On level ground, a 60-foot-tall vertical building casts a 10-foot shadow. at the same time, another vertical building casts a 25-foot shadow. how many feet tall is the second building?
Using the concept of similar triangles, the height of the second building is calculated to be 150 feet, since its 25-foot shadow corresponds proportionally to the 60-foot building's 10-foot shadow.
Explanation:To find the height of the second building given that a 60-foot-tall building casts a 10-foot shadow, and another building casts a 25-foot shadow, we can use the concept of similar triangles. The idea behind similar triangles is that corresponding sides of similar triangles are proportional. Therefore, if one building is 60 feet tall and casts a 10-foot shadow, the ratios of the height to shadow length will be the same for the second building.
To set up the proportion, we have:
We can write the proportion as:
h1/s1 = h2/s2
Substituting the known values into the proportion gives us:
60/10 = x/25
Now we solve for x:
x = (60/10) * 25
x = 6 * 25
x = 150
Therefore, the height of the second building is 150 feet.
show that if k is a positive constant, then the area between the x-axis and one arch of the curve y=sin kx is 2/k
HELP ASAP PLEASE!!!
In the past 3 years, Hannah’s savings account has earned $90 in interest. She initially deposited $600. What simple annual interest rate is the bank paying on this account?
A. 2.7%
B. 3.5%
C. 4.0%
D. 5.0%
1/5n -3/4 + 7/10n
Need to simplify
if x=t^2-1 and y=t^4-2t^3, then when t=1 what's d^2y/dx^2? if x=t^2-1 and y=t^4-2t^3, then when t=1 what's d^2y/dx^2?
To find d^2y/dx^2 when t = 1, we need to first express y in terms of x. Then, differentiate y with respect to x to find dy/dx. Finally, differentiate dy/dx to find d^2y/dx^2 and substitute t = 1.
Explanation:Given the equations x = t^2 - 1 and y = t^4 - 2t^3, we can find d^2y/dx^2 when t = 1.
First, we need to express y in terms of x. From the equation x = t^2 - 1, we can solve for t as t = sqrt(x + 1). Substituting this into the equation y = t^4 - 2t^3, we get y = (sqrt(x + 1))^4 - 2(sqrt(x + 1))^3.
Next, we need to find the first derivative of y with respect to x: dy/dx. Then, we can find the second derivative d^2y/dx^2 by differentiating dy/dx. Finally, substitute t = 1 into d^2y/dx^2 to find the value.
K-X=V-W solve for the letter x
To solve for 'x' in the equation 'K - X = V - W', we rearrange the equation to isolate 'x', resulting in 'X = K - V + W'.
Explanation:To solve the equation for the letter x, you need to isolate x on one side of the equation. It's a simple process of rearranging the equation.
Here we start with the original equation:
K - X = V - W
First, to separate your desired variable, or in this case 'x', we add 'X' to both sides to cancel 'X' from the left hand side:
K = X + V - W
Finally, to isolate 'x', we just need to subtract 'V' and add 'W' to both sides
X = K - V + W
So, the solution to the equation when solved for the letter 'x' is X = K - V + W.
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You need to know the number of different arrangements possible for five distinct letters. You decide to use the permutations rule, but your friends tells you to use 5!. Who is correct? Explain.
Both methods are correct, since you are counting all possible arrangements of 5 items taken 5 at a time.
Your friend is correct because applying the permutations rule in this setting would be inappropriate.
Neither method is correct. The combinations rule should be applied in this setting.
Your method is correct because you are applying the permutations rule in the appropriate setting.
Answer:
Option A
Step-by-step explanation:
Whenever we want to arrange a number of objects or letters or numbers n then we must check whether
i) repitition is allowed
If repitition is allowed then total number of ways = n!
ii) repitition not allowed.
In this case again we have to check whether order matters or not.
If order matters then no of ways nPn.
Here n =5
We find that nPn = 5!
Thus both are correct.
Hence option A
math plzz I got turn it in Monday she just barely sent me it
the smaller of two containers has a capacity of 150 gallons. When it is 4/5 full, its contents are emptied into a larger container, filling exactly 2/3 of it. What is the capacity, in gallons, of the larger container?
On April 11, 2012, two earthquakes were measured off the northwest coast of Sumatra. The first had a magnitude of 8.6. The second had a magnitude of 8.2. By what approximate factor was the intensity of the first earthquake greater than the intensity of the second earthquake?
0.40
1.02
1.05
2.51
Answer:
Option D. 2.51 is correct.
