The probability that the first interview occurs on the fifth resume that you sent is 0.2592.
According to the given question.
The probability of being called for an interview, p = 0.40.
So, the probability of not being called for an interview, q = 1 - 0.40 = 0.60
As we know that binomial distribution summarizes the number of trials, or observations when each trial has the same probability of attaining one particular value. The binomial distribution determines the probability of observing a specified number of successful outcomes in a specified number of trials.
Therefore, the probability that the first interview occurs on the fifth resume that you send out
= [tex]^{5} C_{1} (0.40)^{1} (0.60)^{4}[/tex]
= 5(0.40)(0.1296)
= 0.2592
Hence, the probability that the first interview occurs on the fifth resume that you sent is 0.2592.
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In a given right triangle, If 0 º < x < 90 º and cos x = √ 3 / 2, then sin x = ?
Answer:
1/2
Step-by-step explanation:
The "Pythagorean relation" between trig functions can be used to find the sine.
Pythagorean relationThe relation between sine and cosine is the identity ...
sin(x)² +cos(x)² = 1
This can be solved for sin(x) in terms of cos(x):
sin(x) = √(1 -cos(x)²)
ApplicationFor the present case, using the given cosine value, we find ...
sin(x) = √(1 -(√3/2)²) = √(1 -3/4) = √(1/4)
sin(x) = 1/2
__
Additional comment
The sine and cosine of an angle are the y and x coordinates (respectively) of the corresponding point on the unit circle. The right triangle with these legs will satisfy the Pythagorean theorem with ...
sin(x)² + cos(x)² = 1 . . . . . . where 1 is the hypotenuse (radius of unit circle)
A calculator can always be used to verify the result.
When comparing the f(x) = –x2 + 2x and g(x) = log(2x + 1), on which interval are both functions positive?
(–∞, 0)
(0, 2)
(2, ∞)
(∞, ∞)
Considering their graphs, the interval in which both functions are positive is:
(0, 2)
When are the functions positive?A function is positive when it's graph is positioned above the x-axis.
Looking at the graph, the functions are positive for x between 0 and 2, hence the interval in which both functions are positive is stated as follows:
(0, 2)
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A 6 character computer password is made up of 4 numbers followed by 2 letters. How many different passwords are possible?
Answer: 6,760,000
Step-by-Step Explanation:
Simplify this expression √x4y12
Answer:
4[tex]\sqrt{3xy}[/tex]
Step-by-step explanation:
4 is a perfect square. We can pull 2 out from under the square root symbol.
The prime factor of 12 is 2.2.3. We can pull another 2 outside of the square root symbol. 2 x2 is 4 that will be outside of the square root symbol and the x, y and 3 will be left under the symbol.
. f(x) = Square root of quantity x plus eight. ; g(x) = 8x - 12 Find f(g(x)). (1 point) f(g(x)) = 2 Square root of quantity two x plus one. f(g(x)) = 8 Square root of quantity x plus eight. - 12 f(g(x)) = 2 Square root of quantity two x minus one. f(g(x)) = 8 Square root of quantity two x plus one.
Answer:
[tex]f(g(x))[/tex] = [tex]\sqrt{8x - 4}[/tex]
Step-by-step explanation:
• [tex]f(x) = \sqrt{x + 8}[/tex]
• [tex]g(x) = 8x - 12[/tex]
[tex]f(g(x))[/tex] is the combination of the functions [tex]f(x)[/tex] and [tex]g(x)[/tex] such that [tex]g(x)[/tex] is the input to the function [tex]f(x)[/tex] .
This means, we have to replace the original input of [tex]f(x)[/tex], which is [tex]x[/tex], with the function [tex]g(x)[/tex].
∴ [tex]f(g(x))[/tex] = [tex]f(8x - 12)[/tex]
⇒ [tex]\sqrt{8x - 12 + 8}[/tex]
⇒ [tex]\sqrt{8x - 4}[/tex]
Sketch the graph of the following equation: y=-3x-5
Answer is below attached
Step by step. We know y = -3x -5
The first point on the graph is -5 on the y axis. It is your y intercept.
The second point is your slope, which is the number next to the x, stated as y/x, -3/1.
You will graph this from the y-intercept as shown in red.
Then you can connect the points, shown with the blue line.
help please. which one is right?
