Professor Rodgers can select the group of 4 students in 11880 ways.
Here the professor has to select 4 students from a group of 12. hence we see that
to select the first student, the professor can do so in 12 ways.
To select the second student, the professor now has 11 students left. Hence he can do in 11 ways.
To select the third student, he is left with 10 students, hence the thirst student can be selected in 10 ways
The fourth student can be selected in 9 ways.
Hence, Professor can select the group in 12 X 11 X 10 X 9 ways
= 11880 ways.
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The larger of two numbers is 9 more than twice the smaller. The sum of the numbers is 3 less than five times the smaller. Find the numbers.
By solving a system of equations we will see that the larger number is 21 and the smaller one is 6.
How to find the two numbers?Let's define the variables:
x = smaller number
y = larger number.
We know that the larger of two numbers is 9 more than twice the smaller, so we can write:
y -2x = 9
The sum of the numbers is 3 less than five times the smaller.
x + y = 5x - 3
Then we have a system of equations:
y -2x = 9
x + y = 5x - 3
Now we can isolate y on the first equation to get:
y = 9 + 2x
We can substitute that on the other equation to get:
x + 9 + 2x = 5x - 3
3x + 9 = 5x - 3
9 + 3 = 5x - 3x
12 = 2x
12/2 = x
6 = x
And the value of y is:
y = 9 + 2x
y = 9 + 2*6 = 21
These are the two numbers.
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Sandy sold her homemade strawberry jam for $5 per jar at the farmers’ market. She bought a basket of strawberries for $24 to make the jam. If x represents the number of jars of jam sold, which expression represents Sandy’s earnings?
The expression that represents Sandy’s earnings is 5x - 24
How to determine the earnings expressionFrom the question, we have the following parameters that can be used in our computation:
Cost price = $24
Selling price = 5 per jar
This means that the total sales is
Total = 5 * x
Evaluate
Total = 5x
The earnings is the difference between the total sales and the cost price
Sp, we have
Earnings = 5x - 24
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In the triangle ABC, AB = 6cm and BC = 9cm. Given that the area of the triangle is 18 cm², find the possible values of the angle B.
The angle, ∠B has 2 possible angles, one is 41.81° and the other will be 138.19°
In ΔABC we have been given that
AB = 6 cm
BC = 9 cm
A formula for the area of a triangle is
1/2 X one side X oth sde X sin(common angle)
Hence if we consider AB and BC with common angle, ∠B we get
1/2 X 6 X 9 X sinB = 18
or, sinB = 18/27
or, sinB = 2/3
Now since sin is positive in 2 quadrants, we will have 2 possible values for ∠B
one will be 41.81° and the other will be (180 - 41.81)° = 138.19°
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the track of a bicycle tire that completes one revolution is 54 ft. what are the radius, diameter, and circumference of the wheel?
The radius is 8.59 ft, the diameter is 17.18 ft and the circumference is 54 ft.
How to find the radius, diameter, and circumference of the wheel?The circumference of the wheel will be 54 ft, since that's the distance the tire travels in one revolution.
The diameter of the wheel is twice the radius, so if we can find the radius we can find the diameter.
To find the radius (r), we can use the formula:
circumference = 2 × π × radius
54 = 2 × π × r
r = 54 /2 π = 8.59 ft
The diameter is twice the radius, so:
diameter = 2r
diameter = 2 × 8.59 = 17.18 ft
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Which of these systems of linear equations has no solution?
2x+8y =15
4x+10y =30
2x-y=18
4x+ 2y = 38
4x+7y= 17
8x-14y - 36
4x-3y = 16
8x-by = 34
The system of linear equations: 2x-y=18 & 4x-3y = 16 has no solution.
The system of linear equations has no solution if the equations are inconsistent, meaning that there is no set of values for the variables that satisfies all of the equations simultaneously. One way to check for inconsistency is to try to find the solution by solving for one of the variables in one equation and then substituting it into another equation to see if both equations are satisfied. If the equations yield different values for the same variable, then the system has no solution.
