Answer:
P(15, 10)
Step-by-step explanation:
By definition;
[tex]nC_r=\binom{n}{r}=\frac{n!}{(n-r)!r!}[/tex]
and
[tex]nP_r=\binom{n}{r}=\frac{n!}{(n-r)!}[/tex]
This implies that;
[tex]15P_{10}=\binom{15}{10}=\frac{15!}{(15-10)!}=\frac{15!}{5!}[/tex]
[tex]15C_{10}=\binom{15}{10}=\frac{15!}{(15-10)!10!}=\frac{15!}{5!10!}[/tex]
[tex]15C_{5}=\binom{15}{5}=\frac{15!}{(15-5)!5!}=\frac{15!}{5!10!}[/tex]
Graph y=1000(1+0.06)^x
I don’t have a graphing calculator please help!
Y=1000(1+00.6) so divide y by 92 and get 1
Answer:
y=6x+100
Step-by-step explanation:
im not 100% sure if this is correct but i used an online graphing calculator!
Which expression is equivalent to
Answer:
1/81
Step-by-step explanation:
Remember:
b^-n = 1/b^n
Then
[(3^2)]^-2 = 1/[9^2]
1/81
Best regards
Answer:
The correct answer option is [tex]\frac { 1 } { 81 } [/tex].
Step-by-step explanation:
We are given the following expression and we are to find out whether which of the given answer options is equivalent to this expression:
[tex] ( 3 ^ 2 ) ^ { - 2 } [/tex]
We know the rule for solving the exponents:
[tex] ( b ^ n ) ^ { m } = b ^ { n \cdot m} [/tex]
This means that the exponents are multiplied with each other.
So, if we multiply them, for the given expression we get:
[tex] ( 3 ) ^ { - 4 } [/tex] = [tex] \frac { 1 } { 3 ^ 4 } = \frac { 1 } { 81 } [/tex]
The answer is B. ( that’s why it has the 1 in front of it) but I need help showing how I got that as an answer
Answer: The area is 221.558, with the explanation below.
Step-by-step explanation: The area of a circle is solved by the equation
π x r². You are given the diameter of 16.8, and the radius is half of it, so the radius = 16.8/2 = 8.4
Next, you need to plug your numbers into the equation:
Area = 3.14 x 8.4²
Area = 3.14 x 70.56
Area = 221.558
Kevin and Randy Muise have a jar containing 70 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $7.50. How many of each type of coin do they have.
Answer:
50 nickels, 20 quarters.
Step-by-step explanation:
System of equations (q = # of quarters, n = # of nickels):
q + n = 70, 0.25q + 0.05n = 7.50
the first equation can be changed to q = 70 - n, so we are able to substitute q with 70 - n.
So, it will look like 0.25*70 - 0.25n + 0.05n = 7.50. This can be simplified to 0.2n = 10, which means that n = 50.
Knowing that we can solve q + 50 = 70, which means that q = 20.
By applying algebraic principles, it's determined that Kevin and Randy Muise have 20 quarters and 50 nickels. We've used two equations to solve this two-variable problem. The first equation comes from the total number of coins, and the second comes from the total value of the coins
Explanation:The subject of this question is a classic two-variable algebra problem. We have two unknowns here: the number of quarters (which we'll call Q) and the number of nickels (which we'll call N).
From the given information in the question, we can create the following equations:
Q + N = 700.25Q + 0.05N = 7.50Essentially, the first equation states that the total number of coins is 70, and the second equation is representative of the total value in dollars of the coins.
From the first equation, we can isolate one variable: N = 70 - Q.
Substituting this value into the second equation gives us
0.25Q + 0.05(70 - Q) = 7.50
⇒0.20Q +3.50 =7.50
⇒0.20Q= 4
⇒Q= 20
Solving this equation gives us the value of Q (number of quarters) = 20.
Substituting Q = 20 into our first equation: 20 + N = 70, we can find the value of N (number of nickels) = 50.
So, Kevin and Randy Muise have 20 quarters and 50 nickels.
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can someone explain the quadratic formula real quick lol
Answer: OPTION D
Step-by-step explanation:
THe quadratic formula is shown below:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
Given the quadratic equation shown in the image, you have that:
a=1
b=3
c=4
Therefore, when you susbtityte these values into the formula you obtain the following solution:
[tex]x=\frac{-3\±\sqrt{3^2-4(1)(4)}}{2*1}[/tex]
[tex]x=\frac{-3\±\sqrt{-7}}{2}[/tex]
Answer:
D.x = (-3±√-7) / 2
Step-by-step explanation:
We have given a quadratic equation.
x²+3x+4 = 0
From above equation, a = 1, b = 3 and c = 4
We have to find the solution of given equation bu using quadratic formula.
x = (-b±√b²-4ac) / 2a
Putting given values in above formula, we have
x = (-3±√(3)²-4(1)(4) ) / 2(1)
x = (-3±√9-16) / 2
x = (-3±√-7) / 2 which is the answer.
The first five multiples for the numbers 4 and 6 are shown below. Multiples of 4: 4, 8, 12, 16, 20, . . . Multiples of 6: 6, 12, 18, 24, 30, . . . What is the least common multiple of 4 and 6? 2 4 12 24
Answer:
12
Step-by-step explanation:
We are given first five multiples of 4 and 6 as shown below and we are to find their least common multiple.
Multiples of 4: 4, 8, 12, 16, 20, . . .
Multiples of 6: 6, 12, 18, 24, 30, . . .
From the given multiples, we can see that the number 12 and 24 are the common multiples which means that these numbers are multiples of both 4 and 6.
So the least common multiple will be 12.
The least common multiple (LCM) of 4 and 6 is 12. This is the smallest multiple that both numbers share.
Explanation:The least common multiple (LCM) of two numbers is the smallest number that is evenly divisible by both of those numbers. In this case, we are looking for the LCM of 4 and 6.
To find the LCM, we can list the multiples of both numbers and look for the smallest common multiple.
Multiples of 4: 4, 8, 12, 16, 20, ...
Multiples of 6: 6, 12, 18, 24, 30, ...
From the lists, we can see that 12 is the smallest number that appears in both lists. Therefore, the LCM of 4 and 6 is 12.
So, the correct answer is 12. The LCM of 4 and 6 is 12 because it is the smallest number that is evenly divisible by both 4 and 6, as it appears in the list of multiples for both numbers.
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If 1/5 cup of icing covers 1/3 of a cake, how many total cups of icing are needed to cover the entire cake? Plz show work:)
A. 2/3
B. 3/5
C. 3/2
D. 5/3
Answer:
B. 3/5
Step-by-step explanation
1/5 of icing = 1/3 of a cake
1/3 * 3/1 = 3/3 = 1 (a whole cake)
1/5 * 3/1 = 3/5
The answer to your question is B, 3/5.
use the discriminant to describe the root of each equation 3x^2-10=0
Given a quadratic equation [tex]ax^2+bx+c=0[/tex]
The discriminant is defined as
[tex]\Delta=b^2-4ac[/tex]
In your case, the equation is defined by the coefficients
[tex]a=3,b=0,c=-10[/tex]
So, the discriminant is
[tex]\Delta=0^2-4\cdot 3\cdot (-10) = 120[/tex]
The discriminant is involved in the solving formula as follows:
[tex]x_{1,2} = \dfrac{-b\pm\sqrt{\Delta}}{2a}[/tex]
Which implies that:
If [tex]\Delta>0[/tex] the root exists, and so you have two distinct solution (the one where you choose the plus sign, and the one where you choose the minus sign in the solving formula)If [tex]\Delta=0[/tex] the root is zero, and you have two collpapsed solutions, since there's no difference in adding or subtracting it.If [tex]\Delta<0[/tex], the root is not defined using real numbers, and the equation has no real solutions.In your case, since the discriminant is positive, you have two distinct solutions. Since 120 is not a perfect square, however, you will not get rid of the square root, so you will have two distinct irrational solutions.
The equation 3x² - 10 = 0 has a discriminant of 120, which is greater than zero. This means that there are two distinct real roots for this equation.
To describe the roots of the equation 3x² - 10 = 0 using the discriminant, we must first understand that the discriminant (d) of a quadratic equation of the form ax² + bx + c = 0 is given by b2 - 4ac. For our equation, a = 3, b = 0, and c = -10, so the discriminant
would be:
= (0)2 - 4(3)(-10) = 0 + 120 = 120
Since > 0, this indicates that there are two distinct real roots. When the discriminant is greater than zero, the quadratic equation has two real solutions. Therefore, in this case, 3x2 - 10 = 0 has two real roots, corresponding to the x-values where the parabola intersects the x-axis.
Determine the mean of 28,40,53,39,45
Answer:
41
Step-by-step explanation:
Add the numbers together and divide by 5. 5 is the amount of numbers in the example.
Answer: The mean of all the numbers is 41.
Step-by-step explanation:
To find the mean of a set of numbers you must first add them all together. In this case, all of the numbers added together equaled 205. Then, you divide what ever your previous number was by how many numbers are in the original set all total. In this case, there was 5. So my last step would be dividing 205 / 5 = 41. 41 is my final answer.
Which of the following shows the table representation of the exponential function f(x)=5*2^x
0-5
1-7
2-9
3-11
0-1
1-10
2-100
3-1000
0-10
1-20
2-40
3-60
0-5
1-10
2-20
3-40
Answer:
The correct option is 4.
Step-by-step explanation:
The given function is
[tex]f(x)=5(2)^x[/tex]
Put x=0,
[tex]f(0)=5(2)^0=5\times 1=5[/tex]
Put x=1,
[tex]f(1)=5(2)^1=5\times 2=10[/tex]
Put x=2,
[tex]f(2)=5(2)^2=5\times 4=20[/tex]
Put x=3,
[tex]f(3)=5(2)^3=5\times 8=40[/tex]
Only table 4 represents the correct value of the given function, therefore the correct option is 4.
The table representation of the exponential function f(x)=5*2^x is: for x=0, f(x)=5; for x=1, f(x)=10; for x=2, f(x)=20; for x=3, f(x)=40.
Explanation:To find the table representation of the exponential function f(x)=5*2^x, we need to calculate the values of f(x) for different values of x. Remember, any number raised to the power of 2 is being squared, but in this case, x can be any integer, and we're multiplying the result of 2 raised to that power by 5. Here's how you calculate the first few values:
For x=0: f(0) = 5*2^0 = 5*1 = 5 For x=1: f(1) = 5*2^1 = 5*2 = 10 For x=2: f(2) = 5*2^2 = 5*4 = 20 For x=3: f(3) = 5*2^3 = 5*8 = 40
Therefore, the correct table representation of the function f(x)=5*2^x is:
0 - 5 1 - 10 2 - 20 3 - 40
Two dice are tossed. Find the probability of getting the sum of the dice equal to 1
If the dices have equal probability, that means each number has a 1/6 chance of getting picked because there are 6 sides to a dice with 6 different numbers.
There are a total of 36 combinations, because 6 * 6 is 36.
It would be impossible to have a sum of 1, as the lowest number on both dice is 1. 1 + 1 = 2. Therefore there is a 0/36 probability of getting a sum of 1.
what is the area of the actual playground=_____
[tex]ft {}^{2} [/tex]
Answer:
a: 162 ft^2
Step-by-step explanation:
Lets turn the inches into feet. Every one inch is 3 feet so 3 inches is 9 feet and 6 inches is 18 feet. 9*18=162. The area of the playground is 162 ft^2
Philip needs to incorporate at least 200 roses in his floral arrangements for a wedding. Each centerpiece will have 24 roses, and each bouquet will have 10 roses. Write an inequality to represent the situation, if x represents the number of centerpieces Philip makes, and y represents the number of bouquets.
Answer:
24 x + 10 y >= 200
Step-by-step explanation:
as x represents centerpiece and y represent bouquet and total number of roses should be atleast 200 which means we can use roses more than 200 but not less than 200, the equation will be:
24 x + 10 y >= 200
Answer:
[tex]24x+10y\geq 200[/tex]
Step-by-step explanation:
Givens:
Phillip needs at least 200 roses.There will be 24 roses per centerpiece.There will be 10 roses per bouquet.[tex]x[/tex] represent the number centerpieces, and [tex]y[/tex] represents the number of bouquets.According to the problem, we can define the number of roses per a centerpiece: [tex]24x[/tex]
The number of roses per bouquet: [tex]10y[/tex]
So, the problem restricts the amount of roses, at least 200, that means, 200 or more than 200 roses. Therefore the expression that represent the amount of roses would be:
[tex]24x+10y\geq 200[/tex]
As you can observe, the inequality includes the 200 roses restriction, and the amount of roses per centerpieces and per bouquet.
If we know that p → q is true and p is true, what do we know about q?
a. q is false
b. q is true
c. q must be negated
d. q could be either true or false
Answer:
B
Step-by-step explanation:
If p and q are both true, then p→q is true.
If p is true, q is false, then p→q is false.
If p is false, q is true, then p→q is true.
If p and q are both false, then p→q is true.
So if you know that p→q and p are both true, then q must be true (because if q is false, then p→q must be false).
Trigonometry please help!
See the attached picture:
A rectangle is 6 inches wide. It’s length is 2 inches more than its width. What’s the perimeter of the rectangle
Answer:
28 in
Step-by-step explanation:
6+2= 8 so therefore the length is eight.
To find perimeter, add up all the sides of the rectangle so 6+6+8+8=28
Final answer:
The perimeter of the rectangle is calculated using its length and width. With a width of 6 inches and 2 inches added to determine the length, the perimeter is found to be 28 inches.
Explanation:
To determine the perimeter of the rectangle, we first have to calculate both the width and the length. The width is given as 6 inches. The problem states that the length is 2 inches more than its width, which means the length is 6 inches + 2 inches = 8 inches.
The formula to compute the perimeter (P) of a rectangle is P = 2 * (length + width). Substituting our values, we get P = 2 * (8 inches + 6 inches) = 2 * 14 inches = 28 inches. Therefore, the perimeter of the rectangle is 28 inches.
Which function is represented by this graph?
The last option is not even a function, because it ambiguously defines the endpoints.
The first option doesn't define the endpoint, because they are always excluded.
So, the correct option is the second one, because it includes the left endpoint and excludes the right one.
The function d(x) is given by:
d(x)= 1 if 1≤x<4
2 if 4≤x<6
3.5 if 6≤x<11
and 5 if 11≤x<13
Step-by-step explanation:By looking at the graph of the function we observe that the function takes the value :1 when 1≤x<4
( because the graph is a straight horizontal line i.e. y=1 and the line has a closed circle at x=1 and open circle at x=4 )
also the function takes the value: 2 when 4≤x<6( because the graph is a straight horizontal line i.e. y=2 and the line has a closed circle at x=4 and open circle at x=6 )
also the function takes the value: 3.5 when 6≤x<11( because the graph is a straight horizontal line i.e. y=3.5 and the line has a closed circle at x=6 and open circle at x=11 )
also the function takes the value: 5 when 11≤x<13( because the graph is a straight horizontal line i.e. y=5 and the line has a closed circle at x=11 and open circle at x=13 )
What side lengths form a right triangle
Answer:
A, C
Step-by-step explanation:
I had answered this earlier, so you better look back at that question.
To reiterate, use the Pythagorean Theorem a^2+b^2=c^2.
If a^2+b^2=c^2, it is a right triangle.
*remember that squaring a square root results in just the number inside the square root.
what is the product
Answer:
Step-by-step explanation:
To find the indicated product, multiply each element in the 2x2 matrix by 3:
3(-6) 3(-11)
3(-14) 3(-8)
which comes out to:
-18 -33
-42 -24
This corresponds to the 2nd answer choice.
A rectangle is 2/5 inches long and 1/3 inches wide.
What is the area of the rectangle?
Enter your answer in the box as a fraction in simplest form.
Answer:
The area of the rectangle is 2/15
Step-by-step explanation:
To figure this out you have to multiply the length and the width
2/5×1/3 = 2/15
This is the simplified answer
Kaylee cut half of a loaf of bread into four equal parts. What fraction of the whole loaf does each of the four parts represent?
1 whole divided by 4 parts is the same as saying each part is 1/4 or 25% of the whole.
Determine the total number of roots of each polynomial function using the factores form? F(x) = (x-6)^2(x+2)^2
Answer:
4
Step-by-step explanation:
If we perform the indicated multiplication, the highest powered x term will be 4 (as in x^4). Thus, the total number of roots of this polynomial will be 4.
Answer:
total number of roots =4
Step-by-step explanation:
the total number of roots of each polynomial function using the factored form
[tex]F(x) = (x-6)^2(x+2)^2[/tex]
Given f(x) is in factored form, to get the roots we look at the factors and the exponents.
[tex](x-6)^2[/tex] has exponent 2, so we have two roots 6 and 6
like that [tex](x+2)^2[/tex] gives us two roots because it has exponent 2
So total number of roots for this polynomial function is 4
2x^2+10x+12=0 factor with steps
Answer:
x= -2,-3
Step-by-step explanation:
Evaluate: 5P5.
it's for permutations.
someone help pls
Answer:
120
Step-by-step explanation:
Using the definition
n[tex]P_{r}[/tex] = n! / (n - r ) !
where n! = n(n - 1)(n - 2) ....... × 3 × 2 × 1
Hence
5[tex]P_{5}[/tex] = 5! / 0! = 5! ← 0! = 1
5[tex]P_{5}[/tex] = 5! = 5 × 4 × 3 × 2 × 1 = 120
In mathematics, the permutation '5P5' equals 1 because there is exactly one way to arrange 5 items in 5 spots.
Explanation:The problem you are asked to solve involves understanding permutations, which in mathematics, is a way to calculate the number of possible arrangements of a set of items. Specifically, the permutation you are asked to evaluate is written as '5P5'.
In permutation notation, the expression 'nPn' always equals 1, because there are exactly 1 ways you can arrange 'n' items in 'n' spots.
Therefore, the solution to '5P5' is 1.
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What is the area, in square meters, of a right triangle with sides of length 8 meters, 15 meters and 17 meters?
Answer:
60 square meters
Step-by-step explanation:
The area of a triangle is with the formula A = 1/2 b*h. The base and height are the measurements of the sides of a triangle which form a 90 degree angle. When all three measurements are given, the base and height are the smallest since the largest is the hypotenuse. Here b = 8 and h = 15.
So the area is A = 1/2 * 8 * 15 = 60.
A video rental company offer a plan that includes a membership fee of $8 and charges $2 for every DVD borrowed. They also offer a second plan, that costs $48 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. What is that total cost of either plan? How many DVDs is that?
The cost at which both video rental plans are the same is $48, which occurs when a customer borrows 20 DVDs in a month.
Explanation:The student asked about the cost at which both video rental plans offered by a company would be equal in value. To find this, we need to establish an equation for each plan and set them equal to each other. The first plan includes a membership fee of $8 and charges $2 for every DVD borrowed, which can be represented as cost = $2 × number of DVDs + $8. The second plan is a flat rate of $48 per month for unlimited rentals.
Now we set the equations equal to each other: $2 × number of DVDs + $8 = $48. Solving for the number of DVDs would look like this:
Subtract $8 from both sides: $2 × number of DVDs = $40Divide both sides by $2: number of DVDs = 20Therefore, the break-even point where both plans cost the same amount is at 20 DVDs borrowed. At this point, the customer would pay $48 with either plan.
The sum of two numbers is 21. Their difference is 7. What are the numbers?
Answer:
The numbers are
14
and
7
.
Explanation:
Let the numbers be
x
and
y
.
x
+
y
=
21
x
−
y
=
7
y
=
21
−
x
x
−
(
21
−
x
)
=
7
x
−
21
+
x
=
7
2
x
=
28
x
=
14
∴
14
+
y
=
21
y
=
7
Answer: The required numbers are 14 and 7.
Step-by-step explanation: Given that the sum of two numbers is 21 and their difference is 7.
We are to find the numbers.
Let x and y represents the two numbers.
Then, according to the given information, we have
[tex]x+y=21~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-y=7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Adding equations (i) and (ii), we get
[tex](x+y)+(x-y)=21+7\\\\\Rightarrow 2x=28\\\\\Rightarrow x=\dfrac{28}{2}\\\\\Rightarrow x=14.[/tex]
From equation (i), we get
[tex]x+y=21\\\\\Rightarrow 14+y=21\\\\\Rightarrow y=21-14\\\\\Rightarrow y=7.[/tex]
Thus, the required numbers are 14 and 7.
Between what two integers on a number line would the square root of 29 be plotted?
5 and 6
because 5 squared is 25 and 6 squared is 36 so 29 is in between
What is the quotient?
Answer:
The answer is 1/9.
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Hope this helps. :D
For this case we have that by definition, any number raised to zero results in "1".
That is to say:
[tex]a ^ 0 = 1[/tex]
Then, given the following expression:
[tex]\frac {(- 3) ^ 0} {(- 3) ^ 2} = \frac {1} {(- 3) (- 3)} =[/tex]
Taking into account that:
[tex]- * - = +\\\frac {1} {(- 3) (- 3)} = \frac {1} {9}[/tex]
Answer:
[tex]\frac {1} {(- 3) (- 3)} = \frac {1} {9}[/tex]
Option c
My favorite songdress
Answer:
I'm sorry but is this a question? I don't mean to be rude.
Step-by-step explanation: