Answer:
Yes
Step-by-step explanation:
Yesterday would be Thursday and the day after next would be Sunday
prime factorization of a 4- digit number with at least three distinct factors
Need two examples. SHOW ALL STEPS
Answer:
We know that every number can be written as a product of prime numbers.
The method to find the factorized form of a number depends on the number, we just try to find the different factors by dividing by them, for example for the number 1000 we have:
1000 is an even number, then we can divide it by 2 (2 is a prime number)
1000 = 2*500 (so we already found a prime factor)
500 is also an even number, so we can divide it by 2
1000 = 2*500 = 2*2*250 (we found another prime factor)
dividing by 2 again we get:
1000 = 2*2*250 = 2*2*2*125
1000 = (2*2*2)*125
now we just need to factorize 125
we know that 125 is a multiple of 5, such that:
125 = 5*25 = 5*5*5
(5 is a prime number, so it is completely factorized).
Then the factorization of 1000 is:
1000 = (2*2*2)*(5*5*5) = 2^3*5^3
Now with another example, 1422
1422 is an even number, so we again start using the factor 2:
1422 = 2 = 711
then:
1422 = 2*711
we already found a factor.
711 is a multiple of 3 (the sum of its digits is a multiple of 3), then:
711/3 = 237
We can write our number as:
1422 = 2*3*237
237 is also a multiple of 3
237/3 = 79
then:
1422 = 2*3*3*79
and 79 is a prime number, so we already have 1422 completely factorized.
Put the equation y = x^2- 14x + 48 into the form y = (x-h)^2+k
please help me!
Answer:
Step-by-step explanation:
Answer:
[tex]y=(x-7)^2-1[/tex]
Step-by-step explanation:
We want to convert the equation:
[tex]\displaystyle y=x^2-14x+48[/tex]
Into vertex form, given by:
[tex]\displaystyle y=a(x-h)^2+k[/tex]
Where a is the leading coefficient and (h, k) is the vertex.
There are two methods of doing this. We can either: (1) use the vertex formulas or (2) complete the square.
Method 1) Vertex Formulas
Let's use the vertex formulas. First, note that the leading coefficient a of our equation is 1.
Recall that the vertex is given by:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -14, and c = 48. Find the x-coordinate of the vertex:
[tex]\displaystyle x=-\frac{(-14)}{2(1)}=7[/tex]
To find the y-coordinate, substitute this value back into the equation. Hence:
[tex]y=(7)^2-14(7)+48=-1[/tex]
Therefore, our vertex (h, k) is (7, -1), where h = 7 and k = -1.
And since we already determined a = 1, our equation in vertex form is:
[tex]\displaystyle y=(x-7)^2-1[/tex]
Method 2) Completing the Square
We can also complete the square to acquire the vertex form. We have:
[tex]y=x^2-14x+48[/tex]
Factor out the leading coefficient from the first two terms. Since the leading coefficient is one in this case, we do not need to do anything significant:
[tex]y=(x^2-14x)+48[/tex]
Now, we half b and square it. The value of b in this case is -14. Half of -14 is -7 and its square is 49.
We will add this value inside the parentheses. Since we added 49 inside the parentheses, we will also subtract 49 outside to retain the equality of the equation. Hence:
[tex]y=(x^2-14x+49)+48-49[/tex]
Factor using the perfect square trinomial and simplify:
[tex]y=(x-7)^2-1[/tex]
We acquire the same solution as before, with the vertex being (7, -1).
How many additional teachers will have to be hired to reduce the ratio to 1:20
Answer:
30 additional teachers will have to be hired to reduce the ratio to 1:20.
Step-by-step explanation:
Given that Jefferson School has 1800 students, and the teacher-pupil ratio is 1:30, to determine how many additional teachers will have to be hired to reduce the ratio to 1:20, the following calculation must be performed:
30 = 1800
1 = X
1800/30 = X
60 = X
20 = 1800
1 = X
1800/20 = X
90 = X
90 - 60 = 30
Therefore, 30 additional teachers will have to be hired to reduce the ratio to 1:20.
What is the sum of 4th squared number and the 2nd cube number
Answer:
mark me as brinalist if answers are correct
if 18 : 6 = x : 3 then what is 5 + 3x
Answer:
32
Step-by-step explanation:
18 : 6 = 3
therefore, x : 3 has to equal 3.
X : 3 = 3
X = 3 × 3
X = 9
To verify:
18 : 6 = 9 : 3
3 = 3
It's true that X = 9, so now just replace the X with 9 in the next equation
5 + 3(9) = 32
Answer:
32
Step-by-step explanation:
18 : 6 = x : 3
Product of means = Product of extremes
6 * x = 3*18
x = [tex]\frac{3*18}{6}[/tex]
x = 3*3
x = 9
Now plugin x = 9 in the expression
5 + 3x = 5 + 3*9
= 5 + 27
= 32
Warren drives his car 330 miles and has an average of a certain speed. If the average speed had been 3 mph more. he could have traveled 352 miles in the same length
of time. What was his average speed?
Keypad
Answer:
45 miles per hour
Step-by-step explanation:
d=distance in miles
r=rate miles/hr
t = time in hours
t = 352/(r+3)
330/r = 352/(r+3)
352r = 330r + 990
22r = 990
r = 45
1 Find the value of C to that the function probability density function defined as follow, also calculate the man and variance /4
X -1 0 1
f(x) 3c 3c 6c
Answer:
[tex]c = \frac{1}{12}[/tex]
The mean of the distribution is 0.25.
The variance of the distribution is of 0.6875.
Step-by-step explanation:
Probability density function:
For it to be a probability function, the sum of the probabilities must be 1. The probabilities are 3c, 3c and 6c, so:
[tex]3c + 3c + 6c = 1[/tex]
[tex]12c = 1[/tex]
[tex]c = \frac{1}{12}[/tex]
So the probability distribution is:
[tex]P(X = -1) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]
[tex]P(X = 0) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]
[tex]P(X = 1) = 6c = 6\frac{1}{12} = \frac{1}{2} = 0.5[/tex]
Mean:
Sum of each outcome multiplied by its probability. So
[tex]E(X) = -1(0.25) + 0(0.25) + 1(0.5) = -0.25 + 0.5 = 0.25[/tex]
The mean of the distribution is 0.25.
Variance:
Sum of the difference squared between each value and the mean, multiplied by its probability. So
[tex]V^2(X) = 0.25(-1-0.25)^2 + 0.25(0 - 0.25)^2 + 0.5(1 - 0.25)^2 = 0.6875[/tex]
The variance of the distribution is of 0.6875.
evaluate the expression when b= -6 and c=3
-4c+b
Answer:
-18
Step-by-step explanation:
b = -6
c = 3
-4c + b = ?
Plug in the value of each variable into the equation
-4c + b = ?
= -4(3) + (-6)
= -12 - 6
= -18
Give an example of a function with both a removable and a non-removable discontinuity.
Answer:
(x+5)(x-3) / (x+5)(x+1)
Step-by-step explanation:
A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator. It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x. In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.
!PLEASE HELP WILL GIVE BRAINLIEST!
An internet service charges $34 per month for internet access. Write an equation to represent the total cost based on the number of months of internet access.
Answer:
34m = c
Step-by-step explanation:
For every month (m) you pay 34 dollars. However many months youu use that service time 34 equals your total cost (c).
Answer:
[tex]let \: cost \: be \: { \bf{c}} \: and \: months \: be \: { \bf{n}} \\ { \bf{c \: \alpha \: n}} \\ { \bf{c = kn}} \\ 34 = (k \times 1) \\ k = 34 \: dollars \\ \\ { \boxed{ \bf{c = 34n}}}[/tex]
whether the distribution of the mean of a large number of independent, identically distributed variables. true or false
Answer:
The statement is false
Step-by-step explanation:
Given
See comment for complete statement
Required
Is the statement true or false
From central limit theorem, we understand that a distribution is approximately normal if the distribution takes a sample considered to be large enough from the population.