In this case, the system of linear equations:
2x-y=18
4x-3y = 16
Has no solution. We can solve for x in the first equation and then substitute it into the second equation. If the equation yields a different value for y, then the system has no solution.
2x-y=18
2x=y+18
x=y/2 + 9
Now, substituting x into the second equation:
4x-3y=16
4(y/2 + 9) - 3y = 16
2y + 36 - 3y = 16
-y = -20
This result implies that y is not a real number, so the system of equations has no solution.
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Question Down Below: (Please i really need to complete this right now)
The inequality to represent the constraints will be:
x + y ≥ 325
x + 2y = 600
How to calculate the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
Let x = number of vegetarian meals
Let y = number of meats.
The inequality to represent the constraints will be:
x + y ≥ 325
x + 2y = 600
In this case, the daily budget is 600.
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a cook wants to know what happens to bacon when it is fried in a frying pan versus microwaving it. specifically, the cook wonders if the bacon ends up moister and more flavorful when fried or when microwaved. what are the dependent variables
The dependent variables in the following scenario are whether the bacon becomes moister and more flavorful and the independent variable is the cooking method.
In statistics, a dependent variable is one whose value is determined by another set of variables called independent variables. To put it simply, the dependent variable is the thing that is being tested or calculated. The dependent variable is sometimes known as the "outcome variable." In the given scenario, the chef was curious as to whether or not frying or microwaving the bacon would produce a moister and more flavorful final product. The bacon is the result of the experiment, hence it is a dependent variable.
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50 POINTS (and its easy im just kinda dmb)
find the number of possible outcomes
1. A softball player bats six times in a game. Each at-bat results in an out, getting on base or hitting a homerun.
2. A sandwich shop has three types of sandwiches: ham, turkey, and chicken. Each s andwich can be ordered with white bread or multi-grain bread. Customers can add any combination of the six available toppings
Answer: 1.18 possibilities 2. 36 possibilities
Step-by-step explanation:
1. 1o, 1g, 1h, 2o, 2g, 2h, 3o, 3g, 3h, 4o, 4g, 4h, 5o, 5g, 5h, 6o, 6g, 6h
2. hw1 hw2 hw3 hw4 hw5 hw6, hg1 hg2 hg3 hg4 hg5 hg6, tw1 tw2 tw3 tw4 tw5 tw6, tg1 tg2 tg3 tg4 tg5 tg6, cw1 cw2 cw3 cw4 cw5 cw6, cg1 cg2 cg3 cg4 cg5 cg6
Solve the quadratic inequality in terms of x 3x^2-8x+15>10x
The solution of the inequality in terms of x is x > 3 or x < 5/3.
What is quadratic inequality?
A quadratic inequality is simply a type of equation that does not have an equal sign and includes the highest degree of two. The wavy curve method is a method used to solve quadratic inequalities. Solving quadratic inequalities is the same as solving quadratic equations.
To solve the quadratic inequality 3x^2 - 8x + 15 > 10x, we first need to move all the terms to one side of the inequality sign to create a standard form of quadratic inequality.
3x^2 - 8x + 15 > 10x
3x^2 - 18x + 15 > 0
Now we can factor the left side of the inequality as (3x-5)(x-3) > 0
To solve the inequality, we need to find the values of x that make the expression (3x-5)(x-3) > 0 true. We can do this by setting each factor to zero and solving for x:
3x - 5 = 0, x = 5/3
x - 3 = 0, x = 3
Now we need to test these values of x in the original inequality to see if they make it true or false, and also we need to test values of x between and around these roots.
For x = 5/3, we have 3(5/3)^2 - 8(5/3) + 15 > 10(5/3)
Which is true.
For x = 3, we have 3(3)^2 - 8(3) + 15 > 10(3)
Which is also true.
So, we can conclude that the solution of the inequality is x > 3 or x < 5/3.
Therefore, the solution of the inequality in terms of x is x > 3 or x < 5/3.
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Please answer the question :)
An inequality represented by situation A is x < -4.
