Answer:
The number of passcodes possible is 1,100,000
Step-by-step explanation:
Here , we want to calculate the number of different possible passcodes.
For the five digit code,
each number in the code has a possibility of choosing from the digits 0 to 9, so this means that each of the numbers in the code has 10 options.
So for a five digit code, the number of possible choices would be 10 * 10 * 10 * 10 * 10 = 10^5
For a six digit code, the number of possible choice would be 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10^6
So for 5 or 6 digits code, the number of possible choices would be;
10^5 + 10^6 = 10^5(1 + 10)
= 11(10^5) = 1,100,000
The number of passcodes possible is 1,100,000
Calculation of the no of passcode:For the five-digit code, the no of possible choices should be [tex]10^5[/tex]
For the six-digit code, the no of possible choices should be [tex]10^6[/tex]
So, the possible choices should be
[tex]10^5 + 10^6 = 10^5(1 + 10)\\\\= 11(10^5)[/tex]
= 1,100,000
Hence, The number of passcodes possible is 1,100,000
Learn more about code here: https://brainly.com/question/24418415
A small company that manufactures snowboards uses the relation below to model its profit. In the model,
represents the number of snowboards in thousands, and P represents the profit in ten thousands of dollars.
What is the maximum profit the company can earn? How many snowboards must it produce to earn this
maximum profit?
a. Factor P =
4x2 + 32x + 336 to find the roots.
b. Find the axis of symmetry then use it to find the vertex.
c. Therefore, we need to see snowboards to make a maximum profit of
Answer:
a) x₁ = 14
x₂ = - 6
b) x = 4
c) P(max ) = 4000000 $
Step-by-step explanation:
To find the axis of symmetry we solve the equation
a) -4x² + 32x + 336 = 0
4x² - 32x - 336 = 0 or x² - 8x - 84 = 0
x₁,₂ = [ -b ± √b² -4ac ]/2a
x₁,₂ = [ 8 ±√(64) + 336 ]/2
x₁,₂ = [ 8 ± √400 ]/2
x₁,₂ =( 8 ± 20 )/2
x₁ = 14
x₂ = -6
a) Axis of symmetry must go through the middle point between the roots
x = 4 is the axis of symmetry
c) P = -4x² + 32x + 336
Taking derivatives on both sides of the equation we get
P´(x) = - 8x + 32 ⇒ P´(x) = 0 - 8x + 32
x = 32/8
x = 4 Company has to sell 4 ( 4000 snowboard)
to get a profit :
P = - 4*(4)² + 32*(4) + 336
P(max) = -64 + 128 + 336
P(max) = 400 or 400* 10000 = 4000000
In order to sustain itself in its cold habitat, a Siberian tiger requires 25 pounds of meat per day.
How much meat would seven Siberian tigers need for the month of April?
Select one:
a. 750 pounds
b. 175 pounds
c. 5425 pounds
d. 5250 pounds
Answer:
d. 5250 pounds
Step-by-step explanation:
25 lbs per day
There are 30 days in april
25 lbs/ day * 30 days
1 tiger would eat 750 lbs
There are 7 tigers
7 * 750 =5250 lbs
Answer:
D. 5250 pounds
Step-by-step explanation:
What you need to do is multiply 25 pounds by 30 because there are 30 days in the month of April.
25 x 30 = 750
Then multiply that amount by seven because there are 7 tigers.
750 x 7 = 5250
Which ordered pair is a solution to the system of linear equations? 2x + 3y= 6 –3x + 5y = 10
Answer:
(0,2)
Step-by-step explanation:
solve by addition/elimination
2x + 3y= 6
–3x + 5y = 10
multiply first equation by 3 and second one by 2 to eliminate x)
6x+9y=18
-6x+10y=20 (add the two equations)
6x+9y-6x+10y=38
19y=38
y=38/19=2
2x+3y=6
2x=6-6
x=0
Answer:
a
Step-by-step explanation:
Question 15: (5 points)
Find one possibie missing coordinate so that the point becomes a solution to the given inequality.
(x, 7) is a solution to 2 x - 3<y.
=
In a few sentences, please explain how you arrived at your answer
Answer:
[tex](4,7)[/tex]
Step-by-step explanation:
Given
[tex]2x - 3 < y[/tex]
[tex](x,7)[/tex]
Required
Find one possible value of x
From the given parameters;
[tex](x,7)[/tex] is a possible solution of [tex]2x - 3 < y[/tex] where y= 7
Substitute 7 for y
[tex]2x - 3 < 7[/tex]
Add 3 to both sides
[tex]2x - 3 + 3 < 7 + 3[/tex]
[tex]2x < 10[/tex]
Divide both sides by 2
[tex]2x/2 < 10/2[/tex]
[tex]x < 5[/tex]
The result of the inequality implies that x is less than 5; So, the possible values of x is all real numbers less than 5;
Having said that;
[tex](4,7)[/tex] is one possible coordinate of [tex]2x - 3 < y[/tex]
Use an appropriate series to find Taylor series of the given function centered at the indicated value of a. Write your answer in summation notation.
sinx, a= 2π
Answer:
The Taylor series is [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
Step-by-step explanation:
From the question we are told that
The function is [tex]f(x) = sin (x)[/tex]
This is centered at
[tex]a = 2 \pi[/tex]
Now the next step is to represent the function sin (x) in it Maclaurin series form which is
[tex]sin (x) = \frac{x^3}{3! } + \frac{x^5}{5!} - \frac{x^7}{7 !} +***[/tex]
=> [tex]sin (x) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
Now since the function is centered at [tex]a = 2 \pi[/tex]
We have that
[tex]sin (x - 2 \pi ) = (x-2 \pi ) - \frac{(x - 2 \pi)^3 }{3 \ !} + \frac{(x - 2 \pi)^5 }{5 \ !} - \frac{(x - 2 \pi)^7 }{7 \ !} + ***[/tex]
This above equation is generated because the function is not centered at the origin but at [tex]a = 2 \pi[/tex]
[tex]sin (x-2 \pi ) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x - 2 \pi)^{2n+1}][/tex]
Now due to the fact that [tex]sin (x- 2 \pi) = sin (x)[/tex]
This because [tex]2 \pi[/tex] is a constant
Then it implies that the Taylor series of the function centered at [tex]a = 2 \pi[/tex] is
[tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
On an uphill hike Ted climbs at 3mph. Going back down, he runs at 5mph. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike?
Answer:
10 miles
Step-by-step explanation:
3 mi/1 hr x (h hours + 2/3 hr) = 5 mi/1 hr x h hours
3h + 2 = 5h
2 = 2h
h = 1 hour
3mi/hr x 1 2/3 hr = 5 miles
5 mi/hr x 1 hr = 5 miles
He hiked 10 miles. (
Help ASAP!!!
Identify the correct trigonometry formula to use to solve for x.
Answer:
The answer is option 2.
Step-by-step explanation:
You have to apply Cosine Rule, cosθ = adjacent/hypotenuse. Then, you have to substitute the values into the formula :
[tex]cos(θ) = \frac{adj.}{hypo.} [/tex]
[tex]let \: θ = 55[/tex]
[tex]let \: adj. = 11[/tex]
[tex]let \: hypo. = x[/tex]
[tex]cos(55) = \frac{11}{x} [/tex]
The correct trigonometry formula to use to solve for x is [tex]\frac{11}{x}[/tex] . Thus option 1 is correct.
According to the question, we have
base = 11
hypotenuse = x
here for [tex]cos Ф[/tex]Ф, it is not required to find the value of perpendicular,
we know that in a right-angle triangle using trigonometric ratio, we get
[tex]cos Ф[/tex] Ф = [tex]\frac{base }{hypotenuse}[/tex]
[tex]cos Ф[/tex] Ф = [tex]\frac{11}{x}[/tex]
here Ф = [tex]55 ^0[/tex]
[tex]cos 55^o = \frac{11}{x}[/tex]
Thus, the value of the trigonometry formula to use to solve for x is [tex]\frac{11}{x}[/tex].
Thus option 1 is correct.
Learn more about Trigonometry here :
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What is the total amount of 2/5+5/3+9/3 and the lowest common denominator?
The lowest common denominator is lcm(5, 3), which is 15.
The sum of 2/5 + 5/3 + 9/3 is 6/15 + 25/15 + 45/15, which is 76/15 or [tex]5\frac{1}{15}[/tex].
