Final answer:
The rate at which the tip of the shadow is moving away from the pole when the person is 25 ft from the pole is 0 ft/sec. The rate at which the tip of the shadow is moving away from the person when the person is 25 ft from the pole is 0 ft/sec.
Explanation:
To solve for the rates at which the tip of the shadow is moving away from the pole and from the person, we can use similar triangles and related rates. Let's solve each part step by step:
a. Rate the tip of the shadow is moving away from the pole:
We have a right triangle formed by the pole, the person, and the tip of the shadow. Let x be the distance between the person and the tip of the shadow.
Since the person is moving away from the pole at a rate of 2 ft/sec, dx/dt = 2 ft/sec.
Using the similar triangles, we have:
(12 ft + 5.5 ft) / x = 12 ft / (x + 25 ft)
Simplifying the equation gives:
17.5x + 437.5 = 12x + 300
5.5x = 137.5
x = 25 ft
Now, let's differentiate both sides of the equation with respect to time t:
17.5 (dx/dt) = 12 (dx/dt) + 0
17.5 (dx/dt) - 12 (dx/dt) = 0
5.5 (dx/dt) = 0
dx/dt = 0 ft/sec
So, the rate at which the tip of the shadow is moving away from the pole when the person is 25 ft from the pole is 0 ft/sec.
b. Rate the tip of the shadow is moving away from the person:
Using the similar triangles, we have:
(12 ft + 5.5 ft) / x = 5.5 ft / 25 ft
Simplifying the equation gives:
17.5x = 137.5
x = 7.857 ft
Now, let's differentiate both sides of the equation with respect to time t:
17.5 (dx/dt) = 5.5 (dx/dt) + d(7.857)/dt
12 (dx/dt) = d(7.857)/dt
dx/dt = (d(7.857)/dt) / 12
dx/dt = (0 ft/sec) / 12
So, the rate at which the tip of the shadow is moving away from the person when the person is 25 ft from the pole is 0 ft/sec.
PLEASE HELP I HAVE THE ANSWER JUST NEED THE WORK!
Answer:
in expanded form the summation is
2 + 4 + 6 .... upto 20 + 2 y^6 × 10
= 110 + 20y^6
Find the area of the triangle below.
A.√3/2
B.√3
C.2√3
D.2√2
Answer: A
A= 1/2 x b x h
1/2(1)(1 sq rt 3)= .866
Sq rt 3 /2 = .867
Step-by-step explanation:
best estimate for the quotient of 2 5/6 divided by 1/3
Answer:
the best answer for this is 8.5, if you choose to round up it would be about 9
Step-by-step explanation:
To estimate the quotient of 2 5/6 divided by 1/3, convert the mixed number to an improper fraction and multiply by the reciprocal of the divisor.
Explanation:To find the best estimate for the quotient of 2 ⅝ divided by ⅓, we can convert the mixed number to an improper fraction and then multiply by the reciprocal of the divisor. First, convert 2 ⅝ to an improper fraction: 2 x 6 + 5 = 17/6. Next, multiply 17/6 by the reciprocal of 1/3: 17/6 x 3/1 = 51/6. Simplifying the fraction gives the answer as 8 1/2. Therefore, the best estimate for the quotient is 8 1/2.
Learn more about Estimating quotients here:https://brainly.com/question/16131717
#SPJ2
A fruit stand has to decide what to charge for their produce. They need $ 10 for 4 apples and 4 oranges. They also need $ 15 for 6 apples and 6 oranges. We put this information into a system of linear equations. Can we find a unique price for an apple and an orange?
Answer:
No
Step-by-step explanation:
Say the price of 1 apple is x and the price of 1 orange is y. Then, we can write the two equations:
4x + 4y = 10
6x + 6y = 15
We can try to solve this by elimination, which means getting rid of one variable so that we're left with only 1 variable to solve for. Multiply the top equation by 3 and the bottom equation by 2:
3 * (4x + 4y) = 10 * 3 ⇒ 12x + 12y = 30
2 * (6x + 6y) = 15 * 2 ⇒ 12x + 12y = 30
Subtract the bottom equation from the top:
12x + 12y = 30
- 12x + 12y = 30
______________
0 + 0 = 0
Since we result in 0 = 0, that means any values of x and y we put into the equations will work, so we cannot find a unique price.
