A discounted surfing lesson costs $50, and a discounted parasailing trip costs $80.
Let x represent the discounted cost per person for a surfing class.
Let y represent the reduced cost per person for surfing instruction.
The cost of taking a surfing lesson and going parasailing is $130
x + y = 130--------------(i)
25 people take
Surfing lessons and 30 people go parasailing and a total of $3,650 is collected
25x + 30y = 3650--------------(ii)
We solve for y using equ (i):
y = 130 - x ------------(iii)
Substitute equ (iii) to equ (ii) and solve for x
25x + 30(130 - x) = 3650
25x + 390 - 30x = 3650
-5x = -250
-x = 50
We solve for y using equ (iii):
y = 130 - x
y = 130 - 50
y = 80
Thus, a discounted surfing lesson costs $50, and a discounted parasailing trip costs $80.
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I need the answers, please. It's due today.
Answer the following questions:
1. In a kitchen, the combined number of plates and glasses is 60. If the ratio of the number of plates to glasses is 2 ∶ 3, how many plates should be added so that the ratio of plates to glasses is 1 ∶ 1?
2. Fred has a collection of movie CDs. The ratio of fantasy movies to drama movies is 3 ∶ 2. The ratio of drama movies to comedy movies is 4 ∶ 3. If Fred has 24 fantasy movie CDs in his collection, how many comedy movie CDs does he have?
The number of plates to make the ratio 1 : 1 is 12 and the number of comedy movies is 24
What is RatioA ratio is a way of comparing two or more quantities, typically by expressing them as a fraction. The numerator of the fraction represents one quantity and the denominator represents the other. The ratio can be written in different forms, such as "a to b" or "a:b", which expresses the relationship of a to b.
In this problem, using the ratio 2:3;
Number of glasses and plates = 60
Number of plates = 2 / (2 +3) * 60
number of plates = 2 / 5 * 60
number of plates = 24
Number of glasses = 3 / 5 * 60
Number of glasses = 36
The number of plates to make the ratio 1:1 = 36 - 24 = 12
The number of plates = 12
2.
The ratio of fantasy movie to drama movie = 3 : 2
The ratio of drama to comedy = 4 : 3
The number of fantasy = 24
We will set a ratio between fantasy to drama to comedy = 3 : 2 : 2
The total number of movies ;
24 = 2/ 7 * x
24 * 7 = 2x
2x = 168
x = 168 / 2
x = 84
The number of comedy movie is;
y = 2 / 7 * 84
y = 24
The number of comedy is 24
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What is the height H of the roof?.
Answer:
Step-by-step explanation:
Per ASCE 7, the Mean Roof Height (h) is defined as the average of the roof eave height and the height to the highest point on the roof surface, except that, for roof angles of less than or equal to 10°, the mean roof height is permitted to be taken as the roof eave height
i hope it helps
What is y =- 4 on a graph?.
It is a horizontal line which crosses the y axis at -4
The y-intercept is the point at which the graph crosses the y-axis. The most important step in graphing any function with the formula y = f(x) is finding the intercepts. The x-intercept and the y-intercept are the two possible forms of an intercept for a function. The point on the axis where a function's graph intersects it is known as the intercept.
In this equation, y=-4 which means y-intercept is -4 (i.e., c= -4) and the slope of the line is 0.
Thus, it will be a horizontal line cutting the y-axis at -4
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The spinner is spun 300 times. How many times would you expect the arrow to stop on green if the spinner is fair? The table below shows the number of times the arrow stops on each colour. The spinner is spun once more. Estimate the probobility of it landing on purple. If the spinner is spun another 1000 times, about how many times would you expect it to land on blue?
If the spinner is fair, it means that the probability of the arrow stopping on any given color is the same. Given that there are four colors on the spinner (green, blue, purple, and yellow), we can expect the arrow to stop on green 1/4 of the time. So if the spinner is spun 300 times, we would expect the arrow to stop on green 300 times * 1/4 = 75 times.
Given that the spinner has been spun once more, the table now shows that the spinner has been spun 301 times. We can estimate the probability of it landing on purple by using the number of times it has landed on purple divided by the total number of spins.
Purple: 48/301 = 0.159 or 15.9%
If the spinner is spun another 1000 times, we can expect it to land on blue 1000 * 1/4 = 250 times approximately, this is assuming the spinner is fair.
