Answer:
3 5/8 miles
Step-by-step explanation:
You want miles to go for a 3 7/8 mile trip after 1/4 mile has been taveled.
DifferenceThe remaining mileage is the difference between the total distance and the distance already covered.
3 7/8 -1/4 = 3 7/8 -2/8 = 3 5/8
Kaitlin still has 3 5/8 miles to jog.
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Given the demand function D(p) = 400-4p².
Find the Elasticity of Demand at a price of $8.
At this price, we would say the demand is:
-Inelastic
-Elastic
-Unitary
Based on this, to increase revenue we should:
-Keep Prices Unchanged
-Lower Prices
-Raise Prices
The Elasticity of Demand at a price of $8 is 0.056.
Given the demand function,
D(p) = 400 - 4p²
The formula to find the elasticity of demand is,
e = p/D
Here p is the price and D is the quantity demanded.
When p = $8,
D = 400 - (4 × 8²) = 144
Elasticity of demand = 8 / 144 = 0.056
Hence the elasticity of demand is 0.056.
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Each of P, Q and R had a certain amount of money. P gave some money to Q and R in such a way that the amounts with them were doubled. Now Q gave some money to P and R such that the amounts with them were doubled. Finally R also gave some money with him to P and Q such that the amounts with them were doubled. At this stage, each of them had 240.What was the initial amount with P?
The initial amount of money with P was 2Q0 = 2 * 3Q0 = 6Q0.
What is amount?Amount is the sum of money or quantity of something. It is usually measured in numerical values such as dollars, pounds, or euros. It is used to describe the total of something, such as how much money is in a bank account or the total cost of a purchase. Amount can also be used to describe a quantity of something such as the amount of time spent on a project or the amount of people present at an event.
Let us denote the initial amount of money with P, Q and R as P0, Q0 and R0 respectively. We know that P gave some money to Q and R such that their amounts were doubled, which implies that P0 = 2(Q0 + R0). Similarly, Q gave some money to P and R such that their amounts were doubled, which implies that Q0 = 2(P0 + R0). Finally, R gave some money to P and Q such that their amounts were doubled, which implies that R0 = 2(P0 + Q0). Substituting the value of P0 from the first equation in the third equation, we get:
2(Q0 + R0) = 2(P0 + Q0)
2Q0 + 2R0 = 2P0 + 2Q0
R0 = P0
Substituting the value of R0 in the first equation, we get:
P0 = 2(Q0 + R0)
P0 = 2(Q0 + P0)
P0 = 2Q0 + P0
P0 = 2Q0
Finally, substituting the value of P0 in the second equation, we get:
Q0 = 2(P0 + R0)
Q0 = 2(2Q0 + R0)
Q0 = 4Q0 + R0
R0 = 3Q0
Therefore, the initial amount of money with P, Q and R can be calculated as follows:
P0 = 2Q0
Q0 = 3Q0
R0 = 3Q0
Therefore, the initial amount of money with P was 2Q0 = 2 * 3Q0 = 6Q0.
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Solve the right triangle using the information given. Round answers to two decimal places, if necessary. a = 4, b = 6; Find c, α, and β.
Step-by-step explanation:
first, remember Pythagoras :
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle).
a and b are the legs.
so, in our case
c² = 4² + 6² = 16 + 36 = 52
c = sqrt(52) = 7.211102551... ≈ 7.21
and then remember the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides, A, B, C are the corresponding opposite angles (here also called alpha, beta. gamma would be the 90° angle).
so,
4/sin(alpha) = c/sin(90) = c
4 = c×sin(alpha)
sin(alpha) = 4/c = 4/7.211102551... = 0.554700196...
alpha = 33.69006753...° ≈ 33.69°
we don't need to do that much calculation for the third angle beta, as we know the sum of all angles in a triangle is always 180°.
so,
180 = alpha + beta + 90 = 33.69 + beta + 90
90 = 33.69 + beta
56.30993247... = beta ≈ 56.31°
Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What is your expected net winnings?
Answer:
Expected Value = -1(999/1000) + 499(1/1000) = -500/1000 = -50 cents
Step-by-step explanation:
Suppose it takes John 18 minutes to run 2 miles. How long would it take him to run 5 kilometers? Round your answer to the nearest minute.
The required it would take John 26.3 minutes to run 5 kilometers.
