square root 2x-7 = 1
Answer:
4
Step-by-step explanation:
To solve for x in the equation:
√(2x - 7) = 1
We can start by isolating the square root by squaring both sides of the equation:
(√(2x - 7))^2 = 1^2
2x - 7 = 1
Next, we can isolate the variable by adding 7 to both sides of the equation:
2x = 8
Finally, we can solve for x by dividing both sides by 2:
x = 4
Therefore, the solution to the equation √(2x - 7) = 1 is x = 4.
The subscription rates in the United States and Canada for a civil engineering magazine are 1 year, $7.50;2 years, $12.00;3 years, $16.00; and 5 years, $22.00. Compute the rate of return on the investment for purchasers of: a) 2-year subscriptions b) 3-year subscriptions c) 5-year subscriptions.
a) 2-year subscriptions is approximately 20%.
b) 3-year subscriptions is approximately 29.56%.
c) 5-year subscriptions is approximately 41.33%.
To compute the rate of return on the investment for purchasers of different subscription lengths, we need to calculate the average annual cost of each subscription option.
a) 2-year subscriptions:
The cost of a 2-year subscription is $12.00. To find the average annual cost, we divide the total cost by the number of years:
Average annual cost = $12.00 / 2 = $6.00
b) 3-year subscriptions:
The cost of a 3-year subscription is $16.00. To find the average annual cost, we divide the total cost by the number of years:
Average annual cost = $16.00 / 3 = $5.33 (rounded to two decimal places)
c) 5-year subscriptions:
The cost of a 5-year subscription is $22.00. To find the average annual cost, we divide the total cost by the number of years:
Average annual cost = $22.00 / 5 = $4.40
Now, to calculate the rate of return on the investment, we need to compare the average annual cost to the regular 1-year subscription rate of $7.50.
a) For 2-year subscriptions:
Rate of return = (1 - Average annual cost / 1-year subscription rate) * 100%
Rate of return = (1 - $6.00 / $7.50) * 100% ≈ 20%
b) For 3-year subscriptions:
Rate of return = (1 - Average annual cost / 1-year subscription rate) * 100%
Rate of return = (1 - $5.33 / $7.50) * 100% ≈ 29.56%
c) For 5-year subscriptions:
Rate of return = (1 - Average annual cost / 1-year subscription rate) * 100%
Rate of return = (1 - $4.40 / $7.50) * 100% ≈ 41.33%
Therefore, the rate of return on the investment for purchasers of:
a) 2-year subscriptions is approximately 20%.
b) 3-year subscriptions is approximately 29.56%.
c) 5-year subscriptions is approximately 41.33%.
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Calculate and express your answer in decimal form: 3/4⋅200 *
Answer:
150.00
Step-by-step explanation:
PLEASE HELP ASAP THIS IS TIMED. If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)? On a coordinate plane, a straight line with a negative slope crosses the y-axis at (0, 5) and crosses the x-axis at (1, 0). On a coordinate plane, a parabola opens down. It goes through (negative 2, negative 4), has a vertex at (0, 5), and goes through (2, negative 2) On a coordinate plane, a parabola opens up. It goes through (negative 3, 7), has a vertex at (negative 1, 2), and goes through (0, 5). On a coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5)
Answer:
4th Graph
Step-by-step explanation:
Step 1: Find (f + g)(x)
-x² + 3x + 5 + x² + 2x
3x + 5 + 2x
5x + 5
Step 2: Graph
Answer:
option d on edge trash
Step-by-step explanation:
Find the 12th term of the arithmetic sequence x−4, 3x−11, 5x-18, ...
Answer:
Step-by-step explanation:
x -4 , 3x-11 , 5x - 18 ,.......
first term = a = x -4
Common difference (d) = second term - first term
= 3x -11 - [ x - 4]
= 3x - 11 - x + 4
= 3x - x - 11 + 4
= 2x - 7
nth term = a + (n-1)*d
12th term = x - 4 + 11*(2x - 7)
= x - 4 + 11*2x - 7 *11
= x - 4 + 22x - 77
=x + 22x - 4 - 77
= 23x - 81
Which one of the following statistics can be used to make decisions about retaining or discarding an item based on how well the item discriminates between high- and low-scoring test takers? Item-total correlation p-value level Item bias index
The statistic known as "p-value level" can be used to determine whether to keep or remove a question depending on how well it distinguishes between test takers with high and low scores.
Define the term p-value level statistics?A statistical measurement known as a p-value is employed to check a hypothesis' validity against actual data.
A p-value calculates the likelihood of getting the outcomes that were observed, presuming that null hypothesis is correct. The significance levels of the difference that was found increases with decreasing p-value.The probability value, or p value, indicates the likelihood that your data might be true under null hypothesis. This is accomplished by estimating the probability of given test statistic, that is the figure obtained from a statistical analysis of your data.Thus, the statistic known as "p-value level" can be used to determine whether to keep or remove a question depending on how well it distinguishes between test takers with high and low scores.
