When creating a rubric or criteria for grading students, it is important to establish clear expectations and criteria that align with the learning objectives of the assignment or task. Here is a suggested rubric format:
1. Content Knowledge: Assess the depth and accuracy of the student's understanding of the subject matter.
2. Organization and Structure: Evaluate the clarity and logical flow of the student's work, including the use of headings, subheadings, and transitions.
3. Research and Evidence: Consider the quality and relevance of sources used, as well as the integration of evidence to support arguments or claims.
4. Critical Thinking: Assess the student's ability to analyze, evaluate, and synthesize information, demonstrating higher-order thinking skills.
5. Writing Mechanics: Evaluate the student's grammar, spelling, punctuation, and overall writing style.
6. Creativity and Originality: Acknowledge unique or innovative ideas, approaches, or perspectives.
7. Presentation (if applicable): Assess the student's ability to effectively present their work, including visual aids, organization, and delivery.
Each criterion should have specific descriptors or levels of achievement (e.g., Excellent, Good, Fair, Poor) that clearly communicate expectations. It is also helpful to assign weights to each criterion to reflect their relative importance.
Providing detailed feedback and examples can further enhance the usefulness of the rubric for students' understanding and improvement.
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The length of the longer leg of a right triangle is 20cm more than twice the length of the shorter leg. The length of the hypotenuse is 22cm more than twice the length of the shorter leg. Find the side lengths of the triangle.
Stefan and Roman share some money in the ratio 5:9 which number in the ratio represents Stefans share and who will get more money
The ratio that represents Stefan's share is given as follows:
5/14.
Roman is the person that will get more money.
How to obtain the shares?The shares are obtained applying the proportions in the context of the problem.
Stefan and Roman share some money in the ratio 5:9, hence the denominator of the fraction is given as follows:
5 + 9 = 14.
Then the shares are given as follows:
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need help fast i am in a math escape room
The correct options are 1) B, 2) A and 3) D.
1) The table shows the work hour and earned money of Logan we need to build an equation to relate both the variables,
So, let the earned money be y and the hour worked be h,
So,
He worked 45 hours to earn $495,
So, in one hours he earned = $495/45 = $11
Therefore, the equation that relate both the variables is,
y = 11h
2) To represent the amount Mr. Kelly pays per month; we can divide the total rent paid for the year by the number of months.
So, if his yearly rent is $12564, so per month he must be paying =
12564 / 12 = $1047
Therefore, the equation that represents the amount Mr. Kelly pays per month is: 1047m = c
3) The relation given shows the quantity of apples bought to its corresponding cost,
So, considering the point (4, 10) by which the graph passes,
So, this mean that, 4 pounds of apple cost $10,
So, 1 pound = 10/4 = $2.5
Hence the cost per pound is $2.5.
Hence the answers are 1) B, 2) A and 3) D.
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Fast answer + explanation
The variables in this problem are classified as follows:
Number of siblings: Discrete.Weight: Continuous.Time to answer a puzzle: Continuous.Mark out of 10 on a math test: Continuous.What are continuous and discrete variables?Continuous variables: Can assume decimal values.Discrete variables: Assume only countable values, such as 0, 1, 2, 3, …In the context of this problem, the number of siblings is the only discrete variable, as is the only variable that cannot assume decimal values.
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need some help can anyone help me
The measure of side TR is given as follows:
TR = 6.7.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.As the triangles in this problem are similar, the proportional relationship for the side lengths is given as follows:
TR/35 = 5/26.
Hence the length of side TR is given as follows:
TR = 35 x 5/26
TR = 6.7.
