Answer:
Hence, the probability of an access code “1234”= [tex]\dfrac{1}{10000}[/tex]
Step-by-step explanation:
" The probability of an event is defined as the ratio of total number of favourable outcomes to the total number of possible outcomes ".
A bank requires a four-digit access code for each account. The access code is generated using the digits 0–9, and the digits can be repeated.
The total number of outcomes possible are 10×10×10×10=10000
since the first place any of the 10 digits are possible, similarly for the second, third and fourth place.
Also each code is a unique representation in itself.
Hence the code "1234" is unique.
Hence, the probability of an access code “1234”= [tex]\dfrac{1}{10000}[/tex]
Find the value of x for which p is parallel to q , if m<1=(3x) and m<3=105. The diagram is not scale.
15-28i=3l+(4m)i solve ...?
To solve the equation 15-28i=3l+(4m)i, separate the real and imaginary parts of the equation and solve for l and m separately.
Explanation:To solve the equation 15-28i=3l+(4m)i, we can separate the real and imaginary parts of the equation. The real part is 15, and the imaginary part is -28. Similarly, the real part of the right side is 3l and the imaginary part is 4m. Equating the real parts and imaginary parts separately, we get two equations: 15 = 3l and -28 = 4m. Solving these equations will give us the values of l and m.
In the first equation, dividing both sides by 3 gives us l = 5. In the second equation, dividing both sides by 4 gives us m = -7.
Therefore, the solution to the equation 15-28i=3l+(4m)i is l = 5 and m = -7.
Find a value of the standard normal random variable Z, Call it Z0, such that
a. P(Z ≤ Z0) = .0401
b. P(- Z0 ≤ Z ≤ Z0) = .95
c. P(- Z0 ≤ Z ≤ Z0) = .90
d. P(- Z0 ≤ Z ≤ 0) = .2967
The 0 is subzero, don't know why the site couldn't show it.
Using the normal distribution, it is found that:
a) [tex]Z_0 = -1.75[/tex].
b) [tex]Z_0 = 1.96[/tex].
c) [tex]Z_0 = 1.645[/tex].
d) [tex]Z_0 = -0.83[/tex].
In a normal distribution 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]
Each z-score has a p-value associated with it, which is the percentile of X, and is found at the z-table.Item a:
This is Z with a p-value of 0.0401, thus [tex]Z_0 = -1.75[/tex].
Item b:
Due to the symmetry of the normal distribution, the middle 95% is between the 2.5th and the 97.5th percentile.We want the positive value, so Z with a p-value of 0.975, which is [tex]Z_0 = 1.96[/tex]Item c:
Same logic as b, just middle 90%, thus [tex]Z_0 = 1.645[/tex].
Item d:
This is Z with a p-value of 1 - 0.2967 = 0.2033, thus [tex]Z_0 = -0.83[/tex].
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Final answer:
The value of the standard normal random variable Z that satisfies the equation P(-Z0 ≤ Z ≤ Z0) = 0.90 is approximately 1.28.
Explanation:
The z-score that corresponds to the area 0.90 under the standard normal distribution can be found using a z-table or a calculator.
Using a z-table, locate the area 0.90. The corresponding z-score is approximately 1.28.Using a calculator, the invNorm(0.90) command can be used to find the z-score, which is also approximately 1.28.Therefore, the value of the standard normal random variable Z, denoted as Z0, that satisfies the equation P(-Z0 ≤ Z ≤ Z0) = 0.90 is approximately 1.28.
Jessica's family is on vacation at the Outer Banks. She is going to buy dinner at a local seafood distributor. She can buy shrimp at $8.50 per pound and crab cakes for $3 each. she has $45 to spend and must buy 3 pound of shrimp. What is the largest quantity of crab cakes that she can buy?
he ages of four groups of workers are shown. Which group has the largest range?
Answer:
b
Step-by-step explanation:
Answer:
D) Group D
Step-by-step explanation:
A range: 38
B range: 48
C range: 40
D range: 51
10 is %20 of what number
Answer:
50
Step-by-step explanation:
10=20/100*50/1=1000/100=10
simplify completely 5x^2+9x-2/x^2+12x+20*x^2+17x+70/15x-3 ...?
I HAVE 5 MATH QUESTIONS AND NEED HELP ASAP! ONLY COMMENT IF YOU ARE GOING TO HELP.
A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3 additional seats . How many seats are in thecivic theater
There are 840 seats in total in Cinema Hall.
What is arithmetic Progression?The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.
Given:
First term, [tex]a_1[/tex] = 22
second row = 22 + 3 = 25
Third row = 25 + 3 = 28
So, the Recursive Formula is
[tex]a_n[/tex] = a + (n-1)d
[tex]a_n[/tex] = 10 + (n-1)3
[tex]a_n[/tex] = 10 + 3n - 3
[tex]a_n[/tex] = 7 + 3n
In 21th rows the seats are
= 7 +3 (21)
= 7 + 63 = 70
Now, to find the number of seats in hall we have to find the sum of seats from row 1 to row 21 using Formula
= n×([tex]a_1[/tex]+ [tex]a_n[/tex])/2
= 21 x (10 + 70) /2
= 21 x 80 /2
= 21 x 40
= 840
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Andrea drove 500 miles in 10 hours. find the average number of miles per hour that andrea drove
A sail is in the form of a right triangle that is four times as high as it is wide.The sail is made from 32 square meters of material. What is its height?
To calculate the height of a sail that is four times as high as it is wide and made from 32 square meters of material, we use the area formula for a triangle and find that the height is 16 meters.
The student's question concerns the height of a sail in the shape of a right triangle, where the sail's height is four times its width and the total area of the sail is 32 square meters. To find the height, we can let the width be x meters, which makes the height 4x meters due to the given ratio.
Using the formula for the area of a triangle, A = bh/2, where b is the base and h is the height, we can write an equation for the area in terms of x: 32 m² = x × (4x) / 2.
Simplifying this, we get 32 = 2x2, which can be further simplified to x² = 16. Taking the square root of both sides gives us x = 4. Therefore, the height of the sail, being four times the width, is 16 meters.
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the second equation is substituted into the first equation.
2x – 3y = –29
x + 4y = 13
2(4y + 13) – 3y = –29
2(–4y + 13) – 3y = –29
2x – 3(4y + 13) = –29
2x – 3(–4y + 13) = –29 ...?
Answer:
can confirm that the answer above is correct
hope yall have a nice day
Step-by-step explanation:
What percent of 150 is 135?
find g'(4) given that f(4)=3 and f'(4) = -5. g(x) = f(x)/x
Find the numerical value of cosh (ln5)
The numerical value of cosh(ln5) is 2.55, obtained by using the hyperbolic cosine function definition and the properties of exponential and logarithmic functions.
Explanation:The question asks you to find the numerical value of cosh (ln5). This involves using hyperbolic trigonometry functions, specifically the hyperbolic cosine function.
The hyperbolic cosine, represented by 'cosh', is a mathematical function whose definition is similar to the ordinary trigonometric cosine function. However, it is defined using exponential functions rather than angular measure. The general definition is cosh(x) = (e^x + e^(-x))/2.
Using this formula and substituting ln5 for x results in cosh(ln5) = (e^(ln5) + e^(-ln5))/2.
The expression e^(ln5) simplifies to 5 since e and ln are inverse functions.
For the second term, e^(-ln5), we can use the fact that a negative exponent signifies taking the reciprocal, so this simplifies to 1/5.
Therefore, cosh(ln5) = (5 + 1/5)/2 = 5.1/2 = 2.55.
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The solution to cosh (ln5) is obtained by substituting ln5 in the formula of hyperbolic cosine function, which simplifies it to (5 + 1/5)/2 yielding a result of 2.6.
To find the numerical value of cosh (ln5), we need to know the definition of cosh. It is a hyperbolic function defined as cosh(x) = (e^x + e^-x)/2 where e is Euler's number (approximately 2.71828).
So, to find cosh (ln5), we substitute ln5 in place of x in the formula cosh(x) = (e^x + e^-x)/2.
This gives us cosh(ln5) = (e^ln5 + e^-ln5)/2. However, e and ln are inverse functions, so e^ln5 simplifies to 5. Similarly, for e^-ln5, we need to use the property a^-b = 1/a^b to simplify it to 1/5.
Then we just add and divide, yielding cosh(ln5) = (5 + 1/5)/2 = 2.6.
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Locate the absolute extrema of the function on the closed interval:
y = 3x^(2/3) - 2x, [-1, 1]
The absolute maximum occurs at x = -1, where y = 5. The absolute minimum occurs at x = 1, where y = 1.
Explanation:To find the absolute extrema of a function on a closed interval, we first need to find the critical points of the function within that interval. The critical points occur where the derivative of the function is equal to zero or does not exist.
In this case, the function is y = 3x^(2/3) - 2x, and the closed interval is [-1, 1].
We can find the derivative of the function:
y' = 2x^(-1/3) - 2
Setting the derivative equal to zero and solving for x:
2x^(-1/3) - 2 = 0
x^(-1/3) = 1
Raising both sides to the power of -3 gives:
x = 1
We found one critical point at x = 1. Now we need to check the endpoints of the closed interval, which are -1 and 1. Evaluating the function at these points:
y(-1) = 3(-1)^(2/3) - 2(-1) = 5
y(1) = 3(1)^(2/3) - 2(1) = 1
Therefore, the absolute maximum of the function occurs at x = -1, where y = 5, and the absolute minimum occurs at x = 1, where y = 1.
50 coins is worth $5.20. There areally 12 more nickels and dimes, and the rest Andre quarters. How many coins of each type are there?
40% of the students at Rockledge Middle School are musicians. 75% of those musicians have to read sheet music when they play their instruments If 38 of the students can play their instruments without reading sheet music, how many students are there at Rockledge Middle School?
What is the simplified form of the expression? 7^4
a. 16,384
b. 16,807
c. 343
d. 2,401
Answer:
The correct answer is D. The simplified form of the expression 7^4 is 2,401.
Step-by-step explanation:
7 ^ 4, that is, the exponentiation of 7 to the fourth power, implies the continuous multiplication of the number 7 for 4 times. Therefore, this number will appear 4 times in a multiplication, whose result will be said number exposed to the fourth power.
Simplified, this operation translates into 7x7x7x7, whose result is 2,401.
find the median for the given set of data.
0.6, 1.1, 0.87, 2, 0.87, 1.23
a) 0.87
b)0.985
c)1.1
Can someone answer the questions on the sheet for me please?
Statistics show that the sales force of Golden Wholesalers successfully closed 1,711 sales out of 1,950 sales calls. What was their percent success rate?
9x^2-y^2=1
(a) find y' by implicit differentiation
(b) Solve the equation explicitly for y and differentiate to get y' in terms of x
(c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a)
Finding the rate of change in something with respect to something is known as differentiation. For Example, Change in y with respect to x is known as the derivative of y with respect to x.
How to solve it?(a) [tex]9{x}^2-{y}^2 = 1[/tex]
Differentiating equation with respect to x :
[tex]9*2x - 2y\frac{dy}{dx} = 0\\ 18x = 2y\frac{dy}{dx}\\9\frac{x}{y} =\frac{dy}{dx}[/tex]
(b)
[tex]9{x}^2-{y}^2 = 1\\9{x}^2-1 = {y}^2 \\\sqrt[2]{9{x}^2-1} = y\\[/tex]
differentiating with respect to x gives:
[tex]\frac{1}{2\sqrt{9{x}^2-1} } *(18x) = \frac{dy}{dx}\\\frac{1}{\sqrt{9{x}^2-1} } *(9x) = \frac{dy}{dx}[/tex]
(c) [tex]9\frac{x}{y} =\frac{dy}{dx}[/tex]
substituting value of y
[tex]\sqrt[2]{9{x}^2-1} = y\\\\\frac{9x}{\sqrt[2]{9{x}^2-1}} = \frac{dy}{dx}[/tex]
Hence the solution is consistent.
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Chandra has 2 liters of a 14% solution of sodium hydroxide in a container. What is the amount and concentration of sodium hydroxide solution she must add to this in order to end up with 7 liters of a 34% solution?
A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85. Which system of equations can be used to determine the number of quarters, q, and the number of dimes, d, in the bag?
Answer:
Simultaneous Equation
Step-by-step explanation:
A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85. Which system of equations can be used to determine the number of quarters, q, and the number of dimes, d, in the bag?
To get the number of dimes and the number of quarters q will definitely have to be by simultaneous equation
let the number of dimes be d
let the number of quarters be q
let the cost of quarters/ one be Q
let the cost of dime/one be D
q+d=18--------------1
Qq+Dd=2.85.........2
from equation 1
q=18-d
substituting the value of q into equation 2
Q(18-d)+Dd=2.85
if cost of quarters/ one is given and the cost of dime/one is also given we can go ahead to find
q and d
In this mathematical problem involving a system of equations, we use the information provided about the total number of coins and their total value to form two equations: q + d = 18 and 0.25q + 0.10d = 2.85.
Explanation:The subject of this question is Mathematics, specifically dealing with a system of equations. Given the problem, the system of equations can be formulated from the conditions that the student has 18 coins in total and their combined value is $2.85. These conditions give us two equations:
q + d = 18, this equation represents the total number of quarters (q) and dimes (d).0.25q + 0.10d = 2.85, this equation represents the total value of the quarters and dimes in the bag.Learn more about System of Equations here:
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A triangle has sides of square root of 2 and 3. Which could not be the length of the third side if it is a right triangle?
Answer:
the root of 13
Step-by-step explanation:
Rewrite y = √25-75) + 3 to make it easy to graph using a translation. Describe the graph
A.Rewritten, y = √X-3 + 3. It is the graph of y = √X translated 3 units right and 3 units up.
B. Rewritten, y = √X-3 + 3. It is the graph of y = √X translated 3 units left and 3 units up.
C. Rewritten, y = √X-3 + 3. It is the graph of y = √X translated 3 units left and 3 units up.
D. Rewritten, y = √X-3 + 3. It is the graph of y = √X translated 3 units right and 3 units up.
2. How is the graph of Y=√X) -5 translated from the graph of √X ?
shifted 5 units right
shifted 5 units down
shifted 5 units left
shifted 5 units up
Suppose you buy a car with a value of $9,250. Each year the value of your car will depreciate by 5.1%. How much will your car be worth in 8 years?
Final answer:
To calculate the value of the car in 8 years with a constant yearly depreciation rate of 5.1%, we can use the formula for compound interest.
Explanation:
To calculate the value of the car in 8 years, we can use the formula for compound interest: A = P(1 - r/n)^(nt), where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, the initial amount is $9,250, the interest rate is 5.1%, and the number of times interest is compounded per year is 1. Plugging these values into the formula, we get:
A = 9250(1 - 0.051/1)^(1*8) = $6630.27
Therefore, the car will be worth approximately $6,630.27 in 8 years.
Pre-Calc :
How do you get the direct relationship between y and x and how do you know if the parametric equations determine y as a function of x with the following?
x = 2t and y = 3t -1
A secant is a line or segment that passes through a circle in one and only one place. True or false?
Answer:
false
Step-by-step explanation: