17 cubic units.
Step-by-step explanation:
The volume (V) of a parallelepiped with one vertex at the origin is given by the absolute value of the scalar vector product of the vectors at the adjacent vertices.
V = |(a x b) · c|
In this case,
a = (1,4,0) = i + 4k + 0j
b = (-2,-5,2) = -2i -5j + 2k
c = (-2,2,1) = -2i + 2j + k
First, let's calculate the cross product of vectors a and b. i.e a x b as follows:
(i) Arrange the vectors in a matrix form
a x b = | i j k |
| 1 4 0 |
| -2 -5 2 |
(ii) Calculate the determinant of the matrix
a x b = i(8 - 0) -j(2-0) + k(-5+8)
a x b = i(8) -j(2) + k(3)
a x b = 8i - 2j + 3k
Secondly, calculate the scalar product of the cross product found above and the vector c as follows;
(a x b) . c = (8i - 2j + 3k) · (-2i + 2j + k)
Multiply like terms
(a x b) . c = (8 * -2)(i.i) + (-2 * 2)(j.j) + (3 * 1)(k.k) [i.i = j.j = k.k = 1]
(a x b) . c = (-16) + (-4) + (3)
(a x b) . c = -16 - 4 + 3
(a x b) . c = -17
Thirdly, find the absolute value of the result found above. i.e
|(a x b) . c| = |-17|
|(a x b) . c| = 17
Therefore, the volume of the parallelepiped is 17 cubic units.
Keith is looking at a cliff. He determines that the angle of elevation to the top is 70° from where he is at. 70m away from Keith, Alan estimates the angle between the base of the cliff, himself, and Keith to be 29° while Keith estimates the angle between the base of the cliff, himself, and Alan to be 48°. What is the height, h, of the cliff to the nearest tenth of a metre?
1) 78.8m
2) 83.9m
3) 89.0m
4) 95.7m
This question completely baffled me on my homework, I still haven't done it because I don't even know how to approach it (Since it's a 3D problem)
Please help me out
Also, this homework is due in an hour so I'm starting to sweat
9514 1404 393
Answer:
4) 95.7 m
Step-by-step explanation:
The angle at the cliff base between Alan and Keith is ...
B = 180° -29° -48° = 103°
The law of sines will tell you the distance KB from Keith to the cliff base is
KB/sin(A) = KA/sin(B)
KB = KA×sin(A)/sin(B) = (70 m)sin(29°)/sin(103°) ≈ 34.82935 m
The height of the cliff is found from the tangent relation ...
Tan = Opposite/Adjacent
tan(70°) = height/(34.83 m)
height = (34.83 m)tan(70°) = 95.693 m
The height of the cliff is about 95.7 m.
_____
Additional comment
These problems can usually be resolved into two 2-D problems. Here, we can work out the distance we need from Keith to the cliff by considering only the ground plan of the site. Then we can work out the height of the cliff only considering the vertical plane containing Keith and the base of the cliff.
The attachment shows the ground plan triangle KAB.
4
)
5 + 15x
42x + 4
A) -2
C) -10
B) 3
D) -8
Answer:
D
Step-by-step explanation:
D
Meg makes a dot plot for the data 9, 9, 4, 5, 5, 3,
4,5, 3, 8, 8, 5. Where does a gap occur?
The gap consists of the values 6 and 7.
Check out the dot plot below to see what I mean. We have one cluster on the left from 3 to 5. Then another cluster on the right from 8 to 9.
Answer:
The gap is present around 6 & 7
Step-by-step explanation:
Since there is no evidence of dots above 6 & 7, there must have been a freeze in data around then, called a gap.
4/8 =?/2 please answer
Answer:
? = 1
Step-by-step explanation:
4/8 = ?/2
Change the ? into a variable so it's easier to calculate:
Variable x = ?
4/8 = x/2
Cross multiply:
4 × 2 = 8 × x
8 = 8x
Divide both sides by 8 to isolate the variable:
1 = x
Check your work:
4/8 = 1/2
4 × 2 = 8 × 1
8 = 8
Correct!
Activity IB. FIND ME!
Find the area of each circle. Use = 3.14
3.
1.
2.
om
13cm
19in.
5.