Answer: B
Step-by-step explanation: If it goes through a point, flip that point around and that is the point of the inverse. Do that for multiple points to get your answer, which is B
Please help !!! Need help !!!
The go fish game tank contains 30 fish the probability of catching a purple fish is 1/3 the probability of catching a green fish
Answer:
2/3
Step-by-step explanation:
since they are just two colors of fish inside, since the probability is always 1.. so we have to minus 1/3 from 1,which is 1-1/3=2/3
The coefficient of determination, r, is the amount of variation in _______ that is explained by the regression line.
The coefficient of determination, r, is the amount of variation in the observed values of the response variable that is explained by the regression line.
About Coefficient of Determination:
When forecasting the result of an event, the coefficient of determination is a statistical measurement that looks at how variations in one variable may be explained by differences in a second variable.
In other words, the coefficient of determination, r, which is more frequently used to refer to the strength of a linear relationship between two variables, is a crucial tool for researchers when undertaking trend analysis.
For illustration, this coefficient of determination might be used to consider the possibility that a woman would give birth to her child on a specific date in the future if she became pregnant on a specific day. This metric's objective in this situation is to determine the relationship between the connected occurrences of conception and birth.
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If the first two angles of a triangle measure 45° and 111°, what does the third angle measure?
Answer:
third angle measures 24°
Step-by-step explanation:
triangles are 180°
add up the first two angles and subtract the sum from 180°
45° + 111° = 156°
180 - 156 = 24
Solve this inequality and write the solution using interval notation:
The solution to the inequality in discuss involving a rational expression as indicated in the task content is; t (9, infinity).
What is the solution to the inequality as indicated in the task content in which case, the solution is expressed using interval notation?The inequality given in the task content as evident is; (2t +22)/(2t +2) <= 2.
On this note, the inequality can be solved by cross-multiplication as follows;
2t +22 <= 4t +4
Hence, we have;
-2t <= -18
t >= 9.
Hence, when expressed as an interval notation, we have; t (9, infinity).
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Hundred chart: I am thinking of a number that is greater than 70 but less than 100.
It is not divisible by 10. It is not divisible by 4. It is not an odd number. What can I be
The numbers which is greater than 70 but less than 100, not divisible by 10, not divisible by 4, not an odd number are 74, 78, 82, 86, 94, 98
Even and odd numbersA number greater than 70 but less than 100Not divisible by 10Not divisible by 4Not odd numberA number greater than 70 but less than 100
71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 98
Not odd number
72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98
Not divisible by 10
72, 74, 76, 78, 82, 84, 86, 88, 92, 94, 96, 98
Not divisible by 4
74, 78, 82, 86, 94, 98
Therefore, the numbers which is greater than 70 but less than 100, not divisible by 10, not divisible by 4, not an odd number are 74, 78, 82, 86, 94, 98.
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
○ [tex]3x + 4y = 7[/tex]
Step-by-step explanation:
The general form of the equation of a straight line is as follows:
[tex]\boxed{y = mx + c}[/tex],
where:
m = slope
c = y-intercept.
This means that m, which is the coefficient of [tex]x[/tex], needs to be [tex]-\frac{3}{4}[/tex].
Therefore we have to rearrange each equation given to make y the subject, and then check if the coefficient of [tex]x[/tex] becomes [tex]-\frac{3}{4}[/tex].
• First option:
[tex]4x - 3y = 7[/tex]
⇒ [tex]-3y = -4x + 7[/tex]
⇒ [tex]y = \frac{4}{3}x -{ \frac{7}{3}[/tex]
∴ 'm' is [tex]\bf \frac{4}{3}[/tex], not [tex]-\frac{3}{4}[/tex], therefore this option is incorrect.
• Second option:
[tex]4x + 3y = 7[/tex]
⇒ [tex]3y = -4x + 7[/tex]
⇒ [tex]y = -\frac{4}{3}x + \frac{7}{3}[/tex]
∴ 'm' is [tex]\bf -\frac{4}{3}[/tex], not [tex]-\frac{3}{4}[/tex], therefore this option is incorrect.
• Third option:
[tex]3x + 4y = 7[/tex]
⇒ [tex]4y = -3x + 7[/tex]
⇒ [tex]y = -\frac{3}{4}x + \frac{7}{3}[/tex]
'm' is [tex]\bf -\frac{3}{4}[/tex], therefore this option is correct.
