20+0.15x = 35+0.10x
0.15x=15+0.10x
0.05x=15
x= 15/0.05
x= 300minutes
check:
300*.015 = 45+20=65
300*0.10 = 30 + 35 = 65
they equal
so number of minutes would be 300
The table below shows the surface area y, in square feet, of a shrinking lake in x days: Time (x) (days) 5 10 15 20 Surface area (y) (square feet) 90 85 70 61 Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the lake. [Choose the value of the correlation coefficient from −1, −0.98, −0.5, −0.02.] (4 points) Part B: What is the value of the slope of the graph of surface area versus time between 15 and 20 days, and what does the slope represent? (3 points) Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)
What is the domain of the relation: (0, 7), (8, -1), (2, 3), (-4, 6)?
A. (-4, 0, 2, 8)
B. (-1, 3, 6, 7)
C. (1, 7, 8, -1)
D. (2, 3, -4, 6)
Jonathan deposits $2000 into a bank account that pays 7% annual interest compounded annually. This means the bank pays him 7% of his account balance as interest at the end of each year, and he leaves the original amount and the interest in the account.
1. Write a recursive formula to model the situation described above. Use A0 to represent the initial amount invested. Then describe An, the next year’s balance, in terms of the current year’s balance, An-1.
Can you use matrix multiplication with a matrix with three rows and a matrix with two columns
NEED HELP!!!!!!!!!!!!!!!
Which factorizations can be used to identify the real zeros of the function f(x)=-20x^2+23x-6 ?
A. (-10x+2)(2x+3)
B. -(10x+2)(2x-3)
C. -(4x-3)(5x+2)
D. -(4x-3)(5x-2)
Answer:
Option D. [tex]-(4x-3)(5x-2)[/tex]
Step-by-step explanation:
we have
[tex]f(x)=-20x^{2}+23x-6[/tex]
Equate the function to zero
[tex]-20x^{2}+23x-6=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]-20x^{2}+23x=6[/tex]
Factor the leading coefficient
[tex]-20(x^{2}-(23/20)x)=6[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]-20(x^{2}-(23/20)x+(529/1,600))=6-(529/80)[/tex]
[tex]-20(x^{2}-(23/20)x+(529/1,600))=-(49/80)[/tex]
[tex](x^{2}-(23/20)x+(529/1,600))=(49/1,600)[/tex]
Rewrite as perfect squares
[tex](x-(23/40))^{2}=(49/1,600)[/tex]
[tex](x-(23/40))=(+/-)(7/40)[/tex]
[tex]x=(23/40)(+/-)(7/40)[/tex]
[tex]x=(23/40)(+)(7/40)=30/40=3/4[/tex]
[tex]x=(23/40)(-)(7/40)=16/40=2/5[/tex]
therefore
[tex]-20x^{2}+23x-6=-20(x-(3/4))(x-(2/5))[/tex]
[tex]-20x^{2}+23x-6=-(5)(4)(x-(3/4))(x-(2/5))[/tex]
[tex]-20x^{2}+23x-6=-(4x-3)(5x-2)[/tex]
Which regular polygon can be drawn by using rotations in geometry software?
Answer:
n- regular polygon
Step-by-step explanation:
In order to draw n- regular polygons, 360 must be divisible by n.
Therefore, there are many regular polygons such as 12- polygon using 30° rotations and 15-polygon using 24° rotations.
Triangle LMN has vertexes at L(-1, -6), M(1, -6), and N(1, 1). Find the measure of angle L to the nearest degree.
There were 490 people at play. The admission price was $3.00 for adults and $1.00 for children. The admission receipts were $990. How many adults and children attended
Find the GCF of the first two terms and the GCF of the last two terms of the polynomial. 5h^3+20h^2+4h+16
Give an example of a function that is integrable on the interval [-1,1], but not continuous on [-1,1]. explain.
How can you rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations?
You can rearrange formulas to highlight a specific quantity of interest by identifying it and isolating it using inverse operations.
Explanation:In mathematics, you can rearrange formulas to highlight a specific quantity of interest using the same reasoning as in solving equations. The goal is to isolate the variable or the quantity you want to highlight on one side of the formula. Here are the steps to do it:
Identify the quantity of interest you want to highlight.
