Answer:
(i) y = 5/7x
(ii) 7/3 m/s
Step-by-step explanation:
Shadow problems almost always involve similar triangles, meaning that shadow lengths and object heights generally have the same ratio. We can use this fact to write proportions related to the measures in this problem.
(i)The ratio of shadow-tip distance to the object height is the same for both objects. For distances in meters, we have ...
x/7 = (x-y)/2
2x = 7(x -y) . . . . . multiply by 14
7y = 5x . . . . . . . add 7y-2x
y = 5/7x . . . . . divide by the coefficient of y
__
(ii)Solving the equation from the first part for x, we have ...
x = 7/5y . . . . . multiply by 7/5
The derivative with respect to time is then ...
x' = 7/5y'
The rate of change of y is given as 5/3 m/s, so the rate of change of x will be ...
x' = (7/5)(5/3 m/s) = 7/3 m/s
The top of the man's shadow is moving at 7/3 meters per second.
How do you know 4/5 is already simpless? Explain
Answer:
cause u cant make it more simpler
Step-by-step explanation:
4 and 5 cannot bbe cancelled by any number
Answer:
you can simply a fraction with even and odd numbers
analyzing compositions of functions pls help asap
The second option is correct. The domain of the composite function (g o f) (x) is all real numbers except x = 0.
How to determine the domain of the composite functionTo determine the domain of the composition (g o f)(x), we need to consider the domains of both functions, as well as any restrictions that arise from the composition.
The function f(x) = 3x is defined for all real numbers since there are no restrictions on x.
The function g(x) = 1/x, however, has a restriction. It is not defined for x = 0 because division by zero is undefined.
Thus for the composition (g o f)(x) = g(f(x)):
(g o f)(x) = g(f(x)) = g(3x) = 1/(3x)
Since the function g(x) = 1/x has a restriction at x = 0, it implies that the composition (g o f)(x) = 1/(3x) will also have the same restriction.
Therefore, the domain of the composite function (g o f)(x) is all real numbers except x = 0.
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a bag contains one counter, known to be either white or black. a white counter is put in, the bag is shaken, and a counter is drawn out, which proves to be white. what is now the chance of drawing a white counter?
The chance of drawing a white counter after drawing a white counter from the bag is 1
Let's assume that the probability of drawing a white counter from the bag is represented by the symbol P(W), and the probability of drawing a black counter is represented by P(B).
Initially, there is a 50% chance that the counter in the bag is white and a 50% chance that it is black. Therefore, we can represent the probability of initially having a white counter as P(W) = 0.5 and the probability of initially having a black counter as P(B) = 0.5.
After adding the white counter to the bag, we now have two possible scenarios
The counter in the bag was originally white, and we added another white counter. The probability of this scenario is P(W) × 1 = 0.5 × 1 = 0.5.
The counter in the bag was originally black, and we added a white counter. The probability of this scenario is P(B) × 1 = 0.5 × 1 = 0.5.
Thus, the probability of drawing a white counter after drawing a white counter from the bag is the probability of scenario 1 divided by the probability of both scenarios
P(W|W) = P(W and W) / P(W and W) + P(B and W)
P(W|W) = (0.5 × 1) / ((0.5 × 1) + (0.5 × 0))
P(W|W) = 1
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A 2-column table with 10 rows. the first column is labeled x with entries 0.5, 1, 1, 1.5, 2, 2, 2.5, 3.5, 3.5, 4. the second column is labeled y with entries 1, 1, 2, 3, 2, 5, 4, 5, 6, 7. a graph shows the horizontal axis numbered 1 to 4 and the vertical axis numbered 1 to 7. a line increases from 0 to 4. the regression calculator shows the relationship between the hours devin spent playing a video game, x, and the levels he achieved, y. which number of hours can be used to make an extrapolation of the level he could achieve? 2 3 4 5
Based on the graph of this regression calculator, the number of hours that can be used to make an extrapolation of the level he could achieve is: A. 2.
What is a regression line?A regression line can be defined as a statistical line that best describes the behavior of a data set and such, it is a line that best fits a set of data.
How to determine number of hours?From the graph of this regression calculator, we can deduce that the linear regression is given by this function y ≈ 1.62x + 0.117; r ≈ 0.92.