33cm
25cm
yan paki sagot
How to solve the inequality 8x + 10 ≤ 60
Answer:
x ≤ 6.25
Step-by-step explanation:
8x + 10 ≤ 60
Subtract 10 from both sides
8x ≤ 50
Divide both side by 8
x ≤ 6.25
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Triangle D E F is shown. Angle E F D is a right angle. The length of E F is 24 and the length of D F is 7.
Which trigonometric ratios are correct for triangle DEF? Select three options.
sin(D) = StartFraction 24 Over 25 EndFraction
cos(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 24 Over 7 EndFraction
sin(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 7 Over 24 EndFraction
Answer:
Sin(E) = 7/25
Sin(D) = 24/25
Tan(D)= 24/7
Step-by-step explanation:
Sin=opp/hyp
Tan=opp/adj
Cos=adj/hyp
The trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7
How to determine the trigonometric ratios?The given parameters are:
EF = 24
DF = 7
Start by calculating the length DE using:
DE²= EF² + DF²
So, we have:
DE²= 24² + 7²
Take the square root of both sides
DE= 25
The sine of the angles is calculated using:
sin(Ф) = opp/hyp
So, we have:
sin(E) = 7/25
sin(D) = 24/25
The tangent of the angles is calculated using:
tan(Ф) = opp/adj
So, we have:
tan(D)= 24/7
Hence, the trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7
Read more about trigonometric ratios at:
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Use the diagram to estimate the perimeter, rounding each number to the nearest hundred.
A parallelogram is shown. Two sides are labeled 5,534 feet. The other two sides are labeled 1,566 feet.
14,200 feet
16,000 feet
14,400 feet
14,000 feet
Answer:
14,000 feet.
Step-by-step explanation:
A parallelogram has 4 total sides and the opposite sides are characterized as having the same length. Therefore, If we are provided the lengths of two adjacent sides we can easily calculate the perimeter by multiplying these provided lengths by 2 and then adding them together. Since we are asked to round each number to the nearest hundred, it would be the following...
(5,500 * 2) + (1,500 * 2) = x
11,000 + 3000 = x
14,000 = x
Finally, we can estimate that the perimeter of the parallelogram is 14,000 feet.
lim x->1+( sin(1-x)-(e^(x-1))+1)/ lnx
We're given the one-sided limit,
[tex]\displaystyle\lim_{x\to1^+}\frac{\sin(1-x)-e^{x-1}+1}{\ln(x)}[/tex]
Evaluating the limand directly at x = 1 gives the indeterminate from
(sin(1 - 1) - exp(1 - 1) + 1) / ln(1) = 0/0
so we can potentially solve the limit by applying L'Hopital's rule. Doing so gives
[tex]\displaystyle\lim_{x\to1^+}\frac{\sin(1-x)-e^{x-1}+1}{\ln(x)}=\lim_{x\to1^+}\frac{-\cos(1-x)-e^{x-1}}{\frac1x}=\frac{-\cos(0)-e^0}{\frac11}=\boxed{-2}[/tex]
Ethan is 1.6 metres tall, Uzma is 154 cm tall.
Work out how much taller Ethan is than Uzma.
Answer:
1.6 metres is 160 centimetres
Ethan is 6 centimetres taller than Uzma
please help step by step, please
9514 1404 393
Answer:
title: 300%payday: 650%check cashing: 214%Step-by-step explanation:
The formula for simple interest is ...
I = Prt
where P is the principal amount loaned, r is the annual rate, and t is the time in years. Solving for interest rate, we get ...
r = I/(Pt)
We assume 12 months or 52 weeks in a year.
__
Car title loan
r = 125/(500×1/12) = 3 × 100% = 300%
The APR is 300%.
__
Payday loan
r = 125/(500×2/52) = 6.5 × 100% = 650%
The APR is 650%.
__
Check cashing
r = 19.66/(478.41×1/52) ≈ 2.1369 × 100% ≈ 214%
The APR is about 214%.
There are 3 liters of orange juice at a school party. 10 students want to drink all of the orange juice, and they all want to get exactly the same amount. How much orange juice can each get? (enter your answer as a fraction or mixed number)
Answer:
3 1/3 each
Step-by-step explanation:
10/3=3 1/3
write an equation of the line below
My rule is: y = 1/3x + 11/15
Find y, if x=1
Find y, if x=6
76. In the diagram below, lines land mare
parallel. Both are intersected by
transversal t.
