The smallest number of coins Freddie would need is 4 (one penny, one nickel, one dime, and one quarter).
What is algebra ?
Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It includes the study of operations such as addition, subtraction, multiplication, division, and the extraction of roots, as well as the properties of operations such as commutativity, associativity, and distributivity.
In order to be able to pay any amount of money less than a dollar, Freddie would need to have at least one coin of each denomination: pennies, nickels, dimes, and quarters. The smallest number of coins he would need to achieve this is 4. With one penny, one nickel, one dime, and one quarter, he would be able to pay any amount of money less than a dollar by using combinations of these coins.
Therefore , The smallest number of coins Freddie would need is 4 (one penny, one nickel, one dime, and one quarter).
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Apples are selling 3 for $2:50 and bananas are 0.72
Answer: Apples $0.18 (18 Cents) Bananas $0.14 (14 cents)
Step-by-step explanation:
Math knowledge would give the cost for each item. We have:
4 apples + 6 bananas = $1.56
and
9 apples + 7 bananas = $2.60
To find a cost, we encode an apple as 'a', and a banana as 'b' in the following two main equations:
4a+6b=1.56
9a+7b=2.6
The following formula represents the situation by using elimination method to find, let's say, the banana value:
4a+6b=1.56 , 9a+7b=2.6
9×4a+9×6b=9×1.56, 4×9a+4×7b=4×2.6
36a+54b=14.04, 36a+28b=10.4
36a−36a+54b−28b=14.04−10.4
54b−28b=14.04−10.4
26b=14.04−10.4
26b=3.64
b=3.64÷26
b=0.14
That is a banana costs $0.14 (14¢).
Now we have found the value of a banana, we substitute this new value in one of the main equations above to reduce variables so that we can find the value of an apple as follows:
4a+6b=1.56
4a+(6×0.14)=1.56
4a+0.84=1.56
4a=1.56-0.84
4a=0.72
a=0.72÷4
a=0.18
Simply enough, an apple costs $0.18 (18¢), and a banana costs $0.14 (14¢).
For f(x)=3x+1 and g(x)=x2-6,find (f⋅g)(x)
The required value of the given function is (f ⋅ g)(4) = 130.
What are the functions?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
The functions are given in the question, as follows:
f(x)=3x+1 and g(x)=x²-6
(f ⋅g)(x) is the composition of the functions f and g, which means f(x) × g(x).
(f ⋅ g)(x) = f(x) × g(x)
So, substituting x = 4:
(f ⋅ g)(4) = f(4) × g(4)
= (3 × 4 + 1)×(4² - 6)
= 13 × 10
= 130
So, (f ⋅ g)(4) = 130.
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Which expression is equivalent to cos(3x) sin x?
a. 1/2[sin(4x)+sin(2x)]
b. sin(2x)-sinx
c.1/2[sin(4x)-sin(2x)]
d. sin(2x)+sin x
[tex]\textit{Product to Sum Identities} \\\\ cos(\alpha)sin(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad -\quad sin(\alpha-\beta)] \\\\[-0.35em] ~\dotfill\\\\ cos(3x)sin(x)\implies \cfrac{1}{2}[sin(3x+x)~~ - ~~sin(3x-x)] \\\\\\ ~\hfill {\Large \begin{array}{llll} \cfrac{1}{2}[sin(4x)-sin(2x)] \end{array}}~\hfill[/tex]
The increase in the number of matches produced in California from 1980 to 1990 exceeds by how many million the increase in the number of matches produced in Oregon over the same period
As per the unitary method, the number of matches produced in Oregon over the same period is 64
The term unitary method is known as the method of finding the value of a single unit from the value of multiple units
Here we have given that the increase in the number of matches produced in California from 1980 to 1990 exceeds.
Therefore, the number of increase is calculated as,
CA = 0.33(1.2) = 396
If the increase is calculated as,
=> 0.33(1.6) = 528
Then the difference is calculated as,
=> 528 - 396 = 132
Similarly the number of matches in Oregon is calculated as.
=> 0.17(1.2) =204 M
=> 0.17(1.6) = 272 M
Therefore, the difference is calculated as
=> 272 -204 = 68
Therefore the total difference between increases is written as,
=> 132-68 = 64
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Find the area of the shaded portion if we know the outer circle has a diameter of 4 m and the inner circle has a diameter of 1. 5 m. A Circle
The area of the shaded portion is given by the difference between the area of the outer circle and the area of the inner circle.
