The number of tickets they purchased is 4.
How many tickets did they purchase?The expression that would b used to represent the total cost at the carnival is a linear expression. A linear expression is an expression that has a single variable that is raised to the power of one.
The form of the linear expressions that can be used to represent the total cost at the carnival is:
Total cost = admission fee + (price per ride x number of rides)
Total cost in option 1 = $5 + 0.30r
Total cost in option 2 = $3 + $0.80r
Where r = number of rides
When they pay the same amount of money, the linear functions would be equal:
$5 + 0.30r = $3 + $0.80r
$5 - $3 = $0.80r - 0.30r
$2 = $0.50r
r = 2 / 0.5
r = 4
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Solve the following system of equations using substitution (Enter your answer as an ordered pair, including the parentheses and comma.)
-3x+6y=12
2y=x+4
The system of equations has infinite solutions, both equations represent the same line.
How to solve the system of equations?
Here we have the following system of equations:
-3x+6y=12
2y=x+4
And we want to solve this by substitution, first, we can rewrite the first equation as:
-3x + 3*(2y) = 12
Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:
-3x + 3*(x + 4) = 12
Now we can solve this for x.
-3x + 3x + 12 = 12
12 = 12
So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).
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what is the inverse of (x^2 4)
The inverse function of the given function y = x² + 4 will be y = √(x - 4).
What is the inverse function?Let the function f is given as
y = m(x + a) + c
Then the inverse function of the function f will be given by swapping x with y and y with x.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The function is given below.
y = x² + 4
The inverse function of the function y = x² + 4 is given as,
Replace x with y and y with x, then we have
x = y² + 4
Solve the equation for y, then the equation is rewritten as,
x = y² + 4
y² = x - 4
y = √(x - 4)
The inverse function of the given function y = x² + 4 will be y = √(x - 4).
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Vickie made a recipe for 144 ounce of cented candle wax how many 1 cup candle mold can he fill with the recipe
The number of 1 cup candle mold which the can fill with 144 ounce of cented candle wax is 18.
As we know ,
1-cup= 8 ounces
On dividing ,
144 by 8 = 18
Therefore , the no of cups which can be filled is 18 .
One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal pieces. Every day, we might employ the division approach in various situations.
Any number divided by 0 has no specified result. The outcome in this situation can be expressed as infinite. For instance, 15/0 =, which is undefined.
Dividend :
The division procedure shown below is used to divide any expression.
Dividend is equal to Divisor Quotient + Remainder.
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Elizabeth works for the lawn care company and earns $15 per day plus $35 for every lawn mows. Let x be the amount of lawns she mows and y be the total money she made for the day. Write the linear equation that models her total pay for the day.
Using the information provided, how many money would she make if she mows eight lawns today?
The linear function represents the total cost is y = 15 + 35x and the money made by 8 lawns will be $295.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given,
For x number of lawn mows,
Total earning y = 15 + 35x
For x = 8
y = 15 + 35 x 8 = 295
Hence "The linear function represents the total cost is y = 15 + 35x and the money made by 8 lawns will be $295".
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8 baskets have some apples in them, and the same number of apples are in each basket. 6 apples are added to each basket to make a total of 144 apples. What equation can go with this problem?
Answer:
8(x + 6) = 144
Step-by-step explanation:
We can start building this equation by making everything equal to 144 since the problem is representing the total number of apples:
? = 144
Next, we don't know how many apples are in each basket, so we can represent it with a variable, x.
Since 6 apples are added to each basket we will simply add 6 to the "x" amount of apples in each basket:
x + 6 = 144
Lastly, according to the scenario, we have 8 baskets, each holding "x" amount of apples plus the extra 6 that was added, so it will be multiplied:
8(x + 6) = 144
a = 1212(b1 b2)h find the area of the trapezoid.
The area of trapezoid with sides 125ft and 81ft with height 75ft is: 7,725ft².
What is the area of trapezoid?A trapezoid is a quadrilateral that is convex. There are at least two parallel sides to a trapezoid. The parallel sides are referred to as bases, while the non-parallel sides are referred to as legs.The bases are the two parallel sides, and height is always the perpendicular distance from one base to the opposite. The area of this parallelogram is equal to half of its height (half of the trapezoid's height) times its base (sum of the trapezoid's bases)Area of a trapezoid,
A = 1/2 x (b1 x b2)h
Here given,
b1 = 125ft
b2 = 81ft
h = 75ft
By substituting the values ,
A = 1/2 ( 125 + 81 ) x 75
A = 1/2 x 206 x 75
A = 0.5 x 206 x 75
A = 7,725 ft²
The complete question is "To answer the question, use the formula for the area of a trapezoid A=h((b1+b2)/2), where A is the area, b1 and b2 are the lengths of the bases, and h is the height. What is the area of grass on a trapezoidal field with a height of 75 feet and bases of 125 feet and 81 feet? HINT: Use the values given for h, b1, and b2.".
