Arvilla laid out the stones for a necklace in a big circle, with each stone spaced an equal distance from its neighbors. She then counted the stones in order around the circle. Unfortunately, before she finished counting she lost track of where she had started, but she realized that she could figure out how many stones were in the circle after she noticed that the sixth stone was directly opposite the seventeenth stone. How many stones are in the necklace?
Using proportions, it is found that there are 22 stones in the circle.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, the sixth stone was directly opposite the seventeenth stone, hence over half the circle, there was 11 stones.
Then, we apply the proportion, and get that:
0.5n = 11
n = 22.
There are 22 stones in the circle.
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A university's freshman class has 8900 students. 3471 of those students are majoring in Engineering. What percentage of the freshman class are Engineering majors?
Answer:
39%
Step-by-step explanation:
[tex]\frac{3471}{8900}[/tex] converted to a percentage = 39%, or 0.39 in decimal form.
During a science experiment, Cesar sets up a group of filter that removes contaminants from a liquid sample. Each filter removes 94.8% of the remaining contaminants. Which recursive formula describes the fraction of contaminants still remaining in the liquid sample after passing through n filters?
Using an exponential function, the recursive formula that describes the fraction of contaminants still remaining in the liquid sample after passing through n filters is given by:
[tex]A[n] = (0.052)^n[/tex]
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, considering an initial fraction of A(0) = 100% = 1, the decay rate is of r = 0.948, hence the formula is:
[tex]A[n} = (1 - r)^n[/tex]
[tex]A[n] = (0.052)^n[/tex]
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find the domain and range of the function shown in the graph given
what is the domain and the range?
[tex] - 6 \leqslant x \leqslant 6[/tex]
Range:[tex] - 5 \leqslant y \leqslant 5[/tex]
The graph of f(x) = 2x + 4 shifts six units to the right when it is replaced with the graph of f(x) = 2x-k What is the value of k?
02
04
06
O 10
The value of k in the function f(x) = 2x-k is 6.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
We are given that;
f(x) = 2x + 4
f(x) = 2x-k
Now,
To shift a linear function to the right, we subtract a constant from the input variable x. For example, f (x) = 2x + 4 shifts to the right by 2 units when it is replaced with f (x) = 2 (x - 2) + 4.
In this case, f (x) = 2x + 4 shifts six units to the right when it is replaced with f (x) = 2 (x - k) + 4. To find the value of k, we can equate the expressions inside the parentheses and solve for k:
x - k = x - 6 k = 6
Therefore, by the given functions the answer will be 6.
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Solve the equation by elimination
2x - 5y = -7
=
-2x + 3y = 1
Answer:
Step-by-step explanation:
Find the total number of positive integers of 4 digits or less that can be taken from the digits 1, 2, 3, and 4 in the case that a) repeating figures is not allowed b) repeat figures are allowed
Answer:
1,2,4
Step-by-step explanation:
all are positive intergers
Does the point (2, -2) lie on the line 3x − y = 4? Yes No
Answer:
No
Step-by-step explanation:
(2,-2)
2 is the x coordinate
-2 is the y coordinate
3x - y = 4
3(2) -(-2) = 6 + 2
6 + 2 = 8, not 4
Hope this helps :)
Have a nice day!
Answer:
No, it is not in the line.
Step-by-step explanation:
Let's plug the coordinates of the point and find out
[tex]3(2) -(-2) = 4\\6+2 = 8\ne 4[/tex]
I need help! ASAP PLS
Answer:
The area is 155 ft.
Step-by-step explanation:
To find the area if a trapezoid, you have to add the number on top( in this case 13 ft) and then add that with the bottom number(18 ft.) Then, you take that answer and divide it by 2. After that, multiply it with the height(10.) Thus, the answer is 155 ft.
Triangle ABC and triangle ACD are isosceles. Angle DAB = 86° and angle ADC = 58°. Find the value of x.
The computation of triangle ABC and ACD which are both isosceles shows that the value of x will be 36°.
How to solve the triangle?It should be noted that the sum of angles in a triangle is 180°. In this situation two of the three angles have been given.
Therefore, the value of the third angle will be:
86° + 58° + x = 180°
144° + x = 180°
x = 180° - 144°
x = 36°
In conclusion, x is 36°.
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20-3+12/6x2=N
Helpppppp
Answer:
N=21
Step-by-step explanation:
20-3+12/6x2=N
20-3+2x2=N
20-3+4=N
21=N
N=21
X/3=15/12 Aflați termenul necunoscut din proporție
Answer:
x = 3,75
Step-by-step explanation:
x/3 = 15/12
x/3 = 5/4
4x = 3 × 5
4x = 15
x = 15/4
x = 3,75
Pls help me here on this question
if ms purple gets 81 apples, and a rat eat 51 of them, how many are left? (the rat must have been hungry)
Answer:
There are 30 apples left!
Step-by-step explanation:
81-
51
-----
30
The probability Kayla will score above 70% on a mathematics test is 0.60. Kayla will take four tests this semester. We want to find the probability she will score above 70% on exactly three out of the four tests. What is the probability of Kayla scoring above 70% on exactly three out of the four tests
The probability of Kayla scoring above 70% on exactly three out of the four tests is 8.64%.
ProbabilityGiven that the probability Kayla will score above 70% on a mathematics test is 0.60, and Kayla will take four tests this semester, and we want to find the probability she will score above 70% on exactly three out of the four tests, to determine what is the probability of Kayla scoring above 70% on exactly three out of the four tests, the following calculation must be performed:
0.6 x 0.6 x 0.6 x 0.4 = X0.216 x 0.4 = X0.0864 = X0.0864 x 100 = 8.64Therefore, the probability of Kayla scoring above 70% on exactly three out of the four tests is 8.64%.
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what is the perimeter of square 3/4 inches
Answer:
p=4a
Step-by-step explanation:
The density of a certain material is such that it weighs 1 pound for every 3.5 cups of volume. Express this density in tons per cubic foot. Round your answer to the nearest hundredth.
Answer:
0.02 tons per cubic foot
Step-by-step explanation:
delt math
The density of the material is, 106.36 tons per cubic foot.
What is density?Density is the mass of a material substance per unit volume.
d = M/V, where d is density, M is mass, and V is volume, is the formula for density.
Grams per cubic centimeter are a typical unit of measurement for density.
Given, The density of a certain material is such that it weighs 1 pound for every 3.5 cups.
Therefore, d = 1/3.5 per cubic cup.
d = 0.29 pounds per cubic cup.
Now, We know 1 ton is equal to 2000 pounds and 1 foot is equal to 119688.
Therefore, The density of the material per cubic foot is,
= 119688/(2000×0.29) tons per cubic foot.
= 106.36 tons per cubic foot.
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Jessica’s bank is offering bear a loan with a stated rate of 4.90% interest. If the interest is compounded every two months what will Jessica pay. For interest l?
A. 4.90
B. 5.00
C. 5.01
D. 4.98
Answer:
B no wrok needed
Step-by-step explanation:
What is y 6=2(y+2)
HELP ME PLEASE
What is the average
67,70,66
What's the answer to 8.546 rounded to the nearest ones place
Answer:
8.5
Step-by-step explanation:
because the hundredths place is not above 5
A full bathtub is emptying at a
fixed rate. Which of the following
equations may relates the amount
in water y, in gallons, with the
amount of time, x minutes. Assume
the bathtub is holding 100 liters
of water, and empties at a rate of
5.8 liters per minute.
Answer:
D 5y + 29x = 500
Step-by-step explanation:
Slope-intercept form of a linear equation: y = mx + b
(where m is the slope/rate of change, and b is the y-intercept)
Given:
bathtub holds 100 liters⇒ when x = 0, y = 100
Therefore, b = 100
Given:
the water is emptying at a rate of 5.8 liters/minNote that the water is decreasing in volume as time goes by. Therefore, the rate of change is negative, so m = -5.8
Inputting these values into the equation gives:
y = -5.8x + 100
Multiply the equation by 5:
5y = -29x + 500
Rearrange:
5y + 29x = 500
Therefore, D is the solution.
help pls
part b for Q11
part a & b for Q12
Answer:
x = 2.6, x = -1.6
Step-by-step explanation:
If we compare the graph to points (-1, 2) and (2, 2) [see blue lines on attachment], we can determine that the scale of the y-axis is 1 square per 1 unit. (This is different from the scale of x-axis, which is 2 squares per unit).
Therefore, to use the graph to estimate the x-value when y = 4, count 4 square up the y-axis from 0, then trace along the horizontal line until you meet the curve. Then trace down to the x-axis and read the values of x. (shown by the red lines on the attachment).
So the approximate value of x is -1.6 and 2.6 when y = 4.
The actual answer can be calculated as follows:
x² - x = 4
⇒ x² - x - 4 = 0
Use the quadratic formula:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\implies x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(1)(-4)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{1\pm\sqrt{17}}{2}[/tex]
[tex]\implies x=2.6,x= -1.6 \sf \ (1 \ dp)[/tex]
Answer:
x=-1.56,2.56
please help i'll give brainliest HELP PLLLLEEEEEEEEAAAAAAAASEEEEEEE
Answer:
22
Step-by-step explanation:
which equation shows the correct relationship between the measures of the angles of the two triangles?
m<ABC=m<A'B'C'
Observe both triangles
<A=<A'<B=<B'<C=<C'So<ABC=<A'B'C'
Choose the inverse of y = x2 – 10x.
Answer:
The inverse is 5±sqrt(x+25)
Step-by-step explanation:
y = x^2 - 10x
To find the inverse, exchange x and y and solve for y
x = y^2 -10y
Complete the square
x+25 = y^2 -10y +25
x+25 = (y-5)^2
Take the square root of each side
±sqrt(x+25) = y-5
Add 5 to each side
5±sqrt(x+25) = y
The inverse is 5±sqrt(x+25)
Answer:
[tex]y=\pm\sqrt{x+25}+5[/tex]
Step-by-step explanation:
Given function:
[tex]y=x^2-10x[/tex]
Rearrange to make [tex]x[/tex] the subject.
First, complete the square by adding 25 to both sides and factoring:
[tex]y+25=x^2-10x+25[/tex]
[tex]y+25=(x-5)^2[/tex]
Square root both sides:
[tex]\pm\sqrt{y+25}=x-5[/tex]
Add 5 to both sides:
[tex]x=\pm\sqrt{y+25}+5[/tex]
Finally, swap [tex]x[/tex] and [tex]y[/tex] (since the inverse of a function is its reflection in the line [tex]y = x[/tex])
[tex]y=\pm\sqrt{x+25}+5[/tex]
Translate the verbal expression into an algebraic expression "Four times the sum of a number and 5"?
Answer:
4(x+5)
Step-by-step explanation:
Combing like terms for -8x-11x
Answer:
-19x
Step-by-step explanation:
to make this equation easier, remove the variables (-8-11) which equals -19. You can then say the answer is -19x
6 divided by 3.54 ..
Answer:1.694
Step-by-step explanation:
You take away the decimal from 3.54 and make the 6 the same number place
Ex. 1 ÷ 1.20
1=100
1.20=120
600 ÷ 354 = 1.694
Andrea goes to the movies with her friends. The total cost of ride tickets is given by the equation c = 5.5t, where c is the total cost of tickets and t is the number of tickets.
If Andrea bought 7 tickets, she would spend ______?
A) $18
B) $2.50
C) $35
D) $38.50
Answer:
38.5
D
Step-by-step explanation:
5.5x7=38.5