Since there are 1.60934 kilometers in a mile, we can first convert 2 miles to kilometers:
2 miles = 2 * 1.60934 kilometers = 3.21869 kilometers
Now we can use the formula for speed:
speed = distance/time.
time = distance/speed
We know the distance (5 kilometers), and we can find the speed by dividing the distance by the time it takes to run 2 miles:
speed = 3.21869 kilometers / 18 minutes
speed ≈ 0.19 kilometers per minute
Now we can use this speed to find the time it would take to run 5 kilometers:
time = 5 kilometers / 0.19 kilometers per minute
time ≈ 26.3 minutes
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A two-day environmental clean up started at 9AM on the first day. The number of workers fluctuated as shown in the following figure.
graph of number of workers vs. time; between t=0 hours and t=8 hours the graph behaves as a sine curve with centerline 30, amplitude 10 and period 16; between t=12 and t=20, the graph is constant at 20. Then, at t=20 the graph becomes a sine curve again, starting at its minimum and completing one period between t=20 and t=36. The graph is then constant at 20 until t=44, before increasing as a sine again until t=48.
Suppose that the workers were paid 15 dollars per hour for work during the time period 9 am to 5 pm and were paid 22.5 dollars per hour for work during the rest of the day. What would the total personnel costs of the clean up have been under these conditions?
total cost =
dollars
The total personnel costs of the cleanup would be $8,625.
How to determine?Between 9AM and 5PM, a total of 8 hours, the workers are present during the interval t=0 to t=8. During this interval, the number of workers is given by:
f(t) = 30 + 10sin((2π/16)t)
We can calculate the number of workers for each hour using this formula:
f(0) = 30 + 10sin(0) = 30
f(1) = 30 + 10sin(π/8) ≈ 38.66
f(2) = 30 + 10sin(π/4) = 40
f(3) = 30 + 10sin(3π/8) ≈ 38.66
f(4) = 30 + 10sin(π/2) = 40
f(5) = 30 + 10sin(5π/8) ≈ 38.66
f(6) = 30 + 10sin(3π/4) = 30
f(7) = 30 + 10sin(7π/8) ≈ 21.34
f(8) = 30 + 10sin(π) = 20
So, during the first 8 hours, the number of workers fluctuates between 20 and 40.
Between 5PM and 9AM the next day, a total of 16 hours, the workers are present during the intervals t=8 to t=12, t=20 to t=36, and t=44 to t=48. During these intervals, the number of workers is given by:
Between t=8 and t=12, the number of workers is decreasing from 40 to 20. We can approximate this by a linear function:
f(t) = 40 - 5t
Between t=20 and t=36, the number of workers is constant at 20.
Between t=44 and t=48, the number of workers is increasing from 20 to 40. We can use the same linear function as before, but with t shifted by 44:
f(t) = 40 - 5(t-44)
We can now calculate the total personnel costs by multiplying the number of workers at each time interval by the appropriate hourly rate:
From 9AM to 5PM (8 hours): 30 workers on average, at a rate of $15 per hour:
8 × 30 × 15 = $3,600
From 5PM to 9AM the next day (16 hours):
From t=8 to t=12 (4 hours): average of 30 workers, at a rate of $22.5 per hour:
4 × 30 × 22.5 = $2,700
From t=20 to t=36 (16 hours): constant 20 workers, at a rate of $22.5 per hour:
16 × 20 × 22.5 = $7,200
From t=44 to t=48 (4 hours): average of 30 workers, at a rate of $22.5 per hour:
4 × 30 × 22.5 = $2,700
The total cost is the sum of the costs for each time interval:
$3,600 + $2,700 + $7,200 + $2,700 = $16,200
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The point N lies on the segment MP.
Find the coordinates of N so that the ratio of MN to NP is 3 to 5.
Check
M(-6,-3)
N (?.?)
P (26,13)
Coordinates of N:
4D
2023 McGraw Hill LLC. All Right
The coordinates of point N that divides the line segment formed joining points M(-6,-3) and P(26,13) in the ratio 3:5, evaluated using section-formula is (14,7)
What is section-formula?
The coordinates of the point that splits a specific line segment into two halves are given by the section formula. The line may be split at the point either internally or externally. Their lengths are divided in a way that keeps them in the m: n ratio. The ratio in which the line segment is divided and the coordinates of the points connecting it allow us to calculate the coordinates.
According to section-formula:
(x,y) = ( [tex]\frac{c.m + a. n}{m + n}[/tex] , [tex]\frac{d.m + b. n}{m + n}[/tex]) {where (x,y)are coordinates of point which divides & (a,b) ; (c,d) are coordinates of points forming line segment.
Given P=(a,b) = (26,13)
M=(c,d) = (-6.-3)
m:n = 3 : 5
N=(x,y) = ?
N=(x,y) = ( [tex]\frac{c.m + a. n}{m + n}[/tex] , [tex]\frac{d.m + b. n}{m + n}[/tex])
= {[tex]\frac{(-6)(3)+(26)(5)}{3+5}[/tex] ; [tex]\frac{(-3)(3)+(13)(5)}{3+5}[/tex] }
={ [tex]\frac{-18+130}{8}[/tex] ; [tex]\frac{-9+65}{8}[/tex] }
= {[tex]\frac{112}{8}[/tex] , [tex]\frac{56}{8}[/tex] }
={14 , 7}
The coordinates of point N are (14,7) which divides line joining P(26,13) and M(-6,-3) in ratio 3:5.
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Which graph shows the solution to the system of linear equations? y equals negative one third times x plus 1 y = −2x − 3 a coordinate grid with one line that passes through the points 0 comma 1 and 4 comma 0 and another line that passes through the points 0 comma negative 1 and 1 comma negative 3 a coordinate grid with one line that passes through the points 0 comma 1 and 3 comma 0 and another line that passes through the points 0 comma negative 3 and 1 comma negative 5 a coordinate grid with one line that passes through the points 0 comma 1 and 3 comma negative 1 and another line that passes through the points 0 comma negative 1 and 2 comma negative 5 a coordinate grid with one line that passes through the points 0 comma 1 and 4 comma negative 2 and another line that passes through the points 0 comma negative 2 and 1 comma negative 5
The graph of the system of linear equations can be seen in the image at the end.
Which is the graph of the system of linear equations?Here we have the following system of equations:
y = -(1/3)x + 1
y = -2x - 3
To graph the system of equations, we just need to graph both of these lines in the same coordinate axis. The point where the lines intercept are the solutions of the system.
In the image at the end we can see the graph of the system of equations, there we also can see that the solution is the point (-2.4, 1.8)
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solve 2.1*tan9 to 2d.p
Answer:
Correct question:-
Prove that tan9.tan17.tan45.tan73.tan81=1
LHS
Step-by-step explanation:
Find the equation of a line perpendicular to y=-1/2x+4 that passes through the point (-2,8)
Answer:
y = 2x + 12.
Step-by-step explanation:
To find the equation of a line perpendicular to y=-1/2x+4 and passing through the point (-2,8), we can first determine the slope of the perpendicular line.
Recall that two lines are perpendicular if and only if their slopes are negative reciprocals of each other. Therefore, the slope of the line we want to find is the negative reciprocal of the slope of y=-1/2x+4.
The slope of y=-1/2x+4 is -1/2, so the slope of the line perpendicular to it is 2 (since the negative reciprocal of -1/2 is 2).
Next, we can use the point-slope form of the equation of a line to write the equation of the line perpendicular to y=-1/2x+4 that passes through the point (-2,8):
y - 8 = 2(x + 2)
Simplifying and putting the equation in slope-intercept form, we get:
y = 2x + 12
Therefore, the equation of the line perpendicular to y=-1/2x+4 that passes through the point (-2,8) is y = 2x + 12.
[tex]\sf y =2x+12.[/tex]
Step-by-step explanation:1. Find the slope of the given equation.The slope of any linear equation can be found just by taking a look at the equation when it's solved for "y".
[tex]\sf y=-\dfrac{1}{2} x+4[/tex]
Looking at the given equation, we can clearly tell that the value of slope is [tex]-\dfrac{1}{2}[/tex].
2. Find the slope of the perpendicular line.The slope of any linear equation that is perpendicular to another can be found by writting the multiplicative reciprocal of the original equation's slope, and changing the sign on it.
Let's do it step by step:
a) Write the slope of the original equation.
[tex]-\dfrac{1}{2}[/tex]
b) Write the multiplicative reciprocal.
For this, you just need to change the order in the fraction. In other words, switch places between the numerator and denominator.
[tex]-\dfrac{1}{2}\Longrightarrow-\dfrac{2}{1}=-2[/tex]
c) Change the symbol of the number.[tex]\sf -2\Longrightarrow2[/tex]
Therefore, the slope of the new equation will be 2, and it is perpendicular to the original equation ([tex]\sf y=-\dfrac{1}{2} x+4[/tex]).
3. Identify the values.With the given ordered pair (-2, 8) and the slope (2) we can calculate the formula of the new equation.
Formula to use: [tex]\sf y-y_{1} =m(x-x_{1} )[/tex]
[tex]\sf x_{1} =-2\\ \\\sf y_{1} =8\\ \\m=2[/tex]
4. Calculate.Now we substitute the variables in the equation by the identified values in step 3.
[tex]\sf y-(8) =(2)(x-(-2))\\ \\y-8 =(2)(x+2)\\ \\[/tex]
Use the distributive property of multiplication on the right side of the equation (check the attached image).
[tex]\sf y-8 =(2)(x)+(2)(2)\\\\y-8 =2x+4\\ \\y-8+8 =2x+4+8\\ \\y =2x+12[/tex]
5. Verify.a) Is it perpendicular?
According to the theory explained in step 2, it is, because the slope is 2.
b) Does it pass through point (-2, 8)?.
For this, simply substitute "x" by "-2" in the calculated equation. If y= 8, then the function also meets this requirement.
[tex]\sf y =2(-2)+12\\ \\y=-4+12\\ \\y=8[/tex]
That's correct. We have found the correct answer.
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Ayuda porfavor , cuadros magicos de tal manera que al sumarlos horizontal y vertical den el resultado
hola te hice tres los otros no tuve tiempo espero te sirvan de ayuda :)
Find the accumulated value of an investment of $15,000 for 5 years at an interest rate of 6.5% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly d. compounded continuously. Round answers to the nearest cent.
Answer:
a. Compounded semiannually: $19,216.67
b. Compounded quarterly: $19,338.56
c. Compounded monthly: $19,416.32
d. Compounded continuously: $19,451.08
Step-by-step explanation:
The formula for the accumulated value (A) of an investment with an initial principal (P), an interest rate (r) and a compounding period (n) for a number of years (t) is:
A = P(1 + r/n)^(n*t)
Using this formula, we can calculate the accumulated value for each of the compounding periods given:
a. Compounded semiannually:
A = $15,000(1 + 0.065/2)^(2*5) = $19,216.67
b. Compounded quarterly:
A = $15,000(1 + 0.065/4)^(4*5) = $19,338.56
c. Compounded monthly:
A = $15,000(1 + 0.065/12)^(12*5) = $19,416.32
d. Compounded continuously:
A = $15,000e^(0.0655) = $19,451.08
Therefore, the accumulated value of the investment varies depending on the compounding period, with more frequent compounding resulting in a higher accumulated value.
Use the Quotient Property of Logarithms to write the logarithm as a difference of logarithms, and simplify if possible: log3 3/8
The expression "log₃(3/8)" can be expressed in the form of "difference-of-logarithms" is log₃(3) - log₃(8), and it's simplified value is -0.89278.
The "Quotient-Property" states that logarithm of quotient of "two-numbers" is equal to the difference of logarithms of individual numbers. It is expressed as : logₐ(b/c) = logₐ(b) - logₐ(c);
Using the quotient property, we can write log₃(3/8) as:
⇒ log₃(3) - log₃(8)
We know that log₃(3) = and log₃(8) = ,
So, ⇒ log₃(3) - log₃(8),
⇒ 1 - 1.89278
⇒ -0.89278,
Therefore, the value of log₃(3/8) is -0.89278.
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The given question is incomplete, the complete question is
Use the Quotient Property of Logarithms to write the logarithm as a difference of logarithms, and simplify if possible: log₃(3/8).
Which graph shows the image of ABC after a rotation about the origin
Answer:
I need the rotation in degrees around the origin (flip around x axis, 90 degrees counter clockwise) or send all of the graph options
Step-by-step explanation:
different equation dy÷dx+ytanx=secx
Answer:
First, we rearrange the equation to isolate the y-term on one side:
dy/dx + ytanx = secx
Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1
Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1
Integrating both sides with respect to x, we get: y |secx| = x + C
where C is the constant of integration. Solving for y, we have:
y = (x + C)/|secx|
Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined
there are n people seated at a round table.
Step-by-step explanation:
circular permutations of n objects =(n-1)!
The volume of a cone is 678.24 cubic inches. What is the height of the cone?
The height of the cone is 18 inches.
How to find the height of a cone?The height of the cone can be found as follows:
volume of a cone = 1 / 3 πr²h
where
r = radius of the coneh = height of the coneTherefore,
r = 6 inches
volume of the cone = 678.24
h = ?
Hence,
678.24 = 1 / 3 × 3.14 × 6² × h
678.24 = 1 / 3 × 3.14 × 36 × h
37.68h = 678.24
divide both sides of the equation by 37.68
h = 678.24 / 37.68
h = 18 inches
Therefore,
height of the cone = 18 inches
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The sample space for tossing a coin 4 times is {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}. Determine P(at least 3 heads). 12.5% 25% 31.25% 68.75%
Answer: a
Step-by-step explanation:
Theres 5 times that we could get at least 3 heads and were tossing the coin 4 times so 5/4. 5 divided 4 = 1.25 x100 =12.5 percent
The probability of P(at least 3 heads) is 31.25%
How to determine the probabilityProbability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
From the information given, we have that;
{HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}.
Count the number of events with 3 H's
Now, to determine the P(at least 3 heads).
We get;
P(at least 3 heads) = 5/16 × 100/1
Divide the values, we get;
P(at least 3 heads) = 0.3125×100/1
Multiply the values we get;
P(at least 3 heads) = 31.25%
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
1) c
2) d
3) a
4) b
Step-by-step explanation:
1)
[tex] \frac{13400}{13400 + 52100} = 20.5\%[/tex]
2)
[tex] \frac{9200}{9200 + 25800} = 26.3\% [/tex]
3)
[tex] \frac{52100 + 25800}{52100 + 25800 + 13400 + 9200} = 77.5\%[/tex]
4)
[tex] \frac{25800 + 9200}{25800 + 9200 + 52100 + 13400} = 34.8\%[/tex]
Answer:
1) c
2) d
3) a
4) b
Step-by-step explanation:
1)
[tex] \frac{13400}{13400 + 52100} = 20.5\%[/tex]
2)
[tex] \frac{9200}{9200 + 25800} = 26.3\% [/tex]
3)
[tex] \frac{52100 + 25800}{52100 + 25800 + 13400 + 9200} = 77.5\%[/tex]
4)
[tex] \frac{25800 + 9200}{25800 + 9200 + 52100 + 13400} = 34.8\%[/tex]
4x + 3y = 18
4x - 2y = 18
Answer:
To solve the system of linear equations:
4x + 3y = 18
4x - 2y = 18
we can use the method of elimination or substitution.
Method 1: Elimination
In this method, we eliminate one of the variables by adding or subtracting the equations in a way that eliminates one of the variables. Here's how we can do it:
Multiply the first equation by 2, and the second equation by 3 to eliminate x:
8x + 6y = 36
12x - 6y = 54
Now, subtract the second equation from the first:
8x + 6y - (12x - 6y) = 36 - 54
8x + 6y - 12x + 6y = -18
-4x + 12y = -18
Divide both sides by -4 to isolate x:
-4x/(-4) + 12y/(-4) = -18/(-4)
x - 3y = 4.5
Now, we can substitute this value of x into one of the original equations, let's use the first equation:
4(4.5) + 3y = 18
18 + 3y = 18
3y = 18 - 18
3y = 0
y = 0
So, the solution to the system of equations is x = 4.5 and y = 0.
Method 2: Substitution
In this method, we solve one of the equations for one variable and then substitute that expression into the other equation to solve for the other variable. Here's how we can do it:
Solve the first equation for x:
4x + 3y = 18
4x = 18 - 3y
x = (18 - 3y)/4
Now, substitute this expression for x into the second equation:
4[(18 - 3y)/4] - 2y = 18
18 - 3y - 2y = 18
-5y = 18 - 18
-5y = 0
y = 0
Now, substitute this value of y back into the expression for x:
x = (18 - 3(0))/4
x = 18/4
x = 4.5
So, the solution to the system of equations is x = 4.5 and y = 0, which is consistent with the solution obtained using the elimination method.
Answer:
(4.5,0)
Step-by-step explanation:
The point that makes this system of equations true is (4.5,0.
When x=4.5, and y=0 both of these equations equal each other.
You can find this point either by using your calculator, or graphing the equations and seeing where they intersect.
Can someone help me with this thank you
Answer:
1. 4 tens 2 ones
2. 6 tens 5 ones
3. 3 tens 7 ones
4. 2 tens 6 ones
5. 7 tens 4 ones
6. 5 tens 9 ones
7. 8 tens 1 ones
8. 9 tens 9 ones
9. 1 tens 3 ones
Step-by-step explanation:
not sure if I did it right, lmk if im wrong. Think ur just suppsoed to count the number of boxes that make 10, and those that dont count up to 10, depending on the number, are seen as "ones".
61. You plan to save some money based on the following criteria. On day 1, you save $2, on day 2 you save $22, and on day 3 you save $2³. If you continue along the same pattern for one week, how much do you save in all?
You would save a total of $272 in one week if you continued along the same pattern.
What is pattern?
A pattern is a repeating or predictable sequence of events, numbers, shapes, or objects. In the context of the question you asked earlier, the pattern is the sequence of the amounts saved on each day, which follows a predictable rule: the amount saved doubles each day, starting with $2 on day 1. So the pattern is: $2, $22, $2³, $2⁴, $2⁵, $2⁶, $2⁷. Recognizing and understanding patterns is an important skill in many areas of life, from mathematics and science to language and music.
Based on the given pattern, on day 4, the amount saved would be $2⁴ = $16. On day 5, the amount saved would be $2⁵ = $32. On day 6, the amount saved would be $2⁶ = $64. And on day 7, the amount saved would be $2⁷ = $128.
To calculate the total amount saved for the week, we simply add up the amounts saved on each day:
Total amount saved = $2 + $22 + $2³ + $16 + $32 + $64 + $128
= $2 + $22 + $8 + $16 + $32 + $64 + $128
= $272
Therefore, you would save a total of $272 in one week if you continued along the same pattern.
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15.3
21. A squirrel is standing on the branch of a tree. The angle of elevation from a point on the ground to the squirrel
is 48°. The ground distance from the point to the tree is 28ft. How high above the ground is the squirrel?
Round your answer to the nearest foot.
48⁰
28 ft
21
Answer:
The height of the squirrel is 31 feet.
Step-by-step explanation:
You need to know your Right Triangle Trigonometry to do this problem.
Rt Triangle trig is all about ratios. Angles and ratios.
In your question, there is a rt triangle. The side measure given, 28 is next to the angle. The math word for "next to" is "adjacent" You know the adjacent side. The squirrel's height is the opposite side. The ratio that puts together adjacent and opposite is tangent.
tan Angle = opposite/adjacent
tan 48° = x/28
multiply both sides by 28
28•tan48° = x
You have to use a calculator that has trig functions. It will have buttons that say "sin", "cos", and "tan"
Enter 28 × tan48° =
It will return 31.0971504152
Your question asks you to round to the nearest whole.
x = 31
The squirrel's height in the tree is 31ft.
Select the correct answer. Which statement best describes the zeros of the function h(x) = (x + 9)(x2 − 10x + 25)? A. The function has three complex zeros. B. The function has three distinct real zeros. C. The function has one real zero and two complex zeros. D. The function has two distinct real zeros.
All the zeroes of the function are,
x = - 9, 5, 5
Given that;
The function is,
h (x) = (x + 9) (x² - 10x + 25)
Now, We can find all the zeroes of the function as;
h (x) = (x + 9) (x² - 10x + 25)
h (x) = (x + 9) (x² - 5x - 5x + 25)
h (x) = (x + 9) ((x - 5) - 5 (x - 5))
h (x) = (x + 9) (x - 5) (x - 5)
Thus, All the zeroes of the function are,
x + 9 = 0
x = - 9
(x - 5)² = 0
x = 5, 5
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Calculate the circumference, given the following diameters. Use T[= 22 7 I. 30 cm 2. 15 m 3. 40 ft 4. 20 cm 5. 8 m 6. 12 cm 7. 22 in. 8. 34 m 9. 10m 10. 34 cm
Required circumference of the given diameters are 94.29 cm, 471.43 m, 377.14 ft, 62.86 cm, 251.43 m, 37.71 cm, 69.71 in, 1068.57 m, 314.29 m, 106.86 cm respectively.
What is circumference of circle?
The circumference of a circle is the distance around the edge or boundary of the circle. It is a fundamental geometric property of a circle and is defined as the product of the circle's diameter and pi (π), which is a mathematical constant approximately equal to 3.14.
The formula to calculate the circumference of a circle is C = 2πr or C = πd
where C represents the circumference, r represents the radius, and d represents the diameter of the circle,
1. Diameter = 30 cm
Circumference = π x Diameter
= 22/7 x 30
= 94.29 cm
2. Diameter = 15 m
Circumference = π x Diameter
= 22/7 x 15 x 100
= 471.43 m
3. Diameter = 40 ft
Circumference = π x Diameter
= 22/7 x 40 x 12
= 377.14 ft
4. Diameter = 20 cm
Circumference = π x Diameter
= 22/7 x 20
= 62.86 cm
5. Diameter = 8 m
Circumference = π x Diameter
= 22/7 x 8 x 100
= 251.43 m
6. Diameter = 12 cm
Circumference = π x Diameter
= 22/7 x 12
= 37.71 cm
7. Diameter = 22 in
Circumference = π x Diameter
= 22/7 x 22
= 69.71 in
8. Diameter = 34 m
Circumference = π x Diameter
= 22/7 x 34 x 100
= 1068.57 m
9. Diameter = 10 m
Circumference = π x Diameter
= 22/7 x 10 x 100
= 314.29 m
10. Diameter = 34 cm
Circumference = π x Diameter
= 22/7 x 34
= 106.86 cm
Therefore, the circumference of the given diameters are 94.29 cm, 471.43 m, 377.14 ft, 62.86 cm, 251.43 m, 37.71 cm, 69.71 in, 1068.57 m, 314.29 m, 106.86 cm.
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What are the odds in favor of Dave selecting a gray t-shirt if he has 5 gray in his wardrobe of 16
Answer:
wouldn't it be 5/16
Step-by-step explanation:
honestly not sure but isn't this just a probability question?
The life time of a certain device has CDF
F (x) = 1 − e^−λx2 x > 0; λ > 0
Derive the pdf of X and determine its mean, mode, median and variance.
The probability density function (pdf) of the lifetime of a certain device is expressed as: f (x) = 2λxe^−λx² ; x > 0; λ > 0
Mean: E(x) = -2λ + C
Mode: x = 0
Median: x = ±√(-ln(0.5)/λ)
Variance: Var(x) = 0
What is probability density function?Probability density function (PDF) describes the relative likelihood for a random variable to take on a given value. It is a continuous function that is used to represent the probability distribution of a continuous random variable.
The probability density function (pdf) of the lifetime of a certain device is expressed as:
f (x) = 2λxe^−λx² ; x > 0; λ > 0
Mean: The mean (or expected value) of the probability density function is given by:
E(x) = ∫x.f(x)dx = ∫x.2λxe^−λx²dx
= -2λe^−λx² + C
E(x) = -2λ + C
Mode: The mode of the probability density function is the value at which the maximum density occurs. This occurs at the point where the derivative of the function is equal to 0.
f′(x) = 2λxe^−λx²
= 0
x = 0
Therefore, the mode of the probability density function is 0.
Median: The median is the value of the random variable for which the cumulative distribution function is equal to 0.5.
F(x) = 1 − e^−λx² = 0.5
1 − e^−λx² = 0
e^−λx² = 0.5
−λx² = ln(0.5)
x² = -ln(0.5)/λ
x = ±√(-ln(0.5)/λ)
Therefore, the median of the probability density function is given by:
x = ±√(-ln(0.5)/λ)
Variance: The variance of the probability density function is given by:
Var(x) = E(x²) - (E(x))²
E(x²) = ∫x².f(x)dx
= ∫x^2.2λxe^−λx²dx
= -2λe^−λx² + C
E(x²) = -2λ + C
Var(x) = -2λ + C - (-2λ + C)²
= 0
Therefore, the variance of the probability density function is 0.
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graph the function f(x)=x^2+6x+4 by starting with the graph of y=x^2 and using transformations
The following steps we have to follow to make the graph of the given function:
[tex]f(x) = x^2 + 6x + 4[/tex]
Start with the graph of [tex]y = x^2[/tex], which is a parabola that opens upwards and passes through the origin (0, 0).
To shift the parabola to the left by 3 units (since 6/2 = 3), we subtract 3 from x inside the function. This gives us
[tex]y = (x - 3)^2[/tex],
which is the same parabola shifted 3 units to the right.
To shift the parabola up by 4 units, we add 4 to the function. This gives us f(x) = (x - 3)^2 + 4, which is the final function we want to graph.
To graph f(x), we can plot a few points and sketch the resulting parabola. For example, when x = -2, we have
[tex]f(-2) = ( -2 - 3)^2 + 4 = 9[/tex],
so one point on the graph is (-2, 9). Similarly,
when x = -1, we have
[tex]f(-1) = (-1 - 3)^2 + 4 = 8[/tex], so another point on the graph is (-1, 8). We can continue this process to get more points and sketch the parabola.