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The area of trapezoid is 7725 ft²
What is a trapezoid?
In American and Canadian English, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English.
In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs (or lateral sides); if not, the trapezoid is a parallelogram, and there are two pairs of bases. Unlike the specific situations below, a scalene trapezoid is a trapezoid that lacks equal-sized sides.
Given, the expression for the area a is given as
a = [(b₁ + b₂)/2]*h
where b₁ = 125ft, b₂ = 81ft, h = 75ft.
Substituting these values in the above area expression, we get,
a = [(125+81)/2]*75
a = 103*75
a = 7725 ft²
Thus, the area of trapezoid is 7725 ft²
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13. a prospector thinks there is an even (50-50) chance that his property contains oil. any property suspected to have oil can go through two independent tests. the first test is 80% reliable; if there is oil on the property, it reports positive 80% of the time, and it reports negative 80% of the time whenever there is no oil. for the second test, it reports positive 75% of the time when there is oil, as well as reporting positive 50% of the time when there is no oil. what is the probability the property has oil, given that both tests report positive? assume event a: first test reports positive; event b: second test reports positive; event o: the property has oil.
The probability the property has oil, given that both tests report positive.
P(O|A∩B) = 0.6 * 0.5 / 0.8 = 0.375
P(O|A∩B) = P(A∩B|O)P(O) / P(A∩B)
P(A∩B|O) = 0.8 * 0.75 = 0.6
P(O) = 0.5
P(A∩B) = P(A|O)P(O) + P(A|¬O)P(¬O)
P(A|O) = 0.8, P(¬O) = 0.5
P(A∩B) = 0.8 * 0.5 + 0.8 * 0.5 = 0.8
P(O|A∩B) = 0.6 * 0.5 / 0.8 = 0.375
The probability theory is defined.The study of random events is the focus of probability theory, a subfield of mathematics. It is impossible to predict the outcome of a random event before it happens, although it could take any of numerous different forms. It is believed that chance played a role in how things turned out.
How does probability work?Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures and the risk of health impacts are related.
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What is the antiderivative of 1/sinx?
The anti-derivative in other words integration of the inverse of sine function i.e 1/sinx is
x sin⁻¹x + √(1 - x²) + C.
Integration of a function is the inverse process of differentiation. The integral is just the inverse derivative. The inverse integral of sin is written as
x sin⁻¹x + √(1 - x²) + C.
where ∫ --> the sign of integration, dx --> that the integration of sine inverse with respect to x, C --> the constant of integration.
Integral of Sin Reverse proof by integration by parts :
The formula for integration by parts is ∫f(x)g(x)dx = f(x) ∫g(x)dx - ∫[d(f(x) ) /dx×∫g(x) dx] sin⁻¹x can be written as sin⁻¹x = sin⁻¹x.1.f(x) = sin⁻¹x, g(x) = 1
d(sin⁻¹x)/dx = 1/√(1 - x²)
Using these equations and facts,
∫sin⁻¹x dx = ∫sin⁻¹x.1 dx
= sin⁻¹x ∫1dx - ∫[d(sin⁻¹x)/dx × ∫1 dx] dx
= x sin⁻¹x - ∫[1/√(1 - x²) × x] dx
= x sin⁻¹x - ∫x/√(1 - x²) dx
= x sin⁻¹x + (1/2) ∫-2x/√(1 - x²) dx [multiplication and division by 2]
= x sin⁻¹x + (1/2) ∫(-2x)(1 - x²)-1/2 dx
= x sin⁻¹x + (1/2) [(1 - x²)-1/2 + 1/ (-1/2 + 1)] + C {using the formula ∫[f(x)]nf'(x)dx=[f(x)]n +1/(n + 1) +C}
= x sin⁻¹x + (1/2) [(1 - x²)1/2/ (1/2)] + C
= x sin⁻¹x + (1 - x²)1/2 + C
= x sin⁻¹x + √(1 - x²) + C
Therefore the inverse derivative of 1/sinc is x sin⁻¹x + √(1 - x²) + C.
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What is the smallest possible composite, positive, integer x and y such that [tex]\frac{x}{y}[/tex]=5
x=
y=
The smallest possible composite, positive, integer x and y such that x/y=5 are x=20, y=4.
