The number of possibilities for Jane for making the four letter password (either upper case or lower case) with first letter being a vowel is 1406080
What is the rule of product in combinatorics?If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in [tex]p \times q[/tex] ways.
Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.
Thus, doing A then B is considered same as doing B then A
We need to find the number of ways a four letter password can be made The first letter is fixed to be a vowel.
There are 10 vowels (5 of lowercase and 5 of upper case).
Thus, 10 ways of choosing the first letter.
Second letter can be any of the 52 letters(26 of lowercase and 26 of uppercase).
Similarly, third and fourth letter can be any of the 52 letters.
Thus, using the product rule, the number of ways of making the four letter password is:
[tex]N = 10 \times 52 \times 52 \times 52 = 1406080[/tex]
(the answer can be different if we consider only either lowercase letters or only upper case letters. In those cases, there would be [tex]5 \times 26^3 = 87880[/tex] ways to make such passwords).
We used product rule, since we wanted to do the choosing of all the four letters for password, and we knew the number of ways each of them can be done individually.
Thus, the number of possibilities for Jane for making the four letter password (either upper case or lower case) with first letter being a vowel is 1406080
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Biểu thức sin²x + cos²x có giá trị bằng ?
we have sin²x + cos²x = 1
ok done. Thank to me :>
Find the unit rate.
12 laps in 30minutes
Answer:
0.4/1
Step-by-step explanation:
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 30
Please help me!!! It would really help
Answer:
D'(25, 0)
Step-by-step explanation:
Dilation by a factor of 5 about the origin multiplies each individual coordinate by 5.
(x, y) ⇒ (5x, 5y)
D(5, 0) ⇒ D'(5·5, 5·0) = D'(25, 0)
Help me I don’t understand please explain the answer to me
Answer:
a
Step-by-step explanation:
r and t are same- side exterior angles and sum to 180 , so
t + r = 180 , that is
t + 91 = 180 ( subtract 91 from both sides )
t = 89
t and u are vertically opposite angles and are congruent , so
u = t = 91
Then
t + u = 89 + 89 = 178 → a
What are the values of m and n
Answer:
m = 20°, n = 45°Step-by-step explanation:
Both of the triangles are isosceles as marked on the diagram.
The right triangle has missing angles of:
n = 90°/2 = 45°The missing angles of the bigger triangle:
m + n = 1/2(180° - 50°)m + 45° = 65°m = 20°Given loga (m) = 10 and loga (n) = 25 , find loga (m * n ^ 2)
The result of the log function [tex]log_a (m * n ^ 2)[/tex] is 60
According to the law of logarithm if [tex]log_ab=y[/tex] then [tex]b=a^y[/tex]
Given the following expressions
[tex]log_am=10\\log_an=25[/tex]
This can be expressed as
[tex]m =a^{10} \ and \ n = a^{25}[/tex]
Substitute the value of m and n into the expression [tex]log_a (m * n ^ 2)[/tex] to have:
[tex]log_a (m * n ^ 2) = log_a(a^{10}\times a^{50})\\=log_aa^{60}\\=60log_aa\\=60(1) \\= 60[/tex]
This shows that the result of the log function [tex]log_a (m * n ^ 2)[/tex] is 60
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please help
Jay buys a certain brand of cereal that costs $15 per box. Luke changes to a super-saving brand of the same size. The equation shows the price, y, as a function of the number of boxes, x, for the new brand, y = 10x Part A: How many more dollars is the price of a box of Jay's original brand of cereal than the price of a box of the super-saving brand? Show your work. (5 points) Part B: How much money does Jay save each month with the change in cereal brand if he buys 8 cereal boxes each month? Show your work. (5 points)
A.
Jay's original brand is $5 more than the price of a box of the super-saving brand.
Since Jay's original brand costs $15 per box and the price of Luke's super-saving brand is y = 10x where x = number of boxes. For one box, x = 1.
So, y = 10x
y = 10 × 1
y = $10
So, Jay's brand costs $15 per box and Luke brand cost $10 per box.
So, the difference in price is per box is $15 - 10$ = $5
So, Jay's original brand is $5 more than the price of a box of the super-saving brand.
B.
Jay saves $40 per month with the change in cereal brand if he buys 8 cereal boxes each month
Since the difference in price for each box bought is $5. Jay saves $5 for every super-saving cereal brand he buys.
So, if he buys 8 cereal boxes per month, he saves $5 per box × 8 boxes per month = $40 per month.
So, Jay saves $40 per month with the change in cereal brand if he buys 8 cereal boxes each month
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A corporation earned its profit of 2.5x10^4 for 1x10^3 days in a row. What was the corporation's total profit during this time?
Answer:
$2.6 x 10^4
Step-by-step explanation:
can anyone help me out with this?
Given :
Evaluate the equation.
2x – 4(x – 2y) + 6y = ?When x = 5 and y = 2 then,
2x – 4(x – 2y) + 6y
= 2(5) – 4[(5) – 2(2)] + 6(2)
= 10 – 4(5 – 4) + 12
= 10 – 4*1 + 12
= 10 – 4 + 12
= 22 – 4
= 18
Please explain step-by-step! Thanks!
Random answers will be reported
Step-by-step explanation:
what is your questions?????Find: (4x2y3 + 2xy2 – 2y) – (–7x2y3 + 6xy2 – 2y)
Place the correct coefficients in the difference.
x2y3 +
xy2 +
y
Answer:
final answer: 58xy
Step-by-step explanation:
24xy + 4xy - 2y + 42xy - 12xy + 2y
(24xy + 4xy + 42xy - 2xy) + ( - 2y + 2y)
(24 + 4 + 42 - 12)x xy + ( - 2 + 2)xy
58xy + ( - 2 + 2)xy
58xy + 0y
58xy
Answer:
1st one is 11
2nd one is -4
3rd one is 0
Step-by-step explanation:
no need
you can trust me :)
1
message
Two friends went bowling. One friend scored 130 points and the other friend scored 83 points. How does the value represented by the 3 in 130 compare to the value represented by the 3 in 83?
It is 3 times greater
It is 10 times greater
It is 47 times greater
It is 50 times greater
Answer:
10x greater
Step-by-step explanation:
Two friends let’s say their names are
Molly Polly
130 points 83 points
Molly‘s 3 in her 130 is is the tens place
here a chart: ones Tens. Hundreds. thousands.
1265 1265. 1265. 1265
now let’s go back to Molly and Polly. The 3 in 130 is one place above the 3 in 83 and this ,my friend, technically means it is only 10x greater
hope this helped :3
:3 byeeeeeeeeee
Mary bought 176 flowers for 4 vases. How many flowers are needed for 7 vases?
She planned to have 44 flowers per vase (176/4). 7 vases would mean 308 flowers.
can someone help me solve this question? -6 - (-10) + (-2)
Answer:
2
Step-by-step explanation:
note - (- ) = + and + (- ) = -
- 6 - (- 10) + (- 2)
= - 6 + 10 - 2
= 4 - 2
= 2
Answer:
2
Explanation:
- 6 + 10+ (- 2)
= 4+(-2)
=2
Amy borrows $1,000 on a simple interest loan. She pays an annual rate of 3.5%. She will take 3 years to pay back the loan. How much interest will Amy pay?
Answer:
105
Step-by-step explanation:
1,000 divided by 3.5% is 35
35 x 3 is 105
Since you are just asking for just the interest and not the total the answer is 105
The interest that Amy should pay is $105.
Given that,
Amy borrows $1,000 on a simple interest loan. She pays an annual rate of 3.5%. She will take 3 years to pay back the loan.Based on the above information, the calculation is as follows:
[tex]= 1000 \times 3.5\% \times 3[/tex]
= 105
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Which is NOT a function?
A. y = x + 3^2
B. x + y = 3^2
C. x + 3 = y^2
D. y = x^2 - 3
Answer:
All are functions
Step-by-step explanation:
A. y = x + 9 A graph of a line. There are no x-values that are the same on the graph. The graph passes the vertical line test.
B. x + y = 9
y = -x + 9 A graph of a line. There are no x values that are the same number on the graph. The graph passes the vertical line test
C. x + 3 = y²
[tex]\sqrt{x + 3} = y[/tex] The graph passes the vertical line test. On the graph, there are no x-values that are the same number.
D. y = x² - 3 The graph is a parabola. The graph passes the vertical line test (there are no x- values are the same number on the graph).
Zidan is using the Rational Root Theorem to help find the roots of a 5th degree polynomial. He has discovered five roots and still has 4 to test. What is his next best step?
1-He should test the remaining 4 roots.
2-He should use the Factor Theorem to find the remaining polynomial roots.
3-He needs to pick one of the roots and use the quadratic formula to test it.
4-He can stop testing because he has found all the roots.
Answer:
He can stop testing because he has found all the roots.
Step-by-step explanation:
I took the test and it said I got it right. Hope this helps!
what is the x intercept?
Answerrrrrrrrrr:
- 7/6
Please help me with this I don't get it
50% of 25% is the number. What is the number?
Answer:
1/8
Step-by-step explanation:
50/100 * 25/100
1/2 * 1/4 = 1/8
In ΔNOP, p = 7.5 inches, ∠O=8° and ∠P=25°. Find the length of n, to the nearest 10th of an inch.
Answer: 10.17898 so
About 10.2
Answer: 10.6
Step-by-step explanation:
There are four consecutive integers that add up to 22 what is the greatest integer
Answer:
7
Step-by-step explanation:
We can use the equation:
x + (x + 1) + (x + 2) + (x + 3) = 22
Combine like terms
4x + 6 = 22
Subtract 6 from both sides
4x = 16
Isolate x
x = 4
Plug in x
4 + (4 + 1) + (4 + 2) + (4 + 3) = 22
Solve
4 + 5 + 6 + 7 = 22
7 is the greatest integer
solve for x, find the measure of all angles hurryyyyyy!
Answer:
Step-by-step explanation:
Well the first fact is that you can solve H and J with 1 equation. Two remote (unconnected to) one of the exterior angles when summed, equals the unconnected exterior angle.
H + j are not connected to the exterior angle at I.
Put more directly
2x + 3x = 150 Combine
5x = 150 Divide by 5
x = 150/5
x = 30
So H = 2 * 30 = 60
and J = 3*30 = 90
All triangles have interior angles that add up to 180
We have already accounted for 150.
JIH + 150 = 180 Subtract 150
jIH = 180 - 150 = 30
Summary
x = 30
JIH = 30
H = 60
J = 90
A line passes through the points (4, 6) and (8, 7). What is its equation in point-slope form?
Answer:
y - 6 = 1/4(x - 4).
Step-by-step explanation:
The slope m = (7-6)/(8-4) = 1/4
y - y1 = m(x - x1)
Using the point (4, 6)
y - 6 = 1/4(x - 4) (answer)
The equation of line passes through the points (4, 6) and (8, 7) will be;
⇒ y = 1/4x + 5
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (4, 6) and (8, 7).
Now,
Since, The equation of line passes through the points (4, 6) and (8, 7) .
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (7 - 6) / (8 - 4)
m = 1 / 4
m = 1/4
Thus, The equation of line with slope 1/4 is,
⇒ y - 6 = 1/4 (x - 4)
⇒ 4 (y - 6) = x - 4
⇒ 4y - 24 = x - 4
⇒ 4y = x - 4 + 24
⇒ 4y = x + 20
⇒ y = 1/4x + 5
Therefore, The equation of line passes through the points (4, 6) and
(8, 7) will be;
⇒ y = 1/4x + 5
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at 6 am the temperature was -8ºC. In the afternoon, the temperature was +3ºC. What was the change of temperature during the day?