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Add and simplify: 9sqrt(x)+3root(3)(x)+sqrt(9x)
Group of answer choices
12sqrt(x)+sqrt(9x)
18sqrt(x)+3root(3)(x)
12sqrt(x)+3root(3)(x)
15sqrt(x)
Answer:
C
Step-by-step explanation:
[tex]9\sqrt{x} + 3\sqrt{3x} + \sqrt{9x} \\= \sqrt{x} ( 9 + 3\sqrt{3}+3)\\ = 12\sqrt{x} + 3\sqrt{3x}[/tex]
100 Points! State the amplitude, period, and phase shift for each function. Then graph the function. Photo attached. Thank you!
hello
the answer to the question is:
y = a tan(bx – c) + d
a = 1, b = 1, c = π/2
the midline is y = d, so y = 0 and there's no vertical shift
the vertical stretch is 1, so label the y-axis so the inflection point of the curve is 1 above the midline, 1, and the other inflection point is 1 below the midline, −1
the period is:
T = π/b ----> T = π
the phase shift is:
PS = c/b ----> PS = π/2
and also, there's no amplitude for tangent and cotangent, there is only the vertical stretch that takes the place of an amplitude
For which equation would x = 3 be a solution?
8 - x = 11
x + 7 = 4
5 + x = 9
x - 2 = 1
Giving out 60 points and will mark brainliest
Answer:
Step-by-step explanation:
lets solve all the equations and check:
1 ) 8 - x = 11
-x = 11 - 8
x = -3 ------------- not this one
2 ) x + 7 = 4
x = 4 - 7
x = -3 -------------not this one
3 ) 5 + x = 9
x = 9 - 5
x = 4 ------------- not this one
4 ) x - 2 = 1
x = 1 + 2
x = 3 ----------- this is the correct option
hope this helps!
Question 2 Complex numbers. 2.1. Write the following in the form a+bi 2.1.1(2-√√-225) 3+√-18
.1.1(2-√√-225) = 2.1.1(2-15) = 2.1.1(-13) = -27.31
To solve this problem, we first need to simplify the expression inside the parentheses. The square root of a negative number is an imaginary number, so we can write the expression as follows:
2.1.1(2-√-225) = 2.1.1(2-√(-1)(225))
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We can then simplify the expression as follows:
2.1.1(2-√(-1)(225)) = 2.1.1(2-i*15) = 2.1.1(2-15) = 2.1.1(-13) = -27.31
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The second problem is a bit more complicated. We need to use the fact that the square root of a negative number is an imaginary number. We can write the expression as follows:
3+√-18 = 3+√(-1)(18)
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We can then simplify the expression as follows:
3+√(-1)(18) = 3+i*3 = 3+3i
mariah bought a package of 8 cupcakes. She and her friend ate 5 of the cupcakes.
What fraction of the cupcakes did they eat and what fraction of the cupcakes were left?
Answer:
The fraction of cupcakes they ate is:
5 / 8
The fraction of cupcakes left is:
3 / 8
Cora wants to determine a 95 percent confidence interval for the true proportion p
of high school students in the area who attend their home basketball games. Out of n
randomly selected students she finds that that exactly half attend their home basketball games. About how large would n have to be to get a margin of error less than 0.04 for p
The required sample size for a margin of error of less than 0.04 is given as follows:
n = 601.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is defined as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
We have no estimate, hence the proportion is used as follows:
[tex]\pi = 0.5[/tex]
For a margin of error of 0.04, the sample size is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96 \times 0.5[/tex]
[tex]\sqrt{n} = \frac{1.96 \times 0.5}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 0.5}{0.04}\right)^2[/tex]
n = 601.
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Need help solving this question
The proportion that correctly defines θ is BC/PC = DE/PE = θ.
option C.
What is the length of the arcs?The length of the arcs is calculated as follows;
Length of arc = (θ/360) x 2πr
where;
r is the radius of the circleθ is the central angle of the arcFor sector PCB, the length of the arc is given as;
(θ/360) x 2π(PC) = BC
(θ/360) x 2π = BC/PC
θ = BC/PC ------- (1)
Note: 2π radian = 360⁰
For sector PED, the length of the arc is given as;
(θ/360) x 2π(PE) = DE
(θ/360) x 2π = DE/PE
θ = DE/PE ------- (2)
Compare the two equations as follows;
BC/PC = DE/PE = θ
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Can someone please provide a step-by-step explanation for the answer? I would really appreciate it.
Let f(x)= 2(x-1) / x²-2x-3 - 1/ x-3, x ЄR, x > 3.
(a) Show that f(x) = 1/ x+1
(b) Find the inverse function of ƒ (x).
(c) Find the domain of ƒ−¹(x).
