Final answer:
Calculating possibilities ranges from completing a quiz to creating secret codes, with correct answers including 108 ways to complete a quiz and 234,000 combinations for a secret code. The arrangement of the word EXPERIMENT yields 1,209,600 unique arrangements, and other questions involve calculating probabilities and combinations in different scenarios.
Explanation:
Calculating Various Probabilities and Combinations
Let's break down each part of the question to provide clear and step-by-step solutions.
1. Completing a Quiz
For the quiz with 2 true-or-false questions and 3 multiple-choice questions (each with 3 options), the number of ways to complete the quiz can be calculated as 22 * 33, which equals 4 * 27 = 108. So, the correct answer is 108 ways.
2. Creating a Secret Code
For a secret code consisting of 2 digits (10 options each, but cannot repeat, so 10*9), 2 letters (26 options each, but cannot repeat, so 26*25), followed by 1 symbol from 4 options, the total number of combinations is 10*9*26*25*4 = 234,000. Thus, the correct choice is 234,000 combinations.
3. Arrangements of the Word EXPERIMENT
To find the number of distinct arrangements of the letters in EXPERIMENT, considering the repeated letters, the formula is the total factorial divided by the product of factorials of each repeated letter: 10!/ (2! * 3!), which calculates to 1,209,600. Therefore, option a is correct.
4. Sending Students to a Summer Dance Program
To determine how many ways a dance instructor can send 4 of her 11 students to a summer dance program, we use combinations: 11C4 = 330. So, the answer is 330 ways, option a.
5. Probability of Starting a Car
With 5 keys, the probability that a randomly chosen key starts the car is 1/5, which translates to 20%, option c.
6. Probability of Choosing a Losing Card
If the winning probability is 2.9%, the losing probability is 100% - 2.9% = 97.1%, thus the correct answer is option d.
From a team of five students, you choose two students at random without replacement. Calculate the probability that the first student selected is the team leader and the second is the assistant team leader. Please show all work!!
Answer:
1/20
Step-by-step explanation:
1/4*1/5=1/20
A rectangular garden measures 15 m long and 13.7 m wide. what is the length of a diagonal from one corner of the garden to the other?
The length of the diagonal is:
20.3147
Step-by-step explanation:We know that if we draw a diagonal in a rectangle such that the length and width of a rectangle are a and b then the length of the diagonal act as a hypotenuse of a right angled triangle with two sides of triangle as a and b.
Hence, we will use the Pythagorean Theorem to find the length of the hypotenuse (c) as follows:
[tex]c^2=a^2+b^2[/tex]
[tex]c^2=(15)^2+(13.7)^2\\\\c^2=225+187.69\\\\c^2=412.69\\\\c=\pm \sqrt{412.69}\\\\c=\pm 20.3147[/tex]
Since, length can't be negative.
Hence, we have:
[tex]c=20.3147[/tex]
Final answer:
Using the Pythagorean theorem, the length of the diagonal for a rectangular garden measuring 15 m by 13.7 m is approximately 20.31 meters.
Explanation:
The student is asking about finding the length of the diagonal of a rectangle. The rectangle has dimensions of 15 m (length) and 13.7 m (width). To find the diagonal, we can use the Pythagorean theorem, which is applicable in a right-angled triangle and states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The diagonal of the rectangle can be considered as the hypotenuse (c) of a right-angled triangle with the other two sides being the lengths and the width of the rectangle.
Using the dimensions of the garden:
Length (a) = 15 m
Width (b) = 13.7 m
Diagonal (c) = ?
Applying the Pythagorean theorem:
c^2 = a^2 + b^2
c^2 = 15^2 + 13.7^2
c^2 = 225 + 187.69
c^2 = 412.69
c = [tex]\sqrt{412.69}[/tex]
c ≈ 20.31 m
So, the length of the diagonal from one corner of the garden to the other is approximately 20.31 meters.
