $5,000 for a trip toa national competition. The school agreed to contribute $1,000 toward the trip. Which of theinequalities below shows the amount of money that each glee club member needs to raise to help payfor the trip.a) 60x + 1,000 > 5,000b) 60x + 5,000 > 1,000c) 1,000x + 60 < 5,000
Answers
Let x be the amount raised by each club member. Since there are 60 members, the amount raised by them would be
[tex]60x[/tex]Now, we know the school contributed $1,000. Now, the amount raised is:
[tex]60x+1000[/tex]Since this amount has to be at least $5,000, we have that the inequality that shows the amount of money that each glee club member needs to raise to help pay for the trip is:
[tex]60x+1000>5000[/tex]Answer: Option A
21. What are the modes of the following sets of numbers?
a. 3, 13, 6, 8, 10, 5, 6
b. 12, 0, 15, 15, 13, 19, 16, 13, 16, 16
Answers
Answer:
6 and 16
Step-by-step explanation:
→ Find the most recurring number in sequence A
6
→ Find the most recurring number in sequence B
16
a=3,k=12,z=6,h=4 Evaluate the algebraic expression z+15=?
Answers
since z=6, so z+15 is equal to 21
or a+k+z=21
Write the equation of the line passing through (-3,1) that is perpendicular to 3x-8y=16
Answers
two lines are perpendicular when their slope is inverted and have the opposite sign
the general form of the equation line is-3,1
[tex]y=mx+b[/tex]where m is the slope
rewrite
[tex]\begin{gathered} 3x-8y=16 \\ 3x-16=8y \\ y=\frac{3x-16}{8} \\ y=\frac{3}{8}x-2 \end{gathered}[/tex]so, the slope 3/8
the slope of the other line is
[tex]\frac{3}{8}\longrightarrow-\frac{8}{3}[/tex]to write the new equation of the line we use the slope and replace the point (-3,1)
[tex]\begin{gathered} (1)=(-\frac{8}{3})(-3)+b \\ 1=8+b \\ b=-7 \end{gathered}[/tex]now, replace b and the slope to create the line
[tex]y=-\frac{8}{3}x-7[/tex]what is 11/12 ÷ 1/30 2 1/40 2 3/40 3 1/30 3 2/3
Answers
The given expression is
[tex]\frac{11}{12}\colon\frac{1}{3}[/tex]First, we change 1/3 for its reciprocal to transform the division into a product.
[tex]\frac{11}{12}\cdot\frac{3}{1}[/tex]Then, we multiply the fractions.
[tex]\frac{11\cdot3}{12\cdot1}=\frac{33}{12}=\frac{11}{4}[/tex]At last, we transform the fraction into a mixed fraction.
[tex]\frac{11}{4}=2\frac{3}{4}[/tex]Therefore, the right answer is B. 2 3/4.4. 3. The price of a computer is $699.00. The sales tax rate is 8%. What is the 10 points
sales tax on this computer in dollars and cents?
Mark only one oval.
0000
$55.92
$754.92
$5,592.00
$5.59
Answers
Answer:
$754.92
Step-by-step explanation:
699.00 plus 8% of 699.00 is 754.92
an article suggests that a poisson process can be used to represent the occurrence of structural loads over time. suppose the mean time between occurrences of loads is 0.4 year. (a) how many loads can be expected to occur during a 4-year period? loads (b) what is the probability that more than twelve loads occur during a 4-year period? (round your answer to three decimal places.) (c) how long must a time period be so that the probability of no loads occurring during that period is at most 0.3? (round your answer to four decimal places.) yr
Answers
The probability of no loads occurring during that period is at most 0.3 exists 3.2 years.
