Since Shay's sibling is 7 years younger than twice her age, Shay is therefore 29 years old.
what is unitary method ?Mathematicians use the unitary method, also referred to as the "single unit technique," to answer problems involving proportional relationships between two or more quantities. The unitary technique entails determining the value of a single unit or quantity and using that value to calculate the values of other quantities in relation to that unit or quantity. Problems requiring ratios, proportions, percentages, and other related ideas can be solved using this approach.
given
Shay's age will be denoted by the letter S, and her sister's age will be referred to as "Sister".
The first claim informs us of the following:
Sibling = 2S – 7
And based on the second assertion, we can infer that:
Sibling + S = 80
The result of putting the first equation into the second equation is:
S + (2S - 7) = 80
When we simplify this solution, we obtain:
3S - 7 = 80
7 added to both edges gives us:
3S = 87
When we multiply both parts by 3, we get:
S = 29
Since Shay's sibling is 7 years younger than twice her age, Shay is therefore 29 years old.
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Jen's total assets are $6,964. her liabilities are $1,670 in credit card debt and $3,642 for a student loan. what is her net worth?
The difference between Jen's total assets and liabilities is her net worth. The sum of her credit card debt and school loan debt represents her overall liabilities.
What are the assets and liabilities?Liability can also include owing money or services to someone, even though word usually refers to being responsible for something. For instance, a homeowner's tax obligation may include the sum of city property taxes owed or the sum of federal income taxes owed.
To calculate Jen's net worth, we need to subtract her total liabilities from her total assets:
Net worth = Total assets—Total liabilities
Her total obligations must be subtracted from her total assets in order to determine her net worth:
Total liabilities = $ [tex]1,670[/tex] + $ [tex]3,642 =[/tex] $ [tex]5,312[/tex]
Net worth = $ [tex]6,964[/tex] - $ [tex]5,312[/tex]
Net worth = $ [tex]1,652[/tex]
Therefore, Jen's net worth is $ [tex]1,652[/tex] .
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calculate the percent yield of copper (ii) oxide. 4. explain why you obtained a yield different than g
To calculate the percent yield of copper (II) oxide, you need to have the actual yield and the theoretical yield. The percent yield can be calculated using the following formula: Percent Yield = (Actual Yield / Theoretical Yield) * 100
1. Obtain the actual yield: This is the amount of copper (II) oxide produced in your experiment or reaction, typically measured in grams.
2. Calculate the theoretical yield: Use the balanced chemical equation and the stoichiometry of the reaction to determine the maximum amount of copper (II) oxide that could be produced from the given reactants.
3. Plug the values into the formula: Divide the actual yield by the theoretical yield and multiply the result by 100 to get the percent yield.
If you obtained a yield different than the expected or theoretical yield, there could be several reasons, including experimental errors, impure reactants, or side reactions occurring during the process. These factors can cause the actual yield to be higher or lower than the theoretical yield.
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what is the probability that more than 50 cars will need to be inspected before one with the defect is found?
The probability that more than 50 inspections are required before one with the defect is found is very low , approximately 1.05 x 10^-9.
We can use a geometric distribution to model the number of cars that need to be inspected before one with the defect is found. Since the probability of finding a car with the defect is p = 0.4, the probability of not finding a car with the defect on a given inspection is q = 1 - p = 0.6.
Let's define the random variable X as the number of inspections required until one with the defect is found. The PMF of the geometric distribution is:
P(X = k) = q^(k-1) * p
where k is the number of inspections required.
To find the probability that more than 50 inspections are required, we need to calculate the cumulative probability:
P(X > 50) = Σ(k=51 to ∞) P(X = k)
Using the PMF of the geometric distribution, we get:
P(X > 50) = Σ(k=51 to ∞) q^(k-1) * p
This sum can be simplified using the formula for the sum of an infinite geometric series:
P(X > 50) = q^50 * p / (1 - q)
Substituting in the values of p = 0.4 and q = 0.6, we get:
P(X > 50) = 0.6^50 * 0.4 / 0.4 = 0.6^50
Using a calculator or software, we can calculate that this probability is approximately 1.05 x 10^-9, which is a very small probability.
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Complete question is:
Of the automobiles produced at a particular plant, 40% had a certain defect. what is the probability that more than 50 cars will need to be inspected before one with the defect is found?
if the odds on a bet are 16:1 against, what is the probability of winning? express your answer as a fraction.
The probability of winning is 1/17, which can also be expressed as a decimal (approximately 0.059) or as a percentage (approximately 5.9%).
The odds on a bet represent the ratio of the probability of winning to the probability of losing. In this case, the odds are 16:1 against winning, which means that the probability of winning is 1 out of 16.
To express this probability as a fraction, we can use the formula:
Probability of winning = 1 / (odds + 1)
Plugging in the given odds, we get:
Probability of winning = 1 / (16 + 1)
Probability of winning = 1/17
In this case, the odds of 16:1 against winning correspond to a probability of 1/17, which represents the chance of winning the bet.
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this is so confusing. i have to round to either 106 or 67 in.
The circumference of a circle with a radius of 15 inches is 30π inches, or 94.25 inches
How to calculate the circumferenceThe circumference of a circle can be calculated using the formula:
C = 2πr
where C is the circumference, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14159.
In this case, the radius is 15 inches. Substituting this value into the formula, we get:
C = 2π(15) = 30π
So the circumference of a circle with a radius of 15 inches is 30π inches, or approximately 94.2478 inches.
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Write the slope-intercept form of the equation of the line described.
through: (-4, -1), parallel to y =
-1/2x-2
Answer:
y = - [tex]\frac{1}{2}[/tex] x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{2}[/tex] x - 2 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
• Parallel lines have equal slopes , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute (- 4, - 1 ) into the partial equation
- 1 = - [tex]\frac{1}{2}[/tex] (- 4) + c = 2 + c ( subtract 2 from both sides )
- 3 = c
y = - [tex]\frac{1}{2}[/tex] x - 3 ← equation of parallel line
You must find the sum of the volume of the square prism and the square pyramid.
Enter the letter of the answer.
The sum of the volume of the square prism and the square pyramid is 672 cubic inches.
What is prism ?
A prism is a three-dimensional geometric shape that has two identical, parallel polygonal bases and rectangular sides that connect the bases. The sides are perpendicular to the bases and their shape depends on the shape of the base. For example, if the base is a square, the prism is called a square prism. If the base is a rectangle, the prism is called a rectangular prism. The height of the prism is the perpendicular distance between the bases.
According to the question:
First, let's calculate the volume of the square prism:
The formula for the volume of a square prism is V = lwh, where l is the length, w is the width, and h is the height.
In this case, the length (l) and width (w) of the prism are both equal to a, which is 10 inches, and the height (h) is 6 inches. So, we have:
V_prism = lwh = 10 x 10 x 6 = 600 cubic inches
Next, let's calculate the volume of the square pyramid:
The formula for the volume of a square pyramid is V = (1/3)Bh, where B is the area of the base and h is the height.
In this case, the base of the pyramid is a square with side length b, which is 6 inches, so the area of the base is:
[tex]B = b^2 = 6^2 = 36 square inches[/tex]
The height of the pyramid is also 6 inches, so we have:
V_pyramid = (1/3)Bh = (1/3) x 36 x 6 = 72 cubic inches
Finally, the total volume is the sum of the volumes of the prism and pyramid:
V_total = V_prism + V_pyramid = 600 + 72 = 672 cubic inches
Therefore, the sum of the volume of the square prism and the square pyramid is 672 cubic inches.
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Triangle ABC is congruent to triangle A′′B′′C′′ .
Which sequence of transformations could have been used to transform triangle ABC to produce triangle A′′B′′C′′ ?
Triangle ABC was reflected across the x-axis and then translated 9 units right.
Triangle ABC was translated 7 units down and then 9 units right.
Triangle ABC was translated 10 units right and then reflected across the x-axis.
Triangle ABC was reflected across the y-axis and then translated 7 units down.
Which choice would transform the pre-image to the composite image? Make sure the letter for each vertex matches! Select one: a. Reflect across the y-axis and translate 4 down and three left. b. Rotate 180° and reflect across the x-axis. c. Rotate 90° and translate 4 up and 3 right. d. Reflect across the x-axis and translate up 4 and right 3.
d. Reflect across the x-axis and translate up 4 and right 3, this transforms the pre-image to the composite image.
What is composite image?
A composite image is the result of applying multiple transformations to a given pre-image. It is formed by first applying one transformation to the pre-image and then applying another transformation to the resulting image, and so on. The final result is the composite image.
Let's analyze the given options:
a. Reflect across the y-axis and translate 4 down and three left.
This transformation would reflect the pre-image across the y-axis, which would change the signs of the x-coordinates, and then translate it 4 units down and 3 units left. However, this transformation would not result in the composite image provided.
b. Rotate 180° and reflect across the x-axis.