2(3b+6) =78 : Answer is 11
-2(6c-3) = -72 : Answer is 6.5
Check Right and Left side of the equation
The right side of the first equation is 78 and the right side of the second equation is -72. Both sides of the equations are constants (numbers with no variable in them)
The left side of the first equation is 2(3b+6) and the left side of the second equation is -2(6c-3). Both sides of the equations are products of a constant and a variable or a sum/difference of variables.
To find the value of b and c in the equation, you need to solve the equation.
For the first equation:
2(3b + 6) = 78
3b + 6 = 39
3b = 33
b = 11
For the second equation:
-2(6c - 3) = -72
6c - 3 = 36
6c = 39
c = 6.5
So, the value of b is 11 and the value of c is 6.5
What is the domain of 7?.
The domain of a function is the set of all input values (or independent variables) for which the function is defined, and for which the output values (or dependent variables) are real numbers. In other words, it's the set of all the values that can be plugged into the function without resulting in an error.
The number 7 is not a function, it's a constant value. Therefore, it doesn't have a domain, as it doesn't take any input value. A domain is only applicable for a function, which takes some input and produces an output. It does not make sense to speak of the domain of a constant number.
In contrast, if you have a function like f(x) = 7, the domain of this function would be the set of all real numbers since the function will produce the output of 7 for any real value of x.
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What is a product of a fraction?.
The product of fractions is a fraction or an integer.
We know that the fraction is used to represent the portion or part of the whole thing.
The fraction has two parts: numerator and denominator.
The top part of fraction is numerator and the bottom part is denominator.
consider a fraction 1/8.
Here, numerator is 1, denominator is 8
When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8
The multiplication of fractions is defined as the product of a fraction with a fraction or the product of a fraction with an integer or the product of a fraction with the variables.
The steps to multiply two fraction are:
First multiply the numerator with numerator
Then Multiply the denominator with the denominator
And lastly simplify the fractions, if required
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What are the four rules of multiplication?.
The four rules of multiplication is explained below.
The term multiplication in math is defined as the process of when you take one number and add it together a number of times
Here we need to define the four rules of multiplication.
Here the first rule of multiplication is written as that any number times zero is always zero.
And the next rule is that any number times one is always the same number.
And the another rule is written as add a zero onto the original number when multiplying by 10.
And if the order of factors does not affect the product then switching the roles of multiplier and multiplicand results in the same answer.
Where the other rule is that products are always positive when multiplying numbers with the same signs.
And the final rule is the products are always negative when multiplying numbers with different signs.
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p(x)=x²+x2-10x+8 (b) Using long division express p(x) as product of linear factor (e) Hence solve x¹+x²-10x +8=0 Qu. 3. The polynomial p/x) is given (a) Show that x-2 is a factor of p(x)
Answer:
b. To express p(x) as a product of linear factors using long division, we divide p(x) by (x - 2) and get a quotient of (x + 5) and a remainder of 0. This means that p(x) = (x - 2)(x + 5)
e. To solve p(x) = 0, we set each factor equal to zero and find the solutions:
x - 2 = 0, x = 2
x + 5 = 0, x = -5
Thus, the solutions to the equation p(x) = 0 are x = 2 and x = -5.
a. To show that x-2 is a factor of p(x), we can use synthetic division or polynomial long division.
let's use polynomial long division to divide p(x) by (x-2)
p(x) = x²+x²-10x+8
| x-2 |
x²-2x+x
| -x²-x²+10x+8
--------------
0
As we can see, after dividing p(x) by (x-2) we get remainder as 0, which implies that (x-2) is a factor of p(x)
Hence, we can say that x-2 is a factor of p(x)
16. If AABC-ADBE, find the values of x and y.
The values of x and y for the given similar triangles are 3 and 10 respectively.
Define the term similarity of the triangle?If two figures have the same shape, they are termed to be comparable. In more formal terms, two figures are said to be comparable if their respective angles are congruent and their corresponding side length ratios are identical. The scale factor is the name given to this usual ratio.For the stated question-
Using the similarity for the triangle ABC and DBE,
Taking the ratios of the sides.
x/9 = 4/12
x = 9/3 = 3
And,
5/y = 4/(12 - 4)
5/y = 4/8
y = 5*2 = 10
Thus, the values of x and y for the given similar triangles are 3 and 10 respectively.
