The number of possible different votes for Milan, based on the list of bands is 60 different votes.
How to find the number of possible votes?There are 5 lists of bands that Milan has to choose from to place a vote and there are only 3 bands to be chosen out of the 5 lists.
The total number of different votes possible is therefore possible by performing a permutation:
= 5! / ( 5 - 3) !
= 5 ! / 2 !
= (5 x 4 x 3 x 2 x 1) / (2 x 1)
= 60 different votes
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What is the mean ,Median and mode of these values 300,285,200,50,150,50,80,50,250,50,185,250
Answer: mode 50 Mean x¯¯¯ 158.33333333333
Median x˜ 167.5
Step-by-step explanation: hope this helps
Range 250
Minimum 50
Maximum 300
Count n 12
Sum 1900
Complete the proof by choosing the correct "Reason".
The completed table of the two column method to prove DE = FD is presented as follows;
Statement [tex]{}[/tex] Reason
1. CE = CD + DE[tex]{}[/tex] Segment addition postulate
2. FG = FD + DG [tex]{}[/tex] Segment addition postulate
3. CE = FG [tex]{}[/tex] Given
4. CD + DE = FD + DG [tex]{}[/tex] Substitution property of equality
5. CD = DG [tex]{}[/tex] Given
6. DG + DE = FD + DG [tex]{}[/tex] Substitution property of equality
7. DE = FD [tex]{}[/tex] Subtraction property of equality
What is a two column method, used to prove a statement in mathematics?A two column method consists a number of statements alongside the reasons that are known to make the statements true.
The segment addition postulate state that a point B is located on a segment AC if and only if AB + BC = AC, therefore;
CE = CD + DEFG = FD + DGThe substitution property of equality states that if a = b, and a + c = d, then b + c = d
Which gives;
CE = CD + DEFG = FD + DGCE = FG, then, CD + DE = FD + DGSimilarly; CD = DG, then DG + DE = FD + DG
The subtraction (and addition) property of equality states that a quantity of known value can be subtracted (or added) to both sides of an equation and both sides of the equation remains equal.
Mathematically, if x = y, then x - z = y - z, therefore;
DG + DE = FD + DGThen;
DG + DE - DG = FD + DG - DG∴ DE = FD
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(2x²-3x+1)-(-x² + 2x − 2) - (2x - 3)² =
Answer:
6x^2-17x+12
Step-by-step explanation:
Distribute
2x^2-3x+1+x^2-2x+2(-2x+3)^2
Square (2x+3)
(-2x+3)(-2x+3)
FOIL
4x^2-6x-6x+9
Combine like terms
4x^2-12x+9
re-write equation
2x^2-3x+1+x^2-2x+2+4x^2-12x+9
Combine like terms
6x^2-17x+12
How many three-letter "words" can be made from 10 letters "FGHIJKLMNO" if repetition of letters (a) is allowed? Your answer is (b) is not allowed? Your answer is
a. The number of permutations of three letter words that can be formed with repetition is 1000 words
b. The number of permutations of three letter words that can be formed without repetiton is 720 words
What are permutations?Permutations are the number of ways in which x objects can be arranged out of n objects.
The number of permutations is given by ⁿPₓ = n(n - 1)(n -2)...(n - x + 1)
a. How to find the number of ways in which the 10 letters can be arranged if repetition is allowed?Since we require the number of three-letter "words" can be made from 10 letters "FGHIJKLMNO" with repetition, we note that there are 10 letters.
Since repetition is allowed, for the first slot, we have 10 letters, for the second position, we have 10 letters and for the third position, we have 10 letters.
So, the total number of permutations is n = 10 × 10 × 10
= 1000 words
So, the number of three letter words that can be formed is 1000 words
b. How to find the number of ways in which the 10 letters can be arranged if repetition is not allowed?Since we require the number of three-letter "words" can be made from 10 letters "FGHIJKLMNO" without repetition, we note that there are 10 letters.
Since repetition is not allowed, for the first slot, we have 10 letters, for the second position, we have 9 letters and for the third position, we have 8 letters.
So, the total number of permutations is ¹⁰P₃ = 10 × 9 × 8
= 720 words
So, the number of three letter words that can be formed is 720 words
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Write a sentence for 2(3+5n)=an
The sentence which represents the algebraic equation is; "Twice the sum of 3 and and five times a number n is equal to the product of the number and another number, a".
Which sentence represents the algebraic expression?It follows from the task content that the sentence which represents the equation given be determined.
First, the expression 3 + 5n can be interpreted as; the sum of 3 and 5 times a number, n.
Also, the expression "an" can be interpreted as the product of n and another number a.
Therefore, the whole equation; 2(3+5n)=an can be interpreted as;
"Twice the sum of 3 and and five times a number n is equal to the product of the number and another number, a".
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A road has a speed limit sign at the beginning that is noticed by 84 % of people. 95 % of people who didn't notice the sign speed on the road. Of those who notice the sign, 75 % follow the speed limit.
How many percent of people speeding on this road noticed the sign? In other words, how many people on this road speed on purpose. Give your answer in percentage.
The percentage of people over speeding on this road on purpose is 9%
Find the percent of people speeding on this road who noticed the signPercentage of people who notice the speed limit at the beginning of the road = 84%Percentage of people who didn't notice the sign = 95%Percentage of people who notice the sign and follow the speed limit = 75%Percent of people speeding on this road noticed the sign = Percentage of people who notice the speed limit at the beginning of the road - Percentage of people who notice the sign and follow the speed limit
= 84% - 75%
= 9%
In conclusion, the percentage of people who intentionally speed on purpose is 9%
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¿Cuál es la ordenada en el origen de la recta que pasa por el punto P(-4, 5) y cuya pendiente es 2?
The y-intercept of the line passes through the point (-4,5) with slope 2 is y = 13.
Given:
(-4,5) and slope m = 2
substitute in y=mx+c
5 = 2*(-4) + c
5 = -8 + c
c = 5 + 8
c = 13.
c value in y = 2x + c
y = 2x + 13
To find y-intercept put x = 0.
y = 2(0) + 13
y = 0+13
y = 13
Therefore the y-intercept of the line passes through the point (-4,5) with slope 2 is y = 13.
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7th grade math: can you help? i only need help on 1, 2, 3, & 4
By using percentage, it can be calculated that
1) Percentage increase in area = 25 %
2) Percentage increase in area = 60 %
3) Percentage decrease in area = 25 %
4) Percentage decrease in area = 40 %
What is percentage?
Sometimes there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
For example 2% means [tex]\frac{2}{100}[/tex]. Here 2 is expressed as a fraction of 100
1) Original area = 12 sq. yard
New area = 15 sq. yard
Increase in area = 15 - 12 = 3 sq. yard
Percentage increase = [tex]\frac{3}{12}\times 100 \\[/tex]
= 25 %
1) Original area = 15 sq. yard
New area = 24 sq. yard
Increase in area = 24 - 15 = 9 sq. yard
Percentage increase = [tex]\frac{9}{15}\times 100 \\[/tex]
= 60 %
1) Original area = 12 sq. yard
New area = 9 sq. yard
Increase in area = 12 - 9 = 3 sq. yard
Percentage decrease = [tex]\frac{3}{12}\times 100 \\[/tex]
= 25 %
1) Original area = 10 sq. yard
New area = 6 sq. yard
Increase in area = 10 - 6 = 4 sq. yard
Percentage increase = [tex]\frac{4}{10}\times 100 \\[/tex]
= 40 %
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A caterpillar eats 75 leaves in 5 hours. How many leaves will the caterpillar eat in 8 hours if it continues to eat at the same rate?
How much must be deposited today into the following account in order to have $50,000 in 7 years for a down payment on a house? Assume no additional deposits
are made.
An account with quarterly compounding and an APR of 5.9%
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$50000\\ P=\textit{original amount deposited}\\ r=rate\to 5.9\%\to \frac{5.9}{100}\dotfill &0.059\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}[/tex]
[tex]50000=P\left(1+\frac{0.059}{4}\right)^{4\cdot 7} \implies 50000=P(1.01475)^{28} \\\\\\ \cfrac{50000}{(1.01475)^{28}}=P\implies 33183.05\approx P[/tex]
(−3,y) and (x,2).
y=−2x+2
Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
Complete the table below.
x y
row 1−3 Answer
row 2 Answer
2
The value of x in the second ordered pair is - 0.5 or - 1/2 and that of y in the first ordered pair is 8.
The given ordered pair is (-3,y) and (x,2)
the equation y=-2x+2
In the first step we put the value of x as -3 as given in (-3,y) in the equation y=-2x+2, we get
y=-2(-3)+2
⇒y=6+2
⇒y=8
So the value of y is 8 then the ordered pair will be (-3,8).
Again, in the second step, we put the value of y as 2 as given in (x,2) in the equation y=-2x+2, and we get
2=-2x+2
⇒2x=2-2
⇒2x=0
⇒x=0
So the value of x is 0, and the ordered pair will be (0,2).
The table:
# Value of x Value of y 1 -3 8 2 0 2I have provided a photo of the table:
A motorboat maintained a constant speed of 14 miles per hour relative to the water in going 33 miles upstream and then
returning. The total time for the trip was 7.0 hours. Use this information to find the speed of the current.
What is speed of the current is miles per hour?
The speed of the current is equal to 8 miles per hour.
How to calculate the speed of the current?Mathematically, speed of any physical object can be calculated by using this formula;
Speed = distance/time
Let the variable c represent the speed of the current in miles per hour. Therefore, the downstream and upstream speed relative to the water would be given by this mathematical expression:
Speed downstream = 14 + c.
Speed upstream = 14 - c.
Additionally, the total time would be given by:
Total time = total distance/speed
Time upstream + time downstream = 6.5 hours
33/(14 - c) + 33/(14 + c) = 7.0
Multiplying both sides of the equation by (14 - c)(14 + c), we have:
33(14 + c) + 33(14 - c) = 7.0(14 - c)(14 + c)
462 + 33c + 462 - 33c = 7.0(196 - c²)
924 = 7.0(196 - c²)
Dividing both sides of the equation by 7.0, we have:
132 = 196 - c²
Speed of the current, c² = 196 - 132
Speed of the current, c² = 64
Speed of the current, c = √64
Speed of the current, c = 8 miles per hour.
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Please help I need the answer
The range of function f(x) = 4x + 5 for given input values is {-3, 1, 5, 9, 13}
The correct answer is an option (C)
In this question, we have been given a function f(x) = 4x + 5
We need to find the range of given function for input {-2, -1, 0, 1 , 2}
We know that the range of a function is the set of all output values for given input.
for x = -2,
f(-2) = 4(-2) + 5
f(-2) = -3
for x = -1,
f(-1) = 4(-1) + 5
f(-1) = 1
for x = 0,
f(0) = 4(0) + 5
f(0) = 5
for x = 1,
f(1) = 4(1) + 5
f(1) = 9
for x = 2,
f(2) = 4(2) + 5
f(2) = 13
Therefore, the range of function f(x) = 4x + 5 for given input values is {-3, 1, 5, 9, 13}
The correct answer is an option (C)
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Describe the slope of the line
Find the slope
m=??
Answer: 2.333333...
Step-by-step explanation:
If we apply rise over run, we see that it rises 3.5 spaces, and runs 1.5, which means that [tex]m = \frac{rise}{run} = \frac{3.5}{1.5} = 2.33333...[/tex]
Car Survey 1500 In a survey of people who owned a certain type of car ,675 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
The percent of the people surveyed were satisfied with the car will
be 45%.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
Total number of people in a survey of car = 1,500
And, 675 people said they would buy that type of car again.
Now,
Total number of people in a survey of car = 1,500
And, The people surveyed were satisfied with the car = 675
Hence, The percent of the people surveyed were satisfied with the car is;
= 675 / 1500 x 100
= 0.45 x 100
= 45%
Thus, The percent of the people surveyed were satisfied with the car will
be 45%.
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Select the correct answer.
Consider the function given below.
f(x) = lx-5l +2
Which of the following statements about the y-values of the graph of the function is true?
A. The y-values are all greater than or equal to 5.
B. The y-values are all greater than or equal to 2.
C. The y-values are all less than or equal to 2.
D. The y-values are all less than or equal to 5.
The statement which is true about the y-values of the graph of the function as required is; Choice B; The y-values are all greater than or equal to 2.
Which statement is true regarding the y-values?It follows from the task content that the statement which is true regarding the y-values of the graph defined by; f(x) = lx-5l +2 is to be determined.
Therefore, we must recall that expressions enclosed in the absolute value sign upon evaluation are always greater than or equal to zero.
Hence, it can be concluded that we the y-values of the resulting graph to be greater than or equal to 2 (on the occasion that; lx-5l = 0).
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The first section of a newspaper has 16 pages. Advertisements take up 3 and 3/8 of the pages. How many pages are not advertisements?
A total of 12 5/8 pages is not meant for advertisement
How to determine the number of pages that are not for adverts?From the question, we have the following parameters
First section = 16 pages
Pages for advertisement = 3 and 3/8 pages
Rewrite the above parameters as
First section = 16 pages
Pages for advertisement = 3 3/8 pages
The number of pages that are not for adverts is then calculated as
Pages not for adverts = First section - Pages for advertisement
Substitute the known values in the above equation
So, we have the following equation
Pages not for adverts = 16 - 3 3/8
Evaluate the difference
Pages not for adverts = 12 5/8
Hence, the number of pages that are not for adverts is 12 5/8 pages
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If it takes 1 printer 14 minutes to print a batch of leaflets, how long would it
take 2 printers to print the same number of leaflets?
2 printers takes 7 minutes to print the same number of leaflets.
From the question, we have
1 printers takes 14 minutes to print the leaflets.
2 printers takes = 14/2 = 7 minutes to print the leaflets.
Divide:
Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.
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Answer: 7
Step-by-step explanation: because 1 printer takes 14 mins but if u have 2 u half the 14 it gives you 7 so it will take 2 printers 7 mins to print the same amount of leaflets. hope this helps.
The pH of solution measures its acidity and can be determined using the formula pH= -log(base of 10 )C, where is the concentration of hydronium ions in the solution. measured in moles per litre .A lower pH indicates a more acidic solution.
Determine whether the unknown liquid is more or less acidic then the coffee ( pH=-4.886)
if that liquid has 10 times the concentration ions of the coffee.
The pH of the liquid which is 3.886 indicates that it is more acidic than coffee.
What is the pH of a solution?The pH of a solution gives a measure of the concentration of hydronium ions in the solution, and therefore, indicates the level of acidity or basicity of the solution.
pH = -㏒₁₀CpH values ranges from 0 to 14, with solutions that are more acidic having a pH of less than 7, while basic solutions have a pH of more than 7.
The given pH of coffee = -4.886
The concentration of the liquid = 10 × The concentration of the ions in coffee
Which gives;
-㏒₁₀C = 4.886
Concentration of the hydronium ions in coffee, C = [tex]10^{(-4.886)}[/tex]
Concentration of ions in the unknown liquid = 10 × [tex]10^{(-4.886)}[/tex] = [tex]10^{(-3.886)}[/tex]
pH of the unknown liquid = [tex]-log_{10} \left(10^{(-3.886)}\right) = 3.886[/tex]
The pH of the unknown liquid indicates that it is more acidic than coffee
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Assessment Practice
5. A science teacher has $225 to spend on lab equipment.
He buys 4 posters with a guide to classifying rocks, for
$19 each. Student rock collections cost $9 each. How
many rock collections can he buy? Explain how you solve.
Use one or more equations and bar diagrams in your
explanation. Tell what your variables represent. 4.AR.1.1.4.AR.2.2
Answer:
Assessment Practice 5. A science teacher has $225 to spend on lab equipment. He buys 4 posters with a guide to classifying rocks, for $19 each. Student rock collections cost $9 each. How many rock collections can he buy? Explain how you solve
Let
x -----> number of rock collections that he can buy
so
the algebraic expression that represents this situation is
Solve the inequality for x
subtract 76 both sides
Divide both sides by 9
therefore
The maximum number of rock collections that he can buy is 16
Step-by-step explanation:
The equation is 9x+76=225 and the number of rock collections he can buy is 17.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, a science teacher has $225 to spend on lab equipment.
Let the number of rocks collected be x.
He buys 4 posters with a guide to classifying rocks, for $19 each.
That is 19×4=76
Student rock collections cost $9 each.
Now, 9×x=9x
So, the equation is 9x+76=225
Subtract 76 on both the sides of equation, we get
9x=149
Divide 9 on both the sides of equation, we get
x=16.5
x≈17
Therefore, the number of rock collections he can buy is 17.
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Gayle Miller works 43 hours every week. Her weekly salary is $397.75. How much overtime does Gayle make each week?
Answer:
$9.25
Step-by-step explanation:
$397.75÷43=$9.25
Weekly salary divided by hours of work = hourly pay
Find the solutions of the quadratic equation −x^2 + 3x − 3 = 0
1. How many games did each team play? The men played
E is the midpoint of DF---------- DE=6x+1 and EF=7x−4. Find DE, EF, and DF.
25 points
Answer:
Step-by-step explanation:
x=5
A biologist wants to estimate how many fish are in a lake. The biologist takes a sample of 10 fish from the lake and tags all 10 fish. The biologist then releases the fish back into the lake. The nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. Using this information, estimate the number of fish in the lake.
If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.
How to find the estimated number?Let x represent the estimated number of fish in the lake
Hence,
x /10 = 7/2
Cross multiply
2x = 10 × 7
2x = 70
Divide both side by 2x
x =70/2
x = 35 fish
Therefore 35 is the number of fish.
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write an equivalent ratio for each given ratio.
Answer:
what are the given ratio?
Step-by-step explanation:
in need of help!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
2 pairs of parallel sides
Complete each ordered pair so that it is a solution of the given linear equation. x +2y=4
The ordered pairs that are solutions to the linear equation x + 2y = 4 are given as follows:
(-3,3.5).(18,-7).How to complete the ordered pairs?The linear function in this problem is defined as follows:
x + 2y = 4.
To complete the ordered pairs, we take the given coordinate and then solve for the missing coordinate .
For the first ordered pair, the given coordinate is of x = -3, hence we have to solve for y when x = -3, thus:
-3 + 2y = 4.
2y = 7.
y = 7/2
y = 3.5.
Hence the ordered pair is:
(-3, 3.5).
For the second ordered pair, the given coordinate is of y = -7, hence we have to solve for x when y = -7, thus:
x + 2y = 4.
x - 14 = 4
x = 18.
Hence the ordered pair is:
(18, -7).
Missing InformationThe ordered pairs that we have to complete are given as follows:
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A species of animal that has an initial population of 215 experiences uninhibited growth. The rate of growth is 16.63%. About how long does it take the population to grow to 1134? Round to the nearest tenth.
The exponential growth of 16.63% will take approximately 10.80 years to reach a population of 1134
Exponential FunctionAn exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.
Data;
Initial population = 215rate = 16.63%Final Population - 1134Time = ?f(x) = P(1 + r)ˣ
x = time
Substituting the values
1134 = 215(1 + 0.1663)^ˣ
x = 10.80
It will take approximately 10.8 years to reach a growth of 1134
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Answer: The correct answer is "10.0 years"
Step-by-step explanation:
I took the test
5. During the 2016 presidential election, 58.1% of eligible voters participated. In a recent poll of 1048 randomly selected
eligible voters, 586 responded that they intend to vote.
(a) Test at the 5% significance level if the percent of eligible voters that intend to participate is different from the 2016
participation rate.
(b) Explain a Type II error in the context of the data.
Using the z-distribution to test the hypothesis, it is found that:
a) The conclusion is that there is not enough evidence to conclude that the percentage has changed from 2016.
b) A Type II error would mean finding that there is not enough evidence that the percentage is significantly below 58.1% when in fact it is.
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is the same as in 2016, that is:
[tex]H_0: p = 0.581[/tex]
At the alternative hypothesis, it is tested if the proportion is different, hence:
[tex]H_1: p \neq 0.581[/tex]
A Type II error is the non-rejection of a false null hypothesis, that is, finding that there is not enough evidence that the percentage is significantly below 58.1% when in fact it is.
What is the test statistic?The equation calculating the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which the variables are listed as follows:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the value for these variables is given as follows:
[tex]\overline{p} = \frac{586}{1048} = 0.559, n = 1048, p = 0.581[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.559 - 0.581}{\sqrt{\frac{0.581(0.419)}{1048}}}[/tex]
z = -1.44.
The critical value for a two-tailed test is with a significance level of 0.05 is:
|z| = 1.96.
The absolute value of the test statistic is of |z| = 1.44 < 1.96, meaning that there is not enough evidence to conclude that the percentage has changed from 2016.
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