Using the combination formula, it is found that it would be possible to elect 27,405 different leadership committees.
The order in which the students are selected to the committee is not important, which means that the combination formula is used to solve this question.
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 4 students are chosen from a set of 30, thus:
[tex]C_{30,4} = \frac{30!}{4!26!} = 27405[/tex]
It would be possible to elect 27,405 different leadership committees.
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how do you solve f + 15 = 35
So what we do to one side of the equal sign, we must do to the other side as well.
We want to solve for f, so we need to subtract 15 on both sides of the equal sign in order to get f alone by itself on the left side:
[tex] f=20 [/tex]
So now we know that f = 20.
f + 15 = 35
Isolate the variable (f). Note the equal sign. What you do to one side, you do to the other.
Subtract 15 from both sides
f + 15 (-15) = 35 (-15)
f = 35 - 15
Simplify
f = 20
f = 20 is your answer
hope this helps
The cruise control feature on a car is set to maintain a speed of 65 miles per hour. The car’s actual speed never varies by more than three mph. Select the inequality that represents the speed of the car while cruise control is being used.
Final answer:
The inequality that represents the speed of the car while cruise control is being used is 62 ≤ s ≤ 68, where s is the car's speed and it shows the car's speed will be at least 62 mph and at most 68 mph.
Explanation:
The cruise control feature on a car is designed to maintain a steady speed, in this case, 65 miles per hour. However, it is acknowledged that the car's actual speed can fluctuate slightly. The question asks for an inequality that represents the potential speed of the car while cruise control is in use.
Considering the car's speed can vary by up to 3 mph more or less than the cruise control setting, we can set up an inequality to describe this range of speeds. The car's speed (s) should be no more than 3 mph above 65 mph and no less than 3 mph below 65 mph. Therefore, the inequality that represents the speed s of the car would be:
62 ≤ s ≤ 68
This inequality shows that the car's speed will be at least 62 mph and at most 68 mph, encompassing the 3 mph range of variation allowed by the cruise control setting.
Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?
Rationalize the denominator of square root of negative 9 over open parentheses 4 minus 7 i close parentheses minus open parentheses 6 minus 6 i close parentheses.
The following information is obtained from two independent samples selected from two normally distributed populations.
n1 = 18 x1 = 7.82 σ1 = 2.35
n2 =15 x2 =5.99 σ2 =3.17
A. What is the point estimate of μ1 − μ2? Round to two decimal places.
B. Construct a 99% confidence interval for μ1 − μ2. Find the margin of error for this estimate.
Round to two decimal places.
A. The point estimate of μ1 − μ2 is calculated using the value of x1 - x2, therefore:
μ1 − μ2 = x1 – x2 = 7.82 – 5.99
μ1 − μ2 = 1.83
B. The formula for confidence interval is given as:
Confidence interval = (x1 –x2) ± z σ
where z is a value taken from the standard distribution tables at 99% confidence interval, z = 2.58
and σ is calculated using the formula:
σ = sqrt [(σ1^2 / n1) + (σ2^2 / n2)]
σ = sqrt [(2.35^2 / 18) + (3.17^2 / 15)]
σ = 0.988297
Going back to the confidence interval:
Confidence interval = 1.83 ± (2.58) (0.988297)
Confidence interval = 1.83 ± 2.55
Confidence interval = -0.72, 4.38
How do you turn 1/8 into a fraction
In which situation is the distance traveled proportional to time?
A car moving in stop-and-go traffic
A person biking on a trail at 12
miles per hour for 20
minutes
A baseball hit to center field
A race car slowing down after crossing the finish line
Answer: a person on a trail at 12 miles per hour for 20 minutes
Step-by-step explanation:
just go it right!!!
Rounded to the nearest some, What is the greatest amount of money that rounds to $105.40? What is the least amount of money that rounds to $105.40?
The greatest amount of money that rounds to $105.40 is $105.41, while the least amount that rounds to $105.40 is $105.39.
Explanation:The greatest amount of money that rounds to $105.40 would be the amount slightly greater than $105.40. Since rounding to the nearest cent, we would look at the hundredths place. Any amount greater than $105.405 would round up to $105.41. So the greatest amount of money that rounds to $105.40 would be $105.41.