How long must a time period be so that the probability of no loads occurring during that period?Given: Mean time between occurrence = 0.4 year
A number of loads expected to occur during a 4 year period
Period = 4
Mean time = 0.4
Let the formula = Period/Mean Time
The number of loads expected to occur during a 4-year period
= 4/0.4 = 10 loads
B. Probability that more than 11 loads occur during 4 year period
The expected number of loads during 4-year period = 10 (from A above)
mean = 10
Using Poisson distribution,
P(k events in interval)= (λ^k * e^-k)/k!
where: k = 0, 1, 2,3,4, . . ., 11 and λ = 10.
P(k = 0) = (1[tex]0^0[/tex] × [tex]e^{-10[/tex])/0! = 0.000045
P(k = 1) = (1[tex]0^1[/tex] × [tex]e^{-10[/tex])/1! = 0.000454
P(k = 2) = (10² × [tex]e^{-10[/tex])/2! = 0.00227
P(k = 3) = (10³ × [tex]e^{-10[/tex])/3! = 0.007567
P(k = 4) = (1[tex]0^4[/tex] × [tex]e^{-10[/tex])/4! = 0.018917
P(k = 5) = (1[tex]0^5[/tex] × [tex]e^{-10[/tex])/5! = 0.037833
P(k = 6) = (1[tex]0^6[/tex] × [tex]e^{-10[/tex])/6! = 0.063055
P(k = 7) = (1[tex]0^7[/tex] × [tex]e^{-10[/tex])/7! = 0.090079
P(k = 8) = (1[tex]0^8[/tex] × [tex]e^{-10[/tex])/8! = 0.112599
P(k = 9) = (1[tex]0^9[/tex] × [tex]e^{-10[/tex])/9! = 0.12511
P(k = 10) = (1[tex]0^{10[/tex] × [tex]e^{-10[/tex])/10! = 0.12511
P(k = 11) = (1[tex]0^{11[/tex] × [tex]e^{-10[/tex])/11! = 0.113736
The probability that more than 11 loads occur during a 4-year period is then given by the following Express
1 - [P(k = 0) + P(k = 1) + P(k = 2) + . . . + P(k = 11)]
substitute the values in the above equation, we get
= 1 - [0.000045 + 0.000454 + 0.00227 + 0.007567 + 0.018917 + 0.037833 + 0.063055 + 0.090079 + 0.112599 + 0.12511+ 0.12511 + 0.113736]
simplifying the equation, we get
= 1 - 0.571665 = 0.428335
C. How long must a time period be so that the probability of no loads occurring during that period is at most 0.3
(λ^0 * e^-λ)/0! = 0.3
⇒ e^-λ/1 = 0.3
simplifying the above equation, we get
⇒ e^-λ = 0.3
⇒ -λ = ln 0.3
⇒ -λ = -1.204
⇒ λ = 1.204
The time period = 4 years / 1.204
Time period = 3.2 years
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7. Solve by using extracting square roots 4a²-25= 0
pa answer po rn
w solution po
Answers
[tex]4a^{2} -25=0\\(2a-5)(2a+5)=0\\2a-5=0 \\or 2a+5=0\\\\a=\frac{5}{2} \\\\or\\\\a=-\frac{5}{2}[/tex]
IF YOU CHECK CAREFULLY YOU WILL FIND THAT THIS EQAUTION IS MADE OF DIFFERENCE OF SQUARES.
GOODLUCK!!
this is a super hard one
Answers
Notice that in the given sequence the difference between the first two terms is 7 so the solution must be in terms of multiples of 7 plus a constant. The only two options that have this characteristic are first and last ones, for the sum to consider the first term the sum must start for r=0.
Answer: last option.
17. What are the roots of the equation s² - 7 = 74?
18. One of the roots of x² - 8x = 0 is 8. What is the other root?
paanswer po ngaun
w solution if meron po sana
Answers
Answer:
17. s = 9
18. x = 8x^(½)
Step-by-step explanation:
s² - 7 = 74?
s² = 74 + 7
s² = 81
√(s²) = √(81)
s = 9
x² - 8x = 0
x² = 0 + 8x
x² = 8x
√(x²) = √(8x)
x = 8x^(½)
OR by factoring
x²−8x=0
x(x−8)=0
x=0 or x−8=0
x=0 or x=8
convert improper fractions to mixed number 7/5
Answers
The mixed fraction of the given improper fraction is [tex]1\frac{2}{5}[/tex].
