From a set of whole numbers less than 25, the probability of getting a number either divisible by 5 or divisible by 3 is 11/25
The set of whole numbers = {0, 1,2,3,4,5.....}
The set of whole numbers less than 25 = {0,1,2,3,4,......,24}
The numbers divisible by 5 = {5, 10, 15, 20}
The numbers divisible by 3 = {3, 6, 9, 12, 15, 18, 21, 24}
The common term is 15
The probability = Number of favorable outcomes / Total number of outcomes
The number of favorable outcome = 11
Total number of outcomes = 25
Substitute the values in the equation
The probability = 11/25
Hence, from a set of whole numbers less than 25, the probability of getting a number either divisible by 5 or divisible by 3 is 11/25
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2.2(s + 1) 14.7 = 5.1
Answer:-454/539
Step-by-step explanation:32.34(s+1)=5.1
32.34s+32.34=5.1
32.34s=5.1-32.34
32.34s=-27.24
s=-454/539
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 25 liters per minute. There are 700 liters in the pond to start.
Let W represent the amount of water in the pond (in liters), and let T represent the number of minutes that water has been added. Write an equation relating W to T, and then graph your equation using the axes below.
An equation relating W to T is given by W = 700 + 25T. Also, a graph of this linear equation is shown in the image attached below.
How to write an equation relating W to T?In order to write an equation relating W to T, we would define the variables that represents the amount of water in the pond (in liters) and the number of minutes this water has been added as follows:
Let the variable W represent the amount of water in the pond (in liters).Let the variable T represent the number of minutes that water has been added.The initial volume of water is given by:
700
The volume of water added to this pool would be given by:
25T
Therefore, the total volume of water added to this pool is given by:
W = 700 + 25T
Next, we would determine the points for the graph of this equation:
At T = 0, we have:
W = 700 + 25(0)
W = 700 ⇒ (0, 700)
At T = 1, we have:
W = 700 + 25(1)
W = 725 ⇒ (1, 725)
At T = 2, we have:
W = 700 + 25(2)
W = 750 ⇒ (2, 750)
At T = 3, we have:
W = 700 + 25(3)
W = 775 ⇒ (3, 775)
At T = 4, we have:
W = 700 + 25(4)
W = 800 ⇒ (4, 800)
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a box with an open top and a square base is to be constructed to contain 4000 cubic inches. find the dimension that will require the minimum amount of material to construct the box.
The dimension of the box will be (40 inch × 40 inch × 10 inch).
How to determine the maximum and minimum values of an expression using differentiation?
Any given expression can have both minimum and maximum outcomes for any number in a real world scenario, which can be determined using differentiation; first order differentiation when equated to zero reveals the value that will solute to produce the maximum or minimum and then the upon differentiating the obtained expression again and then substituting the variable in acceptable positions, if the outcome is a positive number then the obtained number in first differentiation suggests a minimum value of the given expression.
Given, the volume of the box described = 4000 inch³
Let the dimension of the base of the box be = 'a' inch × 'a' inch = a² inch²
Therefore, height of the box = (4000 inch³)/(a² inch²) = (4000/a²) inch
Total surface area of the described box = S = a² + [4a×(4000/a²)]
= [a² + 16000/a] inch
For the limiting values of S, dS/da = 0 ⇒ d[a² + 16000/a]/da = 0
⇒ 2a - [16000/a²] = 0 ⇒ 2a = 16000/a² ⇒ a³ = 8000 ⇒ a = ∛8000 = 20
Therefore, the value of a is 20 inch.
Thus, height of the box = 4000/a² = 4000/400 = 10 inch
For S to have the minimum limited value, d²S/da² > 0 for a = 20 inch, which is satisfied by the available value of S.
∴ The minimal surface area = a² + 16000/a = 400 + (16000/400)
= 440 inch²
We are aware that the least amount of material will be needed to build the box when its overall surface area is the smallest.
Thus, to minimize the amount of material in consideration, the dimension of the box will be (40 inch × 40 inch × 10 inch).
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sin(2x)cos(7x) - cos(2x)sin(7x)= -0.1
Answer:
sin(2x)cos(7x) - cos(2x)sin(7x)= -0.1
government employees: in 2013 about 66% of full-time law enforcement workers were sworn officers, and of those, 88.4% were male. females however make up 60.7% of civilian employees. choose one law enforcement worker at random and find the following. b. the probability that he is a male civilian employee
The probability that he is a male civilian employee is 0.13362.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given that 66% of full-time law enforcement employees are sworn officers, 34% of them are civilian employees (100 - 66).
Given that 60.7% of civilian employees are women. Therefore, the percentage of men is (100 - 60.7)% or 39.3%.
Therefore, the likelihood that he works as a male civilian is 39.3% of 34%, which equals 0.393 * 0.34, = 0.13362.
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Which expression shows the distance you would travel from the gym to your science class in this hallway?
The expression that shows the distance you would drive from the gym to the office along this road is b.|-6|+|4|
What is a Distance ?Distance is a numerical or qualitative measurement of the distance between two objects or points. Distance is defined as an object's total movement without regard for direction. The distance can be defined as how much ground an object has covered regardless of its starting or ending point.
To find the distance between two points in a number line we do the absolute value of the points subtracted. That is if we need to find the distance between point a and point b in a number line we do |a-b|.
Now, the Gym is at point -6 in the number line and the office is at point 4 in the number line, then the distance from -6 to 4 is |-6-4| = |-10| = 10.
Now, option a is |-6+4| ≠ |-6-4|.
The option b is |-6|+|4| = 6+4 = 10 =|-6-4|. Then, option b is correct.
Option c is -6+4 ≠ |-6-4|.
The option d is -|6|+|4| = -6+4 ≠ |-6-4|.
Then, the correct answer is b.
The complete question is given below.
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Complete question
Which expression shows the distance you would drive from the gym to the office along this road?
a.|-6 + 4|
b.|-6|+|4|
c.-6+4
d.-|6|+|4|
Can anyone write the equation of the graph?
The equation of the absolute function graph given in the diagram is: y = |x - 3| + 5.
How to Find the Equation of the Graph of an Absolute Value Function?y = a|x – h| + k is the equation, in vertex form, that represents the absolute value function where:
The vertex of the graph of the absolute value function = (h, k) The graph opens up or opens down depends on the value of a.The vertex of the graph is (3, 5). This implies that:
(h, k) = (3, 5)
Substitute h = 3 and k = 5 into the equation in vertex form, y = a|x – h| + k:
y = a|x – h| + k
y = a|x - 3| + 5
To find the value of a, substitute a point on the graph, (5, 7), into the y = a|x - 3| + 5:
7 = a|5 - 3| + 5
7 - 5 = 2a [subtraction property]
2 = 2a
a = 1 [division property of equality]
Substitute a = 1 into the equation y = a|x - 3| + 5:
y = |x - 3| + 5
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A piece of cardboard that is 25 inches by 20 inches is to be made into a box with an open top. Each corner will have a square of the same dimensions cut out to be folded into an open box with no top.
A) What are the dimensions of the square to be cut from each corner?
B) What would the volume be of the open box?
Dimensions of the box are (25-2h) and (20-2h) and Volume of the box will be V=h(25-2h)(20-2h).
What is Three dimensional shape?Three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given,
A piece of cardboard that is 25 inches by 20 inches is to be made into a box with an open top
Each corner will have a square of the same dimensions cut out to be folded into an open box with no top.
Let the cut squares will have side h then h is the height of the box and the two lengths are (25-2h) and (20-2h).
The dimensions of the box are (25-2h) and (20-2h)..
Volume of the box will be V=h(25-2h)(20-2h)
Hence, dimensions of the box are (25-2h) and (20-2h) and Volume of the box will be V=h(25-2h)(20-2h).
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a federal report indicated that 13% of children under age 6 live in poverty in massachusetts, an increase over previous years. how large a sample is needed to estimate the true proportion of children under age 6 living in poverty in massachusetts within 2% with 99% confidence? round the intermediate calculations to three decimal places and round up your final answer to the next whole number.
Using the concepts of statistics, we got that 2004 is the sample size needed to estimate the true proportion of children under age 6 living in poverty in Massachusetts within 2% with 99% confidence.
The number of observations used to calculate estimates for the certain population is known as the sample size. The sample size was actually determined by drawing from the population. Sampling is a practice of choosing a portion of a population from which to draw conclusions about the characteristics of a entire population. A subset of the population is chosen for analysis based on the number of entities in it.
We have Margin of error(E)=0.02,
Significance level([tex]\alpha[/tex])=0.01
Proportion(p)=0.13
Therefore, q is defined by =1-p
=> q =1-0.13
=>q=0.87
So, the Z-score is 2.582
Now, we know that sample size(S) is given by
=>S =[ [ [Z²×p×(1-p)] / e²] / [1+(Z²×p×(1-p)/e²)] ]
=>S=[ [ ( 2.582)²×0.13×0.87/(0.02)²] / [1 + [(2.582)²×0.13×0.87] / (0.02)²]
=>S= ([0.754/0.0004] / [1+(0.754/0.0004)])×1000
=>S=([885.01] / [1+1885.01]) × 1000
=>S=(0.200351)×1000
=>S=2003.51=2004 (approx)
Hence, a federal report indicated that 13% of children under age 6 live in poverty in Massachusetts, an increase over previous years in that case size of sample which is needed to estimate the true proportion of children under age 6 living in poverty in Massachusetts within 2% with 99% confidence is 2004.
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Translate the expression “the product of triple a number and 19”
Answer: 3x+19
Step-by-step explanation:
The length of a rectangle is 5 yd longer than its width.
If the perimeter of the rectangle is 70 yd, find its length and width
Answer:
length is 20 yards, width is 15 yards
Step-by-step explanation:
Length = width + 5
2(W + 5) + 2(W) = 70
2W + 10 + 2W = 70
4W + 10 = 70
4W = 60
W = 60 ÷ 4
W = 15 yards
L = 15 + 5
L = 20 yards
a train goes at a constant speed.it can travel 150 miles
in 2 1/2 hours. what distance will it travel in 2 hours.
PLEASE ANSWER
The distance traveled by the car in 2hours is 120miles
What is speed?Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
from the definition speed= distance/time
since the train has constant speed,therefore the speed of the car = 150/2 1/2
= 60miles/hour
Distance= speed×time
Therefore for a time of 2hours the train will cover
60×2= 120 miles
Therefore the distance covered in 2hours is 120miles
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To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
The equation that can be used to find the price of one tire patch is 22.20 - 4x = 1.90 and 4x + 1.90 = 22.20
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
Rhyan paid using a gift card that had $22.20 on it.
Let x represent the cost of each tire patch needed for the mountain biking trip. Rhyan bought four tire patches and had $1.90 remaining. Hence:
22.20 - 4x = 1.90
4x + 1.90 = 22.20
The equation is 22.20 - 4x = 1.90
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Graph the points of the given function with the x-values x=−4 , x = 0, and x = 5. f(x)=−2x+4−−−−√
The graph is attached and the table of value of the graph is as follows
x y
-4 12
0 4
5 -6
How to get the table of valuesThe function y = −2x + 4 is a linear function and will have a straight line graph
The table of values is gotten form the equation y = −2x + 4
solving for x = -4,
y = −2 * -4 + 4 = 12
solving for x = 0
y = −2 * 0 + 4 = 4
solving for x = 5,
y = −2 * 5 + 4 = -6
x y
-4 12
0 4
5 -6
The graph is plotted by finding the points in the table in the Cartesian plane and joining the points together
Other values are solved for in similar step
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Answer:Here is your answer
Step-by-step explanation:
Click the two inequalities represented by the system of inequalities graph below.
The system of inequalities that best represent the shaded feasible region shown on the graph is
y < x + 1y < -x - 2How to determine the inequalities represented inequalities graphinformation gotten from the question include
inequality graph showing shaded regions
some interpretation on the information from the question include
shading below the is less thandotted lines mean the inequality do not have equal toThis interpretation removes the first and the last options since they contain the equal to sign
positive slope moves from bottom left to top right
y < x + 1
negative slope moves from top left to down right
y < -x - 2
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there are more than 200 pages but fewer than 800 in my book. all thre digits of my number are the same. the number is divisible by 9. how many pages sre in my book
Answer:777
Step-by-step explanation: I do not care
There are 333 pages are in my book.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
There are more than 200 pages but fewer than 800 in my book.
And, All the digits of my number are the same and the number is divisible by 9.
Now,
Let a number with three same digit = xxx
So, We get;
200 < xxx < 800
Since, the number is divisible by 9.
So, By the rule of the number divide by 9, we get;
x + x + x = 9k
3x = 9k
for k = 1;
x = 3
Thus, Number of pages = 333
Therefore,
There are 333 pages are in my book.
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Express 2x=3y-7 in the form of ax+by+c=0 write the values
The final answer of the given quadratic equation is 2x - 3y + 7= 0.
What is the quadratic equation?
Any equation in algebra that can be written in standard form as where x is an unknown and a, b, and c denote known numbers, where a 0 is a quadratic equation.
We have,
2x = 3y - 7
Converting the given equation in the form of ax + by + c = 0, we get
2x - 3y + 7= 0
Hence, the final answer of the quadratic equation is 2x - 3y + 7= 0.
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a sum of money was shareed between aziz and ahmad in the ratio of 4:7. aziz reeceived 21 dollars less than ahmad. find the total sum of money shareed by both of them
The total sum of money is 77 dollars .
Let the total sum of money be x .
⇒ Aziz's share = 4x / 11
Ahmad's share = 7x / 11
Given : Aziz received 21 dollars less than Ahmad
⇒ 4x / 11 = ( 7x / 11 ) - 21
Solving the above linear equation in one variable ,
( 7x - 4x ) / 11 = 21 ( taking like terms together )
3x = 21 * 11
x = 7 * 11
x = 77
Aziz's share = ( 4 / 11 ) * 77 = 28
Ahmad's share = ( 7 / 11 ) * 77 = 49
Total Sum of money = 28 + 49 = 77 dollars .
Hence , the total sum of money = 77 dollars .
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Find the slope (rate of change) of a line that passes through (-2,-3) and (1, 1).
We have coordinates (-2, -3) and (1, 1)
To find: Slope of a line that passes through these two coordinates
Let (-2, -3) be (x₁ , y₁) and (1, 1) be (x₂, y₂)
We will use the formula of Slope :
m = y₂ - y₁ / x₂ - x₁
Where 'm' stands for slope
m = 1 - (-3) / 1 - (-2)
m = 1 + 3 / 1 + 2
m = 4 / 3
The slope of the line is 4/3
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how many three-digit positive integers leave a remainder of 2 when divided by 5 and a remainder of 6 when divided by 7?
There are 180 three-digit numbers that leave a remainder of 2 when divided by 5 and 128 three-digit numbers that leave a remainder of 6 when divided by 7.
The smallest 3-digit number to leave a remainder of 2 when divided by 5 is 102.
The next number will be 107, and then 112,
The last 3 digit number to leave a remainder 2 when divided by 5 is 997
Therefore here we get an Arithmetic Progression
102, 107, 112, ..., 997
We know that for any term of an A.P
aₙ = a + (n - 1)d
where,
a = first term
n = the order number of that particular value
d = common difference
Here,
a = 102
d = 107 - 102
= 5
The number of 3 digit number for the above problem will be the value of n for 997
Hence we get
997 = 102 + (n - 1)5
or, 102 + 5n - 5 = 997
or, 5n + 97 = 997
or, 5n = 997 - 97
or, 5n = 900
or, n = 900/5
or, n = 180
Next, we need to find the no. of three-digit numbers that leave the remainder of 6 when divided by 7
The smallest 3-digit number to leave the remainder of 6 when divided by 7 is 104
The largest is 993
Therefore, just like before, we get the A.P
104, 111, 118, ..., 993
here,
a = 104
d = 7
aₙ = 993
Hence we get,
993 = 104 + (n - 1)7
or, 104 + 7n - 7 = 993
or, 97 + 7n = 993
or, 7n = 993 - 97
or, 7n = 896
or, n = 128
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Omar compro 3.5k de cebolla a 8.90 el kilo. Cuanto pago por las cebollas
The amount that Omar will pay when he bought 3.5k of onions are 8.90 per kilo is $31.15.
What is money?From the information given, Omah wants to know the total amount that he will pay for the onions. It's important to know the cost for each kilogram of onion and then multiply it but the number of kilograms that are bought.
In this case, Omar bought 3.5k of onions are 8.90 per kilo.
The amount that Omar will pay for the onions will be:
= Number of kilograms × Cost per kg
= 3.5 × 8.90
= $31.15
In conclusion, the amount is $31.15.
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Please help!! I need to find the Length of Side EF and The scale factor from both triangles
The required answers for given similar triangles are DF= 3, EF= 2.25, and scale factor 4/3 respectively.
What is Similarity?In geometry, two geometrical triangle are similar if they have the same shape, and corresponding sides are equate by some factor. More accurately, one can be obtained from the other by uniformly scaling.
According to given data:For length of side DF, ratio of corresponding sides is equal.
⇒ [tex]\frac{AB}{DE} =\frac{AC}{DF}[/tex]
⇒ [tex]\frac{2}{1.5}=\frac{4}{DF}[/tex]
⇒ DF = 3
Similarly for EF,
[tex]\frac{AB}{DE} =\frac{BC}{EF}[/tex]
⇒[tex]\frac{2}{1.5}=\frac{3}{EF}[/tex]
⇒ EF = 2.25
At last, by using same concept of similarity scale factor is
[tex]\frac{AB}{DE} =\frac{AC}{DF}[/tex]
⇒ [tex]\frac{AB}{DE} =\frac{4}{3}[/tex]
This is our scale factor for both triangle.
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which of the following is part of the solution of the system?
y-x<=-5, y-2x>-5
a) (0,1)
b) (-1,-6)
Answer:
Neither of them are solutions unless you had a typo in the question.
Step-by-step explanation:
1) plug in the known values into both of the equations
First Coordinate:
y-x[tex]\leq[/tex]-5
(1)-(0)[tex]\leq[/tex]-5
1[tex]\leq[/tex]-5 which is not true.
In this case, we do not need to plug in (0,1) into both of the equations because the coordinate cannot be a solution unless the coordinate works in BOTH of the equations.
Second Coordinate:
1) y-x[tex]\leq[/tex]-5
(-6)-(-1)[tex]\leq[/tex]-5
(-6)+1[tex]\leq[/tex]-5 --> It becomes a +1 because two negatives make a positive
-5 [tex]\leq[/tex]-5 - -> which means this is true because -5 is less than or equal to -5
2) y-2x>-5
(-6)-2(-1)>-5
-6(2)>-5
-12>-5 NOT TRUE
ANSWER: Neither of them are solutions unless you had a typo in the question.
hi please help me..this is a multiple choice
Answer:
Step-by-step explanation:
A and D are the answers that I would pick
Answer:
B and C
Step-by-step explanation:
- 1 / -3 = 1/3, we know negative divide by a negative number = positive
- -1/3 = 1/3, we know negative times negative = positive
You have $8.50 and you need to make copies of a flyer at a store that charges
$0.35 per copy. Find the inequality that represents the number of copies you can
make. Use x as the variable.
What is the maximum number of copies you can afford to make?
copies
The required number maximum number of copies can be afforded x < 24.28.
Given that,
We have $8.50 and you need to make copies of a flyer at a store that charges $0.35 per copy.
Inequality can be defined as the relation of an equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the number of copies be x,
According to the question,
0.35x < 8.50
x < 8.50 / 0.35
x < 24.28
Thus, the required number maximum number of copies can be afforded x < 24.28.
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Factorise completely:
Answer:
2xy(8x + 5)
Step-by-step explanation:
16x²y + 10xy ← factor out 2xy from each term
= 2xy(8x + 5)
The triangles shown below must be congruent.
A. True
• B. False
Answer:
true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
you are about to roll 2 fair six-sided dice, hoping to get a double. (a double is when both dice show the same value on top). which double will occur the least often?
you are about to roll 2 fair six-sided dice, hoping to get a double. (a double is when both dice show the same value on top). Each double will occur once with the probability of 1/36
The sample space for the event of rolling 2 fair six-sided dice is :
S={ (1, 1),(1, 2),(1,3),(1,4),(1,5),(1,6),(2,1)........., (6,5),(6,6) } , So in total for the outcome, we get a total of 36 pairs, with the probability of getting an event as 1/36, now the situation given to us is the vent of getting a double.So the event space for getting a double while rolling 2 dice is E = { (1, 1),(2, 2),(3,3),(4,4),(5,5),(6,6) } , the outcome will be 6 pairs, so the probability for each double pair to come out when we roll the 2 dice is: 1/36 and the probability of getting the least double from the 6 pairs of double is: 1/6
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Write a linear function f with the values ƒ (0) = -3 and ƒ (7) = 11.
The linear function with f values f(0) = -3 and f(7) = 11 is f(x) = 2x - 3
What is a Linear Function?linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to the straight line. In case, if the function contains more variables, then the variables should be constant, or it might be the known variables for the function to remain it in the same linear function condition.
if f(0) = -3, it means at x = 0, f(x) = -3
and if f(7) = 11, it means at x = 7, f(x) = 11
So the Linear equation that will yield these results is f(x) = 2x - 3
In conclusion, the Linear function is f(x) = 2x - 3
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If someone could please answer all 3 points (20 points)
The missing parts of the table for the function are 49, 1 and 49 respectively
How to complete the missing parts of the table?
An exponential function is a type of function which involves exponents. A simple exponential function is of the form y = bˣ
Given: the exponential function y = (1/7)ˣ
In order to find the missing parts, we have to substitute the relevant values into the function. Thus:
For x = -2:
y = (1/7)ˣ
Substitute x = -2 into the function:
y = (1/7)⁻² = 49
For x = 0:
y = (1/7)ˣ
Substitute x = 0 into the function:
y = (1/7)⁰ = 1
For x = 2:
y = (1/7)ˣ
Substitute x = 2 into the function:
y = (1/7)² = 1/49
The missing part is 49
Therefore, the missing parts of the table are 49, 1 and 49 respectively
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