Step-by-step explanation:
Magnitude of first earthquake = 8.6
Let intensity of first earthquake be x
[tex]Magnitude = \log(\frac{x}{S}),\text{ where S is seismographic factor}\\\\\implies 8.6=\log(\frac{x}{S}).......(1)[/tex]
Magnitude of second earthquake = 8.2
Let intensity of second earthquake be y
[tex]Magnitude = \log(\frac{y}{S}),\text{ where S is seismographic factor}\\\\\implies 8.2=\log(\frac{y}{S}).......(2)[/tex]
Now, to find the factor by which intensity of first earthquake is greater than intensity of second : we divide equation (1) by equation (2)
[tex]\implies\log(\frac{x}{y})=8.6 - 8.2\\\\\implies \log(\frac{x}{y})=0.4\\\\\implies\frac{x}{y}=10^{0.4}\\\\\implies\frac{x}{y}=2.51[/tex]
Hence the required factor is 2.51
Therefore, Option D. 2.51 is correct.
Answer:
2.51
Step-by-step explanation:
A child takes a nap averaging three hours and gets an average of 12 hours of sleep at night. Nap time and night time sleep can each vary by 30 mins. What are the possible time lengths for the child's nap and night time sleep? ...?
Final answer:
The possible time lengths for the child's nap are 2.5 to 3.5 hours, and for night time sleep are 11.5 to 12.5 hours, as each can vary by up to 30 minutes.
Explanation:
The question asks about the possible time lengths for a child's nap and night time sleep, given that each can vary by 30 minutes. The average nap time is three hours, so the possible nap lengths range from 2.5 hours (3 hours - 30 minutes) to 3.5 hours (3 hours + 30 minutes). Similarly, the average night time sleep is 12 hours, meaning the possible night time sleep lengths range from 11.5 hours (12 hours - 30 minutes) to 12.5 hours (12 hours + 30 minutes).
The child's nap can be from 2.5 to 3.5 hours and night sleep from 11.5 to 12.5 hours, totaling a possible sleep range of 14 to 16 hours per day.
Explanation:The child's nap time can vary by 30 minutes from the average of 3 hours, meaning the possible lengths for nap time range from 2.5 hours to 3.5 hours. Similarly, the night time sleep also has a variability of 30 minutes from the average of 12 hours, which gives a range of 11.5 hours to 12.5 hours for night time sleep. Therefore, the possible lengths for the child's total sleep time can range from a minimum of 14 hours (2.5 hours nap + 11.5 hours night) to a maximum of 16 hours (3.5 hours nap + 12.5 hours night).
what's is width of a rectangle with an area of 5/8 in and a length of ten inches
A parabola has the equation –5x^2 + 30x – y – 34 = 0. Which equation is that of the parabola in vertex form? ...?
A dvd costs $20 the sales tax is 6.5% how much sales tax do you have to pay
the table below represents the total number of laps jessica swam in the pool this summer.
week 1 18 laps week 2 28 laps week 3 38 laps week 4 48 laps
if the linear function representing the number of laps jessica swam each week is f(w)=10w+8. what does the 10 represent in this function?
In the function f(w) 10w+8, the number 10 represents the number of laps Jessica increased her swim by each week.
To find out what the coefficient 10 represents in the linear function f(w) = 10w + 8, we need to understand the structure of the function.
In this function:
- w represents the week of the summer.
- f(w) represents the number of laps Jessica swam in week w.
- The coefficient 10 is multiplied by w, indicating a relationship.
Since the linear function represents the number of laps Jessica swam each week, the coefficient 10 represents the number of laps Jessica increased her swim by each week.
So, the correct answer is: C. The number of laps Jessica increased her swim by each week
Complete question:
The table below represents the total number of laps Jessica swam in the pool this summer:
Week Laps
1 18
2 28
3 38
4 48
If the linear function representing the number of laps Jessica swam each week is f(w) 10w+8, what does the 10 represent in this function?
The number of laps Jessica swam in total
The week of the summer that Jessica swam
The number of laps Jessica Increased her swim by each week
A The number of laps Jessica swam in week
can -2/5 be simplified
car salesman sells cars with prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of cars he expects to sell over the next
10 years.
The salesman has observed that many students are looking for cars that cost less
than $5,000. If he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years, how will the distribution be affected?
The mean will shift to the right.
The mean and the median will be the same.
The median will shift to the right.
The mean will shift to the left.
I think it's B
Answer:
The mean will shift to the left.
Step-by-step explanation:
using the quadratic formula 3x2 – 13x + 4 = 0
find g'(4) given that f(4)=3 and f'(4) = -5. g(x) = f(x)/x
what is the answer to this : (3m 3 - y)(3m 3 - y)
A restaurant manager recorded the number of people in different age groups who attended her food festival. She then created the following histogram:
Histogram with title Food Festival Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79 and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50.