Here is a rough sketch of the graph of [tex]f(x) = x^2 + 6x + 4:[/tex]
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The following steps we have to follow to make the graph of the given function:
[tex]f(x) = x^2 + 6x + 4[/tex]
Start with the graph of [tex]y = x^2[/tex], which is a parabola that opens upwards and passes through the origin (0, 0).
To shift the parabola to the left by 3 units (since 6/2 = 3), we subtract 3 from x inside the function. This gives us
[tex]y = (x - 3)^2[/tex],
which is the same parabola shifted 3 units to the right.
To shift the parabola up by 4 units, we add 4 to the function. This gives us f(x) = (x - 3)^2 + 4, which is the final function we want to graph.
To graph f(x), we can plot a few points and sketch the resulting parabola. For example, when x = -2, we have
[tex]f(-2) = ( -2 - 3)^2 + 4 = 9[/tex],
so one point on the graph is (-2, 9). Similarly,
when x = -1, we have
[tex]f(-1) = (-1 - 3)^2 + 4 = 8[/tex], so another point on the graph is (-1, 8). We can continue this process to get more points and sketch the parabola.
Here is a rough sketch of the graph of [tex]f(x) = x^2 + 6x + 4:[/tex]
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One can of soda has a capacity of 355mL. How may liters of soda does 12.
12 cans of soda hold 4.26 liters of soda.
The process for determining the total volume of soda would be the same using the specific capacity and number of cans.
We need to determine how many milliliters of soda 12 cans hold. We can do this by multiplying the capacity of one can (355 mL) by the number of cans (12):
355 mL/can x 12 cans = 4,260 mL
Now we need to convert this amount to liters. We know that 1 liter is equal to 1,000 milliliters, so we can divide the total volume in milliliters by 1,000:
4,260 mL ÷ 1,000 mL/L = 4.26 L
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The distance between Anaheim, CA and Sacramento, CA is 420 miles. A map shows the distance to be 20 cm. What does 1 cm on the map represent in miles? Greg says that the scale is 1 cm = 21 miles. Grace says that the scale is 1 cm = 19 miles.
If the distance between Anaheim and Sacramento in real life is 420 miles, then 1 cm on map represents 21 miles, so, Greg's scale is correct.
To determine what 1 cm on the map represents in miles, we calculate the scale-factor, which tells us the ratio of distance on the map to distance in the real world.
The scale factor is = (distance on map)/(distance in real world),
The distance between, "Anaheim" and "Sacramento" in real life is = 420 miles, and on map is 20cm,
So, Scale factor is = 420/20 = 21 miles,
So, we can say that 1 cm on the map represents 21 miles in real-life.
Now, we can compare the scale given by Greg and Grace to the actual scale,
⇒ Greg's scale is 1 cm = 21 miles, which is the same as the actual scale we just calculated. So, Greg is correct.
⇒ Grace's scale is 1 cm = 19 miles, which is not the same as the actual scale we just calculated. So, Grace is incorrect.
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The given question is incomplete, the complete question is
The distance between Anaheim and Sacramento is 420 miles. A map shows the distance to be 20 cm. What does 1 cm on the map represent in miles? Greg says that the scale is 1 cm = 21 miles. Grace says that the scale is 1 cm = 19 miles. Who is correct.
If the distance between Anaheim and Sacramento in real life is 420 miles, then 1 cm on map represents 21 miles, so, Greg's scale is correct.
To determine what 1 cm on the map represents in miles, we calculate the scale-factor, which tells us the ratio of distance on the map to distance in the real world.
The scale factor is = (distance on map)/(distance in real world),
The distance between, "Anaheim" and "Sacramento" in real life is = 420 miles, and on map is 20cm,
So, Scale factor is = 420/20 = 21 miles,
So, we can say that 1 cm on the map represents 21 miles in real-life.
Now, we can compare the scale given by Greg and Grace to the actual scale,
⇒ Greg's scale is 1 cm = 21 miles, which is the same as the actual scale we just calculated. So, Greg is correct.
⇒ Grace's scale is 1 cm = 19 miles, which is not the same as the actual scale we just calculated. So, Grace is incorrect.
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The given question is incomplete, the complete question is
The distance between Anaheim and Sacramento is 420 miles. A map shows the distance to be 20 cm. What does 1 cm on the map represent in miles? Greg says that the scale is 1 cm = 21 miles. Grace says that the scale is 1 cm = 19 miles. Who is correct.