Final answer:
The cross product a~ × b~, where a~ points south and b~ points west, is directed downwards. This direction is determined using the right-hand rule and is perpendicular to the original plane formed by a~ and b~.
Explanation:
If vector a~ points south and vector b~ points west, their cross product a~ × b~ can be determined using the right-hand rule. By pointing the fingers of your right hand towards the direction of a~ (south) and then rotating your wrist to point your fingers towards b~ (west), your thumb will point downwards. Therefore, the direction of a~ × b~ is downwards, which is into the ground if you are standing in the Northern Hemisphere.
The cross product of two vectors is always perpendicular to the plane that contains the original vectors. So in this case, since a~ and b~ are orthogonal and lie in the horizontal plane, their cross product a~ × b~ will be orthogonal to this horizontal plane. As the vectors move from a~ to b~ in an anticlockwise direction, the resultant vector points downward, opposite to the upward direction that would be indicated by b~ × a~.
prove:
when xz= yz then x=y if z is not equal to zero
A flower vase, in the form of a hexagonal prism, is to be filled with 512 cubic inches of water. Find the height of the water if the wet portion of the flower vase and its volume are numerically equal.
Height of water in hexagonal prism vase = 384 inches, given equal volume of water and wet portion.
Let's denote the height of the water in the vase as [tex]\( h \)[/tex] inches.
The volume of a hexagonal prism can be calculated using the formula:
[tex]\[ V = \frac{3\sqrt{3}}{2}a^2h \][/tex]
where [tex]\( a \)[/tex] is the length of one side of the hexagon (which represents the base of the prism), and [tex]\( h \)[/tex] is the height of the prism.
Since the base of the vase is a hexagon, we need to find the side length of this hexagon.
The area of a regular hexagon can be calculated using the formula:
[tex]\[ A = \frac{3\sqrt{3}}{2}a^2 \][/tex]
Given that the volume of water in the vase is 512 cubic inches, and the wet portion's volume and its height are equal, we have:
[tex]\[ 512 = \frac{3\sqrt{3}}{2}a^2h \][/tex]
We are also given that the wet portion's volume is numerically equal to its height, so:
[tex]\[ h = 512 \][/tex]
Substituting this value of [tex]\( h \)[/tex] into the volume equation, we have:
[tex]\[ 512 = \frac{3\sqrt{3}}{2}a^2(512) \][/tex]
Now, we can solve for [tex]\( a \).[/tex]
[tex]\[ a^2 = \frac{512}{\frac{3\sqrt{3}}{2} \times 512} \]\[ a^2 = \frac{512}{\frac{3\sqrt{3}}{2} \times 512} \]\[ a^2 = \frac{2}{3\sqrt{3}} \]\[ a^2 = \frac{2\sqrt{3}}{9} \]\[ a = \sqrt{\frac{2\sqrt{3}}{9}} \]\[ a = \frac{\sqrt{2\sqrt{3}}}{3} \][/tex]
Now, let's find the height of the water by substituting the value of [tex]\( a \)[/tex]into the volume equation:
[tex]\[ 512 = \frac{3\sqrt{3}}{2}\left(\frac{\sqrt{2\sqrt{3}}}{3}\right)^2h \]\[ 512 = \frac{3\sqrt{3}}{2}\left(\frac{2\sqrt{3}}{9}\right)h \]\[ 512 = \frac{3\sqrt{3}}{2}\left(\frac{2\sqrt{3}}{9}\right)h \]\[ 512 = \frac{4}{3}h \]\[ h = \frac{512 \times 3}{4} \]\[ h = 384 \][/tex]
So, the height of the water in the vase is 384 inches.
Find the solution to the equations.
3x - y = -4
x + y = 0
(0, 0)
(-1, 1)
(1, -1)
which of the following is a Pythagorean triple?
A. 3,4,6
B.7,25,26
C.15,21,25
D.9,40,41
the population of a bacteria culture doubles in number every 12 minutes. the ratio of the number of bacteria at the end of 1 hour to the number of bacteria at the beginning of the hour is? ...?
Answer:
32
Step-by-step explanation:
Let X be the number of bacteria at the initial time.
At 12 minutes = 2 X
At 24 minutes = 4X
At 36 minutes = 8X
At 48 minutes = 16X
At 60 minutes = 32X
The ratio between the final and the initial instant will be: 32X / X = 32
the temperature was 8 below zero in the morning and dropped 12 degrees during the afternoon. what was the temperature late in the afternoon
The temperature was -20 in the afternoon.
What are arithmetical operations?The arithmetic operators are addition, subtraction, multiplication and division. The arithmetic operators are applied between two or more numbers or quantities.
Given that, the temperature was 8 below zero in the morning and dropped 12 degrees during the afternoon.
We need to find the temperature late in the afternoon.
We know,
8 below zero is -8 degrees.
Now it is saying that the temperature dropped by 12 degrees,
Therefore,
-8 -12
-8 + (-12) = -20
Hence the temperature was -20 in the afternoon.
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Two groups of students were asked how far they lived from their school. The table below shows the distances in miles:
Group A (distance in miles)1 1.589.26.84.54.82.50.76
Group B (distance in miles)22.53.231.31.82.431.51.8
Which statement best compares the mean distances for the two groups?
A. It is equal for Group A and Group B.
B. It is greater for Group B than Group A.
C. Its value for group A is double the value for Group B.
D. Its value for group B is three times the value for Group A.
One pipe can fill a swimming pool in 8 hours. Another pipe takes 12 hours. How long will it take to fill the pool if both pipes are used simultaneously?
£1800 is invested at4% compound interest per year.
How many years will it take for the investment to be worth £2000?
what is an acrostic poem for the word triangle?
Final answer:
An acrostic poem for the word 'triangle' is a creative way to convey various attributes of the geometric shape or to create a poem with each line starting with the corresponding letter. The poem can be directly related to the properties of a triangle or more abstract.
Explanation:
An acrostic poem uses the first letter of each line to spell out a word vertically. For the word 'triangle', an acrostic poem might be a creative way to describe the characteristics of a triangle, or it could be abstract, using each letter to begin a line that doesn't necessarily relate to the shape but instead creates a coherent poem.
Here is an example of an acrostic poem for the word 'triangle':
Three sides enclosing space,
Reminder of structure and base,
In geometry, an essential grace,
Angles acute, obtuse, or right,
Nestled within, points of light,
Guiding principles of design,
Lines intersect by plan divine,
Eternally, three lines combine.
Remember, while writing an acrostic for 'triangle', you may also use the opportunity to incorporate into your poem mnemonics for the relationships between the sides and angles of a right triangle, such as 'SOHCAHTOA', or explore the figurative and metaphorical implications of the shape as referenced in literary examples or the sciences.
A scientist had 3/ 5 liter of solution. He used 7/ 12 of the solution for an experiment.
How many liters of solution did the scientist use for the experiment
simplify 8a+4b-3a+5b
The simplified form of the expression [tex]8a+4b-3a+5b[/tex] is [tex]\boxed{5a+9b}[/tex].
Further explanation:
The given expression is [tex]8a+4b-3a+5b[/tex].
The given expression consists of [tex]2[/tex] different variables [tex]a[/tex] and [tex]b[/tex]. These variables can take any values since, its value is not fixed.
An algebraic expressions are formed if different variables and are added, subtracted, multiplied and divided.
The given expression is obtained when the variable [tex]a[/tex] and variable [tex]b[/tex] is added and subtracted with multiplication with different integers.
In the given expression there are [tex]4[/tex] terms with each term having different coefficients.
Like terms in the given expression are those whose algebraic factors are same that is [tex]8a[/tex] and [tex]-3a[/tex] are like terms and [tex]4b[/tex] and [tex]5b[/tex] are like terms.
The given expression is a binomial since, it have two unlike terms.
To simplify the given expression first we have to identify the like and unlike terms.
The like terms are [tex]8a[/tex] and [tex]-3a[/tex] and other set of like terms are [tex]4b[/tex] and [tex]5b[/tex]
Since, [tex]a[/tex] and [tex]b[/tex] are variable and they are numbers they can be added or subtracted using distributive property.
[tex]8a[/tex] and [tex]-3a[/tex] are subtracted as follows:
[tex]\begin{aligned}8a-3b&=(8\cdot a)-(3\cdot a)\\&=(8-3)\cdot a\\&=5\cdot a\\&=5a\end{aligned}[/tex]
[tex]4b[/tex] and [tex]5b[/tex] are added as follows:
[tex]\begin{aligned}4b+5b&=(4\cdot b)+(5\cdot b)\\&=(4+5)\cdot b\\&=9\cdot b\\&=9b\end{aligned}[/tex]
Therefore, simplified form of the given expression is [tex]5a+9b[/tex] since both are positive terms.
Thus, the simplified form of the expression [tex]8a+4b-3a+5b[/tex] is [tex]\boxed{5a+9b}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Algebraic expressions
Keywords: Simplify, 8a+4b-3a+5b, expression, 5a+9b, terms, coefficients, like, unlike, addition, subtraction, variables, values, distributive property, like terms, unlike terms.
Need help ASAP
Will upvote!
I think it's A but i'm not sure
Lines A and B are represented by the equations given below:
Line A: x + 2y = 3
Line B: x + y = 3
Which statement is true about the solution to the set of equations?
There are infinitely many solutions.
There are two solutions.
There is one solution.
There is no solution.
What are the zeros of the polynomial function: f(x) = x3 + x2 – 6x ? ...?
-----
0.66 = 6/10
66/100
2/3
Ahmed is taking orders for lunch. A slice of pizza cost $2 and a chicken sandwich costs $3. He collects $24 for the group of 10 people.How many people ordered a chicken sandwich?
1.5x+2.5y=21.50
x+y=9
8 people ordered chicken sandwich
What is the vertex of the absolute value function defined by ƒ(x) = |x - 7| + 1?
(7,1)
(-7,-1)
(-7,1)
(7,-1)
Answer: [ 7,1 ]
Step-by-step explanation:
this is the answer on odyssey ware.
A homemade lip balm consists of coconut oil and beeswax. Coconut oil costs $0.50 per ounce and beeswax costs $2.00 per ounce. If 6 ounces of coconut oil and 5 ounces of beeswax are used to create the lip balm mixture, which values represent a and b in the table?
what does a and b equal
a = $
b = $
Let
a--------> the total cost in dollars of [tex]6[/tex] ounces of coconut oil
b--------> the total cost in dollars of [tex]5[/tex] ounces of beeswax
we know that
[tex]a=0.50 \frac{\$}{ounce}*6=\$3[/tex]
[tex]b=2.00 \frac{\$}{ounce}*5=\$10[/tex]
therefore
the answer is
the total cost in dollars of [tex]6[/tex] ounces of coconut oil is [tex]a=\$3[/tex]
the total cost in dollars of [tex]5[/tex] ounces ofbeeswax is [tex]b=\$10[/tex]
For the function f(x)=x+5, what is the ordered pair for the point on the graph when x=4w?
Answer:
(4w, 4w + 5)
Step-by-step explanation:
Identify the converse of the following conditional:
If a point is in the fourth quadrant, then its coordinates are negative.
A. If a point is in the fourth quadrant, then its coordinates are negative.
B. If the coordinates of a point are not negative, then the point is not in the fourth quadrant.
C. If a point is not in the fourth quadrant, then the coordinates of the point are not negative.
D. If the coordinates of a point are negative, then the point is in the fourth quadrant.
Six different written driving tests are administered by the Motor Vehicle Department. One of these six tests is selected at random for each applicant for a driver's license. A group consisting of two women and three men apply for a license. (Round your answers to three decimal places.)
(a) What is the probability that exactly two of the five will take the same test?
(b) What is the probability that the two women will take the same test?
To find the probability that exactly two of the five will take the same test, we use combinations. The probability is 2/3 or 0.667. To find the probability that the two women will take the same test, we use combinations. The probability is 1/2 or 0.500.
To find the probability that exactly two of the five will take the same test, we can use the concept of combinations. There are six different tests, and we need to choose two of them to be taken by two people. The total number of ways to select two tests out of six is given by the combination formula C(6,2) = 6!/(2!(6-2)!) = 15. Now, for each of these two selected tests, there are two people (either two men or two women) who can take the test, resulting in a total of two possibilities. Therefore, the number of favorable outcomes is 2 * 15 = 30. Finally, the probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes, which is 6!/(2!3!) = 15. So the probability is 30/15 = 2/3 or 0.667 (rounded to three decimal places).
To find the probability that the two women will take the same test, we can use similar reasoning. There are six different tests, and we need to choose one of them to be taken by both women. The total number of ways to choose one test out of six is given by the combination formula C(6,1) = 6!/1!(6-1)! = 6. Now, for the chosen test, there are three possible ways both women can take it, since they can be the first two applicants, the last two applicants, or the middle two applicants. Therefore, the number of favorable outcomes is 3. The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes, which is also 6. So the probability is 3/6 = 1/2 or 0.500 (rounded to three decimal places).
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Final answer:
The probability that exactly two of the five will take the same test is 0.00463. The probability that the two women will take the same test is 1.167.
Explanation:
To find the probability that exactly two of the five will take the same test, we can use combinations. There are 6 different tests and we want to select 2 of them for the same test. Since order doesn't matter, we can use combinations. The number of ways to choose 2 tests out of 6 is 6 choose 2 = 15.
Now, for each pair of tests, we have 5 people who can take those tests. The probability that exactly 2 of the five will take the same test is the probability that exactly 2 people are randomly assigned to the same test out of the 5 people. The total number of possible outcomes is 6^5 since each person has 6 choices for which test to take, and there are 5 people.
So, the probability that exactly two of the five will take the same test is 15/6^5, which is approximately 0.00463.
To find the probability that the two women will take the same test, we consider the different possibilities. The two women can take the same test out of the 6 tests, or they can take different tests.
If they take the same test, there are 5 possible tests for them to choose from. The probability of this happening is 5/6.
If they take different tests, there are 5 possible tests for each of them to choose from. The probability of this happening is (5/6) * (4/5) = 2/3.
Therefore, the probability that the two women will take the same test is (5/6) + (2/3) = 7/6, which is approximately 1.167.
Jarek buys jerseys for his team online. He pays a constant shipping price plus a special rate for each jersey. During the spring season, Jarek paid $151 for 24 jerseys. In the summer season, he paid $79 for 12 jerseys. What is the special rate Jarek pays for each jersey and how much does he pay for shipping?
Thanks to anyone who can help!
Henry wanted to make two bakery items. One recipe called for 1 1/4 cup of sugar and the other for 2/3 cup of sugar. How much sugar does he need?
A. 1 11/12
B. 1 1/12
C. 1 3/7
D. 1 1/4
15 percent of 45.4 is what?
Which represents the inverse of the function f(x) = 4x? a) h(x) = x + 4 b) h(x) = x – 4 c) h(x) = x d) h(x) = x witch is right
The table shows the total number of hamburgers and hot dogs sold at a food stand at a local fair on two separate days. It also shows the dollar amount taken in each day.
Hamburgers Hot Dogs Total
Day 1 200 150 $1,450
Day 2 200 250 $1,750
What is the cost of a hamburger and the cost of a hot dog?
Enter your answers in the boxes.
Hamburger: $
Hot dog: $
x + 2 > -8
a. x > -6
b. x > -10
c. x <-10
d. x < -6
Which point satisfies the equation 2x+3y=8? A) (-1,3) B) (2,2) C) (-2,4) D) (1,4)
The point that satisfies the equation 2x+3y=8 is (1,4).
Explanation:To find the point that satisfies the equation 2x + 3y = 8, we can substitute the x and y values from each option into the equation and see which option makes the equation true.
Let's try option A, (-1,3): 2(-1) + 3(3) = -2 + 9 = 7, which is not equal to 8.
Continuing this process for options B, C, and D, we find that the point (1,4) satisfies the equation 2x + 3y = 8.
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ABCD ~ WXYZ. AD=12, DC=3 AND WZ=35. FIND YZ.
THE FIGURES ARE NOT DRAWN TO SCALE.
The unknown length YZ can be found through the ratios of corresponding sides in similar figures ABCD and WXYZ. Given AD=12, DC=3, WZ=35, the equation 3/YZ = 12/35 is formed. Solving for YZ, we find that YZ is 8.75.
Explanation:In the given question, ABCD and WXYZ are similar figures which mean the ratio of corresponding sides are equal. So, the ratio AD/WZ equals to the ratio DC/YZ. Given, AD=12, DC=3 and WZ=35. The length of YZ can be found by cross multiplying these ratios.
So, DC/YZ = AD/WZ.
By substituting the given values:
3/YZ = 12/35.
To find YZ, we simply cross-multiply and solve for YZ:
3 × 35 = 12 × YZ,
Hence, YZ = (3 × 35) / 12, which is 8.75 units.
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What is an equivalent decimal for 29/30?