This transformation would rotate the pre-image 180 degrees counterclockwise around the origin, which would change the signs of both the x and y-coordinates, and then reflect it across the x-axis. This transformation would not result in the composite image provided.
c. Rotate 90° and translate 4 up and 3 right.
This transformation would rotate the pre-image 90 degrees counterclockwise around the origin, which would swap the x and y-coordinates and negate the new x-coordinate, and then translate it 4 units up and 3 units right. This transformation would not result in the composite image provided.
d. Reflect across the x-axis and translate up 4 and right 3.
This transformation would reflect the pre-image across the x-axis, which would change the signs of the y-coordinates, and then translate it 4 units up and 3 units right. This transformation would result in the composite image provided.
Therefore, the correct answer is d. Reflect across the x-axis and translate up 4 and right 3.
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Whether the economy is in a recession is illustrated in the AD/AS model by how close the _____ is to the potential GDP line.
a. AD curve
b. AS curve
c. AS and AD curve
d. equilibrium
When the equilibrium point is above the potential GDP line, the economy is experiencing inflationary pressure.
In the AD/AS model, whether the economy is in a recession is illustrated by how close the equilibrium is to the potential GDP line. The potential GDP line represents the maximum level of output that an economy can produce with its existing resources and technology.What is the AD/AS model?The AD/AS model is a graphical representation of the macroeconomic relationship between aggregate demand (AD) and aggregate supply (AS). This model is used to explain the behavior of the economy by demonstrating how changes in the level of aggregate demand and aggregate supply can impact the economy's level of output and prices.
The model's AD curve represents the total demand for all goods and services in an economy at different price levels. The AS curve represents the total supply of all goods and services in the economy at different price levels.
The intersection of the AD and AS curves represents the equilibrium point where the economy's output level and price level are determined. The economy is in a recession when the equilibrium point is below the potential GDP line.
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find the product of each pair of complex conjugated.
(4+5i)(4-5i)
The products of pair of complex conjugates is 41
What are Complex Numbers?The product of a real number with an imaginary number is a complex number. A complex number is often symbolised by the symbol z and has the form a + ib. Re(z) is used to represent the value "a" as the real component, and Im is used to represent the value "b" as the imaginary part (z). Ib is sometimes referred to as an imaginary number.
Given:complex conjugates expressed as
=(4+5i)(4-5i)
Expand the expression:
=16-20i+20i-25i²
=16-25i²
According to complex number, i² = -1
Substitute this into the result to have:
=16+25
=41
Hence the products of pair of complex conjugates is 41.
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The Morris family is planning to carpet their entire home. The type of carpet they want is sold at two different stores. The table and graph below show the costs for different amounts of carpet sold by the two stores. Which store sells the carpet for the lesser amount, in cost per square yard? Show work or explain your answer.
By charging $11 per square yard as opposed to $12 per square yard at Shop A, Store B offers the carpet for a lower price per square yard.
What distinguishes a table from a graph?The same data that is displayed in tables is also presented in charts and graphs. Yet, compared to a table, a chart or graph provides less detail or greater imprecision.
We must divide the total cost by the quantity of carpet square yards in order to determine the price per square yard. Seeing from the table that Shop A charges $360 for 30 square yards of carpet, the following information is provided:
Shop A's price per square yard is $360.30 sq yard divided by $12 per sq yd
A similar price of $550 is charged by Store B for 50 square yards of carpet, giving us:
$550 divided by 50 square yards yields $11 per square yard at store B.
The graph also shows that, for all carpet sizes, Shop B consistently charges less per square yard than Store A.
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How many square feet of wood are needed to make a box that is 4 feet long, 2 feet
high, and 21 feet wide?
Answer:
Calculate the surface area
Step-by-step explanation:
A. The answer to this volume problem is incorrect. Describe the error made in finding the volume of the triangular prism.
B. Give the correct volume of the triangular prism.
1. Describe the error in finding the volume of the triangular prism.
2. Give the correct volume of the triangular prism.
175 Cm³ is the correct volume of the triangular prism.
What is prism?
A prism is a solid, three-dimensional object whose two ends are identical. It is a result of the elements of flat faces, identical bases, and equal cross-sections. Without bases, the prism's faces are parallelograms or rectangles.
A prism is a transparent object made of glass or another material that has been cut into precise angles and plane faces for the purpose of reflecting and analyzing light in optics. White light can be divided into its component colors, known as a spectrum, using a standard triangular prism.