What is the value of x?
According to a government study, among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $2,020. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $456. Use Appendix B.3. (Round your z-score computation to 2 decimal places and final answers to 2 decimal places.) What percent of the adults spend more than $2,600 per year on reading and entertainment
Answer:
z = x-u/s
z = 2600 - 2020/456
z = 1.27
= .897
1-.898 = .102
z > 1.27 = 10.2%
The percentage of adults spending more than $2,600 per year on reading and entertainment is 10.2%.
What is the z-score?The standard score in statistics is the number of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.
Given that according to a government study, among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $2,020. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $456.
The percentage will be calculated as,
z = x-u/s
z = 2600 - (2020/456)
z = 1.27
The value of z=1.27 in the table is 0.897. The percentage will be calculated as,
P = 1-.898 = .102
z > 1.27 = 10.2%
Therefore, the percentage of adults spending more than $2,600 per year on reading and entertainment is 10.2%.
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) A desk organizer sells for $35, which includes a markup rate of 60% based on the selling price.
a. Find the markup.
b. Find the cost.
Answer: a. $21
b. $14
Step-by-step explanation:
Selling price of desk organizer = $35
Markup rate = 60%
a. The markup will be:
= Markup rate × Selling price
= 60% × $35
= 0.6 × $35
= $21
Therefore, the markup is $21
b. The cost will then be:
Cost price = Selling price - Markup
= $35 - $21
= $14
Based on the areas of the squares, determine whether the triangle shown is a right triangle.
The given triangle is not a right-angle triangle as the sides don't form a Pythagorean triplet.
What is the Pythagoras theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the le right triangle is equal to the square on the hypotenuse (the Pythagoras the right angle)—or, in familiar algebraic notation, a² + b² = c².
Given her: Three squares whose sides form one Pythagoreans of a triangle .
Now a²=58
b²=10
b=√10
c²=64
c=8
Clearly √10<√58<8
Thus c must be the hypotenuse of the triangle.
Using Pythagoras' theorem we get
√10²+√58²=68≠64
Hence, The given triangle is not a right angle triangle as the sides don't form a Pythagorean triplet.
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Two and three fifths plus one and three fifths
Answer:
2 3 + 1 3 = 3/5 + 3/5 = 1 1/5 + 2+1 = 3 + 1 !/5 = 4 1/5
5 5
Step-by-step explanation: The Slashes mean The number bellow
Please make this answer Brainlist...
Find the perimeter of the triangle whose vertices are the following specified (0,3), (-10,-4) (-9,-7) points in the plane.
Answer:
The perimeter of the triangle is 28.82
Step-by-step explanation:
Please check the image uploaded for the diagram.
Perimeter = d₁ + d₂ + d₃
[tex]d_1 = \sqrt{(-10-0)^2 + (-4-3)^2} = \sqrt{100+49} =\sqrt{149} = 12.21\\\\d_2 = \sqrt{(-9-0)^2 + (-7-3)^2} = \sqrt{81+100} =\sqrt{181} = 13.45\\\\d_3 = \sqrt{(-10+9)^2 + (-4+7)^2} = \sqrt{1+9} =\sqrt{10} = 3.16\\\\Perimeter = 12.21 + 13.45 + 3.16 = 28.82[/tex]
What is the value of X
A. x=20
B. x=15
C. x=10
D. x=5
m(x) = x2 + 4x
n(x) = x
(mn)(x) =
x2 + 4x(x)
(x2 +4x)(x)
Answer:
Answer:
1. B. (x^2 + 4x)(x)
2. A. (x^3+4x^2)
3. 9
4. 0
5. 1
Step-by-step explanation:
Will give Brainliest! 10 points!
Provide reasons for the statements of this proof.
Answer:
See Below.
Step-by-step explanation:
Statements: Reasons:
[tex]\displaystyle 1)\, AD\perp BC\text{ and } D\text{ is the midpoint of } BC[/tex] Given
[tex]\displaystyle 2)\, BD\cong CD[/tex] Definition of Midpoint
[tex]\displaystyle 3)\, m\angle ADB=90^\circ \text{ and } m\angle ADC=90^\circ[/tex] Definition of Perp. Lines
[tex]\displaystyle 4)\, m\angle ADB=m\angle ADC[/tex] Substitution
[tex]\displaystyle 5) \angle ADB\cong \angle ADC[/tex] Definition of Congruence
[tex]\displaystyle 6)\, AD\cong AD[/tex] Reflexive Property
[tex]\displaystyle 7)\Delta BDA\cong\Delta CDA[/tex] SAS Congruence
if a student is selected at random, find the probability that the student is 14 year old
Answer:
If the student is selected at random the answer is if you put 14 years apart of the student selected at random means the answer are not apart.
