suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 14 of you want to go . he decides that the only fair way is to draw names out of a hat. What is the probability that you, Samuel, Emma and Paul are chosen? Into a fraction or round your answer to four decimal places if necessary
total employees=14
probability that you are chosen is P=1/14
probability that Samuel are chosen is P=1/13
the probability that Emma are chosen is P=1/12
the probability that Paul are chosen is P=1/11
therefore
the probability that you, Samuel, Emma and Paul are chosen is
P=(1/14)(1/13)(1/12)(1/11)=4.16x10^-5=0.00004
problem N 2
P=(1/27)(1/26)(1/25)=0.00005698=0.0001
The graph of a periodic function f is shown below.What is the period of this function? What is the amplitude of this function? Write a function formula for f. (Enter "theta" for θ.)f(θ)=
The period of the function is 3.14, amplitude is 3 and the
Function: ,f(θ) = 3*cos(2*θ) + 1
To know the period of this function
The period is the distance between two maximums or two minimums, because that's the part that repeats after. In the graph I've marked two maximums in red: one is at θ = 0 and the other one is at θ = 3.14. Therefore the period is 3.14
The amplitude is the distance between the maximum or minimum to the midline. In other words it's half the distance between the maximum and minimum: 3
Finally, the function is a cosine - because it starts at the higher value while the sine starts at zero - with an amplitude of 3, shifted 1 unit up (because the midline is 1 and not 0) and since the period is 3.14 it is also dilated horizontally by a factor of 2: f(θ) = 3cos(2θ) + 1
Therefore, the period of the function is 3.14, amplitude is 3 and the Function: ,f(θ) = 3*cos(2*θ) + 1
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Use the factor theorem to determine if( x - 2) + (x + 4) are factors of the function below
Here, the dividend is x^3-6x^2+11x+6 and the divisor is x-2.
Put the value of divisor as 0 implies,
[tex]\begin{gathered} x-2=0 \\ x=2 \end{gathered}[/tex]Find f(2) implies,
[tex]\begin{gathered} f(2)=2^3-(6\times2^2)+(11\times2)-6 \\ =8-24+22-6 \\ =0 \end{gathered}[/tex]Therefore, x-2 is a factor of the polynomial.
Pu the value 0 for x+4 gives,
[tex]\begin{gathered} x+4=0 \\ x=-4 \end{gathered}[/tex]Find f(-4) gives,
[tex]\begin{gathered} f(-4)=(-4)^3-(6\times(-4)^2)+(11\times-4)-6 \\ =-64-96-44-6 \\ =-210 \end{gathered}[/tex]Therefore, x+4 is not a factor of polynomial.
Hence, Option C.
guys whatd 3/2000 please help this is due by tomorrow
Answer:
0.0015
Step-by-step explanation:
don't forget to follow rate like
solve the system of equations and choose the correct ordered pair. 2x - 6y = 85x - 4y = 31
We have
[tex]\begin{gathered} 2x-6y=8\text{ (1)} \\ 5x-4y=31\text{ (2)} \end{gathered}[/tex]we must solve the system of equations
First, we will solve for x the first equation
[tex]\begin{gathered} 2x-6y=8 \\ 2x=8+6y \\ x=\frac{8}{2}+\frac{6}{2}y \\ x=4+3y \end{gathered}[/tex]Then, we must replace the value of x in the second equation
[tex]\begin{gathered} 5(4+3y)-4y=31 \\ 20+15y-4y=31 \\ 11y=11 \\ y=\frac{11}{11} \\ y=1 \end{gathered}[/tex]Finally, we replace the value of y in the equation that we solved for x
[tex]\begin{gathered} x=4+3(1) \\ x=4+3 \\ x=7 \end{gathered}[/tex]So, the correct ordered pair is (7, 1)
Solve 3n - 5p + 2n = 10p for n.
Solving for n ,
[tex]\begin{gathered} 3n-5p+2n=10p \\ \rightarrow3n+2n=10p+5p \\ \rightarrow5n=15p \\ \rightarrow n=\frac{15p}{5} \\ \\ \Rightarrow n=3p \end{gathered}[/tex]What is the common ratio of the sequence 18,24,32…
Answer:
4/3
Explanation:
The given sequence is 18, 24, 32, ...
Then, the common ratio can be calculated as
24/18 = 4/3
32/24 = 4/3
Because 24 and 18 are consecutive numbers and 32 and 24 are consecutive numbers.
Therefore, the common ratio is 4/3
Warren buys a bag of cookies that contains 5 chocolate chip cookies, 6 peanut butter cookies, 6 sugar cookies and 6 oatmeal cookies.What is the probability that Warren reaches in the bag and randomly selects 2 peanut butter cookies from the bag? Round your answer to four decimal places. Hint: Did you use conditional probability?
ANSWER
0.0593
EXPLANATION
The total number of cookies in the bag is,
[tex]5+6+6+6=23[/tex]When Warren takes the first cookie, the probability of it being a peanut butter cookie is 6 out of 23,
[tex]P(pb_1)=\frac{6}{23}[/tex]If the first cookie was peanut butter, when he takes the second cookie there are only 5 peanut butter cookies left and a total of 22 cookies, so the probability of that second cookie being peanut butter is,
[tex]P(pb_2)=\frac{5}{22}[/tex]So, the probability that Warren selects 2 peanut butter cookies from the bag is,
[tex]P(2pb)=\frac{6}{23}\times\frac{5}{22}\approx0.0593[/tex]Hence, the probability that he takes 2 peanut butter cookies is 0.0593.
when Nolan left his house this morning, his cell phone was 30% charged and it then started to lose 5% charge for each hour thereafter. Write an equation for B, in terms of t, representing the charge remaining in Nolan's battery, as a percentage, t hour after Nolan left his
b= 30 -5t
1) Gathering the data
30%=0.3
5% = 0.05
Setting a table
charge hour
30% 0
25% 1
20% 2
15% 3
The first part 30-5b is the charge in %, t is the instant
30-5t =b
QRST is a rectangle. Find the value of x and the length of each diagonal. QS = 5x + 12 and RT = 6x – 2
We can draw the rectangle QRST as:
The two diagonals of a rectangle will have the same length, so we can write:
[tex]\begin{gathered} QS=RT \\ 5x+12=6x-2 \\ 5x-6x=-2-12 \\ -x=-14 \\ x=14 \end{gathered}[/tex]With the value of x, we can calculate the length of the diagonal:
[tex]QS=5x+12=5\cdot14+12=70+12=82[/tex]Answer: the lengths of the diagonals QS and RT is 82.
The value of x is 14 and the length of each diagonal would be 82 units.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
We have been given that QRST is a rectangle.
We have to determine the value of x and the length of each diagonal.
QS = 5x + 12 and RT = 6x – 2
Because a rectangle's two diagonals will be the same length, we may write:
QS = RT
5x + 12 = 6x – 2
Rearrange the terms in the above equation,
6x - 5x = 12 + 2
x = 14
The value of x is 14.
So, QS = 5(14) + 12 and RT = 6(14) – 2
So, QS = RT = 82
Therefore, the length of each diagonal would be 82 units.
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It takes approximately 4.65 quarts of milk to make a pound of cheese. Express this amount as a mixed number in simplest form.
The amount of the quarts of milk to prepare a pound of cheese in mixed number is 4 ¹³/₂₀.
What is the meaning of the term mixed number?The mixed number is a representation of both a whole number and a legal fraction. A whole number, one numerator, as well as a denominator are combined to create a mixed number.Creating mixed fractions from incorrect fractions.
Step 1: Divide this numerator by the denominator
Step 2: The quotient should be expressed as a whole number.
Step 3: Input the numerator and denominator as the remainder and the divisor, respectively.
For the given question,
The quantity of 4.65 quarts of milk to make a pound of cheese.
This can be written as-
= 465/100
Dived the numerator and denominator by 5
= 93/20
Write the value in mixed fraction as;
The remainder will be 13 after diving 93 with 20 and with quotient 4.
= 4 ¹³/₂₀.
Thus, the amount of the quarts of milk to prepare a pound of cheese is 4 ¹³/₂₀.
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what is the equation of the line passing through the points (-2,3) and (1,4)?