First, let's find the areas of the circles:
Outer Circle: Area = πr^2 = π (2)^2 = 4π square meters
Inner Circle: Area = πr^2 = π (0.75)^2 = 0.5625π square meters
Area of shaded portion = Area of outer circle - Area of inner circle = 4π - 0.5625π = 3.4375π square meters
So the area of the shaded portion is approximately 10.8 square meters.
Which two numbers below will you set the inside of the absolute value to in the beginning of your work?
|3x-8|=4
A. 4 and -4
B. 2 and -2
C. 3 and -4
D. 8 and -8
Answer:
I think the answer is A. I hope this is helpful
what would be the height of a stack of 8x10^9 books is each book has a thickness of 3.1x10^-4
To find the height of a stack of 8x10^9 books, we need to calculate the total thickness of all the books.
The thickness of one book is 3.1x10^-4 meters. So, the total thickness of 8x10^9 books can be calculated by multiplying the thickness of one book by the number of books:
3.1x10^-4 meters/book * 8x10^9 books = 24.8 meters
Therefore, the height of a stack of 8x10^9 books, each with a thickness of 3.1x10^-4 meters, would be 24.8 meters.
It's equivalent to about 81 ft.
jeff lives 12 miles east of stan jeff lives 16 miles north of wei what is the shortest stan and wei can live from each other
Answer:
20 miles
Step-by-step explanation:
first, draw a diagram. Then, use the pythagorean theorem to calculate.
1) a man flies a kite at a height of 120 m. the wind carries the kite horizontally away from him at a rate of 6 m/sec. how fast is the distance between the man and the kite changing when the kite is 130 m away from him?
So, on solving the provided question, we can say that, here by differential equations So, 2(400)(25) = 2(500)(dy/dt) => [tex]dy/dt = 20 ft/sec[/tex]
What is differential equation?
Sequences in which the difference between succeeding terms is constant are known as arithmetic progressions. For instance, an arithmetic progression with a tolerance of 2 is the sequence 5, 7, 9, 11, 13, and so on. An arithmetic progression (A.P.) is a progression where the tolerance between two succeeding numbers is always the same.
Let x be the girl's distance from the kite at time t and y be the length of the string at that same moment.
The right triangle at time t has a hypotenuse of length y, a hypotenuse of length 300, and a hypotenuse of length x.
[tex]dx/dt = 25[/tex]
By the Pythagorean Theorem,
[tex]x2 + 3002 = y2[/tex]
[tex]2x(dx/dt) = 2y(dy/dt)[/tex]
Since [tex]x2 + 3002 = y2 and y = 500, x = 400[/tex]
So, 2(400)(25) = 2(500)(dy/dt)
[tex]dy/dt = 20 ft/sec[/tex]
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The U.S. Bureau of Labor and Statistics reported that a person between the ages of 18 and 34 has had an average of 9.3 jobs. To see if this average is correct, a researcher selected a random sample of 8 workers between the ages of 18 and 34 and asked how many different places they had worked. The results were as follows:
0.05, fail to reject null hypothesis..
What is hypothesis in math
A proposition is considered to be a hypothesis if it is plausible given the available information but has not been proven true or wrong.
A statement on which hypothesis testing will be based is referred to as a hypothesis in statistics (also known as a statistical hypothesis).
Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 9.2
Alternative Hypothesis: μ ≠ 9.2
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (8.25 - 9.2)/(5.1478/sqrt(8))
t = -0.522
P-value Approach
P-value = 0.6178
As P-value >= 0.05, fail to reject null hypothesis..
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Which of the following statements is false?
1. We use one-sample procedures when our samples are equal in size but aren't independent. II. Everything else being equal, a confidence interval based on 15 degrees
of freedom will be narrower than one based on 10 degrees of freedom. III. We can pool our estimates of the population variance if we want a narrower confidence interval for a given confidence level.
OA. I only
OB. Il only
OC III only
OD. I and II only
OE None are false
OF. I'm not sure.
The only statements that is false is A. I only: 1. We use one-sample procedures when our samples are equal in size but aren't independent.
A one-sample procedure is used when we want to compare a sample mean to a known population mean or when we want to estimate a population mean using a sample mean. In a one-sample procedure, the sample is selected independently and is typically assumed to be random. So, independence of the sample is a requirement for one-sample procedure.
While statement II and III are true.
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Suppose the formula for calculating the cost per one thousand kilowatt hours of electricity is twice the sum of 36 and 4 times the difference of 7 and 2 dollars per thousand kilowatt hours. How many cents does one hundred kilowatt hour cost?
The cost of one hundred kilowatt-hours of electricity is $16.4
What is unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
Given that, the formula for calculating the cost per one thousand kilowatt-hours of electricity is twice the sum of 36 and 4 times the difference of 7 and 2 dollars per thousand kilowatt-hours.
The cost for 1000 kilowatt-hours of electricity =
2(36+36) + 4(7-2)
= 2(72) + 4(5)
= 144 + 20
= $164
Since, 1000 kilowatt-hours of electricity costs $164
Then, 1 kwh will cost = $164 / 1000
And, 100 KWh will cost = $164 / 1000 × 100
= $16.4
Hence, The cost of one hundred kilowatt-hours of electricity is $16.4
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Let V be a vector space, T:V + V be a linear transformation and W be a one dimensional subspace of V. Prove that W is an invariant sub- space under T if and only if all non-zero vectors in W are eigenvectors of T.
W is an invariant sub-space under T if and only if all non-zero vectors in W are eigenvectors of T because T=αI,α∈F.
The vector is an entity with both magnitude and direction. The movement of an item between two points is described by a vector. The directed line segment can be used to graphically represent vector math.
Given that,
For each vector v ∈ V, there exists [tex]a_{v}[/tex] such that [tex]T_{v}=a_{v}v[/tex] (because [tex]T_{v}[/tex] ∈ span(v) ). Suppose there are vectors u, v∈V such that [tex]a_{u}\neq a_{v}[/tex]. Then
T(u+v)=Tu+Tv⇒[tex]a_{u+v}(u+v)=a_{u}u+a_{v}v[/tex]
which means (u,v) is linearly dependent (since both coefficients cannot be zero simultaneously, by assumption). Therefore, either [tex]a_{u}= a_{v}[/tex], and T is a scalar transformation, or V has a dimension of at most 1, which also implies Tx=αx, with constant α.
Hence, T=αI,α∈F
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Write an explicit formula for an,
the nth term of the sequence 3, 8, 13, .
An explicit formula for aₙ, the nth term of the arithmetic sequence is aₙ = 3 + 5(n - 1)..
How to write an explicit formula for the arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.From the information provided, we have the following parameters:
First term, a₁ = 3
Second term, a₂ = 8
Next, we would determine the common difference as follows:
Common difference, d = a₂ - a₁
Common difference, d = 8 - 3
Common difference, d = 5
Substituting the parameters into the mathematical expression, we have;
aₙ = 3 + (n - 1)(5)
aₙ = 3 + 5(n - 1).
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progresión geométrica, 3er termino es 81 y la razón es 3...
Calcula el primer término y la suma de los 20 primeros términos
El primer término de la progresión geométrica es 9 y la suma de los primeros veinte términos es 1.569 × 10¹⁰.
¿Cómo analizar una progresión geométrica?
En este problema tenemos el caso de una progresión geométrica, es decir, una serie de elementos generados por un expresión de la forma:
y = a · rⁿ⁻¹
Where:
a - Valor del primer elemento.r - Razónn - Índice del elemento enésimo de la serie.El primer término se determina como sigue: (y = 81, r = 3, n = 3)
a = y / rⁿ⁻¹
a = 81 / 3³⁻¹
a = 9
Por último, determinamos la suma de los veinte primeros elementos mediante la siguiente fórmula:
S = [y(n) · r - a] / (r - 1)
Primero, determinamos y(20):
y(20) = 9 · 3²⁰⁻¹
y(20) = 1.046 × 10¹⁰
Segundo, calculamos la suma:
S = [(1.046 × 10¹⁰) · 3 - 9] / (3 - 1)
S = 1.569 × 10¹⁰
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The Rockets and the Rangers are in a league where each of the teams plays $100$ games. At some point in the season, the Rockets' ratio of their wins to their losses is $3:2,$ the Rangers' ratio of their wins to their losses is $7:13,$ and both teams have the same number of games left to play. If the Rockets lose all of their remaining games while the Rangers win all of their remaining games, the teams will end the season with the same number of wins. At this point in the season, how many games do the Rockets have left to play?
According to the information, we can infer that there are 20 games left. To solve this problem we have to use a linear equation.
How to calculate how many games do the Rockets have left to play?To calculate how many games do the Rockets have left to play we have to use a linear equation. Additionally, we have to take into account the information that we have:
Ratio wins/loses Rockets: 3:2Ratio wins(loses Rangers: 7:13Total games: 1000Also, we know that if the rockets loses all the remaining games, and the rangers win all the remaining games, both will win the same number of games. Finally, to solve this problem we have to make the following equation:
In this equation, X is equal to the number of games won by both teams.
(100 - X)*(7/20) + X = (100 - X)*(3/5)
X = (100 - X)*(3/5) - (100 - X)*(7/20)
X = (100 - X)*(3/5 - 7/20)
X = (100 - X)*(12/20 - 7/20)
X = (100 - X)*(5/20)
(20/5)*X = 100 - X
4*X = 100 - X
4*X + X = 100
5*X = 100
X = 100/5
X = 20
According to the above, the number of games won by both teams is 20.
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a financial analyst wants to estimate the difference in the mean growth for all large- and small-cap stocks for the last 60 days. he selects a random sample of 30 large-cap stocks and 30 small-cap stocks from the large populations of large- and small-cap stocks. are the conditions for constructing a 90% confidence interval for the difference in the true mean growth of all large- and small-cap stocks for the last 60 days met? random: 10%: normal/large sample:
Yes, the conditions for constructing a 90% confidence interval for the difference in the true mean growth of all large- and small-cap stocks for the last 60 days are met.
Shares of businesses having a market value between $300 million and $2 billion are considered small-cap stocks. Small-cap firms have the potential for rapid development, which makes them attractive investment targets even if their stocks may be more volatile and carry greater risks for buyers.
Large-cap stocks, commonly referred to as large caps, are stocks that are traded for businesses with a market value of at least $10 billion. Because investors gravitate toward quality and stability and become more risk-averse during challenging markets, large-cap companies often exhibit lower volatility.
Thus, the conditions for constructing a 90% confidence interval for the difference in the true mean growth of all large- and small-cap stocks for the last 60 days are met.
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why was the math student so bad at decimals?
A box of peaches is shared among 5 people. Each person will get 3 more peaches than they would get if the peaches were shared among 8 people. How many peaches are there in the box?
Answer:
40 peaches.
Step-by-step explanation:
We can set up an equation using this information:
(x + 3) * 5 = x * 8
Expanding and simplifying the equation:
5x + 15 = 8x
Subtracting 5x from both sides:
15 = 3x
Dividing both sides by 3:
x = 5
So, if the peaches were shared among 8 people, each person would get 5 peaches. If each person got 3 more peaches if the peaches were shared among 5 people, each person would get 8 peaches.
So the box has 8 peaches per 5 people, 8*5 = 40 peaches
Answer:
There are 8 peaches in the box.
Step-by-step explanation:
It states that if the peaches were shared among 8 people, each person would get x/8 peaches, and if the peaches were shared among 5 people, each person would get x/5 + 3 peaches.
To find the total number of peaches in the box, we can use the equation to find the value of x.
We know that x/8 = x/5 + 3 , we can multiply both sides by 8*5 to get rid of the denominator
8(x/8) = 8(x/5 + 3)
x = 8(x/5 + 3)
5x = 8x + 24
Subtracting x from both sides
3x = 24
Dividing both sides by 4
x = 8
There are 8 peaches in the box.
7/8 in decimal and percent give an explanation please
Answer: 0.875 for decimal, 87.5 for percent.
Step-by-step explanation- Pretty easy, all you gotta do is divide the top by the bottom. So 7 divided by 8= 0.875!
For percent, divide 7 by 8 and then multiply by 100, it would be 87.5
two trains leave the station at the same time, one heading east and the other west. the eastbound train travels at miles per hour. the westbound train travels at miles per hour. how long will it take for the two trains to be miles apart? do not do any rounding.
It will take (miles / (mph eastbound + mph westbound)) hours for the two trains to be miles apart.
(miles / (mph eastbound + mph westbound)) * 60 minutes/hour = minutes
The time it takes for two trains to be a certain distance apart depends on the speed of each train and the distance between them. To calculate this, we can use the equation time = distance/speed. We can also use this equation to calculate the time for two trains traveling in opposite directions. To do this, we add the speed of the eastbound train (mph eastbound) and the speed of the westbound train (mph westbound) and divide the distance between the two trains (miles) by the total. This gives us the amount of time it will take for the two trains to be miles apart. After converting the answer to minutes, we get the amount of time it will take for the two trains to be miles apart.