An inequality represented by situation B is x ≤ 3.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two or more numerical values and variables in an algebraic equation based on any of the following inequality symbols:
Less than or equal to (≤).Greater than (>).Greater than or equal to (≥).Less than (<).In this exercise, we would use interpret each of the situations by using an inequality to model them. On the balance in situation A, the tray on the left is denoted with the variable (x) while the tray on the right is denoted with numerical values of "-1" in four places, therefore, we would write the inequality as follows:
x < 4(-1)
x < -4.
In situation B, the circle on the number line (graph) is closed because it represents the less than or equal to (≤) symbol and it decreases to the left of the number line;
x ≤ 3.
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A survey showed that 74% of adults need correction (eyeglasses, contacts, surgery, etc. ) for their eyesight. If 21 adults are randomly selected, find the probability no more than that of them need correction for their eyesight. Is a significantly number of adults requiring eyesight correction?
7.9 x 10⁻¹¹ is the probability of people who need correction for there eyesight.Yes, it is a significantly number of adults requiring eyesight.
The probability of no more than 21 out of 21 randomly selected adults needing correction for their eyesight would be calculated using the binomial probability formula:
(n choose k) × [tex]p^{k}* (1-p)^{n-k}[/tex]
where n is the total number of trail. k is the number of successful trials (the number of adults not needing correction), p is the probability of a successful trial (the probability of an adult not needing correction)which is:
1-0.74 =0.26)
(n choose k) is the binomial coefficient, which is calculated by:
n! / (k! × (n-k)!).
So, the probability of no more than 21 out of 21 randomly selected adults needing correction for their eyesight would be:
(21 choose 21) ×0.26²¹ ×0.74⁰= 0.26²¹ = 7.9 x 10⁻¹¹
This is a very low probability, indicating that it is highly unlikely that no more than 21 out of 21 randomly selected adults would not need correction for their eyesight.
Yes, it is a significantly number of adults requiring eyesight correction. 74% is a high percentage.
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POINTS GIVEN!!! ASAP Alang was out at a restaurant for dinner when the bill came. His dinner came to $18. He wanted to leave a 10% tip. How much was his meal plus the tip, before tax, in dollars and cents? ASAP
Answer: $19.80
Step-by-step explanation:
Step 1:
Multiply to get tip:
18*0.1=1.8
Step 2:
Add:
18+1.8=19.8
Add the zero in the hundredths digit place since there are always two-digit places after the decimal point when dealing with money.
Find an equation for the line through (0, -5) and parallel to y = 1/2x + 1
Answer:
y=1/2x-5
Step-by-step explanation:
Parallel lines always have the same slope. Thus, since you know y=1/2+1 is parallel you know the slope is 1/2 as in y=mx+b, m is the slope. In addition, you know the y-intercept as -5. So the equation is y=1/2x-5
Answer:
y=1/2x-5
Step-by-step explanation:
to be parallel it needs to have the same slope so the slope is the same
0,-5 is the y intercept so -5 is the y intercept
The cafeteria sells each apple at one price and each banana at another price. For 5 apples and 3 bananas Dan pays $5.70. For 3 apples and 5 bananas Chris pays $4.70. The price of one apple is how much more then the price of one banana, in cents?
In this question, why do you multiply by 5 to the top equation and 3 to the bottom equation?
Answer: In this question, we are trying to find the difference in price between one apple and one banana. We can set up a system of two equations with two variables to represent the information given in the problem. Let x be the price of one apple in cents and y be the price of one banana in cents.
The first equation represents the information that Dan paid $5.70 for 5 apples and 3 bananas:
5x + 3y = 570
The second equation represents the information that Chris paid $4.70 for 3 apples and 5 bananas:
3x + 5y = 470
We can use these equations to solve for the value of x (the price of one apple) in terms of y (the price of one banana).
We can use the first equation and solve for x:
5x = 570 - 3y
x = (570 - 3y)/5
We can then substitute this expression of x into the second equation:
3((570 - 3y)/5) + 5y = 470
By multiplying both sides of the equation by 5 and 3 respectively, we can get the equation in a form that we can solve for y and then substitute back for x.
