Step 1: Definition
Arranging people, digits, numbers, alphabets, letters, and colors are examples of permutations. Selection of menu, food, clothes, subjects, the team are examples of combinations.
Step 2:
How many possible ways can a group of 10 runners finish first, second and third?
PERMUTATION because it involved arrangement
Step 3:
How many ways can 2 females and 1 male be selected for a conference from a larger group of 5 females and males?
NOT PERMUTATION because it involved selection, hence it is a combination.
Step 4:
How many 3 letter arrangements of the word OLDWAYS are there?
PERMUTATION because it involved arrangement
Step 5:
How many 5-card hands from a standard deck of cards would result in all spades?
NOT PERMUTATION because it involved selection, hence it is a combination.
Use the given information to select the factors of f(x). f(4)=0 f(-1)=0 f(3/2)=0. Make sure to select all correct answers for full credit.
The binomials x - 4, x + 1 and 2 · x - 3 are factors of the polynomials.
How to derive the equations of the factors of a polynomial
Herein we know the x-values of a polynomial such that the expression is equal to zero. Mathematically speaking, these x-values are known as roots and the mathematical expressions that contain them are known as factors, which are represented by binomials of the form:
a · r - b = 0
Where a, b are real coefficients.
If we know that x₁ = 4, x₂ = - 1, x₃ = 3 / 2, then the factors of the polynomials are listed below:
x₁ = 4:
x - 4 = 0
x₂ = - 1:
x + 1 = 0
x₃ = 3 / 2
2 · x - 3 = 0
x - 4, x + 1 and 2 · x - 3 are factors of the polynomials.
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if A/B and C/D are rational expressions,then which of the following is true?*PHOTO*
In general,
[tex]\begin{gathered} \frac{w}{x}*\frac{y}{z}=\frac{w*y}{x*z} \\ x,z\ne0 \end{gathered}[/tex]Therefore, in our case, (Notice that since A/B and C/D are rational expressions, B and D cannot be equal to zero)
[tex]\frac{A}{B}*\frac{C}{D}=\frac{A*C}{B*D}[/tex]Notice that the left side of each option includes the term
[tex]\frac{A}{B}*\frac{D}{C}[/tex]However, we cannot assure that C is different than zero because it is only stated that C/D is rational.
Furthermore,
[tex]\frac{A}{B}*\frac{D}{C}=\frac{A*D}{B*C}[/tex]And (A*D)/(B*C) is not included among the options.
Therefore, the answer has to be option D as it is the only one that correctly expresses the multiplication of two fractions.Remember that there is a mistake in each option, the left side has to be A/B*D/CHow do you write 6 tens + 4 ones + 5 tenths + 2 hundredths + 8 thousandths
Answer:
Step-by-step explanation:
64.528 is the decimal
Multiply -5 1/2 × 7 5/6 =
You have to multiply:
[tex]-5\frac{1}{2}\cdot7\frac{5}{6}[/tex]First write the compound fractions as impropper fractions.
To do so, divide the whole number by one to express it as a fraction and add both fractions:
[tex]\begin{gathered} 5\frac{1}{2}=\frac{5}{1}+\frac{1}{2}\to\text{ common denominator 2} \\ \\ \frac{5\cdot2}{1\cdot2}+\frac{1}{2}=\frac{10}{2}+\frac{1}{2}=\frac{11}{2} \end{gathered}[/tex][tex]\begin{gathered} 7\frac{5}{6}=\frac{7}{1}+\frac{5}{6}\to\text{ common denominator 6} \\ \frac{7\cdot6}{1\cdot6}+\frac{5}{6}=\frac{42}{6}+\frac{5}{6}=\frac{47}{6} \end{gathered}[/tex]Rewrite the multiplication using the corresponding impropper fractions:
[tex]-\frac{11}{2}\cdot\frac{47}{6}[/tex]And solve the multiplication, numerator * numerator and denominator*denominator:
[tex]-\frac{11}{2}\cdot\frac{47}{6}=-(\frac{11\cdot47}{2\cdot6})=-\frac{517}{12}[/tex]Can you please help me out with a question
Given data:
The given radius is r=16 ft.