Two hundred undergraduate students were randomly selected from a university that has 47,000 students in total. Systolic blood pressure was tested on the 200 students. The sample mean is 118.0 mmHg and the sample standard deviation is 11.0 mmHg. Please construct a 95% confidence interval for the population mean of students' systolic blood pressure. Which one of the following results is the closest to your answer? (Hint: use 1.96 as the critical z-value)
a. [110.5, 125.5]
b. [112.5, 123.5]
c. [114.5, 121.5]
d. [116.5, 119.5]
Answer:
The correct option is d
Step-by-step explanation:
From the question we are told that
The population size is [tex]N = 47000[/tex]
The sample size is [tex]n = 200[/tex]
The sample mean is [tex]\= x = 118.0 \ mmHg[/tex]
The standard deviation is [tex]\sigma = 11.0 \ mmHg[/tex]
Given that the confidence level is 95% then the level of significance can be calculated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from z-table , the value is [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 1.96[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because
[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval ( [tex]1-\alpha[/tex]) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error .
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } *\frac{\sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 *\frac{11.0 }{ \sqrt{200} }[/tex]
[tex]E = 1.5245[/tex]
The 95% confidence level interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]118.0 - 1.5245 < \mu < 118.0 + 1.5245[/tex]
[tex]116.5< \mu < 119.5[/tex]
[tex][116.5 , 119.5][/tex]
In △ABC, m∠A=27 °, c=14 , and m∠B=25 °. Find a to the nearest tenth.
Answer:
a = 8.1
Step-by-step explanation:
Firstly, since we have a triangle, automatically, we have 3 interior angles
Mathematically the sum of these angles = 180
A + B + C = 180
27 + 25 + C = 180
52 + C = 180
C = 180-52
C = 128
We use the sine rule to find a
The sine rule posits that the ratio of a side to the sine of the angle facing that side is equal for all the sides of a triangle
Thus, mathematically according to the sine rule;
c/Sin C = a/Sin A
14/sin 128 = a/sin 27
a = 14sin27/sin 128 = 8.0657
which to the nearest tenth is 8.1
What is the lateral surface area of the cone? A cone with diameter 18 centimeters, height of 12 centimeters, and slant height of 15 centimeters. L A = pi r l 108 pi centimeters squared 135 pi centimeters squared 180 pi centimeters squared 270 pi centimeters squared
Answer:
3051.08 cm squared
Step-by-step explanation:
The equation to find lateral surface area of a cone:
SA = pi r sqrt(h^2 * r^2)
Plug your values in.
SA = 3.14 * 9 * sqrt(144*81)
SA = 3.14 * 9 * 108
SA = 3051.08
The lateral surface area is 3051.08 cm squared.
Answer:
424.12cm^2
Step-by-step explanation:
make sure you have the radius, half of the diameter!
remember to use this formula! Lateral surface area = πrs = πr√(r2 + h2)
hope this helped!
r=radius
h=hight
s=slant
(SAT Prep) In the given figure, a║b. What is the value of x? A. 70° B. 45° C. 80° D. 65° I NEED THIS FAST PLZZZZZZ!!!!!!!!!!!!
Answer:
70
Step-by-step explanation:
You have to find the vertical of x. To the right of the vertical, we see that there is an angle of 25 (since the 25 up top corresponds to that blank angle). Once you add 25 + 85 + x = 180 (since this is a straight line), we see that x is 70, and its vertical is also 70.
helpppppppppppppppppppppp pleaseeeeeeeeeeeeeeeeeeeeeee
Answer:
0.29
Step-by-step explanation:
There are 29 squares shaded in. In all, there are 100 squares in the 10 × 10 square, so there are 29 shaded squares out of 100 squares in all. That is basically:
[tex]\frac{29}{100}[/tex]
[tex]\frac{29}{100}[/tex] can be converted to 0.29.
Answer:
0.29
Step-by-step explanation:
Since the grid is a 10x10, it means there are 100 total 'blocks' in the grid. So, since there are 29 shaded in out of the 100 'blocks total, the decimal would be .29, since the decimal means 29 hundredths, and it also means that there is 29 hundredths of the total grid shaded in.
Could anyone help me with this? T+S+U=130 T=3(U) S= T+10 U= ?? I need to decipher the value of T,S and U.
Answer:
U = 17 1/7
T = 51 3/7
S = 61 3/7
Step-by-step explanation:
Given
T+S+U=130\
T=3(U)
S= T+10 we have to find value of u
First step:
find S and T in terms of U
T is given
T = 3U
S = T +10 , using T = 3U
S = 3U+10
Using the above value in T+S+U=130
3U + 3U+10 + U = 130
=> 7U = 130-10 = 120
=> U = 120/7 = 17 1/7
T = 3U = 3*120/7 = 360/7 = 51 3/7
S = T+10 = 360/7 + 10 = (360+70)/7 = 430/7 = 61 3/7
Thus,
U = 17 1/7
T = 51 3/7
S = 61 3/7
Find the points of intersection of the following function graphs: y=20x−70 and y=70x+30
Answer:
(-2,-110)
Step-by-step explanation:
First solve for x
20x−70=70x+30
x= -2
Now substitute x for -2
y=20x−70
y=20(-2)-70
y = -110
Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 18 of the 52 boxes on the shelf have the secret decoder ring. The other 34 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?