Step-by-step explanation:
14 years selected the problem is that 14-9 is more then 9 and u add that up to get the right equation for the 14 years apart
ACTIVITY 1 Directions: Interpret these circle graphs
A. The pie graph below shows what a normal human body is made of.
Questions:
1. As shown in the graph,what composes the human body?
2. Which makes up the greatest part of the human body? the least?
Step-by-step explanation:
1) it is composed of 20% of fat, 17% of bone, 50% of muscle and 13% others(minerals)
2) muscle makes up the greatest part and the minerals makes up the least.
hope it heals u.
make me brain list Pls.
Find the area
10
7
12
4
5
5
Answer:
[tex]{ \tt{area = (7 \times 10) + (12 \times 4) + (5 \times 5)}} \\ { \tt{ = 70 + 48 + 25}} \\ { \tt{ = 143 \: {in}^{2} }}[/tex]
Answer: break into 2 rect and 1 sqr the sum areas of each
Step-by-step explanation: square = 5x5
Rectangle 1 = 10x7
Rectangle 2 = 12x4
Sum each shape area = total area
An item costs S430 before tax, and the sales tax is $17.20.
Find the sales tax rate. Write your answer as a percentage.
Answer:
Step-by-step explanation:
430
x4%
_________
$17.20+ $430= $447.20
Maddy has a bag of 36 marbles. The probability of picking green is 1 in 2, the probability of picking red is 1 in 3, and the probability of picking blue is 1 in 9. The only other color in the bag is black. Find the probability of Maddy picking a black marble.
Answer: 1 in 18
This is the same as writing the fraction 1/18
==============================================================
Explanation:
Since she has 36 marbles total, and the probability of picking green is 1 in 2, this means (1/2)*36 = 18 marbles are green.
Then she also has (1/3)*36 = 12 red marbles and (1/9)*36 = 4 blue marbles.
So far, that accounts for 18+12+4 = 34 marbles in all. That leaves 36-4 = 2 marbles left over that must be black, as it's the only color left.
From that, the probability of choosing a black marble is 2/36 = 1/18.
There's a 1 in 18 chance of Maddy picking a black marble.
1/18 = 0.0556 = 5.56% approximately
Which is the graph of an even monomial function?
Answer:
The graph of an even function is symmetric about the y-axis. The graph of an odd function is symmetric about the x-axis. It is possible that the use of these two words originated with the observation that the graph of a polynomial function in which all variables are to an even power is symmetric about the y -axis.
Three rectangular prisms each have a height of 1 cm.
. Prism A has a base that is 1 cm by 11 cm
* Prism B has a base that is 2 cm by 7 cm SA +V
Prism C has a base that is 3 cm by 5 cm.
1. Find the surface area and volume of each prism. Use the dot paper to draw the prisms, if needed.
Answer:
A: SA = 46 cm^2; V = 11 cm^3
B: SA = 46 cm^2; V = 14 cm^3
C: SA = 46 cm^2; V = 15 cm^3
Step-by-step explanation:
SA = 2B + PH = 2LW + PH
where SA = total surface area,
B = area of a base
P = perimeter of the base
H = height of the prism
L = length of the base
W = width of the base
V = LWH
Prism A:
SA = 2(11 cm)(1 cm) + 2(11 cm + 1 cm)(1 cm)
SA = 46 cm^2
V = (11 cm)(1 cm)(1 cm) = 11 cm^3
Prism B:
SA = 2(7 cm)(2 cm) + 2(7 cm + 2 cm)(1 cm)
SA = 46 cm^2
V = (7 cm)(2 cm)(1 cm) = 14 cm^3
Prism C:
SA = 2(5 cm)(3 cm) + 2(5 cm + 3 cm)(1 cm)
SA = 46 cm^2
V = (5 cm)(3 cm)(1 cm) = 15 cm^3
