At a meeting for math enthusiasts, two entrance fees are charged. Anyone who knows the code word “algemath” only pays 2 euros. Those who are unlucky and do not know the code word pay three euros more. You know that 7338 people were present and that the cashier received 17487 euros. How many people knew the password?
Answers
Number of People who knows the Code are 6401
What is Linear Equation in Two Variable?
A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Solution:
Let, Number of People who kows the Code be x
Number of Peoplee who do not know the Code be y
According to the Question:
x + y = 7338 ----------(i)
2x + 5y = 17487 ----------(ii)
Multiplying Equation (i) by 2
2x + 2y = 14676 ---------(iii)
Substracting Equation (iii) from Equation (ii)
3y = 2811
y = 937
This means x = 6401
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Related Questions
if 9 kg of sugar cost to 238.50 how much sugar can be bought for 371
Answers
Answer:
14 kg
Step-by-step explanation:
Set up a proportion:
9/238.5 = x/371
Cross multiply.
9 x 371 = 3339
238.5 times x = 238.5x
238.5x = 3339
Divide by 238.5 on both sides.
3339/238.5 = 14
Im so confused- please help
Answers
Step-by-step explanation:
a/q
x + x - 3 + 2x - 9 = 36
4x - 12 = 36
4x = 36 + 12 = 48
x = 48/4 = 12
x = 12
so,
x = 12
x - 3 = 12 - 3 = 9
2x - 9 = 2(12) - 9 = 15
we know,
area = 1/2 × base × height
so,
→ 1/2 × 12 × 9
→ 1 × 6 × 9
→ 54 inches.
HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE
Find the surface area of the regular pyramid.
Answers
The surface area of the regular pyramid as given in the task content is; 16m².
What is the surface are of the regular pyramid?The task content requires that the surface area of the pyramid be determined. This surface area can therefore be evaluated as follows;
Surface area = (2×2) + 4((1/2)×2×3) = 4 + 12 = 16m².
The surface area of the regular pyramid is therefore; 16m².
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6. A company car purchased for $39,600 depreciates at 12% per annum. What is the car
worth after 3 years?
Answers
Answer:
$26,986.29
Step-by-step explanation:
We can use the formula for calculating the depreciation of an asset over time:
wor
\(\bold{D = P(1 - \frac{r}{100} )^t}\)
where:
D= the current value of the asset
P = the initial purchase price of the asset
r = the annual depreciation rate as a decimal
t = the number of years the asset has been in use
In this case, we have:
P = $39,600
r = 12% = 0.12
t = 3 years
Substituting these values into the formula, we get:
\(D= 39,600(1 - \frac{12}{100})^3\\D= 39,600(1 - 0.12)^3\\D= 39,600*0.88^3\\D= 39,600*0.681472\\D=26986.2912\)
Therefore, the car is worth approximately $26,986.29 after 3 years of depreciation at a rate of 12% per annum.
Answer:
$26,986.29
Step-by-step explanation:
As the car's value depreciates at a constant rate of 12% per annum, we can use the exponential decay formula to create a function for the value of the car f(t) after t years.
Exponential Decay formula\(\boxed{f(t)=a(1-r)^t}\)
where:
f(t) is the value of the car (in dollars) after t years.a is the initial value of the car.r is the depreciation rate (as a decimal).t is the time period (number of years after purchase).In this case, the initial value is $39,600, and the rate of depreciation is 12% per year. Therefore, the function that models the value of the car after t years is:
\(f(t)=39600(1-0.12)^t\)
\(f(t)=39600(0.88)^t\)
To calculate the value of the car after 3 years, substitute t = 3 into the function:
\(\begin{aligned} f(3)&=39600(0.88)^3\\&=39600(0.681472)\\&=26986.2912\\&=26986.29\;(\sf 2\;d.p.)\end{aligned}\)
Therefore, the car is worth $26,986.29 after 3 years.
How do I do number 1??
Help me it’s due tomorrow!!!
Answers
The values of x and y are 20 and 12.