Answer:
3/26
Step-by-step explanation:
Probability of the first box to have the secret decoder ring is 18 out of 52:
18/52= 9/26Probability of the second box to have the ring is 17 out of 51, because one box with the ring already selected and not counted:
17/51= 1/3Probability that both of them have the secret decoder ring:
9/26*1/3= 3/26So the answer is 3/26
7987.1569 to the nearest thousandth
Answer:
7987.1569 to the nearest thousandths is 7987.157
Step-by-step explanation:
what is 1.8÷0.004? using long division
Answer:
Hi! Answer will be below.
Step-by-step explanation:
The answer is 450.
If you divide 1.8 and 0.004 the answer you should get is 450.
Below I attached a picture of how to do long division...the picture is an example.
Hope this helps!:)
⭐️Have a wonderful day!⭐️
Jamie's dog eats 3/4 pound of dog food each day. How many pounds of dog
food does Jamie's dog eat in 4 days?
Answer:
The dog will eat 3 lbs
Step-by-step explanation:
Take the amount eaten per day and multiply by the number of days
3/4 * 4 = 3
The dog will eat 3 lbs
Answer:
3 pounds
Step-by-step explanation:
Multiply the amount of dog food per day with the number of days.
[tex]\frac{3}{4} \times 4[/tex]
[tex]\frac{12}{4} =3[/tex]
In 4 days, Jamie's dog will eat 3 pounds of dog food.
help!! I have problem to solve this question
Answer:
Step-by-step explanation:
[tex]\frac{x-1}{2} =t\\\frac{y-2}{3} =t\\\frac{z-3}{4} =t\\so~eq.~of~line~L_{1}~is\\\frac{x-1}{2} =\frac{y-2}{3} =\frac{z-3}{4} \\its~d.r's~are~2,3,4\\again~\frac{x-2}{1} =s\\\frac{y-4}{2} =s\\\frac{z+1}{-4} =s\\so~eq. ~of~line~L_{2}~is\\\frac{x-2}{1} =\frac{y-4}{2} =\frac{z+1}{-4} \\its~d.r's ~are~1,2,-4\\let ~the ~d.r's~of~line~perpendicular~to~both~L_{1}~and~L_{2}~be~a,b,c,~then~\\2a+3b+4c=0\\1a+2b-4c=0\\solving\\\frac{a}{3*-4-4*2} =\frac{b}{4*1-2*-4} =\frac{c}{2*2-3*1} \\[/tex]
[tex]\frac{a}{-20} =\frac{b}{-4} =\frac{c}{1} \\d.r's~of ~reqd~line~is~-20,-4,1~or~20,4,-1[/tex]
now you find the point of intersection.
then calculate the angle.
A sample of radioactive material disintegrates from 6 to 4 grams in 100 days. After how many days will just 3 grams remain?
Answer:
150 days
Step-by-step explanation:
6-4=2
100/2=50
50*3=150
The number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
The rate of disintegration varies directly proportional to the quantity of the material.
As such, we can say:
[tex]\mathbf{=\dfrac{dN}{dt}\ \alpha \ N}[/tex]
[tex]\mathbf{\implies \dfrac{dN}{N}\ = k dt}[/tex]
Taking the integral form;
[tex]\mathbf{\implies \int \dfrac{dN}{N}\ =\int k dt}[/tex]
[tex]\mathbf{\implies In N =kt+ C---- (1)}[/tex]
When t = 0, N = 6 grams
In(6) = C
∴
When t = 100, N = 4 grams
In (4) = 100k + In6
100 k = 1n (4) - In(6)
[tex]\mathbf{100 k = In (\dfrac{4}{6})}[/tex]
[tex]\mathbf{k = \dfrac{1}{100} In(\dfrac{4}{6})}[/tex]
∴
From equation (1):
[tex]\mathbf{In N = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
when,
n = 3 grams; we have:[tex]\mathbf{In (3) = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
[tex]\mathbf{\implies \dfrac{t}{100} In(\dfrac{4}{6}) = In \dfrac{ 3}{ 6}}[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{In (\dfrac{ 3}{ 6})}{ In(\dfrac{4}{6}) }\Big) }[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{0.69314}{ 0.40048}\Big) }[/tex]
t = 173.077 days
Therefore, the number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
Learn more about radioactive materials here:
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what is the answer 2×3+4×100-50+10
Answer:
366
Step-by-step explanation:
2×3+4×100-50+10
PEMDAS says multiply and divide from left to right
6 + 400 - 50 +10
Then add and subtract
406-50+10
356+10
366
Answer:
[tex]\boxed{366}[/tex]
Step-by-step explanation:
[tex]2 \times 3+4 \times 100-50+10[/tex]
Multiplication is first.