Note:
You can rearrange the equation given in the last option, and see that 'm' comes out to be [tex]\frac{3}{4}[/tex], thereby making it incorrect.
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:[tex]\sf{- \dfrac{3}{4}}[/tex]
First, we take all the given options to their slope-intercept form:
[tex]\longrightarrow \sf{y=m x+b}[/tex]
Taking to each equation to its slope-intercept form, you get:
[tex]\small\longrightarrow \sf{-3y = 7 - 4x}[/tex]
[tex]\small\longrightarrow \sf{- \dfrac{4}{ - 3} x + \dfrac{7}{3} }[/tex]
[tex]\small\longrightarrow \sf{y = \dfrac{4}{ 3} x - \dfrac{7}{3} }[/tex]
[tex]\small\longrightarrow \sf{3y = 7 - 4x}[/tex]
[tex]\small\longrightarrow \sf{y = \dfrac{7}{3} - \dfrac{4}{3} x}[/tex]
[tex]\small\longrightarrow \sf{4y y = = 7- 3x}[/tex]
[tex]\small\longrightarrow \sf{y = \dfrac{7}{4} - \dfrac{3}{4} x}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex] \bm{3x+4y=7}[/tex]
Ebony's bank balance 1st reached $400 on Day 4. The last day her balance was $400 was Day 8.
(a) Determine
B(5), B(6), and B(7). Explain how you determined these amounts.
Explain how you determined these amounts.
(b) Estimate
B(1), B(2), and B(3)
(c) Jade said that the amount of money Ebony took out of her account each day between Day 8 and Day
12 was the same amount of money she put into her account each day between Day 0 and Day 4.
Recall that Day 12 is when the balance first reached $0. Without doing any calculations, how could
you show Jade why that cannot be true?
Ebony’s bank balance is $400 was Day 8 and this can be explained below.
How to explain the information?Jade cannot be true because for every transaction made during withdraws, a little amount of money is collected and as such the amount will never remain $400.
Note that the scenario for the above to occur is:
On day 4, her balance = $400
On day 5, her balance = $40
On day 6, her balance = $400
On day 7, her balance = $400
On day 8, her balance = $400
Another fact is that since she deposited 400 at first, on day 8, there will be a 0 increase so the amount will still be 400.
Therefore, if the above is the case, one can deduce the fact that her balance will still be $400.
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Three Algebra 1 students are comparing how fast their social media posts have spread. Their results are shown in the following table:
Student
Amber
Ben
Carter
Description
Amber shared her photo with 3 people. They continued to share it, so the number of shares increases every day, as shown by the function.
Ben shared his post with 2 friends. Each of those friends shares with 3 more every day, so the number of shares triples every day.
Carter shared his post with 10 friends, who each share with only 2 people each day.
Social Media Post Shares
f(x) = 3(4)x
Day
0
1
2
number of shares
2
6
18
Write an exponential function to represent the spread of Carter's social media post.
The exponential model that best represents the data is f(x) = 2(3)x
Exponential equationExponential equations are inverse of logarithmic equation. Exponential equations are written in the form y = ab^x
where
a is the base
x is the exponent
Using the coordinate points (0, 2) and (1, 6)
Substitute
2 = ab^0
6 = ab
Take the ratio
6/2 = ab/a
3 = b
Determine the value of 'a"
Recall that
6 = ab
6 = 3a
Divide both sides by 3
3a/3 = 6/3
a = 2
Hence the exponential model that best represents the data is f(x) = 2(3)x
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PLS HELP ASAP! Ty
Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6
Find (h-g)(2.1)
The value of the function (h-g)(2.1) is -3.51
How to determine the function value?The equations of the functions are given as:
Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6
To calculate or find (h-g)(2.1), we start by calculating h(2.1) and g(2.1)
This is calculated as follows:
g(2.1)= 2(2.1)^2+3(2.1)-9
Evaluate
g(2.1)= 6.12
h(2.1)=(2.1)^2+2(2.1)-6
Evaluate
h(2.1)=2.61
The function is then calculated as:
(h-g)(2.1) = h(2.1) - g(2.1)
This gives
(h-g)(2.1) = 2.61 - 6.12
Evaluate the difference
(h-g)(2.1) = -3.51
Hence, the value of the function (h-g)(2.1) is -3.51
As a breakdown
g(x)= 2x^2+3x-9
h(x)=x^2+2x-6
g(2.1)= 2(2.1)^2+3(2.1)-9
g(2.1)= 6.12
h(2.1)=(2.1)^2+2(2.1)-6
h(2.1)=2.61
(h-g)(2.1) = h(2.1) - g(2.1)
(h-g)(2.1) = 2.61 - 6.12
(h-g)(2.1) = -3.51
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help me with this please
Answer:
48
Step-by-step explanation:
The area of this circle is
[tex]\pi( {4}^{2} ) = 16\pi = 50.27[/tex]
about 50.27 square centimeters. So 48 square centimeters seems reasonable here since 3 is used for π.