The least amount of money that rounds to $105.40 would be the amount slightly less than $105.40. Again, looking at the hundredths place, any amount less than $105.395 would round down to $105.39. So the least amount of money that rounds to $105.40 would be $105.39.
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what else would you need yo show that ABC DEF by ASA APEX ?
What is the value of the expression -225 divided by -15
GIVING BRAINLIEST
-225 divided by -15 is equal to 15.
What is Division?A division is a process of splitting a specific amount into equal parts.
We have to find the value of the expression -225 divided by -15
By means of division we can find this value.
-225/(-15) = 15
Two hundred twenty five is the numerator and fifteen is the denominator.
We get 15
When we divide a negative number by a negative number, the result is a positive number.
Therefore, -225 divided by -15 is equal to 15.
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Create a factorable polynomial with a GCF of 2y. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.
A survey has a margin of error of 4%. In the survey, 67 of the 110 people interviewed said they would vote for candidate A. If there are 9570 people in the district, what is the range of the number of people who will vote for candidate A?
Plz help me answer this
the diagram show a straight line ABC . Find the value of p
it is a fraction. it is greater than 0.5 and less than 0.9. its denominator is a square number.its numerator number is a prime number. what could be the mystery number be?
Fraction with numerator as prime number and denominator as a square number between 0.5 and 0.9 is equals to 7/9.
What is fraction?"Fraction is defined as the part of whole number divided into equal parts."
According to the question,
'x / y' represents the required fraction
'x' represents numerator of the given fraction
'y' represents denominator of the given fraction
Condition given,
0.5 < ( x / y) < 0.9
Denominator is squared number
Numerator is a prime number
(5 / 10) < ( 6 / 10) <( 7 / 10) < (7 / 9)< ( 9 / 10)
Hence, required fraction as per condition is ( 7 / 9).
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solve the system of equations using elimination. 3p+9q=6 5p-5q=30
What is the simplified form of √10000x^64 ? 5000x^32 5000x^8 100x^8 100x^32
Answer:
Option (d) is correct.
[tex]\sqrt{10000x^{64}}=100x^{32}[/tex]
Step-by-step explanation:
Given : Expression [tex]\sqrt{10000x^{64}}[/tex]
We have to write a simplified form of the given expression [tex]\sqrt{10000x^{64}}[/tex]
Consider the given expression [tex]\sqrt{10000x^{64}}[/tex]
[tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0[/tex]
[tex]=\sqrt{10000}\sqrt{x^{64}}[/tex]
Factor 10000 as [tex]10000=100^2[/tex]
[tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a[/tex]
[tex]\sqrt{100^2}=100[/tex]
also, [tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
We have,
[tex]\sqrt{x^{64}}=x^{\frac{64}{2}}=x^{32}[/tex]
Thus, [tex]\sqrt{10000x^{64}}=100x^{32}[/tex]
Answer: D. 100x32
Step-by-step explanation:
What is the constant term in the expression 4x3y + 8x2 + 6x + 5? (Input a numeric value only.)
Answer:
Answer is 5.
Step-by-step explanation:
The given expression is :
[tex]4x^{3}y+8x^{2} +6x+5[/tex]
We have to tell the constant term here.
A constant term is one that remains same and does not change with change in values of x and y.
Here, other terms contains either x or y or both, that will change with change in x and y. Only 5 is the single term that will remain constant.
So, the answer is 5.
8x-12y=84 into slope intercept form
A girl wants to count the steps of a moving escalator which is going up. If she is going up on it, she counts 60 steps. If she is walking down, taking the same time per step, then she counts 90 steps. How many steps would she have to take in either direction, if the escalator were standing still?
What is the simplified form of the expression? (2x^6)(3x^(1/2)
Answer:
[tex](6x^\frac{13}{2})[/tex]
Step-by-step explanation:
[tex](2x^6)(3x^\frac{1}{2})[/tex]
Use property of exponents
a^m * a^n = a^mn
When the exponents with same base are in multiplication then we add the exponents
2 times 3= 6
now we multiply x^6 and x^1/2
[tex](x^6)(x^\frac{1}{2})=x^{6+\frac{1}{2}}[/tex]
Make the denominators same to add the fractions
[tex]\frac{12}{2} +\frac{1}{2} =\frac{13}{2}[/tex]
[tex](6x^\frac{13}{2})[/tex]
Determine the 4th term in the geometric sequence whose first term is -2 and whose common ratio is -5
250.
To determine the 4th term in a geometric sequence, start with the first term and use the common ratio. In this case, the first term is -2 and the common ratio is -5. The formula for finding the nth term of a geometric sequence is an = a1 * r(n-1).
Identify the values: a1 = -2, r = -5, n = 4.
Substitute into the formula: a4 = -2 * (-5)(4-1).
Calculate the 4th term: a4 = -2 * (-5)3 = -2 * (-125) = 250.
FIRST CORRECT ANSWER GETS BRAINLIEST!
Complete the steps in order to write the inverse of f(x) = x + 5
To find the inverse of a function, replace f(x) with y, swap x and y, then solve for y. Thus, the inverse of f(x) = x + 5 is f^-1(x) = x - 5.
Explanation:To find the inverse of a function like f(x) = x + 5, we use the following steps:
Replace the function notation f(x) with y. So, we get y = x + 5.
Swap the roles of x and y. This changes the equation to x = y + 5.
Solve for y to get the inverse function. By subtracting 5 from both sides, we acquire y = x - 5.
This implies that the inverse of the function f(x) = x + 5 is f-1(x) = x - 5.
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The tickets in a box are numbered from 1 to 20 inclusive. If a ticket is drawn at random and replaced, and then a second ticket is drawn at random, what is the probability that the sum of their numbers is even?
Answer:
1/2
Step-by-step explanation:
no guarantees but the guy before me said 10/20 and of course if you divide 10 and 20 you get 0.5, and 0.5 is equal to 1/2.
If trap is an isosceles trapezoid, what is the value of x
Answer:
Option E ⇒ x = 19
Step-by-step explanation:
See the attached figure.
TRAP is an isosceles trapezoid
The shown angles are supplementary angles
So, the sum of (5x+9) and (4x) is 180
So, 5x+9 + 4x = 180
solve for x
9x + 9 = 180
9x = 180-9 = 171
x = 171/9 = 19
The answer is option E
f (x)=4x^2+4x+8, g (x)=4x-7 find (g*f)(x)
randy made a business trip of 204 miles. he averaged 52 mph for the first part of the trip and 50 mph for the second part. if the trip took 4 hours, how long did he travel at each rate?
x+y = 4
x=4-y
52x+50y=204
52(4-y)+50y=204
208-52y+50y=204
208-2y=204
-2y=-4
y=2
x= 4-2=2
check 52*2=104
50*2 = 100
104+100=204
so he traveled 2 hours at both 50 and 52 mph
When adding or subtracting two decimals, what is the first thing you must do
You are given a rectangular sheet of cardboard that measures 11 in. by 8.5 in. (see the diagram below). A small square of the same size is cut from each corner, and each side folded up along the cuts to from a box with no lid. 1. Anya thinks the cut should be 1.5 inches to create the greatest volume, while Terrence thinks it should be 3 inches. Explain how both students can determine the formula for the volume of the box. Determine which student's suggestion would create the larger volume. Explain how there can be two different volumes when each student starts with the same size cardboard. 2. Why is the value of x limited to 0 in. < x < 4.25 in.?
We can solve for the value of x using the formula:
V = l w h
where,
h = x the size of the cut since it would form the walls of the rectangle
w = 8.5 – 2x = it is subtracted by 2x since two sides will be cut
l = 11 – 2x
Substituting:
V = x (8.5 − 2x) (11 − 2x)
Expanding the expression:
V = 93.5 x – 39 x^2 + 4 x^3
To solve the maxima, we have to get the 1st derivative dV / dx then equate to 0. dV / dx = 0:
dV / dx = 93.5 – 78 x + 12 x^2
0 = 93.5 – 78 x + 12 x^2
We get:
x ≈ 1.585 in and x ≈ 4.915 in
Therefore Anya’s suggestion of 1.5 inches would create the larger volume since it is nearer to 1.585 inches.
There can be different volumes since volume refers to the amount of space inside the rectangle. They can only have similar perimeter and surface area, but not volume.
It is restricted to 0 in. < x < 4.25 in. because our w is 8.5 – 2x. Going beyond that value will give negative dimensions.