V = 1/2 x B x H
Find the Base area = l x w
Base area = (10 x 5)
Base area = 50 sq.m
V = (1/2) x (50) x 7
V = 175
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Which of the following equations represents a linear function? x = 9 4x − 3 = 15 y equals one half times x squared y equals negative one third times x minus 3
Therefore , the solution of the given problem of function comes out to be this equation has a single value for x = 4.5 .
What is function?The midterm test questions will cover all of the topics, including actual as well as fictitious locations and arithmetic variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox has a particular spot that might be used as a haven.
Here,
A linear function is represented by the equation:
=> 4x - 3 = 15
The formula for this equation is y = mx plus b, where m denotes the slope and b the y-intercept:
=> 4x - 3 = 15
=> 4x = 18
=> x = 4.5
As a result, this equation has a single value for x as its solution, indicating that it reflects a linear function.
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Find the missing dimension of the triangle.
Area = 14 ft²
6 ft
b
b = ? ft
help pls I'll mark brainlisest
An individual with $35,000 in taxable
income pays $970 for the 10% tax
bracket, and $3,036 for the 12% bracket.
What is the overall federal income tax
payment for this individual?
A. $4,006
C. $3,506
B. $32,036
D. $2,030
Answer:
The overall federal income tax payment for this individual would be $970 + $3,036 = $4,006. So the correct answer is A. $4,006.
Step-by-step explanation:
The individual pays $970 for the 10% tax bracket and $3,036 for the 12% tax bracket. Adding these two amounts together gives us a total federal income tax payment of $4,006.
Question 8 of 10
Floyd's brick house is located in the suburbs. If his building property
insurance is $652.50 per year, how much is his house worth?
Annual Premium per $100 of coverage
Brick
Steel
Area
rating
Building Contents
Building Contents
City
0.39
0 43
Suburb 0.45
0.52
Rural 0.6
0.69
OA. $185,000
OB. $145,000
OC. $125,000
O D. $95,000
05
0.56
0.71
0.54
0.63
0.8
Mixed
Building Contents
0.55
0.72
0.89
0.65
0.74
0.91
Wood
Building Contents
0.66
0.83
1
0.76
0.85
1.02
The right answer is (B), which is $145,000, given that his building property insurance costs $652.50 annually.
what is interest ?In mathematics, interest usually refers to the sum of money that is charged or made over the course of a given period of time on a principal sum of money. In finance and economics, interest—which can be basic or compound—is frequently used to calculate borrowing costs and return on investment. The principal sum, the interest rate, and the duration for which the interest is being charged or earned are the three factors used to compute simple interest.
given
We are informed that Floyd's home is situated in a suburban area, where building property insurance costs $0.45 for every $100 of coverage.
Assume Floyd's home is worth x. Then, the yearly payment for his home's building property insurance is:
0.0045x = $652.50
After finding x, we obtain:
x = $652.50 ÷ 0.0045
x ≈ $145,000
Floyd's home is therefore currently worth about $145,000.
The correct response is (B ) $145,000 as his building property insurance is $652.50 per year.
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Some people on this app scare me-
Sure, some people here are nice but some are just straight up rude and some are just creepy.. one random person on here literally called me "puppy girl" ..
I'm hoping all of these 30 yr olds on this app get off and actually have something to do with their life ..
There was this one person that said, 'hey how old are you?' of course I lied. then another asking me to change my profile to something inappropriate.
Each of the 17 guinea pigs needs its cage cleaned. If it takes 1 hour to clean 4 cages, how many hours will it take to clean all 17 cages?
It will take
hours to clean all the cages.
Answer:
Step-by-step explanation:
4 hours and 30 minutes
The vertices of a square are located at (0, 2), (2, 0), (0, -2), and (-2, 0).
Select all transformations that will carry this square onto itself.
A reflection across the line y = x
B reflection across the line y = -X
C reflection across the x-axis
D 45° rotation about the origin
E 90° rotation about the origin
Answer:
Step-by-step explanation:
A reflection across the line y = x will not carry the square onto itself, since the vertex (0, 2) would be reflected to (2, 0) which is not a vertex of the original square.
A reflection across the line y = -x would also not carry the square onto itself, since the vertex (0, 2) would be reflected to (−2, 0) which is not a vertex of the original square.
However, a reflection across the x-axis would carry the square onto itself since all of the vertices lie in the same quadrant, and reflecting across the x-axis does not change their signs.
A 45° or 90° rotation about the origin would also carry the square onto itself since the square has rotational symmetry of order 4.