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1.1. How many m³ = are there in 3( mile )³
1.2. How many gal/min correspond to 5ft³ /s. 1.3. Convert the following: 9.50 cm to nm/sec² (5)
Using the conversion factors, we find that 3 cubic miles is approximately equal to 1.2504543 × 10^10 cubic meters. 5 cubic feet per second is equal to 2244.156 gallons per minute. 9.50 centimeters is equal to 9.50 * 10^7 nanometers per second squared.
1.1. One mile is equal to 1609.34 meters. Since we're dealing with cubic units, we cube the conversion factor.
1 mile = 1609.34 meters
1 mile³ = (1609.34 meters)³ = 4.168181 × 10^9 cubic meters
Therefore, 3 cubic miles is equal to 3 * 4.168181 × 10^9 cubic meters, which is approximately 1.2504543 × 10^10 cubic meters.
1.2. To convert from cubic feet per second (ft³/s) to gallons per minute (gal/min), we use the appropriate conversion factors.
Here are the conversion factors:
1 cubic foot = 7.48052 gallons
1 minute = 60 seconds
So, we set up the conversion as follows:
5 ft³/s * 7.48052 gal/ft³ * 60 s/min = 2244.156 gal/min
Therefore, 5 cubic feet per second is equal to 2244.156 gallons per minute.
1.3. To convert centimeters (cm) to nanometers per second squared (nm/sec²), we use the appropriate conversion factors. Here are the conversion factors:
1 centimeter = 10^7 nanometers
1 second = 1 second
So, we set up the conversion as follows:
9.50 cm * (10^7 nm/cm) / (1 sec)² = 9.50 * 10^7 nm/sec²
Therefore, 9.50 centimeters is equal to 9.50 * 10^7 nanometers per second squared.
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helpppppp!!!!!!!!!!!!!!
Answer:
Amanda spent $150.31. When 8 is substituted for g and 3 is substituted for t, the expression simplifies to 132.4 + 17.91.
Step-by-step explanation:
g = # of gallons of paint for $16.55 per gallon
t = # of pints of paint thinner for $5.97 per pint
Amanda bought 8 gallons of paint and 3 pints of paint thinner. To find out how much money she spent, just substitute 8 for g and 3 for t in the expression you selected.
16.55(8) + 5.97(3) = $150.31
Hope this helps!
Answer:
A
Step-by-step explanation:
bc everything lines up
What is the answer to 8)555 with the remainder and this is division.
Answer:
69 <-- quotient
---
Step-by-step explanation:
8)555
48
--
75
72
--
3 <-- remainder
40 m divided by 2
Can YOU solve that?
ha! I know the answer
Answer:
20m
Step-by-step explanation:
40m/2
20m
because 40/2=20
Justin bought 3 CDs that were each the same price. Including sales tax, he paid a total of $49.50 Each CD had a tax of $1.10 What was the price of each CD before tax?
Answer:
We know he bought 3 CDs and he paid 49.50 dollars, which the tax included. Now, we can calculate how much did he pay for each CD by dividing the total cost (49.50) by the number of CDs (3):
49.50/3 = 16.50
Now, we know each CD costs 16.50 with tax included so, if it has a tax of1.10 dollars, we only need to substract the price (16.50) and the tax (1.10)
16.50 - 1.10 = 15.40
Without tax, ech CD costs 15.4 dollars ($15.4)
Answer:
The price before sale tax is $15.40
Step-by-step explanation:
$1.10 × 3 = $3.30
$49.50 - $3.30 = $46.20
$46.20 ÷ 3 = $15.40
the project charter must state the key metric to be improved. the key metric is the _____ in y=f(x) for the project
The key metric to be improved in a project can vary depending on the nature and objectives of the project. However, in the context of the equation y = f(x), the key metric would typically be represented by the variable "y."
The specific definition of "y" will depend on the project and its goals. It could represent a wide range of factors, such as cost savings, customer satisfaction, productivity, revenue growth, quality improvement, or any other relevant performance indicator that the project aims to enhance.
When creating a project charter, it is essential to clearly define and specify the key metric (i.e., "y") that will be targeted for improvement throughout the project's duration. This helps align the project team's efforts and provides a clear focus on the desired outcome.
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Find the HCF of ; 3.36,60,84
Answer:
3
Step-by-step explanation:
im guessing 3.36 is a typo and it should be 3,36,60,84
so in that case it would be 3
Answer:
3
Step-by-step explanation:
ok you understand hope
Marcus is going to buy a round swimming pool for his backyard that measures 15 feet across. How much of his backyard would the swimming pool cover, in square feet?