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£1800 is put into an account. It gathers
simple interest at a rate of 3% per year.
a) How much money is added to the
account each year?
b) How much money will be in the account
after two years?
Give your answers in pounds (£).
Answer:
a) To find out how much money is added to the account each year, we use the simple interest formula: I = Prt, where I is the interest, P is the principal (initial deposit), r is the annual interest rate (expressed as a decimal), and t is the number of years.
In this case, P = 1800, r = 0.03, and t = 1 (because we are finding the interest added for 1 year)
So the formula becomes:
I = 1800 * 0.03 * 1 = 54
Therefore, £54 is added to the account each year.
b) To find out how much money will be in the account after two years, we add the original deposit to the total interest earned over two years.
We know that the interest added each year is £54, and since we are trying to find the balance after 2 years, we will multiply it by 2 to find the total interest earned over 2 years:
Interest = 54 * 2 = £108
Now we add the original deposit and the total interest to find the total amount in the account after 2 years:
Total = 1800 + 108 = £1908
So the amount of money in the account after two years will be £1908.
The account will have £1909.62 after two years.
What is simple interest?Simple interest is the amount of interest charged on a specific principal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.
a) The amount of money added to the account each year is determined by multiplying the principal amount (initial amount) by the interest rate. So, the amount added to the account each year is:
Interest = Principal x Rate
Interest = £1800 x 0.03
Interest = £54
Therefore, £54 will be added to the account each year.
b) To find the amount of money in the account after two years, we need to add the interest earned in each year to the principal amount. After one year, the account will have:
Amount after 1 year = £1800 + £54 = £1854
After the second year, the account will have earned another 3% interest on the new balance of £1854. So, the interest earned in the second year is:
Interest = £1854 x 0.03
Interest = £55.62
Therefore, the total amount of money in the account after two years is:
Amount after 2 years = £1854 + £55.62 = £1909.62
So, the account will have £1909.62 after two years.
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The mean value of land and buildings per acre from a sample of farms is $1800, with a standard deviation of $300.
The data set has a bell-shaped distribution. Using the empirical rule, determine which of the following farms, whose
land and building values per acre are given, are unusual (more than two standard deviations from the mean). Are any
of the data values very unusual (more than three standard deviations from the mean)?
$1625 $2493 $1521 $615 $1656 $1664
Which of the farms are unusual (more than two standard deviations from the mean)? Select all that apply.
A. $615
B. $1656
C. $1625
D. $2493
E. $1521
F. $1664
Answer:
A and D
Step-by-step explanation:
The Empirical Rule states that for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean.
Given that the mean value of land and buildings per acre from the sample of farms is $1800 and the standard deviation is $300, we can use this information to determine which farms are unusual (more than two standard deviations from the mean).
A. $615 is unusual, it is more than two standard deviations from the mean, which is $1800. $615 is $1185 less than the mean. Since it is more than $600 less than the mean, it is more than two standard deviations from the mean.
B. $1656 is not unusual, it is less than 2 standard deviations from the mean.
C. $1625 is not unusual, it is less than 2 standard deviations from the mean.
D. $2493 is unusual, it is more than two standard deviations from the mean, which is $1800. $2493 is $693 more than the mean. Since it is more than $600 more than the mean, it is more than two standard deviations from the mean.
E. $1521 is unusual, it is more than two standard deviations from the mean, which is $1800. $1521 is $279 less than the mean. Since it is more than $600 less than the mean, it is more than two standard deviations from the mean.
F. $1664 is not unusual, it is less than 2 standard deviations from the mean.
None of the data values are very unusual (more than three standard deviations from the mean).
So the farms that are unusual (more than two standard deviations from the mean) are A and D.
Answer: Using the empirical rule, if the distribution is bell-shaped, we know that about 68% of the data falls within one standard deviation of the mean, about 95% of the data falls within two standard deviations of the mean, and about 99.7% of the data falls within three standard deviations of the mean.
To determine which of the farms are unusual (more than two standard deviations from the mean), we need to calculate the lower and upper bounds for two standard deviations from the mean:
Lower bound = Mean value - (2 * Standard deviation) = $1800 - (2 * $300) = $1200
Upper bound = Mean value + (2 * Standard deviation) = $1800 + (2 * $300) = $2400
So, any data value outside this range is considered unusual. Therefore, the farms that are unusual are:
$2493 (more than two standard deviation from the mean)
None of the data values are very unusual (more than three standard deviations from the mean)
Step-by-step explanation:
As part of a quality-control program, 3 batteries from a box of 15 is chosen at random for testing. In how many ways can this test batch be chosen?a) 455 b) 3 c) 2,730d) 45 e) 6
This test batch can be chosen is 455 ways. (Option A).
The problem is asking for the number of ways to choose 3 batteries out of a box of 15.
This is a combination problem and the number of ways to choose k items out of a set of n items, without regard to the order of selection, is given by the binomial coefficient:
C(n,k) = n!/(k!(n-k)!)
where ! denotes factorial.
So in this case, we have:
C(15,3) = 15!/(3!(15-3)!) = 151413/(321) = 455
So, the answer is 455.
Therefore, This test batch can be chosen is 455 ways. (Option A).
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A poster is being designed that is to contain 2 150. In of printed material with margins of 2 inches at the top and bottom and 3 inches at each side. What overall dimensions will minimize the amount of paper used?
A poster is being designed that is to contain 2 150. In of printed material with margins of 2 inches at the top and bottom and 3 inches at each side. the dimensions that will minimize the amount of paper used is that should be 12 inches wide by 6 inches tall.
The margins are 2 inches at the top and bottom and 3 inches at each side. The margins are then added to the two 150s, making a total width of 12 inches and a total height of 6 inches. This is the minimum amount of paper that can be used for the poster. In order to minimize the amount of paper used, it is important to consider the size of the margins.
The margins should be kept as small as possible in order to maximize the amount of space available for the printed material. Generally speaking, a margin of 1 inch is sufficient for most printed materials. If a larger margin is necessary, then the overall dimensions of the poster should be adjusted accordingly.
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Evaluate f(-2) if f(x) = x^2 + 3
Answer:
f(-2) = 7
Step-by-step explanation:
For this, we need to substitute -2 for x, giving us:
[tex]-2^{2} + 3[/tex]
Simplifying:
4 + 3 = 7
So, f(-2) = 7.
Hope this helped!
a 20 foot tree stands parallel to a 12 foot flagpole.a 28 foot wire is stretched between the top of the tree and the top of the flagpole.how far apart are the tree and the flagpole
the distance between the tree and the flagpole is approximately 23.29 feet.
To find the distance between the tree and flagpole, we can use the Pythagorean theorem, which states that the square of the distance between the two points (the hypotenuse of the right triangle) is equal to the sum of the squares of the other two sides.
In this case, the distance between the tree and flagpole (the hypotenuse of the triangle) is equal to the square root of (20^2 + 12^2) = square root of (400 + 144) = square root of 544.
So the distance between the tree and the flagpole is approximately 23.29 feet.
Learn more about Pythagorean Theorem here: brainly.com/question/28361847
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At a student bake sale, cakes sold for $4 each and pies sold for $5 each. The students sold a total of 75 cakes and pies, and made $340. Which system of equations would determine the number of each ticket sold?
Answer: The system of equations to determine the number of each item sold would be:
4x + 5y = 340 (where x is the number of cakes and y is the number of pies)
and
x + y = 75 (where x and y is number of cakes and pies)
This system of equations can be solved using methods such as substitution or elimination.
Step-by-step explanation:
you record the number x of runs scored by the winning team and the number y of runs scored by the losing team for each softball game in a team's season. does the relation necessarily represent a function? explain.
No the relation doesn't necessarily represent a function.
The term function is known as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Here we have given that you record the number x of runs scored by the winning team and the number y of runs scored by the losing team for each softball game in a team's season.
As we all know that in any two games here we have given that if the winning teams had the same numbers of runs while the losing teams had different numbers of runs then the given relation is not a function.
Here we have to remember that for a relationship to be a function then it must be fulfilled and it is possible for every input value there must be only one output value
To know more about function here
https://brainly.com/question/28193995
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Simplify the ratio 18ml:24ml:42ml
Answer: 3ml:4ml:7ml
Step-by-step explanation: To simplify ratios you have to find the highest number that you can divide all the parts in the ratio by (AKA as highest common factor)
In this case the common factor of 18,24 and 42 is 6.
so now divide all the parts by 6:
18/6=3
24/6=4
42/6=7
finally put these numbers back into the correct ratio format and for this question put on the units.
final answer= 3ml:4ml:7ml
