\(8.5(3.5 + x)\)
\((8.5 \times 3.5) + (8.5 \times x)\)
\(29.75 + 8.5x\)
I honestly don't know what to do for b. Maybe it tells us that the minimum area possible is 38.25 in²? or maybe it tells us that the area of just the original photo is 29.75 in²? I don't know.
I have the Junior maths challenge (Year 7-8) tomorrow and I would like to do well, to anyone who has done it or has learnt more than I have, what should I revise for?
Also it includes things from the Year 8 curriculum, from there what should I revise for?
To prepare for the Junior Maths Challenge (Year 7-8), you should revise key topics from both Year 7 and Year 8 curriculums.
1. Review basic arithmetic operations, including addition, subtraction, multiplication, and division.
2. Study fractions, decimals, and percentages, and understand how to convert between them.
3. Revise algebraic expressions, equations, and inequalities, as well as simplifying and solving them.
4. Practice geometry, including properties of shapes, angles, area, and perimeter.
5. Familiarize yourself with concepts of probability and statistics, including mean, median, mode, and range.
6. Learn problem-solving strategies, such as identifying patterns, using logical reasoning, and working systematically.
Summary: To do well in the Junior Maths Challenge, focus on revising important topics from Year 7 and Year 8, including arithmetic, algebra, geometry, and probability, as well as practicing problem-solving strategies. Good luck!
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A set of data is approximately normally distributed. In order from highest to lowest, list the range, the Interquartile Range (IQR), and the standard deviation.
A. Range, standard deviation,IQR
B. standard deviation, IQR, Range
C. IQR, Range, standard deviation
D. Range, IQR,standard deviation
The correct order from highest to lowest for a set of data that is approximately normally distributed is C. IQR, Range, standard deviation.
Let's discuss each of these measures and why they are listed in this order:
Interquartile Range (IQR): The IQR is a measure of statistical dispersion and represents the range of the middle 50% of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). By listing the IQR first, we prioritize a measure that captures the spread of the central portion of the data, which is valuable for understanding the variability within the distribution.
Range: The range is the simplest measure of dispersion and represents the difference between the maximum and minimum values in the data set. It provides an overall sense of the spread of the data. While it is informative, it does not take into account the distribution within the dataset or the relative position of the values. Therefore, the range is listed second in this order.
Standard Deviation: The standard deviation is a measure of the dispersion or spread of the data, and it provides information about how closely the data points cluster around the mean. It is calculated as the square root of the variance. The standard deviation is a widely used and important measure in statistics, and it is listed last in this order because it focuses on the overall spread of the data without specifically capturing the central 50% (as the IQR does) or considering the extreme values (as the range does).
By listing the measures in the order of IQR, Range, and then standard deviation, we prioritize the measures that capture the spread of the central portion of the data and provide a more comprehensive understanding of the distribution before considering the overall range and overall spread of the data.
In summary, for a set of data that is approximately normally distributed, the correct order from highest to lowest is C. IQR, Range, standard deviation.
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show how to add 24+9 by making tens.
20 + 2 + 2 + 9, 20 + 4 + 9 add 24+9 by making tens.
What is an example of tens and ones?
There are always tens and ones in two-digit numerals. As an illustration, the tens place of the number 56 is represented by 5 and the ones place by 6, respectively.
Here, each rod is one ten and is made up of ten ones. First fact: As 1 ten, 2 tens, 3 tens, 4 tens, and so on, the numbers 10, 20, 30, 40, and so forth can be written.
Where do the ones and tens go?
A location with a value of 1 in the system of places and values. In the number 23, the one's place is occupied by 3. a place with a value of 10 in the system of place-values. 2, which is in the tens place, is the number 23.
24+9 by making tens
= 20 + 2 + 2 + 9
20 + 4 + 9
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Ajar contains 100 coins. If it is very unlikely that you will randomly choose a quarter out of the jar, how many quarters
could be in the jar?
10
85
50
35
When coding the phrase "supravesical fissure of urinary bladder," the main term to reference in the index is ________ .a. urinaryb. bladderc. fissured. supravesical
The correct option of the given question is option (c) fissure.
When coding the phrase "supravesical fissure of urinary bladder," the main term to reference in the index is c. fissure.
