There are 1250 skiers and 2500 snowboarders bought season passes.
What is substitution method:The substitution technique is a mathematical approach for solving simultaneous linear equations. The value of one variable with one equation is substituted in the second equation, as the name implies.
According to the given information:The ratio of 1:2 indicates that there is one skier for every two snowboarders.
Let S stand in for the skier.
B should symbolize the snowboarder.
This condition is equivalent to = 1:2 = S:B.
Alternatively, 2S = B.
B - S = 1250
2S - S = 1250
Applying substitution method.
s = 1250
B = 2S = 2(1250) = 2500
B = 2500
There are 1250 skiers and 2500 snowboarders.
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I understand that the question you are looking is:
The Speedy Fast Ski Resort has started to keep track of the number of skiers and snowboarders who bought season passes. The Ratio of the number of skiers who bought season passes is 1:2.If 1,250 more snowboarders bought season passes than skiers, how many skiers bought season passes?
PLease help <3 and please dont give an answer just for points. I need it to be correct
The solution to the linear equations in three variable are x = 5, y = -11, and z = 3.
What is a linear equation?It is defined as the relation between three variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The three linear equations:
2x - y + 4z = 33 ..(i)
x + 2y - 3z = -26 ...(ii)
-5x - 3y + 5z = 23 ...(iii)
After solving the above linear equation by elimination method:
From the equation (i):
[tex]x=\dfrac{33+y-4z}{2}[/tex] ....(iv)
Plug the above value in the equation (ii) and (iii)
[tex]\rm \dfrac{33+y-4z}{2}+2y-3z=-26\\\\\\\\ -5\cdot \dfrac{33+y-4z}{2}-3y+5z=23[/tex]
After solving the above linear equation in two variables:
y = -11
z = 3
Plug the above values in the equation (iv)
We get the value of x:
x = (33-11-3(4))/2
x = (33-11-12)/2
x = 10/2
x = 5
Thus, the solution to the linear equations in three variable are x = 5, y = -11, and z = 3.
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Which of the following represents the range of the graph of F(x) below?
A. x<2
B. All real numbers
C. y ≤ 2
-6
D. x≤2
FOX
6
(0, 2)
5
[tex]y \leqslant 2[/tex]
Which unit is a derived unit?
O meter
Odensity
O ampere
O second
density
a derived unit is something that comes from using base units in mathematical operations.
For this 10-point assignment, please describe the context of the mathematics by doing the following:
• Explain how circles are related to the Pythagorean Theorem. You may include triangles in your discussion, too.
• One city is located at (45, -123) and the other is located at (53.65, -6.7). describe how you would compute the distance between the
cities, momentarily ignoring the curvature of the Earth (what would you do if you didn't ignore the curvature?).
Circles are related to Pythagorean theorem in the sense that the equations are alike and the sides conforms to:
radius ≅ hypotenuse(x2 - x1)^2 ≅ opposite(y2 - y1)^2 ≅ adjacentThe distance between the two cities is 116.62 units (ignoring curvature)
If the curvature is not ignored then we sort for the angle subtended
How to compare circle to Pythagorean theoremThe Pythagorean theorem relates the square of hypotenuse, square of the opposite, and the square of the adjacent as follows
hypotenuse^2 = opposite^2 + adjacent^2 equation 1
Representing a circle in a coordinate axis will give it values in coordinate form. Assuming the coordinate of the center is (x1, y1) and a point in the circumference is (x2, y2). The radius of the circle, r is given as
r^2 = (x2 - x1)^2 + (y2 - y1)^2 equation 2
comparing equation 1 and 2 shows that
radius ≅ hypotenuse, (x2 - x1)^2 ≅ opposite, and (y2 - y1)^2 ≅ adjacent
How to find the between two citiessay A = (45, -123)
say B = (53.65, -6.7)
Let the distance between the two cities be d
d^2 = (53.65 - 45)^2 + (-6.7 - (-123) )^2
d^2 = 8.65^2 + 116.3^2
d = √13600.5125
d = 116.62 units (ignoring the earth curvature)
if the curvature is not ignored then we look for the angle subtends
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Compare the number of cars in the world to those that are in the United States.
name the property illustrated by each statement of if t-13=52, then 52=t-13
The property illustrated by each statement of if t-13=52, then 52=t-13 is commutative
t-13=52, then 52=t-13
The property illustrated to each statement is commutative because it shows that for some value of t both statements are equal.
In mathematics, a binary operation is commutative if changing the order of the operands does now not alternate the result. it's far a essential belongings of many binary operations, and lots of mathematical proofs rely on it. most acquainted as the call of the assets that says something like "3 + four = 4 + 3" or "2 × 5 = 5 × 2",
the property also can be utilized in greater superior settings. The name is wanted because there are operations, which includes department and subtraction, that do not have it (for example, "3 − five ≠ 5 − 3");
such operations are not commutative, and so are called noncommutative operations.
The idea that easy operations, along with the multiplication and addition of numbers, are commutative become for many years implicitly assumed.
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How many full cases and additional items are needed to fulfill the order of 60 items ordered and 14 items per case
Answer:
Step-by-step explanation:
Answer:
there are many case and additional
items are needed to fulfill to order
of60items ordered
Step-by-step explanation:
1. The height of a right triangular prism is 1 inches. Each side of the triangular base measures 10 inches, and the height of the base is 82 inches. The triangular prism is placed atop a cube whose side measures 10 inches so that one of the triangular prism's bases lies completely on one side of the cube.
What is the surface area of the solid formed?
If a right triangular prism's height is 1 inch. The produced solid has the following surface area: = 2,930.05 in².
Right triangular prism describing:A polyhedron with six vertices, nine edges, and five faces is a right triangular prism. Regular prisms have all of their triangles faces equilateral. The prism's rectangular faces will be congruent in this situation.
What is the method for determining a triangular prism's total surface area?A triangular prism's total surface area is the sum of the areas of its three lateral faces (rectangles) as well as two bases (triangles). For something like the surface area of any prism, the most generic formula is:
According to the given data:Given:
Hight = 1 inches
Base of the prism = 10 inches.
The Hight if the base = 82 inches.
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
Surface area = 5(10× 10) + (0.5÷ 10 × 1) + 3(10× 82)
Surface area = 5(100) +0.05+ 3(810)
Surface area = 500 +0.05 + 2430
Surface area = 2,930.05 in²
The produced solid has a surface area of approximately = 2,930.05 in².
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Calculate marginal opportunity costs using graph showing oranges and cherries
To calculate marginal cost ; we use "subtract the quantity change from the overall cost change."
The potential cost of increasing orange output from 50 to 80 units was (250 – 200) = 50 cherries.
The potential cost of increasing cherry production from 100 to 200 units was (86-80) = 6 oranges.
Opportunity cost for an orange right now is,
equals 1.67 cherries.
Opportunity cost is therefore 3.34 cherries for two oranges.
One cherry's opportunity cost is,
0.06 orange units
1.8 oranges are the opportunity cost of 30 cherries.
Conclusion
a. Cherry 50
b. Oranges, six
c. Cherry 3.34
d. Oranges, 1.8
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convert 7 yards per minute to feet per second
(3 feet=1 yard)
Answer:
0.35 feet per second
Step-by-step explanation:
To start, there's 3 feet in 1 yard.
So, we have to convert the 7 yards per minute to feet.
7 x 3 = 21
Then, we have to convert 21 feet per minute to X amount of feet per second.
To note, there are 60 seconds in a single minute
Therefore, you have to divide 21 by 60 to find the amount of feet in one second.
21 / 60 = 0.35
The answer is 0.35 feet per second
Please help i will give brainliest :)
The table below displays the student loan balances for two college graduates in 2010 (the year of their graduation).
2010
Mr. Jones
$6,400
Ms. Smith $27,200
Expand each part and complete the questions.
Part 1 - Mr. Jones
In the 3 years since graduation, Mr. Jones' loan balance has decreased by 71.4%. Calculate the change in his loan balance. Round your result
Between 2010 and 2013, Mr. Jones' student loan balance
Part 2-
Using proportions, the correct statement is given as follows:
Between 2010 and 2013, Mr. Jones' student loan balance decreased by 4750 dollars.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
His balance is only 100 - 71.4 = 28.6% of the initial balance of $6,400, hence it is currently of:
0.286 x 6400 = $1830.
The decrease was of:
6400 - 1830 = $4750.
Hence the correct statement is:
Between 2010 and 2013, Mr. Jones' student loan balance decreased by 4750 dollars.
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A seven-digit number has a 9 in the thousands place, a 2 in the
hundred thousands place, a 6 in the greatest place-value position, a 4
in the ten thousands place, a 1 in the tens place, a 5 in the least
place-value position, and a 7 in the hundreds place. What is the
number?
Answer: 6,249,715
Step-by-step explanation:
The number sequence is built like this:
Millions , hundred thousands + ten thousands + thousands , hundred + tens
+ ones
The millions place is the greatest value here, and the ones place is the least value in every situation involving whole numbers.
8.
-2|3x+1|=-10
hsiaodkmakakcmd help
Answer: x=-2, 4/3
Step-by-step explanation:
-2|3x+1|=-10
-2|3x+1| / (-2) = -10/(-2)
-2|3x+1| / (-2) = 5
|3x+1|=5
3x+1=5
3x=4
x=4/3
3x+1=-5
3x=-6
x=-2
x=-2, 4/3
(b) After his first month he had more than he expected to have due to interest the bank provided. This let
Rob come up with a better expression, w^2/25 +45w+155, where w is the number of weeks. How much will he have in 1 year?
The amount he is expected to have due to interest in the bank after a year is; $2603.16
How to solve algebraic equations?We are given the equation;
w²/25 + 45w + 155
where;
w is number of weeks
Now, this equation above represents the function of the amount he is expected to have due to interest in the bank. Thus;
After 1 year, the number of weeks is 52 weeks. Thus, we now have;
A(52) = 52²/25 + 45(52) + 155
A(52) = $2603.16
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To the nearest 10 thousand
When the number given of 15,587,252 is rounded off to the nearest 10 thousand, the result would be 15,590,000.
How to round to the nearest ten thousand?When rounding to the nearest ten thousand, you would look at the thousands number which is the 4th number before the decimal.
If this digit if more than 5, then you round the ten thousandth digit up to the nearest whole number. If the digit is less than 5, then you round down.
The number 15,587,252 has the thousands number as 7 which is more than 5 so the ten thousands number will be round up to:
= 15,590,000
Rest of the question:
Find out 15,587,252 to the nearest 10 thousand.
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help with this please.
Using integrals, it is found that the cumulative distribution function(cdf) at x = 2.27 is given by:
P(X ≤ 2.27) = 0.897.
How to find the cumulative distribution function of a distribution?The cumulative distribution function of a distribution given by f(x) at a value of x = x* is given by the following integral:
[tex]\int_{-\infty}^{x^{\ast}} f(x) dx[/tex]
For this problem, the distribution is given by:
[tex]f(x) = e^{-x}, x > 0[/tex]
Hence, at x = 2.27, the cdf is given by:
[tex]\int_{0}^{2.27} e^{-x} dx[/tex]
The infinity was replaced by 0 because the lower bound of the definition of the distribution is of 0. Hence:
[tex]\int_{0}^{2.27} e^{-x} dx = -e^{-x}|_{x = 0}^{x = 2.27}[/tex]
Applying the Fundamental Theorem of Calculus:
P(X ≤ 2.27) = -e^(-2.27) + e^0 = -e^(-2.27) + 1 = 0.897.
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Find the measure of the exterior angle.
(Click document to see image.)
Answer:
65°
Step-by-step explanation:
Exterior angle property:Exterior angle of a triangle equals the sum of opposite interior (remote) angles.
3x - 10 = x + 15 + 25
3x - 10 = x + 40
Add 10 to both sides,
3x = x + 40 + 10
3x = x +50
Subtract 'x' from both sides,
3x- x = 50
2x = 50
Divide both sides by 2
x = 50÷ 2
x = 25
Exterior angle = 3x -10
= 3*25 - 10
= 75 - 10
= 65°
Find a possible formula for the exponential function graphed below.
Check the picture below.
[tex]{\LARGE \begin{array}{llll} y = ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \textit{we know that} \begin{cases} x=0\\ y=40 \end{cases}\implies 40=ab^0\implies 40=a(1)\implies 40=a \\ ~\hfill \underline{y = 40b^x} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{we also know that} \begin{cases} x=3\\ y= 15 \end{cases}\implies 15 = 40b^3\implies \cfrac{15}{40}=b^3\implies \cfrac{3}{8}=b^3 \\\\\\ \sqrt[3]{\cfrac{3}{8}}=b\implies \cfrac{\sqrt[3]{3}}{\sqrt[3]{8}}=b\implies \cfrac{\sqrt[3]{3}}{2}=b~\hfill \underline{y = 40\left( \frac{\sqrt[3]{3}}{2} \right)^x}[/tex]
Identify the number of solutions of the system Of a linear equation. X+3y-z=2. X+y-z=0 3x+zy_3z=-1
System of liner equation [tex]x+3y-z=2[/tex],[tex]x+y-z=0[/tex] and [tex]3x+2y-3z=-1[/tex] has no solution.
What do you mean by system of linear equation?
A set of two linear equations with two variables is a system of linear equations.
Given:
[tex]x+3y-z=2[/tex] ---1
[tex]x+y-z=0[/tex] ---2
[tex]3x+2y-3z=-1[/tex] ---3
Rearranging the equation 2
[tex]z=x+y[/tex] ---4
Putting equation 4 in equation 1
⇒ [tex]x+3y-(x+y)=2[/tex]
⇒ [tex]x+3y-x-y=2[/tex]
⇒ [tex]2y=2[/tex]
⇒ [tex]y=1[/tex]
Putting equation 4 in equation 3
⇒ [tex]3x+2y-3(x+y)=-1[/tex]
⇒ [tex]3x+2y-3x-3y=-1[/tex]
⇒ [tex]-1y=-1[/tex]
⇒ [tex]y=1[/tex]
Putting value of y above
⇒ [tex]1=1[/tex]
Therefore, system of liner equation has no solution.
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-5x-20+8+16x simplify please show steps
Answer:-12+16x
Step-by-step explanation:
-5x-20+8+16x
-5x-12+16x
-12+16x
Answer: 11x-12
Step-by-step explanation:
(-5x)-(20)+(8)+(16x)It would be easier to rearrange this equation by degree (ie ax^2, ax^1, a)
(16x)-(5x)-(20)+(8)You cannot subtract ax^1 by a, but you can subtract ax^1 by ax^1 (16x-5x)
16x-5x= 11xWe can also subtract a by a (-20+8)
-20+8= -12Remember your positive and negative signs
Answer: 11x-12What’s the volume of the cone in terms of pi?
Answer:
83 [tex]\frac{8}{10}[/tex] π cm3
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] π ([tex]4^{2}[/tex])(5) = 83.7758040957
Lines a & m are parallel. Using the diagram below, what is the degree measure of angle 3?
Enter the numerical answer only. Example, if the answer is 12 degrees, only enter 12.
The angle ∠3 = 153° by alternate angle theorem.
What are parallel lines?Parallel lines are those lines that are equidistant from each other and never meet.
Parallel lines cut by a transversal, forms different angle relationship like alternate angles, corresponding angles, etc.
Line a and m are parallel lines . Therefore, angles 1, 2, 3, 4, 5, 153 degrees are related base on alternate and corresponding relationship.
Hence,
∠3 = 153°(alternate angles)
Alternate angles are congruent.
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What decimal are equivalent to to (5×10)+(2×1/100)?
Answer:50.02
Step-by-step explanation:
This is about proper writing of decimals. We are given;(5 × 10) + (2 × 1/100) From BODMAS, let us first solve what is inside both brackets;5 × 10 = 502 × 1/100 = 2/100 = 0.02Since we have solved what is in the brackets, next is to add both of them;50 + 0.02 = 50.02Thus, the decimal equivalent is 50.02
Answer: it is 50.02
Step-by-step explanation: the decimals are equivalent
A mother wants to invest $13000 for her children's education. She invests a portion of
the money in a bank certificate of deposit (CD account) which earns 4% and the
remainder in a savings bond that earns 7%. If the total interest earned after one year is
$780, how much money was invested at each rate?
The amount invested at 4% is $4,333.33
The amount invested at 7% is $8,666.67
What represents the amount invested at 4%?
Let assume that x is the amount invested in the bank certificate of deposit (CD account) which earns 4%, in essence, the interest earned at 4% is the amount of money invested multiplied by 4%
interest at 4%=4%*x=0.04x
amount invested at 7%=13000-x
interest at 7%=7%*(13000-x)
interest at 7%=910-0.07x
total interest=0.04x+910-0.07x
total interest=910-0.03x
total interest earned=780
780=910-0.03x
0.03x=910-780
0.03x=130
x=130/0.03
x=amount invested at 4%=$4,333.33
amount invested at 7%=$13,000-$4,333.33
amount invested at 7%=$8,666.67
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What is the slope of the line that passes through the points (-4,-7) and
(-2,-19)? Write your answer in simplest form.
Answer:
-1/3
Step-by-step explanation:
The slope of the line passing through the points (-2, 5) and (1, 4) is m = -1/3.
In the past month, Deandre rented 1 video game and 7 DVDs. The rental price for the video game was $3.20. The rental price for each DVD was $4.90. What Is
the total amount that Deandre spent on video game and DVD rentals in the past month?
Answer:
Deandre spent $36.50 on video games and DVD rentals in the past month.
Step-by-step explanation:
values
video game = $3.20
DVD = $4.90
let video games be represented with the variable v
dvd represented by the variable d
make an equation
7d + 1v = ?
plug in values
7(4.90) + 1(3.20) = ?
7 x 4.90 = 34.3
1 x 3.20 = 3.20
34.3 + 3.20 = 36.50
thus 7d + 1v = $36.50
Write the expression |x − 9| + |x − 6| without the absolute value symbols if x is in the given interval.
(−∞, 1)
Recall the definition of absolute value.
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
Now,
[tex]x<1 \implies x-9 \le -8 < 0 \implies |x-9| = -(x-9) = 9 - x[/tex]
and
[tex]x<1 \implies x-6 \le -6 < 0 \implies |x-6| = -(x-6) = 6 - x[/tex]
so that
[tex]|x-9| + |x-6| = (9-x) + (6 - x) = \boxed{15 - 2x}[/tex]
24.
How would the following triangle be classified?
isosceles acute
scalene right
isosceles right
Scalene acute
What is the domain of the function y= 2√x-6?
Answer:
Domain of the function:
In interval notation: [6, ∞)
In set notation: {x: x∈R, x≥6}
Step-by-step explanation:
Remember that the the domain of the square root function are all the values such is is bigger than zero. We can express the later in set notation: {x: x∈R, x≥0}, or in interval notation: [0, ∞)
This is because the square root is not defined, in the real numbers, for negative values.
So, to find the domain of our function, we just need to set the thing inside the radical grater or equal than zero and solve for x:
The domain of the function is all the numbers bigger than 6, including 6.
Domain of the function: x will have values greater than or equal to 6 .
In interval notation: [6, ∞)
In set notation: {x: x∈R, x≥6}
Given, that function y = 2√x-6
Domain of the square root function are all the values which is greater than zero.
Express the later in set notation:
{x: x ∈ R, x≥0},
Interval notation: [0, ∞)
This is because the square root is not defined, in the real numbers, for negative values.
Domain of function y,
[tex]y= 2\sqrt{x-6}[/tex]
[tex]x-6\geq 0 \\x\geq 6[/tex]
The domain of the function is all the numbers greater than 6, including 6. Thus domain of function : [6, ∞) .
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