Hope this helps!
Answer:
No
Step-by-step explanation:
4A + 4O = 10
6A + 6O = 15
The second equation is just a multiple of the first one, so we don't have two distinct equations to solve for the prices
Adam recorded the number of flower blooms on each of his ten rose bushes. 9, 10, 4, 12, 15, 17, 18, 10, 12, 13 If he combined the number of blooms into one data set, which box plot correctly displays the data? A) A B) B C) C D) D
Answer:
The correct option is;
A)
Step-by-step explanation:
The box plot diagram will be constructed as follows
From the question data we have that;
9, 10, 4, 12, 15, 17, 18, 10, 12, 13
Rearranging we have
4, 9, 10, 10, 12, 12, 13, 15, 17,18,
The minimum = 4
The maximum = 18
Median = 12
The lower quartile Q₁ = 10
The upper quartile Q₂ = 15
Therefore, the correct option for the flower blooms on Rose brushes is A.
Answer:
The box plot that correctly displays the data is A.
Correct statement, question and graph:
Adam recorded the number of flower blooms on each of his ten rose bushes.
9, 10, 4, 12, 15, 17, 18, 10, 12, 13
If he combined the number of blooms into one data set, which box plot correctly displays the data?
A)
B)
C)
D)
Source:
Previous question that can be found at brainly
Step-by-step explanation:
1. Let's order the data from smallest to largest.
4, 9, 10, 10, 12, 12, 13, 15, 17, 18
2. Let's find the median, this way:
Median = (5th number + 6th number)/2
Median = 12 + 12/2 = 24/2 = 12
3. Let's find out the quartiles.
The first quartile is the median of the data points to the left of the median.
4, 9, 10, 10, 12
Q₁ = 10
The third quartile is the median of the data points to the right of the median.
12, 13, 15, 17, 18
Q₃ = 15
The box plot that correctly displays Q₁, median and Q₃ is box plot A.
In Box B, Q₁ = 9, median = 10 and Q₃ = 14In Box C, Q₁ = 9, median = 10 and Q₃ = 12 with values from 6 to 12In Box D, Q₁ = 5, median = 9 and Q₃ = 14Jill spent of her money on a new shirt end of her Money on pants with a fraction of her money has she spent money on pants what fraction of her money has she spent
Answer:
This means Jill has spent exactly half of her money and she has exactly half of her money too left.
The fraction of her money she has spent = (1/2)
Step-by-step explanation:
The total fraction of money Jill has spent = (fraction of money she spent on a new shirt) + (fraction of money she spent on pants) = (1/6) + (1/3) = (3/6) = (1/2)
This means Jill has spent exactly half of her money and she has exactly half of her money too left.
Hope this Helps!!!
Pls help me understand.
A students cost for last semester was $2,000. She spent $380 of that on books. What percent of last semesters cost was spent on books?
Answer:
19 %
Step-by-step explanation:
380 : 2000 = 0.19
0.19 X 100%= 19 %
PLEASE HELP!!! SHOW ALL YOUR WORK WORTH 30 Points!!!!
Answer:
A
1) horizontal translation of 2 units towards left
2) vertical translation of 10 units upwards
B)
1) k = -2
2) k = 10
C)
1) g(x) = f(x + 2)
2) g(x) = f(x) + 10
Step-by-step explanation:
A & B)
1) horizontal translation of 2 units towards left
2) vertical translation of 10 units upwards
C)
1) g(x) = f(x + 2)
2) g(x) = f(x) + 10
The diagonal of a rectangle is 25 in. The width is 15 inches. What is the length
Answer:
The length is 20 in
Step-by-step explanation:
Use Pythagorean Theorem to solve for the length
15^2 + b^2 = 25^2 Simplify
225 + b^2 = 625
-225 - 225 Subtract 225 from both sides
b^2 = 400 Take the square root of both sides
b = 20 in
If this answer is correct, please make me Brainliest!
a standard golf ball has a diameter of 1.68 inches. the material used to make the golf ball weighs .6523 ounces per cubic inch. what is the weight, to the nearest hundredth of an ounce, of one golf ball?
Given:
Given that the standard golf ball has a diameter of 1.68 inches.
Radius of the golf ball is 0.84 inches.
The material used to make the golf ball weighs 0.6523 ounces per cubic inch.
We need to determine the weight of one golf ball.
Volume of the golf ball:
The volume of the golf ball can be determined using the formula,
[tex]V=\frac{4}{3} \pi r^3[/tex]
Substituting r = 0.84, we get;
[tex]V=\frac{4}{3} (3.14)(0.84)^3[/tex]
[tex]V=2.481\ in^3[/tex]
Thus, the volume of one golf ball is 2.481 cubic inches.
Weight of one golf ball:
The weight of one golf ball can be determined by multiplying the volume of the golf ball with 0.6523 ounces per cubic inch.
Thus, we have;
[tex]Weight=2.481 \times 0.6523[/tex]
[tex]Weight = 1.62[/tex]
Thus, the weight of one golf ball is 1.62 ounces.
Final answer:
To find the weight of a golf ball, calculate its volume using its diameter, then multiply the volume by the weight of the material. The weight of one golf ball is approximately 1.80 ounces.
Explanation:
To find the weight of one golf ball, we first need to calculate its volume. The diameter of the golf ball is given as 1.68 inches, so the radius is 0.84 inches. Using the formula for the volume of a sphere, V = (4/3)πr³, we find the volume to be approximately 2.759 cubic inches.
Next, we calculate the weight of the golf ball by multiplying the volume by the weight of the material per cubic inch. Given that the material weighs 0.6523 ounces per cubic inch, multiplying this by the volume of the golf ball gives us the weight. Therefore, the weight of one golf ball is approximately 1.80 ounces.
Find the y-intercept for the parabola defined by
this equation:
y=x² + 8x + 12
Separate the values with a comma.
Enter the correct answer.
Answer:
y-intercepts (0,-12)
Step-by-step explanation:
3. What is the area of the circle shown below?
Diameter:
28 inches
Pi=3.14
Step-by-step explanation:
Given diameter (d) = 28 inches
π = 3.14
Radius (r) = 28/2= 14 inches
Now
Area of the circle
= πr²
= 3.14 * 14²
= 615.44 inch ²
Kim and Sam were each given the same pair of numbers. Sam's description of the two numbers was: The larger number is 3 more than three times the smaller number, . Kim's description of the two numbers was: Five times the smaller number decreased by 7 is the larger number. Which equation represents the situation?
Answer:
Sam's description = [tex]3x+3[/tex], Kim's description = [tex]5x-7[/tex]
Step-by-step explanation:
Given:
Kim and Sam were each given the same pair of numbers.
Sam's description of the two numbers was:
The larger number is 3 more than three times the smaller number.
Kim's description of the two numbers was:
Five times the smaller number decreased by 7 is the larger number.
Question asked:
Which equation represents the situation?
Solution:
Let smaller number = [tex]x[/tex]
According to Sam's description of the two numbers, the equation will be:-
Larger number = 3 more than three times the smaller number
= [tex]3x+3\ (eq1)[/tex]
According to Kim's description of the two numbers was, the equation will be:-
Larger number = Five times decreased by 7
= [tex]5x-7\ (eq2)[/tex]
By equating both equation:-
[tex]5x-7=3x+3\\ \\ Subtracting\ both\ sides\ by \ 3x\\ \\ 5x-3x-7=3x-3x+3\\ \\ 2x-7=3\\ \\ Adding\ both\ sides\ by\ 7\\ \\ 2x-7+7=3+7\\ \\ 2x=10\\ \\ Dividing\ both\ sides\ by\ 2\\ \\ x=5[/tex]
Smaller number = [tex]x[/tex] = 5
Larger number = [tex]3\times5+3=15+3=18[/tex]
Therefore, equations represents the situation are [tex]3x+3[/tex] and [tex]5x-7[/tex]
3 markers cost $5.79.
Which equation would help determine the cost of 13 markers?
Choose 1 answer:
A.) 13/$5.79 = x/3
B.) x/13 = 3/$5.79
C.) 3/$5.79 = 13/x
D.)13/x = $5.79/3
E.) None of the above
Answer:
C. 3/$5.79 = 13/x
Step-by-step explanation:
We can write the fact that 3 markers cost $5.79 as a proportion:
3/$5.79
Let x represent the unknown cost of 13 markers. Since 13 markers cost x, we have the following proportion:
13/x
The cost changes along with the number of markers purchased, and so the two proportions are equivalent.
3/$5.79 = 13/x
Find the expression for the area of the figure. Give your answer as a simplified radical.
Answer:
D
Step-by-step explanation:
Area of rectangle= length × breadth
Area of figure
[tex] = ( \sqrt{15x}) ( \sqrt{10x} ) \\ = \sqrt{(10x)(15x)} \\ = \sqrt{150 {x}^{2} } \\ = \sqrt{6(25 {x}^{2}) } \\ = (\sqrt{6} )( \sqrt{( {5x})^{2} } ) \\ = ( \sqrt{6} )(5x) \\ = 5x \sqrt{6} [/tex]
Find the mean of these numbers:
4,2,5,6,3
Answer:
5
Step-by-step explanation:
4,2,5,6,3
cancel one on each side ou till you have 1 number left
Answer:
Mean: 4
Median: 4
Mode: 4, 2, 5, 6, 3
Minimum: 2
Maximum: 6
Range: 4
Count: 5
Sum: 20
Step-by-step explanation:
A sample of 16 atm transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. Find the test statistic to decide whether the mean transaction time exceeds 60 seconds.
Answer:
[tex]t=\frac{67-60}{\frac{12}{\sqrt{16}}}=2.33[/tex]
Step-by-step explanation:
Data given and notation
[tex]\bar X=67[/tex] represent the sample mean
[tex]s=12[/tex] represent the sample standard deviation
[tex]n=16[/tex] sample size
[tex]\mu_o =60[/tex] represent the value that we want to test
t would represent the statistic (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean is higher than 60, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 60[/tex]
Alternative hypothesis:[tex]\mu > 60[/tex]
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{67-60}{\frac{12}{\sqrt{16}}}=2.33[/tex]
Troy is helping his mom make a fence for their rectangular vegetable garden. First, they measure the sides and find that it is 20 feet long and 40 feet wide. Then, they buy fencing from the hardware store. If the store sells fencing in 4-yard packages, how many packages do Troy and his mom need?
Answer:
10 Packages
Step-by-step explanation:
The rectangular vegetable garden has a dimension of Length 20 feet and Width 40 feet.
Perimeter of a Rectangle=2(L+W)
=2(20+40)=2(60)=120 feet
Since the store sells fencing in 4-yard packages, let us convert our perimeter to Yards.
1 Yard= 3 Foot
x Yard =120 Feet
Cross Multiply
3x=120
x=40 Yards
The Perimeter =40 Yards
Therefore the number of Packages which Troy and his Mom needs:
Perimeter of the Garden÷Length Per Package
=40÷4
=10 Packages
Troy and his mom would need 20 Packages of Fencing.
To be able to conclude, we conver
Seven people went to the movies.
The number of adults was one more
than the number of children. How
many adults and children went to the
movies?
Answer:
4 adults 3 children
Step-by-step explanation:
Final answer:
To solve the problem, we set c as the number of children, and deduced that a = c + 1 for the number of adults, leading to 3 children and 4 adults going to the movies.
Explanation:
The question is about solving a basic algebra problem involving a small group of people going to the movies. To find out how many adults and children went to the movies, we can set up an equation based on the information provided. Let c represent the number of children. Since the number of adults is one more than the number of children, we have a = c + 1 for the number of adults. Together, they total seven people, so we can write the equation c + (c + 1) = 7. Simplifying this equation gives us 2c + 1 = 7. Solving for c, we subtract 1 from both sides to get 2c = 6, and then divide by 2 to find c = 3. This means there were 3 children. Since there is one more adult than children, a = 3 + 1 = 4, which gives us 4 adults. Therefore, there were 3 children and 4 adults that went to the movies.
Two apples and five bananas cost £4.20
Three apples and seven bananas cost £5.95
Work out the cost of an apple and the cost of a banana
The cost of an apple is 0.7 dollars and the cost of a banana is 0.35 dollars.
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
Given, Two apples and five bananas cost £4.20.
Assuming no. of apples to be x and no. of bananas to be y.
∴ 2x + 5y = 4.20...(i) and,
Three apples and seven bananas cost £5.95.
∴ 3x + 7y = 5.95...(ii)
Now multiplying eqn(i) by 3 and eqn(ii) by 2 to cancel out x in both equations.
So, 6x + 15y = 12.6...(iii) and 6x + 14y = 11.9...(iv)
Subtracting eqn(iv) from eqn(iii) we get y = 0.7 and substituting value of y in eqn(iv) we get x = 0.35
learn more about linear equations here :
https://brainly.com/question/13738061
#SPJ2
The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 56 ft from a light is 2.7 foot-candles, find the intensity on a screen 70 ft from the light.
Answer:
The intensity on a screen 70 ft from the light is 1.728 foot candle.
Step-by-step explanation:
Given that,
The magnitude of intensity [tex]I[/tex] of light varies inversely as the square of the magnitude of distance D from the source.
That is
[tex]I\propto \frac{1}{D^2}[/tex]
Then,
[tex]\frac{I_1}{I_2}=\frac{D_2^2}{D_1^2}[/tex]
Given that,
The magnitude of intensity of illumination on a screen 56 ft from a light is 2.7 foot-candle.
Here,
[tex]I_1[/tex]=2.7 foot-candle, [tex]D_1[/tex]= 56 ft
[tex]I_2[/tex]=?, [tex]D_2[/tex]= 70 ft.
[tex]\frac{I_1}{I_2}=\frac{D_2^2}{D_1^2}[/tex]
[tex]\Rightarrow \frac{2.7}{I_2}=\frac{70^2}{56^2}[/tex]
[tex]\Rightarrow \frac{I_2}{2.7}=\frac{56^2}{70^2}[/tex]
[tex]\Rightarrow {I_2}=\frac{56^2\times 2.7}{70^2}[/tex]
[tex]\Rightarrow {I_2}=1.728[/tex] foot-candle
The intensity on a screen 70 ft from the light is 1.728 foot candle.
5(1-2x)+8x=15 what the equations
Answer:
x = -5
Step-by-step explanation:
You're asking for the solution? the x value that makes the equation true?
First perform the multiplication: 5 - 10x + 8x = 15
Combining like terms, we get -10 = 2x.
Dividing both sides by 2 yields x = -5.
1. Calculate the H.C.F of a 2 b 5 and a 3 b 3 .
9514 1404 393
Answer:
a^2·b^3
Step-by-step explanation:
Factors of both terms include 'a' to some power, and 'b' to some power. The greatest common factor will use the lowest power of each of these variables.
powers of 'a' are a^2, a^3. Greatest common power is a^2
powers of 'b' are b^5 and b^3. Greatest common power is b^3
The highest common factor of both terms is a^2·b^3.
__
Additional comment
When that is factored out of the sum, you have ...
a^2b^5 +a^3b^3 = a^2·b^3(b^2 +a)
The remaining two terms (b^2+a) have no common factors—as it should be.
Perms and Combos Special Cases
If eight people eat dinner together, in how
many different ways may 3 order chicken, 4
order steak, and l order lobster?
treat each choice as a sonarate combination
Then as a counting principle
x² + 3x + 2
What do I do
Answer:
(x+2)(x+1)
Step-by-step explanation:
it factors to (x+2) and (x+1) then the answers are -2 and -1
IF SOMEONE ANSWERS WITHIN 5 MINUTES THEY WILL GET BRAINLIEST ANSWER
Among a group of 86 investors, 23 owned shares of Stock A, 33 owned shares of Stock B, 44 owned shares of Stock C, 11 owned shares of both Stock A and Stock B, 10 owned shares of Stock A and Stock C, 17 owned shares of Stock B and Stock C, and 7 owned shares of all three. How many investors did not have shares in any of the three? How many owned shares of either Stock A or Stock C but not Stock B?
A. 24,33
B. 17,36
C. 17,33
D. 17,40
Answer:
A
Step-by-step explanation:
Hi!
This one's a bit hard to explain! IF you want explanation, just comment.
Using the data given, we can conclude that [tex]\boxed{A}[/tex] is the correct answer.
Hope this helps!
Students in a marching band want to line up for their performance. The problem is that when they Line up in twos there is 1 left over. When they line up in threes there are 2 left over. When they line up in fours there are 3 left over. When they line up in fives there are 4 left over. When they line up in sixes there are 5 left over. When they line up in sevens there are no students left over. How many students are there?
Answer:
x = 119
Step-by-step explanation:
Solution:-
- The number of students in a marching band = x
- When they Line up in "twos" there is 1 left over, That if we mathematically express it:
Division: x / 2 , Remainder = 1
- When they Line up in "threes" there is 2 left over, That if we mathematically express it:
Division: x / 3 , Remainder = 2
- When they Line up in "fours" there is 3 left over, That if we mathematically express it:
Division: x / 4 , Remainder = 3
When they Line up in "fives" there is 4 left over, That if we mathematically express it:
Division: x / 5 , Remainder = 4
When they Line up in "sixes" there is 5 left over, That if we mathematically express it:
Division: x / 6 , Remainder = 5
When they Line up in "sevens" there are no left over, That if we mathematically express it:
Division: x / 7 , Remainder = 0
- It means that the total number of "x" students are perfectly divisible by 7. If it is not divisible by 2, then it is an odd number.
- So,
x = 7 * a
Where, x > 7 and exclude derivative multiples of (5, 4 , 6)
- So from trial and error, a = 17
x = 119
Using multiples and remainder of divisions, it is found that there were 119 students there.
-------------------------
When they line up in sevens, no students remain, thus, the number of students is a multiple of 7.When they line up in two's, there is 1 left over, thus, the number of students is odd.When they line up in three's, there are 2 left over, thus, the remainder of the division of the number of students n and 3 is 2.When they line up in fives, there are 4 left over, thus, the remainder of the division of the number of students n and 5 is 4.When they line up in sixes there are 5 left over, thus, the remainder of the division of the number of students n and 6 is 5.-------------------------
Shortening the possibilities, we look at odd multiples of 7, which are: {7, 21, 35, 49, 63, 77, 91, 105, 119, ...}
21, 63 and 105 are multiples of 3, so these are not the number of students.35 is multiple of 5, so it is also disconsidered.The remainder of the division of 119 and 3 is 2.The remainder of the division of 119 and 5 is 4.The remainder of the division of 119 and 6 is 5.Thus, 119 is the number of students.
A similar problem is given at https://brainly.com/question/21644206
What does a a isolate variable mean?
Answer:
Isolating a variable means rearranging an algebraic equation so that a different variable is on its own. The goal is to choose a sequence of operations that will leave the variable of interest on one side and put all other terms on the other side of the equal sign.
Step-by-step explanation:
Original price of a book: $90.50
Tax: 4%
Answer:
The tax is $3.62
So the price now is $94.12
Answer:
$94.12
Step-by-step explanation:
If the original price is $90.5 then you would have to multiply
90.50*104%,you multiply 104% because 100% is sopposed to be the original price and the tax adds up the price by 4% so,
100%+4%=104%
104%*90.50=$94.12
Suppose Mr. Kraus is 1.75m tall. When her shadow is 1m, how long would the shadow be of a 265m tall building?
Answer:
151.43 meters
Step-by-step explanation:
We can use ratios to solve
1.75m 265m
--------------- = -----------
1 m x meters
Using cross products
1.75x = 265*1
Divide each side by 1.75
1.75x/1.75 = 265/1.75
x =151.4285714
151.43 meters
Answer:
151.429m
Step-by-step explanation:
This is a proportion problem.
1.75m/1m = 265m/ Xm
1.75m= 265m/ Xm
Xm = 265m/1.75m = 151.429m