We know that the volume of a prism is defined by:
[tex]V=lwh \\ \\ \\ Where: \\ \\ l:length \\ \\ w:width \\ \\ h:height \\ \\ \\ l=\frac{d-2}{3d-9} \\ \\ w=\frac{4}{d-4} \\ \\ h=\frac{2d-6}{2d-4}[/tex]
Substituting values:
[tex]V=\left(\frac{d-2}{3d-9}\right)\left(\frac{4}{d-4}\right)\left(\frac{2d-6}{2d-4}\right) \\ \\ \\ Simplifying: \\ \\ V=\frac{d-2}{3d-9}\cdot \frac{4}{d-4}\cdot \frac{d-3}{d-2} \\ \\ V=\frac{\left(d-2\right)\cdot \:4\left(d-3\right)}{\left(3d-9\right)\left(d-4\right)\left(d-2\right)} \\ \\ V=\frac{4\left(d-3\right)}{\left(3d-9\right)\left(d-4\right)} \\ \\ V=\frac{4\left(d-3\right)}{3\left(d-3\right)\left(d-4\right)}[/tex]
[tex]Finally: \\ \\ \boxed{V=\frac{4}{3\left(d-4\right)}}[/tex]
The volume of the given prism in simplified form is [tex]V = \frac{4}{3(d - 4)}[/tex].
To find the volume of the prism, we use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
Given the dimensions of the prism:
l = \frac{d - 2}{3d - 9}
[tex]l = \frac{d - 2}{3d - 9}\\\\w = \frac{4}{d - 4}\\\\h = \frac{2d - 6}{2d - 4}[/tex]
We substitute these into the formula:
[tex]V = \left(\frac{d - 2}{3d - 9}\right) \left(\frac{4}{d - 4}\right) \left(\frac{2d - 6}{2d - 4}\right)[/tex]
Now we simplify this expression step-by-step:
Simplify the height term:
[tex]\frac{2d - 6}{2d - 4} = \frac{2(d - 3)}{2(d - 2)} = \frac{d - 3}{d - 2}[/tex]
Substitute the simplified height term:
[tex]V = \left(\frac{d - 2}{3(d - 3)}\right) \left(\frac{4}{d - 4}\right) \left(\frac{d - 3}{d - 2}\right)[/tex]
Combine and cancel common terms:
[tex]V = \frac{4}{3(d - 4)}[/tex]
This gives us the volume of the prism in its simplest form.
Complete question:
Using V = lwh, what is an expression for the volume of the following prism? The dimensions of a prism are shown.
The height is (2 d - 6) / (2 d - 4).
The width is 4 / (d - 4 ).
The length is StartFraction (d - 2) / (3 d - 9 ).
This describes the relationship between one set of data that increases as another set of data increases. This is synonymous with directly related.
Answer:
Positive correlation
Step-by-step explanation:
Correlation:
Correlation is a technique that help us to find or define a linear relationship between two variables.It is a measure of linear relationship between two quantities. A positive correlation means that an increase in one quantity leads to an increase in another quantity A negative correlation means with increase in one quantity the other quantity decreases.Positive correlation means that the data sets are directly related with each other.Thus, the correct answer is
Positive correlation
Answer:
Negative Correlation
Step-by-step explanation:
Which statement is not true about the data shown by the box plot below?
a.
The interquartile range is 52.
b.
The median of the upper half of the data is 49.
c.
The median of the data is 37.
d.
Three fourths of the data is less than 49.
The false statement is "the median of the data is 37" because the IQR of the data is 20 option (a) is correct.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
It is given that:
A box plot is shown in the picture;
As we know,
The interquartile range(IQR):
IQR = Q3 - Q1
IQR = 50 - 30
IQR = 20
From the box plot:
The median of the upper half of the data is 49.
The median of the data is 37.
Three-fourths of the data is less than 49.
Thus, the false statement is "the median of the data is 37" because the IQR of the data is 20 option (a) is correct.
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Find the area of the shape shown below.
Answer:
240 square units
Step-by-step explanation:
Area of shape =area of rectangle + area of triangle
[tex] = 20 \times 10 + \frac{1}{2} \times 20 \times 4 \\ = 200 + 40 \\ = 240 \: {units}^{2} [/tex]
Simplify the expression and find the value, if x=2 : 5x-6-x+9
Answer:11
Step-by-step explanation:
5x-6-x+9
When x=2 we have
5(2)-6-2+9
10-6-2+9
10+9-6-2
19-6-2=11
Answer:
11
Step-by-step explanation:
5x - 6 - x + 9
4x + 3
x = 2
4(2) + 3 = 11
(a+1)+(b-2)i=6+7i Solve for a and b
Answer:
a = 5 and b = 9Step-by-step explanation:
(a+1)+(b-2)i=6+7i
⇔
a + 1 = 6
and
b - 2 = 7
⇔
a = 5
and
b = 9
If the base angle of the cone needs to measure 60° and the cone needs to be 24 inches tall, approximately how wide will the base of the resulting cone need to be?
A.
27.72 inches
B.
13.86 inches
C.
41.57 inches
D.
83.14 inches
Final answer:
Using the base angle and the height of the cone, we can use trigonometry to find that the width of the base of the cone needs to be approximately 41.57 inches, making option C the correct answer.
Explanation:
The question asks for the width of the base of a cone given that its base angle is 60° and its height is 24 inches. To solve this, we need to understand that the base angle of 60° creates a right-angled triangle when a line is drawn from the apex of the cone to any point on the base's circumference, with the height of the cone being one side of this triangle and half of the cone's base width being the other side.
Using trigonometry, specifically the tangent function, which is the opposite side (half the base width) over the adjacent side (height), we can solve for the base width. Given that tan(60°) = √3 and the height is 24 inches, the formula becomes √3 = (base width/2) / 24, solving for the base width gives us roughly 41.57 inches, which makes option C correct.
Drivers of semitrucks and other large vehicles pay close attention to signs similar to the one below. These signs indicate a change in the grade or slope of the road. Look at the black scalene triangle in the sign. How can the third-angle theorem be applied to find all three angle measurements in the black triangle? (2 points)
Answer:
A triangles angles equal 180 so add 90 and 60 then subtract that from 180. 2) yes. they have same angles so they must be congruent
A triangle with two angles that measure 34°.
Then the correct option is A.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
here, we have,
In triangle ΔABC, the measure of the third angle is calculated as,
∠C + ∠B + ∠A = 180°
∠C + 112° + 34° = 180°
∠C = 34°
The measure of the two angles of the triangle is identical.
Then the triangle will be an isosceles triangle.
A triangle with two angles that measure 34°.
Then the correct option is A.
More about the triangle link is given below.
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Complete Question:
Triangle ABC is shown.
Which triangle listed below must be similar to triangle ABC?
(1 point)
(A) A triangle with two angles that measure 34°
(B) A triangle with angles that measure 34° and 66°
(C) A scalene triangle with only one angle that measures 112°
(D) An isosceles triangle with two angles that measure 56°
Include with your answer choice below, reasoning why your choice is correct.
(2 points)
Use formulas, definitions, or theorems in your reasoning.
- What is it about the angles?
- Anything with the angle sums?
- What about the type of triangles?
estimated a 3 out of every 25 men are left handed
what percent of men are left ahnded
Answer:
12
Step-by-step explanation:
Percent means out of 100
We have 3/25
Multiply the top and bottom by 4
12/100
The percent is 12
Final answer:
Based on the estimate provided, 12% of men are left-handed, which is calculated by dividing 3 by 25 and then multiplying the result by 100.
Explanation:
To calculate the percentage of men who are left-handed based on the estimate that 3 out of every 25 men are left-handed, you can use the following steps:
Divide the number of left-handed men by the total number of men. In this case, 3 divided by 25 equals 0.12.Multiply the result by 100 to convert it to a percentage. So, 0.12 multiplied by 100 equals 12%.Therefore, based on the given estimate, 12% of men are left-handed.
You randomly draw marble from the bag of marbles contains seven blue marbles two Green marbles and one red marble what is P(not draw a blue marble)?
Answer:
3/10 probability as it is the same as getting 2gm +1rm =3m
Step-by-step explanation:
You add up the numbers 7+2+1=10m
A car traveled 63 miles on 3 gallons of gas. What proportion can you set up to determine how many miles, m, the car can travel on 7 gallons of gas?
