a man 6 ft tall walks at a rate of 6 ft/sec away from a lamppost that is 18 ft high. at what rate is the length of his shadow changing when he is 30 ft away from the lamppost? (do not round your answer)
The rate of change of length of his shadow when he is 30ft away from the lamp post is 3 ft/sec .
In the question ,
it is given that ,
the length of the man is = 6 ft ,
le the distance of the man from the base of the lamp post at time "t" is = x
let the length of the shadow at time "t" = y ,
given that dx/dt = 6 ft/sec .
From the figure given ,
In triangle ABC and triangle ADE ,
AB/BC = AD/DE
that is , y/6 = (x+y)/18
after simplification ,
we get ,
2y = x .
differentiating both with respect to "t" ,
we get
2 * dy/dt = dx/dt
Substituting dx/dt = 6 ,
we get ,
dy/dt = 3 ft/sec .
Therefore , the rate of change of the length of the shadow is 3 ft/sec .
Learn more about Rate Of Change here
https://brainly.com/question/17037953
#SPJ4
What are the 4 theorems to prove two triangles are congruent?
We can use the four theorems - SSS, SAS, ASA, AAS - to prove that two triangles are congruent.
To prove that the given triangles are congruent there are some rules, one of which it must satisfy to show that the two are congruent. The four theorems are stated and explained below-
SSS rule: If the 3 sides of both of the given triangles are equal, then the triangles are congruent.
SAS rule: If the 2 sides and one of the three angles of both of the given triangles are equal, then the triangles are congruent.
ASA rule: If 2 of the total three angles and a side (in the middle of the angles)of both of the given triangles are equal, then the triangles are congruent.
AAS rule: If 2 angles and a side(adjacent to the angles) of the given two triangles are equal, then the triangles are congruent.
Learn more about Congruency on
https://brainly.com/question/19258025?referrer=searchResults
#SPJ4
five people check identical suitcases before boarding an airplane. at the baggage claim, each person takes one of the five suitcases at random. what is the probability that every person ends up with the wrong suitcase?
5% probability is there that every person ends up with the wrong suitcase.
Given,
Number of people checked in = 5
Number of suitcases = 5
We have to find the probability that when each person taken a suitcase randomly and it ends up with the wrong suitcase;
Here,
5 people can take 5 suitcases in 5 different ways.
So,
Probability = possible outcomes / original outcome
Probability = 5 x 5 / 5
Probability = 25/5 = 5
That is,
The probability that every person ends up with the wrong suitcase is 5%
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ4
What is the total number of degrees in a triangle?
60
90°
30°
Answer:
180 degrees in a triangle
you are bored at a lunch meeting and decide to place a raisin in your glass of water. the raisin swells to twice its original size. relative to the water, the raisin must have been:
If the raisin swells to twice its original size, relative to the water, the raisin must have been hypertonic solution.
A response that is hypertonic refers to one that has a larger osmotic strain than another arrangement. In the end, a hypertonic arrangement is one in which the concentration of solute particles outside of a layer is greater than that inside.An arrangement that has a higher solute fixation than another arrangement is said to be hypertonic.The inside of a red platelet compared with the solute concentration of fresh water serve as illustrations of a hypertonic arrangement.When two arrangements come into contact, the solute or dissolvable moves until the arrangements reach harmony and are isotonic with one another.To know more about hypertonic check the below link:
https://brainly.com/question/29309024
#SPJ4
The formula F(C) =
9
5
C + 32 calculates the temperature in degrees Fahrenheit, given a temperature in degrees Celsius.
You can find an equation for the temperature in degrees Celsius for a given temperature in degrees Fahrenheit by finding the function’s
An equation for the temperature in degrees Celsius for a given temperature in degrees Fahrenheit can be determine and it will be: [tex]C = \frac{F - 32}{95}[/tex].
What is temperature?
The degree to which an object is hot or cold is measured by its temperature.
Formula to calculate temperature in degrees Fahrenheit:
F = 95C+32 --- (1)
The given equation (1) can be used to determine the equation to calculate the temperature in degrees Celsius for a given temperature in degrees Fahrenheit.
To determine equation for degrees Celsius following steps can be used:
Subtract 32 from both sides of the above equation,
F - 32 = 95C + 32 - 32
F - 32 = 95C
95C = F - 32
Divide both sides by 95
C = (F - 32)/ 95
Hence, by using some arithmetic operations, equation for the temperature in degrees Celsius for a given temperature in degrees Fahrenheit can be determine and it will be: [tex]C = \frac{F - 32}{95}[/tex].
