A flagpole 3 meters tall casta a shadow of 4 meters long at the same time a nearby building casts a shadow of 62 meters long. How tall is the building
Jim and his dad are building a rectangular flower bed. They have a total of 35 feet of landscaping timber to use, and they want to use all of it. However, they are not sure what width and length they want the flower bed to be. In this activity, you will write a function in which the width of the flower bed, w, is the input, and the length, l, is the output. The perimeter of a rectangle is given by the equation 2l + 2w = p. Part A Jim and his dad want to find the length of the garden once they decide its width. Use function notation to write a function that represents its length in terms of the width.
The perimeter of a rectangle is 35.
So the function that represents the length of the flower bed in terms of its width is:
l(w) = (35 - 2w) / 2.
What is a rectangular perimeter?The whole distance that a rectangle's borders, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.
To write a function that represents the length of the flower bed in terms of its width, we can use the equation for the perimeter of a rectangle:
2l + 2w = p
where l is the length, w is the width, and p is the perimeter. We know that the perimeter is 35 feet, so we can substitute that into the equation:
2l + 2w = 35
We want to solve this equation for l, so we can isolate the variable on one side of the equation:
2l = 35 - 2w
Dividing both sides by 2 gives:
l = (35 - 2w) / 2
So the function that represents the length of the flower bed in terms of its width is:
l(w) = (35 - 2w) / 2
where l(w) is the length of the flower bed for a given width w.
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Find y'' by implicit differentiation. 5x2 + y2 = 3
To find y'' by implicit differentiation, differentiate the equation 5x^2 + y^2 = 3 twice with respect to x. Simplify and isolate y'' to find the second derivative of y.
Explanation:To find y'' by implicit differentiation, we differentiate the equation 5x^2 + y^2 = 3 with respect to x twice.
Step 1: Differentiate both sides of the equation with respect to x using the chain rule.
Step 2: Simplify the equation and isolate y'' to find the second derivative of y.
Step 3: Rewrite the equation with the second derivative of y isolated on one side.
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0/17 into a decimal using long division
when derek planted a tree it was 36 inches tall. the tree grew 1 1/4 inches per year the tree is now 44 3/4 inches tall. how many years ago did derek lant the tree?
What is the perimeter of this shape? A. 26 cm B. 24 cm C. 22 cm D. 18 cm PLEASE HELP
The box plots display the same data for the number of crackers in each snack bag, but one includes the outlier in the data and the other excludes it. 4, 14, 15, 15, 16, 16, 18, 19, 20, 20, 21 Number of Crackers in Each Bag, with Outlier Number of Crackers in Each Bag, without Outlier Which statement comparing the box plots is true? Both the median and the range changed. Both the range and the lower quartile changed. Both the median and the interquartile range changed. Both the interquartile range and the lower quartile changed.
Answer:
Both the median and the range changed.
Step-by-step explanation:
We first ensure this data set is from least to greatest. This one is.
Next we find the median. This is the middle value; in this set, it is 16.
Next we find Q1, the lower quartile. This is the middle of the lower set of data (once the data is "split" by the median). This is 15.
Next we find Q3, the upper quartile. This is the middle of the upper set of data (once the data is "split" by the median). This is 20.
The IQR is Q3-Q1, or 20-15 = 5.
The range is the max subtracted by the min, or 21-4 = 17.
Any outlier will be 1.5 times the IQR below Q1 or 1.5 times the IQR above Q3.
1.5(5) = 7.5; 15-7.5 = 7.5. Any lower outlier would be below this value; this makes 4 an outlier.
20+7.5 = 27.5. Any upper outlier would be above this value; this means there are no outliers on the upper end.
Taking the data value 4 out, the median is now 17. Q1 would still be 15 and Q3 would still be 20; this means the IQR would still be 5.
The range would now be 21-14 = 7.
This means the median and the range have changed.
The true statement comparing the box plots is that Both the median and the range changed.
What are quartiles?When we get data that can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.
Quartiles are then selected as 3 points such that they create four groups in the data, each group approximately possessing 25% of the data.
The box plots display the same data for the number of crackers in each snack bag, but one includes the outlier in the data and the other excludes it.
4, 14, 15, 15, 16, 16, 18, 19, 20, 20, 21 Number of Crackers in Each Bag, with Outlier Number of Crackers in Each Bag, without Outlier
The median in this set is 16.
Q1, the lower quartile. This is the middle of the lower set of data.
This is 15.
Q3, the upper quartile. This is the middle of the upper set of data. This is 20.
The IQR is Q3-Q1
20-15 = 5.
The range will be
21-4 = 17.
Any outlier will be 1.5 times the IQR below Q1 or 1.5 times the IQR above Q3.