(d) Given that g(x) = 2x² – 3, where x Є R. Solve (ƒ o g)(x) = 1/8.
b) The inverse function of ƒ(x) is given by: ƒ⁻¹(x) = (1 - x) / x
c) The domain of ƒ⁻¹(x) is all real numbers except for 1.
d) The solutions for (ƒ o g)(x) = 1/8 are x = √5 and x = -√5.
(a) To show that f(x) = 1 / (x + 1), we need to simplify the expression f(x) and demonstrate that it is equivalent to 1 / (x + 1):
f(x) = [2(x - 1) / (x² - 2x - 3)] - (1 / (x - 3))
f(x) = [2(x - 1) / (x - 3)(x + 1)] - (1 / (x - 3))
f(x) = [2(x - 1) - (x + 1)] / (x - 3)(x + 1)
f(x) = [2x - 2 - x - 1] / (x - 3)(x + 1)
f(x) = (x - 3) / (x - 3)(x + 1)
f(x) = 1 / (x + 1)
Therefore, we have shown that f(x) = 1 / (x + 1).
(b) To find the inverse function of ƒ(x), we interchange the roles of x and y and solve for y:
x = 1 / (y + 1)
xy + x = 1
xy = 1 - x
y = (1 - x) / x
Therefore, the inverse function of ƒ(x) is given by:
ƒ⁻¹(x) = (1 - x) / x
(c) The domain of ƒ⁻¹(x) can be determined by looking at the domain of the original function f(x), which is x > 3.
For ƒ(x), the range is all real numbers except for 1 (since f(x) = 1 / (x + 1)).
Therefore, the domain of ƒ⁻¹(x) is all real numbers except for 1.
(d) Given g(x) = 2x² - 3, we are asked to solve (ƒ o g)(x) = 1/8.
(ƒ o g)(x) means we need to substitute g(x) into ƒ(x):
ƒ(g(x)) = 1 / (g(x) + 1)
Substituting g(x) = 2x² - 3:
ƒ(2x² - 3) = 1 / (2x² - 3 + 1)
ƒ(2x² - 3) = 1 / (2x² - 2)
1 / (2x² - 2) = 1 / 8
8 = 2x² - 2
2x² = 10
x² = 5
x = ±√5
Therefore, the solutions for (ƒ o g)(x) = 1/8 are x = √5 and x = -√5.
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Tamika Clark is the county superintendent. She travels to the
3 schools in her district every month. This month her travel
expenses include: 246 miles traveled at $0.55 per mile; meals,
$180.70; miscellaneous, $46.90. What is her total travel expense
this month?
Tamika Clark's total travel expense this month is $362.90.
Given that the supervisor for the county is Tamika Clark.
Every month, she makes the trip to the three schools in her district.
Her travel costs for this month include 246 miles at a cost of $0.55 per mile, $180.70 for meals, and $46.10 for other expenses.
We must determine the whole cost of her.
To calculate Tamika Clark's total travel expenses this month, we need to add up her expenses for miles traveled, meals, and miscellaneous items.
Miles traveled:
246 miles x $0.55 per mile = $135.30
Meals: $180.70
Miscellaneous: $46.90
Total travel expenses:
$135.30 (miles traveled) + $180.70 (meals) + $46.90 (miscellaneous) = $362.90
Therefore, Tamika Clark's total travel expense this month is $362.90.
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Question 4 help me on please
The true statement is that the box-plot indicates that:
more women earn more than $369 than earn less than $337 more than 50% of men earn more than $406. Do 50% of all women earn less than the minimum weekly salary of men?To determine the validity of this statement, we compare the minimum weekly salary of men (represented by the lower end of the box-plot whisker) to the median of women's earnings (represented by the line inside the box).
If the median of women's earnings is less than the minimum salary of men, then more than 50% of women earn less than the minimum weekly salary of men.
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Determine which of the given points are solutions to the given equation.
2x^2 + y = 4
I. (3, -14) II. (-3, 14) III. (-3, -14)
The points that are solutions to the equation [tex]2x^2 + y = 4[/tex] are:
I. (3, -14)
III. (-3, -14)
To determine which of the given points are solutions to the equation [tex]2x^2 + y = 4[/tex], we need to substitute the x and y values of each point into the equation and check if the equation holds true.
