Therefore , the speed of shadow moving down the wall when he is 5 feet from the wall is 8/3 ft/sec.
What does differentiation mean?A method of determining a function's derivative is differentiation. Mathematicians use the technique of differentiation to determine the instantaneous rate of change in a function based on one of its variables. The most typical example is velocity, which is the rate at which a distance changes in relation to time.
Here,
ΔABC & ΔDBE
=> AC/DE = BC/BE
=> h/6 = 20 /20-x
=> h = 120/20-x
Differentiate w.r.t to t
=> dh/dt = [tex]\frac{120}{{(20-x)}^{2} }[/tex] * dx/dt
given the man is walking towards wall at the rate of 5 ft/s
thus, dx/dt =5 ft/s
=>dh/dt = [tex]\frac{120}{{(20-5)}^{2} }[/tex] * 5
=>dh/dt = 8/3 ft /sec
Therefore , the speed of shadow moving down the wall when he is 5 feet from the wall is 8/3 ft/sec.
To know more about differentiation , visit
https://brainly.com/question/24898810
#SPJ4
The equation 4(2x 1) = 6x − 12 models the change in water level in a lake in one month. solve for x, which is change in height in inches. x equals negative thirteen halves x = −8 x = 8 x equals eleven halves
From the given options, option 2. x= -8 is the correct option. Here, the x is change in height in inches so the, change in height is -8 inches.
A linear equation is simply an equation with the highest degree always being 1. The standard form of a linear equation in one variable is Ax + B = 0. x is a variable in this equation, and A and B are constants. A two-variable linear equation has the standard form Ax + By = C. The variables x and y are variables, their coefficients A and B are variables, and C is a constant.
Given, linear equation is
[tex]4(2x+1)=6x-12\\\\8x+4=6x-12\\\\8x-6x=-4-12\\\\2x=-16\\\\x=-8[/tex]
Hence, the x equals to -8.
To learn more about linear equation refer here
https://brainly.com/question/29739212
#SPJ4
PLEASE ANSWER FAST
Find the missing values in the table below so that it represents a linear function.
The value of y₂, y₃ and y₄ in the linear function are -21, -26 and -31 respectively.
How to represent linear function?Linear function can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, to find the missing values in the table we have to use the equation of the linear function.
y = mx + b
let's find m.
using (4, -16) and (8, -36)
m = slope = -36 + 16 / 8 - 4
m = -20 / 4
m = -5
Hence, let's find y-intercept using (4, -16).
y = -5x + b
-16 = -5(4) + b
-16 + 20 = b
b = 4
Therefore, the equation is y = -5x + 4.
Let's find y₂, y₃ and y₄
y₂ = -5(5) + 4 = -25 + 4 = - 21
y₃ = -5(6) + 4 = -30 + 4 = -26
y₄ = -5(7) + 4 = -35 + 4 = - 31
learn more on linear function here: https://brainly.com/question/29491261
#SPJ1
Hard A level Maths question, please help ASAP cheers
The value of the shaded area from the rectangle ACDE is approximately 52.124 square centimeters.
How to determine the value of the shaded area
In this problem we must calculate the shaded area of the section within the rectangle ACDE, this can be found by the subtracting the area of the region ABDE, which is the combination of the areas of the right triangle ABE and the arc BDE, whose formulas are shown below:
Triangle ABE
S = (1 / 2) · AB · AE
Arc BDE
S = (1 / 2) · α · ED²
Where α is the central angle, in radians.
Rectangle ACDE
S = ED · AE
If we know that AE = 20 cm, ED = 28 cm, α = π / 4 and AB = 20 cm, then the area of the shaded area is:
S = (28 cm) · (20 cm) - (1 / 2) · (π / 4) · (28 cm)² - (1 / 2) · (20 cm) · (20 cm)
S ≈ 52.124 cm²
To learn more on areas: https://brainly.com/question/27683633
#SPJ1
Simplify each expression.
8x+13 - 3x + 9/1/2
Answer:5x+22
there you gooo
Answer:
5x+ 45/2
Step-by-step explanation:
Makayla has 25% as many bags of popcorn as her sister. How many bags of popcorn does her sister have if Makayla has 12 bags?