To gain a pass a student needs to achieve a mean of at least 60% in eight tests. In the first seven
tests the student achieved a mean of 54%. What percentage must the student achieve in test eight
if they are to pass the course?
Step-by-step explanation:
the mean value is the sum of all data points divided by the number of data points.
first we have 7 tests and their mean value :
(t1 + t2 + t3 + t4 + t5 + t6 + t7) / 7 = 54
that means
(t1 + t2 + t3 + t4 + t5 + t6 + t7) = 54 × 7 = 378
in order for the mean value to be at least 60% after 8 tests, we need to add a t8, so that
(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) = 60 × 8 = 480
because only then we have
(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) / 8 = 60
and the student passes.
so,
(t1 + t2 + t3 + t4 + t5 + t6 + t7) + t8 = 480
378 + t8 = 480
t8 = 480 - 378 = 102%
the student would have to achieve 102% on the 8th test.
which would be normally impossible, but maybe the tests involve some bonus points.
A highway sign shows a speed limit of 65 miles per hour. Which of the following car speed measurements represent the same level of accuracy compared to the speed limit sign?
a. 66 ,ph
b. 56mph
c. 60mph
d.64mph
The car speed measurements that represent the same level of accuracy compared to the speed limit sign is 64mph (option D).
What is accuracy?Accuracy is the exact conformity to truth or the degree of conformity of a measure to a true or standard value.
Accuracy is different from precision as precision deals with the closeness of an observed value with a true value.
According to this question, a highway sign shows a speed limit of 65 miles per hour. This suggests that a car speed measurement that will represent the same level of accuracy compared to the speed limit sign is 64mph.
64mph is the closest speed measurement to 65mph that does not exceed this speed limit. However, 66 mph is also close but exceeds the true value for the speed limit.
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Three hens lay 3 eggs any 3 days. in how many days will 3n hens lay at this rate 9nk eggs
Answer: is 48 eggs .
Step-by-step explanation:
3 hens gives 3 eggs in 3 days
Therefore , 1 gives 1 egg in 3 days
So
3days = 1egg
After that 12 days\/3 times = 4 eggs (in 12 times )
So 1 hen offers 4 eggs in 12 days after that
12 hens x 4 eggs = 48 eggs (in 12 days by 12 hens)
the graph of y=-3x+ 2 is:
A population has a mean of 94 and a standard deviation of 18. A sample of 36 observations will be taken. The probability that the sample mean will be between 89.17 and 101.05 is _____. a. 0.9463 b. 0.4369 c. 0.0094 d. 0.9369
The probability that the sample mean will be between 89.17 and 101.05 is: 0.940091407
A sample mean is a data set's average. A data set's central tendency, standard deviation, and variance may all be calculated using the sample mean.
The sample mean may be used to calculate population averages, among other things.
What is the calculation that supports the above answer?The information given are as follows:
μ = 94,
σ = 18
Where Χ = Sample Mean
hence P (89.17 < X< 101.05) =
P [[tex]\frac{89.17 -94}{18/\sqrt{36} } \leq \frac{X -mu}{sd/\sqrt{xn} } \leq \frac{101.5-94}{18/\sqrt{36} }[/tex]]
= P [ -1.61 ≤ Z ≤ 2.5]
= P (Z ≤ -1.61) - P (Z ≤ 2.5)
= NORMSIDST (-1.61) - NORMSDIST (2.5)
= 0.053698928 - 0.993790335
= -0.940091407
Since probability cannot be negative,
The probability that the sample mean will be between 89.17 and 101.05 is: 0.940091407
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1. Find the length of a.