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The main term to reference in the index when coding the phrase "supravesical fissure of urinary bladder" is c. fissure.
In medical coding, the index is typically organized alphabetically based on the main terms or significant words within medical terminology. In this case, "fissure" is the main term that represents the specific condition or anatomical feature being coded.
The other terms, such as "urinary," "bladder," and "supravesical," provide additional context but are not the primary focus when searching for the appropriate code in the index.
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Can someone please help me I don’t get this
Answer:
D is correct.
Step-by-step explanation:
\(3 |x + 1| < 6\)
\( |x + 1| < 2\)
\( - 2 < x + 1 < 2\)
\( - 3 < x < 1\)
x > 3 and x < 1, so D is correct.
Mrs. Newman's famous peanut butter cookies call for 1 cup of peanut butter for every
1
2
of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil. How much peanut butter should she use?
In a case whereby Mrs. Carter's famous peanut butter cookies call for 1 cup of peanut butter for every 1 2 of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil the amount of peanut butter she should use can be expressed as 2 cups of peanut butter.
How can the amount of peanut butter be calculated?The concept that will be used is simplification. Base on the provided information from the question,
(1/2 cup of oil )= (1 cup of peanut butter)
we can represent (1 cup of oil) as (x)
The if we perfor a Cross Multipliplication we have:
(1/2x) =( 1 × 1)
x = (1 × 2/1)
x = 2 cups of peanut butter.
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If a researcher is interested determining if there is a relationship between ethnicity and job type, then a Chi- Square Goodness of Fit test can be used. false true
It is FALSE to state that if a researcher is interested determining if there is a relationship betweenethnicity and job type, then a Chi- Square Goodness of Fit test can be used.
How is this so?A Chi-Square Goodness of Fit test is not appropriate for determining the relationship between ethnicity and job type.
This test is used to assess thedistribution of categorical variables within a single population or sample, comparing observed frequencies with expected frequencies.
To examine the relationship between ethnicity and job type, a Chi-Square test of independence or another suitable statistical test, such as logistic regression,would be more appropriate.
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Determine whether each triangle with sides of given lengths is a right triangle. 2 m, 5 m, 6 m
The triangle with the lengths 2m, 5m and 6m is not a right triangle, as the lengths do not form a Pythagorean triple.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
The sum of the two smaller sides squared is given as follows:
2² + 5² = 4 + 25 = 29.
The square of the largest side is of:
6² = 36.
As 29 is different of 36, the Pythagorean Theorem is not respected, and thus the triangle is not a right triangle.
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Triangle ABC is isosceles with AB = AC.
Angle BAC = 110° and the area of the triangle is 85cm2.
Calculate AC
If Triangle ABC is isosceles with AB = AC is: 13.45 cm.
Triangle ABC∆ABC = 85 cm² .
(1/2) ×AC×AB ×sinA = 85 cm²
AC=AB=x
Hence:
85= (1/2)x²×sin110°
A² × sin 110° = 170
A² ×0.94 = 170
A² = 170/0.94
A² =√ 180.85
A= 13.45 cm
Therefore if Triangle ABC is isosceles with AB = AC is: 13.45 cm.
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A(n) ________ indicates when an object sends or receives a message and is identified by a narrow vertical shape that covers the lifeline. A.. focus. b. subclass. c. instance. d. activity
A(n) focus indicates when an object sends or receives a message and is identified by a narrow vertical shape that covers the lifeline. A) focus.
A focus, in the context of UML, is a graphical element that represents the point in time when an object is actively sending or receiving a message. It is indicated by a narrow vertical shape that covers the lifeline of the object in a sequence diagram.
The other options, subclass and instance, do not refer to elements used in sequence diagrams. Subclass refers to a type of object that inherits attributes and behaviors from a parent class, while instance refers to a specific occurrence of an object with its own unique set of attribute values. Activity is a type of diagram used to model business processes or workflows.
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supply of houses is determined by two variables (I and R) in the following way: h(1,R) = a log1 + b R + CR log1, where a, b, and c are all constants. How does housing supply respond to changes in I (a) and R (OR)? an an Select one: an a. ar an a+cR an I and an = b + clog1 2 an ī and a b+cR log1 = b + cR log1 O b. a1 an a+cR an C. ai and an an d. ar an + CR log 1 and aR = b + c log1
The housing supply function is given by h(I,R) = a log1 + bR + cR log1. The housing supply responds to changes in I with a rate of a, and to changes in R with a rate of b + c log1.
Based on the given equation, the housing supply (h) is determined by two variables: I and R. The equation shows that h is a function of R, with a log-linear relationship. The variable I only appears as a constant (a) in the equation, so changes in I do not directly affect the supply of houses.
On the other hand, changes in R (or OR, which is the same variable) do affect the supply of houses. Specifically, an increase in R leads to an increase in the supply of houses. The magnitude of this increase depends on the values of b and c in the equation.
To see this, we can take the partial derivative of h with respect to R:
dh/dR = b + cR/(ln(10))
This equation tells us how much the housing supply changes in response to a change in R. The derivative is positive (i.e. the supply increases) as long as c is positive. The larger c is, the greater the increase in supply for a given increase in R.
Therefore, the correct answer is:
b + cR/(ln(10))
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Can anyone help me plz thanks
Answer:I believe it is C
Step-by-step explanation:
Its -2 then gets decreased by 5
Answer:
\(optoin \: c. \: is \: correct\)
george's friend clarence, who is even more concerned about consumers, suggests a price ceiling 50% below the monopoly price. at this price, the quantity demanded would be 65 units, and the quantity supplied would be units.
George's friend Clarence, who is concerned about consumers, suggests implementing a price ceiling that is 50% lower than the monopoly price. With this price ceiling in place, the quantity demanded would increase to 65 units. However, the exact quantity supplied at this new price is not provided in your question.
George's friend Clarence is suggesting a price ceiling, which is a government-imposed limit on how high a price can be charged for a good or service. In this case, the price ceiling is set at 50% below the monopoly price. This means that the price charged for the good or service would be significantly lower than what the monopolistic supplier would typically charge.
At this lower price point, Clarence predicts that the quantity demanded would increase to 65 units, indicating that consumers would be more willing to purchase the product due to its lower price. However, it is unclear what the quantity supplied would be at this price point, as that information is missing from the question.
Overall, George's friend Clarence's suggestion of a price ceiling serves to protect consumers by limiting the monopolistic supplier's ability to charge exorbitant prices and instead promoting a more competitive market.
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The diameter of ball bearing are ditributed normally. The mean diameter i 81 millimeter and the variance i 16. Find the probability that the diameter of a elected bearing i greater than 85 millimeter. Round your anwer to four decimal place
the probability that the diameter of a elected bearing is greater than 85 millimeter P(diameter > 85) = P(z > (85-81)/4) = P(z > 1) = 0.1587
The diameter of ball bearings is normally distributed, with a mean of 81 millimeters and a variance of 16.
To calculate the probability that a selected bearing has a diameter greater than 85 millimeters, we first calculate the z-score for 85 millimeters.
We subtract 81 from 85 to get 4, and divide by 4 to get 1 for the z-score.
We the look up the probability for a value of 1 in the z-table, which is 0.1587.
This is the probability that a selected bearing has a diameter greater than 85 millimeters, rounded to four decimal places.
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Write an equivalent equation using the Subtraction Property of Equality
9y = 4y + 10
(explain how to do this to)
The Equivalent equation using the Subtraction Property of Equality is y = 2.
what is Subtraction Property of Equality?According to the Subtraction Property of Equality, if two equal items have an equal value subtracted from them or deleted, the result is a new equal amount. When two equivalent sides of a mathematical statement are separated by an equal sign, an equation is being expressed. The subtraction property is expressed as follows: If a = b, then a - c = b - c.In order to balance an equation, one must apply the same mathematical operation on both sides, which is known as the subtraction property of equality.If we have an expression as ( a + b ) = c
Then as per subtraction property of equality [ (a + b ) - b = c - b ]
Here given 9y = 4y + 10
Simplifying this equation, we get
⇒9y - 4y = 10
⇒( 9 - 4 )y = 10
⇒5y = 10
therefore, y = ( 10 ÷ 5 )
⇒y = 2
Therefore the equivalent equation is y = 2.
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Can someone answer these for me please. I need the answers within the next few hours.
will mark brainliest for correct answer!!
Answer:
50
Step-by-step explanation:
because first you add 22 and 32 and you will get 54. then you round the number 4 in 54 to the nearest foot and you will get 50 so that is the anwser.
Find Laplace transform of the function \( f(t)=5 t^{3}-5 \sin 4 t \) (5 marks)
The Laplace transform of the function \(f(t) = 5t^3 - 5\sin(4t)\) is given by: \[F(s) = \frac{120}{s^4} - \frac{20}{s^2+16}\]
To find the Laplace transform of the given function \(f(t) = 5t^3 - 5\sin(4t)\), we can apply the properties and formulas of Laplace transforms.
The Laplace transform of a function \(f(t)\) is defined as:
\[
F(s) = \mathcal{L}\{f(t)\} = \int_0^\infty f(t)e^{-st}\,dt
\]
where \(s\) is the complex frequency variable.
Let's find the Laplace transform of each term separately:
1. Laplace transform of \(5t^3\):
Using the power rule of Laplace transforms, we have:
\[
\mathcal{L}\{5t^3\} = \frac{3!}{s^{4+1}} = \frac{5\cdot3!}{s^4}
\]
2. Laplace transform of \(-5\sin(4t)\):
Using the Laplace transform of the sine function, we have:
\[
\mathcal{L}\{-5\sin(4t)\} = -\frac{5\cdot4}{s^2+4^2} = -\frac{20}{s^2+16}
\]
Now, we can combine the Laplace transforms of the individual terms to obtain the Laplace transform of the entire function:
\[
\mathcal{L}\{f(t)\} = \mathcal{L}\{5t^3 - 5\sin(4t)\} = \frac{5\cdot3!}{s^4} - \frac{20}{s^2+16} = \frac{120}{s^4} - \frac{20}{s^2+16}
\]
This is the Laplace transform representation of the function \(f(t)\) in the frequency domain. The Laplace transform allows us to analyze the function's behavior in the complex frequency domain, making it easier to solve differential equations and study the system's response to different inputs.
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The point Z(3, 6) is reflected over the line y = x. What are the coordinates of the resulting point, Z′? HELP ASAP!!
Answer:
Z' = (6, 3 )
Step-by-step explanation:
Under a reflection in the line y = x
a point (x, y ) → (y, x ) , then
Z (3, 6 ) → Z' (6, 3 )
Find the 50th term of 6,12,18,24
Answer:
300
Step-by-step explanation:
You simply multiply 50 and 6. I hope you have a nice day. :)
Answer:
300 :3
Step-by-step explanation:
6 x 1 = 6
6 x 2 = 12
6 x 3 = 18
6 x 50 = 300
In your answers below for the variable A type the word lambda for the derivativeX(x) type X for the double derivativeX(x) type X", etc.
Separate variables in the following partial differential equation for u(x, t).
xu₂ − (tu₂ + t²u₂) + zu = 0 • DE for X(z): ________ = 0 .
DE for T(t): ________ = 0
(Simplify your answers so that the highest derivative in each equation is positive.)
The separated variable form of the given partial differential equation is:
DE for X(z): xX" - (tX" + t²X") + zX = 0
DE for T(t): T' - T'' = 0
To separate the variables in the given partial differential equation, we assume that the solution can be expressed as the product of two functions, one dependent on the variable x (X(z)) and the other dependent on the variable t (T(t)).
1. DE for X(z):
We differentiate X(z) with respect to x to obtain X' and differentiate again to obtain X". We substitute these derivatives into the given equation and separate the variables.
xX" - (tX" + t²X") + zX = 0
Simplifying, we have (x - t - t²)X" + zX = 0
Since this equation must hold for all values of x, the coefficients of X" and X must both be zero.
x - t - t² = 0
This is the differential equation for X(z), where X(z) represents the function dependent on the variable z.
2. DE for T(t):
We differentiate T(t) with respect to t to obtain T' and differentiate again to obtain T''. We substitute these derivatives into the given equation and separate the variables.
T' - T'' = 0
This is the differential equation for T(t), where T(t) represents the function dependent on the variable t.
By separating the variables in this way, we obtain two ordinary differential equations: one for X(z) and one for T(t). Each equation involves only a single variable, allowing us to solve them separately.
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HELP is it a, b, c , or d?
Answer:
B
when you input the first value of y which is -2
-2+2=(4/5)(x+9)
0=(4x+36)/5
multiply both sides by 5
0=4x +36
4x =-36
divide both sides by 4
x=-9
if you like my answer mark as brainliest
Netflix charges Geyon $15 per month for a membership, plus a $5 one-time fee for streaming on his phone. How many months will Geyon have his membership for if Netflix charges him $50?
Answer:
2 and a half months
Step-by-step explanation:
You need to divide 50 by 20 (because member ship+netflix)
Two trains leave a city at the same time. One train goes west at a constant rate of 60 mph. The other goes east at a rate of 50 mph. How long will it take the trains to be 550 miles apart?
A. 5 hours
B. 7 hours
C. 9 hours
D. 11 hours
Answer:
A. 5 hours
Step-by-step explanation:
Using factor theorem, factorise x⁴-x³-7x²+x+6
Answer:
Add and subtract the second term to the expression and factor by grouping .
(x-1)(x+1)(x-3)(x+2)
Answer:
(x-1)(x-3)(x+1)(x+2)
Step-by-step explanation:
x⁴-x³-7x²+x+6=
x⁴-x³-x²+x -6x²+6=
x³(x-1)-x(x-1)-6(x²-1)=
x³(x-1)-x(x-1)-6(x-1)(x+1)=
(x-1)(x³-x-6x-6)=
(x-1)(x³-3x²+3x²-9x+2x-6)=
(x-1)(x-3)(x²+3x+2)=
(x-1)(x-3)(x²+x+2x+2)=
(x-1)(x-3)(x+1)(x+2)
From the list below, select the two properties that are NOT necessarily true for a rhombus.
A
Each pair of opposite sides are congruent.
B
Each pair of opposite angles are congruent
С
All sides are congruent.
D
All angles are congruent.
E
Diagonals are congruent.
F
Diagonals are perpendicular.
Answer:
D, E
Step-by-step explanation:
D. all angles do not have to be congruent
E. diagonals do not have to be congruent
Option D is incorrect 100%
Option E should be incorrect aswell.
Someone help me please
Answer:
Step-by-step explanation:
any minus temperature is < 7oC
0 is < 7oC
1 ... 6 is < 7oC
If 28% of students in college are near-sighted, the probability that in a randomly chosen group of 20 college students, exactly 4 are near-sighted is closest to:.
Therefore, the probability that exactly 4 out of 20 randomly chosen college students are near-sighted is closest to 0.7988 or approximately 0.80.
To find the probability that exactly 4 out of 20 randomly chosen college students are near-sighted, we can use the binomial probability formula.
The formula for the probability of k successes in n trials, with a probability of success p in each trial, is given by:
\(P(X = k) = (n choose k) * p^k * (1 - p)^{(n - k)\)
In this case, n = 20, k = 4, and p = 0.28 (probability of a student being near-sighted).
Plugging in these values into the formula, we get:
\(P(X = 4) = (20 choose 4) * (0.28)^4 * (1 - 0.28)^{(20 - 4)\)
Calculating the values:
(20 choose 4) = 4845
\((0.28)^4\) ≈ 0.006859
\((1 - 0.28)^{(20 - 4)\) ≈ 0.19224
P(X = 4) ≈ 4845 * 0.006859 * 0.19224
≈ 0.7988
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The sumerian mathematical system was based on units of sixty, ten, and six and survives in what modern system?
The sumerian mathematical system was based on units of sixty, ten, and six and survives in what modern system time measurement.
What is sumerian mathematical system?
Sumer (a region of Mesopotamia, present-day Iraq) is sometimes referred to as the Cradle of Civilization because it was the origin of writing, the wheel, agriculture, the arch, the plow, irrigation, and many other accomplishments.
We really know more about ancient Sumerian and Babylonian mathematics than we do about early Egyptian mathematics because the Sumerians invented the first known writing system, the pictographic cuneiform script, which uses wedge-shaped symbols engraved on baked clay tablets. In fact, we even have math and geometry problems that seem like school exercises.
The base number 60 was created by adding a "celestial" 6 and a "common" 10 in the Sumerian "sexagesimal" system.
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