What is a composite number?The result of multiplying two smaller positive integers is a positive integer known as a composite number. It is, in other words, an integer that is positive and has at least one divisor besides itself and 1. The composite numbers are exactly the numbers that are not prime and not a unit, since every positive integer is either composite, prime, or the number 1.
Because it is the result of the two smaller integers 2 and 7, for instance, the number 14 is a composite number. The integers 2 and 3 are also not composite numbers because they can only be divided by one another and themselves.
The smallest possible composite, positive, integers are
4 and 20
20/4=5
So, x=20 and y=4
Therefore, the smallest possible composite, positive, integer x and y such that x/y=5 are x=20 and y=4.
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solve this please I need some help
Answer:
x = 85°
Step-by-step explanation:
the angle adjacent to B inside the triangle is corresponding to 70° and are congruent.
the sum of the 3 angles in a triangle is 180° , then
x + 25° + 70° = 180°
x + 95° = 180° ( subtract 95° from both sides )
x = 85°
Shana bought sodas and
popcorn for the movies. Sodas cost $3 each and popcorn costs S4 per bag.
bought 7 things from the concession. all either sodas or bags of popcorn.
Shana
Shana spent a total
system of equations involving the number of sodas, s, and the bags of popcorn,
of $26. Write 8
how many of each Shana bought.
b. Solve the system to see
Shana bought 5 bags of popcorn and 2 bottles of soda.
What is an equation?
An equation is consist of two expressions. At least one of the expression contain a variable.
Given that, the cost unit bottle of soda is $3.
The cost of unit bag popcorn is $4.
Assume that she bought s number of soda bottle and p number of bags of popcorn.
Then the cost of s number of soda bottle is $3s.
The cost of p number of bags of popcorn $4p.
She spent $26 in total.
Therefore
3s + 4p = 26.....(i)
She bought 7 things from the shop.
Therefore,
s + p =7 .....(ii)
Solve equation (i) and (ii) by using elimination method:
Multiply equation (ii) by 3 and subtract it from (i)
3s + 4p = 26.
3s + 3p =21
(-) (-) (-)
_________
p = 5
Putting p = 5 in equation (ii)
s + 5 = 7
s = 2
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A map has a ratio of 1:4000. Find the actual distance, in metres, which is represented by 6.4 cm on the map.
Show working
The scale of a map is the relationship between the distance on the map and the actual distance. In this case, the scale of the map is 1:4000, which means that 1 unit on the map represents 4000 units in the actual distance. To find the actual distance that is represented by 6.4 cm on the map, we need to convert the distance on the map to the same unit as the actual distance. Since 1 cm is equal to 0.01 m, 6.4 cm is equal to 6.4 * 0.01 = 0.064 m.
Now we can use the scale of the map to convert the distance on the map to the actual distance. We can set up the following proportion:
0.064 m / 1 = x / 4000
Where x is the actual distance in metres. Solving for x, we get:
x = 0.064 m * 4000 = 256 m
Therefore, the actual distance represented by 6.4 cm on the map is 256 m.
two dice are thrown. what is the probability that the sum of the numbers appearing on the two dice is 8, if 3 appears on the first?
If 3 appears on the first die, then the sum of the numbers on the two dice can be 8 only if 5 appears on the second die. The probability of rolling a 5 on a single die is 1/6, so the probability of rolling a 3 and a 5 on two dice is 1/6 * 1/6 = 1/36. This means that the probability of rolling a sum of 8 when 3 appears on the first die is 1/36.
Capital Cars rents a compact car for 3
days for $132. How much does it cost
to rent the car for 1 day?
Answer: $44
Step-by-step explanation:
Select the correct answer.
Which expression is equivalent to this quotient?
Answer:
[tex]$\frac{5}{8}$[/tex]
Step-by-step explanation:
. finding numbers the sum of two nonnegative numbers is 20. find the numbers if (a) the sum of their squares is as large as possible; as small as possible. (b) one number plus the square root of the other is as large as possible; as small as possible.
When the sum of their squares is as largest as possible the numbers are 0 and 20, when the sum of their squares is as small as possible, the numbers are 10 and 10
Sum of the two numbers = 20
First we have to find the sum of their squares is as large as possible
Consider the first number as x and second number as y
To get the largest values the value of x or the value of y should be zero
Then the two numbers are 0 and 20
To get the small as possible
x^2 + (20-x)^2 = x^2 + x^2 - 20x +400
= 2x^2 -20x + 400
= 2(x^2 - 10x + 100)
The one number will be 10 and the other number will be 10
Therefore, to get the largest value the numbers will be 0 and 20 and to get the smallest value the numbers will be 10 and 10
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Determine the coordinates of W(−7, 4) after a reflection in the line y=9
The coordinate of the reflection about the line y = 9 is thus (7, 4)
What is reflection?Reflection is a transformation in which an object is flipped over a line.
