Final answer:
The number of ways 12 cheerleaders can line up is calculated using permutations, specifically 12!, which is the product of all positive integers from 1 to 12.
Explanation:
The number of ways the 12 cheerleaders can line up down the football field can be calculated using the concept of permutations. A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement. For 12 cheerleaders, each of whom is distinct, the number of different ways they can line up is the same as the number of permutations of 12 objects, which is given by the factorial of the number of objects.
The formula for permutations of n objects is n! (n factorial), where n represents the total number of objects. Therefore, for 12 cheerleaders, the expression for the number of ways they can line up is:
12!
This is calculated as 12 × 11 × 10 × 9 × ... × 3 × 2 × 1. The value of 12! (12 factorial) gives us the total number of possible arrangements for the 12 cheerleaders.
The longest side of an acute isosceles triangle is 8 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides? 4.0 cm 4.1 cm 5.6 cm 5.7 cm
The smallest possible length of one of the two congruent sides is 5.7 cm and this can be determined by using the Pythagorean theorem for an acute triangle.
Given :
The longest side of an acute isosceles triangle is 8 centimeters.
The following steps can be used in order to determine the smallest possible length of one of the two congruent sides:
Step 1 - The Pythagorean theorem for an acute triangle can be used in order to determine the smallest possible length of one of the two congruent sides.
Step 2 - Let the length of the smaller sides be 'a' and let the length of the larger side be 'b'.
Step 3 - According to the Pythagorean theorem for an acute triangle:
[tex]\rm H^2 < B^2+P^2[/tex]
where H is the hypotenuse, B is the base, and P is the perpendicular.
Step 4 - Substitute the values of the known terms in the above expression.
[tex]a^2+a^2>b^2[/tex]
[tex]2a^2>b^2[/tex]
Step 5 - Substitute the value of x in the above expression.
[tex]2a^2>8^2[/tex]
a > [tex]\sqrt{32}[/tex]
a > 5.6
Therefore, the correct option is D).
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How to solve 19-4c=17?
would you ever get a credit card from a company that would raise your rate even though you pay your credit card bills as agreed?
a.i don't mind throwing money away
b.i didn't now that credit card companies from one another
c.i didn't carefully shop for the right credit card company.
d.both b and c
You invest $300 in an account at 7.5% per year simple interest. How much will you have in the account at the beginning of the 11th year
By investing $300 at a 7.5% per year simple interest rate, the accrued interest over 11 years is $247.50. Adding this to the initial investment, the total in the account at the beginning of the 11th year will be $547.50.
To determine how much you will have in an account at the beginning of the 11th year with simple interest, you can use the formula for simple interest:
Simple Interest (I) = P × r × t
Where:
P is the principal amount ($300)r is the annual interest rate (7.5% or 0.075)t is the time in years (11 years)Let's calculate the simple interest first:
I = 300 × 0.075 × 11I = 247.50So, the interest earned over 11 years is $247.50. Now, add this to the principal amount to get the total amount in the account at the beginning of the 11th year:
Total Amount = Principal + Interest
Total Amount = 300 + 247.50
Total Amount = 547.50
Simplify by combining like terms: -18 + 3 (5x - 2) + 8
what is the probability of flipping a coin 10 times and getting tails8 times? Round your answer to the nearest tenth of a percent
Answer:
4.4%
Step-by-step explanation:
Bodhi has a collection of 175 dimes and nickels. The collection is worth $13.30. Which equation can be used to find n, the number of nickels in the collection?
ANSWER- 0.1(175-n)+0.05n=13.30
Answer:
The equation we can use is 0.1(175-n)+0.05 n=13.30
Step-by-step explanation:
Number of Dimes= d
Number of Nickels= n
n+d=175, so d=175-n
The value of the dime is $0.10 and the value of each nickel is $0.05 and the whole collection is worth $13.30, so
0.1 d+0.05 n=13.30
Replacing
0.1(175-n)+0.05 n=13.30 this is the equation we have to use to get the number of nickels.
Which function is an example of exponential growth? y = 2(0.3)x y = 1.5(0.4)x y = 3(8)x y = 2(0.7)x
(k^3-8k^2+16k-5)/(k-5)
please use the "dividing polynomials format WILL GIVE BRAINIEST
if you do not use this format you will not become brainliest
What is the coefficient of y in the expression 3 ⋅ 4 + 5y?
5
9
12
17
best answer will get brainiest!!!!!
I am a number between 30 and 50 . I am a multiple of 8. My greatest common factor with 25 is 5 what number am I ?
The table shows the estimated number of deer living in a forest over a five-year period. Which type of function best models the data? Write an equation to model the data. Year Estimated Population 0 100 1 79 2 62 3 49 4 39
We are given the following data:
Year Estimated Population
0 100
1 79
2 62
3 49
4 39
Just by looking at the data we can see that the relationship of year and estimated population is not linear. The decrease in the population does not follow a linear path, that is:
79 – 100 is not equal to 62 – 79
-21 is not equal to -17
Therefore, the relationship must be exponential. Let us find the common ratio by dividing the population in year 1 and year 0:
common ratio, r = 79 / 100 = 0.79
This means that the population decreases by 21% every year.
So the model for this data can be written as:
yn = y0 * r^n
Where,
yn = is the population after n years
y0 = initial population
r = growth rate = decreasing
n = number of years
given f(x)=6x+2 find f(x+3)
f(x+3) = 6x+20
What is a function?A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
f(x) = 6x+2
f(x+3) = 6(x+3) + 2
= 6x + 18 + 2
= 6x + 20
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The following data points represent the number of chicken nuggets on each family member's plate. 1, 3, 0, 6? If the mean of the data set is 3 chicken nuggets, find the missing number of chicken nuggets.
The missing number of chicken nuggets will be 5.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
The following data points represent the number of chicken nuggets on each family member's plate.
1, 3, 0, 6, x
If the mean of the data set is 3 chicken nuggets. Then the missing number of chicken nuggets is calculated as,
3 = (1 + 3 + 0 + 6 + x) / 5
15 = 10 + x
x = 5
The missing number of chicken nuggets will be 5.
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A box of grass seed weighs .62 pounds. How much does a box containing .75 times as much grass seed weigh?
Which of these shows 7 + 2y rewritten using the commutative property of addition?
7y + 2
2y + 7
7 − 2y
2y − 7
bets answer gets brainiest!!!!!
which shows the factored form of x2-12x-45
Answer:
[tex](x+3)(x-15)[/tex] is the required factorized form of the given expression.
Step-by-step explanation:
The given equation is:
[tex]x^2-12x-45[/tex], we have to factorized this equation,
Upon solving the above equation, we get
⇒[tex]x^2-15x+3x-45[/tex]
⇒[tex]x(x-15)+3(x-15)[/tex]
⇒[tex](x+3)(x-15)[/tex]
which is the required factorized form of the given expression.
On Ms. Smith's last math test, 60% of her 25 students earned an 83% or better. How many of Ms. Smith's students earned an 83% or better on the last math test? A. 17 B. 14 C. 20 D. 15
The answer is 15.
15 students earned an 83% or better on the last math test.
60% of 25 students means 60% * 25 = 15 students earned an 83% or better on Ms. Smith's last math test. Therefore, the answer is 15.
Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below. x – y = 7 3x – 2y = 8 Step 1: x = y + 7 Step 2: 3(y + 7) – 2y = 8 Step 3: 3y + 7 – 2y = 8 Step 4: y + 7 = 8 Step 5: y = 1 In which step did Ernesto make the first error?
Answer:
answer C
Step-by-step explanation:
NEED HELP ASAP DUE TOMORROW AND ITS REALLY LATE WHERE I AM
How much is Pete's 12% commission on $50,00 in sales
True or False: Every Student's t-distribution with n < N, n the number in the sample and N the number in the population, will be less peaked and have thinner tails.
The statement is false as the Student's t-distribution is actually more peaked and has thicker tails with smaller sample sizes, and it becomes similar to the standard normal distribution as the sample size, and consequently the degrees of freedom, increase.
Explanation:The statement that every Student's t-distribution with n < N, where n is the sample size and N is the population size, will be less peaked and have thinner tails is false. In reality, the t-distribution is more peaked and has thicker tails when the sample size is smaller, which happens due to the reduced degrees of freedom (df).
The shape of the Student's t-distribution is determined by the degrees of freedom, which is n - 1 for a sample size n. As n approaches the population size N, the t-distribution approaches the standard normal distribution. This is further supported by the central limit theorem, which states that as the sample size increases, the sampling distribution of the sample means tends to be normal. Therefore:
The statement in the question is false; the t-distribution becomes less peaked and has thicker tails as the degrees of freedom decrease.
Explanation:The Student's t-distribution is a probability distribution that is used when the sample size is small and the population standard deviation is unknown. It is similar to the standard normal distribution, but has thicker tails and less probability in the center. As the degrees of freedom increase, the t-distribution approaches the standard normal distribution. Therefore, the statement in the question is false. The t-distribution becomes less peaked and has thicker tails as the degrees of freedom decrease.
A television costs $270.25 including 15% tax. How much of cost is the tax
Final answer:
The tax on the television is $35.25.
Explanation:
To find the amount of tax, we first need to determine the original cost of the television. Since the total cost, including tax, is $270.25, we can set up the equation:
$270.25 = x + 0.15x
Where x is the original cost of the television. Combining like terms, we get:
$270.25 = 1.15x
To solve for x, divide both sides of the equation by 1.15:
x = $270.25 ÷ 1.15
Using a calculator, we find that x is approximately $235.00. Therefore, the tax on the television is:
$270.25 - $235.00 = $35.25
I need help with #46!!!!
Remark
There are two formulas for doing this. I'll use the one that does not involve the slope. I think it will be easier for you to understand.
Step One
Decide which point is (x1,y1)
Since point P is 2/5 the way up from point A, we will call (x1,y1) point A
Step Two
Write the givens.
Point(A) = (-2,-3)
Point(B) = (3,2)
Step Three
Write the formula
x1 + ratio*(x2 - x1), y1 + ratio(y2 - y1)
Sub and solve.
-2 + 2/5 *(3 - - 2) , -3 + 2/5*(2 - -3)
-2 + 2/5(5) , - 3 + 2
-2 + 2 , - 1
P = (0 , - 1) <<<<<< Answer
If this turns out to be incorrect please notify me.
First right answer gets brain
Solve the following system. 4x2 + 9y2 =72 x2 - y2 = 5 The solutions are (), (), (), and () (remember to include the commas) there has to be 4 solutions all ordered pairs please help
Answer: The required solutions are
[tex](x,y)=(3,2),~(-3,2),~(3,-2),~(-3, -2).[/tex]
Step-by-step explanation: We are given to solve the following system of equations:
[tex]4x^2+9y^2=72~~~~~~~~~~~~~~~~~~~~(i)\\\\x^2-y^2=5~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Let us consider that
[tex]x^2=a,~~~~~y^2=b.[/tex]
So, equations (i) and (ii) becomes
[tex]4a+9b=72~~~~~~~~~~~~~~~~(iii)\\\\a-b=5~~~~~~~~~~~~~~~~~~~~(iv)[/tex]
Multiplying equation (iv) by 4 and then subtracting from equation (iii), we get
[tex](4a+9b)-(4a-4b)=72-4\times 5\\\\\Rightarrow 4a+9b-4a+4b=72-20\\\\\Rightarrow 13b=52\\\\\Rightarrow b=4.[/tex]
From equation (iv), we get
[tex]a-b=5\\\\\Rightarrow a-4=5\\\\\Rightarrow a=9.[/tex]
Therefore,
[tex]a=9~~~~~\Rightarrow x^2=9~~~~~\Rightarrow x=\pm3,\\\\b=4~~~~~\Rightarrow y^2=4~~~~~\Rightarrow y=\pm2.[/tex]
Thus, the required solutions are
[tex](x,y)=(3,2),~(-3,2),~(3, -2),~(-3, -2).[/tex]
if PA=14 and PD=10 what is the length of PC
To find the length of PC when PA=14 and PD=10, apply the cosine rule formula in trigonometry.
The length of PC can be calculated using trigonometry and the given information.
Since PA=14 and PD=10, we can use the cosine rule to find the length of PC.Applying the cosine rule formula, PC = √(PA2 + PD2 - 2*PA*PD*cos(θ)).Calculate the length of PC by substituting the values: PC = √(142 + 102 - 2*14*10*cos(θ)).(Write the rate as a fraction, then find each unit rate.)
A wheel rotates through 1,800 degrees in 5 revolutions.
From the computation, the rate per revolution will be 360°.
From the information given, it was stated that the wheel rotates through 1,800 degrees in 5 revolutions.
Therefore, the rate per revolution will be:
= 1800/5
= 360°
Therefore, the rate per revolution is 360°.
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which of the following describes the quotient of 2 and -12?
You are stacking books into a shipping box that is 15 inches high. Each book is 1.25 inches thick. How many books can you fit in a stack?
In the equation y = 3x - 1 what is the value of y when x equals -3?
Just plug in -3 for x and solve
y= -10