Roger is renting a tuxedo for prom. Once he has chosen his jacket, he must choose from three types of pants, four colors of vests, and two different styles of shoes. How many different ways can he select his attire for the prom?
The number of ways he can select his attire for the prom to look differently will be twenty-four (24).
What are permutation and combination?A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
Roger is renting a tuxedo for prom.
Once he has chosen his jacket, he must choose from three types of pants, four colors of vests, and two different styles of shoes.
Then the number of the ways he can select his attire for the prom will be
[tex]\rm Number \ of \ ways = ^3C_1 \times ^4C_1 \times ^2C_1 \\\\ Number \ of \ ways = 3 \times 4 \times 2\\\\Number \ of \ ways = 24[/tex]
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A card is drawn at random from a well-shuffled deck of 52 cards. what is the probability of drawing a face card or a spade?
Answer:
11/26
Step-by-step explanation: took the test
What is the quotient of 75,120 ÷ 16?
The quotient of 75,120 divided by 16 is 4,695.
To find the quotient of 75,120 divided by 16, you can follow these steps:
Perform the division: 75,120 ÷ 16 = 4,695.This means that 75,120 divided by 16 equals 4,695.So, the quotient of 75,120 divided by 16 is 4,695.
While crossing the Atlantic, sailors spot two mermaids 120° apart on each end of an island that is 6 miles away. How far apart are the mermaids around the outer edge of the island to the nearest tenth of a mile?
A. 12.6 miles
B. 3.1 miles
C. 7.2 miles
D. 20.2 miles
In a right triangle, the length of one leg is 6 units. The length of the other leg is 8 units. What is the length of the hypotenuse (hint: use Pythagorean Theorem)?
The length of the hypotenuse of given right triangle is 9.2 units.
Given that, in a right triangle, the length of one leg is 6 units. The length of the other leg is 8 units.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Let the length of the hypotenuse be x.
Now, using Pythagoras theorem, we get
x²=6²+7²
⇒x²=36+49
⇒x²=85
⇒x=√85
⇒x=9.2 units
Therefore, the length of the hypotenuse of given right triangle is 9.2 units.
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What is the square root of 64
help please,carlos buys computer parts for $4,000.out of those parts, he can assemble many computers and sell each at $600.how many assembled computers must he sell in order to profit$1,400?
Answer:
9.
Step-by-step explanation: To profit means to make more than originally spent. He Spent 4,000$ and needs to profit 1,400$. Bringing a total of 5,400$. 5,400 divided by 600$ equals 9 computers.
What number must be added to the expression below to complete the square? x2 - 11x
Since we are to complete the square, therefore I believe the correct given should be:
x ^ 2 – 11 x
Take note of the symbol ^ which denotes that 2 is an exponent of x.
The general form of a binomial equation is in the form of:
a x^2 + b x + c
Where in this case:
a = 1
b = -11
c = unknown
To complete the square, we have to find for the value of c. This is calculated using the formula:
c = (b / 2) ^ 2
c = (-11 / 2) ^ 2
c = 30.25
Therefore the complete equation is:
x ^ 2 – 11 x + 30.25
30.25 is correct but apex asks for a fraction so 121/4
What is the length of the third side of the window frame below? (Figure is not drawn to scale.) A picture of a right triangular window frame is shown. The longest side has length labeled as 87 inches. The height of the frame is labeled as 63 inches.
Answer: 60 inches
Step-by-step explanation:
Given: A frame in the shape of right triangle with the longest side = 87 inches
The height of the frame is labeled as 63 inches.
Let 'x' be the third side of the frame then by Pythagoras theorem of right triangle , we have
[tex]87^2=x^2+63^2\\\\\Righatrrow\ x^2=87^2-63^2\\\\\Rightarrow\ x^2=3600\\\\\Rightarrow\ x=\sqrt{3600}=60[/tex]
Hence, the length of the third side of the window frame = 60 inches.
When x is 2, y is 4, p is 0.5, and m is 2. If x varies directly with the product of p and m and inversely with y, which equation models the situation?
b. StartFraction x y Over p m EndFraction = 8
Replace ? with a whole number to make the statements true.
a. 20 ÷ 4 ? means ? × 4 = 20
b. 2,725 ÷ 5 ? means ? × 5 = 2,725
c. ? ÷ 5 = 0
Answer:
a. 5
b. 545
c. 0
Step-by-step explanation:
These are straightforward division problems, easily solved using your own memorized multiplication facts, or using a calculator.
a. 20 ÷ 4 = 5 means 5 × 4 = 20
b. 2725 ÷ 5 = 545 means 545 × 5 = 2725
c. 0 ÷ 5 = 0 means 0 × 5 = 0
_____
When using the Google calculator and standard keyboard symbols, you can use the slash (/) for "divided by" and the asterisk (*) for "times."
An artifact was found to have an original amount of Carbon-14 of 32 grams. Approximately how many grams of Carbon-14 remain after 4300 years? Carbon 14 decays at a rate of -0.00012 grams per year.
9.6 grams
19.1 grams
22.4 grams
31.2 grams
Geometry help please.
The library has at least 5,000 books. Which inequality represents the situation an has an infinite number of solutions?
Which statement is true?
All quadrilaterals are rectangles.
All parallelograms are rectangles.
All squares are rectangles.
All rectangles are squares.
The money collected from selling bacon at a butcher store is given by the function f(x) = 3.55x – 4, where f(x) is the sales revenue in dollars and x is the number of customers visiting the store each day. If {17, 21, 24, 34} customers visited over four days, what is the income from bacon sales each day?
{50.55, 63.45, 80.34, 99.8}
{43.45, 58.75, 73.4, 93.5}
{56.35, 70.55, 81.2, 116.7}
{45.74, 65.7, 83.8, 105.7}
{63.25, 68.35, 79.7, 97.6}
Answer:
Hi!
The correct answer is {56.35, 70.55, 81.2, 116.7} .
Step-by-step explanation:
The set {17, 21, 24, 34} represents the values of x.
If you replace each value in the equation:
f(17) = 3.55 * 17 – 4 = 60.35 - 4 = 56.35f(21) = 3.55 * 17 – 4 = 74.55 - 4 = 70.55f(24) = 3.55 * 17 – 4 = 85.2 - 4 = 81.2f(34) = 3.55 * 17 – 4 = 120.7 - 4 = 116.7Then you have the values {56.35, 70.55, 81.2, 116.7} .
The original value of a car is 18000 and it depreciates by 15% each year. what is the value of the car after three years?
A normal population has a mean of 75 and a standard deviation of 5. you select a sample of 40. compute the probability the sample mean is
The probability that the sample mean is less than 74 is about 10.38%.
To solve the problem step-by-step, let's go through each calculation in detail:
1. Compute the Standard Error (SE):
Given:
- Population mean [tex](\(\mu\))[/tex] = 75
- Population standard deviation [tex](\(\sigma\))[/tex] = 5
- Sample size (n) = 40
The standard error of the mean is calculated using the formula:
[tex]\[ \text{SE} = \frac{\sigma}{\sqrt{n}} \][/tex]
Substituting the given values:
[tex]\[ \text{SE} = \frac{5}{\sqrt{40}} = \frac{5}{6.3246} \approx 0.791 \][/tex]
2. Compute the Z-score for a sample mean of 74:
The Z-score is calculated using the formula:
[tex]\[ Z = \frac{X - \mu}{\text{SE}} \][/tex]
Where:
- (X) is the sample mean.
Given (X = 74):
[tex]\[ Z = \frac{74 - 75}{0.791} = \frac{-1}{0.791} \approx -1.26 \][/tex]
3. Find the probability corresponding to the Z-score:
The Z-score of -1.26 corresponds to the cumulative probability from the standard normal distribution table.
A Z-score of -1.26 gives a cumulative probability (area under the curve to the left of the Z-score) of approximately 0.1038.
Therefore, the probability that the sample mean is less than 74 is about 10.38%.
determine the y-intercept and the equation for the horizontal asymptote of the function.
k(x)= (1/2)^x
Reminder: you might like to graph the function to help you.
a. (0.5, 1) there is no horizontal asymptote
b. (0,1); y= 0
c. (0, 0.5); y=0.5
d. (1,0); y= 1
what key features can be identified from graphs of polynomials with higher degrees and explain how the key features can be used to sketch the graph of the polynomial function.
The key features of graphs of polynomials with higher degrees include the leading coefficient, end behavior, and turning points. These features can be used to sketch the graph of the polynomial function.
Explanation:The key features that can be identified from graphs of polynomials with higher degrees include the leading coefficient, the end behavior, and the number and behavior of the turning points. The leading coefficient determines the orientation of the graph, whether it opens upwards or downwards. The end behavior of the graph shows how the function behaves as x approaches positive or negative infinity. The number and behavior of the turning points indicate the shape and direction of the graph.
These key features can be used to sketch the graph of the polynomial function by following these steps:
Identify the degree of the polynomial and determine the leading coefficient.Use the end behavior to determine the general direction in which the graph will go as x approaches positive or negative infinity.Find the x-intercepts by solving the equation f(x) = 0.Determine the behavior of the turning points by analyzing the sign of the second derivative.Plot the key points on the graph, including the x-intercepts and any turning points.Use the information from steps 2 and 4 to sketch the graph, connecting the key points with a smooth curve.Learn more about Polynomial Graphs here:https://brainly.com/question/4159808
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Which is a correct first step for solving this equation? x+7=2x+5−4x
Answer:x+7=2x+5-4x
x+7=-2x+5
Find the z score so that 25% of the standard normal curve lies to the left of z. remember that this means you are looking for the area (which means you need to find the 4 digit number in the area portion of table 3 that is closet to 25% ).
To locate the z-score where 25% of the standard normal distribution is to the left, one checks a z-table for the area closest to 0.25, which approximately corresponds to a z-score of -0.675.
Explanation:To find the z-score so that 25% of the standard normal curve lies to the left, we need to look up the corresponding area in a z-table. Since most z-tables represent the cumulative area to the left of a z-score, we must find the value closest to 0.25, the decimal equivalent of 25%. Upon checking a standard z-table, we find that the area closest to 0.25 corresponds to a z-score of approximately -0.675. Therefore, the z-score that has 25% of the area under the normal curve to its left is -0.675.
F(x)=4x+7
G(x)=3x^2 find (f+g)(x)
The circumference of the circle shown below is 75 inches. Which expression gives the length in inches of ?
You have 63 coins in your piggy bank, all the quarters and nickles. The total amount is $12.55. Hop many quarters do you have?
A.4
B.47
C.16
D.59
In how many ways can a teacher arrange 5 students in the front row of a classroom with a total of 40 students? Answers:
98,960,960
88,960,960
78,960,960
68,960,960
Find the 6th term of the expansion of (2p - 3q)11. a. -7,185,024p4q7 c. -7,185p4q7 b. -7,185,024p6q5 d. -7,185p6q5
Answer: B. [tex]-7185024p^6q^5[/tex]
Step-by-step explanation:
The (r+1)th term in [tex](a+b)^n[/tex] is given by :
[tex]^nC_r(a)^{n-r}(b)^r[/tex]
The given binomial : [tex](2p - 3q)^{11}[/tex]
For the 6th term, we put r=6-1=5 , we get
[tex]^{11}C_5(2p)^{11-5}(-3q)^5\\\\=\dfrac{11!}{5!(11-5)!}(2p)^6(-243q^5)\\\\=-dfrac{11\times10\times9\times8\times7\times6!}{6!5!}(64p^6)(243q^5)\\\\=-462\times(64p^6)(243q^5)\\\\=-7185024p^6q^5[/tex]
Hence, the 6th term of the expansion of [tex](2p - 3q)^{11}[/tex] = [tex]-7185024p^6q^5[/tex]
Explain how the distributive property helps us multiply the following polynomials and why and how the final products differ:
● (a + b)^2,
● (a – b)^2, and
(a - b)(a + b).
The distributive property is used to expand [tex](a + b)^2[/tex] and [tex](a - b)^2[/tex], resulting in [tex]a^2 + 2ab + b^2[/tex]and [tex]a^2 - 2ab + b^2[/tex]respectively. The product (a - b)(a + b) uses the distributive property to result in [tex]a^2 - b^2[/tex], showcasing how signs affect the final expressions.
Explanation:The distributive property of multiplication over addition is essential when multiplying polynomials. Let's explore how this property is applied to the given expressions:
For [tex](a + b)^2[/tex], we have to multiply (a + b) by itself. According to the distributive property, it becomes a² + 2ab + b².
Similarly, for [tex](a -b)^2[/tex], distributing (a - b) with itself yields a² - 2ab + b².
Lastly, (a - b)(a + b) represents a difference of squares. By applying the distributive property, the middle terms cancel out, leaving us with a² - b².
The final products differ because of the signs in the original binomials. The squared terms result in a positive sign whether the original binomial had a plus or minus (per rules of multiplying signs), but the product of the mixed terms determines whether you have a sum or difference in the final expression, affecting the middle term.
Which statement is correct with respect to f(x) = -3|x − 1| + 12?
The V-shaped graph opens upward, and its vertex lies at (-3, 1).
The V-shaped graph opens downward, and its vertex lies at (-1, 3).
The V-shaped graph opens upward, and its vertex lies at (1, -12).
The V-shaped graph opens downward, and its vertex lies at (1, 12).
How to multiply scientific notation with another scientific notation?
1. Multiply the coefficients and round to the number of significant figures in the coefficient with the smallest number of significant figures.
2. Add the exponents.
3. Convert the result to scientific notation.
Answer:
Let's say that I have to multiply 2.5 x 10^3 and 6.23 x 10^5.
First, Let's multiply 10^3 and 10^5.
It would be 10^8.
next, let's multiply 2.5 and 6.23.
It is 15.575.
So, my answer is 15.575 x 10^8.