The angle between a diagonal of a cube and an adjacent edge is 54.75°;
Assuming the length of a side of the cube as 1 unit, the three sides are given by the vectors;
a = (1, 0, 0)
b = (0, 1, 0)
c = (0, 0, 1)
The diagonal is given by the vector, v = (1, 1, 1)
The angle between the diagonal and one edge of the cube is given by
cos θ = v. a / |v|.|a|
v. a = (1, 1, 1).(1, 0, 0)
= 1(1) + 1(0) + 1(0
= 1 + 0 + 0
v. a = 1
Magnitude of vector V = √[(1)² + (1)² + (1)²]
|v| = √3
Similarly, |a| = √1;
So, |v|.|a| = √3.√1 = √3
Now, cos θ = 1/√3
So, θ = cos¹(1/√3)
θ = 54.75°
Therefore, the required angle is 54.75°.
To learn more about this; visit: https://brainly.com/question/1423361
#SPJ4
give the inverse, contrapositive, and converse for each of the following state- ments: (a) if she finished her homework, then she went to the party. (b) if he trained for the race, then he finished the race. (c) if the patient took the medicine, then she had side effects. 3
The inverse of (a) is If she did not go to the party, then she will not finish her homework.
The inverse of (b) is If he did not finish the race, then he will not have trained for the race.
The inverse of (c) is If she has no side effects then the patient will not take the medicine.
The converse of (a) is if she finished her homework, then she went to the party.
The converse of (b) is if he trained for the race, then he finished the race.
The converse of (c) is if the patient took the medicine, then she had side effects.
The contrapositive of (a) is if she did not finish her homework, then she did not go to the party.
The contrapositive of (b) is if he did not train for the race, then he will not finish the race.
The contrapositive of (c) is if the patient did not take the medicine, then she will not have side effects.
What do you mean by Inverse, Contrapositive, and Converse?Converse: By swapping the hypothesis and the conclusion, a statement can be made to mean the converse. "If two lines don't intersect, then they are parallel" is the inverse of "If two lines overlap, then they are parallel."
Inverse: Each of the original statements is presupposed to be false in an inverted statement. "If it is not snowing" would be the polar opposite of "If it is snowing." "Then it is not chilly" would be the polar opposite of "then it is cold."
Contrapositive: a statement or theorem created by swapping out the hypothesis and conclusion, or the subject and predicate, of a given statement or theorem. The opposite of "if A then B" is "if not-B then not-A."
To learn more about Contrapositive, Inverse, and Converse, Visit:
https://brainly.com/question/1713053
#SPJ4
Suppose your cable company charges its customers $4 to rent a movie. An online membership costs $21 and members pay only $2.50 to rent a movie. For what number of movies is the cost the same?
The number of movies that will give same cost is 14 movies.
How to calculate the number of movies?From the information, the cable company charges its customers $4 to rent a movie and an online membership costs $21 and members pay only $2.50 to rent a movie.
Let the number of movies for same cost be represented by x. This will be:
(4 × x) = 21 + (2.50x)
4x = 21 + 2.50x
Collect like terms
4x - 2.50x = 21
1.50x = 21
Divide
x = 21/1.5
x = 14
The number of movies will be 14
Learn more about expressions on:
brainly.com/question/22048677
#SPJ1
Part A
Fill in the blank question.
SHIPPING The U.S. Department of Commerce regulates how much the actual weight of a package can vary from its labeled weight. A package with a labeled weight of 9.4 pounds can have an actual weight that is plus or minus 0.22 pound.
Part A
Write an absolute value equation to represent the maximum and minimum acceptable weights of the package. Let x be the actual weight of the package.
The simplified value of the maximum weight is 9.62 and the minimum weight is 9.18. Also the function for the maximum and minimum weight is y + x and y - x
Here,
Given that, A package with a labeled weight of 9.4 pounds can have an actual weight plus or minus 0.22 pounds.
Let the weight labeled be y and the actual weight be x
Weight = y ± x
Maximum weight = y + x
Minimum weight = y - x
Weight = 9.4 ± 0.22
Now,
Maximum weight = 9.4 + 0.22 = 9.62 pounds
Minimum weight = 9.4 - 0.22 = 9.18 pounds
Thus, the simplified value of the maximum weight is 9.62 and the minimum weight is 9.18. Also, the function for the maximum and minimum weight is y + x and y - x
Learn more about algebraic expression here:
https://brainly.com/question/953809
#SPJ1
The Spartan basketball team purchased equipment and uniforms for a total cost of $1,860. The equipment that was purchased cost $300, and the uniforms were $120 each. How many uniforms did the school purchase?
The number of uniforms the Spartan Basketball team purchased was 13.
How is the number of uniforms determined?The number of uniforms bought by the Spartan Basketball team can be determined using the mathematical operations of subtraction and division.
In the first place, the cost of equipment is subtracted from the total cost. The remainder is divided by the unit cost of uniforms. The quotient is the number of uniforms bought.
Data and Calculations:Total cost incurred = $1,860
Cost of equipment = $300
Remainder cost = $1,560 ($1,860 - $300)
Unit cost per uniform = $120
The number of uniforms bought = 13 ($1,560/$120)
Thus, the number of uniforms the Spartan basketball team purchased was 13.
Learn more about mathematical operations at https://brainly.com/question/20628271
#SPJ1
I need help please help me if u can
here is the answer
Step-by-step explanation:
it is just changing decimals to normal numbers.
can you help me and solve it
Answer:
I think its $4 I'm not sure tho
Step-by-step explanation:
Answer:
[tex] \large{ \star{ \boxed{ \tt \: answer : \: \$ \: 3.28 }}}[/tex]
Please see the attached picture for full solution!:)
-------- HappY LearninG <3 ----
proof that the span of two noncollinear vectors is the plane containing the origin and the heads of the vectors.
The Span of two noncollinear vectors is the plane containing the origin and the heads of the vectors.
Linear Span of vectors can be represented as
let [tex]x_{1} and x_{2}[/tex] be two non collinear vectors its span be written as [tex]x=a_{1} x_{1} +a_{2} x_{2}[/tex] where [tex]a_{1}, a_{2}[/tex] are arbitrary scalars.
Subspace of vectors : a subset A of a vector space V is called a subspace of V if A is itself a vector space under scalar multiplication and addition defined on V.
The Span of two vectors is a vector space containing two vectors. Hence the span is also a vector space . It is sufficient to notice that any two independent vectors from subspace can be the basis.
Zero vector is the linear combination of these basis vector.
hence it is not possible to have a span of two non collinear vectors that does not contain origin .
Therefore, The span of two noncollinear vectors is the plane containing the origin and the heads of the vectors.
Learn more about Vector Space here https://brainly.com/question/14575871
#SPJ4
10. Before a race, you start 4 5/8 behind your friend. At the halfway point, you are 3 2/3 ahead your friend. What is the change in distance between you and your friend from the beginning of the race?
The change in distance between you and your friend from the beginning of the race is 8 7/24.
How to calculate the value?It should be noted that before the race, you start 4 5/8 behind your friend and at the halfway point, you are 3 2/3 ahead your friend.
Therefore, the change in distance will be the addition of the fractions given.
= 4 5/8 + 3 2/3
= 4 15/24 + 3 16/24
= 7 31/24
= 8 7/24
Therefore, the change in distance between you and your friend from the beginning of the race is 8 7/24.
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
Help needed with geometry.
Answer:
d
Step-by-step explanation:
Answer: d
Terry used a total of 52 inches of ribbon to make 6 decorations. He used the same amount of ribbon for each decoration. How much ribbon did Terry use for each decoration?
Answer:52 x 6=312
Step-by-step explanation:
Terry used 52 inches of ribbon for the same amount. He's multiplying. Hope this helped.
What is the equation of the line?
Answer:
y=-1/3x
Step-by-step explanation:
The line decreasing from left to right. So, the slope of the line is a negative number. The only answer choice that has a negative number for the slope is A. y=-1/3x.
Hope this helps!
Please mark as brainliest if correct!
Answer:
y = 3x
Step-by-step explanation:
To find the equation of a graphed line, find the y-intercept and the slope in order to write the equation in y-intercept (y=mx+b) form. Slope is the change in y over the change in x.
Complete the equation describing how x and y are related.
X 0,1,2,3,4
y -1,3,7,11,15
y = [? ]x + []
Answer:
y = 4 x - 1
Step-by-step explanation:
hope this helps you.
.......
Answer:
.
Step-by-step explanation:
In an arithmetic sequence, if you are given a3=93 and a5=135, find a=100. Must show work to receive full credit.
The 100th term of the sequence is 2130.
How to calculate the value?a3 = a + 2d = 93
a5 = a + 4d = 135
Compute both equations
(4d - 2d) = (135 - 93)
2d = 42
d = 42/2 = 21
a + 2d = 93
a + 2(21) = 93
a + 42 = 93
a = 94 - 42 = 51
100th term will be:
= a + 99d
= 51 + 99(21)
= 51 + 2079
= 2130
Learn more about sequence on:
brainly.com/question/6561461
#SPJ1
A veterinarian is investigating a new type of tick repellant to determine if it reduces the number of ticks on dogs compared to a current popular brand.
Part A: Which of the following design is most appropriate: observational study, experiment, census, or sample survey? Explain your reasoning.
Part B: Explain how you would implement the design you selected in Part A.
Part C: Explain one benefit your design would provide.
The most appropriate design is an experiment (A), this can be applied by having a control and an experimental group (B), and one benefit is that you can identify the effectiveness (C).
Why is the best design an experiment?Different from an observational study, a census or a survey that are used to collect information about people's preferences, an experiment allows you to test the effectiveness of a treatment, which is the main purpose in this case.
How to implement it?The bst is to have a control and an experiment group. For example you select 30 dogs and use the repelant in 15 dogs; then all dogs are exposed to ticks. As a result you can evaluate how effective the repelant is by comparing the two groups.
What benefit will this design provide?You can directly compare the two groups and determine the effectiveness of the repelant.The experiment can be replicated or repeated.Learn more about experiments in: https://brainly.com/question/11256472
#SPJ1
there is a dart that lands uniformly randomly in space on a dartboard. the dartboard is 3 concentric circles with radius 1, 2, and 3
There are 160 possibilities for area codes
We are required to find all the combinations for different area codes
It is given to us that the conditions for the tree digit area code are:
first digit could be any number from 4 through 8,
the second digit was either 4 5 6 or 7, and the third digit could be any number except 2 or 7
Using the conditions above, the digits which can be first digit of code = 4 through 8 =4,5,6,7,8
the digits which can be second digit of code= 4,5,6,7
the digits which can be third digit of code = 0,1,3,4,5,6,8,9
number of possibilities for first digit= 5
number of possibilities for second digit=4
number of possibilities for third digit= 8
Therefore, total number of possibilities of code = number of possibilities of first digit x number of possibilities of second digit x number of possibilities of third digit = 5 x 4 x 8=160
Therefore, there are 160 possibilities for area codes
For further reference:
https://brainly.com/question/17161931?referrer=searchResults
#SPJ9
2-124. Troy is a fan of baseball, and his favorite player is Moe Jauer of the Minnesota Triplets. Troy made a table displaying how many home runs Jauer hit during his first five seasons. Graph Troy’s data.
The scatter plot showing Troy's data is given at the end of the answer.
What is a scatter plot, and why it is used in this problem?A scatter plot shows a series of points (x,y), relating the input x to the output y.
For this problem, it is used because we want to graph a discrete function, as:
The input x is the professional year of the baseball player. The output y is the number of home runs hit by the player in the year.Both professional year and home runs are countable amounts, that cannot assume decimal values, hence we have a discrete function and use a scatter plot.
From the table presented in this problem, the points for the scatter plot are given as follows:
(1,6), (2,9), (3,13), (4,7), (5,9).
The scatter plot, labeled and with the points, is shown by the graph at the end of the answer.
More can be learned about scatter plots at https://brainly.com/question/6592115
#SPJ1
Please help me please
Answer:
A
Step-by-step explanation:
the big triangle is a bigger version of the smaller triangle, so it had to be a dilation.
Dilations of images are also similar, not congruent, so the answer is A.
Phaedrus claims that this graph shows a straight
line. Is he correct? Explain why or why not.
Answer:yes
Step-by-step explanation:
Ria has these two cubes.
The side length of the smaller cube is x cm.
The side length of the larger cube is twice the side length of the
smaller cube.
Write an expression for the side length of the larger cube in
terms of x.
Answer:
2x
Step-by-step explanation:
side length of smaller cube = x
side length of larger cube is two times the side length of smaller cube.
Therefore side length of larger cube = 2x
Express 2^40 × 4^30 in the form 2^n
Answer:
[tex]2^{100}[/tex]
Step-by-step explanation:
Given expression:
[tex]2^{40} \times 4^{30}[/tex]
Rewrite 4 as 2²:
[tex]\implies 2^{40} \times (2^2)^{30}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 2^{40} \times 2^{(2\times30)}[/tex]
[tex]\implies 2^{40} \times 2^{60}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies 2^{(40+60)}[/tex]
[tex]\implies 2^{100}[/tex]
Therefore, n = 100.
4+801542/85*994567789
Answer:9,378,727,447,079.929
Step-by-step explanation:
Answer:
9.37414075 13 squared digit I don’t remember what it is called for that number so yea
Step-by-step explanation:
8011542/84 is 94257.43529 (already added 4) and 94257.43529 is about 9.37414075 13 squared digit I don’t remember what it is called for that number but that is the answer
what the answer to
1 4/5 x 5/6
Answer:
7/3
Step-by-step explanation:
14/5×5/6
=14/6
=7/3
Xio just took a math test with 25 questions, each worth an equal
number of points.
The test is worth 100 points total. If a score of 70
points earns a grade of C, how many questions would Xio need to get
right to get a grade a of C on the test?
solve this please and thank you
Answer:
b 45
Step-by-step explanation:
its b ur welcome parallel
Answer:
Its 6x6
Step-by-step explanation:
because you have to count going up and over
Complete the explanation to identify the set of numbers that best describes the situation.
the amount of water in a glass as it evaporates
The amount can be any
number less than 0
, thus it is a
rational
number.
ms. wilson draws a model of the factorization of a polynomial with integer factors. her model is partially complete. which equation is represented by ms. wilson’s model? n2 3n 40
n²+13n+40,
This is why;
Observe only the right side. The number is (n+8)(n+5).
Let's elaborate on that using FOIL.
F = When we multiply the first two terms, n and n, we obtain n².
O = outer instructs us to multiply n by 5 to get n*5 or 5n from the outer terms.
I = inner instructs us to multiply the inner expressions 8 by 8 and n by n to obtain 8n.
Since 8 and 5 are multiplied by L, we obtain 8*5 = 40.
Add up the outcomes: n²+5n+8n+40 = n²+13n+40
Observe how the phrase is a little bit simplified by the combination of the like terms (5n and 8n).
This demonstrates how (n+8)(n+5) becomes n²+13n+40, becoming the correct response. For all values of n, none of the other options are valid equations;
To learn more about this, visit: https://brainly.com/question/2400307
#SPJ4
Mr. Sowers wants to purchase expo markers for his classroom. He has a budget of $35. A four-pack of markers costs $5.49, including tax. Write and solve an inequality, using x for the variable, to solve for the number of packs of markers Mr. Sowers can purchase.
Answer:
5.49x=35
Step-by-step explanation:
the x is the number of markers
Dan earns £9.20 per hour. How much will he earn for 8 hours work?
Answer:
£73.6
Step-by-step explanation:
Earnings per hour ( means for one hour of work he earns)= £9.20
total no of hours he works for = 8
so,in 8 hours he will earn
9.20× 8=£73.6
Given the following, what is the length, l?
V = lwh
V = 576, w = 6, h = 12
The value of l is. We use simple substitution of values to find the value of l is 48.
We have been given the equation V=lwh where l is the length, we can say that the given equation is that of volume of a cuboid where l is the length, w is the width and h is the height of the cuboid. We know the values of V,w and h. We have to substitute the values of V,w and h in the equation V=lwh inorder to find the value of l. Substitution method is generally used for solving system of equations where we first solve the value of one variable and then substitute the value in the other equation to find the value of the other variable. Since we only have one equation and we know the value of 3 of the 4 variables we only have to solve for one.
V=lwh
l=V/wh =[tex]\frac{576}{6.12} =\frac{576}{72}[/tex]= 48
Thus we get the value of l to be 48 by substituting the values of V,w and h.
Learn more about substitution method from here:
https://brainly.com/question/22340165
#SPJ9
what is the monthly difference in median income for a male versus a female when both have a bachelor's degree
Answer: $1,372
Step-by-step explanation:
If using the Labor Statistics Document
A men’s median weekly earning with Bachelor’s degree only is $1,384 * 4 weeks = $5,536
A women’s medium weekly earning with a Bachelor’s degree only is $1,041 * 4 weeks = $4,164
Subtract $5,536 - $4,164 = $1,372
The full sentences are:
The typical monthly salary for women with bachelor's degrees is $3,020.
The typical annual salary for a guy with an associate's degree is $36,432.
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Every month has four weeks.
The median monthly income is thus:
Earnings = 4 * $755
Earnings = $3020
As a result, the typical monthly salary for women with bachelor's degrees is $3,020.
The median annual income:
A man with an associate's degree makes $759 each week.
A month has four weeks, while a year has twelve months.
Hence, the annual median income is:
Earnings = 4 x 12 x $759
Earnings = $36,432
Thus, the typical annual salary for a guy with an associate's degree is $36,432.
Learn more about Mean here:
https://brainly.com/question/521501
#SPJ5
Complete question:
3. What is your monthly median income if you are a female with a bachelor's degree? _____
4. What is your yearly median income if you are a male with an associates degree? _____