Answer:
Makayla's sister has 48 bags of popcorn
Step-by-step explanation:
25/100 = 4
12x4 = 48
12*4
= 48 is the answer
three hot dogs cost $82.86 and 2 hamburgers cost $55.12. which food has the lower unit price
Answer:
Hamburgers
Step-by-step explanation:
82.86/3 = 27.62
55.12/2 = 27.56
27.56 is smaller so hamburgers it is!
1.
The band and the orchestra are each having a party to celebrate the
results of their latest competition. The band would like to order cupcakes
from Walmart at a cost of $3.35 per cupcake and a $13.00 order fee
The orchestra would like to order cupcakes from Publix at $2.90 each
and a $22.50 order fee. This system {2.90c +22.50 represents the
total cost, T, and the number of cupcakes. Determine how many
cupcakes each club can order if they both have the same amount of
money to spend. Is the solution viable or not viable?
By solving a linear equation, it can be calculated that
Each club can order 21.1 cupcakes if they both have the same amount of
money to spend
What is a linear equation?
Equation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by an equal to sign
A one degree equation is called linear equation
Let the number of cupcakes ordered by each club be c
The band would like to order cupcakes from Walmart at a cost of $3.35 per cupcake and a $13.00 order fee
Total amount spent = $(13 + 3.35c)
The orchestra would like to order cupcakes from Publix at $2.90 each
and a $22.50 order fee
Total amount spent = $(22.5 + 2.90c)
By the problem,
The linear equation is
13 + 3.35c = 22.5 + 2.90c
3.35c - 2.90c = 22.5 - 13
0.45c = 9.5
c = 21.1
This solution is not viable as the number of cupcakes must be an integer not a decimal.
To learn more about linear equation , refer to the link-
https://brainly.com/question/2030026
#SPJ1
1. Which of the following is a perfect cube. (A) 100 (B) 68600 (C) 343000 (D) 400
Answer: 68600
hope it helps!
a doctor claims that people are at most 6 pounds overweight. to test the claim, the doctor randomly selects 81 people and calculates the difference between their ideal weight and actual weight. the sample mean and sample standard deviation of that difference were 7 pounds and 2 pounds respectively. can we conclude at the 1% level of significance that the claim is true? group of answer choices yes, conclude the claim is true by rejecting h0. no, conclude the claim is not true by rejecting h0. no, conclude the claim is not true by accepting h0. yes, conclude the claim is true by accepting h0.
we conclude at the 1% level of significance that the claim is true by accepting H₀
What is Hypothesis?
A hypothesis outlines your expectations for the results of your investigation. It is a speculative, untested response to your research question.
Given,
n = 81
x bar = 7
s= 2
Here, a doctor claims that people are atmost 6 pound over weight
H₀ : μ ≤ 6 versus
H₀ : μ > 6 versus
Now,
The Test Stastistic is
t = x bar - μ / s√n
t = 7-6/2√81
t = 4.5
let ∝ = 0.10, then p value = 0.000
p value >∝
yes, conclude the claim is true by accepting H₀
To learn more about Hypothesis visit:
brainly.com/question/11560606
#SPJ4
2) Given that Y and P are two events and P(Y) = 0.57, P(P) = 0.5 and P(Y UP) = 0.84,
Draw a Venn Diagram and find:
a) P(Yn P)
b) P(Y|P)
c) P(P|Y)
d) P(Y/P')
a) The value of P(Y∩P) =0.23
b) The value of (Y|P) = 0.34
c) The value of (P|Y) = 0.27
d) The value of P(Y/P') = 0.68
What is Venn diagram?
A Venn diagram can also be referred to as a set diagram or a logic diagram that illustrates various set operations including the intersection, union, and difference of sets. Subsets of a set are also represented using it. A subset of whole numbers, which is a subset of integers, is a collection of natural numbers, as an example.
Given that there are two events Y and P.
P(Y) = 0.57
P(P) = 0.5
P(Y∪P) = 0.84
The formula of intersection is P(Y∩P) = P(P) + P(Y) - P(Y∪P)
Putting P(Y) = 0.57, P(P) = 0.5, P(Y∪P) = 0.84
P(Y∩P) = 0.5 + 0.57 - 0.84
P(Y∩P) = 0.23.
b)
P(Y|P) = P(Y) - P(Y∩P)
P(Y|P) = 0.57 - 0.23
P(Y|P) = 0.34
c)
P(P|Y) = P(P) - P(Y∩P)
P(P|Y) = 0.5 - 0.23
P(P|Y) = 0.27
d) P(Y/P') = P(Y∩P') / P(P')
P(Y/P') = P(Y|P)/[1 - P(P)]
P(Y/P') = 0.34/(1- 0.5)
P(Y/P') = 0.68
To learn more about conditional probability, click on below link:
https://brainly.com/question/17888647
#SPJ1
Select ALL the correct answers.
Consider the graph given below.
Determine which sequences of transformations could be applied to the parent function, f(x) = x, to obtain the graph above.
1)Shift left 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2
2)Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2
3)Shift right 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2
4)Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units
5)Shift left 2 units, reflect over the y-axis, and then vertically stretch by a factor of 6
6)Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units
The sequences of transformations that could be applied to the parent function are Reflected over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units i.e. Option (4).
What is transformation?
An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation. Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
The two-dimensional shape without any transformations is known as a preimage or inverse image. The transformed figure is shown in the image.
Given, the parent function, f(x) = x
From the given graph, the equation will be
y = -2x + 6
Then, the transformation will be
Shifted up 6 units
Vertical stretch by a factor of 2
Reflected over the y-axis
Hence, the required answer is Option 4.
To learn more about transformation
https://brainly.com/question/2458900
#SPJ1
Which of the following values is not an irrational number?
5.73, ,√73, √40
O 5.73
O TT
3/73
O√40
The number that is non-irrational is 5.73, because it can be written as a quotient of two integers.
Which of the following options is not an irrational number?A rational number is a number that can be written as a quotient of two integer numbers, while an irrational number can't be written like that.
Also, the square root of a non perfect square is also irrational.
Here the options are:
5.73, ,√73, √40
Notice that neither of the square roots of non perfect square numbers, so these are irrational numbers.
In other hand, if we see the first one:
5.73
We can rewrite this as:
5.73 = 573/100
So this is a quotient of two integers, then this is a rational number, so this is the correct option.
Learn more about rational numbers by reading:
https://brainly.com/question/12088221
#SPJ1
At a football stadium, 4% of the fans in attendance were teenagers. If there were 170 teenagers at the football stadium, what was the total number of people at the stadium?
Answer:
4,250
Step-by-step explanation:
If 4% of all fans were teenagers, and 100 divided by 4 is 25, simply math of 170 times 25 gives you 4,250
Therefore, the answer is 4,250
Answer:
Total number of people = 4,250
Step-by-step explanation:
4% of 4,250 = 170
Help!!!! Please Help Me!!! I need the answer right now!!! Thanks!!!
The subject is Science and Not Mathematics.
I couldn't find the Science option.
The numbers of the atoms of each element are;
Carbon dioxide;6 atoms of carbon, 12 atoms of oxygen
Water ;12 atoms of hydrogen, 6 atoms of oxygen
Glucose;6 atoms of carbon, 12 atoms of hydrogen, 6 atoms of oxygen
Oxygen molecule12 atoms of oxygen
What is a reaction?In a chemical reaction, there is the combination of the atoms of the reactants and a consequent recombination as the products are formed. In accordance with the law of the conservation of mass, we know that the number of atoms before reaction must be equal to the number of atoms after reaction.
Now we have to look at the atoms and count up the number of atoms of each element in each of the compounds and this is how we are able to obtain the number of each atom as shown above.
Learn more about reaction:https://brainly.com/question/28984750
#SPJ1
Express 80 as the product of its prime factors.
Write the prime factors in ascending order.
Answer: [tex]2^4 \times 5[/tex]
Step-by-step explanation:
[tex]80=2 \times 40\\\\80=2 \times 2 \times 20\\\\80=2 \times 2 \times 2 \times 10\\\\80=2 \times 2 \times 2 \times 2 \times 5\\\\80=2^4 \times 5[/tex]
Which stataments are true regarding undifinable terms in geometry?
Answer:
A point has no length or widthA line consists of an infinite number of pointsA plane consists of an infinite set of linesStep-by-step explanation:
The statements that are true regarding undefined terms are;
A point has no length or widthA line consists of an infinite number of pointsA plane consists of an infinite set of linesThe reason these statements above are true are as follows:
Examples of undefined terms includes a point, a plane, a line and a set
A point is for representing a position in space. It has no dimensions
Therefore, the statement, A point has no length or width is true
A plane is defined as an interconnected set of points that lay on the same flat surface, and extends infinitely along the surface in all directions
A line is defined as an infinite set of points that are arranged in straight path and extends without end in opposite directions
Therefore, the statement, a line consists of an infinite number of points is true
Therefore, a plane can be considered as being made up of an infinite set of lines that are located on a flat surface
Therefore, the statement, a plane consists of an infinite set of lines is true
what is this pleasee i give brainliest
The Slope of the line is -3/2
How to find Slope of the Line ?By Substituting x=26
=1/9/8*26+8/3
=-3/2
The slope formula is as follows if P(x1,y1) and Q(x2,y2) are the two points on a straight line:Slope, m = Y-coordinate change / X-coordinate changem = (y2 – y1)/(x2 – x1) (x2 – x1)As a result, using the formula above, we can quickly determine the slope of a line connecting two locations.The rise of the line from one point to another (along the y-axis) over the run is another way to describe the slope of a line between two points (along x-axis). A line's slope provides information on the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them.To learn more about Slope of the Line refer to:
https://brainly.com/question/27212023
#SPJ1
Blaine is going bowling and will need to
pay $4 for shoes and then $3 for every
game. Write an equation for the
situation, if Blaine spends 16 dollars.
Answer: $16 = 4s + 3g
Step-by-step explanation:
s = shoes
g = games
A garden snail travels at a rate of 2.2 feet per minute.
At this rate, how long will it take for the snail to travel 55 feet?
At this rate, it will take the snail [___ minutes to travel 55 feet.
WHAT IS THE ANSWER.
If the snails moves at a constant rate, it will take 25 minutes to travel 55 feet.
How long will it take for the snail to travel 55 feet?We know that the snail travels at a rate of 2.2 feet per minute, so after x minutes, the distance traveled by the snail is:
D = 2.2ft*x
To see how many minutes it takes the snail to travel 55 feet, we need to solve the equation:
55 ft = 2.2ft*x
If we divide both sides by 2.2ft, we will get:
55ft/2.2ft = x
25 = x
So the snail takes 25 minutes to travel the 55 feet.
Learn more about distances:
https://brainly.com/question/7243416
#SPJ1
What is the value of x in the solution to this system of equations?
5x - 5y = 120
y = -7x + 8
Enter your answer in the box.
X = what is x?!?!
Answer:
{x = 4
{y = -20
Step-by-step explanation:
{5x - 5y = 120
{y = -7x + 8
5x - 5(-7x +8) = 120
5x + 35x - 40 = 120
40x - 40 = 120
40x = 120 + 40
40x = 160
x = 160/40
(cross out common factor)
x = 4
-----------
x = 4 (next is y)
y = -7 x 4 + 8 (calculate)
y = 20
y = -20
solution of system;
{x = 4
{y = 20
Lisa has x $5 bills and y $10 bills in her purse. The total value of the bills is more than $100. Which Inequality models this situation?
Answer:
D) 5x + 10y > 100
Step-by-step explanation:
We know that the sum of x $5 bills and y $10 bills in more than $100:
5x + 10y > 100
c) 5x + 10y > 100
The sentence did not say equal or greater than (≥).
for a particular clothing store a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed. suppose six customers are randomly selected and are mailed $10-off coupons. what is the probability that three of the customers redeem the coupon?