Apply inverse operations to isolate that quantity on one side of the equation/formula.
Simplify or solve for the highlighted quantity if needed.
For example, if you have the formula for the area of a rectangle, A = L * W, and you want to solve for the length of the rectangle, you can rearrange the formula as L = A / W, highlighting the length as the quantity of interest.
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How do you find the vertex of this parabola? I just plotted the points down on a graphing calculator, but I figure there's a better way.
Which of the following is FALSE? The diagonals of a parallelogram bisect each other. The diagonals of a rhombus bisect each other. The diagonals of a square bisect each other. The diagonals of a kite bisect each other
Answer:
The diagonals of a kite bisect each other
Step-by-step explanation:
Let analyse all possible answer:
a. The diagonals of a parallelogram bisect each other
True, it is one of the properties of a parallelogram
b. The diagonals of a rhombus bisect each other
True, In any rhombus, the diagonals (lines linking opposite corners) bisect each other at right angles (90°). That is, each diagonal cuts the other into two equal parts, and the angle where they cross is always 90 degrees.
c. The diagonals of a square bisect each other.
True, it is one of the properties of a square
d. The diagonals of a kite bisect each other
Wrong, because we do not know what shape of the kite is, it can have a really strange shape that we can not identify where the diagonals are as you can see in the attached photo.
What is the difference between discrete vs continuous data
And can someone please help me with 1-5
the distance across the center of a circle is called the?
Probability of a lightbulb failing question? If the probability is .001 that a light bulb will fail on any given day, then what is the probability that it will last at least 30 days?
The midpoint of A (-4, 2) and B(8, 5) is
Answer: The midpoint of the points A(-4, 2) and B(8, 5) is M(2, 3.5).
Step-by-step explanation: We are given to find the midpoint of the points A(-4, 2) and B(8, 5).
We know that
the co-ordinates of the midpoint of the points (a, b) and (c, d) are given by
[tex]M=\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]
Therefore, the co-ordinates of the midpoint of the points (-4, 2) and B(8, 5) will be
[tex]M=\left(\dfrac{-4+8}{2},\dfrac{2+5}{2}\right)=\left(\dfrac{4}{2},\dfrac{7}{2}\right)=(2,3.5).[/tex]
Thus, the midpoint of the points A(-4, 2) and B(8, 5) is M(2, 3.5).
Melissa has three different positive integers. she adds their reciprocals together and gets a sum of 1. what is the product of her integers?
First let us assign the three positive integers to be x, y, and z.
From the given problem statement, we know that:
(1/x) + (1/y) + (1/z) = 1
Without loss of generality we can assume x < y
< z.
We know that:
1 = (1/3) + (1/3) + (1/3)
Where x = y = z = 3 would be a solution
However this could not be true because x, y, and z must all be different integers. And x, y, and z cannot all be 3 or bigger than 3 because the sum would then be less than 1. So let us say that x is a denominator that is less than 3. So x = 2, and we have:
(1/2) + (1/y) + (1/z) = 1
Therefore
(1/y) + (1/z) = 1/2
We also know that:
(1/4) + (1/4) = (1/2)
and y = z = 4 would be a solution, however this is also not true because y and z must also be different. And y and z cannot be larger than 4, so y=3, therefore
(1/2) + (1/3) + (1/z) = 1
Now we are left by 1 variable so we calculate for z. Multiply both sides by 6z:
3z + 2z + 6 = 6z
z = 6
Therefore:
(1/2) + (1/3) + (1/6) = 1
so {x,y,z}={2,3,6}
Final answer:
The product of Melissa's integers is 120.
Explanation:
The product of Melissa's integers is 120.
Let the integers be a, b, and c.
According to the given information, 1/a + 1/b + 1/c = 1.
By finding common denominators and simplifying, you can determine that a * b * c = 120.
Graph the hyperbola with equation quantity x plus four squared divided by sixteen minus the quantity of y plus three squared divided by twenty five = 1.
Which point is a solution of x + 2y ≤ 4?
A. (2,4)
B. (1,1)
C. (3,5)
D. (-1,5)
A fast typist can type 120 words in 100 seconds. In 180 seconds, how many words could be typed?
Answer:
216
Step-by-step explanation:
i think
Round 846 to the nearest hundred___________ and 3756 to the nearest thousand ________
How many days are between march the 15th and august the 15th?
Answer:21 weeks and 6 days
Step-by-step explanation:
lol im late its 2021
What is the 12th term of the arithmetic sequence where a1 = 5 and a6 = 20?
what must be done to the expression x + 108 to make it equal x?
To make the expression x + 108 equal to x, subtract 108 from both sides of the equation.
Explanation:To make the expression x + 108 equal to x, we need to subtract 108 from both sides of the equation. This will give us:
x + 108 - 108 = x - 108
Simplifying the equation, we get:
x = x - 108
However, if we are not solving an equation and simply need to simplify the expression x + 108 to make it equal to x, then the answer is that nothing can be done. The expression cannot be simplified to make it equal to x without additional information or context.
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A candy factory made 54 boxes of chocolates. Each box weighs 2 pounds. They packed the boxes in 6 cases with the same number of boxes in each case. How many pounds of chocolates were there in each case?
The number of pounds of chocolates in each case is 18 pounds
How to find the number of pounds in each case?
The candy factory made 54 boxes of chocolates.
Each box weighs 2 pounds
Therefore,
each box = 2 pounds
They packed the boxes in 6 cases with the same number of boxes in each case. Therefore,
Boxes in each case = 54 / 6 = 9 boxes
Therefore,
pounds of chocolates in each case = 9 × 2 = 18 pounds
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What is the length of the diagonal of a cube with a side length of 5 cm? Round to the nearest tenth. 7.1 cm 8.7 cm 21.3 cm 26.7 cm
The required length of the diagonal of a cube with a side length of 5 cm is approximately 8.7 cm.
What is diagonal?A diagonal is a straight line that connects two non-adjacent corners of a polygon, such as a square, rectangle, or any other shape with four or more sides. For a given quesiton, the diagonal of a cube with side length s is given by the formula d = s√3.
Here,
As mentioned in the question, we have given a cube with a length of its side is 5 cm.
We know that the diagonal of a cube with side length s is given by the formula d = s√3.
Substituting s=5 into this formula, we get:
d = s√3.
d = 5√3
Rounding to the nearest tenth, we get d = 8.7 cm.
Therefore, the length of the diagonal of a cube with a side length of 5 cm is approximately 8.7 cm.
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What does "a"equal to?
The mean incubation time for a type of fertilized egg kept at 100.2100.2â°f is 2323 days. suppose that the incubation times are approximately normally distributed with a standard deviation of 11 dayday. â(a) what is the probability that a randomly selected fertilized egg hatches in less than 2121 âdays? â(b) what is the probability that a randomly selected fertilized egg hatches between 2222 and 2323 âdays? â(c) what is the probability that a randomly selected fertilized egg takes over 2525 days toâ hatch?
To solve this problem, what we have to do is to calculate for the z scores of each condition then find the probability using the standard normal probability tables for z.
The formula for z score is:
z = (x – u) / s
where,
x = sample value
u = sample mean = 23 days
s = standard deviation = 1 day
A. P when x < 21 days
z = (21 – 23) / 1
z = -2
Using the table,
P = 0.0228
Therefore there is a 2.28% probability that the hatching period is less than 21 days.
B. P when 23 ≥ x ≥ 22
z (x=22) = (22 – 23) / 1 = -1
P (z=-1) = 0.1587
z (x=23) = (23 – 23) / 1 = 0
P (z=0) = 0.5
P = 0.5 - 0.1587 = 0.3413
Therefore there is a 34.13% probability that the hatching period is between 22 and 23 days.
C. P when x > 25
z = (25 – 23) / 1
z = 2
P = 0.9772
This is not yet the answer since this probability refers to the left of z. Therefore the correct probability is:
P true = 1 – 0.9772
P true = 0.0228
Therefore there is a 2.28% probability that the hatching period is more than 25 days.
One number exceeds another by 11. the sum of the numbers is 3535. what are the numbers?