Solution:
Given the points below;
[tex]\left(-2,3\right)\text{ }and\text{ }(1,4)[/tex]To find the equation of a straight line, the formula is
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Where
[tex]\begin{gathered} (x_1,y_1)=(-2,3) \\ (x_2,y_2)=(1,4) \end{gathered}[/tex]Substitute the values of the coordinates into the formula to find the equation of a straight line above
[tex]\begin{gathered} \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \frac{y-3}{x-(-2)}=\frac{4-3}{1-(-2)} \\ \frac{y-3}{x+2}=\frac{1}{1+2} \\ \frac{y-3}{x+2}=\frac{1}{3} \\ Crossmultiply \\ 3(y-3)=1(x+2) \\ 3y-9=x+2 \\ x+2=3y-9 \\ x+2-(3y-9)=0 \\ x+2-3y+9=0 \\ x-3y+2+9=0 \\ x-3y+11=0 \end{gathered}[/tex]Hence, the general equation of the line is
[tex]x-3y+11=0[/tex]The following data represents the weight of goods in a truck in tons. Find the lower limit of the outlier.1.5, 1.4, 1.7, 1.2, 2, 1.8, 2.5
0.5
Explanations:The given dataset is:
1.5, 1.4, 1.7, 1.2, 2, 1.8, 2.5
Step 1: Rearrange the dataset in ascending order
1.2, 1.4, 1.5, 1.7, 1.8, 2, 2.5
Step 2: Find the lower quartile, Q₁
The lower quartile is the median of the first half of the data set
That is Q₁ is the median of 1.2, 1.4, 1.5
Q₁ = 1.4
Step 3: Find the upper quartile, Q₃
The upper quartile is the median of the second half of the data set
That is Q₃ is the median of 1.8, 2, 2.5
Q₃ = 2
Step 4: Find the interquartile range (IQR)
IQR = Q₃ - Q₁
IQR = 2 - 1.4
IQR = 0.6
Step 5: Find the lower limit of the outlier using the formula below
Lower limit = Q₁ - 1.5(IQR)
Lower limit = 1.4 - 1.5(0.6)
Lower limit = 1.4 - 0.9
Lower limit = 0.5
Eric is exploring the formula for the circumference of a circle. He computed the circumferences of several circles with different radii. He then plotted the results and connected them with a line, as shown below. The graph shows the circumference (in m) versus the radius (in m). Find the domain and the range of the function shown.
Answer:
Domain of a function
The domain of a function is the set of all possible inputs for the function.
Hence,
From the graph below, the domain of the function will be
Hence,
The domain will be
[tex]\Rightarrow0\leq x<\infty[/tex]Step 2:
Range of the function
The range of a function is the set of its possible output values.
From the graph below, the range of the function will be
Hence,
The range of the graph is
[tex]0\leq y<\infty[/tex]What is the conjugate of −1−5i?
The conjugate will be -1 + 5i
Explanation:Given:
[tex]-1\text{ - 5i}[/tex]To find:
the conjugate of the above complex number
A complex number is in the form: a + bi
The conjugate of the complex number is a - bi
When the complex number is -1 - 5i, where a = -1, b = -5i
The conjugate will negate the value of b
a will be -1 while b = -(-5i) = 5i
The conjugate will be -1 + 5i
Rewrite 3^x = 243 as a logarithmic equation. log3(243) = x logx(243) = 3 log3(x) = 243 log243(x) = 3
In general, the logarithmic function definition states that
[tex]y=log_b(x)\Leftrightarrow x=b^y[/tex]Therefore, in our case,
[tex]3^x=243\Leftrightarrow x=log_3(243)[/tex]Thus, the answer is log3(243)=x, the first option.A pitcher has the ability to throw a baseball at 95 mph.a. How fast is the speed in ft/s? b. How long does the hitter have to make a decision about swinging at the ball if the plate and the mound are sepa- rated by 60 ft? c. If the batter wanted a full second to make a decision, what would the speed in mph have to be?
Speed = 95 miles per hour
a. to express it in feet per second
1 mile = 5280 ft
1 hour = 3600 seconds
(95 x 5280 )/3600 = 139.33 ft/s
b. Speed = distance / time
Time = Distance / speed
Distance = 60ft
Time = 60ft / 139.33 ft /s = 0.43 seconds
c.
speed= distance / time
S = 60 ft / 1 sec = 60 ft/s
Solve using substitution.y = -x - 1y = x + 3Submit
y = -x - 1 (a)
y = x + 3 (b)
Replace the value of y in the first equation (a) by the value of y in the second equation (b).
x+3=-x-1
Solve for x
x+x=-1-3
2x=-4
x=-4/2
x= -2
Replace the value of x in (a) or (b)
y=-x-1
y= -(-2)-1
y= 2-1
y=1
Ost< and cost is given. Use the Pythagorean identity sin2 t + cos2 t = 1 to find sin t.18) cos i =316I need help with #18
sin^2t + cos^2t = 1
sint = 1/4
(1/4)^2 + cos^2 t = 1
1/16 + cos^2 t = 1
cos^2 t = 1 - 1/16
cos^2 t = (16 - 1)/16
cos^2 t = 15/16
take root both side,
[tex]\begin{gathered} cost=\sqrt[]{\frac{15}{16}} \\ \cos t=\frac{\sqrt[]{15}}{4} \end{gathered}[/tex]so the answer is option D
Which expression is equivalent to 5(24 - 9)?(5×24)-(5×9)(5×24)+(5×9)(5×24)-9(5×24)+9
5 ( 24 - 9 )
= ( 5 X 24 ) - ( 5 X 9 ) ----------- OPTION A
can you tell me which one is the answer just that I don't need anything else.
Thus the answer is Option (D) 7/15.
simplifying fractions 35/45
Given the fraction: 35/45
We will simplify the fraction as follows:
[tex]\frac{35}{45}=\frac{5\cdot7}{5\cdot9}=\frac{7}{9}[/tex]LCM for 35 and 45 is 5
So, divide both numbers by 5
Watts are units that measure the rate at which energy is used. A kilowatt is equal to 10 to the 3rd power watts. A gigawatt is equivalent to 10 to the 9th power watts. How many kilowatts are in a gigawatt?
Hello, I'm confused on this one. Writing English expression into algebraic language.
STEP-BY-STEP EXPLANATION:
Firstly, you need to understand that are many operations symbols that are used in algebra. The operations are listed below
[tex]+\text{ , - , }\times,\text{ }\frac{\square}{\square}[/tex]When translating a word statement into an algebraic equation, the following points are very important
0. Read the problem carefully and figure out what you are asked to find
,1. Assign a variable to what you are looking for
,2. Write down the variables
,3. Write down the expression or equation
As you can see from the first question given,
A number multiplied by 24
Firstly, we need to assign a variable.
Let the variable be m
The next step is to identify the operation is the statement
The mathematical operation is multiplication
Hence, the expression is written below as
A number multiplied by 24 = m x 24
PART 4
A number multiplied by 2 and then take away 21
Firstly, assign a variable
Let the variable be m
Secondly, multiply the variable by 2
m x 2 = 2m
Take away mean minus
The next thing is to take away 21
Therefore, we have
2m - 21
you can have more than one point slope equation for a single line. true or false?
Given:
Any single line can have more than one point-slope equation.
To check: It is true or false.
Explanation:
The standard form of a point-slope equation is,
[tex]y=mx+c[/tex]Where m is the slope of the line and c is the y-intercept.
Here, (x, y) is any one point of the line.
The slope of the line is the same for every point of the line. Also, there must be a single y-intercept since the straight line has a linear function.
Any single line can have more than one point-slope equation if we change points simultaneously.
That is,
At every point of the line, we can write the point-slope eq
what is the volume of the right prism shown ? the prism is drawn to scale . the volume of the prism is _______
The formula to find the volume of a right trapezoidal prism is
[tex]\begin{gathered} V=\frac{(a+b)}{2}\cdot h\cdot l \\ \text{ Where V is the volume} \\ a\text{ is the long base} \\ \text{b is the short base} \\ h\text{ is the height and } \\ l\text{ is the length of the right trapezoidal prism} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} a=7.5in \\ b=5in \\ h=6in \\ l=8in \end{gathered}[/tex][tex]\begin{gathered} V=\frac{(a+b)}{2}\cdot h\cdot l \\ V=\frac{(7.5in+5in)}{2}\cdot6in\cdot8in \\ V=300in^3 \end{gathered}[/tex]Therefore, the volume of the right trapezoidal prism is 300 cubic inches.
