The rate of change in elevation of the second scuba diver in feet per minute is; 12.5 ft/minute
How to find the rate of change of speed?We are given that;
The elevation of a certain scuba diver changes by 15⁵/₈ ft every minute.
Now, this rate of change was 1¹/₄ times the rate of change for a second scuba diver.
Thus, if the rate of change of elevation for the second scuba diver is x, then it means that;
15⁵/₈ = 1¹/₄x
Converting the fractions to improper fractions gives us;
125/8 = 5x/4
Thus making x the subject gives us;
x = (125 * 4)/(5 * 8)
x = 12.5 ft/minute
This represents the rate of change in elevation of the second diver.
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Prehistoric cave painting were discovered. The paint contained 5% of the original carbon-14. Estimate the age of the paintings using the exponential decay model for carbon-14, A=A_0e ^-0.000121t (round to the nearest whole number as needed.)
About 24 ,758 years have passed since the cave drawings were created.
What is the age formula?If one's age is x now, one's age will be nx in the future. Age n years from now equals x + n if the age at currently is x. Age n years ago equals x - n if the current age is x. The ages will be ax and bx in the ratio a: b.
What is the measure age?The time since birth, which is typically expressed as an exact number of years or a finished number of years, is known as a person's chronological age.
A is the current sum.
A0 is the original sum.
A0 = A0 A0 = A0 0.05 e-0.000121t
A / A0 = e-0.000121t
0.05 = e-0.000121t, 0.05 = ln e-0.000121t, 0.05 = -0.000121t, 0.05 = e, and 0.05 = -0.000121t, respectively.
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The artwork is 24,758 years old, according to the exponential equation's solution.
Is power equivalent to exponential?Exponents are frequently referred to as strengths or indices. In plain English, a power expression is one that depicts the same number being multiplied repeatedly, whereas an exponent is a quantity that depicts the powers to which the value is increased.
Briefing:A = current amount
A₀ = original amount
0.05 A₀ = A
A = A₀ [tex]e^{-0.000121t}[/tex]
A / A₀ = [tex]e^{-0.000121t}[/tex]
0.05 = [tex]e^{-0.000121t}[/tex]
ln 0.05 = ln [tex]e^{-0.000121t}[/tex]
ln 0.05 = -0.000121t ln e
ln 0.05 = -0.000121t
-2.9957 ≈ -0.000121t
24758.11 ≈ t
About 24,758 years have passed since the cave drawings were created.
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Given quadrilateral ABCD with A(-4,-2), B(-3,2), C(2,4) and D(4,-3). Find the area in square units.
The area of the quadrilateral ABCD, with the vertices coordinates A(-4, -2), B(-3, 2), C(2, 4), and D(4, -3), is 18 square units
What is a quadrilateral?A quadrilateral is a four sided polygon, that has a sum of the interior angles of 360°
The area of the quadrilateral can be calculated as comprising of the area of two triangles, with vertices; B(-3, 2), C(2, 4), D(4, -3), and B(-3, 2), C(2, 4), A(-4, -2)
The area of a triangle with known coordinates of the vertices is precented as follows;
Let (x₁, y₁), (x₂, y₂), (x₃, y₃) represent, the vertices of the triangle, we get;
A = 0.5×|x₁·y₂ - x₂·y₁ + x₂·y₃ - x₃·y₂ + x₃·y₁ - x₁·y₃|
Therefore;
The area, A₁ of the triangle ΔBCD with vertices at the coordinates (-3, 2), (2, 4), (4, -3), is found as follows;
A₁ = 0.5 × |(-3)×4 - 2×2 + 2 ×(-3) - 4 × 4 + 4×2 - (-3)×4| = 9
Similarly, the area, A₂, of the triangle, ΔBCA with vertices (-3, 2), (2, 4), (-4, -2), is found as follows;
A₂ = 0.5 × |(-3)×4 - 2×2 + 2 ×(-2) - (-4) × 4 + (-4)×2 - (-3)×(-2)| = 9
The area of the quadrilateral, A = A₁ + A₂, is therefore;
The area of the A = 9 + 9 = 18
The area of the quadrilateral ABCD is 18 square units
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Select all of the algebraic expressions that could represent the phrase below.
