The length of the shadow of man is 0.8 m/s.
How to solve word problems?
Here are some actions to take:
1. Recognize the issue.
Recognize every term used to describe the issue, Recognize what you need to look for, Recognize the issue's context.
2. Convert the issue into an equation. Give the unknown a variable (or variables) to symbolise, Indicate exactly what the variable stands for.
3. Put the strategy into action and find a solution.
dx/dt =1.2 m/s
4.5 / x+ y = 1.8 / y
1.8x + 1.8y = 4.5y
1.8x = 2.7y
2x = 3y
3 dy/dt = 2dx/ dt = dy/dt = 2/3
=0.8
Hence, The length of the shadow of man is 0.8 m/s
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The number of badgers in a forest increases
by 20% each year.
This year, there are 200 badgers in the forest.
Calculate the number of badgers that there will
be in the forest
a) after 1 year.
b) after 2 years.
By evaluating the exponential equation for the population:
P(x) = 200*(1.2)^x
We will get:
a) 240 badgers
b) 288 badgers
How to calculate the number of badgers after x years?We know that the number of badgers increases by 20% each year, that increase after x years is given by the exponential equation:
P(x) = A*(1 + 20%/100%)^x
P(x) = A*(1.2)^x
Where A is the initial amount.
Here we know that the initial population of badgers is 200, then we have:
P(x) = 200*(1.2)^x
a) To find the population after one year, we need to evaluate the exponential equation in x = 1, we will get:
P(1) = 200*1.2^1 =240
b) The population after 2 years is:
P(2) = 200*1.2^2 = 288
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How do you prove SAS congruence rule?
The prove the SAS congruence rule, two sides and one angles between the includes sides of the triangle and the two sides and one angles between the includes sides of the another triangle should be equal
The SAS congruence rule is used to prove the congruence of the one triangle angle and another triangle.
SAS congruence rule stands for the side-angle-side congruence rule of triangles.
Side-angle-side rule of congruence states that if two sides and one angles between the includes sides of the triangle is equal to the two sides and one angles between the includes sides of the another triangle, then the both the triangles are congruent
Therefore, to prove the SAS congruence rule two sides and one angle of both triangle should be equal
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At a bowling alley, the cost of shoe rental is $2. 55 and the cost per game is $3. 75. If f (n) represents the total cost of shoe rental and n games, what is the recursive equation for f (n)?.
The recursive equation for f( n ) is f( n-1 ) + 3.75
Any term of a sequence in terms of its preceding terms is a recursive equation. The equation can be defined as a mathematical statement made up of expressions. For example, b (n ) = 2b ( n-1 ) + 4 is a recursive equation.
As per the question,
The cost of shoe rental ( c ) = 2.55The cost per game ( g ) = 3.75number of games = nThe total cost of shoe rental = f ( n ) The recursive equation for f ( n ) = ?As we know,
⇒ f ( n ) = total cost
= g × n + c
f ( n ) = 3.75 ( n ) + 2.55
Replace n with n - 1,
⇒ f ( n - 1 ) = 3.75 ( n - 1 ) + 2.55
⇒ f ( n - 1 ) = 3.75 n - 3.75 + 2.55
⇒ f ( n - 1 ) = 3.75 n + 2.55 - 3.75
⇒ f ( n - 1 ) = f ( n ) - 3.75
⇒ f ( n ) = f ( n - 1 ) + 3.75
Therefore, f( n-1 ) + 3.75 is the recursive equation for f ( n ).
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At the beginning of spring, Allison planted a small sunflower in her backyard. When it was first planted, the sunflower was 15 inches tall. The sunflower then began to grow at a rate of 2 inches per week. How tall would the sunflower be after 9 weeks? How tall would the sunflower be after w weeks?
Answer:
Hope this helps you out
Step-by-step explanation:
After 9 weeks, the sunflower would be 39 inches tall.
After w weeks, the sunflower would be 15 + (2 * w) inches tall.
Wade Boggs played professional baseball for three different teams in 18 years.
The table shows his total number of hits for each team.
the Red Sox had 2,098 hits, Yankees had 702 hits, and Devil Rays had 210 hits.
Suppose he made the same number of hits each of the 18 years. If t = total number of hits
and a = number of hits per year, which two equations can be used to determine the number
of hits he made each year? Drag these equations into the box.
The two equations that can be used to determine the number of hits that he had each year are given as follows:
t = 2098 + 702 + 210.a = t/18.How to obtain the equations?His hits by team are divided as follows:
Red Sox: 2098 hits.Yankees: 702 hits.Devil Rays: 210 hits.Then the total number of hits is obtained by the sum of the number of hits that he obtained with each of the three teams, as follows:
t = 2098 + 702 + 210 = 3010.
Then the amount of hits that he obtained each year is obtained applying the proportion, dividing t by 18, as follows:
a = t/18.
Hence the result is given as follows:
a = t/18 = 3010/18 = 167 hits per year.
Missing Information
The options are given by the image shown at the end of the answer.
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7) The initial fee to have a website getup using a server is $48. It costs $44 per month to maintain the
website. Write an equation that gives the total cost of setting up and maintaining the website as a
function of the number of months it is maintained.
Find the total of setting up and maintaining the website for 6 months.
Answer:
a.) c(t)=44t+48
b.) the total initial cost of setting up a website and maintaining it for 6 months is $312
Step-by-step explanation:
h
suppose the population of the earth is doubling every 30 years. if the population of the earth is now 7 billion people, approximately how many people will be here when you are 95 years old?
Population after 95 years is more than 28 billion.
What is a growth rate?
The growth rate of a value (such as GDP, turnover, earnings, etc.) gauges how much it has changed over time (month, quarter, year). The percentage is a fairly universal way to communicate it.
Here, we have
The present size of the population is 7 billion.
Assuming that the population starts growing from the age of "0"
The number of people after 30 years is equal to two times the present population i.e 14 billion
The number of people after 60 years is equal to two times the population after 40 years i.e 28 billion
Hence, the population after 95 years is more than 28 billion.
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Which of the statements are true about the function f given by f(x) = 100 • e^-x
Select all that apply. s
A. The y-intercept of the graph off is at (0, 100).
B. The values f increase when x increases.
C. The value of f when x = -1 is a little less than 40.
D. The value of f when x = 5 is less than 1.
E. The value of f is never 0.
Answer:
A. The y-intercept of the graph of f is at (0, 100).
D. The value of f when x = 5 is less than 1.
E. The value of f is never 0.
The first two statements are not true because the function f is defined by the equation f(x) = 100 • e^-x, where e^-x is the base of the natural logarithm (commonly known as "e") raised to the power of -x. Since e is always greater than 1, the value of e^-x will always be between 0 and 1, so the function f will always decrease as x increases. This means that statements B and C are not true.
Step-by-step explanation:
a bakery sells 5800 muffins in 2010. the bakery sells 7420 muffins in 2015. write a linear model that represents the number y of muffins that the bakery sells x years after 2010.
The required linear model is y = 5800 + 324x.
What is a linear equation?
Equations whose variables have a power of one are called linear equations.
Given, a bakery sells 5800 muffins in 2010
the bakery sells 7420 muffins in 2015
So, the number of muffins sold after 2010 through 2015:
7,420 - 5,800 = 1,620
Then, the sales per year:
1,620 muffins sold since 2010 / 5 years = 324 muffins per year.
Then our linear model will be:
y = 5800 + 324x
Hence, the required linear model is y = 5800 + 324x.
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What is an equation of the line that passes through the point (6,1)(6,1) and is perpendicular to the line 2x+3y=182x+3y=18?.
The equation of a line passes through (6,1) is 3x - 2y = 16.
Here we have to find the equation of a line.
Data given:
Point = (6,1)
The equation of another line is 2x + 3y = 18
From the given equation we can find the slope;
So we have
3y = -2x + 18
y = -2/3x + 18/3
So the slope is -2/3
As the line is perpendicular, so the slope of the line perpendicular to it will be 3/2
The general formula of the line is:
(y - y1) = m(x-x1)
(x1, y1) is the point
The point is (6,1 ) and the slope is 3/2
Now put that in the equation we get:
(y - 1) = 3/2(x - 6)
2y - 2 = 3x - 18
3x - 2y = 16
Therefore the equation is 3x - 2y = 16.
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Find the zeros of the equation by factoring. x2 + 9x + 20 = 0 factors should have two whole numbers separated by a: + or - . Do not type parentheses and no spaces. Examples: x+7 x-8
x=
X=
Answer:
Step-by-step explanation:
(x+4)(x+5) = 0
x = -4
x = -5
The area of the triangle formed by x and y intercepts of the parabola y=0. 5(x-3)(x+k).
The possible values of k are -0.56, -3.56, -2, and -1.
We have the equation of the parabola, y=0.5(x-3)(x+k)
When we Substitute x=0, we get that y=0.5*(-3) * k for instance y = -1.5k
So, the y-intercept is (0,-1.5k).
We will now substitute y=0, 0=0.5(x-3)(x+k) for instance 0=0.5(x-3)(x+k) x=3 and x=-k
So, the x-intercepts are (3,0) and (-k,0).
We can see that 'k' cannot be 0 or -3 since height = 0 if k=0, which is not conceivable. If k = -3, the base is also 0, which is not feasible.
We know that area of a triangle is 1/2*base*height
when we substitute we will get
1.5=1/2*(3+k) *(1.5k)
3=4.5k+1.5k^2
k=-0.56 and k=-3.56
or
1.5=1/2*(-3-k) *(1.5k)
3=-4.5k-1.5k^2
k=-2 and k=-1
hence the possible values of k will be -0.56, -3.56, -2, and -1.
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Your question is incomplete, most probably the full question was:
The area of the triangle formed by x− and y− intercepts of the parabola y=0.5(x−3)(x+k) is equal to 1.5 square units. Find all possible values of k.
A company offers premium cable for 39.96 pet month plus a one time set fee. The total cost for setup and 6 months I'd 264.70 wrote and solve a linear equation
The cost per month is 39.96, the setup fee is 24.94, and the equations are x = 39.96 and 6x + y = 264.70.
What is equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given data:
A company offers premium cable for 39.96 per month plus a one-time set fee,
The total cost for setup and 6 months I'd 264.70
Write the equation as shown below,
The number of months × price per month + one-time setup fee = total cost
Calculate the equations,
x = number of months, y = setup fees
1 × x + y = 39.96 ⇒ x = 39.96 (y = 0 for one month)
6 × x + y = 264.70 ⇒ 6x + y = 264.70
Solve the above equation by the elimination method
x = 39.96 and y = 24.94
Therefore, the cost per month is 39.96, the setup fee is 24.94, and the equations are x = 39.96 and 6x + y = 264.70.
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Can you guys work your mathical math ASAP
Answer:
216.025 I think
Answer: S=237.5 in
Step-by-step explanation:
S=2(5)(6,5)+2(6.5)(7.5)+2(5)(7.5)
S=6,5(10)+97.5+7.5(10)
S=65+97.5+75
S=237,5 in
How do you prove ABC isosceles?
Triangle ABC to be isosceles we need to prove that opposite pair of sides of triangle ABC are congruent to each other.
Explanation :
Let us consider a triangle ABC,
To prove : Triangle ABC is an isosceles triangle.
In triangle ABC draw perpendicular bisector through point A to BC at point D.In triangle ADC and triangle ADB,
m ∠CAD ≅ m ∠BAD ( AD bisect angle A )
AD = DA ( common side )
m ∠ADC ≅ m ∠ADB ( each 90° )
By Angle side angle (ASA ) theorem ,
ΔADC ≅ΔADB
By congruence parts congruent triangles :
AC ≅ AB
Therefore, by congruence parts congruent triangles side AC ≅ AB implies ABC is an isosceles triangle.
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What are the next three terms in the sequences below?
(1). 2,5,7,12,__,__,__
(2). 9,11,20,31,__,__,__
(3). 2,5,10,50,__,__,__
(4). 1,3,3,9,__,__,__
a stop sign is a regular octagon, formed by cutting triangles off the corners of a square. if a stop sign measures 36 in. from top to bottom, what is the length of each side of the octagon?
The length of each side of the sign will be 14.81-inch approx.
It is assumed that an Octagon sign is created by cutting out triangles from a square's corners, and that the stop sign's overall length is 36 inches. Since we are aware that squares have right angles on all four sides, we can use Pythagoras' theorem to solve for the side of the sign in the image below.
[tex]s^{2} =x^{2} +x^{2} \\s^{2}=2x^{2} ...................Eq.1[/tex]
Also, it is a square. So, the measurement of length from side to side
[tex]2x+s=36....................Eq.2[/tex]
solving Eq.1 we get,
[tex]s=\sqrt{2} x[/tex]...putting this value in Eq.2,
[tex]s=36-2x\\\\\sqrt{2} x=36-2x\\\\x=\frac{36}{2+\sqrt{2} }[/tex]
Putting this value of x in Eq.1,
s = 14.8
Hence, The length of each side of the sign will be 14.81-inch approx.
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How does the graph of g(x) = (x − 8)3 + 3 compare to the parent function f(x) = x3?
a. g(x) is shifted 8 units to the left and 3 units up.
b. g(x) is shifted 3 units to the right and 8 units down.
c. g(x) is shifted 8 units to the right and 3 units up.
d. g(x) is shifted 3 units to the right and 8 units up.
Answer:
The right answer is C.
Step-by-step explanation:
The parent function is:
[tex]f(x)=x^3[/tex]
If something is subtracted from variable [tex]x[/tex] it means the graph shifted toward right and something is added to [tex]y[/tex] value then the graph is shifted up.
[tex]f(x)=(x-8)^3[/tex]
graph shifted toward right by [tex]8[/tex] units right
[tex]f(x)=(x-8)^3+3[/tex]
graph shifted toward right by [tex]3[/tex] units up
Thus the new function is:
[tex]g(x)=(x-8)^3+3[/tex]
Solve two and four-sevenths times two-thirds equals blank. one and fifteen twenty-firsts two and eight twenty-firsts two and twelve-fourteenths three and two-twelfths
After solving the given fraction, the resultant fraction is (A) 1 15/21.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole.
A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
A fraction appears in the numerator or denominator of a complex fraction.
The numerator of a proper fraction is less than the denominator.
So, we have:
2 4/7 * 2/3
Now, solve the fraction as follows:
2 4/7 * 2/3
14+4/7 * 2/3
18/7 * 2/3
36/21
1 15/21
Therefore, after solving the given fraction, the resultant fraction is (A) 1 15/21.
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find the gradient of the line below
The gradient of the line in the given graph is 1/2.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
From the graph, let us consider two points from where the line is passing.
(-2, 3) and (2, 5).
Gradient is nothing but slope of the line.
m=5-3/2-(-2)
=2/4
=1/2
Hence, the gradient of line in the given graph is 1/2.
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Answer now with steps and I will give brainliest. Use picture for reference.
The value of f(g(2)) is output of the function g(2) is in the input of f(x) which
is equal to 1.
What is a composite function?When the output of one function is given to the input of another function they are called composite functions.
In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
From the graphs f(x) = -x + 5 and g(x) = x².
Now, f(g(2)) is the output of g(2) is the input of f(x).
g(2) = (2)².
g(2) = 4.
Now, f(g(2)) = -(4) + 5.
f(g(2)) = 1.
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Jude types 840 characters in 5 minutes. What is her typing rate in characters per minute?
hippocrates magazine states that 35 percent of all americans take multiple vitamins regularly. suppose a researcher surveyed 750 people to test this claim and found that 296 did regularly take a multiple vitamin. is this sufficient evidence to conclude that the actual percentage is different from 35% at the 5% significance level? select the [p-value, decision to reject (rh0) or failure to reject (frh0
The solution to this problem is , we reject null hypothesis R H0 at p value =0.005 .
What is significance level ?The likelihood of rejecting the null hypothesis when it is true is the significance level, often known as alpha or. A significance level of 0.05, for instance, represents a 5% likelihood of drawing the incorrect conclusion that a difference exists when there isn't one.
Given that Hippocrates magazine states that 35 percent of all Americans take multiple vitamins regularly.
Persons surveyed = 750
Of those survived no of persons who took multiple vitamin = 296
Sample proportion = p =0.395
q =1-p = 0.605
[tex]H_{0}\\[/tex] : p= 0.35
[tex]H_{A}[/tex] : p ≠ 0.35
(Two tailed test)
Assuming H0 is true standard error = [tex]\sqrt{(0.35 * 0.65)/750}[/tex]
=>0.0174
p difference = 0.045
Test statistic = 0.045/0.0174
=>2.58
p value = 0.005 for right tailed
Reject H0:
Therefore , we reject R H0 at p value =0.005 .
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From a hot-air balloon, Adriel measures a 22° angle of depression to a landmark
that's 743 feet away, measuring horizontally. What's the balloon's vertical distance
above the ground? Round your answer to the nearest hundredth of a foot if necessary.
The balloon's vertical distance above the ground is 300.19 feet.
What is angle of depression?
If the line of sight is directed downward from the horizontal line, then an angle is created with the horizontal line. The angle produced between the horizontal line and the observer's line of sight is known as the angle of depression if the object being observed is below the observer's level.
Given that a balloon make 22° angle with a fixed point. The horizontal distance of the balloon along the ground is 743 feet.
Here need to find the vertical distance.
To find the vertical distance, use tangent of 22°. The tangent of angle is the ratio of vertical distance to horizontal distance.
Therefore,
tan 22° = vertical distance/ horizontal distance
tan 22° = vertical distance/ 743
Multiply both sides by 743:
vertical distance = 743 × tan 22°
vertical distance = 300.191
vertical distance = 300.19 ( rounding to the nearest hundredth)
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Which point is on the line that passes through point h and is perpendicular to line fg? (–6, 10) (–2, –12) (0, –2) (4, 2)
The point is on the line that passes through point h and is perpendicular to line fg is (-6, 10).
