Answer:
Step-by-step explanation:
Hello,
What other numbers are of this form have exactly four factors?
[tex]8=2^3\text{ has 4 factors } 1, 2, 2^2, 2^3\\\\\text{For any prime p, }p^3\text{ has 4 factors } 1, p, p^2, p^3\\\\[/tex]
Do all the perfect cubes have exactly four factors?
[tex]\text{If p is not prime, then it is not true anymore} \\ \\\text{For instance, }8^3\text{ has more than 4 factors } 1, 2^2, 2^3, 2^4, etc..[/tex]
Is it true that all numbers that have exactly four factors are perfect cubes?
6 has 4 factors : 1, 2, 3, 6 but this is not a perfect cube.
Thank you.
We know that any number can be decomposed as a product of prime numbers.
For example:
[tex]8 = 1\cdot 2\cdot 2\cdot 2[/tex]
8 has four factors if we count the 1.
Now we need to answer some questions regarding this:
What other numbers are of this form have exactly four factors?
8 is a cube number.
Remember that all cube numbers X can be written as:
[tex]X = n\cdot n\cdot n \cdot 1[/tex]
Now, if n is prime, then we can say that X is of the form of 8 and also has 4 factors.
But let's see the case:
[tex]8\cdot 8\cdot8= 512[/tex]
512 is a perfect cube, and if we decompose it we get:
[tex]512 = 8\cdot 8\cdot 8 = (2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)\cdot 1[/tex]
So we found a perfect cube that has 10 factors.
This means that not all perfect cubes have exactly 4 factors.
Now, all numbers that have exactly four factors are perfect cubes?
This is also false, just let's create a counterexample.
[tex]1\cdot 2\cdot 3\cdot 5 = 30[/tex]
the number 30 is not a perfect cube, and we can see that it has exactly 4 factors.
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Point C is the midpoint of a segment AB . What are the coordinates of point B, if: A(–1, 3), C( 1, –1)
Answer:
(3,-5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates together and divide by 2
The x coordinate is
(x1+x2)/2
We know one point and the midpoint
( -1+x)/2 = 1
Multiply by 2
-1 +x = 2
Add 1
x =2+1
x=3
To find the y coordinate of the midpoint, add the y coordinates together and divide by 2
The y coordinate is
(y1+y2)/2
We know one point and the midpoint
(3+y)/2 = -1
Multiply by 2
3+y = -2
Subtract 3
y = -2-3
y =-5
The other endpoint is (3,-5)
Answer:
B(3, -5)
Step-by-step explantion
We know that these formulas can be used to find the mid point between 2 points on a graph
[tex]\frac{a_{1} +b_{1}}{2}= c_{1}\\ \frac{a_{2} +b_{2}}{2} =c_{2}[/tex]
Now we plot these points in
A(-1, 3), C(1, -1)
[tex]\frac{-1+b_{1}}{2} =1 \\\frac{3+b_{2}}{2} =1[/tex]
And we can find that
[tex]b_{1}= 3\\b_{2}=-5[/tex]
Therefore we get the answer of (3, -5)
Hope that helped you with your problem!! :)
which of the folowing has a value that is less than zero.
a.) (-6)2
Answer:
the answer is the letter A
Answer:
A
Step-by-step explanation:
It's A because -6 * 2 equals -12 which is less than zero
Vivian is going to do some yard work, but she needs to leave her house at 1:00 to go to a football game. She is going to mow the lawn for 1 hour and 10 minutesl, trim some bushes for 30 minutes, and put down some mulch for 35 minutes. She will also need 20 minutes to shower and get dressed. What time should she start the work so she will be ready at 1/00 ?
Answer:
10:25
Step-by-step explanation:
mow the lawn 1:10
trim bushes: 0:30
put down mulch: 0:35
shower: 0:20
Total time = 1:10 + 0:30 + 0:35 + 0:20 = 1:95 = 2:35
She needs 2 hours and 35 minutes to do everything.
1:00 p.m. = 13:00
13:00 - 2:35 = 12:60 - 2:35 = 10:25
She should start work at 10:35 a.m.
8. The ratio of cats to dogs in a particular animal shelter is 11:3. If there are 154 total animals in
the shelter, how many of them are dogs?
33 animals at the shelter are dogs.
City planners are designing a new dog park. The park will be a square. The area of the park is the square of the side length: area=2802 feet2. Without using a calculator, what is the area of the dog park? Use polynomial identities to support your answer. (thank you)
Step-by-step explanation:
A = 280² ft²
A = (200 + 80)² ft²
A = [200² + 2(200)(80) + 80²] ft²
A = (40000 + 32000 + 6400) ft²
A = 78400 ft²
The required area of the dog park using polynomial is 6771204 feet².
What is polynomial?Polynomial is an algebraic expression that has more than two terms. In other words, it is a combination of different variables with mathematical operations.
Given that,
The area of the park = square of the side length a = 2802 feet².
To find the area of the park, using polynomial use
Formula of area of square = (a)²
= (2802)²
= (2800 + 2)²
Use formula (a + b)² = a² + b² + 2ab
= (2800)² + (2)² + 2 x 2800 x 2
= 6,760,000 + 4 + 11200
= 6771204 feet²
The required area of the dog park is 6771204 feet².
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the difference of the product of 2 and x, and 9?
Answer:
2-x-9? If that's the question than it would be -x-7, but your question kinda confuses me.
Step-by-step explanation:
I can’t figure out the answer to 4X+14
Answer:
What is the =
Step-by-step explanation:
4x would be 4x4, 16. Then you add 14!
The coefficient of determination in a simple linear regression model is 64%. What is the correlation level between the dependent and independent variables, assuming a negative relationship between them
Answer: -0.64
Step-by-step explanation:
We know that the coefficient of determination in a simple linear regression model is denoted by [tex]r^2[/tex], which gives the proportion of the variance in the dependent variable that is predictable from the independent variable.
Given, the coefficient of determination in a simple linear regression model is 64%.
i.e.
[tex]r^2= 0.64\\\\\Rightarrow\ r=\sqrt{0.64}=\pm 0.64[/tex]
As there is negative relation between the dependent and independent variables.
Then, the correlation coefficient = -0.64
The number 18 is a counterexample for which of the following conditional statements?
Answer:
The number 18 is a counterexample for Option D - If a number is divisible by 2, then it is also divisible by 4.
Step-by-step explanation:
To find : The number 18 is a counterexample for which of the following conditional statements?
Solution :
For a conditional statement to be true then it is true for all cases that satisfy the condition.
A counterexample is given to prove a conditional statement false.
Now, Examine all the conditions
A. If a number is divisible by 2, it is even.
18 is even and divisible by 2 - True
B. If a number is odd, then it is not divisible by 2.
18 is not odd so it is divisible by 2 - True
C. If a number is even, then it ends with 0, 2, 4, 6, or 8.
18 ends with 8 so it is even - True
D. If a number is divisible by 2, then it is also divisible by 4.
18 is divisible by 2 but 18 is not divisible by 4 - False
Therefore, The number 18 is a counterexample for Option D - If a number is divisible by 2, then it is also divisible by 4.
PLEASE HELP AS QUICKLY AS POSSIBLE THANK YOU :)
Answer:
106
Step-by-step explanation:
The area of one of the triangles is 1/2*5*3
The area is 7.5, but there are 2 triangles so the combined area is 15
The area for whole rectangle is 7*(5+3+5)=7*13=91
So the total area is 91+15= 106
which of the following are properties of a trapezoid? Select all that apply
Answer: b, d, e
Trapezoids are quadrilaterals (a shape with four sides) and they have two pairs of sides; one pair are parallel, and the other pair are not.
Picture shown below.
The correct properties of a trapezoid are:
They are quadrilaterals.It has one pair of opposite sides that are parallel.It has one pair of opposite sides that are not parallel.A trapezoid is a quadrilateral, which means it has four sides. One defining property of a trapezoid is that it has one pair of opposite sides that are parallel. This means that these parallel sides never intersect.
Additionally, a trapezoid has another pair of opposite sides that are not parallel, which means they do intersect. Unlike a rectangle or square, a trapezoid does not have all sides congruent.
Lastly, the diagonals of a trapezoid do not necessarily intersect at right angles. The angle formed by the intersection of the diagonals can vary in size. These properties collectively distinguish a trapezoid from other quadrilaterals and make it a unique shape.
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What is the scale factor & what are the x & y values?
Answer:
Scale Factor = 3
x=45
y=75
Step-by-step explanation:
Scale Factor = 60/20 = 3
x=15*3=45
Y=25*3=75
About Integral-Volume of a Sphere. Could you help me,please?