Answer:
the volume of the right trapezoidal prism is 300 cubic inches.
Step-by-step explanation:
what is 10 reproduced at a 1/2 scale
Scaling
To scale a number by a certain amount, multiply both quantities.
The number 10 reproduced at a 1/2 is:
[tex]\begin{gathered} 10\cdot\frac{1}{2} \\ =\frac{10}{2} \\ =5 \end{gathered}[/tex]Answer: 5
1 point (new-original)x100 = %change Calculate the percent change from 45 ft. to 92 ft. original
Given:
New measurement = 92 ft
Original measurement = 45 ft
To calculate the percentage change, use the formula below:
Michael recently started a new hourly wage job. The equation y=18.75x + 2500 models his total pay, y, in dollars as it relates to the number of hours, x, that he has worked.A. What is Miguel's hourly rate of pay?B. Does it appear the Miguel received a signing bonus? If so, how much was the bonus?How many hours must Miguel worked to receive $10,000 in total pay?
Given
y = 18.75x + 2500
Part A:
Based on the given equation where x is the number of hours worked. Since the coefficient of this term is 18.75, then we can conclude that Miguel's hourly rate is $18.75.
Part B:
The given equation has a constant of 2500, at x = 0, where the number of hours worked is zero, then the value of the equation is 2500. This appears that Miguel has a signing bonus, and the amount of bonus is $2500.
Part C:
Substitute y = 10000, to the equation and solve for x
[tex]\begin{gathered} y=18.75x+2500 \\ 10000=18.75x+2500 \\ 10000-2500=18.75x \\ 7500=18.75x \\ 18.75x=7500 \\ \frac{18.75x}{18.75}=\frac{7500}{18.75} \\ x=400 \end{gathered}[/tex]Therefore, Miguel must work 400 hours to receive $10,000 in total.
Notebook cost $2.50 and pens cost $0.75. The cost of n notebooks and p pens is 2.50n+0.75p.Find the cost2 notebooks and 4 pens3 notebooks and 5 pens
Cost =2.50n + 0.75 p
n= number of notebooks
p = number of pens
2 notebooks and 4 pens
Replace n =2 , p=4 and solve:
C = 2.50(2) + 0.75 (4) = 5 +3 = $8
3 notebooks and 5 pens
Same process
C = 2.50 (3) + 0.75 (5) = 7.5 + 3.75 = $11.25
Help please. I’ve had health issues recently and i’m trying to catch up on work and learn it. Thank you so much
80 mililiters of the 10% solution
120 mililiters of the 30% solution
Explanation:
let the amount of solution for the 10% = x
let the amount of solution for the 30% = y
The sum of the amount for the mixture of 10% solution and amount for the 30% solution = 200 mililiters
x + y = 200 ...(1)
In terms of fraction for each solution:
fraction of the 10% solution + fraction of the 30% solution = fraction of the mixture
percentage of the solution of the mixture = 22%
fraction of the 10% solution = 10% (x) = 0.1(x) = 0.1x
fraction of the 30% solution = 30%(y) = 0.3(y) = 0.3y
fraction of the mixture = 22%(200) = 0.22(200)
substitute the above into the equation for fraction:
0.1x + 0.3y = 0.22(200)
0.1x + 0.3y = 44 ...(2)
combine both equatons:
x + y = 200 ...(1)
0.1x + 0.3y = 44 ...(2)
Using substitution method to solve the equations:
from equation 1, let's make x the subject of formula:
x = 200 - y
substitute for x in equation (2):
0.1(200 - y) + 0.3y = 44
20 - 0.1y + 0.3y = 44
20 + 0.2y = 44
0.2y = 44 - 20
0.2y = 24
divide both sides by 0.2:
0.2y/0.2 = 24/0.2
y = 120
sustitute for y in equation (1):
x + 120 = 200
x = 200 - 120
x = 80
Hence, James must mix:
80 mililiters of the 10% solution
120 mililiters of the 30% solution