The value of x for the given equation is 8.
What is Logarithm?Logarithm function is defined as the inverse of the exponential function.
If a^(b) = c, then b = log(c) at the base of a.
For negative numbers, the logarithm are complex numbers.
The given equation is as below,
x^(-1/3) = 32x^(-2)
It can be solved as follows,
x^(-1/3) = 32x^(-2)
Take logarithm on both sides to obtain,
log (x^(-1/3)) = log (32x^(-2))
=> -1/3 log(x) = log(32) - 2log(x)
=> 2log(x) - 1/3 log(x) = log(32)
=> 5/3log(x) = log(32)
=> log (x^(5/3)) = log(32)
Remove log from both sides to get,
x^(5/3) = 32
=> x = 32^(3/5)
=> x = 8
Hence, the solution of the given equation is x = 8.
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Ethan and Adrian are reading the same book. At the beginning of the month, Ethan was on page 18 and Adrian was on page 45. Ethan will read 12 pages per day and Adrian will read 9 pages per day. Let E represent the page of the book that Ethan is on at the end of t days into the month, and let A represent the page of the book that Adrian is on at the end of t days into the month. Write an equation for each situation, in terms of t,, and determine whether Ethan or Adrian is farther along in the book after 4 days.
Answer: Ethan
Step-by-step explanation:
E:A
18:45 on page
12:9 per day
48:36 after 4 days
Ethan is further along in the book after 4 days
Mary has 96 fliers to post around town. last week she posted 1/6 of them. this week she posted 1/4 of the remaining fliers. How many fliers has she still not posted?
Answer:
Start with 60 fliers
post 1/4 of fliers so 60*.25=15
60-15=45 left
post 1/5 of remaining so 45*.20=9
45-9=36 left
Step-by-step explanation:
Last week: (had 60) (used 1/4)= (60)(1/4)= 15. So, you used 15.
You have 60-15=45 left. This is how many you have to start the week.
This week: (had 45) (used 1/5)= (45)(1/5)= 45/5=9. So, you used 9.
This means that you have 45-9= 36 left.
Mary Still did not post 60 fliers.
Total fliers Mary was having = 96
Fliers she posted last week = 1/6 = 0.16
Fliers left with Mary after posting 1/6 part last week
= 96 x 0.16
= 16
Fliers left with Mary after the posting of 1/6 of them
= 96 - 16
= 80
Now the new remaining number of fliers with Mary = 80
Fliers she posted this week = 1/4 = 0.25
Fliers left with Mary after posting 1/4 part this week
= 80 x 0.25
= 20
Fliers left with Mary after the posting of 1/4 of them this week
= 80 - 20
= 60
Therefore, the fliers that Mary still did not post = 60
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A desk is on sale for $459, discount is 32% less than the regular price
What is the regular price?
Find the slope of the li
16.) (5,-3), (5,8)
Answer:
slope = undefined
Step-by-step explanation:
Find the slope of the line: (5,-3), (5,8)
slope = change in y / change in x
slope = ( -3 - 8) / (5 - 5)
slope = -11/0
slope = undefined
These points graph a vertical line.
answer:
the slope is undefined.
step-by-step explanation:
there is an equation (y2-y1)/(x2-x1) that allows for you to determine the slope. since this line is vertical, the slope is defined because if you plug the points into the equation, you would be dividing by 0.
how is the accuracy rate calculated? how is the accuracy rate calculated? subtract the number of correct predictions from the total number of predictions. divide the number of true positives by the number of true negatives. divide the number of correct predictions by the total number of predictions. add the number of true positives and the number of false negatives.
Accuracy rate is equal to the difference of predicted value and true value divide it by true value and then multiply by 100 to get the rate.
Accuracy value represent the calculated value is more close to the true value.It help us to measure the statistical error.It help us to know what the error given in the measured value of the data.Divide the difference of predicted and true by the true value and then multiply it by 100 to get the accuracy rate.Accuracy test can be done different statistical methods also.Accuracy rate = [ | Predicted value - True vale|/ true value ] × 100
Therefore, the accuracy rate is the percentage of the ratio of difference of predicted value and true value to the true value.
The given question is incomplete, I answer the question in general according to my knowledge:
How is the accuracy rate calculated?
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for a math proficiency exam, it is known that the population mean score is 1100 and the population standard deviation is 100. if the test is administered to 64 randomly selected individuals from this population, what is the probability that the sample mean will lie between 1070 and 1120? after finding the appropriate probability, indicate the interval that includes this probability. group of answer choices .7001 to .8500 .6001 to .7000 .8501 to 1.000 .0000 to .3000 .3001 to .6000
The probability that the sample mean will lie between 1070 and 1120 is .7001 to .8500.
To find the probability that the sample mean will lie between 1070 and 1120, we use the Z-score formula:
Z = (x - μ) / σ
where x is the value we are looking for (in this case 1070 or 1120), μ is the population mean (1100), and σ is the population standard deviation (100).
Using this formula, we can calculate the Z-scores for 1070 and 1120, which are -0.3 and 0.2 respectively.
We can then use a Z-table to find the probability associated with each of these Z-scores. The probability associated with a Z-score of -0.3 is 0.6179, and the probability associated with a Z-score of 0.2 is 0.7886.
The probability that the sample mean will lie between 1070 and 1120 is the difference between these two probabilities, which is 0.1707. This is equivalent to a probability of 0.7001 to 0.8500.
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the radius of the wheel on a bike is 19 inches. if the wheel is revolving at 140 revolutions per minute, what is the linear speed of the bike, in miles per hour?
Therefore, the linear speed of the wheel on a bike is approximately 0.9π miles per hour.
What is meant by linear speed?The pace at which an object travels a specific distance in a predetermined amount of time is known as linear speed. By dividing the distance traveled by the time it takes to cover that distance, it may be used to determine how rapidly an item is travelling in a straight line. For instance, if a car moves 100 meters in 10 seconds, its linear speed is 10 meters per second. Linear speed is distinct from average speed, which takes into account any variations in velocity or direction throughout the duration of a voyage. Linear speed is also distinct from tangential speed, which is the pace at which an item travels along a circular route. Physics' fundamental idea of linear speed.
How to solve?
C=2πr,
C=2π(19)=38π.
linear speed of v=(38π/60)*5280=33.6π feet per second.
final speed of v=(33.6π/3600)*60=0.9π miles per hour.
Therefore, the linear speed of the bike is approximately 0.9π miles per hour.
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Using the equation , describe how to create a system of linear equations with an infinite number of solutions.
In the case of coinciding lines with the same y-intercept, the number of solutions to the equation system is unlimited.
What is Equation?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example.
There are many different types of equations, such as linear, quadratic, cubic, etc.
Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It shows that the expressions printed on the left and right sides have an equal relationship. In any mathematical equation, we have LHS = RHS (left hand side = right hand side).
Equations can be solved to find the value of an unknown variable that represents an unknown quantity. If there is no "equal to" symbol in the sentence, it is not an equation.
Hence, In the case of coinciding lines with the same y-intercept, the number of solutions to the equation system is unlimited.
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Complete question-
Using the equation y = 2/3 x - 5, describe how to create a system of linear equations with an infinite number of solutions.
please help me ASAP MATH!
Answer:
A
Step-by-step explanation:
numerator = exponent of x (in this case is 1, so it can be omitted)
denominator = index of the root
√x
How to write the equation of the line with m = - 3/4 that goes through (2, –5) in
Slope–Intercept Form.
Answer: y=-3/4x-3.5
Step-by-step explanation:
First, set up the equation based on the information we already know. The slope-intercept form is y=mx+b (m being the slop and b is the y-intercept)
We already know the slope, so we can substitute it.
y=-3/4x+b
Now, the only variable we need to find is b (the y-intercept)
To do this we can substitute the point that was given, (2,-5)
Substitute -5 in for y and 2 in for x.
Then you get the equation -5=-3/4(2)+b
Multiply -3/4 and 2 and you get -5=-3/2+b
Add -3/2 from both sides to isolate b
You then get b=-3.5
Substitute b back in the original equation
Your final answer is y=-3/4x-3.5
18. What are the zeroes of the function? (1 point)
y=(x-3)(x + 2)(x-2)
O-3, 2, -2
O-3, 2, 2
03, -2, 2
03, 2, 2
The required zeros of the function y=(x-3)(x + 2)(x-2) is given as 3, -2, and 2. Option C is correct.
Here,
Zero of the function are the values of x, for a function for which the function gives y = 0,
So let y = 0, - - - - - -(1)
Put y = (x-3)(x + 2)(x-2) in equation 1
(x-3)(x + 2)(x-2) = 0
Equating each parenthesis step by step with zero,
x - 3 = 0 ; x + 2 = 0 ; x - 2 = 0
x = 3 ; x = -2 ; x = 2
So the values that came out are 3, -2, and 2, are said to be zeros of the given function,
When we substitute any value in the function then y becomes zero such as,
Put x = 3 in function,
y = (3-3)(3+2)(3 - 2)
y = (0)(5)(1)
y = 0
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In the year 2000, the company made $2. 2 million in profit. For each conecutive year after that, their profit increaed by 13%. How much would the company' profit be in the year 2003, to the nearet tenth of a million dollar?
Rounded to the nearest tenth of a million dollars, the company made $3.2 million in profit in the year 2003.