Answer:Let x be the number of miles driven on 60 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mileage, and show both the set up of the proportion and the steps
Step-by-step explanation:
Answer:
147 miles
Step-by-step explanation:
Let x be the number of miles travelled on 7 gallons, then proportion is of the form
[tex]\frac{miles}{gallons}[/tex], thus
[tex]\frac{63}{3}[/tex] = [tex]\frac{x}{7}[/tex] ( cross- multiply )
3x = 63 × 7 = 441 ( divide both sides by 3 )
x = 147
Thus the car can travel 147 miles on 7 gallons
A slot machine has 3 dials. Each dial has 30 positions, one of which is "Jackpot". To win the jackpot, all three dials must be in the "Jackpot" position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot?
1/30 = 0.03 or 3%
3/(30+30+30) = 3/90 = 0.33 or 33%
3/(30×30×30) = 3/27000 = 0.0001 or 0.01%
1/(30×30×30) = 1/27000 = 0.00003 or 0.003%
Answer:
3/(30×30×30) = 3/27000 = 0.0001 or 0.01%
Step-by-step explanation:
Answer:
here we have 3 dials in the slot machines and each dial has 30 position
so probability of getting a number of the each dial =
30
1
since all dials are independent so probability of getting same number would be
P ( getting jack pot) =
30
1
30
1
30
1
=
27000
1
= 0.003% option D is correct.
Step-by-step explanation:
Why is the reference angle the angle
the terminal side and the x-axis instead of the y-axis?
Answer:
If necessary, first "unwind" the angle: Keep subtracting 360 from it until it is lies between 0 and 360°. (For negative angles add 360 instead).
Sketch the angle to see which quadrant it is in.
Depending on the quadrant, find the reference angle:
Quadrilateral ABCD is an isosceles trapezoid with median EF. Which of the following statements is true?
Select the best answer from the choices provided.
A. EF is parallel to the bases.
B. EF = 2(AB + DC)
C. 1/2EF = AB + DC
D. EF =1/2(AD + CB)
Answer:
The answer is A
Step-by-step explanation:
There is no way to prove any of the others to be true
Final answer:
The median EF in an isosceles trapezoid is parallel to its bases, making option A the correct answer.
Explanation:
The student asked a question related to properties of an isosceles trapezoid and its median. In an isosceles trapezoid, the median is a line segment that connects the midpoints of the non-parallel sides. The properties of a trapezoid's median include that it is parallel to the two bases and that its length is equal to the average of the lengths of the two bases. Therefore, the correct statement from the list provided is that the median EF is parallel to the bases.
For more clarity:
EF is indeed parallel to the bases AB and CD; this corresponds to option A.EF is not twice the sum of the lengths of AB and DC, so option B is incorrect.EF is also not half the sum of the lengths of AB and DC, which means option C is incorrect.The length of EF is not half the sum of the lengths of the non-parallel sides AD and CB, so option D is incorrect.Find f(t-3) for f(×)=4x^2-8×+4
Answer:
4t^2-32t+64=4(t^2-8x+16)
Step-by-step explanation:
f(x)=4x^2-8x+4
f(t-3)=4(t-3)^2 - 8(t-3)+4=
4(t^2-2*t*3+9)-8t+24+4=
4(t^2-6t+9)-8t+28=
4t^2-24t+36-8t+28=
4t^2-32t+64=4(t^2-8x+16)
One step equations
6r=42
R=7
I hope that help you! :)
Rani and her friends are raking leaves as a part of a school service project. The regular price of the supplies they need is 60$,but the store manager is giving them a 20% discount. Rani wants to know the sale price of the supplies.
Rani and her friends can purchase their supplies for $48 after a 20% discount on the original price of $60.
Explanation:Rani and her friends need to calculate the sale price of the supplies after a 20% discount. The original price is $60, and the discounts amount in money can be determined by multiplying this original cost by 20% or 0.20. This gives you a discount amount of $12. To determine the final price after the discount, you subtract the discount amount from the original price. Therefore: $60 - $12 = $48. Hence, the sale price of the supplies that Rani and her friends need is $48.
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Drag & Drop. Thank you to anyone who helps
Answer:
Top Left.) None of these, these are vertical angles.
Top Right.) Alternate Exterior
Middle Left.) None of these
Middle Right.) Corresponding
Bottom.) Alternate interior angles
The sum of k and 5 is 11
Answer:
j
Step-by-step explanation:
j
Answer:
K=6
Step-by-step explanation:
Subtract 5 from 11
Write the equation of the line that passes through the point (-5,5) and has a slope of -8/5
A) y= -8/5 x - 3
B) y= -8/5x+3
C) 3x - 5y =0
D) 5x-3y=0
Answer:
A) y= -8/5x -3
Step-by-step explanation:
This is your current equation: y= -8/5x + b. I would plug in your point to the equation. It should look like this: 5= -8/5(-5)+b. Multiply -8/5 by -5 to get 8. This is what you should have: 5=8+b. Subtract 8 from both sides to get -3=b. So, this is your final answer: y= -8/5x -3. So, A is the correct answer. Hope this helped!
please help, no spam answers please, I will mark brainleist!
Answer:
D.
Step-by-step explanation:
Its given that the rectangle has a perimeter of 60 units. A rectangle has four sides, and to get the perimeter, you add up all four sides. You are given one side is 20 units, and the other as 'x.'
So,
x + x + 20 + 20 = 60
2x + 40 = 60
Example for *wrong* answer:
Letter C, x + 20 = 60, that would'nt equal 60 because youre only adding two sides instead of all four.
Hopefully this helps :)
I'm trying to figure out question 4 but I don't understand it and neither do my friends.
Answer:
A: 88 — 100B: 85 — 87C: 82 — 84D: 80 — 81F: 0 — 79Step-by-step explanation:
You know the relation between X and Z is ...
Z = (X -μ)/σ
Solving for X, we find ...
Zσ +μ = X
You're trying to find the exam scores that correspond to the Z-values you found in question 3.
A = 90th percentile and above = 1.28(8) +78 = 88.24 ≈ 88
B = 80th percentile and above = 0.84(8) +78 = 84.72 ≈ 85
C = 70th percentile and above = 0.52(8) +78 = 82.16 ≈ 82
D = 60th percentile and above = 0.25(8) +78 = 80
So, your blanks are filled like this ...
A: 88 — 100
B: 85 — 87
C: 82 — 84
D: 80 — 81
F: 0 — 79
_____
Comment on this curve
The setup guarantees that 60% of the class will fail. It is more common to have those below Z = -2 get an F, and those above Z = 2 get an A.
The lengths of two sides of a triangle are 26
meters and 48 meters. What is the range of
possible lengths, in meters, for the third side,
x, of this triangle? Write your answers in the
boxes.
Answer:
[tex]22\ m < x < 74\ m[/tex]
Step-by-step explanation:
Let
x ----> the length for the third side
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Applying the triangle inequality theorem
1) [tex]26+48> x[/tex]
solve for x
[tex]74> x[/tex]
Rewrite
[tex]x < 74\ m[/tex]
2) [tex]26+x>48[/tex]
solve for x
subtract 26 both sides
[tex]x> 22\ m[/tex]
therefore
The range of possible lengths, in meters, for the third side is equal to
[tex]22\ m < x < 74\ m[/tex]
The range of the possible length of the third side of the triangle is 22 to 74 (exclusive)
Assume the lengths of a triangle are x, y and z.
The following are the possible inequalities that relate the side lengths
[tex]x + y > z[/tex]
[tex]y + z > x[/tex]
[tex]x + z > y[/tex]
The unknown side length is x.
So, we have:
[tex]x + 26 > 48[/tex]
[tex]48 + 26 > x[/tex]
[tex]x + 48 > 26[/tex]
Solve for x in the three inequalities
[tex]x + 26 > 48[/tex]
[tex]x > 22[/tex]
[tex]48 + 26 > x[/tex]
[tex]74 > x[/tex]
[tex]x + 48 > 26[/tex]
[tex]x > -22[/tex]
The values of x cannot be negative.