Answer:
176.7146 in square feet
give brainlyest
Step-by-step explanation:
The word "and" in probability implies that we use the ____ rule.
A. Subtraction
B. Division
C. Addition
D. Multiplication
The word "and" in probability implies that we use the Multiplication rule.
The correct option is Option D.
What is the Multiplication Rule of Probability?The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.
The relationship between two events is explained by the probability multiplication rule.
Set A∩B represents the events in which both events A and B have occurred for two events A and B related to a sample space S. Consequently, (A∩B) indicates that occurrences A and B happened at the same time. You can write the event A∩B as AB. Using the characteristics of conditional probability, the likelihood of event AB is calculated.
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Verify which of the following are identities.
Answer:
d. only the first equation is an identity
Step-by-step explanation:
You toss a fair coin until you have at least one head and at least one tail. What is the expected number of tosses
What was the difference between the winning butterfly time and the winning backstroke time?
Answer:
It has more time and the other takes less time
Step-by-step explanation:
if you subtract them it should be 4.66 seconds of difference hope this helps :)
In ΔEFG, g = 34 inches, e = 72 inches and ∠F=21°. Find the area of ΔEFG, to the nearest square inch.
The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.
To find the area of triangle EFG, we can use the formula:
\(Area = (1/2) \times base \times height\)
In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.
First, let's find the length of FG. We can use the law of cosines:
FG² = EF² + EG² - 2 * EF * EG * cos(∠F)
EF = 72 inches
EG = 34 inches
∠F = 21°
Plugging these values into the equation:
FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)
Solving for FG, we get:
FG ≈ 83.02 inches
Next, we need to find the height. We can use the formula:
height = \(EF \times sin( \angle F)\)
Plugging in the values:
height = 72 * sin(21°)
height ≈ 25.52 inches
Now we can calculate the area:
\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)
Area ≈ 1060.78 square inches
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PLEASEE GUYS HELP ME WITH THIS QUESTION!!!!
Answer:
y= = -2
Step-by-step explanation:
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.
Shape a is enlarged to give shape b a) what is the scale factor of the enlargement? b) mark with a cross the centre of enlargement
The scale factor of the enlargement will be 3. Then the center of enlargement is marked in the diagram.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
Shape A is enlarged to give shape B.
Then the scale factor of the enlargement will be
⇒ 3 / 1
Then the center of enlargement is marked in the diagram.
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əz 22. Suppose z= z(x, y) is implicitly determined by ln(x+y+z) = x+2y+3z. Then dy (z.y.a)=(-1,5,-3)
the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).
n the given problem, we have an implicit equation ln(x+y+z) = x+2y+3z that defines z as a function of x and y. We are given the values dy = (-1, 5, -3).
To find the derivative dy/dx, we can use the total derivative formula and apply it to the implicit equation. The total derivative is given by dy/dx = - (∂F/∂x)/(∂F/∂y), where F = ln(x+y+z) - x - 2y - 3z.
Differentiating F partially with respect to x and y, we have (∂F/∂x) = 1/(x+y+z) - 1 and (∂F/∂y) = 1/(x+y+z) - 2.
Plugging in the given values of dy = (-1, 5, -3), we can calculate dy/dx = - (∂F/∂x)/(∂F/∂y) = -(-1)/(5-2) = 1/3.
Therefore, the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).
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What is the exponential form of log3 2187 = 7?
Answer:
2187 = \(3^{7}\)
Step-by-step explanation:
Using the rule of logarithms
\(log_{b}\) x = n , then x = \(b^{n}\) , then
\(log_{3}\) 2187 = 7
2187 = \(3^{7}\)
Answer:
3 ^7 = 2187
Step-by-step explanation:
log3 2187 = 7
log a (b) = c
a^c = b
3 ^7 = 2187
our basketball team has 12 members, each of whom can play any position. in how many ways can we choose a starting lineup consisting of a center, a power forward, a shooting forward, a point guard, and a shooting guard?
By permutation, in 95040 ways we can choose a starting lineup consisting of a center, a power forward, a shooting forward, a point guard, and a shooting guard
What does permutation mean?A permutation is a set up of things in a certain sequence. Here, the members of sets or their constituent parts are sorted in a linear or sequential manner.
How is a permutation determined?Take the number of possibilities for each event and multiply it by itself X times, where X is the total number of events in the sequence, to find the number of permutations. For instance, four-character PINs have a total of 10 possible combinations because each digit can vary from 0 to 9.
\(12^P_{5} = \frac{12!}{(12-5)!} =\frac{12!}{5!} = 12 X 11 X 10 X 9 X 8 = 95040\)
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When constructing a perpendicular bisector why must the compass opening be greater than 1/2.
It is critical to open a compass with over half the way in order for the arcs formed to meet for perpendicular bisector.
What is perpendicular bisector?A perpendicular bisector would be a line that cuts a line segment in half and forms a 90-degree angle at the intersection point. In other words, a perpendicular bisector separates a line segment now at midpoint, forming a 90-degree angle.
Now, consider an example;
When you wish to build a perpendicular line on a line segment, like line AB, you do the following;
Set the compass on a radius more than half the length of the line AB.Using A as your center, draw an arc above and below line AB.With the same radius and B as our center, draw additional arcs on top or below line AB to join a first arcs on the both side of the line.Join the two arc intersections to cut line AB at M.A line AB appears to be bisected perpendicularly as a result. The arcs would not have met if the compass is opened less than half way down line AB.
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evaluate and solve for the variable 70 = 7m
Answer:
10= m
Step-by-step explanation:
70 = 7m
70/7 = 7m/7
10= m
hope this helps! :)
Answer: 10m
Step-by-step explanation: m=10
what is the domain of validity for csc 0=1/sin 0
a. all real numbers
b. all real numbers except odd multiples of pi/2
c. all real numbers except even multiples of pi/2
d. all real numbers except multiples of pi
The correct answer is (b) all real numbers except odd multiples of π/2. The domain of validity for cscθ (cosecant) is restricted because cosecant is undefined when the sine of an angle is zero.
In the trigonometric identity cscθ = 1/sinθ, the denominator sinθ becomes zero at odd multiples of π/2 (such as π/2, 3π/2, 5π/2, etc.), resulting in a division by zero error. Therefore, the cosecant function is not defined for these values of θ.
For all other real numbers θ, the sine function is non-zero and well-defined, allowing us to calculate the reciprocal of the sine and determine the value of the cosecant. Hence, the domain of validity for cscθ is all real numbers except odd multiples of π/2, as stated in option (b).
It's important to note that in trigonometry, the domain of validity is determined by avoiding any values that would lead to undefined expressions or division by zero errors.
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The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π, because at these points the sine function equals zero, and division by zero is undefined.
Explanation:In mathematics, the cosecant function (csc), is defined as the reciprocal of the sine function, or 1/sinθ. The domain of a function are all the possible input values that will yield real numbers (output). For the csc function, its domain includes all real numbers except where the denominator is zero because division by zero is undefined.
In the unit circle context, sine equals zero at 0, π, 2π, ..., and the negative counterparts. Basically, these are the multiples of π. Thus, for the csc function, the domain is all real numbers except multiples of π, which matches option d in your choices.
The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π.
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the kutta-joukowski theorem, equation (3.140), was derived exactly for the case of the lifting cylinder. in section 3.16 it is stated without proof that equation (3.140) also applies in general to a two-dimensional body of arbitrary shape. although this general result can be proven mathematically, it also can be accepted by making a physical argument as well. make this physical argument by drawing a closed curve around the body where the closed curve is very far away from the body, so far away that in perspective the body becomes a very small speck in the middle of the domain enclosed by the closed curve.
The Kutta-Joukowski theorem, which is represented by equation (3.140), was originally derived for the case of a lifting cylinder. However, it can also be applied to a two-dimensional body of arbitrary shape, as stated in section 3.16.
A more detailed explanation of the answer.
To make a physical argument for this generalization, we can draw a closed curve around the body.
The key is to draw the curve far enough away from the body such that the body appears as a very small speck in the middle of the domain enclosed by the closed curve.
By doing this, we are essentially treating the body as a point object at the center of the curve. Since the body is now a very small speck in comparison to the large domain, its specific shape becomes insignificant to the overall flow around it.
Therefore, the lifting force calculations derived from the Kutta-Joukowski theorem for the lifting cylinder should also apply to the two-dimensional body of arbitrary shape, as long as the body is small in comparison to the domain enclosed by the closed curve.
This physical argument allows us to accept that equation (3.140) can be applied in general to a two-dimensional body of arbitrary shape without requiring a mathematical proof.
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A survey was taken of a random sampling of residents of New York City and Los Angeles to compare how many
of them own a car
Answer:
The survey represents quantitative data and there is greater percentage of LA residents who own cars than NYC residents who do.
TRUE/FALSE return values are type-specific in php functions (a function only returns a value of a specified data type.)
Return values are type-specific in php functions The answer is False.
What is php function?
A PHP function is a piece of code that is very reusable. It can accept an argument list as input and return a value. Inbuilt functions in PHP number in the thousands.
You can develop your own functions in addition to the built-in PHP functions.
A function is a collection of statements that a programme can use repeatedly.
When a page loads, a function won't start running immediately.
A call to a function will cause the function to run.
In this a function only returns a value of a specified data type.
Hence, the given statement return values are type-specific in php functions is FALSE
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