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The Ahmad family uses propane gas to heat their home in the winter. The cost to fill their
propane tank varies directly with the number of gallons of propane they buy. The Ahmads have a
budget of $750 to buy propane for their tank this winter, and the gas costs $3.83 per gallon. Give
the direct variation equation that describes how much propane the Ahmads can purchase with
their $750 budget and state the meaning of the variables x, y, and k for this situation.
The number of gallons they buy is directly connected to the size of the propane tank: x + $3.83y = $750.
what is equation ?Using the equal symbol (=) to indicate equivalence, a mathematical equation is a formula that joins two statements. An equation in algebra is a statement of mathematics proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign places the variables 3x + 5 and 14 apart. The relationship between two sentences on either side of a letter is described by a mathematical formula. A single variable, which also serves as the symbol, is frequently present. like in 2x - 4 = 2, for instance.
given
Let the direct variation equation
be x + $3.83y = 750,
Let the direct variation equation be x + $3.83y = 750,
The number of gallons they buy is directly connected to the size of the propane tank: x + $3.83y = $750.
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A polar vortex causes the temperature to decrease from 3°C at 3 PM to -2°C at 4 PM the temperature continues to change by the same amount each hour until 8 PM find the total change in temperature for 3 PM to 8 PM
The total change in temperature from 3 PM to 8 PM is 25°C.
The first step is to calculate the temperature difference.
Temperature at 3 PM = 3°C
The temperature at 4 The period2°C
The difference = 3 - (-2) = 3 + 2 =5°C
The second step is to calculate the difference time.
Period from 3 PM to 8 PM:
To find the difference between two numbers, subtract the number with the smallest value from the number with the largest value.
So,
8-3 = 5 hours
The third step is to calculate the total temperature change.
5°C × 5 hours = 25°C.
The total change in temperature from 3 PM to 8 PM is 25°C.
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please help im very confused how to do this.
Step-by-step explanation:
(a)
[tex] \frac{b + x}{3} = \frac{b - x}{4} \\ 4b + 4x = 3b - 3x \\ b = - 7x[/tex]
(b)
[tex]p = \frac{y}{1 + y \\ } \\ p + py = y \\ y - py = p \\ y = \frac{p}{1 - p} [/tex]
(c)
[tex] \frac{1}{a} = \frac{1}{b} - \frac{1}{c} \\ \frac{1}{c } = \frac{1}{b} - \frac{1}{a} \\ \frac{1}{c} = \frac{a - b}{ab} \\ c = \frac{ab}{a - b} [/tex]
What are the 3 rules to solving an equation?.
The Golden Rule to Solve an Equation are:-
Simplify both sides of the equation.Move all parts of the equation that contain the variable you're solving for to the same side.Isolate the variable using multiplication, division, exponentiation, or by taking roots.Check your solution!In arithmetic, an equation is a system that expresses the equality of two expressions, by connecting them with the equals signal =. The phrase equation and its cognates in different languages may additionally have subtly one-of-a-kind meanings; as an example, in French, an équation is defined as containing one or more variables, whilst in English, any well-formed method together with expressions associated with an equals signal is an equation.
solving an equation containing variables includes figuring out which values of the variables make the equality real. The variables for which the equation must be solved are also called unknowns, and the values of the unknowns that fulfill the equality are called answers to the equation. There are kinds of equations: identities and conditional equations. An identity is real for all values of the variables. A conditional equation is handiest authentic for particular values of the variables.
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what number is equivalent to 49 ÷ 9
The value of the equation is A = 5.44
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 49 ÷ 9 be equation (1)
On simplifying the equation , we get
A = 5.44
Therefore , the value of A is 5.44
Hence , the equation is A = 5.44
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determine whether the table repersents a discrete probability distribution
The discrete probability distribution is discussed above.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.Given is discrete probability distribution.
A probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment.A discrete probability distribution is the probability distribution of a random variable that can take on only a countable number of values which means that the probability of any event {E} can be expressed as a (finite or countably infinite) sum.Mathematically, we can write it as : [tex]${\displaystyle P(X\in E)=\sum _{\omega \in A}P(X=\omega )}[/tex].A discrete probability distribution is often represented with Dirac measures, the probability distributions of deterministic random variables. If {E} is any event, then : [tex]${\displaystyle P(X\in E)=\sum _{\omega \in A}p(\omega )\delta _{\omega }(E)}[/tex].Mathematically, we can write the equivalent formula as -[tex]${\displaystyle P(X\in E)=\sum _{\omega \in A}p(\omega )\delta _{\omega }(E)} =[/tex]
[tex]${\displaystyle P(X\in E)=\int _{E}f(x)\,dx=\sum _{\omega \in A}p(\omega )\int _{E}\delta (x-\omega )=\sum _{\omega \in A\cap E}p(\omega )}[/tex]
Therefore, the discrete probability distribution is discussed above.