"nine more than the product of 5 times the number of tires t"
Answer:
a,b,d
Step-by-step explanation:
Answer:
Option A: 9 + 5t
Option B: 5 · t + 9
Option D: (5 × t) + 9
Step-by-step explanation:
Hope This Helped
Henry has a rope that is 5 meters long. He cuts away a piece that is 1.27 meters long. How long is the remaining piece of rope?
need it now pls
The length of the remaining rope is 3.73 meters.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Length of the rope = 5 meters
Length of the rope that is cut away = 1.27 meters
The remaining length of the rope.
= 5 - 1.27
= 3.73 meters
Thus,
The remaining length of the rope is 3.73 meters.
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As part of a survey, 200 boys were asked to name their favorite sport. The results showed that 120 of the boys names football as their favorite sport. What percentage of the boys in the survey named football as their favorite sport?
The percentage of the boys in the survey who named football as their favourite sport is 60%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given as part of a survey, 200 boys were asked to name their favourite sport. The results showed that 120 of the boys names football as their favourite sport.
The percentage of boys who like football as their favourite sport will be calculated as,
Percentage = 120 / 200
Percentage = 0.6 x 100
Percentage = 60%
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Thomas earned $46.50 in 4 hours at his job today. How much can he earn tomorrow if he works 10 hours at the same hourly rate? Do NOT include a dollar sign in your answer.
Answer:
116.25 0r 116.30
Step-by-step explanation:
To find the hourly rate, divide the pay by the number of hours
So 46.50/4 = 11.625
You should round that to 11.63
Then, multiply the hourly rate by the number of hours worked the next day.
So 11.63 x 10 = 116.30
The given point P is located on the unit circle, similar to what is seen in the image below, determine the sine and cos e(P is
not necessarily in Quadrant I).
(0,1)
(-1,0)
(0,-1)
(1,0)
PLS HELP ME ASAP
The sine and cosine of the angle of point P are sin θ = 143/145 and cos θ = -24/145 respectively. Option b. is the answer
How to determine the sine and cosine of the angle of point P?Given the coordinate of the point as P (-24/145, 143/145)
This implies x = -24/145 and y = 143/145
To determine the sine and cosine of the angle of point P, we can make a sketch using this information (see attached image).
opposite = 143/145, adjacent = -24/145
hypotenuse = √[(-24/145)² + (143/145)²] = √1 = 1
Using trigometric ratios:
sin θ = (143/145) / 1 = 143/145 [sin θ = opposite/ hypotenuse]
cos θ = (-24/145) / 1 = -24/145 [cos θ = adjacent/ hypotenuse]
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Find the slope of the line that passes through (3, 14) and (8, 8).
Answer:
-6/5
Step-by-step explanation:
you would find the difference between the ys and the XS then divide the product of those by [tex]\frac{y}{x}[/tex].
Help with this im being called a failure
Roaring Zoo has 76 different species of birds. Because of cold weather, only 32 species stayed at the zoo, while the others were transported to the barn until warmer weather returned.
Which equation shows how many species of birds were transported?
b − 32 = 76
b + 32 = 76
b − 76 = 32
b + 76 = 32
Answer:
b + 32 = 76
Step-by-step explanation:
Solve the inequality
1. 2x
Answer:
where is the question
Step-by-step explanation:
Please you need to write the full question so it can be answered
thanks
find the value of expression of 1/8 + 4 7/8
Answer:
Hope the picture will help you
Which of the following properly expresses the
verbal
statement "The square root of a number, x, is 5
less than
the sum of the number and 2" ?
F. √x = 5-(x + 2)
G√√√x = (x + 2)-5
Answer:F. √x = 5-(x + 2)
Step-by-step explanation:
Write an equation of a line passing through the point (-4, -11) and perpendicular to the line 4x + 5y = -45.
The required equation of the line is given as y = 5x -6.
To determine the equation of a line passing through the point (-4, -11) and perpendicular to the line 4x + 5y = -45.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope of the given line
4x + 5y = -45
y = -4/5 - 45
m = -4/5
The equation of the perpendicular line is given as,
y - y₁ = -1/m (x - x₁)
Substitute the value in the above equation,
y + 11 = -1 / -4/5 (x + 4)
y = 5/4(x + 4) - 11
y = 5x + 5 - 11
y = 5x -6
As a result, the needed equation for the line is y = 5x -6.
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What happens to y = x when the slope is changed to a negative number?
If the slope is a negative number for example, y = - x then it would go up one and to the left one because it's a negative number. Negative slopes will always go through the coordinate plant II and IV
find x . geometry please help
The value of x in the circle is given as follows:
x = 23.
How to calculate the value of x?The value of x in the circle is calculated using the tangent-secant theorem, which states that when a secant and a tangent are drawn to a circle from the same external product, the product of the length of the secant and of it's external segment equals the square length of the tangent segment.
The parameters for this problem are given as follows:
Secant: 27 + 2x + 2 = 2x + 29.External segment: 2x + 2.Tangent: 3x - 9.Then, the value of x is obtained applying the product from the tangent-secant theorem as follows:
(2x + 29)(2x + 2) = (3x - 9)²
4x² + 62x + 58 = 9x² - 54x + 81
5x² - 116x + 23 = 0.
Which is a quadratic equation with the coefficients given as follows:
a = 5, b = -116, c = 23.
Using a quadratic equation calculator, the solutions are given as follows:
x = 0.2 -> extraneous, as the length 3x - 9 would be negative.x = 23.More can be learned about the tangent-secant theorem at https://brainly.com/question/9132922
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Can someone pls help me with this I’ll mark brainliest
Aretha had $180 in her bank
account at the end of the week. She
wrote a check for $120, deposited
$250, and spent $75 on groceries
during the week. How much was
in her account at the start of the
week?
should be about $625
Just add all the number up and then subtract the answer you got with the same number except 180 since that's what she has left over. correct me if I'm wrong.
write
equation parallel
through (4,9) (-3,6) and
passes (14,8)
The equation of the line is 3x - 7y + 51 = 0.
What are Parallel Lines ?
Coplanar, parallel lines that don't cross at any point are called parallel lines. Planes in the same three-dimensional space that never cross each other are said to be parallel.
Since the required line is parallel to the line that passes through (4,9) and (-3,6).
So, The slope will be equal to :
m = (y^2 - y^1) / (x^2 - x^1)
here, x^1 = 4, y^1 = 9, x^2 = -3 and y^2 = 6
∴ m = (6 - 9) / (-3 - 4)
= -3/-7
= 3/7.
We know that, The equation of a line is (y - y^1) = m (x - x^1)
∴ The equation of the required line will be :
y - 9 = 3/7 ( x - 4)
7y - 63 = 3x - 12
3x - 7y + 51 = 0.
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please help! I'm almost out of time on my assignment
A metallurgist has one alloy containing 28% aluminum and another containing 59% aluminum. How many pounds of each alloy must he use to make 42 pounds of a third alloy containing 30%
The number of pounds from one alloy is 2.71.
The number of pounds from another alloy is 39.29.
What is an equation?An equation is a mathematical statement of two expressions connected by an equal sign.
We have,
x = pounds from one alloy
y = pounds from the second alloy
Two equation.
28% of x + 59% of y = 30% of 42
0.28x + 0.59y = 0.30 x 42 ______(1)
x + y = 42 _____(2)
Now,
x = 42 - y ________ (3)
Putting (3) in (2)
0.28(42 - y) + 0.59y = 0.30 x 42
11.76 - 0.28y + 0.59y = 12.6
11.76 + 0.31y = 12.6
0.31y = 12.6 - 11.76
0.31y = 0.84
y = 2.71
Now,
x = 42 - y
x = 42 - 2.71
x = 39.29
Thus,
The number of pounds of each alloy is 2.71 and 39.29.