Let's evaluate each point one by one:
I. (3, -14)
Substituting x = 3 and y = -14 into the equation:
[tex]2(3)^2 + (-14) = 4[/tex]
18 - 14 = 4
4 = 4
Since both sides of the equation are equal, the point (3, -14) is a solution to the equation.
II. (-3, 14)
Substituting x = -3 and y = 14 into the equation:
[tex]2(-3)^2 + 14 = 4[/tex]
18 + 14 = 4
32 = 4
Since the equation is not satisfied (32 is not equal to 4), the point (-3, 14) is not a solution to the equation.
III. (-3, -14)
Substituting x = -3 and y = -14 into the equation:
[tex]2(-3)^2 + (-14) = 4[/tex]
18 - 14 = 4
4 = 4
Since both sides of the equation are equal, the point (-3, -14) is a solution to the equation.
In summary, the points that are solutions to the equation [tex]2x^2 + y = 4[/tex]are:
I. (3, -14)
III. (-3, -14)
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Can I have help please thank u
Answer:
A = 30 cm
B = 14 cm
C = 15 cm
D = 41 cm
Step-by-step explanation:
You can find A by multiplying 10 times 6 (because the other side of the square is ten and the side of A already has that 4 there it would be 6) which would be 60, then since it is a right triangle, you can divide that by two and get 30.
You can find B by multiplying 4 by 7 (because the other part of that side of the square is 3 so that part would be 7) which would be 28, then since it is a right triangle, you can divide that by two and get 14.
You can find C by multiplying 10 times 3 and getting 30, then since it is a right triangle, you can divide that by two and get 15.
You can find D by multiplying 10 by 10 (because it is a square) then you'll get 100 from that. Then you can subtract the rest of the triangles from it which would be 100 minus 30 minus 14 minus 15 and you would get 41 which would be triangle D.
Hope this helps!! Let me know if you need more explanation
Please help O need to know if it’s wrong tell me what’s right
Answer:
The graph of g is a reflection over the y-axis. Let's call the points of a regular function before the reflection is done (x, y). When a function is reflected over the y-axis, you get the opposite y values as (x, -y). So with a point like (-2, -3), a reflection over the y-axis would give us (-2, 3), where x stays the same but y becomes the opposite.
The exact solution to the equation e−5x+1=2
is
Answer:
.343656
Step-by-step explanation:
e-5x+1=2
Subtract the 1 to the other side.
e-5x=1
Subtract e to the other side (e is approximately 2.718)
-5x=-1.718
Divide by -5.
x=.343656
please give me answer to this ixl!!!!!
The probability of getting at one hit is 2/5
What probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100%
Probability = sample space / total outcome
The sample space of getting at least 1 hit.
is 4.
Total outcome = 10
probability to get at least one hit = 4/10
= 2/5
Therefore the probability of getting atleast one hit is 2/5
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write an equation for the line that passes through (4, -5) and (3, -2)
Answer:
y = - 3x + 7
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 )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, - 5 ) and (x₂, y₂ ) = (3, - 2 )
m = [tex]\frac{-2-(-5)}{3-4}[/tex] = [tex]\frac{-2+5}{-1}[/tex] = [tex]\frac{3}{-1}[/tex] = - 3 , then
y = - 3x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (3, - 2 )
- 2 = - 3(3) + c = - 9 + c ( add 9 to both sides )
7 = c
y = - 3x + 7 ← equation of line
I need some help cant find it
Answer:
3.6
Step-by-step explanation:
Sine rule: a/SIN A = b/SIN B = c/SIN C.
right-angled triangle, so angle N = 90°.
x/sin 32 = 6.8/sin 90
x = (6.8 X sin 32) / sin 90
= 3.6
ESTION 2 Given: T = n²-10n-30 2.1.1 Which term is the minimum?
The minimum of this quadratic function is -55.
How to determine the axis of symmetry and the vertex of the function?In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function T = n²- 10n - 30, we have:
Axis of symmetry, Xmax = -(-10)/2(1)
Axis of symmetry, Xmax = 10/2 = 5.
For the vertex of T = n²- 10n - 30, we have:
T = n²- 10n - 30
T(5) = 5²- 10(5) - 30
T(5) = -55.
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Matthew invested $8,000 in an account paying an interest rate of 3 1/8% compounded
continuously. Parker invested $8,000 in an account paying an interest rate of 2 3/4%
compounded annually. To the nearest dollar, how much money would Parker have in
his account when Matthew's money has tripled in value?
Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.
We have,
For Matthew's investment, the continuous compounding formula can be used:
[tex]A = P \times e^{rt}[/tex]
Where:
A = Final amount
P = Principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (in decimal form)
t = Time (in years)
In this case,
Matthew's money has tripled,
So A = 3P.
For Parker's investment, the formula for compound interest compounded annually is used:
[tex]A = P \times (1 + r)^t[/tex]
Where:
A = Final amount
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form)
t = Time (in years)
We need to find t when Matthew's money has tripled in value.
Let's set up the equation:
[tex]3P = P \times e^{rt}[/tex]
Dividing both sides by P, we get:
[tex]3 = e^{rt}[/tex]
Taking the natural logarithm of both sides:
ln(3) = rt
Now we can solve for t
t = ln(3) / r
For Matthew's investment,
r = 3 1/8% = 3.125% = 0.03125 (as a decimal).
For Parker's investment,
r = 2 3/4% = 2.75% = 0.0275 (as a decimal).
Now we can calculate t for Matthew's investment:
t = ln(3) / 0.03125
Using a calculator, we find t ≈ 22.313 years.
Now, we can calculate how much money Parker would have in his account at that time:
[tex]A = P \times (1 + r)^t[/tex]
[tex]A = $8,000 \times (1 + 0.0275)^{22.313}[/tex]
Using a calculator, we find A ≈ $13,774.
Therefore,
Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.
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Answer:
20,763
Step-by-step explanation:
I saw the answer after I got it wrong
I need the answer for this question
The solution is; C. x² + 2x - 1 = 3 equation could be solved using this application of the quadratic formula.
Here,
Quadratic formula: x = -b±√b²-4ac/2a [ +/- is ± ]
You can find the value of a, b, c --> ax² + bx + c = 0
we have,
x = -2±√2² - 4×1× -4 / 2×1
Since this is not simplified, you can find a, b, c:
a = 1
b = 2
c = -4
A.) x² + 1 = 2x − 3 Make the equation into ax² + bx + c = 0.
Subtract 2x on both sides, and add 3 on both sides to set the equation equal to 0
x² + 1 - 2x + 3 = 2x - 2x - 3 + 3
x² - 2x + 4 = 0
a = 1
b = -2
c = 4 This is not the answer because b = 2 not -2, and c = -4 not 4
B.) x² - 2x − 1 = 3 Subtract 3 on both sides to set the equation = 0
x² - 2x - 4 = 0
a = 1
b = -2
c = -4 This is not the answer because b = 2 not -2
C. x² + 2x - 1 = 3 Subtract 3 on both sides to set the equation = 0
x² + 2x - 4 = 0
a = 1
b = 2
c = -4 This is your answer
D. x² + 2x - 1 = -3 Add 3 on both sides to set the equation = 0
x² + 2x + 2 = 0
a = 1
b = 2
c = 2
This is not the answer because c = -4 not 2
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complete question:
Which equation could be solved using this application of the quadratic formula?
x = -2±√2² - 4×1× -4 / 2×1
You deposit $500 in an
account that earns
simple interest at an
annual rate of 5.6%.
How much money is in
the account after 3
years?
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 5.6\%\to \frac{5.6}{100}\dotfill &0.056\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 500[1+(0.056)(3)] \implies A=500(1.168)\implies A = 584[/tex]
Answer:
Answer:
I = $ 84.00
Calculation:
First, converting R percent to r a decimal
r = R/100 = 5.6%/100 = 0.056 per year,
then, solving our equation
I = 500 × 0.056 × 3 = 84
I = $ 84.00
The simple interest accumulated
on a principal of $ 500.00
at a rate of 5.6% per year
for 3 years is $ 84.00.