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What is a solution Class 7?.
In class 7, a solution is typically defined as a type of mixture where one or more substances are evenly dispersed in another substance.
The substance that is being dispersed is called the solute, and the substance that it is being dispersed in is called the solvent. Solutions can be liquids, gases, or even solids, and they can be formed by dissolving a solute in a solvent.
In class 7, students learn about different types of solutions, such as:
Liquid solutions: These are solutions where the solvent is a liquid, such as sugar dissolved in water to make a sweet drink.
Gas solutions: These are solutions where the solvent is a gas, such as air, and the solute is a gas or a solid, such as the dissolved oxygen in the air we breathe.
Solid solutions: These are solutions where the solvent is a solid, such as a metal alloy, and the solute is a metal or a non-metal.
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Finding the final amount given the original amount and a...
Last year, Deandre opened an investment account with $7600. At the end of the year, the amount in the account had decreased by
21.5%. How much is this decrease in dollars? How much money was in his account at the end of last year?
Answer:
The decrease in dollars is $1634
Deandre has $5966 in his bank account at the end of the year
Step-by-step explanation:
7600 times 0.215 = 1634
7600 - 1634 = 5966
o the solutions tell you
y = (x + 1)² + 3
y = 2x + 4
The equation y = (x + 1)² + 3 tells that it is quadratic equation and the equation y = 2x + 4 tells that it is a linear equation.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The first equation is - y = (x + 1)² + 3
The second equation is - y = 2x + 4
The first equation is a quadratic equation.
To solve the first equation use the formula (a + b)² = (a² + 2ab + b²) -
y = (x + 1)² + 3
y = (x² + 2x + 1) + 3
y = x² + 2x + 4
The second equation is a linear equation y = 2x + 4.
On graphing both the equations it is seen that the first equation forms a parabola while the second forms a straight line.
Therefore, first equation is quadratic and second is linear.
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Chris is at the deli and is trying to figure out how much total cheese he has bought. He knows that he bought ½ pound of American cheese and two packs of 2/3 pound Mozzarella cheese. How much total cheese did he buy?
Answer: 7/6 or 1 1/6
Step-by-step explanation:
1/2+2/3= 7/6 or 1 1/6
2x2 and 3x2 which is 4/6 (multiply with 2)
1x3 and 2x3 which is 3/6 (multiply with 3)
4/6+3/6= 7/6 or 1 1/6
100 POINTS AND BRAINIEST
Laisha rides a bike 8 miles in 40 minutes. Jefford rides a bike 5 miles in 30 minutes.
Who will bike the farthest in 1 hour?
2nd question. How much farther?
Step-by-step explanation:
laisha bike farthest in 1 hour
How do you write 2 more than 3 times?.
The correct equation to write 2 more than 3 times is 3x + 2.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Let us assume that, the number is 17 .
So,
→ Three time of x = 3 * x = 3x
then,
→ 2 more than three time of x = (3x + 2)
given that, 2 more than three time of x is equal to 17 .
therefore,
→ 3x + 2 = 17
→ 3x = 17 - 2
→ 3x = 15
→ x = 5 (Ans.)
Hence, the required number is 5 .
Verification :-
→ 2 more than three times of 5 = 17
→ 3 * 5 + 2 = 17
→ 15 + 2 = 17
→ 17 = 17 .
hence, the correct equation to write 2 more than 3 times is 3x + 2.
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Jamar is ordering a taxi from an online taxi service. The taxi charges $3.50 just for the pickup and then an additional $2 per mile driven. How much Would a taxi ride cost if Jamar is riding for 7 miles? How much would a taxi ride cost that is m miles long?
Answer:
Step-by-step explanation: Hello! (Don't read this if you are taking a test, please!)
You know that the taxi will already charge $3.50. Write that down. You know that Jamar is riding for 7 miles. You know that each mile costs $2. Multiply the cost of a single mile by the amount of miles, 7. Then you will get your answer. I hope I helped you out!
stefanie has 18 grams of 20% sugar syrup, and john has 30 grams of 25% sugar syrup. how many grams of sugar are in john's syrup?
John syrup contains 11.1 grams of sugar
How to calculate the number of grams in john's syrup?Stefanie has 18 grams of 20% syrup
John has 30 grams of 25%
Therefore the number of grams of sugar in John's syrup can be calculated as follows
18× 20/100 + 30 × 25/100
= 18×0.2 + 30×0.25
= 3.6 + 7.5
= 11.1
Hence there are 11.1 grams of sugar in John's syrup
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Please help! I’m really bad at math
Answer:
14.6
Step-by-step explanation:
In the example
x =kh
k is the constant of proportionality
For each scatter plot, determine if the relationship shown is linear and positive, linear and negative or nonlinear.
Linear and Positive
Linear and Negative
Nonlinear
For the scatter plots shown;
a) Non linear
b) Linear positive
c) Non linear
d) Linear negative
What is the scatter plot?We know that the scatter plot is used to show the relationship between variables. The variable that is plotted on the vertical axis is the dependent variable while the variable that is plotted on the horizontal is the independent variable.
The points that we have on the scatter plot can help us to be able to know whether or not the relationship between the variables is linear.
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Margaret i purchaing a new cell phone. The phone he want to buy cot $275. If he ha a coupon for the phone tore for 15% off and another coupon for $20 off, which hould he ue?
Coupon 1 will provide more discount and hence he will use coupon 1.
Describe percent discount:Percent discount is a way to express a reduction in price as a percentage of the original price. It is commonly used in sales and promotions. For example, a 20% discount on a $100 item would reduce the price to $80.
In order to check which coupon provides more discount to the Margaret we need to check for both coupon value and the coupon whose value is greater that one we will use
coupon 1 is 15 percent of initial cost.
Coupon 1 value = (15/100) * 275
=> $0.15*275
=> $41.25
Coupon 2 value = $20
so Coupon 1 will provide more discount .
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You are interested in exploring the relationship between hours studying and test grades. which of these statements would be her null hypothesis?
a. There is no relation between hours studying and grades on a test. b. There is a relation between hours studying and grades on a test.
c. There is no relation between hours studying and grades on a test.
d.The more hours one studies, the higher their grades will be.
e. None of the above.
There is no relation between hours studying and grades on a test. this statements would be her null hypothesis .
What is the definition of a null hypothesis?
The null hypothesis presupposes that any variation between the selected attributes you observe in a set of data is the result of chance.
For instance, if the predicted profits from the gambling game genuinely equal zero, then any discrepancy between the data's average profits and zero results from chance.
The null hypothesis doesn't exist.
A null hypothesis may declare, for instance, that the population mean return is equal to zero. The null hypothesis is typically an equality hypothesis for population parameters.
It might be said that the alternative hypothesis is the exact opposite of a null hypothesis (e.g., the population mean return is not equal to zero).
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What is the graph of the inequality y ≤-22 - 3?
Answer:
would look like the picture down below meaning it has a ZERO slope
find sin2x, cos2x, and tanx2x if sinx= 15/17 and x terminates in quadrant 2
The trigonometric identities for double angles can be used to solve for sin2x, cos2x, and tan2x.
What is trigonometric?Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles and circles. Trigonometry is used to calculate the measurements of angles, lengths, and areas of different geometric figures. It is also used to solve problems involving forces, motion, and velocity.
Sin2x = (2*15/17)*(-12/17) = -30/289
Cos2x = (2*15/17)*(-5/17) = -30/289
Tan2x = (2*15/17)/(-12/17) = -5/12
Since sinx = 15/17 and x terminates in quadrant 2, then x = -3π/17. The trigonometric identities for double angles can be used to solve for sin2x, cos2x, and tan2x.
Sin2x = 2*sinx*cosx = 2*(15/17)*(-12/17) = -30/289
Cos2x = 2*cosx*cosx - 1 = 2*(-12/17)*(-12/17) - 1 = -5/289
Tan2x = (2*sinx*cosx)/(cosx*cosx - sinx*sinx) = (2*(15/17)*(-12/17))/((-12/17)*(-12/17) - (15/17)*(15/17)) = -5/12
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