The expression for the surface area is,
[tex]\begin{gathered} SA=4\pi(r)^2 \\ =4\pi(16ft)^2 \\ =1024\pi ft^2 \end{gathered}[/tex]The expression for the volume of the sphere is,
[tex]\begin{gathered} V=\frac{4}{3}\pi(r)^3 \\ =\frac{4}{3}\pi(16ft)^3 \\ =\frac{16384\pi}{3}ft^3 \end{gathered}[/tex]Thus, the surface area is 1024π sq-ft, and volume is (16384π)/3 cube-ft.
Make the following conversions.5 pounds 16 ounces toa. Ounces:? ozb. Pounds: ? lbNote : I have attempted 80 ounces in 1 pound as the answers and it is incorrect
In order to calculate these conversions, we need to know the following conversion rate:
1 pound is equal to 16 ounces.
Knowing that, let's convert:
a. to ounces:
[tex]5\text{ pounds 16 ounces }=5\cdot16\text{ ounces + 16 ounces}=80\text{ + 16 ounces }=96\text{ ounces}[/tex]b. to pounds:
[tex]5\text{ pounds 16 ounces }=5\text{ pounds + 1 pound }=6\text{ pounds}[/tex]Solve the equation 10x+14= - 2x+38 explaining all the steps of your solution as in the examples in this section.
To solve the given equation:
1. Add 2x in both sides of the equation:
[tex]\begin{gathered} 10x+2x+14=-2x+2x+38 \\ \\ \text{Combine like terms:} \\ 12x+14=38 \end{gathered}[/tex]2. Subtract 14 in both sides of the equation:
[tex]\begin{gathered} 12x+14-14=38-14 \\ \\ 12x=24 \end{gathered}[/tex]3. Divide both sides of the equation into 12:
[tex]\begin{gathered} \frac{12}{12}x=\frac{24}{12} \\ \\ x=2 \end{gathered}[/tex]Then, the solution for the given equation is x=2Jordan’s of Boston sold Lee Company of New York computer equipment with a $7,000 list price. Sale terms were 4/10, n/30 FOB Boston. Jordan’s agreed to pay the $400 freight. Lee pays the invoice within the discount period. What does Lee pay Jordan’s?
If Sale terms were 4/10, n/30 FOB Boston and Jordan’s agreed to prepay the $400 freight. Lee pays the invoice within the discount period. The amount that Lee pay Jordan’ s is $7,120.
What is the amount received?Using this formula
Amount received = [ ( Cost of computer equipment × ( 1 - rate )] + Freight
Let plug in the formula
Amount received = [ $7,000 × ( 1 - 0.04) ] +$400
Amount received = ( $7,000 x .96 ) + $400
Amount received = $6,720 + 400
Amount received = $7,120
Therefore Lee pay Jordan the amount of $7,120.
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If z = 12.8, what's is the value of 2(z - 4)?
The given expression is
[tex]2(z-4)[/tex]Let's replace z = 12.8.
[tex]2(12.8-4)=2(8.8)=17.6[/tex]Therefore, the value is 17.6.What would you have to divide 584,900 by in order to have the 4 shift to the onesplace Explain your answer on the lines below.
in order to shift the 4 to the ones place, divide the given number 584,900 by 100. After dividing the the number 584,900 by 100, the new number is 584.900. It is clear that 4 is at ones olace.
Please help with #4. The directions are with the pic below.
sphere: 12 pounds
cylinder: 108 pounds
Explanation:
Data:
. From balance A:
3 cubes + 1 sphere = 1 cylinder + 2 spheres
. From balance B:
3 cubes = 5 spheres
Since 1 cube = 20 pounds
=> From balance B:
3 cubes * 20 pounds = 5 spheres
60 pounds = 5 sphere
60 / 5 = 5 / 5
12 pounds = 1 sphere
=> From balance A:
3 cubes + 1 sphere = 1 cylinder + 2 spheres
3 spheres * 20 pounds + 1 sphere * 12 pounds = 1 cylinder + 2 spheres * 12 pounds
120 pounds + 12 pounds = 1 cylinder + 24 pounds
132 pounds = 1 cylinder + 24 pounds
132 pounds - 24 pounds = 1 cylinder + 24 pounds - 24 pounds
108 pounds = 1 cylinder
so I've been using the formula for the volume of a cylinder but I'm still not getting anything even remotely close to my answer choices. the volume is 438.08π mL and the radius is 3.7 cm. I'm solving for the height
Answer:
H = 32 cm
Explanation:
The area of a cylinder is given by
[tex]V=\pi r^2h[/tex]Now solving for h gives
[tex]h=\frac{V}{\pi r^2}[/tex]Now V = 438.08 π and r = 3.7 cm. Putting these values in the above equations gives
[tex]h=\frac{438.08\pi\operatorname{cm}^3}{\pi(3.7cm)^2}[/tex][tex]\boxed{h=32\operatorname{cm}\text{.}}[/tex]which is our answer!
explain why there are two zeros in the product of 5 x 40
EXPLANATION
There are two zeros in the product of 5x40 because multiplying the number 40 5 times give us the number 200 wich is a hundred type number.
In a newspaper, it was reported that the number of yearly robberies in Springfield in 2013 was 180, and then went down by 40% in 2014. How many robberies were there in Springfield in 2014?
As given that the number of yearly robberies in Springfield in 2013 was 180
And then went down by 40% in 2014.
So robberies were there in Springfield in 2014:
[tex]\begin{gathered} N=180-180\times\frac{40}{100} \\ N=180-72 \\ N=108 \end{gathered}[/tex]So robberies were there in Springfield in 2014 are 72
Use disks and washers to find the volume of the solid the results when the area of the region y=x^3 y = 0, and x = 2 is revolved about the line x= 2
Solution
The functions that define the region in consideration are given below:
[tex]\begin{gathered} y=x^3 \\ y=0 \\ x=2 \end{gathered}[/tex]The Washer Method:
- Plotting these functions would help us visualize the question better. This is done below:
- The question would like us to revolve around the region about line x = 2. The region is bounded by the Blue, Red, and Green line. This requires that we use the formula given below:
[tex]\begin{gathered} V=\int ^b_a{f(y)\mathrm{dy}} \\ \text{where,} \\ a\text{ and }b\text{ are the bounds of the integration along the y-axis} \end{gathered}[/tex]-
We can represent the region bounded by the function by rearranging the functions as follows:
[tex]undefined[/tex]Write an explicit rule for the following arithmetic sequence: 28, 38, 48, 58,
When you have an arithmetic sequence you can use the next general formula to get the explicit formula:
[tex]a(n)=a(1)+d(n-1)[/tex]Where a(1) is the first term in the sequence, d is the difference between each term in the sequence, and n is the nth term
You have the sequence: 28,38,48,58
The difference in this sequence is d=10
The first term is: a(1)=28
Then:
[tex]a(n)=28+10(n-1)[/tex][tex]a(n)=28+10n-10[/tex][tex]a(n)=18+10n[/tex]Then, the explicit rule for the given arithmetic sequence is: a(n)=18+10ni inserted a picture of the questions 19 and 20 that i need help with.
WE are given that 9 tickets have a total cost of $94.50. To determine the price for each ticket we must find the quotient between the total amount spent and the number of tickets, like this:
[tex]\frac{94.50}{9}[/tex]Solving the operations we get:
[tex]\frac{94.50}{9}=10.5[/tex]Therefore, each ticket has a price of $10.50
From least to greatest. -1.4-1.02 -1.20
We could put these values in the number line:
Therefore, the order of the numbers from least to greatest is:
-1.4 , -1.20 , -1.02
The least number between all the options given is -1.4 because if you see, all numbers are negative, so, when a negative number is greater, as the amount after the negative sign becomes greater, the number is going to be least. That's the reason of the order.
How many tiles of 8 cm² is needed to cover a floor of dimension 6 cm by 24 cm? A. 6 B. 12 C. 18 D. 24
Answer:
18 tiles.
Step-by-step explanation:
24x6= 144
144/8= 18
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in a classroom there are 28 tablets which includes 5 that are defective. if seven tablets are chosen at random to be used by student groups. 12. how many total selections can be made? a. 140 b. 98280 c. 11793600 d. 4037880 e. 1184040 13. how many selections contain 2 defective tablets? a. 10 b. 21 c. 336490 d. 706629 e. 33649
Using the combination formula, it is found that:
The number of total selections that can be made is: e. 1184040.The number of selections that contain two defective tablets is: c. 336490.Combination formula[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials. It is used when the order in which the elements are chosen does not matter.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In the context of this problem, we have that seven tablets are chosen from a set of 28 tablets, hence the number of selections that can be made is given by:
[tex]C_{28,7} = \frac{28!}{7!21!} = 1,184,040[/tex]
For two defective tablets, the selections are given as follows:
Two defective from a set of five.Five non-defective from a set of 23.Hence the number of selections is calculated as follows:
[tex]C_{23,5}C_{5,2} = \frac{23!}{5!18!} \times \frac{5!}{2!3!} = 336,490[/tex]
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I have already found X . I need help finding m<2
Given:
[tex]m\angle1=8x-102\text{ and }m\angle4=2x+6[/tex]Required:
[tex]\text{ Find the measure of }\angle2.[/tex]Explanation:
Step 1:
[tex]m\angle1=m\angle4[/tex]Step 2:
[tex]\begin{gathered} 8x-102=2x+6 \\ 6x=108 \\ x=18 \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} m\angle1=8(18)-102 \\ m\angle1=144-102 \\ m\angle1=42 \\ Now, \\ m\angle1+m\angle2=180 \\ 42+m\angle2=180 \\ m\angle2=180-42 \\ m\angle2=138 \end{gathered}[/tex]Answer:
Measure of angle 2 equals 138.
You have a total of 21 coins, all nickels and dimes. The total value is $1.70. Which of the following is the system of linear equations that represent this scenario? Let n = the number of nickels and let d = the number dimes.
n = number of nickels
d = number of dimes
1 nickel = 5 cents
1 dime = 10 cents
total number of 21 coins:
n + d = 21
Total value = $1.70
5n + 10 d = 170
Divide by 100
0.05n + 0.10 d = 1.70
Answer:
n + d = 21
0.05n + 0.10 d = 1.70
For the polynomial below, 1 is a zero.h(x) = x² – 3x? - 2x + 4Express h(x) as a product of linear factors.
Step 1
Given the zero, 1, we can use synthetic division to acquire the other factors
Using synthetic division we will write out all coefficients of the terms of h(x) and proceed thus
1 | 1 -3 -2 +4
1 -2 -4
-----------------------
1 -2 -4 0
Hence the quadratic equation we will need to split into linear factors is given as
[tex]x^2-2x-4[/tex]Since the remainder is 0
Step 2
Factorize the quadratic equation above completely
[tex]\begin{gathered} x^2-2x-4=0 \\ we\text{ will use} \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]Where
a= 1
b= -2
c= -4
[tex]\begin{gathered} x=\frac{-(-2)\pm\sqrt[]{(-2)^2-4\times1\times-4}}{2\times1} \\ x=\frac{2\pm\sqrt[]{4+16}}{2} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{2\pm\sqrt[]{20}}{2} \\ x=\frac{2}{2}+\frac{\sqrt[]{20}}{2}=1+\frac{2\sqrt[]{5}}{2}=1+\sqrt[]{5} \\ Or \\ x=\frac{2}{2}-\frac{\sqrt[]{20}}{2}=1-\frac{2\sqrt[]{5}}{2}=1-\sqrt[]{5} \end{gathered}[/tex]Hence the product of linear factor will be
[tex](x-1)(1+\sqrt[]{5})(1-\sqrt[]{5})[/tex]
Suppose that you follow the same path on the return trip from Dubuque to Council Bluffs. What would be thetotal number of (actual) miles for the round trip?
We know the trip from Council Bluffs to Dubuque had a total distance of 348 miles; if we take the same route to go back this will mean that we need to travel the same distance, 348 miles. The total distance then we will be 696 miles.
Rapheal is traveling in a straight line at a constant speed from point A to point B. His distance from point B in miles is -20t + 45, where t is the number of hours he has been traveling. What is his speed in miles per hour?
Rapheal is traveling in a straight line. Its speed in miles per hour is 20 miles per hour.
A and B are the two points of a straight line.Distance between two points is given as :d₀ = -20t + 45 miles
t = the number of hours of travelling.The starting time = 0
i.e. the initial position = 0
Then
we put t=0
At t=0
d₀ = -20(0) + 45
= 0 + 45
= 45 miles
the distance travel after starting first hour is :
T= d₁ & d₀
than we put t = 1
At t = 1;
d₁ = -20(1) + 45
= -20 + 45
= 25 miles
now
Difference between d₁ & d₀ is
d = d₁ - d₀
45 - 25 = 20 miles
Total distance covered = 20 miles
To find the speed we use formula:
Speed = distance/time
Speed=20/1
Speed = 20 miles/hour
Rapheal is traveling in a straight line. Its speed in miles per hour is 20 miles per hour.
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draw and label: ray LM
To draw a Ray; Draw a line with an arrowhead at one end of the line segmen:
Ray LM:
Help me answer these thank u :)
6. -2
7.-38
8.-15
9.0
10.-13
11.-30
12.38
13.33
14.-23
Find the value of z such that 0.04 of the area lies to the right of z. Round your answer toTwo decimal places.
The total area under the normal distribution curve is 1. z-scores are indicated in the horizontal axis below this curve. This means that the sum of areas under the curve at the left and at the right of a certain z-score must be equal to 1.
Then if the area at the right of the z-score that we are looking for is 0.04 the area at its left must be equal to 1-0.04=0.96. The area at the left of z is important because z-score tables usually show the areas at the left of several z-scores. Then the only thing that we have to do is look for the z-score associated with 0.96 in one of these tables. In your case the table that you should use is the one named "Normal Table -∞ to z". That table should look like this one:
As you can see the value 0.96 is associated with the row 1.7 and the column .05 which means that the z-score that meets that the area under the curve at its right is 0.04 is z=1.7+0.05=1.75.
AnswerThen the answer is 1.75
12 is what percent of 18
We have that
[tex]12\cdot\text{ }\frac{100}{18}=\text{ }\frac{1200}{18}\text{ = 66.6666}[/tex]So the answer is: 66.6666 .
Grandma’s Guide to Cooking MeasurementsDried Seasonings 1 pinch = 2 smidgens1 dash = 2 pinches1 sprinkle = 3 pinches1 teaspoon = 8 dashesBased on Grandma's guide to cooking, how many smidgens are in one teaspoon?Do not include units with your answer.
32
Explanation:1 pinch = 2 smidgens
1 dash = 2 pinches
Therefore, 1 dash = 2 x 2 smidgens
1 dash = 4 smidgens
1 teaspoon = 8 dashes
1 teaspoon = 8 x 4 smidgens
1 teaspoon = 32 smidgens
There are 32 smidgens in 1 teaspoon