Chords AB and CD intersect at point E, AE = 10, EB = 4, and CE = 8. Therefore, ED = A) 4 B) 5 C) 6 D) 7
Answer with explanation:
It is given that two chords AB and CD intersect at point E.
Also, A E= 10, E B=4 , CE=8
So, By Intersecting chord Theorem
⇒A E × E B = CE × E D
⇒10 × 4= 8 × ED
⇒ 40 =8× DE
Dividing both sides by , 8 we get
DE= 5 unit
Option: B, DE=5 unit
Solve for x over the complex numbers.
x^2+10x+41=0
x=____ or x=____
Simplify the expression 96/8
Angle A and Angle B are a linear pair. If the measure of Angle A is 3x multiplied by Angle B, then find the measures of Angle A and Angle B.
Can someone please help. Will you graph the functions and approximate an x-value in which the exponential function surpasses the polynomial function. In your final answer, include a copy of the graph.
y = 2x^2 + 7
y = 5^(x-4)
Answer:
paying a price to keep Mowgli alive would b ur answer
Step-by-step explanation:
You learned from your science teacher that water expands when you freeze it. The next time you freeze your water bottle, you leave room for the water to expand, avoiding the cracking of the bottle.
What kind of reasoning did you use?
Question 6 options:
deductive
geometric reasoning
inductive
Which property is x ( y + z) = xy + xz
how many solutions dose this eqashion have
7w-(2+w)=2(3w-1)
a 1
b 0
c infinity solutions
Based on a poll, 40% of adults believe in reincarnation. Assume that 77 adults are randomly selected, and find the indicated probability. Complete parts (a) through (d) below.
a. What is the probability that exactly 66 of the selected adults believe in reincarnation?
The probability that exactly 66 of the 77 adults believe in reincarnation is
nothing.
(Round to three decimal places as needed.)
b. What is the probability that all of the selected adults believe in reincarnation?
The probability that all of the selected adults believe in reincarnation is
nothing.
(Round to three decimal places as needed.)
c. What is the probability that at least 66 of the selected adults believe in reincarnation?
The probability that at least 66 of the selected adults believe in reincarnation is
nothing.
(Round to three decimal places as needed.)
d. If 77 adults are randomly selected, is 66 a significantly high number who believe in reincarnation?
A.
No, because the probability that 66 or more of the selected adults believe in reincarnation is less than 0.05.
B.
Yes, because the probability that 66 or more of the selected adults believe in reincarnation is greater than 0.05.
C.
Yes, because the probability that 66 or more of the selected adults believe in reincarnation is less than 0.05.
D.
No, because the probability that 66 or more of the selected adults believe in reincarnation is greater than 0.05
a. [tex]\( P(X = 66) \approx 0.014 \)[/tex]
b. [tex]\( P(X = 77) \approx 0 \)[/tex]
c. [tex]\( P(X \geq 66) \approx 0.015 \)[/tex]
d. Option C: Yes, 66 is significantly high; probability [tex]\( < 0.05 \).[/tex]
To solve this problem, we'll use the binomial probability formula:
[tex]\[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^{n - k} \][/tex]
Where:
[tex]- \( n \) is the number of trials (77 adults in this case)\\- \( k \) is the number of successes (the number of adults believing in reincarnation)\\- \( p \) is the probability of success (the proportion of adults believing in reincarnation, which is 0.40 in this case)\\- \( \binom{n}{k} \) is the binomial coefficient, which represents the number of ways to choose \( k \) successes out of \( n \) trials.[/tex]
Now let's calculate the probabilities:
a. Probability that exactly 66 of the selected adults believe in reincarnation:
[tex]\[ P(X = 66) = \binom{77}{66} \cdot (0.40)^{66} \cdot (1 - 0.40)^{77 - 66} \][/tex]
b. Probability that all of the selected adults believe in reincarnation:
[tex]\[ P(X = 77) = \binom{77}{77} \cdot (0.40)^{77} \cdot (1 - 0.40)^{77 - 77} \][/tex]
c. Probability that at least 66 of the selected adults believe in reincarnation:
This is the sum of probabilities from 66 to 77.