1.5(5) = 7.5
15-7.5 = 7.5.
Any lower outlier would be below this value, this makes 4 an outlier.
20+7.5 = 27.5.
Any upper outlier would be above this value, this means there are no outliers on the upper end.
Taking the data value 4 out, the median is now 17.
Q1 would still be 15 and Q3 would still be 20; this means the IQR would still be 5.
The range would now be 21-14 = 7.
Thus, This means the median and the range have changed.
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For what value of a does the equation ax^2−3x−5=0 have 1 as one of its roots?
To determine the value of ↑ which the equation ax²-3x-5=0 has 1 as a root, we substitute x=1 into the equation and solve for a, yielding the result that a=8.
To find the value of a for which the equation ax² - 3x-5=0 has 1 as one of its roots, we can substitute x=1 into the equation and solve for a. When x=1, the equation simplifies to:
a(1)² - 3(1) - 5 = 0
a - 3 - 5 = 0
a - 8 = 0
Therefore, a = 8.
This means that the value of a is 8 for the equation to have 1 as one of its roots. This is a direct application of the fact that if a polynomial has a certain number as a root, then by substituting that number in place of the variable, the equation should result in zero.
Hey guys 25 points!! to help me out
In △DEF, DF = 16 and m∠F=45. Find the length of a leg. Leave your answer in simplest radical form.
As part of their senior project Janus nd Arya collected a total of $306 for the construction of a storage shed at a homeless shelter. Janus collected $88 less than Arya collected. How much money did each collect?
Brad has two lengths of copper pipe to fit together one has a length of 2 5/12 feet and the other has a length of 3 7 12 ft how many feet of Pop does he have
Jan and Jo live 1,170 miles apart. At the same time, they start driving toward each other on the same road. Jo’s constant rate is 60 mph. Jan’s is 70 mph. How long will it take them to meet?
Answer:
the answer is 9 hours
Step-by-step explanation:
I got it right on the test
The time taken by Jan and Jo with constant rate of 70 mph and 60 mph respectively, will meet in 9 hours while driving towards each other along a 1,170-mile road.
To find out how long it will take Jan and Jo to meet, you can use the formula:
Time = Distance / Speed
Since they are driving toward each other, their combined speed is the sum of their individual speeds:
Combined Speed = Jan's Speed + Jo's Speed
Combined Speed = 70 mph + 60 mph
Combined Speed = 130 mph
Now, you can use this combined speed to calculate the time it will take for them to meet:
Time = Distance / Combined Speed
Time = 1,170 miles / 130 mph
Time = 9 hours
Therefore, time taken by Jan and Jo is 9 hours to meet while driving toward each other on the same road.
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An athlete runs around a circular track. The track has a diameter of 200 feet. How many laps does she need to take to run a mile?
Let y=3t+6 be a linear function representing the distance from home for an ant t minutes after starting out from a location near its home. What does the number 3 represent in this function?
Corey drew a sketch of a paper hat as shown below.
If a = 4 in and b = 3 in, what is the area of the sketch?
A.84 in squared
B.60 in squared
C.30.5 in squared
D.40 in squared
Team tool Bella canoed 15 3/4 miles in 5 1/4 hours. What was their average rates of speed in miles per hour?
Answer:
3 miles per hour
Step-by-step explanation:
Using speed formula:
[tex]\text{Speed} = \frac{\text{Distance}}{\text{Time}}[/tex]
As per the statement:
Team tool Bella canoed 15 3/4 miles in 5 1/4 hours.
⇒[tex]\text{Distance} = 15\frac{3}{4} = \frac{63}{4}[/tex] miles and
[tex]\tetx{Time} = 5\frac{1}{4} = \frac{21}{4}[/tex] hours
Using speed formula we have;
[tex]\text{Speed}= \frac{\frac{63}{4} }{\frac{21}{4}} = \frac{63}{4} \cdot \frac{4}{21} = \frac{63}{21}[/tex]
Simplify:
[tex]\text{Speed} =3[/tex] miles per hour
Therefore, their average rates of speed in miles per hour is, 3 miles per hour
I am trying to graduate HS please help me out!!!
In certain county, the number of charter schools is 4 less than twice the numbervof alternative schools. We know that there are 48 charter schools in the county. How many alternative schools are in the county?
Chord AC intersects chord BD at point P in circle Z.
AP=3.5 in.
DP=4 in.
PC=6 in.
What is BP?
Enter your answer as a decimal in the box.
Answer: The value of BP is 5.25.
Step-by-step explanation:
Here's why:
Find the ratio between the two different groups of line segments. If you do it in decimal or fraction, it's the same. So, 4/6 = 0.666666667. Then you must find the number that when 3.5 is divided by it, gives you 0.666666667. So that number is 5.25.
S22 for 161+147+133+119+...
The 22nd term of the arithmetic progression in the series 161, 147, 133, 119.... is -133.
Explanation:This question involves finding the 22nd term in a series of numbers where each term is 14 less than the preceding term. This is an arithmetic progression where the first term, 'a' is 161 and the common difference, 'd' is -14.
The formula for the nth term in an arithmetic progression is: a + (n - 1)*d.
Substituting the given values into the formula, we get:
'a' + (22 - 1)*'d' = 161 + (21)*(-14) = 161 - 294 = -133
So, S22 for 161+147+133+119+... = -133.
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lotA has 4,000 spaces. Today Lot A has 2,500 cars in Lot A. Lot B has 2,000 spaces. If both lots have the same ratio of cars to spaces, how many cars are in parking lot B
Choose the correct simplification of the expression g5h4/g2h3
12÷0.5 explain the division expression in terms of bags of almonds
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. the diameter of the base of the cone is approximately three times the altitude. at what rate is the height of the pile changing when the pile is 12 feet high?
The problem involves the concept of related rates in Calculus. By using the relationship between the height and radius of the cone and the rate of change of the volume, we set up a differential equation. Upon solving, we find the rate at which the height of the pile changes is 5/(18π) feet per minute when the pile is 12 feet high.
Explanation:The subject matter of this question is related to Calculus, specifically the concept of related rates. In this scenario, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. Here, the given rate is the rate of change of the volume of the sand pile. The diameter of the base of the cone is approximately three times the altitude, which gives the relationship between the height and the radius of the cone: r=h/3. The student is asked to find at what rate the height of the pile is changing when the pile is 12 feet high.
First, let's recall the formula for the volume of a cone, which is V=(1/3)*π*r²*h. Based on the relationship between the radius and the height, we can substitute r with h/3. Therefore, the volume V=(1/3)*π*(h/3)²*h = (1/27)*π*h³. By differentiating this equation with respect to time t, we get dV/dt = (1/9)*π*h²*dh/dt.
We are given that dV/dt is 10 cubic feet per minute, and we want to find dh/dt when h = 12 feet. Substituting these values into the differentiated equation, we get 10 = (1/9)*π*(12²)*dh/dt. Solving this for dh/dt, we find that dh/dt = 10 / [(1/9)*π*(12²)] = 5/(18π) feet per minute.
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Point P (-3,-1) is the preimage. Point P’(3,-1) is the image after a reflection is performed. Give the line of reflection.
Suppose x follows a distribution with density function: \begin{equation} f\left(x\right) = \left\{\begin{array}{rl} c\left|x - 2\right|,& 0 \le x \le 3\\ 0, & \text{otherwise}\\ \end{array}\right. \end{equation} (note: for this question you can enter your answer in decimals as well as fractions.) what must the value of c be so that f(x) is a probability density function? tries 0/5 find the cumulative distribution function of f(x) for $ 2 \leq x \leq 3 $. [ the accepted form of answer is an algebraic expression in terms of "x". all algebraically equivalent expressions to the correct answer are accepted. write product as *
e.g 2*3 or 3*x, index/power as superscript,
e.g 2^3 for 2 raised to the power 3, the exponential function as exp(x), the logarithm function as log(x) (and not as ln(x)) ] tries 0/5 find the median of the probability distribution of x tries 0/2 find e(x) tries 0/5 find the cumulative distribution function of f(x) for $ 0 \leq x \leq 2 $. [ the accepted form of answer is an algebraic expression in terms of "x". all algebraically equivalent expressions to the correct answer are accepted. write product as *
e.g 2*3 or 3*x, index/power as superscript,
e.g 2^3 for 2 raised to the power 3, the exponential function as exp(x), the logarithm function as log(x) (and not as ln(x)) ]
the floor plan of a kitchen is shown at the right. if the entire floor is to be tiled, how many square feet of tile are needed
Can you square a negative number
A parabola has a vertex at (0,0). The focus of the parabola is located on the positive x-axis. Which part of the graph will the directrix pass through? the origin the negative part of the x-axis the positive part of the x-axis the negative part of the y-axis
Answer with explanation:
→→Information given about Parabola
Vertex of the Parabola = (0,0)
Focus is located on the positive x- axis.
Definition of Parabola: A parabola is locus of all the points such that distance from a fixed point known as focus to distance from a fixed line called, Directrix is always constant.
Let focus of the parabola be (k,0), where , k>0.
Distance between vertex (0,0) and focus(k,0) = Distance between vertex (0,0) and point on negative x-axis (-k,0).
Directrix will pass through point (-k,0).
So, equation of Directrix will be, x= -k
Directrix will pass through
Option B: The Negative part of the x -axis.
Can someone help me with these two questions?