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y-5=1/2(x-4) what are the coordinates
Answer:
The ordered pair (3, 4) is found in the coordinate system when you move 3 steps to the right on the x-axis and 4 steps upwards on the y-axis.
Step-by-step explanation:
hope this helped:)
brainliest for the brains:)
y=-2x coordinate plane
Answer:
The Y=-2x coordinate plane is a two-dimensional plane that represents all possible points with coordinates that satisfy the equation Y=-2x. The Y axis is the vertical axis, and the X axis is the horizontal axis. A point on the Y=-2x coordinate plane can be represented by an ordered pair (x, y), where x is the distance of the point from the Y axis, and y is the distance of the point from the X axis. In the Y=-2x coordinate plane, the Y coordinate of a point is always equal to -2 times the X coordinate of that point.
Step-by-step explanation:
explain the pattern you found on the table
Picture 1 has 5 green squares. It is one square with a square coming out from each corner.
Describe the table pattern you noticed ? Picture 2 adds an additional square extending out from each corner square, making a total of 9 squares. This pattern continues, adding 4 green squares total each time. This means Picture 3 has 13 squares, Picture 4 has 17 squares, and Picture 5 will have 21 green squares.Picture one has 5 green squares. It is one square with a square coming out from each corner. Picture 2 adds an additional square extending out from each corner square, making a total of 9 squares. This pattern continues, adding 4 squares total each time. This means Picture 3 has 13 squares, Picture 4 has 17 squares, and Picture 5 will have 21 squares.To learn more about table pattern refer
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QUESTION 2
Consider the hyperbolic function (y + 2)(x − 4) = 3.
2.1 Write down the domain and range of the function.
please help me with math i’ll give you brainlist
Answer:
Step-by-step explanation:
Domain = Range = (19,77,10,9\5,0,100)
13. Mark and his brother signed up for the Catch Up
phone plan. They share the minutes every month
equally. How many minutes can Mark use each
day without going over his share of minutes?
Answer: 12 minutes
Let us suppose the number of minutes per month is 720. ( i have assumed this data from myself, you use any data you want, remember the procedure)
Now, Mark and his brother share the minutes every month equally.
So, clearly, Mark and his brother would get 360 minutes each every month.
Now, Mark has 360 minutes each month
therefore, Mark has 360/30 minutes per day
= 12 minutes each day.
Step-by-step explanation:
Rewrite 26/9 as a mixed number
a racing venue wants to make the charity race 5% longer. If the race was 25km, what is the new race length
The length of the racing venue after the increase of 5 % is 26.25 km
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the increased length of the racing venue be = A
Let the total length of the racing venue be = 25 km
The percentage increase in the length of the racing venue = 5 %
So , the equation will be
Increased length of the racing venue = total length of the racing venue + ( percentage increase in the length of the racing venue x total length )
Substituting the values in the equation , we get
Increased length of the racing venue = 25 + ( 5/100 ) x 25
Increased length of the racing venue = 25 + ( 5/4 )
Increased length of the racing venue = 25 + 1.25
Increased length of the racing venue = 26.25 km
Therefore , the value of A is 26.25 km
Hence ,
The length of the racing venue after the increase of 5 % is 26.25 km
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What is the scale factor of the geometric sequence?
4, −12, 36, −108, . . .
Enter your answer in the box.
Answer:
Step-by-step expl
The first three terms of an arithmetic sequence are as follows 17,13,9
please look at the picture and answer all the problems (I GIVE U LIKED AND POINTS!)
Answer:
Inequality
a. x<=5
b. x>12
c. x<=-4
d. x>-6
Word Problems
6. x>65
7. x<90
8. x>985
9. x>12
Step-by-step explanation: