Answer:
the factors of prime numbers are only 1 and itself
Answer:
A factor number can only be divided by itself or 1 meaning it cant be a factor anything more than that.
Step-by-step explanation:
How many randomly chosen guests should I invite to my party so that the probability of having a guest with the same birthday as mine is at least 2/3?
Answer:
At least 401 chosen guests
Step-by-step explanation:
Represent those with same birth day with Same
So:
[tex]P(Same) > \frac{2}{3}[/tex]
Represent number of people with n
There are 365 days in a year and 364 days out of these days is not your birthday.
So, there the probability that n people do not share your birthday is [tex](\frac{364}{365})^n[/tex]
i.e.
[tex]P(none) = (\frac{364}{365})^n[/tex]
Solving further, we have that:
[tex]P(same) + P(none) = 1[/tex]
[tex]P(same) + (\frac{364}{365})^n = 1[/tex]
[tex]P(same) = 1 - (\frac{364}{365})^n[/tex]
We're calculating the probability that [tex]P(Same) > \frac{2}{3}[/tex].
So, we have:
[tex]1 - (\frac{364}{365})^n > \frac{2}{3}[/tex]
Collect Like Terms
[tex]1 - \frac{2}{3}> (\frac{364}{365})^n[/tex]
[tex]\frac{3-2}{3}> (\frac{364}{365})^n[/tex]
[tex]\frac{1}{3}> (\frac{364}{365})^n[/tex]
[tex]3^{-1} > (\frac{364}{365})^n[/tex]
Take natural logarithm (ln) of both sides
[tex]ln(3^{-1}) > ln((\frac{364}{365})^n)[/tex]
[tex]-ln\ 3 > n\ ln\ (\frac{364}{365})[/tex]
Apply laws of logarithm
[tex]-ln\ 3 > n\ (ln(364) - ln(365))[/tex]
Multiply through by -1
[tex]ln\ 3 < n\ (ln(365) - ln(364))[/tex]
Solve for n
[tex]\frac{ln\ 3}{(ln(365) - ln(364))} < n[/tex]
Reorder
[tex]n > \frac{ln\ 3}{(ln(365) - ln(364))}[/tex]
[tex]n > \frac{1.09861228867}{(5.89989735358 - 5.89715386764)}[/tex]
[tex]n> \frac{1.09861228867}{0.00274348594}[/tex]
[tex]n > 400.443928891[/tex]
[tex]n > 400[/tex] (approximated)
This implies that n = 401, 402, 403 .....
i.e
[tex]n \geq 401[/tex]
So, at least 401 people has to be invited
List the transformations of the function. *
5 points
f(x)= (1/2(- 1/4(x-3))+1
Answer:
Transformations of function f(x) = 1/2(-1/4(x-3)) + 1 :
vertical compressionhorizontal stretchreflection across y-axistranslates righttranslates upWhich of the following describes the roots of the polynomial function f (x) = (x + 2) squared (x minus 4) (x + 1) cubed?
–2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3
–2 with multiplicity 3, 4 with multiplicity 2, and –1 with multiplicity 4
2 with multiplicity 2, –4 with multiplicity 1, and 1 with multiplicity 3
2 with multiplicity 3, –4 with multiplicity 2, and 1 with multiplicity 4
Answer:
A
Step-by-step explanation:
[tex]f(x) = (x + 2)^2(x-4)(x + 1)^3[/tex]
x+2=0
x+2-2=0-2
x=-2.....(x+2) was squared...exponent of 2...multiplicity of 2
x-4=0
x-4+4=0+4
x=4....(x-4) has no visible exponent which means it is essentially to the power of 1...multiplicity of 1
x+1=0
x+1-1=0-1
x=-1....(x+1) was cubed...exponent was 3...multiplicity of 3
The roots and their respective multiplicity are –2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3 thus option (A) is correct.
What are the roots of an equation?The roots of an equation are the solution of that equation, since an equation consists of hidden values of the variable so to determine them by different processes and then the resultant is called roots.
For example root of x -4 = 0 is x = 4 so 4 will be the only root of this linear equation.
As per the given function,
f(x) = (x + 2)²(x - 4)(x + 1)³
The roots are the points at which the value of the function is zero.
f(x) = 0
(x + 2)²(x - 4)(x + 1)³ = 0
(x + 2)² = 0
x = -2 (with a multiplicity of 2)
(x - 4) = 0
x = 4 (with a multiplicity of 1)
(x + 1)³ = 0
x = -1 (with a multiplicity of 3)
Hence "The roots and their respective multiplicity are –2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3 thus option (A) is correct".
To learn more about the roots of equations,
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Help me pleaseeeeeee
The answer is the second one
Explanation above
Answer:
The correct answer is "y = 3/4x"
Step-by-step explanation:
Slope-intercept form is y2-y1/x2-x1. If you place the points into slope-intercept form you get 6-3/8-4. After reducing the fractions you will get 3/4. So the equation is y = 3/4x.
Bella is learning to type. She typed a letter to her teacher but misspelled 8 words. If she misspelled 25% of the words she typed. how many words did she type in her letter I'm taking a test I need this ASAP
Answer:
She typed 32 words in her letter
Step-by-step explanation:
Assume that the letter has x words
∵ She typed x words in her letter
∵ She misspelled 8 words
∵ She misspelled 25% of the words she typed
∴ She misspelled 25% of x
→ That means 8 is equivalent to 25% of x
∴ 25% of x = 8
∴ 25% × x = 8
→ Change 25% to decimal by divide it by 100
∵ 25% = 25 ÷ 100 = 0.25
∴ 0.25 × x = 8
∴ 0.25x = 8
→ Divide both sides by 0.25
∵ [tex]\frac{0.25x}{0.25}[/tex] = [tex]\frac{8}{0.25}[/tex]
∴ x = 32
∵ x represents the number of words that she typed in the letter
∴ She typed 32 words in her letter
If AABC = ADEC,
ZB = 48° and ZE = x + 4
Answer:
[tex]x = 44^\circ[/tex]
Step-by-step explanation:
Triangle Congruence
Given triangle ABC is congruent to triangle DEC, then it's true that angle ABC is congruent to angle DEC.
The figure shows that:
[tex]m\angle B = 48^\circ[/tex]
[tex]m\angle E = x + 4^\circ[/tex]
Those angles are congruent, or have the same measure, thus:
[tex]x + 4^\circ = 48^\circ[/tex]
Subtracting 4°:
[tex]x = 48^\circ - 4^\circ[/tex]
[tex]\mathbf{x = 44^\circ}[/tex]
complete the sequence:1,1,2,3,5,_,_,_
Answer:
8,13,21
Step-by-step explanation:
Basically,add the previous number to next number
Answer:8,13,21
Step-by-step explanation:
Solve the equation and describe what your answer. What happens? 5x-7=2x+1+3x
Answer: The Answer is 0
Step-by-step explanation:
The key here is combining like terms. Here:
1) 5x-7=2x+1+3x
2) 5x-7=5x+1
Then you add 7 to both sides anywhere that there is no variable. You also subtract 5x to the other 5x
3) 0x=8
When you divide by zero on both sides, your answer should be 0
What is the maximum for: P = 3x + 2y
Answer:
The maximum value of the function P= 3x + 2y
There is an accompanying graph in this problem. In the graph, there are 4 points to consider. I'll just assign letters on each point.
Point O is found in x = 0 ; y = 0 or (0,0)
Point A is found in x = 8 ; y = 0 or (8,0)
Point B is found in x = 6 ; y = 5 or (6,5)
Point C is found in x = 0 ; y = 8 or (0,8)
We will substitute x and y in the equation by its values per point.
Point A = 3(8) + 2(0) = 24 + 0 = 24
Point B = 3(6) + 2(5) = 18 + 10 = 28
Point C = 3(0) + 2(8) = 0 + 16 = 16
The Jimenez family is bringing 12 packages of hamburger and hotdog buns to the neighborhood picnic. The hamburger buns cost $2.00 per package. The hot-dog buns cost $1.50 per package. They spent $20 for the buns. Create and solve a system of equations that can be used to find the number of packages of each type of bun purchased.
Answer:
The system of equations is x + y = 12 and 2x + 1.5y = 20
The number of packages of the hamburger is 4
The number of packages of the hotdog is 8
Step-by-step explanation:
Assume that they bringing x packages of hamburger y packages of hotdog
∵ x represents the number of packages of hamburger
∵ y represents the number of packages of hotdog
∵ Jimenez family is bringing 12 packages of hamburger and hotdog buns
∴ x + y = 12 ⇒ (1)
∵ The hamburger buns cost $2.00 per package
∵ The hot-dog buns cost $1.50 per package
∵ They spent $20 on the buns
∴ 2x + 1.5y = 20 ⇒ (2)
The system of equations is x + y = 12 and 2x + 1.5y = 20
Let us solve it to find x and y
→ Multiply equation (1) by -1.5 to make the coefficients of y equal in
values and different in signs to eliminate it
∵ -1.5(x) + -1.5(y) = -1.5(12)
∴ -1.5x - 1.5y = -18 ⇒ (3)
→ Add equations (2) and (3)
∵ (2x + -1.5) + (1.5y + -1.5y) = (20 + -18)
∴ 0.5x = 2
→ Divide both sides by 0.5 to find x
∴ x = 4
→ Substitute the value of x in equation (1) or (2) to find y
∵ 4 + y = 12
→ Subtract 4 from both sides
∴ 4 - 4 + y = 12 - 4
∴ y = 8
∴ The number of packages of the hamburger is 4
∴ The number of packages of the hotdog is 8
The 7th grade class took a survey on their faviorte ice cream. 58 people said they perfer vanilla, while 28 people said they pefer chocolate. Write a ratio comparing chocolate to vanilla.
Jason and 4 friends went bowling. Three friends rented shoes for $2 each. The total cost to rent the shoes and the lane fees was $42. What was the cost of the lane fees for each person?
Answer: 7.20$
Step-by-step explanation:
Since there are five people over all, and three of them bought shoes for 2$, you would take 2$ Times that by 3 = 6$, now take that 6$ and subtract that by the 42$, leaving you with 36$ left. Take that 36$ and divide it among the 5 people and you get 7.20$ for a lane
To find 7% of a total you can multiply the total by
(1) 7 (3)
(2) 0.7
(3) 7/10
(4) 0.07
James deposited $575 into a bank account that earned 5.5% simple interest each year. No money was deposited into or withdrawn from the account. How much money was in the account after 2 1/2 years? Round your answer to the nearest cent.
Answer:
$654.06
Step-by-step explanation:
ジオメトリヘルプミープリーズは、速くて正しい場合に最も頭が良くなります
関係のドメインは？ 1）関係の出力（y）値2）関係の入力（x）値3）入力値をペアにするポイントのセット…
f（x）= 16 – x ^ 2、g（x）= 4 –xとします。 （fg）（x）とその定義域を見つけます。
助けてくださいお願いします
助けてください
Answer: the answer would be 79.06
Step-by-step explanation:
The slope of the line is ?
Answer:
slope= 4,
Step-by-step explanation:
y = 4x-6
Solve this system for m and b 342=23m+b 147=10m+b
Answer:
b = − 3
m = 5 ( 39 + 2 m ) /23
Please help thanks :)
Answer:
Distributive Property
Step-by-step explanation:
[tex]x(8x+3y)\\We\ multiply\ the\ term\ outside\ brackets\ with\ terms\ inside\ the\ bracket\ equally,\\through\ the\ distributive\ property\ method\ .\\\\Hence,\\x(8x+3y)\\=8x*x+3y*x\\=8x^2+3xy[/tex]
If the average price of a new one-family home is $246,300 with a standard deviation of $15,000, find the minimum and maximum prices of the houses that a contractor will build to satisfy the middle 60% of the market. Assume that the variable is normally distributed.
Answer:
Step-by-step explanation:
P(-a<z<a)=0.60, from the symmetry of normal distribution, P(z<a) = 0.60+ (1-0.60)/2 =
0.60+0.4/2
0.60+0.2
= 0.8
Considering the standard normal distribution table, we have a = 0.80, thus
z =(x-m)/std = 0.80
the maximum x = m + 0.80×std =
Where m = 246300
Std = 15000
246300+0.80×15000
= 246300+12000
= 258300
For the minimum x
x = m - 0.80×std
x = 246300-0.80×15000
246300-12000
= 234300
If an object moves in a straight line with position function s = f(t), then the average velocity between t = a and t = b is
f(b) − f(a)/b − a
and the velocity at t = c is f '(c). Thus the Mean Value Theorem tells us that at some time t = c between a and b the instantaneous velocity f '(c) is equal to the average velocity. For instance, if a car traveled 150 km in 2 hours, then the speedometer must have read km/h at least once.
In general, the Mean Value Theorem can be interpreted as saying that there is a number at which the instantaneous rate of change is equal to the average rate of change over an interval.
Answer:
75 km/hr
Step-by-step explanation:
So, if a car travels 150 km in 2hours.
Then;
f(t=0) = 0
f(t = 2 hours) = 150 km
Therefore;
f'(c) (speedometer reading) = f(t=2)-f(t=0)/(2-0)
f'(c) (speedometer reading) = 150/2 km/hr
f'(c) (speedometer reading) = 75 km/hr
determine if the relation is a function
(-1, 5), (0,3), (2,3), (3, -1)
Answer:
This relation IS a function
Answer:
This is a function
Step-by-step explanation:
Down below none of them overlap
There is no two points in the lines.
This is for someone that i was suppost to give brainliest to lol
Answer:
ok does that mean me dont get brainliest
Step-by-step explanation:
Linear equation: -1 (6x + (6x + 10) = 13
Step 1: -3x - 5 = 13
Step 2: -3x = 18
Step 3: x= -6
Which sequence describes the inverse operations used for steps 2 and 3 to solve the linear equation?
O the addition property of equality and then the division property of equality
O the addition property of equality and then the multiplication property of equality
O the subtraction property of equality and then the division property of equality
O the subtraction property of equality and then the multiplication property of equality
Answer:
the addition property of equality and then the division property of equality
-4q= 52
HELP!!!!!!!!!!!!!!!!!!!!!
Algebra 1
hi
-4q= 52
q = 52/ -4
a = -13
Answer:
-13
Step-by-step explanation:
-4q=52
divide both side by -4
-4q/-4=52/-4
q=-13
Can anyone help me with this question of m
Answer:
<DBC=31
Step-by-step explanation:
<ABC=<ABD+<DBC
125=94+<DBC
125-94=<DBC
31=<DBC
1. Adding decimals is very similar to adding___________.
2.Line up the number vertically so that all the decimal points are_______.
3. Add extra______to the right of the number so that each number has the same number of digits to the right of the decimal point.
4. Place the______________of the result in line with the other decimal points.
Answers:
1. Adding decimals is very similar to adding whole numbers.
2. Line up the number vertically so that all the decimal points are aligned.
3. Add extra zeros to the right of he number so that each number has the same number of digits the right of the decimal point.
4. Place the decimal point of the result in line with the other decimal points.
I hope this helped you. If it is please click the thanks button. Thank You, Bye! ;-D
1. Adding decimals is very similar to adding whole numbers.
2. Line up the number vertically so that all the decimal points are aligned.
3. Add extra zeros to the right of the number so that each number has the same number of digits to the right of the decimal point.
4. Place the decimal point of the result in line with the other decimal points.
While adding two decimals.
First, the decimals numbers are written under each other so that decimal points are lined up.The numbers are converted to like decimals by attaching the zeros. The number of zeros attached depends on the number with the maximum digits after the decimal point. The digits of each numbers are lined up so that each column contains digits in the same place. Addition is carried out the normal way by starting from the right to the left. The decimal point is then placed in the place as the numbers above it.Learn more about decimal form here:
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Learn more about decimal addition here:
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What is one hundred times greater than 40?
Suppose babies born in a large hospital have a mean weight of 3685 grams, and a variance of 330,625. If 113 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by greater than 50 grams? Round your answer to four decimal places.
its not greater than 50 grams. and the answer rounder to the four decimal places is 32.6106
Five of the 25 girls on Alden Middle School’s soccer team are seventh-grade students. Find the percentage of seventh graders on the team.
Answer:
20%
Step-by-step explanation:
5 divided by 25 multiplied by 100 will give you 20%.
I hope you understand
If f(x) = 2x^2 +1, complete the following:
a. f(-4)
b. f(-2)
c. f(0)
d. f(2)
e. f(4)
This is a timed test please i need help!!
Answer:
Sub the values in the brackets of each question into the equation
Step-by-step explanation:
eg. c. f(0) = 2(0)^2 + 1 = 1
Which is the net force acting on a 1.7-kg object that is accelerating at 5.0 m/s??
A. 8.5 N
B. 2.9 N
C. 0.34 N
D. 3.3 N
Answer:
A. 8.5 N
Step-by-step explanation: F = 8.5 N