You can get the equation of the blue line and then determine which point is on the perpendicular line to that blue line, but you can alternatively work this out physically simply by examining the points.
The slope of the perpendicular lines is negative reciprocals.
So if FG is 3/4, it would be -4/3.
The slope is calculated as m = (y2-y1)/(x2-x1).
So, in order to acquire the solution, we will enter these values (6,6) till we reach the following result: -4/3
m= (10-(-6)/(-6-6) (-6-6)
m = 16/-12
m= -4/3
As a result, the ultimate answer to this question is A) (-6, 10)
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Answer:
The point is on the line that passes through point h and is perpendicular to line fg is (-6, 10).You can get the equation of the blue line and then determine which point is on the perpendicular line to that blue line, but you can alternatively work this out physically simply by examining the points. The slope of the perpendicular lines is negative reciprocals.So if FG is 3/4, it would be -4/3.The slope is calculated as m = (y2-y1)/(x2-x1).So, in order to acquire the solution, we will enter these values (6,6) till we reach the following result: -4/3m= (10-(-6)/(-6-6) (-6-6)m = 16/-12m= -4/3As a result, the ultimate answer to this question is
Step-by-step explanation:
The point is on the line that passes through point h and is perpendicular to line fg is (-6, 10).You can get the equation of the blue line and then determine which point is on the perpendicular line to that blue line, but you can alternatively work this out physically simply by examining the points. The slope of the perpendicular lines is negative reciprocals.So if FG is 3/4, it would be -4/3.The slope is calculated as m = (y2-y1)/(x2-x1).So, in order to acquire the solution, we will enter these values (6,6) till we reach the following result: -4/3m= (10-(-6)/(-6-6) (-6-6)m = 16/-12m= -4/3As a result, the ultimate answer to this question is
Help me please!! Ill rate 5/5 for whoever answers first
Answer:
7) d (21)
6) a (102)
Step-by-step explanation:
For the first question, we should start with what we know first:
When angles are complementary then, their angles add up to 90.
So here we have 69 + something = 90.
We find out that the missing angle (angle B) is 21.
For this second question, we know that a straight line has an angle of 180. Here we have a straight line, but only part of the angle in which we only have 78.
Since we know 78 + x = 180
Then we can figure out that x = 102.
For which of the following x-values is k(x) =80?
By reading the graph we can see that k(x) = 80 for x ∈ (5, 6]
For which value of x is k(x) = 80?Look at the graph and try to identify the line where y = 80, now move to the right until you hit the graph of k(x) (red graph).
Now, move downwards until you intercept the x-axis, that value in the x-axis is the input that gives k(x) = 80.
In this case, there is a set of values.
The open circle means taht the value does not belong to the set.
The closed circle means taht the value does belong to the set.
Then k(x) = 80 for all the values of x in the set:
(5, 6]
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Please hurry and answer these questions, I don't have much time!
Max Points: 100,
I will also give brainliest.
Answer:
1. 20 minutes (segment A)
2. 40 minutes (segment B)
3. 10 minutes (segment C)
4. 10 minutes (Segment D minus Segment B)
5. Segments C & E (approaching x axis)
6. Segment A (greatest slope)
7. 115 minutes
At the fisher farm, the weights of zucchini squash are normally distributed, with a mean of 5 ounces and a standard deviation of 0. 7 ounces. Which weight represents the top 10% of the zucchinis?.
Weight represents the top 10% of the zucchinis is 5.9
The formula for calculating a z-score is z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
We're looking for:
Weight is 10% of zucchinis at the top.
Top 10% = 90% of the population
90th percentile Z score is 1.282.
Hence
1.282 = x - 5 / 0.7
1.282 × 0.7 = x - 5
0.8974 = x - 5
x = 5 + 0.8974
x = 5.8974
5.9 ounces, roughly.
The top 10% of the zucchinis have a weight of 5.9 ounces.
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4. Jennifer has a lemonade stand. She charges $1.25 for a glass of lemonade. It costs her $0.60 to make each glass of lemonade plus $15 a day for other expenses. Write an equation (do not solve) to determine how many glasses of lemonade, 1, Jennifer needs to sell each day in order to break even?
In order to break even,
Total charge for x glasses = Per day cost
1.25x = 0.6x + 15
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let x be the number of glasses of lemonade Jennifer needs to sell each day
Total charge for x glasses = 1.25x
It costs her $0.60 to make each glass of lemonade:
=> For x glasses, cost = 0.6x
Per day cost = 0.6x + 15
In order to break even,
Total charge for x glasses = Per day cost
1.25x = 0.6x + 15
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