Which of the following statements best compares the height of the bars of the histogram?
There are twice as many participants in the 60–79 age group than in the 0–19 age group.
There are 3 times as many participants in the 40–59 age group than in the 0–19 age group.
There are more participants in the 40–59 age group than in the 0–19 and 60–79 groups combined.
There are more participants in the 60–79 age group than in the 0–19 and 20–39 groups combined.
Answer:
Option: B
There are three times as many participants in the 40-59 age group than in the 0-19 age group.
Step-by-step explanation:
From the histogram we have following observations:
Number of people in the age group 0-19= 20
Number of people in the age group 20-39=40
Number of people in the age group 40-59=60
Number of people in the age group 60-79=50
Hence, from the data we could say that there are three times as many participants in the 40-59 age group( which is 60) than in the 0-19 age group(which is 20).
Hence, option B is correct.
Write a real-world prblem in which you would need to convert pints to cups
Find the discriminant of the following equation.
4x2 + 12x + 9 = 0
Which of the following are not congruence theorems for right triangles? Check all that apply.
A. LA
B. HL
C. AA
D. HA
E. HH
F. LL
Answer:
E. HH, C. AA
Step-by-step explanation:
Got these from the quiz
make a conjecture about the next item in the sequence.
6,8,-32,-30,120
answer choices....... a.122 b.-480 c. -488 d. 116 ...?
The sequence alternates between adding 2 and multiplying by -4. Starting with 6, the sequence progresses by these operations to reach 120. Following this pattern, the next term after 120 is a) 122 by adding 2.
The student has asked to make a conjecture about the next item in the sequence 6, 8, -32, -30, 120. To determine the pattern, let's look at the differences between each pair of numbers.
From 6 to 8, we add 2.
From 8 to -32, we multiply 8 by -4.
From -32 to -30, we add 2.
From -30 to 120, we multiply -30 by -4.
It appears that the sequence alternates between adding 2 and multiplying by -4. Following this pattern, after 120 the next operation should be adding 2.
Therefore, the next number in the sequence would be 120 + 2 = 122. Hence, the answer is option a. 122.
b+c=10/a
solve for a ...?
To solve the equation b + c = 10/a for a, isolate a on one side of the equation by multiplying both sides by a, distribute a to both terms inside the parentheses, and then solve for a by dividing both sides by (b + c).
Explanation:To solve the equation b + c = 10/a for a, we need to isolate a on one side of the equation. We can start by multiplying both sides of the equation by a to get rid of the denominator:
a(b + c) = 10
Next, we can distribute a to both terms inside the parentheses:
ab + ac = 10
Finally, we can solve for a by dividing both sides of the equation by (b + c):
a = 10 / (b + c)
Calculate the average rate of change for the function f(x) = −x4 + 4x3 − 2x2 + x + 1, from x = 0 to x = 1.
0
1
2
7
Answer:
C) 2
Step-by-step explanation:
I took the quiz and got a 100%.
Shape 1 and shape 2 are plotted on a coordinate plane. Which rigid transformation can you perform on shape 2 to show that shape 2 is congruent to shape 1?
a 45° rotation clockwise about the origin
a translation 6 units to the left and 8 units up
a reflection across the x-axis
a translation 3 units to the left and 6 units up
Two translation rigid transformations are required to transform shape 1 to shape 2
The rigid transformation that can be performed on shape 2 to show that shape 2 is congruent to shape 1 is the option
A transformation of 6 units to the left and 8Reasons:
The coordinates of the three points on shape 1 are; (2, 12), (4, 14), (6, 14)
The coordinates of the three points shape 2 are; (8, 4), (10, 6), (12, 6)
The difference in the coordinates are;
Difference in x-coordinate are;
Point 1 = 8 - 2 = 6
Point 2 = 10 - 6 = 6
Point 3 = 12 - 6 = 6
Therefore;
To get the x-value of shape 1 from the shape 2, the transform that is to be performed on shape 2 is a transformation of -6 units or 6 units left
Difference in y-coordinate are;
Point 1 = 4 - 12 = -8
Point 2 = 6 - 14 = -8
Point 3 = 6 - 14 = -8
Therefore;
To get the y-value of shape 1 from the shape 2, the transform that is to be performed on shape 2 is a transformation of 8 units or 8 units up
The composite transformation is therefore;
A transformation of 6 units to the left and 8 units upLearn more here:
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Factor the expression.
9x^2 + 48x + 64
Are 8:5 and 4:19 equivalent