The anticipated quantity of coupons as calculated from the data given is 1.6 .
We learn from the question that
The probability of a $10 voucher being redeemed via mail is p = 0.16.
n = 10 is the sample size.
In general, the projected number of coupons redeemed is represented numerically as
E(x) = np [ of PDF ]
= 10 x 0.16
= 1.6
When data follows a normal distribution, the probability density function (PDF) and cumulative distribution function (CDF) assist us in determining probabilities and ranges of probabilities. The CDF is the PDF integration, from left to right. We may construct many forms of probability estimates from our normally distributed data using these two normal distribution functions.
The standard deviation is a technique for us to explain how "spread out" the data is - how far it "deviates" from the mean value. Both and are known as normal distribution parameters.
To learn more about normal distribution
brainly.com/question/27997995
#SPJ4
DUE BY SATURDAY!! please help
Answer:
Step-by-step explanation:
so you don't understand at all
Answer:
a.+1,-1
b.+√13,-√13
c.no real solutions
d.no real solutions
Step-by-step explanation:
question no c&d has no real solutions but they have complex solutions
if you are not taught about complex numbers then the Answers to c&d are no real solutions but for complex solutions
c.+3i,-3i
d.+√5i,-√5i
9. The length of an arc of a circle is 12 cm. The corresponding sector area is 108 cm².
Find:
a) the radius of the circle
b) the angle subtended at the centre of the circle by the arc.
At the circle's center, the arc's radius and angle are 9 cm and 4/3 radians, respectively.
What is the arc of a circle?Any section of a circle's circumference is considered an arc. Remember that the circumference of a circle is its perimeter or distance.
Given the length of the arc is 12cm and the area of the arc is 108 cm Square.
Since the length of the arc = θ × r
Area of the arc (A) = (θ/360°) × πr2
Substituting values in the formulas
12 = θ × r
108 = θ × r²
comparing both equations
r = 9 cm
θ = 4/3 radian
Therefore, the radius and the angle subtended at the center of the circle by the arc are 9 cm and 4/3 radian respectively.
Learn more about the arc of the circle here:
https://brainly.com/question/16930503
#SPJ1
Please help me with this question!
Answer:
Step-by-step explanation:
the answer is 11/12
If slope of a line is 7 and y-intercept is 4, then write the equation of that line.
Answer: The answer is y=7x+4
M is the slope and the y-intercept is b
Consider this right triangle. 20 m 37° Enter the length of side AB, to the nearest tenth.
Answer:
15.1
Step-by-step explanation:
tan(angle) = opposite/adjacent
tan 37 = AB/20
AB = 20 x tan 37 = 20 x 0.754 = 15.08 or 15.1
Geometric Transformations
The four letter code from the transformations is given as follows:
FB H.
How to obtain the four letter code?The four letter code is obtained applying the transformations to the given points.
The coordinates of point 1 are given as follows:
(-4,2).
The transformation is a reflection over the x-axis, which has the rule given as follows:
(x,y) ->(x,-y).
Hence the coordinates of the image of point 1 are given as follows:
1'(-4,-2).
Meaning that the first letter is of F.
The coordinates of point 2 are given as follows:
(-2,3).
The transformation is a reflection over the y-axis, which has the rule given as follows:
(x,y) ->(-x,y).
Hence the coordinates of the image of point 2 are given as follows:
2'(2,3)
Meaning that the second letter is of B.
The coordinates of point 4 are given as follows:
(-1,2)
The transformation is a reflection over the line y = x, which has the rule given as follows:
(x,y) ->(y,x).
Hence the coordinates of the image of point 4 are given as follows:
4'(2,-1)
Meaning that the fourth letter is of H.
Missing InformationThe third transformation is missing.
More can be learned about transformations at https://brainly.com/question/29209050
#SPJ1
Help with question 1
Answer: D
Step-by-step explanation:
Given the tally marks its 16ths, and the point is on the 3rd tally so it would be 10-3/16 Hope this helps!
Julie buys a pair of earrings for $7. Now she would like to buy the same earrings for 2 of her friends. How much will she spend for all 3 pairs of earrings
