⇒I will be using the laws of exponents. As indicated below :
⇒[tex]x^{n} *x^{m} \\=x^{n+m}[/tex]
This just simply means that if you are multiplying powers of the same base you keep one base as a result and add the exponents.
⇒ The other law of exponents is indicated below:
⇒[tex]x^{n} /x^{m} \\=x^{n-m}[/tex]
This means that if you are dividing powers of the same base you keep one base and subtract the exponents.
N.B : BODMAS RULES ALSO APPLY
[tex]\frac{(3^{8} *3^{4} )}{(3^{2}*3^{8} ) } \\=\frac{3^{8+4} }{3^{2+8} } \\=\frac{3^{12} }{3^{10} } \\=3^{12-10} \\=3^{2} \\=9[/tex]
Attached is your solution. Goodluck!!
40 push-ups in 5 days = push-ups in 6 days
Answer:
48 push ups
Step-by-step explanation:
40 push ups in 5 days can be modelled with the fraction 40/5
you can simplify that to 8/1 after dividing both sides by 5
now set that equal to push ups over 6
but first you must declare a variable for push ups
let x = push ups
8/1 = x/6
multiply both sides by 6
48/1 = x
x = 48
that is your answer
48 push ups
To know how many reflections are made per day, a division is made between the days and the total number of reflections.
40 Flexions ➗ 5 days = 8 flexions a day.
Every day it has 8 flexions, in multiply the 6 days for the 8 flexions of each, then.
8 flexions (1 day) ✖ 6 days = 48 flexions.
Answer: 48 flexions = 6 days ✅.
provide an appropriate response. the length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 7.0 minutes and a standard deviation of 1 minute. find the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot.
By the distribution,6.3 minutes is the time limit that 75.8% of college students go over when looking for a parking space in the library parking lot.
Given that,
Finding a parking spot in the library parking lot takes college students an average of 7.0 minutes, with a standard deviation of 1 minute, according to a normal distribution.
Find the window of opportunity that 75.8% of college students miss when looking for a place in the library parking lot.
The following formula calculates the z-score of a measure X of a normally distributed variable with mean μ and standard deviationσ:
Z=(X-μ)/σ
The z-score calculates how far the measure deviates from the mean by standard deviation.
The p-value for this z-score, which is the percentile of X, can be obtained by looking at the z-score table.
The cut-off time is the 100th percentile minus 75.8th percentile, or X, for Z = -0.7, so:
Z=(X-μ)/σ
-0.7=(X-7)/1
-0.7=X-7
X=-0.7+7
X=6.3
Therefore, 6.3 minutes is the time limit that 75.8% of college students go over when looking for a parking space in the library parking lot.
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An archeologist in Turkey discovers a spear head that contains 85% of its original amount of C-14. k = 0.0001 Find the age of the spear head to the nearest year.
The age of the spear head is found to be 1625 years.
What is the age?Let us recall that the age of the sample can be determined by the use of radiometric dating. Let us now define the variables;
The constant of the decay (k) = 0.0001
The amount of the sample originally present (No) = No
The amount of the sample at time t = 0.85No
t = The age of the sample
Given that;
N= Noe^-kt
N/No = e^-kt
0.85No/No = e^-0.0001t
0.85 = e^-0.0001t
ln0.85 = -0.0001t
t = ln0.85/ -0.0001
t = 1625 years
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Find the y intercept: y=3.5x-7
The y-intercept of the function y = 3.5x - 7 is ( 0, - 7 ).
A function is an association between inputs in which each input has a unique link to one or more outputs. Each function has a range, codomain, and domain.
Consider the function,
y = 3.5x - 7
The equation of a straight line is expressed in the slope-intercept form (a linear function). It takes the formula y = mx + b, where m is the slope, b is the y-intercept, and y and x serve as variables.
The value of y at x = 0 can be used to determine the y-intercept. The graph's intersection with the y-axis occurs at this location.
Then,
y = 3.5x - 7
y = 3.5( 0 ) - 7
y = - 7
The y-intercept of the function is ( 0, - 7).
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a group of friends is taking part in a two-day walking event for charity. yesterday, they walked 28 miles in 9 hours and 44 minutes. today, they finished the last 10 miles in 2 hours and 55 minutes. what was the group's average speed for the two-day event?
Average speed of the group for the two day event is 0.105 miles\min.
The average is defined as the mean value that is equal to the ratio of the total sum of the number of a given set of values to the total number of values present in that set.
Time taken on day 1 in minutes = 9x60 + 44
= 540 + 44 = 584 minutes.
Time taken on day 2 in minutes = 2x60 + 55
= 120 + 55 = 157 minutes
Now we will be applying speed-distance formula we get,
Speed= Distance/time
On day 1,
[tex]Speed_{1}[/tex]= 28/584 = 0.0479 miles/min
On day 2,
[tex]Speed_{2}[/tex]= 10/175 = 0.0571 miles/min
Thus,the average speed is:
Average = [tex]Speed_{1} + Speed_{2}[/tex] = 0.0479 + 0.0571= 0.105 miles/min
Hence,the average speed is 0.105 miles/min
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Shelly was shopping and saw that a 14lb turkey costs $13.86. Calculate the unit price for 1 lb of turkey.
the unit price for 1 lb of turky is $0.99
Explanation:The cost of 14 lb of turkey = $13.86
let the cost of 1 lb of turkey = y
The unit price is the cost for 1lb of turkey:
14 lb = 13.86
1 lb = y
cross multiply:
14(y) = 1(13.86)
14y = 13.86
divide both sides by 14:
14y/14 = 13.86/14
y = 0.99
Hence, the unit price for 1 lb of turky is $0.99
Have no clue how to do this if you could help or give best guess that would be awesome.
We are asked to find an equivalent amount to 100 USD in french francs. Acording to the table, on tuesday, a dollar costs 4.3450 french francs, then we can find how many francs we got by multiplying 100 USD and 4.345, then we get:
Francs = 100×4.3450 = 434.50
Then, the answer is 434.5 french francs
Kadeem and Quinn both drive 25 miles. Kadeem drives at a constant speed of 50 miles and hour. Quinn drives at a constant of 75 miles an hour. Who takes longer to drive 25 miles? How much longer?
Kadeem takes 0.5 hours to travel 25 miles, and Quinn 0.33 hours, so Kadeem takes longer.
Who takes longer to drive 25 miles?
Remember the relation:
Speed*time = distance.
Notice that if the distance is fixed, then for a longer speed the time needed will be smaller.
Here we know that:
Kadeem drives at a constant speed of 50mi/h
Quinn drives at a constant speed of 75 mi/h.
Replacing that in the equation:
Kadeem's case:
(50 mi/h)*t = 25mi
t = (25 mi)/(50 mi/h) = 0.5 hours.
Quinn's case:
t = (25mi)/(75 mi/h) = 0.33 hours.
So Kadeem takes longer.
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9TH GRADE MATH HELPPPP
Answer:
The equation in slope-intercept form is:
[tex]y=\frac{1}{3}x+3[/tex]
So the second option is the correct one.
Step-by-step explanation:
Step 1: Identify the gradient
The perpendicular line's equation is given as:
[tex]y=-3x+4[/tex]
This equation is in the form of:
[tex]y=mx+b[/tex]
Upon comparing the [tex]x[/tex] components of both equations, we get[tex]-3x=mx\\\text{Remove the}~ x~ \text{from both sides:}\\-3=m\\m=-3[/tex]
So, the gradient of this 'reference' equation is -3.
The equation we need to find is perpendicular to this 'reference' equation.
So, its gradient should be the negative reciprocal of the gradient of the 'reference' equation.
The negative reciprocal of -3 is:
[tex]-\frac{1}{(-3)}\\=\frac{1}{3}[/tex]
So, the gradient of our equation is [tex]\frac{1}{3}[/tex].
Step 2: Create the equation:
The equation crosses the x-axis at -9, which means its y-coordinate is 0 (at x-axis, y=0) ,so its coordinate is [tex](-9,0)[/tex].
The formula for an equation is:
[tex]y-y_{1}=m(x-x_{1})[/tex]
The coordinate [tex](x_{1},y_{1})[/tex] is [tex](-9,0)[/tex], and the gradient ([tex]m[/tex]) is [tex]\frac{1}{3}[/tex].
Substitute the values into the equation:
[tex]y-y_{1}=m(x-x_{1})\\y-0=\frac{1}{3}(x-(-9))\\\\\text{Simplify}\\y=\frac{1}{3}(x+9)[/tex]
[tex]\text{Simplify further}\\y=\frac{1}{3}x+3[/tex]
Since, the slope-intercept form is:
[tex]y=mx+b[/tex]
We already have our equation in the slope-intercept form.
Alexis has two job offers. Job #1 pays $12 an hour and will allow her to work 40 hours a week. Job #2 pays $8 an hour and also requires a 40-hour week. However, Job #2 also pays bonuses based on sales. The other salespersons told Alexis they average about $100 a week in bonuses. Which job will likely pay the most money per week?
Answer:
$8 an hour and also requires a 40-hour week
Step-by-step explanation:
x-4y=-2
Determine if the given ordered pair, (2, 1), satisfies the given equation.
O YES
O NO
Answer:
Yes.
Step-by-step explanation:
Replace x with 2 and y with 1 and see if the equation is true
x - 4y = -2
2 - 4(1) = -2
2 - 4 = -2
-2 = -2
The statement is true so the point is on the line.
5. Which might be your first step if you want to solve the
system by elimination?
1st equation: 5x + 4y = 7
2nd equation: 2x - 3y = 3
A) Substitute -10y + 7 for x in the second equation.
B) Substitute 3y + 3 for x in the second equation.
C) Multiply the first equation by 3, multiply the second
equation by 4, then add the resulting equations
together.
D Multiply the first equation by 2, multiply the second
equation 5, then add the resulting equations together.
Answer:
C)
Step-by-step explanation:
elimination is not substitution.
therefore, A and B are out.
D does not work, because in the described way the x terms don't get different signs, and the addition does not eliminate any variable.
C brings both y terms to the same absolute value, and their signs are different, so the addition will eliminate the y terms leaving us with one equation in x that we can solve :
15x + 12y = 21
8x - 12y = 12
---------------------
23x 0 = 33
23x = 33
x = 33/23
Answer:
a is the right answer for you
Sydney picked 28 raspberries and 35 blueberries to make two desserts.
She needs 4 raspberries for each raspberry tart and 5 blueberries for each
blueberry tart. She wants to know how many desserts she will be able to
make with the berries.
A recent survey showed that 73% of elementary school students have a pet. What is the ratio of students who have a pet to students who do not have a pet?
Answer:
73 : 27
Step-by-step explanation:
You want the ratio of students that have a pet to students that don't have a pet, given that 73% of students have a pet.
No petIf 73% of students have a pet, then the remaining 100% -73% = 27% of students do not have a pet.
RatioThe ratio of students who have a pet to students who don't have a pet is then ...
(have a pet) : (don't have a pet) = 73% : 27% = 73 : 27
According to a recent survey, 73% of elementary school students have a pet, making the ratio of students with pets to those without pets 73:27.
What is ratio?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
You want the ratio of students that have a pet to students that don't have a pet, given that 73% of students have a pet.
If 73% of students have a pet, then the remaining 100% -73% = 27% of students do not have a pet.
The ratio of students who have a pet to students who don't have a pet is then,(have a pet) : (don't have a pet) = 73% : 27% = 73 : 27
A recent survey found that 73% of elementary school students own a pet, making the proportion of students who own pets to those who don't stand at 73:27.
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A triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers. Is it a right triangle?
If a triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers. No it is not a right triangle.
Determining whether the triangle is a right triangleWe would be making use of converse of Pythagoras' theorem to determine whether the triangle is a right triangle.
In a situation were we have a right triangle the square on longest side will be the same with the sum of square of other sides
Longest side
45² = 2025
Other side
30 ² + 35 ²
900 + 1,225
= 2125
Hence,
2025 ≠ 2125
Based on the above it is not a right triangle because the longest side did not equate the other side.
Therefore it is not a right triangle.
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As 2125 ≠ 2025 therefore it didn't meet the requirements of Pythagoras' theorem, it is not a right-angle triangle.
This type of question makes a right-angled triangle that can be solved by Pythagoras's theorem.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given, A triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers.
∴ 30² + 35² = 45².
900 + 1225 = 2025.
2125 ≠ 2025.
It is not a right-angle triangle because it didn't satisfy the property of Pythagoras's theorem.
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[tex]11/16 - 2/3[/tex]11/16 - 2/3=
Given
\qquad \overline{BA}\perp\overline{BD}
BA
⊥
BD
start overline, B, A, end overline, \perp, start overline, B, D, end overline
\qquad m \angle CBD = 4x + 52^\circm∠CBD=4x+52
∘
m, angle, C, B, D, equals, 4, x, plus, 52, degrees
\qquad m \angle ABC = 8x - 10^\circm∠ABC=8x−10
∘
m, angle, A, B, C, equals, 8, x, minus, 10, degrees
Find m\angle CBDm∠CBDm, angle, C, B, D:
The value of ∠CBD is 68° and the value of ∠ABC is 22°
Given
Angle CBD = 4x + 52
Angle ABC = 8x − 10
If BA is perpendicular to BD, then ∠BAD = 90°
∠BAD = ∠CBD + ∠ABC
On substituting this values into the formula:
4x + 52 + 8x − 10 = 90
12x + 42 = 90
Add -42 to both sides
12x + 42 - 42 = 90 -42
12x = 48
x = 48/12
x = 4°
Here,
∠CBD = 4x + 52
∠CBD = 4 x 4 + 52 = 16 + 52 = 68°
Then,
∠ABC = 8x − 10
∠ABC = 8 x 4 − 10 = 32 - 10 = 22°
That is,
The value of ∠CBD is 68° and the value of ∠ABC is 22°
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Answer:
68 degrees
Step-by-step explanation:
got it right on khan academy
what is 17 = r - 6.7
Answer:
r = 23.7
Step-by-step explanation:
17 = r - 6.7 ( add 6.7 to both sides )
23.7 = r
Checks: 32.96,121.03 and 24.70;cash:22 one dollar bills, 5 ten dollar bills, and 15.21 in coins; less $20 cash recieved
The balance of the checks and cash (receipts and payments) is -$245.90.
How is the balance determined?The balance is the difference between receipts of cash and payments of checks and cash.
Using addition and subtraction operations, the balance is determined as follows:
Check Payments:32.96
121.03
24.70
Total checks = $178.69
Cash Payments:22 one dollar bills = $22.00 (22 x $1)
5 ten dollar bills $50.00 (5 x $10)
15.21 in coins $15.21
Total cash payments = $87.21
Cash Receipts:$20 cash received
Total cash = $67.21
Balance = -$245.90 [$20 - ($87.21 + $178.69)]
Thus, the balance of the checks and cash totals -$245.90, showing that payments outstripped receipts.
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Question Completion:How much is the balance between receipts and payments?
How do you distribute 259 or 3.25 pieces of candy into 80 bags
259 pieces of candy can be distributed in 80 bags to give 3 candy per bag and there will be 19 candies remaining
How to distribute 259pieces of candy in 80 bagsThe concept for distributing the required candies is achieved by the mathematical operation called division.
Division is an inverse of multiplication. With division we can share and determine number of candy per bag
The question is solved by
= 259 ÷ 80
= 259 / 80
= 3 19/80
This means that there will be 3 candies per bag and after sharing among the nags there will be 19 candies remaining.
Putting this in decimal gives
= 3.2375 ≅ 3.24
In a situation where we are to count the candies if they are 3.25 pieces per bag the we multiply as follows
= 3.25 * 80
= 260
in this case the total number of candies should be 260
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a fence is to be built to enclose a rectangular area of 280 square feet. the fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 13 dollars per foot. find the dimensions of the enclosure that is most economical to construct.
Fencing of any rectangular region is basically represent perimeter of that rectangular region.
For most economical fencing, length L = 21.05 feet and width W = 13.301 feet.
How to estimate the length and width of the rectangular region?Area of rectangular region is 280 square feet.
And length is L and width is W.
Area of rectangular region = L × W=280 square feet
W=280 / L
Since, The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 14 dollars per foot.
Therefore, Total cost, C = 6(2L + W) + 13W = 12 L + 19 W
Total cost, C = 12 L+ 5,320 / L
To find most economical cost, differentiate above function and equate to zero.
C' = 12 - 5,320 / L²
simplifying the above equation, we get
⇒ 12 - 5,320 / L² = 0
⇒ L² = 5,320 / 12
L = 21.05 feet
Therefore, L = 21.05 feet
Substituting value of L in area equation.
We get, W = 13.301 feet.
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Please help quickly!! (30 POINTS)
Given f(x)=3x^2 −5x−2.
What is the value of f(−2/3)?
The value of the function f(−2/3) will give the value 8/3.
What is the answer for f(-2/3)?A function is important to show the expression that's given.
Given: f(x) = 3x^2 −5x−2.
To find f(-2/3), we substitute x = -2/3 into the equation:
f(-2/3) = 3 x (-2/3)^2 - 5(-2/3) - 2
= 3 x 4/9 + 10/3 -2
= 12/9 + 10/3 - 2
= (12 + 30 - 18) / 9
= 24 /9
= 8/3
Therefore, f(-2/3) evaluates to 8/3.
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Answer:1700
Step-by-step explanation:
Just the coordinates is fine :)
To give an entity the desired position, orientation, or shape starting from the current position, orientation, or shape, geometric transformations are required. Scaling, rotation, translation, and shear are the fundamental transformations. Projections and mappings are two additional crucial categories of transformation.
Y =- X is what kind of a transformation?
Y = X's reflection:
The x-coordinate and the y-coordinate switch positions when a point is reflected across the line y = x. Y = -x reflection: The x-coordinate and the y-coordinate switch places when you reflect a point across the line y = -x, and they are negated (the signs are changed).