Answer:
Step-by-step explanation:
[tex]\dfrac{ 1 }{ 2 } \times 12\times 15\times \sin ( 110 )[/tex]
==> 84.57
The university theatre department is selling tickets to their
upcoming performance. Three senior citizen tickets and one
student ticket were sold for $38. Three senior citizen ad two
student tickets were sold for $52. Determine the cost of a
senior citizen ticket, x and the price of a student ticket, y. Write
your answer as an ordered pair (x,y).
Answer:
(8,14)
Step-by-step explanation:
3x+2y=52
3x+1y=38 Subtract these equations using elimination method to get y=14
Then substitute y=14 to either equation
the bottom one is easier so
3x+1(14)=38 distribute 1 to 14 and any number times one is 1
3x+14=38 Subtract 14 from both sides
3x=24 Divide by 3
x=8 so check now
3(8)+1(14)=38
24+14=38?
38=38? yes
Use the laplace transform to solve the given initial-value problem. y'' − 4y' + 4y = t3e2t, y(0) = 0, y'(0) = 0
The Laplace of the given equation is [tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex].
According to the statement
we have given that the equation and we have to solve this problem with the help of the Laplace transform.
So, According to the statement
the given equation is
y'' − 4y' + 4y = t^3e^2t, y(0) = 0, y'(0) = 0
And the Laplace transform is an integral transform method which is particularly useful in solving linear ordinary differential equations.
Firstly fill the value of the Laplace of the second order derivative and put x = 0 in the equation
And same it with the first order of the derivative.
And then the Laplace of the equation become
[tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex]
So, The Laplace of the given equation is [tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex]
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Three neon lights are turned on at the same time. One blinks every 4 seconds, the second one blinks every 5 seconds, and the third blinks every 6 seconds. In 5 minutes, how many times will all three lights blink at the same time?
In order to find how many times they will blink at the same time we need to find the common multiple of 4 and 6 between 1 and 60.
The first bulb blinks after every 4 seconds, means it blinks in multiple of 4.
The multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60.
The second bulb blinks after every 6 seconds, means it blinks in multiple of 6.
The multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.
The common multiple of 4 and 6 = 12, 24, 36, 48, 60.
∴
in sixty seconds they will blink 5 times at the same time.
What is the average rate of change of f over the interval -4≤x≤5
The average rate of change over the interval is 2/9
How to determine the average rate of change?The interval is given as:
-4 ≤ x ≤ 5
From the table, we have:
f(5) = 4
f(-4) = 2
The average rate of change is then calculated as:
[tex]m = \frac{f(5) - f(-4)}{5 --4}[/tex]
This gives
[tex]m = \frac{4 - 2}{5 +4}[/tex]
Evaluate
[tex]m = \frac{2}{9}[/tex]
Hence, the average rate of change over the interval is 2/9
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What is the answer please
Answer:
m∠RSU = 10x - 9 = 10(14) - 9 = 140 - 9 = 131
m∠RST = 2x = 2(14) = 28
m∠TSU = 2x + 75 = 2(14) + 75 = 28 + 75 = 103
Step-by-step explanation:
m∠RSU = m∠RST + m∠TSU
10x - 9 = 2x + (2x + 75)
10x - 9 = 2x + 2x + 75
10x - 9 = 4x + 75
-4x +9 -4x +9
6x = 84
x = 14
m∠RSU = 10x - 9 = 10(14) - 9 = 140 - 9 = 131
m∠RST = 2x = 2(14) = 28
m∠TSU = 2x + 75 = 2(14) + 75 = 28 + 75 = 103
Cross-multiplication is helpful in: a. quadratic equations c. linear equations b. solving proportions d. word problems please select the best answer from the choices provided a b c d
Correct option is B)
Cross-multiplication is helpful in Solving proportions.
What is Solving Proportions?Solving proportions is simply a matter of stating the ratios as fractions, setting the two fractions equal to each other, cross-multiplying and solving the resulting equation.
What are the 2 methods for solving proportions?Method I: Draw a double-sided number line, label the parts, set up a proportion and solve.
Method II: Using any method, calculate unit rate and then calculate how many pounds you can get for $30. Method III: Graph a point to represent the original ratio.
What is the rule for solving proportions?The product of the means is equal to the product of the extremes.
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I understand the the question you are looking for is :
Cross-multiplication is helpful in:
a. quadratic equations
b. solving proportions
c. linear equations
d. word problems
please select the best answer from the choices provided a b c d