Answer:
I think -5
Step-by-step explanation:
-8-(3)= -5
if they are the same sings (+or-) you keep and add and different signs subtract, you keep the sign of the bigger number then you'll be exact.
Hope it helps
Fiona has $18 to spend. She spent $4.25, including tax, to buy a notebook. She needs to save $9.75, but she wants to buy a snack. If crackers cost $0.50 per package including tax, what inequality would show the maximum number of packages that Fiona can buy
Answer:
4.25+9.75+0.5x≤18
Step-by-step explanation:
4.25+9.75+0.5x≤18
14+0.5x≤18
0.5x≤4
x≤8
She can buy at most 8 packs of crackers.
Hope this helps :)
Fiona can buy maximum 8 number of packages of crackers.
What is subtraction?Subtraction is mathematic operation. Which is used to remove terms or objects in expression.
Given that Fiona has $18 to spend and she spent $4.25 .
Now, she has the money $18 - $4.25 = $ 13.75
And she needs to save $9.75 from rest of the amount.
Therefore, $13.75 - $ 9.75 = $4
Now she has $4 to spend and one packet of crackers cost $0.50.
So $4 / $0.50 = 8 number of packages Fiona can buy with the rest of money.
Therefore, Fiona can buy maximum 8 number of packages of crackers.
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what is the value of x?
Answer:
x=80
Step-by-step explanation:
70 + 30+x =180 (sum of angles in a triangle =180)
x=80
One-fourth of a number increased by thirteen is less than two.
Answer: x < -44
Step-by-step explanation:
alright my fellow dude gamer, i want you to know that "a number" is basically just x
so lets do this
[tex]\frac{1}{4}x + 13 < 2[/tex]
ok now we are going to solve for x, no?
[tex]\frac{1}{4}x < -11[/tex]
i just subtracted 13 from both sides
now we divide -11 by 1/4
[tex]x < -44[/tex]
MAGIC! ABSOLUTELY FANTASTIC! OH MY GOODNESS AHHHHHHH
The length of the fence is 12 1/2 feet and the width of the fence is 10 3/4 determine the perimeter
Answer:
46 1/2 feet
Step-by-step explanation:
Perimeter is defined as 2 × length + 2 × width which is 12.5 × 2 + 10.75 × 2 which works out to 46 1/2 or 46.5 feet which is the answer.
The perimeter of rectangle with length of the fence is [tex]12\frac{1}{2}[/tex] feet and the width of the fence is [tex]10\frac{3}{4}[/tex] is 46.5 feet.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given,
The length of the fence is [tex]12\frac{1}{2}[/tex] feet
[tex]12\frac{1}{2}[/tex] is changed to improper fraction 25/2
the width of the fence is [tex]10\frac{3}{4}[/tex]
[tex]10\frac{3}{4}[/tex] is changed to improper fraction 43/4
Now we know that perimeter of rectangle =2(Length+width)
=2(25/2+43/4)
LCM of 2 and 4 is 4
=2(50+43)/4
=93/2
=46.5
Hence the perimeter of rectangle with length of the fence is [tex]12\frac{1}{2}[/tex] feet and the width of the fence is [tex]10\frac{3}{4}[/tex] is 46.5 feet.
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-16=m/5 -18 prove m=10
Answer:
[tex]-16 = \frac{m}{5} - 18\\2 = \frac{m}{5}\\10 = m\\[/tex]
Step-by-step explanation:
Given the equation [tex]-16 = \frac{m}{5} - 18[/tex] isolate [tex]m[/tex]
1. The first is sum both sides by 18
[tex]-16 + 18= \frac{m}{5} - 18 + 18\\2 = \frac{m}{5}[/tex]
2. The second is multiply both sides by [tex]5[/tex]
[tex]5 \cdot 2 =5 \cdot \frac{m}{5}\\10 = m[/tex]
So of this way you can proof that [tex]m = 10[/tex]