Thus, the extrapolation would be given by:
0.14999 ≤ x ≤ 4.35.
0.39999 ≤ y ≤ 7.6.
Therefore, two (2) number of hours can be used to make an extrapolation of the level he could achieve.
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Answer:
answer is 5
Step-by-step explanation:
What is the slope? WIL MARK BRAIN 20 POINTS
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
4PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer:
9.3 ft
Step-by-step explanation:
If the original quantity is 8 and the new quantity
is 2, what is the percent decrease?
If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.
How did we figure this out?
For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:
\(\boxed{8-2=6}\\\boxed{6/2=3}\)
We are going to take that 25% and multiply it with 3 to get are final answer.
What is the missing number of 25 and 3?\(\boxed{25*3=75}\\\boxed{So,2=75}\)
Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.
Find all the roots for the polynomial,
32x2 -108 = 0
Answer:
x=-1.837 or 1.837
Step by Step explanation:
Use the standard form,ax²+bx+c=0 , to find the coefficients of our equation, :
q = 32
b= 0
c= -108
x=-1.837 or x=1.837
I hope this is helpful
pls tag brainliest answer
2 1/3 +1/2{2 divided by 4/5}
Answer:
36/5
Step-by-step explanation:
36/5 is the answer.
21/3 +1/2*4/10
7+1/5
36/5
please mark me brainliest
A shipping container will be used to transport several 120-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 12400 kilograms have already been loaded into the container. Which inequality can be used to determine x, the greatest number of
120-kilogram crates that can be loaded onto the shipping container?
Inequality can be used to determine x, the greatest number of 120-kilogram crates that can be loaded onto the shipping container is 8000 + 120C <= 27500
What is inequality?An inequality is a relationship that allows us to contrast two or more mathematical expressions.
Knowing that;
Each carton weighs 120 kg.
The container's maximum weight when loaded is 27500 kg.
Weight of the container as it is currently loaded: 8000 kg
Now that we have merged, we have;
Solution
because 8000 grams have already been loaded kilograms
into the container
each crate weighs 120 kilograms.
so 8000 + 120C <= 27500
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66.67 mph in 1.5 hours
How long does it take the car to travel 26 miles at this speed?
Answer:
5
Step-by-step explanation:
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Find the distance between the given parallel planes. 4x − 5y z = 16, 8x − 10y 2z = 2
The distance between the two planes 4x-5y+z=16 and 8x-10y+2z=2 will be 2.34 units.
What is a plane?
A plane is a flat surface on which a straight line joining any two points on it would wholly lie.
Given equations are
\(4x-5y+z=16\)
\(8x-10y+2z=2\)
The distance between two planes is given by the formula:
\(D=\dfrac{|d_2-d_1|}{\sqrt{a^2+b^2+c^2}}\)
Here from equations
\(4x-5y+z=16\)
\(8x-10y+2z=2\)
We can also write the equation \(8x-10y+2z=2\) as:
\(4x-5y+z=1\)
So now the two equations are:
\(4x-5y+z=16\)
\(4x-5y+z=1\)
here a=4 b=-5 c =1 and d1=16 d2=1
Putting the values in the equation.
\(D=\dfrac{|-16+1|}{\sqrt{4^2+(-5)^2+(10^2)}}\)
\(D=2.34\)
Hence the distance between the two planes 4x-5y+z=16 and 8x-10y+2z=2 will be 2.34 units.
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Suppose X is a normal random variable with mean u=49 and standard deviation=9. (a) Compute the z-value corresponding to X=36. (b) Suppose the area under the standard normal curve to the left of the z-value found in part (a) is 0.0743. What is the area under the normal curve to the left of X-367- (c) What is the area under the normal curve to the right of X-36? -
The area under the normal curve to the right of X = 36 is approximately 0.9257.
(a) To compute the z-value corresponding to X = 36, we use the formula:
z = (X - u) / σ
where X is the value of interest, u is the mean, and σ is the standard deviation.
Plugging in the values, we have:
z = (36 - 49) / 9
= -13 / 9
≈ -1.444
Therefore, the z-value corresponding to X = 36 is approximately -1.444.
(b) Given that the area under the standard normal curve to the left of the z-value found in part (a) is 0.0743, we want to find the corresponding area under the normal curve to the left of X = 36.
We can use the z-score to find this area. From part (a), we have z = -1.444. Using a standard normal distribution table or a calculator, we can find the area corresponding to this z-value, which is approximately 0.0743.
Therefore, the area under the normal curve to the left of X = 36 is approximately 0.0743.
(c) To find the area under the normal curve to the right of X = 36, we subtract the area to the left of X = 36 from 1.
Area to the right of X = 36 = 1 - Area to the left of X = 36
= 1 - 0.0743
= 0.9257
Therefore, the area under the normal curve to the right of X = 36 is approximately 0.9257.
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Please help me anwser this
Answer:
(x + 3)² + (y - 6)² = 9
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (- 3, 6 ) and r = 3 , then
(x - (- 3 )² + (y - 6)² = 3² , that is
(x + 3)² + (y - 6)² = 9
how do I find the Domain and Range for:f(x)=(x-2)^2 -2
Domain: the set of all possible x values of the function.
Since there are no radicals and denominators, the domain of the function is all the real numbers.
Domain= all real numbers
Range = the set of all possible y values of the function
Range= (-2; ∞)
Graph of the function:
A miniature golf course recently provided its customers with a variety of colored golf balls.
red 2
white 1
pink 10
blue 2
green 5
What is the experimental probability that the next customer will receive a pink golf ball?
Write your answer as a fraction or whole number.
P(pink)=
Scott rolled a number cube several times and counted how many times he rolled a 3.
What is the theoretical probability of Scott rolling a 3 if his number cube is fair?
Answer:
The probability of rolling a 3 is : 1/6
Step-by-step explanation:
Select all the expressions that are equivalent to 16x - 12 -24x + 4.
Answer:
Expressions equivalent to 16x - 12 -24x + 4.
-8x - 8 , - (8x + 8) , 8 (-x -1) , -8 (x + 1)
Step-by-step explanation:
16x -12 -24x + 4
Arranging like terms, 16x - 24x - 12 + 4 = -8x - 8
Taking common minus, = - (8x + 8)
Taking common 8, = 8 (-x -1)
Taking common -8, = -8 (x +1)
student researchers wanted to see whether a short delay between seeing a list of words and when people were asked to recall them would hinder memorization. the subjects were shown a list of words to memorize for 1 minute and were then given 1 minute to recall as many words as they could. each subject did this once with no delay between memorizing and recall and another time with a 30-second wait between memorizing and recall. they were randomly assigned the order of the two conditions. the number of words memorized under each condition can be found in the statcrunch data set memorizingwords. questions: use the appropriate simulation applet to calculate an approximate p-value. is there strong evidence that a short delay hinders the memorization process? explain.
The appropriate simulation applet to calculate an approximate p-value is 0.0077.
The strong evidence that a short delay hinders the memorization process is strong data suggests that a brief delay impairs memorization.
Delay or no delay, answer: the number of words remembered
The mean distance between words remembered with and without delay over time is null, or zero.
Alt: The mean distance in words remembered over the long term (with no delay minus with delay) is higher than 0.
Yes, the majority of the lines do skew to the right. The mean for no delay is 10.55 whereas that for with delay is 8.7.
The mean distance in words remembered is 1.85.
1)0.0077 as the p-value
2)Strong data suggests that a brief delay impairs memorization.
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Help with me maths plz ;)
Help plz !!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
275
Donavan is measuring the angles of a triangle. He measures the first two angles and gets 10 and 120. What should be the measure of the third angle
Answer:
the third angle should equal 50 degrees.
Step-by-step explanation:
the angles of a triangle always add up to 180 degrees.
10+120=130
180-130=50
therefore, the last angle=50 degrees
Dora baked 12 cupcakes. She used 1/4 pound of flour for each cupcake. She used 1/2 of the flour in the container. How much flour was in the container?
Answer:
There was 6 pounds of flour in the container.
Step-by-step explanation:
Because each cupcake used a fourth of a pound and she made 12 cupcakes she used a total of 3 pounds. It also said she used half the container which would mean there was originally 6 pounds of flour.
What the answer to the question
Answer:
6.1
Step-by-step explanation:
use law of cosines
d² = e² + f² - 2ef cos D
d² = 9² + 10² - 2(9)(10) cos 37
d² = 81 + 100 - 143.75
d² = 37.25
d = 6.1
Rhombus EFGH is rotated 90° counterclockwise about vertex G. How many pairs of parallel sides does the rotated figure have?
The number of pairs of the parallel lines after the rotation is 2
How to determine the number of pairs of the parallel lines?The transformation is described by
Rotation by 90° counterclockwise about vertex G
There are four types of transformation, and they are:
DilationRotationReflectionTranslationAs a general rule of rotation:
When a shape, line or an angle is rotated, the size of the properties in the rotated figure remains unchanged
Before rotation, a rhombus has two pairs of parallel sides
This means that the parallel sides would remain parallel after rotation
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there are 40 rows of seats in a class.Each row has 120 chairs.How many students can sit in the class?
Answer:
4800 students
Step-by-step explanation:
120x40=4800students
4800 can sit in the class
Can y’all pls help me I need help!!
Answer:
D
Step-by-step explanation:
I hope this helps :) Have a lovely day!!!
A truck is hauling earth from a construction site. The truck has the following specifications: T
Bank density
Loose density
110 pcf
100 pef
The productivity, in bank measure (yd
3
/hr), of this operation is most nearly: (A) 38.8 (B) 35.3 (C) 32.3 (D) 29.5
The productivity of the truck in bank measure is most nearly 32.3 (option C).
To calculate the productivity of the truck in bank measure, we need to convert the loose density to bank density. Bank measure refers to the volume of material when it is compacted or in its natural state, while loose measure refers to the volume of material when it is loose or not compacted.
The formula to convert loose density to bank density is as follows:
Bank Density = Loose Density / (1 + Moisture Content)
Since the moisture content is not provided in the question, we assume it to be zero for simplicity. Therefore, the bank density is equal to the loose density.
Next, we need to calculate the truck's productivity in bank measure. The formula for productivity is:
Productivity = Truck Capacity / Cycle Time
However, the truck capacity and cycle time are not provided in the question. Therefore, we cannot directly calculate the productivity.
Given that we have the specifications of the truck's density, we can make an estimation based on industry standards. A common truck capacity for earth hauling is around 20 cubic yards. The cycle time can vary depending on factors such as loading and dumping time, travel distance, and road conditions. For estimation purposes, let's assume a cycle time of 30 minutes (0.5 hours).
Using these values, we can calculate the productivity as follows:
Productivity = Truck Capacity / Cycle Time
Productivity = 20 / 0.5
Productivity = 40 cubic yards per hour
However, the productivity is measured in bank measure (yd³/hr), so we need to adjust the result based on the bank density.
Adjusted Productivity = Productivity * (Loose Density / Bank Density)
Adjusted Productivity = 40 * (100 / 110)
Adjusted Productivity ≈ 32.3 cubic yards per hour (bank measure)
Therefore, the productivity of the truck in bank measure is most nearly 32.3 (option C).
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please help me!
Compare the graph of f(x) = 6x and the graph of g(x) = 6x – 12. Then complete the sentence. The graph of g is a _____ translation of the graph of f _____ units _____.
Answer:
The graph of g(x) is a vertical translation of f(x). Although both have the same x coordinates but different y coordinates.
The graph of g is a vertical translation of the graph of f 12 units downward.
Step-by-step explanation:
The equation y=f(x)+k represents that when k is negative, the graph moves downward.
The complete the sentence is The graph of g is a vertical translation of the graph of f 12 units downward.
What is Translation?Translation is the act of moving a shape or a figure from one location to another. A figure can move in translation up, down, right, left, or anywhere else in the coordinate system. Only the object's position changes during translation; its size stays the same.
Given:
f(x) = 6x
and, g(x) = 6x – 12.
As, -12 shows the vertical translation of 12 units.
Also, The graph of g(x) is a vertical translation of f(x).
Despite having distinct y coordinates, both objects have the same x coordinates.
So, The graph of g is a vertical translation of the graph of 12 units downward.
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Find the midline of the graph of the function
g(x) = cos (3x)
A) x = 0
B y = 3
C y = 0
D none