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. The cross-sectional reflection of point (x, y)
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What is the graph of f(x) = 3x - 4, where x ≥ 1?
Here is the graph for you!!
What is the effect on the graph of f(x) = 1/xwhen it is transformed to
g(x) = 1/x + 17?
OA. The graph of f(x) is shifted 17 units to the left.
OB. The graph of f(x) is shifted 17 units up.
OC. The graph of f(x) is shifted 17 units down.
O D. The graph of f(x) is shifted 17 units to the right.
The correct option is option B that is "The graph of f(x) is shifted 17 units up". It is shifted 17 units up. By adding 17 to the equation, y increases by 17. If y increases by 17, the graph shifts up by 17.
What is graph?In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to connected and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other types of graphs.
What is transformation in graph?The process of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the modification of algebraic equations, it is a typical kind of algebraic problem.
It is shifted 17 units up.
By adding 17 to the equation, y increases by 17.
If y increases by 17, the graph shifts up by 17.
Option B, "The graph of f(x) is shifted 17 units up," is the answer. It is moved upward 17 units. Adding 17 to the formula causes y to rise by 17. The graph moves up 17 units if y rises by 17.
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O is the center of the regular decagon below. Find its perimeter. Round to the nearest
tenth if necessary.
16
Based on the center of the regular decagon, we can find that the perimeter of the decagon would be 98.9 units.
How to find the perimeter of a decagon?When given the midpoint of a decagon and the measurement of the radius, the perimeter can be found by the formula:
= 10 x ( ( 2 x Radius of the decagon) / (1 + √5)))
Given a radius of 16 units, the perimeter of this decagon is:
= 10 x ( (2 x 16) / (1 + √5)))
= 10 x ( (32 / (1 + √5)))
= 98.9 units
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Perimeter of Decagon with radius and midpoint given is 100 units.
What is Polygon?Polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides.
Given polygon is a decagon. A decagon is a polygon which have ten sides with same length with centre o.
The radius of the decagon is 16.
When radius and midpoint is given the perimeter can be given by formula
Perimeter= 10 x ( ( 2 x Radius of the decagon) / (1 + √5)))
=10×((2×16) / (1 + √5)))
=10×((32) / (1 + √5)
=320/1+√5
=320/1+2.2
=320/3.2
=100 units.
Hence perimeter of Decagon with radius and midpoint given is 100 units.
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Identify the partial quotient in the first step of this problem, as shown:
Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.
-83843/21 is the partial fraction of Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.
4357/21 - 4200
Take LCM as 21.
4357-88200/21
-83843/21
=-3992.5
Hence -83843/21 is the partial fraction of Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.
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the probability of being satisfied with a product purchased online is 0.555. if you buy 8 products online, what is the probability that you will be satisfied with 3 or more of the purchased products? (round your answer to 3 decimal places if necessary.)
The probability that you will be satisfied with 3 or more of the purchased products is 0.916
Given that,
The chance of being pleased with an internet purchase is 0.555. if you purchase 8 items online
Solution -
let X denote the no of success of
Purchased product online
X ~ B(n,p)
n = 8
P= 0. 555
a = 1 - 0 .555 = 0.445
P ( X = x) = [tex]nc_{x} b^{x} a^{n-x}[/tex]
P ( X = x)= [tex]8c_{x} (0.555^{x} )(0.445)^{8-x[/tex]
P ( X>=3)= [tex]\lim_{3 \to 8} 8c_{x} (0.555^{x} )(0.445)^{8-x[/tex]
P ( X>=3)) = 0.91614
=0.916
Therefore we can conclude the probability that you will be satisfied with 3 or more of the purchased products is 0.916
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The table shows the inputs and outputs for the function f (x) = -7x-5.Input-10-5O5Output65?-5-40What is the output value of the function when the input is –5?403050
Answer:
30
Explanation:
To know the output value of the function, we need to replace x by -5 and calculated f(x). So:
[tex]\begin{gathered} f(x)=-7x-5 \\ f(-5)=-7(-5)-5 \\ f(-5)=35-5 \\ f(-5)=30 \end{gathered}[/tex]Therefore, if the input x is -5, the output f(x) is 30
So, the answer is 30.
7/12 x 4x3 =? I need help
Cyphon, this is the solution:
We have to multiply the following fractions:
7/12 * 4/3
7 * 4 / 12 * 3
28/36
Simplifying, we have:
7/9 (Dividing by 4 numerator and denominator)
We have to add the following fractions:
- 1/2 + 4/9
Let's find the lowest common denominator between 2 and 9, as follows:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
9, 18, 27, 36
The lowest common denominator is 18