According to the question,
We have the following improper fraction:
7/5
Now, to convert this into mixed fraction we will divide the numerator by the denominator and add the quotient before the fraction and the remainder will form the numerator and the denominator will remain same as that of this improper fraction.
(More to know: there are three kinds of fraction: proper fraction (in proper fraction, we have denominator larger than numerator), improper fraction and mixed fraction.
So, we will divide 7 by 5:
[tex]1\frac{2}{5}[/tex]
Hence, the mixed fraction of 7/5 is [tex]1\frac{2}{5}[/tex].
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If f(x) = 5x, what is f¹(x)?
O f¹(x) = -5x
○ f¹(x) = -1/2 x
0 r²(x) = ²/1 x
O f¹(x) = 5x
Answers
The value of f¹(x) = x/5
What is function?
A function in maths is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.
We are given f(x) = 5x
and we are to find inverse of f(x).
Replace f(x) by y.
So,
y = 5x
Isolate x
x = y/5
Replace x by f'(y)
So,
f'(y) = y/5
Replace all occurrences of y by x.
So,
f'(x) = x/5
Therefore, the inverse of function f(x) = 5x is f'(x) = x/5
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EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answers
Answer:
c = 23
Step-by-step explanation:
To start, the interior of ∠L is needed to complete the equation. Since the total value of an interior and exterior angle is equal to 180°, we can confirm that 180° - 83° = 97°. Now, we can plug in the numbers.
(2c + 51)° = 97°
Next, you want to subtract 51 from both sides.
(2c + 51) - 51 = 97 - 51
2c = 46
Lastly, you isolate c by dividing 46 by 2.
c = 46 ÷ 2
c = 23
Whileat the fruit stand, ramon bought 3 punds of apples that cost $0.89 per pound and 4 cantaloupes that each cost $1.09. about how much money did he spend, not including tax?
Answers
The total money spent on fruits is $7.03
While at the fruit stand, Ramon bought the following fruits,
3 pounds of apples that cost $0.89 per pound
4 cantaloupes that each cost $1.09
So, the total amount he spent on the materials he bought without including taxes is,
Total money spent = 3 x ( 0.89 ) + 4 x ( 1.09 )
= 2.67 + 4.36
= 7.03
The total money spent on fruits is $7.03
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The carpenter cuts 1-
1
inches off a piece of wood every 2 minutes. How many inches
2
will be cut in 25 min?
Answers
Please help me do my Math Homework ASAP, it is attached.
Answers
Answer:
Step-by-step explanation:
fine the value of x. please help
Answers
Answer:
141 degrees
Step-by-step explanation:
The total angle interior of a triangle is 180 degrees. And the 2 angles opposite of x equal it so x=103+38
What is the lowest common multiple of 19 & 9
Answers
Solution:
LCM of 9 and 19 is the smallest number among all common multiples of 9 and 19.
The first few multiples of 9 and 19 are (9, 18, 27, 36, 45, 54, . . . ) and (19, 38, 57, 76, 95, . . . ) respectively.
There are 3 commonly used methods to find LCM of 9 and 19 - by listing multiples, by division method, and by prime factorization.
To calculate the LCM of 9 and 19 by the division method, we will divide the numbers(9, 19) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 19.
In this case, we get:
Then, the LCM would be:
[tex]3\text{ x 3 x 19 = }171[/tex]so that, the correct answer is:
[tex]171[/tex]if a baker has 7/3 cups of chocolate, the baker can make a maximum of .... cakes.
Answers
She calls for 4/5 cup of chocolate
She had 7/3 cups of chocolate.
[tex]\begin{gathered} \text{The bake can make a ma}\xi mum\text{ of = }\frac{7}{3}\text{ }\frac{.}{.}\text{ }\frac{4}{5} \\ \text{ = }\frac{7}{3}\text{ x }\frac{5}{4} \\ \text{ = }\frac{35}{12} \\ \text{ = 2}\frac{11}{12} \\ \end{gathered}[/tex]Maximum number of cakes a baker can make = 2
Zahra and some friends are going to the movies. At the theater, they sell a bag of
popcorn for $3.50 and a drink for $5. How much would it cost if they bought 8 bags
of popcorn and 5 drinks? How much would it cost if they bought p bags of popcorn
and d drinks?
Total cost, 8 bags of popcorn and 5 drinks:
Total cost, p bags of popcorn and d drinks:
Answers
After performing some mathematical operations, we know that the total cost of 8 popcorn bags and 5 drinks is $53.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving multiple operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).So, the total cost:
1 bag of popcorn costs $3.50.1 drink costs $5.Cost of a total of 8 bags of popcorn and 5 drinks:
(8 × 3.50) + (5 × 5)28 + 25$53Therefore, after performing some mathematical operations, we know that the total cost of 8 popcorn bags and 5 drinks is $53.
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The correct question is given below:
Zahra and some friends are going to the movies. At the theater, they sell a bag of popcorn for $3.50 and a drink for $5. How much would it cost if they bought 8 bags of popcorn and 5 drinks?
in 1982, the us mint changed the composition of pennies from all copper to zinc with copper coating. pennies made prior to 1982 weigh 3.1 grams. pennies made since 1982 weight 2.5 grams. if you have a bag of 1267 pennies, and the bag weighs 3541.9 grams, how many pennies from each time period are there in the bag?
Answers
Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams. 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
Given that,
The 1982 change in pennies composition from all copper to zinc with copper coating was made by the US Mint. Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams.
We have to find how many coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
An issue of quantity and amount. In this context, the term "amount" refers to weight. The variables should be identified with letters that will make them easy to distinguish: Z for largely zinc and C for all copper. Create weight and quantity equations:
C + Z = 1287
3.1 C + 2.5 Z = 3601.5
By multiplying all three components of the first equation by -2.5 and placing them under the second equation, drawing a line, and then subtracting, you can eliminate the Z using this method.
3.1 C + 2.5 Z = 3601.5
-2.5 C - 2.5 Z = -3217.5
--------------------------------
0.6 C = 384
Divide both sides by .6.
C = 640
Subtract 640 from 1287.
Z = 647
Therefore, 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
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4x > 28 solve the inequality for x and simplify your answer as much as possible
Answers
Answer:
x > 7
Step-by-step explanation:
x = 28 ÷ 4
x > 7
that's it
Hey there!
4x > 28
DIVIDE 4 to BOTH SIDES
4x/4 > 28/4
SIMPLIFY it
x > 28/4
x > 7
It is an open circle started at 7 & it’s going to the left of the number line
Therefore, your answer should be:
x > 7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Eli dug a trench
18
20
of a meter long. The next day he dug another 17
20
B
of a meter. What is a reasonable estimate of the total length of the trench?
Answers
The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters so option (C) is correct.
What is summation?A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities.
There could be only two terms, but there could be one hundred, a thousand, or a million.
Here are always an integer number of terms in a summation.
As per the given,
Length of the trench on the first day = 18/20 meters
Length of the trench on the second day = 9/20
Total length of the trench = 18/20 + 9/20
Take LCM as 20
⇒ (18 + 9)/20 = 27/20
⇒ 1.35 which is closest among the given option by 1 1/2 meters.
Hence "The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters".
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passes through (1,4) and perpendicular to y=2x-7
Answers
The equation of the line is found as y = -x/2 + 9/2.
What is meant by the equation of the line?This is an x and y equation for whom solution set is just a line in the (x,y) plane. The "slope-intercept" form is the most commonly used in algebra. y = mx + b. In effect, x is used as a parameter, and y is written as just a function of x: y = f(x) = mx+b.For the given question;
The equation of the perpendicular line is given as;
y = 2x - 7
Compare the equation with the standard form of slope intercept.
y = mx + c
m = slope and c is the y intercept.
m1 = 2
Now, the line is perpendicular, thus the relation between both slopes is;
m1 × m2 = -1
m2 = -1/2
The passing coordinates of the line is (1. 4).
Find the equation using formula.
y - y1 = m2(x - x1)
y - 4 = (-1/2) (x - 1)
Simplifying,
y = -x/2 + 9/2
Thus, the equation of the line is found as y = -x/2 + 9/2.
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1. Write the distance from the Sun to Mercury in scientific notation. Include units with your answer.
NEED HELP ASAP WILL GIVE BRAINLIST TO BEST AWNSER
Answers
Answer:
3.456 × 10^11
Step-by-step explanation:
= 3.456 × 10^11
scientific notation
= 3.456e11
scientific e notation
= 345.6 × 10^9
engineering notation
billion; prefix giga- (G)
= 3.456 × 10^11
standard form
11
Order of Magnitude
for scientific and standard forms
= 345600000000
(real number)
= three hundred forty-five billion six hundred million
word form
I hope this helps!! :D
Whats the midpoint of line segment (-1,6), (3,0)
Answers
Answer:
(1,3)
Step-by-step explanation:
You can use the distance formula to help you solve the answer
Answer:
(1; 3)
Step-by-step explanation:
x = (-1 + 3)/2 = 1
y = (6 + 0)/2 = 3
RS =9y + 2, ST = 2y + 3, and RT = 60
Answers
Answer:
y=5
Step-by-step explanation:
RS + ST = RT
9y+2 + 2y+3 = 60
11y + 5 = 60
11y = 55
Y = 5
Andrew earns 30% on all sales plus a retainer of £125 per week.
If he earns £893 in one week, find the value of his sales for that week.
Answers
If Andrew earns 30% on all sales plus a retainer of $125 per week and If he earns $893 in one week, then the value of the his sales for that week is $2560.
The total amount he earned = $893
The amount of retainer he earned = $125
The percentage he earned = 30%
30% of the sales = The total amount he earned - The amount of retainer he earned
Substitute the values in the equation
= 893-125
= $768
Consider the total sales as x
Then,
x × (30/100) = 768
0.3x = 768
x = 768/0.3
x = $2560
Hence, if Andrew earns 30% on all sales plus a retainer of $125 per week and If he earns $893 in one week, then the value of the his sales for that week is $2560.
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I need help with number 16 can I please get help?
Answers
We will break apart the figure into triangles, rectangles, squares etc. We will then find area of each individual figure and sum it.
We can break apart the figure as shown below:
Suppose each street in the map shown represents a line. Provide an example of
each angle relationship.
Vertical angles
Supplementary
angles
Linear pair
Adjacent angles
Vertical angles
Congruent angles
10
15
16
11
12
17
18
Willow Drive
4
8
13 14 Franklin Drive
19 20
21
23
Sixth Ave
Main Street
22 Fifth Ave
24
Answers
Vertical angles are : 1 and 6
supplementary angles : 1 and 2
linear pair : angle 4 and 8
adjacent angles: 21 and 22
What is a supplementary angle?A supplementary angle is an angle that, when added to another angle, results in a total angle measure of 180 degrees. In other words, if two angles are supplementary, the sum of their angle measures will be equal to 180 degrees.
For example, if angle A measures 100 degrees, its supplementary angle B would measure 80 degrees, since 100 + 80 = 180. Conversely, if angle B measures 120 degrees, its supplementary angle A would measure 60 degrees, since 120 + 60 = 180.
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