Step-by-step explanation:
A rocket is launched in the air. Its height in feet is given by h= -16t^2 + 56t where t represents the time in seconds after launch. What is the appropriate domain for this Solution?
The domain of the function (t) in h = - 16t² + 56t should be greater than
or equal to 43.5 seconds as the height of the rocket can not be negative.
Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given that;
A rocket is launched into the air. Its height in feet is given by
h = - 16t² + 72t.
Where t represents time in seconds and h represents the height in feet.
We know that height can not be negative.
h ≥ 0.
So, - 16t² + 56t ≥ 0.
- 16t² ≥ -56t.
16t² ≥ 56t.
16t ≥ 56.
t ≥ 56/16.
t ≥ 3.5 seconds.
Therefore, the domain of the function (t) in h = - 16t² + 56t should be greater than or equal to 3.5 seconds.
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If side a measures 30 feet and side b measures 40 feet, how many feet of flowers will be planted along side c, the hypotenuse of the triangle? Show your work.
Answer:
You dont have to tell me to show my work twice
Step-by-step explanation:
To find the length of side c (the hypotenuse), we will use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (a and b) is equal to the square of the hypotenuse (c).
In this case, a = 30 feet and b = 40 feet. Therefore:
c^2 = a^2 + b^2
c^2 = 30^2 + 40^2
c^2 = 900 + 1600
c^2 = 2500
c = √2500
c = 50 feet
So the length of side c (the hypotenuse) is 50 feet. To find out how many feet of flowers will be planted along side c, we need to know the perimeter of the triangle (the sum of the lengths of all three sides). The perimeter is:
Perimeter = a + b + c
Perimeter = 30 + 40 + 50
Perimeter = 120 feet
Therefore, 120 feet of flowers will be planted along side c.
Answer: Here, side a = 30ft.
side b = 40ft.
Hence according to, Pythagoras theorem,
h²=p²+b²
where, h= hypotenuse of the triangle
b= base of the triangle
p= perpendicular of the triangle
Step-by-step explanation:
hypotenuse c {according to question} - c=[tex]\sqrt{a^{2} + b^{2}[/tex]
therefore, c=[tex]\sqrt{30^{2} + 40^{2} }[/tex] = 50ft. will be the answer.
Hypotenuse means the longest side of the triangle or in other words the side opposite to the 90° angle of the triangle.
According to United States Census Bureau, in 2013 the four states shown in the table had the highest population density of all states, measured in population per square mile
(mi^2). Which state had the greatest population density in 2013?
New Jersey has the greatest population density in 2013
Since we know that,
Population density is defined as the number of people per square at any given point in time.
Total people / total area = population density
In emerging countries, population density is higher than in developed countries.
Now for the state : Connecticut
Population = 3596080
Area = 4842
Therefore,
Density = 3596080/4842
= 742.68
Now for the state : Massachusetts
Population = 6692824
Area = 7800
Therefore,
Density = 6692824/7800
= 858.05
Now for the state : New Jersey
Population = 8899339
Area = 7354
Therefore,
Density = 8899339/7354
= 1210.13
Now for the state : New Jersey
Population = 1051511
Area = 1034
Therefore,
Density = 8899339/7354
= 1016.93
Hence population Density of New Jersey is greatest.
To learn more about population density visit:
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four times the quantity of 6 minus a number is 8
Answer:
The original number was 4.
Step-by-step explanation:
We can construct an equation to model the given situation, using a variable x to represent the original number:
"the quantity of 6 minus a number"
[tex](6 - x)[/tex]
"four times the quantity"
[tex]4(6 - x)[/tex]
"is 8"
[tex]4(6 - x) = 8[/tex]
We can solve for x in this equation.
[tex]4(6 - x) = 8[/tex]
↓ applying the distributive property ... [tex]A(B+C) = AB + AC[/tex]
[tex]24 - 4x = 8[/tex]
↓ adding 4x to both sides
[tex]24 = 8 + 4x[/tex]
↓ subtracting 8 from both sides
[tex]16 = 4x[/tex]
↓ dividing both sides by 4
[tex]4 = x[/tex]
[tex]\boxed{x = 4}[/tex]
So, the original number was 4.