The values of x and y are -3 and 2.
We have,
In a parallelogram,
- Opposite sides are congruent:
The opposite sides of a parallelogram have equal lengths.
- Opposite angles are congruent:
The opposite angles of a parallelogram have equal
Now,
a)
Opposite angles are congruent:
So,
5x + 29 = 7x - 11
29 + 11 = 7x - 5x
40 = 2x
2x = 40
x = 40/2
x = 20
And,
3y + 15 = 5y - 9
15 + 9 = 5y - 3y
24 = 2y
y = 24/2
y = 12
b)
Opposite sides are congruent:
So,
-6x = -4x + 6
-6x + 4x = 6
-2x = 6
x = -3
And,
7y + 3 = 12y - 7
12y - 7y = 3 + 7
5y = 10
y = 2
Thus,
The values of x and y are 20 and 12.
The values of x and y are -3 and 2.
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Someone please help and show work
Answers
Mean - this is the average. Add up the numbers and divide by the count of the numbers in the data set.
11+13+14+16+17+18+20+20+21+24+25+29 = 228
There are 12 numbers, so divide by 12.
228/12 = 19. The mean is 19.
Median - - - this is the MIDDLE number. Your data is already in numerical order (hooray!) so there are 12 numbers. Since it's even, we'll take the average of the 2 middle numbers. The 6th number is 18 and the 7th number is 20. The average of these is 19. So the median is 19.
(Side note: yes, median and mean can be the same.)
Mode - - - this is repeat/most common numbers! 20 repeats. 20 is the mode.
Range - - - biggest number is 29, littlest is 11. The range is 29-11 = 18.
If PQ¯ is tangent to circle R at point Q, and PS¯ is tangent to ⊙R at point S, what is the perimeter of quadrilateral PQRS?
Answers
The perimeter of PQRS would depend on the lengths of the tangent segments and the lengths of the intercepted arcs. Without specific measurements, we cannot determine the precise perimeter.
To determine the perimeter of quadrilateral PQRS, we need more information about the lengths of the sides or the relationship between the sides and angles. Without specific measurements or additional details, we cannot calculate the exact perimeter of the quadrilateral.
However, we can provide some general information.Since PQ¯ is tangent to circle R at point Q, it is perpendicular to the radius drawn from the center of the circle to point Q. Similarly, PS¯ is tangent to circle R at point S, so it is perpendicular to the radius drawn to point S.
The quadrilateral PQRS is formed by the tangents PQ¯ and PS¯ along with the two arcs intercepted by these tangents on the circle R.
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(x³ ⋅ y⁴ ⋅ z)³ ⋅ (x⁵ ⋅ y ⋅ z³)²
Answers
Answer:
y - x + z
Step-by-step explanation:A good way to tackle this problem is to check for the signs of all the variables. In your original expression, x-y+z, x and y are positive and y is negative.
the two sides of the caution sign form a triangle. Each of those side lengths measure 24 inches. two of the angles in the triangle measure 70 each. classify the triangle and determine the measure of the third angle in the triangle.
Answers
Answer:
Step-by-step explanation:
Since two of the angles in the triangle measure 70 degrees each, the triangle must be an isosceles triangle. An isosceles triangle has two equal sides and two equal angles, so the third angle must also measure 70 degrees. Thus, the measure of the third angle in the triangle is 70 degrees.
A closet in Shivani's house is 2 yards by 1 yard. How much would it cost to put a new floor in the closet if the flooring costs $38.00 per square yard?
Answers
The amount it would cost to put a new floor in the closet is $76.00
Calculating how much it would cost to put a new floor in the closetFrom the question, we are to calculate how much it would cost to put a new floor in the closet
From the given information,
A closet in the house is 2 yards by 1 yard.
To determine how much it would cost to put a new floor in the closet,
First,
We calculate the area of the closet
Area of the closet = 2 yard × 1 yard
Area of the closet = 2 square yards
Now,
From the given information,
The flooring costs $38.00 per square yard
Thus,
The amount it would cost to put a new floor in the closet is
2 × $38.00
= $76.00
Hence,
The amount it would cost is $76.00
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an employer pays 22 for 2 hours. use the ratio table to determine how much she chargesfor 5 hours
Answers
The employer will charge $55 for 5 hours
How to calculate the amount charged for 5 hours ?The first step is to calculate the amount charged for an hour
22= 2
x= 1
cross multiply
2x= 22
x= 22/2
x= 11
The amount charged for 5 hours can be calculated as follows
11= 1
y= 5
cross multiply
y= 55
Hence $55 will be charged for 5 hours
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The figure cda and xyz if cd=26 what is xy
Answers
Answer:
26 mm
Step-by-step explanation:
Δcda ≅ Δxyz
If cd=26 mm then xy=cd= 26 mm
A statue of Abraham Lincoln casts a 9-foot shadow at the same time the White House casts a 48-foot shadow. If the White House is 70 feet tall, how tall is the statue of Abraham Lincoln?
Answers
Answer: The statue, originally intended to be only 10 feet tall, was on further consideration enlarged so that it finally stood 19 feet tall from head to foot, the scale being such that if Lincoln were standing he would be 28 feet tall.
Step-by-step explanation: hope this helps
Answer: 28 ft
Step-by-step explanation:
Determine whether the set {v1, v2} is a basis for R
2.
Answers
The given set {v1,v2} is a basis for \(R^{2}\).
How to determine if set is a basis of vector space?Assume that for some n, V is a subspace of \(R^{n}\). A collection of vectors from V, B = {v1, v2,... vr}, is said to be a basis for V, if B spans V and is linearly independent. The collection cannot serve as a basis for V if either of these conditions is not met.
If a vector spans V and contains enough vectors, it can be written as a linear combination of the vectors in a collection of vectors. The collection doesn't contain so many vectors that some of them start to depend on the others if it is linearly independent. Therefore, a basis seems to be the ideal size: It's big enough to span the space but not so big as to be dependent.
Given collection of vectors v1 and v2 can be represented (as per image given in question) as
v1= (i+j)
v2= (-i+j)
The collection { (i + j), (-i+j)} is a basis for \(R^{2}\).
It is linearly independent, since neither i + j nor -i + j is a multiple of the other. It spans all of \(R^{2}\) because every vector in \(R^{2}\) can be expressed as a linear combination of i + j and -i + j.Hence, the given set {v1,v2} is a basis for \(R^{2}\).
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Amy bought 4 lbs.,8 oz. of turkey cold cuts, and 6 lbs., 15 oz. of ham cold cuts. How much did she buy in total? (You should convert any ounces over 15 into pounds)
Answers
Add the ounces
15+8 is 23 oz
When converting to a pound you can simply divide 23/16 or subtract in this case since it is a small number
23-16 is 7
in 23 oz it is equal to 1lb and 7 oz
Finally add the original 4, the 6 and the1lb and 7oz making it
11lbs,7oz
Which number doesn't share the same pattern as
2,20, 4,8,300
Answers
A square painting has an area of 9 square metres. How long is each side?
Answers
Answer:
2
Step-by-step explanation:
One hundred adults were asked to name
their favorite sport, and the results are
shown in the circle graph. What percent of
adults preferred soccer or baseball?
Volleyball, 3
Other. 4
Golf, 7
Soccer, 11.
Baseball, 14
Football,39
Basketball, 22
Answers
The percentage of adults who preferred soccer or basketball is 25%.
What is circle graph?The size of each slice in a circle graph, also called a pie chart, indicates the proportion or percentage of each category, and the information is displayed as a circle divided into sections or slices. Circle graphs are frequently used to compare various categories in a dataset or to illustrate how various components contribute to the overall. They are particularly helpful when working with data that can be broken down into distinct categories, such survey results or demographic data.
From the circle graph we see that, percentage of adults who preferred soccer is 11%, and the percentage who preferred baseball is 14%.
Thus,
11% + 14% = 25%
Hence, the percentage of adults who preferred soccer or basketball is 25%.
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Select the correct answer.
Simplify:
3x3² +8÷2-(4+3)
A.
30
B. 32
OC. 23
OD. 24
I need it asap pleasee
Answers
Answer:
OD:24
Step-by-step explanation:
3*3”2 = 27
-(4+3) = -7
8divided by 2= 4
27 + 4 -7=24
A gardener has a bag of flower seeds. Half of the seeds are roses, one fourth are gardenias,
and one fourth are irises.
a. P(gardenias)
b. P(not gardenias)
Answers
tyler orders a meal thats 15$ if the tax rate is 6.6% how much will the sales tax be on tylers meal?
Answers
Answer : 0.99
Explanation : 15 * 6.6/100 For The Tax.
Total : 15.99
206) A recipe for cupcakes calls for 3-
3
10
200
7
sugar. Julio accidentally put in 4-
10
How many extra cups did he put in?
cups of
cups.
Answers
Julio accidentally put in an extra 1/10 cup of sugar.
To calculate the number of extra cups of sugar that Julio put in, we need to find the difference between what the recipe called for (3/10 cups) and what he actually added (4/10 cups).
The difference can be calculated as follows:
Actual amount - Required amount = Extra amount
= 4/10 - 3/10
= 1/10
Therefore, Julio accidentally put in an extra 1/10 cup of sugar.
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find the value of x
a) 2:5=8:x
Answers
Step-by-step explanation:
solution:
given,
or, 2:5 = 8:x
or, 2/5 = 8/x [ changing into fraction form ]
or, 2x = 40 [ doing cross-multiplication ]
or, x = 20 [ dividing both sides with 2]
20+8(x-11)=-12 answer and how to solve it?
Answers
Answer: x=7
Step-by-step explanation:
To solve for x, you want to use algebraic properties.
20+8(x-11)=-12 [distribute]
20+8x-88=-12 [combine like terms]
8x-68=-12 [add both sides by 68]
8x=56 [divide both sides by 8]
x=7
Now we know that x=7.
what equation is the blue line
Answers
Hello!
the equation of the blue line is 3y + 0.5x
The given figure shows the intersection of plane S with a square pyramid.
Which shape depicts the cross-section?
OA.
D.
E
Answers
The cross section can be of these shapes square and triangle are; A, D
What is cross-segment ?A cross-segment is a plane segment that is a segment of a three-dimensional item that is parallel to one among its planes of symmetry or perpendicular to considered one of its traces of symmetry.
An instance of a go-segment would be a circle. A cross-section is seen whilst a 3-dimensional picture is reduce through a plane.
Then the case of the cone, a circular go-segment emerges while the cone is cut parallel with its base
The go-sectional region is the location of a 3-dimensional shape which is acquired whilst a three-dimensional object - inclusive of a cylinder - is sliced perpendicular to some designated axis at a point.
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y2-4y+4/(2-6y) x (2y+4)/(3y2-12)
Answers
Answer:
what is the question? please ask a question.
the dimension of the confirms room or 7.2 M * 11 M what is the area of the conference room
Answers
Step-by-step explanation:
Just multiply the two dimensions to get m^2 area
7.2 m * 11 m = 79.2 m^2
The picture below is being enlarged by a scale factor of 2.5 how many inches of framing will the picture require
Answers
Answer:
Multiply the given numbers by a factor of 2.5, then find the perimeter by adding up all 4 of the sides.
Step-by-step explanation:
While there isn't a picture given, it can be assumed that the shape given is a rectangle.
Then, simply multiply all 4 sides by a factor of 2.5, since that's the number it is being enlarged by.
Then to find the "framing" of said rectangle, add up all 4 of the sides that you just calculated to find the perimeter.
-7 = z/-6
\( - 7 = \frac{z}{ - 6} \)
What is the answer?
Answers
-7 (-6) = z
42 = z
Z = 42