What is meant by Profit?Profit is a financial gain that occurs when the revenue from a company activity is more than the costs, costs, and taxes required to support the activity. It is, in other words, the difference between income and costs. Profit is an important aspect in a company's performance and is often quantified in monetary terms, but it may also be viewed .For example, for each consecutive year after that, their profit increased by 13%.
Profits may be divided into two categories: net profit and gross profit. After deducting all costs, taxes, and expenses, a company's net profit is the overall profit it has made. In contrast, gross profit is the profit made by a firm before expenses and costs are deducted.
How to solve?
In the year 2001, the company made $2.2 million * 1.13 = $2.486 million in profit.
In the year 2002, the company made $2.486 million * 1.13 = $2.82778 million in profit.
In the year 2003, the company made $2.82778 million * 1.13 = $3.1987314 million in profit.
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Determine if (2, -1) is a solution to the system of equations:
2x−y=5
y=3x−7
Justify your answer using mathematics.
Is the coordinate a solution?
yes or no
The solution to the system of equations is (x, y) = (2, -1).
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
WE are given the system of equations
2x−y=5
y = 2x - 5
y=3x−7
Adding the two equations Then divide by 2
Subtracting the second equation from the first gives;
0 = x -2
x = 2
y = -1
therefore, The solution is (x, y) = (2, -1).
The solution to the system of equations is (x, y) = (2, -1).
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it takes avery 48 seconds to sprint 365m what is her average speed
Match the variable and angle with the correct value to create the angle measures for the exterior angle theorem.
x=60°, y=15°, angle C is 45°, angle DBC is 105° and angle CBA is 75°.
In the given figure, ∠DBC=7y°, ∠CBA=5y°, ∠C=3y° and ∠D=x°.
What is angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Here,
∠DBC+∠CBA=180° (Sum of adjacent angles is 180°)
⇒ 7y°+5y°=180°
⇒ 12y°=180°
⇒ y°=15°
∠DBC=7y°=105°, ∠CBA=5y°=75° and ∠C=3y°=45°
Now, ∠DBC=∠C+∠A
⇒ 105°=45°+∠A
⇒ ∠A=60°
Therefore, x=60°, y=15°, angle C is 45°, angle DBC is 105° and angle CBA is 75°.
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What is the rate of change between (3.4,-0.1) and (3.5,0.1)?
The rate of change between the points (3.4, -0.1) and (3.5, 0.1) is 2.
How to find rate of change?The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.
The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity.
Therefore,
rate of change = Δy / Δx
rate of change = y₂ - y₁ / x₂ - x₁
Hence, let's find the rate of change of (3.4,-0.1) and (3.5,0.1).
rate of change = 0.1 + 0.1 / 3.5 - 3.4
rate of change = 0.2 / 0.1
rate of change = 2
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A one-cup serving of spaghetti with meatballs contains 260 calories and 32 grams of carbohydrates. A one-cup serving of chopped iceberg lettuce contains 5 calories and 1 gram of
carbohydrates. Determine how many servings of each would be required to obtain 160 calories and 20 grams of carbohydrates
How many serving(s) of spaghetti would be required?
(Round to the nearest tenth.)
For 160 calories and 20 grams of carbohydrates 0.61 cups are required.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a one-cup serving of spaghetti with meatballs contains 260 calories and 32 grams of carbohydrates. A one-cup serving of chopped iceberg lettuce contains 5 calories and 1 gram of carbohydrates.
For 160 calories the number of cups will be calculated as,
1 cup = 260 calories
160 calories = ( 160 ) / 260 cups
160 calories = 0.61 cups
Therefore, for 160 calories and 20 grams of carbohydrates 0.61 cups are required.
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Winston's bill at the restaurant was $32. He left a tip of 20%.
What was the tip amount? Round your answer to the nearest penny.
The round of tip amount.
Total tip = $ 7.00
Total (Bill + Tip) = $ 39.00.
How to Calculate Tip?
To calculate the tip multiply the total check by 1 plus the decimal percentage tip you'd like to leave.
If you wanted to leave a 20% tip, you would add 1 to 0.20 to get 1.20. Multiply the bill by 1.20 to get the total amount you'd leave including tip.
Decide on tip percentageAdd the decimal form of tip percentage to 1 to get your rateMultiply the bill by your rateTo calculate this, you can multiply the bill amount by the tip percentage: $32 * 0.20 = $6.40.
The tip amount was $6.40.
Hence, the round of tip amount.
Total tip = $ 7.00
Total (Bill + Tip) = $ 39.00.
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Tyler made a scale drawing of an apartment. The scale of the drawing was 1 millimeter : 2 meters. The living room is 6 meters long in real life. How long is the living room in the drawing?
In the drawing, the length of the living room is 3 millimeters.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, Tyler made a scale drawing of an apartment. The scale of the drawing was 1 millimeter : 2 meters.
The living room is 6 meters long in real life and assuming in the drawing it is x millimeters.
∴ 1 : 2 : : x : 6.
1/2 = x/6.
x = 6/2.
x = 3.
So, In drawing it is 3 millimeters.
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(4x-7.2)+(-5.3x-8) please help!
Answer:
−1.3x − 15.2
Step-by-step explanation:
step 1: simplify
4x−7.2−5.3x−8
=4x+−7.2+−5.3x+−8
step 2: combine like terms
=4x+−7.2+−5.3x+−8
=(4x+−5.3x)+(−7.2+−8)
=−1.3x+−15.2
For what values of x is y=-7-|x| increasing? Decreasing?
The intervals for which the function y = -7 - |x| is increasing and decreasing is given as follows:
Increasing: x < 0.Decreasing: x > 0.How to obtain the intervals of increase and decrease?The function is defined as follows:
y = -7 - |x|.
The parent absolute value function is increasing for x > 0 and decreasing for x < 0.
For this problem, the multiplication by -1 means that the function was reflected over the x-axis, meaning that the intervals of decrease and increase were exchanged, and thus they are given as follows:
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Please help me with this question
Answer:
D
Step-by-step explanation:
it is a regular pentagon.
so, all side lengths are equal, and also all cross connections between corners are equal.
that makes TR parallel to PQ.
and that makes SPQ an isoceles triangle (both legs are equally long). and the smaller triangle S to x to the angle to the right of x is similar to SPQ, which means they have the same angles.
so, the triangle interior angle at P = the triangle interior angle Q = y.
and they must be the same as the bottom 2 interior angles of the small triangle.
x and the angle right to x are equal too, as they are the triangle exterior (supplementary) angles to the bottom 2 interior angles of the small triangle.
we know that the sum of all angles of the internal trapezoid (PQ to x and its right neighbor) is 360.
and based on the EqualLogic found above these angles are
2×x + 2×y = 360°
x + y = 180°
If James Handerson wants to see a 15% increase in his bench press, and he can lift 210 pounds now, what goal weight should he shoot for?
James Handerson should shoot for 241.5 lbs.
Step-by-step explanation:Here are the steps to figuring out your problem:First, convert 15% into a decimal by moving the decimal place over twice to get 0.15.
Then, set up this equation:
0.15 x 210 = 31.5
Now, 31.5 is the percent increase, so now we add to the original weight:
210 + 31.5 = 241.5
Solution:
241.5 lbs.
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
What is the domain of this function?(–10,3)(3,2)(0,–8)(8,–4)(7,6)
Answer:
d = {-10, 0, 3, 7, 8}
Step-by-step explanation:
the domain is the set of x values in a function
Label the slope for each line.
Miss Muffet's Spider
Answer:
A=1 B=2 C=7
Step-by-step explanation:
Look at the graph!!!!
x/2 -5 = -3
Answers: A.4 B.1 C.-4 D.-16
Answer:
A. 4
Step-by-step explanation:
x/2 - 5 = -3
x/2 = 2
x = 4
Multiply both sides of the equation by 2.
x - 10 = -6Add 10 to both sides.
x = -6 + 10Add −6 and 10 to get 4.
x = 4slope is 1/4 the line passes through the point 8,5
Answer:
Go up by 1 and run 4, remeber slope: rise over run. If the point is 8,5 then find 8 on the x axis and 5 and the y, wherever they meet, that's your answer.
Step-by-step explanation:
Which graph shows a system with no solutions?
help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
Answer:
Step-by-step explanation:
a.) The population is years measured after 2000 so 2000 is 0. Any number to the 0 power is 1 so the population is 23.1 (million).
b.) 28.3 = [tex]23.1e^{0.0152t}[/tex]
1.22510823 ≈ [tex]e^{0.0152t}[/tex]
ln 1.22510823 ≈ 0.0152t
t≈13.4 MILLION
Kate wants to install an in ground pool in five years. She estimates the cost will be $50,000. How
much should she deposit monthly into an account that pays 1. 6% interest compounded
monthly in order to have enough money to pay for the pool in 5 years? Round your answer to
the nearest dollar
Kate should deposit $46,158.28 monthly into an account
In this question, we have been given the amount A = $50,000,
interest rate R = 1.6%
period t = 5 years
We need to find the principal amount (P)
First, convert R as a percent to decimal
r = 1.6/100
r = 0.016
Using the formula of compound interest for P,
P = A / (1 + r/n)nt
P = 50,000.00 / (1 + 0.016/12)(12)(5)
P = $46,158.28
Therefore, Kate should deposit $46,158.28
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