Also, the mean and the standard deviation are known.
However, the given statement implies that the distribution will be normal depending on an underlying distribution; this is false.
Find the volume of the cone. Round to the nearest hundredth.
Answer:
Step-by-step explanation:
volume of cone=1/3 πr²h
=1/3×π×5²×11
=275/3 ×3.14
≈287.33 in³
The average of 6,10,x,20 and 30 is 18. what is the value of x
Answer:
24
Step-by-step explanation:
18 times 5 is 90 so that means that the given numbers have to add up to 90 (including x)
so,
6+10+20+30=66
90-66=24
I hope this helps!
Answer:
[tex]x = 24[/tex]
Step-by-step explanation:
[tex]6 + 10 + x + 20 + 30 = 18[/tex]
There are 5 numbers that we must add to average out to get 18 so let set this equation up
[tex] \frac{6 + 10 + x + 20 + 30}{5} = 18[/tex]
[tex]6 + 10 + x + 20 + 30 = 90[/tex]
[tex]x = 24[/tex]
In an examination every student took history or geography or both of 500 candidates 60% took history whiles 72% took geography. How many students took both subjects
Answer:
80 students
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
60% of 500 = 300
72% of 500 = 360
40% of 500 = 200
28% of 500 = 140
300+360 = 660
660 - 2x = 500
660 - 500 = 2x
160 = 2x
2x = 160
x = 80
The perimeter of an equilateral triangle is 126mm.
State the length of one of its sides.
Explanation:
Divide 126 over 3. This is because any equilateral triangle has all three sides the same length
126/3 = 42
Each side is 42 mm long
So its perimeter is 3*42 = 126 mm
Side note: if your teacher says a triangle is equiangular, then it's automatically equilateral as well (and vice versa).
The length of one of its sides of an equilateral triangle is 42 mm.
What is equilateral triangle?In geometry, an equilateral triangle exists as a triangle that contains all its sides equivalent in length. Since the three sides stand equivalent therefore the three angles, opposite to the equivalent sides, stand equivalent in measure. Thus, it stands also named an equiangular triangle, where each angle measure 60 degrees.
The perimeter of an equilateral triangle exists 126 mm.
The equilateral triangle contains all three sides of the same length
126/3 = 42
Each side stands 42 mm long
So its perimeter stands 3 [tex]*[/tex] 42 = 126 mm
Therefore, the length of one of its sides = 42 mm.
To learn more about equilateral triangle
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Joyce paid $60.00 for an item at the store that was 50 percent off the original price. What was the original price?
$
Give your answer to the nearest cent.
A statistician calculates that 7% of Americans are vegetarians. If the statistician is correct, what is the probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%
Answer:
0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A statistician calculates that 7% of Americans are vegetarians.
This means that [tex]p = 0.07[/tex]
Sample of 403 Americans
This means that [tex]n = 403[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.07[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.07*0.93}{403}} = 0.0127[/tex]
What is the probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%?
Proportion below 7 - 3 = 4% or above 7 + 3 = 10%. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them, and multiply by 2.
Probability the proportion is below 4%
p-value of Z when X = 0.04.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.04 - 0.07}{0.0127}[/tex]
[tex]Z = -2.36[/tex]
[tex]Z = -2.36[/tex] has a p-value of 0.0091
2*0.0091 = 0.0182
0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.
What is the lcd for 3/6 and 2/9
9514 1404 393
Answer:
LCD = 18
Step-by-step explanation:
6 and 9 have a common factor of 3, so the LCD is ...
(6×9)/3 = 18
Then the fractions can be written as ...
3/6 = 9/18
2/9 = 4/18
what type of number cannot be written as a fraction p/q, where p and q are intergers and q is not equal to zero
Answer:
irrational numbers
Step-by-step explanation:
An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q.
Hi there!
»»————- ★ ————-««
I believe your answer is:
Irrational Number
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
The definition that is given in the question was the definition of a irrational number.A number that cannot be written as a fraction with two integers is called a irrational number. Some examples of irrational numbers are non-terminating decimals that do not repeat and non-perfect squares. A number that CAN be written as a fraction with two integers is called a rational number.⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Use the parametric equations of an ellipse, x=acosθ, y=bsinθ, 0≤θ≤2π , to find the area that it encloses.
Answer:
Area of ellipse=[tex]\pi ab[/tex]
Step-by-step explanation:
We are given that
[tex]x=acos\theta[/tex]
[tex]y=bsin\theta[/tex]
[tex]0\leq\theta\leq 2\pi[/tex]
We have to find the area enclose by it.
[tex]x/a=cos\theta, y/b=sin\theta[/tex]
[tex]sin^2\theta+cos^2\theta=x^2/a^2+y^2/b^2[/tex]
Using the formula
[tex]sin^2x+cos^2x=1[/tex]
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
This is the equation of ellipse.
Area of ellipse
=[tex]4\int_{0}^{a}\frac{b}{a}\sqrt{a^2-x^2}dx[/tex]
When x=0,[tex]\theta=\pi/2[/tex]
When x=a, [tex]\theta=0[/tex]
Using the formula
Area of ellipse
=[tex]\frac{4b}{a}\int_{\pi/2}^{0}\sqrt{a^2-a^2cos^2\theta}(-asin\theta)d\theta[/tex]
Area of ellipse=[tex]-4ba\int_{\pi/2}^{0}\sqrt{1-cos^2\theta}(sin\theta)d\theta[/tex]
Area of ellipse=[tex]-4ba\int_{\pi/2}^{0} sin^2\theta d\theta[/tex]
Area of ellipse=[tex]-2ba\int_{\pi/2}^{0}(2sin^2\theta)d\theta[/tex]
Area of ellipse=[tex]-2ba\int_{\pi/2}^{0}(1-cos2\theta)d\theta[/tex]
Using the formula
[tex]1-cos2\theta=2sin^2\theta[/tex]
Area of ellipse=[tex]-2ba[\theta-1/2sin(2\theta)]^{0}_{\pi/2}[/tex]
Area of ellipse[tex]=-2ba(-\pi/2-0)[/tex]
Area of ellipse=[tex]\pi ab[/tex]
HELP ASAP! I don’t know how to solve this problem nor where to start. Can someone please help me out here?
===============================================
Explanation:
It might help to draw out the picture as shown below. The pool itself (just the water only) is the inner rectangle. The outer rectangle is the pool plus the border of those 1 by 1 tiles.
The pool is a rectangle 90 feet by 80 feet. If we add on the tiles, then we get a larger rectangle that is 90+2 = 92 feet by 80+2 = 82 feet.
We add on 2 since we're adding two copies of "1" on either side of each dimension.
The larger rectangle's area is 92*82 = 7544 square feet
The smaller rectangle's area is 90*80 = 7200 square feet
The difference in areas is 7544-7200 = 344 square feet.
Each 1 by 1 tile is of area 1*1 = 1 sq foot, meaning that 344 tiles will get us the 344 square foot border around the pool.
what is a value between 1/4 and 1/3 is
9514 1404 393
Answer:
2/7
Step-by-step explanation:
Any unit fraction with a denominator between 3 and 4 will be between 1/3 and 1/4. For example, ...
1/3.5 = 2/7 . . . . is between 1/3 and 1/4
__
You can also go at this considering decimal equivalents.
1/4 = 0.25
1/3 = 0.333... (repeating)
So, decimal numbers like 0.26, 0.295, 0.3330 are all values that are between 1/4 and 1/3.
In which quadrant do the points have negative x-coordinates and negative y-coordinates?
Hi there!
»»————- ★ ————-««
I believe your answer is:
Quadrant III
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
The plane is split into four quadrants. Quadrant III houses all the points with negative signs for both X and Y values.⸻⸻⸻⸻
See the attached picture for reference.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
please help me i begging.
Answer:
The two equivalent expressions are 6(x − y) and 6x − 6y.
Step-by-step explanation:
Which of the following numbers is rational? Assume that the decimal patterns continue.
Answer:
[tex]\sqrt{49}[/tex]
Step-by-step explanation:
Define a rational number by a number able to expressed a fraction where the denominator is not 0 or 1.
Non-terminating (never-ending) decimals cannot be expressed as a fraction and therefore are irrational. However, recall that [tex]\sqrt{49}=7[/tex], which can be expressed as a fraction (e.g. [tex]\frac{14}{2}[/tex], etc). Thus, the answer is [tex]\boxed{\sqrt{49}}[/tex].
im stuck on this question!!!!
Answer:
reflected across the y axis: (5,2)
reflected across the x axis: (-2,5)
Answer:
Answer: (5,2) when reflected off the y-axis. (-5,-2) when reflected off the x-axis
Evaluate the expression below for x = 2, y = -3, and z = -1.
x?2? - y? (x +z)
A. -23
B. -5
C 13
D
27
Please select the best answer from the choices provided
Ο Α
ОВ
ОС
OD
The value of the expression for the given values of x, y and z is B. -5.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given expression is,
x²z² - y²(x + z)
We have certain values for x, y and z.
x = 2, y = -3 and z = -1.
Substituting the values,
(2²)(-1²) - (-3²) (2 + -1) = (4 × 1) - (9 × 1)
= 4 - 9
= -5
Hence the value of the expression is -5.
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What type of line is PQ⎯⎯⎯⎯⎯⎯⎯⎯?
Answer:
median
Step-by-step explanation:
Q is at the midpoint of RS and so PQ is a median
A median is a segment from a vertex to the midpoint of the opposite side.
We want to define what type of line is PQ (the line that passes through points P and Q) by looking at the given image, one can easily see that the line PQ is a median, now let's explain why.
First, let's analyze the image:
In the image, we can see that P is one vertex of the triangle, and Q is the midpoint of the segment RS (you can see that RQ = 4 and QS = 4) , where R and S are the other two vertexes of the triangle.
Particularly, we can define a median of a triangle as the line that passes through the midpoint of one side of the triangle and by the vertex that does not belong to that side.
With that definition, we can see that PQ is a median because Q is the midpoint of one side of the triangle and P is the vertex that does not belong to that side.
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Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision.
The question is incomplete. The complete question is :
Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision.
[tex]$\{ x^5, x^5-1,3 \} \text{ on } (- \infty, \infty)$[/tex]
Solution :
Given :
Function : [tex]$\{ x^5, x^5-1,3 \} \text{ on } (- \infty, \infty)$[/tex]
We have to determine whether the given function is linear dependent or linearly independent for the interval [tex]$(-\infty, \infty)$[/tex].
The given function are linearly dependent because for the constants, [tex]c_1[/tex] and [tex]c_2[/tex], the equation is :
[tex]$c_1x^5 + c_23 = x^5-1$[/tex] has the solution [tex]$c_1 = 1$[/tex] and [tex]$c_2 = -\frac{1}{3}$[/tex]
Therefore,
[tex]$1x^5 + \left(-\frac{1}{3}\right)3 = x^5-1$[/tex]
The measure of angle theta is 7x/6. The measure of its reference angle is _ °, and sin theta is _
Answer:
30° and -1/2. This is pretty easy to do on a piece of paper but I recommend googling "unit circle" and clicking images, it tells you everything you need to know.
Step-by-step explanation:
