Hello,
3y + 4 < 16
⇔ 3y < 16 - 4
⇔ 3y < 12
⇔ y < 12/3
⇔ y < 4
⇒ S = ] - ∞ ; 4 [
At Hinsdale College, students are employed by the college library to re-shelve books.
The students claim that a 15-minute coffee break every hour would relive boredom and
increase the average number of books re-shelved per hour. To test the student's claim,
the following data were gathered on a random sample of seven student employees.
Over a period of one week, each student worked a normal schedule without coffee
breaks. Then, during the next week, the students were allowed coffee breaks.
Unknown to the students, a member of the library staff secretly recorded the average
number of books shelved per hour and computed the averages with and without the
coffee break system. The results are below. Test the claim that the students shelve
more books when they have a coffee break, use a 0.05 level of significance.
Student 1 2 3 4 5 6 7
Without
Coffee
breaks
75 63 82 53 79 96 73
With
Coffee
Breaks
90 72 95 50 85 110 89
The p value is less, therefore one should reject the null hypothesis.
How to illustrate the information?From the information given, the test statistic will be:
t = (10 - 0)/(6.733/✓7)
t = 3.930.
The degree of freedom will be:
= 7 - 1 = 6
Using the table, the p value will be 0.0039.
Since the p value is less than 0.05 one should reject the null hypothesis.
Learn more about hypothesis on:
brainly.com/question/11555274
#SPJ1
I need help with this one can someone show me step by step
Answer:
A
Step-by-step explanation:
You are given one angle and one side are similar
for Angle-Side-Angle you obviously need one more angle attached to the given side
A angle r = ~ angle c
A high school baseball player has a 0.229 batting average. in one game, he gets 5 at bat. what is the probability he will get at least 2 hits in the game? round your answer to four places.
The probability he will get at least 2 hits in the game is 0.470
GivenThe batting average is 0.229
In one game he gets 5 at bat
To find the probability he will get at least 2 hits we use binomial distribution.
What is Binomial distribution?The binomial distribution is also a Frequency distribution used for the possible no. of successful outcomes in a given no. of trials in each of which there is the same probability of success.
So we have
n = 5
p = 0.299
q = 1 - p
= 0.701
[tex]P(X) = nC_{x} p^x q^(n-x)[/tex]
P(at least 2 hits in the game) = 1 - P(less than 2 hits)
= 1 - P(0) - P(1)
[tex]= 1 - 0.701^5 - 5C1 x 0.299 x 0.701^4[/tex]
= 1 - 0.169 - 0.361
= 0.470
Learn more on binomial distribution probability here:
https://brainly.com/question/10559687
#SPJ4
what is the best estimate of the sum of the fraction? 31/4 +17/3 +8/18
The best estimate of the sum of the expression given is [tex]\rm 13 \dfrac {31}{26}[/tex]
What is a Fraction ?
A fraction is written as p/q , where q [tex]\rm \ne[/tex] 0
It is asked to determine the sum of the fraction
31/4 + 17/3 + 8/18
Taking the LCM of 4 , 3 , 18
LCM of 4 , 3 ,18 is 36
Therefore
[tex]\rm \dfrac{ 31 *9 + 17 *12 + 8 *2}{36 }[/tex]
(279+204+16) /36
499 / 36
[tex]\rm 13 \dfrac {31}{26}[/tex]
Therefore the best estimate of the sum of the expression given is [tex]\rm 13 \dfrac {31}{26}[/tex].
To know more about Fraction
https://brainly.com/question/10354322
#SPJ1
which shows a correct step in using substitution to slove the system of equation y=2x-1 4x+y=2
The solution using correct step of substitution in the equation y=2x-1 4x+y=2 is x = 1/2 and y = 0
Simultaneous equationy = 2x - 1
4x + y = 2
Substitute the value of y in equation (1) into (2)4x + y = 2
4x + (2x - 1) = 2
4x + 2x - 1 = 2
6x - 1 = 2
6x = 2 + 1
6x = 3
x = 3/6
x = 1/2
substitute the value of x into equation (1)y = 2x - 1
y = 2(1/2) - 1
= 2/2 - 1
= 1 - 1
y = 0
Learn more about simultaneous equation:
https://brainly.com/question/16863577
#SPJ1
Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients.[tex]\frac{t^4+t^2+1}{(t^2+4)(t^2+2)^2}[/tex]
The form of the partial fraction decomposition is [tex]\frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]
How to decompose the function?The fraction is given as:
[tex]\frac{t^4 + t^2 + 1}{(t^2 + 4)(t^2 + 2)^2}[/tex]
To decompose the above, we make use of the following rule:
[tex]\frac{px^n + qx^m +....+ r}{(x^2 + a)(x^2 + b)^2} = \frac{Ax + B}{(x^2 + a)} + \frac{Cx + D}{(x^2 + b)} + \frac{Ex + F}{(x^2 + b)^2}[/tex]
So, we have:
[tex]\frac{t^4 + t^2 + 1}{(t^2 + 4)(t^2 + 2)^2} = \frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]
Hence, the form of the partial fraction decomposition is [tex]\frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]
Read more about partial fraction decomposition at:
https://brainly.com/question/2516522
#SPJ1
This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so that it is circumscribed about the
candy bar. If AD = 2.5 cm, what is the smallest diameter of wrapper that will fit the candy bar?
TheThe smallest diameter of wrapper that will fit the candy bar is 5cm.
Smallest diameterGiven:
AD = DC
AC = AD + DC
Segment AD = 2.5cm
Hence:
AC = AD + AD (AD = DC)
AC = 2AD
Where:
AD=2.5
So,
AC = 2(2.5cm)
AC = 5cm
Therefore the smallest diameter of wrapper that will fit the candy bar is 5cm.
Learn more about smallest diameter here: https://brainly.com/question/12944899
#SPJ1
Answer: 5cm.
Step-by-step explanation:
If 3 times a certain number is increased by 4 the result is 28. What is the number?
If x is "the number," which of the following equations could be used to solve for the number?
3 x + 4 = 28
3 x = 4 + 28
3( x + 4) = 28
Answer:3x+4=28
Step-by-step explanation:
the second one would equal 3x=32
And the third one would equal 3x+12=28 which isn’t right either
How is the theoretical probability of an event computed?
The theoretical probability of an event computed as
Theoretical Probability = [tex]\frac{ Number of desired outcomes}{ Number of possible outcomes.}[/tex] This is further explained below.
What is theoretical probability?Generally, The theoretical probability formula is the ratio of the number of successful outcomes to the total number of possible possibilities. We may write this formula out as follows:
In conclusion, the theoretical probability is mathematically given as
Theoretical Probability = [tex]\frac{ Number of desired outcomes}{ Number of possible outcomes.}[/tex]
Read more about theoretical probability
https://brainly.com/question/24037367
#SPJ1
The price of an item has been reduced by $3.49. The new sale price is $84.42. What was the original price?
$
X
3
x+7/|x+7| for x> -7
absolute value
Answer: 1
Step-by-step explanation:
If [tex]x > -7[/tex], then [tex]x+7 > 0 \implies |x+7|=x+7[/tex]
So, we have the original fraction is equal to
[tex]\frac{x+7}{x+7}=\boxed{1}[/tex]
Solve 5x-4<2x+5. Enter your answer as an inequality.(Need help ASAP pls!!!)
Answer: x < 3
Step-by-step explanation:
To solve this inequality, we will simplify and isolate the x variable.
Given:
5x - 4 < 2x + 5
Add 4 to both sides:
5x < 2x + 9
Subtract 2x from both sides:
3x< + 9
Divide both sides by 3:
x < 3
Answer:
x < 3
Step-by-step explanation:
Well you want to isolate x so start by subtracting 2x from both equations that way you remove it from the right side and it's only on the left side.
subtract 2x from both equations
[tex]3x-4 < 5[/tex]
add 4 to both equations
[tex]3x < 9[/tex]
divide both sides by 3
[tex]x < 3[/tex]
What is the value of g(f(x)) when x=-2 if f(x)=x3
Answer:
The answer would be A: -15
3. Which graph represents the solution to 13k-21> 7?
Answer: Option (2)
Step-by-step explanation:
[tex]|3k-2| > 7[/tex] means [tex]3k-2 < -7[/tex] or [tex]3k-2 > 7[/tex].
Solving each of these cases gives [tex]k < -\frac{5}{3}[/tex] or [tex]k > 3[/tex].
So, the answer is Option (2).
Chris is mixing 2 different types of fruit juice together for a summer drink. The two types of juices he is using is one that is 30% strawberry concentrate and the other is 55% lemon concentrate. If he wants 2 L that is 40% concentrate of the fruit juices, how much of each should be used to create the drink?
The total amount of the drink is 2L. Strawberry concentrate will be X amount, and lemon concentrate will be the other part which is 2 - X.
---Note that we can only use one variable because there is only one equation to be set up here. That's why "the other part" is simply the total amount minus the strawberry amount.
0.4(2) = 0.3(x) + 0.55(2 - x)
---0.4, 0.3 and 0.55 are the decimal equivalents of 40%, 30% and 55%
0.8 = 0.3x + 1.1 - 0.55x
0.8 = -0.25x + 1.1
-0.3 = -0.25x
x = 1.2
Therefore, Chris should use 1.2L of strawberry concentrate and 0.8L of lemon concentrate to get 2L of a 40% concentrate mixture.
Hope this helps!
What is addition and subtraction
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{What is addition \& subtraction?}[/tex]
[tex]\huge\textbf{What is addition?}[/tex]
[tex]\bullet\large\textbf{ Well, \underline{addition} simply means when you're ADDING}\\\large\textbf{2 or more numbers from each other to get the result of}\\\large\textbf{a number.}[/tex]
[tex]\huge\textbf{Random notes}[/tex]
[tex]\star\large\textbf{ Usually, you start working with addition when you're in}\\\large\textbf{pre-kindergarten (pre-k also known as head-start)}\\\\\star\large\textbf{ When, you're adding you are going upward.}\\\\\star\large\textbf{ Addition sometimes come after you learn how to count}\\\large\textbf{the basic numbers and so forth because adding never}\\\large\textbf{ends if you really think about.}[/tex]
[tex]\huge\textbf{Example:}[/tex]
[tex]\heartsuit\large\textbf{ 2 \boxed{\bf +} 5 = 7}\\\\\\\heartsuit\large\textbf{ You got the result of 7 because you started at 2 \& went}\\\larg\textbf{up 5 spaces to your right on your number and you landed}\\\large\textbf{on 7.}[/tex]
[tex]\huge\textbf{What is subtraction?}[/tex]
[tex]\bullet\large\textbf{ Well, subtraction simply means you're taking away. Often}\\\large\textbf{people call it take aways.}[/tex]
[tex]\huge\textbf{Random notes:}[/tex]
[tex]\star\large\textbf{ Usually, you start working with subtraction when you're}\\\large\textbf{in pre-kindergarten (pre-k also known as headstart)}\\\\\star\large\textbf{When you're subtracting you are doing downward.}\\\\\star\large\textbf{You focus more on subtraction when you're counting}\\\large\textbf{backwards.}[/tex]
[tex]\huge\textbf{Example:}[/tex]
[tex]\heartsuit\large\textbf{ 7 \boxed{\bf -} 5 = 2 }\\\\\\\heartsuit\large\textbf{ 7 \boxed{\bf -} 2 = 5}\\\\\\\heartsuit\large\textbf{ For equation \#1. you begin at 7 and go BACK 5 spaces}\\\large\textbf{and you should have landed on 2.}\\\\\\\heartsuit\large\textbf{ For equation \#2. you begin at 7 \& go BACK 2 spaces}\\\large\textbf{and you should have landed on 5.}[/tex]
[tex]\huge\textsf{KEEP IN MIND:}[/tex]
[tex]\circ\large\textsf{ Addition OPPOSITE is subtraction \& subtraction OPPOSITE is}\\\large\textsf{addition.}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitirite1040:)}[/tex]
Which of the following illustrates the truth value of the following conditional?
p: 7 + 1 = 0
q: 2 + 2 = 5
F F → T
T T → T
F T → F
T F → T
The truth table for implication of the equations is F F ⇒ T
What is a truth table?A truth table is a mathematical logic table that shows the truth values of different logic statements combined by a given logic rule.