To know more about temperature, click on the link
https://brainly.com/question/4658134
#SPJ1
Answer:
inverse
Step-by-step explanation:
ed 2023
how many miles are there
At the end, the distance to the car will be 17 miles, and the distance that they walked is 13 miles.
How many miles are there?We want to find the total distance at which the hikers are at the end.
Notice that each little square represents one mile. And the line ends at two little squares above the marking of 15 miles, then the distance to the car at the end is:
15mi + 2 mi = 17 miles.
We also could want to find the distance they walked on the given graph. To find that, we need to take the difference between the final distance and the initial distance.
The final distance is 17 miles, we already know this, and the initial distance is the y-intercept, which in this case is 4 miles.
Then the distance that they walked is:
D = 17mi - 4mi = 13mi
Learn more about distances at:
https://brainly.com/question/7243416
#SPJ1
Evaluate the expression for the given value of the variable. 32 + 1/9t. T = - 1/2
Answer: 32 1/18
Step-by-step explanation: So first, I did 1/9 (-1/2) and I got 1/18. Yes although it was negative, when multiplying, it will become positive, then 1 x 1 is 1, and 9 x 2 is 18. Then, when adding it to 32, you get 32 1/18. I hoped this helped!
An auto mechanic's current annual gross wage is $43,500. For retirement, the mechanic wants to have enough saved to live off 80% of the
current annual gross wage and draw 4% the first year. What is the total amount the mechanic will need in retirement savings to meet their
retirement income goal?
A 780,000
B 1,392,000
C 870,000
D 807,000
The total amount the mechanic will need in retirement savings to meet their retirement income goal is 870,000. The correct option is C.
What is an expression?In mathematics, an expression is a combination of numbers, symbols, and operations (such as addition, subtraction, multiplication, and division) that represents a quantity or a value.
Expressions can be very simple, such as a single number or variable, or they can be more complex, such as a combination of multiple terms with different operators.
The mechanic wants to live off 80% of their current annual gross wage, which is:
0.8 x 43,500 = $34,800 per year
The mechanic plans to draw 4% the first year from their retirement savings, which means the total retirement savings needed are:
34,800 / 0.04 = $870,000
Therefore, the answer is C) 870,000.
To know more about an expression follow
https://brainly.com/question/12247643
#SPJ2
the soccer filed has a width of 6.its length is double the size of the width what is the total area of the soccer field
Answer:72 lol
Step-by-step explanation: do the math 6 x 2 = 12
6 x 12 = 72
can anyone help me I don't know how to do this
Step-by-step explanation:
its me ryan , 15 from michigan . Its just that i needed friends . If you want to be my good friend , please do comment below and we can be real good friends. ?
11. suppose the spot rate over a 3-year period is 2.658%, the forward rate for the first year is f0;1 54:5%, and the forward rate for the second year is f1;2 51:5%. what is the forward rate for the third year?
The forward rate for the third year 3.06%
The forward rate is the interest rate applied to future financial transactions. The forward rate is calculated from the spot rate, adjusted for maintenance costs to determine future interest rates that equalize the strategy to extend short-term investments and the total return on long-term investments.
This term can also refer to interest rates charged on future financial obligations, such as interest rates on loan payments.
(n1 – n2) reservation rate calculation number. A few years later n2 no. The number of years of Forward rate = [(1 + S1)n1 / (1 + S2)n2]1/(n1-n2) – 1.
According the question:
S3 = [(1 + S₁) × (1 + F(1,2))²]¹/³ ⁻¹
= [(1 + 2.658%) × (1 + 2.340%)²]¹/³ ⁻¹
= [1.02658 × 11.1556]¹/³ ⁻¹
= (12.18)¹/³ ⁻¹
= 3.06
Therefore, calculation of spot rate for three years will be, 3.06%
Learn more about Forward rate:
https://brainly.com/question/14029507
#SPJ4
To lift a load of 100 n a distance of 1 m an effort of 25 n must be applied over an inclined plane of length 4 m. What must be done to lift the load 2 m, using the same effort?.
An inclined plane of length 8 m is used to lift the load 2 m, using the same effort.
A ramp that helps lift and lower heavy things is called an inclined plane. It is a flat surface that is positioned against a horizontal surface at an angle other than a right angle.
Work is defined as the use of force to move an object over a distance. It is derived as the product of displacement (d) and force (F). Work is given by W = F×d = 25 N×d.
When a body is lifted, we can express work as W = m×g×h where g is gravity and h is height. And the force is written as F = m×g where m is the mass of an object. Then, W = F×h
Calculating the work done to lift the load to 2 m, we get,
W = 100 N×2 m = 200 Nm.
Substitute this value in W = F×h, we get,
200 Nm = 25 N×d
Divide both sides by 25 N, and we get,
[tex]\begin{aligned}\frac{\mathrm{200\;Nm}}{\mathrm{25\;N}}&=\frac{\mathrm{25\;N\times d}}{\mathrm{25\;N}}\\d&=\mathrm{8\;m}\end{aligned}[/tex]
The value is 8 m. Therefore, the first statement is correct.
The complete question is -
To lift a load of 100 N a distance of 1 m an effort of 25 N must be applied over an inclined plane of length 4 m. What must be done to lift the load 2 m, using the same effort?
A. Use an inclined plane of length 8 m.
B. Use an inclined plane of length 2 m.
C. Use an inclined plane of length 10 m
D. Use an inclined plane of length 16 m.
To know more about work:
https://brainly.com/question/2005605
#SPJ4
approximately 40 % of the population have type o blood . if 4 people are randomly selected to be donors . find the probability that at least one is type o.
The probability that at least one is type O is 0.8704.
What is a binomial distribution probability?
A value's likelihood of taking one of two independent values is summarised by the statistical distribution known as the binomial distribution.
Given, 40 % of the population has type O blood and 4 people are randomly selected to be donors
Then, binomial distribution can be given by
X ~ = Binomial(n = 4, p = 0.4)
P(at least one type O)
P[X ≥ 1]
= 1- P[X < 1]
= 1- P[X = 0]
= [tex]1 -C(4,0) * (0.4)^{0} * (1 - 0.4)^{4-0}[/tex]
=1-0.1296
=0.8704
Hence, the probability that at least one is type O is 0.8704.
To learn more about a binomial distribution probability
https://brainly.com/question/14578727
#SPJ4
Gavin deposited $12,000 at 2% interest mounted quarterly what is the value after 16 years round to the nearest cent
Answer:
final amount = $16512.36
Step-by-step explanation:
The question asks us to find the value of Gavin's deposit of $12,000 after 16 years, given that the interest rate of 2% is compounded quarterly.
To do this, we have to use the following formula for compound interest:
[tex]\boxed{A = P(1 + \frac{r}{n})^{nt}}[/tex],
where:
A → amount at the end
P → principal (original) amount
r → interest rate (in decimal)
n → number of times per year that the interest is compounded
t → time (in years).
From the question, we know that the initial amount deposited is $12,000. Therefore, P = 12000. We also know that the interest rate is 2%, but the formula requires the rate to be in decimal, so r = 0.02. The time for which the money is deposited is 16 years, and therefore, t = 16. We are told that the interest is compounded quarterly, that is, every 3 months. This means that the interest is compounded 4 times yearly, so n = 4.
From the above information and formula, we can calculate the final amount:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
⇒ [tex]A = 12000(1 + \frac{0.02}{4})^{4 \times 16}[/tex]
⇒ A = $16512.36
Therefore, the final amount after 16 years is $16512.36.
What is the length of DE?
Answer:
6.3
Step-by-step explanation:
probability is a measure of how likely an event is to occur. match one of the probabilities that follow with each statement of likelihood given. (the probability is usually a more exact measure of likelihood than is the verbal statement.)this event is impossible. it can never occur. b. this event is certain. it will occur on every trial. c. this event is very unlikely, but it will occur once in a while in a long sequence of trials. d. this event will occur more often than not.
Therefore the answer to following is probabilities of following problems are (a) 0 ,(b) 1 ,(c) 0.01 and (d) 0.6 .
What is probability ?To investigate unpredictability, mathematicians utilize probability. It discusses the possibility (the likelihood) of an event happening. For instance, if you flip a fair coin four times, you might not get two heads and two tails each time.
Here,
(A) The event cannot happen if the probability is zero.
(b) The event is guaranteed to occur if the probability is 1.
(c) An event is very unlikely to happen if the probability is less than 0.01.
(d) The occurrence is more likely to happen if the probability is 0.6. (because the probability is greater than 0.6).
(a) 0
(b) 1
(c) 0.01
(d) 0.6
Therefore the answer to following is probabilities of following problems are (a) 0 ,(b) 1 ,(c) 0.01 and (d) 0.6
To know more about probability , visit
https://brainly.com/question/11234923
#SPJ4
Complete the following questions.
Winona and Takoda are shopping for a present for their mother. The chart shows several possible presents. There is no sales tax in the state where they live.
a. Write two expressions in terms of d to show how much Winona and Takoda would pay in total if they buy their mother the set of power tools.
b. Let the value of d equal $79.00. Calculate the total cost of each of the possible presents for the value you chose. Then write a sentence telling Winona and Takoda which preset to buy for their mother if they want to spend the least amount of money.
a) The expressions are given as follows:
Power tools: 0.85d.Water skis: 0.75(d + 15).Jewelry: 0.9(d - 5).b) The total cost for each present is of:
Power tools: $67.15.Water skis: $69.56.Jewelry: $63.Hence the present that they can buy with the least amount of money is:
Jewelry.
How to obtain the costs?The costs are found applying the proportions in this problem.
As a function of d, the functions are found multiplying the decimal equivalents of each discount by the cost expression.
The decimal equivalents of each discount are given as follows:
Discount of 15% -> 0.85, as 85% of the price is paid.Discount of 25% -> 0.75, as 75% of the price is paid.Discount of 10% -> 0.9, as 90% of the price is paid.Then the actual costs are calculated replacing the instances of d in each item with the numeric value d = 79.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Which type of rigid transformation is the equivalent of two reflections across intersecting lines?
according to the question,
given data in the question,
the type of rigid transformation is the equivalent of two across intersecting lines
Rotation is the process of changing the orientation of a shape by mirroring two intersecting line segments.
The intersection of the two reflection lines is the center of rotation.
An isometric drawing is a composite of two isometric drawings. The combination of two reflections on two parallel lines corresponds to translation.
The configuration of the two reflections is either translational or rotational. A translation occurs when a reflection is followed by a parallel reflection. Reflections following reflections from intersecting lines cause rotation
To know more about rotation visit
https://brainly.com/question/6202925
#SPJ1
The type of transformation that is equivalent to 2 reflections across intersecting lines is rotation
Which transformation is equivalent to a double reflection over parallel lines?A slide or a shift is a translation. By executing two composite reflections along parallel lines, translations may be produced. Translations maintain orientation and are isometric.
Which type of isometry is the equivalent of two reflections in parallel lines?An isometry is made up of two other isometries. The translation is equal to the combination of two reflections over two parallel lines.
according to the question,
the type of rigid transformation is the equivalent of two across intersecting lines
Rotation is the process of changing the orientation of a shape by mirroring two intersecting line segments.
The intersection of the two reflection lines is the center of rotation.
An isometric drawing is a composite of two isometric drawings. The combination of two reflections on two parallel lines corresponds to translation.
The configuration of the two reflections is either translational or rotational. A translation occurs when a reflection is followed by a parallel reflection. Reflections following reflections from intersecting lines cause rotation
To know more about rotation visit:-
https://brainly.com/question/26249005
#SPJ4
How can you summarize the ruler placement postulate? you can measure the between points a and b by using as zero.
The summary of the ruler placement postulate is: A direct relationship exists between the set of points on the line and the collection of real numbers, where each point is matched to a single real number and The magnitude of the gap between two points is equal to the absolute value of the subtraction of the two associated values.
The ruler placement postulate states that if two points are given, it is possible to measure the distance between them by taking the point of reference as zero. This means that any point can be chosen as an origin, and the distance between the two points can be calculated by measuring the number of units between them. This postulate also applies to curves, and the distance between two points on a curve can be measured by taking a point of reference as zero and measuring the number of units between them. This postulate is essential in the measurement of distances between points and curves in geometry.
To know more about ruler placement postulate refer to the link brainly.com/question/25097538
#SPJ4
Carly is a catcher on the school softball team. By the end of the season she had played in 45 percent of the 40 games the team played. In how many games did Carly NOT play.
Number of games did Carly NOT play is 22.
How to calculate percentage?
A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Given:
Total number of games = 40
It is given that she had played in 45 percent of the 40 games the team played.
Number of games she played = 45% of 40
= [tex]\frac{45}{100}\times 40= 18[/tex]
Number of games she did not play = 40 - 18 = 22
Therefore, number of games did Carly NOT play is 22.
To learn more about the percentage from the given link.
https://brainly.com/question/24877689
#SPJ1
Mr. Patrick has 30 students in his class working on a project. Show at least 3 different ways he could equally group his students.
I will offer more points soon
Answer:
10 groups of 3, 3 groups of 10 and 5 groups of 6
Step-by-step explanation:
Joy had 939 stuffed animals. She gave some away. Now she has 402 stuffed animals. How many did she gave away?
Answer: 537 stuffed animals
Step-by-step explanation:
Take 939 - 402 = 537
So she gave away 537 stuffed animals
find a polynomial f(x) of degree 3 that has the following zeros: 1, 7, -2
leave your answer in factored form
pls !!!!!!!!! do ti. 24 3/5 +4^3x(8 1/5 -2) ??????????
The solution is, the simplified value is 2107/5 = 421.4.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
24 3/5 +4^3x(8 1/5 -2)
we have to
Simplify the Equation
With Converting 24 3/5 to a improper fraction
Calculate the Power of 4^3
Then convert 8 1/5 to a improper fraction
Subtract 41/5 and 2 to get 31/5
Then Multiple the product,
64 • 31/5 to get 1984/5
After add the fractions up
123/5 + 1984/5
=2107/5
=421.4
Hence, The solution is, the simplified value is 2107/5 = 421.4.
To learn more on simplification click:
brainly.com/question/28996879
#SPJ2
How long does it take to travel 1 km by bus?
Tt takes 1.5 min of time to travel a distance of 1 km by bus
Since here we need to find the time, which basically depends on the speed of the bus, as we know the formula we refer to for calculating the time is distance/speed, here we are provided with the distance which is 1km also equal to 1000m. Now considering a normal condition where the speed of the bus is h 40km per hour, therefore
=>Distance = Speed × Time
=?1km = 40 Km/hr × Time
Time = 1/40 hr = 0.025 hr ,Which is almost 1.5 min
To know more about time refer to the link brainly.com/question/16963199
#SPJ4
how many times can 64 go into 51
There are 2times 64 in 151. The answer you divide 151 by 64 which would get you 2.359375. The remainder is 23
none
Step-by-step explanation:
64 is a bigger number so unless I am wrong it should not be able to go into 51.
How do i solve this?
Answer:
7, 14,21 28
4,8,12,16
Step-by-step explanation:
Answer:
8, 21, 16
Step-by-step explanation:
The ratio from sugar to cups is 7:4, which is 1.75.
Divide and multiply to solve.
14 / 1.75 = 8
12 * 1.75 = 21
28 / 1.75 = 16
Which ordered pairs represent points on the graph of this equation? Select all that apply.
3X + y = 0
Answer:
Do you have a picture of the graph?
Step-by-step explanation:
If so can you pls insert :)
I need help pleaseeee
The words that fills the blank space on the method used to find the length of the diagonal AG, using Pythagorean Theorem are as follows;
Blank 1; The Pythagorean Theorem
Blank 2; Square root of 73
Blank 3; A leg
Blank 4; The hypotenuse
Blank 5; 9.4 cm
What is the Pythagorean Theorem?Pythagoras Theorem indicates that the square of the longest side of a right triangle is equivalent to the sum of the square of the other two sides.
The diagonals from point A to point G in the cuboid can be found using Pythagoras Theorem as follows;
The diagonal of the base rectangle, ABCD, is found as follows;
AC = √(8² + 3²) = √(73)
Using the side CG as the leg of the right triangle ΔACG, with AG being the hypotenuse, we get;
CG = 4 indicated in the diagram in the question
(AG)² = (AC)² + (CG)²
(AG)² = 73 + 4² = 89
AG = √(89) ≈ 9.4
The completed statement is therefore;
To find the length of the diagonal from point A (front/bottom /left) to point G (back/top/right); You would first use the Pythagorean Theorem on the bottom of the box rectangle to find the diagonal AC = square root 73 cm. Then use CG as a leg of the triangle ACG, with AG being the hypotenuse. AG is approximately 9.4 cm.Learn more about Pythagorean Theorem here:
https://brainly.com/question/15252776
#SPJ1