Therefore, the correct answers are C, D, and E.
Near Pittsburgh, a cable car transports people from the Monongahela River valley to the community on top of the overlooking bluff. The Monongahela Incline has a grade of 78%. Find the measure of the angle the cable car track makes. with the valley floor. If necessary, round to the nearest degree.
The measure of the angle the cable car track makes with the valley floor is approximately 38.7 degrees.
What is grade?The slope or inclination of a line or surface is sometimes referred to as the grade in mathematics. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on a line or surface is what is meant by this term. Usually, the grade is given as a percentage or a fraction. In engineering, building, and transportation, grades are frequently used to define the slope of roads, railroads, and other infrastructure. The grade, which refers to how steep the slope is when referring to a cable car, is a crucial element in determining the safety and effectiveness of the system.
To find the angle we use the trigonometric functions:
tan(θ) = grade = rise/run
Given that, the grade of the incline is 78%, then grade = 0.78.
θ = arctan(0.78) ≈ 38.7 degrees.
Hence, the measure of the angle the cable car track makes with the valley floor is approximately 38.7 degrees.
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Dalton's weekly allowance is $5. He can also earn $1 each time he walks the family dog.
Write an equation that shows how the amount of money Dalton gets in a week, y, depends
on the number of times he walks the dog, x.
Do not include dollar signs in the equation.
y =
The equation that shows how the amount of money Dalton gets in a week, y, depends on the number of times he walks the dog, x is y = 5 + x
Calulating the equation of the number amount of moneyGiven that
Weekly allowance = $5
Amount earned for walking the dog = $1
The above means that
Total money = Weekly allowance + Amount earned for walking the dog * Number of times
So, we have
y = 5 + 1 * x
Evaluate
y = 5 + x
Hence, the equation is y = 5 + x
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if x and y are positive integers, find the domain and the range of 2y = 30 - 3x
The domain of the equation is {1, 3, 5, 7, 9}. and the range of the equation is {6, 8, 10, 12, 14}.
What is range and domain of a function?
The domain of a function in mathematics is the set of all possible input values (usually denoted by x) for which the function is defined. It is the set of all values of the independent variable (input) for which the function is defined.
A function's range, on the other hand, is the set of all potential output values (typically indicated by y) that the function may generate. It is the set of all values of the dependent variable (output) that the function can take.
Now,
To solve for y:
2y = 30 - 3x
y = (30 - 3x)/2
The domain of the equation is the set of all possible values of x that will make the equation valid. Since x and y are positive integers, we need to find integer solutions for x that will also result in integer values for y.
Let's look at the equation (30 - 3x)/2 = y. For y to be an integer, (30 - 3x) must be even. This means that x can only take on odd integer values between 1 and 9, inclusive. Therefore, the domain of the equation is {1, 3, 5, 7, 9}.
To find the range of the equation, we need to find the possible values of y that correspond to the values of x in the domain. We can substitute each value of x into the equation y = (30 - 3x)/2 and simplify to find the corresponding value of y.
When x = 1, y = 14
When x = 3, y = 12
When x = 5, y = 10
When x = 7, y = 8
When x = 9, y = 6
Therefore, the range of the equation is {6, 8, 10, 12, 14}.
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Wendall and Stacey measured the lengths of several wooden planks. Wendall recorded his measurements in inches, and Stacey recorded her measurements in feet. In order to compare the lengths of the wooden planks, they recorded their measurements in the table below. Find the measurements of the wooden planks Wendall measured in feet, and then find the measurements of the wooden planks Stacey measured in inches.
To convert Wendall's measurements from inches to feet, we need to divide each measurement by 12, since there are 12 inches in a foot. So, the measurements in feet are:Length (in)Length (ft)242363484605To convert Stacey's measurements from feet to inches, we need to multiply each measurement by 12. So, the measurements in inches are:Length (ft)Length (in)6727848969108Therefore, the measurements of the wooden planks Wendall measured in feet are 2, 3, 4, and 5 feet, and the measurements of the wooden planks Stacey measured in inches are 72, 84, 96, and 108 inches.
solve the inequality and please show work !!
The solution to the inequality 2√(x-3) < √(x+3) is x ∈ (3, 7].
What is an inequality?
In mathematics, an inequality is a statement that compares two values or expressions and states that one is greater than, less than, or not equal to the other. An inequality is typically written using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to). Inequalities are used to represent a wide range of mathematical concepts, such as the relationships between two quantities, the constraints on a system, or the conditions for a particular outcome to occur. Solving inequalities involves finding the set of values that satisfy the inequality, which may be a single value, a range of values, or no values at all.
What are the key steps to solve this inequality?
To solve the inequality, we need to isolate the variable x on one side of the inequality and then square both sides to eliminate the square roots. However, we need to be careful when squaring both sides because this may introduce extraneous solutions. To avoid this, we need to check our solutions at the end to make sure they satisfy the original inequality.
Isolate the square root term on one side of the inequality
2√(x-3) < √(x+3)
Square both sides:
4(x-3) < x+3
Simplify and rearrange the inequality to get x on one side
4x - 15 < 0
x < 15/4
Check the solution by plugging it into the original inequality
2√(15/4 - 3) < √(15/4 + 3)
2√(3/4) < √27/4
2(√3/2) < 3/2
√3 < 3/2 (This is true)
Therefore, the solution to the inequality is x ∈ (3, 7].
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A certain computer can perform a maximum number of operations per second. If this computer is running at 40%
of the maximum and is performing 30 operations per second, what is the maximum number of operations the
computer can perform per second? Round your answer to the nearest whole number.
1. 70 operations per second
2. 12 operations per second
3. 1,200 operations per second
4. 75 operations per second
Answer:
Step-by-step explanation:
Let's represent the maximum number of operations per second as "x".
If the computer is running at 40% of the maximum, it is performing 0.4x operations per second.
We are given that the computer is performing 30 operations per second, so we can set up an equation:
0.4x = 30
Solving for x:
x = 75
Therefore, the maximum number of operations the computer can perform per second is 75.
So, the correct answer is 4. 75 operations per second.
what is 2.5<1/3(x-18) ??
Answer:
x > 25.5
Step-by-step explanation:
2.5 < [tex]\frac{1}{3}[/tex] (x - 18 ) ← multiply both sides by 3 to clear the fraction
7.5 < x - 18 ( ad 18 to both sides )
25.5 < x , then
x > 25.5
State the vertex for the quadratic function, and determine if the vertex is the highest or lowest point on the graph. Then state the range of the function. y = - 32 - 2)2 - 1 The vertex, (), is the Select an answer point on the graph. The range is Preview
The vertex for the quadratic function and the range of the function are determined in the following answer.The given quadratic function [tex]isy = -32 - 2(x - 1)²[/tex]
It is noted that the quadratic function is in the vertex form, i.e.,[tex]y = a(x - h)² + k[/tex]
where (h, k) is the vertex of the parabola. Comparing the given function with the vertex form of the quadratic equation, we get the value of the vertex, i.e.,(h, k) = (1, -32).This implies that the vertex of the given quadratic function is located at (1, -32).Since the coefficient of the quadratic term is negative in the given function, the parabola opens downwards, and the vertex is the highest point on the graph.Therefore, the vertex (-32, 1) is the highest point on the graph of the given quadratic function. The range of a function is the set of all possible values that the function can attain. The given quadratic function is in the form y = a(x - h)² + k where a, h, and k are constants.
Since the coefficient of the quadratic term is negative in the given function, the parabola opens downwards. Therefore, the range of the given function is (-∞, -32].Hence, the range of the given quadratic function is[tex](-∞, -32].[/tex]
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william can mulch a garden in 20 minutes. together, william and tina can mulch the same garden in 11 minutes. how long will it take tina to mulch the garden when working alone?
Tina can mulch the garden alone in 25 minutes.
Let's use the formula for the work rate to solve the problem. If William can mulch the garden alone in 20 minutes, his work rate is 1/20. Similarly, let's assume that Tina can mulch the garden alone in x minutes, so her work rate is 1/x.
When they work together, their work rates add up, so we have:
1/20 + 1/x = 1/11
Now we can solve for x:
1/x = 1/11 - 1/20
1/x = (20 - 11) / (11 x 20)
1/x = 9 / 220
x = 220 / 9
x ≈ 24.4
So it would take Tina 24.4 minutes to mulch the garden alone.
However, we need to round this up to the nearest minute because you can't have a fraction of a minute. Therefore, Tina can mulch the garden alone in 25 minutes.
Alternatively, we can use the inverse formula for the work rate to solve for Tina's time alone:
1/20 + 1/t = 1/11
1/t = 1/11 - 1/20
1/t = (20 - 11) / (11 x 20)
1/t = 9 / 220
t = 220 / 9
t ≈ 24.4
So Tina can mulch the garden alone in 24.4 minutes, which rounds up to 25 minutes.
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