Analysis:
P: 7 +1 is not equal to 0 making P to be false(F)
q: 2+2 is not equal to 5 making q to be false(F)
so for conditional or implication, F F⇒ T
Learn more about truth tables: brainly.com/question/14458200
#SPJ1
5. Lucinda is a babysitter. Her hourly rate is $5.00. fin one week, she baby sat 13 hours and
received tips of $14.50. How much did she earn?
put the events in order of what is most likely to happen, to least likely to happen. If you were to win a million dollars for winning one of these events, which would you pick to play? Use probability to explain your answers
Answer:
no man you should reconsider the question again
try typing again i guess its wrong
Step-by-step explanation:
no man you should reconsider the question again
try typing again i guess its wrong
winning a lottery would be correct one i guess
Factor by Grouping.
25x^2-20x-12
Answer:
ac = -300-20 = -30 +10(5x +2)(5x +(-6))Step-by-step explanation:
The sequence of required answers provides a step-by-step solution to the problem.
Factors of acIn the given trinomial, we identify the coefficients as ...
ax² +bx +c = 25x² -20x -12 ⇒ a=25; b=-20; c=-12
Then the ac product is ...
ac = (25)(-12) = -300
The factor pairs that make this product can be listed as ...
-300 = (-300)(1) = (-150)(2) = (-100)(3) = (-75)(4) = (-60)(5) = (-50)(6) = (-30)(10) = (-25)(12) = (-20)(15) . . . . (only pairs with a negative sum are listed)
The sums of these pairs are -299, -148, -97, -71, -55, -44, -20, -13, -5.
The factors of the ac product that add to -20 are -30 and 10.
Factor by groupingThese factors are used to rewrite the -20x term as a sum.
25x² -20x -12 = 25x² -30x +10x -12
Grouping these terms in pairs, we can identify common factors:
= (25x² -30x) +(10x -12)
= 5x(5x -6) +2(5x -6)
= (5x +2)(5x +(-6))
A metallurgist has one alloy containing 45% copper and another containing 69% copper. How many pounds of each alloy must be use to make 42 pounds of a third alloy containing 66% copper
5.25 pounds of one alloy containing 45% copper and 36.75 pounds of 69% copper is used to make 42 pounds of 66% copper
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the amount of 45% copper and y represent the amount of 66% copper needed to make 42 pounds of a third alloy containing 66% copper. Hence:
x + y = 42 (1)
Also:
0.45x + 0.69y = 42(0.66) (2)
This gives:
x = 5.25, y = 36.75
5.25 pounds of one alloy containing 45% copper and 36.75 pounds of 69% copper is used to make 42 pounds of 66% copper
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
To measure voltage (V), the formula V = √P. R is used. In this formula, P represents power measured in watts and
R represents resistance measured in ohms. What is the resistance (to the nearest ohm) if the volts are 130 and power is
1200 watts?
The resistance measured in ohms according to the given task is; 3.75 ohms.
What is the resistance in the given set-up?Since it follows that the three quantities are related by the formula; V = √P. R can be used to estimate the required resistance.
Hence, when V = 130 and P = 1200; we have;
130 = √1200 × R
R = 3.75 ohm
Read more on voltage and resistance;
https://brainly.com/question/24858512
#SPJ1
Solve-2x-8> 3x + 12.
A. x < -4
OB. x>-4
C. x > -3
D. x < -3
Answer:
x < -4
Step-by-step explanation:
add 8 to both sides
Simplify
Subtract 3x from both sides
Simplify, again
Multiply both sides by -1 ( reverse inequality)
Simplify, again
Divide both sides by 5
And vwola x < -4
HOPE THAT HELPS! :)
factor equation step by step.
Answer:
no solution
Step-by-step explanation:
use grouping method:
f(x) = x^2 - 4x + 2
factor it:
when we try to factor the above equation, we see that there is no ordered pair in which the numbers multiple to -4 and add to 2, so there is no solution
What are the slope and the y-intercept of the linear function that is represented by the table? x y Negative three-fourths Negative StartFraction 1 Over 30 EndFraction Negative one-half Negative StartFraction 2 Over 15 EndFraction One-fourth Negative StartFraction 13 Over 30 EndFraction Two-thirds Negative three-fifths a The slope is Negative two-fifths, and the y-intercept is Negative one-third. b The slope is Negative one-third, and the y-intercept is Negative two-fifths. c The slope is One-third, and the y-intercept is Negative two-fifths. d The slope is Two-fifths, and the y-intercept is Negative one-third.
The slope and the y-intercept of the function are: A. Slope = -2/5; y-intercept = -1/3.