How to find the coordinates of W(−7, 4) after a reflection in the line y = 9?We know that to reflect W(-7, 4) over the line y = 9, the distance of the point W and its reflection from the line y = 9 must be the same.
The distance of point W(-7, 4) from the line y = 9 is d = 9 - (- 7) = 9 + 7 = 15
So, the x - coordinate of the reflection from the line y = 9 is x = 15 - 9 = 7
Since the y - coordinate of the point W, does not change, the coordinate of the reflection about the line y = 9 is thus (7, 4)
So, the coordinate of the reflection about the line y = 9 is thus (7, 4)
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Pls Help also don't make it plagiarized, please look at the image
Proportional functions are used to express direct variation in graphs.
The graph shows a straight difference.
How to determine the type of graph?
From the graph, we have the following ordered pairs
(x, y) = (0, 0), (2, 4) and (3, 9)
We can rewrite it as:
(x,x^2) = (0,0^2), (2,2^2) and (3,3^2)
The above means that, the equation of the graph is:
y = x²
It means, y varies directly to the square of x
Where, the proportionality constant is equal to 1
Therefore, the graph represents a direct variation
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which triangle pairs are not necessarily congruent? select all that apply
The second triangle pairs are not necessarily congruent.
Option 2 is true.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
There are some triangles is shown in figure.
Now,
We know that;
Two triangles are congruent by theorem of SAS , ASA theorem.
So, When the ''two sides and one angle'' or ''two angle and one side'' are equal to another triangle then the triangles are congruent.
Here, In second option we have;
Only angles are equal, which make them similar not congruent.
Thus, We get;
The second triangle pairs are not necessarily congruent.
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what number would you be rather guessing correctly? the number of rolls of a fair six-sided die will
The number of rolls of a fair six sided die will be 1/6.
A cube (plural "cubes") is a solid with marks on each face. Since the faces are usually all of the same shape, the dual of the Platonic solids and the Archimedean solids is a natural choice. You can "roll" a die by throwing it in the air and letting it rest on one of its faces. Dice are used in many games to choose random numbers to bet on, and are used in board and role-playing games to determine how many squares to move, the outcome of a competition, etc. Coins are a degenerate two-sided case of dice.
In probability theory, an outcome is the possible outcome of an experiment or trial. Each possible outcome of a given experiment is unique, and different outcomes are mutually exclusive (only one outcome occurs in each trial of the experiment). All possible outcomes of an experiment form an element of sample space.
According to the question,
When a dice is thrown, number of possible outcomes =
1, 2, 3, 4, 5, 6 = 6 = n
Here, 6 occurs one time, i.e. m = 1
Thus, Probability of getting a number 6 = 1/6
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Construct the simplest polynomial with integer coefficients with the given roots:
√5,7,-1
Sasha and Jeffrey each want to run for president of their school's student body council. In order to do so, they must collect a certain number of signatures and get a nomination. So far, Sasha has 15 signatures, and Jeffrey has 17. Sasha is collecting signatures at an average rate of 6 per day, whereas Jeffrey is averaging 4 signatures every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How long will that take? How many signatures will they both have?
Candice and Porter will have collected 23 signatures each in one day using a system of equations.
What are equations?Equations are mathematical statements that claim that two expressions are equal or equivalent.
Equality is depicted using the equation sign (=). Candice Porter
The number of signatures collected for nomination 21 18
Average collection of signatures per day 2 5
Let the total signatures collected by Candice on day x = 21 + 2x
Let the total signatures collected by Porter on day x = 18 + 5x
The day the two candidates will have collected the same signatures is set as equality:
21 + 2x = 18 + 5x
21 - 18 = 5x - 2x
3 = 3x
x = 1
Total signatures collected by on day 1:
Candice = 21 + 2x = 21 + 2(1) = 23
Porter = 18 + 5x = 18 + 5(1) = 23
Thus, using a system of equations, it will take Candice and Porter 1 day to collect the same number of signatures, and each will have 23 signatures.
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How do you write 0.85 as a percent?
Answer: 85%
Step-by-step explanation:
Since percentages are numbers/ratios expressed as a fraction of 100, 85/100 becomes 85%
How do you simplify the expression 1+tan^2θ?