We can solve for y by subtracting 3((570 - 3y)/5) from both sides:
5y = 470 - 3((570 - 3y)/5)
Expanding and simplifying the right side of the equation:
5y = 470 - 3(114 - y)
5y = 470 - 342 + 3y
y = (470 - 342)/8
We can substitute this value of y back into the first equation and solve for x
x = (570 - 3y)/5
x = (570 - 3(470 - 342)/8)/5
x = (570 - 441)/5
Therefore, the price of one apple is (570 - 441)/5 = 129 cents more than the price of one banana.
Step-by-step explanation:
After you have constructed a 60° angle, what other appropriately used construction will get you a 30° angle?
Answer:
Construct an angel bisector
how to determine if a function is even or odd algebraically
If f(-x) = -f(x), the function is odd. and if f(-x) = f(x), the function is even.
What are functions?A function is defined as a relation between a set of inputs having one output each, a function is a relationship between inputs where each input is related to exactly one output.
We can decide algebraically if a function is even, odd or neither by replacing x by -x and computing f(-x).
If f(-x) = f(x), the function is even.
If f(-x) = -f(x), the function is odd.
In order to "determine algebraically" whether a function is even, odd, or neither, you take the function and plug − x in for x, simplify, and compare the results with what you'd started with.
If you end up with the exact same function that you started with (that is, if f (− x) = f (x), so all the signs are the same), then the function is even; if you end up with the exact opposite of what you started with (that is, if f (− x) = − f (x), so all the signs are switched), then the function is odd.
If the result is neither exactly the same nor exactly opposite (that is, nor having all the same terms but with all the signs reversed), then the function is neither even nor odd.
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if vector c is added to vector b, the result is -9i - 8j. if b is subtracted from c, the result is 5i 4j. what direction is b to the nearest degree
221 degree is the direction of B to the nearest degree.
We have to find the vector B. We will substructure Equations
-9i - 8j - 5i - 4j = -14i -12j
= 2(-7i-6j)
From here you get the value of vector B. That is minus seven i and minus of six j. Now we can see that this is both. The signs are negative so it should lie in 3rd chord event.
And for third quarter went in their direction or we can say Angelo factor B is want A D. Plus theater. So when I. D. Plus and universal marvelous of -6 divided by -7 that provides us one or d. plus 41 degree. That is 221 degree.
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Several friends each want to buy new basketball shoes that cost $60. To earn money, they do yard work for $9 an hour. The table shows the number of hours each person did yard work for each day. Who earned enough money to buy the basketball shoes? What inequality can you write to represent this situation?
Indicate whether or not each friend earned enough money to buy the basketball shoes.
Answer:
Step-by-step explanation:
There's no table or image attached to your question, but they would have to work at least 7 hours in order to earn enough money. In 7 hours, they would earn $63.
What property is 4 x (X •10) = (4•x) • 10
Answer:
Your answer is Identitive property
please help ! Identify the special angle pair created by angles 1 and 2 in each diagram.
The angle relationship between ∠1 and ∠2 are as follows:
Same side interior anglesalternate interior angles corresponding angles.How to find angle relationships in parallel lines?When parallel lines are cross by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, same interior angles, vertically opposite angles etc.
Therefore. let's find the relationship of the angle 1 and 2 in the parallel lines cut by the transversal.
Hence, the relationship are:
1. Same side interior angles
2. alternate interior angles
3. corresponding angles.
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√196
What is the square root?
Answer: √196 = 14
Step-by-step explanation: mere guess
Fifth term of (x-3y)^6
The fifth term of the expression is 1215x²y⁴.
What is Binomial Theorem?Binomial theorem is the method of expanding an expression consisting of two terms raised to any power.
By binomial theorem,
(x - 3y)⁶ = 6C₀ x⁶ + 6C₁ x⁵ (3y) + 6C₂ x⁴ (3y)² + 6C₃ x³ (3y)³ + 6C₄ x² (3y)⁴ + 6C₅ x (3y)⁵ + 6C₆ (3y)⁶
Simplifying the combination part,
= x⁶ + 6x⁵(3y) + 15x⁴(3y)² + 20x³(3y)³ + 15x²(3y)⁴ + 6x(3y)⁵ + (3y)⁶
= x⁶ + 18x⁵y + 135x⁴y² + 540x³y³ + 1215x²y⁴ + 1458xy⁵ + 729y⁶
Hence the fifth term of the expression is 1215x²y⁴.
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A sculpture needs to lift a piece of marble.
It is a cuboid with dimensions 1 m by 0.6 m by 0.3 m.
Marble has a density of 2.7g/cm cubed.
What is the mass of the marble in kg?
The mass of the marble lifter by a sculpture is 0.0306 kg.
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.
We know the volume of a cuboid is (length×width×height).
Therefore, The volume of this cuboid is (1×0.6×0.3) = 0.18 m³.
The marble has a density of 2.7g/cm which is equivalent to 0.17kg/meter.
We know Mass = volume×density.
Therefore, The mass of the marble is 0.17×10.18 kg.
= 0.0306 kg.
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What’s the missing angles??
Try multiplying the 91 and 65 then that's an answer for one. Then try dividing them for another angle.
solve for [tex]tan\frac{17\pi }{12}[/tex]
After calculating , The value of given expression is -3.73
What is Tanx in terms of sinx and cosx?
Tanx can be defined as the ratio of sinx and cosx or tanx also can be defined as the ratio opposite side and adjacent side.
Given
expression,
tan(17pi/12)
The value of pi = 180
so by putting the value we get,
tan(17*180 / 12 )
tan ( 3060 / 12 )
as we know the value of 3060/12 = 255.
tan(255)
= -3.73
so we got the value of tan(255) is -3.73 approximately
Hence, The value of given expression is -3.73
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what is the probability of spinning a three on the first spinner, the color orange on the second spinner, and rolling an even number of the fair number cube?
A. 1/12
B. 1/16
C. 1/24
D. 1/48
Show your work please!!
Answer:
D. 1/48
Step-by-step explanation:
Each event (spinning a 3, spinning orange, rolling an even number) is an independent event, so the overall probability is the product of the three individual probabilities.
For each event,
p(event) = (number of desired outcomes)/(total number of possible outcomes)
p(spinning a 3) = 1/6
p(spinning orange) = 1/4
p(even number) = 3/6 = 1/2
p(spinning a 3 then spinning orange then rolling an even number) =
= 1/6 × 1/4 × 1/2
= 1/48
Answer: D. 1/48
Answer:
1/48
Step-by-step explanation:
First look at the spinner- there is only one three out of six, so the spinner is 1/6
Now looking at the second spinner- there are four spaces and one orange- giving us 1/4
And finally for the die there are six sides and three are even- which is 3/6
And in order to get our final answer we will multiply 1/6 * 1/4 * 3/6 which equals 1/48
How many miles is the diagonal path from Jim house to the mall
The distance from Jim's house to the mall is given as follows:
11.25 miles.
How to obtain the distance between two points?Suppose that we have two points with coordinates given as follows:
[tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]
Then the equation for the distance between these two points is given as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The coordinates are given as follows:
Jim's house: (17, 13).Mall: (8,1).Hence the distance is given as follows:
[tex]D = \sqrt{(17 - 8)^2+(13 - 1)^2}[/tex]
D = 15 units.
Each unit represents 0.75 miles, hence the distance in miles is given as follows:
15 x 0.75 = 11.25 miles.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Yusuf drove 156 miles in 3 hours. If he continued at the same rate, how far would he travel in 2 hours?
Answer:104 miles in 2 hours.
Step-by-step explanation:
so first since we need to know how much he drove in 2 hours we just divide 156 by 3 to get 52 and then multiply 52 by 2 since we need to know how many miles he traveled in 2 hours then you get your final answer of
104
Find veda and kalbes climming speeds
(b) A workshop produces 360 chairs in
5 days.
The rate of production is ?
chairs/day.
Answer:
72
Step-by-step explanation:
just divide 360 by 5
ez
To find the rate of production, you have to divide the number of chairs produced by the amount of days.
Given:
Chairs produced - 360
Days - 5
[tex]360\div5[/tex]
[tex]\fbox{72 chairs per day}[/tex]