[tex]\[ P(X \geq 66) = \sum_{k=66}^{77} \binom{77}{k} \cdot (0.40)^{k} \cdot (1 - 0.40)^{77 - k} \][/tex]
Let's calculate these probabilities.
a. Probability that exactly 66 of the selected adults believe in reincarnation:
[tex]\[ P(X = 66) = \binom{77}{66} \cdot (0.40)^{66} \cdot (0.60)^{11} \]\[ = \frac{77!}{66!(77-66)!} \cdot (0.40)^{66} \cdot (0.60)^{11} \]\[ \approx 0.014 \][/tex]
b. Probability that all of the selected adults believe in reincarnation:
[tex]\[ P(X = 77) = \binom{77}{77} \cdot (0.40)^{77} \cdot (0.60)^{0} \]\[ = (0.40)^{77} \]\[ \approx 0 \][/tex]
c. Probability that at least 66 of the selected adults believe in reincarnation:
[tex]\[ P(X \geq 66) = \sum_{k=66}^{77} \binom{77}{k} \cdot (0.40)^{k} \cdot (0.60)^{77 - k} \]\[ \approx 0.015 \][/tex]
So, for the options:
d. If 77 adults are randomly selected, is 66 a significantly high number who believe in reincarnation?
C. Yes, because the probability that 66 or more of the selected adults believe in reincarnation is less than 0.05.
You pay $30 each month for satellite TV, plus $2.50 for every movie you purchase. Write and solve an equation to find the number of movies purchased during a month with a total bill of $45.
Answer:
6 movies
Step-by-step explanation:
You pay each month for satellite TV = $30
and for every movie you purchase = $2.50
Let the number of the movies you purchase be x
The equation will be
30 + 2.50x = 45
2.50x = 45 - 30
2.50x = 15
x = [tex]\frac{15}{2.5}[/tex]
x = 6
You purchased 6 movies during the month.
While hiking, Emily recorded that she climbed 125 feet, descended 31 feet to find a new trail and then went 145 feet further up the mountain to end her hike. How far up the mountain was Emily when she stopped climbing for the day
Lisa earns $8.10 an hour and worked 40 hours. Jamie earns $10.80 an hour. How many hours would Jamie need to work to equal Lisa’s earnings over 40 hours
Answer:
it takes 30 hours for Jamie to equal Lisa's earnings
Step-by-step explanation:
Lisa earns $8.10 an hour and worked 40 hours.
Total amount Lisa earns = rate times hours
Total amount Lisa earns =[tex]8.10 \cdot 40=324[/tex]
Jamie earns $10.80 an hour
LEt 'n' be the number of hours Jamie works
Total amount Jamie earns =[tex]10.80 \cdot n=10.80n[/tex]
we need to find out 'n' when Jamie earnings is equal to Lisa earnings
[tex]10.80n= 324[/tex]
Divide by 10.80 on both sides
n= 30
So it takes 30 hours for Jamie to equal Lisa's earnings
Solve for m and show your work. 4n=3m-1
Assume your favorite soccer team has 2 games left to finish the season. the outcome of each game can be win, lose or tie. the number of possible outcomes is
The number of possible outcomes for the two remaining games is 9.
Explanation:The number of possible outcomes for the two remaining games can be found by multiplying the number of outcomes for each game. Since each game can have three possible outcomes (win, lose, or tie), there are a total of 3 outcomes for each game. Therefore, the number of possible outcomes for the two games is 3 x 3 = 9.
Can Anyone Help Me
Real-world problems that have more than one answer can be described by relations.
A. True
B. False
How do you find the width of a rectangle when the perimeter is given?
when adding 3 and -9, how do you know that the sun is negative?
what is the approximate circumference of the circle shown below
The correct option is [tex]\boxed{\bf option A}[/tex] i.e, [tex]\boxed{\bf 129\text{ cm}}[/tex].
Further explanation:
A circle is the set of all points on a plane whose distance from a fixed point is constant.
There are infinite points on the circle and distance of these points from the center of circle is always constant.
The distance from the center of the circle to any point on the circle is called as radius of the circle.
The circumference is the length of the circle and the formula of the circumference [tex]C[/tex] for the circle is as follows:
[tex]\boxed{C=2\pi r}[/tex] …… (1)
Here, [tex]r[/tex] is the radius of the circle and the value of [tex]\pi[/tex] is approximately equal to [tex]3.14[/tex].
The formula of the circumference for circle is terms of diameter is as follows:
[tex]\boxed{C=d\pi}[/tex]
Here, [tex]d[/tex] is the diameter of the circle.
The relationship between diameter and the radius is as follows:
[tex]\boxed{d=2r}[/tex].
From attached Figure 1 it is observed that the radius of the circle is [tex]20.5\text{ cm}[/tex].
Substitute [tex]r=20.5[/tex] in the equation (1) to obtain the value of circumference [tex]C[/tex] as follows:
[tex]\begin{aligned}C&=2\pi r\\&=2\cdot 3.14 \cdot 20.5\\&=128.74\\ &\approx129\end{aligned}[/tex]
Therefore, the circumference of the circle is [tex]\boxed{\bf 129\text{\bf cm}}[/tex].
Thus, the correct option is [tex]\boxed{\bf option A}[/tex].
Learn more:
1. Learn more about circle https://brainly.com/question/1952668
2. Learn more about radius of circle https://brainly.com/question/1506955
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Circle
Keywords: Circle, radius of a circle, point, distance, diameter, circumference, d=2r, C=2pir, 129. centimeter, locus of circle, approximate, value, shown below.
HELP ASAP PLEASE!
Evaluate the numerical expression.
− 1/3 − (− 4/9 )
Scott earns 16.85 per hour at his job. He works 7 hour per day , 4 days per week. What Scott's gross income in 4 weeks
Scott's gross income in 4 weeks, rounded to the nearest cent, is $1887.20.
Calculate Scott's daily earnings:
Scott earns $16.85 per hour, and he works for 7 hours per day.
Daily earnings = $16.85/hour × 7 hours = $117.95
Calculate Scott's weekly earnings:
Scott works 4 days per week.
Weekly earnings = Daily earnings × Number of days worked per week
= $117.95/day × 4 days/week
= $471.80
Calculate Scott's gross income for 4 weeks:
Scott works for 4 weeks.
Gross income for 4 weeks = Weekly earnings × Number of weeks
= $471.80/week × 4 weeks
= $1887.20
However, we need to ensure the precision of the final answer. As currency involves cents, it's important to round appropriately.
Since we're dealing with money, we'll round to the nearest cent.
After rounding, the gross income for 4 weeks is $1887.20.
Solve each equation. Leave the answer as an improper fraction. 16x2 = 49
Answer:
[tex]x= +-\frac{7}{4}[/tex]
Step-by-step explanation:
[tex]16x^2= 49[/tex]
Solve the equation for x
To solve the equation , we need to isolate x
To get x alone , we need to remove the numbers attached with x
To remove 16 we divide both sides by 16
[tex]x^2 = \frac{49}{16}[/tex]
Now to remove square from x we take square root on both sides
[tex]\sqrt{x^2} = \sqrt{\frac{49}{16}}[/tex]
square root (49) = 7
square root (16)= 4
So , [tex]x= +-\frac{7}{4}[/tex]
When we take square root we include +-
Translate the following word phrase into an algebraic expression.
" The product of 8 and a number increased by 2"
A. 8x-2
B. 8(x+2)
C. 8x+2
D. x÷8+2
How does the graph of g(x)=⌊x⌋−3 differ from the graph of f(x)=⌊x⌋?
Final answer:
The graph of g(x)=⌊x⌋-3 is the same as the graph of f(x)=⌊x⌋ but shifted downward by 3 units because of the subtraction of 3, resulting in each step being 3 units lower.
Explanation:
The student has asked how the graph of g(x)=⌊x⌋-3 differs from the graph of f(x)=⌊x⌋. The function ⌊x⌋ represents the greatest integer function or floor function, which maps a real number to the largest integer less than or equal to it. The graph of f(x) is a step function that jumps up by 1 at each integer value of x. The graph of g(x) will be exactly the same as f(x) but will be shifted downward by 3 units due to the -3 in the function. This means that each step on the graph of g(x) will occur at an integer value of y that is 3 less than the corresponding step on the graph of f(x). For example, where f(x) has a step at y=0, g(x) will have a step at y=-3.
Combine the radical below 2√27-√48
Pam buys a shirt that costs $11.99 , pants that cost $23.98 , and a belt that costs $9.95 she has a coupon for 20% off the entire purchase. about how much will the three items cost ?
A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line? Check all that apply.
(–2, 0) and (2, 5)
(–4, 5) and (4, –5)
(–3, 4) and (2, 0)
(1, –1) and (6, –5)
(2, –1) and (10, 9)
Answer:
Options A and Option E.
Step-by-step explanation:
A line has a slope of -4/5. Now a line perpendicular to this line will have the slope as [tex]m_{1}.m_{2}=-1[/tex]
Therefore [tex]m_{2}=-\frac{1}{m_{1}}=\frac{1}{\frac{4}{5} }=\frac{5}{4}[/tex]
Now we will find the slope with the help of points given in the options if they lie on the perpendicular line.
A). [tex]m=\frac{5-0}{2+2}=\frac{5}{4}[/tex]
B). [tex]m=\frac{-5-5}{4+4}=\frac{-10}{8}=-\frac{5}{4}[/tex]
C). [tex]m=\frac{0-4}{2+3}=-\frac{4}{5}[/tex]
D). [tex]m=\frac{-5+1}{6-1}=\frac{-4}{5}=-\frac{4}{5}[/tex]
E). [tex]m=\frac{9+1}{10-2}=\frac{10}{8}=\frac{5}{4}[/tex]
Options A and E are the correct options.
What is the equation of a line that is parallel to 2x+3y=3 and passes through the point (3, −4) ? Enter your answer in the box.
Final answer:
The equation of the line that is parallel to 2x+3y=3 and passes through the point (3, −4) is y = −(2/3)x − 2. We found this by first converting the given line into slope-intercept form to find the slope, and then using the point-slope form with the given point.
Explanation:
To find the equation of the line that is parallel to 2x+3y=3 and passes through the point (3, −4), we first need to determine the slope of the given line. The equation of a line in slope-intercept form is y = mx + b, where m represents the slope. We can rewrite the given equation in slope-intercept form by isolating y:
2x + 3y = 3
3y = −2x + 3
y = −(2/3)x + 1
This shows that the slope (m) of the given line is −(2/3). Since parallel lines have the same slope, the slope of the new line will also be −(2/3). Now we use the point-slope form of a line which is y − y1 = m(x − x1), where (x1,y1) is a point on the line. Plugging in the given point (3, −4) and the slope −(2/3), we get:
y − (−4) = −(2/3)(x − 3)
Distributing the slope on the right side and moving −4 to the other side gives us the final equation:
y = −(2/3)x + 2 + −4
y = −(2/3)x − 2
This is the equation of the line that is parallel to 2x+3y=3 and passes through the point (3, −4).
What is one point on a graph for the equation y=-3x-1 and how do we substitute it?
use the slope intercept equation to find the slope and the y intercept
y = mx-b
m = slope
b = y intercept
m is the number before the x so -3 is the slope
and -1 is the y intercept
so a point on the graph would be the y intercept at (0,-1)