Answer:
check the answer
Step-by-step explanation:
find the answer in the attached file
If eight persons are having dinner together, in how many different ways can three order chicken, four order steak, and one order lobster
Answer:
Total number of ways= 144 ways
Step-by-step explanation:
Number of ways 3 can order chicken
= 3!
= 3*2*1
= 6
Number of ways 4 can order steak
= 4!
= 4*3*2*1
= 24
Number of ways 1 can order lobster
= 1!
= 1
Total number of ways= 24*6*1
Total number of ways= 144 ways
The total number of different ways is 144.
Calculation of the total no of ways:Since If eight persons are having dinner together.And, there is three order chicken, four order steak, and one order lobster
Now
Number of ways 3 can order chicken
= 3!
[tex]= 3\times 2\times 1[/tex]
= 6
Now
Number of ways 4 can order steak
= 4!
[tex]= 4\times 3\times 2\times 1[/tex]
= 24
Now Number of ways 1 can order lobster
= 1!
= 1
So, total should be
[tex]= 24\times 6\times 1[/tex]
= 144 ways
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Course Activity: Relationships Betwee
5 of 16
Question
Mark says that the number 2 is a rational number
because he can write it as the fraction ?
Is Mark correct? Why or why not?
Answer:
yes
Step-by-step explanation:
A rational number is in the form p/q where p and q are both integers and the denominator q is not equal to zero. This means that the set of all real numbers are rational numbers.
Since q can be any integer apart from zero, it means that all integers are rational numbers i.e for q = 1.
Hence 2 which can be written as fraction as 2/1 is a rational number since the denominator (q = 1) is a non zero number
Answer:
Mark is not correct because a fraction is rational only if the numerator and the denominator are both integers.
Step-by-step explanation:
Which expression has a value of 74?
Please help
Answer:
x+5y+2z sry if itss wrong lol
Step-by-step explanation:
Solve the following math problem. Show your work.
My mom gave me 25 cents. I shared 10 cents with my brother. How much money do I have left?
Answer:
15
Step-by-step explanation:
25-10=15
You take out 10 cents and u have 15 left
- + 10.8 is: rational irrational
Answer:
i think it is rational but if u guess u have a 50/50 chance
Step-by-step explanation:
Answer:
Rational
Step-by-step explanation:
I believe the answer is rational because it’s a decimal and goes with the rational category.
help a girl out pls.........
Answer:
Hey there!
The solution is (1, 2) because that is where the lines intersect.
Hope this helps :)
Find all values of in the interval [0, 2π] that satisfy the equation. Enter your answers from smallest to largest. (Enter NONE in any unused answer blanks.) $$ 2\sin^2(x) = 1 $$
Answer:
π/4 and 3π/4Step-by-step explanation:
Given the equation [tex]2\sin^2(x) = 1 \\[/tex], we are to find all the values of x in the interval [0, 2π] that satisfies the equation.
Simplifying the equation:
[tex]2\sin^2(x) = 1 \\\\sin^2x = \frac{1}{2} \\\\[/tex]
Square both sides of the equation;
[tex]\sqrt{sin^2x } = \sqrt{\frac{1}{2} } \\\\sin(x) = \sqrt{0.5}\\ \\sin(x) = 0.7071\\\\x = sin^{-1}0.7071\\\\x \approx 45^0[/tex]
The general formula for sin(x) is x = nπ + (-1)ⁿ∝ where n = 0, 1, 2, 3...
Since ∝ = 45° = π/4.
x = nπ + (-1)ⁿπ/4
when n = 1
x = π + (-1)¹π/4
x = π - π/4
x = 3π/4
Hence the values of x within the given interval are π/4 and 3π/4
Which set of numbers may represent the lengths of the sides of a triangle? (A) {2,5,9} (B) {6,6,7} (C) {6,4,2} (D) {7,8,1}
Answer:
(B) {6,6,7}
Step-by-step explanation:
A criterion to determine if each triplet represents a triangle is the Law of Cosine, which states that:
[tex]a^{2} = b^{2}+c^{2}-2\cdot b \cdot c \cdot \cos \theta[/tex]
Where [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex] are sides of the triangle and [tex]\theta[/tex] is the angle opposite to side [tex]a[/tex]. Now, let is clear the cosine function:
[tex]2\cdot a \cdot b\cdot \cos \theta = b^{2}+c^{2}-a^{2}[/tex]
[tex]\cos \theta = \frac{b^{2}+c^{2}-a^{2}}{2\cdot b \cdot c}[/tex]
Cosine is a bounded function between -1 and 1, a triplet corresponds to a triangle if and only if result is located between upper and lower bounds. Now let is evaluate each triplet:
a) [tex]a = 2[/tex], [tex]b = 5[/tex], [tex]c = 9[/tex]
[tex]\cos \theta =\frac{5^{2}+9^{2}-2^{2}}{2\cdot (5)\cdot (9)}[/tex]
[tex]\cos \theta = 1.133[/tex] (Absurd)
The triplet does not represent a triangle.
b) [tex]a = 6[/tex], [tex]b = 6[/tex], [tex]c = 7[/tex]
[tex]\cos \theta =\frac{6^{2}+7^{2}-6^{2}}{2\cdot (6)\cdot (7)}[/tex]
[tex]\cos \theta = 0.583[/tex] (Reasonable)
The triplet represents a triangle.
c) [tex]a = 6[/tex], [tex]b = 4[/tex], [tex]c = 2[/tex]
[tex]\cos \theta = \frac{4^{2}+2^{2}-6^{2}}{2\cdot (4)\cdot (2)}[/tex]
[tex]\cos \theta = -1[/tex] (Absurd)
The triplet does not represent a triangle, but a straight line.
d) [tex]a = 7[/tex], [tex]b = 8[/tex], [tex]c = 1[/tex]
[tex]\cos \theta = \frac{8^{2}+1^{2}-7^{2}}{2\cdot (8)\cdot (1)}[/tex]
[tex]\cos \theta = 1[/tex] (Absurd)
The triplet does not represent a triangle, but a straight line.
Hence, the correct answer is B.
There are 14 books on a shelf. .5 of them are new. The rest of them are used. What is the ratio of all books on the shelf to used books?
Answer:
9/14
Step-by-step explanation:
A square has an area of 121 square feet. What is the side length of the square
Answer:
11 feet
Step-by-step explanation:
The area of a square is simply the side of the square squared. This can be written as an equation as follows:
A = l^2
where A is the area of the square and l is the length of a side of the square.
Using this, we can find the length of the side.
121 = l^2
sqrt(121) = sqrt (l^2)
11 = l
Hence, the side length of the square is 11 feet.
Cheers.
Answer:
11
Step-by-step explanation:
[tex]Area = s^2[/tex]
s = side
[tex]A =121\\121 = s^2\\Square\:root\:both\:sides\:of\:the\:equation\\\sqrt{121}=\sqrt{x^2} \\\\11 =x\\x=11[/tex]
The graph shows the solution to a system of equations. What is that solution?
Answer:
(-2,2)
Step-by-step explanation:
Usually in these types of questions, the solution is the intersection point between the two equations. These two lines intersect at what looks like the point (-2,2) so that is the solution.
Hope this helped!
I have 30 ones 2 thousands,4 hundred thousands 60 tens, and 100 hundreds
Answer:
52630
Step-by-step explanation:
Simplify into numbers.
30 + 2000 + 40000 + 600 + 10000
Add.
52630
A movie rental company offers a membership plan that costs $10/month and charges $2 to rent each movie.How many movies can a member rent in one month and spend at most $24
Answer:
7 movies
Step-by-step explanation:
Given
membership cost for 1 month = $10
rent for 1 movie = $2
Maximum money to be spent by a member = $24
Let the no. of movie rented by x
Thus, total rent for x movies = x* rent for 1 movie = x*$2 = $2x
Total spending for 1 month = membership cost for 1 month + total rent for x movies
Total spending for 1 month = 10 +2x
Given that he can spend at most $24
Total spending for 1 month <= 24
10 + 2x <= 24
2x <= 24-10
2x <= 14
x <= 14/2
x <= 7
Thus, movies rented can be less than or equal to 7.
since we have to find the maximum movies rented in 23, it will be 7
Thus, at most 7 movies can be rented.
Match the input values on the left with the output values on the right. y = x/2 + 1
1)3 X
2)Y 2
3)2 4
4)4.5 7
5)5.5 9
Answer:
x, y
2, 2
4, 3
7, 4.5
9, 5.5
Step-by-step explanation:
matching input / output values.
insert each values into the equation.
1. x y = (x)/2 + 1
2. 2 y = (2)/2 + 1 y = 2
3. 4 y = (4)/2 + 1 y = 3
4. 7 y = (7)/2 + 1 y = 4.5
5. 9 y = (9)/2 + 1 y = 5.5
therefore,
x, y
2, 2
4, 3
7, 4.5
9, 5.5
i hope the above solution is what you are lookin'
This exercise examines the accuracy of various branch predictors for the following repeating pattern (e.g., in a loop) of branch outcomes: T, NT, T, T, NT.
a. What is the accuracy of always-taken and always-not-taken predictors for this sequence of branch outcomes?
b. What is the accuracy of the 2-bit predictor for the first four branches in this pattern, assuming that the predictor starts off in the bottom left state (predict not taken)?
c. What is the accuracy of the 2-bit predictor if this pattern is repeated forever?
Answer:
attached below is the missing part of the question and the solution
A) 60%, 40%
B) 25%
C) 60%
Step-by-step explanation:
a) The accuracy of always-taken for this sequence of branch outcomes = 60%
The accuracy of always -not-taken for this sequence of branch outcomes = 40%
b) The accuracy of the 2-bit predictor for the first four branches assuming that the predictor starts off in the bottom left state = 25%
C)the accuracy of the 2-bit predictor if this pattern is repeated forever = 60% ( was stopped after the fourth iteration because the fourth and third iterations are the same) =
Part C
Kelvin wants to know whether his father, Arnold, skied three times as long without falling as anyone else in the family did. He can check using the
inequality 3w < 356, where w is the time in seconds that each person skied. Plug the values for the time skied by each person into the inequality to
find the answer
B
I
u
X
Font Sizes
A- A - E 3 E 3
Person
Time Skied Plugged into True or False?
(seconds) 3w <356
Answer
Kelvin 223 669 < 356
Lori 55 165 < 356
Vanessa 265 795 < 356
Devon 172 516 < 356
Celia 112 336 < 356
Step-by-step explanation:
Suppose that a box contains 6 cameras and that 3 of them are defective. A sample of 2 cameras is selected at random. Define the random variable X as the number of defective cameras in the sample.
Answer: 1/5, 1/2, 0.
Step-by-step explanation:
given data:
no of cameras = 6
no of cameras defective = 3
no of cameras selected = 2
Let p(t):=P(X=t)
p(2)=m/n,
m=binomial(3,2)=3!/2!= 3
n=binomial(6,2)=6!/2!/4! = 15
p(3)= 3/15
= 1/5.
p(1)=m/n,
m=binomial(6,1)*binomial(2,2)=6!/1!/4!*2!/2!/0!= 7.5
n=binomial(6,2)= 15
p(2)= 7.5/15
= 1/2
p(0)=m/n,
m=0
p(0)=0
Answer:
a.
The probability of X
k P(X=k)
0 0.25
1 0.5
2 0.25
b. The expected variable value of X; E(X) = 1
Step-by-step explanation:
Given that:
number of cameras = 6
numbers of defective = 3
the probability of defective camera p = 3/6 = 0.5
sample size n = 2
Then X = {0,1,2}
Suppose X is the given variable that represents the number of defective cameras in the sample.
∴
X [tex]\sim[/tex] Bin (n =2, p = 0.5)
The probability mass function of binomial distribution can be computed as :
[tex]P(X =x) = (^n_x) p^x (1-p)^{n-x}[/tex]
For ;
x = 0
The probability P(X=0) [tex]= (^2_0) 0.5^0 (1-0.5)^{2-0}[/tex]
[tex]P(X=0) = \dfrac{2!}{0!(2-0)!} \times 1 \times 0.5^2[/tex]
[tex]P(X=0) =1\times 1 \times 0.25[/tex]
[tex]P(X=0) = 0.25[/tex]
For :
x = 1
The probability P(X=1) [tex]= (^2_1) 0.5^1 (1-0.5)^{2-1}[/tex]
[tex]P(X=1) = \dfrac{2!}{1!(2-1)!} \times 0.5^1 \times 0.5^1[/tex]
[tex]P(X=1) =2 \times 0.5 \times 0.5[/tex]
[tex]P(X=1) =0.5[/tex]
For :
x = 2
The probability P(X=2) [tex]= (^2_2) 0.5^2 (1-0.5)^{2-2}[/tex]
[tex]P(X=2) = \dfrac{2!}{2!(2-2)!} \times 0.5^2 \times 0.5^0[/tex]
[tex]P(X=2) =1 \times 0.5^2 \times 1[/tex]
[tex]P(X=2) =0.25[/tex]
The probability of X
k P(X=k)
0 0.25
1 0.5
2 0.25
The expected variable value of X can be computed as:
E(X) = np
E(X) = 2 × 0.5
E(X) = 1