So, we ignore the inequality [tex]x > -22[/tex]
We are left with
[tex]74 > x[/tex] and [tex]x > 22[/tex]
Combine the inequalities
[tex]74 > x > 22[/tex]
Rewrite as:
[tex]22 < x < 74[/tex]
Hence, the range of the possible length is 22 to 74 (exclusive)
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if cos x=2/3 and x is in quadrant 4 then sin x/2=
A. 1/3
B. Sqrt 1/6
C. -Sqrt 1/6
D. -1/3
Options are above will mark brainliest
Answer: B, [tex]\sqrt{\frac{1}{6} }[/tex]
Step-by-step explanation:
Using half-angle identities
Using half angle identities, we know that
[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1-cosx}{2} }[/tex]
Plug in 2/3 for cosx
[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1-2/3}{2} }[/tex]
[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1/3}{2} }[/tex]
[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1}{6} }[/tex]
Determining sign
Since the angle x is in quadrant 4 from 270 to 360 degrees, if we divide the angle by 2, the angle x should be somewhere from 135 to 180 degrees, which would all fall in quadrant 2
all sin values in quadrant 2 are positive
Final answer
[tex]sinx = \sqrt{\frac{1}{6} }[/tex]
If cos x=2/3 and x is in quadrant 4 then value of sin x/2 is -√(1/6), option C is correct.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To find sin(x/2), we can use the half-angle formula for sine:
sin(x/2) = ±√[(1 - cos x)/2]
Since x is in quadrant 4, cosine is positive and sine is negative. We are given that cos x = 2/3
so we can substitute this value into the formula:
sin(x/2) = -√[(1 - 2/3)/2]
sin(x/2) = -√(1/6)
Hence, if cos x=2/3 and x is in quadrant 4 then sin x/2 is -√(1/6)
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21 3/4 as a improper fraction
Answer:
87/4
Step-by-step explanation:
Step 1: Convert 21 3/4 into an improper fraction
21 3/4 is same as 21 * 4/4 + 3/4
21 * 4/4 = 84/4
Step 2: Add them up
84/4 + 3/4
87/4
Answer: 87/4
Answer: 87/4
Step-by-step explanation:
Multiply:
21*4=84
Add:
84+3=87
Your answer should be: 87/4
The denominator stays the same
points [50] Amelie's bird cage is shaped like a rectangular prism. The cage has a height of 26 inches and a volume of 7,280 cubic inches. Amelie puts a piece of newspaper on the bottom of the cage. The newspaper fits the bottom of the cage perfectly.
What is the area of the newspaper on the bottom of the cage?
Enter your answer in the box.
Solve the provides equation verify the solution and state the answer using solution set notation. 126= w+38
Answer:
88
Step-by-step explanation:
126=w+38
w=126-38
=88
What's the snaller angle?
Answer:
the (2x) obviously because it is close to an acute angle and the (13x) is closer to a right angle
Step-by-step explanation:
Write the point-slope form of the line passing through (2, -12) and parallel to y=3x.
y - 12 = -(x + 2)
y + 12 = -(x - 2)
y + 12 = 3(x - 2)
y + 12 = -3(x - 2)
Answer:
y + 12 = 3(x-2)
Step-by-step explanation:
To start, you want the slope of the other line. Well, the slope of a parallel line is the same, so since the first line's slope is 3, so will the other one. then, because there is no other answer with a slope of 3, you automatically know it is the third answer. you don't need to work this problem further, but if you need to in the future, just comment and I will help you.
How much money invested at 5% compounded continuously for 3 years will result in $852
Answer:
Step-by-step explanation:
Rate of interest is 5%.
Time =3years
Amount =$852
Then, we need to find P
Generally compound interest is given as
A=P(1+r/n)^nt
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period=12
t=number of time periods elapsed
A=P(1+r/n)^nt
852=P(1+0.05/12)^(12×5)
852=P(1+0.004167)^60
852=P(1.004167)^60
852=1.2834P
Then, P=852/1.2834
P=$663.88
Then the principal amount invested is $663.88
Approximately $664
The ratio of the number of boys to the number of girls at school is 4:5. a. What fraction of the students are boys? b. If there are 120 boys, how many students are there altogether? *
Answer: a. 4/9
b. 270 students
Step-by-step explanation:
Answer:
270
Step-by-step explanation:
120÷4= 30
30×5=150
150+120=270