The tangent theta is a Trigonometric function, the simplified value of 1 + tan²θ is sec²θ.
What is Trigonometry function ?Trigonometric functions are also called circular functions. They are easily defined as functions of triangle angles. This means that the relationships between the angles and sides of triangles are given by these trigonometric functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant. Also read the triangle identity here.
We have given an expression, 1 + tan²θ
we know that , tanθ = sinθ /cosθ
sin²θ + cos²θ =1 and 1/cosθ = secθ
Now, 1 + tan²θ = 1 + sin²θ/cos²θ
taking LCM cos²θ
=> 1 + tan²θ = (cos²θ + sin²θ )/cos²θ
=> 1 + tan²θ = 1/cos²θ
=> 1 + tan²θ = sec²θ
Hence, the required expression is sec²θ.
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How do you solve 2^x=20?
Answer:
x=4.321928
Here’s your explanation
Let's solve your equation step-by-step.
2^x=20
Solve Exponent.
2^x=20
log(2^x)=log(20) (Take log of both sides)
x*(log(2))=log(20)
x=log(20)
log(2)
Then you get your answer x=4.321928
Step-by-step explanation:
Take the log of both sides:
log2(2^x) = log2(20)
xlog2(2) = log2(20)
x(1) = log2(20)
x = log2(20) ≈ 4.322
Which of the following iS benefit to using The random sample allows for different treatments to be assigned: causal relationship can be determined_ The results of the observational study can be generalized to the population. A random sample is the easiest method of data collection. The distribution of the sample will match the distribution of the population
The advantage of employing a random sample is (C) that the population can be generalized from the findings of the observational study.
What is a random sample?In statistics, a simple random sample is a subset of persons taken from a larger set in which a subset of individuals is chosen randomly, all with the same probability.
It is a method of choosing a sample at random.
The outcomes of the observational study can be generalized to the population.
To construct a simple random sample, there are six steps: (a) defining the population; (b) picking your sample size; (c) listing the population; (d) assigning numbers to the units; (e) discovering random numbers, and (f) selecting your sample.
Therefore, the advantage of employing a random sample is (C) that the population can be generalized from the findings of the observational study.
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Correct question:
Which of the following is a benefit to using a random sample for an observational study?
a. The random sample allows for different treatments to be assigned.
b. A causal relationship can be determined.
c. The results of the observational study can be generalized to the population.
d. A random sample is the easiest method of data collection.
e. The distribution of the sample will match the distribution of the population.
What number is 32% of 50?
Answer: 16
Step-by-step explanation:
32% of 50 = 16
15. Find m
X=3
please help due today
Answer:
11x - 2 = 6x + 13 (corresponding angles)
5x = 15
x = 3
This graph shows the weights of some squashes at farmers' market: Weights of squashes W X 8 3 8 5 6 3 Pounds How much heavier is the heaviest squash than the lightest squash? Write your answer as proper fraction, mixed number, or whole number: pounds Submit dontt know thls yet > 9.52
1/2
what is whole number?
All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well.
According to question,
heaviest squash than the lightest squash are,
[tex]7/8-3/8=4/8[/tex]
[tex]=1/2[/tex]
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a landscaper is designing a flower garden in the shape of a trapezoid he wants the shorter base to be 2 yards greater than the height of the trapezoid h and the longer base to be
The length of the bases of the trapezoid shape yard will be 18 yards and 22 yards.
What is a Trapezoid?A quadrilateral with at least one set of parallel sides is called a trapezoid in American and Canadian English.
In British and other varieties of English, it is termed a trapezium.
In Euclidean geometry, a trapezoid is a convex quadrilateral by definition.
The parallel sides are called the basis of the trapezoid.
So, we have:
The height should be 3 yards higher than the shorter base.
b₁=h+3
The height should be 3 yards higher than the shorter base.
b₂=h+7
Formula for Area of trapezoid = 1/2(b₁+b₂)h
Now, using the formula, calculate as follows:
150=1/2(h+3+h+7)h
150=(2h+10)h/2
150=2h²+10h/2
150=2h²+5h
h²+5h-150=0
h²+15h-10h-150=0
h(h+15)-10(h+15)=0
(h-10)(h+15)=0
h=10 or h-15
h should be positive:
b₁=h+3=15+3=18
b₂=h+7=15+7=22
Therefore, the length of the bases of the trapezoid shape yard will be 18 yards and 22 yards.
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Complete question:
A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. the total area of the flower garden is 150 square yards. what will the length of each base be