[tex]6+400-50+10[/tex]
Add or subtract the numbers.
[tex]350+10+6[/tex]
[tex]366[/tex]
HELP WILL GIVE BRAINLIEST FOR ANSWER QUICKLY PLEASE HELP
Answer:
We have sinθ = 12/13
The method here is to figure out the value of θ
Using a calculator sin^(-1)(12/13) =67.38°
67.38° is in quadrant 1 so we must substract 67.38° from 180° wich is π
180-67.38= 112.61° ⇒ θ= 112.61°Now time to calculate cos2θ and cosθ using a calculator
cosθ = -5/13 cos2θ = -0.7The values we got make sense since θ is in quadrant 2 and 2θ in quadrant 3
the result of two forces acting on a body has a magnitude of 80 pounds. The angles between the resultant and the forces are 20 degrees and 52 degrees. find the magnitude of the large force
Answer:
Larger force= 66.28 pounds
Step-by-step explanation:
The angle of the resultant force 80 pounds = 180-(52+20)
The angle of the resultant force 80 pounds = 180-72
The angle of the resultant force 80 pounds = 108°
The larger force is the force with 52°
Let the larger force be x
Magnitude of the larger force
x/sin52 = 80/sin108
X= sin52 *(80/sin 108)
X= 0.7880*(80/0.9511)
X = 0.7780*(84.1131)
X = 66.28 pounds
Solve.
1/3-6<24
{s | s<6}
O {S | s < 10}
O {S | s < 54}
O {S | s < 90}
Answer:
The answer is:
The fourth option,
{s | s <90}
Step-by-step explanation:
yes
Answer:
[tex]\boxed{s|s<90}[/tex]
Step-by-step explanation:
1/3s-6<24
Add 6 on both sides.
1/3s<30
Multiply both sides by 3.
s<90
Determine whether the following problem involves a permutation or a combination and explain your answer. How many different -letter passwords can be formed from the letters , , , , , , and if no repetition of letters is allowed? Choose the correct answer below. A. The problem involves a permutation because the order in which the letters are selected does matter. B. The problem involves a combination because the order in which the letters are selected does not matter. C. The problem involves a combination because the order in which the letters are selected does matter. D. The problem involves a permutation because the order in which the letters are selected does not matter.
Answer:
B. The problem involves a combination because the order in which the letters are selected does not matter.
Step-by-step explanation:
Computation technique is a method of statistics to find possible ways of combination. In computation technique it is assumed that order does not matter and letters will be selected at random. Permutation is a statistics technique to find possible ways of combination when the order does matter. Permutation technique cannot be used when order does not matter.
i give you brailenst
Answer:
The answer is #3 which is 24%.
Step-by-step explanation:
6 × 100
25
25 into 100 is 4, then 6×4 = 24%
I really hope this helps :)
Which algebraic expression represents the phrase "six less than a number"?
SERE
6x - X
X-6
6- X
X - 6x
Answer:
The answer is option B.
Step-by-step explanation:
six less than a number is written as
x - 6
Hope this helps you
what is the answer. plz heelp 5h+2(11-h)= -5
Answer:
h = -9
Step-by-step explanation:
5h+2(11-h)= -5
Distribute
5h +22 -2h = -5
Combine like terms
3h +22 = -5
Subtract 22 from each side
3h +22-22 = -5-22
3h = -27
Divide by 3
3h/3 = -27/3
h = -9
Which graph best models the inequality y<_ -2/5x+2
Answer:
Step-by-step explanation:
Simplify each term.
y ≤ −2x/5 + 2
Find the slope and the y-intercept for the boundary line.
Slope: -2/5
Y-intercept: 2
Graph a solid line, then shade the area below the boundary line since
y is less than -2x/5 + 2
y ≤ −2x/5 + 2
Hope this can help