How to Find Slope and Y-intercept of a Linear Function?Slope (m) = change in y / change in x.
Using two pairs of points form the table value, (1/4, -13/30) and (2/3, -3/5)"
Slope (m) = (-13/30 - (-3/5))/(1/4 - 2/3)
Slope (m) = (-13/30 + 3/5))/(1/4 - 2/3)
Slope (m) = (1/6)/(-5/12)
Slope (m) = (1/6)(12/-5) = 12/-30
Slope (m) = -2/5
Plug in m = -2/5 and (x, y) = (2/3, -3/5) into y = mx + b to find the y-intercept (b).
-3/5 = -2/5(2/3) + b
-3/5 = -4/15 + b
-3/5 + 4/15 = b
-1/3 = b
b = -1/3
Learn more about the slope and y-intercept on:
https://brainly.com/question/10700419
#SPJ1
Answer:
A. Slope = -2/5; y-intercept = -1/3.
Step-by-step explanation:
Hope this helps!!
Solve the quadratic equation by using the quadratic formula. If the solutions are not real, enter NA.
2x2−7x+1=0
Enter the exact answers.
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter.
Enclose numerators and denominators in parentheses. Remember that (a−b)/1+n is not the same as (a−b)/(1+n) .
By using the quadratic formula, the roots of the quadratic equation 2 · x² - 7 · x + 1 are represented by the irrational number x = (7 ± √41) / 4.
How to find the roots of quadratic equation by quadratic formula
For polynomials of the form a · x² + b · x + c = 0, the two roots can be found analytically by quadratic formula, whose expression is described below:
[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]
If we know that a = 2, b = - 7 and c = 1, then the roots of the polynomial are:
x = 7/4 ± (1/4) · √41
x = (7 ± √41) / 4
By using the quadratic formula, the roots of the quadratic equation 2 · x² - 7 · x + 1 are represented by the irrational number x = (7 ± √41) / 4.
To learn more on quadratic equations: https://brainly.com/question/17177510
#SPJ1
Choose the letter of the equation for
the graph.
KIN
2
a. y =
sin x + 2
b. y = cos x + 2
c. y = cos(x - π)
d. y =
sin(x - π)
e. y = sin(x + π/2)
Enter
Answer:
a
Step-by-step explanation:
The midline is at y=2.
Eliminate c, d, e
Also, since there is no horizontal shift amongst the remaining options, we know that since y=2 when x=0, this means it must be a sine curve.
This means the answer is a.
answer the questions below to find the total surface area of the can
The total surface area of the tomato ketchup given in the diagram can be determined as follows:
The total surface area of a shape is the addition of the areas of its individual surface.
So that the questions can be answered as thus:
A. To find the area of the given circle;
i. Area of a circle = [tex]\pi r^{2}[/tex]
where r is the radius of the circle.
area of the circle = π[tex](2.5)^{2}[/tex]
= 6.25[tex]\pi[/tex]
ii. There are two identical circles in the cylinder.
iii. The total area of all circles = 2(6.25[tex]\pi[/tex])
= 12.5[tex]\pi[/tex] square inches
B. To find the area of the rectangle;
i. one side of the rectangle is 5 inches.
ii. The other side of the rectangle = 2[tex]\pi[/tex]r
= 2(2.5)[tex]\pi[/tex]
= 5[tex]\pi[/tex] inches
iii. The area of the rectangle = l x b
= 5[tex]\pi[/tex] x 5
= 25[tex]\pi[/tex] square inches
C. Total surfce area of the cylinder = 5[tex]\pi[/tex] + 25[tex]\pi[/tex]
= 30[tex]\pi[/tex] square inches
For more clarifications on total surface area of a cylinder, check: https://brainly.com/question/16990329
#SPJ1
Answer:
Step-by-step explanation:
First box
6.25
2
12.5
------
Second box
------
5
5
25
------
Last box
------
37.5
Margo borrows $1500, agreeing to pay it back with 3% annual interest after 18 months. How much interest will she pay?
Answer:
67.5
Step-by-step explanation:
I'm assuming this is simple interest.
1500x0.03x1.5=67.5
Megan has 5 yards of cloth to make
napkins. She needs yard for each
napkin. How many napkins can
Megan make with the cloth?
napkins
Answer: 5
5yards = 5napkins